xref: /petsc/src/dm/impls/plex/plexfem.c (revision feff33ee0b5b037fa8f9f294dede656a2f85cc47)

#include <petsc/private/dmpleximpl.h>   /*I      "petscdmplex.h"   I*/
#include <petscsf.h>

#include <petsc/private/petscfeimpl.h>
#include <petsc/private/petscfvimpl.h>

/*@
  DMPlexGetScale - Get the scale for the specified fundamental unit

  Not collective

  Input Arguments:
+ dm   - the DM
- unit - The SI unit

  Output Argument:
. scale - The value used to scale all quantities with this unit

  Level: advanced

.seealso: DMPlexSetScale(), PetscUnit
@*/
PetscErrorCode DMPlexGetScale(DM dm, PetscUnit unit, PetscReal *scale)
{
  DM_Plex *mesh = (DM_Plex*) dm->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidPointer(scale, 3);
  *scale = mesh->scale[unit];
  PetscFunctionReturn(0);
}

/*@
  DMPlexSetScale - Set the scale for the specified fundamental unit

  Not collective

  Input Arguments:
+ dm   - the DM
. unit - The SI unit
- scale - The value used to scale all quantities with this unit

  Level: advanced

.seealso: DMPlexGetScale(), PetscUnit
@*/
PetscErrorCode DMPlexSetScale(DM dm, PetscUnit unit, PetscReal scale)
{
  DM_Plex *mesh = (DM_Plex*) dm->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  mesh->scale[unit] = scale;
  PetscFunctionReturn(0);
}

static PetscErrorCode DMPlexProjectRigidBody_Private(PetscInt dim, PetscReal t, const PetscReal X[], PetscInt Nf, PetscScalar *mode, void *ctx)
{
  const PetscInt eps[3][3][3] = {{{0, 0, 0}, {0, 0, 1}, {0, -1, 0}}, {{0, 0, -1}, {0, 0, 0}, {1, 0, 0}}, {{0, 1, 0}, {-1, 0, 0}, {0, 0, 0}}};
  PetscInt *ctxInt  = (PetscInt *) ctx;
  PetscInt  dim2    = ctxInt[0];
  PetscInt  d       = ctxInt[1];
  PetscInt  i, j, k = dim > 2 ? d - dim : d;

  PetscFunctionBegin;
  if (dim != dim2) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Input dimension %d does not match context dimension %d", dim, dim2);
  for (i = 0; i < dim; i++) mode[i] = 0.;
  if (d < dim) {
    mode[d] = 1.; /* Translation along axis d */
  } else {
    for (i = 0; i < dim; i++) {
      for (j = 0; j < dim; j++) {
        mode[j] += eps[i][j][k]*X[i]; /* Rotation about axis d */
      }
    }
  }
  PetscFunctionReturn(0);
}

/*@C
  DMPlexCreateRigidBody - For the default global section, create rigid body modes by function space interpolation

  Collective on DM

  Input Arguments:
. dm - the DM

  Output Argument:
. sp - the null space

  Note: This is necessary to provide a suitable coarse space for algebraic multigrid

  Level: advanced

.seealso: MatNullSpaceCreate(), PCGAMG
@*/
PetscErrorCode DMPlexCreateRigidBody(DM dm, MatNullSpace *sp)
{
  MPI_Comm       comm;
  Vec            mode[6];
  PetscSection   section, globalSection;
  PetscInt       dim, dimEmbed, n, m, d, i, j;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscObjectGetComm((PetscObject)dm,&comm);CHKERRQ(ierr);
  ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
  ierr = DMGetCoordinateDim(dm, &dimEmbed);CHKERRQ(ierr);
  if (dim == 1) {
    ierr = MatNullSpaceCreate(comm, PETSC_TRUE, 0, NULL, sp);CHKERRQ(ierr);
    PetscFunctionReturn(0);
  }
  ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
  ierr = DMGetDefaultGlobalSection(dm, &globalSection);CHKERRQ(ierr);
  ierr = PetscSectionGetConstrainedStorageSize(globalSection, &n);CHKERRQ(ierr);
  m    = (dim*(dim+1))/2;
  ierr = VecCreate(comm, &mode[0]);CHKERRQ(ierr);
  ierr = VecSetSizes(mode[0], n, PETSC_DETERMINE);CHKERRQ(ierr);
  ierr = VecSetUp(mode[0]);CHKERRQ(ierr);
  for (i = 1; i < m; ++i) {ierr = VecDuplicate(mode[0], &mode[i]);CHKERRQ(ierr);}
  for (d = 0; d < m; d++) {
    PetscInt         ctx[2];
    PetscErrorCode (*func)(PetscInt, PetscReal, const PetscReal *, PetscInt, PetscScalar *, void *) = DMPlexProjectRigidBody_Private;
    void            *voidctx = (void *) (&ctx[0]);

    ctx[0] = dimEmbed;
    ctx[1] = d;
    ierr = DMProjectFunction(dm, 0.0, &func, &voidctx, INSERT_VALUES, mode[d]);CHKERRQ(ierr);
  }
  for (i = 0; i < dim; ++i) {ierr = VecNormalize(mode[i], NULL);CHKERRQ(ierr);}
  /* Orthonormalize system */
  for (i = dim; i < m; ++i) {
    PetscScalar dots[6];

    ierr = VecMDot(mode[i], i, mode, dots);CHKERRQ(ierr);
    for (j = 0; j < i; ++j) dots[j] *= -1.0;
    ierr = VecMAXPY(mode[i], i, dots, mode);CHKERRQ(ierr);
    ierr = VecNormalize(mode[i], NULL);CHKERRQ(ierr);
  }
  ierr = MatNullSpaceCreate(comm, PETSC_FALSE, m, mode, sp);CHKERRQ(ierr);
  for (i = 0; i< m; ++i) {ierr = VecDestroy(&mode[i]);CHKERRQ(ierr);}
  PetscFunctionReturn(0);
}

/*@C
  DMPlexCreateRigidBodies - For the default global section, create rigid body modes by function space interpolation

  Collective on DM

  Input Arguments:
+ dm    - the DM
. nb    - The number of bodies
. label - The DMLabel marking each domain
. nids  - The number of ids per body
- ids   - An array of the label ids in sequence for each domain

  Output Argument:
. sp - the null space

  Note: This is necessary to provide a suitable coarse space for algebraic multigrid

  Level: advanced

.seealso: MatNullSpaceCreate()
@*/
PetscErrorCode DMPlexCreateRigidBodies(DM dm, PetscInt nb, DMLabel label, const PetscInt nids[], const PetscInt ids[], MatNullSpace *sp)
{
  MPI_Comm       comm;
  PetscSection   section, globalSection;
  Vec           *mode;
  PetscScalar   *dots;
  PetscInt       dim, dimEmbed, n, m, b, d, i, j, off;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscObjectGetComm((PetscObject)dm,&comm);CHKERRQ(ierr);
  ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
  ierr = DMGetCoordinateDim(dm, &dimEmbed);CHKERRQ(ierr);
  ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
  ierr = DMGetDefaultGlobalSection(dm, &globalSection);CHKERRQ(ierr);
  ierr = PetscSectionGetConstrainedStorageSize(globalSection, &n);CHKERRQ(ierr);
  m    = nb * (dim*(dim+1))/2;
  ierr = PetscMalloc2(m, &mode, m, &dots);CHKERRQ(ierr);
  ierr = VecCreate(comm, &mode[0]);CHKERRQ(ierr);
  ierr = VecSetSizes(mode[0], n, PETSC_DETERMINE);CHKERRQ(ierr);
  ierr = VecSetUp(mode[0]);CHKERRQ(ierr);
  for (i = 1; i < m; ++i) {ierr = VecDuplicate(mode[0], &mode[i]);CHKERRQ(ierr);}
  for (b = 0, off = 0; b < nb; ++b) {
    for (d = 0; d < m/nb; ++d) {
      PetscInt         ctx[2];
      PetscErrorCode (*func)(PetscInt, PetscReal, const PetscReal *, PetscInt, PetscScalar *, void *) = DMPlexProjectRigidBody_Private;
      void            *voidctx = (void *) (&ctx[0]);

      ctx[0] = dimEmbed;
      ctx[1] = d;
      ierr = DMProjectFunctionLabel(dm, 0.0, label, nids[b], &ids[off], 0, NULL, &func, &voidctx, INSERT_VALUES, mode[d]);CHKERRQ(ierr);
      off   += nids[b];
    }
  }
  for (i = 0; i < dim; ++i) {ierr = VecNormalize(mode[i], NULL);CHKERRQ(ierr);}
  /* Orthonormalize system */
  for (i = 0; i < m; ++i) {
    ierr = VecMDot(mode[i], i, mode, dots);CHKERRQ(ierr);
    for (j = 0; j < i; ++j) dots[j] *= -1.0;
    ierr = VecMAXPY(mode[i], i, dots, mode);CHKERRQ(ierr);
    ierr = VecNormalize(mode[i], NULL);CHKERRQ(ierr);
  }
  ierr = MatNullSpaceCreate(comm, PETSC_FALSE, m, mode, sp);CHKERRQ(ierr);
  for (i = 0; i< m; ++i) {ierr = VecDestroy(&mode[i]);CHKERRQ(ierr);}
  ierr = PetscFree2(mode, dots);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@
  DMPlexSetMaxProjectionHeight - In DMPlexProjectXXXLocal() functions, the projected values of a basis function's dofs
  are computed by associating the basis function with one of the mesh points in its transitively-closed support, and
  evaluating the dual space basis of that point.  A basis function is associated with the point in its
  transitively-closed support whose mesh height is highest (w.r.t. DAG height), but not greater than the maximum
  projection height, which is set with this function.  By default, the maximum projection height is zero, which means
  that only mesh cells are used to project basis functions.  A height of one, for example, evaluates a cell-interior
  basis functions using its cells dual space basis, but all other basis functions with the dual space basis of a face.

  Input Parameters:
+ dm - the DMPlex object
- height - the maximum projection height >= 0

  Level: advanced

.seealso: DMPlexGetMaxProjectionHeight(), DMProjectFunctionLocal(), DMProjectFunctionLabelLocal()
@*/
PetscErrorCode DMPlexSetMaxProjectionHeight(DM dm, PetscInt height)
{
  DM_Plex *plex = (DM_Plex *) dm->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  plex->maxProjectionHeight = height;
  PetscFunctionReturn(0);
}

/*@
  DMPlexGetMaxProjectionHeight - Get the maximum height (w.r.t. DAG) of mesh points used to evaluate dual bases in
  DMPlexProjectXXXLocal() functions.

  Input Parameters:
. dm - the DMPlex object

  Output Parameters:
. height - the maximum projection height

  Level: intermediate

.seealso: DMPlexSetMaxProjectionHeight(), DMProjectFunctionLocal(), DMProjectFunctionLabelLocal()
@*/
PetscErrorCode DMPlexGetMaxProjectionHeight(DM dm, PetscInt *height)
{
  DM_Plex *plex = (DM_Plex *) dm->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  *height = plex->maxProjectionHeight;
  PetscFunctionReturn(0);
}

/*@C
  DMPlexInsertBoundaryValuesEssential - Insert boundary values into a local vector

  Input Parameters:
+ dm     - The DM, with a PetscDS that matches the problem being constrained
. time   - The time
. field  - The field to constrain
. Nc     - The number of constrained field components, or 0 for all components
. comps  - An array of constrained component numbers, or NULL for all components
. label  - The DMLabel defining constrained points
. numids - The number of DMLabel ids for constrained points
. ids    - An array of ids for constrained points
. func   - A pointwise function giving boundary values
- ctx    - An optional user context for bcFunc

  Output Parameter:
. locX   - A local vector to receives the boundary values

  Level: developer

.seealso: DMPlexInsertBoundaryValuesEssentialField(), DMAddBoundary()
@*/
PetscErrorCode DMPlexInsertBoundaryValuesEssential(DM dm, PetscReal time, PetscInt field, PetscInt Nc, const PetscInt comps[], DMLabel label, PetscInt numids, const PetscInt ids[], PetscErrorCode (*func)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *), void *ctx, Vec locX)
{
  PetscErrorCode (**funcs)(PetscInt, PetscReal, const PetscReal x[], PetscInt, PetscScalar *u, void *ctx);
  void            **ctxs;
  PetscInt          numFields;
  PetscErrorCode    ierr;

  PetscFunctionBegin;
  ierr = DMGetNumFields(dm, &numFields);CHKERRQ(ierr);
  ierr = PetscCalloc2(numFields,&funcs,numFields,&ctxs);CHKERRQ(ierr);
  funcs[field] = func;
  ctxs[field]  = ctx;
  ierr = DMProjectFunctionLabelLocal(dm, time, label, numids, ids, Nc, comps, funcs, ctxs, INSERT_BC_VALUES, locX);CHKERRQ(ierr);
  ierr = PetscFree2(funcs,ctxs);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@C
  DMPlexInsertBoundaryValuesEssentialField - Insert boundary values into a local vector

  Input Parameters:
+ dm     - The DM, with a PetscDS that matches the problem being constrained
. time   - The time
. locU   - A local vector with the input solution values
. field  - The field to constrain
. Nc     - The number of constrained field components, or 0 for all components
. comps  - An array of constrained component numbers, or NULL for all components
. label  - The DMLabel defining constrained points
. numids - The number of DMLabel ids for constrained points
. ids    - An array of ids for constrained points
. func   - A pointwise function giving boundary values
- ctx    - An optional user context for bcFunc

  Output Parameter:
. locX   - A local vector to receives the boundary values

  Level: developer

.seealso: DMPlexInsertBoundaryValuesEssential(), DMAddBoundary()
@*/
PetscErrorCode DMPlexInsertBoundaryValuesEssentialField(DM dm, PetscReal time, Vec locU, PetscInt field, PetscInt Nc, const PetscInt comps[], DMLabel label, PetscInt numids, const PetscInt ids[],
                                                        void (*func)(PetscInt, PetscInt, PetscInt,
                                                                     const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[],
                                                                     const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[],
                                                                     PetscReal, const PetscReal[], PetscInt, const PetscScalar[],
                                                                     PetscScalar[]),
                                                        void *ctx, Vec locX)
{
  void (**funcs)(PetscInt, PetscInt, PetscInt,
                 const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[],
                 const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[],
                 PetscReal, const PetscReal[], PetscInt, const PetscScalar[], PetscScalar[]);
  void            **ctxs;
  PetscInt          numFields;
  PetscErrorCode    ierr;

  PetscFunctionBegin;
  ierr = DMGetNumFields(dm, &numFields);CHKERRQ(ierr);
  ierr = PetscCalloc2(numFields,&funcs,numFields,&ctxs);CHKERRQ(ierr);
  funcs[field] = func;
  ctxs[field]  = ctx;
  ierr = DMProjectFieldLabelLocal(dm, time, label, numids, ids, Nc, comps, locU, funcs, INSERT_BC_VALUES, locX);CHKERRQ(ierr);
  ierr = PetscFree2(funcs,ctxs);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@C
  DMPlexInsertBoundaryValuesRiemann - Insert boundary values into a local vector

  Input Parameters:
+ dm     - The DM, with a PetscDS that matches the problem being constrained
. time   - The time
. faceGeometry - A vector with the FVM face geometry information
. cellGeometry - A vector with the FVM cell geometry information
. Grad         - A vector with the FVM cell gradient information
. field  - The field to constrain
. Nc     - The number of constrained field components, or 0 for all components
. comps  - An array of constrained component numbers, or NULL for all components
. label  - The DMLabel defining constrained points
. numids - The number of DMLabel ids for constrained points
. ids    - An array of ids for constrained points
. func   - A pointwise function giving boundary values
- ctx    - An optional user context for bcFunc

  Output Parameter:
. locX   - A local vector to receives the boundary values

  Note: This implementation currently ignores the numcomps/comps argument from DMAddBoundary()

  Level: developer

.seealso: DMPlexInsertBoundaryValuesEssential(), DMPlexInsertBoundaryValuesEssentialField(), DMAddBoundary()
@*/
PetscErrorCode DMPlexInsertBoundaryValuesRiemann(DM dm, PetscReal time, Vec faceGeometry, Vec cellGeometry, Vec Grad, PetscInt field, PetscInt Nc, const PetscInt comps[], DMLabel label, PetscInt numids, const PetscInt ids[],
                                                 PetscErrorCode (*func)(PetscReal,const PetscReal*,const PetscReal*,const PetscScalar*,PetscScalar*,void*), void *ctx, Vec locX)
{
  PetscDS            prob;
  PetscSF            sf;
  DM                 dmFace, dmCell, dmGrad;
  const PetscScalar *facegeom, *cellgeom = NULL, *grad;
  const PetscInt    *leaves;
  PetscScalar       *x, *fx;
  PetscInt           dim, nleaves, loc, fStart, fEnd, pdim, i;
  PetscErrorCode     ierr, ierru = 0;

