xref: /petsc/src/dm/impls/plex/plex.c (revision 39d7646b82f3c61fed60464cb8cf8b037dcb3c88)

#include <petsc-private/dmpleximpl.h>   /*I      "petscdmplex.h"   I*/
#include <../src/sys/utils/hash.h>
#include <petsc-private/vecimpl.h>
#include <petsc-private/isimpl.h>

/* Logging support */
PetscLogEvent DMPLEX_Distribute, DMPLEX_Stratify;

PETSC_EXTERN PetscErrorCode VecView_Seq(Vec, PetscViewer);
PETSC_EXTERN PetscErrorCode VecView_MPI(Vec, PetscViewer);

#undef __FUNCT__
#define __FUNCT__ "VecView_Plex_Local"
PetscErrorCode VecView_Plex_Local(Vec v, PetscViewer viewer)
{
  DM             dm;
  PetscBool      isvtk;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = VecGetDM(v, &dm);CHKERRQ(ierr);
  if (!dm) SETERRQ(PetscObjectComm((PetscObject)v), PETSC_ERR_ARG_WRONG, "Vector not generated from a DM");
  ierr = PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERVTK, &isvtk);CHKERRQ(ierr);
  if (isvtk) {
    PetscViewerVTKFieldType ft = PETSC_VTK_POINT_FIELD;
    PetscSection            section;
    PetscInt                dim, pStart, pEnd, cStart, fStart, vStart, cdof = 0, fdof = 0, vdof = 0;

    ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
    ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
    ierr = DMPlexGetHeightStratum(dm, 0, &cStart, NULL);CHKERRQ(ierr);
    ierr = DMPlexGetHeightStratum(dm, 1, &fStart, NULL);CHKERRQ(ierr);
    ierr = DMPlexGetDepthStratum(dm, 0, &vStart, NULL);CHKERRQ(ierr);
    ierr = PetscSectionGetChart(section, &pStart, &pEnd);CHKERRQ(ierr);
    /* Assumes that numer of dofs per point of each stratum is constant, natural for VTK */
    if ((cStart >= pStart) && (cStart < pEnd)) {ierr = PetscSectionGetDof(section, cStart, &cdof);CHKERRQ(ierr);}
    if ((fStart >= pStart) && (fStart < pEnd)) {ierr = PetscSectionGetDof(section, fStart, &fdof);CHKERRQ(ierr);}
    if ((vStart >= pStart) && (vStart < pEnd)) {ierr = PetscSectionGetDof(section, vStart, &vdof);CHKERRQ(ierr);}
    if (cdof && fdof && vdof) { /* Actually Q2 or some such, but visualize as Q1 */
      ft = (cdof == dim) ? PETSC_VTK_POINT_VECTOR_FIELD : PETSC_VTK_POINT_FIELD;
    } else if (cdof && vdof) {
      SETERRQ(PetscObjectComm((PetscObject)viewer),PETSC_ERR_SUP,"No support for viewing mixed space with dofs at both vertices and cells");
    } else if (cdof) {
      /* TODO: This assumption should be removed when there is a way of identifying whether a space is conceptually a
       * vector or just happens to have the same number of dofs as the dimension. */
      if (cdof == dim) {
        ft = PETSC_VTK_CELL_VECTOR_FIELD;
      } else {
        ft = PETSC_VTK_CELL_FIELD;
      }
    } else if (vdof) {
      if (vdof == dim) {
        ft = PETSC_VTK_POINT_VECTOR_FIELD;
      } else {
        ft = PETSC_VTK_POINT_FIELD;
      }
    } else SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Could not classify input Vec for VTK");

    ierr = PetscObjectReference((PetscObject) dm);CHKERRQ(ierr); /* viewer drops reference */
    ierr = PetscObjectReference((PetscObject) v);CHKERRQ(ierr);  /* viewer drops reference */
    ierr = PetscViewerVTKAddField(viewer, (PetscObject) dm, DMPlexVTKWriteAll, ft, (PetscObject) v);CHKERRQ(ierr);
  } else {
    PetscBool isseq;

    ierr = PetscObjectTypeCompare((PetscObject) v, VECSEQ, &isseq);CHKERRQ(ierr);
    if (isseq) {
      ierr = VecView_Seq(v, viewer);CHKERRQ(ierr);
    } else {
      ierr = VecView_MPI(v, viewer);CHKERRQ(ierr);
    }
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "VecView_Plex"
PetscErrorCode VecView_Plex(Vec v, PetscViewer viewer)
{
  DM             dm;
  PetscBool      isvtk;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = VecGetDM(v, &dm);CHKERRQ(ierr);
  if (!dm) SETERRQ(PetscObjectComm((PetscObject)v), PETSC_ERR_ARG_WRONG, "Vector not generated from a DM");
  ierr = PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERVTK, &isvtk);CHKERRQ(ierr);
  if (isvtk) {
    Vec         locv;
    const char *name;

    ierr = DMGetLocalVector(dm, &locv);CHKERRQ(ierr);
    ierr = PetscObjectGetName((PetscObject) v, &name);CHKERRQ(ierr);
    ierr = PetscObjectSetName((PetscObject) locv, name);CHKERRQ(ierr);
    ierr = DMGlobalToLocalBegin(dm, v, INSERT_VALUES, locv);CHKERRQ(ierr);
    ierr = DMGlobalToLocalEnd(dm, v, INSERT_VALUES, locv);CHKERRQ(ierr);
    ierr = VecView_Plex_Local(locv, viewer);CHKERRQ(ierr);
    ierr = DMRestoreLocalVector(dm, &locv);CHKERRQ(ierr);
  } else {
    PetscBool isseq;

    ierr = PetscObjectTypeCompare((PetscObject) v, VECSEQ, &isseq);CHKERRQ(ierr);
    if (isseq) {
      ierr = VecView_Seq(v, viewer);CHKERRQ(ierr);
    } else {
      ierr = VecView_MPI(v, viewer);CHKERRQ(ierr);
    }
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexView_Ascii"
PetscErrorCode DMPlexView_Ascii(DM dm, PetscViewer viewer)
{
  DM_Plex          *mesh = (DM_Plex*) dm->data;
  DM                cdm;
  DMLabel           markers;
  PetscSection      coordSection;
  Vec               coordinates;
  PetscViewerFormat format;
  PetscErrorCode    ierr;

  PetscFunctionBegin;
  ierr = DMGetCoordinateDM(dm, &cdm);CHKERRQ(ierr);
  ierr = DMGetDefaultSection(cdm, &coordSection);CHKERRQ(ierr);
  ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
  ierr = PetscViewerGetFormat(viewer, &format);CHKERRQ(ierr);
  if (format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
    const char *name;
    PetscInt    maxConeSize, maxSupportSize;
    PetscInt    pStart, pEnd, p;
    PetscMPIInt rank, size;

    ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);CHKERRQ(ierr);
    ierr = MPI_Comm_size(PetscObjectComm((PetscObject)dm), &size);CHKERRQ(ierr);
    ierr = PetscObjectGetName((PetscObject) dm, &name);CHKERRQ(ierr);
    ierr = DMPlexGetChart(dm, &pStart, &pEnd);CHKERRQ(ierr);
    ierr = DMPlexGetMaxSizes(dm, &maxConeSize, &maxSupportSize);CHKERRQ(ierr);
    ierr = PetscViewerASCIISynchronizedAllow(viewer, PETSC_TRUE);CHKERRQ(ierr);
    ierr = PetscViewerASCIIPrintf(viewer, "Mesh '%s':\n", name);CHKERRQ(ierr);
    ierr = PetscViewerASCIISynchronizedPrintf(viewer, "Max sizes cone: %D support: %D\n", maxConeSize, maxSupportSize);CHKERRQ(ierr);
    ierr = PetscViewerASCIIPrintf(viewer, "orientation is missing\n", name);CHKERRQ(ierr);
    ierr = PetscViewerASCIIPrintf(viewer, "cap --> base:\n", name);CHKERRQ(ierr);
    for (p = pStart; p < pEnd; ++p) {
      PetscInt dof, off, s;

      ierr = PetscSectionGetDof(mesh->supportSection, p, &dof);CHKERRQ(ierr);
      ierr = PetscSectionGetOffset(mesh->supportSection, p, &off);CHKERRQ(ierr);
      for (s = off; s < off+dof; ++s) {
        ierr = PetscViewerASCIISynchronizedPrintf(viewer, "[%D]: %D ----> %D\n", rank, p, mesh->supports[s]);CHKERRQ(ierr);
      }
    }
    ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
    ierr = PetscViewerASCIIPrintf(viewer, "base <-- cap:\n", name);CHKERRQ(ierr);
    for (p = pStart; p < pEnd; ++p) {
      PetscInt dof, off, c;

      ierr = PetscSectionGetDof(mesh->coneSection, p, &dof);CHKERRQ(ierr);
      ierr = PetscSectionGetOffset(mesh->coneSection, p, &off);CHKERRQ(ierr);
      for (c = off; c < off+dof; ++c) {
        ierr = PetscViewerASCIISynchronizedPrintf(viewer, "[%D]: %D <---- %D (%D)\n", rank, p, mesh->cones[c], mesh->coneOrientations[c]);CHKERRQ(ierr);
      }
    }
    ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
    ierr = PetscSectionGetChart(coordSection, &pStart, NULL);CHKERRQ(ierr);
    if (pStart >= 0) {ierr = PetscSectionVecView(coordSection, coordinates, viewer);CHKERRQ(ierr);}
    ierr = DMPlexGetLabel(dm, "marker", &markers);CHKERRQ(ierr);
    ierr = DMLabelView(markers,viewer);CHKERRQ(ierr);
    if (size > 1) {
      PetscSF sf;

      ierr = DMGetPointSF(dm, &sf);CHKERRQ(ierr);
      ierr = PetscSFView(sf, viewer);CHKERRQ(ierr);
    }
    ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
  } else if (format == PETSC_VIEWER_ASCII_LATEX) {
    const char  *name;
    const char  *colors[3] = {"red", "blue", "green"};
    const int    numColors  = 3;
    PetscReal    scale      = 2.0;
    PetscScalar *coords;
    PetscInt     depth, cStart, cEnd, c, vStart, vEnd, v, eStart = 0, eEnd = 0, e, p;
    PetscMPIInt  rank, size;

    ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
    ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);CHKERRQ(ierr);
    ierr = MPI_Comm_size(PetscObjectComm((PetscObject)dm), &size);CHKERRQ(ierr);
    ierr = PetscObjectGetName((PetscObject) dm, &name);CHKERRQ(ierr);
    ierr = PetscViewerASCIISynchronizedAllow(viewer, PETSC_TRUE);CHKERRQ(ierr);
    ierr = PetscViewerASCIIPrintf(viewer, "\
\\documentclass[crop,multi=false]{standalone}\n\n\
\\usepackage{tikz}\n\
\\usepackage{pgflibraryshapes}\n\
\\usetikzlibrary{backgrounds}\n\
\\usetikzlibrary{arrows}\n\
\\begin{document}\n\
\\section{%s}\n\
\\begin{center}\n", name, 8.0/scale);CHKERRQ(ierr);
    ierr = PetscViewerASCIIPrintf(viewer, "Mesh for process ");CHKERRQ(ierr);
    for (p = 0; p < size; ++p) {
      if (p > 0 && p == size-1) {
        ierr = PetscViewerASCIIPrintf(viewer, ", and ", colors[p%numColors], p);CHKERRQ(ierr);
      } else if (p > 0) {
        ierr = PetscViewerASCIIPrintf(viewer, ", ", colors[p%numColors], p);CHKERRQ(ierr);
      }
      ierr = PetscViewerASCIIPrintf(viewer, "{\\textcolor{%s}%D}", colors[p%numColors], p);CHKERRQ(ierr);
    }
    ierr = PetscViewerASCIIPrintf(viewer, ".\n\n\n\
\\begin{tikzpicture}[scale = %g,font=\\fontsize{8}{8}\\selectfont]\n");CHKERRQ(ierr);
    /* Plot vertices */
    ierr = DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);CHKERRQ(ierr);
    ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
    ierr = PetscViewerASCIIPrintf(viewer, "\\path\n");CHKERRQ(ierr);
    for (v = vStart; v < vEnd; ++v) {
      PetscInt off, dof, d;

      ierr = PetscSectionGetDof(coordSection, v, &dof);CHKERRQ(ierr);
      ierr = PetscSectionGetOffset(coordSection, v, &off);CHKERRQ(ierr);
      ierr = PetscViewerASCIISynchronizedPrintf(viewer, "(");CHKERRQ(ierr);
      for (d = 0; d < dof; ++d) {
        if (d > 0) {ierr = PetscViewerASCIISynchronizedPrintf(viewer, ",");CHKERRQ(ierr);}
        ierr = PetscViewerASCIISynchronizedPrintf(viewer, "%G", scale*PetscRealPart(coords[off+d]));CHKERRQ(ierr);
      }
      ierr = PetscViewerASCIISynchronizedPrintf(viewer, ") node(%D_%D) [draw,shape=circle,color=%s] {%D} --\n", v, rank, colors[rank%numColors], v);CHKERRQ(ierr);
    }
    ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
    ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
    ierr = PetscViewerASCIIPrintf(viewer, "(0,0);\n");CHKERRQ(ierr);
    /* Plot edges */
    ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
    ierr = PetscViewerASCIIPrintf(viewer, "\\path\n");CHKERRQ(ierr);
    if (depth > 1) {ierr = DMPlexGetDepthStratum(dm, 1, &eStart, &eEnd);CHKERRQ(ierr);}
    for (e = eStart; e < eEnd; ++e) {
      const PetscInt *cone;
      PetscInt        coneSize, offA, offB, dof, d;

      ierr = DMPlexGetConeSize(dm, e, &coneSize);CHKERRQ(ierr);
      if (coneSize != 2) SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Edge %d cone should have two vertices, not %d", e, coneSize);
      ierr = DMPlexGetCone(dm, e, &cone);CHKERRQ(ierr);
      ierr = PetscSectionGetDof(coordSection, cone[0], &dof);CHKERRQ(ierr);
      ierr = PetscSectionGetOffset(coordSection, cone[0], &offA);CHKERRQ(ierr);
      ierr = PetscSectionGetOffset(coordSection, cone[1], &offB);CHKERRQ(ierr);
      ierr = PetscViewerASCIISynchronizedPrintf(viewer, "(");CHKERRQ(ierr);
      for (d = 0; d < dof; ++d) {
        if (d > 0) {ierr = PetscViewerASCIISynchronizedPrintf(viewer, ",");CHKERRQ(ierr);}
        ierr = PetscViewerASCIISynchronizedPrintf(viewer, "%G", scale*0.5*PetscRealPart(coords[offA+d]+coords[offB+d]));CHKERRQ(ierr);
      }
      ierr = PetscViewerASCIISynchronizedPrintf(viewer, ") node(%D_%D) [draw,shape=circle,color=%s] {%D} --\n", e, rank, colors[rank%numColors], e);CHKERRQ(ierr);
    }
    ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
    ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
    ierr = PetscViewerASCIIPrintf(viewer, "(0,0);\n");CHKERRQ(ierr);
    /* Plot cells */
    ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
    for (c = cStart; c < cEnd; ++c) {
      PetscInt *closure = NULL;
      PetscInt  closureSize, firstPoint = -1;

      ierr = DMPlexGetTransitiveClosure(dm, c, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
      ierr = PetscViewerASCIISynchronizedPrintf(viewer, "\\draw[color=%s] ", colors[rank%numColors]);CHKERRQ(ierr);
      for (p = 0; p < closureSize*2; p += 2) {
        const PetscInt point = closure[p];

        if ((point < vStart) || (point >= vEnd)) continue;
        if (firstPoint >= 0) {ierr = PetscViewerASCIISynchronizedPrintf(viewer, " -- ");CHKERRQ(ierr);}
        ierr = PetscViewerASCIISynchronizedPrintf(viewer, "(%D_%D)", point, rank);CHKERRQ(ierr);
        if (firstPoint < 0) firstPoint = point;
      }
      /* Why doesn't this work? ierr = PetscViewerASCIISynchronizedPrintf(viewer, " -- cycle;\n");CHKERRQ(ierr); */
      ierr = PetscViewerASCIISynchronizedPrintf(viewer, " -- (%D_%D);\n", firstPoint, rank);CHKERRQ(ierr);
      ierr = DMPlexRestoreTransitiveClosure(dm, c, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
    }
    ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
    ierr = PetscViewerASCIIPrintf(viewer, "\\end{tikzpicture}\n\\end{center}\n");CHKERRQ(ierr);
    ierr = PetscViewerASCIIPrintf(viewer, "\\end{document}\n", name);CHKERRQ(ierr);
  } else {
    MPI_Comm    comm;
    PetscInt   *sizes;
    PetscInt    locDepth, depth, dim, d;
    PetscInt    pStart, pEnd, p;
    PetscInt    numLabels, l;
    PetscMPIInt size;

    ierr = PetscObjectGetComm((PetscObject)dm,&comm);CHKERRQ(ierr);
    ierr = MPI_Comm_size(comm, &size);CHKERRQ(ierr);
    ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
    ierr = PetscViewerASCIIPrintf(viewer, "Mesh in %D dimensions:\n", dim);CHKERRQ(ierr);
    ierr = DMPlexGetDepth(dm, &locDepth);CHKERRQ(ierr);
    ierr = MPI_Allreduce(&locDepth, &depth, 1, MPIU_INT, MPI_MAX, comm);CHKERRQ(ierr);
    ierr = PetscMalloc(size * sizeof(PetscInt), &sizes);CHKERRQ(ierr);
    if (depth == 1) {
      ierr = DMPlexGetDepthStratum(dm, 0, &pStart, &pEnd);CHKERRQ(ierr);
      pEnd = pEnd - pStart;
      ierr = MPI_Gather(&pEnd, 1, MPIU_INT, sizes, 1, MPIU_INT, 0, comm);CHKERRQ(ierr);
      ierr = PetscViewerASCIIPrintf(viewer, "  %D-cells:", 0);CHKERRQ(ierr);
      for (p = 0; p < size; ++p) {ierr = PetscViewerASCIIPrintf(viewer, " %D", sizes[p]);CHKERRQ(ierr);}
      ierr = PetscViewerASCIIPrintf(viewer, "\n");CHKERRQ(ierr);
      ierr = DMPlexGetHeightStratum(dm, 0, &pStart, &pEnd);CHKERRQ(ierr);
      pEnd = pEnd - pStart;
      ierr = MPI_Gather(&pEnd, 1, MPIU_INT, sizes, 1, MPIU_INT, 0, comm);CHKERRQ(ierr);
      ierr = PetscViewerASCIIPrintf(viewer, "  %D-cells:", dim);CHKERRQ(ierr);
      for (p = 0; p < size; ++p) {ierr = PetscViewerASCIIPrintf(viewer, " %D", sizes[p]);CHKERRQ(ierr);}
      ierr = PetscViewerASCIIPrintf(viewer, "\n");CHKERRQ(ierr);
    } else {
      for (d = 0; d <= dim; d++) {
        ierr = DMPlexGetDepthStratum(dm, d, &pStart, &pEnd);CHKERRQ(ierr);
        pEnd = pEnd - pStart;
        ierr = MPI_Gather(&pEnd, 1, MPIU_INT, sizes, 1, MPIU_INT, 0, comm);CHKERRQ(ierr);
        ierr = PetscViewerASCIIPrintf(viewer, "  %D-cells:", d);CHKERRQ(ierr);
        for (p = 0; p < size; ++p) {ierr = PetscViewerASCIIPrintf(viewer, " %D", sizes[p]);CHKERRQ(ierr);}
        ierr = PetscViewerASCIIPrintf(viewer, "\n");CHKERRQ(ierr);
      }
    }
    ierr = PetscFree(sizes);CHKERRQ(ierr);
    ierr = DMPlexGetNumLabels(dm, &numLabels);CHKERRQ(ierr);
    if (numLabels) {ierr = PetscViewerASCIIPrintf(viewer, "Labels:\n");CHKERRQ(ierr);}
    for (l = 0; l < numLabels; ++l) {
      DMLabel         label;
      const char     *name;
      IS              valueIS;
      const PetscInt *values;
      PetscInt        numValues, v;

      ierr = DMPlexGetLabelName(dm, l, &name);CHKERRQ(ierr);
      ierr = DMPlexGetLabel(dm, name, &label);CHKERRQ(ierr);
      ierr = DMLabelGetNumValues(label, &numValues);CHKERRQ(ierr);
      ierr = PetscViewerASCIIPrintf(viewer, "  %s: %d strata of sizes (", name, numValues);CHKERRQ(ierr);
      ierr = DMLabelGetValueIS(label, &valueIS);CHKERRQ(ierr);
      ierr = ISGetIndices(valueIS, &values);CHKERRQ(ierr);
      for (v = 0; v < numValues; ++v) {
        PetscInt size;

        ierr = DMLabelGetStratumSize(label, values[v], &size);CHKERRQ(ierr);
        if (v > 0) {ierr = PetscViewerASCIIPrintf(viewer, ", ");CHKERRQ(ierr);}
        ierr = PetscViewerASCIIPrintf(viewer, "%d", size);CHKERRQ(ierr);
      }
      ierr = PetscViewerASCIIPrintf(viewer, ")\n");CHKERRQ(ierr);
      ierr = ISRestoreIndices(valueIS, &values);CHKERRQ(ierr);
    }
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMView_Plex"
PetscErrorCode DMView_Plex(DM dm, PetscViewer viewer)
{
  PetscBool      iascii, isbinary;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidHeaderSpecific(viewer, PETSC_VIEWER_CLASSID, 2);
  ierr = PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERASCII, &iascii);CHKERRQ(ierr);
  ierr = PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERBINARY, &isbinary);CHKERRQ(ierr);
  if (iascii) {
    ierr = DMPlexView_Ascii(dm, viewer);CHKERRQ(ierr);
#if 0
  } else if (isbinary) {
    ierr = DMPlexView_Binary(dm, viewer);CHKERRQ(ierr);
#endif
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMDestroy_Plex"
PetscErrorCode DMDestroy_Plex(DM dm)
{
  DM_Plex       *mesh = (DM_Plex*) dm->data;
  DMLabel        next  = mesh->labels;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if (--mesh->refct > 0) PetscFunctionReturn(0);
  ierr = PetscSectionDestroy(&mesh->coneSection);CHKERRQ(ierr);
  ierr = PetscFree(mesh->cones);CHKERRQ(ierr);
  ierr = PetscFree(mesh->coneOrientations);CHKERRQ(ierr);
  ierr = PetscSectionDestroy(&mesh->supportSection);CHKERRQ(ierr);
  ierr = PetscFree(mesh->supports);CHKERRQ(ierr);
  ierr = PetscFree(mesh->facesTmp);CHKERRQ(ierr);
  while (next) {
    DMLabel tmp = next->next;

    ierr = DMLabelDestroy(&next);CHKERRQ(ierr);
    next = tmp;
  }
  ierr = DMLabelDestroy(&mesh->subpointMap);CHKERRQ(ierr);
  ierr = ISDestroy(&mesh->globalVertexNumbers);CHKERRQ(ierr);
  ierr = ISDestroy(&mesh->globalCellNumbers);CHKERRQ(ierr);
  /* This was originally freed in DMDestroy(), but that prevents reference counting of backend objects */
  ierr = PetscFree(mesh);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetAdjacencySingleLevel_Private"
PetscErrorCode DMPlexGetAdjacencySingleLevel_Private(DM dm, PetscInt p, PetscBool useClosure, const PetscInt *tmpClosure, PetscInt *adjSize, PetscInt adj[])
{
  const PetscInt *support = NULL;
  PetscInt        numAdj   = 0, maxAdjSize = *adjSize, supportSize, s;
  PetscErrorCode  ierr;

  PetscFunctionBegin;
  if (useClosure) {
    ierr = DMPlexGetConeSize(dm, p, &supportSize);CHKERRQ(ierr);
    ierr = DMPlexGetCone(dm, p, &support);CHKERRQ(ierr);
    for (s = 0; s < supportSize; ++s) {
      const PetscInt *cone = NULL;
      PetscInt        coneSize, c, q;

      ierr = DMPlexGetSupportSize(dm, support[s], &coneSize);CHKERRQ(ierr);
      ierr = DMPlexGetSupport(dm, support[s], &cone);CHKERRQ(ierr);
      for (c = 0; c < coneSize; ++c) {
        for (q = 0; q < numAdj || (adj[numAdj++] = cone[c],0); ++q) {
          if (cone[c] == adj[q]) break;
        }
        if (numAdj > maxAdjSize) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid mesh exceeded adjacency allocation (%D)", maxAdjSize);
      }
    }
  } else {
    ierr = DMPlexGetSupportSize(dm, p, &supportSize);CHKERRQ(ierr);
    ierr = DMPlexGetSupport(dm, p, &support);CHKERRQ(ierr);
    for (s = 0; s < supportSize; ++s) {
      const PetscInt *cone = NULL;
      PetscInt        coneSize, c, q;

      ierr = DMPlexGetConeSize(dm, support[s], &coneSize);CHKERRQ(ierr);
      ierr = DMPlexGetCone(dm, support[s], &cone);CHKERRQ(ierr);
      for (c = 0; c < coneSize; ++c) {
        for (q = 0; q < numAdj || (adj[numAdj++] = cone[c],0); ++q) {
          if (cone[c] == adj[q]) break;
        }
        if (numAdj > maxAdjSize) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid mesh exceeded adjacency allocation (%D)", maxAdjSize);
      }
    }
  }
  *adjSize = numAdj;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetAdjacency_Private"
PetscErrorCode DMPlexGetAdjacency_Private(DM dm, PetscInt p, PetscBool useClosure, const PetscInt *tmpClosure, PetscInt *adjSize, PetscInt adj[])
{
  const PetscInt *star  = tmpClosure;
  PetscInt        numAdj = 0, maxAdjSize = *adjSize, starSize, s;
  PetscErrorCode  ierr;

  PetscFunctionBegin;
  ierr = DMPlexGetTransitiveClosure(dm, p, useClosure, &starSize, (PetscInt**) &star);CHKERRQ(ierr);
  for (s = 2; s < starSize*2; s += 2) {
    const PetscInt *closure = NULL;
    PetscInt        closureSize, c, q;

    ierr = DMPlexGetTransitiveClosure(dm, star[s], (PetscBool)!useClosure, &closureSize, (PetscInt**) &closure);CHKERRQ(ierr);
    for (c = 0; c < closureSize*2; c += 2) {
      for (q = 0; q < numAdj || (adj[numAdj++] = closure[c],0); ++q) {
        if (closure[c] == adj[q]) break;
      }
      if (numAdj > maxAdjSize) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid mesh exceeded adjacency allocation (%D)", maxAdjSize);
    }
    ierr = DMPlexRestoreTransitiveClosure(dm, star[s], (PetscBool)!useClosure, &closureSize, (PetscInt**) &closure);CHKERRQ(ierr);
  }
  *adjSize = numAdj;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexSetPreallocationCenterDimension"
PetscErrorCode DMPlexSetPreallocationCenterDimension(DM dm, PetscInt preallocCenterDim)
{
  DM_Plex *mesh = (DM_Plex*) dm->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  mesh->preallocCenterDim = preallocCenterDim;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexPreallocateOperator"
PetscErrorCode DMPlexPreallocateOperator(DM dm, PetscInt bs, PetscSection section, PetscSection sectionGlobal, PetscInt dnz[], PetscInt onz[], PetscInt dnzu[], PetscInt onzu[], Mat A, PetscBool fillMatrix)
{
  DM_Plex           *mesh = (DM_Plex*) dm->data;
  MPI_Comm           comm;
  PetscSF            sf, sfDof, sfAdj;
  PetscSection       leafSectionAdj, rootSectionAdj, sectionAdj;
  PetscInt           nleaves, l, p;
  const PetscInt    *leaves;
  const PetscSFNode *remotes;
  PetscInt           dim, pStart, pEnd, numDof, globalOffStart, globalOffEnd, numCols;
  PetscInt          *tmpClosure, *tmpAdj, *adj, *rootAdj, *cols, *remoteOffsets;
  PetscInt           depth, maxConeSize, maxSupportSize, maxClosureSize, maxAdjSize, adjSize;
  PetscLayout        rLayout;
  PetscInt           locRows, rStart, rEnd, r;
  PetscMPIInt        size;
  PetscBool          useClosure, debug = PETSC_FALSE;
  PetscErrorCode     ierr;

  PetscFunctionBegin;
  ierr = PetscObjectGetComm((PetscObject)dm,&comm);CHKERRQ(ierr);
  ierr = PetscOptionsGetBool(NULL, "-dm_view_preallocation", &debug, NULL);CHKERRQ(ierr);
  ierr = MPI_Comm_size(comm, &size);CHKERRQ(ierr);
  ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
  ierr = DMGetPointSF(dm, &sf);CHKERRQ(ierr);
  /* Create dof SF based on point SF */
  if (debug) {
    ierr = PetscPrintf(comm, "Input Section for Preallocation:\n");CHKERRQ(ierr);
    ierr = PetscSectionView(section, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
    ierr = PetscPrintf(comm, "Input Global Section for Preallocation:\n");CHKERRQ(ierr);
    ierr = PetscSectionView(sectionGlobal, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
    ierr = PetscPrintf(comm, "Input SF for Preallocation:\n");CHKERRQ(ierr);
    ierr = PetscSFView(sf, NULL);CHKERRQ(ierr);
  }
  ierr = PetscSFCreateRemoteOffsets(sf, section, section, &remoteOffsets);CHKERRQ(ierr);
  ierr = PetscSFCreateSectionSF(sf, section, remoteOffsets, section, &sfDof);CHKERRQ(ierr);
  if (debug) {
    ierr = PetscPrintf(comm, "Dof SF for Preallocation:\n");CHKERRQ(ierr);
    ierr = PetscSFView(sfDof, NULL);CHKERRQ(ierr);
  }
  /* Create section for dof adjacency (dof ==> # adj dof) */
  /*   FEM:   Two points p and q are adjacent if q \in closure(star(p)), preallocCenterDim = dim   */
  /*   FVM:   Two points p and q are adjacent if q \in star(cone(p)),    preallocCenterDim = dim-1 */
  /*   FVM++: Two points p and q are adjacent if q \in star(closure(p)), preallocCenterDim = 0     */
  if (mesh->preallocCenterDim == dim) {
    useClosure = PETSC_FALSE;
  } else if (mesh->preallocCenterDim == 0) {
    useClosure = PETSC_TRUE;
  } else SETERRQ1(comm, PETSC_ERR_ARG_OUTOFRANGE, "Do not support preallocation with center points of dimension %d", mesh->preallocCenterDim);

  ierr = PetscSectionGetChart(section, &pStart, &pEnd);CHKERRQ(ierr);
  ierr = PetscSectionGetStorageSize(section, &numDof);CHKERRQ(ierr);
  ierr = PetscSectionCreate(comm, &leafSectionAdj);CHKERRQ(ierr);
  ierr = PetscSectionSetChart(leafSectionAdj, 0, numDof);CHKERRQ(ierr);
  ierr = PetscSectionCreate(comm, &rootSectionAdj);CHKERRQ(ierr);
  ierr = PetscSectionSetChart(rootSectionAdj, 0, numDof);CHKERRQ(ierr);
  /*   Fill in the ghost dofs on the interface */
  ierr = PetscSFGetGraph(sf, NULL, &nleaves, &leaves, &remotes);CHKERRQ(ierr);
  ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
  ierr = DMPlexGetMaxSizes(dm, &maxConeSize, &maxSupportSize);CHKERRQ(ierr);

  maxClosureSize = 2*PetscMax(PetscPowInt(mesh->maxConeSize,depth),PetscPowInt(mesh->maxSupportSize,depth)) + 2;
  maxAdjSize     = PetscPowInt(mesh->maxConeSize,depth) * PetscPowInt(mesh->maxSupportSize,depth) + 1;

  ierr = PetscMalloc2(maxClosureSize,PetscInt,&tmpClosure,maxAdjSize,PetscInt,&tmpAdj);CHKERRQ(ierr);

