xref: /petsc/src/dm/impls/plex/plex.c (revision 472b984436794f5b5f82c9039f5d768939e601a1)

#include <petsc/private/dmpleximpl.h> /*I      "petscdmplex.h"   I*/
#include <petsc/private/dmlabelimpl.h>
#include <petsc/private/isimpl.h>
#include <petsc/private/vecimpl.h>
#include <petsc/private/glvisvecimpl.h>
#include <petscsf.h>
#include <petscds.h>
#include <petscdraw.h>
#include <petscdmfield.h>
#include <petscdmplextransform.h>
#include <petscblaslapack.h>

/* Logging support */
PetscLogEvent DMPLEX_Interpolate, DMPLEX_Partition, DMPLEX_Distribute, DMPLEX_DistributeCones, DMPLEX_DistributeLabels, DMPLEX_DistributeSF, DMPLEX_DistributeOverlap, DMPLEX_DistributeField, DMPLEX_DistributeData, DMPLEX_Migrate, DMPLEX_InterpolateSF, DMPLEX_GlobalToNaturalBegin, DMPLEX_GlobalToNaturalEnd, DMPLEX_NaturalToGlobalBegin, DMPLEX_NaturalToGlobalEnd, DMPLEX_Stratify, DMPLEX_Symmetrize, DMPLEX_Preallocate, DMPLEX_ResidualFEM, DMPLEX_JacobianFEM, DMPLEX_InterpolatorFEM, DMPLEX_InjectorFEM, DMPLEX_IntegralFEM, DMPLEX_CreateGmsh, DMPLEX_RebalanceSharedPoints, DMPLEX_PartSelf, DMPLEX_PartLabelInvert, DMPLEX_PartLabelCreateSF, DMPLEX_PartStratSF, DMPLEX_CreatePointSF, DMPLEX_LocatePoints, DMPLEX_TopologyView, DMPLEX_LabelsView, DMPLEX_CoordinatesView, DMPLEX_SectionView, DMPLEX_GlobalVectorView, DMPLEX_LocalVectorView, DMPLEX_TopologyLoad, DMPLEX_LabelsLoad, DMPLEX_CoordinatesLoad, DMPLEX_SectionLoad, DMPLEX_GlobalVectorLoad, DMPLEX_LocalVectorLoad;
PetscLogEvent DMPLEX_RebalBuildGraph, DMPLEX_RebalRewriteSF, DMPLEX_RebalGatherGraph, DMPLEX_RebalPartition, DMPLEX_RebalScatterPart, DMPLEX_Generate, DMPLEX_Transform, DMPLEX_GetLocalOffsets, DMPLEX_Uninterpolate;

PetscBool  Plexcite       = PETSC_FALSE;
const char PlexCitation[] = "@article{LangeMitchellKnepleyGorman2015,\n"
                            "title     = {Efficient mesh management in {Firedrake} using {PETSc-DMPlex}},\n"
                            "author    = {Michael Lange and Lawrence Mitchell and Matthew G. Knepley and Gerard J. Gorman},\n"
                            "journal   = {SIAM Journal on Scientific Computing},\n"
                            "volume    = {38},\n"
                            "number    = {5},\n"
                            "pages     = {S143--S155},\n"
                            "eprint    = {http://arxiv.org/abs/1506.07749},\n"
                            "doi       = {10.1137/15M1026092},\n"
                            "year      = {2016},\n"
                            "petsc_uses={DMPlex},\n}\n";

PETSC_EXTERN PetscErrorCode VecView_MPI(Vec, PetscViewer);

/*@
  DMPlexIsSimplex - Is the first cell in this mesh a simplex?

  Input Parameter:
. dm - The `DMPLEX` object

  Output Parameter:
. simplex - Flag checking for a simplex

  Level: intermediate

  Note:
  This just gives the first range of cells found. If the mesh has several cell types, it will only give the first.
  If the mesh has no cells, this returns `PETSC_FALSE`.

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexGetSimplexOrBoxCells()`, `DMPlexGetCellType()`, `DMPlexGetHeightStratum()`, `DMPolytopeTypeGetNumVertices()`
@*/
PetscErrorCode DMPlexIsSimplex(DM dm, PetscBool *simplex)
{
  DMPolytopeType ct;
  PetscInt       cStart, cEnd;

  PetscFunctionBegin;
  PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
  if (cEnd <= cStart) {
    *simplex = PETSC_FALSE;
    PetscFunctionReturn(PETSC_SUCCESS);
  }
  PetscCall(DMPlexGetCellType(dm, cStart, &ct));
  *simplex = DMPolytopeTypeGetNumVertices(ct) == DMPolytopeTypeGetDim(ct) + 1 ? PETSC_TRUE : PETSC_FALSE;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexGetSimplexOrBoxCells - Get the range of cells which are neither prisms nor ghost FV cells

  Input Parameters:
+ dm     - The `DMPLEX` object
- height - The cell height in the Plex, 0 is the default

  Output Parameters:
+ cStart - The first "normal" cell
- cEnd   - The upper bound on "normal" cells

  Level: developer

  Note:
  This function requires that tensor cells are ordered last.

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexConstructGhostCells()`, `DMPlexGetCellTypeStratum()`
@*/
PetscErrorCode DMPlexGetSimplexOrBoxCells(DM dm, PetscInt height, PetscInt *cStart, PetscInt *cEnd)
{
  DMLabel         ctLabel;
  IS              valueIS;
  const PetscInt *ctypes;
  PetscBool       found = PETSC_FALSE;
  PetscInt        Nct, cS = PETSC_MAX_INT, cE = 0;

  PetscFunctionBegin;
  PetscCall(DMPlexGetCellTypeLabel(dm, &ctLabel));
  PetscCall(DMLabelGetValueIS(ctLabel, &valueIS));
  PetscCall(ISGetLocalSize(valueIS, &Nct));
  PetscCall(ISGetIndices(valueIS, &ctypes));
  for (PetscInt t = 0; t < Nct; ++t) {
    const DMPolytopeType ct = (DMPolytopeType)ctypes[t];
    PetscInt             ctS, ctE, ht;

    if (ct == DM_POLYTOPE_UNKNOWN) {
      // If any cells are not typed, just use all cells
      PetscCall(DMPlexGetHeightStratum(dm, PetscMax(height, 0), cStart, cEnd));
      break;
    }
    if (DMPolytopeTypeIsHybrid(ct) || ct == DM_POLYTOPE_FV_GHOST) continue;
    PetscCall(DMLabelGetStratumBounds(ctLabel, ct, &ctS, &ctE));
    if (ctS >= ctE) continue;
    // Check that a point has the right height
    PetscCall(DMPlexGetPointHeight(dm, ctS, &ht));
    if (ht != height) continue;
    cS    = PetscMin(cS, ctS);
    cE    = PetscMax(cE, ctE);
    found = PETSC_TRUE;
  }
  if (!Nct || !found) cS = cE = 0;
  PetscCall(ISDestroy(&valueIS));
  // Reset label for fast lookup
  PetscCall(DMLabelMakeAllInvalid_Internal(ctLabel));
  if (cStart) *cStart = cS;
  if (cEnd) *cEnd = cE;
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode DMPlexGetFieldTypes_Internal(DM dm, PetscSection section, PetscInt field, PetscInt *types, PetscInt **ssStart, PetscInt **ssEnd, PetscViewerVTKFieldType **sft)
{
  PetscInt                 cdim, pStart, pEnd, vStart, vEnd, cStart, cEnd, c, depth, cellHeight, t;
  PetscInt                *sStart, *sEnd;
  PetscViewerVTKFieldType *ft;
  PetscInt                 vcdof[DM_NUM_POLYTOPES + 1], globalvcdof[DM_NUM_POLYTOPES + 1];
  DMLabel                  depthLabel, ctLabel;

  PetscFunctionBegin;
  /* the vcdof and globalvcdof are sized to allow every polytope type and simple vertex at DM_NUM_POLYTOPES */
  PetscCall(PetscArrayzero(vcdof, DM_NUM_POLYTOPES + 1));
  PetscCall(DMGetCoordinateDim(dm, &cdim));
  PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
  PetscCall(PetscSectionGetChart(section, &pStart, &pEnd));
  if (field >= 0) {
    if ((vStart >= pStart) && (vStart < pEnd)) PetscCall(PetscSectionGetFieldDof(section, vStart, field, &vcdof[DM_NUM_POLYTOPES]));
  } else {
    if ((vStart >= pStart) && (vStart < pEnd)) PetscCall(PetscSectionGetDof(section, vStart, &vcdof[DM_NUM_POLYTOPES]));
  }

  PetscCall(DMPlexGetVTKCellHeight(dm, &cellHeight));
  PetscCall(DMPlexGetDepth(dm, &depth));
  PetscCall(DMPlexGetDepthLabel(dm, &depthLabel));
  PetscCall(DMPlexGetCellTypeLabel(dm, &ctLabel));
  for (c = 0; c < DM_NUM_POLYTOPES; ++c) {
    const DMPolytopeType ict = (DMPolytopeType)c;
    PetscInt             dep;

    if (ict == DM_POLYTOPE_FV_GHOST) continue;
    PetscCall(DMLabelGetStratumBounds(ctLabel, ict, &cStart, &cEnd));
    if (pStart >= 0) {
      PetscCall(DMLabelGetValue(depthLabel, cStart, &dep));
      if (dep != depth - cellHeight) continue;
    }
    if (field >= 0) {
      if ((cStart >= pStart) && (cStart < pEnd)) PetscCall(PetscSectionGetFieldDof(section, cStart, field, &vcdof[c]));
    } else {
      if ((cStart >= pStart) && (cStart < pEnd)) PetscCall(PetscSectionGetDof(section, cStart, &vcdof[c]));
    }
  }

  PetscCall(MPIU_Allreduce(vcdof, globalvcdof, DM_NUM_POLYTOPES + 1, MPIU_INT, MPI_MAX, PetscObjectComm((PetscObject)dm)));
  *types = 0;

  for (c = 0; c < DM_NUM_POLYTOPES + 1; ++c) {
    if (globalvcdof[c]) ++(*types);
  }

  PetscCall(PetscMalloc3(*types, &sStart, *types, &sEnd, *types, &ft));
  t = 0;
  if (globalvcdof[DM_NUM_POLYTOPES]) {
    sStart[t] = vStart;
    sEnd[t]   = vEnd;
    ft[t]     = (globalvcdof[t] == cdim) ? PETSC_VTK_POINT_VECTOR_FIELD : PETSC_VTK_POINT_FIELD;
    ++t;
  }

  for (c = 0; c < DM_NUM_POLYTOPES; ++c) {
    if (globalvcdof[c]) {
      const DMPolytopeType ict = (DMPolytopeType)c;

      PetscCall(DMLabelGetStratumBounds(ctLabel, ict, &cStart, &cEnd));
      sStart[t] = cStart;
      sEnd[t]   = cEnd;
      ft[t]     = (globalvcdof[c] == cdim) ? PETSC_VTK_CELL_VECTOR_FIELD : PETSC_VTK_CELL_FIELD;
      ++t;
    }
  }

  if (!*types) {
    if (field >= 0) {
      const char *fieldname;

      PetscCall(PetscSectionGetFieldName(section, field, &fieldname));
      PetscCall(PetscInfo((PetscObject)dm, "Could not classify VTK output type of section field %" PetscInt_FMT " \"%s\"\n", field, fieldname));
    } else {
      PetscCall(PetscInfo((PetscObject)dm, "Could not classify VTK output type of section\n"));
    }
  }

  *ssStart = sStart;
  *ssEnd   = sEnd;
  *sft     = ft;
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode DMPlexRestoreFieldTypes_Internal(DM dm, PetscSection section, PetscInt field, PetscInt *types, PetscInt **sStart, PetscInt **sEnd, PetscViewerVTKFieldType **ft)
{
  PetscFunctionBegin;
  PetscCall(PetscFree3(*sStart, *sEnd, *ft));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode DMPlexGetFieldType_Internal(DM dm, PetscSection section, PetscInt field, PetscInt *sStart, PetscInt *sEnd, PetscViewerVTKFieldType *ft)
{
  PetscInt cdim, pStart, pEnd, vStart, vEnd, cStart, cEnd;
  PetscInt vcdof[2] = {0, 0}, globalvcdof[2];

  PetscFunctionBegin;
  *ft = PETSC_VTK_INVALID;
  PetscCall(DMGetCoordinateDim(dm, &cdim));
  PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
  PetscCall(DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd));
  PetscCall(PetscSectionGetChart(section, &pStart, &pEnd));
  if (field >= 0) {
    if ((vStart >= pStart) && (vStart < pEnd)) PetscCall(PetscSectionGetFieldDof(section, vStart, field, &vcdof[0]));
    if ((cStart >= pStart) && (cStart < pEnd)) PetscCall(PetscSectionGetFieldDof(section, cStart, field, &vcdof[1]));
  } else {
    if ((vStart >= pStart) && (vStart < pEnd)) PetscCall(PetscSectionGetDof(section, vStart, &vcdof[0]));
    if ((cStart >= pStart) && (cStart < pEnd)) PetscCall(PetscSectionGetDof(section, cStart, &vcdof[1]));
  }
  PetscCall(MPIU_Allreduce(vcdof, globalvcdof, 2, MPIU_INT, MPI_MAX, PetscObjectComm((PetscObject)dm)));
  if (globalvcdof[0]) {
    *sStart = vStart;
    *sEnd   = vEnd;
    if (globalvcdof[0] == cdim) *ft = PETSC_VTK_POINT_VECTOR_FIELD;
    else *ft = PETSC_VTK_POINT_FIELD;
  } else if (globalvcdof[1]) {
    *sStart = cStart;
    *sEnd   = cEnd;
    if (globalvcdof[1] == cdim) *ft = PETSC_VTK_CELL_VECTOR_FIELD;
    else *ft = PETSC_VTK_CELL_FIELD;
  } else {
    if (field >= 0) {
      const char *fieldname;

      PetscCall(PetscSectionGetFieldName(section, field, &fieldname));
      PetscCall(PetscInfo((PetscObject)dm, "Could not classify VTK output type of section field %" PetscInt_FMT " \"%s\"\n", field, fieldname));
    } else {
      PetscCall(PetscInfo((PetscObject)dm, "Could not classify VTK output type of section\n"));
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexVecView1D - Plot many 1D solutions on the same line graph

  Collective

  Input Parameters:
+ dm     - The `DMPLEX` object
. n      - The number of vectors
. u      - The array of local vectors
- viewer - The `PetscViewer`

  Level: advanced

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `VecViewFromOptions()`, `VecView()`
@*/
PetscErrorCode DMPlexVecView1D(DM dm, PetscInt n, Vec u[], PetscViewer viewer)
{
  PetscDS            ds;
  PetscDraw          draw = NULL;
  PetscDrawLG        lg;
  Vec                coordinates;
  const PetscScalar *coords, **sol;
  PetscReal         *vals;
  PetscInt          *Nc;
  PetscInt           Nf, f, c, Nl, l, i, vStart, vEnd, v;
  char             **names;

  PetscFunctionBegin;
  PetscCall(DMGetDS(dm, &ds));
  PetscCall(PetscDSGetNumFields(ds, &Nf));
  PetscCall(PetscDSGetTotalComponents(ds, &Nl));
  PetscCall(PetscDSGetComponents(ds, &Nc));

  PetscCall(PetscViewerDrawGetDraw(viewer, 0, &draw));
  if (!draw) PetscFunctionReturn(PETSC_SUCCESS);
  PetscCall(PetscDrawLGCreate(draw, n * Nl, &lg));

  PetscCall(PetscMalloc3(n, &sol, n * Nl, &names, n * Nl, &vals));
  for (i = 0, l = 0; i < n; ++i) {
    const char *vname;

    PetscCall(PetscObjectGetName((PetscObject)u[i], &vname));
    for (f = 0; f < Nf; ++f) {
      PetscObject disc;
      const char *fname;
      char        tmpname[PETSC_MAX_PATH_LEN];

      PetscCall(PetscDSGetDiscretization(ds, f, &disc));
      /* TODO Create names for components */
      for (c = 0; c < Nc[f]; ++c, ++l) {
        PetscCall(PetscObjectGetName(disc, &fname));
        PetscCall(PetscStrncpy(tmpname, vname, sizeof(tmpname)));
        PetscCall(PetscStrlcat(tmpname, ":", sizeof(tmpname)));
        PetscCall(PetscStrlcat(tmpname, fname, sizeof(tmpname)));
        PetscCall(PetscStrallocpy(tmpname, &names[l]));
      }
    }
  }
  PetscCall(PetscDrawLGSetLegend(lg, (const char *const *)names));
  /* Just add P_1 support for now */
  PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
  PetscCall(DMGetCoordinatesLocal(dm, &coordinates));
  PetscCall(VecGetArrayRead(coordinates, &coords));
  for (i = 0; i < n; ++i) PetscCall(VecGetArrayRead(u[i], &sol[i]));
  for (v = vStart; v < vEnd; ++v) {
    PetscScalar *x, *svals;

    PetscCall(DMPlexPointLocalRead(dm, v, coords, &x));
    for (i = 0; i < n; ++i) {
      PetscCall(DMPlexPointLocalRead(dm, v, sol[i], &svals));
      for (l = 0; l < Nl; ++l) vals[i * Nl + l] = PetscRealPart(svals[l]);
    }
    PetscCall(PetscDrawLGAddCommonPoint(lg, PetscRealPart(x[0]), vals));
  }
  PetscCall(VecRestoreArrayRead(coordinates, &coords));
  for (i = 0; i < n; ++i) PetscCall(VecRestoreArrayRead(u[i], &sol[i]));
  for (l = 0; l < n * Nl; ++l) PetscCall(PetscFree(names[l]));
  PetscCall(PetscFree3(sol, names, vals));

  PetscCall(PetscDrawLGDraw(lg));
  PetscCall(PetscDrawLGDestroy(&lg));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode VecView_Plex_Local_Draw_1D(Vec u, PetscViewer viewer)
{
  DM dm;

  PetscFunctionBegin;
  PetscCall(VecGetDM(u, &dm));
  PetscCall(DMPlexVecView1D(dm, 1, &u, viewer));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode VecView_Plex_Local_Draw_2D(Vec v, PetscViewer viewer)
{
  DM                 dm;
  PetscSection       s;
  PetscDraw          draw, popup;
  DM                 cdm;
  PetscSection       coordSection;
  Vec                coordinates;
  const PetscScalar *array;
  PetscReal          lbound[3], ubound[3];
  PetscReal          vbound[2], time;
  PetscBool          flg;
  PetscInt           dim, Nf, f, Nc, comp, vStart, vEnd, cStart, cEnd, c, N, level, step, w = 0;
  const char        *name;
  char               title[PETSC_MAX_PATH_LEN];

  PetscFunctionBegin;
  PetscCall(PetscViewerDrawGetDraw(viewer, 0, &draw));
  PetscCall(VecGetDM(v, &dm));
  PetscCall(DMGetCoordinateDim(dm, &dim));
  PetscCall(DMGetLocalSection(dm, &s));
  PetscCall(PetscSectionGetNumFields(s, &Nf));
  PetscCall(DMGetCoarsenLevel(dm, &level));
  PetscCall(DMGetCoordinateDM(dm, &cdm));
  PetscCall(DMGetLocalSection(cdm, &coordSection));
  PetscCall(DMGetCoordinatesLocal(dm, &coordinates));
  PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
  PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));

  PetscCall(PetscObjectGetName((PetscObject)v, &name));
  PetscCall(DMGetOutputSequenceNumber(dm, &step, &time));

  PetscCall(VecGetLocalSize(coordinates, &N));
  PetscCall(DMGetBoundingBox(dm, lbound, ubound));
  PetscCall(PetscDrawClear(draw));

  /* Could implement something like DMDASelectFields() */
  for (f = 0; f < Nf; ++f) {
    DM          fdm = dm;
    Vec         fv  = v;
    IS          fis;
    char        prefix[PETSC_MAX_PATH_LEN];
    const char *fname;

    PetscCall(PetscSectionGetFieldComponents(s, f, &Nc));
    PetscCall(PetscSectionGetFieldName(s, f, &fname));

    if (v->hdr.prefix) PetscCall(PetscStrncpy(prefix, v->hdr.prefix, sizeof(prefix)));
    else prefix[0] = '\0';
    if (Nf > 1) {
      PetscCall(DMCreateSubDM(dm, 1, &f, &fis, &fdm));
      PetscCall(VecGetSubVector(v, fis, &fv));
      PetscCall(PetscStrlcat(prefix, fname, sizeof(prefix)));
      PetscCall(PetscStrlcat(prefix, "_", sizeof(prefix)));
    }
    for (comp = 0; comp < Nc; ++comp, ++w) {
      PetscInt nmax = 2;

      PetscCall(PetscViewerDrawGetDraw(viewer, w, &draw));
      if (Nc > 1) PetscCall(PetscSNPrintf(title, sizeof(title), "%s:%s_%" PetscInt_FMT " Step: %" PetscInt_FMT " Time: %.4g", name, fname, comp, step, (double)time));
      else PetscCall(PetscSNPrintf(title, sizeof(title), "%s:%s Step: %" PetscInt_FMT " Time: %.4g", name, fname, step, (double)time));
      PetscCall(PetscDrawSetTitle(draw, title));

      /* TODO Get max and min only for this component */
      PetscCall(PetscOptionsGetRealArray(NULL, prefix, "-vec_view_bounds", vbound, &nmax, &flg));
      if (!flg) {
        PetscCall(VecMin(fv, NULL, &vbound[0]));
        PetscCall(VecMax(fv, NULL, &vbound[1]));
        if (vbound[1] <= vbound[0]) vbound[1] = vbound[0] + 1.0;
      }

      PetscCall(PetscDrawGetPopup(draw, &popup));
      PetscCall(PetscDrawScalePopup(popup, vbound[0], vbound[1]));
      PetscCall(PetscDrawSetCoordinates(draw, lbound[0], lbound[1], ubound[0], ubound[1]));
      PetscCall(VecGetArrayRead(fv, &array));
      for (c = cStart; c < cEnd; ++c) {
        DMPolytopeType     ct;
        PetscScalar       *coords = NULL, *a = NULL;
        const PetscScalar *coords_arr;
        PetscBool          isDG;
        PetscInt           numCoords, color[4] = {-1, -1, -1, -1};

        PetscCall(DMPlexGetCellType(dm, c, &ct));
        PetscCall(DMPlexPointLocalRead(fdm, c, array, &a));
        if (a) {
          color[0] = PetscDrawRealToColor(PetscRealPart(a[comp]), vbound[0], vbound[1]);
          color[1] = color[2] = color[3] = color[0];
        } else {
          PetscScalar *vals = NULL;
          PetscInt     numVals, va;

          PetscCall(DMPlexVecGetClosure(fdm, NULL, fv, c, &numVals, &vals));
          if (!numVals) {
            PetscCall(DMPlexVecRestoreClosure(fdm, NULL, fv, c, &numVals, &vals));
            continue;
          }
          PetscCheck(numVals % Nc == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of components %" PetscInt_FMT " does not divide the number of values in the closure %" PetscInt_FMT, Nc, numVals);
          switch (numVals / Nc) {
          case 1: /* P1 Clamped Segment Prism */
          case 2: /* P1 Segment Prism, P2 Clamped Segment Prism */
            PetscCheck(ct == DM_POLYTOPE_SEG_PRISM_TENSOR, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cell should be a tensor segment, but it is a %s", DMPolytopeTypes[ct]);
            for (va = 0; va < numVals / Nc; ++va) color[va] = PetscDrawRealToColor(PetscRealPart(vals[va * Nc + comp]), vbound[0], vbound[1]);
            break;
          case 3: /* P1 Triangle */
          case 4: /* P1 Quadrangle */
            PetscCheck(ct == DM_POLYTOPE_TRIANGLE || ct == DM_POLYTOPE_QUADRILATERAL || ct == DM_POLYTOPE_SEG_PRISM_TENSOR, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cell should be a triangle or quad, but it is a %s", DMPolytopeTypes[ct]);
            for (va = 0; va < numVals / Nc; ++va) color[va] = PetscDrawRealToColor(PetscRealPart(vals[va * Nc + comp]), vbound[0], vbound[1]);
            break;
          case 6: /* P2 Triangle */
          case 8: /* P2 Quadrangle */
            PetscCheck(ct == DM_POLYTOPE_TRIANGLE || ct == DM_POLYTOPE_QUADRILATERAL || ct == DM_POLYTOPE_SEG_PRISM_TENSOR, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cell should be a triangle or quad, but it is a %s", DMPolytopeTypes[ct]);
            for (va = 0; va < numVals / (Nc * 2); ++va) color[va] = PetscDrawRealToColor(PetscRealPart(vals[va * Nc + comp + numVals / (Nc * 2)]), vbound[0], vbound[1]);
            break;
          default:
            SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Number of values for cell closure %" PetscInt_FMT " cannot be handled", numVals / Nc);
          }
          PetscCall(DMPlexVecRestoreClosure(fdm, NULL, fv, c, &numVals, &vals));
        }
        PetscCall(DMPlexGetCellCoordinates(dm, c, &isDG, &numCoords, &coords_arr, &coords));
        switch (numCoords) {
        case 6:
        case 12: /* Localized triangle */
          PetscCall(PetscDrawTriangle(draw, PetscRealPart(coords[0]), PetscRealPart(coords[1]), PetscRealPart(coords[2]), PetscRealPart(coords[3]), PetscRealPart(coords[4]), PetscRealPart(coords[5]), color[0], color[1], color[2]));
          break;
        case 8:
        case 16: /* Localized quadrilateral */
          if (ct == DM_POLYTOPE_SEG_PRISM_TENSOR) {
            PetscCall(PetscDrawLine(draw, PetscRealPart(coords[0]), PetscRealPart(coords[1]), PetscRealPart(coords[2]), PetscRealPart(coords[3]), PetscMax(color[0], color[1])));
          } else {
            PetscCall(PetscDrawTriangle(draw, PetscRealPart(coords[0]), PetscRealPart(coords[1]), PetscRealPart(coords[2]), PetscRealPart(coords[3]), PetscRealPart(coords[4]), PetscRealPart(coords[5]), color[0], color[1], color[2]));
            PetscCall(PetscDrawTriangle(draw, PetscRealPart(coords[4]), PetscRealPart(coords[5]), PetscRealPart(coords[6]), PetscRealPart(coords[7]), PetscRealPart(coords[0]), PetscRealPart(coords[1]), color[2], color[3], color[0]));
          }
          break;
        default:
          SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Cannot draw cells with %" PetscInt_FMT " coordinates", numCoords);
        }
        PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &coords_arr, &coords));
      }
      PetscCall(VecRestoreArrayRead(fv, &array));
      PetscCall(PetscDrawFlush(draw));
      PetscCall(PetscDrawPause(draw));
      PetscCall(PetscDrawSave(draw));
    }
    if (Nf > 1) {
      PetscCall(VecRestoreSubVector(v, fis, &fv));
      PetscCall(ISDestroy(&fis));
      PetscCall(DMDestroy(&fdm));
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode VecView_Plex_Local_Draw(Vec v, PetscViewer viewer)
{
  DM        dm;
  PetscDraw draw;
  PetscInt  dim;
  PetscBool isnull;

  PetscFunctionBegin;
  PetscCall(PetscViewerDrawGetDraw(viewer, 0, &draw));
  PetscCall(PetscDrawIsNull(draw, &isnull));
  if (isnull) PetscFunctionReturn(PETSC_SUCCESS);

  PetscCall(VecGetDM(v, &dm));
  PetscCall(DMGetCoordinateDim(dm, &dim));
  switch (dim) {
  case 1:
    PetscCall(VecView_Plex_Local_Draw_1D(v, viewer));
    break;
  case 2:
    PetscCall(VecView_Plex_Local_Draw_2D(v, viewer));
    break;
  default:
    SETERRQ(PetscObjectComm((PetscObject)v), PETSC_ERR_SUP, "Cannot draw meshes of dimension %" PetscInt_FMT ". Try PETSCVIEWERGLVIS", dim);
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode VecView_Plex_Local_VTK(Vec v, PetscViewer viewer)
{
  DM                      dm;
  Vec                     locv;
  const char             *name;
  PetscSection            section;
  PetscInt                pStart, pEnd;
  PetscInt                numFields;
  PetscViewerVTKFieldType ft;

  PetscFunctionBegin;
  PetscCall(VecGetDM(v, &dm));
  PetscCall(DMCreateLocalVector(dm, &locv)); /* VTK viewer requires exclusive ownership of the vector */
  PetscCall(PetscObjectGetName((PetscObject)v, &name));
  PetscCall(PetscObjectSetName((PetscObject)locv, name));
  PetscCall(VecCopy(v, locv));
  PetscCall(DMGetLocalSection(dm, &section));
  PetscCall(PetscSectionGetNumFields(section, &numFields));
  if (!numFields) {
    PetscCall(DMPlexGetFieldType_Internal(dm, section, PETSC_DETERMINE, &pStart, &pEnd, &ft));
    PetscCall(PetscViewerVTKAddField(viewer, (PetscObject)dm, DMPlexVTKWriteAll, PETSC_DEFAULT, ft, PETSC_TRUE, (PetscObject)locv));
  } else {
    PetscInt f;

    for (f = 0; f < numFields; f++) {
      PetscCall(DMPlexGetFieldType_Internal(dm, section, f, &pStart, &pEnd, &ft));
      if (ft == PETSC_VTK_INVALID) continue;
      PetscCall(PetscObjectReference((PetscObject)locv));
      PetscCall(PetscViewerVTKAddField(viewer, (PetscObject)dm, DMPlexVTKWriteAll, f, ft, PETSC_TRUE, (PetscObject)locv));
    }
    PetscCall(VecDestroy(&locv));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode VecView_Plex_Local(Vec v, PetscViewer viewer)
{
  DM        dm;
  PetscBool isvtk, ishdf5, isdraw, isglvis, iscgns;

  PetscFunctionBegin;
  PetscCall(VecGetDM(v, &dm));
  PetscCheck(dm, PetscObjectComm((PetscObject)v), PETSC_ERR_ARG_WRONG, "Vector not generated from a DM");
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERVTK, &isvtk));
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERHDF5, &ishdf5));
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERDRAW, &isdraw));
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERGLVIS, &isglvis));
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERCGNS, &iscgns));
  if (isvtk || ishdf5 || isdraw || isglvis || iscgns) {
    PetscInt    i, numFields;
    PetscObject fe;
    PetscBool   fem  = PETSC_FALSE;
    Vec         locv = v;
    const char *name;
    PetscInt    step;
    PetscReal   time;

    PetscCall(DMGetNumFields(dm, &numFields));
    for (i = 0; i < numFields; i++) {
      PetscCall(DMGetField(dm, i, NULL, &fe));
      if (fe->classid == PETSCFE_CLASSID) {
        fem = PETSC_TRUE;
        break;
      }
    }
    if (fem) {
      PetscObject isZero;

      PetscCall(DMGetLocalVector(dm, &locv));
      PetscCall(PetscObjectGetName((PetscObject)v, &name));
      PetscCall(PetscObjectSetName((PetscObject)locv, name));
      PetscCall(PetscObjectQuery((PetscObject)v, "__Vec_bc_zero__", &isZero));
      PetscCall(PetscObjectCompose((PetscObject)locv, "__Vec_bc_zero__", isZero));
      PetscCall(VecCopy(v, locv));
      PetscCall(DMGetOutputSequenceNumber(dm, NULL, &time));
      PetscCall(DMPlexInsertBoundaryValues(dm, PETSC_TRUE, locv, time, NULL, NULL, NULL));
    }
    if (isvtk) {
      PetscCall(VecView_Plex_Local_VTK(locv, viewer));
    } else if (ishdf5) {
#if defined(PETSC_HAVE_HDF5)
      PetscCall(VecView_Plex_Local_HDF5_Internal(locv, viewer));
#else
      SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "HDF5 not supported in this build.\nPlease reconfigure using --download-hdf5");
#endif
    } else if (isdraw) {
      PetscCall(VecView_Plex_Local_Draw(locv, viewer));
    } else if (isglvis) {
      PetscCall(DMGetOutputSequenceNumber(dm, &step, NULL));
      PetscCall(PetscViewerGLVisSetSnapId(viewer, step));
      PetscCall(VecView_GLVis(locv, viewer));
    } else if (iscgns) {
#if defined(PETSC_HAVE_CGNS)
      PetscCall(VecView_Plex_Local_CGNS(locv, viewer));
#else
      SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "CGNS not supported in this build.\nPlease reconfigure using --download-cgns");
#endif
    }
    if (fem) {
      PetscCall(PetscObjectCompose((PetscObject)locv, "__Vec_bc_zero__", NULL));
      PetscCall(DMRestoreLocalVector(dm, &locv));
    }
  } else {
    PetscBool isseq;

    PetscCall(PetscObjectTypeCompare((PetscObject)v, VECSEQ, &isseq));
    if (isseq) PetscCall(VecView_Seq(v, viewer));
    else PetscCall(VecView_MPI(v, viewer));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode VecView_Plex(Vec v, PetscViewer viewer)
{
  DM        dm;
  PetscBool isvtk, ishdf5, isdraw, isglvis, isexodusii, iscgns;

  PetscFunctionBegin;
  PetscCall(VecGetDM(v, &dm));
  PetscCheck(dm, PetscObjectComm((PetscObject)v), PETSC_ERR_ARG_WRONG, "Vector not generated from a DM");
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERVTK, &isvtk));
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERHDF5, &ishdf5));
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERDRAW, &isdraw));
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERGLVIS, &isglvis));
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERCGNS, &iscgns));
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWEREXODUSII, &isexodusii));
  if (isvtk || isdraw || isglvis || iscgns) {
    Vec         locv;
    PetscObject isZero;
    const char *name;

    PetscCall(DMGetLocalVector(dm, &locv));
    PetscCall(PetscObjectGetName((PetscObject)v, &name));
    PetscCall(PetscObjectSetName((PetscObject)locv, name));
    PetscCall(DMGlobalToLocalBegin(dm, v, INSERT_VALUES, locv));
    PetscCall(DMGlobalToLocalEnd(dm, v, INSERT_VALUES, locv));
    PetscCall(PetscObjectQuery((PetscObject)v, "__Vec_bc_zero__", &isZero));
    PetscCall(PetscObjectCompose((PetscObject)locv, "__Vec_bc_zero__", isZero));
    PetscCall(VecView_Plex_Local(locv, viewer));
    PetscCall(PetscObjectCompose((PetscObject)locv, "__Vec_bc_zero__", NULL));
    PetscCall(DMRestoreLocalVector(dm, &locv));
    /* Call flush for proper logging of VecView timings */
    if (isvtk) PetscCall(PetscViewerFlush(viewer));
  } else if (ishdf5) {
#if defined(PETSC_HAVE_HDF5)
    PetscCall(VecView_Plex_HDF5_Internal(v, viewer));
#else
    SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "HDF5 not supported in this build.\nPlease reconfigure using --download-hdf5");
#endif
  } else if (isexodusii) {
#if defined(PETSC_HAVE_EXODUSII)
    PetscCall(VecView_PlexExodusII_Internal(v, viewer));
#else
    SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "ExodusII not supported in this build.\nPlease reconfigure using --download-exodusii");
#endif
  } else {
    PetscBool isseq;

    PetscCall(PetscObjectTypeCompare((PetscObject)v, VECSEQ, &isseq));
    if (isseq) PetscCall(VecView_Seq(v, viewer));
    else PetscCall(VecView_MPI(v, viewer));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode VecView_Plex_Native(Vec originalv, PetscViewer viewer)
{
  DM                dm;
  MPI_Comm          comm;
  PetscViewerFormat format;
  Vec               v;
  PetscBool         isvtk, ishdf5;

  PetscFunctionBegin;
  PetscCall(VecGetDM(originalv, &dm));
  PetscCall(PetscObjectGetComm((PetscObject)originalv, &comm));
  PetscCheck(dm, comm, PETSC_ERR_ARG_WRONG, "Vector not generated from a DM");
  PetscCall(PetscViewerGetFormat(viewer, &format));
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERHDF5, &ishdf5));
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERVTK, &isvtk));
  if (format == PETSC_VIEWER_NATIVE) {
    /* Natural ordering is the common case for DMDA, NATIVE means plain vector, for PLEX is the opposite */
    /* this need a better fix */
    if (dm->useNatural) {
      if (dm->sfNatural) {
        const char *vecname;
        PetscInt    n, nroots;

        PetscCall(VecGetLocalSize(originalv, &n));
        PetscCall(PetscSFGetGraph(dm->sfNatural, &nroots, NULL, NULL, NULL));
        if (n == nroots) {
          PetscCall(DMPlexCreateNaturalVector(dm, &v));
          PetscCall(DMPlexGlobalToNaturalBegin(dm, originalv, v));
          PetscCall(DMPlexGlobalToNaturalEnd(dm, originalv, v));
          PetscCall(PetscObjectGetName((PetscObject)originalv, &vecname));
          PetscCall(PetscObjectSetName((PetscObject)v, vecname));
        } else SETERRQ(comm, PETSC_ERR_ARG_WRONG, "DM global to natural SF only handles global vectors");
      } else SETERRQ(comm, PETSC_ERR_ARG_WRONGSTATE, "DM global to natural SF was not created");
    } else v = originalv;
  } else v = originalv;

  if (ishdf5) {
#if defined(PETSC_HAVE_HDF5)
    PetscCall(VecView_Plex_HDF5_Native_Internal(v, viewer));
#else
    SETERRQ(comm, PETSC_ERR_SUP, "HDF5 not supported in this build.\nPlease reconfigure using --download-hdf5");
#endif
  } else if (isvtk) {
    SETERRQ(comm, PETSC_ERR_SUP, "VTK format does not support viewing in natural order. Please switch to HDF5.");
  } else {
    PetscBool isseq;

    PetscCall(PetscObjectTypeCompare((PetscObject)v, VECSEQ, &isseq));
    if (isseq) PetscCall(VecView_Seq(v, viewer));
    else PetscCall(VecView_MPI(v, viewer));
  }
  if (v != originalv) PetscCall(VecDestroy(&v));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode VecLoad_Plex_Local(Vec v, PetscViewer viewer)
{
  DM        dm;
  PetscBool ishdf5;

  PetscFunctionBegin;
  PetscCall(VecGetDM(v, &dm));
  PetscCheck(dm, PetscObjectComm((PetscObject)v), PETSC_ERR_ARG_WRONG, "Vector not generated from a DM");
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERHDF5, &ishdf5));
  if (ishdf5) {
    DM          dmBC;
    Vec         gv;
    const char *name;

    PetscCall(DMGetOutputDM(dm, &dmBC));
    PetscCall(DMGetGlobalVector(dmBC, &gv));
    PetscCall(PetscObjectGetName((PetscObject)v, &name));
    PetscCall(PetscObjectSetName((PetscObject)gv, name));
    PetscCall(VecLoad_Default(gv, viewer));
    PetscCall(DMGlobalToLocalBegin(dmBC, gv, INSERT_VALUES, v));
    PetscCall(DMGlobalToLocalEnd(dmBC, gv, INSERT_VALUES, v));
    PetscCall(DMRestoreGlobalVector(dmBC, &gv));
  } else PetscCall(VecLoad_Default(v, viewer));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode VecLoad_Plex(Vec v, PetscViewer viewer)
{
  DM        dm;
  PetscBool ishdf5, isexodusii, iscgns;

  PetscFunctionBegin;
  PetscCall(VecGetDM(v, &dm));
  PetscCheck(dm, PetscObjectComm((PetscObject)v), PETSC_ERR_ARG_WRONG, "Vector not generated from a DM");
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERHDF5, &ishdf5));
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWEREXODUSII, &isexodusii));
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERCGNS, &iscgns));
  if (ishdf5) {
#if defined(PETSC_HAVE_HDF5)
    PetscCall(VecLoad_Plex_HDF5_Internal(v, viewer));
#else
    SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "HDF5 not supported in this build.\nPlease reconfigure using --download-hdf5");
#endif
  } else if (isexodusii) {
#if defined(PETSC_HAVE_EXODUSII)
    PetscCall(VecLoad_PlexExodusII_Internal(v, viewer));
#else
    SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "ExodusII not supported in this build.\nPlease reconfigure using --download-exodusii");
#endif
  } else if (iscgns) {
#if defined(PETSC_HAVE_CGNS)
    PetscCall(VecLoad_Plex_CGNS_Internal(v, viewer));
#else
    SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "CGNS not supported in this build.\nPlease reconfigure using --download-cgns");
#endif
  } else PetscCall(VecLoad_Default(v, viewer));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode VecLoad_Plex_Native(Vec originalv, PetscViewer viewer)
{
  DM                dm;
  PetscViewerFormat format;
  PetscBool         ishdf5;

  PetscFunctionBegin;
  PetscCall(VecGetDM(originalv, &dm));
  PetscCheck(dm, PetscObjectComm((PetscObject)originalv), PETSC_ERR_ARG_WRONG, "Vector not generated from a DM");
  PetscCall(PetscViewerGetFormat(viewer, &format));
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERHDF5, &ishdf5));
  if (format == PETSC_VIEWER_NATIVE) {
    if (dm->useNatural) {
      if (dm->sfNatural) {
        if (ishdf5) {
#if defined(PETSC_HAVE_HDF5)
          Vec         v;
          const char *vecname;

          PetscCall(DMPlexCreateNaturalVector(dm, &v));
          PetscCall(PetscObjectGetName((PetscObject)originalv, &vecname));
          PetscCall(PetscObjectSetName((PetscObject)v, vecname));
          PetscCall(VecLoad_Plex_HDF5_Native_Internal(v, viewer));
          PetscCall(DMPlexNaturalToGlobalBegin(dm, v, originalv));
          PetscCall(DMPlexNaturalToGlobalEnd(dm, v, originalv));
          PetscCall(VecDestroy(&v));
#else
          SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "HDF5 not supported in this build.\nPlease reconfigure using --download-hdf5");
#endif
        } else SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Reading in natural order is not supported for anything but HDF5.");
      }
    } else PetscCall(VecLoad_Default(originalv, viewer));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

PETSC_UNUSED static PetscErrorCode DMPlexView_Ascii_Geometry(DM dm, PetscViewer viewer)
{
  PetscSection       coordSection;
  Vec                coordinates;
  DMLabel            depthLabel, celltypeLabel;
  const char        *name[4];
  const PetscScalar *a;
  PetscInt           dim, pStart, pEnd, cStart, cEnd, c;

  PetscFunctionBegin;
  PetscCall(DMGetDimension(dm, &dim));
  PetscCall(DMGetCoordinatesLocal(dm, &coordinates));
  PetscCall(DMGetCoordinateSection(dm, &coordSection));
  PetscCall(DMPlexGetDepthLabel(dm, &depthLabel));
  PetscCall(DMPlexGetCellTypeLabel(dm, &celltypeLabel));
  PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
  PetscCall(PetscSectionGetChart(coordSection, &pStart, &pEnd));
  PetscCall(VecGetArrayRead(coordinates, &a));
  name[0]       = "vertex";
  name[1]       = "edge";
  name[dim - 1] = "face";
  name[dim]     = "cell";
  for (c = cStart; c < cEnd; ++c) {
    PetscInt *closure = NULL;
    PetscInt  closureSize, cl, ct;

    PetscCall(DMLabelGetValue(celltypeLabel, c, &ct));
    PetscCall(PetscViewerASCIIPrintf(viewer, "Geometry for cell %" PetscInt_FMT " polytope type %s:\n", c, DMPolytopeTypes[ct]));
    PetscCall(DMPlexGetTransitiveClosure(dm, c, PETSC_TRUE, &closureSize, &closure));
    PetscCall(PetscViewerASCIIPushTab(viewer));
    for (cl = 0; cl < closureSize * 2; cl += 2) {
      PetscInt point = closure[cl], depth, dof, off, d, p;

      if ((point < pStart) || (point >= pEnd)) continue;
      PetscCall(PetscSectionGetDof(coordSection, point, &dof));
      if (!dof) continue;
      PetscCall(DMLabelGetValue(depthLabel, point, &depth));
      PetscCall(PetscSectionGetOffset(coordSection, point, &off));
      PetscCall(PetscViewerASCIIPrintf(viewer, "%s %" PetscInt_FMT " coords:", name[depth], point));
      for (p = 0; p < dof / dim; ++p) {
        PetscCall(PetscViewerASCIIPrintf(viewer, " ("));
        for (d = 0; d < dim; ++d) {
          if (d > 0) PetscCall(PetscViewerASCIIPrintf(viewer, ", "));
          PetscCall(PetscViewerASCIIPrintf(viewer, "%g", (double)PetscRealPart(a[off + p * dim + d])));
        }
        PetscCall(PetscViewerASCIIPrintf(viewer, ")"));
      }
      PetscCall(PetscViewerASCIIPrintf(viewer, "\n"));
    }
    PetscCall(DMPlexRestoreTransitiveClosure(dm, c, PETSC_TRUE, &closureSize, &closure));
    PetscCall(PetscViewerASCIIPopTab(viewer));
  }
  PetscCall(VecRestoreArrayRead(coordinates, &a));
  PetscFunctionReturn(PETSC_SUCCESS);
}

typedef enum {
  CS_CARTESIAN,
  CS_POLAR,
  CS_CYLINDRICAL,
  CS_SPHERICAL
} CoordSystem;
const char *CoordSystems[] = {"cartesian", "polar", "cylindrical", "spherical", "CoordSystem", "CS_", NULL};

static PetscErrorCode DMPlexView_Ascii_Coordinates(PetscViewer viewer, CoordSystem cs, PetscInt dim, const PetscScalar x[])
{
  PetscInt i;

  PetscFunctionBegin;
  if (dim > 3) {
    for (i = 0; i < dim; ++i) PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, " %g", (double)PetscRealPart(x[i])));
  } else {
    PetscReal coords[3], trcoords[3] = {0., 0., 0.};

    for (i = 0; i < dim; ++i) coords[i] = PetscRealPart(x[i]);
    switch (cs) {
    case CS_CARTESIAN:
      for (i = 0; i < dim; ++i) trcoords[i] = coords[i];
      break;
    case CS_POLAR:
      PetscCheck(dim == 2, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Polar coordinates are for 2 dimension, not %" PetscInt_FMT, dim);
      trcoords[0] = PetscSqrtReal(PetscSqr(coords[0]) + PetscSqr(coords[1]));
      trcoords[1] = PetscAtan2Real(coords[1], coords[0]);
      break;
    case CS_CYLINDRICAL:
      PetscCheck(dim == 3, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cylindrical coordinates are for 3 dimension, not %" PetscInt_FMT, dim);
      trcoords[0] = PetscSqrtReal(PetscSqr(coords[0]) + PetscSqr(coords[1]));
      trcoords[1] = PetscAtan2Real(coords[1], coords[0]);
      trcoords[2] = coords[2];
      break;
    case CS_SPHERICAL:
      PetscCheck(dim == 3, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Spherical coordinates are for 3 dimension, not %" PetscInt_FMT, dim);
      trcoords[0] = PetscSqrtReal(PetscSqr(coords[0]) + PetscSqr(coords[1]) + PetscSqr(coords[2]));
      trcoords[1] = PetscAtan2Real(PetscSqrtReal(PetscSqr(coords[0]) + PetscSqr(coords[1])), coords[2]);
      trcoords[2] = PetscAtan2Real(coords[1], coords[0]);
      break;
    }
    for (i = 0; i < dim; ++i) PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, " %g", (double)trcoords[i]));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode DMPlexView_Ascii(DM dm, PetscViewer viewer)
{
  DM_Plex          *mesh = (DM_Plex *)dm->data;
  DM                cdm, cdmCell;
  PetscSection      coordSection, coordSectionCell;
  Vec               coordinates, coordinatesCell;
  PetscViewerFormat format;

  PetscFunctionBegin;
  PetscCall(PetscViewerGetFormat(viewer, &format));
  if (format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
    const char *name;
    PetscInt    dim, cellHeight, maxConeSize, maxSupportSize;
    PetscInt    pStart, pEnd, p, numLabels, l;
    PetscMPIInt rank, size;

    PetscCall(DMGetCoordinateDM(dm, &cdm));
    PetscCall(DMGetCoordinateSection(dm, &coordSection));
    PetscCall(DMGetCoordinatesLocal(dm, &coordinates));
    PetscCall(DMGetCellCoordinateDM(dm, &cdmCell));
    PetscCall(DMGetCellCoordinateSection(dm, &coordSectionCell));
    PetscCall(DMGetCellCoordinatesLocal(dm, &coordinatesCell));
    PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank));
    PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)dm), &size));
    PetscCall(PetscObjectGetName((PetscObject)dm, &name));
    PetscCall(DMPlexGetChart(dm, &pStart, &pEnd));
    PetscCall(DMPlexGetMaxSizes(dm, &maxConeSize, &maxSupportSize));
    PetscCall(DMGetDimension(dm, &dim));
    PetscCall(DMPlexGetVTKCellHeight(dm, &cellHeight));
    if (name) PetscCall(PetscViewerASCIIPrintf(viewer, "%s in %" PetscInt_FMT " dimension%s:\n", name, dim, dim == 1 ? "" : "s"));
    else PetscCall(PetscViewerASCIIPrintf(viewer, "Mesh in %" PetscInt_FMT " dimension%s:\n", dim, dim == 1 ? "" : "s"));
    if (cellHeight) PetscCall(PetscViewerASCIIPrintf(viewer, "  Cells are at height %" PetscInt_FMT "\n", cellHeight));
    PetscCall(PetscViewerASCIIPrintf(viewer, "Supports:\n"));
    PetscCall(PetscViewerASCIIPushSynchronized(viewer));
    PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "[%d] Max support size: %" PetscInt_FMT "\n", rank, maxSupportSize));
    for (p = pStart; p < pEnd; ++p) {
      PetscInt dof, off, s;

      PetscCall(PetscSectionGetDof(mesh->supportSection, p, &dof));
      PetscCall(PetscSectionGetOffset(mesh->supportSection, p, &off));
      for (s = off; s < off + dof; ++s) PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "[%d]: %" PetscInt_FMT " ----> %" PetscInt_FMT "\n", rank, p, mesh->supports[s]));
    }
    PetscCall(PetscViewerFlush(viewer));
    PetscCall(PetscViewerASCIIPrintf(viewer, "Cones:\n"));
    PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "[%d] Max cone size: %" PetscInt_FMT "\n", rank, maxConeSize));
    for (p = pStart; p < pEnd; ++p) {
      PetscInt dof, off, c;

      PetscCall(PetscSectionGetDof(mesh->coneSection, p, &dof));
      PetscCall(PetscSectionGetOffset(mesh->coneSection, p, &off));
      for (c = off; c < off + dof; ++c) PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "[%d]: %" PetscInt_FMT " <---- %" PetscInt_FMT " (%" PetscInt_FMT ")\n", rank, p, mesh->cones[c], mesh->coneOrientations[c]));
    }
    PetscCall(PetscViewerFlush(viewer));
    PetscCall(PetscViewerASCIIPopSynchronized(viewer));
    if (coordSection && coordinates) {
      CoordSystem        cs = CS_CARTESIAN;
      const PetscScalar *array, *arrayCell = NULL;
      PetscInt           Nf, Nc, pvStart, pvEnd, pcStart = PETSC_MAX_INT, pcEnd = PETSC_MIN_INT, pStart, pEnd, p;
      PetscMPIInt        rank;
      const char        *name;

      PetscCall(PetscOptionsGetEnum(((PetscObject)viewer)->options, ((PetscObject)viewer)->prefix, "-dm_plex_view_coord_system", CoordSystems, (PetscEnum *)&cs, NULL));
      PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)viewer), &rank));
      PetscCall(PetscSectionGetNumFields(coordSection, &Nf));
      PetscCheck(Nf == 1, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Coordinate section should have 1 field, not %" PetscInt_FMT, Nf);
      PetscCall(PetscSectionGetFieldComponents(coordSection, 0, &Nc));
      PetscCall(PetscSectionGetChart(coordSection, &pvStart, &pvEnd));
      if (coordSectionCell) PetscCall(PetscSectionGetChart(coordSectionCell, &pcStart, &pcEnd));
      pStart = PetscMin(pvStart, pcStart);
      pEnd   = PetscMax(pvEnd, pcEnd);
      PetscCall(PetscObjectGetName((PetscObject)coordinates, &name));
      PetscCall(PetscViewerASCIIPrintf(viewer, "%s with %" PetscInt_FMT " fields\n", name, Nf));
      PetscCall(PetscViewerASCIIPrintf(viewer, "  field 0 with %" PetscInt_FMT " components\n", Nc));
      if (cs != CS_CARTESIAN) PetscCall(PetscViewerASCIIPrintf(viewer, "  output coordinate system: %s\n", CoordSystems[cs]));

      PetscCall(VecGetArrayRead(coordinates, &array));
      if (coordinatesCell) PetscCall(VecGetArrayRead(coordinatesCell, &arrayCell));
      PetscCall(PetscViewerASCIIPushSynchronized(viewer));
      PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "Process %d:\n", rank));
      for (p = pStart; p < pEnd; ++p) {
        PetscInt dof, off;

        if (p >= pvStart && p < pvEnd) {
          PetscCall(PetscSectionGetDof(coordSection, p, &dof));
          PetscCall(PetscSectionGetOffset(coordSection, p, &off));
          if (dof) {
            PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "  (%4" PetscInt_FMT ") dim %2" PetscInt_FMT " offset %3" PetscInt_FMT, p, dof, off));
            PetscCall(DMPlexView_Ascii_Coordinates(viewer, cs, dof, &array[off]));
            PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "\n"));
          }
        }
        if (cdmCell && p >= pcStart && p < pcEnd) {
          PetscCall(PetscSectionGetDof(coordSectionCell, p, &dof));
          PetscCall(PetscSectionGetOffset(coordSectionCell, p, &off));
          if (dof) {
            PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "  (%4" PetscInt_FMT ") dim %2" PetscInt_FMT " offset %3" PetscInt_FMT, p, dof, off));
            PetscCall(DMPlexView_Ascii_Coordinates(viewer, cs, dof, &arrayCell[off]));
            PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "\n"));
          }
        }
      }
      PetscCall(PetscViewerFlush(viewer));
      PetscCall(PetscViewerASCIIPopSynchronized(viewer));
      PetscCall(VecRestoreArrayRead(coordinates, &array));
      if (coordinatesCell) PetscCall(VecRestoreArrayRead(coordinatesCell, &arrayCell));
    }
    PetscCall(DMGetNumLabels(dm, &numLabels));
    if (numLabels) PetscCall(PetscViewerASCIIPrintf(viewer, "Labels:\n"));
    for (l = 0; l < numLabels; ++l) {
      DMLabel     label;
      PetscBool   isdepth;
      const char *name;

      PetscCall(DMGetLabelName(dm, l, &name));
      PetscCall(PetscStrcmp(name, "depth", &isdepth));
      if (isdepth) continue;
      PetscCall(DMGetLabel(dm, name, &label));
      PetscCall(DMLabelView(label, viewer));
    }
    if (size > 1) {
      PetscSF sf;

      PetscCall(DMGetPointSF(dm, &sf));
      PetscCall(PetscSFView(sf, viewer));
    }
    if (mesh->periodic.face_sfs)
      for (PetscInt i = 0; i < mesh->periodic.num_face_sfs; i++) PetscCall(PetscSFView(mesh->periodic.face_sfs[i], viewer));
    PetscCall(PetscViewerFlush(viewer));
  } else if (format == PETSC_VIEWER_ASCII_LATEX) {
    const char  *name, *color;
    const char  *defcolors[3]  = {"gray", "orange", "green"};
    const char  *deflcolors[4] = {"blue", "cyan", "red", "magenta"};
    char         lname[PETSC_MAX_PATH_LEN];
    PetscReal    scale      = 2.0;
    PetscReal    tikzscale  = 1.0;
    PetscBool    useNumbers = PETSC_TRUE, drawNumbers[4], drawColors[4], useLabels, useColors, plotEdges, drawHasse = PETSC_FALSE;
    double       tcoords[3];
    PetscScalar *coords;
    PetscInt     numLabels, l, numColors, numLColors, dim, d, depth, cStart, cEnd, c, vStart, vEnd, v, eStart = 0, eEnd = 0, fStart = 0, fEnd = 0, e, p, n;
    PetscMPIInt  rank, size;
    char       **names, **colors, **lcolors;
    PetscBool    flg, lflg;
    PetscBT      wp = NULL;
    PetscInt     pEnd, pStart;

    PetscCall(DMGetCoordinateDM(dm, &cdm));
    PetscCall(DMGetCoordinateSection(dm, &coordSection));
    PetscCall(DMGetCoordinatesLocal(dm, &coordinates));
    PetscCall(DMGetCellCoordinateDM(dm, &cdmCell));
    PetscCall(DMGetCellCoordinateSection(dm, &coordSectionCell));
    PetscCall(DMGetCellCoordinatesLocal(dm, &coordinatesCell));
    PetscCall(DMGetDimension(dm, &dim));
    PetscCall(DMPlexGetDepth(dm, &depth));
    PetscCall(DMGetNumLabels(dm, &numLabels));
    numLabels  = PetscMax(numLabels, 10);
    numColors  = 10;
    numLColors = 10;
    PetscCall(PetscCalloc3(numLabels, &names, numColors, &colors, numLColors, &lcolors));
    PetscCall(PetscOptionsGetReal(((PetscObject)viewer)->options, ((PetscObject)viewer)->prefix, "-dm_plex_view_scale", &scale, NULL));
    PetscCall(PetscOptionsGetReal(((PetscObject)viewer)->options, ((PetscObject)viewer)->prefix, "-dm_plex_view_tikzscale", &tikzscale, NULL));
    PetscCall(PetscOptionsGetBool(((PetscObject)viewer)->options, ((PetscObject)viewer)->prefix, "-dm_plex_view_numbers", &useNumbers, NULL));
    for (d = 0; d < 4; ++d) drawNumbers[d] = useNumbers;
    for (d = 0; d < 4; ++d) drawColors[d] = PETSC_TRUE;
    n = 4;
    PetscCall(PetscOptionsGetBoolArray(((PetscObject)viewer)->options, ((PetscObject)viewer)->prefix, "-dm_plex_view_numbers_depth", drawNumbers, &n, &flg));
    PetscCheck(!flg || n == dim + 1, PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_SIZ, "Number of flags %" PetscInt_FMT " != %" PetscInt_FMT " dim+1", n, dim + 1);
    n = 4;
    PetscCall(PetscOptionsGetBoolArray(((PetscObject)viewer)->options, ((PetscObject)viewer)->prefix, "-dm_plex_view_colors_depth", drawColors, &n, &flg));
    PetscCheck(!flg || n == dim + 1, PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_SIZ, "Number of flags %" PetscInt_FMT " != %" PetscInt_FMT " dim+1", n, dim + 1);
    PetscCall(PetscOptionsGetStringArray(((PetscObject)viewer)->options, ((PetscObject)viewer)->prefix, "-dm_plex_view_labels", names, &numLabels, &useLabels));
    if (!useLabels) numLabels = 0;
    PetscCall(PetscOptionsGetStringArray(((PetscObject)viewer)->options, ((PetscObject)viewer)->prefix, "-dm_plex_view_colors", colors, &numColors, &useColors));
    if (!useColors) {
      numColors = 3;
      for (c = 0; c < numColors; ++c) PetscCall(PetscStrallocpy(defcolors[c], &colors[c]));
    }
    PetscCall(PetscOptionsGetStringArray(((PetscObject)viewer)->options, ((PetscObject)viewer)->prefix, "-dm_plex_view_lcolors", lcolors, &numLColors, &useColors));
    if (!useColors) {
      numLColors = 4;
      for (c = 0; c < numLColors; ++c) PetscCall(PetscStrallocpy(deflcolors[c], &lcolors[c]));
    }
    PetscCall(PetscOptionsGetString(((PetscObject)viewer)->options, ((PetscObject)viewer)->prefix, "-dm_plex_view_label_filter", lname, sizeof(lname), &lflg));
    plotEdges = (PetscBool)(depth > 1 && drawNumbers[1] && dim < 3);
    PetscCall(PetscOptionsGetBool(((PetscObject)viewer)->options, ((PetscObject)viewer)->prefix, "-dm_plex_view_edges", &plotEdges, &flg));
    PetscCheck(!flg || !plotEdges || depth >= dim, PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Mesh must be interpolated");
    if (depth < dim) plotEdges = PETSC_FALSE;
    PetscCall(PetscOptionsGetBool(((PetscObject)viewer)->options, ((PetscObject)viewer)->prefix, "-dm_plex_view_hasse", &drawHasse, NULL));

    /* filter points with labelvalue != labeldefaultvalue */
    PetscCall(DMPlexGetChart(dm, &pStart, &pEnd));
    PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
    PetscCall(DMPlexGetDepthStratum(dm, 1, &eStart, &eEnd));
    PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
    PetscCall(DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd));
    if (lflg) {
      DMLabel lbl;

      PetscCall(DMGetLabel(dm, lname, &lbl));
      if (lbl) {
        PetscInt val, defval;

        PetscCall(DMLabelGetDefaultValue(lbl, &defval));
        PetscCall(PetscBTCreate(pEnd - pStart, &wp));
        for (c = pStart; c < pEnd; c++) {
          PetscInt *closure = NULL;
          PetscInt  closureSize;

          PetscCall(DMLabelGetValue(lbl, c, &val));
          if (val == defval) continue;

          PetscCall(DMPlexGetTransitiveClosure(dm, c, PETSC_TRUE, &closureSize, &closure));
          for (p = 0; p < closureSize * 2; p += 2) PetscCall(PetscBTSet(wp, closure[p] - pStart));
          PetscCall(DMPlexRestoreTransitiveClosure(dm, c, PETSC_TRUE, &closureSize, &closure));
        }
      }
    }

    PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank));
    PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)dm), &size));
    PetscCall(PetscObjectGetName((PetscObject)dm, &name));
    PetscCall(PetscViewerASCIIPrintf(viewer, "\
\\documentclass[tikz]{standalone}\n\n\
\\usepackage{pgflibraryshapes}\n\
\\usetikzlibrary{backgrounds}\n\
\\usetikzlibrary{arrows}\n\
\\begin{document}\n"));
    if (size > 1) {
      PetscCall(PetscViewerASCIIPrintf(viewer, "%s for process ", name));
      for (p = 0; p < size; ++p) {
        if (p) PetscCall(PetscViewerASCIIPrintf(viewer, (p == size - 1) ? ", and " : ", "));
        PetscCall(PetscViewerASCIIPrintf(viewer, "{\\textcolor{%s}%" PetscInt_FMT "}", colors[p % numColors], p));
      }
      PetscCall(PetscViewerASCIIPrintf(viewer, ".\n\n\n"));
    }
    if (drawHasse) {
      PetscInt maxStratum = PetscMax(vEnd - vStart, PetscMax(eEnd - eStart, PetscMax(fEnd - fStart, cEnd - cStart)));