  PetscFunctionBegin;
  ierr = DMGetPointSF(dm, &sf);CHKERRQ(ierr);
  ierr = PetscSFGetGraph(sf, NULL, &nleaves, &leaves, NULL);CHKERRQ(ierr);
  nleaves = PetscMax(0, nleaves);
  ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
  ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
  ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
  ierr = VecGetDM(faceGeometry, &dmFace);CHKERRQ(ierr);
  ierr = VecGetArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
  if (cellGeometry) {
    ierr = VecGetDM(cellGeometry, &dmCell);CHKERRQ(ierr);
    ierr = VecGetArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);
  }
  if (Grad) {
    PetscFV fv;

    ierr = PetscDSGetDiscretization(prob, field, (PetscObject *) &fv);CHKERRQ(ierr);
    ierr = VecGetDM(Grad, &dmGrad);CHKERRQ(ierr);
    ierr = VecGetArrayRead(Grad, &grad);CHKERRQ(ierr);
    ierr = PetscFVGetNumComponents(fv, &pdim);CHKERRQ(ierr);
    ierr = DMGetWorkArray(dm, pdim, MPIU_SCALAR, &fx);CHKERRQ(ierr);
  }
  ierr = VecGetArray(locX, &x);CHKERRQ(ierr);
  for (i = 0; i < numids; ++i) {
    IS              faceIS;
    const PetscInt *faces;
    PetscInt        numFaces, f;

    ierr = DMLabelGetStratumIS(label, ids[i], &faceIS);CHKERRQ(ierr);
    if (!faceIS) continue; /* No points with that id on this process */
    ierr = ISGetLocalSize(faceIS, &numFaces);CHKERRQ(ierr);
    ierr = ISGetIndices(faceIS, &faces);CHKERRQ(ierr);
    for (f = 0; f < numFaces; ++f) {
      const PetscInt         face = faces[f], *cells;
      PetscFVFaceGeom        *fg;

      if ((face < fStart) || (face >= fEnd)) continue; /* Refinement adds non-faces to labels */
      ierr = PetscFindInt(face, nleaves, (PetscInt *) leaves, &loc);CHKERRQ(ierr);
      if (loc >= 0) continue;
      ierr = DMPlexPointLocalRead(dmFace, face, facegeom, &fg);CHKERRQ(ierr);
      ierr = DMPlexGetSupport(dm, face, &cells);CHKERRQ(ierr);
      if (Grad) {
        PetscFVCellGeom       *cg;
        PetscScalar           *cx, *cgrad;
        PetscScalar           *xG;
        PetscReal              dx[3];
        PetscInt               d;

        ierr = DMPlexPointLocalRead(dmCell, cells[0], cellgeom, &cg);CHKERRQ(ierr);
        ierr = DMPlexPointLocalRead(dm, cells[0], x, &cx);CHKERRQ(ierr);
        ierr = DMPlexPointLocalRead(dmGrad, cells[0], grad, &cgrad);CHKERRQ(ierr);
        ierr = DMPlexPointLocalFieldRef(dm, cells[1], field, x, &xG);CHKERRQ(ierr);
        DMPlex_WaxpyD_Internal(dim, -1, cg->centroid, fg->centroid, dx);
        for (d = 0; d < pdim; ++d) fx[d] = cx[d] + DMPlex_DotD_Internal(dim, &cgrad[d*dim], dx);
        ierru = (*func)(time, fg->centroid, fg->normal, fx, xG, ctx);
        if (ierru) {
          ierr = ISRestoreIndices(faceIS, &faces);CHKERRQ(ierr);
          ierr = ISDestroy(&faceIS);CHKERRQ(ierr);
          goto cleanup;
        }
      } else {
        PetscScalar       *xI;
        PetscScalar       *xG;

        ierr = DMPlexPointLocalRead(dm, cells[0], x, &xI);CHKERRQ(ierr);
        ierr = DMPlexPointLocalFieldRef(dm, cells[1], field, x, &xG);CHKERRQ(ierr);
        ierru = (*func)(time, fg->centroid, fg->normal, xI, xG, ctx);
        if (ierru) {
          ierr = ISRestoreIndices(faceIS, &faces);CHKERRQ(ierr);
          ierr = ISDestroy(&faceIS);CHKERRQ(ierr);
          goto cleanup;
        }
      }
    }
    ierr = ISRestoreIndices(faceIS, &faces);CHKERRQ(ierr);
    ierr = ISDestroy(&faceIS);CHKERRQ(ierr);
  }
  cleanup:
  ierr = VecRestoreArray(locX, &x);CHKERRQ(ierr);
  if (Grad) {
    ierr = DMRestoreWorkArray(dm, pdim, MPIU_SCALAR, &fx);CHKERRQ(ierr);
    ierr = VecRestoreArrayRead(Grad, &grad);CHKERRQ(ierr);
  }
  if (cellGeometry) {ierr = VecRestoreArrayRead(cellGeometry, &cellgeom);CHKERRQ(ierr);}
  ierr = VecRestoreArrayRead(faceGeometry, &facegeom);CHKERRQ(ierr);
  CHKERRQ(ierru);
  PetscFunctionReturn(0);
}

PetscErrorCode DMPlexInsertBoundaryValues_Plex(DM dm, PetscBool insertEssential, Vec locX, PetscReal time, Vec faceGeomFVM, Vec cellGeomFVM, Vec gradFVM)
{
  PetscInt       numBd, b;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscDSGetNumBoundary(dm->prob, &numBd);CHKERRQ(ierr);
  for (b = 0; b < numBd; ++b) {
    DMBoundaryConditionType type;
    const char             *labelname;
    DMLabel                 label;
    PetscInt                field, Nc;
    const PetscInt         *comps;
    PetscObject             obj;
    PetscClassId            id;
    void                    (*func)(void);
    PetscInt                numids;
    const PetscInt         *ids;
    void                   *ctx;

    ierr = DMGetBoundary(dm, b, &type, NULL, &labelname, &field, &Nc, &comps, &func, &numids, &ids, &ctx);CHKERRQ(ierr);
    if (insertEssential != (type & DM_BC_ESSENTIAL)) continue;
    ierr = DMGetLabel(dm, labelname, &label);CHKERRQ(ierr);
    ierr = DMGetField(dm, field, &obj);CHKERRQ(ierr);
    ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
    if (id == PETSCFE_CLASSID) {
      switch (type) {
        /* for FEM, there is no insertion to be done for non-essential boundary conditions */
      case DM_BC_ESSENTIAL:
        ierr = DMPlexLabelAddCells(dm,label);CHKERRQ(ierr);
        ierr = DMPlexInsertBoundaryValuesEssential(dm, time, field, Nc, comps, label, numids, ids, (PetscErrorCode (*)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *)) func, ctx, locX);CHKERRQ(ierr);
        ierr = DMPlexLabelClearCells(dm,label);CHKERRQ(ierr);
        break;
      case DM_BC_ESSENTIAL_FIELD:
        ierr = DMPlexLabelAddCells(dm,label);CHKERRQ(ierr);
        ierr = DMPlexInsertBoundaryValuesEssentialField(dm, time, locX, field, Nc, comps, label, numids, ids,
                                                        (void (*)(PetscInt, PetscInt, PetscInt, const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[],
                                                                  const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[],
                                                                  PetscReal, const PetscReal[], PetscInt, const PetscScalar[], PetscScalar[])) func, ctx, locX);CHKERRQ(ierr);
        ierr = DMPlexLabelClearCells(dm,label);CHKERRQ(ierr);
        break;
      default: break;
      }
    } else if (id == PETSCFV_CLASSID) {
      if (!faceGeomFVM) continue;
      ierr = DMPlexInsertBoundaryValuesRiemann(dm, time, faceGeomFVM, cellGeomFVM, gradFVM, field, Nc, comps, label, numids, ids,
                                               (PetscErrorCode (*)(PetscReal,const PetscReal*,const PetscReal*,const PetscScalar*,PetscScalar*,void*)) func, ctx, locX);CHKERRQ(ierr);
    } else SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", field);
  }
  PetscFunctionReturn(0);
}

/*@
  DMPlexInsertBoundaryValues - Puts coefficients which represent boundary values into the local solution vector

  Input Parameters:
+ dm - The DM
. insertEssential - Should I insert essential (e.g. Dirichlet) or inessential (e.g. Neumann) boundary conditions
. time - The time
. faceGeomFVM - Face geometry data for FV discretizations
. cellGeomFVM - Cell geometry data for FV discretizations
- gradFVM - Gradient reconstruction data for FV discretizations

  Output Parameters:
. locX - Solution updated with boundary values

  Level: developer

.seealso: DMProjectFunctionLabelLocal()
@*/
PetscErrorCode DMPlexInsertBoundaryValues(DM dm, PetscBool insertEssential, Vec locX, PetscReal time, Vec faceGeomFVM, Vec cellGeomFVM, Vec gradFVM)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidHeaderSpecific(locX, VEC_CLASSID, 2);
  if (faceGeomFVM) {PetscValidHeaderSpecific(faceGeomFVM, VEC_CLASSID, 4);}
  if (cellGeomFVM) {PetscValidHeaderSpecific(cellGeomFVM, VEC_CLASSID, 5);}
  if (gradFVM)     {PetscValidHeaderSpecific(gradFVM, VEC_CLASSID, 6);}
  ierr = PetscTryMethod(dm,"DMPlexInsertBoundaryValues_C",(DM,PetscBool,Vec,PetscReal,Vec,Vec,Vec),(dm,insertEssential,locX,time,faceGeomFVM,cellGeomFVM,gradFVM));CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode DMComputeL2Diff_Plex(DM dm, PetscReal time, PetscErrorCode (**funcs)(PetscInt, PetscReal, const PetscReal [], PetscInt, PetscScalar *, void *), void **ctxs, Vec X, PetscReal *diff)
{
  Vec              localX;
  PetscErrorCode   ierr;

  PetscFunctionBegin;
  ierr = DMGetLocalVector(dm, &localX);CHKERRQ(ierr);
  ierr = DMPlexInsertBoundaryValues(dm, PETSC_TRUE, localX, time, NULL, NULL, NULL);CHKERRQ(ierr);
  ierr = DMGlobalToLocalBegin(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
  ierr = DMGlobalToLocalEnd(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
  ierr = DMPlexComputeL2DiffLocal(dm, time, funcs, ctxs, localX, diff);CHKERRQ(ierr);
  ierr = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@C
  DMComputeL2Diff - This function computes the L_2 difference between a function u and an FEM interpolant solution u_h.

  Input Parameters:
+ dm     - The DM
. time   - The time
. funcs  - The functions to evaluate for each field component
. ctxs   - Optional array of contexts to pass to each function, or NULL.
- localX - The coefficient vector u_h, a local vector

  Output Parameter:
. diff - The diff ||u - u_h||_2

  Level: developer

.seealso: DMProjectFunction(), DMComputeL2FieldDiff(), DMComputeL2GradientDiff()
@*/
PetscErrorCode DMPlexComputeL2DiffLocal(DM dm, PetscReal time, PetscErrorCode (**funcs)(PetscInt, PetscReal, const PetscReal [], PetscInt, PetscScalar *, void *), void **ctxs, Vec localX, PetscReal *diff)
{
  const PetscInt   debug = 0;
  PetscSection     section;
  PetscQuadrature  quad;
  PetscScalar     *funcVal, *interpolant;
  PetscReal       *coords, *detJ, *J;
  PetscReal        localDiff = 0.0;
  const PetscReal *quadWeights;
  PetscInt         dim, coordDim, numFields, numComponents = 0, qNc, Nq, cellHeight, cStart, cEnd, cEndInterior, c, field, fieldOffset;
  PetscErrorCode   ierr;

  PetscFunctionBegin;
  ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
  ierr = DMGetCoordinateDim(dm, &coordDim);CHKERRQ(ierr);
  ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
  ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
  for (field = 0; field < numFields; ++field) {
    PetscObject  obj;
    PetscClassId id;
    PetscInt     Nc;

    ierr = DMGetField(dm, field, &obj);CHKERRQ(ierr);
    ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
    if (id == PETSCFE_CLASSID) {
      PetscFE fe = (PetscFE) obj;

      ierr = PetscFEGetQuadrature(fe, &quad);CHKERRQ(ierr);
      ierr = PetscFEGetNumComponents(fe, &Nc);CHKERRQ(ierr);
    } else if (id == PETSCFV_CLASSID) {
      PetscFV fv = (PetscFV) obj;

      ierr = PetscFVGetQuadrature(fv, &quad);CHKERRQ(ierr);
      ierr = PetscFVGetNumComponents(fv, &Nc);CHKERRQ(ierr);
    } else SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", field);
    numComponents += Nc;
  }
  ierr = PetscQuadratureGetData(quad, NULL, &qNc, &Nq, NULL, &quadWeights);CHKERRQ(ierr);
  if ((qNc != 1) && (qNc != numComponents)) SETERRQ2(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_SIZ, "Quadrature components %D != %D field components", qNc, numComponents);
  ierr = PetscMalloc5(numComponents,&funcVal,numComponents,&interpolant,coordDim*Nq,&coords,Nq,&detJ,coordDim*coordDim*Nq,&J);CHKERRQ(ierr);
  ierr = DMPlexGetVTKCellHeight(dm, &cellHeight);CHKERRQ(ierr);
  ierr = DMPlexGetHeightStratum(dm, cellHeight, &cStart, &cEnd);CHKERRQ(ierr);
  ierr = DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
  cEnd = cEndInterior < 0 ? cEnd : cEndInterior;
  for (c = cStart; c < cEnd; ++c) {
    PetscScalar *x = NULL;
    PetscReal    elemDiff = 0.0;
    PetscInt     qc = 0;

    ierr = DMPlexComputeCellGeometryFEM(dm, c, quad, coords, J, NULL, detJ);CHKERRQ(ierr);
    ierr = DMPlexVecGetClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);

    for (field = 0, fieldOffset = 0; field < numFields; ++field) {
      PetscObject  obj;
      PetscClassId id;
      void * const ctx = ctxs ? ctxs[field] : NULL;
      PetscInt     Nb, Nc, q, fc;

      ierr = DMGetField(dm, field, &obj);CHKERRQ(ierr);
      ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
      if (id == PETSCFE_CLASSID)      {ierr = PetscFEGetNumComponents((PetscFE) obj, &Nc);CHKERRQ(ierr);ierr = PetscFEGetDimension((PetscFE) obj, &Nb);CHKERRQ(ierr);}
      else if (id == PETSCFV_CLASSID) {ierr = PetscFVGetNumComponents((PetscFV) obj, &Nc);CHKERRQ(ierr);Nb = 1;}
      else SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", field);
      if (debug) {
        char title[1024];
        ierr = PetscSNPrintf(title, 1023, "Solution for Field %d", field);CHKERRQ(ierr);
        ierr = DMPrintCellVector(c, title, Nb, &x[fieldOffset]);CHKERRQ(ierr);
      }
      for (q = 0; q < Nq; ++q) {
        if (detJ[q] <= 0.0) SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %D, point %D", detJ[q], c, q);
        ierr = (*funcs[field])(coordDim, time, &coords[coordDim * q], Nc, funcVal, ctx);
        if (ierr) {
          PetscErrorCode ierr2;
          ierr2 = DMPlexVecRestoreClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr2);
          ierr2 = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr2);
          ierr2 = PetscFree5(funcVal,interpolant,coords,detJ,J);CHKERRQ(ierr2);
          CHKERRQ(ierr);
        }
        if (id == PETSCFE_CLASSID)      {ierr = PetscFEInterpolate_Static((PetscFE) obj, &x[fieldOffset], q, interpolant);CHKERRQ(ierr);}
        else if (id == PETSCFV_CLASSID) {ierr = PetscFVInterpolate_Static((PetscFV) obj, &x[fieldOffset], q, interpolant);CHKERRQ(ierr);}
        else SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", field);
        for (fc = 0; fc < Nc; ++fc) {
          const PetscReal wt = quadWeights[q*qNc+(qNc == 1 ? 0 : qc+fc)];
          if (debug) {ierr = PetscPrintf(PETSC_COMM_SELF, "    elem %d field %d diff %g\n", c, field, PetscSqr(PetscRealPart(interpolant[fc] - funcVal[fc]))*wt*detJ[q]);CHKERRQ(ierr);}
          elemDiff += PetscSqr(PetscRealPart(interpolant[fc] - funcVal[fc]))*wt*detJ[q];
        }
      }
      fieldOffset += Nb;
      qc += Nc;
    }
    ierr = DMPlexVecRestoreClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
    if (debug) {ierr = PetscPrintf(PETSC_COMM_SELF, "  elem %d diff %g\n", c, elemDiff);CHKERRQ(ierr);}
    localDiff += elemDiff;
  }
  ierr  = PetscFree5(funcVal,interpolant,coords,detJ,J);CHKERRQ(ierr);
  ierr  = MPIU_Allreduce(&localDiff, diff, 1, MPIU_REAL, MPIU_SUM, PetscObjectComm((PetscObject)dm));CHKERRQ(ierr);
  *diff = PetscSqrtReal(*diff);
  PetscFunctionReturn(0);
}