  /*
   ** The bootstrapping process involves six rounds with similar structure of visiting neighbors of each point.
    1. Visit unowned points on interface, count adjacencies placing in leafSectionAdj
       Reduce those counts to rootSectionAdj (now redundantly counting some interface points)
    2. Visit owned points on interface, count adjacencies placing in rootSectionAdj
       Create sfAdj connecting rootSectionAdj and leafSectionAdj
    3. Visit unowned points on interface, write adjacencies to adj
       Gather adj to rootAdj (note that there is redundancy in rootAdj when multiple procs find the same adjacencies)
    4. Visit owned points on interface, write adjacencies to rootAdj
       Remove redundancy in rootAdj
   ** The last two traversals use transitive closure
    5. Visit all owned points in the subdomain, count dofs for each point (sectionAdj)
       Allocate memory addressed by sectionAdj (cols)
    6. Visit all owned points in the subdomain, insert dof adjacencies into cols
   ** Knowing all the column adjacencies, check ownership and sum into dnz and onz
  */

  for (l = 0; l < nleaves; ++l) {
    PetscInt dof, off, d, q;
    PetscInt p = leaves[l], numAdj = maxAdjSize;

    ierr = PetscSectionGetDof(section, p, &dof);CHKERRQ(ierr);
    ierr = PetscSectionGetOffset(section, p, &off);CHKERRQ(ierr);
    ierr = DMPlexGetAdjacency_Private(dm, p, useClosure, tmpClosure, &numAdj, tmpAdj);CHKERRQ(ierr);
    for (q = 0; q < numAdj; ++q) {
      const PetscInt padj = tmpAdj[q];
      PetscInt ndof, ncdof;

      if ((padj < pStart) || (padj >= pEnd)) continue;
      ierr = PetscSectionGetDof(section, padj, &ndof);CHKERRQ(ierr);
      ierr = PetscSectionGetConstraintDof(section, padj, &ncdof);CHKERRQ(ierr);
      for (d = off; d < off+dof; ++d) {
        ierr = PetscSectionAddDof(leafSectionAdj, d, ndof-ncdof);CHKERRQ(ierr);
      }
    }
  }
  ierr = PetscSectionSetUp(leafSectionAdj);CHKERRQ(ierr);
  if (debug) {
    ierr = PetscPrintf(comm, "Adjacency Section for Preallocation on Leaves:\n");CHKERRQ(ierr);
    ierr = PetscSectionView(leafSectionAdj, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
  }
  /* Get maximum remote adjacency sizes for owned dofs on interface (roots) */
  if (size > 1) {
    ierr = PetscSFReduceBegin(sfDof, MPIU_INT, leafSectionAdj->atlasDof, rootSectionAdj->atlasDof, MPI_SUM);CHKERRQ(ierr);
    ierr = PetscSFReduceEnd(sfDof, MPIU_INT, leafSectionAdj->atlasDof, rootSectionAdj->atlasDof, MPI_SUM);CHKERRQ(ierr);
  }
  if (debug) {
    ierr = PetscPrintf(comm, "Adjancency Section for Preallocation on Roots:\n");CHKERRQ(ierr);
    ierr = PetscSectionView(rootSectionAdj, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
  }
  /* Add in local adjacency sizes for owned dofs on interface (roots) */
  for (p = pStart; p < pEnd; ++p) {
    PetscInt numAdj = maxAdjSize, adof, dof, off, d, q;

    ierr = PetscSectionGetDof(section, p, &dof);CHKERRQ(ierr);
    ierr = PetscSectionGetOffset(section, p, &off);CHKERRQ(ierr);
    if (!dof) continue;
    ierr = PetscSectionGetDof(rootSectionAdj, off, &adof);CHKERRQ(ierr);
    if (adof <= 0) continue;
    ierr = DMPlexGetAdjacency_Private(dm, p, useClosure, tmpClosure, &numAdj, tmpAdj);CHKERRQ(ierr);
    for (q = 0; q < numAdj; ++q) {
      const PetscInt padj = tmpAdj[q];
      PetscInt ndof, ncdof;

      if ((padj < pStart) || (padj >= pEnd)) continue;
      ierr = PetscSectionGetDof(section, padj, &ndof);CHKERRQ(ierr);
      ierr = PetscSectionGetConstraintDof(section, padj, &ncdof);CHKERRQ(ierr);
      for (d = off; d < off+dof; ++d) {
        ierr = PetscSectionAddDof(rootSectionAdj, d, ndof-ncdof);CHKERRQ(ierr);
      }
    }
  }
  ierr = PetscSectionSetUp(rootSectionAdj);CHKERRQ(ierr);
  if (debug) {
    ierr = PetscPrintf(comm, "Adjancency Section for Preallocation on Roots after local additions:\n");CHKERRQ(ierr);
    ierr = PetscSectionView(rootSectionAdj, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
  }
  /* Create adj SF based on dof SF */
  ierr = PetscSFCreateRemoteOffsets(sfDof, rootSectionAdj, leafSectionAdj, &remoteOffsets);CHKERRQ(ierr);
  ierr = PetscSFCreateSectionSF(sfDof, rootSectionAdj, remoteOffsets, leafSectionAdj, &sfAdj);CHKERRQ(ierr);
  if (debug) {
    ierr = PetscPrintf(comm, "Adjacency SF for Preallocation:\n");CHKERRQ(ierr);
    ierr = PetscSFView(sfAdj, NULL);CHKERRQ(ierr);
  }
  ierr = PetscSFDestroy(&sfDof);CHKERRQ(ierr);
  /* Create leaf adjacency */
  ierr = PetscSectionSetUp(leafSectionAdj);CHKERRQ(ierr);
  ierr = PetscSectionGetStorageSize(leafSectionAdj, &adjSize);CHKERRQ(ierr);
  ierr = PetscMalloc(adjSize * sizeof(PetscInt), &adj);CHKERRQ(ierr);
  ierr = PetscMemzero(adj, adjSize * sizeof(PetscInt));CHKERRQ(ierr);
  for (l = 0; l < nleaves; ++l) {
    PetscInt dof, off, d, q;
    PetscInt p = leaves[l], numAdj = maxAdjSize;

    ierr = PetscSectionGetDof(section, p, &dof);CHKERRQ(ierr);
    ierr = PetscSectionGetOffset(section, p, &off);CHKERRQ(ierr);
    ierr = DMPlexGetAdjacency_Private(dm, p, useClosure, tmpClosure, &numAdj, tmpAdj);CHKERRQ(ierr);
    for (d = off; d < off+dof; ++d) {
      PetscInt aoff, i = 0;

      ierr = PetscSectionGetOffset(leafSectionAdj, d, &aoff);CHKERRQ(ierr);
      for (q = 0; q < numAdj; ++q) {
        const PetscInt padj = tmpAdj[q];
        PetscInt ndof, ncdof, ngoff, nd;

        if ((padj < pStart) || (padj >= pEnd)) continue;
        ierr = PetscSectionGetDof(section, padj, &ndof);CHKERRQ(ierr);
        ierr = PetscSectionGetConstraintDof(section, padj, &ncdof);CHKERRQ(ierr);
        ierr = PetscSectionGetOffset(sectionGlobal, padj, &ngoff);CHKERRQ(ierr);
        for (nd = 0; nd < ndof-ncdof; ++nd) {
          adj[aoff+i] = (ngoff < 0 ? -(ngoff+1) : ngoff) + nd;
          ++i;
        }
      }
    }
  }
  /* Debugging */
  if (debug) {
    IS tmp;
    ierr = PetscPrintf(comm, "Leaf adjacency indices\n");CHKERRQ(ierr);
    ierr = ISCreateGeneral(comm, adjSize, adj, PETSC_USE_POINTER, &tmp);CHKERRQ(ierr);
    ierr = ISView(tmp, NULL);CHKERRQ(ierr);
  }
  /* Gather adjacenct indices to root */
  ierr = PetscSectionGetStorageSize(rootSectionAdj, &adjSize);CHKERRQ(ierr);
  ierr = PetscMalloc(adjSize * sizeof(PetscInt), &rootAdj);CHKERRQ(ierr);
  for (r = 0; r < adjSize; ++r) rootAdj[r] = -1;
  if (size > 1) {
    ierr = PetscSFGatherBegin(sfAdj, MPIU_INT, adj, rootAdj);CHKERRQ(ierr);
    ierr = PetscSFGatherEnd(sfAdj, MPIU_INT, adj, rootAdj);CHKERRQ(ierr);
  }
  ierr = PetscSFDestroy(&sfAdj);CHKERRQ(ierr);
  ierr = PetscFree(adj);CHKERRQ(ierr);
  /* Debugging */
  if (debug) {
    IS tmp;
    ierr = PetscPrintf(comm, "Root adjacency indices after gather\n");CHKERRQ(ierr);
    ierr = ISCreateGeneral(comm, adjSize, rootAdj, PETSC_USE_POINTER, &tmp);CHKERRQ(ierr);
    ierr = ISView(tmp, NULL);CHKERRQ(ierr);
  }
  /* Add in local adjacency indices for owned dofs on interface (roots) */
  for (p = pStart; p < pEnd; ++p) {
    PetscInt numAdj = maxAdjSize, adof, dof, off, d, q;

    ierr = PetscSectionGetDof(section, p, &dof);CHKERRQ(ierr);
    ierr = PetscSectionGetOffset(section, p, &off);CHKERRQ(ierr);
    if (!dof) continue;
    ierr = PetscSectionGetDof(rootSectionAdj, off, &adof);CHKERRQ(ierr);
    if (adof <= 0) continue;
    ierr = DMPlexGetAdjacency_Private(dm, p, useClosure, tmpClosure, &numAdj, tmpAdj);CHKERRQ(ierr);
    for (d = off; d < off+dof; ++d) {
      PetscInt adof, aoff, i;

      ierr = PetscSectionGetDof(rootSectionAdj, d, &adof);CHKERRQ(ierr);
      ierr = PetscSectionGetOffset(rootSectionAdj, d, &aoff);CHKERRQ(ierr);
      i    = adof-1;
      for (q = 0; q < numAdj; ++q) {
        const PetscInt padj = tmpAdj[q];
        PetscInt ndof, ncdof, ngoff, nd;

        if ((padj < pStart) || (padj >= pEnd)) continue;
        ierr = PetscSectionGetDof(section, padj, &ndof);CHKERRQ(ierr);
        ierr = PetscSectionGetConstraintDof(section, padj, &ncdof);CHKERRQ(ierr);
        ierr = PetscSectionGetOffset(sectionGlobal, padj, &ngoff);CHKERRQ(ierr);
        for (nd = 0; nd < ndof-ncdof; ++nd) {
          rootAdj[aoff+i] = ngoff < 0 ? -(ngoff+1)+nd : ngoff+nd;
          --i;
        }
      }
    }
  }
  /* Debugging */
  if (debug) {
    IS tmp;
    ierr = PetscPrintf(comm, "Root adjacency indices\n");CHKERRQ(ierr);
    ierr = ISCreateGeneral(comm, adjSize, rootAdj, PETSC_USE_POINTER, &tmp);CHKERRQ(ierr);
    ierr = ISView(tmp, NULL);CHKERRQ(ierr);
  }
  /* Compress indices */
  ierr = PetscSectionSetUp(rootSectionAdj);CHKERRQ(ierr);
  for (p = pStart; p < pEnd; ++p) {
    PetscInt dof, cdof, off, d;
    PetscInt adof, aoff;

    ierr = PetscSectionGetDof(section, p, &dof);CHKERRQ(ierr);
    ierr = PetscSectionGetConstraintDof(section, p, &cdof);CHKERRQ(ierr);
    ierr = PetscSectionGetOffset(section, p, &off);CHKERRQ(ierr);
    if (!dof) continue;
    ierr = PetscSectionGetDof(rootSectionAdj, off, &adof);CHKERRQ(ierr);
    if (adof <= 0) continue;
    for (d = off; d < off+dof-cdof; ++d) {
      ierr = PetscSectionGetDof(rootSectionAdj, d, &adof);CHKERRQ(ierr);
      ierr = PetscSectionGetOffset(rootSectionAdj, d, &aoff);CHKERRQ(ierr);
      ierr = PetscSortRemoveDupsInt(&adof, &rootAdj[aoff]);CHKERRQ(ierr);
      ierr = PetscSectionSetDof(rootSectionAdj, d, adof);CHKERRQ(ierr);
    }
  }
  /* Debugging */
  if (debug) {
    IS tmp;
    ierr = PetscPrintf(comm, "Adjancency Section for Preallocation on Roots after compression:\n");CHKERRQ(ierr);
    ierr = PetscSectionView(rootSectionAdj, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
    ierr = PetscPrintf(comm, "Root adjacency indices after compression\n");CHKERRQ(ierr);
    ierr = ISCreateGeneral(comm, adjSize, rootAdj, PETSC_USE_POINTER, &tmp);CHKERRQ(ierr);
    ierr = ISView(tmp, NULL);CHKERRQ(ierr);
  }
  /* Build adjacency section: Maps global indices to sets of adjacent global indices */
  ierr = PetscSectionGetOffsetRange(sectionGlobal, &globalOffStart, &globalOffEnd);CHKERRQ(ierr);
  ierr = PetscSectionCreate(comm, &sectionAdj);CHKERRQ(ierr);
  ierr = PetscSectionSetChart(sectionAdj, globalOffStart, globalOffEnd);CHKERRQ(ierr);
  for (p = pStart; p < pEnd; ++p) {
    PetscInt  numAdj = maxAdjSize, dof, cdof, off, goff, d, q;
    PetscBool found  = PETSC_TRUE;

    ierr = PetscSectionGetDof(section, p, &dof);CHKERRQ(ierr);
    ierr = PetscSectionGetConstraintDof(section, p, &cdof);CHKERRQ(ierr);
    ierr = PetscSectionGetOffset(section, p, &off);CHKERRQ(ierr);
    ierr = PetscSectionGetOffset(sectionGlobal, p, &goff);CHKERRQ(ierr);
    for (d = 0; d < dof-cdof; ++d) {
      PetscInt ldof, rdof;

      ierr = PetscSectionGetDof(leafSectionAdj, off+d, &ldof);CHKERRQ(ierr);
      ierr = PetscSectionGetDof(rootSectionAdj, off+d, &rdof);CHKERRQ(ierr);
      if (ldof > 0) {
        /* We do not own this point */
      } else if (rdof > 0) {
        ierr = PetscSectionSetDof(sectionAdj, goff+d, rdof);CHKERRQ(ierr);
      } else {
        found = PETSC_FALSE;
      }
    }
    if (found) continue;
    ierr = PetscSectionGetDof(section, p, &dof);CHKERRQ(ierr);
    ierr = PetscSectionGetOffset(sectionGlobal, p, &goff);CHKERRQ(ierr);
    ierr = DMPlexGetAdjacency_Private(dm, p, useClosure, tmpClosure, &numAdj, tmpAdj);CHKERRQ(ierr);
    for (q = 0; q < numAdj; ++q) {
      const PetscInt padj = tmpAdj[q];
      PetscInt ndof, ncdof, noff;

      if ((padj < pStart) || (padj >= pEnd)) continue;
      ierr = PetscSectionGetDof(section, padj, &ndof);CHKERRQ(ierr);
      ierr = PetscSectionGetConstraintDof(section, padj, &ncdof);CHKERRQ(ierr);
      ierr = PetscSectionGetOffset(section, padj, &noff);CHKERRQ(ierr);
      for (d = goff; d < goff+dof-cdof; ++d) {
        ierr = PetscSectionAddDof(sectionAdj, d, ndof-ncdof);CHKERRQ(ierr);
      }
    }
  }
  ierr = PetscSectionSetUp(sectionAdj);CHKERRQ(ierr);
  if (debug) {
    ierr = PetscPrintf(comm, "Adjacency Section for Preallocation:\n");CHKERRQ(ierr);
    ierr = PetscSectionView(sectionAdj, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
  }
  /* Get adjacent indices */
  ierr = PetscSectionGetStorageSize(sectionAdj, &numCols);CHKERRQ(ierr);
  ierr = PetscMalloc(numCols * sizeof(PetscInt), &cols);CHKERRQ(ierr);
  for (p = pStart; p < pEnd; ++p) {
    PetscInt  numAdj = maxAdjSize, dof, cdof, off, goff, d, q;
    PetscBool found  = PETSC_TRUE;

    ierr = PetscSectionGetDof(section, p, &dof);CHKERRQ(ierr);
    ierr = PetscSectionGetConstraintDof(section, p, &cdof);CHKERRQ(ierr);
    ierr = PetscSectionGetOffset(section, p, &off);CHKERRQ(ierr);
    ierr = PetscSectionGetOffset(sectionGlobal, p, &goff);CHKERRQ(ierr);
    for (d = 0; d < dof-cdof; ++d) {
      PetscInt ldof, rdof;

      ierr = PetscSectionGetDof(leafSectionAdj, off+d, &ldof);CHKERRQ(ierr);
      ierr = PetscSectionGetDof(rootSectionAdj, off+d, &rdof);CHKERRQ(ierr);
      if (ldof > 0) {
        /* We do not own this point */
      } else if (rdof > 0) {
        PetscInt aoff, roff;

        ierr = PetscSectionGetOffset(sectionAdj, goff+d, &aoff);CHKERRQ(ierr);
        ierr = PetscSectionGetOffset(rootSectionAdj, off+d, &roff);CHKERRQ(ierr);
        ierr = PetscMemcpy(&cols[aoff], &rootAdj[roff], rdof * sizeof(PetscInt));CHKERRQ(ierr);
      } else {
        found = PETSC_FALSE;
      }
    }
    if (found) continue;
    ierr = DMPlexGetAdjacency_Private(dm, p, useClosure, tmpClosure, &numAdj, tmpAdj);CHKERRQ(ierr);
    for (d = goff; d < goff+dof-cdof; ++d) {
      PetscInt adof, aoff, i = 0;

      ierr = PetscSectionGetDof(sectionAdj, d, &adof);CHKERRQ(ierr);
      ierr = PetscSectionGetOffset(sectionAdj, d, &aoff);CHKERRQ(ierr);
      for (q = 0; q < numAdj; ++q) {
        const PetscInt  padj = tmpAdj[q];
        PetscInt        ndof, ncdof, ngoff, nd;
        const PetscInt *ncind;

        /* Adjacent points may not be in the section chart */
        if ((padj < pStart) || (padj >= pEnd)) continue;
        ierr = PetscSectionGetDof(section, padj, &ndof);CHKERRQ(ierr);
        ierr = PetscSectionGetConstraintDof(section, padj, &ncdof);CHKERRQ(ierr);
        ierr = PetscSectionGetConstraintIndices(section, padj, &ncind);CHKERRQ(ierr);
        ierr = PetscSectionGetOffset(sectionGlobal, padj, &ngoff);CHKERRQ(ierr);
        for (nd = 0; nd < ndof-ncdof; ++nd, ++i) {
          cols[aoff+i] = ngoff < 0 ? -(ngoff+1)+nd : ngoff+nd;
        }
      }
      if (i != adof) SETERRQ4(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid number of entries %D != %D for dof %D (point %D)", i, adof, d, p);
    }
  }
  ierr = PetscSectionDestroy(&leafSectionAdj);CHKERRQ(ierr);
  ierr = PetscSectionDestroy(&rootSectionAdj);CHKERRQ(ierr);
  ierr = PetscFree(rootAdj);CHKERRQ(ierr);
  ierr = PetscFree2(tmpClosure, tmpAdj);CHKERRQ(ierr);
  /* Debugging */
  if (debug) {
    IS tmp;
    ierr = PetscPrintf(comm, "Column indices\n");CHKERRQ(ierr);
    ierr = ISCreateGeneral(comm, numCols, cols, PETSC_USE_POINTER, &tmp);CHKERRQ(ierr);
    ierr = ISView(tmp, NULL);CHKERRQ(ierr);
  }
  /* Create allocation vectors from adjacency graph */
  ierr = MatGetLocalSize(A, &locRows, NULL);CHKERRQ(ierr);
  ierr = PetscLayoutCreate(PetscObjectComm((PetscObject)A), &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);
  /* Only loop over blocks of rows */
  if (rStart%bs || rEnd%bs) SETERRQ3(PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONG, "Invalid layout [%d, %d) for matrix, must be divisible by block size %d", rStart, rEnd, bs);
  for (r = rStart/bs; r < rEnd/bs; ++r) {
    const PetscInt row = r*bs;
    PetscInt       numCols, cStart, c;

    ierr = PetscSectionGetDof(sectionAdj, row, &numCols);CHKERRQ(ierr);
    ierr = PetscSectionGetOffset(sectionAdj, row, &cStart);CHKERRQ(ierr);
    for (c = cStart; c < cStart+numCols; ++c) {
      if ((cols[c] >= rStart*bs) && (cols[c] < rEnd*bs)) {
        ++dnz[r-rStart];
        if (cols[c] >= row) ++dnzu[r-rStart];
      } else {
        ++onz[r-rStart];
        if (cols[c] >= row) ++onzu[r-rStart];
      }
    }
  }
  if (bs > 1) {
    for (r = 0; r < locRows/bs; ++r) {
      dnz[r]  /= bs;
      onz[r]  /= bs;
      dnzu[r] /= bs;
      onzu[r] /= bs;
    }
  }
  /* Set matrix pattern */
  ierr = MatXAIJSetPreallocation(A, bs, dnz, onz, dnzu, onzu);CHKERRQ(ierr);
  ierr = MatSetOption(A, MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
  /* Fill matrix with zeros */
  if (fillMatrix) {
    PetscScalar *values;
    PetscInt     maxRowLen = 0;

    for (r = rStart; r < rEnd; ++r) {
      PetscInt len;

      ierr      = PetscSectionGetDof(sectionAdj, r, &len);CHKERRQ(ierr);
      maxRowLen = PetscMax(maxRowLen, len);
    }
    ierr = PetscMalloc(maxRowLen * sizeof(PetscScalar), &values);CHKERRQ(ierr);
    ierr = PetscMemzero(values, maxRowLen * sizeof(PetscScalar));CHKERRQ(ierr);
    for (r = rStart; r < rEnd; ++r) {
      PetscInt numCols, cStart;

      ierr = PetscSectionGetDof(sectionAdj, r, &numCols);CHKERRQ(ierr);
      ierr = PetscSectionGetOffset(sectionAdj, r, &cStart);CHKERRQ(ierr);
      ierr = MatSetValues(A, 1, &r, numCols, &cols[cStart], values, INSERT_VALUES);CHKERRQ(ierr);
    }
    ierr = PetscFree(values);CHKERRQ(ierr);
    ierr = MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
    ierr = MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  }
  ierr = PetscSectionDestroy(&sectionAdj);CHKERRQ(ierr);
  ierr = PetscFree(cols);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#if 0
#undef __FUNCT__
#define __FUNCT__ "DMPlexPreallocateOperator_2"
PetscErrorCode DMPlexPreallocateOperator_2(DM dm, PetscInt bs, PetscSection section, PetscSection sectionGlobal, PetscInt dnz[], PetscInt onz[], PetscInt dnzu[], PetscInt onzu[], Mat A, PetscBool fillMatrix)
{
  PetscInt       *tmpClosure,*tmpAdj,*visits;
  PetscInt        c,cStart,cEnd,pStart,pEnd;
  PetscErrorCode  ierr;

  PetscFunctionBegin;
  ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
  ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
  ierr = DMPlexGetMaxSizes(dm, &maxConeSize, &maxSupportSize);CHKERRQ(ierr);

  maxClosureSize = 2*PetscMax(PetscPowInt(mesh->maxConeSize,depth),PetscPowInt(mesh->maxSupportSize,depth));

  ierr    = PetscSectionGetChart(section, &pStart, &pEnd);CHKERRQ(ierr);
  npoints = pEnd - pStart;

  ierr = PetscMalloc3(maxClosureSize,PetscInt,&tmpClosure,npoints,PetscInt,&lvisits,npoints,PetscInt,&visits);CHKERRQ(ierr);
  ierr = PetscMemzero(lvisits,(pEnd-pStart)*sizeof(PetscInt));CHKERRQ(ierr);
  ierr = PetscMemzero(visits,(pEnd-pStart)*sizeof(PetscInt));CHKERRQ(ierr);
  ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
  for (c=cStart; c<cEnd; c++) {
    PetscInt *support = tmpClosure;
    ierr = DMPlexGetTransitiveClosure(dm, c, PETSC_FALSE, &supportSize, (PetscInt**)&support);CHKERRQ(ierr);
    for (p=0; p<supportSize; p++) lvisits[support[p]]++;
  }
  ierr = PetscSFReduceBegin(sf,MPIU_INT,lvisits,visits,MPI_SUM);CHKERRQ(ierr);
  ierr = PetscSFReduceEnd  (sf,MPIU_INT,lvisits,visits,MPI_SUM);CHKERRQ(ierr);
  ierr = PetscSFBcastBegin(sf,MPIU_INT,visits,lvisits);CHKERRQ(ierr);
  ierr = PetscSFBcastEnd  (sf,MPIU_INT,visits,lvisits);CHKERRQ(ierr);

  ierr = PetscSFGetRanks();CHKERRQ(ierr);


  ierr = PetscMalloc2(maxClosureSize*maxClosureSize,PetscInt,&cellmat,npoints,PetscInt,&owner);CHKERRQ(ierr);
  for (c=cStart; c<cEnd; c++) {
    ierr = PetscMemzero(cellmat,maxClosureSize*maxClosureSize*sizeof(PetscInt));CHKERRQ(ierr);
    /*
     Depth-first walk of transitive closure.
     At each leaf frame f of transitive closure that we see, add 1/visits[f] to each pair (p,q) not marked as done in cellmat.
     This contribution is added to dnz if owning ranks of p and q match, to onz otherwise.
     */
  }

  ierr = PetscSFReduceBegin(sf,MPIU_INT,ldnz,dnz,MPI_SUM);CHKERRQ(ierr);
  ierr = PetscSFReduceEnd  (sf,MPIU_INT,lonz,onz,MPI_SUM);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}
#endif

#undef __FUNCT__
#define __FUNCT__ "DMCreateMatrix_Plex"
PetscErrorCode DMCreateMatrix_Plex(DM dm, MatType mtype, Mat *J)
{
  PetscSection   section, sectionGlobal;
  PetscInt       bs = -1;
  PetscInt       localSize;
  PetscBool      isShell, isBlock, isSeqBlock, isMPIBlock, isSymBlock, isSymSeqBlock, isSymMPIBlock, isSymmetric;
  PetscErrorCode ierr;

  PetscFunctionBegin;
#if !defined(PETSC_USE_DYNAMIC_LIBRARIES)
  ierr = MatInitializePackage(NULL);CHKERRQ(ierr);
#endif
  if (!mtype) mtype = MATAIJ;
  ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
  ierr = DMGetDefaultGlobalSection(dm, &sectionGlobal);CHKERRQ(ierr);
  /* ierr = PetscSectionGetStorageSize(sectionGlobal, &localSize);CHKERRQ(ierr); */
  ierr = PetscSectionGetConstrainedStorageSize(sectionGlobal, &localSize);CHKERRQ(ierr);
  ierr = MatCreate(PetscObjectComm((PetscObject)dm), J);CHKERRQ(ierr);
  ierr = MatSetSizes(*J, localSize, localSize, PETSC_DETERMINE, PETSC_DETERMINE);CHKERRQ(ierr);
  ierr = MatSetType(*J, mtype);CHKERRQ(ierr);
  ierr = MatSetFromOptions(*J);CHKERRQ(ierr);
  ierr = PetscStrcmp(mtype, MATSHELL, &isShell);CHKERRQ(ierr);
  ierr = PetscStrcmp(mtype, MATBAIJ, &isBlock);CHKERRQ(ierr);
  ierr = PetscStrcmp(mtype, MATSEQBAIJ, &isSeqBlock);CHKERRQ(ierr);
  ierr = PetscStrcmp(mtype, MATMPIBAIJ, &isMPIBlock);CHKERRQ(ierr);
  ierr = PetscStrcmp(mtype, MATSBAIJ, &isSymBlock);CHKERRQ(ierr);
  ierr = PetscStrcmp(mtype, MATSEQSBAIJ, &isSymSeqBlock);CHKERRQ(ierr);
  ierr = PetscStrcmp(mtype, MATMPISBAIJ, &isSymMPIBlock);CHKERRQ(ierr);
  /* Check for symmetric storage */
  isSymmetric = (PetscBool) (isSymBlock || isSymSeqBlock || isSymMPIBlock);
  if (isSymmetric) {
    ierr = MatSetOption(*J, MAT_IGNORE_LOWER_TRIANGULAR, PETSC_TRUE);CHKERRQ(ierr);
  }
  if (!isShell) {
    PetscBool fillMatrix = (PetscBool) !dm->prealloc_only;
    PetscInt *dnz, *onz, *dnzu, *onzu, bsLocal, bsMax, bsMin;

    if (bs < 0) {
      if (isBlock || isSeqBlock || isMPIBlock || isSymBlock || isSymSeqBlock || isSymMPIBlock) {
        PetscInt pStart, pEnd, p, dof, cdof;

        ierr = PetscSectionGetChart(sectionGlobal, &pStart, &pEnd);CHKERRQ(ierr);
        for (p = pStart; p < pEnd; ++p) {
          ierr = PetscSectionGetDof(sectionGlobal, p, &dof);CHKERRQ(ierr);
          ierr = PetscSectionGetConstraintDof(sectionGlobal, p, &cdof);CHKERRQ(ierr);
          if (dof-cdof) {
            if (bs < 0) {
              bs = dof-cdof;
            } else if (bs != dof-cdof) {
              /* Layout does not admit a pointwise block size */
              bs = 1;
              break;
            }
          }
        }
        /* Must have same blocksize on all procs (some might have no points) */
        bsLocal = bs;
        ierr = MPI_Allreduce(&bsLocal, &bsMax, 1, MPIU_INT, MPI_MAX, PetscObjectComm((PetscObject)dm));CHKERRQ(ierr);
        bsLocal = bs < 0 ? bsMax : bs;
        ierr = MPI_Allreduce(&bsLocal, &bsMin, 1, MPIU_INT, MPI_MIN, PetscObjectComm((PetscObject)dm));CHKERRQ(ierr);
        if (bsMin != bsMax) {
          bs = 1;
        } else {
          bs = bsMax;
        }
      } else {
        bs = 1;
      }
    }
    ierr = PetscMalloc4(localSize/bs, PetscInt, &dnz, localSize/bs, PetscInt, &onz, localSize/bs, PetscInt, &dnzu, localSize/bs, PetscInt, &onzu);CHKERRQ(ierr);
    ierr = PetscMemzero(dnz,  localSize/bs * sizeof(PetscInt));CHKERRQ(ierr);
    ierr = PetscMemzero(onz,  localSize/bs * sizeof(PetscInt));CHKERRQ(ierr);
    ierr = PetscMemzero(dnzu, localSize/bs * sizeof(PetscInt));CHKERRQ(ierr);
    ierr = PetscMemzero(onzu, localSize/bs * sizeof(PetscInt));CHKERRQ(ierr);
    ierr = DMPlexPreallocateOperator(dm, bs, section, sectionGlobal, dnz, onz, dnzu, onzu, *J, fillMatrix);CHKERRQ(ierr);
    ierr = PetscFree4(dnz, onz, dnzu, onzu);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetDimension"
/*@
  DMPlexGetDimension - Return the topological mesh dimension

  Not collective

  Input Parameter:
. mesh - The DMPlex

  Output Parameter:
. dim - The topological mesh dimension

  Level: beginner

.seealso: DMPlexCreate()
@*/
PetscErrorCode DMPlexGetDimension(DM dm, PetscInt *dim)
{
  DM_Plex *mesh = (DM_Plex*) dm->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidPointer(dim, 2);
  *dim = mesh->dim;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexSetDimension"
/*@
  DMPlexSetDimension - Set the topological mesh dimension

  Collective on mesh

  Input Parameters:
+ mesh - The DMPlex
- dim - The topological mesh dimension

  Level: beginner

.seealso: DMPlexCreate()
@*/
PetscErrorCode DMPlexSetDimension(DM dm, PetscInt dim)
{
  DM_Plex *mesh = (DM_Plex*) dm->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidLogicalCollectiveInt(dm, dim, 2);
  mesh->dim               = dim;
  mesh->preallocCenterDim = dim;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetChart"
/*@
  DMPlexGetChart - Return the interval for all mesh points [pStart, pEnd)

  Not collective

  Input Parameter:
. mesh - The DMPlex

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

  Level: beginner

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

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  ierr = PetscSectionGetChart(mesh->coneSection, pStart, pEnd);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexSetChart"
/*@
  DMPlexSetChart - Set the interval for all mesh points [pStart, pEnd)

  Not collective

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

  Output Parameters:

  Level: beginner

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

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  ierr = PetscSectionSetChart(mesh->coneSection, pStart, pEnd);CHKERRQ(ierr);
  ierr = PetscSectionSetChart(mesh->supportSection, pStart, pEnd);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetConeSize"
/*@
  DMPlexGetConeSize - Return the number of in-edges for this point in the Sieve DAG

  Not collective

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

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

  Level: beginner

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

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidPointer(size, 3);
  ierr = PetscSectionGetDof(mesh->coneSection, p, size);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexSetConeSize"
/*@
  DMPlexSetConeSize - Set the number of in-edges for this point in the Sieve DAG

  Not collective

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

  Output Parameter:

  Note:
  This should be called after DMPlexSetChart().

  Level: beginner

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

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  ierr = PetscSectionSetDof(mesh->coneSection, p, size);CHKERRQ(ierr);

  mesh->maxConeSize = PetscMax(mesh->maxConeSize, size);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetCone"
/*@C
  DMPlexGetCone - Return the points on the in-edges for this point in the Sieve DAG

  Not collective

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

  Output Parameter:
. cone - An array of points which are on the in-edges for point p

  Level: beginner

  Note:
  This routine is not available in Fortran.

.seealso: DMPlexCreate(), DMPlexSetCone(), DMPlexSetChart()
@*/
PetscErrorCode DMPlexGetCone(DM dm, PetscInt p, const PetscInt *cone[])
{
  DM_Plex       *mesh = (DM_Plex*) dm->data;
  PetscInt       off;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidPointer(cone, 3);
  ierr  = PetscSectionGetOffset(mesh->coneSection, p, &off);CHKERRQ(ierr);
  *cone = &mesh->cones[off];
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexSetCone"
/*@
  DMPlexSetCone - Set the points on the in-edges for this point in the Sieve DAG

  Not collective

  Input Parameters:
+ mesh - The DMPlex
. p - The Sieve point, which must lie in the chart set with DMPlexSetChart()
- cone - An array of points which are on the in-edges for point p

  Output Parameter:

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

  Level: beginner

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

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  ierr = PetscSectionGetChart(mesh->coneSection, &pStart, &pEnd);CHKERRQ(ierr);
  ierr = PetscSectionGetDof(mesh->coneSection, p, &dof);CHKERRQ(ierr);
  if (dof) PetscValidPointer(cone, 3);
  ierr = PetscSectionGetOffset(mesh->coneSection, p, &off);CHKERRQ(ierr);
  if ((p < pStart) || (p >= pEnd)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "Mesh point %D is not in the valid range [%D, %D)", p, pStart, pEnd);
  for (c = 0; c < dof; ++c) {
    if ((cone[c] < pStart) || (cone[c] >= pEnd)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "Cone point %D is not in the valid range [%D, %D)", cone[c], pStart, pEnd);
    mesh->cones[off+c] = cone[c];
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetConeOrientation"
/*@C
  DMPlexGetConeOrientation - Return the orientations on the in-edges for this point in the Sieve DAG

  Not collective

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

  Output Parameter:
. coneOrientation - An array of orientations which are on the in-edges for point p. An orientation is an
                    integer giving the prescription for cone traversal. If it is negative, the cone is
                    traversed in the opposite direction. Its value 'o', or if negative '-(o+1)', gives
                    the index of the cone point on which to start.

  Level: beginner

  Note:
  This routine is not available in Fortran.