      PetscCall(PetscViewerASCIIPrintf(viewer, "\\newcommand{\\vStart}{%" PetscInt_FMT "}\n", vStart));
      PetscCall(PetscViewerASCIIPrintf(viewer, "\\newcommand{\\vEnd}{%" PetscInt_FMT "}\n", vEnd - 1));
      PetscCall(PetscViewerASCIIPrintf(viewer, "\\newcommand{\\numVertices}{%" PetscInt_FMT "}\n", vEnd - vStart));
      PetscCall(PetscViewerASCIIPrintf(viewer, "\\newcommand{\\vShift}{%.2f}\n", 3 + (maxStratum - (vEnd - vStart)) / 2.));
      PetscCall(PetscViewerASCIIPrintf(viewer, "\\newcommand{\\eStart}{%" PetscInt_FMT "}\n", eStart));
      PetscCall(PetscViewerASCIIPrintf(viewer, "\\newcommand{\\eEnd}{%" PetscInt_FMT "}\n", eEnd - 1));
      PetscCall(PetscViewerASCIIPrintf(viewer, "\\newcommand{\\eShift}{%.2f}\n", 3 + (maxStratum - (eEnd - eStart)) / 2.));
      PetscCall(PetscViewerASCIIPrintf(viewer, "\\newcommand{\\numEdges}{%" PetscInt_FMT "}\n", eEnd - eStart));
      PetscCall(PetscViewerASCIIPrintf(viewer, "\\newcommand{\\fStart}{%" PetscInt_FMT "}\n", fStart));
      PetscCall(PetscViewerASCIIPrintf(viewer, "\\newcommand{\\fEnd}{%" PetscInt_FMT "}\n", fEnd - 1));
      PetscCall(PetscViewerASCIIPrintf(viewer, "\\newcommand{\\fShift}{%.2f}\n", 3 + (maxStratum - (fEnd - fStart)) / 2.));
      PetscCall(PetscViewerASCIIPrintf(viewer, "\\newcommand{\\numFaces}{%" PetscInt_FMT "}\n", fEnd - fStart));
      PetscCall(PetscViewerASCIIPrintf(viewer, "\\newcommand{\\cStart}{%" PetscInt_FMT "}\n", cStart));
      PetscCall(PetscViewerASCIIPrintf(viewer, "\\newcommand{\\cEnd}{%" PetscInt_FMT "}\n", cEnd - 1));
      PetscCall(PetscViewerASCIIPrintf(viewer, "\\newcommand{\\numCells}{%" PetscInt_FMT "}\n", cEnd - cStart));
      PetscCall(PetscViewerASCIIPrintf(viewer, "\\newcommand{\\cShift}{%.2f}\n", 3 + (maxStratum - (cEnd - cStart)) / 2.));
    }
    PetscCall(PetscViewerASCIIPrintf(viewer, "\\begin{tikzpicture}[scale = %g,font=\\fontsize{8}{8}\\selectfont]\n", (double)tikzscale));

    /* Plot vertices */
    PetscCall(VecGetArray(coordinates, &coords));
    PetscCall(PetscViewerASCIIPushSynchronized(viewer));
    for (v = vStart; v < vEnd; ++v) {
      PetscInt  off, dof, d;
      PetscBool isLabeled = PETSC_FALSE;

      if (wp && !PetscBTLookup(wp, v - pStart)) continue;
      PetscCall(PetscSectionGetDof(coordSection, v, &dof));
      PetscCall(PetscSectionGetOffset(coordSection, v, &off));
      PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "\\path ("));
      PetscCheck(dof <= 3, PETSC_COMM_SELF, PETSC_ERR_PLIB, "coordSection vertex %" PetscInt_FMT " has dof %" PetscInt_FMT " > 3", v, dof);
      for (d = 0; d < dof; ++d) {
        tcoords[d] = (double)(scale * PetscRealPart(coords[off + d]));
        tcoords[d] = PetscAbs(tcoords[d]) < 1e-10 ? 0.0 : tcoords[d];
      }
      /* Rotate coordinates since PGF makes z point out of the page instead of up */
      if (dim == 3) {
        PetscReal tmp = tcoords[1];
        tcoords[1]    = tcoords[2];
        tcoords[2]    = -tmp;
      }
      for (d = 0; d < dof; ++d) {
        if (d > 0) PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, ","));
        PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "%g", (double)tcoords[d]));
      }
      if (drawHasse) color = colors[0 % numColors];
      else color = colors[rank % numColors];
      for (l = 0; l < numLabels; ++l) {
        PetscInt val;
        PetscCall(DMGetLabelValue(dm, names[l], v, &val));
        if (val >= 0) {
          color     = lcolors[l % numLColors];
          isLabeled = PETSC_TRUE;
          break;
        }
      }
      if (drawNumbers[0]) {
        PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, ") node(%" PetscInt_FMT "_%d) [draw,shape=circle,color=%s] {%" PetscInt_FMT "};\n", v, rank, color, v));
      } else if (drawColors[0]) {
        PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, ") node(%" PetscInt_FMT "_%d) [fill,inner sep=%dpt,shape=circle,color=%s] {};\n", v, rank, !isLabeled ? 1 : 2, color));
      } else PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, ") node(%" PetscInt_FMT "_%d) [] {};\n", v, rank));
    }
    PetscCall(VecRestoreArray(coordinates, &coords));
    PetscCall(PetscViewerFlush(viewer));
    /* Plot edges */
    if (plotEdges) {
      PetscCall(VecGetArray(coordinates, &coords));
      PetscCall(PetscViewerASCIIPrintf(viewer, "\\path\n"));
      for (e = eStart; e < eEnd; ++e) {
        const PetscInt *cone;
        PetscInt        coneSize, offA, offB, dof, d;

        if (wp && !PetscBTLookup(wp, e - pStart)) continue;
        PetscCall(DMPlexGetConeSize(dm, e, &coneSize));
        PetscCheck(coneSize == 2, PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Edge %" PetscInt_FMT " cone should have two vertices, not %" PetscInt_FMT, e, coneSize);
        PetscCall(DMPlexGetCone(dm, e, &cone));
        PetscCall(PetscSectionGetDof(coordSection, cone[0], &dof));
        PetscCall(PetscSectionGetOffset(coordSection, cone[0], &offA));
        PetscCall(PetscSectionGetOffset(coordSection, cone[1], &offB));
        PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "("));
        for (d = 0; d < dof; ++d) {
          tcoords[d] = (double)(0.5 * scale * PetscRealPart(coords[offA + d] + coords[offB + d]));
          tcoords[d] = PetscAbs(tcoords[d]) < 1e-10 ? 0.0 : tcoords[d];
        }
        /* Rotate coordinates since PGF makes z point out of the page instead of up */
        if (dim == 3) {
          PetscReal tmp = tcoords[1];
          tcoords[1]    = tcoords[2];
          tcoords[2]    = -tmp;
        }
        for (d = 0; d < dof; ++d) {
          if (d > 0) PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, ","));
          PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "%g", (double)tcoords[d]));
        }
        if (drawHasse) color = colors[1 % numColors];
        else color = colors[rank % numColors];
        for (l = 0; l < numLabels; ++l) {
          PetscInt val;
          PetscCall(DMGetLabelValue(dm, names[l], e, &val));
          if (val >= 0) {
            color = lcolors[l % numLColors];
            break;
          }
        }
        PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, ") node(%" PetscInt_FMT "_%d) [draw,shape=circle,color=%s] {%" PetscInt_FMT "} --\n", e, rank, color, e));
      }
      PetscCall(VecRestoreArray(coordinates, &coords));
      PetscCall(PetscViewerFlush(viewer));
      PetscCall(PetscViewerASCIIPrintf(viewer, "(0,0);\n"));
    }
    /* Plot cells */
    if (dim == 3 || !drawNumbers[1]) {
      for (e = eStart; e < eEnd; ++e) {
        const PetscInt *cone;

        if (wp && !PetscBTLookup(wp, e - pStart)) continue;
        color = colors[rank % numColors];
        for (l = 0; l < numLabels; ++l) {
          PetscInt val;
          PetscCall(DMGetLabelValue(dm, names[l], e, &val));
          if (val >= 0) {
            color = lcolors[l % numLColors];
            break;
          }
        }
        PetscCall(DMPlexGetCone(dm, e, &cone));
        PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "\\draw[color=%s] (%" PetscInt_FMT "_%d) -- (%" PetscInt_FMT "_%d);\n", color, cone[0], rank, cone[1], rank));
      }
    } else {
      DMPolytopeType ct;

      /* Drawing a 2D polygon */
      for (c = cStart; c < cEnd; ++c) {
        if (wp && !PetscBTLookup(wp, c - pStart)) continue;
        PetscCall(DMPlexGetCellType(dm, c, &ct));
        if (DMPolytopeTypeIsHybrid(ct)) {
          const PetscInt *cone;
          PetscInt        coneSize, e;

          PetscCall(DMPlexGetCone(dm, c, &cone));
          PetscCall(DMPlexGetConeSize(dm, c, &coneSize));
          for (e = 0; e < coneSize; ++e) {
            const PetscInt *econe;

            PetscCall(DMPlexGetCone(dm, cone[e], &econe));
            PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "\\draw[color=%s] (%" PetscInt_FMT "_%d) -- (%" PetscInt_FMT "_%d) -- (%" PetscInt_FMT "_%d);\n", colors[rank % numColors], econe[0], rank, cone[e], rank, econe[1], rank));
          }
        } else {
          PetscInt *closure = NULL;
          PetscInt  closureSize, Nv = 0, v;

          PetscCall(DMPlexGetTransitiveClosure(dm, c, PETSC_TRUE, &closureSize, &closure));
          for (p = 0; p < closureSize * 2; p += 2) {
            const PetscInt point = closure[p];

            if ((point >= vStart) && (point < vEnd)) closure[Nv++] = point;
          }
          PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "\\draw[color=%s] ", colors[rank % numColors]));
          for (v = 0; v <= Nv; ++v) {
            const PetscInt vertex = closure[v % Nv];

            if (v > 0) {
              if (plotEdges) {
                const PetscInt *edge;
                PetscInt        endpoints[2], ne;

                endpoints[0] = closure[v - 1];
                endpoints[1] = vertex;
                PetscCall(DMPlexGetJoin(dm, 2, endpoints, &ne, &edge));
                PetscCheck(ne == 1, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Could not find edge for vertices %" PetscInt_FMT ", %" PetscInt_FMT, endpoints[0], endpoints[1]);
                PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, " -- (%" PetscInt_FMT "_%d) -- ", edge[0], rank));
                PetscCall(DMPlexRestoreJoin(dm, 2, endpoints, &ne, &edge));
              } else PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, " -- "));
            }
            PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "(%" PetscInt_FMT "_%d)", vertex, rank));
          }
          PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, ";\n"));
          PetscCall(DMPlexRestoreTransitiveClosure(dm, c, PETSC_TRUE, &closureSize, &closure));
        }
      }
    }
    for (c = cStart; c < cEnd; ++c) {
      double             ccoords[3] = {0.0, 0.0, 0.0};
      PetscBool          isLabeled  = PETSC_FALSE;
      PetscScalar       *cellCoords = NULL;
      const PetscScalar *array;
      PetscInt           numCoords, cdim, d;
      PetscBool          isDG;

      if (wp && !PetscBTLookup(wp, c - pStart)) continue;
      PetscCall(DMGetCoordinateDim(dm, &cdim));
      PetscCall(DMPlexGetCellCoordinates(dm, c, &isDG, &numCoords, &array, &cellCoords));
      PetscCheck(!(numCoords % cdim), PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "coordinate dim %" PetscInt_FMT " does not divide numCoords %" PetscInt_FMT, cdim, numCoords);
      PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "\\path ("));
      for (p = 0; p < numCoords / cdim; ++p) {
        for (d = 0; d < cdim; ++d) {
          tcoords[d] = (double)(scale * PetscRealPart(cellCoords[p * cdim + d]));
          tcoords[d] = PetscAbs(tcoords[d]) < 1e-10 ? 0.0 : tcoords[d];
        }
        /* Rotate coordinates since PGF makes z point out of the page instead of up */
        if (cdim == 3) {
          PetscReal tmp = tcoords[1];
          tcoords[1]    = tcoords[2];
          tcoords[2]    = -tmp;
        }
        for (d = 0; d < dim; ++d) ccoords[d] += tcoords[d];
      }
      for (d = 0; d < cdim; ++d) ccoords[d] /= (numCoords / cdim);
      PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &array, &cellCoords));
      for (d = 0; d < cdim; ++d) {
        if (d > 0) PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, ","));
        PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "%g", (double)ccoords[d]));
      }
      if (drawHasse) color = colors[depth % numColors];
      else color = colors[rank % numColors];
      for (l = 0; l < numLabels; ++l) {
        PetscInt val;
        PetscCall(DMGetLabelValue(dm, names[l], c, &val));
        if (val >= 0) {
          color     = lcolors[l % numLColors];
          isLabeled = PETSC_TRUE;
          break;
        }
      }
      if (drawNumbers[dim]) {
        PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, ") node(%" PetscInt_FMT "_%d) [draw,shape=circle,color=%s] {%" PetscInt_FMT "};\n", c, rank, color, c));
      } else if (drawColors[dim]) {
        PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, ") node(%" PetscInt_FMT "_%d) [fill,inner sep=%dpt,shape=circle,color=%s] {};\n", c, rank, !isLabeled ? 1 : 2, color));
      } else PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, ") node(%" PetscInt_FMT "_%d) [] {};\n", c, rank));
    }
    if (drawHasse) {
      int height = 0;

      color = colors[depth % numColors];
      PetscCall(PetscViewerASCIIPrintf(viewer, "%% Cells\n"));
      PetscCall(PetscViewerASCIIPrintf(viewer, "\\foreach \\c in {\\cStart,...,\\cEnd}\n"));
      PetscCall(PetscViewerASCIIPrintf(viewer, "{\n"));
      PetscCall(PetscViewerASCIIPrintf(viewer, "  \\node(\\c_%d) [draw,shape=circle,color=%s,minimum size = 6mm] at (\\cShift+\\c-\\cStart,%d) {\\c};\n", rank, color, height++));
      PetscCall(PetscViewerASCIIPrintf(viewer, "}\n"));

      if (depth > 2) {
        color = colors[1 % numColors];
        PetscCall(PetscViewerASCIIPrintf(viewer, "%% Faces\n"));
        PetscCall(PetscViewerASCIIPrintf(viewer, "\\foreach \\f in {\\fStart,...,\\fEnd}\n"));
        PetscCall(PetscViewerASCIIPrintf(viewer, "{\n"));
        PetscCall(PetscViewerASCIIPrintf(viewer, "  \\node(\\f_%d) [draw,shape=circle,color=%s,minimum size = 6mm] at (\\fShift+\\f-\\fStart,%d) {\\f};\n", rank, color, height++));
        PetscCall(PetscViewerASCIIPrintf(viewer, "}\n"));
      }

      color = colors[1 % numColors];
      PetscCall(PetscViewerASCIIPrintf(viewer, "%% Edges\n"));
      PetscCall(PetscViewerASCIIPrintf(viewer, "\\foreach \\e in {\\eStart,...,\\eEnd}\n"));
      PetscCall(PetscViewerASCIIPrintf(viewer, "{\n"));
      PetscCall(PetscViewerASCIIPrintf(viewer, "  \\node(\\e_%d) [draw,shape=circle,color=%s,minimum size = 6mm] at (\\eShift+\\e-\\eStart,%d) {\\e};\n", rank, color, height++));
      PetscCall(PetscViewerASCIIPrintf(viewer, "}\n"));

      color = colors[0 % numColors];
      PetscCall(PetscViewerASCIIPrintf(viewer, "%% Vertices\n"));
      PetscCall(PetscViewerASCIIPrintf(viewer, "\\foreach \\v in {\\vStart,...,\\vEnd}\n"));
      PetscCall(PetscViewerASCIIPrintf(viewer, "{\n"));
      PetscCall(PetscViewerASCIIPrintf(viewer, "  \\node(\\v_%d) [draw,shape=circle,color=%s,minimum size = 6mm] at (\\vShift+\\v-\\vStart,%d) {\\v};\n", rank, color, height++));
      PetscCall(PetscViewerASCIIPrintf(viewer, "}\n"));

      for (p = pStart; p < pEnd; ++p) {
        const PetscInt *cone;
        PetscInt        coneSize, cp;

        PetscCall(DMPlexGetCone(dm, p, &cone));
        PetscCall(DMPlexGetConeSize(dm, p, &coneSize));
        for (cp = 0; cp < coneSize; ++cp) PetscCall(PetscViewerASCIIPrintf(viewer, "\\draw[->, shorten >=1pt] (%" PetscInt_FMT "_%d) -- (%" PetscInt_FMT "_%d);\n", cone[cp], rank, p, rank));
      }
    }
    PetscCall(PetscViewerFlush(viewer));
    PetscCall(PetscViewerASCIIPopSynchronized(viewer));
    PetscCall(PetscViewerASCIIPrintf(viewer, "\\end{tikzpicture}\n"));
    PetscCall(PetscViewerASCIIPrintf(viewer, "\\end{document}\n"));
    for (l = 0; l < numLabels; ++l) PetscCall(PetscFree(names[l]));
    for (c = 0; c < numColors; ++c) PetscCall(PetscFree(colors[c]));
    for (c = 0; c < numLColors; ++c) PetscCall(PetscFree(lcolors[c]));
    PetscCall(PetscFree3(names, colors, lcolors));
    PetscCall(PetscBTDestroy(&wp));
  } else if (format == PETSC_VIEWER_LOAD_BALANCE) {
    Vec                    cown, acown;
    VecScatter             sct;
    ISLocalToGlobalMapping g2l;
    IS                     gid, acis;
    MPI_Comm               comm, ncomm = MPI_COMM_NULL;
    MPI_Group              ggroup, ngroup;
    PetscScalar           *array, nid;
    const PetscInt        *idxs;
    PetscInt              *idxs2, *start, *adjacency, *work;
    PetscInt64             lm[3], gm[3];
    PetscInt               i, c, cStart, cEnd, cum, numVertices, ect, ectn, cellHeight;
    PetscMPIInt            d1, d2, rank;

    PetscCall(PetscObjectGetComm((PetscObject)dm, &comm));
    PetscCallMPI(MPI_Comm_rank(comm, &rank));
#if defined(PETSC_HAVE_MPI_PROCESS_SHARED_MEMORY)
    PetscCallMPI(MPI_Comm_split_type(comm, MPI_COMM_TYPE_SHARED, rank, MPI_INFO_NULL, &ncomm));
#endif
    if (ncomm != MPI_COMM_NULL) {
      PetscCallMPI(MPI_Comm_group(comm, &ggroup));
      PetscCallMPI(MPI_Comm_group(ncomm, &ngroup));
      d1 = 0;
      PetscCallMPI(MPI_Group_translate_ranks(ngroup, 1, &d1, ggroup, &d2));
      nid = d2;
      PetscCallMPI(MPI_Group_free(&ggroup));
      PetscCallMPI(MPI_Group_free(&ngroup));
      PetscCallMPI(MPI_Comm_free(&ncomm));
    } else nid = 0.0;

    /* Get connectivity */
    PetscCall(DMPlexGetVTKCellHeight(dm, &cellHeight));
    PetscCall(DMPlexCreatePartitionerGraph(dm, cellHeight, &numVertices, &start, &adjacency, &gid));

    /* filter overlapped local cells */
    PetscCall(DMPlexGetHeightStratum(dm, cellHeight, &cStart, &cEnd));
    PetscCall(ISGetIndices(gid, &idxs));
    PetscCall(ISGetLocalSize(gid, &cum));
    PetscCall(PetscMalloc1(cum, &idxs2));
    for (c = cStart, cum = 0; c < cEnd; c++) {
      if (idxs[c - cStart] < 0) continue;
      idxs2[cum++] = idxs[c - cStart];
    }
    PetscCall(ISRestoreIndices(gid, &idxs));
    PetscCheck(numVertices == cum, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Unexpected %" PetscInt_FMT " != %" PetscInt_FMT, numVertices, cum);
    PetscCall(ISDestroy(&gid));
    PetscCall(ISCreateGeneral(comm, numVertices, idxs2, PETSC_OWN_POINTER, &gid));

    /* support for node-aware cell locality */
    PetscCall(ISCreateGeneral(comm, start[numVertices], adjacency, PETSC_USE_POINTER, &acis));
    PetscCall(VecCreateSeq(PETSC_COMM_SELF, start[numVertices], &acown));
    PetscCall(VecCreateMPI(comm, numVertices, PETSC_DECIDE, &cown));
    PetscCall(VecGetArray(cown, &array));
    for (c = 0; c < numVertices; c++) array[c] = nid;
    PetscCall(VecRestoreArray(cown, &array));
    PetscCall(VecScatterCreate(cown, acis, acown, NULL, &sct));
    PetscCall(VecScatterBegin(sct, cown, acown, INSERT_VALUES, SCATTER_FORWARD));
    PetscCall(VecScatterEnd(sct, cown, acown, INSERT_VALUES, SCATTER_FORWARD));
    PetscCall(ISDestroy(&acis));
    PetscCall(VecScatterDestroy(&sct));
    PetscCall(VecDestroy(&cown));

    /* compute edgeCut */
    for (c = 0, cum = 0; c < numVertices; c++) cum = PetscMax(cum, start[c + 1] - start[c]);
    PetscCall(PetscMalloc1(cum, &work));
    PetscCall(ISLocalToGlobalMappingCreateIS(gid, &g2l));
    PetscCall(ISLocalToGlobalMappingSetType(g2l, ISLOCALTOGLOBALMAPPINGHASH));
    PetscCall(ISDestroy(&gid));
    PetscCall(VecGetArray(acown, &array));
    for (c = 0, ect = 0, ectn = 0; c < numVertices; c++) {
      PetscInt totl;

      totl = start[c + 1] - start[c];
      PetscCall(ISGlobalToLocalMappingApply(g2l, IS_GTOLM_MASK, totl, adjacency + start[c], NULL, work));
      for (i = 0; i < totl; i++) {
        if (work[i] < 0) {
          ect += 1;
          ectn += (array[i + start[c]] != nid) ? 0 : 1;
        }
      }
    }
    PetscCall(PetscFree(work));
    PetscCall(VecRestoreArray(acown, &array));
    lm[0] = numVertices > 0 ? numVertices : PETSC_MAX_INT;
    lm[1] = -numVertices;
    PetscCall(MPIU_Allreduce(lm, gm, 2, MPIU_INT64, MPI_MIN, comm));
    PetscCall(PetscViewerASCIIPrintf(viewer, "  Cell balance: %.2f (max %" PetscInt_FMT ", min %" PetscInt_FMT, -((double)gm[1]) / ((double)gm[0]), -(PetscInt)gm[1], (PetscInt)gm[0]));
    lm[0] = ect;                     /* edgeCut */
    lm[1] = ectn;                    /* node-aware edgeCut */
    lm[2] = numVertices > 0 ? 0 : 1; /* empty processes */
    PetscCall(MPIU_Allreduce(lm, gm, 3, MPIU_INT64, MPI_SUM, comm));
    PetscCall(PetscViewerASCIIPrintf(viewer, ", empty %" PetscInt_FMT ")\n", (PetscInt)gm[2]));
#if defined(PETSC_HAVE_MPI_PROCESS_SHARED_MEMORY)
    PetscCall(PetscViewerASCIIPrintf(viewer, "  Edge Cut: %" PetscInt_FMT " (on node %.3f)\n", (PetscInt)(gm[0] / 2), gm[0] ? ((double)gm[1]) / ((double)gm[0]) : 1.));
#else
    PetscCall(PetscViewerASCIIPrintf(viewer, "  Edge Cut: %" PetscInt_FMT " (on node %.3f)\n", (PetscInt)(gm[0] / 2), 0.0));
#endif
    PetscCall(ISLocalToGlobalMappingDestroy(&g2l));
    PetscCall(PetscFree(start));
    PetscCall(PetscFree(adjacency));
    PetscCall(VecDestroy(&acown));
  } else {
    const char    *name;
    PetscInt      *sizes, *hybsizes, *ghostsizes;
    PetscInt       locDepth, depth, cellHeight, dim, d;
    PetscInt       pStart, pEnd, p, gcStart, gcEnd, gcNum;
    PetscInt       numLabels, l, maxSize = 17;
    DMPolytopeType ct0 = DM_POLYTOPE_UNKNOWN;
    MPI_Comm       comm;
    PetscMPIInt    size, rank;

    PetscCall(PetscObjectGetComm((PetscObject)dm, &comm));
    PetscCallMPI(MPI_Comm_size(comm, &size));
    PetscCallMPI(MPI_Comm_rank(comm, &rank));
    PetscCall(DMGetDimension(dm, &dim));
    PetscCall(DMPlexGetVTKCellHeight(dm, &cellHeight));
    PetscCall(PetscObjectGetName((PetscObject)dm, &name));
    if (name) PetscCall(PetscViewerASCIIPrintf(viewer, "%s in %" PetscInt_FMT " dimension%s:\n", name, dim, dim == 1 ? "" : "s"));
    else PetscCall(PetscViewerASCIIPrintf(viewer, "Mesh in %" PetscInt_FMT " dimension%s:\n", dim, dim == 1 ? "" : "s"));
    if (cellHeight) PetscCall(PetscViewerASCIIPrintf(viewer, "  Cells are at height %" PetscInt_FMT "\n", cellHeight));
    PetscCall(DMPlexGetDepth(dm, &locDepth));
    PetscCall(MPIU_Allreduce(&locDepth, &depth, 1, MPIU_INT, MPI_MAX, comm));
    PetscCall(DMPlexGetCellTypeStratum(dm, DM_POLYTOPE_FV_GHOST, &gcStart, &gcEnd));
    gcNum = gcEnd - gcStart;
    if (size < maxSize) PetscCall(PetscCalloc3(size, &sizes, size, &hybsizes, size, &ghostsizes));
    else PetscCall(PetscCalloc3(3, &sizes, 3, &hybsizes, 3, &ghostsizes));
    for (d = 0; d <= depth; d++) {
      PetscInt Nc[2] = {0, 0}, ict;

      PetscCall(DMPlexGetDepthStratum(dm, d, &pStart, &pEnd));
      if (pStart < pEnd) PetscCall(DMPlexGetCellType(dm, pStart, &ct0));
      ict = ct0;
      PetscCallMPI(MPI_Bcast(&ict, 1, MPIU_INT, 0, comm));
      ct0 = (DMPolytopeType)ict;
      for (p = pStart; p < pEnd; ++p) {
        DMPolytopeType ct;

        PetscCall(DMPlexGetCellType(dm, p, &ct));
        if (ct == ct0) ++Nc[0];
        else ++Nc[1];
      }
      if (size < maxSize) {
        PetscCallMPI(MPI_Gather(&Nc[0], 1, MPIU_INT, sizes, 1, MPIU_INT, 0, comm));
        PetscCallMPI(MPI_Gather(&Nc[1], 1, MPIU_INT, hybsizes, 1, MPIU_INT, 0, comm));
        if (d == depth) PetscCallMPI(MPI_Gather(&gcNum, 1, MPIU_INT, ghostsizes, 1, MPIU_INT, 0, comm));
        PetscCall(PetscViewerASCIIPrintf(viewer, "  Number of %" PetscInt_FMT "-cells per rank:", (depth == 1) && d ? dim : d));
        for (p = 0; p < size; ++p) {
          if (rank == 0) {
            PetscCall(PetscViewerASCIIPrintf(viewer, " %" PetscInt_FMT, sizes[p] + hybsizes[p]));
            if (hybsizes[p] > 0) PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT ")", hybsizes[p]));
            if (ghostsizes[p] > 0) PetscCall(PetscViewerASCIIPrintf(viewer, " [%" PetscInt_FMT "]", ghostsizes[p]));
          }
        }
      } else {
        PetscInt locMinMax[2];

        locMinMax[0] = Nc[0] + Nc[1];
        locMinMax[1] = Nc[0] + Nc[1];
        PetscCall(PetscGlobalMinMaxInt(comm, locMinMax, sizes));
        locMinMax[0] = Nc[1];
        locMinMax[1] = Nc[1];
        PetscCall(PetscGlobalMinMaxInt(comm, locMinMax, hybsizes));
        if (d == depth) {
          locMinMax[0] = gcNum;
          locMinMax[1] = gcNum;
          PetscCall(PetscGlobalMinMaxInt(comm, locMinMax, ghostsizes));
        }
        PetscCall(PetscViewerASCIIPrintf(viewer, "  Min/Max of %" PetscInt_FMT "-cells per rank:", (depth == 1) && d ? dim : d));
        PetscCall(PetscViewerASCIIPrintf(viewer, " %" PetscInt_FMT "/%" PetscInt_FMT, sizes[0], sizes[1]));
        if (hybsizes[0] > 0) PetscCall(PetscViewerASCIIPrintf(viewer, " (%" PetscInt_FMT "/%" PetscInt_FMT ")", hybsizes[0], hybsizes[1]));
        if (ghostsizes[0] > 0) PetscCall(PetscViewerASCIIPrintf(viewer, " [%" PetscInt_FMT "/%" PetscInt_FMT "]", ghostsizes[0], ghostsizes[1]));
      }
      PetscCall(PetscViewerASCIIPrintf(viewer, "\n"));
    }
    PetscCall(PetscFree3(sizes, hybsizes, ghostsizes));
    {
      const PetscReal *maxCell;
      const PetscReal *L;
      PetscBool        localized;

      PetscCall(DMGetPeriodicity(dm, &maxCell, NULL, &L));
      PetscCall(DMGetCoordinatesLocalized(dm, &localized));
      if (L || localized) {
        PetscCall(PetscViewerASCIIPrintf(viewer, "Periodic mesh"));
        PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_FALSE));
        if (L) {
          PetscCall(PetscViewerASCIIPrintf(viewer, " ("));
          for (d = 0; d < dim; ++d) {
            if (d > 0) PetscCall(PetscViewerASCIIPrintf(viewer, ", "));
            PetscCall(PetscViewerASCIIPrintf(viewer, "%s", L[d] > 0.0 ? "PERIODIC" : "NONE"));
          }
          PetscCall(PetscViewerASCIIPrintf(viewer, ")"));
        }
        PetscCall(PetscViewerASCIIPrintf(viewer, " coordinates %s\n", localized ? "localized" : "not localized"));
        PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_TRUE));
      }
    }
    PetscCall(DMGetNumLabels(dm, &numLabels));
    if (numLabels) PetscCall(PetscViewerASCIIPrintf(viewer, "Labels:\n"));
    for (l = 0; l < numLabels; ++l) {
      DMLabel     label;
      const char *name;
      PetscInt   *values;
      PetscInt    numValues, v;

      PetscCall(DMGetLabelName(dm, l, &name));
      PetscCall(DMGetLabel(dm, name, &label));
      PetscCall(DMLabelGetNumValues(label, &numValues));
      PetscCall(PetscViewerASCIIPrintf(viewer, "  %s: %" PetscInt_FMT " strata with value/size (", name, numValues));

      { // Extract array of DMLabel values so it can be sorted
        IS              is_values;
        const PetscInt *is_values_local = NULL;

        PetscCall(DMLabelGetValueIS(label, &is_values));
        PetscCall(ISGetIndices(is_values, &is_values_local));
        PetscCall(PetscMalloc1(numValues, &values));
        PetscCall(PetscArraycpy(values, is_values_local, numValues));
        PetscCall(PetscSortInt(numValues, values));
        PetscCall(ISRestoreIndices(is_values, &is_values_local));
        PetscCall(ISDestroy(&is_values));
      }
      PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_FALSE));
      for (v = 0; v < numValues; ++v) {
        PetscInt size;

        PetscCall(DMLabelGetStratumSize(label, values[v], &size));
        if (v > 0) PetscCall(PetscViewerASCIIPrintf(viewer, ", "));
        PetscCall(PetscViewerASCIIPrintf(viewer, "%" PetscInt_FMT " (%" PetscInt_FMT ")", values[v], size));
      }
      PetscCall(PetscViewerASCIIPrintf(viewer, ")\n"));
      PetscCall(PetscViewerASCIIUseTabs(viewer, PETSC_TRUE));
      PetscCall(PetscFree(values));
    }
    {
      char    **labelNames;
      PetscInt  Nl = numLabels;
      PetscBool flg;

      PetscCall(PetscMalloc1(Nl, &labelNames));
      PetscCall(PetscOptionsGetStringArray(((PetscObject)dm)->options, ((PetscObject)dm)->prefix, "-dm_plex_view_labels", labelNames, &Nl, &flg));
      for (l = 0; l < Nl; ++l) {
        DMLabel label;

        PetscCall(DMHasLabel(dm, labelNames[l], &flg));
        if (flg) {
          PetscCall(DMGetLabel(dm, labelNames[l], &label));
          PetscCall(DMLabelView(label, viewer));
        }
        PetscCall(PetscFree(labelNames[l]));
      }
      PetscCall(PetscFree(labelNames));
    }
    /* If no fields are specified, people do not want to see adjacency */
    if (dm->Nf) {
      PetscInt f;

      for (f = 0; f < dm->Nf; ++f) {
        const char *name;

        PetscCall(PetscObjectGetName(dm->fields[f].disc, &name));
        if (numLabels) PetscCall(PetscViewerASCIIPrintf(viewer, "Field %s:\n", name));
        PetscCall(PetscViewerASCIIPushTab(viewer));
        if (dm->fields[f].label) PetscCall(DMLabelView(dm->fields[f].label, viewer));
        if (dm->fields[f].adjacency[0]) {
          if (dm->fields[f].adjacency[1]) PetscCall(PetscViewerASCIIPrintf(viewer, "adjacency FVM++\n"));
          else PetscCall(PetscViewerASCIIPrintf(viewer, "adjacency FVM\n"));
        } else {
          if (dm->fields[f].adjacency[1]) PetscCall(PetscViewerASCIIPrintf(viewer, "adjacency FEM\n"));
          else PetscCall(PetscViewerASCIIPrintf(viewer, "adjacency FUNKY\n"));
        }
        PetscCall(PetscViewerASCIIPopTab(viewer));
      }
    }
    PetscCall(DMGetCoarseDM(dm, &cdm));
    if (cdm) {
      PetscCall(PetscViewerASCIIPushTab(viewer));
      PetscCall(PetscViewerASCIIPrintf(viewer, "Defined by transform from:\n"));
      PetscCall(DMPlexView_Ascii(cdm, viewer));
      PetscCall(PetscViewerASCIIPopTab(viewer));
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode DMPlexDrawCell(DM dm, PetscDraw draw, PetscInt cell, const PetscScalar coords[])
{
  DMPolytopeType ct;
  PetscMPIInt    rank;
  PetscInt       cdim;

  PetscFunctionBegin;
  PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank));
  PetscCall(DMPlexGetCellType(dm, cell, &ct));
  PetscCall(DMGetCoordinateDim(dm, &cdim));
  switch (ct) {
  case DM_POLYTOPE_SEGMENT:
  case DM_POLYTOPE_POINT_PRISM_TENSOR:
    switch (cdim) {
    case 1: {
      const PetscReal y  = 0.5;  /* TODO Put it in the middle of the viewport */
      const PetscReal dy = 0.05; /* TODO Make it a fraction of the total length */

      PetscCall(PetscDrawLine(draw, PetscRealPart(coords[0]), y, PetscRealPart(coords[1]), y, PETSC_DRAW_BLACK));
      PetscCall(PetscDrawLine(draw, PetscRealPart(coords[0]), y + dy, PetscRealPart(coords[0]), y - dy, PETSC_DRAW_BLACK));
      PetscCall(PetscDrawLine(draw, PetscRealPart(coords[1]), y + dy, PetscRealPart(coords[1]), y - dy, PETSC_DRAW_BLACK));
    } break;
    case 2: {
      const PetscReal dx = (PetscRealPart(coords[3]) - PetscRealPart(coords[1]));
      const PetscReal dy = (PetscRealPart(coords[2]) - PetscRealPart(coords[0]));
      const PetscReal l  = 0.1 / PetscSqrtReal(dx * dx + dy * dy);

      PetscCall(PetscDrawLine(draw, PetscRealPart(coords[0]), PetscRealPart(coords[1]), PetscRealPart(coords[2]), PetscRealPart(coords[3]), PETSC_DRAW_BLACK));
      PetscCall(PetscDrawLine(draw, PetscRealPart(coords[0]) + l * dx, PetscRealPart(coords[1]) + l * dy, PetscRealPart(coords[0]) - l * dx, PetscRealPart(coords[1]) - l * dy, PETSC_DRAW_BLACK));
      PetscCall(PetscDrawLine(draw, PetscRealPart(coords[2]) + l * dx, PetscRealPart(coords[3]) + l * dy, PetscRealPart(coords[2]) - l * dx, PetscRealPart(coords[3]) - l * dy, PETSC_DRAW_BLACK));
    } break;
    default:
      SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Cannot draw cells of dimension %" PetscInt_FMT, cdim);
    }
    break;
  case DM_POLYTOPE_TRIANGLE:
    PetscCall(PetscDrawTriangle(draw, PetscRealPart(coords[0]), PetscRealPart(coords[1]), PetscRealPart(coords[2]), PetscRealPart(coords[3]), PetscRealPart(coords[4]), PetscRealPart(coords[5]), PETSC_DRAW_WHITE + rank % (PETSC_DRAW_BASIC_COLORS - 2) + 2, PETSC_DRAW_WHITE + rank % (PETSC_DRAW_BASIC_COLORS - 2) + 2, PETSC_DRAW_WHITE + rank % (PETSC_DRAW_BASIC_COLORS - 2) + 2));
    PetscCall(PetscDrawLine(draw, PetscRealPart(coords[0]), PetscRealPart(coords[1]), PetscRealPart(coords[2]), PetscRealPart(coords[3]), PETSC_DRAW_BLACK));
    PetscCall(PetscDrawLine(draw, PetscRealPart(coords[2]), PetscRealPart(coords[3]), PetscRealPart(coords[4]), PetscRealPart(coords[5]), PETSC_DRAW_BLACK));
    PetscCall(PetscDrawLine(draw, PetscRealPart(coords[4]), PetscRealPart(coords[5]), PetscRealPart(coords[0]), PetscRealPart(coords[1]), PETSC_DRAW_BLACK));
    break;
  case DM_POLYTOPE_QUADRILATERAL:
    PetscCall(PetscDrawTriangle(draw, PetscRealPart(coords[0]), PetscRealPart(coords[1]), PetscRealPart(coords[2]), PetscRealPart(coords[3]), PetscRealPart(coords[4]), PetscRealPart(coords[5]), PETSC_DRAW_WHITE + rank % (PETSC_DRAW_BASIC_COLORS - 2) + 2, PETSC_DRAW_WHITE + rank % (PETSC_DRAW_BASIC_COLORS - 2) + 2, PETSC_DRAW_WHITE + rank % (PETSC_DRAW_BASIC_COLORS - 2) + 2));
    PetscCall(PetscDrawTriangle(draw, PetscRealPart(coords[0]), PetscRealPart(coords[1]), PetscRealPart(coords[4]), PetscRealPart(coords[5]), PetscRealPart(coords[6]), PetscRealPart(coords[7]), PETSC_DRAW_WHITE + rank % (PETSC_DRAW_BASIC_COLORS - 2) + 2, PETSC_DRAW_WHITE + rank % (PETSC_DRAW_BASIC_COLORS - 2) + 2, PETSC_DRAW_WHITE + rank % (PETSC_DRAW_BASIC_COLORS - 2) + 2));
    PetscCall(PetscDrawLine(draw, PetscRealPart(coords[0]), PetscRealPart(coords[1]), PetscRealPart(coords[2]), PetscRealPart(coords[3]), PETSC_DRAW_BLACK));
    PetscCall(PetscDrawLine(draw, PetscRealPart(coords[2]), PetscRealPart(coords[3]), PetscRealPart(coords[4]), PetscRealPart(coords[5]), PETSC_DRAW_BLACK));
    PetscCall(PetscDrawLine(draw, PetscRealPart(coords[4]), PetscRealPart(coords[5]), PetscRealPart(coords[6]), PetscRealPart(coords[7]), PETSC_DRAW_BLACK));
    PetscCall(PetscDrawLine(draw, PetscRealPart(coords[6]), PetscRealPart(coords[7]), PetscRealPart(coords[0]), PetscRealPart(coords[1]), PETSC_DRAW_BLACK));
    break;
  case DM_POLYTOPE_SEG_PRISM_TENSOR:
    PetscCall(PetscDrawTriangle(draw, PetscRealPart(coords[0]), PetscRealPart(coords[1]), PetscRealPart(coords[2]), PetscRealPart(coords[3]), PetscRealPart(coords[4]), PetscRealPart(coords[5]), PETSC_DRAW_WHITE + rank % (PETSC_DRAW_BASIC_COLORS - 2) + 2, PETSC_DRAW_WHITE + rank % (PETSC_DRAW_BASIC_COLORS - 2) + 2, PETSC_DRAW_WHITE + rank % (PETSC_DRAW_BASIC_COLORS - 2) + 2));
    PetscCall(PetscDrawTriangle(draw, PetscRealPart(coords[2]), PetscRealPart(coords[3]), PetscRealPart(coords[6]), PetscRealPart(coords[7]), PetscRealPart(coords[4]), PetscRealPart(coords[5]), PETSC_DRAW_WHITE + rank % (PETSC_DRAW_BASIC_COLORS - 2) + 2, PETSC_DRAW_WHITE + rank % (PETSC_DRAW_BASIC_COLORS - 2) + 2, PETSC_DRAW_WHITE + rank % (PETSC_DRAW_BASIC_COLORS - 2) + 2));
    PetscCall(PetscDrawLine(draw, PetscRealPart(coords[0]), PetscRealPart(coords[1]), PetscRealPart(coords[2]), PetscRealPart(coords[3]), PETSC_DRAW_BLACK));
    PetscCall(PetscDrawLine(draw, PetscRealPart(coords[2]), PetscRealPart(coords[3]), PetscRealPart(coords[6]), PetscRealPart(coords[7]), PETSC_DRAW_BLACK));
    PetscCall(PetscDrawLine(draw, PetscRealPart(coords[6]), PetscRealPart(coords[7]), PetscRealPart(coords[4]), PetscRealPart(coords[5]), PETSC_DRAW_BLACK));
    PetscCall(PetscDrawLine(draw, PetscRealPart(coords[4]), PetscRealPart(coords[5]), PetscRealPart(coords[0]), PetscRealPart(coords[1]), PETSC_DRAW_BLACK));
    break;
  case DM_POLYTOPE_FV_GHOST:
    break;
  default:
    SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Cannot draw cells of type %s", DMPolytopeTypes[ct]);
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode DrawPolygon_Private(DM dm, PetscDraw draw, PetscInt cell, PetscInt Nv, const PetscReal refVertices[], const PetscScalar coords[], PetscInt edgeDiv, PetscReal refCoords[], PetscReal edgeCoords[])
{
  PetscReal   centroid[2] = {0., 0.};
  PetscMPIInt rank;
  PetscInt    fillColor;

  PetscFunctionBegin;
  PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank));
  fillColor = PETSC_DRAW_WHITE + rank % (PETSC_DRAW_BASIC_COLORS - 2) + 2;
  for (PetscInt v = 0; v < Nv; ++v) {
    centroid[0] += PetscRealPart(coords[v * 2 + 0]) / Nv;
    centroid[1] += PetscRealPart(coords[v * 2 + 1]) / Nv;
  }
  for (PetscInt e = 0; e < Nv; ++e) {
    refCoords[0] = refVertices[e * 2 + 0];
    refCoords[1] = refVertices[e * 2 + 1];
    for (PetscInt d = 1; d <= edgeDiv; ++d) {
      refCoords[d * 2 + 0] = refCoords[0] + (refVertices[(e + 1) % Nv * 2 + 0] - refCoords[0]) * d / edgeDiv;
      refCoords[d * 2 + 1] = refCoords[1] + (refVertices[(e + 1) % Nv * 2 + 1] - refCoords[1]) * d / edgeDiv;
    }
    PetscCall(DMPlexReferenceToCoordinates(dm, cell, edgeDiv + 1, refCoords, edgeCoords));
    for (PetscInt d = 0; d < edgeDiv; ++d) {
      PetscCall(PetscDrawTriangle(draw, centroid[0], centroid[1], edgeCoords[d * 2 + 0], edgeCoords[d * 2 + 1], edgeCoords[(d + 1) * 2 + 0], edgeCoords[(d + 1) * 2 + 1], fillColor, fillColor, fillColor));
      PetscCall(PetscDrawLine(draw, edgeCoords[d * 2 + 0], edgeCoords[d * 2 + 1], edgeCoords[(d + 1) * 2 + 0], edgeCoords[(d + 1) * 2 + 1], PETSC_DRAW_BLACK));
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode DMPlexDrawCellHighOrder(DM dm, PetscDraw draw, PetscInt cell, const PetscScalar coords[], PetscInt edgeDiv, PetscReal refCoords[], PetscReal edgeCoords[])
{
  DMPolytopeType ct;

  PetscFunctionBegin;
  PetscCall(DMPlexGetCellType(dm, cell, &ct));
  switch (ct) {
  case DM_POLYTOPE_TRIANGLE: {
    PetscReal refVertices[6] = {-1., -1., 1., -1., -1., 1.};

    PetscCall(DrawPolygon_Private(dm, draw, cell, 3, refVertices, coords, edgeDiv, refCoords, edgeCoords));
  } break;
  case DM_POLYTOPE_QUADRILATERAL: {
    PetscReal refVertices[8] = {-1., -1., 1., -1., 1., 1., -1., 1.};

    PetscCall(DrawPolygon_Private(dm, draw, cell, 4, refVertices, coords, edgeDiv, refCoords, edgeCoords));
  } break;
  default:
    SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Cannot draw cells of type %s", DMPolytopeTypes[ct]);
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode DMPlexView_Draw(DM dm, PetscViewer viewer)
{
  PetscDraw    draw;
  DM           cdm;
  PetscSection coordSection;
  Vec          coordinates;
  PetscReal    xyl[3], xyr[3];
  PetscReal   *refCoords, *edgeCoords;
  PetscBool    isnull, drawAffine;
  PetscInt     dim, vStart, vEnd, cStart, cEnd, c, cDegree, edgeDiv;

  PetscFunctionBegin;
  PetscCall(DMGetCoordinateDim(dm, &dim));
  PetscCheck(dim <= 2, PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Cannot draw meshes of dimension %" PetscInt_FMT, dim);
  PetscCall(DMGetCoordinateDegree_Internal(dm, &cDegree));
  drawAffine = cDegree > 1 ? PETSC_FALSE : PETSC_TRUE;
  edgeDiv    = cDegree + 1;
  PetscCall(PetscOptionsGetBool(((PetscObject)dm)->options, ((PetscObject)dm)->prefix, "-dm_view_draw_affine", &drawAffine, NULL));
  if (!drawAffine) PetscCall(PetscMalloc2((edgeDiv + 1) * dim, &refCoords, (edgeDiv + 1) * dim, &edgeCoords));
  PetscCall(DMGetCoordinateDM(dm, &cdm));
  PetscCall(DMGetLocalSection(cdm, &coordSection));
  PetscCall(DMGetCoordinatesLocal(dm, &coordinates));
  PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
  PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));

  PetscCall(PetscViewerDrawGetDraw(viewer, 0, &draw));
  PetscCall(PetscDrawIsNull(draw, &isnull));
  if (isnull) PetscFunctionReturn(PETSC_SUCCESS);
  PetscCall(PetscDrawSetTitle(draw, "Mesh"));

  PetscCall(DMGetBoundingBox(dm, xyl, xyr));
  PetscCall(PetscDrawSetCoordinates(draw, xyl[0], xyl[1], xyr[0], xyr[1]));
  PetscCall(PetscDrawClear(draw));

  for (c = cStart; c < cEnd; ++c) {
    PetscScalar       *coords = NULL;
    const PetscScalar *coords_arr;
    PetscInt           numCoords;
    PetscBool          isDG;

    PetscCall(DMPlexGetCellCoordinates(dm, c, &isDG, &numCoords, &coords_arr, &coords));
    if (drawAffine) PetscCall(DMPlexDrawCell(dm, draw, c, coords));
    else PetscCall(DMPlexDrawCellHighOrder(dm, draw, c, coords, edgeDiv, refCoords, edgeCoords));
    PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &coords_arr, &coords));
  }
  if (!drawAffine) PetscCall(PetscFree2(refCoords, edgeCoords));
  PetscCall(PetscDrawFlush(draw));
  PetscCall(PetscDrawPause(draw));
  PetscCall(PetscDrawSave(draw));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode DMPlexCreateHighOrderSurrogate_Internal(DM dm, DM *hdm)
{
  DM           odm = dm, rdm = dm, cdm;
  PetscFE      fe;
  PetscSpace   sp;
  PetscClassId id;
  PetscInt     degree;
  PetscBool    hoView = PETSC_TRUE;

  PetscFunctionBegin;
  PetscObjectOptionsBegin((PetscObject)dm);
  PetscCall(PetscOptionsBool("-dm_plex_high_order_view", "Subsample to view meshes with high order coordinates", "DMPlexCreateHighOrderSurrogate_Internal", hoView, &hoView, NULL));
  PetscOptionsEnd();
  PetscCall(PetscObjectReference((PetscObject)dm));
  *hdm = dm;
  if (!hoView) PetscFunctionReturn(PETSC_SUCCESS);
  PetscCall(DMGetCoordinateDM(dm, &cdm));
  PetscCall(DMGetField(cdm, 0, NULL, (PetscObject *)&fe));
  PetscCall(PetscObjectGetClassId((PetscObject)fe, &id));
  if (id != PETSCFE_CLASSID) PetscFunctionReturn(PETSC_SUCCESS);
  PetscCall(PetscFEGetBasisSpace(fe, &sp));
  PetscCall(PetscSpaceGetDegree(sp, &degree, NULL));
  for (PetscInt r = 0, rd = PetscCeilReal(((PetscReal)degree) / 2.); r < (PetscInt)PetscCeilReal(PetscLog2Real(degree)); ++r, rd = PetscCeilReal(((PetscReal)rd) / 2.)) {
    DM  cdm, rcdm;
    Mat In;
    Vec cl, rcl;

    PetscCall(DMRefine(odm, PetscObjectComm((PetscObject)odm), &rdm));
    PetscCall(DMPlexCreateCoordinateSpace(rdm, rd, PETSC_FALSE, NULL));
    PetscCall(PetscObjectSetName((PetscObject)rdm, "Refined Mesh with Linear Coordinates"));
    PetscCall(DMGetCoordinateDM(odm, &cdm));
    PetscCall(DMGetCoordinateDM(rdm, &rcdm));
    PetscCall(DMGetCoordinatesLocal(odm, &cl));
    PetscCall(DMGetCoordinatesLocal(rdm, &rcl));
    PetscCall(DMSetCoarseDM(rcdm, cdm));
    PetscCall(DMCreateInterpolation(cdm, rcdm, &In, NULL));
    PetscCall(MatMult(In, cl, rcl));
    PetscCall(MatDestroy(&In));
    PetscCall(DMSetCoordinatesLocal(rdm, rcl));
    PetscCall(DMDestroy(&odm));
    odm = rdm;
  }
  *hdm = rdm;
  PetscFunctionReturn(PETSC_SUCCESS);
}

#if defined(PETSC_HAVE_EXODUSII)
  #include <exodusII.h>
  #include <petscviewerexodusii.h>
#endif

PetscErrorCode DMView_Plex(DM dm, PetscViewer viewer)
{
  PetscBool iascii, ishdf5, isvtk, isdraw, flg, isglvis, isexodus, iscgns;
  char      name[PETSC_MAX_PATH_LEN];

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidHeaderSpecific(viewer, PETSC_VIEWER_CLASSID, 2);
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERVTK, &isvtk));
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERHDF5, &ishdf5));
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERDRAW, &isdraw));
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERGLVIS, &isglvis));
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWEREXODUSII, &isexodus));
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERCGNS, &iscgns));
  if (iascii) {
    PetscViewerFormat format;
    PetscCall(PetscViewerGetFormat(viewer, &format));
    if (format == PETSC_VIEWER_ASCII_GLVIS) PetscCall(DMPlexView_GLVis(dm, viewer));
    else PetscCall(DMPlexView_Ascii(dm, viewer));
  } else if (ishdf5) {
#if defined(PETSC_HAVE_HDF5)
    PetscCall(DMPlexView_HDF5_Internal(dm, viewer));
#else
    SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "HDF5 not supported in this build.\nPlease reconfigure using --download-hdf5");
#endif
  } else if (isvtk) {
    PetscCall(DMPlexVTKWriteAll((PetscObject)dm, viewer));
  } else if (isdraw) {
    DM hdm;

    PetscCall(DMPlexCreateHighOrderSurrogate_Internal(dm, &hdm));
    PetscCall(DMPlexView_Draw(hdm, viewer));
    PetscCall(DMDestroy(&hdm));
  } else if (isglvis) {
    PetscCall(DMPlexView_GLVis(dm, viewer));
#if defined(PETSC_HAVE_EXODUSII)
  } else if (isexodus) {
    /*
      exodusII requires that all sets be part of exactly one cell set.
      If the dm does not have a "Cell Sets" label defined, we create one
      with ID 1, containing all cells.
      Note that if the Cell Sets label is defined but does not cover all cells,
      we may still have a problem. This should probably be checked here or in the viewer;
    */
    PetscInt numCS;
    PetscCall(DMGetLabelSize(dm, "Cell Sets", &numCS));
    if (!numCS) {
      PetscInt cStart, cEnd, c;
      PetscCall(DMCreateLabel(dm, "Cell Sets"));
      PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
      for (c = cStart; c < cEnd; ++c) PetscCall(DMSetLabelValue(dm, "Cell Sets", c, 1));
    }
    PetscCall(DMView_PlexExodusII(dm, viewer));
#endif
#if defined(PETSC_HAVE_CGNS)
  } else if (iscgns) {
    PetscCall(DMView_PlexCGNS(dm, viewer));
#endif
  } else SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Viewer type %s not yet supported for DMPlex writing", ((PetscObject)viewer)->type_name);
  /* Optionally view the partition */
  PetscCall(PetscOptionsHasName(((PetscObject)dm)->options, ((PetscObject)dm)->prefix, "-dm_partition_view", &flg));
  if (flg) {
    Vec ranks;
    PetscCall(DMPlexCreateRankField(dm, &ranks));
    PetscCall(VecView(ranks, viewer));
    PetscCall(VecDestroy(&ranks));
  }
  /* Optionally view a label */
  PetscCall(PetscOptionsGetString(((PetscObject)dm)->options, ((PetscObject)dm)->prefix, "-dm_label_view", name, sizeof(name), &flg));
  if (flg) {
    DMLabel label;
    Vec     val;

    PetscCall(DMGetLabel(dm, name, &label));
    PetscCheck(label, PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Label %s provided to -dm_label_view does not exist in this DM", name);
    PetscCall(DMPlexCreateLabelField(dm, label, &val));
    PetscCall(VecView(val, viewer));
    PetscCall(VecDestroy(&val));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexTopologyView - Saves a `DMPLEX` topology into a file

  Collective

  Input Parameters:
+ dm     - The `DM` whose topology is to be saved
- viewer - The `PetscViewer` to save it in

  Level: advanced

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMView()`, `DMPlexCoordinatesView()`, `DMPlexLabelsView()`, `DMPlexTopologyLoad()`, `PetscViewer`
@*/
PetscErrorCode DMPlexTopologyView(DM dm, PetscViewer viewer)
{
  PetscBool ishdf5;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidHeaderSpecific(viewer, PETSC_VIEWER_CLASSID, 2);
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERHDF5, &ishdf5));
  PetscCall(PetscLogEventBegin(DMPLEX_TopologyView, viewer, 0, 0, 0));
  if (ishdf5) {
#if defined(PETSC_HAVE_HDF5)
    PetscViewerFormat format;
    PetscCall(PetscViewerGetFormat(viewer, &format));
    if (format == PETSC_VIEWER_HDF5_PETSC || format == PETSC_VIEWER_DEFAULT || format == PETSC_VIEWER_NATIVE) {
      IS globalPointNumbering;

      PetscCall(DMPlexCreatePointNumbering(dm, &globalPointNumbering));
      PetscCall(DMPlexTopologyView_HDF5_Internal(dm, globalPointNumbering, viewer));
      PetscCall(ISDestroy(&globalPointNumbering));
    } else SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "PetscViewerFormat %s not supported for HDF5 output.", PetscViewerFormats[format]);
#else
    SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "HDF5 not supported in this build.\nPlease reconfigure using --download-hdf5");
#endif
  }
  PetscCall(PetscLogEventEnd(DMPLEX_TopologyView, viewer, 0, 0, 0));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexCoordinatesView - Saves `DMPLEX` coordinates into a file

  Collective

  Input Parameters:
+ dm     - The `DM` whose coordinates are to be saved
- viewer - The `PetscViewer` for saving

  Level: advanced

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMView()`, `DMPlexTopologyView()`, `DMPlexLabelsView()`, `DMPlexCoordinatesLoad()`, `PetscViewer`
@*/
PetscErrorCode DMPlexCoordinatesView(DM dm, PetscViewer viewer)
{
  PetscBool ishdf5;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidHeaderSpecific(viewer, PETSC_VIEWER_CLASSID, 2);
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERHDF5, &ishdf5));
  PetscCall(PetscLogEventBegin(DMPLEX_CoordinatesView, viewer, 0, 0, 0));
  if (ishdf5) {
#if defined(PETSC_HAVE_HDF5)
    PetscViewerFormat format;
    PetscCall(PetscViewerGetFormat(viewer, &format));
    if (format == PETSC_VIEWER_HDF5_PETSC || format == PETSC_VIEWER_DEFAULT || format == PETSC_VIEWER_NATIVE) {
      PetscCall(DMPlexCoordinatesView_HDF5_Internal(dm, viewer));
    } else SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "PetscViewerFormat %s not supported for HDF5 output.", PetscViewerFormats[format]);
#else
    SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "HDF5 not supported in this build.\nPlease reconfigure using --download-hdf5");
#endif
  }
  PetscCall(PetscLogEventEnd(DMPLEX_CoordinatesView, viewer, 0, 0, 0));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexLabelsView - Saves `DMPLEX` labels into a file

  Collective

  Input Parameters:
+ dm     - The `DM` whose labels are to be saved
- viewer - The `PetscViewer` for saving

  Level: advanced

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMView()`, `DMPlexTopologyView()`, `DMPlexCoordinatesView()`, `DMPlexLabelsLoad()`, `PetscViewer`
@*/
PetscErrorCode DMPlexLabelsView(DM dm, PetscViewer viewer)
{
  PetscBool ishdf5;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidHeaderSpecific(viewer, PETSC_VIEWER_CLASSID, 2);
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERHDF5, &ishdf5));
  PetscCall(PetscLogEventBegin(DMPLEX_LabelsView, viewer, 0, 0, 0));
  if (ishdf5) {
#if defined(PETSC_HAVE_HDF5)
    IS                globalPointNumbering;
    PetscViewerFormat format;

    PetscCall(PetscViewerGetFormat(viewer, &format));
    if (format == PETSC_VIEWER_HDF5_PETSC || format == PETSC_VIEWER_DEFAULT || format == PETSC_VIEWER_NATIVE) {
      PetscCall(DMPlexCreatePointNumbering(dm, &globalPointNumbering));
      PetscCall(DMPlexLabelsView_HDF5_Internal(dm, globalPointNumbering, viewer));
      PetscCall(ISDestroy(&globalPointNumbering));
    } else SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "PetscViewerFormat %s not supported for HDF5 input.", PetscViewerFormats[format]);
#else
    SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "HDF5 not supported in this build.\nPlease reconfigure using --download-hdf5");
#endif
  }
  PetscCall(PetscLogEventEnd(DMPLEX_LabelsView, viewer, 0, 0, 0));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexSectionView - Saves a section associated with a `DMPLEX`

  Collective

  Input Parameters:
+ dm        - The `DM` that contains the topology on which the section to be saved is defined
. viewer    - The `PetscViewer` for saving
- sectiondm - The `DM` that contains the section to be saved, can be `NULL`

  Level: advanced

  Notes:
  This function is a wrapper around `PetscSectionView()`; in addition to the raw section, it saves information that associates the section points to the topology (`dm`) points. When the topology (`dm`) and the section are later loaded with `DMPlexTopologyLoad()` and `DMPlexSectionLoad()`, respectively, this information is used to match section points with topology points.

  In general `dm` and `sectiondm` are two different objects, the former carrying the topology and the latter carrying the section, and have been given a topology name and a section name, respectively, with `PetscObjectSetName()`. In practice, however, they can be the same object (or in case `sectiondm` is `NULL`) if it carries both topology and section; in that case the name of the object is used as both the topology name and the section name.

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMView()`, `DMPlexTopologyView()`, `DMPlexCoordinatesView()`, `DMPlexLabelsView()`, `DMPlexGlobalVectorView()`, `DMPlexLocalVectorView()`, `PetscSectionView()`, `DMPlexSectionLoad()`, `PetscViewer`
@*/
PetscErrorCode DMPlexSectionView(DM dm, PetscViewer viewer, DM sectiondm)
{
  PetscBool ishdf5;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidHeaderSpecific(viewer, PETSC_VIEWER_CLASSID, 2);
  if (!sectiondm) sectiondm = dm;
  PetscValidHeaderSpecific(sectiondm, DM_CLASSID, 3);
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERHDF5, &ishdf5));
  PetscCall(PetscLogEventBegin(DMPLEX_SectionView, viewer, 0, 0, 0));
  if (ishdf5) {
#if defined(PETSC_HAVE_HDF5)
    PetscCall(DMPlexSectionView_HDF5_Internal(dm, viewer, sectiondm));
#else
    SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "HDF5 not supported in this build.\nPlease reconfigure using --download-hdf5");
#endif
  }
  PetscCall(PetscLogEventEnd(DMPLEX_SectionView, viewer, 0, 0, 0));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexGlobalVectorView - Saves a global vector

  Collective

  Input Parameters:
+ dm        - The `DM` that represents the topology
. viewer    - The `PetscViewer` to save data with
. sectiondm - The `DM` that contains the global section on which vec is defined, can be `NULL`
- vec       - The global vector to be saved

  Level: advanced

  Notes:
  In general `dm` and `sectiondm` are two different objects, the former carrying the topology and the latter carrying the section, and have been given a topology name and a section name, respectively, with `PetscObjectSetName()`. In practice, however, they can be the same object (or in case `sectiondm` is `NULL`) if it carries both topology and section; in that case the name of the object is used as both the topology name and the section name.

  Calling sequence:
.vb
       DMCreate(PETSC_COMM_WORLD, &dm);
       DMSetType(dm, DMPLEX);
       PetscObjectSetName((PetscObject)dm, "topologydm_name");
       DMClone(dm, &sectiondm);
       PetscObjectSetName((PetscObject)sectiondm, "sectiondm_name");
       PetscSectionCreate(PETSC_COMM_WORLD, &section);
       DMPlexGetChart(sectiondm, &pStart, &pEnd);
       PetscSectionSetChart(section, pStart, pEnd);
       PetscSectionSetUp(section);
       DMSetLocalSection(sectiondm, section);
       PetscSectionDestroy(&section);
       DMGetGlobalVector(sectiondm, &vec);
       PetscObjectSetName((PetscObject)vec, "vec_name");
       DMPlexTopologyView(dm, viewer);
       DMPlexSectionView(dm, viewer, sectiondm);
       DMPlexGlobalVectorView(dm, viewer, sectiondm, vec);
       DMRestoreGlobalVector(sectiondm, &vec);
       DMDestroy(&sectiondm);
       DMDestroy(&dm);
.ve

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexTopologyView()`, `DMPlexSectionView()`, `DMPlexLocalVectorView()`, `DMPlexGlobalVectorLoad()`, `DMPlexLocalVectorLoad()`
@*/
PetscErrorCode DMPlexGlobalVectorView(DM dm, PetscViewer viewer, DM sectiondm, Vec vec)
{
  PetscBool ishdf5;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidHeaderSpecific(viewer, PETSC_VIEWER_CLASSID, 2);
  if (!sectiondm) sectiondm = dm;
  PetscValidHeaderSpecific(sectiondm, DM_CLASSID, 3);
  PetscValidHeaderSpecific(vec, VEC_CLASSID, 4);
  /* Check consistency */
  {
    PetscSection section;
    PetscBool    includesConstraints;
    PetscInt     m, m1;

    PetscCall(VecGetLocalSize(vec, &m1));
    PetscCall(DMGetGlobalSection(sectiondm, &section));
    PetscCall(PetscSectionGetIncludesConstraints(section, &includesConstraints));
    if (includesConstraints) PetscCall(PetscSectionGetStorageSize(section, &m));
    else PetscCall(PetscSectionGetConstrainedStorageSize(section, &m));
    PetscCheck(m1 == m, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Global vector size (%" PetscInt_FMT ") != global section storage size (%" PetscInt_FMT ")", m1, m);
  }
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERHDF5, &ishdf5));
  PetscCall(PetscLogEventBegin(DMPLEX_GlobalVectorView, viewer, 0, 0, 0));
  if (ishdf5) {
#if defined(PETSC_HAVE_HDF5)
    PetscCall(DMPlexGlobalVectorView_HDF5_Internal(dm, viewer, sectiondm, vec));
#else
    SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "HDF5 not supported in this build.\nPlease reconfigure using --download-hdf5");
#endif
  }
  PetscCall(PetscLogEventEnd(DMPLEX_GlobalVectorView, viewer, 0, 0, 0));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexLocalVectorView - Saves a local vector

  Collective

  Input Parameters:
+ dm        - The `DM` that represents the topology
. viewer    - The `PetscViewer` to save data with
. sectiondm - The `DM` that contains the local section on which `vec` is defined, can be `NULL`
- vec       - The local vector to be saved

  Level: advanced

  Note:
  In general `dm` and `sectiondm` are two different objects, the former carrying the topology and the latter carrying the section, and have been given a topology name and a section name, respectively, with `PetscObjectSetName()`. In practice, however, they can be the same object (or in case `sectiondm` is `NULL`) if it carries both topology and section; in that case the name of the object is used as both the topology name and the section name.