PetscErrorCode DMComputeL2GradientDiff_Plex(DM dm, PetscReal time, PetscErrorCode (**funcs)(PetscInt, PetscReal, const PetscReal [], const PetscReal [], PetscInt, PetscScalar *, void *), void **ctxs, Vec X, const PetscReal n[], PetscReal *diff)
{
  const PetscInt   debug = 0;
  PetscSection     section;
  PetscQuadrature  quad;
  Vec              localX;
  PetscScalar     *funcVal, *interpolant;
  const PetscReal *quadPoints, *quadWeights;
  PetscReal       *coords, *realSpaceDer, *J, *invJ, *detJ;
  PetscReal        localDiff = 0.0;
  PetscInt         dim, coordDim, qNc = 0, Nq = 0, numFields, numComponents = 0, cStart, cEnd, cEndInterior, c, field, fieldOffset;
  PetscErrorCode   ierr;

  PetscFunctionBegin;
  ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
  ierr = DMGetCoordinateDim(dm, &coordDim);CHKERRQ(ierr);
  ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
  ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
  ierr = DMGetLocalVector(dm, &localX);CHKERRQ(ierr);
  ierr = DMGlobalToLocalBegin(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
  ierr = DMGlobalToLocalEnd(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
  for (field = 0; field < numFields; ++field) {
    PetscFE  fe;
    PetscInt Nc;

    ierr = DMGetField(dm, field, (PetscObject *) &fe);CHKERRQ(ierr);
    ierr = PetscFEGetQuadrature(fe, &quad);CHKERRQ(ierr);
    ierr = PetscFEGetNumComponents(fe, &Nc);CHKERRQ(ierr);
    numComponents += Nc;
  }
  ierr = PetscQuadratureGetData(quad, NULL, &qNc, &Nq, &quadPoints, &quadWeights);CHKERRQ(ierr);
  if ((qNc != 1) && (qNc != numComponents)) SETERRQ2(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_SIZ, "Quadrature components %D != %D field components", qNc, numComponents);
  /* ierr = DMProjectFunctionLocal(dm, fe, funcs, INSERT_BC_VALUES, localX);CHKERRQ(ierr); */
  ierr = PetscMalloc7(numComponents,&funcVal,coordDim*Nq,&coords,coordDim*Nq,&realSpaceDer,coordDim*coordDim*Nq,&J,coordDim*coordDim*Nq,&invJ,numComponents,&interpolant,Nq,&detJ);CHKERRQ(ierr);
  ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
  ierr = DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
  cEnd = cEndInterior < 0 ? cEnd : cEndInterior;
  for (c = cStart; c < cEnd; ++c) {
    PetscScalar *x = NULL;
    PetscReal    elemDiff = 0.0;
    PetscInt     qc = 0;

    ierr = DMPlexComputeCellGeometryFEM(dm, c, quad, coords, J, invJ, detJ);CHKERRQ(ierr);
    ierr = DMPlexVecGetClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);

    for (field = 0, fieldOffset = 0; field < numFields; ++field) {
      PetscFE          fe;
      void * const     ctx = ctxs ? ctxs[field] : NULL;
      PetscReal       *basisDer;
      PetscInt         Nb, Nc, q, fc;

      ierr = DMGetField(dm, field, (PetscObject *) &fe);CHKERRQ(ierr);
      ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
      ierr = PetscFEGetNumComponents(fe, &Nc);CHKERRQ(ierr);
      ierr = PetscFEGetDefaultTabulation(fe, NULL, &basisDer, NULL);CHKERRQ(ierr);
      if (debug) {
        char title[1024];
        ierr = PetscSNPrintf(title, 1023, "Solution for Field %d", field);CHKERRQ(ierr);
        ierr = DMPrintCellVector(c, title, Nb, &x[fieldOffset]);CHKERRQ(ierr);
      }
      for (q = 0; q < Nq; ++q) {
        if (detJ[q] <= 0.0) SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %D, quadrature points %D", detJ[q], c, q);
        ierr = (*funcs[field])(coordDim, time, &coords[q*coordDim], n, numFields, funcVal, ctx);
        if (ierr) {
          PetscErrorCode ierr2;
          ierr2 = DMPlexVecRestoreClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr2);
          ierr2 = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr2);
          ierr2 = PetscFree7(funcVal,coords,realSpaceDer,J,invJ,interpolant,detJ);CHKERRQ(ierr2);
          CHKERRQ(ierr);
        }
        ierr = PetscFEInterpolateGradient_Static(fe, &x[fieldOffset], coordDim, invJ, n, q, interpolant);CHKERRQ(ierr);
        for (fc = 0; fc < Nc; ++fc) {
          const PetscReal wt = quadWeights[q*qNc+(qNc == 1 ? 0 : qc+fc)];
          if (debug) {ierr = PetscPrintf(PETSC_COMM_SELF, "    elem %d fieldDer %d diff %g\n", c, field, PetscSqr(PetscRealPart(interpolant[fc] - funcVal[fc]))*wt*detJ[q]);CHKERRQ(ierr);}
          elemDiff += PetscSqr(PetscRealPart(interpolant[fc] - funcVal[fc]))*wt*detJ[q];
        }
      }
      fieldOffset += Nb;
      qc          += Nc;
    }
    ierr = DMPlexVecRestoreClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
    if (debug) {ierr = PetscPrintf(PETSC_COMM_SELF, "  elem %d diff %g\n", c, elemDiff);CHKERRQ(ierr);}
    localDiff += elemDiff;
  }
  ierr  = PetscFree7(funcVal,coords,realSpaceDer,J,invJ,interpolant,detJ);CHKERRQ(ierr);
  ierr  = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr);
  ierr  = MPIU_Allreduce(&localDiff, diff, 1, MPIU_REAL, MPIU_SUM, PetscObjectComm((PetscObject)dm));CHKERRQ(ierr);
  *diff = PetscSqrtReal(*diff);
  PetscFunctionReturn(0);
}

PetscErrorCode DMComputeL2FieldDiff_Plex(DM dm, PetscReal time, PetscErrorCode (**funcs)(PetscInt, PetscReal, const PetscReal [], PetscInt, PetscScalar *, void *), void **ctxs, Vec X, PetscReal *diff)
{
  const PetscInt   debug = 0;
  PetscSection     section;
  PetscQuadrature  quad;
  Vec              localX;
  PetscScalar     *funcVal, *interpolant;
  PetscReal       *coords, *detJ, *J;
  PetscReal       *localDiff;
  const PetscReal *quadPoints, *quadWeights;
  PetscInt         dim, coordDim, numFields, numComponents = 0, qNc, Nq, cStart, cEnd, cEndInterior, c, field, fieldOffset;
  PetscErrorCode   ierr;

  PetscFunctionBegin;
  ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
  ierr = DMGetCoordinateDim(dm, &coordDim);CHKERRQ(ierr);
  ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
  ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
  ierr = DMGetLocalVector(dm, &localX);CHKERRQ(ierr);
  ierr = DMProjectFunctionLocal(dm, time, funcs, ctxs, INSERT_BC_VALUES, localX);CHKERRQ(ierr);
  ierr = DMGlobalToLocalBegin(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
  ierr = DMGlobalToLocalEnd(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
  for (field = 0; field < numFields; ++field) {
    PetscObject  obj;
    PetscClassId id;
    PetscInt     Nc;

    ierr = DMGetField(dm, field, &obj);CHKERRQ(ierr);
    ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
    if (id == PETSCFE_CLASSID) {
      PetscFE fe = (PetscFE) obj;

      ierr = PetscFEGetQuadrature(fe, &quad);CHKERRQ(ierr);
      ierr = PetscFEGetNumComponents(fe, &Nc);CHKERRQ(ierr);
    } else if (id == PETSCFV_CLASSID) {
      PetscFV fv = (PetscFV) obj;

      ierr = PetscFVGetQuadrature(fv, &quad);CHKERRQ(ierr);
      ierr = PetscFVGetNumComponents(fv, &Nc);CHKERRQ(ierr);
    } else SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", field);
    numComponents += Nc;
  }
  ierr = PetscQuadratureGetData(quad, NULL, &qNc, &Nq, &quadPoints, &quadWeights);CHKERRQ(ierr);
  if ((qNc != 1) && (qNc != numComponents)) SETERRQ2(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_SIZ, "Quadrature components %D != %D field components", qNc, numComponents);
  ierr = PetscCalloc6(numFields,&localDiff,numComponents,&funcVal,numComponents,&interpolant,coordDim*Nq,&coords,Nq,&detJ,coordDim*coordDim*Nq,&J);CHKERRQ(ierr);
  ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
  ierr = DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
  cEnd = cEndInterior < 0 ? cEnd : cEndInterior;
  for (c = cStart; c < cEnd; ++c) {
    PetscScalar *x = NULL;
    PetscInt     qc = 0;

    ierr = DMPlexComputeCellGeometryFEM(dm, c, quad, coords, J, NULL, detJ);CHKERRQ(ierr);
    ierr = DMPlexVecGetClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);

    for (field = 0, fieldOffset = 0; field < numFields; ++field) {
      PetscObject  obj;
      PetscClassId id;
      void * const ctx = ctxs ? ctxs[field] : NULL;
      PetscInt     Nb, Nc, q, fc;

      PetscReal       elemDiff = 0.0;

      ierr = DMGetField(dm, field, &obj);CHKERRQ(ierr);
      ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
      if (id == PETSCFE_CLASSID)      {ierr = PetscFEGetNumComponents((PetscFE) obj, &Nc);CHKERRQ(ierr);ierr = PetscFEGetDimension((PetscFE) obj, &Nb);CHKERRQ(ierr);}
      else if (id == PETSCFV_CLASSID) {ierr = PetscFVGetNumComponents((PetscFV) obj, &Nc);CHKERRQ(ierr);Nb = 1;}
      else SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", field);
      if (debug) {
        char title[1024];
        ierr = PetscSNPrintf(title, 1023, "Solution for Field %d", field);CHKERRQ(ierr);
        ierr = DMPrintCellVector(c, title, Nb*Nc, &x[fieldOffset]);CHKERRQ(ierr);
      }
      for (q = 0; q < Nq; ++q) {
        if (detJ[q] <= 0.0) SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %D, quadrature point %D", detJ, c, q);
        ierr = (*funcs[field])(coordDim, time, &coords[coordDim*q], numFields, funcVal, ctx);
        if (ierr) {
          PetscErrorCode ierr2;
          ierr2 = DMPlexVecRestoreClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr2);
          ierr2 = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr2);
          ierr2 = PetscFree6(localDiff,funcVal,interpolant,coords,detJ,J);CHKERRQ(ierr2);
          CHKERRQ(ierr);
        }
        if (id == PETSCFE_CLASSID)      {ierr = PetscFEInterpolate_Static((PetscFE) obj, &x[fieldOffset], q, interpolant);CHKERRQ(ierr);}
        else if (id == PETSCFV_CLASSID) {ierr = PetscFVInterpolate_Static((PetscFV) obj, &x[fieldOffset], q, interpolant);CHKERRQ(ierr);}
        else SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", field);
        for (fc = 0; fc < Nc; ++fc) {
          const PetscReal wt = quadWeights[q*qNc+(qNc == 1 ? 0 : qc+fc)];
          if (debug) {ierr = PetscPrintf(PETSC_COMM_SELF, "    elem %d field %d point %g %g %g diff %g\n", c, field, coordDim > 0 ? coords[0] : 0., coordDim > 1 ? coords[1] : 0., coordDim > 2 ? coords[2] : 0., PetscSqr(PetscRealPart(interpolant[fc] - funcVal[fc]))*wt*detJ[q]);CHKERRQ(ierr);}
          elemDiff += PetscSqr(PetscRealPart(interpolant[fc] - funcVal[fc]))*wt*detJ[q];
        }
      }
      fieldOffset += Nb;
      qc          += Nc;
      localDiff[field] += elemDiff;
    }
    ierr = DMPlexVecRestoreClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
  }
  ierr = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr);
  ierr = MPIU_Allreduce(localDiff, diff, numFields, MPIU_REAL, MPIU_SUM, PetscObjectComm((PetscObject)dm));CHKERRQ(ierr);
  for (field = 0; field < numFields; ++field) diff[field] = PetscSqrtReal(diff[field]);
  ierr = PetscFree6(localDiff,funcVal,interpolant,coords,detJ,J);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@C
  DMPlexComputeL2DiffVec - This function computes the cellwise L_2 difference between a function u and an FEM interpolant solution u_h, and stores it in a Vec.

  Input Parameters:
+ dm    - The DM
. time  - The time
. funcs - The functions to evaluate for each field component: NULL means that component does not contribute to error calculation
. ctxs  - Optional array of contexts to pass to each function, or NULL.
- X     - The coefficient vector u_h

  Output Parameter:
. D - A Vec which holds the difference ||u - u_h||_2 for each cell

  Level: developer

.seealso: DMProjectFunction(), DMComputeL2Diff(), DMPlexComputeL2FieldDiff(), DMComputeL2GradientDiff()
@*/
PetscErrorCode DMPlexComputeL2DiffVec(DM dm, PetscReal time, PetscErrorCode (**funcs)(PetscInt, PetscReal, const PetscReal [], PetscInt, PetscScalar *, void *), void **ctxs, Vec X, Vec D)
{
  PetscSection     section;
  PetscQuadrature  quad;
  Vec              localX;
  PetscScalar     *funcVal, *interpolant;
  PetscReal       *coords, *detJ, *J;
  const PetscReal *quadPoints, *quadWeights;
  PetscInt         dim, coordDim, numFields, numComponents = 0, qNc, Nq, cStart, cEnd, cEndInterior, c, field, fieldOffset;
  PetscErrorCode   ierr;