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

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
#if defined(PETSC_USE_DEBUG)
  {
    PetscInt dof;
    ierr = PetscSectionGetDof(mesh->coneSection, p, &dof);CHKERRQ(ierr);
    if (dof) PetscValidPointer(coneOrientation, 3);
  }
#endif
  ierr = PetscSectionGetOffset(mesh->coneSection, p, &off);CHKERRQ(ierr);

  *coneOrientation = &mesh->coneOrientations[off];
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexSetConeOrientation"
/*@
  DMPlexSetConeOrientation - Set the orientations on the in-edges for this point in the Sieve DAG

  Not collective

  Input Parameters:
+ mesh - The DMPlex
. p - The Sieve point, which must lie in the chart set with DMPlexSetChart()
- coneOrientation - An array of orientations which are on the in-edges for point p. An orientation is an
                    integer giving the prescription for cone traversal. If it is negative, the cone is
                    traversed in the opposite direction. Its value 'o', or if negative '-(o+1)', gives
                    the index of the cone point on which to start.

  Output Parameter:

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

  Level: beginner

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

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  ierr = PetscSectionGetChart(mesh->coneSection, &pStart, &pEnd);CHKERRQ(ierr);
  ierr = PetscSectionGetDof(mesh->coneSection, p, &dof);CHKERRQ(ierr);
  if (dof) PetscValidPointer(coneOrientation, 3);
  ierr = PetscSectionGetOffset(mesh->coneSection, p, &off);CHKERRQ(ierr);
  if ((p < pStart) || (p >= pEnd)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "Mesh point %D is not in the valid range [%D, %D)", p, pStart, pEnd);
  for (c = 0; c < dof; ++c) {
    PetscInt cdof, o = coneOrientation[c];

    ierr = PetscSectionGetDof(mesh->coneSection, mesh->cones[off+c], &cdof);CHKERRQ(ierr);
    if (o && ((o < -(cdof+1)) || (o >= cdof))) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "Cone orientation %D is not in the valid range [%D. %D)", o, -(cdof+1), cdof);
    mesh->coneOrientations[off+c] = o;
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexInsertCone"
PetscErrorCode DMPlexInsertCone(DM dm, PetscInt p, PetscInt conePos, PetscInt conePoint)
{
  DM_Plex       *mesh = (DM_Plex*) dm->data;
  PetscInt       pStart, pEnd;
  PetscInt       dof, off;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  ierr = PetscSectionGetChart(mesh->coneSection, &pStart, &pEnd);CHKERRQ(ierr);
  if ((p < pStart) || (p >= pEnd)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "Mesh point %D is not in the valid range [%D, %D)", p, pStart, pEnd);
  if ((conePoint < pStart) || (conePoint >= pEnd)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "Cone point %D is not in the valid range [%D, %D)", conePoint, pStart, pEnd);
  ierr = PetscSectionGetDof(mesh->coneSection, p, &dof);CHKERRQ(ierr);
  ierr = PetscSectionGetOffset(mesh->coneSection, p, &off);CHKERRQ(ierr);
  if ((conePos < 0) || (conePos >= dof)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "Cone position %D of point %D is not in the valid range [0, %D)", conePos, p, dof);
  mesh->cones[off+conePos] = conePoint;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexInsertConeOrientation"
PetscErrorCode DMPlexInsertConeOrientation(DM dm, PetscInt p, PetscInt conePos, PetscInt coneOrientation)
{
  DM_Plex       *mesh = (DM_Plex*) dm->data;
  PetscInt       pStart, pEnd;
  PetscInt       dof, off;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  ierr = PetscSectionGetChart(mesh->coneSection, &pStart, &pEnd);CHKERRQ(ierr);
  if ((p < pStart) || (p >= pEnd)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "Mesh point %D is not in the valid range [%D, %D)", p, pStart, pEnd);
  ierr = PetscSectionGetDof(mesh->coneSection, p, &dof);CHKERRQ(ierr);
  ierr = PetscSectionGetOffset(mesh->coneSection, p, &off);CHKERRQ(ierr);
  if ((conePos < 0) || (conePos >= dof)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "Cone position %D of point %D is not in the valid range [0, %D)", conePos, p, dof);
  mesh->coneOrientations[off+conePos] = coneOrientation;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetSupportSize"
/*@
  DMPlexGetSupportSize - Return the number of out-edges for this point in the Sieve DAG

  Not collective

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

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

  Level: beginner

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

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidPointer(size, 3);
  ierr = PetscSectionGetDof(mesh->supportSection, p, size);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexSetSupportSize"
/*@
  DMPlexSetSupportSize - Set the number of out-edges for this point in the Sieve DAG

  Not collective

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

  Output Parameter:

  Note:
  This should be called after DMPlexSetChart().

  Level: beginner

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

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  ierr = PetscSectionSetDof(mesh->supportSection, p, size);CHKERRQ(ierr);

  mesh->maxSupportSize = PetscMax(mesh->maxSupportSize, size);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetSupport"
/*@C
  DMPlexGetSupport - Return the points on the out-edges for this point in the Sieve DAG

  Not collective

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

  Output Parameter:
. support - An array of points which are on the out-edges for point p

  Level: beginner

.seealso: DMPlexCreate(), DMPlexSetCone(), DMPlexSetChart(), DMPlexGetCone()
@*/
PetscErrorCode DMPlexGetSupport(DM dm, PetscInt p, const PetscInt *support[])
{
  DM_Plex       *mesh = (DM_Plex*) dm->data;
  PetscInt       off;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidPointer(support, 3);
  ierr     = PetscSectionGetOffset(mesh->supportSection, p, &off);CHKERRQ(ierr);
  *support = &mesh->supports[off];
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexSetSupport"
/*@
  DMPlexSetSupport - Set the points on the out-edges for this point in the Sieve DAG

  Not collective

  Input Parameters:
+ mesh - The DMPlex
. p - The Sieve point, which must lie in the chart set with DMPlexSetChart()
- support - An array of points which are on the in-edges for point p

  Output Parameter:

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

  Level: beginner

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

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  ierr = PetscSectionGetChart(mesh->supportSection, &pStart, &pEnd);CHKERRQ(ierr);
  ierr = PetscSectionGetDof(mesh->supportSection, p, &dof);CHKERRQ(ierr);
  if (dof) PetscValidPointer(support, 3);
  ierr = PetscSectionGetOffset(mesh->supportSection, p, &off);CHKERRQ(ierr);
  if ((p < pStart) || (p >= pEnd)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "Mesh point %D is not in the valid range [%D, %D)", p, pStart, pEnd);
  for (c = 0; c < dof; ++c) {
    if ((support[c] < pStart) || (support[c] >= pEnd)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "Support point %D is not in the valid range [%D, %D)", support[c], pStart, pEnd);
    mesh->supports[off+c] = support[c];
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexInsertSupport"
PetscErrorCode DMPlexInsertSupport(DM dm, PetscInt p, PetscInt supportPos, PetscInt supportPoint)
{
  DM_Plex       *mesh = (DM_Plex*) dm->data;
  PetscInt       pStart, pEnd;
  PetscInt       dof, off;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  ierr = PetscSectionGetChart(mesh->supportSection, &pStart, &pEnd);CHKERRQ(ierr);
  ierr = PetscSectionGetDof(mesh->supportSection, p, &dof);CHKERRQ(ierr);
  ierr = PetscSectionGetOffset(mesh->supportSection, p, &off);CHKERRQ(ierr);
  if ((p < pStart) || (p >= pEnd)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "Mesh point %D is not in the valid range [%D, %D)", p, pStart, pEnd);
  if ((supportPoint < pStart) || (supportPoint >= pEnd)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "Support point %D is not in the valid range [%D, %D)", supportPoint, pStart, pEnd);
  if (supportPos >= dof) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "Support position %D of point %D is not in the valid range [0, %D)", supportPos, p, dof);
  mesh->supports[off+supportPos] = supportPoint;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetTransitiveClosure"
/*@C
  DMPlexGetTransitiveClosure - Return the points on the transitive closure of the in-edges or out-edges for this point in the Sieve DAG

  Not collective

  Input Parameters:
+ mesh - The DMPlex
. p - The Sieve point, which must lie in the chart set with DMPlexSetChart()
. useCone - PETSC_TRUE for in-edges,  otherwise use out-edges
- points - If points is NULL on input, internal storage will be returned, otherwise the provided array is used

  Output Parameters:
+ numPoints - The number of points in the closure, so points[] is of size 2*numPoints
- points - The points and point orientations, interleaved as pairs [p0, o0, p1, o1, ...]

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

  Level: beginner

.seealso: DMPlexRestoreTransitiveClosure(), DMPlexCreate(), DMPlexSetCone(), DMPlexSetChart(), DMPlexGetCone()
@*/
PetscErrorCode DMPlexGetTransitiveClosure(DM dm, PetscInt p, PetscBool useCone, PetscInt *numPoints, PetscInt *points[])
{
  DM_Plex        *mesh = (DM_Plex*) dm->data;
  PetscInt       *closure, *fifo;
  const PetscInt *tmp = NULL, *tmpO = NULL;
  PetscInt        tmpSize, t;
  PetscInt        depth       = 0, maxSize;
  PetscInt        closureSize = 2, fifoSize = 0, fifoStart = 0;
  PetscErrorCode  ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  ierr    = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
  maxSize = 2*PetscMax(PetscMax(PetscPowInt(mesh->maxConeSize,depth),PetscPowInt(mesh->maxSupportSize,depth)),depth) + 2;
  ierr    = DMGetWorkArray(dm, maxSize, PETSC_INT, &fifo);CHKERRQ(ierr);
  if (*points) {
    closure = *points;
  } else {
    ierr = DMGetWorkArray(dm, maxSize, PETSC_INT, &closure);CHKERRQ(ierr);
  }
  closure[0] = p; closure[1] = 0;
  /* This is only 1-level */
  if (useCone) {
    ierr = DMPlexGetConeSize(dm, p, &tmpSize);CHKERRQ(ierr);
    ierr = DMPlexGetCone(dm, p, &tmp);CHKERRQ(ierr);
    ierr = DMPlexGetConeOrientation(dm, p, &tmpO);CHKERRQ(ierr);
  } else {
    ierr = DMPlexGetSupportSize(dm, p, &tmpSize);CHKERRQ(ierr);
    ierr = DMPlexGetSupport(dm, p, &tmp);CHKERRQ(ierr);
  }
  for (t = 0; t < tmpSize; ++t, closureSize += 2, fifoSize += 2) {
    const PetscInt cp = tmp[t];
    const PetscInt co = tmpO ? tmpO[t] : 0;

    closure[closureSize]   = cp;
    closure[closureSize+1] = co;
    fifo[fifoSize]         = cp;
    fifo[fifoSize+1]       = co;
  }
  while (fifoSize - fifoStart) {
    const PetscInt q   = fifo[fifoStart];
    const PetscInt o   = fifo[fifoStart+1];
    const PetscInt rev = o >= 0 ? 0 : 1;
    const PetscInt off = rev ? -(o+1) : o;

    if (useCone) {
      ierr = DMPlexGetConeSize(dm, q, &tmpSize);CHKERRQ(ierr);
      ierr = DMPlexGetCone(dm, q, &tmp);CHKERRQ(ierr);
      ierr = DMPlexGetConeOrientation(dm, q, &tmpO);CHKERRQ(ierr);
    } else {
      ierr = DMPlexGetSupportSize(dm, q, &tmpSize);CHKERRQ(ierr);
      ierr = DMPlexGetSupport(dm, q, &tmp);CHKERRQ(ierr);
      tmpO = NULL;
    }
    for (t = 0; t < tmpSize; ++t) {
      const PetscInt i  = ((rev ? tmpSize-t : t) + off)%tmpSize;
      const PetscInt cp = tmp[i];
      /* Must propogate orientation */
      const PetscInt co = tmpO ? (rev ? -(tmpO[i]+1) : tmpO[i]) : 0;
      PetscInt       c;

      /* Check for duplicate */
      for (c = 0; c < closureSize; c += 2) {
        if (closure[c] == cp) break;
      }
      if (c == closureSize) {
        closure[closureSize]   = cp;
        closure[closureSize+1] = co;
        fifo[fifoSize]         = cp;
        fifo[fifoSize+1]       = co;
        closureSize           += 2;
        fifoSize              += 2;
      }
    }
    fifoStart += 2;
  }
  if (numPoints) *numPoints = closureSize/2;
  if (points)    *points    = closure;
  ierr = DMRestoreWorkArray(dm, maxSize, PETSC_INT, &fifo);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexRestoreTransitiveClosure"
/*@C
  DMPlexRestoreTransitiveClosure - Restore the array of points on the transitive closure of the in-edges or out-edges for this point in the Sieve DAG

  Not collective

  Input Parameters:
+ mesh - The DMPlex
. p - The Sieve point, which must lie in the chart set with DMPlexSetChart()
. useCone - PETSC_TRUE for in-edges,  otherwise use out-edges
- points - If points is NULL on input, internal storage will be returned, otherwise the provided array is used

  Output Parameters:
+ numPoints - The number of points in the closure, so points[] is of size 2*numPoints
- points - The points and point orientations, interleaved as pairs [p0, o0, p1, o1, ...]

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

  Level: beginner

.seealso: DMPlexGetTransitiveClosure(), DMPlexCreate(), DMPlexSetCone(), DMPlexSetChart(), DMPlexGetCone()
@*/
PetscErrorCode DMPlexRestoreTransitiveClosure(DM dm, PetscInt p, PetscBool useCone, PetscInt *numPoints, PetscInt *points[])
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  ierr = DMRestoreWorkArray(dm, 0, PETSC_INT, points);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetMaxSizes"
/*@
  DMPlexGetMaxSizes - Return the maximum number of in-edges (cone) and out-edges (support) for any point in the Sieve DAG

  Not collective

  Input Parameter:
. mesh - The DMPlex

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

  Level: beginner

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

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (maxConeSize)    *maxConeSize    = mesh->maxConeSize;
  if (maxSupportSize) *maxSupportSize = mesh->maxSupportSize;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMSetUp_Plex"
PetscErrorCode DMSetUp_Plex(DM dm)
{
  DM_Plex       *mesh = (DM_Plex*) dm->data;
  PetscInt       size;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  ierr = PetscSectionSetUp(mesh->coneSection);CHKERRQ(ierr);
  ierr = PetscSectionGetStorageSize(mesh->coneSection, &size);CHKERRQ(ierr);
  ierr = PetscMalloc(size * sizeof(PetscInt), &mesh->cones);CHKERRQ(ierr);
  ierr = PetscMalloc(size * sizeof(PetscInt), &mesh->coneOrientations);CHKERRQ(ierr);
  ierr = PetscMemzero(mesh->coneOrientations, size * sizeof(PetscInt));CHKERRQ(ierr);
  if (mesh->maxSupportSize) {
    ierr = PetscSectionSetUp(mesh->supportSection);CHKERRQ(ierr);
    ierr = PetscSectionGetStorageSize(mesh->supportSection, &size);CHKERRQ(ierr);
    ierr = PetscMalloc(size * sizeof(PetscInt), &mesh->supports);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMCreateSubDM_Plex"
PetscErrorCode DMCreateSubDM_Plex(DM dm, PetscInt numFields, PetscInt fields[], IS *is, DM *subdm)
{
  PetscSection   section, sectionGlobal;
  PetscInt      *subIndices;
  PetscInt       subSize = 0, subOff = 0, nF, f, pStart, pEnd, p;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if (!numFields) PetscFunctionReturn(0);
  ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
  ierr = DMGetDefaultGlobalSection(dm, &sectionGlobal);CHKERRQ(ierr);
  if (!section) SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Must set default section for DMPlex before splitting fields");
  if (!sectionGlobal) SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Must set default global section for DMPlex before splitting fields");
  ierr = PetscSectionGetNumFields(section, &nF);CHKERRQ(ierr);
  if (numFields > nF) SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Number of requested fields %d greater than number of DM fields %d", numFields, nF);
  ierr = PetscSectionGetChart(sectionGlobal, &pStart, &pEnd);CHKERRQ(ierr);
  for (p = pStart; p < pEnd; ++p) {
    PetscInt gdof;

    ierr = PetscSectionGetDof(sectionGlobal, p, &gdof);CHKERRQ(ierr);
    if (gdof > 0) {
      for (f = 0; f < numFields; ++f) {
        PetscInt fdof, fcdof;

        ierr     = PetscSectionGetFieldDof(section, p, fields[f], &fdof);CHKERRQ(ierr);
        ierr     = PetscSectionGetFieldConstraintDof(section, p, fields[f], &fcdof);CHKERRQ(ierr);
        subSize += fdof-fcdof;
      }
    }
  }
  ierr = PetscMalloc(subSize * sizeof(PetscInt), &subIndices);CHKERRQ(ierr);
  for (p = pStart; p < pEnd; ++p) {
    PetscInt gdof, goff;

    ierr = PetscSectionGetDof(sectionGlobal, p, &gdof);CHKERRQ(ierr);
    if (gdof > 0) {
      ierr = PetscSectionGetOffset(sectionGlobal, p, &goff);CHKERRQ(ierr);
      for (f = 0; f < numFields; ++f) {
        PetscInt fdof, fcdof, fc, f2, poff = 0;

        /* Can get rid of this loop by storing field information in the global section */
        for (f2 = 0; f2 < fields[f]; ++f2) {
          ierr  = PetscSectionGetFieldDof(section, p, f2, &fdof);CHKERRQ(ierr);
          ierr  = PetscSectionGetFieldConstraintDof(section, p, f2, &fcdof);CHKERRQ(ierr);
          poff += fdof-fcdof;
        }
        ierr = PetscSectionGetFieldDof(section, p, fields[f], &fdof);CHKERRQ(ierr);
        ierr = PetscSectionGetFieldConstraintDof(section, p, fields[f], &fcdof);CHKERRQ(ierr);
        for (fc = 0; fc < fdof-fcdof; ++fc, ++subOff) {
          subIndices[subOff] = goff+poff+fc;
        }
      }
    }
  }
  if (is) {ierr = ISCreateGeneral(PetscObjectComm((PetscObject)dm), subSize, subIndices, PETSC_OWN_POINTER, is);CHKERRQ(ierr);}
  if (subdm) {
    PetscSection subsection;
    PetscBool    haveNull = PETSC_FALSE;
    PetscInt     f, nf = 0;

    ierr = DMPlexClone(dm, subdm);CHKERRQ(ierr);
    ierr = PetscSectionCreateSubsection(section, numFields, fields, &subsection);CHKERRQ(ierr);
    ierr = DMSetDefaultSection(*subdm, subsection);CHKERRQ(ierr);
    ierr = PetscSectionDestroy(&subsection);CHKERRQ(ierr);
    for (f = 0; f < numFields; ++f) {
      (*subdm)->nullspaceConstructors[f] = dm->nullspaceConstructors[fields[f]];
      if ((*subdm)->nullspaceConstructors[f]) {
        haveNull = PETSC_TRUE;
        nf       = f;
      }
    }
    if (haveNull) {
      MatNullSpace nullSpace;

      ierr = (*(*subdm)->nullspaceConstructors[nf])(*subdm, nf, &nullSpace);CHKERRQ(ierr);
      ierr = PetscObjectCompose((PetscObject) *is, "nullspace", (PetscObject) nullSpace);CHKERRQ(ierr);
      ierr = MatNullSpaceDestroy(&nullSpace);CHKERRQ(ierr);
    }
    if (dm->fields) {
      if (nF != dm->numFields) SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "The number of DM fields %d does not match the number of Section fields %d", dm->numFields, nF);
      ierr = DMSetNumFields(*subdm, numFields);CHKERRQ(ierr);
      for (f = 0; f < numFields; ++f) {
        ierr = PetscObjectListDuplicate(dm->fields[fields[f]]->olist, &(*subdm)->fields[f]->olist);CHKERRQ(ierr);
      }
      if (numFields == 1) {
        MatNullSpace space;
        Mat          pmat;

        ierr = PetscObjectQuery((*subdm)->fields[0], "nullspace", (PetscObject*) &space);CHKERRQ(ierr);
        if (space) {ierr = PetscObjectCompose((PetscObject) *is, "nullspace", (PetscObject) space);CHKERRQ(ierr);}
        ierr = PetscObjectQuery((*subdm)->fields[0], "nearnullspace", (PetscObject*) &space);CHKERRQ(ierr);
        if (space) {ierr = PetscObjectCompose((PetscObject) *is, "nearnullspace", (PetscObject) space);CHKERRQ(ierr);}
        ierr = PetscObjectQuery((*subdm)->fields[0], "pmat", (PetscObject*) &pmat);CHKERRQ(ierr);
        if (pmat) {ierr = PetscObjectCompose((PetscObject) *is, "pmat", (PetscObject) pmat);CHKERRQ(ierr);}
      }
    }
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexSymmetrize"
/*@
  DMPlexSymmetrize - Creates support (out-edge) information from cone (in-edge) inoformation

  Not collective

  Input Parameter:
. mesh - The DMPlex

  Output Parameter:

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

  Level: beginner

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

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

    ierr = PetscSectionGetDof(mesh->coneSection, p, &dof);CHKERRQ(ierr);
    ierr = PetscSectionGetOffset(mesh->coneSection, p, &off);CHKERRQ(ierr);
    for (c = off; c < off+dof; ++c) {
      ierr = PetscSectionAddDof(mesh->supportSection, mesh->cones[c], 1);CHKERRQ(ierr);
    }
  }
  for (p = pStart; p < pEnd; ++p) {
    PetscInt dof;

    ierr = PetscSectionGetDof(mesh->supportSection, p, &dof);CHKERRQ(ierr);

    mesh->maxSupportSize = PetscMax(mesh->maxSupportSize, dof);
  }
  ierr = PetscSectionSetUp(mesh->supportSection);CHKERRQ(ierr);
  /* Calculate supports */
  ierr = PetscSectionGetStorageSize(mesh->supportSection, &supportSize);CHKERRQ(ierr);
  ierr = PetscMalloc(supportSize * sizeof(PetscInt), &mesh->supports);CHKERRQ(ierr);
  ierr = PetscMalloc((pEnd - pStart) * sizeof(PetscInt), &offsets);CHKERRQ(ierr);
  ierr = PetscMemzero(offsets, (pEnd - pStart) * sizeof(PetscInt));CHKERRQ(ierr);
  for (p = pStart; p < pEnd; ++p) {
    PetscInt dof, off, c;

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

      ierr = PetscSectionGetOffset(mesh->supportSection, q, &offS);CHKERRQ(ierr);

      mesh->supports[offS+offsets[q]] = p;
      ++offsets[q];
    }
  }
  ierr = PetscFree(offsets);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexSetDepth_Private"
PetscErrorCode DMPlexSetDepth_Private(DM dm, PetscInt p, PetscInt *depth)
{
  PetscInt       d;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = DMPlexGetLabelValue(dm, "depth", p, &d);CHKERRQ(ierr);
  if (d < 0) {
    /* We are guaranteed that the point has a cone since the depth was not yet set */
    const PetscInt *cone = NULL;
    PetscInt        dCone;

    ierr = DMPlexGetCone(dm, p, &cone);CHKERRQ(ierr);
    ierr = DMPlexSetDepth_Private(dm, cone[0], &dCone);CHKERRQ(ierr);
    d    = dCone+1;
    ierr = DMPlexSetLabelValue(dm, "depth", p, d);CHKERRQ(ierr);
  }
  *depth = d;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexStratify"
/*@
  DMPlexStratify - The Sieve DAG for most topologies is a graded poset (http://en.wikipedia.org/wiki/Graded_poset), and
  can be illustrated by Hasse Diagram (a http://en.wikipedia.org/wiki/Hasse_diagram). The strata group all points of the
  same grade, and this function calculates the strata. This grade can be seen as the height (or depth) of the point in
  the DAG.

  Not collective

  Input Parameter:
. mesh - The DMPlex

  Output Parameter:

  Notes:
  The normal association for the point grade is element dimension (or co-dimension). For instance, all vertices would
  have depth 0, and all edges depth 1. Likewise, all cells heights would have height 0, and all faces height 1.

  This should be called after all calls to DMPlexSymmetrize()

  Level: beginner

.seealso: DMPlexCreate(), DMPlexSymmetrize()
@*/
PetscErrorCode DMPlexStratify(DM dm)
{
  DM_Plex       *mesh = (DM_Plex*) dm->data;
  PetscInt       pStart, pEnd, p;
  PetscInt       numRoots = 0, numLeaves = 0;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  ierr = PetscLogEventBegin(DMPLEX_Stratify,dm,0,0,0);CHKERRQ(ierr);
  /* Calculate depth */
  ierr = PetscSectionGetChart(mesh->coneSection, &pStart, &pEnd);CHKERRQ(ierr);
  /* Initialize roots and count leaves */
  for (p = pStart; p < pEnd; ++p) {
    PetscInt coneSize, supportSize;

    ierr = DMPlexGetConeSize(dm, p, &coneSize);CHKERRQ(ierr);
    ierr = DMPlexGetSupportSize(dm, p, &supportSize);CHKERRQ(ierr);
    if (!coneSize && supportSize) {
      ++numRoots;
      ierr = DMPlexSetLabelValue(dm, "depth", p, 0);CHKERRQ(ierr);
    } else if (!supportSize && coneSize) {
      ++numLeaves;
    } else if (!supportSize && !coneSize) {
      /* Isolated points */
      ierr = DMPlexSetLabelValue(dm, "depth", p, 0);CHKERRQ(ierr);
    }
  }
  if (numRoots + numLeaves == (pEnd - pStart)) {
    for (p = pStart; p < pEnd; ++p) {
      PetscInt coneSize, supportSize;

      ierr = DMPlexGetConeSize(dm, p, &coneSize);CHKERRQ(ierr);
      ierr = DMPlexGetSupportSize(dm, p, &supportSize);CHKERRQ(ierr);
      if (!supportSize && coneSize) {
        ierr = DMPlexSetLabelValue(dm, "depth", p, 1);CHKERRQ(ierr);
      }
    }
  } else {
    /* This might be slow since lookup is not fast */
    for (p = pStart; p < pEnd; ++p) {
      PetscInt depth;

      ierr = DMPlexSetDepth_Private(dm, p, &depth);CHKERRQ(ierr);
    }
  }
  ierr = PetscLogEventEnd(DMPLEX_Stratify,dm,0,0,0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetJoin"
/*@C
  DMPlexGetJoin - Get an array for the join of the set of points

  Not Collective

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

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

  Level: intermediate

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

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

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidPointer(points, 2);
  PetscValidPointer(numCoveredPoints, 3);
  PetscValidPointer(coveredPoints, 4);
  ierr = DMGetWorkArray(dm, mesh->maxSupportSize, PETSC_INT, &join[0]);CHKERRQ(ierr);
  ierr = DMGetWorkArray(dm, mesh->maxSupportSize, PETSC_INT, &join[1]);CHKERRQ(ierr);
  /* Copy in support of first point */
  ierr = PetscSectionGetDof(mesh->supportSection, points[0], &dof);CHKERRQ(ierr);
  ierr = PetscSectionGetOffset(mesh->supportSection, points[0], &off);CHKERRQ(ierr);
  for (joinSize = 0; joinSize < dof; ++joinSize) {
    join[i][joinSize] = mesh->supports[off+joinSize];
  }
  /* Check each successive support */
  for (p = 1; p < numPoints; ++p) {
    PetscInt newJoinSize = 0;

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

      for (m = 0; m < joinSize; ++m) {
        if (point == join[i][m]) {
          join[1-i][newJoinSize++] = point;
          break;
        }
      }
    }
    joinSize = newJoinSize;
    i        = 1-i;
  }
  *numCoveredPoints = joinSize;
  *coveredPoints    = join[i];
  ierr              = DMRestoreWorkArray(dm, mesh->maxSupportSize, PETSC_INT, &join[1-i]);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexRestoreJoin"
/*@C
  DMPlexRestoreJoin - Restore an array for the join of the set of points

  Not Collective

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

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

  Level: intermediate

.keywords: mesh
.seealso: DMPlexGetJoin(), DMPlexGetFullJoin(), DMPlexGetMeet()
@*/
PetscErrorCode DMPlexRestoreJoin(DM dm, PetscInt numPoints, const PetscInt points[], PetscInt *numCoveredPoints, const PetscInt **coveredPoints)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidPointer(coveredPoints, 4);
  ierr = DMRestoreWorkArray(dm, 0, PETSC_INT, (void*) coveredPoints);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetFullJoin"
/*@C
  DMPlexGetFullJoin - Get an array for the join of the set of points

  Not Collective

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

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

  Level: intermediate

.keywords: mesh
.seealso: DMPlexGetJoin(), DMPlexRestoreJoin(), DMPlexGetMeet()
@*/
PetscErrorCode DMPlexGetFullJoin(DM dm, PetscInt numPoints, const PetscInt points[], PetscInt *numCoveredPoints, const PetscInt **coveredPoints)
{
  DM_Plex       *mesh = (DM_Plex*) dm->data;
  PetscInt      *offsets, **closures;
  PetscInt      *join[2];
  PetscInt       depth = 0, maxSize, joinSize = 0, i = 0;
  PetscInt       p, d, c, m;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidPointer(points, 2);
  PetscValidPointer(numCoveredPoints, 3);
  PetscValidPointer(coveredPoints, 4);

  ierr    = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
  ierr    = PetscMalloc(numPoints * sizeof(PetscInt*), &closures);CHKERRQ(ierr);
  ierr    = PetscMemzero(closures,numPoints*sizeof(PetscInt*));CHKERRQ(ierr);
  ierr    = DMGetWorkArray(dm, numPoints*(depth+2), PETSC_INT, &offsets);CHKERRQ(ierr);
  maxSize = PetscPowInt(mesh->maxSupportSize,depth);
  ierr    = DMGetWorkArray(dm, maxSize, PETSC_INT, &join[0]);CHKERRQ(ierr);
  ierr    = DMGetWorkArray(dm, maxSize, PETSC_INT, &join[1]);CHKERRQ(ierr);

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

    ierr = DMPlexGetTransitiveClosure(dm, points[p], PETSC_FALSE, &closureSize, &closures[p]);CHKERRQ(ierr);

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

      ierr = DMPlexGetDepthStratum(dm, d, &pStart, &pEnd);CHKERRQ(ierr);
      for (i = offsets[p*(depth+2)+d]; i < closureSize; ++i) {
        if ((pStart > closures[p][i*2]) || (pEnd <= closures[p][i*2])) {
          offsets[p*(depth+2)+d+1] = i;
          break;
        }
      }
      if (i == closureSize) offsets[p*(depth+2)+d+1] = i;
    }
    if (offsets[p*(depth+2)+depth+1] != closureSize) SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Total size of closure %D should be %D", offsets[p*(depth+2)+depth+1], closureSize);
  }
  for (d = 0; d < depth+1; ++d) {
    PetscInt dof;

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

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

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

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetMeet"
/*@C
  DMPlexGetMeet - Get an array for the meet of the set of points

  Not Collective

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

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

  Level: intermediate

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

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

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidPointer(points, 2);
  PetscValidPointer(numCoveringPoints, 3);
  PetscValidPointer(coveringPoints, 4);
  ierr = DMGetWorkArray(dm, mesh->maxConeSize, PETSC_INT, &meet[0]);CHKERRQ(ierr);
  ierr = DMGetWorkArray(dm, mesh->maxConeSize, PETSC_INT, &meet[1]);CHKERRQ(ierr);
  /* Copy in cone of first point */
  ierr = PetscSectionGetDof(mesh->coneSection, points[0], &dof);CHKERRQ(ierr);
  ierr = PetscSectionGetOffset(mesh->coneSection, points[0], &off);CHKERRQ(ierr);
  for (meetSize = 0; meetSize < dof; ++meetSize) {
    meet[i][meetSize] = mesh->cones[off+meetSize];
  }
  /* Check each successive cone */
  for (p = 1; p < numPoints; ++p) {
    PetscInt newMeetSize = 0;

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

      for (m = 0; m < meetSize; ++m) {
        if (point == meet[i][m]) {
          meet[1-i][newMeetSize++] = point;
          break;
        }
      }
    }
    meetSize = newMeetSize;
    i        = 1-i;
  }
  *numCoveringPoints = meetSize;
  *coveringPoints    = meet[i];
  ierr               = DMRestoreWorkArray(dm, mesh->maxConeSize, PETSC_INT, &meet[1-i]);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexRestoreMeet"
/*@C
  DMPlexRestoreMeet - Restore an array for the meet of the set of points

  Not Collective

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

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

  Level: intermediate

.keywords: mesh
.seealso: DMPlexGetMeet(), DMPlexGetFullMeet(), DMPlexGetJoin()
@*/
PetscErrorCode DMPlexRestoreMeet(DM dm, PetscInt numPoints, const PetscInt points[], PetscInt *numCoveredPoints, const PetscInt **coveredPoints)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidPointer(coveredPoints, 4);
  ierr = DMRestoreWorkArray(dm, 0, PETSC_INT, (void*) coveredPoints);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetFullMeet"
/*@C
  DMPlexGetFullMeet - Get an array for the meet of the set of points

  Not Collective

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

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

  Level: intermediate

.keywords: mesh
.seealso: DMPlexGetMeet(), DMPlexRestoreMeet(), DMPlexGetJoin()
@*/
PetscErrorCode DMPlexGetFullMeet(DM dm, PetscInt numPoints, const PetscInt points[], PetscInt *numCoveredPoints, const PetscInt **coveredPoints)
{
  DM_Plex       *mesh = (DM_Plex*) dm->data;
  PetscInt      *offsets, **closures;
  PetscInt      *meet[2];
  PetscInt       height = 0, maxSize, meetSize = 0, i = 0;
  PetscInt       p, h, c, m;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidPointer(points, 2);
  PetscValidPointer(numCoveredPoints, 3);
  PetscValidPointer(coveredPoints, 4);

  ierr    = DMPlexGetDepth(dm, &height);CHKERRQ(ierr);
  ierr    = PetscMalloc(numPoints * sizeof(PetscInt*), &closures);CHKERRQ(ierr);
  ierr    = DMGetWorkArray(dm, numPoints*(height+2), PETSC_INT, &offsets);CHKERRQ(ierr);
  maxSize = PetscPowInt(mesh->maxConeSize,height);
  ierr    = DMGetWorkArray(dm, maxSize, PETSC_INT, &meet[0]);CHKERRQ(ierr);
  ierr    = DMGetWorkArray(dm, maxSize, PETSC_INT, &meet[1]);CHKERRQ(ierr);