  Calling sequence:
.vb
       DMCreate(PETSC_COMM_WORLD, &dm);
       DMSetType(dm, DMPLEX);
       PetscObjectSetName((PetscObject)dm, "topologydm_name");
       DMClone(dm, &sectiondm);
       PetscObjectSetName((PetscObject)sectiondm, "sectiondm_name");
       PetscSectionCreate(PETSC_COMM_WORLD, &section);
       DMPlexGetChart(sectiondm, &pStart, &pEnd);
       PetscSectionSetChart(section, pStart, pEnd);
       PetscSectionSetUp(section);
       DMSetLocalSection(sectiondm, section);
       DMGetLocalVector(sectiondm, &vec);
       PetscObjectSetName((PetscObject)vec, "vec_name");
       DMPlexTopologyView(dm, viewer);
       DMPlexSectionView(dm, viewer, sectiondm);
       DMPlexLocalVectorView(dm, viewer, sectiondm, vec);
       DMRestoreLocalVector(sectiondm, &vec);
       DMDestroy(&sectiondm);
       DMDestroy(&dm);
.ve

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexTopologyView()`, `DMPlexSectionView()`, `DMPlexGlobalVectorView()`, `DMPlexGlobalVectorLoad()`, `DMPlexLocalVectorLoad()`
@*/
PetscErrorCode DMPlexLocalVectorView(DM dm, PetscViewer viewer, DM sectiondm, Vec vec)
{
  PetscBool ishdf5;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidHeaderSpecific(viewer, PETSC_VIEWER_CLASSID, 2);
  if (!sectiondm) sectiondm = dm;
  PetscValidHeaderSpecific(sectiondm, DM_CLASSID, 3);
  PetscValidHeaderSpecific(vec, VEC_CLASSID, 4);
  /* Check consistency */
  {
    PetscSection section;
    PetscBool    includesConstraints;
    PetscInt     m, m1;

    PetscCall(VecGetLocalSize(vec, &m1));
    PetscCall(DMGetLocalSection(sectiondm, &section));
    PetscCall(PetscSectionGetIncludesConstraints(section, &includesConstraints));
    if (includesConstraints) PetscCall(PetscSectionGetStorageSize(section, &m));
    else PetscCall(PetscSectionGetConstrainedStorageSize(section, &m));
    PetscCheck(m1 == m, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Local vector size (%" PetscInt_FMT ") != local section storage size (%" PetscInt_FMT ")", m1, m);
  }
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERHDF5, &ishdf5));
  PetscCall(PetscLogEventBegin(DMPLEX_LocalVectorView, viewer, 0, 0, 0));
  if (ishdf5) {
#if defined(PETSC_HAVE_HDF5)
    PetscCall(DMPlexLocalVectorView_HDF5_Internal(dm, viewer, sectiondm, vec));
#else
    SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "HDF5 not supported in this build.\nPlease reconfigure using --download-hdf5");
#endif
  }
  PetscCall(PetscLogEventEnd(DMPLEX_LocalVectorView, viewer, 0, 0, 0));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode DMLoad_Plex(DM dm, PetscViewer viewer)
{
  PetscBool ishdf5;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidHeaderSpecific(viewer, PETSC_VIEWER_CLASSID, 2);
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERHDF5, &ishdf5));
  if (ishdf5) {
#if defined(PETSC_HAVE_HDF5)
    PetscViewerFormat format;
    PetscCall(PetscViewerGetFormat(viewer, &format));
    if (format == PETSC_VIEWER_HDF5_XDMF || format == PETSC_VIEWER_HDF5_VIZ) {
      PetscCall(DMPlexLoad_HDF5_Xdmf_Internal(dm, viewer));
    } else if (format == PETSC_VIEWER_HDF5_PETSC || format == PETSC_VIEWER_DEFAULT || format == PETSC_VIEWER_NATIVE) {
      PetscCall(DMPlexLoad_HDF5_Internal(dm, viewer));
    } else SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "PetscViewerFormat %s not supported for HDF5 input.", PetscViewerFormats[format]);
    PetscFunctionReturn(PETSC_SUCCESS);
#else
    SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "HDF5 not supported in this build.\nPlease reconfigure using --download-hdf5");
#endif
  } else SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Viewer type %s not yet supported for DMPlex loading", ((PetscObject)viewer)->type_name);
}

/*@
  DMPlexTopologyLoad - Loads a topology into a `DMPLEX`

  Collective

  Input Parameters:
+ dm     - The `DM` into which the topology is loaded
- viewer - The `PetscViewer` for the saved topology

  Output Parameter:
. globalToLocalPointSF - The `PetscSF` that pushes points in [0, N) to the associated points in the loaded `DMPLEX`, where N is the global number of points;
  `NULL` if unneeded

  Level: advanced

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMLoad()`, `DMPlexCoordinatesLoad()`, `DMPlexLabelsLoad()`, `DMView()`, `PetscViewerHDF5Open()`, `PetscViewerPushFormat()`,
          `PetscViewer`, `PetscSF`
@*/
PetscErrorCode DMPlexTopologyLoad(DM dm, PetscViewer viewer, PetscSF *globalToLocalPointSF)
{
  PetscBool ishdf5;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidHeaderSpecific(viewer, PETSC_VIEWER_CLASSID, 2);
  if (globalToLocalPointSF) PetscAssertPointer(globalToLocalPointSF, 3);
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERHDF5, &ishdf5));
  PetscCall(PetscLogEventBegin(DMPLEX_TopologyLoad, viewer, 0, 0, 0));
  if (ishdf5) {
#if defined(PETSC_HAVE_HDF5)
    PetscViewerFormat format;
    PetscCall(PetscViewerGetFormat(viewer, &format));
    if (format == PETSC_VIEWER_HDF5_PETSC || format == PETSC_VIEWER_DEFAULT || format == PETSC_VIEWER_NATIVE) {
      PetscCall(DMPlexTopologyLoad_HDF5_Internal(dm, viewer, globalToLocalPointSF));
    } else SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "PetscViewerFormat %s not supported for HDF5 input.", PetscViewerFormats[format]);
#else
    SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "HDF5 not supported in this build.\nPlease reconfigure using --download-hdf5");
#endif
  }
  PetscCall(PetscLogEventEnd(DMPLEX_TopologyLoad, viewer, 0, 0, 0));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexCoordinatesLoad - Loads coordinates into a `DMPLEX`

  Collective

  Input Parameters:
+ dm                   - The `DM` into which the coordinates are loaded
. viewer               - The `PetscViewer` for the saved coordinates
- globalToLocalPointSF - The `PetscSF` returned by `DMPlexTopologyLoad()` when loading dm from viewer

  Level: advanced

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMLoad()`, `DMPlexTopologyLoad()`, `DMPlexLabelsLoad()`, `DMView()`, `PetscViewerHDF5Open()`, `PetscViewerPushFormat()`,
          `PetscSF`, `PetscViewer`
@*/
PetscErrorCode DMPlexCoordinatesLoad(DM dm, PetscViewer viewer, PetscSF globalToLocalPointSF)
{
  PetscBool ishdf5;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidHeaderSpecific(viewer, PETSC_VIEWER_CLASSID, 2);
  PetscValidHeaderSpecific(globalToLocalPointSF, PETSCSF_CLASSID, 3);
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERHDF5, &ishdf5));
  PetscCall(PetscLogEventBegin(DMPLEX_CoordinatesLoad, viewer, 0, 0, 0));
  if (ishdf5) {
#if defined(PETSC_HAVE_HDF5)
    PetscViewerFormat format;
    PetscCall(PetscViewerGetFormat(viewer, &format));
    if (format == PETSC_VIEWER_HDF5_PETSC || format == PETSC_VIEWER_DEFAULT || format == PETSC_VIEWER_NATIVE) {
      PetscCall(DMPlexCoordinatesLoad_HDF5_Internal(dm, viewer, globalToLocalPointSF));
    } else SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "PetscViewerFormat %s not supported for HDF5 input.", PetscViewerFormats[format]);
#else
    SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "HDF5 not supported in this build.\nPlease reconfigure using --download-hdf5");
#endif
  }
  PetscCall(PetscLogEventEnd(DMPLEX_CoordinatesLoad, viewer, 0, 0, 0));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexLabelsLoad - Loads labels into a `DMPLEX`

  Collective

  Input Parameters:
+ dm                   - The `DM` into which the labels are loaded
. viewer               - The `PetscViewer` for the saved labels
- globalToLocalPointSF - The `PetscSF` returned by `DMPlexTopologyLoad()` when loading `dm` from viewer

  Level: advanced

  Note:
  The `PetscSF` argument must not be `NULL` if the `DM` is distributed, otherwise an error occurs.

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMLoad()`, `DMPlexTopologyLoad()`, `DMPlexCoordinatesLoad()`, `DMView()`, `PetscViewerHDF5Open()`, `PetscViewerPushFormat()`,
          `PetscSF`, `PetscViewer`
@*/
PetscErrorCode DMPlexLabelsLoad(DM dm, PetscViewer viewer, PetscSF globalToLocalPointSF)
{
  PetscBool ishdf5;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidHeaderSpecific(viewer, PETSC_VIEWER_CLASSID, 2);
  if (globalToLocalPointSF) PetscValidHeaderSpecific(globalToLocalPointSF, PETSCSF_CLASSID, 3);
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERHDF5, &ishdf5));
  PetscCall(PetscLogEventBegin(DMPLEX_LabelsLoad, viewer, 0, 0, 0));
  if (ishdf5) {
#if defined(PETSC_HAVE_HDF5)
    PetscViewerFormat format;

    PetscCall(PetscViewerGetFormat(viewer, &format));
    if (format == PETSC_VIEWER_HDF5_PETSC || format == PETSC_VIEWER_DEFAULT || format == PETSC_VIEWER_NATIVE) {
      PetscCall(DMPlexLabelsLoad_HDF5_Internal(dm, viewer, globalToLocalPointSF));
    } else SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "PetscViewerFormat %s not supported for HDF5 input.", PetscViewerFormats[format]);
#else
    SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "HDF5 not supported in this build.\nPlease reconfigure using --download-hdf5");
#endif
  }
  PetscCall(PetscLogEventEnd(DMPLEX_LabelsLoad, viewer, 0, 0, 0));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexSectionLoad - Loads section into a `DMPLEX`

  Collective

  Input Parameters:
+ dm                   - The `DM` that represents the topology
. viewer               - The `PetscViewer` that represents the on-disk section (sectionA)
. sectiondm            - The `DM` into which the on-disk section (sectionA) is migrated, can be `NULL`
- globalToLocalPointSF - The `PetscSF` returned by `DMPlexTopologyLoad(`) when loading dm from viewer

  Output Parameters:
+ globalDofSF - The `PetscSF` that migrates any on-disk `Vec` data associated with sectionA into a global `Vec` associated with the `sectiondm`'s global section (`NULL` if not needed)
- localDofSF  - The `PetscSF` that migrates any on-disk `Vec` data associated with sectionA into a local `Vec` associated with the `sectiondm`'s local section (`NULL` if not needed)

  Level: advanced

  Notes:
  This function is a wrapper around `PetscSectionLoad()`; it loads, in addition to the raw section, a list of global point numbers that associates each on-disk section point with a global point number in [0, NX), where NX is the number of topology points in `dm`. Noting that globalToLocalPointSF associates each topology point in dm with a global number in [0, NX), one can readily establish an association of the on-disk section points with the topology points.

  In general `dm` and `sectiondm` are two different objects, the former carrying the topology and the latter carrying the section, and have been given a topology name and a section name, respectively, with `PetscObjectSetName()`. In practice, however, they can be the same object (or in case `sectiondm` is `NULL`) if it carries both topology and section; in that case the name of the object is used as both the topology name and the section name.

  The output parameter, `globalDofSF` (`localDofSF`), can later be used with `DMPlexGlobalVectorLoad()` (`DMPlexLocalVectorLoad()`) to load on-disk vectors into global (local) vectors associated with sectiondm's global (local) section.

  Example using 2 processes:
.vb
  NX (number of points on dm): 4
  sectionA                   : the on-disk section
  vecA                       : a vector associated with sectionA
  sectionB                   : sectiondm's local section constructed in this function
  vecB (local)               : a vector associated with sectiondm's local section
  vecB (global)              : a vector associated with sectiondm's global section

                                     rank 0    rank 1
  vecA (global)                  : [.0 .4 .1 | .2 .3]        <- to be loaded in DMPlexGlobalVectorLoad() or DMPlexLocalVectorLoad()
  sectionA->atlasOff             :       0 2 | 1             <- loaded in PetscSectionLoad()
  sectionA->atlasDof             :       1 3 | 1             <- loaded in PetscSectionLoad()
  sectionA's global point numbers:       0 2 | 3             <- loaded in DMPlexSectionLoad()
  [0, NX)                        :       0 1 | 2 3           <- conceptual partition used in globalToLocalPointSF
  sectionB's global point numbers:     0 1 3 | 3 2           <- associated with [0, NX) by globalToLocalPointSF
  sectionB->atlasDof             :     1 0 1 | 1 3
  sectionB->atlasOff (no perm)   :     0 1 1 | 0 1
  vecB (local)                   :   [.0 .4] | [.4 .1 .2 .3] <- to be constructed by calling DMPlexLocalVectorLoad() with localDofSF
  vecB (global)                  :    [.0 .4 | .1 .2 .3]     <- to be constructed by calling DMPlexGlobalVectorLoad() with globalDofSF
.ve
  where "|" represents a partition of loaded data, and global point 3 is assumed to be owned by rank 0.

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMLoad()`, `DMPlexTopologyLoad()`, `DMPlexCoordinatesLoad()`, `DMPlexLabelsLoad()`, `DMPlexGlobalVectorLoad()`, `DMPlexLocalVectorLoad()`, `PetscSectionLoad()`, `DMPlexSectionView()`, `PetscSF`, `PetscViewer`
@*/
PetscErrorCode DMPlexSectionLoad(DM dm, PetscViewer viewer, DM sectiondm, PetscSF globalToLocalPointSF, PetscSF *globalDofSF, PetscSF *localDofSF)
{
  PetscBool ishdf5;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidHeaderSpecific(viewer, PETSC_VIEWER_CLASSID, 2);
  if (!sectiondm) sectiondm = dm;
  PetscValidHeaderSpecific(sectiondm, DM_CLASSID, 3);
  PetscValidHeaderSpecific(globalToLocalPointSF, PETSCSF_CLASSID, 4);
  if (globalDofSF) PetscAssertPointer(globalDofSF, 5);
  if (localDofSF) PetscAssertPointer(localDofSF, 6);
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERHDF5, &ishdf5));
  PetscCall(PetscLogEventBegin(DMPLEX_SectionLoad, viewer, 0, 0, 0));
  if (ishdf5) {
#if defined(PETSC_HAVE_HDF5)
    PetscCall(DMPlexSectionLoad_HDF5_Internal(dm, viewer, sectiondm, globalToLocalPointSF, globalDofSF, localDofSF));
#else
    SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "HDF5 not supported in this build.\nPlease reconfigure using --download-hdf5");
#endif
  }
  PetscCall(PetscLogEventEnd(DMPLEX_SectionLoad, viewer, 0, 0, 0));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexGlobalVectorLoad - Loads on-disk vector data into a global vector

  Collective

  Input Parameters:
+ dm        - The `DM` that represents the topology
. viewer    - The `PetscViewer` that represents the on-disk vector data
. sectiondm - The `DM` that contains the global section on which vec is defined, can be `NULL`
. sf        - The `PetscSF` that migrates the on-disk vector data into vec
- vec       - The global vector to set values of

  Level: advanced

  Notes:
  In general dm and sectiondm are two different objects, the former carrying the topology and the latter carrying the section, and have been given a topology name and a section name, respectively, with `PetscObjectSetName()`. In practice, however, they can be the same object (or in case `sectiondm` is `NULL`) if it carries both topology and section; in that case the name of the object is used as both the topology name and the section name.

  Calling sequence:
.vb
       DMCreate(PETSC_COMM_WORLD, &dm);
       DMSetType(dm, DMPLEX);
       PetscObjectSetName((PetscObject)dm, "topologydm_name");
       DMPlexTopologyLoad(dm, viewer, &sfX);
       DMClone(dm, &sectiondm);
       PetscObjectSetName((PetscObject)sectiondm, "sectiondm_name");
       DMPlexSectionLoad(dm, viewer, sectiondm, sfX, &gsf, NULL);
       DMGetGlobalVector(sectiondm, &vec);
       PetscObjectSetName((PetscObject)vec, "vec_name");
       DMPlexGlobalVectorLoad(dm, viewer, sectiondm, gsf, vec);
       DMRestoreGlobalVector(sectiondm, &vec);
       PetscSFDestroy(&gsf);
       PetscSFDestroy(&sfX);
       DMDestroy(&sectiondm);
       DMDestroy(&dm);
.ve

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexTopologyLoad()`, `DMPlexSectionLoad()`, `DMPlexLocalVectorLoad()`, `DMPlexGlobalVectorView()`, `DMPlexLocalVectorView()`,
          `PetscSF`, `PetscViewer`
@*/
PetscErrorCode DMPlexGlobalVectorLoad(DM dm, PetscViewer viewer, DM sectiondm, PetscSF sf, Vec vec)
{
  PetscBool ishdf5;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidHeaderSpecific(viewer, PETSC_VIEWER_CLASSID, 2);
  if (!sectiondm) sectiondm = dm;
  PetscValidHeaderSpecific(sectiondm, DM_CLASSID, 3);
  PetscValidHeaderSpecific(sf, PETSCSF_CLASSID, 4);
  PetscValidHeaderSpecific(vec, VEC_CLASSID, 5);
  /* Check consistency */
  {
    PetscSection section;
    PetscBool    includesConstraints;
    PetscInt     m, m1;

    PetscCall(VecGetLocalSize(vec, &m1));
    PetscCall(DMGetGlobalSection(sectiondm, &section));
    PetscCall(PetscSectionGetIncludesConstraints(section, &includesConstraints));
    if (includesConstraints) PetscCall(PetscSectionGetStorageSize(section, &m));
    else PetscCall(PetscSectionGetConstrainedStorageSize(section, &m));
    PetscCheck(m1 == m, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Global vector size (%" PetscInt_FMT ") != global section storage size (%" PetscInt_FMT ")", m1, m);
  }
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERHDF5, &ishdf5));
  PetscCall(PetscLogEventBegin(DMPLEX_GlobalVectorLoad, viewer, 0, 0, 0));
  if (ishdf5) {
#if defined(PETSC_HAVE_HDF5)
    PetscCall(DMPlexVecLoad_HDF5_Internal(dm, viewer, sectiondm, sf, vec));
#else
    SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "HDF5 not supported in this build.\nPlease reconfigure using --download-hdf5");
#endif
  }
  PetscCall(PetscLogEventEnd(DMPLEX_GlobalVectorLoad, viewer, 0, 0, 0));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexLocalVectorLoad - Loads on-disk vector data into a local vector

  Collective

  Input Parameters:
+ dm        - The `DM` that represents the topology
. viewer    - The `PetscViewer` that represents the on-disk vector data
. sectiondm - The `DM` that contains the local section on which vec is defined, can be `NULL`
. sf        - The `PetscSF` that migrates the on-disk vector data into vec
- vec       - The local vector to set values of

  Level: advanced

  Notes:
  In general `dm` and `sectiondm` are two different objects, the former carrying the topology and the latter carrying the section, and have been given a topology name and a section name, respectively, with `PetscObjectSetName()`. In practice, however, they can be the same object (or in case `sectiondm` is `NULL`) if it carries both topology and section; in that case the name of the object is used as both the topology name and the section name.

  Calling sequence:
.vb
       DMCreate(PETSC_COMM_WORLD, &dm);
       DMSetType(dm, DMPLEX);
       PetscObjectSetName((PetscObject)dm, "topologydm_name");
       DMPlexTopologyLoad(dm, viewer, &sfX);
       DMClone(dm, &sectiondm);
       PetscObjectSetName((PetscObject)sectiondm, "sectiondm_name");
       DMPlexSectionLoad(dm, viewer, sectiondm, sfX, NULL, &lsf);
       DMGetLocalVector(sectiondm, &vec);
       PetscObjectSetName((PetscObject)vec, "vec_name");
       DMPlexLocalVectorLoad(dm, viewer, sectiondm, lsf, vec);
       DMRestoreLocalVector(sectiondm, &vec);
       PetscSFDestroy(&lsf);
       PetscSFDestroy(&sfX);
       DMDestroy(&sectiondm);
       DMDestroy(&dm);
.ve

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexTopologyLoad()`, `DMPlexSectionLoad()`, `DMPlexGlobalVectorLoad()`, `DMPlexGlobalVectorView()`, `DMPlexLocalVectorView()`,
          `PetscSF`, `PetscViewer`
@*/
PetscErrorCode DMPlexLocalVectorLoad(DM dm, PetscViewer viewer, DM sectiondm, PetscSF sf, Vec vec)
{
  PetscBool ishdf5;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidHeaderSpecific(viewer, PETSC_VIEWER_CLASSID, 2);
  if (!sectiondm) sectiondm = dm;
  PetscValidHeaderSpecific(sectiondm, DM_CLASSID, 3);
  PetscValidHeaderSpecific(sf, PETSCSF_CLASSID, 4);
  PetscValidHeaderSpecific(vec, VEC_CLASSID, 5);
  /* Check consistency */
  {
    PetscSection section;
    PetscBool    includesConstraints;
    PetscInt     m, m1;

    PetscCall(VecGetLocalSize(vec, &m1));
    PetscCall(DMGetLocalSection(sectiondm, &section));
    PetscCall(PetscSectionGetIncludesConstraints(section, &includesConstraints));
    if (includesConstraints) PetscCall(PetscSectionGetStorageSize(section, &m));
    else PetscCall(PetscSectionGetConstrainedStorageSize(section, &m));
    PetscCheck(m1 == m, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Local vector size (%" PetscInt_FMT ") != local section storage size (%" PetscInt_FMT ")", m1, m);
  }
  PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERHDF5, &ishdf5));
  PetscCall(PetscLogEventBegin(DMPLEX_LocalVectorLoad, viewer, 0, 0, 0));
  if (ishdf5) {
#if defined(PETSC_HAVE_HDF5)
    PetscCall(DMPlexVecLoad_HDF5_Internal(dm, viewer, sectiondm, sf, vec));
#else
    SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "HDF5 not supported in this build.\nPlease reconfigure using --download-hdf5");
#endif
  }
  PetscCall(PetscLogEventEnd(DMPLEX_LocalVectorLoad, viewer, 0, 0, 0));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode DMDestroy_Plex(DM dm)
{
  DM_Plex *mesh = (DM_Plex *)dm->data;

  PetscFunctionBegin;
  PetscCall(PetscObjectComposeFunction((PetscObject)dm, "DMSetUpGLVisViewer_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)dm, "DMPlexInsertBoundaryValues_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)dm, "DMCreateNeumannOverlap_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)dm, "DMInterpolateSolution_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)dm, "DMPlexInsertTimeDerivativeBoundaryValues_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)dm, "DMPlexGetOverlap_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)dm, "DMPlexDistributeGetDefault_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)dm, "DMPlexDistributeSetDefault_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)dm, "MatComputeNeumannOverlap_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)dm, "DMPlexReorderGetDefault_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)dm, "DMPlexReorderSetDefault_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)dm, "DMReorderSectionGetDefault_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)dm, "DMReorderSectionSetDefault_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)dm, "DMReorderSectionGetType_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)dm, "DMReorderSectionSetType_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)dm, "DMPlexGetOverlap_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)dm, "DMPlexSetOverlap_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)dm, "DMPlexGetUseCeed_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)dm, "DMPlexSetUseCeed_C", NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)dm, "DMGetIsoperiodicPointSF_C", NULL));
  if (--mesh->refct > 0) PetscFunctionReturn(PETSC_SUCCESS);
  PetscCall(PetscSectionDestroy(&mesh->coneSection));
  PetscCall(PetscFree(mesh->cones));
  PetscCall(PetscFree(mesh->coneOrientations));
  PetscCall(PetscSectionDestroy(&mesh->supportSection));
  PetscCall(PetscSectionDestroy(&mesh->subdomainSection));
  PetscCall(PetscFree(mesh->supports));
  PetscCall(PetscFree(mesh->cellTypes));
  PetscCall(DMPlexTransformDestroy(&mesh->tr));
  PetscCall(PetscFree(mesh->tetgenOpts));
  PetscCall(PetscFree(mesh->triangleOpts));
  PetscCall(PetscFree(mesh->transformType));
  PetscCall(PetscFree(mesh->distributionName));
  PetscCall(PetscPartitionerDestroy(&mesh->partitioner));
  PetscCall(DMLabelDestroy(&mesh->subpointMap));
  PetscCall(ISDestroy(&mesh->subpointIS));
  PetscCall(ISDestroy(&mesh->globalVertexNumbers));
  PetscCall(ISDestroy(&mesh->globalCellNumbers));
  if (mesh->periodic.face_sfs) {
    for (PetscInt i = 0; i < mesh->periodic.num_face_sfs; i++) PetscCall(PetscSFDestroy(&mesh->periodic.face_sfs[i]));
    PetscCall(PetscFree(mesh->periodic.face_sfs));
  }
  PetscCall(PetscSFDestroy(&mesh->periodic.composed_sf));
  if (mesh->periodic.periodic_points) {
    for (PetscInt i = 0; i < mesh->periodic.num_face_sfs; i++) PetscCall(ISDestroy(&mesh->periodic.periodic_points[i]));
    PetscCall(PetscFree(mesh->periodic.periodic_points));
  }
  if (mesh->periodic.transform) PetscCall(PetscFree(mesh->periodic.transform));
  PetscCall(PetscSectionDestroy(&mesh->anchorSection));
  PetscCall(ISDestroy(&mesh->anchorIS));
  PetscCall(PetscSectionDestroy(&mesh->parentSection));
  PetscCall(PetscFree(mesh->parents));
  PetscCall(PetscFree(mesh->childIDs));
  PetscCall(PetscSectionDestroy(&mesh->childSection));
  PetscCall(PetscFree(mesh->children));
  PetscCall(DMDestroy(&mesh->referenceTree));
  PetscCall(PetscGridHashDestroy(&mesh->lbox));
  PetscCall(PetscFree(mesh->neighbors));
  if (mesh->metricCtx) PetscCall(PetscFree(mesh->metricCtx));
  if (mesh->nonempty_comm != MPI_COMM_NULL && mesh->nonempty_comm != MPI_COMM_SELF) PetscCallMPI(MPI_Comm_free(&mesh->nonempty_comm));
  /* This was originally freed in DMDestroy(), but that prevents reference counting of backend objects */
  PetscCall(PetscFree(mesh));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode DMCreateMatrix_Plex(DM dm, Mat *J)
{
  PetscSection           sectionGlobal, sectionLocal;
  PetscInt               bs = -1, mbs;
  PetscInt               localSize, localStart = 0;
  PetscBool              isShell, isBlock, isSeqBlock, isMPIBlock, isSymBlock, isSymSeqBlock, isSymMPIBlock, isMatIS;
  MatType                mtype;
  ISLocalToGlobalMapping ltog;

  PetscFunctionBegin;
  PetscCall(MatInitializePackage());
  mtype = dm->mattype;
  PetscCall(DMGetLocalSection(dm, &sectionLocal));
  PetscCall(DMGetGlobalSection(dm, &sectionGlobal));
  /* PetscCall(PetscSectionGetStorageSize(sectionGlobal, &localSize)); */
  PetscCall(PetscSectionGetConstrainedStorageSize(sectionGlobal, &localSize));
  PetscCallMPI(MPI_Exscan(&localSize, &localStart, 1, MPIU_INT, MPI_SUM, PetscObjectComm((PetscObject)dm)));
  PetscCall(MatCreate(PetscObjectComm((PetscObject)dm), J));
  PetscCall(MatSetSizes(*J, localSize, localSize, PETSC_DETERMINE, PETSC_DETERMINE));
  PetscCall(MatSetType(*J, mtype));
  PetscCall(MatSetFromOptions(*J));
  PetscCall(MatGetBlockSize(*J, &mbs));
  if (mbs > 1) bs = mbs;
  PetscCall(PetscStrcmp(mtype, MATSHELL, &isShell));
  PetscCall(PetscStrcmp(mtype, MATBAIJ, &isBlock));
  PetscCall(PetscStrcmp(mtype, MATSEQBAIJ, &isSeqBlock));
  PetscCall(PetscStrcmp(mtype, MATMPIBAIJ, &isMPIBlock));
  PetscCall(PetscStrcmp(mtype, MATSBAIJ, &isSymBlock));
  PetscCall(PetscStrcmp(mtype, MATSEQSBAIJ, &isSymSeqBlock));
  PetscCall(PetscStrcmp(mtype, MATMPISBAIJ, &isSymMPIBlock));
  PetscCall(PetscStrcmp(mtype, MATIS, &isMatIS));
  if (!isShell) {
    // There are three states with pblocks, since block starts can have no dofs:
    // UNKNOWN) New Block:   An open block has been signalled by pblocks[p] == 1
    // TRUE)    Block Start: The first entry in a block has been added
    // FALSE)   Block Add:   An additional block entry has been added, since pblocks[p] == 0
    PetscBT         blst;
    PetscBool3      bstate     = PETSC_BOOL3_UNKNOWN;
    PetscBool       fillMatrix = (PetscBool)(!dm->prealloc_only && !isMatIS);
    const PetscInt *perm       = NULL;
    PetscInt       *dnz, *onz, *dnzu, *onzu, bsLocal[2], bsMinMax[2], *pblocks;
    PetscInt        pStart, pEnd, dof, cdof, num_fields;

    PetscCall(DMGetLocalToGlobalMapping(dm, &ltog));
    PetscCall(PetscSectionGetBlockStarts(sectionLocal, &blst));
    if (sectionLocal->perm) PetscCall(ISGetIndices(sectionLocal->perm, &perm));

    PetscCall(PetscCalloc1(localSize, &pblocks));
    PetscCall(PetscSectionGetChart(sectionGlobal, &pStart, &pEnd));
    PetscCall(PetscSectionGetNumFields(sectionGlobal, &num_fields));
    // We need to process in the permuted order to get block sizes right
    for (PetscInt point = pStart; point < pEnd; ++point) {
      const PetscInt p = perm ? perm[point] : point;

      switch (dm->blocking_type) {
      case DM_BLOCKING_TOPOLOGICAL_POINT: { // One block per topological point
        PetscInt bdof, offset;

        PetscCall(PetscSectionGetDof(sectionGlobal, p, &dof));
        PetscCall(PetscSectionGetOffset(sectionGlobal, p, &offset));
        PetscCall(PetscSectionGetConstraintDof(sectionGlobal, p, &cdof));
        if (blst && PetscBTLookup(blst, p)) bstate = PETSC_BOOL3_UNKNOWN;
        if (dof > 0) {
          // State change
          if (bstate == PETSC_BOOL3_UNKNOWN) bstate = PETSC_BOOL3_TRUE;
          else if (bstate == PETSC_BOOL3_TRUE && blst && !PetscBTLookup(blst, p)) bstate = PETSC_BOOL3_FALSE;

          for (PetscInt i = 0; i < dof - cdof; ++i) pblocks[offset - localStart + i] = dof - cdof;
          // Signal block concatenation
          if (bstate == PETSC_BOOL3_FALSE && dof - cdof) pblocks[offset - localStart] = -(dof - cdof);
        }
        dof  = dof < 0 ? -(dof + 1) : dof;
        bdof = cdof && (dof - cdof) ? 1 : dof;
        if (dof) {
          if (bs < 0) {
            bs = bdof;
          } else if (bs != bdof) {
            bs = 1;
          }
        }
      } break;
      case DM_BLOCKING_FIELD_NODE: {
        for (PetscInt field = 0; field < num_fields; field++) {
          PetscInt num_comp, bdof, offset;
          PetscCall(PetscSectionGetFieldComponents(sectionGlobal, field, &num_comp));
          PetscCall(PetscSectionGetFieldDof(sectionGlobal, p, field, &dof));
          if (dof < 0) continue;
          PetscCall(PetscSectionGetFieldOffset(sectionGlobal, p, field, &offset));
          PetscCall(PetscSectionGetFieldConstraintDof(sectionGlobal, p, field, &cdof));
          PetscAssert(dof % num_comp == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Point %" PetscInt_FMT " field %" PetscInt_FMT " has %" PetscInt_FMT " dof, not divisible by %" PetscInt_FMT " component ", p, field, dof, num_comp);
          PetscInt num_nodes = dof / num_comp;
          for (PetscInt i = 0; i < dof - cdof; i++) pblocks[offset - localStart + i] = (dof - cdof) / num_nodes;
          // Handle possibly constant block size (unlikely)
          bdof = cdof && (dof - cdof) ? 1 : dof;
          if (dof) {
            if (bs < 0) {
              bs = bdof;
            } else if (bs != bdof) {
              bs = 1;
            }
          }
        }
      } break;
      }
    }
    if (sectionLocal->perm) PetscCall(ISRestoreIndices(sectionLocal->perm, &perm));
    /* Must have same blocksize on all procs (some might have no points) */
    bsLocal[0] = bs < 0 ? PETSC_MAX_INT : bs;
    bsLocal[1] = bs;
    PetscCall(PetscGlobalMinMaxInt(PetscObjectComm((PetscObject)dm), bsLocal, bsMinMax));
    if (bsMinMax[0] != bsMinMax[1]) bs = 1;
    else bs = bsMinMax[0];
    bs = PetscMax(1, bs);
    PetscCall(MatSetLocalToGlobalMapping(*J, ltog, ltog));
    if (dm->prealloc_skip) { // User will likely use MatSetPreallocationCOO(), but still set structural parameters
      PetscCall(MatSetBlockSize(*J, bs));
      PetscCall(MatSetUp(*J));
    } else {
      PetscCall(PetscCalloc4(localSize / bs, &dnz, localSize / bs, &onz, localSize / bs, &dnzu, localSize / bs, &onzu));
      PetscCall(DMPlexPreallocateOperator(dm, bs, dnz, onz, dnzu, onzu, *J, fillMatrix));
      PetscCall(PetscFree4(dnz, onz, dnzu, onzu));
    }
    if (pblocks) { // Consolidate blocks
      PetscInt nblocks = 0;
      pblocks[0]       = PetscAbs(pblocks[0]);
      for (PetscInt i = 0; i < localSize; i += PetscMax(1, pblocks[i])) {
        if (pblocks[i] == 0) continue;
        // Negative block size indicates the blocks should be concatenated
        if (pblocks[i] < 0) {
          pblocks[i] = -pblocks[i];
          pblocks[nblocks - 1] += pblocks[i];
        } else {
          pblocks[nblocks++] = pblocks[i]; // nblocks always <= i
        }
        for (PetscInt j = 1; j < pblocks[i]; j++)
          PetscCheck(pblocks[i + j] == pblocks[i], PETSC_COMM_SELF, PETSC_ERR_PLIB, "Block of size %" PetscInt_FMT " at %" PetscInt_FMT " mismatches entry %" PetscInt_FMT " at %" PetscInt_FMT, pblocks[i], i, pblocks[i + j], i + j);
      }
      PetscCall(MatSetVariableBlockSizes(*J, nblocks, pblocks));
    }
    PetscCall(PetscFree(pblocks));
  }
  PetscCall(MatSetDM(*J, dm));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexGetSubdomainSection - Returns the section associated with the subdomain

  Not Collective

  Input Parameter:
. dm - The `DMPLEX`

  Output Parameter:
. subsection - The subdomain section

  Level: developer

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `PetscSection`
@*/
PetscErrorCode DMPlexGetSubdomainSection(DM dm, PetscSection *subsection)
{
  DM_Plex *mesh = (DM_Plex *)dm->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (!mesh->subdomainSection) {
    PetscSection section;
    PetscSF      sf;

    PetscCall(PetscSFCreate(PETSC_COMM_SELF, &sf));
    PetscCall(DMGetLocalSection(dm, &section));
    PetscCall(PetscSectionCreateGlobalSection(section, sf, PETSC_TRUE, PETSC_FALSE, PETSC_TRUE, &mesh->subdomainSection));
    PetscCall(PetscSFDestroy(&sf));
  }
  *subsection = mesh->subdomainSection;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexGetChart - Return the interval for all mesh points [`pStart`, `pEnd`)

  Not Collective

  Input Parameter:
. dm - The `DMPLEX`

  Output Parameters:
+ pStart - The first mesh point
- pEnd   - The upper bound for mesh points

  Level: beginner

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexCreate()`, `DMPlexSetChart()`
@*/
PetscErrorCode DMPlexGetChart(DM dm, PetscInt *pStart, PetscInt *pEnd)
{
  DM_Plex *mesh = (DM_Plex *)dm->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (mesh->tr) PetscCall(DMPlexTransformGetChart(mesh->tr, pStart, pEnd));
  else PetscCall(PetscSectionGetChart(mesh->coneSection, pStart, pEnd));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexSetChart - Set the interval for all mesh points [`pStart`, `pEnd`)

  Not Collective

  Input Parameters:
+ dm     - The `DMPLEX`
. pStart - The first mesh point
- pEnd   - The upper bound for mesh points

  Level: beginner

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexCreate()`, `DMPlexGetChart()`
@*/
PetscErrorCode DMPlexSetChart(DM dm, PetscInt pStart, PetscInt pEnd)
{
  DM_Plex *mesh = (DM_Plex *)dm->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscCall(PetscSectionSetChart(mesh->coneSection, pStart, pEnd));
  PetscCall(PetscSectionSetChart(mesh->supportSection, pStart, pEnd));
  PetscCall(PetscFree(mesh->cellTypes));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexGetConeSize - Return the number of in-edges for this point in the DAG

  Not Collective

  Input Parameters:
+ dm - The `DMPLEX`
- p  - The point, which must lie in the chart set with `DMPlexSetChart()`

  Output Parameter:
. size - The cone size for point `p`

  Level: beginner

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexCreate()`, `DMPlexSetConeSize()`, `DMPlexSetChart()`
@*/
PetscErrorCode DMPlexGetConeSize(DM dm, PetscInt p, PetscInt *size)
{
  DM_Plex *mesh = (DM_Plex *)dm->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscAssertPointer(size, 3);
  if (mesh->tr) PetscCall(DMPlexTransformGetConeSize(mesh->tr, p, size));
  else PetscCall(PetscSectionGetDof(mesh->coneSection, p, size));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexSetConeSize - Set the number of in-edges for this point in the DAG

  Not Collective

  Input Parameters:
+ dm   - The `DMPLEX`
. p    - The point, which must lie in the chart set with `DMPlexSetChart()`
- size - The cone size for point `p`

  Level: beginner

  Note:
  This should be called after `DMPlexSetChart()`.

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexSetCone()`, `DMPlexCreate()`, `DMPlexGetConeSize()`, `DMPlexSetChart()`
@*/
PetscErrorCode DMPlexSetConeSize(DM dm, PetscInt p, PetscInt size)
{
  DM_Plex *mesh = (DM_Plex *)dm->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscCheck(!mesh->tr, PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Cannot call DMPlexSetConeSize() on a mesh with a transform defined.");
  PetscCall(PetscSectionSetDof(mesh->coneSection, p, size));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  DMPlexGetCone - Return the points on the in-edges for this point in the DAG

  Not Collective

  Input Parameters:
+ dm - The `DMPLEX`
- p  - The point, which must lie in the chart set with `DMPlexSetChart()`

  Output Parameter:
. cone - An array of points which are on the in-edges for point `p`, the length of `cone` is the result of `DMPlexGetConeSize()`

  Level: beginner

  Fortran Notes:
  `cone` must be declared with
.vb
  PetscInt, pointer :: cone(:)
.ve

  You must also call `DMPlexRestoreCone()` after you finish using the array.
  `DMPlexRestoreCone()` is not needed/available in C.

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexGetConeSize()`, `DMPlexSetCone()`, `DMPlexGetConeTuple()`, `DMPlexSetChart()`, `DMPlexRestoreCone()`
@*/
PetscErrorCode DMPlexGetCone(DM dm, PetscInt p, const PetscInt *cone[])
{
  DM_Plex *mesh = (DM_Plex *)dm->data;
  PetscInt off;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscAssertPointer(cone, 3);
  PetscCall(PetscSectionGetOffset(mesh->coneSection, p, &off));
  *cone = PetscSafePointerPlusOffset(mesh->cones, off);
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexGetConeTuple - Return the points on the in-edges of several points in the DAG

  Not Collective

  Input Parameters:
+ dm - The `DMPLEX`
- p  - The `IS` of points, which must lie in the chart set with `DMPlexSetChart()`

  Output Parameters:
+ pConesSection - `PetscSection` describing the layout of `pCones`
- pCones        - An `IS` containing the points which are on the in-edges for the point set `p`

  Level: intermediate

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexCreate()`, `DMPlexGetCone()`, `DMPlexGetConeRecursive()`, `DMPlexSetChart()`, `PetscSection`, `IS`
@*/
PetscErrorCode DMPlexGetConeTuple(DM dm, IS p, PetscSection *pConesSection, IS *pCones)
{
  PetscSection cs, newcs;
  PetscInt    *cones;
  PetscInt    *newarr = NULL;
  PetscInt     n;

  PetscFunctionBegin;
  PetscCall(DMPlexGetCones(dm, &cones));
  PetscCall(DMPlexGetConeSection(dm, &cs));
  PetscCall(PetscSectionExtractDofsFromArray(cs, MPIU_INT, cones, p, &newcs, pCones ? ((void **)&newarr) : NULL));
  if (pConesSection) *pConesSection = newcs;
  if (pCones) {
    PetscCall(PetscSectionGetStorageSize(newcs, &n));
    PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)p), n, newarr, PETSC_OWN_POINTER, pCones));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexGetConeRecursiveVertices - Expand each given point into its cone points and do that recursively until we end up just with vertices.

  Not Collective

  Input Parameters:
+ dm     - The `DMPLEX`
- points - The `IS` of points, which must lie in the chart set with `DMPlexSetChart()`

  Output Parameter:
. expandedPoints - An `IS` containing the of vertices recursively expanded from input points

  Level: advanced

  Notes:
  Like `DMPlexGetConeRecursive()` but returns only the 0-depth `IS` (i.e. vertices only) and no sections.

  There is no corresponding Restore function, just call `ISDestroy()` on the returned `IS` to deallocate.

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexCreate()`, `DMPlexGetCone()`, `DMPlexGetConeTuple()`, `DMPlexGetConeRecursive()`, `DMPlexRestoreConeRecursive()`,
          `DMPlexGetDepth()`, `IS`
@*/
PetscErrorCode DMPlexGetConeRecursiveVertices(DM dm, IS points, IS *expandedPoints)
{
  IS      *expandedPointsAll;
  PetscInt depth;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidHeaderSpecific(points, IS_CLASSID, 2);
  PetscAssertPointer(expandedPoints, 3);
  PetscCall(DMPlexGetConeRecursive(dm, points, &depth, &expandedPointsAll, NULL));
  *expandedPoints = expandedPointsAll[0];
  PetscCall(PetscObjectReference((PetscObject)expandedPointsAll[0]));
  PetscCall(DMPlexRestoreConeRecursive(dm, points, &depth, &expandedPointsAll, NULL));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexGetConeRecursive - Expand each given point into its cone points and do that recursively until we end up just with vertices
  (DAG points of depth 0, i.e., without cones).

  Not Collective

  Input Parameters:
+ dm     - The `DMPLEX`
- points - The `IS` of points, which must lie in the chart set with `DMPlexSetChart()`

  Output Parameters:
+ depth          - (optional) Size of the output arrays, equal to `DMPLEX` depth, returned by `DMPlexGetDepth()`
. expandedPoints - (optional) An array of index sets with recursively expanded cones
- sections       - (optional) An array of sections which describe mappings from points to their cone points

  Level: advanced

  Notes:
  Like `DMPlexGetConeTuple()` but recursive.

  Array `expandedPoints` has size equal to `depth`. Each `expandedPoints`[d] contains DAG points with maximum depth d, recursively cone-wise expanded from the input points.
  For example, for d=0 it contains only vertices, for d=1 it can contain vertices and edges, etc.

  Array section has size equal to `depth`.  Each `PetscSection` `sections`[d] realizes mapping from `expandedPoints`[d+1] (section points) to `expandedPoints`[d] (section dofs) as follows\:
  (1) DAG points in `expandedPoints`[d+1] with `depth` d+1 to their cone points in `expandedPoints`[d];
  (2) DAG points in `expandedPoints`[d+1] with `depth` in [0,d] to the same points in `expandedPoints`[d].

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexCreate()`, `DMPlexGetCone()`, `DMPlexGetConeTuple()`, `DMPlexRestoreConeRecursive()`, `DMPlexGetConeRecursiveVertices()`,
          `DMPlexGetDepth()`, `PetscSection`, `IS`
@*/
PetscErrorCode DMPlexGetConeRecursive(DM dm, IS points, PetscInt *depth, IS *expandedPoints[], PetscSection *sections[])
{
  const PetscInt *arr0 = NULL, *cone = NULL;
  PetscInt       *arr = NULL, *newarr = NULL;
  PetscInt        d, depth_, i, n, newn, cn, co, start, end;
  IS             *expandedPoints_;
  PetscSection   *sections_;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidHeaderSpecific(points, IS_CLASSID, 2);
  if (depth) PetscAssertPointer(depth, 3);
  if (expandedPoints) PetscAssertPointer(expandedPoints, 4);
  if (sections) PetscAssertPointer(sections, 5);
  PetscCall(ISGetLocalSize(points, &n));
  PetscCall(ISGetIndices(points, &arr0));
  PetscCall(DMPlexGetDepth(dm, &depth_));
  PetscCall(PetscCalloc1(depth_, &expandedPoints_));
  PetscCall(PetscCalloc1(depth_, &sections_));
  arr = (PetscInt *)arr0; /* this is ok because first generation of arr is not modified */
  for (d = depth_ - 1; d >= 0; d--) {
    PetscCall(PetscSectionCreate(PETSC_COMM_SELF, &sections_[d]));
    PetscCall(PetscSectionSetChart(sections_[d], 0, n));
    for (i = 0; i < n; i++) {
      PetscCall(DMPlexGetDepthStratum(dm, d + 1, &start, &end));
      if (arr[i] >= start && arr[i] < end) {
        PetscCall(DMPlexGetConeSize(dm, arr[i], &cn));
        PetscCall(PetscSectionSetDof(sections_[d], i, cn));
      } else {
        PetscCall(PetscSectionSetDof(sections_[d], i, 1));
      }
    }
    PetscCall(PetscSectionSetUp(sections_[d]));
    PetscCall(PetscSectionGetStorageSize(sections_[d], &newn));
    PetscCall(PetscMalloc1(newn, &newarr));
    for (i = 0; i < n; i++) {
      PetscCall(PetscSectionGetDof(sections_[d], i, &cn));
      PetscCall(PetscSectionGetOffset(sections_[d], i, &co));
      if (cn > 1) {
        PetscCall(DMPlexGetCone(dm, arr[i], &cone));
        PetscCall(PetscMemcpy(&newarr[co], cone, cn * sizeof(PetscInt)));
      } else {
        newarr[co] = arr[i];
      }
    }
    PetscCall(ISCreateGeneral(PETSC_COMM_SELF, newn, newarr, PETSC_OWN_POINTER, &expandedPoints_[d]));
    arr = newarr;
    n   = newn;
  }
  PetscCall(ISRestoreIndices(points, &arr0));
  *depth = depth_;
  if (expandedPoints) *expandedPoints = expandedPoints_;
  else {
    for (d = 0; d < depth_; d++) PetscCall(ISDestroy(&expandedPoints_[d]));
    PetscCall(PetscFree(expandedPoints_));
  }
  if (sections) *sections = sections_;
  else {
    for (d = 0; d < depth_; d++) PetscCall(PetscSectionDestroy(&sections_[d]));
    PetscCall(PetscFree(sections_));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexRestoreConeRecursive - Deallocates arrays created by `DMPlexGetConeRecursive()`

  Not Collective

  Input Parameters:
+ dm     - The `DMPLEX`
- points - The `IS` of points, which must lie in the chart set with `DMPlexSetChart()`

  Output Parameters:
+ depth          - (optional) Size of the output arrays, equal to `DMPLEX` depth, returned by `DMPlexGetDepth()`
. expandedPoints - (optional) An array of recursively expanded cones
- sections       - (optional) An array of sections which describe mappings from points to their cone points

  Level: advanced

  Note:
  See `DMPlexGetConeRecursive()`

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexCreate()`, `DMPlexGetCone()`, `DMPlexGetConeTuple()`, `DMPlexGetConeRecursive()`, `DMPlexGetConeRecursiveVertices()`,
          `DMPlexGetDepth()`, `IS`, `PetscSection`
@*/
PetscErrorCode DMPlexRestoreConeRecursive(DM dm, IS points, PetscInt *depth, IS *expandedPoints[], PetscSection *sections[])
{
  PetscInt d, depth_;

  PetscFunctionBegin;
  PetscCall(DMPlexGetDepth(dm, &depth_));
  PetscCheck(!depth || *depth == depth_, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "depth changed since last call to DMPlexGetConeRecursive");
  if (depth) *depth = 0;
  if (expandedPoints) {
    for (d = 0; d < depth_; d++) PetscCall(ISDestroy(&((*expandedPoints)[d])));
    PetscCall(PetscFree(*expandedPoints));
  }
  if (sections) {
    for (d = 0; d < depth_; d++) PetscCall(PetscSectionDestroy(&((*sections)[d])));
    PetscCall(PetscFree(*sections));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexSetCone - Set the points on the in-edges for this point in the DAG; that is these are the points that cover the specific point

  Not Collective

  Input Parameters:
+ dm   - The `DMPLEX`
. p    - The point, which must lie in the chart set with `DMPlexSetChart()`
- cone - An array of points which are on the in-edges for point `p`, its length must have been previously provided with `DMPlexSetConeSize()`

  Level: beginner

  Note:
  This should be called after all calls to `DMPlexSetConeSize()` and `DMSetUp()`.

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexCreate()`, `DMPlexGetCone()`, `DMPlexSetChart()`, `DMPlexSetConeSize()`, `DMSetUp()`, `DMPlexSetSupport()`, `DMPlexSetSupportSize()`
@*/
PetscErrorCode DMPlexSetCone(DM dm, PetscInt p, const PetscInt cone[])
{
  DM_Plex *mesh = (DM_Plex *)dm->data;
  PetscInt dof, off, c;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscCall(PetscSectionGetDof(mesh->coneSection, p, &dof));
  if (dof) PetscAssertPointer(cone, 3);
  PetscCall(PetscSectionGetOffset(mesh->coneSection, p, &off));
  if (PetscDefined(USE_DEBUG)) {
    PetscInt pStart, pEnd;
    PetscCall(PetscSectionGetChart(mesh->coneSection, &pStart, &pEnd));
    PetscCheck(!(p < pStart) && !(p >= pEnd), PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "Mesh point %" PetscInt_FMT " is not in the valid range [%" PetscInt_FMT ", %" PetscInt_FMT ")", p, pStart, pEnd);
    for (c = 0; c < dof; ++c) {
      PetscCheck(!(cone[c] < pStart) && !(cone[c] >= pEnd), PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "Cone point %" PetscInt_FMT " is not in the valid range [%" PetscInt_FMT ", %" PetscInt_FMT ")", cone[c], pStart, pEnd);
      mesh->cones[off + c] = cone[c];
    }
  } else {
    for (c = 0; c < dof; ++c) mesh->cones[off + c] = cone[c];
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  DMPlexGetConeOrientation - Return the orientations on the in-edges for this point in the DAG

  Not Collective

  Input Parameters:
+ dm - The `DMPLEX`
- p  - The point, which must lie in the chart set with `DMPlexSetChart()`

  Output Parameter:
. coneOrientation - An array of orientations which are on the in-edges for point `p`. An orientation is an
                    integer giving the prescription for cone traversal. Its length is given by the result of `DMPlexSetConeSize()`

  Level: beginner

  Note:
  The number indexes the symmetry transformations for the cell type (see manual). Orientation 0 is always
  the identity transformation. Negative orientation indicates reflection so that -(o+1) is the reflection
  of o, however it is not necessarily the inverse. To get the inverse, use `DMPolytopeTypeComposeOrientationInv()`
  with the identity.

  Fortran Notes:
  You must call `DMPlexRestoreConeOrientation()` after you finish using the returned array.
  `DMPlexRestoreConeOrientation()` is not needed/available in C.

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexSetConeSize()`, `DMPolytopeTypeComposeOrientation()`, `DMPolytopeTypeComposeOrientationInv()`,
          `DMPlexCreate()`, `DMPlexGetCone()`, `DMPlexSetCone()`, `DMPlexSetChart()`
@*/
PetscErrorCode DMPlexGetConeOrientation(DM dm, PetscInt p, const PetscInt *coneOrientation[])
{
  DM_Plex *mesh = (DM_Plex *)dm->data;
  PetscInt off;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (PetscDefined(USE_DEBUG)) {
    PetscInt dof;
    PetscCall(PetscSectionGetDof(mesh->coneSection, p, &dof));
    if (dof) PetscAssertPointer(coneOrientation, 3);
  }
  PetscCall(PetscSectionGetOffset(mesh->coneSection, p, &off));

  *coneOrientation = &mesh->coneOrientations[off];
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexSetConeOrientation - Set the orientations on the in-edges for this point in the DAG

  Not Collective

  Input Parameters:
+ dm              - The `DMPLEX`
. p               - The point, which must lie in the chart set with `DMPlexSetChart()`
- coneOrientation - An array of orientations. Its length is given by the result of `DMPlexSetConeSize()`

  Level: beginner

  Notes:
  This should be called after all calls to `DMPlexSetConeSize()` and `DMSetUp()`.

  The meaning of coneOrientation is detailed in `DMPlexGetConeOrientation()`.

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexCreate()`, `DMPlexGetConeOrientation()`, `DMPlexSetCone()`, `DMPlexSetChart()`, `DMPlexSetConeSize()`, `DMSetUp()`
@*/
PetscErrorCode DMPlexSetConeOrientation(DM dm, PetscInt p, const PetscInt coneOrientation[])
{
  DM_Plex *mesh = (DM_Plex *)dm->data;
  PetscInt pStart, pEnd;
  PetscInt dof, off, c;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscCall(PetscSectionGetDof(mesh->coneSection, p, &dof));
  if (dof) PetscAssertPointer(coneOrientation, 3);
  PetscCall(PetscSectionGetOffset(mesh->coneSection, p, &off));
  if (PetscDefined(USE_DEBUG)) {
    PetscCall(PetscSectionGetChart(mesh->coneSection, &pStart, &pEnd));
    PetscCheck(!(p < pStart) && !(p >= pEnd), PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "Mesh point %" PetscInt_FMT " is not in the valid range [%" PetscInt_FMT ", %" PetscInt_FMT ")", p, pStart, pEnd);
    for (c = 0; c < dof; ++c) {
      PetscInt cdof, o = coneOrientation[c];

      PetscCall(PetscSectionGetDof(mesh->coneSection, mesh->cones[off + c], &cdof));
      PetscCheck(!o || (o >= -(cdof + 1) && o < cdof), PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "Cone orientation %" PetscInt_FMT " is not in the valid range [%" PetscInt_FMT ". %" PetscInt_FMT ")", o, -(cdof + 1), cdof);
      mesh->coneOrientations[off + c] = o;
    }
  } else {
    for (c = 0; c < dof; ++c) mesh->coneOrientations[off + c] = coneOrientation[c];
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexInsertCone - Insert a point into the in-edges for the point p in the DAG

  Not Collective

  Input Parameters:
+ dm        - The `DMPLEX`
. p         - The point, which must lie in the chart set with `DMPlexSetChart()`
. conePos   - The local index in the cone where the point should be put
- conePoint - The mesh point to insert

  Level: beginner

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexCreate()`, `DMPlexGetCone()`, `DMPlexSetChart()`, `DMPlexSetConeSize()`, `DMSetUp()`
@*/
PetscErrorCode DMPlexInsertCone(DM dm, PetscInt p, PetscInt conePos, PetscInt conePoint)
{
  DM_Plex *mesh = (DM_Plex *)dm->data;
  PetscInt pStart, pEnd;
  PetscInt dof, off;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (PetscDefined(USE_DEBUG)) {
    PetscCall(PetscSectionGetChart(mesh->coneSection, &pStart, &pEnd));
    PetscCheck(!(p < pStart) && !(p >= pEnd), PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "Mesh point %" PetscInt_FMT " is not in the valid range [%" PetscInt_FMT ", %" PetscInt_FMT ")", p, pStart, pEnd);
    PetscCheck(!(conePoint < pStart) && !(conePoint >= pEnd), PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "Cone point %" PetscInt_FMT " is not in the valid range [%" PetscInt_FMT ", %" PetscInt_FMT ")", conePoint, pStart, pEnd);
    PetscCall(PetscSectionGetDof(mesh->coneSection, p, &dof));
    PetscCheck(!(conePos < 0) && !(conePos >= dof), PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "Cone position %" PetscInt_FMT " of point %" PetscInt_FMT " is not in the valid range [0, %" PetscInt_FMT ")", conePos, p, dof);
  }
  PetscCall(PetscSectionGetOffset(mesh->coneSection, p, &off));
  mesh->cones[off + conePos] = conePoint;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexInsertConeOrientation - Insert a point orientation for the in-edge for the point p in the DAG

  Not Collective

  Input Parameters:
+ dm              - The `DMPLEX`
. p               - The point, which must lie in the chart set with `DMPlexSetChart()`
. conePos         - The local index in the cone where the point should be put
- coneOrientation - The point orientation to insert

  Level: beginner

  Note:
  The meaning of coneOrientation values is detailed in `DMPlexGetConeOrientation()`.

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexCreate()`, `DMPlexGetCone()`, `DMPlexSetChart()`, `DMPlexSetConeSize()`, `DMSetUp()`
@*/
PetscErrorCode DMPlexInsertConeOrientation(DM dm, PetscInt p, PetscInt conePos, PetscInt coneOrientation)
{
  DM_Plex *mesh = (DM_Plex *)dm->data;
  PetscInt pStart, pEnd;
  PetscInt dof, off;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (PetscDefined(USE_DEBUG)) {
    PetscCall(PetscSectionGetChart(mesh->coneSection, &pStart, &pEnd));
    PetscCheck(!(p < pStart) && !(p >= pEnd), PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "Mesh point %" PetscInt_FMT " is not in the valid range [%" PetscInt_FMT ", %" PetscInt_FMT ")", p, pStart, pEnd);
    PetscCall(PetscSectionGetDof(mesh->coneSection, p, &dof));
    PetscCheck(!(conePos < 0) && !(conePos >= dof), PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "Cone position %" PetscInt_FMT " of point %" PetscInt_FMT " is not in the valid range [0, %" PetscInt_FMT ")", conePos, p, dof);
  }
  PetscCall(PetscSectionGetOffset(mesh->coneSection, p, &off));
  mesh->coneOrientations[off + conePos] = coneOrientation;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  DMPlexGetOrientedCone - Return the points and orientations on the in-edges for this point in the DAG

  Not collective

  Input Parameters:
+ dm - The DMPlex
- p  - The point, which must lie in the chart set with DMPlexSetChart()

  Output Parameters:
+ cone - An array of points which are on the in-edges for point `p`
- ornt - An array of orientations which are on the in-edges for point `p`. An orientation is an
         integer giving the prescription for cone traversal.

  Level: beginner

  Notes:
  The number indexes the symmetry transformations for the cell type (see manual). Orientation 0 is always
  the identity transformation. Negative orientation indicates reflection so that -(o+1) is the reflection
  of o, however it is not necessarily the inverse. To get the inverse, use `DMPolytopeTypeComposeOrientationInv()`
  with the identity.

  You must also call `DMPlexRestoreOrientedCone()` after you finish using the returned array.

  Fortran Notes:
  `cone` and `ornt` must be declared with
.vb
  PetscInt, pointer :: cone(:)
  PetscInt, pointer :: ornt(:)
.ve

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexRestoreOrientedCone()`, `DMPlexGetConeSize()`, `DMPlexGetCone()`, `DMPlexGetChart()`
@*/
PetscErrorCode DMPlexGetOrientedCone(DM dm, PetscInt p, const PetscInt *cone[], const PetscInt *ornt[])
{
  DM_Plex *mesh = (DM_Plex *)dm->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (mesh->tr) {
    PetscCall(DMPlexTransformGetCone(mesh->tr, p, cone, ornt));
  } else {
    PetscInt off;
    if (PetscDefined(USE_DEBUG)) {
      PetscInt dof;
      PetscCall(PetscSectionGetDof(mesh->coneSection, p, &dof));
      if (dof) {
        if (cone) PetscAssertPointer(cone, 3);
        if (ornt) PetscAssertPointer(ornt, 4);
      }
    }
    PetscCall(PetscSectionGetOffset(mesh->coneSection, p, &off));
    if (cone) *cone = PetscSafePointerPlusOffset(mesh->cones, off);
    if (ornt) *ornt = PetscSafePointerPlusOffset(mesh->coneOrientations, off);
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  DMPlexRestoreOrientedCone - Restore the points and orientations on the in-edges for this point in the DAG obtained with `DMPlexGetOrientedCone()`

  Not Collective

  Input Parameters:
+ dm   - The DMPlex
. p    - The point, which must lie in the chart set with `DMPlexSetChart()`
. cone - An array of points which are on the in-edges for point p
- ornt - An array of orientations which are on the in-edges for point `p`. An orientation is an
         integer giving the prescription for cone traversal.

  Level: beginner

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexGetOrientedCone()`, `DMPlexGetConeSize()`, `DMPlexGetCone()`, `DMPlexGetChart()`
@*/
PetscErrorCode DMPlexRestoreOrientedCone(DM dm, PetscInt p, const PetscInt *cone[], const PetscInt *ornt[])
{
  DM_Plex *mesh = (DM_Plex *)dm->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (mesh->tr) PetscCall(DMPlexTransformRestoreCone(mesh->tr, p, cone, ornt));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexGetSupportSize - Return the number of out-edges for this point in the DAG

  Not Collective

  Input Parameters:
+ dm - The `DMPLEX`
- p  - The point, which must lie in the chart set with `DMPlexSetChart()`

  Output Parameter:
. size - The support size for point `p`

  Level: beginner

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexCreate()`, `DMPlexSetConeSize()`, `DMPlexSetChart()`, `DMPlexGetConeSize()`
@*/
PetscErrorCode DMPlexGetSupportSize(DM dm, PetscInt p, PetscInt *size)
{
  DM_Plex *mesh = (DM_Plex *)dm->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscAssertPointer(size, 3);
  PetscCall(PetscSectionGetDof(mesh->supportSection, p, size));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexSetSupportSize - Set the number of out-edges for this point in the DAG

  Not Collective

  Input Parameters:
+ dm   - The `DMPLEX`
. p    - The point, which must lie in the chart set with `DMPlexSetChart()`
- size - The support size for point `p`

  Level: beginner

  Note:
  This should be called after `DMPlexSetChart()`.