  PetscFunctionBegin;
  ierr = VecSet(D, 0.0);CHKERRQ(ierr);
  ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
  ierr = DMGetCoordinateDim(dm, &coordDim);CHKERRQ(ierr);
  ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
  ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
  ierr = DMGetLocalVector(dm, &localX);CHKERRQ(ierr);
  ierr = DMProjectFunctionLocal(dm, time, funcs, ctxs, INSERT_BC_VALUES, localX);CHKERRQ(ierr);
  ierr = DMGlobalToLocalBegin(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
  ierr = DMGlobalToLocalEnd(dm, X, INSERT_VALUES, localX);CHKERRQ(ierr);
  for (field = 0; field < numFields; ++field) {
    PetscObject  obj;
    PetscClassId id;
    PetscInt     Nc;

    ierr = DMGetField(dm, field, &obj);CHKERRQ(ierr);
    ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
    if (id == PETSCFE_CLASSID) {
      PetscFE fe = (PetscFE) obj;

      ierr = PetscFEGetQuadrature(fe, &quad);CHKERRQ(ierr);
      ierr = PetscFEGetNumComponents(fe, &Nc);CHKERRQ(ierr);
    } else if (id == PETSCFV_CLASSID) {
      PetscFV fv = (PetscFV) obj;

      ierr = PetscFVGetQuadrature(fv, &quad);CHKERRQ(ierr);
      ierr = PetscFVGetNumComponents(fv, &Nc);CHKERRQ(ierr);
    } else SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", field);
    numComponents += Nc;
  }
  ierr = PetscQuadratureGetData(quad, NULL, &qNc, &Nq, &quadPoints, &quadWeights);CHKERRQ(ierr);
  if ((qNc != 1) && (qNc != numComponents)) SETERRQ2(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_SIZ, "Quadrature components %D != %D field components", qNc, numComponents);
  ierr = PetscMalloc5(numComponents,&funcVal,numComponents,&interpolant,coordDim*Nq,&coords,Nq,&detJ,coordDim*coordDim*Nq,&J);CHKERRQ(ierr);
  ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
  ierr = DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
  cEnd = cEndInterior < 0 ? cEnd : cEndInterior;
  for (c = cStart; c < cEnd; ++c) {
    PetscScalar *x = NULL;
    PetscScalar  elemDiff = 0.0;
    PetscInt     qc = 0;

    ierr = DMPlexComputeCellGeometryFEM(dm, c, quad, coords, J, NULL, detJ);CHKERRQ(ierr);
    ierr = DMPlexVecGetClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);

    for (field = 0, fieldOffset = 0; field < numFields; ++field) {
      PetscObject  obj;
      PetscClassId id;
      void * const ctx = ctxs ? ctxs[field] : NULL;
      PetscInt     Nb, Nc, q, fc;

      ierr = DMGetField(dm, field, &obj);CHKERRQ(ierr);
      ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
      if (id == PETSCFE_CLASSID)      {ierr = PetscFEGetNumComponents((PetscFE) obj, &Nc);CHKERRQ(ierr);ierr = PetscFEGetDimension((PetscFE) obj, &Nb);CHKERRQ(ierr);}
      else if (id == PETSCFV_CLASSID) {ierr = PetscFVGetNumComponents((PetscFV) obj, &Nc);CHKERRQ(ierr);Nb = 1;}
      else SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", field);
      if (funcs[field]) {
        for (q = 0; q < Nq; ++q) {
          if (detJ[q] <= 0.0) SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %D, quadrature points %D", (double)detJ[q], c, q);
          ierr = (*funcs[field])(dim, time, &coords[q*coordDim], Nc, funcVal, ctx);
          if (ierr) {
            PetscErrorCode ierr2;
            ierr2 = DMPlexVecRestoreClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr2);
            ierr2 = PetscFree5(funcVal,interpolant,coords,detJ,J);CHKERRQ(ierr2);
            ierr2 = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr2);
            CHKERRQ(ierr);
          }
          if (id == PETSCFE_CLASSID)      {ierr = PetscFEInterpolate_Static((PetscFE) obj, &x[fieldOffset], q, interpolant);CHKERRQ(ierr);}
          else if (id == PETSCFV_CLASSID) {ierr = PetscFVInterpolate_Static((PetscFV) obj, &x[fieldOffset], q, interpolant);CHKERRQ(ierr);}
          else SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", field);
          for (fc = 0; fc < Nc; ++fc) {
            const PetscReal wt = quadWeights[q*qNc+(qNc == 1 ? 0 : qc+fc)];
            elemDiff += PetscSqr(PetscRealPart(interpolant[fc] - funcVal[fc]))*wt*detJ[q];
          }
        }
      }
      fieldOffset += Nb;
      qc          += Nc;
    }
    ierr = DMPlexVecRestoreClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);
    ierr = VecSetValue(D, c - cStart, elemDiff, INSERT_VALUES);CHKERRQ(ierr);
  }
  ierr = PetscFree5(funcVal,interpolant,coords,detJ,J);CHKERRQ(ierr);
  ierr = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr);
  ierr = VecSqrtAbs(D);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@C
  DMPlexComputeGradientClementInterpolant - This function computes the L2 projection of the cellwise gradient of a function u onto P1, and stores it in a Vec.

  Input Parameters:
+ dm - The DM
- LocX  - The coefficient vector u_h

  Output Parameter:
. locC - A Vec which holds the Clement interpolant of the gradient

  Notes: Add citation to (Clement, 1975) and definition of the interpolant
  \nabla u_h(v_i) = \sum_{T_i \in support(v_i)} |T_i| \nabla u_h(T_i) / \sum_{T_i \in support(v_i)} |T_i| where |T_i| is the cell volume

  Level: developer

.seealso: DMProjectFunction(), DMComputeL2Diff(), DMPlexComputeL2FieldDiff(), DMComputeL2GradientDiff()
@*/
PetscErrorCode DMPlexComputeGradientClementInterpolant(DM dm, Vec locX, Vec locC)
{
  DM_Plex         *mesh  = (DM_Plex *) dm->data;
  PetscInt         debug = mesh->printFEM;
  DM               dmC;
  PetscSection     section;
  PetscQuadrature  quad;
  PetscScalar     *interpolant, *gradsum;
  PetscReal       *coords, *detJ, *J, *invJ;
  const PetscReal *quadPoints, *quadWeights;
  PetscInt         dim, coordDim, numFields, numComponents = 0, qNc, Nq, cStart, cEnd, cEndInterior, vStart, vEnd, v, field, fieldOffset;
  PetscErrorCode   ierr;

  PetscFunctionBegin;
  ierr = VecGetDM(locC, &dmC);CHKERRQ(ierr);
  ierr = VecSet(locC, 0.0);CHKERRQ(ierr);
  ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
  ierr = DMGetCoordinateDim(dm, &coordDim);CHKERRQ(ierr);
  ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
  ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
  for (field = 0; field < numFields; ++field) {
    PetscObject  obj;
    PetscClassId id;
    PetscInt     Nc;

    ierr = DMGetField(dm, field, &obj);CHKERRQ(ierr);
    ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
    if (id == PETSCFE_CLASSID) {
      PetscFE fe = (PetscFE) obj;

      ierr = PetscFEGetQuadrature(fe, &quad);CHKERRQ(ierr);
      ierr = PetscFEGetNumComponents(fe, &Nc);CHKERRQ(ierr);
    } else if (id == PETSCFV_CLASSID) {
      PetscFV fv = (PetscFV) obj;

      ierr = PetscFVGetQuadrature(fv, &quad);CHKERRQ(ierr);
      ierr = PetscFVGetNumComponents(fv, &Nc);CHKERRQ(ierr);
    } else SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", field);
    numComponents += Nc;
  }
  ierr = PetscQuadratureGetData(quad, NULL, &qNc, &Nq, &quadPoints, &quadWeights);CHKERRQ(ierr);
  if ((qNc != 1) && (qNc != numComponents)) SETERRQ2(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_SIZ, "Quadrature components %D != %D field components", qNc, numComponents);
  ierr = PetscMalloc6(coordDim*numComponents*2,&gradsum,coordDim*numComponents,&interpolant,coordDim*Nq,&coords,Nq,&detJ,coordDim*coordDim*Nq,&J,coordDim*coordDim*Nq,&invJ);CHKERRQ(ierr);
  ierr = DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);CHKERRQ(ierr);
  ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
  ierr = DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
  cEnd = cEndInterior < 0 ? cEnd : cEndInterior;
  for (v = vStart; v < vEnd; ++v) {
    PetscScalar volsum = 0.0;
    PetscInt   *star = NULL;
    PetscInt    starSize, st, d, fc;

    ierr = PetscMemzero(gradsum, coordDim*numComponents * sizeof(PetscScalar));CHKERRQ(ierr);
    ierr = DMPlexGetTransitiveClosure(dm, v, PETSC_FALSE, &starSize, &star);CHKERRQ(ierr);
    for (st = 0; st < starSize*2; st += 2) {
      const PetscInt cell = star[st];
      PetscScalar   *grad = &gradsum[coordDim*numComponents];
      PetscScalar   *x    = NULL;
      PetscReal      vol  = 0.0;

      if ((cell < cStart) || (cell >= cEnd)) continue;
      ierr = DMPlexComputeCellGeometryFEM(dm, cell, quad, coords, J, invJ, detJ);CHKERRQ(ierr);
      ierr = DMPlexVecGetClosure(dm, NULL, locX, cell, NULL, &x);CHKERRQ(ierr);
      for (field = 0, fieldOffset = 0; field < numFields; ++field) {
        PetscObject  obj;
        PetscClassId id;
        PetscInt     Nb, Nc, q, qc = 0;

        ierr = PetscMemzero(grad, coordDim*numComponents * sizeof(PetscScalar));CHKERRQ(ierr);
        ierr = DMGetField(dm, field, &obj);CHKERRQ(ierr);
        ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
        if (id == PETSCFE_CLASSID)      {ierr = PetscFEGetNumComponents((PetscFE) obj, &Nc);CHKERRQ(ierr);ierr = PetscFEGetDimension((PetscFE) obj, &Nb);CHKERRQ(ierr);}
        else if (id == PETSCFV_CLASSID) {ierr = PetscFVGetNumComponents((PetscFV) obj, &Nc);CHKERRQ(ierr);Nb = 1;}
        else SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", field);
        for (q = 0; q < Nq; ++q) {
          if (detJ[q] <= 0.0) SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %D, quadrature points %D", (double)detJ[q], cell, q);
          if (ierr) {
            PetscErrorCode ierr2;
            ierr2 = DMPlexVecRestoreClosure(dm, NULL, locX, cell, NULL, &x);CHKERRQ(ierr2);
            ierr2 = DMPlexRestoreTransitiveClosure(dm, v, PETSC_FALSE, &starSize, &star);CHKERRQ(ierr2);
            ierr2 = PetscFree4(interpolant,coords,detJ,J);CHKERRQ(ierr2);
            CHKERRQ(ierr);
          }
          if (id == PETSCFE_CLASSID)      {ierr = PetscFEInterpolateGradient_Static((PetscFE) obj, &x[fieldOffset], coordDim, invJ, NULL, q, interpolant);CHKERRQ(ierr);}
          else SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", field);
          for (fc = 0; fc < Nc; ++fc) {
            const PetscReal wt = quadWeights[q*qNc+qc+fc];

            for (d = 0; d < coordDim; ++d) grad[fc*coordDim+d] += interpolant[fc*dim+d]*wt*detJ[q];
          }
          vol += quadWeights[q*qNc]*detJ[q];
        }
        fieldOffset += Nb;
        qc          += Nc;
      }
      ierr = DMPlexVecRestoreClosure(dm, NULL, locX, cell, NULL, &x);CHKERRQ(ierr);
      for (fc = 0; fc < numComponents; ++fc) {
        for (d = 0; d < coordDim; ++d) {
          gradsum[fc*coordDim+d] += grad[fc*coordDim+d];
        }
      }
      volsum += vol;
      if (debug) {
        ierr = PetscPrintf(PETSC_COMM_SELF, "Cell %D gradient: [", cell);CHKERRQ(ierr);
        for (fc = 0; fc < numComponents; ++fc) {
          for (d = 0; d < coordDim; ++d) {
            if (fc || d > 0) {ierr = PetscPrintf(PETSC_COMM_SELF, ", ");CHKERRQ(ierr);}
            ierr = PetscPrintf(PETSC_COMM_SELF, "%g", (double)PetscRealPart(grad[fc*coordDim+d]));CHKERRQ(ierr);
          }
        }
        ierr = PetscPrintf(PETSC_COMM_SELF, "]\n");CHKERRQ(ierr);
      }
    }
    for (fc = 0; fc < numComponents; ++fc) {
      for (d = 0; d < coordDim; ++d) gradsum[fc*coordDim+d] /= volsum;
    }
    ierr = DMPlexRestoreTransitiveClosure(dm, v, PETSC_FALSE, &starSize, &star);CHKERRQ(ierr);
    ierr = DMPlexVecSetClosure(dmC, NULL, locC, v, gradsum, INSERT_VALUES);CHKERRQ(ierr);
  }
  ierr = PetscFree6(gradsum,interpolant,coords,detJ,J,invJ);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

static PetscErrorCode DMPlexComputeIntegral_Internal(DM dm, Vec X, PetscInt cStart, PetscInt cEnd, PetscScalar *cintegral, void *user)
{
  DM                 dmAux = NULL;
  PetscDS            prob,    probAux;
  PetscSection       section, sectionAux;
  Vec                locX,    locA;
  PetscInt           dim, numCells = cEnd - cStart, cell, c, f;
  PetscBool          useFEM = PETSC_FALSE, useFVM = PETSC_FALSE;
  /* DS */
  PetscInt           Nf,    totDim,    *uOff, *uOff_x, numConstants;
  PetscInt           NfAux, totDimAux, *aOff;
  PetscScalar       *u, *a;
  const PetscScalar *constants;
  /* Geometry */
  PetscFECellGeom   *cgeomFEM;
  DM                 dmGrad;
  Vec                cellGeometryFVM = NULL, faceGeometryFVM = NULL, locGrad = NULL;
  PetscFVCellGeom   *cgeomFVM;
  const PetscScalar *lgrad;
  PetscErrorCode     ierr;

  PetscFunctionBegin;
  ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
  ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
  ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
  ierr = PetscSectionGetNumFields(section, &Nf);CHKERRQ(ierr);
  /* Determine which discretizations we have */
  for (f = 0; f < Nf; ++f) {
    PetscObject  obj;
    PetscClassId id;

    ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
    ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
    if (id == PETSCFE_CLASSID) useFEM = PETSC_TRUE;
    if (id == PETSCFV_CLASSID) useFVM = PETSC_TRUE;
  }
  /* Get local solution with boundary values */
  ierr = DMGetLocalVector(dm, &locX);CHKERRQ(ierr);
  ierr = DMPlexInsertBoundaryValues(dm, PETSC_TRUE, locX, 0.0, NULL, NULL, NULL);CHKERRQ(ierr);
  ierr = DMGlobalToLocalBegin(dm, X, INSERT_VALUES, locX);CHKERRQ(ierr);
  ierr = DMGlobalToLocalEnd(dm, X, INSERT_VALUES, locX);CHKERRQ(ierr);
  /* Read DS information */
  ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
  ierr = PetscDSGetComponentOffsets(prob, &uOff);CHKERRQ(ierr);
  ierr = PetscDSGetComponentDerivativeOffsets(prob, &uOff_x);CHKERRQ(ierr);
  ierr = PetscDSGetConstants(prob, &numConstants, &constants);CHKERRQ(ierr);
  /* Read Auxiliary DS information */
  ierr = PetscObjectQuery((PetscObject) dm, "dmAux", (PetscObject *) &dmAux);CHKERRQ(ierr);
  ierr = PetscObjectQuery((PetscObject) dm, "A", (PetscObject *) &locA);CHKERRQ(ierr);
  if (dmAux) {
    ierr = DMGetDS(dmAux, &probAux);CHKERRQ(ierr);
    ierr = PetscDSGetNumFields(probAux, &NfAux);CHKERRQ(ierr);
    ierr = DMGetDefaultSection(dmAux, &sectionAux);CHKERRQ(ierr);
    ierr = PetscDSGetTotalDimension(probAux, &totDimAux);CHKERRQ(ierr);
    ierr = PetscDSGetComponentOffsets(probAux, &aOff);CHKERRQ(ierr);
  }
  /* Allocate data  arrays */
  ierr = PetscCalloc1(numCells*totDim, &u);CHKERRQ(ierr);
  if (useFEM) {ierr = PetscMalloc1(numCells, &cgeomFEM);CHKERRQ(ierr);}
  if (dmAux) {ierr = PetscMalloc1(numCells*totDimAux, &a);CHKERRQ(ierr);}
  /* Read out geometry */
  if (useFEM) {
    for (cell = cStart; cell < cEnd; ++cell) {
      const PetscInt c = cell - cStart;

      ierr = DMPlexComputeCellGeometryFEM(dm, cell, NULL, cgeomFEM[c].v0, cgeomFEM[c].J, cgeomFEM[c].invJ, &cgeomFEM[c].detJ);CHKERRQ(ierr);
      if (cgeomFEM[c].detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", cgeomFEM[c].detJ, c);
    }
  }
  if (useFVM) {
    PetscFV   fv = NULL;
    Vec       grad;
    PetscInt  fStart, fEnd;
    PetscBool compGrad;

    for (f = 0; f < Nf; ++f) {
      PetscObject  obj;
      PetscClassId id;

      ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
      ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
      if (id == PETSCFV_CLASSID) {fv = (PetscFV) obj; break;}
    }
    ierr = PetscFVGetComputeGradients(fv, &compGrad);CHKERRQ(ierr);
    ierr = PetscFVSetComputeGradients(fv, PETSC_TRUE);CHKERRQ(ierr);
    ierr = DMPlexComputeGeometryFVM(dm, &cellGeometryFVM, &faceGeometryFVM);CHKERRQ(ierr);
    ierr = DMPlexComputeGradientFVM(dm, fv, faceGeometryFVM, cellGeometryFVM, &dmGrad);CHKERRQ(ierr);
    ierr = PetscFVSetComputeGradients(fv, compGrad);CHKERRQ(ierr);
    ierr = VecGetArrayRead(cellGeometryFVM, (const PetscScalar **) &cgeomFVM);CHKERRQ(ierr);
    /* Reconstruct and limit cell gradients */
    ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
    ierr = DMGetGlobalVector(dmGrad, &grad);CHKERRQ(ierr);
    ierr = DMPlexReconstructGradients_Internal(dm, fv, fStart, fEnd, faceGeometryFVM, cellGeometryFVM, locX, grad);CHKERRQ(ierr);
    /* Communicate gradient values */
    ierr = DMGetLocalVector(dmGrad, &locGrad);CHKERRQ(ierr);
    ierr = DMGlobalToLocalBegin(dmGrad, grad, INSERT_VALUES, locGrad);CHKERRQ(ierr);
    ierr = DMGlobalToLocalEnd(dmGrad, grad, INSERT_VALUES, locGrad);CHKERRQ(ierr);
    ierr = DMRestoreGlobalVector(dmGrad, &grad);CHKERRQ(ierr);
    /* Handle non-essential (e.g. outflow) boundary values */
    ierr = DMPlexInsertBoundaryValues(dm, PETSC_FALSE, locX, 0.0, faceGeometryFVM, cellGeometryFVM, locGrad);CHKERRQ(ierr);
    ierr = VecGetArrayRead(locGrad, &lgrad);CHKERRQ(ierr);
  }
  /* Read out data from inputs */
  for (c = cStart; c < cEnd; ++c) {
    PetscScalar *x = NULL;
    PetscInt     i;

    ierr = DMPlexVecGetClosure(dm, section, locX, c, NULL, &x);CHKERRQ(ierr);
    for (i = 0; i < totDim; ++i) u[c*totDim+i] = x[i];
    ierr = DMPlexVecRestoreClosure(dm, section, locX, c, NULL, &x);CHKERRQ(ierr);
    if (dmAux) {
      ierr = DMPlexVecGetClosure(dmAux, sectionAux, locA, c, NULL, &x);CHKERRQ(ierr);
      for (i = 0; i < totDimAux; ++i) a[c*totDimAux+i] = x[i];
      ierr = DMPlexVecRestoreClosure(dmAux, sectionAux, locA, c, NULL, &x);CHKERRQ(ierr);
    }
  }
  /* Do integration for each field */
  for (f = 0; f < Nf; ++f) {
    PetscObject  obj;
    PetscClassId id;
    PetscInt     numChunks, numBatches, batchSize, numBlocks, blockSize, Ne, Nr, offset;

    ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
    ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
    if (id == PETSCFE_CLASSID) {
      PetscFE         fe = (PetscFE) obj;
      PetscQuadrature q;
      PetscInt        Nq, Nb;

      ierr = PetscFEGetTileSizes(fe, NULL, &numBlocks, NULL, &numBatches);CHKERRQ(ierr);
      ierr = PetscFEGetQuadrature(fe, &q);CHKERRQ(ierr);
      ierr = PetscQuadratureGetData(q, NULL, NULL, &Nq, NULL, NULL);CHKERRQ(ierr);
      ierr = PetscFEGetDimension(fe, &Nb);CHKERRQ(ierr);
      blockSize = Nb*Nq;
      batchSize = numBlocks * blockSize;
      ierr = PetscFESetTileSizes(fe, blockSize, numBlocks, batchSize, numBatches);CHKERRQ(ierr);
      numChunks = numCells / (numBatches*batchSize);
      Ne        = numChunks*numBatches*batchSize;
      Nr        = numCells % (numBatches*batchSize);
      offset    = numCells - Nr;
      ierr = PetscFEIntegrate(fe, prob, f, Ne, cgeomFEM, u, probAux, a, cintegral);CHKERRQ(ierr);
      ierr = PetscFEIntegrate(fe, prob, f, Nr, &cgeomFEM[offset], &u[offset*totDim], probAux, &a[offset*totDimAux], &cintegral[offset*Nf]);CHKERRQ(ierr);
    } else if (id == PETSCFV_CLASSID) {
      PetscInt       foff;
      PetscPointFunc obj_func;
      PetscScalar    lint;

      ierr = PetscDSGetObjective(prob, f, &obj_func);CHKERRQ(ierr);
      ierr = PetscDSGetFieldOffset(prob, f, &foff);CHKERRQ(ierr);
      if (obj_func) {
        for (c = 0; c < numCells; ++c) {
          PetscScalar *u_x;

          ierr = DMPlexPointLocalRead(dmGrad, c, lgrad, &u_x);CHKERRQ(ierr);
          obj_func(dim, Nf, NfAux, uOff, uOff_x, &u[totDim*c+foff], NULL, u_x, aOff, NULL, &a[totDimAux*c], NULL, NULL, 0.0, cgeomFVM[c].centroid, numConstants, constants, &lint);
          cintegral[c*Nf+f] += PetscRealPart(lint)*cgeomFVM[c].volume;
        }
      }
    } else SETERRQ1(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_WRONG, "Unknown discretization type for field %d", f);
  }
  /* Cleanup data arrays */
  if (useFVM) {
    ierr = VecRestoreArrayRead(locGrad, &lgrad);CHKERRQ(ierr);
    ierr = VecRestoreArrayRead(cellGeometryFVM, (const PetscScalar **) &cgeomFVM);CHKERRQ(ierr);
    ierr = DMRestoreLocalVector(dmGrad, &locGrad);CHKERRQ(ierr);
    ierr = VecDestroy(&faceGeometryFVM);CHKERRQ(ierr);
    ierr = VecDestroy(&cellGeometryFVM);CHKERRQ(ierr);
    ierr = DMDestroy(&dmGrad);CHKERRQ(ierr);
  }
  if (useFEM) {ierr = PetscFree(cgeomFEM);CHKERRQ(ierr);}
  if (dmAux) {ierr = PetscFree(a);CHKERRQ(ierr);}
  ierr = PetscFree(u);CHKERRQ(ierr);
  /* Cleanup */
  ierr = DMRestoreLocalVector(dm, &locX);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@
  DMPlexComputeIntegralFEM - Form the integral over the domain from the global input X using pointwise functions specified by the user

  Input Parameters:
+ dm - The mesh
. X  - Global input vector
- user - The user context

  Output Parameter:
. integral - Integral for each field

  Level: developer

.seealso: DMPlexComputeResidualFEM()
@*/
PetscErrorCode DMPlexComputeIntegralFEM(DM dm, Vec X, PetscScalar *integral, void *user)
{
  DM_Plex       *mesh = (DM_Plex *) dm->data;
  PetscScalar   *cintegral, *lintegral;
  PetscInt       Nf, f, cellHeight, cStart, cEnd, cEndInterior[4], cell;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidHeaderSpecific(X, VEC_CLASSID, 2);
  PetscValidPointer(integral, 3);
  ierr = PetscLogEventBegin(DMPLEX_IntegralFEM,dm,0,0,0);CHKERRQ(ierr);
  ierr = DMGetNumFields(dm, &Nf);CHKERRQ(ierr);
  ierr = DMPlexGetVTKCellHeight(dm, &cellHeight);CHKERRQ(ierr);
  ierr = DMPlexGetHeightStratum(dm, cellHeight, &cStart, &cEnd);CHKERRQ(ierr);
  ierr = DMPlexGetHybridBounds(dm, &cEndInterior[0], &cEndInterior[1], &cEndInterior[2], &cEndInterior[3]);CHKERRQ(ierr);
  cEnd = cEndInterior[cellHeight] < 0 ? cEnd : cEndInterior[cellHeight];
  /* TODO Introduce a loop over large chunks (right now this is a single chunk) */
  ierr = PetscCalloc2(Nf, &lintegral, (cEnd-cStart)*Nf, &cintegral);CHKERRQ(ierr);
  ierr = DMPlexComputeIntegral_Internal(dm, X, cStart, cEnd, cintegral, user);CHKERRQ(ierr);
  /* Sum up values */
  for (cell = cStart; cell < cEnd; ++cell) {
    const PetscInt c = cell - cStart;

    if (mesh->printFEM > 1) {ierr = DMPrintCellVector(cell, "Cell Integral", Nf, &cintegral[c*Nf]);CHKERRQ(ierr);}
    for (f = 0; f < Nf; ++f) lintegral[f] += cintegral[c*Nf+f];
  }
  ierr = MPIU_Allreduce(lintegral, integral, Nf, MPIU_SCALAR, MPIU_SUM, PetscObjectComm((PetscObject) dm));CHKERRQ(ierr);
  if (mesh->printFEM) {
    ierr = PetscPrintf(PetscObjectComm((PetscObject) dm), "Integral:");CHKERRQ(ierr);
    for (f = 0; f < Nf; ++f) {ierr = PetscPrintf(PetscObjectComm((PetscObject) dm), " %g", (double) PetscRealPart(integral[f]));CHKERRQ(ierr);}
    ierr = PetscPrintf(PetscObjectComm((PetscObject) dm), "\n");CHKERRQ(ierr);
  }
  ierr = PetscFree2(lintegral, cintegral);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(DMPLEX_IntegralFEM,dm,0,0,0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@
  DMPlexComputeCellwiseIntegralFEM - Form the vector of cellwise integrals F from the global input X using pointwise functions specified by the user

  Input Parameters:
+ dm - The mesh
. X  - Global input vector
- user - The user context

  Output Parameter:
. integral - Cellwise integrals for each field

  Level: developer

.seealso: DMPlexComputeResidualFEM()
@*/
PetscErrorCode DMPlexComputeCellwiseIntegralFEM(DM dm, Vec X, Vec F, void *user)
{
  DM_Plex       *mesh = (DM_Plex *) dm->data;
  DM             dmF;
  PetscSection   sectionF;
  PetscScalar   *cintegral, *af;
  PetscInt       Nf, f, cellHeight, cStart, cEnd, cEndInterior[4], cell;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidHeaderSpecific(X, VEC_CLASSID, 2);
  PetscValidHeaderSpecific(F, VEC_CLASSID, 3);
  ierr = PetscLogEventBegin(DMPLEX_IntegralFEM,dm,0,0,0);CHKERRQ(ierr);
  ierr = DMGetNumFields(dm, &Nf);CHKERRQ(ierr);
  ierr = DMPlexGetVTKCellHeight(dm, &cellHeight);CHKERRQ(ierr);
  ierr = DMPlexGetHeightStratum(dm, cellHeight, &cStart, &cEnd);CHKERRQ(ierr);
  ierr = DMPlexGetHybridBounds(dm, &cEndInterior[0], &cEndInterior[1], &cEndInterior[2], &cEndInterior[3]);CHKERRQ(ierr);
  cEnd = cEndInterior[cellHeight] < 0 ? cEnd : cEndInterior[cellHeight];
  /* TODO Introduce a loop over large chunks (right now this is a single chunk) */
  ierr = PetscCalloc1((cEnd-cStart)*Nf, &cintegral);CHKERRQ(ierr);
  ierr = DMPlexComputeIntegral_Internal(dm, X, cStart, cEnd, cintegral, user);CHKERRQ(ierr);
  /* Put values in F*/
  ierr = VecGetDM(F, &dmF);CHKERRQ(ierr);
  ierr = DMGetDefaultSection(dmF, &sectionF);CHKERRQ(ierr);
  ierr = VecGetArray(F, &af);CHKERRQ(ierr);
  for (cell = cStart; cell < cEnd; ++cell) {
    const PetscInt c = cell - cStart;
    PetscInt       dof, off;

    if (mesh->printFEM > 1) {ierr = DMPrintCellVector(cell, "Cell Integral", Nf, &cintegral[c*Nf]);CHKERRQ(ierr);}
    ierr = PetscSectionGetDof(sectionF, cell, &dof);CHKERRQ(ierr);
    ierr = PetscSectionGetOffset(sectionF, cell, &off);CHKERRQ(ierr);
    if (dof != Nf) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "The number of cell dofs %D != %D", dof, Nf);
    for (f = 0; f < Nf; ++f) af[off+f] = cintegral[c*Nf+f];
  }
  ierr = VecRestoreArray(F, &af);CHKERRQ(ierr);
  ierr = PetscFree(cintegral);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(DMPLEX_IntegralFEM,dm,0,0,0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@
  DMPlexComputeInterpolatorNested - Form the local portion of the interpolation matrix I from the coarse DM to the uniformly refined DM.

  Input Parameters:
+ dmf  - The fine mesh
. dmc  - The coarse mesh
- user - The user context

  Output Parameter:
. In  - The interpolation matrix

  Level: developer

.seealso: DMPlexComputeInterpolatorGeneral(), DMPlexComputeJacobianFEM()
@*/
PetscErrorCode DMPlexComputeInterpolatorNested(DM dmc, DM dmf, Mat In, void *user)
{
  DM_Plex          *mesh  = (DM_Plex *) dmc->data;
  const char       *name  = "Interpolator";
  PetscDS           prob;
  PetscFE          *feRef;
  PetscFV          *fvRef;
  PetscSection      fsection, fglobalSection;
  PetscSection      csection, cglobalSection;
  PetscScalar      *elemMat;
  PetscInt          dim, Nf, f, fieldI, fieldJ, offsetI, offsetJ, cStart, cEnd, cEndInterior, c;
  PetscInt          cTotDim, rTotDim = 0;
  PetscErrorCode    ierr;

  PetscFunctionBegin;
  ierr = PetscLogEventBegin(DMPLEX_InterpolatorFEM,dmc,dmf,0,0);CHKERRQ(ierr);
  ierr = DMGetDimension(dmf, &dim);CHKERRQ(ierr);
  ierr = DMGetDefaultSection(dmf, &fsection);CHKERRQ(ierr);
  ierr = DMGetDefaultGlobalSection(dmf, &fglobalSection);CHKERRQ(ierr);
  ierr = DMGetDefaultSection(dmc, &csection);CHKERRQ(ierr);
  ierr = DMGetDefaultGlobalSection(dmc, &cglobalSection);CHKERRQ(ierr);
  ierr = PetscSectionGetNumFields(fsection, &Nf);CHKERRQ(ierr);
  ierr = DMPlexGetHeightStratum(dmc, 0, &cStart, &cEnd);CHKERRQ(ierr);
  ierr = DMPlexGetHybridBounds(dmc, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
  cEnd = cEndInterior < 0 ? cEnd : cEndInterior;
  ierr = DMGetDS(dmf, &prob);CHKERRQ(ierr);
  ierr = PetscCalloc2(Nf,&feRef,Nf,&fvRef);CHKERRQ(ierr);
  for (f = 0; f < Nf; ++f) {
    PetscObject  obj;
    PetscClassId id;
    PetscInt     rNb = 0, Nc = 0;

    ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
    ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
    if (id == PETSCFE_CLASSID) {
      PetscFE fe = (PetscFE) obj;

      ierr = PetscFERefine(fe, &feRef[f]);CHKERRQ(ierr);
      ierr = PetscFEGetDimension(feRef[f], &rNb);CHKERRQ(ierr);
      ierr = PetscFEGetNumComponents(fe, &Nc);CHKERRQ(ierr);
    } else if (id == PETSCFV_CLASSID) {
      PetscFV        fv = (PetscFV) obj;
      PetscDualSpace Q;

      ierr = PetscFVRefine(fv, &fvRef[f]);CHKERRQ(ierr);
      ierr = PetscFVGetDualSpace(fvRef[f], &Q);CHKERRQ(ierr);
      ierr = PetscDualSpaceGetDimension(Q, &rNb);CHKERRQ(ierr);
      ierr = PetscFVGetNumComponents(fv, &Nc);CHKERRQ(ierr);
    }
    rTotDim += rNb;
  }
  ierr = PetscDSGetTotalDimension(prob, &cTotDim);CHKERRQ(ierr);
  ierr = PetscMalloc1(rTotDim*cTotDim,&elemMat);CHKERRQ(ierr);
  ierr = PetscMemzero(elemMat, rTotDim*cTotDim * sizeof(PetscScalar));CHKERRQ(ierr);
  for (fieldI = 0, offsetI = 0; fieldI < Nf; ++fieldI) {
    PetscDualSpace   Qref;
    PetscQuadrature  f;
    const PetscReal *qpoints, *qweights;
    PetscReal       *points;
    PetscInt         npoints = 0, Nc, Np, fpdim, i, k, p, d;