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

    ierr = DMPlexGetTransitiveClosure(dm, points[p], PETSC_TRUE, &closureSize, &closures[p]);CHKERRQ(ierr);

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

      ierr = DMPlexGetHeightStratum(dm, h, &pStart, &pEnd);CHKERRQ(ierr);
      for (i = offsets[p*(height+2)+h]; i < closureSize; ++i) {
        if ((pStart > closures[p][i*2]) || (pEnd <= closures[p][i*2])) {
          offsets[p*(height+2)+h+1] = i;
          break;
        }
      }
      if (i == closureSize) offsets[p*(height+2)+h+1] = i;
    }
    if (offsets[p*(height+2)+height+1] != closureSize) SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Total size of closure %D should be %D", offsets[p*(height+2)+height+1], closureSize);
  }
  for (h = 0; h < height+1; ++h) {
    PetscInt dof;

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

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

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

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetNumFaceVertices_Internal"
PetscErrorCode DMPlexGetNumFaceVertices_Internal(DM dm, PetscInt cellDim, PetscInt numCorners, PetscInt *numFaceVertices)
{
  MPI_Comm       comm;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscObjectGetComm((PetscObject)dm,&comm);CHKERRQ(ierr);
  PetscValidPointer(numFaceVertices,3);
  switch (cellDim) {
  case 0:
    *numFaceVertices = 0;
    break;
  case 1:
    *numFaceVertices = 1;
    break;
  case 2:
    switch (numCorners) {
    case 3: /* triangle */
      *numFaceVertices = 2; /* Edge has 2 vertices */
      break;
    case 4: /* quadrilateral */
      *numFaceVertices = 2; /* Edge has 2 vertices */
      break;
    case 6: /* quadratic triangle, tri and quad cohesive Lagrange cells */
      *numFaceVertices = 3; /* Edge has 3 vertices */
      break;
    case 9: /* quadratic quadrilateral, quadratic quad cohesive Lagrange cells */
      *numFaceVertices = 3; /* Edge has 3 vertices */
      break;
    default:
      SETERRQ2(comm, PETSC_ERR_ARG_OUTOFRANGE, "Invalid number of face corners %d for dimension %d", numCorners, cellDim);
    }
    break;
  case 3:
    switch (numCorners) {
    case 4: /* tetradehdron */
      *numFaceVertices = 3; /* Face has 3 vertices */
      break;
    case 6: /* tet cohesive cells */
      *numFaceVertices = 4; /* Face has 4 vertices */
      break;
    case 8: /* hexahedron */
      *numFaceVertices = 4; /* Face has 4 vertices */
      break;
    case 9: /* tet cohesive Lagrange cells */
      *numFaceVertices = 6; /* Face has 6 vertices */
      break;
    case 10: /* quadratic tetrahedron */
      *numFaceVertices = 6; /* Face has 6 vertices */
      break;
    case 12: /* hex cohesive Lagrange cells */
      *numFaceVertices = 6; /* Face has 6 vertices */
      break;
    case 18: /* quadratic tet cohesive Lagrange cells */
      *numFaceVertices = 6; /* Face has 6 vertices */
      break;
    case 27: /* quadratic hexahedron, quadratic hex cohesive Lagrange cells */
      *numFaceVertices = 9; /* Face has 9 vertices */
      break;
    default:
      SETERRQ2(comm, PETSC_ERR_ARG_OUTOFRANGE, "Invalid number of face corners %d for dimension %d", numCorners, cellDim);
    }
    break;
  default:
    SETERRQ1(comm, PETSC_ERR_ARG_OUTOFRANGE, "Invalid cell dimension %d", cellDim);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexCreateNeighborCSR"
PetscErrorCode DMPlexCreateNeighborCSR(DM dm, PetscInt cellHeight, PetscInt *numVertices, PetscInt **offsets, PetscInt **adjacency)
{
  const PetscInt maxFaceCases = 30;
  PetscInt       numFaceCases = 0;
  PetscInt       numFaceVertices[30]; /* maxFaceCases, C89 sucks sucks sucks */
  PetscInt      *off, *adj;
  PetscInt      *neighborCells, *tmpClosure;
  PetscInt       maxConeSize, maxSupportSize, maxClosure, maxNeighbors;
  PetscInt       dim, cellDim, depth = 0, faceDepth, cStart, cEnd, c, numCells, cell;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  /* For parallel partitioning, I think you have to communicate supports */
  ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
  cellDim = dim - cellHeight;
  ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
  ierr = DMPlexGetHeightStratum(dm, cellHeight, &cStart, &cEnd);CHKERRQ(ierr);
  ierr = DMPlexGetMaxSizes(dm, &maxConeSize, &maxSupportSize);CHKERRQ(ierr);
  if (cEnd - cStart == 0) {
    if (numVertices) *numVertices = 0;
    if (offsets)   *offsets   = NULL;
    if (adjacency) *adjacency = NULL;
    PetscFunctionReturn(0);
  }
  numCells  = cEnd - cStart;
  faceDepth = depth - cellHeight;
  /* Setup face recognition */
  if (faceDepth == 1) {
    PetscInt cornersSeen[30] = {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}; /* Could use PetscBT */

    for (c = cStart; c < cEnd; ++c) {
      PetscInt corners;

      ierr = DMPlexGetConeSize(dm, c, &corners);CHKERRQ(ierr);
      if (!cornersSeen[corners]) {
        PetscInt nFV;

        if (numFaceCases >= maxFaceCases) SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Exceeded maximum number of face recognition cases");
        cornersSeen[corners] = 1;

        ierr = DMPlexGetNumFaceVertices_Internal(dm, cellDim, corners, &nFV);CHKERRQ(ierr);

        numFaceVertices[numFaceCases++] = nFV;
      }
    }
  }
  maxClosure   = 2*PetscMax(PetscPowInt(maxConeSize,depth),PetscPowInt(maxSupportSize,depth));
  maxNeighbors = PetscPowInt(maxConeSize,depth)*PetscPowInt(maxSupportSize,depth);
  ierr         = PetscMalloc2(maxNeighbors,PetscInt,&neighborCells,maxClosure,PetscInt,&tmpClosure);CHKERRQ(ierr);
  ierr         = PetscMalloc((numCells+1) * sizeof(PetscInt), &off);CHKERRQ(ierr);
  ierr         = PetscMemzero(off, (numCells+1) * sizeof(PetscInt));CHKERRQ(ierr);
  /* Count neighboring cells */
  for (cell = cStart; cell < cEnd; ++cell) {
    PetscInt numNeighbors = maxNeighbors, n;

    ierr = DMPlexGetAdjacencySingleLevel_Private(dm, cell, PETSC_TRUE, tmpClosure, &numNeighbors, neighborCells);CHKERRQ(ierr);
    /* Get meet with each cell, and check with recognizer (could optimize to check each pair only once) */
    for (n = 0; n < numNeighbors; ++n) {
      PetscInt        cellPair[2];
      PetscBool       found    = faceDepth > 1 ? PETSC_TRUE : PETSC_FALSE;
      PetscInt        meetSize = 0;
      const PetscInt *meet    = NULL;

      cellPair[0] = cell; cellPair[1] = neighborCells[n];
      if (cellPair[0] == cellPair[1]) continue;
      if (!found) {
        ierr = DMPlexGetMeet(dm, 2, cellPair, &meetSize, &meet);CHKERRQ(ierr);
        if (meetSize) {
          PetscInt f;

          for (f = 0; f < numFaceCases; ++f) {
            if (numFaceVertices[f] == meetSize) {
              found = PETSC_TRUE;
              break;
            }
          }
        }
        ierr = DMPlexRestoreMeet(dm, 2, cellPair, &meetSize, &meet);CHKERRQ(ierr);
      }
      if (found) ++off[cell-cStart+1];
    }
  }
  /* Prefix sum */
  for (cell = 1; cell <= numCells; ++cell) off[cell] += off[cell-1];

  if (adjacency) {
    ierr = PetscMalloc(off[numCells] * sizeof(PetscInt), &adj);CHKERRQ(ierr);
    /* Get neighboring cells */
    for (cell = cStart; cell < cEnd; ++cell) {
      PetscInt numNeighbors = maxNeighbors, n;
      PetscInt cellOffset   = 0;

      ierr = DMPlexGetAdjacencySingleLevel_Private(dm, cell, PETSC_TRUE, tmpClosure, &numNeighbors, neighborCells);CHKERRQ(ierr);
      /* Get meet with each cell, and check with recognizer (could optimize to check each pair only once) */
      for (n = 0; n < numNeighbors; ++n) {
        PetscInt        cellPair[2];
        PetscBool       found    = faceDepth > 1 ? PETSC_TRUE : PETSC_FALSE;
        PetscInt        meetSize = 0;
        const PetscInt *meet    = NULL;

        cellPair[0] = cell; cellPair[1] = neighborCells[n];
        if (cellPair[0] == cellPair[1]) continue;
        if (!found) {
          ierr = DMPlexGetMeet(dm, 2, cellPair, &meetSize, &meet);CHKERRQ(ierr);
          if (meetSize) {
            PetscInt f;

            for (f = 0; f < numFaceCases; ++f) {
              if (numFaceVertices[f] == meetSize) {
                found = PETSC_TRUE;
                break;
              }
            }
          }
          ierr = DMPlexRestoreMeet(dm, 2, cellPair, &meetSize, &meet);CHKERRQ(ierr);
        }
        if (found) {
          adj[off[cell-cStart]+cellOffset] = neighborCells[n];
          ++cellOffset;
        }
      }
    }
  }
  ierr = PetscFree2(neighborCells,tmpClosure);CHKERRQ(ierr);
  if (numVertices) *numVertices = numCells;
  if (offsets)   *offsets   = off;
  if (adjacency) *adjacency = adj;
  PetscFunctionReturn(0);
}

#if defined(PETSC_HAVE_CHACO)
#if defined(PETSC_HAVE_UNISTD_H)
#include <unistd.h>
#endif
/* Chaco does not have an include file */
PETSC_EXTERN int interface(int nvtxs, int *start, int *adjacency, int *vwgts,
                       float *ewgts, float *x, float *y, float *z, char *outassignname,
                       char *outfilename, short *assignment, int architecture, int ndims_tot,
                       int mesh_dims[3], double *goal, int global_method, int local_method,
                       int rqi_flag, int vmax, int ndims, double eigtol, long seed);

extern int FREE_GRAPH;

#undef __FUNCT__
#define __FUNCT__ "DMPlexPartition_Chaco"
PetscErrorCode DMPlexPartition_Chaco(DM dm, PetscInt numVertices, PetscInt start[], PetscInt adjacency[], PetscSection *partSection, IS *partition)
{
  enum {DEFAULT_METHOD = 1, INERTIAL_METHOD = 3};
  MPI_Comm       comm;
  int            nvtxs          = numVertices; /* number of vertices in full graph */
  int           *vwgts          = NULL;   /* weights for all vertices */
  float         *ewgts          = NULL;   /* weights for all edges */
  float         *x              = NULL, *y = NULL, *z = NULL; /* coordinates for inertial method */
  char          *outassignname  = NULL;   /*  name of assignment output file */
  char          *outfilename    = NULL;   /* output file name */
  int            architecture   = 1;      /* 0 => hypercube, d => d-dimensional mesh */
  int            ndims_tot      = 0;      /* total number of cube dimensions to divide */
  int            mesh_dims[3];            /* dimensions of mesh of processors */
  double        *goal          = NULL;    /* desired set sizes for each set */
  int            global_method = 1;       /* global partitioning algorithm */
  int            local_method  = 1;       /* local partitioning algorithm */
  int            rqi_flag      = 0;       /* should I use RQI/Symmlq eigensolver? */
  int            vmax          = 200;     /* how many vertices to coarsen down to? */
  int            ndims         = 1;       /* number of eigenvectors (2^d sets) */
  double         eigtol        = 0.001;   /* tolerance on eigenvectors */
  long           seed          = 123636512; /* for random graph mutations */
  short int     *assignment;              /* Output partition */
  int            fd_stdout, fd_pipe[2];
  PetscInt      *points;
  PetscMPIInt    commSize;
  int            i, v, p;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscObjectGetComm((PetscObject)dm,&comm);CHKERRQ(ierr);
  ierr = MPI_Comm_size(comm, &commSize);CHKERRQ(ierr);
  if (!numVertices) {
    ierr = PetscSectionCreate(comm, partSection);CHKERRQ(ierr);
    ierr = PetscSectionSetChart(*partSection, 0, commSize);CHKERRQ(ierr);
    ierr = PetscSectionSetUp(*partSection);CHKERRQ(ierr);
    ierr = ISCreateGeneral(comm, 0, NULL, PETSC_OWN_POINTER, partition);CHKERRQ(ierr);
    PetscFunctionReturn(0);
  }
  FREE_GRAPH = 0;                         /* Do not let Chaco free my memory */
  for (i = 0; i < start[numVertices]; ++i) ++adjacency[i];

  if (global_method == INERTIAL_METHOD) {
    /* manager.createCellCoordinates(nvtxs, &x, &y, &z); */
    SETERRQ(comm, PETSC_ERR_SUP, "Inertial partitioning not yet supported");
  }
  mesh_dims[0] = commSize;
  mesh_dims[1] = 1;
  mesh_dims[2] = 1;
  ierr = PetscMalloc(nvtxs * sizeof(short int), &assignment);CHKERRQ(ierr);
  /* Chaco outputs to stdout. We redirect this to a buffer. */
  /* TODO: check error codes for UNIX calls */
#if defined(PETSC_HAVE_UNISTD_H)
  {
    int piperet;
    piperet = pipe(fd_pipe);
    if (piperet) SETERRQ(comm,PETSC_ERR_SYS,"Could not create pipe");
    fd_stdout = dup(1);
    close(1);
    dup2(fd_pipe[1], 1);
  }
#endif
  ierr = interface(nvtxs, (int*) start, (int*) adjacency, vwgts, ewgts, x, y, z, outassignname, outfilename,
                   assignment, architecture, ndims_tot, mesh_dims, goal, global_method, local_method, rqi_flag,
                   vmax, ndims, eigtol, seed);
#if defined(PETSC_HAVE_UNISTD_H)
  {
    char msgLog[10000];
    int  count;

    fflush(stdout);
    count = read(fd_pipe[0], msgLog, (10000-1)*sizeof(char));
    if (count < 0) count = 0;
    msgLog[count] = 0;
    close(1);
    dup2(fd_stdout, 1);
    close(fd_stdout);
    close(fd_pipe[0]);
    close(fd_pipe[1]);
    if (ierr) SETERRQ1(comm, PETSC_ERR_LIB, "Error in Chaco library: %s", msgLog);
  }
#endif
  /* Convert to PetscSection+IS */
  ierr = PetscSectionCreate(comm, partSection);CHKERRQ(ierr);
  ierr = PetscSectionSetChart(*partSection, 0, commSize);CHKERRQ(ierr);
  for (v = 0; v < nvtxs; ++v) {
    ierr = PetscSectionAddDof(*partSection, assignment[v], 1);CHKERRQ(ierr);
  }
  ierr = PetscSectionSetUp(*partSection);CHKERRQ(ierr);
  ierr = PetscMalloc(nvtxs * sizeof(PetscInt), &points);CHKERRQ(ierr);
  for (p = 0, i = 0; p < commSize; ++p) {
    for (v = 0; v < nvtxs; ++v) {
      if (assignment[v] == p) points[i++] = v;
    }
  }
  if (i != nvtxs) SETERRQ2(comm, PETSC_ERR_PLIB, "Number of points %D should be %D", i, nvtxs);
  ierr = ISCreateGeneral(comm, nvtxs, points, PETSC_OWN_POINTER, partition);CHKERRQ(ierr);
  if (global_method == INERTIAL_METHOD) {
    /* manager.destroyCellCoordinates(nvtxs, &x, &y, &z); */
  }
  ierr = PetscFree(assignment);CHKERRQ(ierr);
  for (i = 0; i < start[numVertices]; ++i) --adjacency[i];
  PetscFunctionReturn(0);
}
#endif

#if defined(PETSC_HAVE_PARMETIS)
#undef __FUNCT__
#define __FUNCT__ "DMPlexPartition_ParMetis"
PetscErrorCode DMPlexPartition_ParMetis(DM dm, PetscInt numVertices, PetscInt start[], PetscInt adjacency[], PetscSection *partSection, IS *partition)
{
  PetscFunctionBegin;
  SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "ParMetis not yet supported");
  PetscFunctionReturn(0);
}
#endif

#undef __FUNCT__
#define __FUNCT__ "DMPlexEnlargePartition"
/* Expand the partition by BFS on the adjacency graph */
PetscErrorCode DMPlexEnlargePartition(DM dm, const PetscInt start[], const PetscInt adjacency[], PetscSection origPartSection, IS origPartition, PetscSection *partSection, IS *partition)
{
  PetscHashI      h;
  const PetscInt *points;
  PetscInt      **tmpPoints, *newPoints, totPoints = 0;
  PetscInt        pStart, pEnd, part, q;
  PetscErrorCode  ierr;

  PetscFunctionBegin;
  PetscHashICreate(h);
  ierr = PetscSectionCreate(PetscObjectComm((PetscObject)dm), partSection);CHKERRQ(ierr);
  ierr = PetscSectionGetChart(origPartSection, &pStart, &pEnd);CHKERRQ(ierr);
  ierr = PetscSectionSetChart(*partSection, pStart, pEnd);CHKERRQ(ierr);
  ierr = ISGetIndices(origPartition, &points);CHKERRQ(ierr);
  ierr = PetscMalloc((pEnd - pStart) * sizeof(PetscInt*), &tmpPoints);CHKERRQ(ierr);
  for (part = pStart; part < pEnd; ++part) {
    PetscInt numPoints, nP, numNewPoints, off, p, n = 0;

    PetscHashIClear(h);
    ierr = PetscSectionGetDof(origPartSection, part, &numPoints);CHKERRQ(ierr);
    ierr = PetscSectionGetOffset(origPartSection, part, &off);CHKERRQ(ierr);
    /* Add all existing points to h */
    for (p = 0; p < numPoints; ++p) {
      const PetscInt point = points[off+p];
      PetscHashIAdd(h, point, 1);
    }
    PetscHashISize(h, nP);
    if (nP != numPoints) SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Invalid partition has %d points, but only %d were unique", numPoints, nP);
    /* Add all points in next BFS level */
    /*   TODO We are brute forcing here, but could check the adjacency size to find the boundary */
    for (p = 0; p < numPoints; ++p) {
      const PetscInt point = points[off+p];
      PetscInt       s     = start[point], e = start[point+1], a;

      for (a = s; a < e; ++a) PetscHashIAdd(h, adjacency[a], 1);
    }
    PetscHashISize(h, numNewPoints);
    ierr = PetscSectionSetDof(*partSection, part, numNewPoints);CHKERRQ(ierr);
    ierr = PetscMalloc(numNewPoints * sizeof(PetscInt), &tmpPoints[part]);CHKERRQ(ierr);
    if (numNewPoints) PetscHashIGetKeys(h, n, tmpPoints[part]); /* Should not need this conditional */
    totPoints += numNewPoints;
  }
  ierr = ISRestoreIndices(origPartition, &points);CHKERRQ(ierr);
  PetscHashIDestroy(h);
  ierr = PetscSectionSetUp(*partSection);CHKERRQ(ierr);
  ierr = PetscMalloc(totPoints * sizeof(PetscInt), &newPoints);CHKERRQ(ierr);
  for (part = pStart, q = 0; part < pEnd; ++part) {
    PetscInt numPoints, p;

    ierr = PetscSectionGetDof(*partSection, part, &numPoints);CHKERRQ(ierr);
    for (p = 0; p < numPoints; ++p, ++q) newPoints[q] = tmpPoints[part][p];
    ierr = PetscFree(tmpPoints[part]);CHKERRQ(ierr);
  }
  ierr = PetscFree(tmpPoints);CHKERRQ(ierr);
  ierr = ISCreateGeneral(PetscObjectComm((PetscObject)dm), totPoints, newPoints, PETSC_OWN_POINTER, partition);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexCreatePartition"
/*
  DMPlexCreatePartition - Create a non-overlapping partition of the points at the given height

  Collective on DM

  Input Parameters:
  + dm - The DM
  . height - The height for points in the partition
  - enlarge - Expand each partition with neighbors

  Output Parameters:
  + partSection - The PetscSection giving the division of points by partition
  . partition - The list of points by partition
  . origPartSection - If enlarge is true, the PetscSection giving the division of points before enlarging by partition, otherwise NULL
  - origPartition - If enlarge is true, the list of points before enlarging by partition, otherwise NULL

  Level: developer

.seealso DMPlexDistribute()
*/
PetscErrorCode DMPlexCreatePartition(DM dm, PetscInt height, PetscBool enlarge, PetscSection *partSection, IS *partition, PetscSection *origPartSection, IS *origPartition)
{
  PetscMPIInt    size;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = MPI_Comm_size(PetscObjectComm((PetscObject)dm), &size);CHKERRQ(ierr);

  *origPartSection = NULL;
  *origPartition   = NULL;
  if (size == 1) {
    PetscInt *points;
    PetscInt  cStart, cEnd, c;

    ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
    ierr = PetscSectionCreate(PetscObjectComm((PetscObject)dm), partSection);CHKERRQ(ierr);
    ierr = PetscSectionSetChart(*partSection, 0, size);CHKERRQ(ierr);
    ierr = PetscSectionSetDof(*partSection, 0, cEnd-cStart);CHKERRQ(ierr);
    ierr = PetscSectionSetUp(*partSection);CHKERRQ(ierr);
    ierr = PetscMalloc((cEnd - cStart) * sizeof(PetscInt), &points);CHKERRQ(ierr);
    for (c = cStart; c < cEnd; ++c) points[c] = c;
    ierr = ISCreateGeneral(PetscObjectComm((PetscObject)dm), cEnd-cStart, points, PETSC_OWN_POINTER, partition);CHKERRQ(ierr);
    PetscFunctionReturn(0);
  }
  if (height == 0) {
    PetscInt  numVertices;
    PetscInt *start     = NULL;
    PetscInt *adjacency = NULL;

    ierr = DMPlexCreateNeighborCSR(dm, 0, &numVertices, &start, &adjacency);CHKERRQ(ierr);
    if (1) {
#if defined(PETSC_HAVE_CHACO)
      ierr = DMPlexPartition_Chaco(dm, numVertices, start, adjacency, partSection, partition);CHKERRQ(ierr);
#endif
    } else {
#if defined(PETSC_HAVE_PARMETIS)
      ierr = DMPlexPartition_ParMetis(dm, numVertices, start, adjacency, partSection, partition);CHKERRQ(ierr);
#endif
    }
    if (enlarge) {
      *origPartSection = *partSection;
      *origPartition   = *partition;

      ierr = DMPlexEnlargePartition(dm, start, adjacency, *origPartSection, *origPartition, partSection, partition);CHKERRQ(ierr);
    }
    ierr = PetscFree(start);CHKERRQ(ierr);
    ierr = PetscFree(adjacency);CHKERRQ(ierr);
# if 0
  } else if (height == 1) {
    /* Build the dual graph for faces and partition the hypergraph */
    PetscInt numEdges;

    buildFaceCSRV(mesh, mesh->getFactory()->getNumbering(mesh, mesh->depth()-1), &numEdges, &start, &adjacency, GraphPartitioner::zeroBase());
    GraphPartitioner().partition(numEdges, start, adjacency, partition, manager);
    destroyCSR(numEdges, start, adjacency);
#endif
  } else SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "Invalid partition height %D", height);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexCreatePartitionClosure"
PetscErrorCode DMPlexCreatePartitionClosure(DM dm, PetscSection pointSection, IS pointPartition, PetscSection *section, IS *partition)
{
  /* const PetscInt  height = 0; */
  const PetscInt *partArray;
  PetscInt       *allPoints, *partPoints = NULL;
  PetscInt        rStart, rEnd, rank, maxPartSize = 0, newSize;
  PetscErrorCode  ierr;

  PetscFunctionBegin;
  ierr = PetscSectionGetChart(pointSection, &rStart, &rEnd);CHKERRQ(ierr);
  ierr = ISGetIndices(pointPartition, &partArray);CHKERRQ(ierr);
  ierr = PetscSectionCreate(PetscObjectComm((PetscObject)dm), section);CHKERRQ(ierr);
  ierr = PetscSectionSetChart(*section, rStart, rEnd);CHKERRQ(ierr);
  for (rank = rStart; rank < rEnd; ++rank) {
    PetscInt partSize = 0;
    PetscInt numPoints, offset, p;

    ierr = PetscSectionGetDof(pointSection, rank, &numPoints);CHKERRQ(ierr);
    ierr = PetscSectionGetOffset(pointSection, rank, &offset);CHKERRQ(ierr);
    for (p = 0; p < numPoints; ++p) {
      PetscInt  point   = partArray[offset+p], closureSize, c;
      PetscInt *closure = NULL;

      /* TODO Include support for height > 0 case */
      ierr = DMPlexGetTransitiveClosure(dm, point, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
      /* Merge into existing points */
      if (partSize+closureSize > maxPartSize) {
        PetscInt *tmpPoints;

        maxPartSize = PetscMax(partSize+closureSize, 2*maxPartSize);
        ierr = PetscMalloc(maxPartSize * sizeof(PetscInt), &tmpPoints);CHKERRQ(ierr);
        ierr = PetscMemcpy(tmpPoints, partPoints, partSize * sizeof(PetscInt));CHKERRQ(ierr);
        ierr = PetscFree(partPoints);CHKERRQ(ierr);

        partPoints = tmpPoints;
      }
      for (c = 0; c < closureSize; ++c) partPoints[partSize+c] = closure[c*2];
      partSize += closureSize;

      ierr = PetscSortRemoveDupsInt(&partSize, partPoints);CHKERRQ(ierr);
      ierr = DMPlexRestoreTransitiveClosure(dm, point, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
    }
    ierr = PetscSectionSetDof(*section, rank, partSize);CHKERRQ(ierr);
  }
  ierr = PetscSectionSetUp(*section);CHKERRQ(ierr);
  ierr = PetscSectionGetStorageSize(*section, &newSize);CHKERRQ(ierr);
  ierr = PetscMalloc(newSize * sizeof(PetscInt), &allPoints);CHKERRQ(ierr);

  for (rank = rStart; rank < rEnd; ++rank) {
    PetscInt partSize = 0, newOffset;
    PetscInt numPoints, offset, p;

    ierr = PetscSectionGetDof(pointSection, rank, &numPoints);CHKERRQ(ierr);
    ierr = PetscSectionGetOffset(pointSection, rank, &offset);CHKERRQ(ierr);
    for (p = 0; p < numPoints; ++p) {
      PetscInt  point   = partArray[offset+p], closureSize, c;
      PetscInt *closure = NULL;

      /* TODO Include support for height > 0 case */
      ierr = DMPlexGetTransitiveClosure(dm, point, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
      /* Merge into existing points */
      for (c = 0; c < closureSize; ++c) partPoints[partSize+c] = closure[c*2];
      partSize += closureSize;

      ierr = PetscSortRemoveDupsInt(&partSize, partPoints);CHKERRQ(ierr);
      ierr = DMPlexRestoreTransitiveClosure(dm, point, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
    }
    ierr = PetscSectionGetOffset(*section, rank, &newOffset);CHKERRQ(ierr);
    ierr = PetscMemcpy(&allPoints[newOffset], partPoints, partSize * sizeof(PetscInt));CHKERRQ(ierr);
  }
  ierr = ISRestoreIndices(pointPartition, &partArray);CHKERRQ(ierr);
  ierr = PetscFree(partPoints);CHKERRQ(ierr);
  ierr = ISCreateGeneral(PetscObjectComm((PetscObject)dm), newSize, allPoints, PETSC_OWN_POINTER, partition);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexDistributeField"
/*
  Input Parameters:
. originalSection
, originalVec

  Output Parameters:
. newSection
. newVec
*/
PetscErrorCode DMPlexDistributeField(DM dm, PetscSF pointSF, PetscSection originalSection, Vec originalVec, PetscSection newSection, Vec newVec)
{
  PetscSF        fieldSF;
  PetscInt      *remoteOffsets, fieldSize;
  PetscScalar   *originalValues, *newValues;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscSFDistributeSection(pointSF, originalSection, &remoteOffsets, newSection);CHKERRQ(ierr);

  ierr = PetscSectionGetStorageSize(newSection, &fieldSize);CHKERRQ(ierr);
  ierr = VecSetSizes(newVec, fieldSize, PETSC_DETERMINE);CHKERRQ(ierr);
  ierr = VecSetFromOptions(newVec);CHKERRQ(ierr);

  ierr = VecGetArray(originalVec, &originalValues);CHKERRQ(ierr);
  ierr = VecGetArray(newVec, &newValues);CHKERRQ(ierr);
  ierr = PetscSFCreateSectionSF(pointSF, originalSection, remoteOffsets, newSection, &fieldSF);CHKERRQ(ierr);
  ierr = PetscSFBcastBegin(fieldSF, MPIU_SCALAR, originalValues, newValues);CHKERRQ(ierr);
  ierr = PetscSFBcastEnd(fieldSF, MPIU_SCALAR, originalValues, newValues);CHKERRQ(ierr);
  ierr = PetscSFDestroy(&fieldSF);CHKERRQ(ierr);
  ierr = VecRestoreArray(newVec, &newValues);CHKERRQ(ierr);
  ierr = VecRestoreArray(originalVec, &originalValues);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexDistribute"
/*@C
  DMPlexDistribute - Distributes the mesh and any associated sections.