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexCreate()`, `DMPlexGetSupportSize()`, `DMPlexSetChart()`
@*/
PetscErrorCode DMPlexSetSupportSize(DM dm, PetscInt p, PetscInt size)
{
  DM_Plex *mesh = (DM_Plex *)dm->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscCall(PetscSectionSetDof(mesh->supportSection, p, size));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  DMPlexGetSupport - Return the points on the out-edges for this point in the DAG

  Not Collective

  Input Parameters:
+ dm - The `DMPLEX`
- p  - The point, which must lie in the chart set with `DMPlexSetChart()`

  Output Parameter:
. support - An array of points which are on the out-edges for point `p`, its length is that obtained from `DMPlexGetSupportSize()`

  Level: beginner

  Fortran Notes:
  `support` must be declared with
.vb
  PetscInt, pointer :: support(:)
.ve

  You must also call `DMPlexRestoreSupport()` after you finish using the returned array.
  `DMPlexRestoreSupport()` is not needed/available in C.

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexGetSupportSize()`, `DMPlexSetSupport()`, `DMPlexGetCone()`, `DMPlexSetChart()`
@*/
PetscErrorCode DMPlexGetSupport(DM dm, PetscInt p, const PetscInt *support[])
{
  DM_Plex *mesh = (DM_Plex *)dm->data;
  PetscInt off;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscAssertPointer(support, 3);
  PetscCall(PetscSectionGetOffset(mesh->supportSection, p, &off));
  *support = PetscSafePointerPlusOffset(mesh->supports, off);
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexSetSupport - Set the points on the out-edges for this point in the DAG, that is the list of points that this point covers

  Not Collective

  Input Parameters:
+ dm      - The `DMPLEX`
. p       - The point, which must lie in the chart set with `DMPlexSetChart()`
- support - An array of points which are on the out-edges for point `p`, its length is that obtained from `DMPlexGetSupportSize()`

  Level: beginner

  Note:
  This should be called after all calls to `DMPlexSetSupportSize()` and `DMSetUp()`.

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexSetCone()`, `DMPlexSetConeSize()`, `DMPlexCreate()`, `DMPlexGetSupport()`, `DMPlexSetChart()`, `DMPlexSetSupportSize()`, `DMSetUp()`
@*/
PetscErrorCode DMPlexSetSupport(DM dm, PetscInt p, const PetscInt support[])
{
  DM_Plex *mesh = (DM_Plex *)dm->data;
  PetscInt pStart, pEnd;
  PetscInt dof, off, c;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscCall(PetscSectionGetChart(mesh->supportSection, &pStart, &pEnd));
  PetscCall(PetscSectionGetDof(mesh->supportSection, p, &dof));
  if (dof) PetscAssertPointer(support, 3);
  PetscCall(PetscSectionGetOffset(mesh->supportSection, p, &off));
  PetscCheck(!(p < pStart) && !(p >= pEnd), PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "Mesh point %" PetscInt_FMT " is not in the valid range [%" PetscInt_FMT ", %" PetscInt_FMT ")", p, pStart, pEnd);
  for (c = 0; c < dof; ++c) {
    PetscCheck(!(support[c] < pStart) && !(support[c] >= pEnd), PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "Support point %" PetscInt_FMT " is not in the valid range [%" PetscInt_FMT ", %" PetscInt_FMT ")", support[c], pStart, pEnd);
    mesh->supports[off + c] = support[c];
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexInsertSupport - Insert a point into the out-edges for the point p in the DAG

  Not Collective

  Input Parameters:
+ dm           - The `DMPLEX`
. p            - The point, which must lie in the chart set with `DMPlexSetChart()`
. supportPos   - The local index in the cone where the point should be put
- supportPoint - The mesh point to insert

  Level: beginner

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexCreate()`, `DMPlexGetCone()`, `DMPlexSetChart()`, `DMPlexSetConeSize()`, `DMSetUp()`
@*/
PetscErrorCode DMPlexInsertSupport(DM dm, PetscInt p, PetscInt supportPos, PetscInt supportPoint)
{
  DM_Plex *mesh = (DM_Plex *)dm->data;
  PetscInt pStart, pEnd;
  PetscInt dof, off;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscCall(PetscSectionGetChart(mesh->supportSection, &pStart, &pEnd));
  PetscCall(PetscSectionGetDof(mesh->supportSection, p, &dof));
  PetscCall(PetscSectionGetOffset(mesh->supportSection, p, &off));
  PetscCheck(!(p < pStart) && !(p >= pEnd), PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "Mesh point %" PetscInt_FMT " is not in the valid range [%" PetscInt_FMT ", %" PetscInt_FMT ")", p, pStart, pEnd);
  PetscCheck(!(supportPoint < pStart) && !(supportPoint >= pEnd), PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "Support point %" PetscInt_FMT " is not in the valid range [%" PetscInt_FMT ", %" PetscInt_FMT ")", supportPoint, pStart, pEnd);
  PetscCheck(supportPos < dof, PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "Support position %" PetscInt_FMT " of point %" PetscInt_FMT " is not in the valid range [0, %" PetscInt_FMT ")", supportPos, p, dof);
  mesh->supports[off + supportPos] = supportPoint;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* Converts an orientation o in the current numbering to the previous scheme used in Plex */
PetscInt DMPolytopeConvertNewOrientation_Internal(DMPolytopeType ct, PetscInt o)
{
  switch (ct) {
  case DM_POLYTOPE_SEGMENT:
    if (o == -1) return -2;
    break;
  case DM_POLYTOPE_TRIANGLE:
    if (o == -3) return -1;
    if (o == -2) return -3;
    if (o == -1) return -2;
    break;
  case DM_POLYTOPE_QUADRILATERAL:
    if (o == -4) return -2;
    if (o == -3) return -1;
    if (o == -2) return -4;
    if (o == -1) return -3;
    break;
  default:
    return o;
  }
  return o;
}

/* Converts an orientation o in the previous scheme used in Plex to the current numbering */
PetscInt DMPolytopeConvertOldOrientation_Internal(DMPolytopeType ct, PetscInt o)
{
  switch (ct) {
  case DM_POLYTOPE_SEGMENT:
    if ((o == -2) || (o == 1)) return -1;
    if (o == -1) return 0;
    break;
  case DM_POLYTOPE_TRIANGLE:
    if (o == -3) return -2;
    if (o == -2) return -1;
    if (o == -1) return -3;
    break;
  case DM_POLYTOPE_QUADRILATERAL:
    if (o == -4) return -2;
    if (o == -3) return -1;
    if (o == -2) return -4;
    if (o == -1) return -3;
    break;
  default:
    return o;
  }
  return o;
}

/* Takes in a mesh whose orientations are in the previous scheme and converts them all to the current numbering */
PetscErrorCode DMPlexConvertOldOrientations_Internal(DM dm)
{
  PetscInt pStart, pEnd, p;

  PetscFunctionBegin;
  PetscCall(DMPlexGetChart(dm, &pStart, &pEnd));
  for (p = pStart; p < pEnd; ++p) {
    const PetscInt *cone, *ornt;
    PetscInt        coneSize, c;

    PetscCall(DMPlexGetConeSize(dm, p, &coneSize));
    PetscCall(DMPlexGetCone(dm, p, &cone));
    PetscCall(DMPlexGetConeOrientation(dm, p, &ornt));
    for (c = 0; c < coneSize; ++c) {
      DMPolytopeType ct;
      const PetscInt o = ornt[c];

      PetscCall(DMPlexGetCellType(dm, cone[c], &ct));
      switch (ct) {
      case DM_POLYTOPE_SEGMENT:
        if ((o == -2) || (o == 1)) PetscCall(DMPlexInsertConeOrientation(dm, p, c, -1));
        if (o == -1) PetscCall(DMPlexInsertConeOrientation(dm, p, c, 0));
        break;
      case DM_POLYTOPE_TRIANGLE:
        if (o == -3) PetscCall(DMPlexInsertConeOrientation(dm, p, c, -2));
        if (o == -2) PetscCall(DMPlexInsertConeOrientation(dm, p, c, -1));
        if (o == -1) PetscCall(DMPlexInsertConeOrientation(dm, p, c, -3));
        break;
      case DM_POLYTOPE_QUADRILATERAL:
        if (o == -4) PetscCall(DMPlexInsertConeOrientation(dm, p, c, -2));
        if (o == -3) PetscCall(DMPlexInsertConeOrientation(dm, p, c, -1));
        if (o == -2) PetscCall(DMPlexInsertConeOrientation(dm, p, c, -4));
        if (o == -1) PetscCall(DMPlexInsertConeOrientation(dm, p, c, -3));
        break;
      default:
        break;
      }
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static inline PetscErrorCode DMPlexGetTransitiveClosure_Hot_Private(DM dm, PetscInt p, PetscBool useCone, PetscInt *size, const PetscInt *arr[], const PetscInt *ornt[])
{
  DM_Plex *mesh = (DM_Plex *)dm->data;

  PetscFunctionBeginHot;
  if (PetscDefined(USE_DEBUG) || mesh->tr) {
    if (useCone) {
      PetscCall(DMPlexGetConeSize(dm, p, size));
      PetscCall(DMPlexGetOrientedCone(dm, p, arr, ornt));
    } else {
      PetscCall(DMPlexGetSupportSize(dm, p, size));
      PetscCall(DMPlexGetSupport(dm, p, arr));
    }
  } else {
    if (useCone) {
      const PetscSection s   = mesh->coneSection;
      const PetscInt     ps  = p - s->pStart;
      const PetscInt     off = s->atlasOff[ps];

      *size = s->atlasDof[ps];
      *arr  = mesh->cones + off;
      *ornt = mesh->coneOrientations + off;
    } else {
      const PetscSection s   = mesh->supportSection;
      const PetscInt     ps  = p - s->pStart;
      const PetscInt     off = s->atlasOff[ps];

      *size = s->atlasDof[ps];
      *arr  = mesh->supports + off;
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static inline PetscErrorCode DMPlexRestoreTransitiveClosure_Hot_Private(DM dm, PetscInt p, PetscBool useCone, PetscInt *size, const PetscInt *arr[], const PetscInt *ornt[])
{
  DM_Plex *mesh = (DM_Plex *)dm->data;

  PetscFunctionBeginHot;
  if (PetscDefined(USE_DEBUG) || mesh->tr) {
    if (useCone) PetscCall(DMPlexRestoreOrientedCone(dm, p, arr, ornt));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode DMPlexGetTransitiveClosure_Depth1_Private(DM dm, PetscInt p, PetscInt ornt, PetscBool useCone, PetscInt *numPoints, PetscInt *points[])
{
  DMPolytopeType  ct = DM_POLYTOPE_UNKNOWN;
  PetscInt       *closure;
  const PetscInt *tmp = NULL, *tmpO = NULL;
  PetscInt        off = 0, tmpSize, t;

  PetscFunctionBeginHot;
  if (ornt) {
    PetscCall(DMPlexGetCellType(dm, p, &ct));
    if (ct == DM_POLYTOPE_FV_GHOST || ct == DM_POLYTOPE_INTERIOR_GHOST || ct == DM_POLYTOPE_UNKNOWN || ct == DM_POLYTOPE_UNKNOWN_CELL || ct == DM_POLYTOPE_UNKNOWN_FACE) ct = DM_POLYTOPE_UNKNOWN;
  }
  if (*points) {
    closure = *points;
  } else {
    PetscInt maxConeSize, maxSupportSize;
    PetscCall(DMPlexGetMaxSizes(dm, &maxConeSize, &maxSupportSize));
    PetscCall(DMGetWorkArray(dm, 2 * (PetscMax(maxConeSize, maxSupportSize) + 1), MPIU_INT, &closure));
  }
  PetscCall(DMPlexGetTransitiveClosure_Hot_Private(dm, p, useCone, &tmpSize, &tmp, &tmpO));
  if (ct == DM_POLYTOPE_UNKNOWN) {
    closure[off++] = p;
    closure[off++] = 0;
    for (t = 0; t < tmpSize; ++t) {
      closure[off++] = tmp[t];
      closure[off++] = tmpO ? tmpO[t] : 0;
    }
  } else {
    const PetscInt *arr = DMPolytopeTypeGetArrangement(ct, ornt);

    /* We assume that cells with a valid type have faces with a valid type */
    closure[off++] = p;
    closure[off++] = ornt;
    for (t = 0; t < tmpSize; ++t) {
      DMPolytopeType ft;

      PetscCall(DMPlexGetCellType(dm, tmp[t], &ft));
      closure[off++] = tmp[arr[t]];
      closure[off++] = tmpO ? DMPolytopeTypeComposeOrientation(ft, ornt, tmpO[t]) : 0;
    }
  }
  PetscCall(DMPlexRestoreTransitiveClosure_Hot_Private(dm, p, useCone, &tmpSize, &tmp, &tmpO));
  if (numPoints) *numPoints = tmpSize + 1;
  if (points) *points = closure;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* We need a special tensor version because we want to allow duplicate points in the endcaps for hybrid cells */
static PetscErrorCode DMPlexTransitiveClosure_Tensor_Internal(DM dm, PetscInt point, DMPolytopeType ct, PetscInt o, PetscBool useCone, PetscInt *numPoints, PetscInt **points)
{
  const PetscInt *arr = DMPolytopeTypeGetArrangement(ct, o);
  const PetscInt *cone, *ornt;
  PetscInt       *pts, *closure = NULL;
  DMPolytopeType  ft;
  PetscInt        maxConeSize, maxSupportSize, coneSeries, supportSeries, maxSize;
  PetscInt        dim, coneSize, c, d, clSize, cl;

  PetscFunctionBeginHot;
  PetscCall(DMGetDimension(dm, &dim));
  PetscCall(DMPlexGetTransitiveClosure_Hot_Private(dm, point, PETSC_TRUE, &coneSize, &cone, &ornt));
  PetscCall(DMPlexGetMaxSizes(dm, &maxConeSize, &maxSupportSize));
  coneSeries    = (maxConeSize > 1) ? ((PetscPowInt(maxConeSize, dim + 1) - 1) / (maxConeSize - 1)) : dim + 1;
  supportSeries = (maxSupportSize > 1) ? ((PetscPowInt(maxSupportSize, dim + 1) - 1) / (maxSupportSize - 1)) : dim + 1;
  maxSize       = PetscMax(coneSeries, supportSeries);
  if (*points) {
    pts = *points;
  } else PetscCall(DMGetWorkArray(dm, 2 * maxSize, MPIU_INT, &pts));
  c        = 0;
  pts[c++] = point;
  pts[c++] = o;
  PetscCall(DMPlexGetCellType(dm, cone[arr[0 * 2 + 0]], &ft));
  PetscCall(DMPlexGetTransitiveClosure_Internal(dm, cone[arr[0 * 2 + 0]], DMPolytopeTypeComposeOrientation(ft, arr[0 * 2 + 1], ornt[0]), useCone, &clSize, &closure));
  for (cl = 0; cl < clSize * 2; cl += 2) {
    pts[c++] = closure[cl];
    pts[c++] = closure[cl + 1];
  }
  PetscCall(DMPlexGetTransitiveClosure_Internal(dm, cone[arr[1 * 2 + 0]], DMPolytopeTypeComposeOrientation(ft, arr[1 * 2 + 1], ornt[1]), useCone, &clSize, &closure));
  for (cl = 0; cl < clSize * 2; cl += 2) {
    pts[c++] = closure[cl];
    pts[c++] = closure[cl + 1];
  }
  PetscCall(DMPlexRestoreTransitiveClosure(dm, cone[0], useCone, &clSize, &closure));
  for (d = 2; d < coneSize; ++d) {
    PetscCall(DMPlexGetCellType(dm, cone[arr[d * 2 + 0]], &ft));
    pts[c++] = cone[arr[d * 2 + 0]];
    pts[c++] = DMPolytopeTypeComposeOrientation(ft, arr[d * 2 + 1], ornt[d]);
  }
  PetscCall(DMPlexRestoreTransitiveClosure_Hot_Private(dm, point, PETSC_TRUE, &coneSize, &cone, &ornt));
  if (dim >= 3) {
    for (d = 2; d < coneSize; ++d) {
      const PetscInt  fpoint = cone[arr[d * 2 + 0]];
      const PetscInt *fcone, *fornt;
      PetscInt        fconeSize, fc, i;

      PetscCall(DMPlexGetCellType(dm, fpoint, &ft));
      const PetscInt *farr = DMPolytopeTypeGetArrangement(ft, DMPolytopeTypeComposeOrientation(ft, arr[d * 2 + 1], ornt[d]));
      PetscCall(DMPlexGetTransitiveClosure_Hot_Private(dm, fpoint, PETSC_TRUE, &fconeSize, &fcone, &fornt));
      for (fc = 0; fc < fconeSize; ++fc) {
        const PetscInt cp = fcone[farr[fc * 2 + 0]];
        const PetscInt co = farr[fc * 2 + 1];

        for (i = 0; i < c; i += 2)
          if (pts[i] == cp) break;
        if (i == c) {
          PetscCall(DMPlexGetCellType(dm, cp, &ft));
          pts[c++] = cp;
          pts[c++] = DMPolytopeTypeComposeOrientation(ft, co, fornt[farr[fc * 2 + 0]]);
        }
      }
      PetscCall(DMPlexRestoreTransitiveClosure_Hot_Private(dm, fpoint, PETSC_TRUE, &fconeSize, &fcone, &fornt));
    }
  }
  *numPoints = c / 2;
  *points    = pts;
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode DMPlexGetTransitiveClosure_Internal(DM dm, PetscInt p, PetscInt ornt, PetscBool useCone, PetscInt *numPoints, PetscInt *points[])
{
  DMPolytopeType ct;
  PetscInt      *closure, *fifo;
  PetscInt       closureSize = 0, fifoStart = 0, fifoSize = 0;
  PetscInt       maxConeSize, maxSupportSize, coneSeries, supportSeries;
  PetscInt       depth, maxSize;

  PetscFunctionBeginHot;
  PetscCall(DMPlexGetDepth(dm, &depth));
  if (depth == 1) {
    PetscCall(DMPlexGetTransitiveClosure_Depth1_Private(dm, p, ornt, useCone, numPoints, points));
    PetscFunctionReturn(PETSC_SUCCESS);
  }
  PetscCall(DMPlexGetCellType(dm, p, &ct));
  if (ct == DM_POLYTOPE_FV_GHOST || ct == DM_POLYTOPE_INTERIOR_GHOST || ct == DM_POLYTOPE_UNKNOWN || ct == DM_POLYTOPE_UNKNOWN_CELL || ct == DM_POLYTOPE_UNKNOWN_FACE) ct = DM_POLYTOPE_UNKNOWN;
  if (DMPolytopeTypeIsHybrid(ct) && ct != DM_POLYTOPE_POINT_PRISM_TENSOR) {
    PetscCall(DMPlexTransitiveClosure_Tensor_Internal(dm, p, ct, ornt, useCone, numPoints, points));
    PetscFunctionReturn(PETSC_SUCCESS);
  }
  PetscCall(DMPlexGetMaxSizes(dm, &maxConeSize, &maxSupportSize));
  coneSeries    = (maxConeSize > 1) ? ((PetscPowInt(maxConeSize, depth + 1) - 1) / (maxConeSize - 1)) : depth + 1;
  supportSeries = (maxSupportSize > 1) ? ((PetscPowInt(maxSupportSize, depth + 1) - 1) / (maxSupportSize - 1)) : depth + 1;
  maxSize       = PetscMax(coneSeries, supportSeries);
  PetscCall(DMGetWorkArray(dm, 3 * maxSize, MPIU_INT, &fifo));
  if (*points) {
    closure = *points;
  } else PetscCall(DMGetWorkArray(dm, 2 * maxSize, MPIU_INT, &closure));
  closure[closureSize++] = p;
  closure[closureSize++] = ornt;
  fifo[fifoSize++]       = p;
  fifo[fifoSize++]       = ornt;
  fifo[fifoSize++]       = ct;
  /* Should kick out early when depth is reached, rather than checking all vertices for empty cones */
  while (fifoSize - fifoStart) {
    const PetscInt       q    = fifo[fifoStart++];
    const PetscInt       o    = fifo[fifoStart++];
    const DMPolytopeType qt   = (DMPolytopeType)fifo[fifoStart++];
    const PetscInt      *qarr = DMPolytopeTypeGetArrangement(qt, o);
    const PetscInt      *tmp, *tmpO = NULL;
    PetscInt             tmpSize, t;

    if (PetscDefined(USE_DEBUG)) {
      PetscInt nO = DMPolytopeTypeGetNumArrangements(qt) / 2;
      PetscCheck(!o || !(o >= nO || o < -nO), PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid orientation %" PetscInt_FMT " not in [%" PetscInt_FMT ",%" PetscInt_FMT ") for %s %" PetscInt_FMT, o, -nO, nO, DMPolytopeTypes[qt], q);
    }
    PetscCall(DMPlexGetTransitiveClosure_Hot_Private(dm, q, useCone, &tmpSize, &tmp, &tmpO));
    for (t = 0; t < tmpSize; ++t) {
      const PetscInt ip = useCone && qarr ? qarr[t * 2] : t;
      const PetscInt io = useCone && qarr ? qarr[t * 2 + 1] : 0;
      const PetscInt cp = tmp[ip];
      PetscCall(DMPlexGetCellType(dm, cp, &ct));
      const PetscInt co = tmpO ? DMPolytopeTypeComposeOrientation(ct, io, tmpO[ip]) : 0;
      PetscInt       c;

      /* Check for duplicate */
      for (c = 0; c < closureSize; c += 2) {
        if (closure[c] == cp) break;
      }
      if (c == closureSize) {
        closure[closureSize++] = cp;
        closure[closureSize++] = co;
        fifo[fifoSize++]       = cp;
        fifo[fifoSize++]       = co;
        fifo[fifoSize++]       = ct;
      }
    }
    PetscCall(DMPlexRestoreTransitiveClosure_Hot_Private(dm, q, useCone, &tmpSize, &tmp, &tmpO));
  }
  PetscCall(DMRestoreWorkArray(dm, 3 * maxSize, MPIU_INT, &fifo));
  if (numPoints) *numPoints = closureSize / 2;
  if (points) *points = closure;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  DMPlexGetTransitiveClosure - Return the points on the transitive closure of the in-edges or out-edges for this point in the DAG

  Not Collective

  Input Parameters:
+ dm      - The `DMPLEX`
. p       - The mesh point
- useCone - `PETSC_TRUE` for the closure, otherwise return the star

  Input/Output Parameter:
. points - The points and point orientations, interleaved as pairs [p0, o0, p1, o1, ...];
           if *points is `NULL` on input, internal storage will be returned, use `DMPlexRestoreTransitiveClosure()`,
           otherwise the provided array is used to hold the values

  Output Parameter:
. numPoints - The number of points in the closure, so `points` is of size 2*`numPoints`

  Level: beginner

  Note:
  If using internal storage (points is `NULL` on input), each call overwrites the last output.

  Fortran Notes:
  `points` must be declared with
.vb
  PetscInt, pointer :: points(:)
.ve
  and is always allocated by the function.

  The `numPoints` argument is not present in the Fortran binding.

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexRestoreTransitiveClosure()`, `DMPlexCreate()`, `DMPlexSetCone()`, `DMPlexSetChart()`, `DMPlexGetCone()`
@*/
PetscErrorCode DMPlexGetTransitiveClosure(DM dm, PetscInt p, PetscBool useCone, PetscInt *numPoints, PetscInt *points[])
{
  PetscFunctionBeginHot;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (numPoints) PetscAssertPointer(numPoints, 4);
  if (points) PetscAssertPointer(points, 5);
  if (PetscDefined(USE_DEBUG)) {
    PetscInt pStart, pEnd;
    PetscCall(DMPlexGetChart(dm, &pStart, &pEnd));
    PetscCheck(p >= pStart && p < pEnd, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Point %" PetscInt_FMT " is not in [%" PetscInt_FMT ", %" PetscInt_FMT ")", p, pStart, pEnd);
  }
  PetscCall(DMPlexGetTransitiveClosure_Internal(dm, p, 0, useCone, numPoints, points));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  DMPlexRestoreTransitiveClosure - Restore the array of points on the transitive closure of the in-edges or out-edges for this point in the DAG

  Not Collective

  Input Parameters:
+ dm        - The `DMPLEX`
. p         - The mesh point
. useCone   - `PETSC_TRUE` for the closure, otherwise return the star
. numPoints - The number of points in the closure, so points[] is of size 2*`numPoints`
- points    - The points and point orientations, interleaved as pairs [p0, o0, p1, o1, ...]

  Level: beginner

  Note:
  If not using internal storage (points is not `NULL` on input), this call is unnecessary

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexGetTransitiveClosure()`, `DMPlexCreate()`, `DMPlexSetCone()`, `DMPlexSetChart()`, `DMPlexGetCone()`
@*/
PetscErrorCode DMPlexRestoreTransitiveClosure(DM dm, PetscInt p, PetscBool useCone, PetscInt *numPoints, PetscInt *points[])
{
  PetscFunctionBeginHot;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (numPoints) *numPoints = 0;
  PetscCall(DMRestoreWorkArray(dm, 0, MPIU_INT, points));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexGetMaxSizes - Return the maximum number of in-edges (cone) and out-edges (support) for any point in the DAG

  Not Collective

  Input Parameter:
. dm - The `DMPLEX`

  Output Parameters:
+ maxConeSize    - The maximum number of in-edges
- maxSupportSize - The maximum number of out-edges

  Level: beginner

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexCreate()`, `DMPlexSetConeSize()`, `DMPlexSetChart()`
@*/
PetscErrorCode DMPlexGetMaxSizes(DM dm, PetscInt *maxConeSize, PetscInt *maxSupportSize)
{
  DM_Plex *mesh = (DM_Plex *)dm->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (maxConeSize) PetscCall(PetscSectionGetMaxDof(mesh->coneSection, maxConeSize));
  if (maxSupportSize) PetscCall(PetscSectionGetMaxDof(mesh->supportSection, maxSupportSize));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode DMSetUp_Plex(DM dm)
{
  DM_Plex *mesh = (DM_Plex *)dm->data;
  PetscInt size, maxSupportSize;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscCall(PetscSectionSetUp(mesh->coneSection));
  PetscCall(PetscSectionGetStorageSize(mesh->coneSection, &size));
  PetscCall(PetscMalloc1(size, &mesh->cones));
  PetscCall(PetscCalloc1(size, &mesh->coneOrientations));
  PetscCall(PetscSectionGetMaxDof(mesh->supportSection, &maxSupportSize));
  if (maxSupportSize) {
    PetscCall(PetscSectionSetUp(mesh->supportSection));
    PetscCall(PetscSectionGetStorageSize(mesh->supportSection, &size));
    PetscCall(PetscMalloc1(size, &mesh->supports));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode DMCreateSubDM_Plex(DM dm, PetscInt numFields, const PetscInt fields[], IS *is, DM *subdm)
{
  PetscFunctionBegin;
  if (subdm) PetscCall(DMClone(dm, subdm));
  PetscCall(DMCreateSectionSubDM(dm, numFields, fields, NULL, NULL, is, subdm));
  if (subdm) (*subdm)->useNatural = dm->useNatural;
  if (dm->useNatural && dm->sfMigration) {
    PetscSF sfNatural;

    (*subdm)->sfMigration = dm->sfMigration;
    PetscCall(PetscObjectReference((PetscObject)dm->sfMigration));
    PetscCall(DMPlexCreateGlobalToNaturalSF(*subdm, NULL, (*subdm)->sfMigration, &sfNatural));
    (*subdm)->sfNatural = sfNatural;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode DMCreateSuperDM_Plex(DM dms[], PetscInt len, IS **is, DM *superdm)
{
  PetscInt i = 0;

  PetscFunctionBegin;
  PetscCall(DMClone(dms[0], superdm));
  PetscCall(DMCreateSectionSuperDM(dms, len, is, superdm));
  (*superdm)->useNatural = PETSC_FALSE;
  for (i = 0; i < len; i++) {
    if (dms[i]->useNatural && dms[i]->sfMigration) {
      PetscSF sfNatural;

      (*superdm)->sfMigration = dms[i]->sfMigration;
      PetscCall(PetscObjectReference((PetscObject)dms[i]->sfMigration));
      (*superdm)->useNatural = PETSC_TRUE;
      PetscCall(DMPlexCreateGlobalToNaturalSF(*superdm, NULL, (*superdm)->sfMigration, &sfNatural));
      (*superdm)->sfNatural = sfNatural;
      break;
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexSymmetrize - Create support (out-edge) information from cone (in-edge) information

  Not Collective

  Input Parameter:
. dm - The `DMPLEX`

  Level: beginner

  Note:
  This should be called after all calls to `DMPlexSetCone()`

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexCreate()`, `DMPlexSetChart()`, `DMPlexSetConeSize()`, `DMPlexSetCone()`
@*/
PetscErrorCode DMPlexSymmetrize(DM dm)
{
  DM_Plex  *mesh = (DM_Plex *)dm->data;
  PetscInt *offsets;
  PetscInt  supportSize;
  PetscInt  pStart, pEnd, p;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscCheck(!mesh->supports, PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONGSTATE, "Supports were already setup in this DMPlex");
  PetscCall(PetscLogEventBegin(DMPLEX_Symmetrize, dm, 0, 0, 0));
  /* Calculate support sizes */
  PetscCall(DMPlexGetChart(dm, &pStart, &pEnd));
  for (p = pStart; p < pEnd; ++p) {
    PetscInt dof, off, c;

    PetscCall(PetscSectionGetDof(mesh->coneSection, p, &dof));
    PetscCall(PetscSectionGetOffset(mesh->coneSection, p, &off));
    for (c = off; c < off + dof; ++c) PetscCall(PetscSectionAddDof(mesh->supportSection, mesh->cones[c], 1));
  }
  PetscCall(PetscSectionSetUp(mesh->supportSection));
  /* Calculate supports */
  PetscCall(PetscSectionGetStorageSize(mesh->supportSection, &supportSize));
  PetscCall(PetscMalloc1(supportSize, &mesh->supports));
  PetscCall(PetscCalloc1(pEnd - pStart, &offsets));
  for (p = pStart; p < pEnd; ++p) {
    PetscInt dof, off, c;

    PetscCall(PetscSectionGetDof(mesh->coneSection, p, &dof));
    PetscCall(PetscSectionGetOffset(mesh->coneSection, p, &off));
    for (c = off; c < off + dof; ++c) {
      const PetscInt q = mesh->cones[c];
      PetscInt       offS;

      PetscCall(PetscSectionGetOffset(mesh->supportSection, q, &offS));

      mesh->supports[offS + offsets[q]] = p;
      ++offsets[q];
    }
  }
  PetscCall(PetscFree(offsets));
  PetscCall(PetscLogEventEnd(DMPLEX_Symmetrize, dm, 0, 0, 0));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode DMPlexCreateDepthStratum(DM dm, DMLabel label, PetscInt depth, PetscInt pStart, PetscInt pEnd)
{
  IS stratumIS;

  PetscFunctionBegin;
  if (pStart >= pEnd) PetscFunctionReturn(PETSC_SUCCESS);
  if (PetscDefined(USE_DEBUG)) {
    PetscInt  qStart, qEnd, numLevels, level;
    PetscBool overlap = PETSC_FALSE;
    PetscCall(DMLabelGetNumValues(label, &numLevels));
    for (level = 0; level < numLevels; level++) {
      PetscCall(DMLabelGetStratumBounds(label, level, &qStart, &qEnd));
      if ((pStart >= qStart && pStart < qEnd) || (pEnd > qStart && pEnd <= qEnd)) {
        overlap = PETSC_TRUE;
        break;
      }
    }
    PetscCheck(!overlap, PETSC_COMM_SELF, PETSC_ERR_PLIB, "New depth %" PetscInt_FMT " range [%" PetscInt_FMT ",%" PetscInt_FMT ") overlaps with depth %" PetscInt_FMT " range [%" PetscInt_FMT ",%" PetscInt_FMT ")", depth, pStart, pEnd, level, qStart, qEnd);
  }
  PetscCall(ISCreateStride(PETSC_COMM_SELF, pEnd - pStart, pStart, 1, &stratumIS));
  PetscCall(DMLabelSetStratumIS(label, depth, stratumIS));
  PetscCall(ISDestroy(&stratumIS));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode DMPlexStratify_CellType_Private(DM dm, DMLabel label)
{
  PetscInt *pMin, *pMax;
  PetscInt  pStart, pEnd;
  PetscInt  dmin = PETSC_MAX_INT, dmax = PETSC_MIN_INT;

  PetscFunctionBegin;
  {
    DMLabel label2;

    PetscCall(DMPlexGetCellTypeLabel(dm, &label2));
    PetscCall(PetscObjectViewFromOptions((PetscObject)label2, NULL, "-ct_view"));
  }
  PetscCall(DMPlexGetChart(dm, &pStart, &pEnd));
  for (PetscInt p = pStart; p < pEnd; ++p) {
    DMPolytopeType ct;

    PetscCall(DMPlexGetCellType(dm, p, &ct));
    dmin = PetscMin(DMPolytopeTypeGetDim(ct), dmin);
    dmax = PetscMax(DMPolytopeTypeGetDim(ct), dmax);
  }
  PetscCall(PetscMalloc2(dmax + 1, &pMin, dmax + 1, &pMax));
  for (PetscInt d = dmin; d <= dmax; ++d) {
    pMin[d] = PETSC_MAX_INT;
    pMax[d] = PETSC_MIN_INT;
  }
  for (PetscInt p = pStart; p < pEnd; ++p) {
    DMPolytopeType ct;
    PetscInt       d;

    PetscCall(DMPlexGetCellType(dm, p, &ct));
    d       = DMPolytopeTypeGetDim(ct);
    pMin[d] = PetscMin(p, pMin[d]);
    pMax[d] = PetscMax(p, pMax[d]);
  }
  for (PetscInt d = dmin; d <= dmax; ++d) {
    if (pMin[d] > pMax[d]) continue;
    PetscCall(DMPlexCreateDepthStratum(dm, label, d, pMin[d], pMax[d] + 1));
  }
  PetscCall(PetscFree2(pMin, pMax));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode DMPlexStratify_Topological_Private(DM dm, DMLabel label)
{
  PetscInt pStart, pEnd;
  PetscInt numRoots = 0, numLeaves = 0;

  PetscFunctionBegin;
  PetscCall(DMPlexGetChart(dm, &pStart, &pEnd));
  {
    /* Initialize roots and count leaves */
    PetscInt sMin = PETSC_MAX_INT;
    PetscInt sMax = PETSC_MIN_INT;
    PetscInt coneSize, supportSize;

    for (PetscInt p = pStart; p < pEnd; ++p) {
      PetscCall(DMPlexGetConeSize(dm, p, &coneSize));
      PetscCall(DMPlexGetSupportSize(dm, p, &supportSize));
      if (!coneSize && supportSize) {
        sMin = PetscMin(p, sMin);
        sMax = PetscMax(p, sMax);
        ++numRoots;
      } else if (!supportSize && coneSize) {
        ++numLeaves;
      } else if (!supportSize && !coneSize) {
        /* Isolated points */
        sMin = PetscMin(p, sMin);
        sMax = PetscMax(p, sMax);
      }
    }
    PetscCall(DMPlexCreateDepthStratum(dm, label, 0, sMin, sMax + 1));
  }

  if (numRoots + numLeaves == (pEnd - pStart)) {
    PetscInt sMin = PETSC_MAX_INT;
    PetscInt sMax = PETSC_MIN_INT;
    PetscInt coneSize, supportSize;

    for (PetscInt p = pStart; p < pEnd; ++p) {
      PetscCall(DMPlexGetConeSize(dm, p, &coneSize));
      PetscCall(DMPlexGetSupportSize(dm, p, &supportSize));
      if (!supportSize && coneSize) {
        sMin = PetscMin(p, sMin);
        sMax = PetscMax(p, sMax);
      }
    }
    PetscCall(DMPlexCreateDepthStratum(dm, label, 1, sMin, sMax + 1));
  } else {
    PetscInt level = 0;
    PetscInt qStart, qEnd;

    PetscCall(DMLabelGetStratumBounds(label, level, &qStart, &qEnd));
    while (qEnd > qStart) {
      PetscInt sMin = PETSC_MAX_INT;
      PetscInt sMax = PETSC_MIN_INT;

      for (PetscInt q = qStart; q < qEnd; ++q) {
        const PetscInt *support;
        PetscInt        supportSize;

        PetscCall(DMPlexGetSupportSize(dm, q, &supportSize));
        PetscCall(DMPlexGetSupport(dm, q, &support));
        for (PetscInt s = 0; s < supportSize; ++s) {
          sMin = PetscMin(support[s], sMin);
          sMax = PetscMax(support[s], sMax);
        }
      }
      PetscCall(DMLabelGetNumValues(label, &level));
      PetscCall(DMPlexCreateDepthStratum(dm, label, level, sMin, sMax + 1));
      PetscCall(DMLabelGetStratumBounds(label, level, &qStart, &qEnd));
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexStratify - Computes the strata for all points in the `DMPLEX`

  Collective

  Input Parameter:
. dm - The `DMPLEX`

  Level: beginner

  Notes:
  The strata group all points of the same grade, and this function calculates the strata. This
  grade can be seen as the height (or depth) of the point in the DAG.

  The DAG for most topologies is a graded poset (https://en.wikipedia.org/wiki/Graded_poset), and
  can be illustrated by a Hasse Diagram (https://en.wikipedia.org/wiki/Hasse_diagram).
  Concretely, `DMPlexStratify()` creates a new label named "depth" containing the depth in the DAG of each point. For cell-vertex
  meshes, vertices are depth 0 and cells are depth 1. For fully interpolated meshes, depth 0 for vertices, 1 for edges, and so on
  until cells have depth equal to the dimension of the mesh. The depth label can be accessed through `DMPlexGetDepthLabel()` or `DMPlexGetDepthStratum()`, or
  manually via `DMGetLabel()`.  The height is defined implicitly by height = maxDimension - depth, and can be accessed
  via `DMPlexGetHeightStratum()`.  For example, cells have height 0 and faces have height 1.

  The depth of a point is calculated by executing a breadth-first search (BFS) on the DAG. This could produce surprising results
  if run on a partially interpolated mesh, meaning one that had some edges and faces, but not others. For example, suppose that
  we had a mesh consisting of one triangle (c0) and three vertices (v0, v1, v2), and only one edge is on the boundary so we choose
  to interpolate only that one (e0), so that
.vb
  cone(c0) = {e0, v2}
  cone(e0) = {v0, v1}
.ve
  If `DMPlexStratify()` is run on this mesh, it will give depths
.vb
   depth 0 = {v0, v1, v2}
   depth 1 = {e0, c0}
.ve
  where the triangle has been given depth 1, instead of 2, because it is reachable from vertex v2.

  `DMPlexStratify()` should be called after all calls to `DMPlexSymmetrize()`

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexCreate()`, `DMPlexSymmetrize()`, `DMPlexComputeCellTypes()`
@*/
PetscErrorCode DMPlexStratify(DM dm)
{
  DM_Plex  *mesh = (DM_Plex *)dm->data;
  DMLabel   label;
  PetscBool flg = PETSC_FALSE;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscCall(PetscLogEventBegin(DMPLEX_Stratify, dm, 0, 0, 0));

  // Create depth label
  PetscCall(DMRemoveLabel(dm, "depth", NULL));
  PetscCall(DMCreateLabel(dm, "depth"));
  PetscCall(DMPlexGetDepthLabel(dm, &label));

  PetscCall(PetscOptionsGetBool(NULL, dm->hdr.prefix, "-dm_plex_stratify_celltype", &flg, NULL));
  if (flg) PetscCall(DMPlexStratify_CellType_Private(dm, label));
  else PetscCall(DMPlexStratify_Topological_Private(dm, label));

  { /* just in case there is an empty process */
    PetscInt numValues, maxValues = 0, v;

    PetscCall(DMLabelGetNumValues(label, &numValues));
    PetscCall(MPIU_Allreduce(&numValues, &maxValues, 1, MPIU_INT, MPI_MAX, PetscObjectComm((PetscObject)dm)));
    for (v = numValues; v < maxValues; v++) PetscCall(DMLabelAddStratum(label, v));
  }
  PetscCall(PetscObjectStateGet((PetscObject)label, &mesh->depthState));
  PetscCall(PetscLogEventEnd(DMPLEX_Stratify, dm, 0, 0, 0));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode DMPlexComputeCellType_Internal(DM dm, PetscInt p, PetscInt pdepth, DMPolytopeType *pt)
{
  DMPolytopeType ct = DM_POLYTOPE_UNKNOWN;
  PetscInt       dim, depth, pheight, coneSize;

  PetscFunctionBeginHot;
  PetscCall(DMGetDimension(dm, &dim));
  PetscCall(DMPlexGetDepth(dm, &depth));
  PetscCall(DMPlexGetConeSize(dm, p, &coneSize));
  pheight = depth - pdepth;
  if (depth <= 1) {
    switch (pdepth) {
    case 0:
      ct = DM_POLYTOPE_POINT;
      break;
    case 1:
      switch (coneSize) {
      case 2:
        ct = DM_POLYTOPE_SEGMENT;
        break;
      case 3:
        ct = DM_POLYTOPE_TRIANGLE;
        break;
      case 4:
        switch (dim) {
        case 2:
          ct = DM_POLYTOPE_QUADRILATERAL;
          break;
        case 3:
          ct = DM_POLYTOPE_TETRAHEDRON;
          break;
        default:
          break;
        }
        break;
      case 5:
        ct = DM_POLYTOPE_PYRAMID;
        break;
      case 6:
        ct = DM_POLYTOPE_TRI_PRISM_TENSOR;
        break;
      case 8:
        ct = DM_POLYTOPE_HEXAHEDRON;
        break;
      default:
        break;
      }
    }
  } else {
    if (pdepth == 0) {
      ct = DM_POLYTOPE_POINT;
    } else if (pheight == 0) {
      switch (dim) {
      case 1:
        switch (coneSize) {
        case 2:
          ct = DM_POLYTOPE_SEGMENT;
          break;
        default:
          break;
        }
        break;
      case 2:
        switch (coneSize) {
        case 3:
          ct = DM_POLYTOPE_TRIANGLE;
          break;
        case 4:
          ct = DM_POLYTOPE_QUADRILATERAL;
          break;
        default:
          break;
        }
        break;
      case 3:
        switch (coneSize) {
        case 4:
          ct = DM_POLYTOPE_TETRAHEDRON;
          break;
        case 5: {
          const PetscInt *cone;
          PetscInt        faceConeSize;

          PetscCall(DMPlexGetCone(dm, p, &cone));
          PetscCall(DMPlexGetConeSize(dm, cone[0], &faceConeSize));
          switch (faceConeSize) {
          case 3:
            ct = DM_POLYTOPE_TRI_PRISM_TENSOR;
            break;
          case 4:
            ct = DM_POLYTOPE_PYRAMID;
            break;
          }
        } break;
        case 6:
          ct = DM_POLYTOPE_HEXAHEDRON;
          break;
        default:
          break;
        }
        break;
      default:
        break;
      }
    } else if (pheight > 0) {
      switch (coneSize) {
      case 2:
        ct = DM_POLYTOPE_SEGMENT;
        break;
      case 3:
        ct = DM_POLYTOPE_TRIANGLE;
        break;
      case 4:
        ct = DM_POLYTOPE_QUADRILATERAL;
        break;
      default:
        break;
      }
    }
  }
  *pt = ct;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexComputeCellTypes - Infer the polytope type of every cell using its dimension and cone size.

  Collective

  Input Parameter:
. dm - The `DMPLEX`

  Level: developer

  Note:
  This function is normally called automatically when a cell type is requested. It creates an
  internal `DMLabel` named "celltype" which can be directly accessed using `DMGetLabel()`. A user may disable
  automatic creation by creating the label manually, using `DMCreateLabel`(dm, "celltype").

  `DMPlexComputeCellTypes()` should be called after all calls to `DMPlexSymmetrize()` and `DMPlexStratify()`

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexCreate()`, `DMPlexSymmetrize()`, `DMPlexStratify()`, `DMGetLabel()`, `DMCreateLabel()`
@*/
PetscErrorCode DMPlexComputeCellTypes(DM dm)
{
  DM_Plex *mesh;
  DMLabel  ctLabel;
  PetscInt pStart, pEnd, p;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  mesh = (DM_Plex *)dm->data;
  PetscCall(DMCreateLabel(dm, "celltype"));
  PetscCall(DMPlexGetCellTypeLabel(dm, &ctLabel));
  PetscCall(DMPlexGetChart(dm, &pStart, &pEnd));
  PetscCall(PetscFree(mesh->cellTypes));
  PetscCall(PetscMalloc1(pEnd - pStart, &mesh->cellTypes));
  for (p = pStart; p < pEnd; ++p) {
    DMPolytopeType ct = DM_POLYTOPE_UNKNOWN;
    PetscInt       pdepth;

    PetscCall(DMPlexGetPointDepth(dm, p, &pdepth));
    PetscCall(DMPlexComputeCellType_Internal(dm, p, pdepth, &ct));
    PetscCheck(ct != DM_POLYTOPE_UNKNOWN && ct != DM_POLYTOPE_UNKNOWN_CELL && ct != DM_POLYTOPE_UNKNOWN_FACE, PETSC_COMM_SELF, PETSC_ERR_SUP, "Point %" PetscInt_FMT " has invalid celltype (%s)", p, DMPolytopeTypes[ct]);
    PetscCall(DMLabelSetValue(ctLabel, p, ct));
    mesh->cellTypes[p - pStart].value_as_uint8 = ct;
  }
  PetscCall(PetscObjectStateGet((PetscObject)ctLabel, &mesh->celltypeState));
  PetscCall(PetscObjectViewFromOptions((PetscObject)ctLabel, NULL, "-dm_plex_celltypes_view"));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  DMPlexGetJoin - Get an array for the join of the set of points

  Not Collective

  Input Parameters:
+ dm        - The `DMPLEX` object
. numPoints - The number of input points for the join
- points    - The input points

  Output Parameters:
+ numCoveredPoints - The number of points in the join
- coveredPoints    - The points in the join

  Level: intermediate

  Note:
  Currently, this is restricted to a single level join

  Fortran Notes:
  `converedPoints` must be declared with
.vb
  PetscInt, pointer :: coveredPints(:)
.ve

  The `numCoveredPoints` argument is not present in the Fortran binding.

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexRestoreJoin()`, `DMPlexGetMeet()`
@*/
PetscErrorCode DMPlexGetJoin(DM dm, PetscInt numPoints, const PetscInt points[], PetscInt *numCoveredPoints, const PetscInt *coveredPoints[])
{
  DM_Plex  *mesh = (DM_Plex *)dm->data;
  PetscInt *join[2];
  PetscInt  joinSize, i = 0;
  PetscInt  dof, off, p, c, m;
  PetscInt  maxSupportSize;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscAssertPointer(points, 3);
  PetscAssertPointer(numCoveredPoints, 4);
  PetscAssertPointer(coveredPoints, 5);
  PetscCall(PetscSectionGetMaxDof(mesh->supportSection, &maxSupportSize));
  PetscCall(DMGetWorkArray(dm, maxSupportSize, MPIU_INT, &join[0]));
  PetscCall(DMGetWorkArray(dm, maxSupportSize, MPIU_INT, &join[1]));
  /* Copy in support of first point */
  PetscCall(PetscSectionGetDof(mesh->supportSection, points[0], &dof));
  PetscCall(PetscSectionGetOffset(mesh->supportSection, points[0], &off));
  for (joinSize = 0; joinSize < dof; ++joinSize) join[i][joinSize] = mesh->supports[off + joinSize];
  /* Check each successive support */
  for (p = 1; p < numPoints; ++p) {
    PetscInt newJoinSize = 0;

    PetscCall(PetscSectionGetDof(mesh->supportSection, points[p], &dof));
    PetscCall(PetscSectionGetOffset(mesh->supportSection, points[p], &off));
    for (c = 0; c < dof; ++c) {
      const PetscInt point = mesh->supports[off + c];

      for (m = 0; m < joinSize; ++m) {
        if (point == join[i][m]) {
          join[1 - i][newJoinSize++] = point;
          break;
        }
      }
    }
    joinSize = newJoinSize;
    i        = 1 - i;
  }
  *numCoveredPoints = joinSize;
  *coveredPoints    = join[i];
  PetscCall(DMRestoreWorkArray(dm, maxSupportSize, MPIU_INT, &join[1 - i]));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  DMPlexRestoreJoin - Restore an array for the join of the set of points obtained with `DMPlexGetJoin()`

  Not Collective

  Input Parameters:
+ dm        - The `DMPLEX` object
. numPoints - The number of input points for the join
- points    - The input points

  Output Parameters:
+ numCoveredPoints - The number of points in the join
- coveredPoints    - The points in the join

  Level: intermediate

  Fortran Notes:
  The `numCoveredPoints` argument is not present in the Fortran binding since it is internal to the array.

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexGetJoin()`, `DMPlexGetFullJoin()`, `DMPlexGetMeet()`
@*/
PetscErrorCode DMPlexRestoreJoin(DM dm, PetscInt numPoints, const PetscInt points[], PetscInt *numCoveredPoints, const PetscInt *coveredPoints[])
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (points) PetscAssertPointer(points, 3);
  if (numCoveredPoints) PetscAssertPointer(numCoveredPoints, 4);
  PetscAssertPointer(coveredPoints, 5);
  PetscCall(DMRestoreWorkArray(dm, 0, MPIU_INT, (void *)coveredPoints));
  if (numCoveredPoints) *numCoveredPoints = 0;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  DMPlexGetFullJoin - Get an array for the join of the set of points

  Not Collective

  Input Parameters:
+ dm        - The `DMPLEX` object
. numPoints - The number of input points for the join
- points    - The input points, its length is `numPoints`

  Output Parameters:
+ numCoveredPoints - The number of points in the join
- coveredPoints    - The points in the join, its length is `numCoveredPoints`

  Level: intermediate

  Fortran Notes:
  `points` and `converedPoints` must be declared with
.vb
  PetscInt, pointer :: points(:)
  PetscInt, pointer :: coveredPints(:)
.ve

  The `numCoveredPoints` argument is not present in the Fortran binding.

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexGetJoin()`, `DMPlexRestoreJoin()`, `DMPlexGetMeet()`
@*/
PetscErrorCode DMPlexGetFullJoin(DM dm, PetscInt numPoints, const PetscInt points[], PetscInt *numCoveredPoints, const PetscInt *coveredPoints[])
{
  PetscInt *offsets, **closures;
  PetscInt *join[2];
  PetscInt  depth = 0, maxSize, joinSize = 0, i = 0;
  PetscInt  p, d, c, m, ms;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscAssertPointer(points, 3);
  PetscAssertPointer(numCoveredPoints, 4);
  PetscAssertPointer(coveredPoints, 5);

  PetscCall(DMPlexGetDepth(dm, &depth));
  PetscCall(PetscCalloc1(numPoints, &closures));
  PetscCall(DMGetWorkArray(dm, numPoints * (depth + 2), MPIU_INT, &offsets));
  PetscCall(DMPlexGetMaxSizes(dm, NULL, &ms));
  maxSize = (ms > 1) ? ((PetscPowInt(ms, depth + 1) - 1) / (ms - 1)) : depth + 1;
  PetscCall(DMGetWorkArray(dm, maxSize, MPIU_INT, &join[0]));
  PetscCall(DMGetWorkArray(dm, maxSize, MPIU_INT, &join[1]));

  for (p = 0; p < numPoints; ++p) {
    PetscInt closureSize;

    PetscCall(DMPlexGetTransitiveClosure(dm, points[p], PETSC_FALSE, &closureSize, &closures[p]));

    offsets[p * (depth + 2) + 0] = 0;
    for (d = 0; d < depth + 1; ++d) {
      PetscInt pStart, pEnd, i;

      PetscCall(DMPlexGetDepthStratum(dm, d, &pStart, &pEnd));
      for (i = offsets[p * (depth + 2) + d]; i < closureSize; ++i) {
        if ((pStart > closures[p][i * 2]) || (pEnd <= closures[p][i * 2])) {
          offsets[p * (depth + 2) + d + 1] = i;
          break;
        }
      }
      if (i == closureSize) offsets[p * (depth + 2) + d + 1] = i;
    }
    PetscCheck(offsets[p * (depth + 2) + depth + 1] == closureSize, PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Total size of closure %" PetscInt_FMT " should be %" PetscInt_FMT, offsets[p * (depth + 2) + depth + 1], closureSize);
  }
  for (d = 0; d < depth + 1; ++d) {
    PetscInt dof;

    /* Copy in support of first point */
    dof = offsets[d + 1] - offsets[d];
    for (joinSize = 0; joinSize < dof; ++joinSize) join[i][joinSize] = closures[0][(offsets[d] + joinSize) * 2];
    /* Check each successive cone */
    for (p = 1; p < numPoints && joinSize; ++p) {
      PetscInt newJoinSize = 0;

      dof = offsets[p * (depth + 2) + d + 1] - offsets[p * (depth + 2) + d];
      for (c = 0; c < dof; ++c) {
        const PetscInt point = closures[p][(offsets[p * (depth + 2) + d] + c) * 2];

        for (m = 0; m < joinSize; ++m) {
          if (point == join[i][m]) {
            join[1 - i][newJoinSize++] = point;
            break;
          }
        }
      }
      joinSize = newJoinSize;
      i        = 1 - i;
    }
    if (joinSize) break;
  }
  *numCoveredPoints = joinSize;
  *coveredPoints    = join[i];
  for (p = 0; p < numPoints; ++p) PetscCall(DMPlexRestoreTransitiveClosure(dm, points[p], PETSC_FALSE, NULL, &closures[p]));
  PetscCall(PetscFree(closures));
  PetscCall(DMRestoreWorkArray(dm, numPoints * (depth + 2), MPIU_INT, &offsets));
  PetscCall(DMRestoreWorkArray(dm, ms, MPIU_INT, &join[1 - i]));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  DMPlexGetMeet - Get an array for the meet of the set of points

  Not Collective

  Input Parameters:
+ dm        - The `DMPLEX` object
. numPoints - The number of input points for the meet
- points    - The input points, of length `numPoints`

  Output Parameters:
+ numCoveringPoints - The number of points in the meet
- coveringPoints    - The points in the meet, of length `numCoveringPoints`

  Level: intermediate

  Note:
  Currently, this is restricted to a single level meet

  Fortran Notes:
  `coveringPoints` must be declared with
.vb
  PetscInt, pointer :: coveringPoints(:)
.ve

  The `numCoveredPoints` argument is not present in the Fortran binding since it is internal to the array.

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexRestoreMeet()`, `DMPlexGetJoin()`
@*/
PetscErrorCode DMPlexGetMeet(DM dm, PetscInt numPoints, const PetscInt points[], PetscInt *numCoveringPoints, const PetscInt *coveringPoints[])
{
  DM_Plex  *mesh = (DM_Plex *)dm->data;
  PetscInt *meet[2];
  PetscInt  meetSize, i = 0;
  PetscInt  dof, off, p, c, m;
  PetscInt  maxConeSize;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscAssertPointer(points, 3);
  PetscAssertPointer(numCoveringPoints, 4);
  PetscAssertPointer(coveringPoints, 5);
  PetscCall(PetscSectionGetMaxDof(mesh->coneSection, &maxConeSize));
  PetscCall(DMGetWorkArray(dm, maxConeSize, MPIU_INT, &meet[0]));
  PetscCall(DMGetWorkArray(dm, maxConeSize, MPIU_INT, &meet[1]));
  /* Copy in cone of first point */
  PetscCall(PetscSectionGetDof(mesh->coneSection, points[0], &dof));
  PetscCall(PetscSectionGetOffset(mesh->coneSection, points[0], &off));
  for (meetSize = 0; meetSize < dof; ++meetSize) meet[i][meetSize] = mesh->cones[off + meetSize];
  /* Check each successive cone */
  for (p = 1; p < numPoints; ++p) {
    PetscInt newMeetSize = 0;

    PetscCall(PetscSectionGetDof(mesh->coneSection, points[p], &dof));
    PetscCall(PetscSectionGetOffset(mesh->coneSection, points[p], &off));
    for (c = 0; c < dof; ++c) {
      const PetscInt point = mesh->cones[off + c];

      for (m = 0; m < meetSize; ++m) {
        if (point == meet[i][m]) {
          meet[1 - i][newMeetSize++] = point;
          break;
        }
      }
    }
    meetSize = newMeetSize;
    i        = 1 - i;
  }
  *numCoveringPoints = meetSize;
  *coveringPoints    = meet[i];
  PetscCall(DMRestoreWorkArray(dm, maxConeSize, MPIU_INT, &meet[1 - i]));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  DMPlexRestoreMeet - Restore an array for the meet of the set of points obtained with `DMPlexGetMeet()`

  Not Collective

  Input Parameters:
+ dm        - The `DMPLEX` object
. numPoints - The number of input points for the meet
- points    - The input points

  Output Parameters:
+ numCoveredPoints - The number of points in the meet
- coveredPoints    - The points in the meet

  Level: intermediate

  Fortran Notes:
  The `numCoveredPoints` argument is not present in the Fortran binding since it is internal to the array.

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexGetMeet()`, `DMPlexGetFullMeet()`, `DMPlexGetJoin()`
@*/
PetscErrorCode DMPlexRestoreMeet(DM dm, PetscInt numPoints, const PetscInt points[], PetscInt *numCoveredPoints, const PetscInt *coveredPoints[])
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (points) PetscAssertPointer(points, 3);
  if (numCoveredPoints) PetscAssertPointer(numCoveredPoints, 4);
  PetscAssertPointer(coveredPoints, 5);
  PetscCall(DMRestoreWorkArray(dm, 0, MPIU_INT, (void *)coveredPoints));
  if (numCoveredPoints) *numCoveredPoints = 0;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  DMPlexGetFullMeet - Get an array for the meet of the set of points

  Not Collective

  Input Parameters:
+ dm        - The `DMPLEX` object
. numPoints - The number of input points for the meet
- points    - The input points, of length  `numPoints`

  Output Parameters:
+ numCoveredPoints - The number of points in the meet
- coveredPoints    - The points in the meet, of length  `numCoveredPoints`

  Level: intermediate

  Fortran Notes:
  `points` and `coveredPoints` must be declared with
.vb
  PetscInt, pointer :: points(:)
  PetscInt, pointer :: coveredPoints(:)
.ve

  The `numCoveredPoints` argument is not present in the Fortran binding since it is internal to the array.

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexGetMeet()`, `DMPlexRestoreMeet()`, `DMPlexGetJoin()`
@*/
PetscErrorCode DMPlexGetFullMeet(DM dm, PetscInt numPoints, const PetscInt points[], PetscInt *numCoveredPoints, const PetscInt *coveredPoints[])
{
  PetscInt *offsets, **closures;
  PetscInt *meet[2];
  PetscInt  height = 0, maxSize, meetSize = 0, i = 0;
  PetscInt  p, h, c, m, mc;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscAssertPointer(points, 3);
  PetscAssertPointer(numCoveredPoints, 4);
  PetscAssertPointer(coveredPoints, 5);

  PetscCall(DMPlexGetDepth(dm, &height));
  PetscCall(PetscMalloc1(numPoints, &closures));
  PetscCall(DMGetWorkArray(dm, numPoints * (height + 2), MPIU_INT, &offsets));
  PetscCall(DMPlexGetMaxSizes(dm, &mc, NULL));
  maxSize = (mc > 1) ? ((PetscPowInt(mc, height + 1) - 1) / (mc - 1)) : height + 1;
  PetscCall(DMGetWorkArray(dm, maxSize, MPIU_INT, &meet[0]));
  PetscCall(DMGetWorkArray(dm, maxSize, MPIU_INT, &meet[1]));

  for (p = 0; p < numPoints; ++p) {
    PetscInt closureSize;

    PetscCall(DMPlexGetTransitiveClosure(dm, points[p], PETSC_TRUE, &closureSize, &closures[p]));

    offsets[p * (height + 2) + 0] = 0;
    for (h = 0; h < height + 1; ++h) {
      PetscInt pStart, pEnd, i;

      PetscCall(DMPlexGetHeightStratum(dm, h, &pStart, &pEnd));
      for (i = offsets[p * (height + 2) + h]; i < closureSize; ++i) {
        if ((pStart > closures[p][i * 2]) || (pEnd <= closures[p][i * 2])) {
          offsets[p * (height + 2) + h + 1] = i;
          break;
        }
      }
      if (i == closureSize) offsets[p * (height + 2) + h + 1] = i;
    }
    PetscCheck(offsets[p * (height + 2) + height + 1] == closureSize, PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Total size of closure %" PetscInt_FMT " should be %" PetscInt_FMT, offsets[p * (height + 2) + height + 1], closureSize);
  }
  for (h = 0; h < height + 1; ++h) {
    PetscInt dof;

    /* Copy in cone of first point */
    dof = offsets[h + 1] - offsets[h];
    for (meetSize = 0; meetSize < dof; ++meetSize) meet[i][meetSize] = closures[0][(offsets[h] + meetSize) * 2];
    /* Check each successive cone */
    for (p = 1; p < numPoints && meetSize; ++p) {
      PetscInt newMeetSize = 0;

      dof = offsets[p * (height + 2) + h + 1] - offsets[p * (height + 2) + h];
      for (c = 0; c < dof; ++c) {
        const PetscInt point = closures[p][(offsets[p * (height + 2) + h] + c) * 2];

        for (m = 0; m < meetSize; ++m) {
          if (point == meet[i][m]) {
            meet[1 - i][newMeetSize++] = point;
            break;
          }
        }
      }
      meetSize = newMeetSize;
      i        = 1 - i;
    }
    if (meetSize) break;
  }
  *numCoveredPoints = meetSize;
  *coveredPoints    = meet[i];
  for (p = 0; p < numPoints; ++p) PetscCall(DMPlexRestoreTransitiveClosure(dm, points[p], PETSC_TRUE, NULL, &closures[p]));
  PetscCall(PetscFree(closures));
  PetscCall(DMRestoreWorkArray(dm, numPoints * (height + 2), MPIU_INT, &offsets));
  PetscCall(DMRestoreWorkArray(dm, mc, MPIU_INT, &meet[1 - i]));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexEqual - Determine if two `DM` have the same topology

  Not Collective

  Input Parameters:
+ dmA - A `DMPLEX` object
- dmB - A `DMPLEX` object

  Output Parameter:
. equal - `PETSC_TRUE` if the topologies are identical

  Level: intermediate

  Note:
  We are not solving graph isomorphism, so we do not permute.