    /* Compose points from all dual basis functionals */
    if (feRef[fieldI]) {
      ierr = PetscFEGetDualSpace(feRef[fieldI], &Qref);CHKERRQ(ierr);
      ierr = PetscFEGetNumComponents(feRef[fieldI], &Nc);CHKERRQ(ierr);
    } else {
      ierr = PetscFVGetDualSpace(fvRef[fieldI], &Qref);CHKERRQ(ierr);
      ierr = PetscFVGetNumComponents(fvRef[fieldI], &Nc);CHKERRQ(ierr);
    }
    ierr = PetscDualSpaceGetDimension(Qref, &fpdim);CHKERRQ(ierr);
    for (i = 0; i < fpdim; ++i) {
      ierr = PetscDualSpaceGetFunctional(Qref, i, &f);CHKERRQ(ierr);
      ierr = PetscQuadratureGetData(f, NULL, NULL, &Np, NULL, NULL);CHKERRQ(ierr);
      npoints += Np;
    }
    ierr = PetscMalloc1(npoints*dim,&points);CHKERRQ(ierr);
    for (i = 0, k = 0; i < fpdim; ++i) {
      ierr = PetscDualSpaceGetFunctional(Qref, i, &f);CHKERRQ(ierr);
      ierr = PetscQuadratureGetData(f, NULL, NULL, &Np, &qpoints, NULL);CHKERRQ(ierr);
      for (p = 0; p < Np; ++p, ++k) for (d = 0; d < dim; ++d) points[k*dim+d] = qpoints[p*dim+d];
    }

    for (fieldJ = 0, offsetJ = 0; fieldJ < Nf; ++fieldJ) {
      PetscObject  obj;
      PetscClassId id;
      PetscReal   *B;
      PetscInt     NcJ = 0, cpdim = 0, j, qNc;

      ierr = PetscDSGetDiscretization(prob, fieldJ, &obj);CHKERRQ(ierr);
      ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
      if (id == PETSCFE_CLASSID) {
        PetscFE fe = (PetscFE) obj;

        /* Evaluate basis at points */
        ierr = PetscFEGetNumComponents(fe, &NcJ);CHKERRQ(ierr);
        ierr = PetscFEGetDimension(fe, &cpdim);CHKERRQ(ierr);
        /* For now, fields only interpolate themselves */
        if (fieldI == fieldJ) {
          if (Nc != NcJ) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Number of components in fine space field %D does not match coarse field %D", Nc, NcJ);
          ierr = PetscFEGetTabulation(fe, npoints, points, &B, NULL, NULL);CHKERRQ(ierr);
          for (i = 0, k = 0; i < fpdim; ++i) {
            ierr = PetscDualSpaceGetFunctional(Qref, i, &f);CHKERRQ(ierr);
            ierr = PetscQuadratureGetData(f, NULL, &qNc, &Np, NULL, &qweights);CHKERRQ(ierr);
            if (qNc != NcJ) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Number of components in quadrature %D does not match coarse field %D", qNc, NcJ);
            for (p = 0; p < Np; ++p, ++k) {
              for (j = 0; j < cpdim; ++j) {
                /* NOTE: This is not quite right, unless fpdim == number of fine grid functional quad points */
                for (c = 0; c < Nc; ++c) elemMat[(offsetI + i)*cTotDim + offsetJ + j] += B[k*cpdim*NcJ+j*Nc+c]*qweights[p*qNc+c];
              }
            }
          }
          ierr = PetscFERestoreTabulation(fe, npoints, points, &B, NULL, NULL);CHKERRQ(ierr);CHKERRQ(ierr);
        }
      } else if (id == PETSCFV_CLASSID) {
        PetscFV        fv = (PetscFV) obj;

        /* Evaluate constant function at points */
        ierr = PetscFVGetNumComponents(fv, &NcJ);CHKERRQ(ierr);
        cpdim = 1;
        /* For now, fields only interpolate themselves */
        if (fieldI == fieldJ) {
          if (Nc != NcJ) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Number of components in fine space field %d does not match coarse field %d", Nc, NcJ);
          for (i = 0, k = 0; i < fpdim; ++i) {
            ierr = PetscDualSpaceGetFunctional(Qref, i, &f);CHKERRQ(ierr);
            ierr = PetscQuadratureGetData(f, NULL, &qNc, &Np, NULL, &qweights);CHKERRQ(ierr);
            if (qNc != NcJ) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Number of components in quadrature %D does not match coarse field %D", qNc, NcJ);
            for (p = 0; p < Np; ++p, ++k) {
              for (j = 0; j < cpdim; ++j) {
                for (c = 0; c < Nc; ++c) elemMat[(offsetI + i*Nc + c)*cTotDim + offsetJ + j*NcJ + c] += 1.0*qweights[p*qNc+c];
              }
            }
          }
        }
      }
      offsetJ += cpdim*NcJ;
    }
    offsetI += fpdim*Nc;
    ierr = PetscFree(points);CHKERRQ(ierr);
  }
  if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(0, name, rTotDim, cTotDim, elemMat);CHKERRQ(ierr);}
  /* Preallocate matrix */
  {
    Mat          preallocator;
    PetscScalar *vals;
    PetscInt    *cellCIndices, *cellFIndices;
    PetscInt     locRows, locCols, cell;

    ierr = MatGetLocalSize(In, &locRows, &locCols);CHKERRQ(ierr);
    ierr = MatCreate(PetscObjectComm((PetscObject) In), &preallocator);CHKERRQ(ierr);
    ierr = MatSetType(preallocator, MATPREALLOCATOR);CHKERRQ(ierr);
    ierr = MatSetSizes(preallocator, locRows, locCols, PETSC_DETERMINE, PETSC_DETERMINE);CHKERRQ(ierr);
    ierr = MatSetUp(preallocator);CHKERRQ(ierr);
    ierr = PetscCalloc3(rTotDim*cTotDim, &vals,cTotDim,&cellCIndices,rTotDim,&cellFIndices);CHKERRQ(ierr);
    for (cell = cStart; cell < cEnd; ++cell) {
      ierr = DMPlexMatGetClosureIndicesRefined(dmf, fsection, fglobalSection, dmc, csection, cglobalSection, cell, cellCIndices, cellFIndices);CHKERRQ(ierr);
      ierr = MatSetValues(preallocator, rTotDim, cellFIndices, cTotDim, cellCIndices, vals, INSERT_VALUES);CHKERRQ(ierr);
    }
    ierr = PetscFree3(vals,cellCIndices,cellFIndices);CHKERRQ(ierr);
    ierr = MatAssemblyBegin(preallocator, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
    ierr = MatAssemblyEnd(preallocator, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
    ierr = MatPreallocatorPreallocate(preallocator, PETSC_TRUE, In);CHKERRQ(ierr);
    ierr = MatDestroy(&preallocator);CHKERRQ(ierr);
  }
  /* Fill matrix */
  ierr = MatZeroEntries(In);CHKERRQ(ierr);
  for (c = cStart; c < cEnd; ++c) {
    ierr = DMPlexMatSetClosureRefined(dmf, fsection, fglobalSection, dmc, csection, cglobalSection, In, c, elemMat, INSERT_VALUES);CHKERRQ(ierr);
  }
  for (f = 0; f < Nf; ++f) {ierr = PetscFEDestroy(&feRef[f]);CHKERRQ(ierr);}
  ierr = PetscFree2(feRef,fvRef);CHKERRQ(ierr);
  ierr = PetscFree(elemMat);CHKERRQ(ierr);
  ierr = MatAssemblyBegin(In, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(In, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  if (mesh->printFEM) {
    ierr = PetscPrintf(PETSC_COMM_WORLD, "%s:\n", name);CHKERRQ(ierr);
    ierr = MatChop(In, 1.0e-10);CHKERRQ(ierr);
    ierr = MatView(In, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
  }
  ierr = PetscLogEventEnd(DMPLEX_InterpolatorFEM,dmc,dmf,0,0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode DMPlexComputeMassMatrixNested(DM dmc, DM dmf, Mat mass, void *user)
{
  SETERRQ(PetscObjectComm((PetscObject) dmc), PETSC_ERR_SUP, "Laziness");
}

/*@
  DMPlexComputeInterpolatorGeneral - Form the local portion of the interpolation matrix I from the coarse DM to a non-nested fine DM.

  Input Parameters:
+ dmf  - The fine mesh
. dmc  - The coarse mesh
- user - The user context

  Output Parameter:
. In  - The interpolation matrix

  Level: developer

.seealso: DMPlexComputeInterpolatorNested(), DMPlexComputeJacobianFEM()
@*/
PetscErrorCode DMPlexComputeInterpolatorGeneral(DM dmc, DM dmf, Mat In, void *user)
{
  DM_Plex       *mesh = (DM_Plex *) dmf->data;
  const char    *name = "Interpolator";
  PetscDS        prob;
  PetscSection   fsection, csection, globalFSection, globalCSection;
  PetscHashJK    ht;
  PetscLayout    rLayout;
  PetscInt      *dnz, *onz;
  PetscInt       locRows, rStart, rEnd;
  PetscReal     *x, *v0, *J, *invJ, detJ;
  PetscReal     *v0c, *Jc, *invJc, detJc;
  PetscScalar   *elemMat;
  PetscInt       dim, Nf, field, totDim, cStart, cEnd, cell, ccell;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscLogEventBegin(DMPLEX_InterpolatorFEM,dmc,dmf,0,0);CHKERRQ(ierr);
  ierr = DMGetCoordinateDim(dmc, &dim);CHKERRQ(ierr);
  ierr = DMGetDS(dmc, &prob);CHKERRQ(ierr);
  ierr = PetscDSGetRefCoordArrays(prob, &x, NULL);CHKERRQ(ierr);
  ierr = PetscDSGetNumFields(prob, &Nf);CHKERRQ(ierr);
  ierr = PetscMalloc3(dim,&v0,dim*dim,&J,dim*dim,&invJ);CHKERRQ(ierr);
  ierr = PetscMalloc3(dim,&v0c,dim*dim,&Jc,dim*dim,&invJc);CHKERRQ(ierr);
  ierr = DMGetDefaultSection(dmf, &fsection);CHKERRQ(ierr);
  ierr = DMGetDefaultGlobalSection(dmf, &globalFSection);CHKERRQ(ierr);
  ierr = DMGetDefaultSection(dmc, &csection);CHKERRQ(ierr);
  ierr = DMGetDefaultGlobalSection(dmc, &globalCSection);CHKERRQ(ierr);
  ierr = DMPlexGetHeightStratum(dmf, 0, &cStart, &cEnd);CHKERRQ(ierr);
  ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
  ierr = PetscMalloc1(totDim, &elemMat);CHKERRQ(ierr);

  ierr = MatGetLocalSize(In, &locRows, NULL);CHKERRQ(ierr);
  ierr = PetscLayoutCreate(PetscObjectComm((PetscObject) In), &rLayout);CHKERRQ(ierr);
  ierr = PetscLayoutSetLocalSize(rLayout, locRows);CHKERRQ(ierr);
  ierr = PetscLayoutSetBlockSize(rLayout, 1);CHKERRQ(ierr);
  ierr = PetscLayoutSetUp(rLayout);CHKERRQ(ierr);
  ierr = PetscLayoutGetRange(rLayout, &rStart, &rEnd);CHKERRQ(ierr);
  ierr = PetscLayoutDestroy(&rLayout);CHKERRQ(ierr);
  ierr = PetscCalloc2(locRows,&dnz,locRows,&onz);CHKERRQ(ierr);
  ierr = PetscHashJKCreate(&ht);CHKERRQ(ierr);
  for (field = 0; field < Nf; ++field) {
    PetscObject      obj;
    PetscClassId     id;
    PetscDualSpace   Q = NULL;
    PetscQuadrature  f;
    const PetscReal *qpoints;
    PetscInt         Nc, Np, fpdim, i, d;

    ierr = PetscDSGetDiscretization(prob, field, &obj);CHKERRQ(ierr);
    ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
    if (id == PETSCFE_CLASSID) {
      PetscFE fe = (PetscFE) obj;

      ierr = PetscFEGetDualSpace(fe, &Q);CHKERRQ(ierr);
      ierr = PetscFEGetNumComponents(fe, &Nc);CHKERRQ(ierr);
    } else if (id == PETSCFV_CLASSID) {
      PetscFV fv = (PetscFV) obj;

      ierr = PetscFVGetDualSpace(fv, &Q);CHKERRQ(ierr);
      Nc   = 1;
    }
    ierr = PetscDualSpaceGetDimension(Q, &fpdim);CHKERRQ(ierr);
    /* For each fine grid cell */
    for (cell = cStart; cell < cEnd; ++cell) {
      PetscInt *findices,   *cindices;
      PetscInt  numFIndices, numCIndices;

      ierr = DMPlexGetClosureIndices(dmf, fsection, globalFSection, cell, &numFIndices, &findices, NULL);CHKERRQ(ierr);
      ierr = DMPlexComputeCellGeometryFEM(dmf, cell, NULL, v0, J, invJ, &detJ);CHKERRQ(ierr);
      if (numFIndices != fpdim) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Number of fine indices %d != %d dual basis vecs", numFIndices, fpdim);
      for (i = 0; i < fpdim; ++i) {
        Vec             pointVec;
        PetscScalar    *pV;
        PetscSF         coarseCellSF = NULL;
        const PetscSFNode *coarseCells;
        PetscInt        numCoarseCells, q, c;

        /* Get points from the dual basis functional quadrature */
        ierr = PetscDualSpaceGetFunctional(Q, i, &f);CHKERRQ(ierr);
        ierr = PetscQuadratureGetData(f, NULL, NULL, &Np, &qpoints, NULL);CHKERRQ(ierr);
        ierr = VecCreateSeq(PETSC_COMM_SELF, Np*dim, &pointVec);CHKERRQ(ierr);
        ierr = VecSetBlockSize(pointVec, dim);CHKERRQ(ierr);
        ierr = VecGetArray(pointVec, &pV);CHKERRQ(ierr);
        for (q = 0; q < Np; ++q) {
          /* Transform point to real space */
          CoordinatesRefToReal(dim, dim, v0, J, &qpoints[q*dim], x);
          for (d = 0; d < dim; ++d) pV[q*dim+d] = x[d];
        }
        ierr = VecRestoreArray(pointVec, &pV);CHKERRQ(ierr);
        /* Get set of coarse cells that overlap points (would like to group points by coarse cell) */
        /* OPT: Pack all quad points from fine cell */
        ierr = DMLocatePoints(dmc, pointVec, DM_POINTLOCATION_NEAREST, &coarseCellSF);CHKERRQ(ierr);
        ierr = PetscSFViewFromOptions(coarseCellSF, NULL, "-interp_sf_view");CHKERRQ(ierr);
        /* Update preallocation info */
        ierr = PetscSFGetGraph(coarseCellSF, NULL, &numCoarseCells, NULL, &coarseCells);CHKERRQ(ierr);
        if (numCoarseCells != Np) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Not all closure points located");
        {
          PetscHashJKKey  key;
          PetscHashJKIter missing, iter;

          key.j = findices[i];
          if (key.j >= 0) {
            /* Get indices for coarse elements */
            for (ccell = 0; ccell < numCoarseCells; ++ccell) {
              ierr = DMPlexGetClosureIndices(dmc, csection, globalCSection, coarseCells[ccell].index, &numCIndices, &cindices, NULL);CHKERRQ(ierr);
              for (c = 0; c < numCIndices; ++c) {
                key.k = cindices[c];
                if (key.k < 0) continue;
                ierr = PetscHashJKPut(ht, key, &missing, &iter);CHKERRQ(ierr);
                if (missing) {
                  ierr = PetscHashJKSet(ht, iter, 1);CHKERRQ(ierr);
                  if ((key.k >= rStart) && (key.k < rEnd)) ++dnz[key.j-rStart];
                  else                                     ++onz[key.j-rStart];
                }
              }
              ierr = DMPlexRestoreClosureIndices(dmc, csection, globalCSection, coarseCells[ccell].index, &numCIndices, &cindices, NULL);CHKERRQ(ierr);
            }
          }
        }
        ierr = PetscSFDestroy(&coarseCellSF);CHKERRQ(ierr);
        ierr = VecDestroy(&pointVec);CHKERRQ(ierr);
      }
      ierr = DMPlexRestoreClosureIndices(dmf, fsection, globalFSection, cell, &numFIndices, &findices, NULL);CHKERRQ(ierr);
    }
  }
  ierr = PetscHashJKDestroy(&ht);CHKERRQ(ierr);
  ierr = MatXAIJSetPreallocation(In, 1, dnz, onz, NULL, NULL);CHKERRQ(ierr);
  ierr = MatSetOption(In, MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
  ierr = PetscFree2(dnz,onz);CHKERRQ(ierr);
  for (field = 0; field < Nf; ++field) {
    PetscObject      obj;
    PetscClassId     id;
    PetscDualSpace   Q = NULL;
    PetscQuadrature  f;
    const PetscReal *qpoints, *qweights;
    PetscInt         Nc, qNc, Np, fpdim, i, d;