  Not Collective

  Input Parameter:
+ dm  - The original DMPlex object
. partitioner - The partitioning package, or NULL for the default
- overlap - The overlap of partitions, 0 is the default

  Output Parameter:
. parallelMesh - The distributed DMPlex object, or NULL

  Note: If the mesh was not distributed, the return value is NULL

  Level: intermediate

.keywords: mesh, elements
.seealso: DMPlexCreate(), DMPlexDistributeByFace()
@*/
PetscErrorCode DMPlexDistribute(DM dm, const char partitioner[], PetscInt overlap, DM *dmParallel)
{
  DM_Plex               *mesh   = (DM_Plex*) dm->data, *pmesh;
  MPI_Comm               comm;
  const PetscInt         height = 0;
  PetscInt               dim, numRemoteRanks;
  IS                     origCellPart,        cellPart,        part;
  PetscSection           origCellPartSection, cellPartSection, partSection;
  PetscSFNode           *remoteRanks;
  PetscSF                partSF, pointSF, coneSF;
  ISLocalToGlobalMapping renumbering;
  PetscSection           originalConeSection, newConeSection;
  PetscInt              *remoteOffsets;
  PetscInt              *cones, *newCones, newConesSize;
  PetscBool              flg;
  PetscMPIInt            rank, numProcs, p;
  PetscErrorCode         ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidPointer(dmParallel,4);

  ierr = PetscLogEventBegin(DMPLEX_Distribute,dm,0,0,0);CHKERRQ(ierr);
  ierr = PetscObjectGetComm((PetscObject)dm,&comm);CHKERRQ(ierr);
  ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
  ierr = MPI_Comm_size(comm, &numProcs);CHKERRQ(ierr);

  *dmParallel = NULL;
  if (numProcs == 1) PetscFunctionReturn(0);

  ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
  /* Create cell partition - We need to rewrite to use IS, use the MatPartition stuff */
  if (overlap > 1) SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Overlap > 1 not yet implemented");
  ierr = DMPlexCreatePartition(dm, height, overlap > 0 ? PETSC_TRUE : PETSC_FALSE, &cellPartSection, &cellPart, &origCellPartSection, &origCellPart);CHKERRQ(ierr);
  /* Create SF assuming a serial partition for all processes: Could check for IS length here */
  if (!rank) numRemoteRanks = numProcs;
  else       numRemoteRanks = 0;
  ierr = PetscMalloc(numRemoteRanks * sizeof(PetscSFNode), &remoteRanks);CHKERRQ(ierr);
  for (p = 0; p < numRemoteRanks; ++p) {
    remoteRanks[p].rank  = p;
    remoteRanks[p].index = 0;
  }
  ierr = PetscSFCreate(comm, &partSF);CHKERRQ(ierr);
  ierr = PetscSFSetGraph(partSF, 1, numRemoteRanks, NULL, PETSC_OWN_POINTER, remoteRanks, PETSC_OWN_POINTER);CHKERRQ(ierr);
  ierr = PetscOptionsHasName(((PetscObject) dm)->prefix, "-partition_view", &flg);CHKERRQ(ierr);
  if (flg) {
    ierr = PetscPrintf(comm, "Cell Partition:\n");CHKERRQ(ierr);
    ierr = PetscSectionView(cellPartSection, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
    ierr = ISView(cellPart, NULL);CHKERRQ(ierr);
    if (origCellPart) {
      ierr = PetscPrintf(comm, "Original Cell Partition:\n");CHKERRQ(ierr);
      ierr = PetscSectionView(origCellPartSection, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
      ierr = ISView(origCellPart, NULL);CHKERRQ(ierr);
    }
    ierr = PetscSFView(partSF, NULL);CHKERRQ(ierr);
  }
  /* Close the partition over the mesh */
  ierr = DMPlexCreatePartitionClosure(dm, cellPartSection, cellPart, &partSection, &part);CHKERRQ(ierr);
  ierr = ISDestroy(&cellPart);CHKERRQ(ierr);
  ierr = PetscSectionDestroy(&cellPartSection);CHKERRQ(ierr);
  /* Create new mesh */
  ierr  = DMPlexCreate(comm, dmParallel);CHKERRQ(ierr);
  ierr  = DMPlexSetDimension(*dmParallel, dim);CHKERRQ(ierr);
  ierr  = PetscObjectSetName((PetscObject) *dmParallel, "Parallel Mesh");CHKERRQ(ierr);
  pmesh = (DM_Plex*) (*dmParallel)->data;
  /* Distribute sieve points and the global point numbering (replaces creating remote bases) */
  ierr = PetscSFConvertPartition(partSF, partSection, part, &renumbering, &pointSF);CHKERRQ(ierr);
  if (flg) {
    ierr = PetscPrintf(comm, "Point Partition:\n");CHKERRQ(ierr);
    ierr = PetscSectionView(partSection, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
    ierr = ISView(part, NULL);CHKERRQ(ierr);
    ierr = PetscSFView(pointSF, NULL);CHKERRQ(ierr);
    ierr = PetscPrintf(comm, "Point Renumbering after partition:\n");CHKERRQ(ierr);
    ierr = ISLocalToGlobalMappingView(renumbering, NULL);CHKERRQ(ierr);
  }
  /* Distribute cone section */
  ierr = DMPlexGetConeSection(dm, &originalConeSection);CHKERRQ(ierr);
  ierr = DMPlexGetConeSection(*dmParallel, &newConeSection);CHKERRQ(ierr);
  ierr = PetscSFDistributeSection(pointSF, originalConeSection, &remoteOffsets, newConeSection);CHKERRQ(ierr);
  ierr = DMSetUp(*dmParallel);CHKERRQ(ierr);
  {
    PetscInt pStart, pEnd, p;

    ierr = PetscSectionGetChart(newConeSection, &pStart, &pEnd);CHKERRQ(ierr);
    for (p = pStart; p < pEnd; ++p) {
      PetscInt coneSize;
      ierr               = PetscSectionGetDof(newConeSection, p, &coneSize);CHKERRQ(ierr);
      pmesh->maxConeSize = PetscMax(pmesh->maxConeSize, coneSize);
    }
  }
  /* Communicate and renumber cones */
  ierr = PetscSFCreateSectionSF(pointSF, originalConeSection, remoteOffsets, newConeSection, &coneSF);CHKERRQ(ierr);
  ierr = DMPlexGetCones(dm, &cones);CHKERRQ(ierr);
  ierr = DMPlexGetCones(*dmParallel, &newCones);CHKERRQ(ierr);
  ierr = PetscSFBcastBegin(coneSF, MPIU_INT, cones, newCones);CHKERRQ(ierr);
  ierr = PetscSFBcastEnd(coneSF, MPIU_INT, cones, newCones);CHKERRQ(ierr);
  ierr = PetscSectionGetStorageSize(newConeSection, &newConesSize);CHKERRQ(ierr);
  ierr = ISGlobalToLocalMappingApply(renumbering, IS_GTOLM_MASK, newConesSize, newCones, NULL, newCones);CHKERRQ(ierr);
  ierr = PetscOptionsHasName(((PetscObject) dm)->prefix, "-cones_view", &flg);CHKERRQ(ierr);
  if (flg) {
    ierr = PetscPrintf(comm, "Serial Cone Section:\n");CHKERRQ(ierr);
    ierr = PetscSectionView(originalConeSection, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
    ierr = PetscPrintf(comm, "Parallel Cone Section:\n");CHKERRQ(ierr);
    ierr = PetscSectionView(newConeSection, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
    ierr = PetscSFView(coneSF, NULL);CHKERRQ(ierr);
  }
  ierr = DMPlexGetConeOrientations(dm, &cones);CHKERRQ(ierr);
  ierr = DMPlexGetConeOrientations(*dmParallel, &newCones);CHKERRQ(ierr);
  ierr = PetscSFBcastBegin(coneSF, MPIU_INT, cones, newCones);CHKERRQ(ierr);
  ierr = PetscSFBcastEnd(coneSF, MPIU_INT, cones, newCones);CHKERRQ(ierr);
  ierr = PetscSFDestroy(&coneSF);CHKERRQ(ierr);
  /* Create supports and stratify sieve */
  {
    PetscInt pStart, pEnd;

    ierr = PetscSectionGetChart(pmesh->coneSection, &pStart, &pEnd);CHKERRQ(ierr);
    ierr = PetscSectionSetChart(pmesh->supportSection, pStart, pEnd);CHKERRQ(ierr);
  }
  ierr = DMPlexSymmetrize(*dmParallel);CHKERRQ(ierr);
  ierr = DMPlexStratify(*dmParallel);CHKERRQ(ierr);
  /* Distribute Coordinates */
  {
    PetscSection originalCoordSection, newCoordSection;
    Vec          originalCoordinates, newCoordinates;
    const char  *name;

    ierr = DMPlexGetCoordinateSection(dm, &originalCoordSection);CHKERRQ(ierr);
    ierr = DMPlexGetCoordinateSection(*dmParallel, &newCoordSection);CHKERRQ(ierr);
    ierr = DMGetCoordinatesLocal(dm, &originalCoordinates);CHKERRQ(ierr);
    ierr = VecCreate(comm, &newCoordinates);CHKERRQ(ierr);
    ierr = PetscObjectGetName((PetscObject) originalCoordinates, &name);CHKERRQ(ierr);
    ierr = PetscObjectSetName((PetscObject) newCoordinates, name);CHKERRQ(ierr);

    ierr = DMPlexDistributeField(dm, pointSF, originalCoordSection, originalCoordinates, newCoordSection, newCoordinates);CHKERRQ(ierr);
    ierr = DMSetCoordinatesLocal(*dmParallel, newCoordinates);CHKERRQ(ierr);
    ierr = VecDestroy(&newCoordinates);CHKERRQ(ierr);
  }
  /* Distribute labels */
  {
    DMLabel  next      = mesh->labels, newNext = pmesh->labels;
    PetscInt numLabels = 0, l;

    /* Bcast number of labels */
    while (next) {
      ++numLabels; next = next->next;
    }
    ierr = MPI_Bcast(&numLabels, 1, MPIU_INT, 0, comm);CHKERRQ(ierr);
    next = mesh->labels;
    for (l = 0; l < numLabels; ++l) {
      DMLabel         newLabel;
      const PetscInt *partArray;
      char           *name;
      PetscInt       *stratumSizes = NULL, *points = NULL;
      PetscMPIInt    *sendcnts     = NULL, *offsets = NULL, *displs = NULL;
      PetscInt        nameSize, s, p;
      PetscBool       isdepth;
      size_t          len = 0;

      /* Bcast name (could filter for no points) */
      if (!rank) {ierr = PetscStrlen(next->name, &len);CHKERRQ(ierr);}
      nameSize = len;
      ierr     = MPI_Bcast(&nameSize, 1, MPIU_INT, 0, comm);CHKERRQ(ierr);
      ierr     = PetscMalloc(nameSize+1, &name);CHKERRQ(ierr);
      if (!rank) {ierr = PetscMemcpy(name, next->name, nameSize+1);CHKERRQ(ierr);}
      ierr = MPI_Bcast(name, nameSize+1, MPI_CHAR, 0, comm);CHKERRQ(ierr);
      ierr = PetscStrcmp(name, "depth", &isdepth);CHKERRQ(ierr);
      if (isdepth) {ierr = PetscFree(name);CHKERRQ(ierr); continue;}
      ierr           = PetscNew(struct _n_DMLabel, &newLabel);CHKERRQ(ierr);
      newLabel->name = name;
      /* Bcast numStrata (could filter for no points in stratum) */
      if (!rank) newLabel->numStrata = next->numStrata;
      ierr = MPI_Bcast(&newLabel->numStrata, 1, MPIU_INT, 0, comm);CHKERRQ(ierr);
      ierr = PetscMalloc3(newLabel->numStrata,PetscInt,&newLabel->stratumValues,
                          newLabel->numStrata,PetscInt,&newLabel->stratumSizes,
                          newLabel->numStrata+1,PetscInt,&newLabel->stratumOffsets);CHKERRQ(ierr);
      /* Bcast stratumValues (could filter for no points in stratum) */
      if (!rank) {ierr = PetscMemcpy(newLabel->stratumValues, next->stratumValues, next->numStrata * sizeof(PetscInt));CHKERRQ(ierr);}
      ierr = MPI_Bcast(newLabel->stratumValues, newLabel->numStrata, MPIU_INT, 0, comm);CHKERRQ(ierr);
      /* Find size on each process and Scatter */
      if (!rank) {
        ierr = ISGetIndices(part, &partArray);CHKERRQ(ierr);
        ierr = PetscMalloc(numProcs*next->numStrata * sizeof(PetscInt), &stratumSizes);CHKERRQ(ierr);
        ierr = PetscMemzero(stratumSizes, numProcs*next->numStrata * sizeof(PetscInt));CHKERRQ(ierr);
        for (s = 0; s < next->numStrata; ++s) {
          for (p = next->stratumOffsets[s]; p < next->stratumOffsets[s]+next->stratumSizes[s]; ++p) {
            const PetscInt point = next->points[p];
            PetscInt       proc;

            for (proc = 0; proc < numProcs; ++proc) {
              PetscInt dof, off, pPart;

              ierr = PetscSectionGetDof(partSection, proc, &dof);CHKERRQ(ierr);
              ierr = PetscSectionGetOffset(partSection, proc, &off);CHKERRQ(ierr);
              for (pPart = off; pPart < off+dof; ++pPart) {
                if (partArray[pPart] == point) {
                  ++stratumSizes[proc*next->numStrata+s];
                  break;
                }
              }
            }
          }
        }
        ierr = ISRestoreIndices(part, &partArray);CHKERRQ(ierr);
      }
      ierr = MPI_Scatter(stratumSizes, newLabel->numStrata, MPIU_INT, newLabel->stratumSizes, newLabel->numStrata, MPIU_INT, 0, comm);CHKERRQ(ierr);
      /* Calculate stratumOffsets */
      newLabel->stratumOffsets[0] = 0;
      for (s = 0; s < newLabel->numStrata; ++s) {
        newLabel->stratumOffsets[s+1] = newLabel->stratumSizes[s] + newLabel->stratumOffsets[s];
      }
      /* Pack points and Scatter */
      if (!rank) {
        ierr = PetscMalloc3(numProcs,PetscMPIInt,&sendcnts,numProcs,PetscMPIInt,&offsets,numProcs+1,PetscMPIInt,&displs);CHKERRQ(ierr);
        displs[0] = 0;
        for (p = 0; p < numProcs; ++p) {
          sendcnts[p] = 0;
          for (s = 0; s < next->numStrata; ++s) {
            sendcnts[p] += stratumSizes[p*next->numStrata+s];
          }
          offsets[p]  = displs[p];
          displs[p+1] = displs[p] + sendcnts[p];
        }
        ierr = PetscMalloc(displs[numProcs] * sizeof(PetscInt), &points);CHKERRQ(ierr);
        for (s = 0; s < next->numStrata; ++s) {
          for (p = next->stratumOffsets[s]; p < next->stratumOffsets[s]+next->stratumSizes[s]; ++p) {
            const PetscInt point = next->points[p];
            PetscInt       proc;

            for (proc = 0; proc < numProcs; ++proc) {
              PetscInt dof, off, pPart;

              ierr = PetscSectionGetDof(partSection, proc, &dof);CHKERRQ(ierr);
              ierr = PetscSectionGetOffset(partSection, proc, &off);CHKERRQ(ierr);
              for (pPart = off; pPart < off+dof; ++pPart) {
                if (partArray[pPart] == point) {
                  points[offsets[proc]++] = point;
                  break;
                }
              }
            }
          }
        }
      }
      ierr = PetscMalloc(newLabel->stratumOffsets[newLabel->numStrata] * sizeof(PetscInt), &newLabel->points);CHKERRQ(ierr);
      ierr = MPI_Scatterv(points, sendcnts, displs, MPIU_INT, newLabel->points, newLabel->stratumOffsets[newLabel->numStrata], MPIU_INT, 0, comm);CHKERRQ(ierr);
      ierr = PetscFree(points);CHKERRQ(ierr);
      ierr = PetscFree3(sendcnts,offsets,displs);CHKERRQ(ierr);
      ierr = PetscFree(stratumSizes);CHKERRQ(ierr);
      /* Renumber points */
      ierr = ISGlobalToLocalMappingApply(renumbering, IS_GTOLM_MASK, newLabel->stratumOffsets[newLabel->numStrata], newLabel->points, NULL, newLabel->points);CHKERRQ(ierr);
      /* Sort points */
      for (s = 0; s < newLabel->numStrata; ++s) {
        ierr = PetscSortInt(newLabel->stratumSizes[s], &newLabel->points[newLabel->stratumOffsets[s]]);CHKERRQ(ierr);
      }
      /* Insert into list */
      if (newNext) newNext->next = newLabel;
      else pmesh->labels = newLabel;
      newNext = newLabel;
      if (!rank) next = next->next;
    }
  }
  /* Cleanup Partition */
  ierr = ISLocalToGlobalMappingDestroy(&renumbering);CHKERRQ(ierr);
  ierr = PetscSFDestroy(&partSF);CHKERRQ(ierr);
  ierr = PetscSectionDestroy(&partSection);CHKERRQ(ierr);
  ierr = ISDestroy(&part);CHKERRQ(ierr);
  /* Create point SF for parallel mesh */
  {
    const PetscInt *leaves;
    PetscSFNode    *remotePoints, *rowners, *lowners;
    PetscInt        numRoots, numLeaves, numGhostPoints = 0, p, gp, *ghostPoints;
    PetscInt        pStart, pEnd;

    ierr = DMPlexGetChart(*dmParallel, &pStart, &pEnd);CHKERRQ(ierr);
    ierr = PetscSFGetGraph(pointSF, &numRoots, &numLeaves, &leaves, NULL);CHKERRQ(ierr);
    ierr = PetscMalloc2(numRoots,PetscSFNode,&rowners,numLeaves,PetscSFNode,&lowners);CHKERRQ(ierr);
    for (p=0; p<numRoots; p++) {
      rowners[p].rank  = -1;
      rowners[p].index = -1;
    }
    if (origCellPart) {
      /* Make sure cells in the original partition are not assigned to other procs */
      const PetscInt *origCells;

      ierr = ISGetIndices(origCellPart, &origCells);CHKERRQ(ierr);
      for (p = 0; p < numProcs; ++p) {
        PetscInt dof, off, d;

        ierr = PetscSectionGetDof(origCellPartSection, p, &dof);CHKERRQ(ierr);
        ierr = PetscSectionGetOffset(origCellPartSection, p, &off);CHKERRQ(ierr);
        for (d = off; d < off+dof; ++d) {
          rowners[origCells[d]].rank = p;
        }
      }
      ierr = ISRestoreIndices(origCellPart, &origCells);CHKERRQ(ierr);
    }
    ierr = ISDestroy(&origCellPart);CHKERRQ(ierr);
    ierr = PetscSectionDestroy(&origCellPartSection);CHKERRQ(ierr);

    ierr = PetscSFBcastBegin(pointSF, MPIU_2INT, rowners, lowners);CHKERRQ(ierr);
    ierr = PetscSFBcastEnd(pointSF, MPIU_2INT, rowners, lowners);CHKERRQ(ierr);
    for (p = 0; p < numLeaves; ++p) {
      if (lowners[p].rank < 0 || lowners[p].rank == rank) { /* Either put in a bid or we know we own it */
        lowners[p].rank  = rank;
        lowners[p].index = leaves ? leaves[p] : p;
      } else if (lowners[p].rank >= 0) { /* Point already claimed so flag so that MAXLOC does not listen to us */
        lowners[p].rank  = -2;
        lowners[p].index = -2;
      }
    }
    for (p=0; p<numRoots; p++) { /* Root must not participate in the rediction, flag so that MAXLOC does not use */
      rowners[p].rank  = -3;
      rowners[p].index = -3;
    }
    ierr = PetscSFReduceBegin(pointSF, MPIU_2INT, lowners, rowners, MPI_MAXLOC);CHKERRQ(ierr);
    ierr = PetscSFReduceEnd(pointSF, MPIU_2INT, lowners, rowners, MPI_MAXLOC);CHKERRQ(ierr);
    ierr = PetscSFBcastBegin(pointSF, MPIU_2INT, rowners, lowners);CHKERRQ(ierr);
    ierr = PetscSFBcastEnd(pointSF, MPIU_2INT, rowners, lowners);CHKERRQ(ierr);
    for (p = 0; p < numLeaves; ++p) {
      if (lowners[p].rank < 0 || lowners[p].index < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Cell partition corrupt: point not claimed");
      if (lowners[p].rank != rank) ++numGhostPoints;
    }
    ierr = PetscMalloc(numGhostPoints * sizeof(PetscInt),    &ghostPoints);CHKERRQ(ierr);
    ierr = PetscMalloc(numGhostPoints * sizeof(PetscSFNode), &remotePoints);CHKERRQ(ierr);
    for (p = 0, gp = 0; p < numLeaves; ++p) {
      if (lowners[p].rank != rank) {
        ghostPoints[gp]        = leaves ? leaves[p] : p;
        remotePoints[gp].rank  = lowners[p].rank;
        remotePoints[gp].index = lowners[p].index;
        ++gp;
      }
    }
    ierr = PetscFree2(rowners,lowners);CHKERRQ(ierr);
    ierr = PetscSFSetGraph((*dmParallel)->sf, pEnd - pStart, numGhostPoints, ghostPoints, PETSC_OWN_POINTER, remotePoints, PETSC_OWN_POINTER);CHKERRQ(ierr);
    ierr = PetscSFSetFromOptions((*dmParallel)->sf);CHKERRQ(ierr);
  }
  /* Cleanup */
  ierr = PetscSFDestroy(&pointSF);CHKERRQ(ierr);
  ierr = DMSetFromOptions(*dmParallel);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(DMPLEX_Distribute,dm,0,0,0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#if defined(PETSC_HAVE_TRIANGLE)
#include <triangle.h>

#undef __FUNCT__
#define __FUNCT__ "InitInput_Triangle"
PetscErrorCode InitInput_Triangle(struct triangulateio *inputCtx)
{
  PetscFunctionBegin;
  inputCtx->numberofpoints             = 0;
  inputCtx->numberofpointattributes    = 0;
  inputCtx->pointlist                  = NULL;
  inputCtx->pointattributelist         = NULL;
  inputCtx->pointmarkerlist            = NULL;
  inputCtx->numberofsegments           = 0;
  inputCtx->segmentlist                = NULL;
  inputCtx->segmentmarkerlist          = NULL;
  inputCtx->numberoftriangleattributes = 0;
  inputCtx->trianglelist               = NULL;
  inputCtx->numberofholes              = 0;
  inputCtx->holelist                   = NULL;
  inputCtx->numberofregions            = 0;
  inputCtx->regionlist                 = NULL;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "InitOutput_Triangle"
PetscErrorCode InitOutput_Triangle(struct triangulateio *outputCtx)
{
  PetscFunctionBegin;
  outputCtx->numberofpoints        = 0;
  outputCtx->pointlist             = NULL;
  outputCtx->pointattributelist    = NULL;
  outputCtx->pointmarkerlist       = NULL;
  outputCtx->numberoftriangles     = 0;
  outputCtx->trianglelist          = NULL;
  outputCtx->triangleattributelist = NULL;
  outputCtx->neighborlist          = NULL;
  outputCtx->segmentlist           = NULL;
  outputCtx->segmentmarkerlist     = NULL;
  outputCtx->numberofedges         = 0;
  outputCtx->edgelist              = NULL;
  outputCtx->edgemarkerlist        = NULL;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "FiniOutput_Triangle"
PetscErrorCode FiniOutput_Triangle(struct triangulateio *outputCtx)
{
  PetscFunctionBegin;
  free(outputCtx->pointmarkerlist);
  free(outputCtx->edgelist);
  free(outputCtx->edgemarkerlist);
  free(outputCtx->trianglelist);
  free(outputCtx->neighborlist);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexGenerate_Triangle"
PetscErrorCode DMPlexGenerate_Triangle(DM boundary, PetscBool interpolate, DM *dm)
{
  MPI_Comm             comm;
  PetscInt             dim              = 2;
  const PetscBool      createConvexHull = PETSC_FALSE;
  const PetscBool      constrained      = PETSC_FALSE;
  struct triangulateio in;
  struct triangulateio out;
  PetscInt             vStart, vEnd, v, eStart, eEnd, e;
  PetscMPIInt          rank;
  PetscErrorCode       ierr;

  PetscFunctionBegin;
  ierr = PetscObjectGetComm((PetscObject)boundary,&comm);CHKERRQ(ierr);
  ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
  ierr = InitInput_Triangle(&in);CHKERRQ(ierr);
  ierr = InitOutput_Triangle(&out);CHKERRQ(ierr);
  ierr = DMPlexGetDepthStratum(boundary, 0, &vStart, &vEnd);CHKERRQ(ierr);

  in.numberofpoints = vEnd - vStart;
  if (in.numberofpoints > 0) {
    PetscSection coordSection;
    Vec          coordinates;
    PetscScalar *array;

    ierr = PetscMalloc(in.numberofpoints*dim * sizeof(double), &in.pointlist);CHKERRQ(ierr);
    ierr = PetscMalloc(in.numberofpoints * sizeof(int), &in.pointmarkerlist);CHKERRQ(ierr);
    ierr = DMGetCoordinatesLocal(boundary, &coordinates);CHKERRQ(ierr);
    ierr = DMPlexGetCoordinateSection(boundary, &coordSection);CHKERRQ(ierr);
    ierr = VecGetArray(coordinates, &array);CHKERRQ(ierr);
    for (v = vStart; v < vEnd; ++v) {
      const PetscInt idx = v - vStart;
      PetscInt       off, d;

      ierr = PetscSectionGetOffset(coordSection, v, &off);CHKERRQ(ierr);
      for (d = 0; d < dim; ++d) {
        in.pointlist[idx*dim + d] = PetscRealPart(array[off+d]);
      }
      ierr = DMPlexGetLabelValue(boundary, "marker", v, &in.pointmarkerlist[idx]);CHKERRQ(ierr);
    }
    ierr = VecRestoreArray(coordinates, &array);CHKERRQ(ierr);
  }
  ierr  = DMPlexGetHeightStratum(boundary, 0, &eStart, &eEnd);CHKERRQ(ierr);
  in.numberofsegments = eEnd - eStart;
  if (in.numberofsegments > 0) {
    ierr = PetscMalloc(in.numberofsegments*2 * sizeof(int), &in.segmentlist);CHKERRQ(ierr);
    ierr = PetscMalloc(in.numberofsegments   * sizeof(int), &in.segmentmarkerlist);CHKERRQ(ierr);
    for (e = eStart; e < eEnd; ++e) {
      const PetscInt  idx = e - eStart;
      const PetscInt *cone;

      ierr = DMPlexGetCone(boundary, e, &cone);CHKERRQ(ierr);

      in.segmentlist[idx*2+0] = cone[0] - vStart;
      in.segmentlist[idx*2+1] = cone[1] - vStart;

      ierr = DMPlexGetLabelValue(boundary, "marker", e, &in.segmentmarkerlist[idx]);CHKERRQ(ierr);
    }
  }
#if 0 /* Do not currently support holes */
  PetscReal *holeCoords;
  PetscInt   h, d;

  ierr = DMPlexGetHoles(boundary, &in.numberofholes, &holeCords);CHKERRQ(ierr);
  if (in.numberofholes > 0) {
    ierr = PetscMalloc(in.numberofholes*dim * sizeof(double), &in.holelist);CHKERRQ(ierr);
    for (h = 0; h < in.numberofholes; ++h) {
      for (d = 0; d < dim; ++d) {
        in.holelist[h*dim+d] = holeCoords[h*dim+d];
      }
    }
  }
#endif
  if (!rank) {
    char args[32];

    /* Take away 'Q' for verbose output */
    ierr = PetscStrcpy(args, "pqezQ");CHKERRQ(ierr);
    if (createConvexHull) {
      ierr = PetscStrcat(args, "c");CHKERRQ(ierr);
    }
    if (constrained) {
      ierr = PetscStrcpy(args, "zepDQ");CHKERRQ(ierr);
    }
    triangulate(args, &in, &out, NULL);
  }
  ierr = PetscFree(in.pointlist);CHKERRQ(ierr);
  ierr = PetscFree(in.pointmarkerlist);CHKERRQ(ierr);
  ierr = PetscFree(in.segmentlist);CHKERRQ(ierr);
  ierr = PetscFree(in.segmentmarkerlist);CHKERRQ(ierr);
  ierr = PetscFree(in.holelist);CHKERRQ(ierr);

  {
    const PetscInt numCorners  = 3;
    const PetscInt numCells    = out.numberoftriangles;
    const PetscInt numVertices = out.numberofpoints;
    const int     *cells      = out.trianglelist;
    const double  *meshCoords = out.pointlist;

    ierr = DMPlexCreateFromCellList(comm, dim, numCells, numVertices, numCorners, interpolate, cells, dim, meshCoords, dm);CHKERRQ(ierr);
    /* Set labels */
    for (v = 0; v < numVertices; ++v) {
      if (out.pointmarkerlist[v]) {
        ierr = DMPlexSetLabelValue(*dm, "marker", v+numCells, out.pointmarkerlist[v]);CHKERRQ(ierr);
      }
    }
    if (interpolate) {
      for (e = 0; e < out.numberofedges; e++) {
        if (out.edgemarkerlist[e]) {
          const PetscInt  vertices[2] = {out.edgelist[e*2+0]+numCells, out.edgelist[e*2+1]+numCells};
          const PetscInt *edges;
          PetscInt        numEdges;

          ierr = DMPlexGetJoin(*dm, 2, vertices, &numEdges, &edges);CHKERRQ(ierr);
          if (numEdges != 1) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Two vertices must cover only one edge, not %D", numEdges);
          ierr = DMPlexSetLabelValue(*dm, "marker", edges[0], out.edgemarkerlist[e]);CHKERRQ(ierr);
          ierr = DMPlexRestoreJoin(*dm, 2, vertices, &numEdges, &edges);CHKERRQ(ierr);
        }
      }
    }
    ierr = DMPlexSetRefinementUniform(*dm, PETSC_FALSE);CHKERRQ(ierr);
  }
#if 0 /* Do not currently support holes */
  ierr = DMPlexCopyHoles(*dm, boundary);CHKERRQ(ierr);
#endif
  ierr = FiniOutput_Triangle(&out);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexRefine_Triangle"
PetscErrorCode DMPlexRefine_Triangle(DM dm, double *maxVolumes, DM *dmRefined)
{
  MPI_Comm             comm;
  PetscInt             dim  = 2;
  struct triangulateio in;
  struct triangulateio out;
  PetscInt             vStart, vEnd, v, cStart, cEnd, c, depth, depthGlobal;
  PetscMPIInt          rank;
  PetscErrorCode       ierr;

  PetscFunctionBegin;
  ierr = PetscObjectGetComm((PetscObject)dm,&comm);CHKERRQ(ierr);
  ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
  ierr = InitInput_Triangle(&in);CHKERRQ(ierr);
  ierr = InitOutput_Triangle(&out);CHKERRQ(ierr);
  ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
  ierr = MPI_Allreduce(&depth, &depthGlobal, 1, MPIU_INT, MPI_MAX, comm);CHKERRQ(ierr);
  ierr = DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);CHKERRQ(ierr);

  in.numberofpoints = vEnd - vStart;
  if (in.numberofpoints > 0) {
    PetscSection coordSection;
    Vec          coordinates;
    PetscScalar *array;

    ierr = PetscMalloc(in.numberofpoints*dim * sizeof(double), &in.pointlist);CHKERRQ(ierr);
    ierr = PetscMalloc(in.numberofpoints * sizeof(int), &in.pointmarkerlist);CHKERRQ(ierr);
    ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
    ierr = DMPlexGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
    ierr = VecGetArray(coordinates, &array);CHKERRQ(ierr);
    for (v = vStart; v < vEnd; ++v) {
      const PetscInt idx = v - vStart;
      PetscInt       off, d;

      ierr = PetscSectionGetOffset(coordSection, v, &off);CHKERRQ(ierr);
      for (d = 0; d < dim; ++d) {
        in.pointlist[idx*dim + d] = PetscRealPart(array[off+d]);
      }
      ierr = DMPlexGetLabelValue(dm, "marker", v, &in.pointmarkerlist[idx]);CHKERRQ(ierr);
    }
    ierr = VecRestoreArray(coordinates, &array);CHKERRQ(ierr);
  }
  ierr  = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);

  in.numberofcorners   = 3;
  in.numberoftriangles = cEnd - cStart;

  in.trianglearealist  = (double*) maxVolumes;
  if (in.numberoftriangles > 0) {
    ierr = PetscMalloc(in.numberoftriangles*in.numberofcorners * sizeof(int), &in.trianglelist);CHKERRQ(ierr);
    for (c = cStart; c < cEnd; ++c) {
      const PetscInt idx      = c - cStart;
      PetscInt      *closure = NULL;
      PetscInt       closureSize;

      ierr = DMPlexGetTransitiveClosure(dm, c, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
      if ((closureSize != 4) && (closureSize != 7)) SETERRQ1(comm, PETSC_ERR_ARG_WRONG, "Mesh has cell which is not a triangle, %D vertices in closure", closureSize);
      for (v = 0; v < 3; ++v) {
        in.trianglelist[idx*in.numberofcorners + v] = closure[(v+closureSize-3)*2] - vStart;
      }
      ierr = DMPlexRestoreTransitiveClosure(dm, c, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
    }
  }
  /* TODO: Segment markers are missing on input */
#if 0 /* Do not currently support holes */
  PetscReal *holeCoords;
  PetscInt   h, d;

  ierr = DMPlexGetHoles(boundary, &in.numberofholes, &holeCords);CHKERRQ(ierr);
  if (in.numberofholes > 0) {
    ierr = PetscMalloc(in.numberofholes*dim * sizeof(double), &in.holelist);CHKERRQ(ierr);
    for (h = 0; h < in.numberofholes; ++h) {
      for (d = 0; d < dim; ++d) {
        in.holelist[h*dim+d] = holeCoords[h*dim+d];
      }
    }
  }
#endif
  if (!rank) {
    char args[32];

    /* Take away 'Q' for verbose output */
    ierr = PetscStrcpy(args, "pqezQra");CHKERRQ(ierr);
    triangulate(args, &in, &out, NULL);
  }
  ierr = PetscFree(in.pointlist);CHKERRQ(ierr);
  ierr = PetscFree(in.pointmarkerlist);CHKERRQ(ierr);
  ierr = PetscFree(in.segmentlist);CHKERRQ(ierr);
  ierr = PetscFree(in.segmentmarkerlist);CHKERRQ(ierr);
  ierr = PetscFree(in.trianglelist);CHKERRQ(ierr);

  {
    const PetscInt numCorners  = 3;
    const PetscInt numCells    = out.numberoftriangles;
    const PetscInt numVertices = out.numberofpoints;
    const int     *cells      = out.trianglelist;
    const double  *meshCoords = out.pointlist;
    PetscBool      interpolate = depthGlobal > 1 ? PETSC_TRUE : PETSC_FALSE;

    ierr = DMPlexCreateFromCellList(comm, dim, numCells, numVertices, numCorners, interpolate, cells, dim, meshCoords, dmRefined);CHKERRQ(ierr);
    /* Set labels */
    for (v = 0; v < numVertices; ++v) {
      if (out.pointmarkerlist[v]) {
        ierr = DMPlexSetLabelValue(*dmRefined, "marker", v+numCells, out.pointmarkerlist[v]);CHKERRQ(ierr);
      }
    }
    if (interpolate) {
      PetscInt e;

      for (e = 0; e < out.numberofedges; e++) {
        if (out.edgemarkerlist[e]) {
          const PetscInt  vertices[2] = {out.edgelist[e*2+0]+numCells, out.edgelist[e*2+1]+numCells};
          const PetscInt *edges;
          PetscInt        numEdges;

          ierr = DMPlexGetJoin(*dmRefined, 2, vertices, &numEdges, &edges);CHKERRQ(ierr);
          if (numEdges != 1) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Two vertices must cover only one edge, not %D", numEdges);
          ierr = DMPlexSetLabelValue(*dmRefined, "marker", edges[0], out.edgemarkerlist[e]);CHKERRQ(ierr);
          ierr = DMPlexRestoreJoin(*dmRefined, 2, vertices, &numEdges, &edges);CHKERRQ(ierr);
        }
      }
    }
    ierr = DMPlexSetRefinementUniform(*dmRefined, PETSC_FALSE);CHKERRQ(ierr);
  }
#if 0 /* Do not currently support holes */
  ierr = DMPlexCopyHoles(*dm, boundary);CHKERRQ(ierr);
#endif
  ierr = FiniOutput_Triangle(&out);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}
#endif