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexGetCone()`
@*/
PetscErrorCode DMPlexEqual(DM dmA, DM dmB, PetscBool *equal)
{
  PetscInt depth, depthB, pStart, pEnd, pStartB, pEndB, p;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dmA, DM_CLASSID, 1);
  PetscValidHeaderSpecific(dmB, DM_CLASSID, 2);
  PetscAssertPointer(equal, 3);

  *equal = PETSC_FALSE;
  PetscCall(DMPlexGetDepth(dmA, &depth));
  PetscCall(DMPlexGetDepth(dmB, &depthB));
  if (depth != depthB) PetscFunctionReturn(PETSC_SUCCESS);
  PetscCall(DMPlexGetChart(dmA, &pStart, &pEnd));
  PetscCall(DMPlexGetChart(dmB, &pStartB, &pEndB));
  if ((pStart != pStartB) || (pEnd != pEndB)) PetscFunctionReturn(PETSC_SUCCESS);
  for (p = pStart; p < pEnd; ++p) {
    const PetscInt *cone, *coneB, *ornt, *orntB, *support, *supportB;
    PetscInt        coneSize, coneSizeB, c, supportSize, supportSizeB, s;

    PetscCall(DMPlexGetConeSize(dmA, p, &coneSize));
    PetscCall(DMPlexGetCone(dmA, p, &cone));
    PetscCall(DMPlexGetConeOrientation(dmA, p, &ornt));
    PetscCall(DMPlexGetConeSize(dmB, p, &coneSizeB));
    PetscCall(DMPlexGetCone(dmB, p, &coneB));
    PetscCall(DMPlexGetConeOrientation(dmB, p, &orntB));
    if (coneSize != coneSizeB) PetscFunctionReturn(PETSC_SUCCESS);
    for (c = 0; c < coneSize; ++c) {
      if (cone[c] != coneB[c]) PetscFunctionReturn(PETSC_SUCCESS);
      if (ornt[c] != orntB[c]) PetscFunctionReturn(PETSC_SUCCESS);
    }
    PetscCall(DMPlexGetSupportSize(dmA, p, &supportSize));
    PetscCall(DMPlexGetSupport(dmA, p, &support));
    PetscCall(DMPlexGetSupportSize(dmB, p, &supportSizeB));
    PetscCall(DMPlexGetSupport(dmB, p, &supportB));
    if (supportSize != supportSizeB) PetscFunctionReturn(PETSC_SUCCESS);
    for (s = 0; s < supportSize; ++s) {
      if (support[s] != supportB[s]) PetscFunctionReturn(PETSC_SUCCESS);
    }
  }
  *equal = PETSC_TRUE;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexGetNumFaceVertices - Returns the number of vertices on a face

  Not Collective

  Input Parameters:
+ dm         - The `DMPLEX`
. cellDim    - The cell dimension
- numCorners - The number of vertices on a cell

  Output Parameter:
. numFaceVertices - The number of vertices on a face

  Level: developer

  Note:
  Of course this can only work for a restricted set of symmetric shapes

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexGetCone()`
@*/
PetscErrorCode DMPlexGetNumFaceVertices(DM dm, PetscInt cellDim, PetscInt numCorners, PetscInt *numFaceVertices)
{
  MPI_Comm comm;

  PetscFunctionBegin;
  PetscCall(PetscObjectGetComm((PetscObject)dm, &comm));
  PetscAssertPointer(numFaceVertices, 4);
  switch (cellDim) {
  case 0:
    *numFaceVertices = 0;
    break;
  case 1:
    *numFaceVertices = 1;
    break;
  case 2:
    switch (numCorners) {
    case 3:                 /* triangle */
      *numFaceVertices = 2; /* Edge has 2 vertices */
      break;
    case 4:                 /* quadrilateral */
      *numFaceVertices = 2; /* Edge has 2 vertices */
      break;
    case 6:                 /* quadratic triangle, tri and quad cohesive Lagrange cells */
      *numFaceVertices = 3; /* Edge has 3 vertices */
      break;
    case 9:                 /* quadratic quadrilateral, quadratic quad cohesive Lagrange cells */
      *numFaceVertices = 3; /* Edge has 3 vertices */
      break;
    default:
      SETERRQ(comm, PETSC_ERR_ARG_OUTOFRANGE, "Invalid number of face corners %" PetscInt_FMT " for dimension %" PetscInt_FMT, numCorners, cellDim);
    }
    break;
  case 3:
    switch (numCorners) {
    case 4:                 /* tetradehdron */
      *numFaceVertices = 3; /* Face has 3 vertices */
      break;
    case 6:                 /* tet cohesive cells */
      *numFaceVertices = 4; /* Face has 4 vertices */
      break;
    case 8:                 /* hexahedron */
      *numFaceVertices = 4; /* Face has 4 vertices */
      break;
    case 9:                 /* tet cohesive Lagrange cells */
      *numFaceVertices = 6; /* Face has 6 vertices */
      break;
    case 10:                /* quadratic tetrahedron */
      *numFaceVertices = 6; /* Face has 6 vertices */
      break;
    case 12:                /* hex cohesive Lagrange cells */
      *numFaceVertices = 6; /* Face has 6 vertices */
      break;
    case 18:                /* quadratic tet cohesive Lagrange cells */
      *numFaceVertices = 6; /* Face has 6 vertices */
      break;
    case 27:                /* quadratic hexahedron, quadratic hex cohesive Lagrange cells */
      *numFaceVertices = 9; /* Face has 9 vertices */
      break;
    default:
      SETERRQ(comm, PETSC_ERR_ARG_OUTOFRANGE, "Invalid number of face corners %" PetscInt_FMT " for dimension %" PetscInt_FMT, numCorners, cellDim);
    }
    break;
  default:
    SETERRQ(comm, PETSC_ERR_ARG_OUTOFRANGE, "Invalid cell dimension %" PetscInt_FMT, cellDim);
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexGetDepthLabel - Get the `DMLabel` recording the depth of each point

  Not Collective

  Input Parameter:
. dm - The `DMPLEX` object

  Output Parameter:
. depthLabel - The `DMLabel` recording point depth

  Level: developer

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexGetDepth()`, `DMPlexGetHeightStratum()`, `DMPlexGetDepthStratum()`, `DMPlexGetPointDepth()`,
@*/
PetscErrorCode DMPlexGetDepthLabel(DM dm, DMLabel *depthLabel)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscAssertPointer(depthLabel, 2);
  *depthLabel = dm->depthLabel;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexGetDepth - Get the depth of the DAG representing this mesh

  Not Collective

  Input Parameter:
. dm - The `DMPLEX` object

  Output Parameter:
. depth - The number of strata (breadth first levels) in the DAG

  Level: developer

  Notes:
  This returns maximum of point depths over all points, i.e. maximum value of the label returned by `DMPlexGetDepthLabel()`.

  The point depth is described more in detail in `DMPlexGetDepthStratum()`.

  An empty mesh gives -1.

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexGetDepthLabel()`, `DMPlexGetDepthStratum()`, `DMPlexGetPointDepth()`, `DMPlexSymmetrize()`
@*/
PetscErrorCode DMPlexGetDepth(DM dm, PetscInt *depth)
{
  DM_Plex *mesh = (DM_Plex *)dm->data;
  DMLabel  label;
  PetscInt d = -1;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscAssertPointer(depth, 2);
  if (mesh->tr) {
    PetscCall(DMPlexTransformGetDepth(mesh->tr, depth));
  } else {
    PetscCall(DMPlexGetDepthLabel(dm, &label));
    // Allow missing depths
    if (label) PetscCall(DMLabelGetValueBounds(label, NULL, &d));
    *depth = d;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexGetDepthStratum - Get the bounds [`start`, `end`) for all points at a certain depth.

  Not Collective

  Input Parameters:
+ dm    - The `DMPLEX` object
- depth - The requested depth

  Output Parameters:
+ start - The first point at this `depth`
- end   - One beyond the last point at this `depth`

  Level: developer

  Notes:
  Depth indexing is related to topological dimension.  Depth stratum 0 contains the lowest topological dimension points,
  often "vertices".  If the mesh is "interpolated" (see `DMPlexInterpolate()`), then depth stratum 1 contains the next
  higher dimension, e.g., "edges".

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexGetHeightStratum()`, `DMPlexGetCellTypeStratum()`, `DMPlexGetDepth()`, `DMPlexGetDepthLabel()`, `DMPlexGetPointDepth()`, `DMPlexSymmetrize()`, `DMPlexInterpolate()`
@*/
PetscErrorCode DMPlexGetDepthStratum(DM dm, PetscInt depth, PetscInt *start, PetscInt *end)
{
  DM_Plex *mesh = (DM_Plex *)dm->data;
  DMLabel  label;
  PetscInt pStart, pEnd;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (start) {
    PetscAssertPointer(start, 3);
    *start = 0;
  }
  if (end) {
    PetscAssertPointer(end, 4);
    *end = 0;
  }
  PetscCall(DMPlexGetChart(dm, &pStart, &pEnd));
  if (pStart == pEnd) PetscFunctionReturn(PETSC_SUCCESS);
  if (depth < 0) {
    if (start) *start = pStart;
    if (end) *end = pEnd;
    PetscFunctionReturn(PETSC_SUCCESS);
  }
  if (mesh->tr) {
    PetscCall(DMPlexTransformGetDepthStratum(mesh->tr, depth, start, end));
  } else {
    PetscCall(DMPlexGetDepthLabel(dm, &label));
    PetscCheck(label, PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "No label named depth was found");
    PetscCall(DMLabelGetStratumBounds(label, depth, start, end));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexGetHeightStratum - Get the bounds [`start`, `end`) for all points at a certain height.

  Not Collective

  Input Parameters:
+ dm     - The `DMPLEX` object
- height - The requested height

  Output Parameters:
+ start - The first point at this `height`
- end   - One beyond the last point at this `height`

  Level: developer

  Notes:
  Height indexing is related to topological codimension.  Height stratum 0 contains the highest topological dimension
  points, often called "cells" or "elements".  If the mesh is "interpolated" (see `DMPlexInterpolate()`), then height
  stratum 1 contains the boundary of these "cells", often called "faces" or "facets".

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexGetDepthStratum()`, `DMPlexGetCellTypeStratum()`, `DMPlexGetDepth()`, `DMPlexGetPointHeight()`
@*/
PetscErrorCode DMPlexGetHeightStratum(DM dm, PetscInt height, PetscInt *start, PetscInt *end)
{
  DMLabel  label;
  PetscInt depth, pStart, pEnd;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (start) {
    PetscAssertPointer(start, 3);
    *start = 0;
  }
  if (end) {
    PetscAssertPointer(end, 4);
    *end = 0;
  }
  PetscCall(DMPlexGetChart(dm, &pStart, &pEnd));
  if (pStart == pEnd) PetscFunctionReturn(PETSC_SUCCESS);
  if (height < 0) {
    if (start) *start = pStart;
    if (end) *end = pEnd;
    PetscFunctionReturn(PETSC_SUCCESS);
  }
  PetscCall(DMPlexGetDepthLabel(dm, &label));
  if (label) PetscCall(DMLabelGetNumValues(label, &depth));
  else PetscCall(DMGetDimension(dm, &depth));
  PetscCheck(depth >= 0, PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Depth not yet computed");
  PetscCall(DMPlexGetDepthStratum(dm, depth - 1 - height, start, end));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexGetPointDepth - Get the `depth` of a given point

  Not Collective

  Input Parameters:
+ dm    - The `DMPLEX` object
- point - The point

  Output Parameter:
. depth - The depth of the `point`

  Level: intermediate

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexGetCellType()`, `DMPlexGetDepthLabel()`, `DMPlexGetDepth()`, `DMPlexGetPointHeight()`
@*/
PetscErrorCode DMPlexGetPointDepth(DM dm, PetscInt point, PetscInt *depth)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscAssertPointer(depth, 3);
  PetscCall(DMLabelGetValue(dm->depthLabel, point, depth));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexGetPointHeight - Get the `height` of a given point

  Not Collective

  Input Parameters:
+ dm    - The `DMPLEX` object
- point - The point

  Output Parameter:
. height - The height of the `point`

  Level: intermediate

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexGetCellType()`, `DMPlexGetDepthLabel()`, `DMPlexGetDepth()`, `DMPlexGetPointDepth()`
@*/
PetscErrorCode DMPlexGetPointHeight(DM dm, PetscInt point, PetscInt *height)
{
  PetscInt n, pDepth;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscAssertPointer(height, 3);
  PetscCall(DMLabelGetNumValues(dm->depthLabel, &n));
  PetscCall(DMLabelGetValue(dm->depthLabel, point, &pDepth));
  *height = n - 1 - pDepth; /* DAG depth is n-1 */
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexGetCellTypeLabel - Get the `DMLabel` recording the polytope type of each cell

  Not Collective

  Input Parameter:
. dm - The `DMPLEX` object

  Output Parameter:
. celltypeLabel - The `DMLabel` recording cell polytope type

  Level: developer

  Note:
  This function will trigger automatica computation of cell types. This can be disabled by calling
  `DMCreateLabel`(dm, "celltype") beforehand.

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexGetCellType()`, `DMPlexGetDepthLabel()`, `DMCreateLabel()`
@*/
PetscErrorCode DMPlexGetCellTypeLabel(DM dm, DMLabel *celltypeLabel)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscAssertPointer(celltypeLabel, 2);
  if (!dm->celltypeLabel) PetscCall(DMPlexComputeCellTypes(dm));
  *celltypeLabel = dm->celltypeLabel;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexGetCellType - Get the polytope type of a given cell

  Not Collective

  Input Parameters:
+ dm   - The `DMPLEX` object
- cell - The cell

  Output Parameter:
. celltype - The polytope type of the cell

  Level: intermediate

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPolytopeType`, `DMPlexGetCellTypeLabel()`, `DMPlexGetDepthLabel()`, `DMPlexGetDepth()`
@*/
PetscErrorCode DMPlexGetCellType(DM dm, PetscInt cell, DMPolytopeType *celltype)
{
  DM_Plex *mesh = (DM_Plex *)dm->data;
  DMLabel  label;
  PetscInt ct;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscAssertPointer(celltype, 3);
  if (mesh->tr) {
    PetscCall(DMPlexTransformGetCellType(mesh->tr, cell, celltype));
  } else {
    PetscInt pStart, pEnd;

    PetscCall(PetscSectionGetChart(mesh->coneSection, &pStart, NULL));
    if (!mesh->cellTypes) { /* XXX remove? optimize? */
      PetscCall(PetscSectionGetChart(mesh->coneSection, NULL, &pEnd));
      PetscCall(PetscMalloc1(pEnd - pStart, &mesh->cellTypes));
      PetscCall(DMPlexGetCellTypeLabel(dm, &label));
      for (PetscInt p = pStart; p < pEnd; p++) {
        PetscCall(DMLabelGetValue(label, p, &ct));
        mesh->cellTypes[p - pStart].value_as_uint8 = (DMPolytopeType)ct;
      }
    }
    *celltype = (DMPolytopeType)mesh->cellTypes[cell - pStart].value_as_uint8;
    if (PetscDefined(USE_DEBUG)) {
      PetscCall(DMPlexGetCellTypeLabel(dm, &label));
      PetscCall(DMLabelGetValue(label, cell, &ct));
      PetscCheck(ct >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Cell %" PetscInt_FMT " has not been assigned a cell type", cell);
      PetscCheck(ct == (PetscInt)*celltype, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid cellType for %" PetscInt_FMT ": %d != %" PetscInt_FMT, cell, (int)*celltype, ct);
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexSetCellType - Set the polytope type of a given cell

  Not Collective

  Input Parameters:
+ dm       - The `DMPLEX` object
. cell     - The cell
- celltype - The polytope type of the cell

  Level: advanced

  Note:
  By default, cell types will be automatically computed using `DMPlexComputeCellTypes()` before this function
  is executed. This function will override the computed type. However, if automatic classification will not succeed
  and a user wants to manually specify all types, the classification must be disabled by calling
  DMCreateLabel(dm, "celltype") before getting or setting any cell types.

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexGetCellTypeLabel()`, `DMPlexGetDepthLabel()`, `DMPlexGetDepth()`, `DMPlexComputeCellTypes()`, `DMCreateLabel()`
@*/
PetscErrorCode DMPlexSetCellType(DM dm, PetscInt cell, DMPolytopeType celltype)
{
  DM_Plex *mesh = (DM_Plex *)dm->data;
  DMLabel  label;
  PetscInt pStart, pEnd;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscCall(PetscSectionGetChart(mesh->coneSection, &pStart, &pEnd));
  PetscCall(DMPlexGetCellTypeLabel(dm, &label));
  PetscCall(DMLabelSetValue(label, cell, celltype));
  if (!mesh->cellTypes) PetscCall(PetscMalloc1(pEnd - pStart, &mesh->cellTypes));
  mesh->cellTypes[cell - pStart].value_as_uint8 = celltype;
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode DMCreateCoordinateDM_Plex(DM dm, DM *cdm)
{
  PetscSection section;
  PetscInt     maxHeight;
  const char  *prefix;

  PetscFunctionBegin;
  PetscCall(DMClone(dm, cdm));
  PetscCall(PetscObjectGetOptionsPrefix((PetscObject)dm, &prefix));
  PetscCall(PetscObjectSetOptionsPrefix((PetscObject)*cdm, prefix));
  PetscCall(PetscObjectAppendOptionsPrefix((PetscObject)*cdm, "cdm_"));
  PetscCall(DMPlexGetMaxProjectionHeight(dm, &maxHeight));
  PetscCall(DMPlexSetMaxProjectionHeight(*cdm, maxHeight));
  PetscCall(PetscSectionCreate(PetscObjectComm((PetscObject)dm), &section));
  PetscCall(DMSetLocalSection(*cdm, section));
  PetscCall(PetscSectionDestroy(&section));

  PetscCall(DMSetNumFields(*cdm, 1));
  PetscCall(DMCreateDS(*cdm));
  (*cdm)->cloneOpts = PETSC_TRUE;
  if (dm->setfromoptionscalled) PetscCall(DMSetFromOptions(*cdm));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode DMCreateCoordinateField_Plex(DM dm, DMField *field)
{
  Vec coordsLocal, cellCoordsLocal;
  DM  coordsDM, cellCoordsDM;

  PetscFunctionBegin;
  *field = NULL;
  PetscCall(DMGetCoordinatesLocal(dm, &coordsLocal));
  PetscCall(DMGetCoordinateDM(dm, &coordsDM));
  PetscCall(DMGetCellCoordinatesLocal(dm, &cellCoordsLocal));
  PetscCall(DMGetCellCoordinateDM(dm, &cellCoordsDM));
  if (coordsLocal && coordsDM) {
    if (cellCoordsLocal && cellCoordsDM) PetscCall(DMFieldCreateDSWithDG(coordsDM, cellCoordsDM, 0, coordsLocal, cellCoordsLocal, field));
    else PetscCall(DMFieldCreateDS(coordsDM, 0, coordsLocal, field));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexGetConeSection - Return a section which describes the layout of cone data

  Not Collective

  Input Parameter:
. dm - The `DMPLEX` object

  Output Parameter:
. section - The `PetscSection` object

  Level: developer

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexGetSupportSection()`, `DMPlexGetCones()`, `DMPlexGetConeOrientations()`, `PetscSection`
@*/
PetscErrorCode DMPlexGetConeSection(DM dm, PetscSection *section)
{
  DM_Plex *mesh = (DM_Plex *)dm->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (section) *section = mesh->coneSection;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexGetSupportSection - Return a section which describes the layout of support data

  Not Collective

  Input Parameter:
. dm - The `DMPLEX` object

  Output Parameter:
. section - The `PetscSection` object

  Level: developer

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexGetConeSection()`, `PetscSection`
@*/
PetscErrorCode DMPlexGetSupportSection(DM dm, PetscSection *section)
{
  DM_Plex *mesh = (DM_Plex *)dm->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (section) *section = mesh->supportSection;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  DMPlexGetCones - Return cone data

  Not Collective

  Input Parameter:
. dm - The `DMPLEX` object

  Output Parameter:
. cones - The cone for each point

  Level: developer

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexGetConeSection()`
@*/
PetscErrorCode DMPlexGetCones(DM dm, PetscInt *cones[])
{
  DM_Plex *mesh = (DM_Plex *)dm->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (cones) *cones = mesh->cones;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  DMPlexGetConeOrientations - Return cone orientation data

  Not Collective

  Input Parameter:
. dm - The `DMPLEX` object

  Output Parameter:
. coneOrientations - The array of cone orientations for all points

  Level: developer

  Notes:
  The `PetscSection` returned by `DMPlexGetConeSection()` partitions coneOrientations into cone orientations of particular points
  as returned by `DMPlexGetConeOrientation()`.

  The meaning of coneOrientations values is detailed in `DMPlexGetConeOrientation()`.

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexGetConeSection()`, `DMPlexGetConeOrientation()`, `PetscSection`
@*/
PetscErrorCode DMPlexGetConeOrientations(DM dm, PetscInt *coneOrientations[])
{
  DM_Plex *mesh = (DM_Plex *)dm->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (coneOrientations) *coneOrientations = mesh->coneOrientations;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* FEM Support */

PetscErrorCode DMPlexGetAllCells_Internal(DM plex, IS *cellIS)
{
  PetscInt depth;

  PetscFunctionBegin;
  PetscCall(DMPlexGetDepth(plex, &depth));
  PetscCall(DMGetStratumIS(plex, "dim", depth, cellIS));
  if (!*cellIS) PetscCall(DMGetStratumIS(plex, "depth", depth, cellIS));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode DMPlexGetAllFaces_Internal(DM plex, IS *faceIS)
{
  PetscInt depth;

  PetscFunctionBegin;
  PetscCall(DMPlexGetDepth(plex, &depth));
  PetscCall(DMGetStratumIS(plex, "dim", depth - 1, faceIS));
  if (!*faceIS) PetscCall(DMGetStratumIS(plex, "depth", depth - 1, faceIS));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
 Returns number of components and tensor degree for the field.  For interpolated meshes, line should be a point
 representing a line in the section.
*/
static PetscErrorCode PetscSectionFieldGetTensorDegree_Private(DM dm, PetscSection section, PetscInt field, PetscInt line, PetscInt *Nc, PetscInt *k, PetscBool *continuous, PetscBool *tensor)
{
  PetscObject  obj;
  PetscClassId id;
  PetscFE      fe = NULL;

  PetscFunctionBeginHot;
  PetscCall(PetscSectionGetFieldComponents(section, field, Nc));
  PetscCall(DMGetField(dm, field, NULL, &obj));
  PetscCall(PetscObjectGetClassId(obj, &id));
  if (id == PETSCFE_CLASSID) fe = (PetscFE)obj;

  if (!fe) {
    /* Assume the full interpolated mesh is in the chart; lines in particular */
    /* An order k SEM disc has k-1 dofs on an edge */
    PetscCall(PetscSectionGetFieldDof(section, line, field, k));
    *k = *k / *Nc + 1;
  } else {
    PetscInt       dual_space_size, dim;
    PetscDualSpace dsp;

    PetscCall(DMGetDimension(dm, &dim));
    PetscCall(PetscFEGetDualSpace(fe, &dsp));
    PetscCall(PetscDualSpaceGetDimension(dsp, &dual_space_size));
    *k = (PetscInt)PetscCeilReal(PetscPowReal(dual_space_size / *Nc, 1.0 / dim)) - 1;
    PetscCall(PetscDualSpaceLagrangeGetContinuity(dsp, continuous));
    PetscCall(PetscDualSpaceLagrangeGetTensor(dsp, tensor));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode GetFieldSize_Private(PetscInt dim, PetscInt k, PetscBool tensor, PetscInt *dof)
{
  PetscFunctionBeginHot;
  if (tensor) {
    *dof = PetscPowInt(k + 1, dim);
  } else {
    switch (dim) {
    case 1:
      *dof = k + 1;
      break;
    case 2:
      *dof = ((k + 1) * (k + 2)) / 2;
      break;
    case 3:
      *dof = ((k + 1) * (k + 2) * (k + 3)) / 6;
      break;
    default:
      *dof = 0;
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexSetClosurePermutationTensor - Create a permutation from the default (BFS) point ordering in the closure, to a
  lexicographic ordering over the tensor product cell (i.e., line, quad, hex, etc.), and set this permutation in the
  section provided (or the section of the `DM`).

  Input Parameters:
+ dm      - The `DM`
. point   - Either a cell (highest dim point) or an edge (dim 1 point), or `PETSC_DETERMINE`
- section - The `PetscSection` to reorder, or `NULL` for the default section

  Example:
  A typical interpolated single-quad mesh might order points as
.vb
  [c0, v1, v2, v3, v4, e5, e6, e7, e8]

  v4 -- e6 -- v3
  |           |
  e7    c0    e8
  |           |
  v1 -- e5 -- v2
.ve

  (There is no significance to the ordering described here.)  The default section for a Q3 quad might typically assign
  dofs in the order of points, e.g.,
.vb
    c0 -> [0,1,2,3]
    v1 -> [4]
    ...
    e5 -> [8, 9]
.ve

  which corresponds to the dofs
.vb
    6   10  11  7
    13  2   3   15
    12  0   1   14
    4   8   9   5
.ve

  The closure in BFS ordering works through height strata (cells, edges, vertices) to produce the ordering
.vb
  0 1 2 3 8 9 14 15 11 10 13 12 4 5 7 6
.ve

  After calling DMPlexSetClosurePermutationTensor(), the closure will be ordered lexicographically,
.vb
   4 8 9 5 12 0 1 14 13 2 3 15 6 10 11 7
.ve

  Level: developer

  Notes:
  The point is used to determine the number of dofs/field on an edge. For SEM, this is related to the polynomial
  degree of the basis.

  This is required to run with libCEED.

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMGetLocalSection()`, `PetscSectionSetClosurePermutation()`, `DMSetGlobalSection()`
@*/
PetscErrorCode DMPlexSetClosurePermutationTensor(DM dm, PetscInt point, PetscSection section)
{
  DMLabel   label;
  PetscInt  dim, depth = -1, eStart = -1, Nf;
  PetscBool continuous = PETSC_TRUE, tensor = PETSC_TRUE;

  PetscFunctionBegin;
  PetscCall(DMGetDimension(dm, &dim));
  if (dim < 1) PetscFunctionReturn(PETSC_SUCCESS);
  if (point < 0) {
    PetscInt sStart, sEnd;

    PetscCall(DMPlexGetDepthStratum(dm, 1, &sStart, &sEnd));
    point = sEnd - sStart ? sStart : point;
  }
  PetscCall(DMPlexGetDepthLabel(dm, &label));
  if (point >= 0) PetscCall(DMLabelGetValue(label, point, &depth));
  if (!section) PetscCall(DMGetLocalSection(dm, &section));
  if (depth == 1) {
    eStart = point;
  } else if (depth == dim) {
    const PetscInt *cone;

    PetscCall(DMPlexGetCone(dm, point, &cone));
    if (dim == 2) eStart = cone[0];
    else if (dim == 3) {
      const PetscInt *cone2;
      PetscCall(DMPlexGetCone(dm, cone[0], &cone2));
      eStart = cone2[0];
    } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Point %" PetscInt_FMT " of depth %" PetscInt_FMT " cannot be used to bootstrap spectral ordering for dim %" PetscInt_FMT, point, depth, dim);
  } else PetscCheck(depth < 0, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Point %" PetscInt_FMT " of depth %" PetscInt_FMT " cannot be used to bootstrap spectral ordering for dim %" PetscInt_FMT, point, depth, dim);

  PetscCall(PetscSectionGetNumFields(section, &Nf));
  for (PetscInt d = 1; d <= dim; d++) {
    PetscInt  k, f, Nc, c, i, j, size = 0, offset = 0, foffset = 0;
    PetscInt *perm;

    for (f = 0; f < Nf; ++f) {
      PetscInt dof;

      PetscCall(PetscSectionFieldGetTensorDegree_Private(dm, section, f, eStart, &Nc, &k, &continuous, &tensor));
      PetscCheck(dim == 1 || tensor || !continuous, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Continuous field %" PetscInt_FMT " must have a tensor product discretization", f);
      if (!continuous && d < dim) continue;
      PetscCall(GetFieldSize_Private(d, k, tensor, &dof));
      size += dof * Nc;
    }
    PetscCall(PetscMalloc1(size, &perm));
    for (f = 0; f < Nf; ++f) {
      switch (d) {
      case 1:
        PetscCall(PetscSectionFieldGetTensorDegree_Private(dm, section, f, eStart, &Nc, &k, &continuous, &tensor));
        if (!continuous && d < dim) continue;
        /*
         Original ordering is [ edge of length k-1; vtx0; vtx1 ]
         We want              [ vtx0; edge of length k-1; vtx1 ]
         */
        if (continuous) {
          for (c = 0; c < Nc; c++, offset++) perm[offset] = (k - 1) * Nc + c + foffset;
          for (i = 0; i < k - 1; i++)
            for (c = 0; c < Nc; c++, offset++) perm[offset] = i * Nc + c + foffset;
          for (c = 0; c < Nc; c++, offset++) perm[offset] = k * Nc + c + foffset;
          foffset = offset;
        } else {
          PetscInt dof;

          PetscCall(GetFieldSize_Private(d, k, tensor, &dof));
          for (i = 0; i < dof * Nc; ++i, ++offset) perm[offset] = i + foffset;
          foffset = offset;
        }
        break;
      case 2:
        /* The original quad closure is oriented clockwise, {f, e_b, e_r, e_t, e_l, v_lb, v_rb, v_tr, v_tl} */
        PetscCall(PetscSectionFieldGetTensorDegree_Private(dm, section, f, eStart, &Nc, &k, &continuous, &tensor));
        if (!continuous && d < dim) continue;
        /* The SEM order is

         v_lb, {e_b}, v_rb,
         e^{(k-1)-i}_l, {f^{i*(k-1)}}, e^i_r,
         v_lt, reverse {e_t}, v_rt
         */
        if (continuous) {
          const PetscInt of   = 0;
          const PetscInt oeb  = of + PetscSqr(k - 1);
          const PetscInt oer  = oeb + (k - 1);
          const PetscInt oet  = oer + (k - 1);
          const PetscInt oel  = oet + (k - 1);
          const PetscInt ovlb = oel + (k - 1);
          const PetscInt ovrb = ovlb + 1;
          const PetscInt ovrt = ovrb + 1;
          const PetscInt ovlt = ovrt + 1;
          PetscInt       o;

          /* bottom */
          for (c = 0; c < Nc; ++c, ++offset) perm[offset] = ovlb * Nc + c + foffset;
          for (o = oeb; o < oer; ++o)
            for (c = 0; c < Nc; ++c, ++offset) perm[offset] = o * Nc + c + foffset;
          for (c = 0; c < Nc; ++c, ++offset) perm[offset] = ovrb * Nc + c + foffset;
          /* middle */
          for (i = 0; i < k - 1; ++i) {
            for (c = 0; c < Nc; ++c, ++offset) perm[offset] = (oel + (k - 2) - i) * Nc + c + foffset;
            for (o = of + (k - 1) * i; o < of + (k - 1) * (i + 1); ++o)
              for (c = 0; c < Nc; ++c, ++offset) perm[offset] = o * Nc + c + foffset;
            for (c = 0; c < Nc; ++c, ++offset) perm[offset] = (oer + i) * Nc + c + foffset;
          }
          /* top */
          for (c = 0; c < Nc; ++c, ++offset) perm[offset] = ovlt * Nc + c + foffset;
          for (o = oel - 1; o >= oet; --o)
            for (c = 0; c < Nc; ++c, ++offset) perm[offset] = o * Nc + c + foffset;
          for (c = 0; c < Nc; ++c, ++offset) perm[offset] = ovrt * Nc + c + foffset;
          foffset = offset;
        } else {
          PetscInt dof;

          PetscCall(GetFieldSize_Private(d, k, tensor, &dof));
          for (i = 0; i < dof * Nc; ++i, ++offset) perm[offset] = i + foffset;
          foffset = offset;
        }
        break;
      case 3:
        /* The original hex closure is

         {c,
         f_b, f_t, f_f, f_b, f_r, f_l,
         e_bl, e_bb, e_br, e_bf,  e_tf, e_tr, e_tb, e_tl,  e_rf, e_lf, e_lb, e_rb,
         v_blf, v_blb, v_brb, v_brf, v_tlf, v_trf, v_trb, v_tlb}
         */
        PetscCall(PetscSectionFieldGetTensorDegree_Private(dm, section, f, eStart, &Nc, &k, &continuous, &tensor));
        if (!continuous && d < dim) continue;
        /* The SEM order is
         Bottom Slice
         v_blf, {e^{(k-1)-n}_bf}, v_brf,
         e^{i}_bl, f^{n*(k-1)+(k-1)-i}_b, e^{(k-1)-i}_br,
         v_blb, {e_bb}, v_brb,

         Middle Slice (j)
         {e^{(k-1)-j}_lf}, {f^{j*(k-1)+n}_f}, e^j_rf,
         f^{i*(k-1)+j}_l, {c^{(j*(k-1) + i)*(k-1)+n}_t}, f^{j*(k-1)+i}_r,
         e^j_lb, {f^{j*(k-1)+(k-1)-n}_b}, e^{(k-1)-j}_rb,

         Top Slice
         v_tlf, {e_tf}, v_trf,
         e^{(k-1)-i}_tl, {f^{i*(k-1)}_t}, e^{i}_tr,
         v_tlb, {e^{(k-1)-n}_tb}, v_trb,
         */
        if (continuous) {
          const PetscInt oc    = 0;
          const PetscInt ofb   = oc + PetscSqr(k - 1) * (k - 1);
          const PetscInt oft   = ofb + PetscSqr(k - 1);
          const PetscInt off   = oft + PetscSqr(k - 1);
          const PetscInt ofk   = off + PetscSqr(k - 1);
          const PetscInt ofr   = ofk + PetscSqr(k - 1);
          const PetscInt ofl   = ofr + PetscSqr(k - 1);
          const PetscInt oebl  = ofl + PetscSqr(k - 1);
          const PetscInt oebb  = oebl + (k - 1);
          const PetscInt oebr  = oebb + (k - 1);
          const PetscInt oebf  = oebr + (k - 1);
          const PetscInt oetf  = oebf + (k - 1);
          const PetscInt oetr  = oetf + (k - 1);
          const PetscInt oetb  = oetr + (k - 1);
          const PetscInt oetl  = oetb + (k - 1);
          const PetscInt oerf  = oetl + (k - 1);
          const PetscInt oelf  = oerf + (k - 1);
          const PetscInt oelb  = oelf + (k - 1);
          const PetscInt oerb  = oelb + (k - 1);
          const PetscInt ovblf = oerb + (k - 1);
          const PetscInt ovblb = ovblf + 1;
          const PetscInt ovbrb = ovblb + 1;
          const PetscInt ovbrf = ovbrb + 1;
          const PetscInt ovtlf = ovbrf + 1;
          const PetscInt ovtrf = ovtlf + 1;
          const PetscInt ovtrb = ovtrf + 1;
          const PetscInt ovtlb = ovtrb + 1;
          PetscInt       o, n;

          /* Bottom Slice */
          /*   bottom */
          for (c = 0; c < Nc; ++c, ++offset) perm[offset] = ovblf * Nc + c + foffset;
          for (o = oetf - 1; o >= oebf; --o)
            for (c = 0; c < Nc; ++c, ++offset) perm[offset] = o * Nc + c + foffset;
          for (c = 0; c < Nc; ++c, ++offset) perm[offset] = ovbrf * Nc + c + foffset;
          /*   middle */
          for (i = 0; i < k - 1; ++i) {
            for (c = 0; c < Nc; ++c, ++offset) perm[offset] = (oebl + i) * Nc + c + foffset;
            for (n = 0; n < k - 1; ++n) {
              o = ofb + n * (k - 1) + i;
              for (c = 0; c < Nc; ++c, ++offset) perm[offset] = o * Nc + c + foffset;
            }
            for (c = 0; c < Nc; ++c, ++offset) perm[offset] = (oebr + (k - 2) - i) * Nc + c + foffset;
          }
          /*   top */
          for (c = 0; c < Nc; ++c, ++offset) perm[offset] = ovblb * Nc + c + foffset;
          for (o = oebb; o < oebr; ++o)
            for (c = 0; c < Nc; ++c, ++offset) perm[offset] = o * Nc + c + foffset;
          for (c = 0; c < Nc; ++c, ++offset) perm[offset] = ovbrb * Nc + c + foffset;

          /* Middle Slice */
          for (j = 0; j < k - 1; ++j) {
            /*   bottom */
            for (c = 0; c < Nc; ++c, ++offset) perm[offset] = (oelf + (k - 2) - j) * Nc + c + foffset;
            for (o = off + j * (k - 1); o < off + (j + 1) * (k - 1); ++o)
              for (c = 0; c < Nc; ++c, ++offset) perm[offset] = o * Nc + c + foffset;
            for (c = 0; c < Nc; ++c, ++offset) perm[offset] = (oerf + j) * Nc + c + foffset;
            /*   middle */
            for (i = 0; i < k - 1; ++i) {
              for (c = 0; c < Nc; ++c, ++offset) perm[offset] = (ofl + i * (k - 1) + j) * Nc + c + foffset;
              for (n = 0; n < k - 1; ++n)
                for (c = 0; c < Nc; ++c, ++offset) perm[offset] = (oc + (j * (k - 1) + i) * (k - 1) + n) * Nc + c + foffset;
              for (c = 0; c < Nc; ++c, ++offset) perm[offset] = (ofr + j * (k - 1) + i) * Nc + c + foffset;
            }
            /*   top */
            for (c = 0; c < Nc; ++c, ++offset) perm[offset] = (oelb + j) * Nc + c + foffset;
            for (o = ofk + j * (k - 1) + (k - 2); o >= ofk + j * (k - 1); --o)
              for (c = 0; c < Nc; ++c, ++offset) perm[offset] = o * Nc + c + foffset;
            for (c = 0; c < Nc; ++c, ++offset) perm[offset] = (oerb + (k - 2) - j) * Nc + c + foffset;
          }

          /* Top Slice */
          /*   bottom */
          for (c = 0; c < Nc; ++c, ++offset) perm[offset] = ovtlf * Nc + c + foffset;
          for (o = oetf; o < oetr; ++o)
            for (c = 0; c < Nc; ++c, ++offset) perm[offset] = o * Nc + c + foffset;
          for (c = 0; c < Nc; ++c, ++offset) perm[offset] = ovtrf * Nc + c + foffset;
          /*   middle */
          for (i = 0; i < k - 1; ++i) {
            for (c = 0; c < Nc; ++c, ++offset) perm[offset] = (oetl + (k - 2) - i) * Nc + c + foffset;
            for (n = 0; n < k - 1; ++n)
              for (c = 0; c < Nc; ++c, ++offset) perm[offset] = (oft + i * (k - 1) + n) * Nc + c + foffset;
            for (c = 0; c < Nc; ++c, ++offset) perm[offset] = (oetr + i) * Nc + c + foffset;
          }
          /*   top */
          for (c = 0; c < Nc; ++c, ++offset) perm[offset] = ovtlb * Nc + c + foffset;
          for (o = oetl - 1; o >= oetb; --o)
            for (c = 0; c < Nc; ++c, ++offset) perm[offset] = o * Nc + c + foffset;
          for (c = 0; c < Nc; ++c, ++offset) perm[offset] = ovtrb * Nc + c + foffset;

          foffset = offset;
        } else {
          PetscInt dof;

          PetscCall(GetFieldSize_Private(d, k, tensor, &dof));
          for (i = 0; i < dof * Nc; ++i, ++offset) perm[offset] = i + foffset;
          foffset = offset;
        }
        break;
      default:
        SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No spectral ordering for dimension %" PetscInt_FMT, d);
      }
    }
    PetscCheck(offset == size, PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Number of permutation entries %" PetscInt_FMT " != %" PetscInt_FMT, offset, size);
    /* Check permutation */
    {
      PetscInt *check;

      PetscCall(PetscMalloc1(size, &check));
      for (i = 0; i < size; ++i) {
        check[i] = -1;
        PetscCheck(perm[i] >= 0 && perm[i] < size, PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Invalid permutation index p[%" PetscInt_FMT "] = %" PetscInt_FMT, i, perm[i]);
      }
      for (i = 0; i < size; ++i) check[perm[i]] = i;
      for (i = 0; i < size; ++i) PetscCheck(check[i] >= 0, PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Missing permutation index %" PetscInt_FMT, i);
      PetscCall(PetscFree(check));
    }
    PetscCall(PetscSectionSetClosurePermutation_Internal(section, (PetscObject)dm, d, size, PETSC_OWN_POINTER, perm));
    if (d == dim) { // Add permutation for localized (in case this is a coordinate DM)
      PetscInt *loc_perm;
      PetscCall(PetscMalloc1(size * 2, &loc_perm));
      for (PetscInt i = 0; i < size; i++) {
        loc_perm[i]        = perm[i];
        loc_perm[size + i] = size + perm[i];
      }
      PetscCall(PetscSectionSetClosurePermutation_Internal(section, (PetscObject)dm, d, size * 2, PETSC_OWN_POINTER, loc_perm));
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode DMPlexGetPointDualSpaceFEM(DM dm, PetscInt point, PetscInt field, PetscDualSpace *dspace)
{
  PetscDS  prob;
  PetscInt depth, Nf, h;
  DMLabel  label;

  PetscFunctionBeginHot;
  PetscCall(DMGetDS(dm, &prob));
  Nf      = prob->Nf;
  label   = dm->depthLabel;
  *dspace = NULL;
  if (field < Nf) {
    PetscObject disc = prob->disc[field];

    if (disc->classid == PETSCFE_CLASSID) {
      PetscDualSpace dsp;

      PetscCall(PetscFEGetDualSpace((PetscFE)disc, &dsp));
      PetscCall(DMLabelGetNumValues(label, &depth));
      PetscCall(DMLabelGetValue(label, point, &h));
      h = depth - 1 - h;
      if (h) {
        PetscCall(PetscDualSpaceGetHeightSubspace(dsp, h, dspace));
      } else {
        *dspace = dsp;
      }
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static inline PetscErrorCode DMPlexVecGetClosure_Depth1_Static(DM dm, PetscSection section, Vec v, PetscInt point, PetscInt *csize, PetscScalar *values[])
{
  PetscScalar       *array;
  const PetscScalar *vArray;
  const PetscInt    *cone, *coneO;
  PetscInt           pStart, pEnd, p, numPoints, size = 0, offset = 0;

  PetscFunctionBeginHot;
  PetscCall(PetscSectionGetChart(section, &pStart, &pEnd));
  PetscCall(DMPlexGetConeSize(dm, point, &numPoints));
  PetscCall(DMPlexGetCone(dm, point, &cone));
  PetscCall(DMPlexGetConeOrientation(dm, point, &coneO));
  if (!values || !*values) {
    if ((point >= pStart) && (point < pEnd)) {
      PetscInt dof;

      PetscCall(PetscSectionGetDof(section, point, &dof));
      size += dof;
    }
    for (p = 0; p < numPoints; ++p) {
      const PetscInt cp = cone[p];
      PetscInt       dof;

      if ((cp < pStart) || (cp >= pEnd)) continue;
      PetscCall(PetscSectionGetDof(section, cp, &dof));
      size += dof;
    }
    if (!values) {
      if (csize) *csize = size;
      PetscFunctionReturn(PETSC_SUCCESS);
    }
    PetscCall(DMGetWorkArray(dm, size, MPIU_SCALAR, &array));
  } else {
    array = *values;
  }
  size = 0;
  PetscCall(VecGetArrayRead(v, &vArray));
  if ((point >= pStart) && (point < pEnd)) {
    PetscInt           dof, off, d;
    const PetscScalar *varr;

    PetscCall(PetscSectionGetDof(section, point, &dof));
    PetscCall(PetscSectionGetOffset(section, point, &off));
    varr = PetscSafePointerPlusOffset(vArray, off);
    for (d = 0; d < dof; ++d, ++offset) array[offset] = varr[d];
    size += dof;
  }
  for (p = 0; p < numPoints; ++p) {
    const PetscInt     cp = cone[p];
    PetscInt           o  = coneO[p];
    PetscInt           dof, off, d;
    const PetscScalar *varr;

    if ((cp < pStart) || (cp >= pEnd)) continue;
    PetscCall(PetscSectionGetDof(section, cp, &dof));
    PetscCall(PetscSectionGetOffset(section, cp, &off));
    varr = PetscSafePointerPlusOffset(vArray, off);
    if (o >= 0) {
      for (d = 0; d < dof; ++d, ++offset) array[offset] = varr[d];
    } else {
      for (d = dof - 1; d >= 0; --d, ++offset) array[offset] = varr[d];
    }
    size += dof;
  }
  PetscCall(VecRestoreArrayRead(v, &vArray));
  if (!*values) {
    if (csize) *csize = size;
    *values = array;
  } else {
    PetscCheck(size <= *csize, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Size of input array %" PetscInt_FMT " < actual size %" PetscInt_FMT, *csize, size);
    *csize = size;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* Compress out points not in the section */
static inline PetscErrorCode CompressPoints_Private(PetscSection section, PetscInt *numPoints, PetscInt points[])
{
  const PetscInt np = *numPoints;
  PetscInt       pStart, pEnd, p, q;

  PetscCall(PetscSectionGetChart(section, &pStart, &pEnd));
  for (p = 0, q = 0; p < np; ++p) {
    const PetscInt r = points[p * 2];
    if ((r >= pStart) && (r < pEnd)) {
      points[q * 2]     = r;
      points[q * 2 + 1] = points[p * 2 + 1];
      ++q;
    }
  }
  *numPoints = q;
  return PETSC_SUCCESS;
}

/* Compressed closure does not apply closure permutation */
PetscErrorCode DMPlexGetCompressedClosure(DM dm, PetscSection section, PetscInt point, PetscInt ornt, PetscInt *numPoints, PetscInt **points, PetscSection *clSec, IS *clPoints, const PetscInt **clp)
{
  const PetscInt *cla = NULL;
  PetscInt        np, *pts = NULL;

  PetscFunctionBeginHot;
  PetscCall(PetscSectionGetClosureIndex(section, (PetscObject)dm, clSec, clPoints));
  if (!ornt && *clPoints) {
    PetscInt dof, off;

    PetscCall(PetscSectionGetDof(*clSec, point, &dof));
    PetscCall(PetscSectionGetOffset(*clSec, point, &off));
    PetscCall(ISGetIndices(*clPoints, &cla));
    np  = dof / 2;
    pts = PetscSafePointerPlusOffset((PetscInt *)cla, off);
  } else {
    PetscCall(DMPlexGetTransitiveClosure_Internal(dm, point, ornt, PETSC_TRUE, &np, &pts));
    PetscCall(CompressPoints_Private(section, &np, pts));
  }
  *numPoints = np;
  *points    = pts;
  *clp       = cla;
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode DMPlexRestoreCompressedClosure(DM dm, PetscSection section, PetscInt point, PetscInt *numPoints, PetscInt **points, PetscSection *clSec, IS *clPoints, const PetscInt **clp)
{
  PetscFunctionBeginHot;
  if (!*clPoints) {
    PetscCall(DMPlexRestoreTransitiveClosure(dm, point, PETSC_TRUE, numPoints, points));
  } else {
    PetscCall(ISRestoreIndices(*clPoints, clp));
  }
  *numPoints = 0;
  *points    = NULL;
  *clSec     = NULL;
  *clPoints  = NULL;
  *clp       = NULL;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static inline PetscErrorCode DMPlexVecGetClosure_Static(DM dm, PetscSection section, PetscInt numPoints, const PetscInt points[], const PetscInt clperm[], const PetscScalar vArray[], PetscInt *size, PetscScalar array[])
{
  PetscInt            offset = 0, p;
  const PetscInt    **perms  = NULL;
  const PetscScalar **flips  = NULL;

  PetscFunctionBeginHot;
  *size = 0;
  PetscCall(PetscSectionGetPointSyms(section, numPoints, points, &perms, &flips));
  for (p = 0; p < numPoints; p++) {
    const PetscInt     point = points[2 * p];
    const PetscInt    *perm  = perms ? perms[p] : NULL;
    const PetscScalar *flip  = flips ? flips[p] : NULL;
    PetscInt           dof, off, d;
    const PetscScalar *varr;

    PetscCall(PetscSectionGetDof(section, point, &dof));
    PetscCall(PetscSectionGetOffset(section, point, &off));
    varr = PetscSafePointerPlusOffset(vArray, off);
    if (clperm) {
      if (perm) {
        for (d = 0; d < dof; d++) array[clperm[offset + perm[d]]] = varr[d];
      } else {
        for (d = 0; d < dof; d++) array[clperm[offset + d]] = varr[d];
      }
      if (flip) {
        for (d = 0; d < dof; d++) array[clperm[offset + d]] *= flip[d];
      }
    } else {
      if (perm) {
        for (d = 0; d < dof; d++) array[offset + perm[d]] = varr[d];
      } else {
        for (d = 0; d < dof; d++) array[offset + d] = varr[d];
      }
      if (flip) {
        for (d = 0; d < dof; d++) array[offset + d] *= flip[d];
      }
    }
    offset += dof;
  }
  PetscCall(PetscSectionRestorePointSyms(section, numPoints, points, &perms, &flips));
  *size = offset;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static inline PetscErrorCode DMPlexVecGetClosure_Fields_Static(DM dm, PetscSection section, PetscInt numPoints, const PetscInt points[], PetscInt numFields, const PetscInt clperm[], const PetscScalar vArray[], PetscInt *size, PetscScalar array[])
{
  PetscInt offset = 0, f;

  PetscFunctionBeginHot;
  *size = 0;
  for (f = 0; f < numFields; ++f) {
    PetscInt            p;
    const PetscInt    **perms = NULL;
    const PetscScalar **flips = NULL;

    PetscCall(PetscSectionGetFieldPointSyms(section, f, numPoints, points, &perms, &flips));
    for (p = 0; p < numPoints; p++) {
      const PetscInt     point = points[2 * p];
      PetscInt           fdof, foff, b;
      const PetscScalar *varr;
      const PetscInt    *perm = perms ? perms[p] : NULL;
      const PetscScalar *flip = flips ? flips[p] : NULL;

      PetscCall(PetscSectionGetFieldDof(section, point, f, &fdof));
      PetscCall(PetscSectionGetFieldOffset(section, point, f, &foff));
      varr = &vArray[foff];
      if (clperm) {
        if (perm) {
          for (b = 0; b < fdof; b++) array[clperm[offset + perm[b]]] = varr[b];
        } else {
          for (b = 0; b < fdof; b++) array[clperm[offset + b]] = varr[b];
        }
        if (flip) {
          for (b = 0; b < fdof; b++) array[clperm[offset + b]] *= flip[b];
        }
      } else {
        if (perm) {
          for (b = 0; b < fdof; b++) array[offset + perm[b]] = varr[b];
        } else {
          for (b = 0; b < fdof; b++) array[offset + b] = varr[b];
        }
        if (flip) {
          for (b = 0; b < fdof; b++) array[offset + b] *= flip[b];
        }
      }
      offset += fdof;
    }
    PetscCall(PetscSectionRestoreFieldPointSyms(section, f, numPoints, points, &perms, &flips));
  }
  *size = offset;
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode DMPlexVecGetOrientedClosure_Internal(DM dm, PetscSection section, PetscBool useClPerm, Vec v, PetscInt point, PetscInt ornt, PetscInt *csize, PetscScalar *values[])
{
  PetscSection    clSection;
  IS              clPoints;
  PetscInt       *points = NULL;
  const PetscInt *clp, *perm = NULL;
  PetscInt        depth, numFields, numPoints, asize;

  PetscFunctionBeginHot;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (!section) PetscCall(DMGetLocalSection(dm, &section));
  PetscValidHeaderSpecific(section, PETSC_SECTION_CLASSID, 2);
  PetscValidHeaderSpecific(v, VEC_CLASSID, 4);
  PetscCall(DMPlexGetDepth(dm, &depth));
  PetscCall(PetscSectionGetNumFields(section, &numFields));
  if (depth == 1 && numFields < 2) {
    PetscCall(DMPlexVecGetClosure_Depth1_Static(dm, section, v, point, csize, values));
    PetscFunctionReturn(PETSC_SUCCESS);
  }
  /* Get points */
  PetscCall(DMPlexGetCompressedClosure(dm, section, point, ornt, &numPoints, &points, &clSection, &clPoints, &clp));
  /* Get sizes */
  asize = 0;
  for (PetscInt p = 0; p < numPoints * 2; p += 2) {
    PetscInt dof;
    PetscCall(PetscSectionGetDof(section, points[p], &dof));
    asize += dof;
  }
  if (values) {
    const PetscScalar *vArray;
    PetscInt           size;

    if (*values) {
      PetscCheck(*csize >= asize, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Provided array size %" PetscInt_FMT " not sufficient to hold closure size %" PetscInt_FMT, *csize, asize);
    } else PetscCall(DMGetWorkArray(dm, asize, MPIU_SCALAR, values));
    if (useClPerm) PetscCall(PetscSectionGetClosureInversePermutation_Internal(section, (PetscObject)dm, depth, asize, &perm));
    PetscCall(VecGetArrayRead(v, &vArray));
    /* Get values */
    if (numFields > 0) PetscCall(DMPlexVecGetClosure_Fields_Static(dm, section, numPoints, points, numFields, perm, vArray, &size, *values));
    else PetscCall(DMPlexVecGetClosure_Static(dm, section, numPoints, points, perm, vArray, &size, *values));
    PetscCheck(asize == size, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Section size %" PetscInt_FMT " does not match Vec closure size %" PetscInt_FMT, asize, size);
    /* Cleanup array */
    PetscCall(VecRestoreArrayRead(v, &vArray));
  }
  if (csize) *csize = asize;
  /* Cleanup points */
  PetscCall(DMPlexRestoreCompressedClosure(dm, section, point, &numPoints, &points, &clSection, &clPoints, &clp));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  DMPlexVecGetClosure - Get an array of the values on the closure of 'point'

  Not collective

  Input Parameters:
+ dm      - The `DM`
. section - The section describing the layout in `v`, or `NULL` to use the default section
. v       - The local vector
- point   - The point in the `DM`

  Input/Output Parameters:
+ csize  - The size of the input values array, or `NULL`; on output the number of values in the closure
- values - An array to use for the values, or *values = `NULL` to have it allocated automatically;
           if the user provided `NULL`, it is a borrowed array and should not be freed, use  `DMPlexVecRestoreClosure()` to return it

  Level: intermediate

  Notes:
  `DMPlexVecGetClosure()`/`DMPlexVecRestoreClosure()` only allocates the values array if it set to `NULL` in the
  calling function. This is because `DMPlexVecGetClosure()` is typically called in the inner loop of a `Vec` or `Mat`
  assembly function, and a user may already have allocated storage for this operation.

  A typical use could be
.vb
   values = NULL;
   PetscCall(DMPlexVecGetClosure(dm, NULL, v, p, &clSize, &values));
   for (cl = 0; cl < clSize; ++cl) {
     <Compute on closure>
   }
   PetscCall(DMPlexVecRestoreClosure(dm, NULL, v, p, &clSize, &values));
.ve
  or
.vb
   PetscMalloc1(clMaxSize, &values);
   for (p = pStart; p < pEnd; ++p) {
     clSize = clMaxSize;
     PetscCall(DMPlexVecGetClosure(dm, NULL, v, p, &clSize, &values));
     for (cl = 0; cl < clSize; ++cl) {
       <Compute on closure>
     }
   }
   PetscFree(values);
.ve

  Fortran Notes:
  The `csize` argument is not present in the Fortran binding.

  `values` must be declared with
.vb
  PetscScalar,dimension(:),pointer   :: values
.ve
  and it will be allocated internally by PETSc to hold the values returned

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexVecRestoreClosure()`, `DMPlexVecSetClosure()`, `DMPlexMatSetClosure()`
@*/
PetscErrorCode DMPlexVecGetClosure(DM dm, PetscSection section, Vec v, PetscInt point, PetscInt *csize, PetscScalar *values[])
{
  PetscFunctionBeginHot;
  PetscCall(DMPlexVecGetOrientedClosure_Internal(dm, section, PETSC_TRUE, v, point, 0, csize, values));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode DMPlexVecGetClosureAtDepth_Internal(DM dm, PetscSection section, Vec v, PetscInt point, PetscInt depth, PetscInt *csize, PetscScalar *values[])
{
  DMLabel            depthLabel;
  PetscSection       clSection;
  IS                 clPoints;
  PetscScalar       *array;
  const PetscScalar *vArray;
  PetscInt          *points = NULL;
  const PetscInt    *clp, *perm = NULL;
  PetscInt           mdepth, numFields, numPoints, Np = 0, p, clsize, size;

  PetscFunctionBeginHot;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (!section) PetscCall(DMGetLocalSection(dm, &section));
  PetscValidHeaderSpecific(section, PETSC_SECTION_CLASSID, 2);
  PetscValidHeaderSpecific(v, VEC_CLASSID, 3);
  PetscCall(DMPlexGetDepth(dm, &mdepth));
  PetscCall(DMPlexGetDepthLabel(dm, &depthLabel));
  PetscCall(PetscSectionGetNumFields(section, &numFields));
  if (mdepth == 1 && numFields < 2) {
    PetscCall(DMPlexVecGetClosure_Depth1_Static(dm, section, v, point, csize, values));
    PetscFunctionReturn(PETSC_SUCCESS);
  }
  /* Get points */
  PetscCall(DMPlexGetCompressedClosure(dm, section, point, 0, &numPoints, &points, &clSection, &clPoints, &clp));
  for (clsize = 0, p = 0; p < Np; p++) {
    PetscInt dof;
    PetscCall(PetscSectionGetDof(section, points[2 * p], &dof));
    clsize += dof;
  }
  PetscCall(PetscSectionGetClosureInversePermutation_Internal(section, (PetscObject)dm, depth, clsize, &perm));
  /* Filter points */
  for (p = 0; p < numPoints * 2; p += 2) {
    PetscInt dep;

    PetscCall(DMLabelGetValue(depthLabel, points[p], &dep));
    if (dep != depth) continue;
    points[Np * 2 + 0] = points[p];
    points[Np * 2 + 1] = points[p + 1];
    ++Np;
  }
  /* Get array */
  if (!values || !*values) {
    PetscInt asize = 0, dof;

    for (p = 0; p < Np * 2; p += 2) {
      PetscCall(PetscSectionGetDof(section, points[p], &dof));
      asize += dof;
    }
    if (!values) {
      PetscCall(DMPlexRestoreCompressedClosure(dm, section, point, &numPoints, &points, &clSection, &clPoints, &clp));
      if (csize) *csize = asize;
      PetscFunctionReturn(PETSC_SUCCESS);
    }
    PetscCall(DMGetWorkArray(dm, asize, MPIU_SCALAR, &array));
  } else {
    array = *values;
  }
  PetscCall(VecGetArrayRead(v, &vArray));
  /* Get values */
  if (numFields > 0) PetscCall(DMPlexVecGetClosure_Fields_Static(dm, section, Np, points, numFields, perm, vArray, &size, array));
  else PetscCall(DMPlexVecGetClosure_Static(dm, section, Np, points, perm, vArray, &size, array));
  /* Cleanup points */
  PetscCall(DMPlexRestoreCompressedClosure(dm, section, point, &numPoints, &points, &clSection, &clPoints, &clp));
  /* Cleanup array */
  PetscCall(VecRestoreArrayRead(v, &vArray));
  if (!*values) {
    if (csize) *csize = size;
    *values = array;
  } else {
    PetscCheck(size <= *csize, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Size of input array %" PetscInt_FMT " < actual size %" PetscInt_FMT, *csize, size);
    *csize = size;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  DMPlexVecRestoreClosure - Restore the array of the values on the closure of 'point' obtained with `DMPlexVecGetClosure()`

  Not collective

  Input Parameters:
+ dm      - The `DM`
. section - The section describing the layout in `v`, or `NULL` to use the default section
. v       - The local vector
. point   - The point in the `DM`
. csize   - The number of values in the closure, or `NULL`
- values  - The array of values

  Level: intermediate

  Note:
  The array values are discarded and not copied back into `v`. In order to copy values back to `v`, use `DMPlexVecSetClosure()`

  Fortran Note:
  The `csize` argument is not present in the Fortran binding since it is internal to the array.