    ierr = PetscDSGetDiscretization(prob, field, &obj);CHKERRQ(ierr);
    ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
    if (id == PETSCFE_CLASSID) {
      PetscFE fe = (PetscFE) obj;

      ierr = PetscFEGetDualSpace(fe, &Q);CHKERRQ(ierr);
      ierr = PetscFEGetNumComponents(fe, &Nc);CHKERRQ(ierr);
    } else if (id == PETSCFV_CLASSID) {
      PetscFV fv = (PetscFV) obj;

      ierr = PetscFVGetDualSpace(fv, &Q);CHKERRQ(ierr);
      Nc   = 1;
    } else SETERRQ1(PetscObjectComm((PetscObject)dmc),PETSC_ERR_ARG_WRONG,"Unknown discretization type for field %d",field);
    ierr = PetscDualSpaceGetDimension(Q, &fpdim);CHKERRQ(ierr);
    /* For each fine grid cell */
    for (cell = cStart; cell < cEnd; ++cell) {
      PetscInt *findices,   *cindices;
      PetscInt  numFIndices, numCIndices;

      ierr = DMPlexGetClosureIndices(dmf, fsection, globalFSection, cell, &numFIndices, &findices, NULL);CHKERRQ(ierr);
      ierr = DMPlexComputeCellGeometryFEM(dmf, cell, NULL, v0, J, invJ, &detJ);CHKERRQ(ierr);
      if (numFIndices != fpdim) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Number of fine indices %d != %d dual basis vecs", numFIndices, fpdim);
      for (i = 0; i < fpdim; ++i) {
        Vec             pointVec;
        PetscScalar    *pV;
        PetscSF         coarseCellSF = NULL;
        const PetscSFNode *coarseCells;
        PetscInt        numCoarseCells, cpdim, q, c, j;

        /* Get points from the dual basis functional quadrature */
        ierr = PetscDualSpaceGetFunctional(Q, i, &f);CHKERRQ(ierr);
        ierr = PetscQuadratureGetData(f, NULL, &qNc, &Np, &qpoints, &qweights);CHKERRQ(ierr);
        if (qNc != Nc) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Number of components in quadrature %D does not match coarse field %D", qNc, Nc);
        ierr = VecCreateSeq(PETSC_COMM_SELF, Np*dim, &pointVec);CHKERRQ(ierr);
        ierr = VecSetBlockSize(pointVec, dim);CHKERRQ(ierr);
        ierr = VecGetArray(pointVec, &pV);CHKERRQ(ierr);
        for (q = 0; q < Np; ++q) {
          /* Transform point to real space */
          CoordinatesRefToReal(dim, dim, v0, J, &qpoints[q*dim], x);
          for (d = 0; d < dim; ++d) pV[q*dim+d] = x[d];
        }
        ierr = VecRestoreArray(pointVec, &pV);CHKERRQ(ierr);
        /* Get set of coarse cells that overlap points (would like to group points by coarse cell) */
        /* OPT: Read this out from preallocation information */
        ierr = DMLocatePoints(dmc, pointVec, DM_POINTLOCATION_NEAREST, &coarseCellSF);CHKERRQ(ierr);
        /* Update preallocation info */
        ierr = PetscSFGetGraph(coarseCellSF, NULL, &numCoarseCells, NULL, &coarseCells);CHKERRQ(ierr);
        if (numCoarseCells != Np) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Not all closure points located");
        ierr = VecGetArray(pointVec, &pV);CHKERRQ(ierr);
        for (ccell = 0; ccell < numCoarseCells; ++ccell) {
          PetscReal pVReal[3];

          ierr = DMPlexGetClosureIndices(dmc, csection, globalCSection, coarseCells[ccell].index, &numCIndices, &cindices, NULL);CHKERRQ(ierr);
          /* Transform points from real space to coarse reference space */
          ierr = DMPlexComputeCellGeometryFEM(dmc, coarseCells[ccell].index, NULL, v0c, Jc, invJc, &detJc);CHKERRQ(ierr);
          for (d = 0; d < dim; ++d) pVReal[d] = PetscRealPart(pV[ccell*dim+d]);
          CoordinatesRealToRef(dim, dim, v0c, invJc, pVReal, x);

          if (id == PETSCFE_CLASSID) {
            PetscFE    fe = (PetscFE) obj;
            PetscReal *B;

            /* Evaluate coarse basis on contained point */
            ierr = PetscFEGetDimension(fe, &cpdim);CHKERRQ(ierr);
            ierr = PetscFEGetTabulation(fe, 1, x, &B, NULL, NULL);CHKERRQ(ierr);
            ierr = PetscMemzero(elemMat, cpdim * sizeof(PetscScalar));CHKERRQ(ierr);
            /* Get elemMat entries by multiplying by weight */
            for (j = 0; j < cpdim; ++j) {
              for (c = 0; c < Nc; ++c) elemMat[j] += B[j*Nc + c]*qweights[ccell*qNc + c];
            }
            ierr = PetscFERestoreTabulation(fe, 1, x, &B, NULL, NULL);CHKERRQ(ierr);CHKERRQ(ierr);
          } else {
            cpdim = 1;
            for (j = 0; j < cpdim; ++j) {
              for (c = 0; c < Nc; ++c) elemMat[j] += 1.0*qweights[ccell*qNc + c];
            }
          }
          /* Update interpolator */
          if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(cell, name, 1, numCIndices, elemMat);CHKERRQ(ierr);}
          if (numCIndices != cpdim) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Number of element matrix columns %D != %D", numCIndices, cpdim);
          ierr = MatSetValues(In, 1, &findices[i], numCIndices, cindices, elemMat, INSERT_VALUES);CHKERRQ(ierr);
          ierr = DMPlexRestoreClosureIndices(dmc, csection, globalCSection, coarseCells[ccell].index, &numCIndices, &cindices, NULL);CHKERRQ(ierr);
        }
        ierr = VecRestoreArray(pointVec, &pV);CHKERRQ(ierr);
        ierr = PetscSFDestroy(&coarseCellSF);CHKERRQ(ierr);
        ierr = VecDestroy(&pointVec);CHKERRQ(ierr);
      }
      ierr = DMPlexRestoreClosureIndices(dmf, fsection, globalFSection, cell, &numFIndices, &findices, NULL);CHKERRQ(ierr);
    }
  }
  ierr = PetscFree3(v0,J,invJ);CHKERRQ(ierr);
  ierr = PetscFree3(v0c,Jc,invJc);CHKERRQ(ierr);
  ierr = PetscFree(elemMat);CHKERRQ(ierr);
  ierr = MatAssemblyBegin(In, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(In, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(DMPLEX_InterpolatorFEM,dmc,dmf,0,0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@
  DMPlexComputeMassMatrixGeneral - Form the local portion of the mass matrix M from the coarse DM to a non-nested fine DM.

  Input Parameters:
+ dmf  - The fine mesh
. dmc  - The coarse mesh
- user - The user context

  Output Parameter:
. mass  - The mass matrix

  Level: developer

.seealso: DMPlexComputeMassMatrixNested(), DMPlexComputeInterpolatorNested(), DMPlexComputeInterpolatorGeneral(), DMPlexComputeJacobianFEM()
@*/
PetscErrorCode DMPlexComputeMassMatrixGeneral(DM dmc, DM dmf, Mat mass, void *user)
{
  DM_Plex       *mesh = (DM_Plex *) dmf->data;
  const char    *name = "Mass Matrix";
  PetscDS        prob;
  PetscSection   fsection, csection, globalFSection, globalCSection;
  PetscHashJK    ht;
  PetscLayout    rLayout;
  PetscInt      *dnz, *onz;
  PetscInt       locRows, rStart, rEnd;
  PetscReal     *x, *v0, *J, *invJ, detJ;
  PetscReal     *v0c, *Jc, *invJc, detJc;
  PetscScalar   *elemMat;
  PetscInt       dim, Nf, field, totDim, cStart, cEnd, cell, ccell;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = DMGetCoordinateDim(dmc, &dim);CHKERRQ(ierr);
  ierr = DMGetDS(dmc, &prob);CHKERRQ(ierr);
  ierr = PetscDSGetRefCoordArrays(prob, &x, NULL);CHKERRQ(ierr);
  ierr = PetscDSGetNumFields(prob, &Nf);CHKERRQ(ierr);
  ierr = PetscMalloc3(dim,&v0,dim*dim,&J,dim*dim,&invJ);CHKERRQ(ierr);
  ierr = PetscMalloc3(dim,&v0c,dim*dim,&Jc,dim*dim,&invJc);CHKERRQ(ierr);
  ierr = DMGetDefaultSection(dmf, &fsection);CHKERRQ(ierr);
  ierr = DMGetDefaultGlobalSection(dmf, &globalFSection);CHKERRQ(ierr);
  ierr = DMGetDefaultSection(dmc, &csection);CHKERRQ(ierr);
  ierr = DMGetDefaultGlobalSection(dmc, &globalCSection);CHKERRQ(ierr);
  ierr = DMPlexGetHeightStratum(dmf, 0, &cStart, &cEnd);CHKERRQ(ierr);
  ierr = PetscDSGetTotalDimension(prob, &totDim);CHKERRQ(ierr);
  ierr = PetscMalloc1(totDim, &elemMat);CHKERRQ(ierr);

  ierr = MatGetLocalSize(mass, &locRows, NULL);CHKERRQ(ierr);
  ierr = PetscLayoutCreate(PetscObjectComm((PetscObject) mass), &rLayout);CHKERRQ(ierr);
  ierr = PetscLayoutSetLocalSize(rLayout, locRows);CHKERRQ(ierr);
  ierr = PetscLayoutSetBlockSize(rLayout, 1);CHKERRQ(ierr);
  ierr = PetscLayoutSetUp(rLayout);CHKERRQ(ierr);
  ierr = PetscLayoutGetRange(rLayout, &rStart, &rEnd);CHKERRQ(ierr);
  ierr = PetscLayoutDestroy(&rLayout);CHKERRQ(ierr);
  ierr = PetscCalloc2(locRows,&dnz,locRows,&onz);CHKERRQ(ierr);
  ierr = PetscHashJKCreate(&ht);CHKERRQ(ierr);
  for (field = 0; field < Nf; ++field) {
    PetscObject      obj;
    PetscClassId     id;
    PetscQuadrature  quad;
    const PetscReal *qpoints;
    PetscInt         Nq, Nc, i, d;

    ierr = PetscDSGetDiscretization(prob, field, &obj);CHKERRQ(ierr);
    ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
    if (id == PETSCFE_CLASSID) {ierr = PetscFEGetQuadrature((PetscFE) obj, &quad);CHKERRQ(ierr);}
    else                       {ierr = PetscFVGetQuadrature((PetscFV) obj, &quad);CHKERRQ(ierr);}
    ierr = PetscQuadratureGetData(quad, NULL, &Nc, &Nq, &qpoints, NULL);CHKERRQ(ierr);
    /* For each fine grid cell */
    for (cell = cStart; cell < cEnd; ++cell) {
      Vec                pointVec;
      PetscScalar       *pV;
      PetscSF            coarseCellSF = NULL;
      const PetscSFNode *coarseCells;
      PetscInt           numCoarseCells, q, c;
      PetscInt          *findices,   *cindices;
      PetscInt           numFIndices, numCIndices;

      ierr = DMPlexGetClosureIndices(dmf, fsection, globalFSection, cell, &numFIndices, &findices, NULL);CHKERRQ(ierr);
      ierr = DMPlexComputeCellGeometryFEM(dmf, cell, NULL, v0, J, invJ, &detJ);CHKERRQ(ierr);
      /* Get points from the quadrature */
      ierr = VecCreateSeq(PETSC_COMM_SELF, Nq*dim, &pointVec);CHKERRQ(ierr);
      ierr = VecSetBlockSize(pointVec, dim);CHKERRQ(ierr);
      ierr = VecGetArray(pointVec, &pV);CHKERRQ(ierr);
      for (q = 0; q < Nq; ++q) {
        /* Transform point to real space */
        CoordinatesRefToReal(dim, dim, v0, J, &qpoints[q*dim], x);
        for (d = 0; d < dim; ++d) pV[q*dim+d] = x[d];
      }
      ierr = VecRestoreArray(pointVec, &pV);CHKERRQ(ierr);
      /* Get set of coarse cells that overlap points (would like to group points by coarse cell) */
      ierr = DMLocatePoints(dmc, pointVec, DM_POINTLOCATION_NEAREST, &coarseCellSF);CHKERRQ(ierr);
      ierr = PetscSFViewFromOptions(coarseCellSF, NULL, "-interp_sf_view");CHKERRQ(ierr);
      /* Update preallocation info */
      ierr = PetscSFGetGraph(coarseCellSF, NULL, &numCoarseCells, NULL, &coarseCells);CHKERRQ(ierr);
      if (numCoarseCells != Nq) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Not all closure points located");
      {
        PetscHashJKKey  key;
        PetscHashJKIter missing, iter;

        for (i = 0; i < numFIndices; ++i) {
          key.j = findices[i];
          if (key.j >= 0) {
            /* Get indices for coarse elements */
            for (ccell = 0; ccell < numCoarseCells; ++ccell) {
              ierr = DMPlexGetClosureIndices(dmc, csection, globalCSection, coarseCells[ccell].index, &numCIndices, &cindices, NULL);CHKERRQ(ierr);
              for (c = 0; c < numCIndices; ++c) {
                key.k = cindices[c];
                if (key.k < 0) continue;
                ierr = PetscHashJKPut(ht, key, &missing, &iter);CHKERRQ(ierr);
                if (missing) {
                  ierr = PetscHashJKSet(ht, iter, 1);CHKERRQ(ierr);
                  if ((key.k >= rStart) && (key.k < rEnd)) ++dnz[key.j-rStart];
                  else                                     ++onz[key.j-rStart];
                }
              }
              ierr = DMPlexRestoreClosureIndices(dmc, csection, globalCSection, coarseCells[ccell].index, &numCIndices, &cindices, NULL);CHKERRQ(ierr);
            }
          }
        }
      }
      ierr = PetscSFDestroy(&coarseCellSF);CHKERRQ(ierr);
      ierr = VecDestroy(&pointVec);CHKERRQ(ierr);
      ierr = DMPlexRestoreClosureIndices(dmf, fsection, globalFSection, cell, &numFIndices, &findices, NULL);CHKERRQ(ierr);
    }
  }
  ierr = PetscHashJKDestroy(&ht);CHKERRQ(ierr);
  ierr = MatXAIJSetPreallocation(mass, 1, dnz, onz, NULL, NULL);CHKERRQ(ierr);
  ierr = MatSetOption(mass, MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
  ierr = PetscFree2(dnz,onz);CHKERRQ(ierr);
  for (field = 0; field < Nf; ++field) {
    PetscObject      obj;
    PetscClassId     id;
    PetscQuadrature  quad;
    PetscReal       *Bfine;
    const PetscReal *qpoints, *qweights;
    PetscInt         Nq, Nc, i, d;

    ierr = PetscDSGetDiscretization(prob, field, &obj);CHKERRQ(ierr);
    ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
    if (id == PETSCFE_CLASSID) {ierr = PetscFEGetQuadrature((PetscFE) obj, &quad);CHKERRQ(ierr);ierr = PetscFEGetDefaultTabulation((PetscFE) obj, &Bfine, NULL, NULL);CHKERRQ(ierr);}
    else                       {ierr = PetscFVGetQuadrature((PetscFV) obj, &quad);CHKERRQ(ierr);}
    ierr = PetscQuadratureGetData(quad, NULL, &Nc, &Nq, &qpoints, &qweights);CHKERRQ(ierr);
    /* For each fine grid cell */
    for (cell = cStart; cell < cEnd; ++cell) {
      Vec                pointVec;
      PetscScalar       *pV;
      PetscSF            coarseCellSF = NULL;
      const PetscSFNode *coarseCells;
      PetscInt           numCoarseCells, cpdim, q, c, j;
      PetscInt          *findices,   *cindices;
      PetscInt           numFIndices, numCIndices;