#if defined(PETSC_HAVE_TETGEN)
#include <tetgen.h>
#undef __FUNCT__
#define __FUNCT__ "DMPlexGenerate_Tetgen"
PetscErrorCode DMPlexGenerate_Tetgen(DM boundary, PetscBool interpolate, DM *dm)
{
  MPI_Comm       comm;
  const PetscInt dim  = 3;
  ::tetgenio     in;
  ::tetgenio     out;
  PetscInt       vStart, vEnd, v, fStart, fEnd, f;
  PetscMPIInt    rank;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr              = PetscObjectGetComm((PetscObject)boundary,&comm);CHKERRQ(ierr);
  ierr              = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
  ierr              = DMPlexGetDepthStratum(boundary, 0, &vStart, &vEnd);CHKERRQ(ierr);
  in.numberofpoints = vEnd - vStart;
  if (in.numberofpoints > 0) {
    PetscSection coordSection;
    Vec          coordinates;
    PetscScalar *array;

    in.pointlist       = new double[in.numberofpoints*dim];
    in.pointmarkerlist = new int[in.numberofpoints];

    ierr = DMGetCoordinatesLocal(boundary, &coordinates);CHKERRQ(ierr);
    ierr = DMPlexGetCoordinateSection(boundary, &coordSection);CHKERRQ(ierr);
    ierr = VecGetArray(coordinates, &array);CHKERRQ(ierr);
    for (v = vStart; v < vEnd; ++v) {
      const PetscInt idx = v - vStart;
      PetscInt       off, d;

      ierr = PetscSectionGetOffset(coordSection, v, &off);CHKERRQ(ierr);
      for (d = 0; d < dim; ++d) in.pointlist[idx*dim + d] = array[off+d];
      ierr = DMPlexGetLabelValue(boundary, "marker", v, &in.pointmarkerlist[idx]);CHKERRQ(ierr);
    }
    ierr = VecRestoreArray(coordinates, &array);CHKERRQ(ierr);
  }
  ierr  = DMPlexGetHeightStratum(boundary, 0, &fStart, &fEnd);CHKERRQ(ierr);

  in.numberoffacets = fEnd - fStart;
  if (in.numberoffacets > 0) {
    in.facetlist       = new tetgenio::facet[in.numberoffacets];
    in.facetmarkerlist = new int[in.numberoffacets];
    for (f = fStart; f < fEnd; ++f) {
      const PetscInt idx     = f - fStart;
      PetscInt      *points = NULL, numPoints, p, numVertices = 0, v;

      in.facetlist[idx].numberofpolygons = 1;
      in.facetlist[idx].polygonlist      = new tetgenio::polygon[in.facetlist[idx].numberofpolygons];
      in.facetlist[idx].numberofholes    = 0;
      in.facetlist[idx].holelist         = NULL;

      ierr = DMPlexGetTransitiveClosure(boundary, f, PETSC_TRUE, &numPoints, &points);CHKERRQ(ierr);
      for (p = 0; p < numPoints*2; p += 2) {
        const PetscInt point = points[p];
        if ((point >= vStart) && (point < vEnd)) points[numVertices++] = point;
      }

      tetgenio::polygon *poly = in.facetlist[idx].polygonlist;
      poly->numberofvertices = numVertices;
      poly->vertexlist       = new int[poly->numberofvertices];
      for (v = 0; v < numVertices; ++v) {
        const PetscInt vIdx = points[v] - vStart;
        poly->vertexlist[v] = vIdx;
      }
      ierr = DMPlexGetLabelValue(boundary, "marker", f, &in.facetmarkerlist[idx]);CHKERRQ(ierr);
      ierr = DMPlexRestoreTransitiveClosure(boundary, f, PETSC_TRUE, &numPoints, &points);CHKERRQ(ierr);
    }
  }
  if (!rank) {
    char args[32];

    /* Take away 'Q' for verbose output */
    ierr = PetscStrcpy(args, "pqezQ");CHKERRQ(ierr);
    ::tetrahedralize(args, &in, &out);
  }
  {
    const PetscInt numCorners  = 4;
    const PetscInt numCells    = out.numberoftetrahedra;
    const PetscInt numVertices = out.numberofpoints;
    const int     *cells      = out.tetrahedronlist;
    const double  *meshCoords = out.pointlist;

    ierr = DMPlexCreateFromCellList(comm, dim, numCells, numVertices, numCorners, interpolate, cells, dim, meshCoords, dm);CHKERRQ(ierr);
    /* Set labels */
    for (v = 0; v < numVertices; ++v) {
      if (out.pointmarkerlist[v]) {
        ierr = DMPlexSetLabelValue(*dm, "marker", v+numCells, out.pointmarkerlist[v]);CHKERRQ(ierr);
      }
    }
    if (interpolate) {
      PetscInt e;

      for (e = 0; e < out.numberofedges; e++) {
        if (out.edgemarkerlist[e]) {
          const PetscInt  vertices[2] = {out.edgelist[e*2+0]+numCells, out.edgelist[e*2+1]+numCells};
          const PetscInt *edges;
          PetscInt        numEdges;

          ierr = DMPlexGetJoin(*dm, 2, vertices, &numEdges, &edges);CHKERRQ(ierr);
          if (numEdges != 1) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Two vertices must cover only one edge, not %D", numEdges);
          ierr = DMPlexSetLabelValue(*dm, "marker", edges[0], out.edgemarkerlist[e]);CHKERRQ(ierr);
          ierr = DMPlexRestoreJoin(*dm, 2, vertices, &numEdges, &edges);CHKERRQ(ierr);
        }
      }
      for (f = 0; f < out.numberoftrifaces; f++) {
        if (out.trifacemarkerlist[f]) {
          const PetscInt  vertices[3] = {out.trifacelist[f*3+0]+numCells, out.trifacelist[f*3+1]+numCells, out.trifacelist[f*3+2]+numCells};
          const PetscInt *faces;
          PetscInt        numFaces;

          ierr = DMPlexGetJoin(*dm, 3, vertices, &numFaces, &faces);CHKERRQ(ierr);
          if (numFaces != 1) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Three vertices must cover only one face, not %D", numFaces);
          ierr = DMPlexSetLabelValue(*dm, "marker", faces[0], out.trifacemarkerlist[f]);CHKERRQ(ierr);
          ierr = DMPlexRestoreJoin(*dm, 3, vertices, &numFaces, &faces);CHKERRQ(ierr);
        }
      }
    }
    ierr = DMPlexSetRefinementUniform(*dm, PETSC_FALSE);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexRefine_Tetgen"
PetscErrorCode DMPlexRefine_Tetgen(DM dm, double *maxVolumes, DM *dmRefined)
{
  MPI_Comm       comm;
  const PetscInt dim  = 3;
  ::tetgenio     in;
  ::tetgenio     out;
  PetscInt       vStart, vEnd, v, cStart, cEnd, c, depth, depthGlobal;
  PetscMPIInt    rank;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscObjectGetComm((PetscObject)dm,&comm);CHKERRQ(ierr);
  ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
  ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
  ierr = MPI_Allreduce(&depth, &depthGlobal, 1, MPIU_INT, MPI_MAX, comm);CHKERRQ(ierr);
  ierr = DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);CHKERRQ(ierr);

  in.numberofpoints = vEnd - vStart;
  if (in.numberofpoints > 0) {
    PetscSection coordSection;
    Vec          coordinates;
    PetscScalar *array;

    in.pointlist       = new double[in.numberofpoints*dim];
    in.pointmarkerlist = new int[in.numberofpoints];

    ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
    ierr = DMPlexGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
    ierr = VecGetArray(coordinates, &array);CHKERRQ(ierr);
    for (v = vStart; v < vEnd; ++v) {
      const PetscInt idx = v - vStart;
      PetscInt       off, d;

      ierr = PetscSectionGetOffset(coordSection, v, &off);CHKERRQ(ierr);
      for (d = 0; d < dim; ++d) in.pointlist[idx*dim + d] = array[off+d];
      ierr = DMPlexGetLabelValue(dm, "marker", v, &in.pointmarkerlist[idx]);CHKERRQ(ierr);
    }
    ierr = VecRestoreArray(coordinates, &array);CHKERRQ(ierr);
  }
  ierr  = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);

  in.numberofcorners       = 4;
  in.numberoftetrahedra    = cEnd - cStart;
  in.tetrahedronvolumelist = (double*) maxVolumes;
  if (in.numberoftetrahedra > 0) {
    in.tetrahedronlist = new int[in.numberoftetrahedra*in.numberofcorners];
    for (c = cStart; c < cEnd; ++c) {
      const PetscInt idx      = c - cStart;
      PetscInt      *closure = NULL;
      PetscInt       closureSize;

      ierr = DMPlexGetTransitiveClosure(dm, c, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
      if ((closureSize != 5) && (closureSize != 15)) SETERRQ1(comm, PETSC_ERR_ARG_WRONG, "Mesh has cell which is not a tetrahedron, %D vertices in closure", closureSize);
      for (v = 0; v < 4; ++v) {
        in.tetrahedronlist[idx*in.numberofcorners + v] = closure[(v+closureSize-4)*2] - vStart;
      }
      ierr = DMPlexRestoreTransitiveClosure(dm, c, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
    }
  }
  /* TODO: Put in boundary faces with markers */
  if (!rank) {
    char args[32];

    /* Take away 'Q' for verbose output */
    /*ierr = PetscStrcpy(args, "qezQra");CHKERRQ(ierr); */
    ierr = PetscStrcpy(args, "qezraVVVV");CHKERRQ(ierr);
    ::tetrahedralize(args, &in, &out);
  }
  in.tetrahedronvolumelist = NULL;

  {
    const PetscInt numCorners  = 4;
    const PetscInt numCells    = out.numberoftetrahedra;
    const PetscInt numVertices = out.numberofpoints;
    const int     *cells      = out.tetrahedronlist;
    const double  *meshCoords = out.pointlist;
    PetscBool      interpolate = depthGlobal > 1 ? PETSC_TRUE : PETSC_FALSE;

    ierr = DMPlexCreateFromCellList(comm, dim, numCells, numVertices, numCorners, interpolate, cells, dim, meshCoords, dmRefined);CHKERRQ(ierr);
    /* Set labels */
    for (v = 0; v < numVertices; ++v) {
      if (out.pointmarkerlist[v]) {
        ierr = DMPlexSetLabelValue(*dmRefined, "marker", v+numCells, out.pointmarkerlist[v]);CHKERRQ(ierr);
      }
    }
    if (interpolate) {
      PetscInt e, f;

      for (e = 0; e < out.numberofedges; e++) {
        if (out.edgemarkerlist[e]) {
          const PetscInt  vertices[2] = {out.edgelist[e*2+0]+numCells, out.edgelist[e*2+1]+numCells};
          const PetscInt *edges;
          PetscInt        numEdges;

          ierr = DMPlexGetJoin(*dmRefined, 2, vertices, &numEdges, &edges);CHKERRQ(ierr);
          if (numEdges != 1) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Two vertices must cover only one edge, not %D", numEdges);
          ierr = DMPlexSetLabelValue(*dmRefined, "marker", edges[0], out.edgemarkerlist[e]);CHKERRQ(ierr);
          ierr = DMPlexRestoreJoin(*dmRefined, 2, vertices, &numEdges, &edges);CHKERRQ(ierr);
        }
      }
      for (f = 0; f < out.numberoftrifaces; f++) {
        if (out.trifacemarkerlist[f]) {
          const PetscInt  vertices[3] = {out.trifacelist[f*3+0]+numCells, out.trifacelist[f*3+1]+numCells, out.trifacelist[f*3+2]+numCells};
          const PetscInt *faces;
          PetscInt        numFaces;

          ierr = DMPlexGetJoin(*dmRefined, 3, vertices, &numFaces, &faces);CHKERRQ(ierr);
          if (numFaces != 1) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Three vertices must cover only one face, not %D", numFaces);
          ierr = DMPlexSetLabelValue(*dmRefined, "marker", faces[0], out.trifacemarkerlist[f]);CHKERRQ(ierr);
          ierr = DMPlexRestoreJoin(*dmRefined, 3, vertices, &numFaces, &faces);CHKERRQ(ierr);
        }
      }
    }
    ierr = DMPlexSetRefinementUniform(*dmRefined, PETSC_FALSE);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}
#endif

#if defined(PETSC_HAVE_CTETGEN)
#include "ctetgen.h"

#undef __FUNCT__
#define __FUNCT__ "DMPlexGenerate_CTetgen"
PetscErrorCode DMPlexGenerate_CTetgen(DM boundary, PetscBool interpolate, DM *dm)
{
  MPI_Comm       comm;
  const PetscInt dim  = 3;
  PLC           *in, *out;
  PetscInt       verbose = 0, vStart, vEnd, v, fStart, fEnd, f;
  PetscMPIInt    rank;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscObjectGetComm((PetscObject)boundary,&comm);CHKERRQ(ierr);
  ierr = PetscOptionsGetInt(((PetscObject) boundary)->prefix, "-ctetgen_verbose", &verbose, NULL);CHKERRQ(ierr);
  ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
  ierr = DMPlexGetDepthStratum(boundary, 0, &vStart, &vEnd);CHKERRQ(ierr);
  ierr = PLCCreate(&in);CHKERRQ(ierr);
  ierr = PLCCreate(&out);CHKERRQ(ierr);

  in->numberofpoints = vEnd - vStart;
  if (in->numberofpoints > 0) {
    PetscSection coordSection;
    Vec          coordinates;
    PetscScalar *array;

    ierr = PetscMalloc(in->numberofpoints*dim * sizeof(PetscReal), &in->pointlist);CHKERRQ(ierr);
    ierr = PetscMalloc(in->numberofpoints     * sizeof(int),       &in->pointmarkerlist);CHKERRQ(ierr);
    ierr = DMGetCoordinatesLocal(boundary, &coordinates);CHKERRQ(ierr);
    ierr = DMPlexGetCoordinateSection(boundary, &coordSection);CHKERRQ(ierr);
    ierr = VecGetArray(coordinates, &array);CHKERRQ(ierr);
    for (v = vStart; v < vEnd; ++v) {
      const PetscInt idx = v - vStart;
      PetscInt       off, d, m;

      ierr = PetscSectionGetOffset(coordSection, v, &off);CHKERRQ(ierr);
      for (d = 0; d < dim; ++d) {
        in->pointlist[idx*dim + d] = PetscRealPart(array[off+d]);
      }
      ierr = DMPlexGetLabelValue(boundary, "marker", v, &m);CHKERRQ(ierr);

      in->pointmarkerlist[idx] = (int) m;
    }
    ierr = VecRestoreArray(coordinates, &array);CHKERRQ(ierr);
  }
  ierr  = DMPlexGetHeightStratum(boundary, 0, &fStart, &fEnd);CHKERRQ(ierr);

  in->numberoffacets = fEnd - fStart;
  if (in->numberoffacets > 0) {
    ierr = PetscMalloc(in->numberoffacets * sizeof(facet), &in->facetlist);CHKERRQ(ierr);
    ierr = PetscMalloc(in->numberoffacets * sizeof(int),   &in->facetmarkerlist);CHKERRQ(ierr);
    for (f = fStart; f < fEnd; ++f) {
      const PetscInt idx     = f - fStart;
      PetscInt      *points = NULL, numPoints, p, numVertices = 0, v, m;
      polygon       *poly;

      in->facetlist[idx].numberofpolygons = 1;

      ierr = PetscMalloc(in->facetlist[idx].numberofpolygons * sizeof(polygon), &in->facetlist[idx].polygonlist);CHKERRQ(ierr);

      in->facetlist[idx].numberofholes    = 0;
      in->facetlist[idx].holelist         = NULL;

      ierr = DMPlexGetTransitiveClosure(boundary, f, PETSC_TRUE, &numPoints, &points);CHKERRQ(ierr);
      for (p = 0; p < numPoints*2; p += 2) {
        const PetscInt point = points[p];
        if ((point >= vStart) && (point < vEnd)) points[numVertices++] = point;
      }

      poly                   = in->facetlist[idx].polygonlist;
      poly->numberofvertices = numVertices;
      ierr                   = PetscMalloc(poly->numberofvertices * sizeof(int), &poly->vertexlist);CHKERRQ(ierr);
      for (v = 0; v < numVertices; ++v) {
        const PetscInt vIdx = points[v] - vStart;
        poly->vertexlist[v] = vIdx;
      }
      ierr                     = DMPlexGetLabelValue(boundary, "marker", f, &m);CHKERRQ(ierr);
      in->facetmarkerlist[idx] = (int) m;
      ierr                     = DMPlexRestoreTransitiveClosure(boundary, f, PETSC_TRUE, &numPoints, &points);CHKERRQ(ierr);
    }
  }
  if (!rank) {
    TetGenOpts t;

    ierr        = TetGenOptsInitialize(&t);CHKERRQ(ierr);
    t.in        = boundary; /* Should go away */
    t.plc       = 1;
    t.quality   = 1;
    t.edgesout  = 1;
    t.zeroindex = 1;
    t.quiet     = 1;
    t.verbose   = verbose;
    ierr        = TetGenCheckOpts(&t);CHKERRQ(ierr);
    ierr        = TetGenTetrahedralize(&t, in, out);CHKERRQ(ierr);
  }
  {
    const PetscInt numCorners  = 4;
    const PetscInt numCells    = out->numberoftetrahedra;
    const PetscInt numVertices = out->numberofpoints;
    const int     *cells      = out->tetrahedronlist;
    const double  *meshCoords = out->pointlist;

    ierr = DMPlexCreateFromCellList(comm, dim, numCells, numVertices, numCorners, interpolate, cells, dim, meshCoords, dm);CHKERRQ(ierr);
    /* Set labels */
    for (v = 0; v < numVertices; ++v) {
      if (out->pointmarkerlist[v]) {
        ierr = DMPlexSetLabelValue(*dm, "marker", v+numCells, out->pointmarkerlist[v]);CHKERRQ(ierr);
      }
    }
    if (interpolate) {
      PetscInt e;

      for (e = 0; e < out->numberofedges; e++) {
        if (out->edgemarkerlist[e]) {
          const PetscInt  vertices[2] = {out->edgelist[e*2+0]+numCells, out->edgelist[e*2+1]+numCells};
          const PetscInt *edges;
          PetscInt        numEdges;

          ierr = DMPlexGetJoin(*dm, 2, vertices, &numEdges, &edges);CHKERRQ(ierr);
          if (numEdges != 1) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Two vertices must cover only one edge, not %D", numEdges);
          ierr = DMPlexSetLabelValue(*dm, "marker", edges[0], out->edgemarkerlist[e]);CHKERRQ(ierr);
          ierr = DMPlexRestoreJoin(*dm, 2, vertices, &numEdges, &edges);CHKERRQ(ierr);
        }
      }
      for (f = 0; f < out->numberoftrifaces; f++) {
        if (out->trifacemarkerlist[f]) {
          const PetscInt  vertices[3] = {out->trifacelist[f*3+0]+numCells, out->trifacelist[f*3+1]+numCells, out->trifacelist[f*3+2]+numCells};
          const PetscInt *faces;
          PetscInt        numFaces;

          ierr = DMPlexGetFullJoin(*dm, 3, vertices, &numFaces, &faces);CHKERRQ(ierr);
          if (numFaces != 1) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Three vertices must cover only one face, not %D", numFaces);
          ierr = DMPlexSetLabelValue(*dm, "marker", faces[0], out->trifacemarkerlist[f]);CHKERRQ(ierr);
          ierr = DMPlexRestoreJoin(*dm, 3, vertices, &numFaces, &faces);CHKERRQ(ierr);
        }
      }
    }
    ierr = DMPlexSetRefinementUniform(*dm, PETSC_FALSE);CHKERRQ(ierr);
  }

  ierr = PLCDestroy(&in);CHKERRQ(ierr);
  ierr = PLCDestroy(&out);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexRefine_CTetgen"
PetscErrorCode DMPlexRefine_CTetgen(DM dm, PetscReal *maxVolumes, DM *dmRefined)
{
  MPI_Comm       comm;
  const PetscInt dim  = 3;
  PLC           *in, *out;
  PetscInt       verbose = 0, vStart, vEnd, v, cStart, cEnd, c, depth, depthGlobal;
  PetscMPIInt    rank;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscObjectGetComm((PetscObject)dm,&comm);CHKERRQ(ierr);
  ierr = PetscOptionsGetInt(((PetscObject) dm)->prefix, "-ctetgen_verbose", &verbose, NULL);CHKERRQ(ierr);
  ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
  ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
  ierr = MPI_Allreduce(&depth, &depthGlobal, 1, MPIU_INT, MPI_MAX, comm);CHKERRQ(ierr);
  ierr = DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);CHKERRQ(ierr);
  ierr = PLCCreate(&in);CHKERRQ(ierr);
  ierr = PLCCreate(&out);CHKERRQ(ierr);

  in->numberofpoints = vEnd - vStart;
  if (in->numberofpoints > 0) {
    PetscSection coordSection;
    Vec          coordinates;
    PetscScalar *array;

    ierr = PetscMalloc(in->numberofpoints*dim * sizeof(PetscReal), &in->pointlist);CHKERRQ(ierr);
    ierr = PetscMalloc(in->numberofpoints     * sizeof(int),       &in->pointmarkerlist);CHKERRQ(ierr);
    ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
    ierr = DMPlexGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
    ierr = VecGetArray(coordinates, &array);CHKERRQ(ierr);
    for (v = vStart; v < vEnd; ++v) {
      const PetscInt idx = v - vStart;
      PetscInt       off, d, m;

      ierr = PetscSectionGetOffset(coordSection, v, &off);CHKERRQ(ierr);
      for (d = 0; d < dim; ++d) {
        in->pointlist[idx*dim + d] = PetscRealPart(array[off+d]);
      }
      ierr = DMPlexGetLabelValue(dm, "marker", v, &m);CHKERRQ(ierr);

      in->pointmarkerlist[idx] = (int) m;
    }
    ierr = VecRestoreArray(coordinates, &array);CHKERRQ(ierr);
  }
  ierr  = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);

  in->numberofcorners       = 4;
  in->numberoftetrahedra    = cEnd - cStart;
  in->tetrahedronvolumelist = maxVolumes;
  if (in->numberoftetrahedra > 0) {
    ierr = PetscMalloc(in->numberoftetrahedra*in->numberofcorners * sizeof(int), &in->tetrahedronlist);CHKERRQ(ierr);
    for (c = cStart; c < cEnd; ++c) {
      const PetscInt idx      = c - cStart;
      PetscInt      *closure = NULL;
      PetscInt       closureSize;

      ierr = DMPlexGetTransitiveClosure(dm, c, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
      if ((closureSize != 5) && (closureSize != 15)) SETERRQ1(comm, PETSC_ERR_ARG_WRONG, "Mesh has cell which is not a tetrahedron, %D vertices in closure", closureSize);
      for (v = 0; v < 4; ++v) {
        in->tetrahedronlist[idx*in->numberofcorners + v] = closure[(v+closureSize-4)*2] - vStart;
      }
      ierr = DMPlexRestoreTransitiveClosure(dm, c, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
    }
  }
  if (!rank) {
    TetGenOpts t;

    ierr = TetGenOptsInitialize(&t);CHKERRQ(ierr);

    t.in        = dm; /* Should go away */
    t.refine    = 1;
    t.varvolume = 1;
    t.quality   = 1;
    t.edgesout  = 1;
    t.zeroindex = 1;
    t.quiet     = 1;
    t.verbose   = verbose; /* Change this */

    ierr = TetGenCheckOpts(&t);CHKERRQ(ierr);
    ierr = TetGenTetrahedralize(&t, in, out);CHKERRQ(ierr);
  }
  {
    const PetscInt numCorners  = 4;
    const PetscInt numCells    = out->numberoftetrahedra;
    const PetscInt numVertices = out->numberofpoints;
    const int     *cells       = out->tetrahedronlist;
    const double  *meshCoords  = out->pointlist;
    PetscBool      interpolate = depthGlobal > 1 ? PETSC_TRUE : PETSC_FALSE;

    ierr = DMPlexCreateFromCellList(comm, dim, numCells, numVertices, numCorners, interpolate, cells, dim, meshCoords, dmRefined);CHKERRQ(ierr);
    /* Set labels */
    for (v = 0; v < numVertices; ++v) {
      if (out->pointmarkerlist[v]) {
        ierr = DMPlexSetLabelValue(*dmRefined, "marker", v+numCells, out->pointmarkerlist[v]);CHKERRQ(ierr);
      }
    }
    if (interpolate) {
      PetscInt e, f;

      for (e = 0; e < out->numberofedges; e++) {
        if (out->edgemarkerlist[e]) {
          const PetscInt  vertices[2] = {out->edgelist[e*2+0]+numCells, out->edgelist[e*2+1]+numCells};
          const PetscInt *edges;
          PetscInt        numEdges;

          ierr = DMPlexGetJoin(*dmRefined, 2, vertices, &numEdges, &edges);CHKERRQ(ierr);
          if (numEdges != 1) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Two vertices must cover only one edge, not %D", numEdges);
          ierr = DMPlexSetLabelValue(*dmRefined, "marker", edges[0], out->edgemarkerlist[e]);CHKERRQ(ierr);
          ierr = DMPlexRestoreJoin(*dmRefined, 2, vertices, &numEdges, &edges);CHKERRQ(ierr);
        }
      }
      for (f = 0; f < out->numberoftrifaces; f++) {
        if (out->trifacemarkerlist[f]) {
          const PetscInt  vertices[3] = {out->trifacelist[f*3+0]+numCells, out->trifacelist[f*3+1]+numCells, out->trifacelist[f*3+2]+numCells};
          const PetscInt *faces;
          PetscInt        numFaces;

          ierr = DMPlexGetFullJoin(*dmRefined, 3, vertices, &numFaces, &faces);CHKERRQ(ierr);
          if (numFaces != 1) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Three vertices must cover only one face, not %D", numFaces);
          ierr = DMPlexSetLabelValue(*dmRefined, "marker", faces[0], out->trifacemarkerlist[f]);CHKERRQ(ierr);
          ierr = DMPlexRestoreJoin(*dmRefined, 3, vertices, &numFaces, &faces);CHKERRQ(ierr);
        }
      }
    }
    ierr = DMPlexSetRefinementUniform(*dmRefined, PETSC_FALSE);CHKERRQ(ierr);
  }
  ierr = PLCDestroy(&in);CHKERRQ(ierr);
  ierr = PLCDestroy(&out);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}
#endif

#undef __FUNCT__
#define __FUNCT__ "DMPlexGenerate"
/*@C
  DMPlexGenerate - Generates a mesh.

  Not Collective

  Input Parameters:
+ boundary - The DMPlex boundary object
. name - The mesh generation package name
- interpolate - Flag to create intermediate mesh elements

  Output Parameter:
. mesh - The DMPlex object

  Level: intermediate

.keywords: mesh, elements
.seealso: DMPlexCreate(), DMRefine()
@*/
PetscErrorCode DMPlexGenerate(DM boundary, const char name[], PetscBool interpolate, DM *mesh)
{
  PetscInt       dim;
  char           genname[1024];
  PetscBool      isTriangle = PETSC_FALSE, isTetgen = PETSC_FALSE, isCTetgen = PETSC_FALSE, flg;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(boundary, DM_CLASSID, 1);
  PetscValidLogicalCollectiveBool(boundary, interpolate, 2);
  ierr = DMPlexGetDimension(boundary, &dim);CHKERRQ(ierr);
  ierr = PetscOptionsGetString(((PetscObject) boundary)->prefix, "-dm_plex_generator", genname, 1024, &flg);CHKERRQ(ierr);
  if (flg) name = genname;
  if (name) {
    ierr = PetscStrcmp(name, "triangle", &isTriangle);CHKERRQ(ierr);
    ierr = PetscStrcmp(name, "tetgen",   &isTetgen);CHKERRQ(ierr);
    ierr = PetscStrcmp(name, "ctetgen",  &isCTetgen);CHKERRQ(ierr);
  }
  switch (dim) {
  case 1:
    if (!name || isTriangle) {
#if defined(PETSC_HAVE_TRIANGLE)
      ierr = DMPlexGenerate_Triangle(boundary, interpolate, mesh);CHKERRQ(ierr);
#else
      SETERRQ(PetscObjectComm((PetscObject)boundary), PETSC_ERR_SUP, "Mesh generation needs external package support.\nPlease reconfigure with --download-triangle.");
#endif
    } else SETERRQ1(PetscObjectComm((PetscObject)boundary), PETSC_ERR_SUP, "Unknown 2D mesh generation package %s", name);
    break;
  case 2:
    if (!name || isCTetgen) {
#if defined(PETSC_HAVE_CTETGEN)
      ierr = DMPlexGenerate_CTetgen(boundary, interpolate, mesh);CHKERRQ(ierr);
#else
      SETERRQ(PetscObjectComm((PetscObject)boundary), PETSC_ERR_SUP, "CTetgen needs external package support.\nPlease reconfigure with --download-ctetgen.");
#endif
    } else if (isTetgen) {
#if defined(PETSC_HAVE_TETGEN)
      ierr = DMPlexGenerate_Tetgen(boundary, interpolate, mesh);CHKERRQ(ierr);
#else
      SETERRQ(PetscObjectComm((PetscObject)boundary), PETSC_ERR_SUP, "Tetgen needs external package support.\nPlease reconfigure with --with-c-language=cxx --download-tetgen.");
#endif
    } else SETERRQ1(PetscObjectComm((PetscObject)boundary), PETSC_ERR_SUP, "Unknown 3D mesh generation package %s", name);
    break;
  default:
    SETERRQ1(PetscObjectComm((PetscObject)boundary), PETSC_ERR_SUP, "Mesh generation for a dimension %d boundary is not supported.", dim);
  }
  PetscFunctionReturn(0);
}

typedef PetscInt CellRefiner;

#undef __FUNCT__
#define __FUNCT__ "GetDepthStart_Private"
PETSC_STATIC_INLINE PetscErrorCode GetDepthStart_Private(PetscInt depth, PetscInt depthSize[], PetscInt *cStart, PetscInt *fStart, PetscInt *eStart, PetscInt *vStart)
{
  PetscFunctionBegin;
  if (cStart) *cStart = 0;
  if (vStart) *vStart = depthSize[depth];
  if (fStart) *fStart = depthSize[depth] + depthSize[0];
  if (eStart) *eStart = depthSize[depth] + depthSize[0] + depthSize[depth-1];
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "GetDepthEnd_Private"
PETSC_STATIC_INLINE PetscErrorCode GetDepthEnd_Private(PetscInt depth, PetscInt depthSize[], PetscInt *cEnd, PetscInt *fEnd, PetscInt *eEnd, PetscInt *vEnd)
{
  PetscFunctionBegin;
  if (cEnd) *cEnd = depthSize[depth];
  if (vEnd) *vEnd = depthSize[depth] + depthSize[0];
  if (fEnd) *fEnd = depthSize[depth] + depthSize[0] + depthSize[depth-1];
  if (eEnd) *eEnd = depthSize[depth] + depthSize[0] + depthSize[depth-1] + depthSize[1];
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "CellRefinerGetSizes"
PetscErrorCode CellRefinerGetSizes(CellRefiner refiner, DM dm, PetscInt depthSize[])
{
  PetscInt       cStart, cEnd, cMax, vStart, vEnd, vMax, fStart, fEnd, fMax, eStart, eEnd, eMax;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);CHKERRQ(ierr);
  ierr = DMPlexGetDepthStratum(dm, 1, &eStart, &eEnd);CHKERRQ(ierr);
  ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
  ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
  ierr = DMPlexGetHybridBounds(dm, &cMax, &fMax, &eMax, &vMax);CHKERRQ(ierr);
  switch (refiner) {
  case 1:
    /* Simplicial 2D */
    depthSize[0] = vEnd - vStart + fEnd - fStart;         /* Add a vertex on every face */
    depthSize[1] = 2*(fEnd - fStart) + 3*(cEnd - cStart); /* Every face is split into 2 faces and 3 faces are added for each cell */
    depthSize[2] = 4*(cEnd - cStart);                     /* Every cell split into 4 cells */
    break;
  case 3:
    /* Hybrid 2D */
    if (cMax < 0) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "No cell maximum specified in hybrid mesh");
    cMax = PetscMin(cEnd, cMax);
    if (fMax < 0) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "No face maximum specified in hybrid mesh");
    fMax         = PetscMin(fEnd, fMax);
    depthSize[0] = vEnd - vStart + fMax - fStart;                                         /* Add a vertex on every face, but not hybrid faces */
    depthSize[1] = 2*(fMax - fStart) + 3*(cMax - cStart) + (fEnd - fMax) + (cEnd - cMax); /* Every interior face is split into 2 faces, 3 faces are added for each interior cell, and one in each hybrid cell */
    depthSize[2] = 4*(cMax - cStart) + 2*(cEnd - cMax);                                   /* Interior cells split into 4 cells, Hybrid cells split into 2 cells */
    break;
  case 2:
    /* Hex 2D */
    depthSize[0] = vEnd - vStart + cEnd - cStart + fEnd - fStart; /* Add a vertex on every face and cell */
    depthSize[1] = 2*(fEnd - fStart) + 4*(cEnd - cStart);         /* Every face is split into 2 faces and 4 faces are added for each cell */
    depthSize[2] = 4*(cEnd - cStart);                             /* Every cell split into 4 cells */
    break;
  default:
    SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unknown cell refiner %d", refiner);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "CellRefinerSetConeSizes"
PetscErrorCode CellRefinerSetConeSizes(CellRefiner refiner, DM dm, PetscInt depthSize[], DM rdm)
{
  PetscInt       depth, cStart, cStartNew, cEnd, cMax, c, vStart, vStartNew, vEnd, vMax, v, fStart, fStartNew, fEnd, fMax, f, eStart, eStartNew, eEnd, eMax, r;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
  ierr = DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);CHKERRQ(ierr);
  ierr = DMPlexGetDepthStratum(dm, 1, &eStart, &eEnd);CHKERRQ(ierr);
  ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
  ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
  ierr = DMPlexGetHybridBounds(dm, &cMax, &fMax, &eMax, &vMax);CHKERRQ(ierr);
  ierr = GetDepthStart_Private(depth, depthSize, &cStartNew, &fStartNew, &eStartNew, &vStartNew);CHKERRQ(ierr);
  switch (refiner) {
  case 1:
    /* Simplicial 2D */
    /* All cells have 3 faces */
    for (c = cStart; c < cEnd; ++c) {
      for (r = 0; r < 4; ++r) {
        const PetscInt newp = (c - cStart)*4 + r;

        ierr = DMPlexSetConeSize(rdm, newp, 3);CHKERRQ(ierr);
      }
    }
    /* Split faces have 2 vertices and the same cells as the parent */
    for (f = fStart; f < fEnd; ++f) {
      for (r = 0; r < 2; ++r) {
        const PetscInt newp = fStartNew + (f - fStart)*2 + r;
        PetscInt       size;

        ierr = DMPlexSetConeSize(rdm, newp, 2);CHKERRQ(ierr);
        ierr = DMPlexGetSupportSize(dm, f, &size);CHKERRQ(ierr);
        ierr = DMPlexSetSupportSize(rdm, newp, size);CHKERRQ(ierr);
      }
    }
    /* Interior faces have 2 vertices and 2 cells */
    for (c = cStart; c < cEnd; ++c) {
      for (r = 0; r < 3; ++r) {
        const PetscInt newp = fStartNew + (fEnd - fStart)*2 + (c - cStart)*3 + r;

        ierr = DMPlexSetConeSize(rdm, newp, 2);CHKERRQ(ierr);
        ierr = DMPlexSetSupportSize(rdm, newp, 2);CHKERRQ(ierr);
      }
    }
    /* Old vertices have identical supports */
    for (v = vStart; v < vEnd; ++v) {
      const PetscInt newp = vStartNew + (v - vStart);
      PetscInt       size;