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexVecGetClosure()`, `DMPlexVecSetClosure()`, `DMPlexMatSetClosure()`
@*/
PetscErrorCode DMPlexVecRestoreClosure(DM dm, PetscSection section, Vec v, PetscInt point, PetscInt *csize, PetscScalar *values[])
{
  PetscInt size = 0;

  PetscFunctionBegin;
  /* Should work without recalculating size */
  PetscCall(DMRestoreWorkArray(dm, size, MPIU_SCALAR, (void *)values));
  *values = NULL;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static inline void add(PetscScalar *x, PetscScalar y)
{
  *x += y;
}
static inline void insert(PetscScalar *x, PetscScalar y)
{
  *x = y;
}

static inline PetscErrorCode updatePoint_private(PetscSection section, PetscInt point, PetscInt dof, void (*fuse)(PetscScalar *, PetscScalar), PetscBool setBC, const PetscInt perm[], const PetscScalar flip[], const PetscInt clperm[], const PetscScalar values[], PetscInt offset, PetscScalar array[])
{
  PetscInt        cdof;  /* The number of constraints on this point */
  const PetscInt *cdofs; /* The indices of the constrained dofs on this point */
  PetscScalar    *a;
  PetscInt        off, cind = 0, k;

  PetscFunctionBegin;
  PetscCall(PetscSectionGetConstraintDof(section, point, &cdof));
  PetscCall(PetscSectionGetOffset(section, point, &off));
  a = &array[off];
  if (!cdof || setBC) {
    if (clperm) {
      if (perm) {
        for (k = 0; k < dof; ++k) fuse(&a[k], values[clperm[offset + perm[k]]] * (flip ? flip[perm[k]] : 1.));
      } else {
        for (k = 0; k < dof; ++k) fuse(&a[k], values[clperm[offset + k]] * (flip ? flip[k] : 1.));
      }
    } else {
      if (perm) {
        for (k = 0; k < dof; ++k) fuse(&a[k], values[offset + perm[k]] * (flip ? flip[perm[k]] : 1.));
      } else {
        for (k = 0; k < dof; ++k) fuse(&a[k], values[offset + k] * (flip ? flip[k] : 1.));
      }
    }
  } else {
    PetscCall(PetscSectionGetConstraintIndices(section, point, &cdofs));
    if (clperm) {
      if (perm) {
        for (k = 0; k < dof; ++k) {
          if ((cind < cdof) && (k == cdofs[cind])) {
            ++cind;
            continue;
          }
          fuse(&a[k], values[clperm[offset + perm[k]]] * (flip ? flip[perm[k]] : 1.));
        }
      } else {
        for (k = 0; k < dof; ++k) {
          if ((cind < cdof) && (k == cdofs[cind])) {
            ++cind;
            continue;
          }
          fuse(&a[k], values[clperm[offset + k]] * (flip ? flip[k] : 1.));
        }
      }
    } else {
      if (perm) {
        for (k = 0; k < dof; ++k) {
          if ((cind < cdof) && (k == cdofs[cind])) {
            ++cind;
            continue;
          }
          fuse(&a[k], values[offset + perm[k]] * (flip ? flip[perm[k]] : 1.));
        }
      } else {
        for (k = 0; k < dof; ++k) {
          if ((cind < cdof) && (k == cdofs[cind])) {
            ++cind;
            continue;
          }
          fuse(&a[k], values[offset + k] * (flip ? flip[k] : 1.));
        }
      }
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static inline PetscErrorCode updatePointBC_private(PetscSection section, PetscInt point, PetscInt dof, void (*fuse)(PetscScalar *, PetscScalar), const PetscInt perm[], const PetscScalar flip[], const PetscInt clperm[], const PetscScalar values[], PetscInt offset, PetscScalar array[])
{
  PetscInt        cdof;  /* The number of constraints on this point */
  const PetscInt *cdofs; /* The indices of the constrained dofs on this point */
  PetscScalar    *a;
  PetscInt        off, cind = 0, k;

  PetscFunctionBegin;
  PetscCall(PetscSectionGetConstraintDof(section, point, &cdof));
  PetscCall(PetscSectionGetOffset(section, point, &off));
  a = &array[off];
  if (cdof) {
    PetscCall(PetscSectionGetConstraintIndices(section, point, &cdofs));
    if (clperm) {
      if (perm) {
        for (k = 0; k < dof; ++k) {
          if ((cind < cdof) && (k == cdofs[cind])) {
            fuse(&a[k], values[clperm[offset + perm[k]]] * (flip ? flip[perm[k]] : 1.));
            cind++;
          }
        }
      } else {
        for (k = 0; k < dof; ++k) {
          if ((cind < cdof) && (k == cdofs[cind])) {
            fuse(&a[k], values[clperm[offset + k]] * (flip ? flip[k] : 1.));
            cind++;
          }
        }
      }
    } else {
      if (perm) {
        for (k = 0; k < dof; ++k) {
          if ((cind < cdof) && (k == cdofs[cind])) {
            fuse(&a[k], values[offset + perm[k]] * (flip ? flip[perm[k]] : 1.));
            cind++;
          }
        }
      } else {
        for (k = 0; k < dof; ++k) {
          if ((cind < cdof) && (k == cdofs[cind])) {
            fuse(&a[k], values[offset + k] * (flip ? flip[k] : 1.));
            cind++;
          }
        }
      }
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static inline PetscErrorCode updatePointFields_private(PetscSection section, PetscInt point, const PetscInt *perm, const PetscScalar *flip, PetscInt f, void (*fuse)(PetscScalar *, PetscScalar), PetscBool setBC, const PetscInt clperm[], const PetscScalar values[], PetscInt *offset, PetscScalar array[])
{
  PetscScalar    *a;
  PetscInt        fdof, foff, fcdof, foffset = *offset;
  const PetscInt *fcdofs; /* The indices of the constrained dofs for field f on this point */
  PetscInt        cind = 0, b;

  PetscFunctionBegin;
  PetscCall(PetscSectionGetFieldDof(section, point, f, &fdof));
  PetscCall(PetscSectionGetFieldConstraintDof(section, point, f, &fcdof));
  PetscCall(PetscSectionGetFieldOffset(section, point, f, &foff));
  a = &array[foff];
  if (!fcdof || setBC) {
    if (clperm) {
      if (perm) {
        for (b = 0; b < fdof; b++) fuse(&a[b], values[clperm[foffset + perm[b]]] * (flip ? flip[perm[b]] : 1.));
      } else {
        for (b = 0; b < fdof; b++) fuse(&a[b], values[clperm[foffset + b]] * (flip ? flip[b] : 1.));
      }
    } else {
      if (perm) {
        for (b = 0; b < fdof; b++) fuse(&a[b], values[foffset + perm[b]] * (flip ? flip[perm[b]] : 1.));
      } else {
        for (b = 0; b < fdof; b++) fuse(&a[b], values[foffset + b] * (flip ? flip[b] : 1.));
      }
    }
  } else {
    PetscCall(PetscSectionGetFieldConstraintIndices(section, point, f, &fcdofs));
    if (clperm) {
      if (perm) {
        for (b = 0; b < fdof; b++) {
          if ((cind < fcdof) && (b == fcdofs[cind])) {
            ++cind;
            continue;
          }
          fuse(&a[b], values[clperm[foffset + perm[b]]] * (flip ? flip[perm[b]] : 1.));
        }
      } else {
        for (b = 0; b < fdof; b++) {
          if ((cind < fcdof) && (b == fcdofs[cind])) {
            ++cind;
            continue;
          }
          fuse(&a[b], values[clperm[foffset + b]] * (flip ? flip[b] : 1.));
        }
      }
    } else {
      if (perm) {
        for (b = 0; b < fdof; b++) {
          if ((cind < fcdof) && (b == fcdofs[cind])) {
            ++cind;
            continue;
          }
          fuse(&a[b], values[foffset + perm[b]] * (flip ? flip[perm[b]] : 1.));
        }
      } else {
        for (b = 0; b < fdof; b++) {
          if ((cind < fcdof) && (b == fcdofs[cind])) {
            ++cind;
            continue;
          }
          fuse(&a[b], values[foffset + b] * (flip ? flip[b] : 1.));
        }
      }
    }
  }
  *offset += fdof;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static inline PetscErrorCode updatePointFieldsBC_private(PetscSection section, PetscInt point, const PetscInt perm[], const PetscScalar flip[], PetscInt f, PetscInt Ncc, const PetscInt comps[], void (*fuse)(PetscScalar *, PetscScalar), const PetscInt clperm[], const PetscScalar values[], PetscInt *offset, PetscScalar array[])
{
  PetscScalar    *a;
  PetscInt        fdof, foff, fcdof, foffset = *offset;
  const PetscInt *fcdofs; /* The indices of the constrained dofs for field f on this point */
  PetscInt        Nc, cind = 0, ncind = 0, b;
  PetscBool       ncSet, fcSet;

  PetscFunctionBegin;
  PetscCall(PetscSectionGetFieldComponents(section, f, &Nc));
  PetscCall(PetscSectionGetFieldDof(section, point, f, &fdof));
  PetscCall(PetscSectionGetFieldConstraintDof(section, point, f, &fcdof));
  PetscCall(PetscSectionGetFieldOffset(section, point, f, &foff));
  a = &array[foff];
  if (fcdof) {
    /* We just override fcdof and fcdofs with Ncc and comps */
    PetscCall(PetscSectionGetFieldConstraintIndices(section, point, f, &fcdofs));
    if (clperm) {
      if (perm) {
        if (comps) {
          for (b = 0; b < fdof; b++) {
            ncSet = fcSet = PETSC_FALSE;
            if (b % Nc == comps[ncind]) {
              ncind = (ncind + 1) % Ncc;
              ncSet = PETSC_TRUE;
            }
            if ((cind < fcdof) && (b == fcdofs[cind])) {
              ++cind;
              fcSet = PETSC_TRUE;
            }
            if (ncSet && fcSet) fuse(&a[b], values[clperm[foffset + perm[b]]] * (flip ? flip[perm[b]] : 1.));
          }
        } else {
          for (b = 0; b < fdof; b++) {
            if ((cind < fcdof) && (b == fcdofs[cind])) {
              fuse(&a[b], values[clperm[foffset + perm[b]]] * (flip ? flip[perm[b]] : 1.));
              ++cind;
            }
          }
        }
      } else {
        if (comps) {
          for (b = 0; b < fdof; b++) {
            ncSet = fcSet = PETSC_FALSE;
            if (b % Nc == comps[ncind]) {
              ncind = (ncind + 1) % Ncc;
              ncSet = PETSC_TRUE;
            }
            if ((cind < fcdof) && (b == fcdofs[cind])) {
              ++cind;
              fcSet = PETSC_TRUE;
            }
            if (ncSet && fcSet) fuse(&a[b], values[clperm[foffset + b]] * (flip ? flip[b] : 1.));
          }
        } else {
          for (b = 0; b < fdof; b++) {
            if ((cind < fcdof) && (b == fcdofs[cind])) {
              fuse(&a[b], values[clperm[foffset + b]] * (flip ? flip[b] : 1.));
              ++cind;
            }
          }
        }
      }
    } else {
      if (perm) {
        if (comps) {
          for (b = 0; b < fdof; b++) {
            ncSet = fcSet = PETSC_FALSE;
            if (b % Nc == comps[ncind]) {
              ncind = (ncind + 1) % Ncc;
              ncSet = PETSC_TRUE;
            }
            if ((cind < fcdof) && (b == fcdofs[cind])) {
              ++cind;
              fcSet = PETSC_TRUE;
            }
            if (ncSet && fcSet) fuse(&a[b], values[foffset + perm[b]] * (flip ? flip[perm[b]] : 1.));
          }
        } else {
          for (b = 0; b < fdof; b++) {
            if ((cind < fcdof) && (b == fcdofs[cind])) {
              fuse(&a[b], values[foffset + perm[b]] * (flip ? flip[perm[b]] : 1.));
              ++cind;
            }
          }
        }
      } else {
        if (comps) {
          for (b = 0; b < fdof; b++) {
            ncSet = fcSet = PETSC_FALSE;
            if (b % Nc == comps[ncind]) {
              ncind = (ncind + 1) % Ncc;
              ncSet = PETSC_TRUE;
            }
            if ((cind < fcdof) && (b == fcdofs[cind])) {
              ++cind;
              fcSet = PETSC_TRUE;
            }
            if (ncSet && fcSet) fuse(&a[b], values[foffset + b] * (flip ? flip[b] : 1.));
          }
        } else {
          for (b = 0; b < fdof; b++) {
            if ((cind < fcdof) && (b == fcdofs[cind])) {
              fuse(&a[b], values[foffset + b] * (flip ? flip[b] : 1.));
              ++cind;
            }
          }
        }
      }
    }
  }
  *offset += fdof;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static inline PetscErrorCode DMPlexVecSetClosure_Depth1_Static(DM dm, PetscSection section, Vec v, PetscInt point, const PetscScalar values[], InsertMode mode)
{
  PetscScalar    *array;
  const PetscInt *cone, *coneO;
  PetscInt        pStart, pEnd, p, numPoints, off, dof;

  PetscFunctionBeginHot;
  PetscCall(PetscSectionGetChart(section, &pStart, &pEnd));
  PetscCall(DMPlexGetConeSize(dm, point, &numPoints));
  PetscCall(DMPlexGetCone(dm, point, &cone));
  PetscCall(DMPlexGetConeOrientation(dm, point, &coneO));
  PetscCall(VecGetArray(v, &array));
  for (p = 0, off = 0; p <= numPoints; ++p, off += dof) {
    const PetscInt cp = !p ? point : cone[p - 1];
    const PetscInt o  = !p ? 0 : coneO[p - 1];

    if ((cp < pStart) || (cp >= pEnd)) {
      dof = 0;
      continue;
    }
    PetscCall(PetscSectionGetDof(section, cp, &dof));
    /* ADD_VALUES */
    {
      const PetscInt *cdofs; /* The indices of the constrained dofs on this point */
      PetscScalar    *a;
      PetscInt        cdof, coff, cind = 0, k;

      PetscCall(PetscSectionGetConstraintDof(section, cp, &cdof));
      PetscCall(PetscSectionGetOffset(section, cp, &coff));
      a = &array[coff];
      if (!cdof) {
        if (o >= 0) {
          for (k = 0; k < dof; ++k) a[k] += values[off + k];
        } else {
          for (k = 0; k < dof; ++k) a[k] += values[off + dof - k - 1];
        }
      } else {
        PetscCall(PetscSectionGetConstraintIndices(section, cp, &cdofs));
        if (o >= 0) {
          for (k = 0; k < dof; ++k) {
            if ((cind < cdof) && (k == cdofs[cind])) {
              ++cind;
              continue;
            }
            a[k] += values[off + k];
          }
        } else {
          for (k = 0; k < dof; ++k) {
            if ((cind < cdof) && (k == cdofs[cind])) {
              ++cind;
              continue;
            }
            a[k] += values[off + dof - k - 1];
          }
        }
      }
    }
  }
  PetscCall(VecRestoreArray(v, &array));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  DMPlexVecSetClosure - Set an array of the values on the closure of `point`

  Not collective

  Input Parameters:
+ dm      - The `DM`
. section - The section describing the layout in `v`, or `NULL` to use the default section
. v       - The local vector
. point   - The point in the `DM`
. values  - The array of values
- mode    - The insert mode. One of `INSERT_ALL_VALUES`, `ADD_ALL_VALUES`, `INSERT_VALUES`, `ADD_VALUES`, `INSERT_BC_VALUES`, and `ADD_BC_VALUES`,
            where `INSERT_ALL_VALUES` and `ADD_ALL_VALUES` also overwrite boundary conditions.

  Level: intermediate

  Note:
  Usually the input arrays were obtained with `DMPlexVecGetClosure()`

  Fortran Note:
  `values` must be declared with
.vb
  PetscScalar,dimension(:),pointer   :: values
.ve

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexVecGetClosure()`, `DMPlexMatSetClosure()`
@*/
PetscErrorCode DMPlexVecSetClosure(DM dm, PetscSection section, Vec v, PetscInt point, const PetscScalar values[], InsertMode mode)
{
  PetscSection    clSection;
  IS              clPoints;
  PetscScalar    *array;
  PetscInt       *points = NULL;
  const PetscInt *clp, *clperm = NULL;
  PetscInt        depth, numFields, numPoints, p, clsize;

  PetscFunctionBeginHot;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (!section) PetscCall(DMGetLocalSection(dm, &section));
  PetscValidHeaderSpecific(section, PETSC_SECTION_CLASSID, 2);
  PetscValidHeaderSpecific(v, VEC_CLASSID, 3);
  PetscCall(DMPlexGetDepth(dm, &depth));
  PetscCall(PetscSectionGetNumFields(section, &numFields));
  if (depth == 1 && numFields < 2 && mode == ADD_VALUES) {
    PetscCall(DMPlexVecSetClosure_Depth1_Static(dm, section, v, point, values, mode));
    PetscFunctionReturn(PETSC_SUCCESS);
  }
  /* Get points */
  PetscCall(DMPlexGetCompressedClosure(dm, section, point, 0, &numPoints, &points, &clSection, &clPoints, &clp));
  for (clsize = 0, p = 0; p < numPoints; p++) {
    PetscInt dof;
    PetscCall(PetscSectionGetDof(section, points[2 * p], &dof));
    clsize += dof;
  }
  PetscCall(PetscSectionGetClosureInversePermutation_Internal(section, (PetscObject)dm, depth, clsize, &clperm));
  /* Get array */
  PetscCall(VecGetArray(v, &array));
  /* Get values */
  if (numFields > 0) {
    PetscInt offset = 0, f;
    for (f = 0; f < numFields; ++f) {
      const PetscInt    **perms = NULL;
      const PetscScalar **flips = NULL;

      PetscCall(PetscSectionGetFieldPointSyms(section, f, numPoints, points, &perms, &flips));
      switch (mode) {
      case INSERT_VALUES:
        for (p = 0; p < numPoints; p++) {
          const PetscInt     point = points[2 * p];
          const PetscInt    *perm  = perms ? perms[p] : NULL;
          const PetscScalar *flip  = flips ? flips[p] : NULL;
          PetscCall(updatePointFields_private(section, point, perm, flip, f, insert, PETSC_FALSE, clperm, values, &offset, array));
        }
        break;
      case INSERT_ALL_VALUES:
        for (p = 0; p < numPoints; p++) {
          const PetscInt     point = points[2 * p];
          const PetscInt    *perm  = perms ? perms[p] : NULL;
          const PetscScalar *flip  = flips ? flips[p] : NULL;
          PetscCall(updatePointFields_private(section, point, perm, flip, f, insert, PETSC_TRUE, clperm, values, &offset, array));
        }
        break;
      case INSERT_BC_VALUES:
        for (p = 0; p < numPoints; p++) {
          const PetscInt     point = points[2 * p];
          const PetscInt    *perm  = perms ? perms[p] : NULL;
          const PetscScalar *flip  = flips ? flips[p] : NULL;
          PetscCall(updatePointFieldsBC_private(section, point, perm, flip, f, -1, NULL, insert, clperm, values, &offset, array));
        }
        break;
      case ADD_VALUES:
        for (p = 0; p < numPoints; p++) {
          const PetscInt     point = points[2 * p];
          const PetscInt    *perm  = perms ? perms[p] : NULL;
          const PetscScalar *flip  = flips ? flips[p] : NULL;
          PetscCall(updatePointFields_private(section, point, perm, flip, f, add, PETSC_FALSE, clperm, values, &offset, array));
        }
        break;
      case ADD_ALL_VALUES:
        for (p = 0; p < numPoints; p++) {
          const PetscInt     point = points[2 * p];
          const PetscInt    *perm  = perms ? perms[p] : NULL;
          const PetscScalar *flip  = flips ? flips[p] : NULL;
          PetscCall(updatePointFields_private(section, point, perm, flip, f, add, PETSC_TRUE, clperm, values, &offset, array));
        }
        break;
      case ADD_BC_VALUES:
        for (p = 0; p < numPoints; p++) {
          const PetscInt     point = points[2 * p];
          const PetscInt    *perm  = perms ? perms[p] : NULL;
          const PetscScalar *flip  = flips ? flips[p] : NULL;
          PetscCall(updatePointFieldsBC_private(section, point, perm, flip, f, -1, NULL, add, clperm, values, &offset, array));
        }
        break;
      default:
        SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "Invalid insert mode %d", mode);
      }
      PetscCall(PetscSectionRestoreFieldPointSyms(section, f, numPoints, points, &perms, &flips));
    }
  } else {
    PetscInt            dof, off;
    const PetscInt    **perms = NULL;
    const PetscScalar **flips = NULL;

    PetscCall(PetscSectionGetPointSyms(section, numPoints, points, &perms, &flips));
    switch (mode) {
    case INSERT_VALUES:
      for (p = 0, off = 0; p < numPoints; p++, off += dof) {
        const PetscInt     point = points[2 * p];
        const PetscInt    *perm  = perms ? perms[p] : NULL;
        const PetscScalar *flip  = flips ? flips[p] : NULL;
        PetscCall(PetscSectionGetDof(section, point, &dof));
        PetscCall(updatePoint_private(section, point, dof, insert, PETSC_FALSE, perm, flip, clperm, values, off, array));
      }
      break;
    case INSERT_ALL_VALUES:
      for (p = 0, off = 0; p < numPoints; p++, off += dof) {
        const PetscInt     point = points[2 * p];
        const PetscInt    *perm  = perms ? perms[p] : NULL;
        const PetscScalar *flip  = flips ? flips[p] : NULL;
        PetscCall(PetscSectionGetDof(section, point, &dof));
        PetscCall(updatePoint_private(section, point, dof, insert, PETSC_TRUE, perm, flip, clperm, values, off, array));
      }
      break;
    case INSERT_BC_VALUES:
      for (p = 0, off = 0; p < numPoints; p++, off += dof) {
        const PetscInt     point = points[2 * p];
        const PetscInt    *perm  = perms ? perms[p] : NULL;
        const PetscScalar *flip  = flips ? flips[p] : NULL;
        PetscCall(PetscSectionGetDof(section, point, &dof));
        PetscCall(updatePointBC_private(section, point, dof, insert, perm, flip, clperm, values, off, array));
      }
      break;
    case ADD_VALUES:
      for (p = 0, off = 0; p < numPoints; p++, off += dof) {
        const PetscInt     point = points[2 * p];
        const PetscInt    *perm  = perms ? perms[p] : NULL;
        const PetscScalar *flip  = flips ? flips[p] : NULL;
        PetscCall(PetscSectionGetDof(section, point, &dof));
        PetscCall(updatePoint_private(section, point, dof, add, PETSC_FALSE, perm, flip, clperm, values, off, array));
      }
      break;
    case ADD_ALL_VALUES:
      for (p = 0, off = 0; p < numPoints; p++, off += dof) {
        const PetscInt     point = points[2 * p];
        const PetscInt    *perm  = perms ? perms[p] : NULL;
        const PetscScalar *flip  = flips ? flips[p] : NULL;
        PetscCall(PetscSectionGetDof(section, point, &dof));
        PetscCall(updatePoint_private(section, point, dof, add, PETSC_TRUE, perm, flip, clperm, values, off, array));
      }
      break;
    case ADD_BC_VALUES:
      for (p = 0, off = 0; p < numPoints; p++, off += dof) {
        const PetscInt     point = points[2 * p];
        const PetscInt    *perm  = perms ? perms[p] : NULL;
        const PetscScalar *flip  = flips ? flips[p] : NULL;
        PetscCall(PetscSectionGetDof(section, point, &dof));
        PetscCall(updatePointBC_private(section, point, dof, add, perm, flip, clperm, values, off, array));
      }
      break;
    default:
      SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "Invalid insert mode %d", mode);
    }
    PetscCall(PetscSectionRestorePointSyms(section, numPoints, points, &perms, &flips));
  }
  /* Cleanup points */
  PetscCall(DMPlexRestoreCompressedClosure(dm, section, point, &numPoints, &points, &clSection, &clPoints, &clp));
  /* Cleanup array */
  PetscCall(VecRestoreArray(v, &array));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* Check whether the given point is in the label. If not, update the offset to skip this point */
static inline PetscErrorCode CheckPoint_Private(DMLabel label, PetscInt labelId, PetscSection section, PetscInt point, PetscInt f, PetscInt *offset, PetscBool *contains)
{
  PetscFunctionBegin;
  *contains = PETSC_TRUE;
  if (label) {
    PetscInt fdof;

    PetscCall(DMLabelStratumHasPoint(label, labelId, point, contains));
    if (!*contains) {
      PetscCall(PetscSectionGetFieldDof(section, point, f, &fdof));
      *offset += fdof;
      PetscFunctionReturn(PETSC_SUCCESS);
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* Unlike DMPlexVecSetClosure(), this uses plex-native closure permutation, not a user-specified permutation such as DMPlexSetClosurePermutationTensor(). */
PetscErrorCode DMPlexVecSetFieldClosure_Internal(DM dm, PetscSection section, Vec v, PetscBool fieldActive[], PetscInt point, PetscInt Ncc, const PetscInt comps[], DMLabel label, PetscInt labelId, const PetscScalar values[], InsertMode mode)
{
  PetscSection    clSection;
  IS              clPoints;
  PetscScalar    *array;
  PetscInt       *points = NULL;
  const PetscInt *clp;
  PetscInt        numFields, numPoints, p;
  PetscInt        offset = 0, f;

  PetscFunctionBeginHot;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (!section) PetscCall(DMGetLocalSection(dm, &section));
  PetscValidHeaderSpecific(section, PETSC_SECTION_CLASSID, 2);
  PetscValidHeaderSpecific(v, VEC_CLASSID, 3);
  PetscCall(PetscSectionGetNumFields(section, &numFields));
  /* Get points */
  PetscCall(DMPlexGetCompressedClosure(dm, section, point, 0, &numPoints, &points, &clSection, &clPoints, &clp));
  /* Get array */
  PetscCall(VecGetArray(v, &array));
  /* Get values */
  for (f = 0; f < numFields; ++f) {
    const PetscInt    **perms = NULL;
    const PetscScalar **flips = NULL;
    PetscBool           contains;

    if (!fieldActive[f]) {
      for (p = 0; p < numPoints * 2; p += 2) {
        PetscInt fdof;
        PetscCall(PetscSectionGetFieldDof(section, points[p], f, &fdof));
        offset += fdof;
      }
      continue;
    }
    PetscCall(PetscSectionGetFieldPointSyms(section, f, numPoints, points, &perms, &flips));
    switch (mode) {
    case INSERT_VALUES:
      for (p = 0; p < numPoints; p++) {
        const PetscInt     point = points[2 * p];
        const PetscInt    *perm  = perms ? perms[p] : NULL;
        const PetscScalar *flip  = flips ? flips[p] : NULL;
        PetscCall(CheckPoint_Private(label, labelId, section, point, f, &offset, &contains));
        if (!contains) continue;
        PetscCall(updatePointFields_private(section, point, perm, flip, f, insert, PETSC_FALSE, NULL, values, &offset, array));
      }
      break;
    case INSERT_ALL_VALUES:
      for (p = 0; p < numPoints; p++) {
        const PetscInt     point = points[2 * p];
        const PetscInt    *perm  = perms ? perms[p] : NULL;
        const PetscScalar *flip  = flips ? flips[p] : NULL;
        PetscCall(CheckPoint_Private(label, labelId, section, point, f, &offset, &contains));
        if (!contains) continue;
        PetscCall(updatePointFields_private(section, point, perm, flip, f, insert, PETSC_TRUE, NULL, values, &offset, array));
      }
      break;
    case INSERT_BC_VALUES:
      for (p = 0; p < numPoints; p++) {
        const PetscInt     point = points[2 * p];
        const PetscInt    *perm  = perms ? perms[p] : NULL;
        const PetscScalar *flip  = flips ? flips[p] : NULL;
        PetscCall(CheckPoint_Private(label, labelId, section, point, f, &offset, &contains));
        if (!contains) continue;
        PetscCall(updatePointFieldsBC_private(section, point, perm, flip, f, Ncc, comps, insert, NULL, values, &offset, array));
      }
      break;
    case ADD_VALUES:
      for (p = 0; p < numPoints; p++) {
        const PetscInt     point = points[2 * p];
        const PetscInt    *perm  = perms ? perms[p] : NULL;
        const PetscScalar *flip  = flips ? flips[p] : NULL;
        PetscCall(CheckPoint_Private(label, labelId, section, point, f, &offset, &contains));
        if (!contains) continue;
        PetscCall(updatePointFields_private(section, point, perm, flip, f, add, PETSC_FALSE, NULL, values, &offset, array));
      }
      break;
    case ADD_ALL_VALUES:
      for (p = 0; p < numPoints; p++) {
        const PetscInt     point = points[2 * p];
        const PetscInt    *perm  = perms ? perms[p] : NULL;
        const PetscScalar *flip  = flips ? flips[p] : NULL;
        PetscCall(CheckPoint_Private(label, labelId, section, point, f, &offset, &contains));
        if (!contains) continue;
        PetscCall(updatePointFields_private(section, point, perm, flip, f, add, PETSC_TRUE, NULL, values, &offset, array));
      }
      break;
    default:
      SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "Invalid insert mode %d", mode);
    }
    PetscCall(PetscSectionRestoreFieldPointSyms(section, f, numPoints, points, &perms, &flips));
  }
  /* Cleanup points */
  PetscCall(DMPlexRestoreCompressedClosure(dm, section, point, &numPoints, &points, &clSection, &clPoints, &clp));
  /* Cleanup array */
  PetscCall(VecRestoreArray(v, &array));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode DMPlexPrintMatSetValues(PetscViewer viewer, Mat A, PetscInt point, PetscInt numRIndices, const PetscInt rindices[], PetscInt numCIndices, const PetscInt cindices[], const PetscScalar values[])
{
  PetscMPIInt rank;
  PetscInt    i, j;

  PetscFunctionBegin;
  PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)A), &rank));
  PetscCall(PetscViewerASCIIPrintf(viewer, "[%d]mat for point %" PetscInt_FMT "\n", rank, point));
  for (i = 0; i < numRIndices; i++) PetscCall(PetscViewerASCIIPrintf(viewer, "[%d]mat row indices[%" PetscInt_FMT "] = %" PetscInt_FMT "\n", rank, i, rindices[i]));
  for (i = 0; i < numCIndices; i++) PetscCall(PetscViewerASCIIPrintf(viewer, "[%d]mat col indices[%" PetscInt_FMT "] = %" PetscInt_FMT "\n", rank, i, cindices[i]));
  numCIndices = numCIndices ? numCIndices : numRIndices;
  if (!values) PetscFunctionReturn(PETSC_SUCCESS);
  for (i = 0; i < numRIndices; i++) {
    PetscCall(PetscViewerASCIIPrintf(viewer, "[%d]", rank));
    for (j = 0; j < numCIndices; j++) {
#if defined(PETSC_USE_COMPLEX)
      PetscCall(PetscViewerASCIIPrintf(viewer, " (%g,%g)", (double)PetscRealPart(values[i * numCIndices + j]), (double)PetscImaginaryPart(values[i * numCIndices + j])));
#else
      PetscCall(PetscViewerASCIIPrintf(viewer, " %g", (double)values[i * numCIndices + j]));
#endif
    }
    PetscCall(PetscViewerASCIIPrintf(viewer, "\n"));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
  DMPlexGetIndicesPoint_Internal - Add the indices for dofs on a point to an index array

  Input Parameters:
+ section - The section for this data layout
. islocal - Is the section (and thus indices being requested) local or global?
. point   - The point contributing dofs with these indices
. off     - The global offset of this point
. loff    - The local offset of each field
. setBC   - The flag determining whether to include indices of boundary values
. perm    - A permutation of the dofs on this point, or NULL
- indperm - A permutation of the entire indices array, or NULL

  Output Parameter:
. indices - Indices for dofs on this point

  Level: developer

  Note: The indices could be local or global, depending on the value of 'off'.
*/
PetscErrorCode DMPlexGetIndicesPoint_Internal(PetscSection section, PetscBool islocal, PetscInt point, PetscInt off, PetscInt *loff, PetscBool setBC, const PetscInt perm[], const PetscInt indperm[], PetscInt indices[])
{
  PetscInt        dof;   /* The number of unknowns on this point */
  PetscInt        cdof;  /* The number of constraints on this point */
  const PetscInt *cdofs; /* The indices of the constrained dofs on this point */
  PetscInt        cind = 0, k;

  PetscFunctionBegin;
  PetscCheck(islocal || !setBC, PetscObjectComm((PetscObject)section), PETSC_ERR_ARG_INCOMP, "setBC incompatible with global indices; use a local section or disable setBC");
  PetscCall(PetscSectionGetDof(section, point, &dof));
  PetscCall(PetscSectionGetConstraintDof(section, point, &cdof));
  if (!cdof || setBC) {
    for (k = 0; k < dof; ++k) {
      const PetscInt preind = perm ? *loff + perm[k] : *loff + k;
      const PetscInt ind    = indperm ? indperm[preind] : preind;

      indices[ind] = off + k;
    }
  } else {
    PetscCall(PetscSectionGetConstraintIndices(section, point, &cdofs));
    for (k = 0; k < dof; ++k) {
      const PetscInt preind = perm ? *loff + perm[k] : *loff + k;
      const PetscInt ind    = indperm ? indperm[preind] : preind;

      if ((cind < cdof) && (k == cdofs[cind])) {
        /* Insert check for returning constrained indices */
        indices[ind] = -(off + k + 1);
        ++cind;
      } else {
        indices[ind] = off + k - (islocal ? 0 : cind);
      }
    }
  }
  *loff += dof;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
 DMPlexGetIndicesPointFields_Internal - gets section indices for a point in its canonical ordering.

 Input Parameters:
+ section - a section (global or local)
- islocal - `PETSC_TRUE` if requesting local indices (i.e., section is local); `PETSC_FALSE` for global
. point - point within section
. off - The offset of this point in the (local or global) indexed space - should match islocal and (usually) the section
. foffs - array of length numFields containing the offset in canonical point ordering (the location in indices) of each field
. setBC - identify constrained (boundary condition) points via involution.
. perms - perms[f][permsoff][:] is a permutation of dofs within each field
. permsoff - offset
- indperm - index permutation

 Output Parameter:
. foffs - each entry is incremented by the number of (unconstrained if setBC=FALSE) dofs in that field
. indices - array to hold indices (as defined by section) of each dof associated with point

 Notes:
 If section is local and setBC=true, there is no distinction between constrained and unconstrained dofs.
 If section is local and setBC=false, the indices for constrained points are the involution -(i+1) of their position
 in the local vector.

 If section is global and setBC=false, the indices for constrained points are negative (and their value is not
 significant).  It is invalid to call with a global section and setBC=true.

 Developer Note:
 The section is only used for field layout, so islocal is technically a statement about the offset (off).  At some point
 in the future, global sections may have fields set, in which case we could pass the global section and obtain the
 offset could be obtained from the section instead of passing it explicitly as we do now.

 Example:
 Suppose a point contains one field with three components, and for which the unconstrained indices are {10, 11, 12}.
 When the middle component is constrained, we get the array {10, -12, 12} for (islocal=TRUE, setBC=FALSE).
 Note that -12 is the involution of 11, so the user can involute negative indices to recover local indices.
 The global vector does not store constrained dofs, so when this function returns global indices, say {110, -112, 111}, the value of -112 is an arbitrary flag that should not be interpreted beyond its sign.

 Level: developer
*/
PetscErrorCode DMPlexGetIndicesPointFields_Internal(PetscSection section, PetscBool islocal, PetscInt point, PetscInt off, PetscInt foffs[], PetscBool setBC, const PetscInt ***perms, PetscInt permsoff, const PetscInt indperm[], PetscInt indices[])
{
  PetscInt numFields, foff, f;

  PetscFunctionBegin;
  PetscCheck(islocal || !setBC, PetscObjectComm((PetscObject)section), PETSC_ERR_ARG_INCOMP, "setBC incompatible with global indices; use a local section or disable setBC");
  PetscCall(PetscSectionGetNumFields(section, &numFields));
  for (f = 0, foff = 0; f < numFields; ++f) {
    PetscInt        fdof, cfdof;
    const PetscInt *fcdofs; /* The indices of the constrained dofs for field f on this point */
    PetscInt        cind = 0, b;
    const PetscInt *perm = (perms && perms[f]) ? perms[f][permsoff] : NULL;

    PetscCall(PetscSectionGetFieldDof(section, point, f, &fdof));
    PetscCall(PetscSectionGetFieldConstraintDof(section, point, f, &cfdof));
    if (!cfdof || setBC) {
      for (b = 0; b < fdof; ++b) {
        const PetscInt preind = perm ? foffs[f] + perm[b] : foffs[f] + b;
        const PetscInt ind    = indperm ? indperm[preind] : preind;

        indices[ind] = off + foff + b;
      }
    } else {
      PetscCall(PetscSectionGetFieldConstraintIndices(section, point, f, &fcdofs));
      for (b = 0; b < fdof; ++b) {
        const PetscInt preind = perm ? foffs[f] + perm[b] : foffs[f] + b;
        const PetscInt ind    = indperm ? indperm[preind] : preind;

        if ((cind < cfdof) && (b == fcdofs[cind])) {
          indices[ind] = -(off + foff + b + 1);
          ++cind;
        } else {
          indices[ind] = off + foff + b - (islocal ? 0 : cind);
        }
      }
    }
    foff += (setBC || islocal ? fdof : (fdof - cfdof));
    foffs[f] += fdof;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
  This version believes the globalSection offsets for each field, rather than just the point offset

 . foffs - The offset into 'indices' for each field, since it is segregated by field

 Notes:
 The semantics of this function relate to that of setBC=FALSE in DMPlexGetIndicesPointFields_Internal.
 Since this function uses global indices, setBC=TRUE would be invalid, so no such argument exists.
*/
static PetscErrorCode DMPlexGetIndicesPointFieldsSplit_Internal(PetscSection section, PetscSection globalSection, PetscInt point, PetscInt foffs[], const PetscInt ***perms, PetscInt permsoff, const PetscInt indperm[], PetscInt indices[])
{
  PetscInt numFields, foff, f;

  PetscFunctionBegin;
  PetscCall(PetscSectionGetNumFields(section, &numFields));
  for (f = 0; f < numFields; ++f) {
    PetscInt        fdof, cfdof;
    const PetscInt *fcdofs; /* The indices of the constrained dofs for field f on this point */
    PetscInt        cind = 0, b;
    const PetscInt *perm = (perms && perms[f]) ? perms[f][permsoff] : NULL;

    PetscCall(PetscSectionGetFieldDof(section, point, f, &fdof));
    PetscCall(PetscSectionGetFieldConstraintDof(section, point, f, &cfdof));
    PetscCall(PetscSectionGetFieldOffset(globalSection, point, f, &foff));
    if (!cfdof) {
      for (b = 0; b < fdof; ++b) {
        const PetscInt preind = perm ? foffs[f] + perm[b] : foffs[f] + b;
        const PetscInt ind    = indperm ? indperm[preind] : preind;

        indices[ind] = foff + b;
      }
    } else {
      PetscCall(PetscSectionGetFieldConstraintIndices(section, point, f, &fcdofs));
      for (b = 0; b < fdof; ++b) {
        const PetscInt preind = perm ? foffs[f] + perm[b] : foffs[f] + b;
        const PetscInt ind    = indperm ? indperm[preind] : preind;

        if ((cind < cfdof) && (b == fcdofs[cind])) {
          indices[ind] = -(foff + b + 1);
          ++cind;
        } else {
          indices[ind] = foff + b - cind;
        }
      }
    }
    foffs[f] += fdof;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode DMPlexAnchorsGetSubMatIndices(PetscInt nPoints, const PetscInt pnts[], PetscSection section, PetscSection cSec, PetscInt tmpIndices[], PetscInt fieldOffsets[], PetscInt indices[], const PetscInt ***perms)
{
  PetscInt numFields, sStart, sEnd, cStart, cEnd;

  PetscFunctionBegin;
  PetscCall(PetscSectionGetNumFields(section, &numFields));
  PetscCall(PetscSectionGetChart(section, &sStart, &sEnd));
  PetscCall(PetscSectionGetChart(cSec, &cStart, &cEnd));
  for (PetscInt p = 0; p < nPoints; p++) {
    PetscInt     b       = pnts[2 * p];
    PetscInt     bSecDof = 0, bOff;
    PetscInt     cSecDof = 0;
    PetscSection indices_section;

    if (b >= sStart && b < sEnd) PetscCall(PetscSectionGetDof(section, b, &bSecDof));
    if (!bSecDof) continue;
    if (b >= cStart && b < cEnd) PetscCall(PetscSectionGetDof(cSec, b, &cSecDof));
    indices_section = cSecDof > 0 ? cSec : section;
    if (numFields) {
      PetscInt fStart[32], fEnd[32];

      fStart[0] = 0;
      fEnd[0]   = 0;
      for (PetscInt f = 0; f < numFields; f++) {
        PetscInt fDof = 0;

        PetscCall(PetscSectionGetFieldDof(indices_section, b, f, &fDof));
        fStart[f + 1] = fStart[f] + fDof;
        fEnd[f + 1]   = fStart[f + 1];
      }
      PetscCall(PetscSectionGetOffset(indices_section, b, &bOff));
      // only apply permutations on one side
      PetscCall(DMPlexGetIndicesPointFields_Internal(indices_section, PETSC_TRUE, b, bOff, fEnd, PETSC_TRUE, perms, perms ? p : -1, NULL, tmpIndices));
      for (PetscInt f = 0; f < numFields; f++) {
        for (PetscInt i = fStart[f]; i < fEnd[f]; i++) { indices[fieldOffsets[f]++] = (cSecDof > 0) ? tmpIndices[i] : -(tmpIndices[i] + 1); }
      }
    } else {
      PetscInt bEnd = 0;

      PetscCall(PetscSectionGetOffset(indices_section, b, &bOff));
      PetscCall(DMPlexGetIndicesPoint_Internal(indices_section, PETSC_TRUE, b, bOff, &bEnd, PETSC_TRUE, (perms && perms[0]) ? perms[0][p] : NULL, NULL, tmpIndices));

      for (PetscInt i = 0; i < bEnd; i++) indices[fieldOffsets[0]++] = (cSecDof > 0) ? tmpIndices[i] : -(tmpIndices[i] + 1);
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

PETSC_INTERN PetscErrorCode DMPlexAnchorsGetSubMatModification(DM dm, PetscSection section, PetscInt numPoints, PetscInt numIndices, const PetscInt points[], const PetscInt ***perms, PetscInt *outNumPoints, PetscInt *outNumIndices, PetscInt *outPoints[], PetscInt offsets[], PetscScalar *outMat[])
{
  Mat             cMat;
  PetscSection    aSec, cSec;
  IS              aIS;
  PetscInt        aStart = -1, aEnd = -1;
  PetscInt        sStart = -1, sEnd = -1;
  PetscInt        cStart = -1, cEnd = -1;
  const PetscInt *anchors;
  PetscInt        numFields, p;
  PetscInt        newNumPoints = 0, newNumIndices = 0;
  PetscInt       *newPoints, *indices, *newIndices, *tmpIndices, *tmpNewIndices;
  PetscInt        oldOffsets[32];
  PetscInt        newOffsets[32];
  PetscInt        oldOffsetsCopy[32];
  PetscInt        newOffsetsCopy[32];
  PetscScalar    *modMat         = NULL;
  PetscBool       anyConstrained = PETSC_FALSE;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidHeaderSpecific(section, PETSC_SECTION_CLASSID, 2);
  PetscCall(PetscSectionGetNumFields(section, &numFields));

  PetscCall(DMPlexGetAnchors(dm, &aSec, &aIS));
  /* if there are point-to-point constraints */
  if (aSec) {
    PetscCall(PetscArrayzero(newOffsets, 32));
    PetscCall(PetscArrayzero(oldOffsets, 32));
    PetscCall(ISGetIndices(aIS, &anchors));
    PetscCall(PetscSectionGetChart(aSec, &aStart, &aEnd));
    PetscCall(PetscSectionGetChart(section, &sStart, &sEnd));
    /* figure out how many points are going to be in the new element matrix
     * (we allow double counting, because it's all just going to be summed
     * into the global matrix anyway) */
    for (p = 0; p < 2 * numPoints; p += 2) {
      PetscInt b    = points[p];
      PetscInt bDof = 0, bSecDof = 0;

      if (b >= sStart && b < sEnd) PetscCall(PetscSectionGetDof(section, b, &bSecDof));
      if (!bSecDof) continue;

      for (PetscInt f = 0; f < numFields; f++) {
        PetscInt fDof = 0;

        PetscCall(PetscSectionGetFieldDof(section, b, f, &fDof));
        oldOffsets[f + 1] += fDof;
      }
      if (b >= aStart && b < aEnd) PetscCall(PetscSectionGetDof(aSec, b, &bDof));
      if (bDof) {
        /* this point is constrained */
        /* it is going to be replaced by its anchors */
        PetscInt bOff, q;

        PetscCall(PetscSectionGetOffset(aSec, b, &bOff));
        for (q = 0; q < bDof; q++) {
          PetscInt a    = anchors[bOff + q];
          PetscInt aDof = 0;

          if (a >= sStart && a < sEnd) PetscCall(PetscSectionGetDof(section, a, &aDof));
          if (aDof) {
            anyConstrained = PETSC_TRUE;
            newNumPoints += 1;
          }
          newNumIndices += aDof;
          for (PetscInt f = 0; f < numFields; ++f) {
            PetscInt fDof = 0;

            if (a >= sStart && a < sEnd) PetscCall(PetscSectionGetFieldDof(section, a, f, &fDof));
            newOffsets[f + 1] += fDof;
          }
        }
      } else {
        /* this point is not constrained */
        newNumPoints++;
        newNumIndices += bSecDof;
        for (PetscInt f = 0; f < numFields; ++f) {
          PetscInt fDof;

          PetscCall(PetscSectionGetFieldDof(section, b, f, &fDof));
          newOffsets[f + 1] += fDof;
        }
      }
    }
  }
  if (!anyConstrained) {
    if (outNumPoints) *outNumPoints = 0;
    if (outNumIndices) *outNumIndices = 0;
    if (outPoints) *outPoints = NULL;
    if (outMat) *outMat = NULL;
    if (aSec) PetscCall(ISRestoreIndices(aIS, &anchors));
    PetscFunctionReturn(PETSC_SUCCESS);
  }

  if (outNumPoints) *outNumPoints = newNumPoints;
  if (outNumIndices) *outNumIndices = newNumIndices;

  for (PetscInt f = 0; f < numFields; ++f) newOffsets[f + 1] += newOffsets[f];
  for (PetscInt f = 0; f < numFields; ++f) oldOffsets[f + 1] += oldOffsets[f];

  if (!outPoints && !outMat) {
    if (offsets) {
      for (PetscInt f = 0; f <= numFields; f++) offsets[f] = newOffsets[f];
    }
    if (aSec) PetscCall(ISRestoreIndices(aIS, &anchors));
    PetscFunctionReturn(PETSC_SUCCESS);
  }

  PetscCheck(!numFields || newOffsets[numFields] == newNumIndices, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid size for closure %" PetscInt_FMT " should be %" PetscInt_FMT, newOffsets[numFields], newNumIndices);
  PetscCheck(!numFields || oldOffsets[numFields] == numIndices, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid size for closure %" PetscInt_FMT " should be %" PetscInt_FMT, oldOffsets[numFields], numIndices);

  PetscCall(DMGetDefaultConstraints(dm, &cSec, &cMat, NULL));
  PetscCall(PetscSectionGetChart(cSec, &cStart, &cEnd));

  /* output arrays */
  PetscCall(DMGetWorkArray(dm, 2 * newNumPoints, MPIU_INT, &newPoints));
  PetscCall(PetscArrayzero(newPoints, 2 * newNumPoints));

  // get the new Points
  for (PetscInt p = 0, newP = 0; p < numPoints; p++) {
    PetscInt b    = points[2 * p];
    PetscInt bDof = 0, bSecDof = 0, bOff;

    if (b >= sStart && b < sEnd) PetscCall(PetscSectionGetDof(section, b, &bSecDof));
    if (!bSecDof) continue;
    if (b >= aStart && b < aEnd) PetscCall(PetscSectionGetDof(aSec, b, &bDof));
    if (bDof) {
      PetscCall(PetscSectionGetOffset(aSec, b, &bOff));
      for (PetscInt q = 0; q < bDof; q++) {
        PetscInt a = anchors[bOff + q], aDof = 0;

        if (a >= sStart && a < sEnd) PetscCall(PetscSectionGetDof(section, a, &aDof));
        if (aDof) {
          newPoints[2 * newP]     = a;
          newPoints[2 * newP + 1] = 0; // orientations are accounted for in constructing the matrix, newly added points are in default orientation
          newP++;
        }
      }
    } else {
      newPoints[2 * newP]     = b;
      newPoints[2 * newP + 1] = points[2 * p + 1];
      newP++;
    }
  }

  if (outMat) {
    PetscScalar *tmpMat;
    PetscCall(PetscArraycpy(oldOffsetsCopy, oldOffsets, 32));
    PetscCall(PetscArraycpy(newOffsetsCopy, newOffsets, 32));

    PetscCall(DMGetWorkArray(dm, numIndices, MPIU_INT, &indices));
    PetscCall(DMGetWorkArray(dm, numIndices, MPIU_INT, &tmpIndices));
    PetscCall(DMGetWorkArray(dm, newNumIndices, MPIU_INT, &newIndices));
    PetscCall(DMGetWorkArray(dm, newNumIndices, MPIU_INT, &tmpNewIndices));

    for (PetscInt i = 0; i < numIndices; i++) indices[i] = -1;
    for (PetscInt i = 0; i < newNumIndices; i++) newIndices[i] = -1;

    PetscCall(DMPlexAnchorsGetSubMatIndices(numPoints, points, section, cSec, tmpIndices, oldOffsetsCopy, indices, perms));
    PetscCall(DMPlexAnchorsGetSubMatIndices(newNumPoints, newPoints, section, section, tmpNewIndices, newOffsetsCopy, newIndices, NULL));

    PetscCall(DMGetWorkArray(dm, numIndices * newNumIndices, MPIU_SCALAR, &modMat));
    PetscCall(DMGetWorkArray(dm, numIndices * newNumIndices, MPIU_SCALAR, &tmpMat));
    PetscCall(PetscArrayzero(modMat, newNumIndices * numIndices));
    // for each field, insert the anchor modification into modMat
    for (PetscInt f = 0; f < PetscMax(1, numFields); f++) {
      PetscInt fStart    = oldOffsets[f];
      PetscInt fNewStart = newOffsets[f];
      for (PetscInt p = 0, newP = 0, o = fStart, oNew = fNewStart; p < numPoints; p++) {
        PetscInt b    = points[2 * p];
        PetscInt bDof = 0, bSecDof = 0, bOff;

        if (b >= sStart && b < sEnd) {
          if (numFields) {
            PetscCall(PetscSectionGetFieldDof(section, b, f, &bSecDof));
          } else {
            PetscCall(PetscSectionGetDof(section, b, &bSecDof));
          }
        }
        if (!bSecDof) continue;
        if (b >= aStart && b < aEnd) PetscCall(PetscSectionGetDof(aSec, b, &bDof));
        if (bDof) {
          PetscCall(PetscSectionGetOffset(aSec, b, &bOff));
          for (PetscInt q = 0; q < bDof; q++, newP++) {
            PetscInt a = anchors[bOff + q], aDof = 0;

            if (a >= sStart && a < sEnd) {
              if (numFields) {
                PetscCall(PetscSectionGetFieldDof(section, a, f, &aDof));
              } else {
                PetscCall(PetscSectionGetDof(section, a, &aDof));
              }
            }
            if (aDof) {
              PetscCall(MatGetValues(cMat, bSecDof, &indices[o], aDof, &newIndices[oNew], tmpMat));
              for (PetscInt d = 0; d < bSecDof; d++) {
                for (PetscInt e = 0; e < aDof; e++) modMat[(o + d) * newNumIndices + oNew + e] = tmpMat[d * aDof + e];
              }
            }
            oNew += aDof;
          }
        } else {
          // Insert the identity matrix in this block
          for (PetscInt d = 0; d < bSecDof; d++) modMat[(o + d) * newNumIndices + oNew + d] = 1;
          oNew += bSecDof;
          newP++;
        }
        o += bSecDof;
      }
    }

    *outMat = modMat;

    PetscCall(DMRestoreWorkArray(dm, numIndices * newNumIndices, MPIU_SCALAR, &tmpMat));
    PetscCall(DMRestoreWorkArray(dm, newNumIndices, MPIU_INT, &tmpNewIndices));
    PetscCall(DMRestoreWorkArray(dm, newNumIndices, MPIU_INT, &newIndices));
    PetscCall(DMRestoreWorkArray(dm, numIndices, MPIU_INT, &tmpIndices));
    PetscCall(DMRestoreWorkArray(dm, numIndices, MPIU_INT, &indices));
  }
  PetscCall(ISRestoreIndices(aIS, &anchors));

  /* output */
  if (outPoints) {
    *outPoints = newPoints;
  } else {
    PetscCall(DMRestoreWorkArray(dm, 2 * newNumPoints, MPIU_INT, &newPoints));
  }
  for (PetscInt f = 0; f <= numFields; f++) offsets[f] = newOffsets[f];
  PetscFunctionReturn(PETSC_SUCCESS);
}

PETSC_INTERN PetscErrorCode DMPlexAnchorsModifyMat_Internal(DM dm, PetscSection section, PetscInt numPoints, PetscInt numIndices, const PetscInt points[], const PetscInt ***perms, PetscInt numRows, PetscInt numCols, const PetscScalar values[], PetscInt *outNumPoints, PetscInt *outNumIndices, PetscInt *outPoints[], PetscScalar *outValues[], PetscInt offsets[], PetscBool multiplyRight, PetscBool multiplyLeft)
{
  PetscScalar *modMat        = NULL;
  PetscInt     newNumIndices = -1;

  PetscFunctionBegin;
  /* If M is the matrix represented by values, get the matrix C such that we will add M * C (or, if multiplyLeft, C^T * M * C) into the global matrix.
     modMat is that matrix C */
  PetscCall(DMPlexAnchorsGetSubMatModification(dm, section, numPoints, numIndices, points, perms, outNumPoints, &newNumIndices, outPoints, offsets, outValues ? &modMat : NULL));
  if (outNumIndices) *outNumIndices = newNumIndices;
  if (modMat) {
    const PetscScalar *newValues = values;

    if (multiplyRight) {
      PetscScalar *newNewValues = NULL;
      PetscBLASInt M            = newNumIndices;
      PetscBLASInt N            = numRows;
      PetscBLASInt K            = numIndices;
      PetscScalar  a = 1.0, b = 0.0;

      PetscCheck(numCols == numIndices, PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_SIZ, "values matrix has the wrong number of columns: %" PetscInt_FMT ", expected %" PetscInt_FMT, numCols, numIndices);

      PetscCall(DMGetWorkArray(dm, numRows * newNumIndices, MPIU_SCALAR, &newNewValues));
      // row-major to column-major conversion, right multiplication becomes left multiplication
      PetscCallBLAS("BLASgemm", BLASgemm_("N", "N", &M, &N, &K, &a, modMat, &M, newValues, &K, &b, newNewValues, &M));

      numCols   = newNumIndices;
      newValues = newNewValues;
    }

    if (multiplyLeft) {
      PetscScalar *newNewValues = NULL;
      PetscBLASInt M            = numCols;
      PetscBLASInt N            = newNumIndices;
      PetscBLASInt K            = numIndices;
      PetscScalar  a = 1.0, b = 0.0;

      PetscCheck(numRows == numIndices, PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_SIZ, "values matrix has the wrong number of rows: %" PetscInt_FMT ", expected %" PetscInt_FMT, numRows, numIndices);

      PetscCall(DMGetWorkArray(dm, newNumIndices * numCols, MPIU_SCALAR, &newNewValues));
      // row-major to column-major conversion, left multiplication becomes right multiplication
      PetscCallBLAS("BLASgemm", BLASgemm_("N", "T", &M, &N, &K, &a, newValues, &M, modMat, &N, &b, newNewValues, &M));
      if (newValues != values) PetscCall(DMRestoreWorkArray(dm, numIndices * newNumIndices, MPIU_SCALAR, &newValues));
      newValues = newNewValues;
    }
    *outValues = (PetscScalar *)newValues;
    PetscCall(DMRestoreWorkArray(dm, numIndices * newNumIndices, MPIU_SCALAR, &modMat));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

PETSC_INTERN PetscErrorCode DMPlexAnchorsModifyMat(DM dm, PetscSection section, PetscInt numPoints, PetscInt numIndices, const PetscInt points[], const PetscInt ***perms, const PetscScalar values[], PetscInt *outNumPoints, PetscInt *outNumIndices, PetscInt *outPoints[], PetscScalar *outValues[], PetscInt offsets[], PetscBool multiplyLeft)
{
  PetscFunctionBegin;
  PetscCall(DMPlexAnchorsModifyMat_Internal(dm, section, numPoints, numIndices, points, perms, numIndices, numIndices, values, outNumPoints, outNumIndices, outPoints, outValues, offsets, PETSC_TRUE, multiplyLeft));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode DMPlexGetClosureIndicesSize_Internal(DM dm, PetscSection section, PetscInt point, PetscInt *closureSize)
{
  /* Closure ordering */
  PetscSection    clSection;
  IS              clPoints;
  const PetscInt *clp;
  PetscInt       *points;
  PetscInt        Ncl, Ni = 0;

  PetscFunctionBeginHot;
  PetscCall(DMPlexGetCompressedClosure(dm, section, point, 0, &Ncl, &points, &clSection, &clPoints, &clp));
  for (PetscInt p = 0; p < Ncl * 2; p += 2) {
    PetscInt dof;

    PetscCall(PetscSectionGetDof(section, points[p], &dof));
    Ni += dof;
  }
  PetscCall(DMPlexRestoreCompressedClosure(dm, section, point, &Ncl, &points, &clSection, &clPoints, &clp));
  *closureSize = Ni;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode DMPlexGetClosureIndices_Internal(DM dm, PetscSection section, PetscSection idxSection, PetscInt point, PetscBool useClPerm, PetscInt *numRows, PetscInt *numCols, PetscInt *indices[], PetscInt outOffsets[], PetscScalar *values[], PetscBool multiplyRight, PetscBool multiplyLeft)
{
  /* Closure ordering */
  PetscSection    clSection;
  IS              clPoints;
  const PetscInt *clp;
  PetscInt       *points;
  const PetscInt *clperm = NULL;
  /* Dof permutation and sign flips */
  const PetscInt    **perms[32] = {NULL};
  const PetscScalar **flips[32] = {NULL};
  PetscScalar        *valCopy   = NULL;
  /* Hanging node constraints */
  PetscInt    *pointsC = NULL;
  PetscScalar *valuesC = NULL;
  PetscInt     NclC, NiC;

  PetscInt *idx;
  PetscInt  Nf, Ncl, Ni = 0, offsets[32], p, f;
  PetscBool isLocal = (section == idxSection) ? PETSC_TRUE : PETSC_FALSE;
  PetscInt  idxStart, idxEnd;
  PetscInt  nRows, nCols;

  PetscFunctionBeginHot;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidHeaderSpecific(section, PETSC_SECTION_CLASSID, 2);
  PetscValidHeaderSpecific(idxSection, PETSC_SECTION_CLASSID, 3);
  PetscAssertPointer(numRows, 6);
  PetscAssertPointer(numCols, 7);
  if (indices) PetscAssertPointer(indices, 8);
  if (outOffsets) PetscAssertPointer(outOffsets, 9);
  if (values) PetscAssertPointer(values, 10);
  PetscCall(PetscSectionGetNumFields(section, &Nf));
  PetscCheck(Nf <= 31, PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "Number of fields %" PetscInt_FMT " limited to 31", Nf);
  PetscCall(PetscArrayzero(offsets, 32));
  /* 1) Get points in closure */
  PetscCall(DMPlexGetCompressedClosure(dm, section, point, 0, &Ncl, &points, &clSection, &clPoints, &clp));
  if (useClPerm) {
    PetscInt depth, clsize;
    PetscCall(DMPlexGetPointDepth(dm, point, &depth));
    for (clsize = 0, p = 0; p < Ncl; p++) {
      PetscInt dof;
      PetscCall(PetscSectionGetDof(section, points[2 * p], &dof));
      clsize += dof;
    }
    PetscCall(PetscSectionGetClosureInversePermutation_Internal(section, (PetscObject)dm, depth, clsize, &clperm));
  }
  /* 2) Get number of indices on these points and field offsets from section */
  for (p = 0; p < Ncl * 2; p += 2) {
    PetscInt dof, fdof;

    PetscCall(PetscSectionGetDof(section, points[p], &dof));
    for (f = 0; f < Nf; ++f) {
      PetscCall(PetscSectionGetFieldDof(section, points[p], f, &fdof));
      offsets[f + 1] += fdof;
    }
    Ni += dof;
  }
  if (*numRows == -1) *numRows = Ni;
  if (*numCols == -1) *numCols = Ni;
  nRows = *numRows;
  nCols = *numCols;
  for (f = 1; f < Nf; ++f) offsets[f + 1] += offsets[f];
  PetscCheck(!Nf || offsets[Nf] == Ni, PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Invalid size for closure %" PetscInt_FMT " should be %" PetscInt_FMT, offsets[Nf], Ni);
  /* 3) Get symmetries and sign flips. Apply sign flips to values if passed in (only works for square values matrix) */
  if (multiplyRight) PetscCheck(nCols == Ni, PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_SIZ, "Expected %" PetscInt_FMT " columns, got %" PetscInt_FMT, Ni, nCols);
  if (multiplyLeft) PetscCheck(nRows == Ni, PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_SIZ, "Expected %" PetscInt_FMT " rows, got %" PetscInt_FMT, Ni, nRows);
  for (f = 0; f < PetscMax(1, Nf); ++f) {
    if (Nf) PetscCall(PetscSectionGetFieldPointSyms(section, f, Ncl, points, &perms[f], &flips[f]));
    else PetscCall(PetscSectionGetPointSyms(section, Ncl, points, &perms[f], &flips[f]));
    /* may need to apply sign changes to the element matrix */
    if (values && flips[f]) {
      PetscInt foffset = offsets[f];

      for (p = 0; p < Ncl; ++p) {
        PetscInt           pnt  = points[2 * p], fdof;
        const PetscScalar *flip = flips[f] ? flips[f][p] : NULL;

        if (!Nf) PetscCall(PetscSectionGetDof(section, pnt, &fdof));
        else PetscCall(PetscSectionGetFieldDof(section, pnt, f, &fdof));
        if (flip) {
          PetscInt i, j, k;

          if (!valCopy) {
            PetscCall(DMGetWorkArray(dm, Ni * Ni, MPIU_SCALAR, &valCopy));
            for (j = 0; j < Ni * Ni; ++j) valCopy[j] = (*values)[j];
            *values = valCopy;
          }
          for (i = 0; i < fdof; ++i) {
            PetscScalar fval = flip[i];

            if (multiplyRight) {
              for (k = 0; k < nRows; ++k) { valCopy[Ni * k + (foffset + i)] *= fval; }
            }
            if (multiplyLeft) {
              for (k = 0; k < nCols; ++k) { valCopy[nCols * (foffset + i) + k] *= fval; }
            }
          }
        }
        foffset += fdof;
      }
    }
  }
  /* 4) Apply hanging node constraints. Get new symmetries and replace all storage with constrained storage */
  PetscCall(DMPlexAnchorsModifyMat_Internal(dm, section, Ncl, Ni, points, perms, nRows, nCols, values ? *values : NULL, &NclC, &NiC, &pointsC, values ? &valuesC : NULL, offsets, multiplyRight, multiplyLeft));
  if (NclC) {
    if (multiplyRight) { *numCols = nCols = NiC; }
    if (multiplyLeft) { *numRows = nRows = NiC; }
    if (valCopy) PetscCall(DMRestoreWorkArray(dm, Ni * Ni, MPIU_SCALAR, &valCopy));
    for (f = 0; f < PetscMax(1, Nf); ++f) {
      if (Nf) PetscCall(PetscSectionRestoreFieldPointSyms(section, f, Ncl, points, &perms[f], &flips[f]));
      else PetscCall(PetscSectionRestorePointSyms(section, Ncl, points, &perms[f], &flips[f]));
    }
    for (f = 0; f < PetscMax(1, Nf); ++f) {
      if (Nf) PetscCall(PetscSectionGetFieldPointSyms(section, f, NclC, pointsC, &perms[f], &flips[f]));
      else PetscCall(PetscSectionGetPointSyms(section, NclC, pointsC, &perms[f], &flips[f]));
    }
    PetscCall(DMPlexRestoreCompressedClosure(dm, section, point, &Ncl, &points, &clSection, &clPoints, &clp));
    Ncl    = NclC;
    Ni     = NiC;
    points = pointsC;
    if (values) *values = valuesC;
  }
  /* 5) Calculate indices */
  PetscCall(DMGetWorkArray(dm, Ni, MPIU_INT, &idx));
  PetscCall(PetscSectionGetChart(idxSection, &idxStart, &idxEnd));
  if (Nf) {
    PetscInt  idxOff;
    PetscBool useFieldOffsets;

    if (outOffsets) {
      for (f = 0; f <= Nf; f++) outOffsets[f] = offsets[f];
    }
    PetscCall(PetscSectionGetUseFieldOffsets(idxSection, &useFieldOffsets));
    if (useFieldOffsets) {
      for (p = 0; p < Ncl; ++p) {
        const PetscInt pnt = points[p * 2];

        PetscCall(DMPlexGetIndicesPointFieldsSplit_Internal(section, idxSection, pnt, offsets, perms, p, clperm, idx));
      }
    } else {
      for (p = 0; p < Ncl; ++p) {
        const PetscInt pnt = points[p * 2];

        if (pnt < idxStart || pnt >= idxEnd) continue;
        PetscCall(PetscSectionGetOffset(idxSection, pnt, &idxOff));
        /* Note that we pass a local section even though we're using global offsets.  This is because global sections do
         * not (at the time of this writing) have fields set. They probably should, in which case we would pass the
         * global section. */
        PetscCall(DMPlexGetIndicesPointFields_Internal(section, isLocal, pnt, idxOff < 0 ? -(idxOff + 1) : idxOff, offsets, PETSC_FALSE, perms, p, clperm, idx));
      }
    }
  } else {
    PetscInt off = 0, idxOff;

    for (p = 0; p < Ncl; ++p) {
      const PetscInt  pnt  = points[p * 2];
      const PetscInt *perm = perms[0] ? perms[0][p] : NULL;

      if (pnt < idxStart || pnt >= idxEnd) continue;
      PetscCall(PetscSectionGetOffset(idxSection, pnt, &idxOff));
      /* Note that we pass a local section even though we're using global offsets.  This is because global sections do
       * not (at the time of this writing) have fields set. They probably should, in which case we would pass the global section. */
      PetscCall(DMPlexGetIndicesPoint_Internal(section, isLocal, pnt, idxOff < 0 ? -(idxOff + 1) : idxOff, &off, PETSC_FALSE, perm, clperm, idx));
    }
  }
  /* 6) Cleanup */
  for (f = 0; f < PetscMax(1, Nf); ++f) {
    if (Nf) PetscCall(PetscSectionRestoreFieldPointSyms(section, f, Ncl, points, &perms[f], &flips[f]));
    else PetscCall(PetscSectionRestorePointSyms(section, Ncl, points, &perms[f], &flips[f]));
  }
  if (NclC) {
    PetscCall(DMRestoreWorkArray(dm, NclC * 2, MPIU_INT, &pointsC));
  } else {
    PetscCall(DMPlexRestoreCompressedClosure(dm, section, point, &Ncl, &points, &clSection, &clPoints, &clp));
  }

  if (indices) *indices = idx;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  DMPlexGetClosureIndices - Gets the global dof indices associated with the closure of the given point within the provided sections.