      ierr = DMPlexGetClosureIndices(dmf, fsection, globalFSection, cell, &numFIndices, &findices, NULL);CHKERRQ(ierr);
      ierr = DMPlexComputeCellGeometryFEM(dmf, cell, NULL, v0, J, invJ, &detJ);CHKERRQ(ierr);
      /* Get points from the quadrature */
      ierr = VecCreateSeq(PETSC_COMM_SELF, Nq*dim, &pointVec);CHKERRQ(ierr);
      ierr = VecSetBlockSize(pointVec, dim);CHKERRQ(ierr);
      ierr = VecGetArray(pointVec, &pV);CHKERRQ(ierr);
      for (q = 0; q < Nq; ++q) {
        /* Transform point to real space */
        CoordinatesRefToReal(dim, dim, v0, J, &qpoints[q*dim], x);
        for (d = 0; d < dim; ++d) pV[q*dim+d] = x[d];
      }
      ierr = VecRestoreArray(pointVec, &pV);CHKERRQ(ierr);
      /* Get set of coarse cells that overlap points (would like to group points by coarse cell) */
      ierr = DMLocatePoints(dmc, pointVec, DM_POINTLOCATION_NEAREST, &coarseCellSF);CHKERRQ(ierr);
      /* Update matrix */
      ierr = PetscSFGetGraph(coarseCellSF, NULL, &numCoarseCells, NULL, &coarseCells);CHKERRQ(ierr);
      if (numCoarseCells != Nq) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Not all closure points located");
      ierr = VecGetArray(pointVec, &pV);CHKERRQ(ierr);
      for (ccell = 0; ccell < numCoarseCells; ++ccell) {
        PetscReal pVReal[3];

        ierr = DMPlexGetClosureIndices(dmc, csection, globalCSection, coarseCells[ccell].index, &numCIndices, &cindices, NULL);CHKERRQ(ierr);
        /* Transform points from real space to coarse reference space */
        ierr = DMPlexComputeCellGeometryFEM(dmc, coarseCells[ccell].index, NULL, v0c, Jc, invJc, &detJc);CHKERRQ(ierr);
        for (d = 0; d < dim; ++d) pVReal[d] = PetscRealPart(pV[ccell*dim+d]);
        CoordinatesRealToRef(dim, dim, v0c, invJc, pVReal, x);

        if (id == PETSCFE_CLASSID) {
          PetscFE    fe = (PetscFE) obj;
          PetscReal *B;

          /* Evaluate coarse basis on contained point */
          ierr = PetscFEGetDimension(fe, &cpdim);CHKERRQ(ierr);
          ierr = PetscFEGetTabulation(fe, 1, x, &B, NULL, NULL);CHKERRQ(ierr);
          /* Get elemMat entries by multiplying by weight */
          for (i = 0; i < numFIndices; ++i) {
            ierr = PetscMemzero(elemMat, cpdim * sizeof(PetscScalar));CHKERRQ(ierr);
            for (j = 0; j < cpdim; ++j) {
              for (c = 0; c < Nc; ++c) elemMat[j] += B[j*Nc + c]*Bfine[(ccell*numFIndices + i)*Nc + c]*qweights[ccell*Nc + c]*detJ;
            }
            /* Update interpolator */
            if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(cell, name, 1, numCIndices, elemMat);CHKERRQ(ierr);}
            if (numCIndices != cpdim) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Number of element matrix columns %D != %D", numCIndices, cpdim);
            ierr = MatSetValues(mass, 1, &findices[i], numCIndices, cindices, elemMat, ADD_VALUES);CHKERRQ(ierr);
          }
          ierr = PetscFERestoreTabulation(fe, 1, x, &B, NULL, NULL);CHKERRQ(ierr);CHKERRQ(ierr);
        } else {
          cpdim = 1;
          for (i = 0; i < numFIndices; ++i) {
            ierr = PetscMemzero(elemMat, cpdim * sizeof(PetscScalar));CHKERRQ(ierr);
            for (j = 0; j < cpdim; ++j) {
              for (c = 0; c < Nc; ++c) elemMat[j] += 1.0*1.0*qweights[ccell*Nc + c]*detJ;
            }
            /* Update interpolator */
            if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(cell, name, 1, numCIndices, elemMat);CHKERRQ(ierr);}
            ierr = PetscPrintf(PETSC_COMM_SELF, "Nq: %d %d Nf: %d %d Nc: %d %d\n", ccell, Nq, i, numFIndices, j, numCIndices);CHKERRQ(ierr);
            if (numCIndices != cpdim) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Number of element matrix columns %D != %D", numCIndices, cpdim);
            ierr = MatSetValues(mass, 1, &findices[i], numCIndices, cindices, elemMat, ADD_VALUES);CHKERRQ(ierr);
          }
        }
        ierr = DMPlexRestoreClosureIndices(dmc, csection, globalCSection, coarseCells[ccell].index, &numCIndices, &cindices, NULL);CHKERRQ(ierr);
      }
      ierr = VecRestoreArray(pointVec, &pV);CHKERRQ(ierr);
      ierr = PetscSFDestroy(&coarseCellSF);CHKERRQ(ierr);
      ierr = VecDestroy(&pointVec);CHKERRQ(ierr);
      ierr = DMPlexRestoreClosureIndices(dmf, fsection, globalFSection, cell, &numFIndices, &findices, NULL);CHKERRQ(ierr);
    }
  }
  ierr = PetscFree3(v0,J,invJ);CHKERRQ(ierr);
  ierr = PetscFree3(v0c,Jc,invJc);CHKERRQ(ierr);
  ierr = PetscFree(elemMat);CHKERRQ(ierr);
  ierr = MatAssemblyBegin(mass, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(mass, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@
  DMPlexComputeInjectorFEM - Compute a mapping from coarse unknowns to fine unknowns

  Input Parameters:
+ dmc  - The coarse mesh
- dmf  - The fine mesh
- user - The user context

  Output Parameter:
. sc   - The mapping

  Level: developer

.seealso: DMPlexComputeInterpolatorNested(), DMPlexComputeJacobianFEM()
@*/
PetscErrorCode DMPlexComputeInjectorFEM(DM dmc, DM dmf, VecScatter *sc, void *user)
{
  PetscDS        prob;
  PetscFE       *feRef;
  PetscFV       *fvRef;
  Vec            fv, cv;
  IS             fis, cis;
  PetscSection   fsection, fglobalSection, csection, cglobalSection;
  PetscInt      *cmap, *cellCIndices, *cellFIndices, *cindices, *findices;
  PetscInt       cTotDim, fTotDim = 0, Nf, f, field, cStart, cEnd, cEndInterior, c, dim, d, startC, endC, offsetC, offsetF, m;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscLogEventBegin(DMPLEX_InjectorFEM,dmc,dmf,0,0);CHKERRQ(ierr);
  ierr = DMGetDimension(dmf, &dim);CHKERRQ(ierr);
  ierr = DMGetDefaultSection(dmf, &fsection);CHKERRQ(ierr);
  ierr = DMGetDefaultGlobalSection(dmf, &fglobalSection);CHKERRQ(ierr);
  ierr = DMGetDefaultSection(dmc, &csection);CHKERRQ(ierr);
  ierr = DMGetDefaultGlobalSection(dmc, &cglobalSection);CHKERRQ(ierr);
  ierr = PetscSectionGetNumFields(fsection, &Nf);CHKERRQ(ierr);
  ierr = DMPlexGetHeightStratum(dmc, 0, &cStart, &cEnd);CHKERRQ(ierr);
  ierr = DMPlexGetHybridBounds(dmc, &cEndInterior, NULL, NULL, NULL);CHKERRQ(ierr);
  cEnd = cEndInterior < 0 ? cEnd : cEndInterior;
  ierr = DMGetDS(dmc, &prob);CHKERRQ(ierr);
  ierr = PetscCalloc2(Nf,&feRef,Nf,&fvRef);CHKERRQ(ierr);
  for (f = 0; f < Nf; ++f) {
    PetscObject  obj;
    PetscClassId id;
    PetscInt     fNb = 0, Nc = 0;

    ierr = PetscDSGetDiscretization(prob, f, &obj);CHKERRQ(ierr);
    ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
    if (id == PETSCFE_CLASSID) {
      PetscFE fe = (PetscFE) obj;

      ierr = PetscFERefine(fe, &feRef[f]);CHKERRQ(ierr);
      ierr = PetscFEGetDimension(feRef[f], &fNb);CHKERRQ(ierr);
      ierr = PetscFEGetNumComponents(fe, &Nc);CHKERRQ(ierr);
    } else if (id == PETSCFV_CLASSID) {
      PetscFV        fv = (PetscFV) obj;
      PetscDualSpace Q;

      ierr = PetscFVRefine(fv, &fvRef[f]);CHKERRQ(ierr);
      ierr = PetscFVGetDualSpace(fvRef[f], &Q);CHKERRQ(ierr);
      ierr = PetscDualSpaceGetDimension(Q, &fNb);CHKERRQ(ierr);
      ierr = PetscFVGetNumComponents(fv, &Nc);CHKERRQ(ierr);
    }
    fTotDim += fNb*Nc;
  }
  ierr = PetscDSGetTotalDimension(prob, &cTotDim);CHKERRQ(ierr);
  ierr = PetscMalloc1(cTotDim,&cmap);CHKERRQ(ierr);
  for (field = 0, offsetC = 0, offsetF = 0; field < Nf; ++field) {
    PetscFE        feC;
    PetscFV        fvC;
    PetscDualSpace QF, QC;
    PetscInt       NcF, NcC, fpdim, cpdim;

    if (feRef[field]) {
      ierr = PetscDSGetDiscretization(prob, field, (PetscObject *) &feC);CHKERRQ(ierr);
      ierr = PetscFEGetNumComponents(feC, &NcC);CHKERRQ(ierr);
      ierr = PetscFEGetNumComponents(feRef[field], &NcF);CHKERRQ(ierr);
      ierr = PetscFEGetDualSpace(feRef[field], &QF);CHKERRQ(ierr);
      ierr = PetscDualSpaceGetDimension(QF, &fpdim);CHKERRQ(ierr);
      ierr = PetscFEGetDualSpace(feC, &QC);CHKERRQ(ierr);
      ierr = PetscDualSpaceGetDimension(QC, &cpdim);CHKERRQ(ierr);
    } else {
      ierr = PetscDSGetDiscretization(prob, field, (PetscObject *) &fvC);CHKERRQ(ierr);
      ierr = PetscFVGetNumComponents(fvC, &NcC);CHKERRQ(ierr);
      ierr = PetscFVGetNumComponents(fvRef[field], &NcF);CHKERRQ(ierr);
      ierr = PetscFVGetDualSpace(fvRef[field], &QF);CHKERRQ(ierr);
      ierr = PetscDualSpaceGetDimension(QF, &fpdim);CHKERRQ(ierr);
      ierr = PetscFVGetDualSpace(fvC, &QC);CHKERRQ(ierr);
      ierr = PetscDualSpaceGetDimension(QC, &cpdim);CHKERRQ(ierr);
    }
    if (NcF != NcC) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Number of components in fine space field %d does not match coarse field %d", NcF, NcC);
    for (c = 0; c < cpdim; ++c) {
      PetscQuadrature  cfunc;
      const PetscReal *cqpoints;
      PetscInt         NpC;
      PetscBool        found = PETSC_FALSE;

      ierr = PetscDualSpaceGetFunctional(QC, c, &cfunc);CHKERRQ(ierr);
      ierr = PetscQuadratureGetData(cfunc, NULL, NULL, &NpC, &cqpoints, NULL);CHKERRQ(ierr);
      if (NpC != 1 && feRef[field]) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Do not know how to do injection for moments");
      for (f = 0; f < fpdim; ++f) {
        PetscQuadrature  ffunc;
        const PetscReal *fqpoints;
        PetscReal        sum = 0.0;
        PetscInt         NpF, comp;

        ierr = PetscDualSpaceGetFunctional(QF, f, &ffunc);CHKERRQ(ierr);
        ierr = PetscQuadratureGetData(ffunc, NULL, NULL, &NpF, &fqpoints, NULL);CHKERRQ(ierr);
        if (NpC != NpF) continue;
        for (d = 0; d < dim; ++d) sum += PetscAbsReal(cqpoints[d] - fqpoints[d]);
        if (sum > 1.0e-9) continue;
        for (comp = 0; comp < NcC; ++comp) {
          cmap[(offsetC+c)*NcC+comp] = (offsetF+f)*NcF+comp;
        }
        found = PETSC_TRUE;
        break;
      }
      if (!found) {
        /* TODO We really want the average here, but some asshole put VecScatter in the interface */
        if (fvRef[field]) {
          PetscInt comp;
          for (comp = 0; comp < NcC; ++comp) {
            cmap[(offsetC+c)*NcC+comp] = (offsetF+0)*NcF+comp;
          }
        } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Could not locate matching functional for injection");
      }
    }
    offsetC += cpdim*NcC;
    offsetF += fpdim*NcF;
  }
  for (f = 0; f < Nf; ++f) {ierr = PetscFEDestroy(&feRef[f]);CHKERRQ(ierr);ierr = PetscFVDestroy(&fvRef[f]);CHKERRQ(ierr);}
  ierr = PetscFree2(feRef,fvRef);CHKERRQ(ierr);

  ierr = DMGetGlobalVector(dmf, &fv);CHKERRQ(ierr);
  ierr = DMGetGlobalVector(dmc, &cv);CHKERRQ(ierr);
  ierr = VecGetOwnershipRange(cv, &startC, &endC);CHKERRQ(ierr);
  ierr = PetscSectionGetConstrainedStorageSize(cglobalSection, &m);CHKERRQ(ierr);
  ierr = PetscMalloc2(cTotDim,&cellCIndices,fTotDim,&cellFIndices);CHKERRQ(ierr);
  ierr = PetscMalloc1(m,&cindices);CHKERRQ(ierr);
  ierr = PetscMalloc1(m,&findices);CHKERRQ(ierr);
  for (d = 0; d < m; ++d) cindices[d] = findices[d] = -1;
  for (c = cStart; c < cEnd; ++c) {
    ierr = DMPlexMatGetClosureIndicesRefined(dmf, fsection, fglobalSection, dmc, csection, cglobalSection, c, cellCIndices, cellFIndices);CHKERRQ(ierr);
    for (d = 0; d < cTotDim; ++d) {
      if ((cellCIndices[d] < startC) || (cellCIndices[d] >= endC)) continue;
      if ((findices[cellCIndices[d]-startC] >= 0) && (findices[cellCIndices[d]-startC] != cellFIndices[cmap[d]])) SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Coarse dof %d maps to both %d and %d", cindices[cellCIndices[d]-startC], findices[cellCIndices[d]-startC], cellFIndices[cmap[d]]);
      cindices[cellCIndices[d]-startC] = cellCIndices[d];
      findices[cellCIndices[d]-startC] = cellFIndices[cmap[d]];
    }
  }
  ierr = PetscFree(cmap);CHKERRQ(ierr);
  ierr = PetscFree2(cellCIndices,cellFIndices);CHKERRQ(ierr);

  ierr = ISCreateGeneral(PETSC_COMM_SELF, m, cindices, PETSC_OWN_POINTER, &cis);CHKERRQ(ierr);
  ierr = ISCreateGeneral(PETSC_COMM_SELF, m, findices, PETSC_OWN_POINTER, &fis);CHKERRQ(ierr);
  ierr = VecScatterCreate(cv, cis, fv, fis, sc);CHKERRQ(ierr);
  ierr = ISDestroy(&cis);CHKERRQ(ierr);
  ierr = ISDestroy(&fis);CHKERRQ(ierr);
  ierr = DMRestoreGlobalVector(dmf, &fv);CHKERRQ(ierr);
  ierr = DMRestoreGlobalVector(dmc, &cv);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(DMPLEX_InjectorFEM,dmc,dmf,0,0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}