      ierr = DMPlexGetSupportSize(dm, v, &size);CHKERRQ(ierr);
      ierr = DMPlexSetSupportSize(rdm, newp, size);CHKERRQ(ierr);
    }
    /* Face vertices have 2 + cells*2 supports */
    for (f = fStart; f < fEnd; ++f) {
      const PetscInt newp = vStartNew + (vEnd - vStart) + (f - fStart);
      PetscInt       size;

      ierr = DMPlexGetSupportSize(dm, f, &size);CHKERRQ(ierr);
      ierr = DMPlexSetSupportSize(rdm, newp, 2 + size*2);CHKERRQ(ierr);
    }
    break;
  case 2:
    /* Hex 2D */
    /* All cells have 4 faces */
    for (c = cStart; c < cEnd; ++c) {
      for (r = 0; r < 4; ++r) {
        const PetscInt newp = (c - cStart)*4 + r;

        ierr = DMPlexSetConeSize(rdm, newp, 4);CHKERRQ(ierr);
      }
    }
    /* Split faces have 2 vertices and the same cells as the parent */
    for (f = fStart; f < fEnd; ++f) {
      for (r = 0; r < 2; ++r) {
        const PetscInt newp = fStartNew + (f - fStart)*2 + r;
        PetscInt       size;

        ierr = DMPlexSetConeSize(rdm, newp, 2);CHKERRQ(ierr);
        ierr = DMPlexGetSupportSize(dm, f, &size);CHKERRQ(ierr);
        ierr = DMPlexSetSupportSize(rdm, newp, size);CHKERRQ(ierr);
      }
    }
    /* Interior faces have 2 vertices and 2 cells */
    for (c = cStart; c < cEnd; ++c) {
      for (r = 0; r < 4; ++r) {
        const PetscInt newp = fStartNew + (fEnd - fStart)*2 + (c - cStart)*4 + r;

        ierr = DMPlexSetConeSize(rdm, newp, 2);CHKERRQ(ierr);
        ierr = DMPlexSetSupportSize(rdm, newp, 2);CHKERRQ(ierr);
      }
    }
    /* Old vertices have identical supports */
    for (v = vStart; v < vEnd; ++v) {
      const PetscInt newp = vStartNew + (v - vStart);
      PetscInt       size;

      ierr = DMPlexGetSupportSize(dm, v, &size);CHKERRQ(ierr);
      ierr = DMPlexSetSupportSize(rdm, newp, size);CHKERRQ(ierr);
    }
    /* Face vertices have 2 + cells supports */
    for (f = fStart; f < fEnd; ++f) {
      const PetscInt newp = vStartNew + (vEnd - vStart) + (f - fStart);
      PetscInt       size;

      ierr = DMPlexGetSupportSize(dm, f, &size);CHKERRQ(ierr);
      ierr = DMPlexSetSupportSize(rdm, newp, 2 + size);CHKERRQ(ierr);
    }
    /* Cell vertices have 4 supports */
    for (c = cStart; c < cEnd; ++c) {
      const PetscInt newp = vStartNew + (vEnd - vStart) + (fEnd - fStart) + (c - cStart);

      ierr = DMPlexSetSupportSize(rdm, newp, 4);CHKERRQ(ierr);
    }
    break;
  case 3:
    /* Hybrid 2D */
    if (cMax < 0) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "No cell maximum specified in hybrid mesh");
    cMax = PetscMin(cEnd, cMax);
    if (fMax < 0) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "No face maximum specified in hybrid mesh");
    fMax = PetscMin(fEnd, fMax);
    ierr = DMPlexSetHybridBounds(rdm, cStartNew + (cMax - cStart)*4, fStartNew + (fMax - fStart)*2 + (cMax - cStart)*3, PETSC_DETERMINE, PETSC_DETERMINE);CHKERRQ(ierr);
    /* Interior cells have 3 faces */
    for (c = cStart; c < cMax; ++c) {
      for (r = 0; r < 4; ++r) {
        const PetscInt newp = cStartNew + (c - cStart)*4 + r;

        ierr = DMPlexSetConeSize(rdm, newp, 3);CHKERRQ(ierr);
      }
    }
    /* Hybrid cells have 4 faces */
    for (c = cMax; c < cEnd; ++c) {
      for (r = 0; r < 2; ++r) {
        const PetscInt newp = cStartNew + (cMax - cStart)*4 + (c - cMax)*2 + r;

        ierr = DMPlexSetConeSize(rdm, newp, 4);CHKERRQ(ierr);
      }
    }
    /* Interior split faces have 2 vertices and the same cells as the parent */
    for (f = fStart; f < fMax; ++f) {
      for (r = 0; r < 2; ++r) {
        const PetscInt newp = fStartNew + (f - fStart)*2 + r;
        PetscInt       size;

        ierr = DMPlexSetConeSize(rdm, newp, 2);CHKERRQ(ierr);
        ierr = DMPlexGetSupportSize(dm, f, &size);CHKERRQ(ierr);
        ierr = DMPlexSetSupportSize(rdm, newp, size);CHKERRQ(ierr);
      }
    }
    /* Interior cell faces have 2 vertices and 2 cells */
    for (c = cStart; c < cMax; ++c) {
      for (r = 0; r < 3; ++r) {
        const PetscInt newp = fStartNew + (fMax - fStart)*2 + (c - cStart)*3 + r;

        ierr = DMPlexSetConeSize(rdm, newp, 2);CHKERRQ(ierr);
        ierr = DMPlexSetSupportSize(rdm, newp, 2);CHKERRQ(ierr);
      }
    }
    /* Hybrid faces have 2 vertices and the same cells */
    for (f = fMax; f < fEnd; ++f) {
      const PetscInt newp = fStartNew + (fMax - fStart)*2 + (cMax - cStart)*3 + (f - fMax);
      PetscInt       size;

      ierr = DMPlexSetConeSize(rdm, newp, 2);CHKERRQ(ierr);
      ierr = DMPlexGetSupportSize(dm, f, &size);CHKERRQ(ierr);
      ierr = DMPlexSetSupportSize(rdm, newp, size);CHKERRQ(ierr);
    }
    /* Hybrid cell faces have 2 vertices and 2 cells */
    for (c = cMax; c < cEnd; ++c) {
      const PetscInt newp = fStartNew + (fMax - fStart)*2 + (cMax - cStart)*3 + (fEnd - fMax) + (c - cMax);

      ierr = DMPlexSetConeSize(rdm, newp, 2);CHKERRQ(ierr);
      ierr = DMPlexSetSupportSize(rdm, newp, 2);CHKERRQ(ierr);
    }
    /* Old vertices have identical supports */
    for (v = vStart; v < vEnd; ++v) {
      const PetscInt newp = vStartNew + (v - vStart);
      PetscInt       size;

      ierr = DMPlexGetSupportSize(dm, v, &size);CHKERRQ(ierr);
      ierr = DMPlexSetSupportSize(rdm, newp, size);CHKERRQ(ierr);
    }
    /* Face vertices have 2 + (2 interior, 1 hybrid) supports */
    for (f = fStart; f < fMax; ++f) {
      const PetscInt newp = vStartNew + (vEnd - vStart) + (f - fStart);
      const PetscInt *support;
      PetscInt       size, newSize = 2, s;

      ierr = DMPlexGetSupportSize(dm, f, &size);CHKERRQ(ierr);
      ierr = DMPlexGetSupport(dm, f, &support);CHKERRQ(ierr);
      for (s = 0; s < size; ++s) {
        if (support[s] >= cMax) newSize += 1;
        else newSize += 2;
      }
      ierr = DMPlexSetSupportSize(rdm, newp, newSize);CHKERRQ(ierr);
    }
    break;
  default:
    SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unknown cell refiner %d", refiner);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "CellRefinerSetCones"
PetscErrorCode CellRefinerSetCones(CellRefiner refiner, DM dm, PetscInt depthSize[], DM rdm)
{
  PetscInt       depth, cStart, cEnd, cMax, cStartNew, cEndNew, c, vStart, vEnd, vMax, vStartNew, vEndNew, v, fStart, fEnd, fMax, fStartNew, fEndNew, f, eStart, eEnd, eMax, eStartNew, eEndNew, r, p;
  PetscInt       maxSupportSize, *supportRef;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
  ierr = DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);CHKERRQ(ierr);
  ierr = DMPlexGetDepthStratum(dm, 1, &eStart, &eEnd);CHKERRQ(ierr);
  ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
  ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
  ierr = DMPlexGetHybridBounds(dm, &cMax, &fMax, &eMax, &vMax);CHKERRQ(ierr);
  ierr = GetDepthStart_Private(depth, depthSize, &cStartNew, &fStartNew, &eStartNew, &vStartNew);CHKERRQ(ierr);
  ierr = GetDepthEnd_Private(depth, depthSize, &cEndNew, &fEndNew, &eEndNew, &vEndNew);CHKERRQ(ierr);
  switch (refiner) {
  case 1:
    /* Simplicial 2D */
    /*
     2
     |\
     | \
     |  \
     |   \
     | C  \
     |     \
     |      \
     2---1---1
     |\  D  / \
     | 2   0   \
     |A \ /  B  \
     0---0-------1
     */
    /* All cells have 3 faces */
    for (c = cStart; c < cEnd; ++c) {
      const PetscInt  newp = cStartNew + (c - cStart)*4;
      const PetscInt *cone, *ornt;
      PetscInt        coneNew[3], orntNew[3];

      ierr = DMPlexGetCone(dm, c, &cone);CHKERRQ(ierr);
      ierr = DMPlexGetConeOrientation(dm, c, &ornt);CHKERRQ(ierr);
      /* A triangle */
      coneNew[0] = fStartNew + (cone[0] - fStart)*2 + (ornt[0] < 0 ? 1 : 0);
      orntNew[0] = ornt[0];
      coneNew[1] = fStartNew + (fEnd    - fStart)*2 + (c - cStart)*3 + 2;
      orntNew[1] = -2;
      coneNew[2] = fStartNew + (cone[2] - fStart)*2 + (ornt[2] < 0 ? 0 : 1);
      orntNew[2] = ornt[2];
      ierr       = DMPlexSetCone(rdm, newp+0, coneNew);CHKERRQ(ierr);
      ierr       = DMPlexSetConeOrientation(rdm, newp+0, orntNew);CHKERRQ(ierr);
#if 1
      if ((newp+0 < cStartNew) || (newp+0 >= cEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a cell [%d, %d)", newp+0, cStartNew, cEndNew);
      for (p = 0; p < 3; ++p) {
        if ((coneNew[p] < fStartNew) || (coneNew[p] >= fEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a face [%d, %d)", coneNew[p], fStartNew, fEndNew);
      }
#endif
      /* B triangle */
      coneNew[0] = fStartNew + (cone[0] - fStart)*2 + (ornt[0] < 0 ? 0 : 1);
      orntNew[0] = ornt[0];
      coneNew[1] = fStartNew + (cone[1] - fStart)*2 + (ornt[1] < 0 ? 1 : 0);
      orntNew[1] = ornt[1];
      coneNew[2] = fStartNew + (fEnd    - fStart)*2 + (c - cStart)*3 + 0;
      orntNew[2] = -2;
      ierr       = DMPlexSetCone(rdm, newp+1, coneNew);CHKERRQ(ierr);
      ierr       = DMPlexSetConeOrientation(rdm, newp+1, orntNew);CHKERRQ(ierr);
#if 1
      if ((newp+1 < cStartNew) || (newp+1 >= cEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a cell [%d, %d)", newp+1, cStartNew, cEndNew);
      for (p = 0; p < 3; ++p) {
        if ((coneNew[p] < fStartNew) || (coneNew[p] >= fEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a face [%d, %d)", coneNew[p], fStartNew, fEndNew);
      }
#endif
      /* C triangle */
      coneNew[0] = fStartNew + (fEnd    - fStart)*2 + (c - cStart)*3 + 1;
      orntNew[0] = -2;
      coneNew[1] = fStartNew + (cone[1] - fStart)*2 + (ornt[1] < 0 ? 0 : 1);
      orntNew[1] = ornt[1];
      coneNew[2] = fStartNew + (cone[2] - fStart)*2 + (ornt[2] < 0 ? 1 : 0);
      orntNew[2] = ornt[2];
      ierr       = DMPlexSetCone(rdm, newp+2, coneNew);CHKERRQ(ierr);
      ierr       = DMPlexSetConeOrientation(rdm, newp+2, orntNew);CHKERRQ(ierr);
#if 1
      if ((newp+2 < cStartNew) || (newp+2 >= cEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a cell [%d, %d)", newp+2, cStartNew, cEndNew);
      for (p = 0; p < 3; ++p) {
        if ((coneNew[p] < fStartNew) || (coneNew[p] >= fEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a face [%d, %d)", coneNew[p], fStartNew, fEndNew);
      }
#endif
      /* D triangle */
      coneNew[0] = fStartNew + (fEnd    - fStart)*2 + (c - cStart)*3 + 0;
      orntNew[0] = 0;
      coneNew[1] = fStartNew + (fEnd    - fStart)*2 + (c - cStart)*3 + 1;
      orntNew[1] = 0;
      coneNew[2] = fStartNew + (fEnd    - fStart)*2 + (c - cStart)*3 + 2;
      orntNew[2] = 0;
      ierr       = DMPlexSetCone(rdm, newp+3, coneNew);CHKERRQ(ierr);
      ierr       = DMPlexSetConeOrientation(rdm, newp+3, orntNew);CHKERRQ(ierr);
#if 1
      if ((newp+3 < cStartNew) || (newp+3 >= cEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a cell [%d, %d)", newp+3, cStartNew, cEndNew);
      for (p = 0; p < 3; ++p) {
        if ((coneNew[p] < fStartNew) || (coneNew[p] >= fEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a face [%d, %d)", coneNew[p], fStartNew, fEndNew);
      }
#endif
    }
    /* Split faces have 2 vertices and the same cells as the parent */
    ierr = DMPlexGetMaxSizes(dm, NULL, &maxSupportSize);CHKERRQ(ierr);
    ierr = PetscMalloc((2 + maxSupportSize*2) * sizeof(PetscInt), &supportRef);CHKERRQ(ierr);
    for (f = fStart; f < fEnd; ++f) {
      const PetscInt newv = vStartNew + (vEnd - vStart) + (f - fStart);

      for (r = 0; r < 2; ++r) {
        const PetscInt  newp = fStartNew + (f - fStart)*2 + r;
        const PetscInt *cone, *support;
        PetscInt        coneNew[2], coneSize, c, supportSize, s;

        ierr             = DMPlexGetCone(dm, f, &cone);CHKERRQ(ierr);
        coneNew[0]       = vStartNew + (cone[0] - vStart);
        coneNew[1]       = vStartNew + (cone[1] - vStart);
        coneNew[(r+1)%2] = newv;
        ierr             = DMPlexSetCone(rdm, newp, coneNew);CHKERRQ(ierr);
#if 1
        if ((newp < fStartNew) || (newp >= fEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a face [%d, %d)", newp, fStartNew, fEndNew);
        for (p = 0; p < 2; ++p) {
          if ((coneNew[p] < vStartNew) || (coneNew[p] >= vEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a vertex [%d, %d)", coneNew[p], vStartNew, vEndNew);
        }
#endif
        ierr = DMPlexGetSupportSize(dm, f, &supportSize);CHKERRQ(ierr);
        ierr = DMPlexGetSupport(dm, f, &support);CHKERRQ(ierr);
        for (s = 0; s < supportSize; ++s) {
          ierr = DMPlexGetConeSize(dm, support[s], &coneSize);CHKERRQ(ierr);
          ierr = DMPlexGetCone(dm, support[s], &cone);CHKERRQ(ierr);
          for (c = 0; c < coneSize; ++c) {
            if (cone[c] == f) break;
          }
          supportRef[s] = cStartNew + (support[s] - cStart)*4 + (c+r)%3;
        }
        ierr = DMPlexSetSupport(rdm, newp, supportRef);CHKERRQ(ierr);
#if 1
        if ((newp < fStartNew) || (newp >= fEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a face [%d, %d)", newp, fStartNew, fEndNew);
        for (p = 0; p < supportSize; ++p) {
          if ((supportRef[p] < cStartNew) || (supportRef[p] >= cEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a cell [%d, %d)", supportRef[p], cStartNew, cEndNew);
        }
#endif
      }
    }
    /* Interior faces have 2 vertices and 2 cells */
    for (c = cStart; c < cEnd; ++c) {
      const PetscInt *cone;

      ierr = DMPlexGetCone(dm, c, &cone);CHKERRQ(ierr);
      for (r = 0; r < 3; ++r) {
        const PetscInt newp = fStartNew + (fEnd - fStart)*2 + (c - cStart)*3 + r;
        PetscInt       coneNew[2];
        PetscInt       supportNew[2];

        coneNew[0] = vStartNew + (vEnd - vStart) + (cone[r]       - fStart);
        coneNew[1] = vStartNew + (vEnd - vStart) + (cone[(r+1)%3] - fStart);
        ierr       = DMPlexSetCone(rdm, newp, coneNew);CHKERRQ(ierr);
#if 1
        if ((newp < fStartNew) || (newp >= fEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a face [%d, %d)", newp, fStartNew, fEndNew);
        for (p = 0; p < 2; ++p) {
          if ((coneNew[p] < vStartNew) || (coneNew[p] >= vEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a vertex [%d, %d)", coneNew[p], vStartNew, vEndNew);
        }
#endif
        supportNew[0] = (c - cStart)*4 + (r+1)%3;
        supportNew[1] = (c - cStart)*4 + 3;
        ierr          = DMPlexSetSupport(rdm, newp, supportNew);CHKERRQ(ierr);
#if 1
        if ((newp < fStartNew) || (newp >= fEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a face [%d, %d)", newp, fStartNew, fEndNew);
        for (p = 0; p < 2; ++p) {
          if ((supportNew[p] < cStartNew) || (supportNew[p] >= cEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a cell [%d, %d)", supportNew[p], cStartNew, cEndNew);
        }
#endif
      }
    }
    /* Old vertices have identical supports */
    for (v = vStart; v < vEnd; ++v) {
      const PetscInt  newp = vStartNew + (v - vStart);
      const PetscInt *support, *cone;
      PetscInt        size, s;

      ierr = DMPlexGetSupportSize(dm, v, &size);CHKERRQ(ierr);
      ierr = DMPlexGetSupport(dm, v, &support);CHKERRQ(ierr);
      for (s = 0; s < size; ++s) {
        PetscInt r = 0;

        ierr = DMPlexGetCone(dm, support[s], &cone);CHKERRQ(ierr);
        if (cone[1] == v) r = 1;
        supportRef[s] = fStartNew + (support[s] - fStart)*2 + r;
      }
      ierr = DMPlexSetSupport(rdm, newp, supportRef);CHKERRQ(ierr);
#if 1
      if ((newp < vStartNew) || (newp >= vEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a vertex [%d, %d)", newp, vStartNew, vEndNew);
      for (p = 0; p < size; ++p) {
        if ((supportRef[p] < fStartNew) || (supportRef[p] >= fEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a face [%d, %d)", supportRef[p], fStartNew, fEndNew);
      }
#endif
    }
    /* Face vertices have 2 + cells*2 supports */
    for (f = fStart; f < fEnd; ++f) {
      const PetscInt  newp = vStartNew + (vEnd - vStart) + (f - fStart);
      const PetscInt *cone, *support;
      PetscInt        size, s;

      ierr          = DMPlexGetSupportSize(dm, f, &size);CHKERRQ(ierr);
      ierr          = DMPlexGetSupport(dm, f, &support);CHKERRQ(ierr);
      supportRef[0] = fStartNew + (f - fStart)*2 + 0;
      supportRef[1] = fStartNew + (f - fStart)*2 + 1;
      for (s = 0; s < size; ++s) {
        PetscInt r = 0;

        ierr = DMPlexGetCone(dm, support[s], &cone);CHKERRQ(ierr);
        if      (cone[1] == f) r = 1;
        else if (cone[2] == f) r = 2;
        supportRef[2+s*2+0] = fStartNew + (fEnd - fStart)*2 + (support[s] - cStart)*3 + (r+2)%3;
        supportRef[2+s*2+1] = fStartNew + (fEnd - fStart)*2 + (support[s] - cStart)*3 + r;
      }
      ierr = DMPlexSetSupport(rdm, newp, supportRef);CHKERRQ(ierr);
#if 1
      if ((newp < vStartNew) || (newp >= vEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a vertex [%d, %d)", newp, vStartNew, vEndNew);
      for (p = 0; p < 2+size*2; ++p) {
        if ((supportRef[p] < fStartNew) || (supportRef[p] >= fEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a face [%d, %d)", supportRef[p], fStartNew, fEndNew);
      }
#endif
    }
    ierr = PetscFree(supportRef);CHKERRQ(ierr);
    break;
  case 2:
    /* Hex 2D */
    /*
     3---------2---------2
     |         |         |
     |    D    2    C    |
     |         |         |
     3----3----0----1----1
     |         |         |
     |    A    0    B    |
     |         |         |
     0---------0---------1
     */
    /* All cells have 4 faces */
    for (c = cStart; c < cEnd; ++c) {
      const PetscInt  newp = (c - cStart)*4;
      const PetscInt *cone, *ornt;
      PetscInt        coneNew[4], orntNew[4];

      ierr = DMPlexGetCone(dm, c, &cone);CHKERRQ(ierr);
      ierr = DMPlexGetConeOrientation(dm, c, &ornt);CHKERRQ(ierr);
      /* A quad */
      coneNew[0] = fStartNew + (cone[0] - fStart)*2 + (ornt[0] < 0 ? 1 : 0);
      orntNew[0] = ornt[0];
      coneNew[1] = fStartNew + (fEnd    - fStart)*2 + (c - cStart)*4 + 0;
      orntNew[1] = 0;
      coneNew[2] = fStartNew + (fEnd    - fStart)*2 + (c - cStart)*4 + 3;
      orntNew[2] = -2;
      coneNew[3] = fStartNew + (cone[3] - fStart)*2 + (ornt[3] < 0 ? 0 : 1);
      orntNew[3] = ornt[3];
      ierr       = DMPlexSetCone(rdm, newp+0, coneNew);CHKERRQ(ierr);
      ierr       = DMPlexSetConeOrientation(rdm, newp+0, orntNew);CHKERRQ(ierr);
#if 1
      if ((newp+0 < cStartNew) || (newp+0 >= cEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a cell [%d, %d)", newp+0, cStartNew, cEndNew);
      for (p = 0; p < 4; ++p) {
        if ((coneNew[p] < fStartNew) || (coneNew[p] >= fEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a face [%d, %d)", coneNew[p], fStartNew, fEndNew);
      }
#endif
      /* B quad */
      coneNew[0] = fStartNew + (cone[0] - fStart)*2 + (ornt[0] < 0 ? 0 : 1);
      orntNew[0] = ornt[0];
      coneNew[1] = fStartNew + (cone[1] - fStart)*2 + (ornt[1] < 0 ? 1 : 0);
      orntNew[1] = ornt[1];
      coneNew[2] = fStartNew + (fEnd    - fStart)*2 + (c - cStart)*4 + 1;
      orntNew[2] = 0;
      coneNew[3] = fStartNew + (fEnd    - fStart)*2 + (c - cStart)*4 + 0;
      orntNew[3] = -2;
      ierr       = DMPlexSetCone(rdm, newp+1, coneNew);CHKERRQ(ierr);
      ierr       = DMPlexSetConeOrientation(rdm, newp+1, orntNew);CHKERRQ(ierr);
#if 1
      if ((newp+1 < cStartNew) || (newp+1 >= cEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a cell [%d, %d)", newp+1, cStartNew, cEndNew);
      for (p = 0; p < 4; ++p) {
        if ((coneNew[p] < fStartNew) || (coneNew[p] >= fEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a face [%d, %d)", coneNew[p], fStartNew, fEndNew);
      }
#endif
      /* C quad */
      coneNew[0] = fStartNew + (fEnd    - fStart)*2 + (c - cStart)*4 + 1;
      orntNew[0] = -2;
      coneNew[1] = fStartNew + (cone[1] - fStart)*2 + (ornt[1] < 0 ? 0 : 1);
      orntNew[1] = ornt[1];
      coneNew[2] = fStartNew + (cone[2] - fStart)*2 + (ornt[2] < 0 ? 1 : 0);
      orntNew[2] = ornt[2];
      coneNew[3] = fStartNew + (fEnd    - fStart)*2 + (c - cStart)*4 + 2;
      orntNew[3] = 0;
      ierr       = DMPlexSetCone(rdm, newp+2, coneNew);CHKERRQ(ierr);
      ierr       = DMPlexSetConeOrientation(rdm, newp+2, orntNew);CHKERRQ(ierr);
#if 1
      if ((newp+2 < cStartNew) || (newp+2 >= cEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a cell [%d, %d)", newp+2, cStartNew, cEndNew);
      for (p = 0; p < 4; ++p) {
        if ((coneNew[p] < fStartNew) || (coneNew[p] >= fEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a face [%d, %d)", coneNew[p], fStartNew, fEndNew);
      }
#endif
      /* D quad */
      coneNew[0] = fStartNew + (fEnd    - fStart)*2 + (c - cStart)*4 + 3;
      orntNew[0] = 0;
      coneNew[1] = fStartNew + (fEnd    - fStart)*2 + (c - cStart)*4 + 2;
      orntNew[1] = -2;
      coneNew[2] = fStartNew + (cone[2] - fStart)*2 + (ornt[2] < 0 ? 0 : 1);
      orntNew[2] = ornt[2];
      coneNew[3] = fStartNew + (cone[3] - fStart)*2 + (ornt[3] < 0 ? 1 : 0);
      orntNew[3] = ornt[3];
      ierr       = DMPlexSetCone(rdm, newp+3, coneNew);CHKERRQ(ierr);
      ierr       = DMPlexSetConeOrientation(rdm, newp+3, orntNew);CHKERRQ(ierr);
#if 1
      if ((newp+3 < cStartNew) || (newp+3 >= cEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a cell [%d, %d)", newp+3, cStartNew, cEndNew);
      for (p = 0; p < 4; ++p) {
        if ((coneNew[p] < fStartNew) || (coneNew[p] >= fEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a face [%d, %d)", coneNew[p], fStartNew, fEndNew);
      }
#endif
    }
    /* Split faces have 2 vertices and the same cells as the parent */
    ierr = DMPlexGetMaxSizes(dm, NULL, &maxSupportSize);CHKERRQ(ierr);
    ierr = PetscMalloc((2 + maxSupportSize*2) * sizeof(PetscInt), &supportRef);CHKERRQ(ierr);
    for (f = fStart; f < fEnd; ++f) {
      const PetscInt newv = vStartNew + (vEnd - vStart) + (f - fStart);

      for (r = 0; r < 2; ++r) {
        const PetscInt  newp = fStartNew + (f - fStart)*2 + r;
        const PetscInt *cone, *support;
        PetscInt        coneNew[2], coneSize, c, supportSize, s;

        ierr             = DMPlexGetCone(dm, f, &cone);CHKERRQ(ierr);
        coneNew[0]       = vStartNew + (cone[0] - vStart);
        coneNew[1]       = vStartNew + (cone[1] - vStart);
        coneNew[(r+1)%2] = newv;
        ierr             = DMPlexSetCone(rdm, newp, coneNew);CHKERRQ(ierr);
#if 1
        if ((newp < fStartNew) || (newp >= fEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a face [%d, %d)", newp, fStartNew, fEndNew);
        for (p = 0; p < 2; ++p) {
          if ((coneNew[p] < vStartNew) || (coneNew[p] >= vEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a vertex [%d, %d)", coneNew[p], vStartNew, vEndNew);
        }
#endif
        ierr = DMPlexGetSupportSize(dm, f, &supportSize);CHKERRQ(ierr);
        ierr = DMPlexGetSupport(dm, f, &support);CHKERRQ(ierr);
        for (s = 0; s < supportSize; ++s) {
          ierr = DMPlexGetConeSize(dm, support[s], &coneSize);CHKERRQ(ierr);
          ierr = DMPlexGetCone(dm, support[s], &cone);CHKERRQ(ierr);
          for (c = 0; c < coneSize; ++c) {
            if (cone[c] == f) break;
          }
          supportRef[s] = cStartNew + (support[s] - cStart)*4 + (c+r)%4;
        }
        ierr = DMPlexSetSupport(rdm, newp, supportRef);CHKERRQ(ierr);
#if 1
        if ((newp < fStartNew) || (newp >= fEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a face [%d, %d)", newp, fStartNew, fEndNew);
        for (p = 0; p < supportSize; ++p) {
          if ((supportRef[p] < cStartNew) || (supportRef[p] >= cEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a cell [%d, %d)", supportRef[p], cStartNew, cEndNew);
        }
#endif
      }
    }
    /* Interior faces have 2 vertices and 2 cells */
    for (c = cStart; c < cEnd; ++c) {
      const PetscInt *cone;
      PetscInt        coneNew[2], supportNew[2];

      ierr = DMPlexGetCone(dm, c, &cone);CHKERRQ(ierr);
      for (r = 0; r < 4; ++r) {
        const PetscInt newp = fStartNew + (fEnd - fStart)*2 + (c - cStart)*4 + r;

        coneNew[0] = vStartNew + (vEnd - vStart) + (cone[r] - fStart);
        coneNew[1] = vStartNew + (vEnd - vStart) + (fEnd    - fStart) + (c - cStart);
        ierr       = DMPlexSetCone(rdm, newp, coneNew);CHKERRQ(ierr);
#if 1
        if ((newp < fStartNew) || (newp >= fEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a face [%d, %d)", newp, fStartNew, fEndNew);
        for (p = 0; p < 2; ++p) {
          if ((coneNew[p] < vStartNew) || (coneNew[p] >= vEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a vertex [%d, %d)", coneNew[p], vStartNew, vEndNew);
        }
#endif
        supportNew[0] = (c - cStart)*4 + r;
        supportNew[1] = (c - cStart)*4 + (r+1)%4;
        ierr          = DMPlexSetSupport(rdm, newp, supportNew);CHKERRQ(ierr);
#if 1
        if ((newp < fStartNew) || (newp >= fEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a face [%d, %d)", newp, fStartNew, fEndNew);
        for (p = 0; p < 2; ++p) {
          if ((supportNew[p] < cStartNew) || (supportNew[p] >= cEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a cell [%d, %d)", supportNew[p], cStartNew, cEndNew);
        }
#endif
      }
    }
    /* Old vertices have identical supports */
    for (v = vStart; v < vEnd; ++v) {
      const PetscInt  newp = vStartNew + (v - vStart);
      const PetscInt *support, *cone;
      PetscInt        size, s;

      ierr = DMPlexGetSupportSize(dm, v, &size);CHKERRQ(ierr);
      ierr = DMPlexGetSupport(dm, v, &support);CHKERRQ(ierr);
      for (s = 0; s < size; ++s) {
        PetscInt r = 0;

        ierr = DMPlexGetCone(dm, support[s], &cone);CHKERRQ(ierr);
        if (cone[1] == v) r = 1;
        supportRef[s] = fStartNew + (support[s] - fStart)*2 + r;
      }
      ierr = DMPlexSetSupport(rdm, newp, supportRef);CHKERRQ(ierr);
#if 1
      if ((newp < vStartNew) || (newp >= vEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a vertex [%d, %d)", newp, vStartNew, vEndNew);
      for (p = 0; p < size; ++p) {
        if ((supportRef[p] < fStartNew) || (supportRef[p] >= fEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a face [%d, %d)", supportRef[p], fStartNew, fEndNew);
      }
#endif
    }
    /* Face vertices have 2 + cells supports */
    for (f = fStart; f < fEnd; ++f) {
      const PetscInt  newp = vStartNew + (vEnd - vStart) + (f - fStart);
      const PetscInt *cone, *support;
      PetscInt        size, s;

      ierr          = DMPlexGetSupportSize(dm, f, &size);CHKERRQ(ierr);
      ierr          = DMPlexGetSupport(dm, f, &support);CHKERRQ(ierr);
      supportRef[0] = fStartNew + (f - fStart)*2 + 0;
      supportRef[1] = fStartNew + (f - fStart)*2 + 1;
      for (s = 0; s < size; ++s) {
        PetscInt r = 0;

        ierr = DMPlexGetCone(dm, support[s], &cone);CHKERRQ(ierr);
        if      (cone[1] == f) r = 1;
        else if (cone[2] == f) r = 2;
        else if (cone[3] == f) r = 3;
        supportRef[2+s] = fStartNew + (fEnd - fStart)*2 + (support[s] - cStart)*4 + r;
      }
      ierr = DMPlexSetSupport(rdm, newp, supportRef);CHKERRQ(ierr);
#if 1
      if ((newp < vStartNew) || (newp >= vEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a vertex [%d, %d)", newp, vStartNew, vEndNew);
      for (p = 0; p < 2+size; ++p) {
        if ((supportRef[p] < fStartNew) || (supportRef[p] >= fEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a face [%d, %d)", supportRef[p], fStartNew, fEndNew);
      }
#endif
    }
    /* Cell vertices have 4 supports */
    for (c = cStart; c < cEnd; ++c) {
      const PetscInt newp = vStartNew + (vEnd - vStart) + (fEnd - fStart) + (c - cStart);
      PetscInt       supportNew[4];

      for (r = 0; r < 4; ++r) {
        supportNew[r] = fStartNew + (fEnd - fStart)*2 + (c - cStart)*4 + r;
      }
      ierr = DMPlexSetSupport(rdm, newp, supportNew);CHKERRQ(ierr);
    }
    break;
  case 3:
    if (cMax < 0) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "No cell maximum specified in hybrid mesh");
    cMax = PetscMin(cEnd, cMax);
    if (fMax < 0) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "No face maximum specified in hybrid mesh");
    fMax = PetscMin(fEnd, fMax);
    /* Interior cells have 3 faces */
    for (c = cStart; c < cMax; ++c) {
      const PetscInt  newp = cStartNew + (c - cStart)*4;
      const PetscInt *cone, *ornt;
      PetscInt        coneNew[3], orntNew[3];