  Not collective

  Input Parameters:
+ dm         - The `DM`
. section    - The `PetscSection` describing the points (a local section)
. idxSection - The `PetscSection` from which to obtain indices (may be local or global)
. point      - The point defining the closure
- useClPerm  - Use the closure point permutation if available

  Output Parameters:
+ numIndices - The number of dof indices in the closure of point with the input sections
. indices    - The dof indices
. outOffsets - Array to write the field offsets into, or `NULL`
- values     - The input values, which may be modified if sign flips are induced by the point symmetries, or `NULL`

  Level: advanced

  Notes:
  Call `DMPlexRestoreClosureIndices()` to free allocated memory

  If `idxSection` is global, any constrained dofs (see `DMAddBoundary()`, for example) will get negative indices.  The value
  of those indices is not significant.  If `idxSection` is local, the constrained dofs will yield the involution -(idx+1)
  of their index in a local vector.  A caller who does not wish to distinguish those points may recover the nonnegative
  indices via involution, -(-(idx+1)+1)==idx.  Local indices are provided when `idxSection` == section, otherwise global
  indices (with the above semantics) are implied.

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexRestoreClosureIndices()`, `DMPlexVecGetClosure()`, `DMPlexMatSetClosure()`, `DMGetLocalSection()`,
          `PetscSection`, `DMGetGlobalSection()`
@*/
PetscErrorCode DMPlexGetClosureIndices(DM dm, PetscSection section, PetscSection idxSection, PetscInt point, PetscBool useClPerm, PetscInt *numIndices, PetscInt *indices[], PetscInt outOffsets[], PetscScalar *values[])
{
  PetscInt numRows = -1, numCols = -1;

  PetscFunctionBeginHot;
  PetscCall(DMPlexGetClosureIndices_Internal(dm, section, idxSection, point, useClPerm, &numRows, &numCols, indices, outOffsets, values, PETSC_TRUE, PETSC_TRUE));
  PetscCheck(numRows == numCols, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Symmetric matrix transformation produces rectangular dimensions (%" PetscInt_FMT ", %" PetscInt_FMT ")", numRows, numCols);
  *numIndices = numRows;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  DMPlexRestoreClosureIndices - Restores the global dof indices associated with the closure of the given point within the provided sections.

  Not collective

  Input Parameters:
+ dm         - The `DM`
. section    - The `PetscSection` describing the points (a local section)
. idxSection - The `PetscSection` from which to obtain indices (may be local or global)
. point      - The point defining the closure
- useClPerm  - Use the closure point permutation if available

  Output Parameters:
+ numIndices - The number of dof indices in the closure of point with the input sections
. indices    - The dof indices
. outOffsets - Array to write the field offsets into, or `NULL`
- values     - The input values, which may be modified if sign flips are induced by the point symmetries, or `NULL`

  Level: advanced

  Notes:
  If values were modified, the user is responsible for calling `DMRestoreWorkArray`(dm, 0, `MPIU_SCALAR`, &values).

  If idxSection is global, any constrained dofs (see `DMAddBoundary()`, for example) will get negative indices.  The value
  of those indices is not significant.  If idxSection is local, the constrained dofs will yield the involution -(idx+1)
  of their index in a local vector.  A caller who does not wish to distinguish those points may recover the nonnegative
  indices via involution, -(-(idx+1)+1)==idx.  Local indices are provided when idxSection == section, otherwise global
  indices (with the above semantics) are implied.

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexGetClosureIndices()`, `DMPlexVecGetClosure()`, `DMPlexMatSetClosure()`, `DMGetLocalSection()`, `DMGetGlobalSection()`
@*/
PetscErrorCode DMPlexRestoreClosureIndices(DM dm, PetscSection section, PetscSection idxSection, PetscInt point, PetscBool useClPerm, PetscInt *numIndices, PetscInt *indices[], PetscInt outOffsets[], PetscScalar *values[])
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscAssertPointer(indices, 7);
  PetscCall(DMRestoreWorkArray(dm, 0, MPIU_INT, indices));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode DMPlexMatSetClosure_Internal(DM dm, PetscSection section, PetscSection globalSection, PetscBool useClPerm, Mat A, PetscInt point, const PetscScalar values[], InsertMode mode)
{
  DM_Plex           *mesh = (DM_Plex *)dm->data;
  PetscInt          *indices;
  PetscInt           numIndices;
  const PetscScalar *valuesOrig = values;
  PetscErrorCode     ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (!section) PetscCall(DMGetLocalSection(dm, &section));
  PetscValidHeaderSpecific(section, PETSC_SECTION_CLASSID, 2);
  if (!globalSection) PetscCall(DMGetGlobalSection(dm, &globalSection));
  PetscValidHeaderSpecific(globalSection, PETSC_SECTION_CLASSID, 3);
  PetscValidHeaderSpecific(A, MAT_CLASSID, 5);

  PetscCall(DMPlexGetClosureIndices(dm, section, globalSection, point, useClPerm, &numIndices, &indices, NULL, (PetscScalar **)&values));

  if (mesh->printSetValues) PetscCall(DMPlexPrintMatSetValues(PETSC_VIEWER_STDOUT_SELF, A, point, numIndices, indices, 0, NULL, values));
  /* TODO: fix this code to not use error codes as handle-able exceptions! */
  ierr = MatSetValues(A, numIndices, indices, numIndices, indices, values, mode);
  if (ierr) {
    PetscMPIInt rank;

    PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)A), &rank));
    PetscCall((*PetscErrorPrintf)("[%d]ERROR in DMPlexMatSetClosure\n", rank));
    PetscCall(DMPlexPrintMatSetValues(PETSC_VIEWER_STDERR_SELF, A, point, numIndices, indices, 0, NULL, values));
    PetscCall(DMPlexRestoreClosureIndices(dm, section, globalSection, point, PETSC_TRUE, &numIndices, &indices, NULL, (PetscScalar **)&values));
    if (values != valuesOrig) PetscCall(DMRestoreWorkArray(dm, 0, MPIU_SCALAR, &values));
    SETERRQ(PetscObjectComm((PetscObject)dm), ierr, "Not possible to set matrix values");
  }
  if (mesh->printFEM > 1) {
    PetscInt i;
    PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Indices:"));
    for (i = 0; i < numIndices; ++i) PetscCall(PetscPrintf(PETSC_COMM_SELF, " %" PetscInt_FMT, indices[i]));
    PetscCall(PetscPrintf(PETSC_COMM_SELF, "\n"));
  }

  PetscCall(DMPlexRestoreClosureIndices(dm, section, globalSection, point, PETSC_TRUE, &numIndices, &indices, NULL, (PetscScalar **)&values));
  if (values != valuesOrig) PetscCall(DMRestoreWorkArray(dm, 0, MPIU_SCALAR, &values));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  DMPlexMatSetClosure - Set an array of the values on the closure of 'point'

  Not collective

  Input Parameters:
+ dm            - The `DM`
. section       - The section describing the layout in `v`, or `NULL` to use the default section
. globalSection - The section describing the layout in `v`, or `NULL` to use the default global section
. A             - The matrix
. point         - The point in the `DM`
. values        - The array of values
- mode          - The insert mode, where `INSERT_ALL_VALUES` and `ADD_ALL_VALUES` also overwrite boundary conditions

  Level: intermediate

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexMatSetClosureGeneral()`, `DMPlexVecGetClosure()`, `DMPlexVecSetClosure()`
@*/
PetscErrorCode DMPlexMatSetClosure(DM dm, PetscSection section, PetscSection globalSection, Mat A, PetscInt point, const PetscScalar values[], InsertMode mode)
{
  PetscFunctionBegin;
  PetscCall(DMPlexMatSetClosure_Internal(dm, section, globalSection, PETSC_TRUE, A, point, values, mode));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
  DMPlexMatSetClosureGeneral - Set an array of the values on the closure of 'point' using a different row and column section

  Not collective

  Input Parameters:
+ dmRow            - The `DM` for the row fields
. sectionRow       - The section describing the layout, or `NULL` to use the default section in `dmRow`
. useRowPerm       - The flag to use the closure permutation of the `dmRow` if available
. globalSectionRow - The section describing the layout, or `NULL` to use the default global section in `dmRow`
. dmCol            - The `DM` for the column fields
. sectionCol       - The section describing the layout, or `NULL` to use the default section in `dmCol`
. useColPerm       - The flag to use the closure permutation of the `dmCol` if available
. globalSectionCol - The section describing the layout, or `NULL` to use the default global section in `dmCol`
. A                - The matrix
. point            - The point in the `DM`
. values           - The array of values
- mode             - The insert mode, where `INSERT_ALL_VALUES` and `ADD_ALL_VALUES` also overwrite boundary conditions

  Level: intermediate

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexMatSetClosure()`, `DMPlexVecGetClosure()`, `DMPlexVecSetClosure()`
@*/
PetscErrorCode DMPlexMatSetClosureGeneral(DM dmRow, PetscSection sectionRow, PetscSection globalSectionRow, PetscBool useRowPerm, DM dmCol, PetscSection sectionCol, PetscSection globalSectionCol, PetscBool useColPerm, Mat A, PetscInt point, const PetscScalar values[], InsertMode mode)
{
  DM_Plex           *mesh = (DM_Plex *)dmRow->data;
  PetscInt          *indicesRow, *indicesCol;
  PetscInt           numIndicesRow = -1, numIndicesCol = -1;
  const PetscScalar *valuesV0 = values, *valuesV1, *valuesV2;

  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dmRow, DM_CLASSID, 1);
  if (!sectionRow) PetscCall(DMGetLocalSection(dmRow, &sectionRow));
  PetscValidHeaderSpecific(sectionRow, PETSC_SECTION_CLASSID, 2);
  if (!globalSectionRow) PetscCall(DMGetGlobalSection(dmRow, &globalSectionRow));
  PetscValidHeaderSpecific(globalSectionRow, PETSC_SECTION_CLASSID, 3);
  PetscValidHeaderSpecific(dmCol, DM_CLASSID, 5);
  if (!sectionCol) PetscCall(DMGetLocalSection(dmCol, &sectionCol));
  PetscValidHeaderSpecific(sectionCol, PETSC_SECTION_CLASSID, 6);
  if (!globalSectionCol) PetscCall(DMGetGlobalSection(dmCol, &globalSectionCol));
  PetscValidHeaderSpecific(globalSectionCol, PETSC_SECTION_CLASSID, 7);
  PetscValidHeaderSpecific(A, MAT_CLASSID, 9);

  PetscCall(DMPlexGetClosureIndicesSize_Internal(dmRow, sectionRow, point, &numIndicesRow));
  PetscCall(DMPlexGetClosureIndicesSize_Internal(dmCol, sectionCol, point, &numIndicesCol));
  valuesV1 = valuesV0;
  PetscCall(DMPlexGetClosureIndices_Internal(dmRow, sectionRow, globalSectionRow, point, useRowPerm, &numIndicesRow, &numIndicesCol, &indicesRow, NULL, (PetscScalar **)&valuesV1, PETSC_FALSE, PETSC_TRUE));
  valuesV2 = valuesV1;
  PetscCall(DMPlexGetClosureIndices_Internal(dmCol, sectionCol, globalSectionCol, point, useColPerm, &numIndicesRow, &numIndicesCol, &indicesCol, NULL, (PetscScalar **)&valuesV2, PETSC_TRUE, PETSC_FALSE));

  if (mesh->printSetValues) PetscCall(DMPlexPrintMatSetValues(PETSC_VIEWER_STDOUT_SELF, A, point, numIndicesRow, indicesRow, numIndicesCol, indicesCol, valuesV2));
  /* TODO: fix this code to not use error codes as handle-able exceptions! */
  ierr = MatSetValues(A, numIndicesRow, indicesRow, numIndicesCol, indicesCol, valuesV2, mode);
  if (ierr) {
    PetscMPIInt rank;

    PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)A), &rank));
    PetscCall((*PetscErrorPrintf)("[%d]ERROR in DMPlexMatSetClosure\n", rank));
    PetscCall(DMPlexPrintMatSetValues(PETSC_VIEWER_STDERR_SELF, A, point, numIndicesRow, indicesRow, numIndicesCol, indicesCol, values));
    PetscCall(DMPlexRestoreClosureIndices(dmCol, sectionCol, globalSectionCol, point, PETSC_TRUE, &numIndicesCol, &indicesRow, NULL, (PetscScalar **)&valuesV2));
    PetscCall(DMPlexRestoreClosureIndices(dmRow, sectionRow, globalSectionRow, point, PETSC_TRUE, &numIndicesRow, &indicesRow, NULL, (PetscScalar **)&valuesV1));
    if (valuesV2 != valuesV1) PetscCall(DMRestoreWorkArray(dmCol, 0, MPIU_SCALAR, &valuesV2));
    if (valuesV1 != valuesV0) PetscCall(DMRestoreWorkArray(dmRow, 0, MPIU_SCALAR, &valuesV1));
  }

  PetscCall(DMPlexRestoreClosureIndices(dmCol, sectionCol, globalSectionCol, point, useColPerm, &numIndicesCol, &indicesCol, NULL, (PetscScalar **)&valuesV2));
  PetscCall(DMPlexRestoreClosureIndices(dmRow, sectionRow, globalSectionRow, point, useRowPerm, &numIndicesRow, &indicesRow, NULL, (PetscScalar **)&valuesV1));
  if (valuesV2 != valuesV1) PetscCall(DMRestoreWorkArray(dmCol, 0, MPIU_SCALAR, &valuesV2));
  if (valuesV1 != valuesV0) PetscCall(DMRestoreWorkArray(dmRow, 0, MPIU_SCALAR, &valuesV1));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode DMPlexMatSetClosureRefined(DM dmf, PetscSection fsection, PetscSection globalFSection, DM dmc, PetscSection csection, PetscSection globalCSection, Mat A, PetscInt point, const PetscScalar values[], InsertMode mode)
{
  DM_Plex        *mesh    = (DM_Plex *)dmf->data;
  PetscInt       *fpoints = NULL, *ftotpoints = NULL;
  PetscInt       *cpoints = NULL;
  PetscInt       *findices, *cindices;
  const PetscInt *fclperm = NULL, *cclperm = NULL; /* Closure permutations cannot work here */
  PetscInt        foffsets[32], coffsets[32];
  DMPolytopeType  ct;
  PetscInt        numFields, numSubcells, maxFPoints, numFPoints, numCPoints, numFIndices, numCIndices, dof, off, globalOff, pStart, pEnd, p, q, r, s, f;
  PetscErrorCode  ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dmf, DM_CLASSID, 1);
  PetscValidHeaderSpecific(dmc, DM_CLASSID, 4);
  if (!fsection) PetscCall(DMGetLocalSection(dmf, &fsection));
  PetscValidHeaderSpecific(fsection, PETSC_SECTION_CLASSID, 2);
  if (!csection) PetscCall(DMGetLocalSection(dmc, &csection));
  PetscValidHeaderSpecific(csection, PETSC_SECTION_CLASSID, 5);
  if (!globalFSection) PetscCall(DMGetGlobalSection(dmf, &globalFSection));
  PetscValidHeaderSpecific(globalFSection, PETSC_SECTION_CLASSID, 3);
  if (!globalCSection) PetscCall(DMGetGlobalSection(dmc, &globalCSection));
  PetscValidHeaderSpecific(globalCSection, PETSC_SECTION_CLASSID, 6);
  PetscValidHeaderSpecific(A, MAT_CLASSID, 7);
  PetscCall(PetscSectionGetNumFields(fsection, &numFields));
  PetscCheck(numFields <= 31, PetscObjectComm((PetscObject)dmf), PETSC_ERR_ARG_OUTOFRANGE, "Number of fields %" PetscInt_FMT " limited to 31", numFields);
  PetscCall(PetscArrayzero(foffsets, 32));
  PetscCall(PetscArrayzero(coffsets, 32));
  /* Column indices */
  PetscCall(DMPlexGetTransitiveClosure(dmc, point, PETSC_TRUE, &numCPoints, &cpoints));
  maxFPoints = numCPoints;
  /* Compress out points not in the section */
  /*   TODO: Squeeze out points with 0 dof as well */
  PetscCall(PetscSectionGetChart(csection, &pStart, &pEnd));
  for (p = 0, q = 0; p < numCPoints * 2; p += 2) {
    if ((cpoints[p] >= pStart) && (cpoints[p] < pEnd)) {
      cpoints[q * 2]     = cpoints[p];
      cpoints[q * 2 + 1] = cpoints[p + 1];
      ++q;
    }
  }
  numCPoints = q;
  for (p = 0, numCIndices = 0; p < numCPoints * 2; p += 2) {
    PetscInt fdof;

    PetscCall(PetscSectionGetDof(csection, cpoints[p], &dof));
    if (!dof) continue;
    for (f = 0; f < numFields; ++f) {
      PetscCall(PetscSectionGetFieldDof(csection, cpoints[p], f, &fdof));
      coffsets[f + 1] += fdof;
    }
    numCIndices += dof;
  }
  for (f = 1; f < numFields; ++f) coffsets[f + 1] += coffsets[f];
  /* Row indices */
  PetscCall(DMPlexGetCellType(dmc, point, &ct));
  {
    DMPlexTransform tr;
    DMPolytopeType *rct;
    PetscInt       *rsize, *rcone, *rornt, Nt;

    PetscCall(DMPlexTransformCreate(PETSC_COMM_SELF, &tr));
    PetscCall(DMPlexTransformSetType(tr, DMPLEXREFINEREGULAR));
    PetscCall(DMPlexTransformCellTransform(tr, ct, point, NULL, &Nt, &rct, &rsize, &rcone, &rornt));
    numSubcells = rsize[Nt - 1];
    PetscCall(DMPlexTransformDestroy(&tr));
  }
  PetscCall(DMGetWorkArray(dmf, maxFPoints * 2 * numSubcells, MPIU_INT, &ftotpoints));
  for (r = 0, q = 0; r < numSubcells; ++r) {
    /* TODO Map from coarse to fine cells */
    PetscCall(DMPlexGetTransitiveClosure(dmf, point * numSubcells + r, PETSC_TRUE, &numFPoints, &fpoints));
    /* Compress out points not in the section */
    PetscCall(PetscSectionGetChart(fsection, &pStart, &pEnd));
    for (p = 0; p < numFPoints * 2; p += 2) {
      if ((fpoints[p] >= pStart) && (fpoints[p] < pEnd)) {
        PetscCall(PetscSectionGetDof(fsection, fpoints[p], &dof));
        if (!dof) continue;
        for (s = 0; s < q; ++s)
          if (fpoints[p] == ftotpoints[s * 2]) break;
        if (s < q) continue;
        ftotpoints[q * 2]     = fpoints[p];
        ftotpoints[q * 2 + 1] = fpoints[p + 1];
        ++q;
      }
    }
    PetscCall(DMPlexRestoreTransitiveClosure(dmf, point, PETSC_TRUE, &numFPoints, &fpoints));
  }
  numFPoints = q;
  for (p = 0, numFIndices = 0; p < numFPoints * 2; p += 2) {
    PetscInt fdof;

    PetscCall(PetscSectionGetDof(fsection, ftotpoints[p], &dof));
    if (!dof) continue;
    for (f = 0; f < numFields; ++f) {
      PetscCall(PetscSectionGetFieldDof(fsection, ftotpoints[p], f, &fdof));
      foffsets[f + 1] += fdof;
    }
    numFIndices += dof;
  }
  for (f = 1; f < numFields; ++f) foffsets[f + 1] += foffsets[f];

  PetscCheck(!numFields || foffsets[numFields] == numFIndices, PetscObjectComm((PetscObject)dmf), PETSC_ERR_PLIB, "Invalid size for closure %" PetscInt_FMT " should be %" PetscInt_FMT, foffsets[numFields], numFIndices);
  PetscCheck(!numFields || coffsets[numFields] == numCIndices, PetscObjectComm((PetscObject)dmc), PETSC_ERR_PLIB, "Invalid size for closure %" PetscInt_FMT " should be %" PetscInt_FMT, coffsets[numFields], numCIndices);
  PetscCall(DMGetWorkArray(dmf, numFIndices, MPIU_INT, &findices));
  PetscCall(DMGetWorkArray(dmc, numCIndices, MPIU_INT, &cindices));
  if (numFields) {
    const PetscInt **permsF[32] = {NULL};
    const PetscInt **permsC[32] = {NULL};

    for (f = 0; f < numFields; f++) {
      PetscCall(PetscSectionGetFieldPointSyms(fsection, f, numFPoints, ftotpoints, &permsF[f], NULL));
      PetscCall(PetscSectionGetFieldPointSyms(csection, f, numCPoints, cpoints, &permsC[f], NULL));
    }
    for (p = 0; p < numFPoints; p++) {
      PetscCall(PetscSectionGetOffset(globalFSection, ftotpoints[2 * p], &globalOff));
      PetscCall(DMPlexGetIndicesPointFields_Internal(fsection, PETSC_FALSE, ftotpoints[2 * p], globalOff < 0 ? -(globalOff + 1) : globalOff, foffsets, PETSC_FALSE, permsF, p, fclperm, findices));
    }
    for (p = 0; p < numCPoints; p++) {
      PetscCall(PetscSectionGetOffset(globalCSection, cpoints[2 * p], &globalOff));
      PetscCall(DMPlexGetIndicesPointFields_Internal(csection, PETSC_FALSE, cpoints[2 * p], globalOff < 0 ? -(globalOff + 1) : globalOff, coffsets, PETSC_FALSE, permsC, p, cclperm, cindices));
    }
    for (f = 0; f < numFields; f++) {
      PetscCall(PetscSectionRestoreFieldPointSyms(fsection, f, numFPoints, ftotpoints, &permsF[f], NULL));
      PetscCall(PetscSectionRestoreFieldPointSyms(csection, f, numCPoints, cpoints, &permsC[f], NULL));
    }
  } else {
    const PetscInt **permsF = NULL;
    const PetscInt **permsC = NULL;

    PetscCall(PetscSectionGetPointSyms(fsection, numFPoints, ftotpoints, &permsF, NULL));
    PetscCall(PetscSectionGetPointSyms(csection, numCPoints, cpoints, &permsC, NULL));
    for (p = 0, off = 0; p < numFPoints; p++) {
      const PetscInt *perm = permsF ? permsF[p] : NULL;

      PetscCall(PetscSectionGetOffset(globalFSection, ftotpoints[2 * p], &globalOff));
      PetscCall(DMPlexGetIndicesPoint_Internal(fsection, PETSC_FALSE, ftotpoints[2 * p], globalOff < 0 ? -(globalOff + 1) : globalOff, &off, PETSC_FALSE, perm, fclperm, findices));
    }
    for (p = 0, off = 0; p < numCPoints; p++) {
      const PetscInt *perm = permsC ? permsC[p] : NULL;

      PetscCall(PetscSectionGetOffset(globalCSection, cpoints[2 * p], &globalOff));
      PetscCall(DMPlexGetIndicesPoint_Internal(csection, PETSC_FALSE, cpoints[2 * p], globalOff < 0 ? -(globalOff + 1) : globalOff, &off, PETSC_FALSE, perm, cclperm, cindices));
    }
    PetscCall(PetscSectionRestorePointSyms(fsection, numFPoints, ftotpoints, &permsF, NULL));
    PetscCall(PetscSectionRestorePointSyms(csection, numCPoints, cpoints, &permsC, NULL));
  }
  if (mesh->printSetValues) PetscCall(DMPlexPrintMatSetValues(PETSC_VIEWER_STDOUT_SELF, A, point, numFIndices, findices, numCIndices, cindices, values));
  /* TODO: flips */
  /* TODO: fix this code to not use error codes as handle-able exceptions! */
  ierr = MatSetValues(A, numFIndices, findices, numCIndices, cindices, values, mode);
  if (ierr) {
    PetscMPIInt rank;

    PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)A), &rank));
    PetscCall((*PetscErrorPrintf)("[%d]ERROR in DMPlexMatSetClosure\n", rank));
    PetscCall(DMPlexPrintMatSetValues(PETSC_VIEWER_STDERR_SELF, A, point, numFIndices, findices, numCIndices, cindices, values));
    PetscCall(DMRestoreWorkArray(dmf, numFIndices, MPIU_INT, &findices));
    PetscCall(DMRestoreWorkArray(dmc, numCIndices, MPIU_INT, &cindices));
  }
  PetscCall(DMRestoreWorkArray(dmf, numCPoints * 2 * 4, MPIU_INT, &ftotpoints));
  PetscCall(DMPlexRestoreTransitiveClosure(dmc, point, PETSC_TRUE, &numCPoints, &cpoints));
  PetscCall(DMRestoreWorkArray(dmf, numFIndices, MPIU_INT, &findices));
  PetscCall(DMRestoreWorkArray(dmc, numCIndices, MPIU_INT, &cindices));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode DMPlexMatGetClosureIndicesRefined(DM dmf, PetscSection fsection, PetscSection globalFSection, DM dmc, PetscSection csection, PetscSection globalCSection, PetscInt point, PetscInt cindices[], PetscInt findices[])
{
  PetscInt       *fpoints = NULL, *ftotpoints = NULL;
  PetscInt       *cpoints      = NULL;
  PetscInt        foffsets[32] = {0}, coffsets[32] = {0};
  const PetscInt *fclperm = NULL, *cclperm = NULL; /* Closure permutations cannot work here */
  DMPolytopeType  ct;
  PetscInt        numFields, numSubcells, maxFPoints, numFPoints, numCPoints, numFIndices, numCIndices, dof, off, globalOff, pStart, pEnd, p, q, r, s, f;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dmf, DM_CLASSID, 1);
  PetscValidHeaderSpecific(dmc, DM_CLASSID, 4);
  if (!fsection) PetscCall(DMGetLocalSection(dmf, &fsection));
  PetscValidHeaderSpecific(fsection, PETSC_SECTION_CLASSID, 2);
  if (!csection) PetscCall(DMGetLocalSection(dmc, &csection));
  PetscValidHeaderSpecific(csection, PETSC_SECTION_CLASSID, 5);
  if (!globalFSection) PetscCall(DMGetGlobalSection(dmf, &globalFSection));
  PetscValidHeaderSpecific(globalFSection, PETSC_SECTION_CLASSID, 3);
  if (!globalCSection) PetscCall(DMGetGlobalSection(dmc, &globalCSection));
  PetscValidHeaderSpecific(globalCSection, PETSC_SECTION_CLASSID, 6);
  PetscCall(PetscSectionGetNumFields(fsection, &numFields));
  PetscCheck(numFields <= 31, PetscObjectComm((PetscObject)dmf), PETSC_ERR_ARG_OUTOFRANGE, "Number of fields %" PetscInt_FMT " limited to 31", numFields);
  /* Column indices */
  PetscCall(DMPlexGetTransitiveClosure(dmc, point, PETSC_TRUE, &numCPoints, &cpoints));
  maxFPoints = numCPoints;
  /* Compress out points not in the section */
  /*   TODO: Squeeze out points with 0 dof as well */
  PetscCall(PetscSectionGetChart(csection, &pStart, &pEnd));
  for (p = 0, q = 0; p < numCPoints * 2; p += 2) {
    if ((cpoints[p] >= pStart) && (cpoints[p] < pEnd)) {
      cpoints[q * 2]     = cpoints[p];
      cpoints[q * 2 + 1] = cpoints[p + 1];
      ++q;
    }
  }
  numCPoints = q;
  for (p = 0, numCIndices = 0; p < numCPoints * 2; p += 2) {
    PetscInt fdof;

    PetscCall(PetscSectionGetDof(csection, cpoints[p], &dof));
    if (!dof) continue;
    for (f = 0; f < numFields; ++f) {
      PetscCall(PetscSectionGetFieldDof(csection, cpoints[p], f, &fdof));
      coffsets[f + 1] += fdof;
    }
    numCIndices += dof;
  }
  for (f = 1; f < numFields; ++f) coffsets[f + 1] += coffsets[f];
  /* Row indices */
  PetscCall(DMPlexGetCellType(dmc, point, &ct));
  {
    DMPlexTransform tr;
    DMPolytopeType *rct;
    PetscInt       *rsize, *rcone, *rornt, Nt;

    PetscCall(DMPlexTransformCreate(PETSC_COMM_SELF, &tr));
    PetscCall(DMPlexTransformSetType(tr, DMPLEXREFINEREGULAR));
    PetscCall(DMPlexTransformCellTransform(tr, ct, point, NULL, &Nt, &rct, &rsize, &rcone, &rornt));
    numSubcells = rsize[Nt - 1];
    PetscCall(DMPlexTransformDestroy(&tr));
  }
  PetscCall(DMGetWorkArray(dmf, maxFPoints * 2 * numSubcells, MPIU_INT, &ftotpoints));
  for (r = 0, q = 0; r < numSubcells; ++r) {
    /* TODO Map from coarse to fine cells */
    PetscCall(DMPlexGetTransitiveClosure(dmf, point * numSubcells + r, PETSC_TRUE, &numFPoints, &fpoints));
    /* Compress out points not in the section */
    PetscCall(PetscSectionGetChart(fsection, &pStart, &pEnd));
    for (p = 0; p < numFPoints * 2; p += 2) {
      if ((fpoints[p] >= pStart) && (fpoints[p] < pEnd)) {
        PetscCall(PetscSectionGetDof(fsection, fpoints[p], &dof));
        if (!dof) continue;
        for (s = 0; s < q; ++s)
          if (fpoints[p] == ftotpoints[s * 2]) break;
        if (s < q) continue;
        ftotpoints[q * 2]     = fpoints[p];
        ftotpoints[q * 2 + 1] = fpoints[p + 1];
        ++q;
      }
    }
    PetscCall(DMPlexRestoreTransitiveClosure(dmf, point, PETSC_TRUE, &numFPoints, &fpoints));
  }
  numFPoints = q;
  for (p = 0, numFIndices = 0; p < numFPoints * 2; p += 2) {
    PetscInt fdof;

    PetscCall(PetscSectionGetDof(fsection, ftotpoints[p], &dof));
    if (!dof) continue;
    for (f = 0; f < numFields; ++f) {
      PetscCall(PetscSectionGetFieldDof(fsection, ftotpoints[p], f, &fdof));
      foffsets[f + 1] += fdof;
    }
    numFIndices += dof;
  }
  for (f = 1; f < numFields; ++f) foffsets[f + 1] += foffsets[f];

  PetscCheck(!numFields || foffsets[numFields] == numFIndices, PetscObjectComm((PetscObject)dmf), PETSC_ERR_PLIB, "Invalid size for closure %" PetscInt_FMT " should be %" PetscInt_FMT, foffsets[numFields], numFIndices);
  PetscCheck(!numFields || coffsets[numFields] == numCIndices, PetscObjectComm((PetscObject)dmc), PETSC_ERR_PLIB, "Invalid size for closure %" PetscInt_FMT " should be %" PetscInt_FMT, coffsets[numFields], numCIndices);
  if (numFields) {
    const PetscInt **permsF[32] = {NULL};
    const PetscInt **permsC[32] = {NULL};

    for (f = 0; f < numFields; f++) {
      PetscCall(PetscSectionGetFieldPointSyms(fsection, f, numFPoints, ftotpoints, &permsF[f], NULL));
      PetscCall(PetscSectionGetFieldPointSyms(csection, f, numCPoints, cpoints, &permsC[f], NULL));
    }
    for (p = 0; p < numFPoints; p++) {
      PetscCall(PetscSectionGetOffset(globalFSection, ftotpoints[2 * p], &globalOff));
      PetscCall(DMPlexGetIndicesPointFields_Internal(fsection, PETSC_FALSE, ftotpoints[2 * p], globalOff < 0 ? -(globalOff + 1) : globalOff, foffsets, PETSC_FALSE, permsF, p, fclperm, findices));
    }
    for (p = 0; p < numCPoints; p++) {
      PetscCall(PetscSectionGetOffset(globalCSection, cpoints[2 * p], &globalOff));
      PetscCall(DMPlexGetIndicesPointFields_Internal(csection, PETSC_FALSE, cpoints[2 * p], globalOff < 0 ? -(globalOff + 1) : globalOff, coffsets, PETSC_FALSE, permsC, p, cclperm, cindices));
    }
    for (f = 0; f < numFields; f++) {
      PetscCall(PetscSectionRestoreFieldPointSyms(fsection, f, numFPoints, ftotpoints, &permsF[f], NULL));
      PetscCall(PetscSectionRestoreFieldPointSyms(csection, f, numCPoints, cpoints, &permsC[f], NULL));
    }
  } else {
    const PetscInt **permsF = NULL;
    const PetscInt **permsC = NULL;

    PetscCall(PetscSectionGetPointSyms(fsection, numFPoints, ftotpoints, &permsF, NULL));
    PetscCall(PetscSectionGetPointSyms(csection, numCPoints, cpoints, &permsC, NULL));
    for (p = 0, off = 0; p < numFPoints; p++) {
      const PetscInt *perm = permsF ? permsF[p] : NULL;

      PetscCall(PetscSectionGetOffset(globalFSection, ftotpoints[2 * p], &globalOff));
      PetscCall(DMPlexGetIndicesPoint_Internal(fsection, PETSC_FALSE, ftotpoints[2 * p], globalOff < 0 ? -(globalOff + 1) : globalOff, &off, PETSC_FALSE, perm, fclperm, findices));
    }
    for (p = 0, off = 0; p < numCPoints; p++) {
      const PetscInt *perm = permsC ? permsC[p] : NULL;

      PetscCall(PetscSectionGetOffset(globalCSection, cpoints[2 * p], &globalOff));
      PetscCall(DMPlexGetIndicesPoint_Internal(csection, PETSC_FALSE, cpoints[2 * p], globalOff < 0 ? -(globalOff + 1) : globalOff, &off, PETSC_FALSE, perm, cclperm, cindices));
    }
    PetscCall(PetscSectionRestorePointSyms(fsection, numFPoints, ftotpoints, &permsF, NULL));
    PetscCall(PetscSectionRestorePointSyms(csection, numCPoints, cpoints, &permsC, NULL));
  }
  PetscCall(DMRestoreWorkArray(dmf, numCPoints * 2 * 4, MPIU_INT, &ftotpoints));
  PetscCall(DMPlexRestoreTransitiveClosure(dmc, point, PETSC_TRUE, &numCPoints, &cpoints));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexGetVTKCellHeight - Returns the height in the DAG used to determine which points are cells (normally 0)

  Input Parameter:
. dm - The `DMPLEX` object

  Output Parameter:
. cellHeight - The height of a cell

  Level: developer

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexSetVTKCellHeight()`
@*/
PetscErrorCode DMPlexGetVTKCellHeight(DM dm, PetscInt *cellHeight)
{
  DM_Plex *mesh = (DM_Plex *)dm->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscAssertPointer(cellHeight, 2);
  *cellHeight = mesh->vtkCellHeight;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexSetVTKCellHeight - Sets the height in the DAG used to determine which points are cells (normally 0)

  Input Parameters:
+ dm         - The `DMPLEX` object
- cellHeight - The height of a cell

  Level: developer

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexGetVTKCellHeight()`
@*/
PetscErrorCode DMPlexSetVTKCellHeight(DM dm, PetscInt cellHeight)
{
  DM_Plex *mesh = (DM_Plex *)dm->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  mesh->vtkCellHeight = cellHeight;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexGetCellTypeStratum - Get the range of cells of a given celltype

  Input Parameters:
+ dm - The `DMPLEX` object
- ct - The `DMPolytopeType` of the cell

  Output Parameters:
+ start - The first cell of this type, or `NULL`
- end   - The upper bound on this celltype, or `NULL`

  Level: advanced

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexConstructGhostCells()`, `DMPlexGetDepthStratum()`, `DMPlexGetHeightStratum()`
@*/
PetscErrorCode DMPlexGetCellTypeStratum(DM dm, DMPolytopeType ct, PetscInt *start, PetscInt *end)
{
  DM_Plex *mesh = (DM_Plex *)dm->data;
  DMLabel  label;
  PetscInt pStart, pEnd;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (start) {
    PetscAssertPointer(start, 3);
    *start = 0;
  }
  if (end) {
    PetscAssertPointer(end, 4);
    *end = 0;
  }
  PetscCall(DMPlexGetChart(dm, &pStart, &pEnd));
  if (pStart == pEnd) PetscFunctionReturn(PETSC_SUCCESS);
  if (mesh->tr) {
    PetscCall(DMPlexTransformGetCellTypeStratum(mesh->tr, ct, start, end));
  } else {
    PetscCall(DMPlexGetCellTypeLabel(dm, &label));
    PetscCheck(label, PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "No label named celltype was found");
    PetscCall(DMLabelGetStratumBounds(label, ct, start, end));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode DMPlexCreateNumbering_Plex(DM dm, PetscInt pStart, PetscInt pEnd, PetscInt shift, PetscInt *globalSize, PetscSF sf, IS *numbering)
{
  PetscSection section, globalSection;
  PetscInt    *numbers, p;

  PetscFunctionBegin;
  if (PetscDefined(USE_DEBUG)) PetscCall(DMPlexCheckPointSF(dm, sf, PETSC_TRUE));
  PetscCall(PetscSectionCreate(PetscObjectComm((PetscObject)dm), &section));
  PetscCall(PetscSectionSetChart(section, pStart, pEnd));
  for (p = pStart; p < pEnd; ++p) PetscCall(PetscSectionSetDof(section, p, 1));
  PetscCall(PetscSectionSetUp(section));
  PetscCall(PetscSectionCreateGlobalSection(section, sf, PETSC_TRUE, PETSC_FALSE, PETSC_FALSE, &globalSection));
  PetscCall(PetscMalloc1(pEnd - pStart, &numbers));
  for (p = pStart; p < pEnd; ++p) {
    PetscCall(PetscSectionGetOffset(globalSection, p, &numbers[p - pStart]));
    if (numbers[p - pStart] < 0) numbers[p - pStart] -= shift;
    else numbers[p - pStart] += shift;
  }
  PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)dm), pEnd - pStart, numbers, PETSC_OWN_POINTER, numbering));
  if (globalSize) {
    PetscLayout layout;
    PetscCall(PetscSectionGetPointLayout(PetscObjectComm((PetscObject)dm), globalSection, &layout));
    PetscCall(PetscLayoutGetSize(layout, globalSize));
    PetscCall(PetscLayoutDestroy(&layout));
  }
  PetscCall(PetscSectionDestroy(&section));
  PetscCall(PetscSectionDestroy(&globalSection));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexCreateCellNumbering - Get a global cell numbering for all cells on this process

  Input Parameters:
+ dm         - The `DMPLEX` object
- includeAll - Whether to include all cells, or just the simplex and box cells

  Output Parameter:
. globalCellNumbers - Global cell numbers for all cells on this process

  Level: developer

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexGetCellNumbering()`, `DMPlexGetVertexNumbering()`
@*/
PetscErrorCode DMPlexCreateCellNumbering(DM dm, PetscBool includeAll, IS *globalCellNumbers)
{
  PetscInt cellHeight, cStart, cEnd;

  PetscFunctionBegin;
  PetscCall(DMPlexGetVTKCellHeight(dm, &cellHeight));
  if (includeAll) PetscCall(DMPlexGetHeightStratum(dm, cellHeight, &cStart, &cEnd));
  else PetscCall(DMPlexGetSimplexOrBoxCells(dm, cellHeight, &cStart, &cEnd));
  PetscCall(DMPlexCreateNumbering_Plex(dm, cStart, cEnd, 0, NULL, dm->sf, globalCellNumbers));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexGetCellNumbering - Get a global cell numbering for all cells on this process

  Input Parameter:
. dm - The `DMPLEX` object

  Output Parameter:
. globalCellNumbers - Global cell numbers for all cells on this process

  Level: developer

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexCreateCellNumbering()`, `DMPlexGetVertexNumbering()`
@*/
PetscErrorCode DMPlexGetCellNumbering(DM dm, IS *globalCellNumbers)
{
  DM_Plex *mesh = (DM_Plex *)dm->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (!mesh->globalCellNumbers) PetscCall(DMPlexCreateCellNumbering(dm, PETSC_FALSE, &mesh->globalCellNumbers));
  *globalCellNumbers = mesh->globalCellNumbers;
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode DMPlexCreateVertexNumbering_Internal(DM dm, PetscBool includeHybrid, IS *globalVertexNumbers)
{
  PetscInt vStart, vEnd;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
  PetscCall(DMPlexCreateNumbering_Plex(dm, vStart, vEnd, 0, NULL, dm->sf, globalVertexNumbers));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexGetVertexNumbering - Get a global vertex numbering for all vertices on this process

  Input Parameter:
. dm - The `DMPLEX` object

  Output Parameter:
. globalVertexNumbers - Global vertex numbers for all vertices on this process

  Level: developer

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexGetCellNumbering()`
@*/
PetscErrorCode DMPlexGetVertexNumbering(DM dm, IS *globalVertexNumbers)
{
  DM_Plex *mesh = (DM_Plex *)dm->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (!mesh->globalVertexNumbers) PetscCall(DMPlexCreateVertexNumbering_Internal(dm, PETSC_FALSE, &mesh->globalVertexNumbers));
  *globalVertexNumbers = mesh->globalVertexNumbers;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexCreatePointNumbering - Create a global numbering for all points.

  Collective

  Input Parameter:
. dm - The `DMPLEX` object

  Output Parameter:
. globalPointNumbers - Global numbers for all points on this process

  Level: developer

  Notes:
  The point numbering `IS` is parallel, with local portion indexed by local points (see `DMGetLocalSection()`). The global
  points are taken as stratified, with each MPI rank owning a contiguous subset of each stratum. In the IS, owned points
  will have their non-negative value while points owned by different ranks will be involuted -(idx+1). As an example,
  consider a parallel mesh in which the first two elements and first two vertices are owned by rank 0.

  The partitioned mesh is
  ```
  (2)--0--(3)--1--(4)    (1)--0--(2)
  ```
  and its global numbering is
  ```
  (3)--0--(4)--1--(5)--2--(6)
  ```
  Then the global numbering is provided as
  ```
  [0] Number of indices in set 5
  [0] 0 0
  [0] 1 1
  [0] 2 3
  [0] 3 4
  [0] 4 -6
  [1] Number of indices in set 3
  [1] 0 2
  [1] 1 5
  [1] 2 6
  ```

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexGetCellNumbering()`
@*/
PetscErrorCode DMPlexCreatePointNumbering(DM dm, IS *globalPointNumbers)
{
  IS        nums[4];
  PetscInt  depths[4], gdepths[4], starts[4];
  PetscInt  depth, d, shift = 0;
  PetscBool empty = PETSC_FALSE;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscCall(DMPlexGetDepth(dm, &depth));
  // For unstratified meshes use dim instead of depth
  if (depth < 0) PetscCall(DMGetDimension(dm, &depth));
  // If any stratum is empty, we must mark all empty
  for (d = 0; d <= depth; ++d) {
    PetscInt end;

    depths[d] = depth - d;
    PetscCall(DMPlexGetDepthStratum(dm, depths[d], &starts[d], &end));
    if (!(starts[d] - end)) empty = PETSC_TRUE;
  }
  if (empty)
    for (d = 0; d <= depth; ++d) {
      depths[d] = -1;
      starts[d] = -1;
    }
  else PetscCall(PetscSortIntWithArray(depth + 1, starts, depths));
  PetscCall(MPIU_Allreduce(depths, gdepths, depth + 1, MPIU_INT, MPI_MAX, PetscObjectComm((PetscObject)dm)));
  for (d = 0; d <= depth; ++d) PetscCheck(starts[d] < 0 || depths[d] == gdepths[d], PETSC_COMM_SELF, PETSC_ERR_PLIB, "Expected depth %" PetscInt_FMT ", found %" PetscInt_FMT, depths[d], gdepths[d]);
  // Note here that 'shift' is collective, so that the numbering is stratified by depth
  for (d = 0; d <= depth; ++d) {
    PetscInt pStart, pEnd, gsize;

    PetscCall(DMPlexGetDepthStratum(dm, gdepths[d], &pStart, &pEnd));
    PetscCall(DMPlexCreateNumbering_Plex(dm, pStart, pEnd, shift, &gsize, dm->sf, &nums[d]));
    shift += gsize;
  }
  PetscCall(ISConcatenate(PETSC_COMM_SELF, depth + 1, nums, globalPointNumbers));
  for (d = 0; d <= depth; ++d) PetscCall(ISDestroy(&nums[d]));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexCreateEdgeNumbering - Create a global numbering for edges.

  Collective

  Input Parameter:
. dm - The `DMPLEX` object

  Output Parameter:
. globalEdgeNumbers - Global numbers for all edges on this process

  Level: developer

  Notes:
  The point numbering `IS` is parallel, with local portion indexed by local points (see `DMGetLocalSection()`). In the IS, owned edges will have their non-negative value while edges owned by different ranks will be involuted -(idx+1).

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexGetCellNumbering()`, `DMPlexGetVertexNumbering()`, `DMPlexCreatePointNumbering()`
@*/
PetscErrorCode DMPlexCreateEdgeNumbering(DM dm, IS *globalEdgeNumbers)
{
  PetscSF  sf;
  PetscInt eStart, eEnd;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscCall(DMGetPointSF(dm, &sf));
  PetscCall(DMPlexGetDepthStratum(dm, 1, &eStart, &eEnd));
  PetscCall(DMPlexCreateNumbering_Plex(dm, eStart, eEnd, 0, NULL, sf, globalEdgeNumbers));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexCreateRankField - Create a cell field whose value is the rank of the owner

  Input Parameter:
. dm - The `DMPLEX` object

  Output Parameter:
. ranks - The rank field

  Options Database Key:
. -dm_partition_view - Adds the rank field into the `DM` output from `-dm_view` using the same viewer

  Level: intermediate

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMView()`
@*/
PetscErrorCode DMPlexCreateRankField(DM dm, Vec *ranks)
{
  DM             rdm;
  PetscFE        fe;
  PetscScalar   *r;
  PetscMPIInt    rank;
  DMPolytopeType ct;
  PetscInt       dim, cStart, cEnd, c;
  PetscBool      simplex;

  PetscFunctionBeginUser;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscAssertPointer(ranks, 2);
  PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank));
  PetscCall(DMClone(dm, &rdm));
  PetscCall(DMGetDimension(rdm, &dim));
  PetscCall(DMPlexGetHeightStratum(rdm, 0, &cStart, &cEnd));
  PetscCall(DMPlexGetCellType(dm, cStart, &ct));
  simplex = DMPolytopeTypeGetNumVertices(ct) == DMPolytopeTypeGetDim(ct) + 1 ? PETSC_TRUE : PETSC_FALSE;
  PetscCall(PetscFECreateDefault(PETSC_COMM_SELF, dim, 1, simplex, "PETSc___rank_", -1, &fe));
  PetscCall(PetscObjectSetName((PetscObject)fe, "rank"));
  PetscCall(DMSetField(rdm, 0, NULL, (PetscObject)fe));
  PetscCall(PetscFEDestroy(&fe));
  PetscCall(DMCreateDS(rdm));
  PetscCall(DMCreateGlobalVector(rdm, ranks));
  PetscCall(PetscObjectSetName((PetscObject)*ranks, "partition"));
  PetscCall(VecGetArray(*ranks, &r));
  for (c = cStart; c < cEnd; ++c) {
    PetscScalar *lr;

    PetscCall(DMPlexPointGlobalRef(rdm, c, r, &lr));
    if (lr) *lr = rank;
  }
  PetscCall(VecRestoreArray(*ranks, &r));
  PetscCall(DMDestroy(&rdm));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexCreateLabelField - Create a field whose value is the label value for that point

  Input Parameters:
+ dm    - The `DMPLEX`
- label - The `DMLabel`

  Output Parameter:
. val - The label value field

  Options Database Key:
. -dm_label_view - Adds the label value field into the `DM` output from `-dm_view` using the same viewer

  Level: intermediate

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMView()`
@*/
PetscErrorCode DMPlexCreateLabelField(DM dm, DMLabel label, Vec *val)
{
  DM             rdm, plex;
  Vec            lval;
  PetscSection   section;
  PetscFE        fe;
  PetscScalar   *v;
  PetscInt       dim, pStart, pEnd, p, cStart;
  DMPolytopeType ct;
  char           name[PETSC_MAX_PATH_LEN];
  const char    *lname, *prefix;

  PetscFunctionBeginUser;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscAssertPointer(label, 2);
  PetscAssertPointer(val, 3);
  PetscCall(DMClone(dm, &rdm));
  PetscCall(DMConvert(rdm, DMPLEX, &plex));
  PetscCall(DMPlexGetHeightStratum(plex, 0, &cStart, NULL));
  PetscCall(DMPlexGetCellType(plex, cStart, &ct));
  PetscCall(DMDestroy(&plex));
  PetscCall(DMGetDimension(rdm, &dim));
  PetscCall(DMGetOptionsPrefix(dm, &prefix));
  PetscCall(PetscObjectGetName((PetscObject)label, &lname));
  PetscCall(PetscSNPrintf(name, sizeof(name), "%s%s_", prefix ? prefix : "", lname));
  PetscCall(PetscFECreateByCell(PETSC_COMM_SELF, dim, 1, ct, name, -1, &fe));
  PetscCall(PetscObjectSetName((PetscObject)fe, ""));
  PetscCall(DMSetField(rdm, 0, NULL, (PetscObject)fe));
  PetscCall(PetscFEDestroy(&fe));
  PetscCall(DMCreateDS(rdm));
  PetscCall(DMCreateGlobalVector(rdm, val));
  PetscCall(DMCreateLocalVector(rdm, &lval));
  PetscCall(PetscObjectSetName((PetscObject)*val, lname));
  PetscCall(DMGetLocalSection(rdm, &section));
  PetscCall(PetscSectionGetChart(section, &pStart, &pEnd));
  PetscCall(VecGetArray(lval, &v));
  for (p = pStart; p < pEnd; ++p) {
    PetscInt cval, dof, off;

    PetscCall(PetscSectionGetDof(section, p, &dof));
    if (!dof) continue;
    PetscCall(DMLabelGetValue(label, p, &cval));
    PetscCall(PetscSectionGetOffset(section, p, &off));
    for (PetscInt d = 0; d < dof; d++) v[off + d] = cval;
  }
  PetscCall(VecRestoreArray(lval, &v));
  PetscCall(DMLocalToGlobal(rdm, lval, INSERT_VALUES, *val));
  PetscCall(VecDestroy(&lval));
  PetscCall(DMDestroy(&rdm));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexCheckSymmetry - Check that the adjacency information in the mesh is symmetric.

  Input Parameter:
. dm - The `DMPLEX` object

  Level: developer

  Notes:
  This is a useful diagnostic when creating meshes programmatically.

  For the complete list of DMPlexCheck* functions, see `DMSetFromOptions()`.

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMCreate()`, `DMSetFromOptions()`
@*/
PetscErrorCode DMPlexCheckSymmetry(DM dm)
{
  PetscSection    coneSection, supportSection;
  const PetscInt *cone, *support;
  PetscInt        coneSize, c, supportSize, s;
  PetscInt        pStart, pEnd, p, pp, csize, ssize;
  PetscBool       storagecheck = PETSC_TRUE;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscCall(DMViewFromOptions(dm, NULL, "-sym_dm_view"));
  PetscCall(DMPlexGetConeSection(dm, &coneSection));
  PetscCall(DMPlexGetSupportSection(dm, &supportSection));
  /* Check that point p is found in the support of its cone points, and vice versa */
  PetscCall(DMPlexGetChart(dm, &pStart, &pEnd));
  for (p = pStart; p < pEnd; ++p) {
    PetscCall(DMPlexGetConeSize(dm, p, &coneSize));
    PetscCall(DMPlexGetCone(dm, p, &cone));
    for (c = 0; c < coneSize; ++c) {
      PetscBool dup = PETSC_FALSE;
      PetscInt  d;
      for (d = c - 1; d >= 0; --d) {
        if (cone[c] == cone[d]) {
          dup = PETSC_TRUE;
          break;
        }
      }
      PetscCall(DMPlexGetSupportSize(dm, cone[c], &supportSize));
      PetscCall(DMPlexGetSupport(dm, cone[c], &support));
      for (s = 0; s < supportSize; ++s) {
        if (support[s] == p) break;
      }
      if ((s >= supportSize) || (dup && (support[s + 1] != p))) {
        PetscCall(PetscPrintf(PETSC_COMM_SELF, "p: %" PetscInt_FMT " cone: ", p));
        for (s = 0; s < coneSize; ++s) PetscCall(PetscPrintf(PETSC_COMM_SELF, "%" PetscInt_FMT ", ", cone[s]));
        PetscCall(PetscPrintf(PETSC_COMM_SELF, "\n"));
        PetscCall(PetscPrintf(PETSC_COMM_SELF, "p: %" PetscInt_FMT " support: ", cone[c]));
        for (s = 0; s < supportSize; ++s) PetscCall(PetscPrintf(PETSC_COMM_SELF, "%" PetscInt_FMT ", ", support[s]));
        PetscCall(PetscPrintf(PETSC_COMM_SELF, "\n"));
        PetscCheck(!dup, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Point %" PetscInt_FMT " not repeatedly found in support of repeated cone point %" PetscInt_FMT, p, cone[c]);
        SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Point %" PetscInt_FMT " not found in support of cone point %" PetscInt_FMT, p, cone[c]);
      }
    }
    PetscCall(DMPlexGetTreeParent(dm, p, &pp, NULL));
    if (p != pp) {
      storagecheck = PETSC_FALSE;
      continue;
    }
    PetscCall(DMPlexGetSupportSize(dm, p, &supportSize));
    PetscCall(DMPlexGetSupport(dm, p, &support));
    for (s = 0; s < supportSize; ++s) {
      PetscCall(DMPlexGetConeSize(dm, support[s], &coneSize));
      PetscCall(DMPlexGetCone(dm, support[s], &cone));
      for (c = 0; c < coneSize; ++c) {
        PetscCall(DMPlexGetTreeParent(dm, cone[c], &pp, NULL));
        if (cone[c] != pp) {
          c = 0;
          break;
        }
        if (cone[c] == p) break;
      }
      if (c >= coneSize) {
        PetscCall(PetscPrintf(PETSC_COMM_SELF, "p: %" PetscInt_FMT " support: ", p));
        for (c = 0; c < supportSize; ++c) PetscCall(PetscPrintf(PETSC_COMM_SELF, "%" PetscInt_FMT ", ", support[c]));
        PetscCall(PetscPrintf(PETSC_COMM_SELF, "\n"));
        PetscCall(PetscPrintf(PETSC_COMM_SELF, "p: %" PetscInt_FMT " cone: ", support[s]));
        for (c = 0; c < coneSize; ++c) PetscCall(PetscPrintf(PETSC_COMM_SELF, "%" PetscInt_FMT ", ", cone[c]));
        PetscCall(PetscPrintf(PETSC_COMM_SELF, "\n"));
        SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Point %" PetscInt_FMT " not found in cone of support point %" PetscInt_FMT, p, support[s]);
      }
    }
  }
  if (storagecheck) {
    PetscCall(PetscSectionGetStorageSize(coneSection, &csize));
    PetscCall(PetscSectionGetStorageSize(supportSection, &ssize));
    PetscCheck(csize == ssize, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Total cone size %" PetscInt_FMT " != Total support size %" PetscInt_FMT, csize, ssize);
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
  For submeshes with cohesive cells (see DMPlexConstructCohesiveCells()), we allow a special case where some of the boundary of a face (edges and vertices) are not duplicated. We call these special boundary points "unsplit", since the same edge or vertex appears in both copies of the face. These unsplit points throw off our counting, so we have to explicitly account for them here.
*/
static PetscErrorCode DMPlexCellUnsplitVertices_Private(DM dm, PetscInt c, DMPolytopeType ct, PetscInt *unsplit)
{
  DMPolytopeType  cct;
  PetscInt        ptpoints[4];
  const PetscInt *cone, *ccone, *ptcone;
  PetscInt        coneSize, cp, cconeSize, ccp, npt = 0, pt;

  PetscFunctionBegin;
  *unsplit = 0;
  switch (ct) {
  case DM_POLYTOPE_POINT_PRISM_TENSOR:
    ptpoints[npt++] = c;
    break;
  case DM_POLYTOPE_SEG_PRISM_TENSOR:
    PetscCall(DMPlexGetCone(dm, c, &cone));
    PetscCall(DMPlexGetConeSize(dm, c, &coneSize));
    for (cp = 0; cp < coneSize; ++cp) {
      PetscCall(DMPlexGetCellType(dm, cone[cp], &cct));
      if (cct == DM_POLYTOPE_POINT_PRISM_TENSOR) ptpoints[npt++] = cone[cp];
    }
    break;
  case DM_POLYTOPE_TRI_PRISM_TENSOR:
  case DM_POLYTOPE_QUAD_PRISM_TENSOR:
    PetscCall(DMPlexGetCone(dm, c, &cone));
    PetscCall(DMPlexGetConeSize(dm, c, &coneSize));
    for (cp = 0; cp < coneSize; ++cp) {
      PetscCall(DMPlexGetCone(dm, cone[cp], &ccone));
      PetscCall(DMPlexGetConeSize(dm, cone[cp], &cconeSize));
      for (ccp = 0; ccp < cconeSize; ++ccp) {
        PetscCall(DMPlexGetCellType(dm, ccone[ccp], &cct));
        if (cct == DM_POLYTOPE_POINT_PRISM_TENSOR) {
          PetscInt p;
          for (p = 0; p < npt; ++p)
            if (ptpoints[p] == ccone[ccp]) break;
          if (p == npt) ptpoints[npt++] = ccone[ccp];
        }
      }
    }
    break;
  default:
    break;
  }
  for (pt = 0; pt < npt; ++pt) {
    PetscCall(DMPlexGetCone(dm, ptpoints[pt], &ptcone));
    if (ptcone[0] == ptcone[1]) ++(*unsplit);
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexCheckSkeleton - Check that each cell has the correct number of vertices

  Input Parameters:
+ dm         - The `DMPLEX` object
- cellHeight - Normally 0

  Level: developer

  Notes:
  This is a useful diagnostic when creating meshes programmatically.
  Currently applicable only to homogeneous simplex or tensor meshes.

  For the complete list of DMPlexCheck* functions, see `DMSetFromOptions()`.

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMCreate()`, `DMSetFromOptions()`
@*/
PetscErrorCode DMPlexCheckSkeleton(DM dm, PetscInt cellHeight)
{
  DMPlexInterpolatedFlag interp;
  DMPolytopeType         ct;
  PetscInt               vStart, vEnd, cStart, cEnd, c;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscCall(DMPlexIsInterpolated(dm, &interp));
  PetscCall(DMPlexGetHeightStratum(dm, cellHeight, &cStart, &cEnd));
  PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
  for (c = cStart; c < cEnd; ++c) {
    PetscInt *closure = NULL;
    PetscInt  coneSize, closureSize, cl, Nv = 0;

    PetscCall(DMPlexGetCellType(dm, c, &ct));
    if (ct == DM_POLYTOPE_UNKNOWN) continue;
    if (interp == DMPLEX_INTERPOLATED_FULL) {
      PetscCall(DMPlexGetConeSize(dm, c, &coneSize));
      PetscCheck(coneSize == DMPolytopeTypeGetConeSize(ct), PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cell %" PetscInt_FMT " of type %s has cone size %" PetscInt_FMT " != %" PetscInt_FMT, c, DMPolytopeTypes[ct], coneSize, DMPolytopeTypeGetConeSize(ct));
    }
    PetscCall(DMPlexGetTransitiveClosure(dm, c, PETSC_TRUE, &closureSize, &closure));
    for (cl = 0; cl < closureSize * 2; cl += 2) {
      const PetscInt p = closure[cl];
      if ((p >= vStart) && (p < vEnd)) ++Nv;
    }
    PetscCall(DMPlexRestoreTransitiveClosure(dm, c, PETSC_TRUE, &closureSize, &closure));
    /* Special Case: Tensor faces with identified vertices */
    if (Nv < DMPolytopeTypeGetNumVertices(ct)) {
      PetscInt unsplit;

      PetscCall(DMPlexCellUnsplitVertices_Private(dm, c, ct, &unsplit));
      if (Nv + unsplit == DMPolytopeTypeGetNumVertices(ct)) continue;
    }
    PetscCheck(Nv == DMPolytopeTypeGetNumVertices(ct), PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cell %" PetscInt_FMT " of type %s has %" PetscInt_FMT " vertices != %" PetscInt_FMT, c, DMPolytopeTypes[ct], Nv, DMPolytopeTypeGetNumVertices(ct));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexCheckFaces - Check that the faces of each cell give a vertex order this is consistent with what we expect from the cell type

  Collective

  Input Parameters:
+ dm         - The `DMPLEX` object
- cellHeight - Normally 0

  Level: developer

  Notes:
  This is a useful diagnostic when creating meshes programmatically.
  This routine is only relevant for meshes that are fully interpolated across all ranks.
  It will error out if a partially interpolated mesh is given on some rank.
  It will do nothing for locally uninterpolated mesh (as there is nothing to check).

  For the complete list of DMPlexCheck* functions, see `DMSetFromOptions()`.

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMCreate()`, `DMPlexGetVTKCellHeight()`, `DMSetFromOptions()`
@*/
PetscErrorCode DMPlexCheckFaces(DM dm, PetscInt cellHeight)
{
  PetscInt               dim, depth, vStart, vEnd, cStart, cEnd, c, h;
  DMPlexInterpolatedFlag interpEnum;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscCall(DMPlexIsInterpolatedCollective(dm, &interpEnum));
  if (interpEnum == DMPLEX_INTERPOLATED_NONE) PetscFunctionReturn(PETSC_SUCCESS);
  if (interpEnum != DMPLEX_INTERPOLATED_FULL) {
    PetscCall(PetscPrintf(PetscObjectComm((PetscObject)dm), "DMPlexCheckFaces() warning: Mesh is only partially interpolated, this is currently not supported"));
    PetscFunctionReturn(PETSC_SUCCESS);
  }

  PetscCall(DMGetDimension(dm, &dim));
  PetscCall(DMPlexGetDepth(dm, &depth));
  PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
  for (h = cellHeight; h < PetscMin(depth, dim); ++h) {
    PetscCall(DMPlexGetHeightStratum(dm, h, &cStart, &cEnd));
    for (c = cStart; c < cEnd; ++c) {
      const PetscInt       *cone, *ornt, *faceSizes, *faces;
      const DMPolytopeType *faceTypes;
      DMPolytopeType        ct;
      PetscInt              numFaces, coneSize, f;
      PetscInt             *closure = NULL, closureSize, cl, numCorners = 0, fOff = 0, unsplit;

      PetscCall(DMPlexGetCellType(dm, c, &ct));
      PetscCall(DMPlexCellUnsplitVertices_Private(dm, c, ct, &unsplit));
      if (unsplit) continue;
      PetscCall(DMPlexGetConeSize(dm, c, &coneSize));
      PetscCall(DMPlexGetCone(dm, c, &cone));
      PetscCall(DMPlexGetConeOrientation(dm, c, &ornt));
      PetscCall(DMPlexGetTransitiveClosure(dm, c, PETSC_TRUE, &closureSize, &closure));
      for (cl = 0; cl < closureSize * 2; cl += 2) {
        const PetscInt p = closure[cl];
        if ((p >= vStart) && (p < vEnd)) closure[numCorners++] = p;
      }
      PetscCall(DMPlexGetRawFaces_Internal(dm, ct, closure, &numFaces, &faceTypes, &faceSizes, &faces));
      PetscCheck(coneSize == numFaces, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cell %" PetscInt_FMT " of type %s has %" PetscInt_FMT " faces but should have %" PetscInt_FMT, c, DMPolytopeTypes[ct], coneSize, numFaces);
      for (f = 0; f < numFaces; ++f) {
        DMPolytopeType fct;
        PetscInt      *fclosure = NULL, fclosureSize, cl, fnumCorners = 0, v;

        PetscCall(DMPlexGetCellType(dm, cone[f], &fct));
        PetscCall(DMPlexGetTransitiveClosure_Internal(dm, cone[f], ornt[f], PETSC_TRUE, &fclosureSize, &fclosure));
        for (cl = 0; cl < fclosureSize * 2; cl += 2) {
          const PetscInt p = fclosure[cl];
          if ((p >= vStart) && (p < vEnd)) fclosure[fnumCorners++] = p;
        }
        PetscCheck(fnumCorners == faceSizes[f], PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Face %" PetscInt_FMT " of type %s (cone idx %" PetscInt_FMT ") of cell %" PetscInt_FMT " of type %s has %" PetscInt_FMT " vertices but should have %" PetscInt_FMT, cone[f], DMPolytopeTypes[fct], f, c, DMPolytopeTypes[ct], fnumCorners, faceSizes[f]);
        for (v = 0; v < fnumCorners; ++v) {
          if (fclosure[v] != faces[fOff + v]) {
            PetscInt v1;

            PetscCall(PetscPrintf(PETSC_COMM_SELF, "face closure:"));
            for (v1 = 0; v1 < fnumCorners; ++v1) PetscCall(PetscPrintf(PETSC_COMM_SELF, " %" PetscInt_FMT, fclosure[v1]));
            PetscCall(PetscPrintf(PETSC_COMM_SELF, "\ncell face:"));
            for (v1 = 0; v1 < fnumCorners; ++v1) PetscCall(PetscPrintf(PETSC_COMM_SELF, " %" PetscInt_FMT, faces[fOff + v1]));
            PetscCall(PetscPrintf(PETSC_COMM_SELF, "\n"));
            SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Face %" PetscInt_FMT " of type %s (cone idx %" PetscInt_FMT ", ornt %" PetscInt_FMT ") of cell %" PetscInt_FMT " of type %s vertex %" PetscInt_FMT ", %" PetscInt_FMT " != %" PetscInt_FMT, cone[f], DMPolytopeTypes[fct], f, ornt[f], c, DMPolytopeTypes[ct], v, fclosure[v], faces[fOff + v]);
          }
        }
        PetscCall(DMPlexRestoreTransitiveClosure(dm, cone[f], PETSC_TRUE, &fclosureSize, &fclosure));
        fOff += faceSizes[f];
      }
      PetscCall(DMPlexRestoreRawFaces_Internal(dm, ct, closure, &numFaces, &faceTypes, &faceSizes, &faces));
      PetscCall(DMPlexRestoreTransitiveClosure(dm, c, PETSC_TRUE, &closureSize, &closure));
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexCheckGeometry - Check the geometry of mesh cells

  Input Parameter:
. dm - The `DMPLEX` object

  Level: developer

  Notes:
  This is a useful diagnostic when creating meshes programmatically.

  For the complete list of DMPlexCheck* functions, see `DMSetFromOptions()`.

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMCreate()`, `DMSetFromOptions()`
@*/
PetscErrorCode DMPlexCheckGeometry(DM dm)
{
  Vec       coordinates;
  PetscReal detJ, J[9], refVol = 1.0;
  PetscReal vol;
  PetscInt  dim, depth, dE, d, cStart, cEnd, c;

  PetscFunctionBegin;
  PetscCall(DMGetDimension(dm, &dim));
  PetscCall(DMGetCoordinateDim(dm, &dE));
  if (dim != dE) PetscFunctionReturn(PETSC_SUCCESS);
  PetscCall(DMPlexGetDepth(dm, &depth));
  for (d = 0; d < dim; ++d) refVol *= 2.0;
  PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
  /* Make sure local coordinates are created, because that step is collective */
  PetscCall(DMGetCoordinatesLocal(dm, &coordinates));
  if (!coordinates) PetscFunctionReturn(PETSC_SUCCESS);
  for (c = cStart; c < cEnd; ++c) {
    DMPolytopeType ct;
    PetscInt       unsplit;
    PetscBool      ignoreZeroVol = PETSC_FALSE;

    PetscCall(DMPlexGetCellType(dm, c, &ct));
    switch (ct) {
    case DM_POLYTOPE_SEG_PRISM_TENSOR:
    case DM_POLYTOPE_TRI_PRISM_TENSOR:
    case DM_POLYTOPE_QUAD_PRISM_TENSOR:
      ignoreZeroVol = PETSC_TRUE;
      break;
    default:
      break;
    }
    switch (ct) {
    case DM_POLYTOPE_TRI_PRISM:
    case DM_POLYTOPE_TRI_PRISM_TENSOR:
    case DM_POLYTOPE_QUAD_PRISM_TENSOR:
    case DM_POLYTOPE_PYRAMID:
      continue;
    default:
      break;
    }
    PetscCall(DMPlexCellUnsplitVertices_Private(dm, c, ct, &unsplit));
    if (unsplit) continue;
    PetscCall(DMPlexComputeCellGeometryFEM(dm, c, NULL, NULL, J, NULL, &detJ));
    PetscCheck(detJ >= -PETSC_SMALL && (detJ > 0.0 || ignoreZeroVol), PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Mesh cell %" PetscInt_FMT " of type %s is inverted, |J| = %g", c, DMPolytopeTypes[ct], (double)detJ);
    PetscCall(PetscInfo(dm, "Cell %" PetscInt_FMT " FEM Volume %g\n", c, (double)(detJ * refVol)));
    /* This should work with periodicity since DG coordinates should be used */
    if (depth > 1) {
      PetscCall(DMPlexComputeCellGeometryFVM(dm, c, &vol, NULL, NULL));
      PetscCheck(vol >= -PETSC_SMALL && (vol > 0.0 || ignoreZeroVol), PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Mesh cell %" PetscInt_FMT " of type %s is inverted, vol = %g", c, DMPolytopeTypes[ct], (double)vol);
      PetscCall(PetscInfo(dm, "Cell %" PetscInt_FMT " FVM Volume %g\n", c, (double)vol));
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexCheckPointSF - Check that several necessary conditions are met for the point `PetscSF` of this plex.

  Collective

  Input Parameters:
+ dm              - The `DMPLEX` object
. pointSF         - The `PetscSF`, or `NULL` for `PointSF` attached to `DM`
- allowExtraRoots - Flag to allow extra points not present in the `DM`

  Level: developer

  Notes:
  This is mainly intended for debugging/testing purposes.

  For the complete list of DMPlexCheck* functions, see `DMSetFromOptions()`.

  Extra roots can come from periodic cuts, where additional points appear on the boundary

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMGetPointSF()`, `DMSetFromOptions()`
@*/
PetscErrorCode DMPlexCheckPointSF(DM dm, PetscSF pointSF, PetscBool allowExtraRoots)
{
  PetscInt           l, nleaves, nroots, overlap;
  const PetscInt    *locals;
  const PetscSFNode *remotes;
  PetscBool          distributed;
  MPI_Comm           comm;
  PetscMPIInt        rank;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (pointSF) PetscValidHeaderSpecific(pointSF, PETSCSF_CLASSID, 2);
  else pointSF = dm->sf;
  PetscCall(PetscObjectGetComm((PetscObject)dm, &comm));
  PetscCheck(pointSF, comm, PETSC_ERR_ARG_WRONGSTATE, "DMPlex must have Point SF attached");
  PetscCallMPI(MPI_Comm_rank(comm, &rank));
  {
    PetscMPIInt mpiFlag;

    PetscCallMPI(MPI_Comm_compare(comm, PetscObjectComm((PetscObject)pointSF), &mpiFlag));
    PetscCheck(mpiFlag == MPI_CONGRUENT || mpiFlag == MPI_IDENT, PETSC_COMM_SELF, PETSC_ERR_ARG_NOTSAMECOMM, "DM and Point SF have different communicators (flag %d)", mpiFlag);
  }
  PetscCall(PetscSFGetGraph(pointSF, &nroots, &nleaves, &locals, &remotes));
  PetscCall(DMPlexIsDistributed(dm, &distributed));
  if (!distributed) {
    PetscCheck(nroots < 0 || nleaves == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Undistributed DMPlex cannot have non-empty PointSF (has %" PetscInt_FMT " roots, %" PetscInt_FMT " leaves)", nroots, nleaves);
    PetscFunctionReturn(PETSC_SUCCESS);
  }
  PetscCheck(nroots >= 0, comm, PETSC_ERR_ARG_WRONGSTATE, "This DMPlex is distributed but its PointSF has no graph set (has %" PetscInt_FMT " roots, %" PetscInt_FMT " leaves)", nroots, nleaves);
  PetscCall(DMPlexGetOverlap(dm, &overlap));

  /* Check SF graph is compatible with DMPlex chart */
  {
    PetscInt pStart, pEnd, maxLeaf;

    PetscCall(DMPlexGetChart(dm, &pStart, &pEnd));
    PetscCall(PetscSFGetLeafRange(pointSF, NULL, &maxLeaf));
    PetscCheck(allowExtraRoots || pEnd - pStart == nroots, PETSC_COMM_SELF, PETSC_ERR_PLIB, "pEnd - pStart = %" PetscInt_FMT " != nroots = %" PetscInt_FMT, pEnd - pStart, nroots);
    PetscCheck(maxLeaf < pEnd, PETSC_COMM_SELF, PETSC_ERR_PLIB, "maxLeaf = %" PetscInt_FMT " >= pEnd = %" PetscInt_FMT, maxLeaf, pEnd);
  }

  /* Check Point SF has no local points referenced */
  for (l = 0; l < nleaves; l++) {
    PetscAssert(remotes[l].rank != (PetscInt)rank, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Point SF contains local point %" PetscInt_FMT " <- (%" PetscInt_FMT ",%" PetscInt_FMT ")", locals ? locals[l] : l, remotes[l].rank, remotes[l].index);
  }

  /* Check there are no cells in interface */
  if (!overlap) {
    PetscInt cellHeight, cStart, cEnd;

    PetscCall(DMPlexGetVTKCellHeight(dm, &cellHeight));
    PetscCall(DMPlexGetHeightStratum(dm, cellHeight, &cStart, &cEnd));
    for (l = 0; l < nleaves; ++l) {
      const PetscInt point = locals ? locals[l] : l;

      PetscCheck(point < cStart || point >= cEnd, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Point SF contains %" PetscInt_FMT " which is a cell", point);
    }
  }

  /* If some point is in interface, then all its cone points must be also in interface (either as leaves or roots) */
  {
    const PetscInt *rootdegree;

    PetscCall(PetscSFComputeDegreeBegin(pointSF, &rootdegree));
    PetscCall(PetscSFComputeDegreeEnd(pointSF, &rootdegree));
    for (l = 0; l < nleaves; ++l) {
      const PetscInt  point = locals ? locals[l] : l;
      const PetscInt *cone;
      PetscInt        coneSize, c, idx;

      PetscCall(DMPlexGetConeSize(dm, point, &coneSize));
      PetscCall(DMPlexGetCone(dm, point, &cone));
      for (c = 0; c < coneSize; ++c) {
        if (!rootdegree[cone[c]]) {
          if (locals) {
            PetscCall(PetscFindInt(cone[c], nleaves, locals, &idx));
          } else {
            idx = (cone[c] < nleaves) ? cone[c] : -1;
          }
          PetscCheck(idx >= 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Point SF contains %" PetscInt_FMT " but not %" PetscInt_FMT " from its cone", point, cone[c]);
        }
      }
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexCheckOrphanVertices - Check that no vertices are disconnected from the mesh, unless the mesh only consists of disconnected vertices.

  Collective

  Input Parameter:
. dm - The `DMPLEX` object

  Level: developer

  Notes:
  This is mainly intended for debugging/testing purposes.

  Other cell types which are disconnected would be caught by the symmetry and face checks.

  For the complete list of DMPlexCheck* functions, see `DMSetFromOptions()`.

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexCheck()`, `DMSetFromOptions()`
@*/
PetscErrorCode DMPlexCheckOrphanVertices(DM dm)
{
  PetscInt pStart, pEnd, vStart, vEnd;

  PetscFunctionBegin;
  PetscCall(DMPlexGetChart(dm, &pStart, &pEnd));
  PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
  if (pStart == vStart && pEnd == vEnd) PetscFunctionReturn(PETSC_SUCCESS);
  for (PetscInt v = vStart; v < vEnd; ++v) {
    PetscInt suppSize;

    PetscCall(DMPlexGetSupportSize(dm, v, &suppSize));
    PetscCheck(suppSize, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Vertex %" PetscInt_FMT " is disconnected from the mesh", v);
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexCheck - Perform various checks of `DMPLEX` sanity

  Input Parameter:
. dm - The `DMPLEX` object

  Level: developer

  Notes:
  This is a useful diagnostic when creating meshes programmatically.

  For the complete list of DMPlexCheck* functions, see `DMSetFromOptions()`.

  Currently does not include `DMPlexCheckCellShape()`.

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMCreate()`, `DMSetFromOptions()`
@*/
PetscErrorCode DMPlexCheck(DM dm)
{
  PetscInt cellHeight;

  PetscFunctionBegin;
  PetscCall(DMPlexGetVTKCellHeight(dm, &cellHeight));
  PetscCall(DMPlexCheckSymmetry(dm));
  PetscCall(DMPlexCheckSkeleton(dm, cellHeight));
  PetscCall(DMPlexCheckFaces(dm, cellHeight));
  PetscCall(DMPlexCheckGeometry(dm));
  PetscCall(DMPlexCheckPointSF(dm, NULL, PETSC_FALSE));
  PetscCall(DMPlexCheckInterfaceCones(dm));
  PetscCall(DMPlexCheckOrphanVertices(dm));
  PetscFunctionReturn(PETSC_SUCCESS);
}

typedef struct cell_stats {
  PetscReal min, max, sum, squaresum;
  PetscInt  count;
} cell_stats_t;

static void MPIAPI cell_stats_reduce(void *a, void *b, int *len, MPI_Datatype *datatype)
{
  PetscInt i, N = *len;

  for (i = 0; i < N; i++) {
    cell_stats_t *A = (cell_stats_t *)a;
    cell_stats_t *B = (cell_stats_t *)b;

    B->min = PetscMin(A->min, B->min);
    B->max = PetscMax(A->max, B->max);
    B->sum += A->sum;
    B->squaresum += A->squaresum;
    B->count += A->count;
  }
}

/*@
  DMPlexCheckCellShape - Checks the Jacobian of the mapping from reference to real cells and computes some minimal statistics.

  Collective

  Input Parameters:
+ dm        - The `DMPLEX` object
. output    - If true, statistics will be displayed on `stdout`
- condLimit - Display all cells above this condition number, or `PETSC_DETERMINE` for no cell output

  Level: developer

  Notes:
  This is mainly intended for debugging/testing purposes.

  For the complete list of DMPlexCheck* functions, see `DMSetFromOptions()`.

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMSetFromOptions()`, `DMPlexComputeOrthogonalQuality()`
@*/
PetscErrorCode DMPlexCheckCellShape(DM dm, PetscBool output, PetscReal condLimit)
{
  DM           dmCoarse;
  cell_stats_t stats, globalStats;
  MPI_Comm     comm = PetscObjectComm((PetscObject)dm);
  PetscReal   *J, *invJ, min = 0, max = 0, mean = 0, stdev = 0;
  PetscReal    limit = condLimit > 0 ? condLimit : PETSC_MAX_REAL;
  PetscInt     cdim, cStart, cEnd, c, eStart, eEnd, count = 0;
  PetscMPIInt  rank, size;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  stats.min = PETSC_MAX_REAL;
  stats.max = PETSC_MIN_REAL;
  stats.sum = stats.squaresum = 0.;
  stats.count                 = 0;

  PetscCallMPI(MPI_Comm_size(comm, &size));
  PetscCallMPI(MPI_Comm_rank(comm, &rank));
  PetscCall(DMGetCoordinateDim(dm, &cdim));
  PetscCall(PetscMalloc2(PetscSqr(cdim), &J, PetscSqr(cdim), &invJ));
  PetscCall(DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd));
  PetscCall(DMPlexGetDepthStratum(dm, 1, &eStart, &eEnd));
  for (c = cStart; c < cEnd; c++) {
    PetscInt  i;
    PetscReal frobJ = 0., frobInvJ = 0., cond2, cond, detJ;

    PetscCall(DMPlexComputeCellGeometryAffineFEM(dm, c, NULL, J, invJ, &detJ));
    PetscCheck(detJ >= 0.0, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Mesh cell %" PetscInt_FMT " is inverted", c);
    for (i = 0; i < PetscSqr(cdim); ++i) {
      frobJ += J[i] * J[i];
      frobInvJ += invJ[i] * invJ[i];
    }
    cond2 = frobJ * frobInvJ;
    cond  = PetscSqrtReal(cond2);

    stats.min = PetscMin(stats.min, cond);
    stats.max = PetscMax(stats.max, cond);
    stats.sum += cond;
    stats.squaresum += cond2;
    stats.count++;
    if (output && cond > limit) {
      PetscSection coordSection;
      Vec          coordsLocal;
      PetscScalar *coords = NULL;
      PetscInt     Nv, d, clSize, cl, *closure = NULL;

      PetscCall(DMGetCoordinatesLocal(dm, &coordsLocal));
      PetscCall(DMGetCoordinateSection(dm, &coordSection));
      PetscCall(DMPlexVecGetClosure(dm, coordSection, coordsLocal, c, &Nv, &coords));
      PetscCall(PetscSynchronizedPrintf(comm, "[%d] Cell %" PetscInt_FMT " cond %g\n", rank, c, (double)cond));
      for (i = 0; i < Nv / cdim; ++i) {
        PetscCall(PetscSynchronizedPrintf(comm, "  Vertex %" PetscInt_FMT ": (", i));
        for (d = 0; d < cdim; ++d) {
          if (d > 0) PetscCall(PetscSynchronizedPrintf(comm, ", "));
          PetscCall(PetscSynchronizedPrintf(comm, "%g", (double)PetscRealPart(coords[i * cdim + d])));
        }
        PetscCall(PetscSynchronizedPrintf(comm, ")\n"));
      }
      PetscCall(DMPlexGetTransitiveClosure(dm, c, PETSC_TRUE, &clSize, &closure));
      for (cl = 0; cl < clSize * 2; cl += 2) {
        const PetscInt edge = closure[cl];

        if ((edge >= eStart) && (edge < eEnd)) {
          PetscReal len;

          PetscCall(DMPlexComputeCellGeometryFVM(dm, edge, &len, NULL, NULL));
          PetscCall(PetscSynchronizedPrintf(comm, "  Edge %" PetscInt_FMT ": length %g\n", edge, (double)len));
        }
      }
      PetscCall(DMPlexRestoreTransitiveClosure(dm, c, PETSC_TRUE, &clSize, &closure));
      PetscCall(DMPlexVecRestoreClosure(dm, coordSection, coordsLocal, c, &Nv, &coords));
    }
  }
  if (output) PetscCall(PetscSynchronizedFlush(comm, NULL));

  if (size > 1) {
    PetscMPIInt  blockLengths[2] = {4, 1};
    MPI_Aint     blockOffsets[2] = {offsetof(cell_stats_t, min), offsetof(cell_stats_t, count)};
    MPI_Datatype blockTypes[2]   = {MPIU_REAL, MPIU_INT}, statType;
    MPI_Op       statReduce;

    PetscCallMPI(MPI_Type_create_struct(2, blockLengths, blockOffsets, blockTypes, &statType));
    PetscCallMPI(MPI_Type_commit(&statType));
    PetscCallMPI(MPI_Op_create(cell_stats_reduce, PETSC_TRUE, &statReduce));
    PetscCallMPI(MPI_Reduce(&stats, &globalStats, 1, statType, statReduce, 0, comm));
    PetscCallMPI(MPI_Op_free(&statReduce));
    PetscCallMPI(MPI_Type_free(&statType));
  } else {
    PetscCall(PetscArraycpy(&globalStats, &stats, 1));
  }
  if (rank == 0) {
    count = globalStats.count;
    min   = globalStats.min;
    max   = globalStats.max;
    mean  = globalStats.sum / globalStats.count;
    stdev = globalStats.count > 1 ? PetscSqrtReal(PetscMax((globalStats.squaresum - globalStats.count * mean * mean) / (globalStats.count - 1), 0)) : 0.0;
  }

  if (output) PetscCall(PetscPrintf(comm, "Mesh with %" PetscInt_FMT " cells, shape condition numbers: min = %g, max = %g, mean = %g, stddev = %g\n", count, (double)min, (double)max, (double)mean, (double)stdev));
  PetscCall(PetscFree2(J, invJ));

  PetscCall(DMGetCoarseDM(dm, &dmCoarse));
  if (dmCoarse) {
    PetscBool isplex;

    PetscCall(PetscObjectTypeCompare((PetscObject)dmCoarse, DMPLEX, &isplex));
    if (isplex) PetscCall(DMPlexCheckCellShape(dmCoarse, output, condLimit));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexComputeOrthogonalQuality - Compute cell-wise orthogonal quality mesh statistic. Optionally tags all cells with
  orthogonal quality below given tolerance.

  Collective

  Input Parameters:
+ dm   - The `DMPLEX` object
. fv   - Optional `PetscFV` object for pre-computed cell/face centroid information
- atol - [0, 1] Absolute tolerance for tagging cells.

  Output Parameters:
+ OrthQual      - `Vec` containing orthogonal quality per cell
- OrthQualLabel - `DMLabel` tagging cells below atol with `DM_ADAPT_REFINE`

  Options Database Keys:
+ -dm_plex_orthogonal_quality_label_view - view OrthQualLabel if label is requested. Currently only `PETSCVIEWERASCII` is supported.
- -dm_plex_orthogonal_quality_vec_view   - view OrthQual vector.

  Level: intermediate

  Notes:
  Orthogonal quality is given by the following formula\:

  $ \min \left[ \frac{A_i \cdot f_i}{\|A_i\| \|f_i\|} , \frac{A_i \cdot c_i}{\|A_i\| \|c_i\|} \right]$

  Where A_i is the i'th face-normal vector, f_i is the vector from the cell centroid to the i'th face centroid, and c_i
  is the vector from the current cells centroid to the centroid of its i'th neighbor (which shares a face with the
  current cell). This computes the vector similarity between each cell face and its corresponding neighbor centroid by
  calculating the cosine of the angle between these vectors.

  Orthogonal quality ranges from 1 (best) to 0 (worst).

  This routine is mainly useful for FVM, however is not restricted to only FVM. The `PetscFV` object is optionally used to check for
  pre-computed FVM cell data, but if it is not passed in then this data will be computed.

  Cells are tagged if they have an orthogonal quality less than or equal to the absolute tolerance.

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexCheckCellShape()`, `DMCreateLabel()`, `PetscFV`, `DMLabel`, `Vec`
@*/
PetscErrorCode DMPlexComputeOrthogonalQuality(DM dm, PetscFV fv, PetscReal atol, Vec *OrthQual, DMLabel *OrthQualLabel)
{
  PetscInt               nc, cellHeight, cStart, cEnd, cell, cellIter = 0;
  PetscInt              *idx;
  PetscScalar           *oqVals;
  const PetscScalar     *cellGeomArr, *faceGeomArr;
  PetscReal             *ci, *fi, *Ai;
  MPI_Comm               comm;
  Vec                    cellgeom, facegeom;
  DM                     dmFace, dmCell;
  IS                     glob;
  ISLocalToGlobalMapping ltog;
  PetscViewer            vwr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (fv) PetscValidHeaderSpecific(fv, PETSCFV_CLASSID, 2);
  PetscAssertPointer(OrthQual, 4);
  PetscCheck(atol >= 0.0 && atol <= 1.0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Absolute tolerance %g not in [0,1]", (double)atol);
  PetscCall(PetscObjectGetComm((PetscObject)dm, &comm));
  PetscCall(DMGetDimension(dm, &nc));
  PetscCheck(nc >= 2, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "DM must have dimension >= 2 (current %" PetscInt_FMT ")", nc);
  {
    DMPlexInterpolatedFlag interpFlag;

    PetscCall(DMPlexIsInterpolated(dm, &interpFlag));
    if (interpFlag != DMPLEX_INTERPOLATED_FULL) {
      PetscMPIInt rank;

      PetscCallMPI(MPI_Comm_rank(comm, &rank));
      SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "DM must be fully interpolated, DM on rank %d is not fully interpolated", rank);
    }
  }
  if (OrthQualLabel) {
    PetscAssertPointer(OrthQualLabel, 5);
    PetscCall(DMCreateLabel(dm, "Orthogonal_Quality"));
    PetscCall(DMGetLabel(dm, "Orthogonal_Quality", OrthQualLabel));
  } else {
    *OrthQualLabel = NULL;
  }
  PetscCall(DMPlexGetVTKCellHeight(dm, &cellHeight));
  PetscCall(DMPlexGetHeightStratum(dm, cellHeight, &cStart, &cEnd));
  PetscCall(DMPlexCreateCellNumbering(dm, PETSC_TRUE, &glob));
  PetscCall(ISLocalToGlobalMappingCreateIS(glob, &ltog));
  PetscCall(ISLocalToGlobalMappingSetType(ltog, ISLOCALTOGLOBALMAPPINGHASH));
  PetscCall(VecCreate(comm, OrthQual));
  PetscCall(VecSetType(*OrthQual, VECSTANDARD));
  PetscCall(VecSetSizes(*OrthQual, cEnd - cStart, PETSC_DETERMINE));
  PetscCall(VecSetLocalToGlobalMapping(*OrthQual, ltog));
  PetscCall(VecSetUp(*OrthQual));
  PetscCall(ISDestroy(&glob));
  PetscCall(ISLocalToGlobalMappingDestroy(&ltog));
  PetscCall(DMPlexGetDataFVM(dm, fv, &cellgeom, &facegeom, NULL));
  PetscCall(VecGetArrayRead(cellgeom, &cellGeomArr));
  PetscCall(VecGetArrayRead(facegeom, &faceGeomArr));
  PetscCall(VecGetDM(cellgeom, &dmCell));
  PetscCall(VecGetDM(facegeom, &dmFace));
  PetscCall(PetscMalloc5(cEnd - cStart, &idx, cEnd - cStart, &oqVals, nc, &ci, nc, &fi, nc, &Ai));
  for (cell = cStart; cell < cEnd; cellIter++, cell++) {
    PetscInt         cellneigh, cellneighiter = 0, adjSize = PETSC_DETERMINE;
    PetscInt         cellarr[2], *adj = NULL;
    PetscScalar     *cArr, *fArr;
    PetscReal        minvalc = 1.0, minvalf = 1.0;
    PetscFVCellGeom *cg;

    idx[cellIter] = cell - cStart;
    cellarr[0]    = cell;
    /* Make indexing into cellGeom easier */
    PetscCall(DMPlexPointLocalRead(dmCell, cell, cellGeomArr, &cg));
    PetscCall(DMPlexGetAdjacency_Internal(dm, cell, PETSC_TRUE, PETSC_FALSE, PETSC_FALSE, &adjSize, &adj));
    /* Technically 1 too big, but easier than fiddling with empty adjacency array */
    PetscCall(PetscCalloc2(adjSize, &cArr, adjSize, &fArr));
    for (cellneigh = 0; cellneigh < adjSize; cellneighiter++, cellneigh++) {
      PetscInt         i;
      const PetscInt   neigh  = adj[cellneigh];
      PetscReal        normci = 0, normfi = 0, normai = 0;
      PetscFVCellGeom *cgneigh;
      PetscFVFaceGeom *fg;

      /* Don't count ourselves in the neighbor list */
      if (neigh == cell) continue;
      PetscCall(DMPlexPointLocalRead(dmCell, neigh, cellGeomArr, &cgneigh));
      cellarr[1] = neigh;
      {
        PetscInt        numcovpts;
        const PetscInt *covpts;

        PetscCall(DMPlexGetMeet(dm, 2, cellarr, &numcovpts, &covpts));
        PetscCall(DMPlexPointLocalRead(dmFace, covpts[0], faceGeomArr, &fg));
        PetscCall(DMPlexRestoreMeet(dm, 2, cellarr, &numcovpts, &covpts));
      }

      /* Compute c_i, f_i and their norms */
      for (i = 0; i < nc; i++) {
        ci[i] = cgneigh->centroid[i] - cg->centroid[i];
        fi[i] = fg->centroid[i] - cg->centroid[i];
        Ai[i] = fg->normal[i];
        normci += PetscPowReal(ci[i], 2);
        normfi += PetscPowReal(fi[i], 2);
        normai += PetscPowReal(Ai[i], 2);
      }
      normci = PetscSqrtReal(normci);
      normfi = PetscSqrtReal(normfi);
      normai = PetscSqrtReal(normai);

      /* Normalize and compute for each face-cell-normal pair */
      for (i = 0; i < nc; i++) {
        ci[i] = ci[i] / normci;
        fi[i] = fi[i] / normfi;
        Ai[i] = Ai[i] / normai;
        /* PetscAbs because I don't know if normals are guaranteed to point out */
        cArr[cellneighiter] += PetscAbs(Ai[i] * ci[i]);
        fArr[cellneighiter] += PetscAbs(Ai[i] * fi[i]);
      }
      if (PetscRealPart(cArr[cellneighiter]) < minvalc) minvalc = PetscRealPart(cArr[cellneighiter]);
      if (PetscRealPart(fArr[cellneighiter]) < minvalf) minvalf = PetscRealPart(fArr[cellneighiter]);
    }
    PetscCall(PetscFree(adj));
    PetscCall(PetscFree2(cArr, fArr));
    /* Defer to cell if they're equal */
    oqVals[cellIter] = PetscMin(minvalf, minvalc);
    if (OrthQualLabel) {
      if (PetscRealPart(oqVals[cellIter]) <= atol) PetscCall(DMLabelSetValue(*OrthQualLabel, cell, DM_ADAPT_REFINE));
    }
  }
  PetscCall(VecSetValuesLocal(*OrthQual, cEnd - cStart, idx, oqVals, INSERT_VALUES));
  PetscCall(VecAssemblyBegin(*OrthQual));
  PetscCall(VecAssemblyEnd(*OrthQual));
  PetscCall(VecRestoreArrayRead(cellgeom, &cellGeomArr));
  PetscCall(VecRestoreArrayRead(facegeom, &faceGeomArr));
  PetscCall(PetscOptionsCreateViewer(comm, NULL, NULL, "-dm_plex_orthogonal_quality_label_view", &vwr, NULL, NULL));
  if (OrthQualLabel) {
    if (vwr) PetscCall(DMLabelView(*OrthQualLabel, vwr));
  }
  PetscCall(PetscFree5(idx, oqVals, ci, fi, Ai));
  PetscCall(PetscViewerDestroy(&vwr));
  PetscCall(VecViewFromOptions(*OrthQual, NULL, "-dm_plex_orthogonal_quality_vec_view"));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* this is here instead of DMGetOutputDM because output DM still has constraints in the local indices that affect
 * interpolator construction */
static PetscErrorCode DMGetFullDM(DM dm, DM *odm)
{
  PetscSection section, newSection, gsection;
  PetscSF      sf;
  PetscBool    hasConstraints, ghasConstraints;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscAssertPointer(odm, 2);
  PetscCall(DMGetLocalSection(dm, &section));
  PetscCall(PetscSectionHasConstraints(section, &hasConstraints));
  PetscCall(MPIU_Allreduce(&hasConstraints, &ghasConstraints, 1, MPIU_BOOL, MPI_LOR, PetscObjectComm((PetscObject)dm)));
  if (!ghasConstraints) {
    PetscCall(PetscObjectReference((PetscObject)dm));
    *odm = dm;
    PetscFunctionReturn(PETSC_SUCCESS);
  }
  PetscCall(DMClone(dm, odm));
  PetscCall(DMCopyFields(dm, PETSC_DETERMINE, PETSC_DETERMINE, *odm));
  PetscCall(DMGetLocalSection(*odm, &newSection));
  PetscCall(DMGetPointSF(*odm, &sf));
  PetscCall(PetscSectionCreateGlobalSection(newSection, sf, PETSC_TRUE, PETSC_TRUE, PETSC_FALSE, &gsection));
  PetscCall(DMSetGlobalSection(*odm, gsection));
  PetscCall(PetscSectionDestroy(&gsection));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode DMCreateAffineInterpolationCorrection_Plex(DM dmc, DM dmf, Vec *shift)
{
  DM        dmco, dmfo;
  Mat       interpo;
  Vec       rscale;
  Vec       cglobalo, clocal;
  Vec       fglobal, fglobalo, flocal;
  PetscBool regular;

  PetscFunctionBegin;
  PetscCall(DMGetFullDM(dmc, &dmco));
  PetscCall(DMGetFullDM(dmf, &dmfo));
  PetscCall(DMSetCoarseDM(dmfo, dmco));
  PetscCall(DMPlexGetRegularRefinement(dmf, &regular));
  PetscCall(DMPlexSetRegularRefinement(dmfo, regular));
  PetscCall(DMCreateInterpolation(dmco, dmfo, &interpo, &rscale));
  PetscCall(DMCreateGlobalVector(dmco, &cglobalo));
  PetscCall(DMCreateLocalVector(dmc, &clocal));
  PetscCall(VecSet(cglobalo, 0.));
  PetscCall(VecSet(clocal, 0.));
  PetscCall(DMCreateGlobalVector(dmf, &fglobal));
  PetscCall(DMCreateGlobalVector(dmfo, &fglobalo));
  PetscCall(DMCreateLocalVector(dmf, &flocal));
  PetscCall(VecSet(fglobal, 0.));
  PetscCall(VecSet(fglobalo, 0.));
  PetscCall(VecSet(flocal, 0.));
  PetscCall(DMPlexInsertBoundaryValues(dmc, PETSC_TRUE, clocal, 0., NULL, NULL, NULL));
  PetscCall(DMLocalToGlobalBegin(dmco, clocal, INSERT_VALUES, cglobalo));
  PetscCall(DMLocalToGlobalEnd(dmco, clocal, INSERT_VALUES, cglobalo));
  PetscCall(MatMult(interpo, cglobalo, fglobalo));
  PetscCall(DMGlobalToLocalBegin(dmfo, fglobalo, INSERT_VALUES, flocal));
  PetscCall(DMGlobalToLocalEnd(dmfo, fglobalo, INSERT_VALUES, flocal));
  PetscCall(DMLocalToGlobalBegin(dmf, flocal, INSERT_VALUES, fglobal));
  PetscCall(DMLocalToGlobalEnd(dmf, flocal, INSERT_VALUES, fglobal));
  *shift = fglobal;
  PetscCall(VecDestroy(&flocal));
  PetscCall(VecDestroy(&fglobalo));
  PetscCall(VecDestroy(&clocal));
  PetscCall(VecDestroy(&cglobalo));
  PetscCall(VecDestroy(&rscale));
  PetscCall(MatDestroy(&interpo));
  PetscCall(DMDestroy(&dmfo));
  PetscCall(DMDestroy(&dmco));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PETSC_INTERN PetscErrorCode DMInterpolateSolution_Plex(DM coarse, DM fine, Mat interp, Vec coarseSol, Vec fineSol)
{
  PetscObject shifto;
  Vec         shift;

  PetscFunctionBegin;
  if (!interp) {
    Vec rscale;

    PetscCall(DMCreateInterpolation(coarse, fine, &interp, &rscale));
    PetscCall(VecDestroy(&rscale));
  } else {
    PetscCall(PetscObjectReference((PetscObject)interp));
  }
  PetscCall(PetscObjectQuery((PetscObject)interp, "_DMInterpolateSolution_Plex_Vec", &shifto));
  if (!shifto) {
    PetscCall(DMCreateAffineInterpolationCorrection_Plex(coarse, fine, &shift));
    PetscCall(PetscObjectCompose((PetscObject)interp, "_DMInterpolateSolution_Plex_Vec", (PetscObject)shift));
    shifto = (PetscObject)shift;
    PetscCall(VecDestroy(&shift));
  }
  shift = (Vec)shifto;
  PetscCall(MatInterpolate(interp, coarseSol, fineSol));
  PetscCall(VecAXPY(fineSol, 1.0, shift));
  PetscCall(MatDestroy(&interp));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* Pointwise interpolation
     Just code FEM for now
     u^f = I u^c
     sum_k u^f_k phi^f_k = I sum_j u^c_j phi^c_j
     u^f_i = sum_j psi^f_i I phi^c_j u^c_j
     I_{ij} = psi^f_i phi^c_j
*/
PetscErrorCode DMCreateInterpolation_Plex(DM dmCoarse, DM dmFine, Mat *interpolation, Vec *scaling)
{
  PetscSection gsc, gsf;
  PetscInt     m, n;
  void        *ctx;
  DM           cdm;
  PetscBool    regular, ismatis, isRefined = dmCoarse->data == dmFine->data ? PETSC_FALSE : PETSC_TRUE;

  PetscFunctionBegin;
  PetscCall(DMGetGlobalSection(dmFine, &gsf));
  PetscCall(PetscSectionGetConstrainedStorageSize(gsf, &m));
  PetscCall(DMGetGlobalSection(dmCoarse, &gsc));
  PetscCall(PetscSectionGetConstrainedStorageSize(gsc, &n));

  PetscCall(PetscStrcmp(dmCoarse->mattype, MATIS, &ismatis));
  PetscCall(MatCreate(PetscObjectComm((PetscObject)dmCoarse), interpolation));
  PetscCall(MatSetSizes(*interpolation, m, n, PETSC_DETERMINE, PETSC_DETERMINE));
  PetscCall(MatSetType(*interpolation, ismatis ? MATAIJ : dmCoarse->mattype));
  PetscCall(DMGetApplicationContext(dmFine, &ctx));

  PetscCall(DMGetCoarseDM(dmFine, &cdm));
  PetscCall(DMPlexGetRegularRefinement(dmFine, &regular));
  if (!isRefined || (regular && cdm == dmCoarse)) PetscCall(DMPlexComputeInterpolatorNested(dmCoarse, dmFine, isRefined, *interpolation, ctx));
  else PetscCall(DMPlexComputeInterpolatorGeneral(dmCoarse, dmFine, *interpolation, ctx));
  PetscCall(MatViewFromOptions(*interpolation, NULL, "-interp_mat_view"));
  if (scaling) {
    /* Use naive scaling */
    PetscCall(DMCreateInterpolationScale(dmCoarse, dmFine, *interpolation, scaling));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode DMCreateInjection_Plex(DM dmCoarse, DM dmFine, Mat *mat)
{
  VecScatter ctx;

  PetscFunctionBegin;
  PetscCall(DMPlexComputeInjectorFEM(dmCoarse, dmFine, &ctx, NULL));
  PetscCall(MatCreateScatter(PetscObjectComm((PetscObject)ctx), ctx, mat));
  PetscCall(VecScatterDestroy(&ctx));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static void g0_identity_private(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[])
{
  const PetscInt f  = (PetscInt)PetscRealPart(constants[numConstants]);
  const PetscInt Nc = uOff[f + 1] - uOff[f];
  for (PetscInt c = 0; c < Nc; ++c) g0[c * Nc + c] = 1.0;
}

PetscErrorCode DMCreateMassMatrixLumped_Plex(DM dm, Vec *lmass, Vec *mass)
{
  DM           dmc;
  PetscDS      ds;
  Vec          ones, locmass;
  IS           cellIS;
  PetscFormKey key;
  PetscInt     depth;

  PetscFunctionBegin;
  PetscCall(DMClone(dm, &dmc));
  PetscCall(DMCopyDisc(dm, dmc));
  PetscCall(DMGetDS(dmc, &ds));
  for (PetscInt f = 0; f < dmc->Nf; ++f) PetscCall(PetscDSSetJacobian(ds, f, f, g0_identity_private, NULL, NULL, NULL));
  if (mass) PetscCall(DMCreateGlobalVector(dm, mass));
  if (lmass) PetscCall(DMCreateLocalVector(dm, &locmass));
  else PetscCall(DMGetLocalVector(dm, &locmass));
  PetscCall(DMGetLocalVector(dm, &ones));
  PetscCall(DMPlexGetDepth(dm, &depth));
  PetscCall(DMGetStratumIS(dm, "depth", depth, &cellIS));
  PetscCall(VecSet(locmass, 0.0));
  PetscCall(VecSet(ones, 1.0));
  key.label = NULL;
  key.value = 0;
  key.field = 0;
  key.part  = 0;
  PetscCall(DMPlexComputeJacobian_Action_Internal(dmc, key, cellIS, 0.0, 0.0, ones, NULL, ones, locmass, NULL));
  PetscCall(ISDestroy(&cellIS));
  if (mass) {
    PetscCall(DMLocalToGlobalBegin(dm, locmass, ADD_VALUES, *mass));
    PetscCall(DMLocalToGlobalEnd(dm, locmass, ADD_VALUES, *mass));
  }
  PetscCall(DMRestoreLocalVector(dm, &ones));
  if (lmass) *lmass = locmass;
  else PetscCall(DMRestoreLocalVector(dm, &locmass));
  PetscCall(DMDestroy(&dmc));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode DMCreateMassMatrix_Plex(DM dmCoarse, DM dmFine, Mat *mass)
{
  PetscSection gsc, gsf;
  PetscInt     m, n;
  void        *ctx;
  DM           cdm;
  PetscBool    regular;

  PetscFunctionBegin;
  if (dmFine == dmCoarse) {
    DM            dmc;
    PetscDS       ds;
    PetscWeakForm wf;
    Vec           u;
    IS            cellIS;
    PetscFormKey  key;
    PetscInt      depth;

    PetscCall(DMClone(dmFine, &dmc));
    PetscCall(DMCopyDisc(dmFine, dmc));
    PetscCall(DMGetDS(dmc, &ds));
    PetscCall(PetscDSGetWeakForm(ds, &wf));
    PetscCall(PetscWeakFormClear(wf));
    for (PetscInt f = 0; f < dmc->Nf; ++f) PetscCall(PetscDSSetJacobian(ds, f, f, g0_identity_private, NULL, NULL, NULL));
    PetscCall(DMCreateMatrix(dmc, mass));
    PetscCall(DMGetLocalVector(dmc, &u));
    PetscCall(DMPlexGetDepth(dmc, &depth));
    PetscCall(DMGetStratumIS(dmc, "depth", depth, &cellIS));
    PetscCall(MatZeroEntries(*mass));
    key.label = NULL;
    key.value = 0;
    key.field = 0;
    key.part  = 0;
    PetscCall(DMPlexComputeJacobian_Internal(dmc, key, cellIS, 0.0, 0.0, u, NULL, *mass, *mass, NULL));
    PetscCall(ISDestroy(&cellIS));
    PetscCall(DMRestoreLocalVector(dmc, &u));
    PetscCall(DMDestroy(&dmc));
  } else {
    PetscCall(DMGetGlobalSection(dmFine, &gsf));
    PetscCall(PetscSectionGetConstrainedStorageSize(gsf, &m));
    PetscCall(DMGetGlobalSection(dmCoarse, &gsc));
    PetscCall(PetscSectionGetConstrainedStorageSize(gsc, &n));

    PetscCall(MatCreate(PetscObjectComm((PetscObject)dmCoarse), mass));
    PetscCall(MatSetSizes(*mass, m, n, PETSC_DETERMINE, PETSC_DETERMINE));
    PetscCall(MatSetType(*mass, dmCoarse->mattype));
    PetscCall(DMGetApplicationContext(dmFine, &ctx));

    PetscCall(DMGetCoarseDM(dmFine, &cdm));
    PetscCall(DMPlexGetRegularRefinement(dmFine, &regular));
    if (regular && cdm == dmCoarse) PetscCall(DMPlexComputeMassMatrixNested(dmCoarse, dmFine, *mass, ctx));
    else PetscCall(DMPlexComputeMassMatrixGeneral(dmCoarse, dmFine, *mass, ctx));
  }
  PetscCall(MatViewFromOptions(*mass, NULL, "-mass_mat_view"));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexGetRegularRefinement - Get the flag indicating that this mesh was obtained by regular refinement from its coarse mesh

  Input Parameter:
. dm - The `DMPLEX` object

  Output Parameter:
. regular - The flag

  Level: intermediate

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexSetRegularRefinement()`
@*/
PetscErrorCode DMPlexGetRegularRefinement(DM dm, PetscBool *regular)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscAssertPointer(regular, 2);
  *regular = ((DM_Plex *)dm->data)->regularRefinement;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexSetRegularRefinement - Set the flag indicating that this mesh was obtained by regular refinement from its coarse mesh

  Input Parameters:
+ dm      - The `DMPLEX` object
- regular - The flag

  Level: intermediate

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexGetRegularRefinement()`
@*/
PetscErrorCode DMPlexSetRegularRefinement(DM dm, PetscBool regular)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  ((DM_Plex *)dm->data)->regularRefinement = regular;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexGetAnchors - Get the layout of the anchor (point-to-point) constraints.  Typically, the user will not have to
  call DMPlexGetAnchors() directly: if there are anchors, then `DMPlexGetAnchors()` is called during `DMGetDefaultConstraints()`.

  Not Collective

  Input Parameter:
. dm - The `DMPLEX` object

  Output Parameters:
+ anchorSection - If not `NULL`, set to the section describing which points anchor the constrained points.
- anchorIS      - If not `NULL`, set to the list of anchors indexed by `anchorSection`

  Level: intermediate

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexSetAnchors()`, `DMGetDefaultConstraints()`, `DMSetDefaultConstraints()`, `IS`, `PetscSection`
@*/
PetscErrorCode DMPlexGetAnchors(DM dm, PetscSection *anchorSection, IS *anchorIS)
{
  DM_Plex *plex = (DM_Plex *)dm->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (!plex->anchorSection && !plex->anchorIS && plex->createanchors) PetscCall((*plex->createanchors)(dm));
  if (anchorSection) *anchorSection = plex->anchorSection;
  if (anchorIS) *anchorIS = plex->anchorIS;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexSetAnchors - Set the layout of the local anchor (point-to-point) constraints.

  Collective

  Input Parameters:
+ dm            - The `DMPLEX` object
. anchorSection - The section that describes the mapping from constrained points to the anchor points listed in anchorIS.
                  Must have a local communicator (`PETSC_COMM_SELF` or derivative).
- anchorIS      - The list of all anchor points.  Must have a local communicator (`PETSC_COMM_SELF` or derivative).

  Level: intermediate

  Notes:
  Unlike boundary conditions, when a point's degrees of freedom in a section are constrained to
  an outside value, the anchor constraints set a point's degrees of freedom to be a linear
  combination of other points' degrees of freedom.

  After specifying the layout of constraints with `DMPlexSetAnchors()`, one specifies the constraints by calling
  `DMGetDefaultConstraints()` and filling in the entries in the constraint matrix.

  The reference counts of `anchorSection` and `anchorIS` are incremented.

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexGetAnchors()`, `DMGetDefaultConstraints()`, `DMSetDefaultConstraints()`
@*/
PetscErrorCode DMPlexSetAnchors(DM dm, PetscSection anchorSection, IS anchorIS)
{
  DM_Plex    *plex = (DM_Plex *)dm->data;
  PetscMPIInt result;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (anchorSection) {
    PetscValidHeaderSpecific(anchorSection, PETSC_SECTION_CLASSID, 2);
    PetscCallMPI(MPI_Comm_compare(PETSC_COMM_SELF, PetscObjectComm((PetscObject)anchorSection), &result));
    PetscCheck(result == MPI_CONGRUENT || result == MPI_IDENT, PETSC_COMM_SELF, PETSC_ERR_ARG_NOTSAMECOMM, "anchor section must have local communicator");
  }
  if (anchorIS) {
    PetscValidHeaderSpecific(anchorIS, IS_CLASSID, 3);
    PetscCallMPI(MPI_Comm_compare(PETSC_COMM_SELF, PetscObjectComm((PetscObject)anchorIS), &result));
    PetscCheck(result == MPI_CONGRUENT || result == MPI_IDENT, PETSC_COMM_SELF, PETSC_ERR_ARG_NOTSAMECOMM, "anchor IS must have local communicator");
  }

  PetscCall(PetscObjectReference((PetscObject)anchorSection));
  PetscCall(PetscSectionDestroy(&plex->anchorSection));
  plex->anchorSection = anchorSection;

  PetscCall(PetscObjectReference((PetscObject)anchorIS));
  PetscCall(ISDestroy(&plex->anchorIS));
  plex->anchorIS = anchorIS;

  if (PetscUnlikelyDebug(anchorIS && anchorSection)) {
    PetscInt        size, a, pStart, pEnd;
    const PetscInt *anchors;

    PetscCall(PetscSectionGetChart(anchorSection, &pStart, &pEnd));
    PetscCall(ISGetLocalSize(anchorIS, &size));
    PetscCall(ISGetIndices(anchorIS, &anchors));
    for (a = 0; a < size; a++) {
      PetscInt p;

      p = anchors[a];
      if (p >= pStart && p < pEnd) {
        PetscInt dof;

        PetscCall(PetscSectionGetDof(anchorSection, p, &dof));
        if (dof) {
          PetscCall(ISRestoreIndices(anchorIS, &anchors));
          SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Point %" PetscInt_FMT " cannot be constrained and an anchor", p);
        }
      }
    }
    PetscCall(ISRestoreIndices(anchorIS, &anchors));
  }
  /* reset the generic constraints */
  PetscCall(DMSetDefaultConstraints(dm, NULL, NULL, NULL));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode DMPlexCreateConstraintSection_Anchors(DM dm, PetscSection section, PetscSection *cSec)
{
  PetscSection anchorSection;
  PetscInt     pStart, pEnd, sStart, sEnd, p, dof, numFields, f;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscCall(DMPlexGetAnchors(dm, &anchorSection, NULL));
  PetscCall(PetscSectionCreate(PETSC_COMM_SELF, cSec));
  PetscCall(PetscSectionGetNumFields(section, &numFields));
  if (numFields) {
    PetscInt f;
    PetscCall(PetscSectionSetNumFields(*cSec, numFields));

    for (f = 0; f < numFields; f++) {
      PetscInt numComp;

      PetscCall(PetscSectionGetFieldComponents(section, f, &numComp));
      PetscCall(PetscSectionSetFieldComponents(*cSec, f, numComp));
    }
  }
  PetscCall(PetscSectionGetChart(anchorSection, &pStart, &pEnd));
  PetscCall(PetscSectionGetChart(section, &sStart, &sEnd));
  pStart = PetscMax(pStart, sStart);
  pEnd   = PetscMin(pEnd, sEnd);
  pEnd   = PetscMax(pStart, pEnd);
  PetscCall(PetscSectionSetChart(*cSec, pStart, pEnd));
  for (p = pStart; p < pEnd; p++) {
    PetscCall(PetscSectionGetDof(anchorSection, p, &dof));
    if (dof) {
      PetscCall(PetscSectionGetDof(section, p, &dof));
      PetscCall(PetscSectionSetDof(*cSec, p, dof));
      for (f = 0; f < numFields; f++) {
        PetscCall(PetscSectionGetFieldDof(section, p, f, &dof));
        PetscCall(PetscSectionSetFieldDof(*cSec, p, f, dof));
      }
    }
  }
  PetscCall(PetscSectionSetUp(*cSec));
  PetscCall(PetscObjectSetName((PetscObject)*cSec, "Constraint Section"));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode DMPlexCreateConstraintMatrix_Anchors(DM dm, PetscSection section, PetscSection cSec, Mat *cMat)
{
  PetscSection    aSec;
  PetscInt        pStart, pEnd, p, sStart, sEnd, dof, aDof, aOff, off, nnz, annz, m, n, q, a, offset, *i, *j;
  const PetscInt *anchors;
  PetscInt        numFields, f;
  IS              aIS;
  MatType         mtype;
  PetscBool       iscuda, iskokkos;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscCall(PetscSectionGetStorageSize(cSec, &m));
  PetscCall(PetscSectionGetStorageSize(section, &n));
  PetscCall(MatCreate(PETSC_COMM_SELF, cMat));
  PetscCall(MatSetSizes(*cMat, m, n, m, n));
  PetscCall(PetscStrcmp(dm->mattype, MATSEQAIJCUSPARSE, &iscuda));
  if (!iscuda) PetscCall(PetscStrcmp(dm->mattype, MATMPIAIJCUSPARSE, &iscuda));
  PetscCall(PetscStrcmp(dm->mattype, MATSEQAIJKOKKOS, &iskokkos));
  if (!iskokkos) PetscCall(PetscStrcmp(dm->mattype, MATMPIAIJKOKKOS, &iskokkos));
  if (iscuda) mtype = MATSEQAIJCUSPARSE;
  else if (iskokkos) mtype = MATSEQAIJKOKKOS;
  else mtype = MATSEQAIJ;
  PetscCall(MatSetType(*cMat, mtype));
  PetscCall(DMPlexGetAnchors(dm, &aSec, &aIS));
  PetscCall(ISGetIndices(aIS, &anchors));
  /* cSec will be a subset of aSec and section */
  PetscCall(PetscSectionGetChart(cSec, &pStart, &pEnd));
  PetscCall(PetscSectionGetChart(section, &sStart, &sEnd));
  PetscCall(PetscMalloc1(m + 1, &i));
  i[0] = 0;
  PetscCall(PetscSectionGetNumFields(section, &numFields));
  for (p = pStart; p < pEnd; p++) {
    PetscInt rDof, rOff, r;

    PetscCall(PetscSectionGetDof(aSec, p, &rDof));
    if (!rDof) continue;
    PetscCall(PetscSectionGetOffset(aSec, p, &rOff));
    if (numFields) {
      for (f = 0; f < numFields; f++) {
        annz = 0;
        for (r = 0; r < rDof; r++) {
          a = anchors[rOff + r];
          if (a < sStart || a >= sEnd) continue;
          PetscCall(PetscSectionGetFieldDof(section, a, f, &aDof));
          annz += aDof;
        }
        PetscCall(PetscSectionGetFieldDof(cSec, p, f, &dof));
        PetscCall(PetscSectionGetFieldOffset(cSec, p, f, &off));
        for (q = 0; q < dof; q++) i[off + q + 1] = i[off + q] + annz;
      }
    } else {
      annz = 0;
      PetscCall(PetscSectionGetDof(cSec, p, &dof));
      for (q = 0; q < dof; q++) {
        a = anchors[rOff + q];
        if (a < sStart || a >= sEnd) continue;
        PetscCall(PetscSectionGetDof(section, a, &aDof));
        annz += aDof;
      }
      PetscCall(PetscSectionGetDof(cSec, p, &dof));
      PetscCall(PetscSectionGetOffset(cSec, p, &off));
      for (q = 0; q < dof; q++) i[off + q + 1] = i[off + q] + annz;
    }
  }
  nnz = i[m];
  PetscCall(PetscMalloc1(nnz, &j));
  offset = 0;
  for (p = pStart; p < pEnd; p++) {
    if (numFields) {
      for (f = 0; f < numFields; f++) {
        PetscCall(PetscSectionGetFieldDof(cSec, p, f, &dof));
        for (q = 0; q < dof; q++) {
          PetscInt rDof, rOff, r;
          PetscCall(PetscSectionGetDof(aSec, p, &rDof));
          PetscCall(PetscSectionGetOffset(aSec, p, &rOff));
          for (r = 0; r < rDof; r++) {
            PetscInt s;

            a = anchors[rOff + r];
            if (a < sStart || a >= sEnd) continue;
            PetscCall(PetscSectionGetFieldDof(section, a, f, &aDof));
            PetscCall(PetscSectionGetFieldOffset(section, a, f, &aOff));
            for (s = 0; s < aDof; s++) j[offset++] = aOff + s;
          }
        }
      }
    } else {
      PetscCall(PetscSectionGetDof(cSec, p, &dof));
      for (q = 0; q < dof; q++) {
        PetscInt rDof, rOff, r;
        PetscCall(PetscSectionGetDof(aSec, p, &rDof));
        PetscCall(PetscSectionGetOffset(aSec, p, &rOff));
        for (r = 0; r < rDof; r++) {
          PetscInt s;

          a = anchors[rOff + r];
          if (a < sStart || a >= sEnd) continue;
          PetscCall(PetscSectionGetDof(section, a, &aDof));
          PetscCall(PetscSectionGetOffset(section, a, &aOff));
          for (s = 0; s < aDof; s++) j[offset++] = aOff + s;
        }
      }
    }
  }
  PetscCall(MatSeqAIJSetPreallocationCSR(*cMat, i, j, NULL));
  PetscCall(PetscFree(i));
  PetscCall(PetscFree(j));
  PetscCall(ISRestoreIndices(aIS, &anchors));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode DMCreateDefaultConstraints_Plex(DM dm)
{
  DM_Plex     *plex = (DM_Plex *)dm->data;
  PetscSection anchorSection, section, cSec;
  Mat          cMat;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscCall(DMPlexGetAnchors(dm, &anchorSection, NULL));
  if (anchorSection) {
    PetscInt Nf;

    PetscCall(DMGetLocalSection(dm, &section));
    PetscCall(DMPlexCreateConstraintSection_Anchors(dm, section, &cSec));
    PetscCall(DMPlexCreateConstraintMatrix_Anchors(dm, section, cSec, &cMat));
    PetscCall(DMGetNumFields(dm, &Nf));
    if (Nf && plex->computeanchormatrix) PetscCall((*plex->computeanchormatrix)(dm, section, cSec, cMat));
    PetscCall(DMSetDefaultConstraints(dm, cSec, cMat, NULL));
    PetscCall(PetscSectionDestroy(&cSec));
    PetscCall(MatDestroy(&cMat));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode DMCreateSubDomainDM_Plex(DM dm, DMLabel label, PetscInt value, IS *is, DM *subdm)
{
  IS           subis;
  PetscSection section, subsection;

  PetscFunctionBegin;
  PetscCall(DMGetLocalSection(dm, &section));
  PetscCheck(section, PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Must set default section for DM before splitting subdomain");
  PetscCheck(subdm, PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Must set output subDM for splitting subdomain");
  /* Create subdomain */
  PetscCall(DMPlexFilter(dm, label, value, PETSC_FALSE, PETSC_FALSE, NULL, subdm));
  /* Create submodel */
  PetscCall(DMPlexGetSubpointIS(*subdm, &subis));
  PetscCall(PetscSectionCreateSubmeshSection(section, subis, &subsection));
  PetscCall(DMSetLocalSection(*subdm, subsection));
  PetscCall(PetscSectionDestroy(&subsection));
  PetscCall(DMCopyDisc(dm, *subdm));
  /* Create map from submodel to global model */
  if (is) {
    PetscSection    sectionGlobal, subsectionGlobal;
    IS              spIS;
    const PetscInt *spmap;
    PetscInt       *subIndices;
    PetscInt        subSize = 0, subOff = 0, pStart, pEnd, p;
    PetscInt        Nf, f, bs = -1, bsLocal[2], bsMinMax[2];

    PetscCall(DMPlexGetSubpointIS(*subdm, &spIS));
    PetscCall(ISGetIndices(spIS, &spmap));
    PetscCall(PetscSectionGetNumFields(section, &Nf));
    PetscCall(DMGetGlobalSection(dm, &sectionGlobal));
    PetscCall(DMGetGlobalSection(*subdm, &subsectionGlobal));
    PetscCall(PetscSectionGetChart(subsection, &pStart, &pEnd));
    for (p = pStart; p < pEnd; ++p) {
      PetscInt gdof, pSubSize = 0;

      PetscCall(PetscSectionGetDof(sectionGlobal, p, &gdof));
      if (gdof > 0) {
        for (f = 0; f < Nf; ++f) {
          PetscInt fdof, fcdof;

          PetscCall(PetscSectionGetFieldDof(subsection, p, f, &fdof));
          PetscCall(PetscSectionGetFieldConstraintDof(subsection, p, f, &fcdof));
          pSubSize += fdof - fcdof;
        }
        subSize += pSubSize;
        if (pSubSize) {
          if (bs < 0) {
            bs = pSubSize;
          } else if (bs != pSubSize) {
            /* Layout does not admit a pointwise block size */
            bs = 1;
          }
        }
      }
    }
    /* Must have same blocksize on all procs (some might have no points) */
    bsLocal[0] = bs < 0 ? PETSC_MAX_INT : bs;
    bsLocal[1] = bs;
    PetscCall(PetscGlobalMinMaxInt(PetscObjectComm((PetscObject)dm), bsLocal, bsMinMax));
    if (bsMinMax[0] != bsMinMax[1]) {
      bs = 1;
    } else {
      bs = bsMinMax[0];
    }
    PetscCall(PetscMalloc1(subSize, &subIndices));
    for (p = pStart; p < pEnd; ++p) {
      PetscInt gdof, goff;

      PetscCall(PetscSectionGetDof(subsectionGlobal, p, &gdof));
      if (gdof > 0) {
        const PetscInt point = spmap[p];

        PetscCall(PetscSectionGetOffset(sectionGlobal, point, &goff));
        for (f = 0; f < Nf; ++f) {
          PetscInt fdof, fcdof, fc, f2, poff = 0;

          /* Can get rid of this loop by storing field information in the global section */
          for (f2 = 0; f2 < f; ++f2) {
            PetscCall(PetscSectionGetFieldDof(section, p, f2, &fdof));
            PetscCall(PetscSectionGetFieldConstraintDof(section, p, f2, &fcdof));
            poff += fdof - fcdof;
          }
          PetscCall(PetscSectionGetFieldDof(section, p, f, &fdof));
          PetscCall(PetscSectionGetFieldConstraintDof(section, p, f, &fcdof));
          for (fc = 0; fc < fdof - fcdof; ++fc, ++subOff) subIndices[subOff] = goff + poff + fc;
        }
      }
    }
    PetscCall(ISRestoreIndices(spIS, &spmap));
    PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)dm), subSize, subIndices, PETSC_OWN_POINTER, is));
    if (bs > 1) {
      /* We need to check that the block size does not come from non-contiguous fields */
      PetscInt i, j, set = 1;
      for (i = 0; i < subSize; i += bs) {
        for (j = 0; j < bs; ++j) {
          if (subIndices[i + j] != subIndices[i] + j) {
            set = 0;
            break;
          }
        }
      }
      if (set) PetscCall(ISSetBlockSize(*is, bs));
    }
    /* Attach nullspace */
    for (f = 0; f < Nf; ++f) {
      (*subdm)->nullspaceConstructors[f] = dm->nullspaceConstructors[f];
      if ((*subdm)->nullspaceConstructors[f]) break;
    }
    if (f < Nf) {
      MatNullSpace nullSpace;
      PetscCall((*(*subdm)->nullspaceConstructors[f])(*subdm, f, f, &nullSpace));

      PetscCall(PetscObjectCompose((PetscObject)*is, "nullspace", (PetscObject)nullSpace));
      PetscCall(MatNullSpaceDestroy(&nullSpace));
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMPlexMonitorThroughput - Report the cell throughput of FE integration

  Input Parameters:
+ dm    - The `DM`
- dummy - unused argument

  Options Database Key:
. -dm_plex_monitor_throughput - Activate the monitor

  Level: developer

.seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMSetFromOptions()`, `DMPlexCreate()`
@*/
PetscErrorCode DMPlexMonitorThroughput(DM dm, void *dummy)
{
  PetscLogHandler default_handler;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscCall(PetscLogGetDefaultHandler(&default_handler));
  if (default_handler) {
    PetscLogEvent      event;
    PetscEventPerfInfo eventInfo;
    PetscReal          cellRate, flopRate;
    PetscInt           cStart, cEnd, Nf, N;
    const char        *name;

    PetscCall(PetscObjectGetName((PetscObject)dm, &name));
    PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
    PetscCall(DMGetNumFields(dm, &Nf));
    PetscCall(PetscLogEventGetId("DMPlexResidualFE", &event));
    PetscCall(PetscLogEventGetPerfInfo(PETSC_DEFAULT, event, &eventInfo));
    N        = (cEnd - cStart) * Nf * eventInfo.count;
    flopRate = eventInfo.flops / eventInfo.time;
    cellRate = N / eventInfo.time;
    PetscCall(PetscPrintf(PetscObjectComm((PetscObject)dm), "DM (%s) FE Residual Integration: %" PetscInt_FMT " integrals %d reps\n  Cell rate: %.2g/s flop rate: %.2g MF/s\n", name ? name : "unknown", N, eventInfo.count, (double)cellRate, (double)(flopRate / 1.e6)));
  } else {
    SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Plex Throughput Monitor is not supported if logging is turned off or the default log handler is not running. Reconfigure using --with-log and run with -log_view.");
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}