      ierr = DMPlexGetCone(dm, c, &cone);CHKERRQ(ierr);
      ierr = DMPlexGetConeOrientation(dm, c, &ornt);CHKERRQ(ierr);
      /* A triangle */
      coneNew[0] = fStartNew + (cone[0] - fStart)*2 + (ornt[0] < 0 ? 1 : 0);
      orntNew[0] = ornt[0];
      coneNew[1] = fStartNew + (fMax    - fStart)*2 + (c - cStart)*3 + 2;
      orntNew[1] = -2;
      coneNew[2] = fStartNew + (cone[2] - fStart)*2 + (ornt[2] < 0 ? 0 : 1);
      orntNew[2] = ornt[2];
      ierr       = DMPlexSetCone(rdm, newp+0, coneNew);CHKERRQ(ierr);
      ierr       = DMPlexSetConeOrientation(rdm, newp+0, orntNew);CHKERRQ(ierr);
#if 1
      if ((newp+0 < cStartNew) || (newp+0 >= cEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a cell [%d, %d)", newp+0, cStartNew, cEndNew);
      for (p = 0; p < 3; ++p) {
        if ((coneNew[p] < fStartNew) || (coneNew[p] >= fEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a face [%d, %d)", coneNew[p], fStartNew, fEndNew);
      }
#endif
      /* B triangle */
      coneNew[0] = fStartNew + (cone[0] - fStart)*2 + (ornt[0] < 0 ? 0 : 1);
      orntNew[0] = ornt[0];
      coneNew[1] = fStartNew + (cone[1] - fStart)*2 + (ornt[1] < 0 ? 1 : 0);
      orntNew[1] = ornt[1];
      coneNew[2] = fStartNew + (fMax    - fStart)*2 + (c - cStart)*3 + 0;
      orntNew[2] = -2;
      ierr       = DMPlexSetCone(rdm, newp+1, coneNew);CHKERRQ(ierr);
      ierr       = DMPlexSetConeOrientation(rdm, newp+1, orntNew);CHKERRQ(ierr);
#if 1
      if ((newp+1 < cStartNew) || (newp+1 >= cEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a cell [%d, %d)", newp+1, cStartNew, cEndNew);
      for (p = 0; p < 3; ++p) {
        if ((coneNew[p] < fStartNew) || (coneNew[p] >= fEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a face [%d, %d)", coneNew[p], fStartNew, fEndNew);
      }
#endif
      /* C triangle */
      coneNew[0] = fStartNew + (fMax    - fStart)*2 + (c - cStart)*3 + 1;
      orntNew[0] = -2;
      coneNew[1] = fStartNew + (cone[1] - fStart)*2 + (ornt[1] < 0 ? 0 : 1);
      orntNew[1] = ornt[1];
      coneNew[2] = fStartNew + (cone[2] - fStart)*2 + (ornt[2] < 0 ? 1 : 0);
      orntNew[2] = ornt[2];
      ierr       = DMPlexSetCone(rdm, newp+2, coneNew);CHKERRQ(ierr);
      ierr       = DMPlexSetConeOrientation(rdm, newp+2, orntNew);CHKERRQ(ierr);
#if 1
      if ((newp+2 < cStartNew) || (newp+2 >= cEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a cell [%d, %d)", newp+2, cStartNew, cEndNew);
      for (p = 0; p < 3; ++p) {
        if ((coneNew[p] < fStartNew) || (coneNew[p] >= fEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a face [%d, %d)", coneNew[p], fStartNew, fEndNew);
      }
#endif
      /* D triangle */
      coneNew[0] = fStartNew + (fMax    - fStart)*2 + (c - cStart)*3 + 0;
      orntNew[0] = 0;
      coneNew[1] = fStartNew + (fMax    - fStart)*2 + (c - cStart)*3 + 1;
      orntNew[1] = 0;
      coneNew[2] = fStartNew + (fMax    - fStart)*2 + (c - cStart)*3 + 2;
      orntNew[2] = 0;
      ierr       = DMPlexSetCone(rdm, newp+3, coneNew);CHKERRQ(ierr);
      ierr       = DMPlexSetConeOrientation(rdm, newp+3, orntNew);CHKERRQ(ierr);
#if 1
      if ((newp+3 < cStartNew) || (newp+3 >= cEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a cell [%d, %d)", newp+3, cStartNew, cEndNew);
      for (p = 0; p < 3; ++p) {
        if ((coneNew[p] < fStartNew) || (coneNew[p] >= fEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a face [%d, %d)", coneNew[p], fStartNew, fEndNew);
      }
#endif
    }
    /*
     2----3----3
     |         |
     |    B    |
     |         |
     0----4--- 1
     |         |
     |    A    |
     |         |
     0----2----1
     */
    /* Hybrid cells have 4 faces */
    for (c = cMax; c < cEnd; ++c) {
      const PetscInt  newp = cStartNew + (cMax - cStart)*4 + (c - cMax)*2;
      const PetscInt *cone, *ornt;
      PetscInt        coneNew[4], orntNew[4];

      ierr = DMPlexGetCone(dm, c, &cone);CHKERRQ(ierr);
      ierr = DMPlexGetConeOrientation(dm, c, &ornt);CHKERRQ(ierr);
      /* A quad */
      coneNew[0] = fStartNew + (cone[0] - fStart)*2 + (ornt[0] < 0 ? 1 : 0);
      orntNew[0] = ornt[0];
      coneNew[1] = fStartNew + (cone[1] - fStart)*2 + (ornt[1] < 0 ? 1 : 0);
      orntNew[1] = ornt[1];
      coneNew[2] = fStartNew + (fMax    - fStart)*2 + (cMax - cStart)*3 + (cone[2] - fMax);
      orntNew[2] = 0;
      coneNew[3] = fStartNew + (fMax    - fStart)*2 + (cMax - cStart)*3 + (fEnd    - fMax) + (c - cMax);
      orntNew[3] = 0;
      ierr       = DMPlexSetCone(rdm, newp+0, coneNew);CHKERRQ(ierr);
      ierr       = DMPlexSetConeOrientation(rdm, newp+0, orntNew);CHKERRQ(ierr);
#if 1
      if ((newp+0 < cStartNew) || (newp+0 >= cEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a cell [%d, %d)", newp+0, cStartNew, cEndNew);
      for (p = 0; p < 4; ++p) {
        if ((coneNew[p] < fStartNew) || (coneNew[p] >= fEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a face [%d, %d)", coneNew[p], fStartNew, fEndNew);
      }
#endif
      /* B quad */
      coneNew[0] = fStartNew + (cone[0] - fStart)*2 + (ornt[0] < 0 ? 0 : 1);
      orntNew[0] = ornt[0];
      coneNew[1] = fStartNew + (cone[1] - fStart)*2 + (ornt[1] < 0 ? 0 : 1);
      orntNew[1] = ornt[1];
      coneNew[2] = fStartNew + (fMax    - fStart)*2 + (cMax - cStart)*3 + (fEnd    - fMax) + (c - cMax);
      orntNew[2] = 0;
      coneNew[3] = fStartNew + (fMax    - fStart)*2 + (cMax - cStart)*3 + (cone[3] - fMax);
      orntNew[3] = 0;
      ierr       = DMPlexSetCone(rdm, newp+1, coneNew);CHKERRQ(ierr);
      ierr       = DMPlexSetConeOrientation(rdm, newp+1, orntNew);CHKERRQ(ierr);
#if 1
      if ((newp+1 < cStartNew) || (newp+1 >= cEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a cell [%d, %d)", newp+1, cStartNew, cEndNew);
      for (p = 0; p < 4; ++p) {
        if ((coneNew[p] < fStartNew) || (coneNew[p] >= fEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a face [%d, %d)", coneNew[p], fStartNew, fEndNew);
      }
#endif
    }
    /* Interior split faces have 2 vertices and the same cells as the parent */
    ierr = DMPlexGetMaxSizes(dm, NULL, &maxSupportSize);CHKERRQ(ierr);
    ierr = PetscMalloc((2 + maxSupportSize*2) * sizeof(PetscInt), &supportRef);CHKERRQ(ierr);
    for (f = fStart; f < fMax; ++f) {
      const PetscInt newv = vStartNew + (vEnd - vStart) + (f - fStart);

      for (r = 0; r < 2; ++r) {
        const PetscInt  newp = fStartNew + (f - fStart)*2 + r;
        const PetscInt *cone, *support;
        PetscInt        coneNew[2], coneSize, c, supportSize, s;

        ierr             = DMPlexGetCone(dm, f, &cone);CHKERRQ(ierr);
        coneNew[0]       = vStartNew + (cone[0] - vStart);
        coneNew[1]       = vStartNew + (cone[1] - vStart);
        coneNew[(r+1)%2] = newv;
        ierr             = DMPlexSetCone(rdm, newp, coneNew);CHKERRQ(ierr);
#if 1
        if ((newp < fStartNew) || (newp >= fEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a face [%d, %d)", newp, fStartNew, fEndNew);
        for (p = 0; p < 2; ++p) {
          if ((coneNew[p] < vStartNew) || (coneNew[p] >= vEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a vertex [%d, %d)", coneNew[p], vStartNew, vEndNew);
        }
#endif
        ierr = DMPlexGetSupportSize(dm, f, &supportSize);CHKERRQ(ierr);
        ierr = DMPlexGetSupport(dm, f, &support);CHKERRQ(ierr);
        for (s = 0; s < supportSize; ++s) {
          if (support[s] >= cMax) {
            supportRef[s] = cStartNew + (cMax - cStart)*4 + (support[s] - cMax)*2 + r;
          } else {
            ierr = DMPlexGetConeSize(dm, support[s], &coneSize);CHKERRQ(ierr);
            ierr = DMPlexGetCone(dm, support[s], &cone);CHKERRQ(ierr);
            for (c = 0; c < coneSize; ++c) {
              if (cone[c] == f) break;
            }
            supportRef[s] = cStartNew + (support[s] - cStart)*4 + (c+r)%3;
          }
        }
        ierr = DMPlexSetSupport(rdm, newp, supportRef);CHKERRQ(ierr);
#if 1
        if ((newp < fStartNew) || (newp >= fEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a face [%d, %d)", newp, fStartNew, fEndNew);
        for (p = 0; p < supportSize; ++p) {
          if ((supportRef[p] < cStartNew) || (supportRef[p] >= cEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a cell [%d, %d)", supportRef[p], cStartNew, cEndNew);
        }
#endif
      }
    }
    /* Interior cell faces have 2 vertices and 2 cells */
    for (c = cStart; c < cMax; ++c) {
      const PetscInt *cone;

      ierr = DMPlexGetCone(dm, c, &cone);CHKERRQ(ierr);
      for (r = 0; r < 3; ++r) {
        const PetscInt newp = fStartNew + (fMax - fStart)*2 + (c - cStart)*3 + r;
        PetscInt       coneNew[2];
        PetscInt       supportNew[2];

        coneNew[0] = vStartNew + (vEnd - vStart) + (cone[r]       - fStart);
        coneNew[1] = vStartNew + (vEnd - vStart) + (cone[(r+1)%3] - fStart);
        ierr       = DMPlexSetCone(rdm, newp, coneNew);CHKERRQ(ierr);
#if 1
        if ((newp < fStartNew) || (newp >= fEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a face [%d, %d)", newp, fStartNew, fEndNew);
        for (p = 0; p < 2; ++p) {
          if ((coneNew[p] < vStartNew) || (coneNew[p] >= vEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a vertex [%d, %d)", coneNew[p], vStartNew, vEndNew);
        }
#endif
        supportNew[0] = (c - cStart)*4 + (r+1)%3;
        supportNew[1] = (c - cStart)*4 + 3;
        ierr          = DMPlexSetSupport(rdm, newp, supportNew);CHKERRQ(ierr);
#if 1
        if ((newp < fStartNew) || (newp >= fEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a face [%d, %d)", newp, fStartNew, fEndNew);
        for (p = 0; p < 2; ++p) {
          if ((supportNew[p] < cStartNew) || (supportNew[p] >= cEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a cell [%d, %d)", supportNew[p], cStartNew, cEndNew);
        }
#endif
      }
    }
    /* Interior hybrid faces have 2 vertices and the same cells */
    for (f = fMax; f < fEnd; ++f) {
      const PetscInt  newp = fStartNew + (fMax - fStart)*2 + (cMax - cStart)*3 + (f - fMax);
      const PetscInt *cone;
      const PetscInt *support;
      PetscInt        coneNew[2];
      PetscInt        supportNew[2];
      PetscInt        size, s, r;

      ierr       = DMPlexGetCone(dm, f, &cone);CHKERRQ(ierr);
      coneNew[0] = vStartNew + (cone[0] - vStart);
      coneNew[1] = vStartNew + (cone[1] - vStart);
      ierr       = DMPlexSetCone(rdm, newp, coneNew);CHKERRQ(ierr);
#if 1
      if ((newp < fStartNew) || (newp >= fEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a face [%d, %d)", newp, fStartNew, fEndNew);
      for (p = 0; p < 2; ++p) {
        if ((coneNew[p] < vStartNew) || (coneNew[p] >= vEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a vertex [%d, %d)", coneNew[p], vStartNew, vEndNew);
      }
#endif
      ierr = DMPlexGetSupportSize(dm, f, &size);CHKERRQ(ierr);
      ierr = DMPlexGetSupport(dm, f, &support);CHKERRQ(ierr);
      for (s = 0; s < size; ++s) {
        ierr = DMPlexGetCone(dm, support[s], &cone);CHKERRQ(ierr);
        for (r = 0; r < 2; ++r) {
          if (cone[r+2] == f) break;
        }
        supportNew[s] = (cMax - cStart)*4 + (support[s] - cMax)*2 + r;
      }
      ierr = DMPlexSetSupport(rdm, newp, supportNew);CHKERRQ(ierr);
#if 1
      if ((newp < fStartNew) || (newp >= fEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a face [%d, %d)", newp, fStartNew, fEndNew);
      for (p = 0; p < size; ++p) {
        if ((supportNew[p] < cStartNew) || (supportNew[p] >= cEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a cell [%d, %d)", supportNew[p], cStartNew, cEndNew);
      }
#endif
    }
    /* Cell hybrid faces have 2 vertices and 2 cells */
    for (c = cMax; c < cEnd; ++c) {
      const PetscInt  newp = fStartNew + (fMax - fStart)*2 + (cMax - cStart)*3 + (fEnd - fMax) + (c - cMax);
      const PetscInt *cone;
      PetscInt        coneNew[2];
      PetscInt        supportNew[2];

      ierr       = DMPlexGetCone(dm, c, &cone);CHKERRQ(ierr);
      coneNew[0] = vStartNew + (vEnd - vStart) + (cone[0] - fStart);
      coneNew[1] = vStartNew + (vEnd - vStart) + (cone[1] - fStart);
      ierr       = DMPlexSetCone(rdm, newp, coneNew);CHKERRQ(ierr);
#if 1
      if ((newp < fStartNew) || (newp >= fEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a face [%d, %d)", newp, fStartNew, fEndNew);
      for (p = 0; p < 2; ++p) {
        if ((coneNew[p] < vStartNew) || (coneNew[p] >= vEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a vertex [%d, %d)", coneNew[p], vStartNew, vEndNew);
      }
#endif
      supportNew[0] = (cMax - cStart)*4 + (c - cMax)*2 + 0;
      supportNew[1] = (cMax - cStart)*4 + (c - cMax)*2 + 1;
      ierr          = DMPlexSetSupport(rdm, newp, supportNew);CHKERRQ(ierr);
#if 1
      if ((newp < fStartNew) || (newp >= fEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a face [%d, %d)", newp, fStartNew, fEndNew);
      for (p = 0; p < 2; ++p) {
        if ((supportNew[p] < cStartNew) || (supportNew[p] >= cEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a cell [%d, %d)", supportNew[p], cStartNew, cEndNew);
      }
#endif
    }
    /* Old vertices have identical supports */
    for (v = vStart; v < vEnd; ++v) {
      const PetscInt  newp = vStartNew + (v - vStart);
      const PetscInt *support, *cone;
      PetscInt        size, s;

      ierr = DMPlexGetSupportSize(dm, v, &size);CHKERRQ(ierr);
      ierr = DMPlexGetSupport(dm, v, &support);CHKERRQ(ierr);
      for (s = 0; s < size; ++s) {
        if (support[s] >= fMax) {
          supportRef[s] = fStartNew + (fMax - fStart)*2 + (cMax - cStart)*3 + (support[s] - fMax);
        } else {
          PetscInt r = 0;

          ierr = DMPlexGetCone(dm, support[s], &cone);CHKERRQ(ierr);
          if (cone[1] == v) r = 1;
          supportRef[s] = fStartNew + (support[s] - fStart)*2 + r;
        }
      }
      ierr = DMPlexSetSupport(rdm, newp, supportRef);CHKERRQ(ierr);
#if 1
      if ((newp < vStartNew) || (newp >= vEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a vertex [%d, %d)", newp, vStartNew, vEndNew);
      for (p = 0; p < size; ++p) {
        if ((supportRef[p] < fStartNew) || (supportRef[p] >= fEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a face [%d, %d)", supportRef[p], fStartNew, fEndNew);
      }
#endif
    }
    /* Face vertices have 2 + (2 interior, 1 hybrid) supports */
    for (f = fStart; f < fMax; ++f) {
      const PetscInt  newp = vStartNew + (vEnd - vStart) + (f - fStart);
      const PetscInt *cone, *support;
      PetscInt        size, newSize = 2, s;

      ierr          = DMPlexGetSupportSize(dm, f, &size);CHKERRQ(ierr);
      ierr          = DMPlexGetSupport(dm, f, &support);CHKERRQ(ierr);
      supportRef[0] = fStartNew + (f - fStart)*2 + 0;
      supportRef[1] = fStartNew + (f - fStart)*2 + 1;
      for (s = 0; s < size; ++s) {
        PetscInt r = 0;

        ierr = DMPlexGetCone(dm, support[s], &cone);CHKERRQ(ierr);
        if (support[s] >= cMax) {
          supportRef[newSize+0] = fStartNew + (fMax - fStart)*2 + (cMax - cStart)*3 + (fEnd - fMax) + (support[s] - cMax);

          newSize += 1;
        } else {
          if      (cone[1] == f) r = 1;
          else if (cone[2] == f) r = 2;
          supportRef[newSize+0] = fStartNew + (fMax - fStart)*2 + (support[s] - cStart)*3 + (r+2)%3;
          supportRef[newSize+1] = fStartNew + (fMax - fStart)*2 + (support[s] - cStart)*3 + r;

          newSize += 2;
        }
      }
      ierr = DMPlexSetSupport(rdm, newp, supportRef);CHKERRQ(ierr);
#if 1
      if ((newp < vStartNew) || (newp >= vEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a vertex [%d, %d)", newp, vStartNew, vEndNew);
      for (p = 0; p < newSize; ++p) {
        if ((supportRef[p] < fStartNew) || (supportRef[p] >= fEndNew)) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d is not a face [%d, %d)", supportRef[p], fStartNew, fEndNew);
      }
#endif
    }
    ierr = PetscFree(supportRef);CHKERRQ(ierr);
    break;
  default:
    SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unknown cell refiner %d", refiner);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "CellRefinerSetCoordinates"
PetscErrorCode CellRefinerSetCoordinates(CellRefiner refiner, DM dm, PetscInt depthSize[], DM rdm)
{
  PetscSection   coordSection, coordSectionNew;
  Vec            coordinates, coordinatesNew;
  PetscScalar   *coords, *coordsNew;
  PetscInt       dim, depth, coordSizeNew, cStart, cEnd, c, vStart, vStartNew, vEnd, v, fStart, fEnd, fMax, f;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
  ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
  ierr = DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);CHKERRQ(ierr);
  ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
  ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
  ierr = DMPlexGetHybridBounds(dm, NULL, &fMax, NULL, NULL);CHKERRQ(ierr);
  ierr = GetDepthStart_Private(depth, depthSize, NULL, NULL, NULL, &vStartNew);CHKERRQ(ierr);
  ierr = DMPlexGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
  ierr = PetscSectionCreate(PetscObjectComm((PetscObject)dm), &coordSectionNew);CHKERRQ(ierr);
  ierr = PetscSectionSetNumFields(coordSectionNew, 1);CHKERRQ(ierr);
  ierr = PetscSectionSetFieldComponents(coordSectionNew, 0, dim);CHKERRQ(ierr);
  ierr = PetscSectionSetChart(coordSectionNew, vStartNew, vStartNew+depthSize[0]);CHKERRQ(ierr);
  if (fMax < 0) fMax = fEnd;
  switch (refiner) {
  case 1:
  case 2:
  case 3:
    /* Simplicial and Hex 2D */
    /* All vertices have the dim coordinates */
    for (v = vStartNew; v < vStartNew+depthSize[0]; ++v) {
      ierr = PetscSectionSetDof(coordSectionNew, v, dim);CHKERRQ(ierr);
      ierr = PetscSectionSetFieldDof(coordSectionNew, v, 0, dim);CHKERRQ(ierr);
    }
    ierr = PetscSectionSetUp(coordSectionNew);CHKERRQ(ierr);
    ierr = DMPlexSetCoordinateSection(rdm, coordSectionNew);CHKERRQ(ierr);
    ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
    ierr = PetscSectionGetStorageSize(coordSectionNew, &coordSizeNew);CHKERRQ(ierr);
    ierr = VecCreate(PetscObjectComm((PetscObject)dm), &coordinatesNew);CHKERRQ(ierr);
    ierr = PetscObjectSetName((PetscObject) coordinatesNew, "coordinates");CHKERRQ(ierr);
    ierr = VecSetSizes(coordinatesNew, coordSizeNew, PETSC_DETERMINE);CHKERRQ(ierr);
    ierr = VecSetFromOptions(coordinatesNew);CHKERRQ(ierr);
    ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
    ierr = VecGetArray(coordinatesNew, &coordsNew);CHKERRQ(ierr);
    /* Old vertices have the same coordinates */
    for (v = vStart; v < vEnd; ++v) {
      const PetscInt newv = vStartNew + (v - vStart);
      PetscInt       off, offnew, d;

      ierr = PetscSectionGetOffset(coordSection, v, &off);CHKERRQ(ierr);
      ierr = PetscSectionGetOffset(coordSectionNew, newv, &offnew);CHKERRQ(ierr);
      for (d = 0; d < dim; ++d) {
        coordsNew[offnew+d] = coords[off+d];
      }
    }
    /* Face vertices have the average of endpoint coordinates */
    for (f = fStart; f < fMax; ++f) {
      const PetscInt  newv = vStartNew + (vEnd - vStart) + (f - fStart);
      const PetscInt *cone;
      PetscInt        coneSize, offA, offB, offnew, d;

      ierr = DMPlexGetConeSize(dm, f, &coneSize);CHKERRQ(ierr);
      if (coneSize != 2) SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Face %d cone should have two vertices, not %d", f, coneSize);
      ierr = DMPlexGetCone(dm, f, &cone);CHKERRQ(ierr);
      ierr = PetscSectionGetOffset(coordSection, cone[0], &offA);CHKERRQ(ierr);
      ierr = PetscSectionGetOffset(coordSection, cone[1], &offB);CHKERRQ(ierr);
      ierr = PetscSectionGetOffset(coordSectionNew, newv, &offnew);CHKERRQ(ierr);
      for (d = 0; d < dim; ++d) {
        coordsNew[offnew+d] = 0.5*(coords[offA+d] + coords[offB+d]);
      }
    }
    /* Just Hex 2D */
    if (refiner == 2) {
      /* Cell vertices have the average of corner coordinates */
      for (c = cStart; c < cEnd; ++c) {
        const PetscInt newv = vStartNew + (vEnd - vStart) + (fEnd - fStart) + (c - cStart);
        PetscInt      *cone = NULL;
        PetscInt       closureSize, coneSize = 0, offA, offB, offC, offD, offnew, p, d;

        ierr = DMPlexGetTransitiveClosure(dm, c, PETSC_TRUE, &closureSize, &cone);CHKERRQ(ierr);
        for (p = 0; p < closureSize*2; p += 2) {
          const PetscInt point = cone[p];
          if ((point >= vStart) && (point < vEnd)) cone[coneSize++] = point;
        }
        if (coneSize != 4) SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Quad %d cone should have four vertices, not %d", c, coneSize);
        ierr = PetscSectionGetOffset(coordSection, cone[0], &offA);CHKERRQ(ierr);
        ierr = PetscSectionGetOffset(coordSection, cone[1], &offB);CHKERRQ(ierr);
        ierr = PetscSectionGetOffset(coordSection, cone[2], &offC);CHKERRQ(ierr);
        ierr = PetscSectionGetOffset(coordSection, cone[3], &offD);CHKERRQ(ierr);
        ierr = PetscSectionGetOffset(coordSectionNew, newv, &offnew);CHKERRQ(ierr);
        for (d = 0; d < dim; ++d) {
          coordsNew[offnew+d] = 0.25*(coords[offA+d] + coords[offB+d] + coords[offC+d] + coords[offD+d]);
        }
        ierr = DMPlexRestoreTransitiveClosure(dm, c, PETSC_TRUE, &closureSize, &cone);CHKERRQ(ierr);
      }
    }
    ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
    ierr = VecRestoreArray(coordinatesNew, &coordsNew);CHKERRQ(ierr);
    ierr = DMSetCoordinatesLocal(rdm, coordinatesNew);CHKERRQ(ierr);
    ierr = VecDestroy(&coordinatesNew);CHKERRQ(ierr);
    ierr = PetscSectionDestroy(&coordSectionNew);CHKERRQ(ierr);
    break;
  default:
    SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unknown cell refiner %d", refiner);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexCreateProcessSF"
PetscErrorCode DMPlexCreateProcessSF(DM dm, PetscSF sfPoint, IS *processRanks, PetscSF *sfProcess)
{
  PetscInt           numRoots, numLeaves, l;
  const PetscInt    *localPoints;
  const PetscSFNode *remotePoints;
  PetscInt          *localPointsNew;
  PetscSFNode       *remotePointsNew;
  PetscInt          *ranks, *ranksNew;
  PetscErrorCode     ierr;

  PetscFunctionBegin;
  ierr = PetscSFGetGraph(sfPoint, &numRoots, &numLeaves, &localPoints, &remotePoints);CHKERRQ(ierr);
  ierr = PetscMalloc(numLeaves * sizeof(PetscInt), &ranks);CHKERRQ(ierr);
  for (l = 0; l < numLeaves; ++l) {
    ranks[l] = remotePoints[l].rank;
  }
  ierr = PetscSortRemoveDupsInt(&numLeaves, ranks);CHKERRQ(ierr);
  ierr = PetscMalloc(numLeaves * sizeof(PetscInt),    &ranksNew);CHKERRQ(ierr);
  ierr = PetscMalloc(numLeaves * sizeof(PetscInt),    &localPointsNew);CHKERRQ(ierr);
  ierr = PetscMalloc(numLeaves * sizeof(PetscSFNode), &remotePointsNew);CHKERRQ(ierr);
  for (l = 0; l < numLeaves; ++l) {
    ranksNew[l]              = ranks[l];
    localPointsNew[l]        = l;
    remotePointsNew[l].index = 0;
    remotePointsNew[l].rank  = ranksNew[l];
  }
  ierr = PetscFree(ranks);CHKERRQ(ierr);
  ierr = ISCreateGeneral(PetscObjectComm((PetscObject)dm), numLeaves, ranksNew, PETSC_OWN_POINTER, processRanks);CHKERRQ(ierr);
  ierr = PetscSFCreate(PetscObjectComm((PetscObject)dm), sfProcess);CHKERRQ(ierr);
  ierr = PetscSFSetFromOptions(*sfProcess);CHKERRQ(ierr);
  ierr = PetscSFSetGraph(*sfProcess, 1, numLeaves, localPointsNew, PETSC_OWN_POINTER, remotePointsNew, PETSC_OWN_POINTER);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "CellRefinerCreateSF"
PetscErrorCode CellRefinerCreateSF(CellRefiner refiner, DM dm, PetscInt depthSize[], DM rdm)
{
  PetscSF            sf, sfNew, sfProcess;
  IS                 processRanks;
  MPI_Datatype       depthType;
  PetscInt           numRoots, numLeaves, numLeavesNew = 0, l, m;
  const PetscInt    *localPoints, *neighbors;
  const PetscSFNode *remotePoints;
  PetscInt          *localPointsNew;
  PetscSFNode       *remotePointsNew;
  PetscInt          *depthSizeOld, *rdepthSize, *rdepthSizeOld, *rdepthMaxOld, *rvStart, *rvStartNew, *reStart, *reStartNew, *rfStart, *rfStartNew, *rcStart, *rcStartNew;
  PetscInt           depth, numNeighbors, pStartNew, pEndNew, cStart, cStartNew, cEnd, cMax, vStart, vStartNew, vEnd, vMax, fStart, fStartNew, fEnd, fMax, eStart, eStartNew, eEnd, eMax, r, n;
  PetscErrorCode     ierr;

  PetscFunctionBegin;
  ierr = DMPlexGetChart(rdm, &pStartNew, &pEndNew);CHKERRQ(ierr);
  ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
  ierr = DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);CHKERRQ(ierr);
  ierr = DMPlexGetDepthStratum(dm, 1, &eStart, &eEnd);CHKERRQ(ierr);
  ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
  ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
  ierr = DMPlexGetHybridBounds(dm, &cMax, &fMax, &eMax, &vMax);CHKERRQ(ierr);
  ierr = GetDepthStart_Private(depth, depthSize, &cStartNew, &fStartNew, &eStartNew, &vStartNew);CHKERRQ(ierr);
  switch (refiner) {
  case 3:
    if (cMax < 0) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "No cell maximum specified in hybrid mesh");
    cMax = PetscMin(cEnd, cMax);
    if (fMax < 0) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "No face maximum specified in hybrid mesh");
    fMax = PetscMin(fEnd, fMax);
  }
  ierr = DMGetPointSF(dm, &sf);CHKERRQ(ierr);
  ierr = DMGetPointSF(rdm, &sfNew);CHKERRQ(ierr);
  /* Caculate size of new SF */
  ierr = PetscSFGetGraph(sf, &numRoots, &numLeaves, &localPoints, &remotePoints);CHKERRQ(ierr);
  if (numRoots < 0) PetscFunctionReturn(0);
  for (l = 0; l < numLeaves; ++l) {
    const PetscInt p = localPoints[l];

    switch (refiner) {
    case 1:
      /* Simplicial 2D */
      if ((p >= vStart) && (p < vEnd)) {
        /* Old vertices stay the same */
        ++numLeavesNew;
      } else if ((p >= fStart) && (p < fEnd)) {
        /* Old faces add new faces and vertex */
        numLeavesNew += 1 + 2;
      } else if ((p >= cStart) && (p < cEnd)) {
        /* Old cells add new cells and interior faces */
        numLeavesNew += 4 + 3;
      }
      break;
    case 2:
      /* Hex 2D */
      if ((p >= vStart) && (p < vEnd)) {
        /* Old vertices stay the same */
        ++numLeavesNew;
      } else if ((p >= fStart) && (p < fEnd)) {
        /* Old faces add new faces and vertex */
        numLeavesNew += 1 + 2;
      } else if ((p >= cStart) && (p < cEnd)) {
        /* Old cells add new cells and interior faces */
        numLeavesNew += 4 + 4;
      }
      break;
    default:
      SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unknown cell refiner %d", refiner);
    }
  }
  /* Communicate depthSizes for each remote rank */
  ierr = DMPlexCreateProcessSF(dm, sf, &processRanks, &sfProcess);CHKERRQ(ierr);
  ierr = ISGetLocalSize(processRanks, &numNeighbors);CHKERRQ(ierr);
  ierr = PetscMalloc5((depth+1)*numNeighbors,PetscInt,&rdepthSize,numNeighbors,PetscInt,&rvStartNew,numNeighbors,PetscInt,&reStartNew,numNeighbors,PetscInt,&rfStartNew,numNeighbors,PetscInt,&rcStartNew);CHKERRQ(ierr);
  ierr = PetscMalloc7(depth+1,PetscInt,&depthSizeOld,(depth+1)*numNeighbors,PetscInt,&rdepthSizeOld,(depth+1)*numNeighbors,PetscInt,&rdepthMaxOld,numNeighbors,PetscInt,&rvStart,numNeighbors,PetscInt,&reStart,numNeighbors,PetscInt,&rfStart,numNeighbors,PetscInt,&rcStart);CHKERRQ(ierr);
  ierr = MPI_Type_contiguous(depth+1, MPIU_INT, &depthType);CHKERRQ(ierr);
  ierr = MPI_Type_commit(&depthType);CHKERRQ(ierr);
  ierr = PetscSFBcastBegin(sfProcess, depthType, depthSize, rdepthSize);CHKERRQ(ierr);
  ierr = PetscSFBcastEnd(sfProcess, depthType, depthSize, rdepthSize);CHKERRQ(ierr);
  for (n = 0; n < numNeighbors; ++n) {
    ierr = GetDepthStart_Private(depth, &rdepthSize[n*(depth+1)], &rcStartNew[n], &rfStartNew[n], &reStartNew[n], &rvStartNew[n]);CHKERRQ(ierr);
  }
  depthSizeOld[depth]   = cMax;
  depthSizeOld[0]       = vMax;
  depthSizeOld[depth-1] = fMax;
  depthSizeOld[1]       = eMax;

  ierr = PetscSFBcastBegin(sfProcess, depthType, depthSizeOld, rdepthMaxOld);CHKERRQ(ierr);
  ierr = PetscSFBcastEnd(sfProcess, depthType, depthSizeOld, rdepthMaxOld);CHKERRQ(ierr);

  depthSizeOld[depth]   = cEnd - cStart;
  depthSizeOld[0]       = vEnd - vStart;
  depthSizeOld[depth-1] = fEnd - fStart;
  depthSizeOld[1]       = eEnd - eStart;

  ierr = PetscSFBcastBegin(sfProcess, depthType, depthSizeOld, rdepthSizeOld);CHKERRQ(ierr);
  ierr = PetscSFBcastEnd(sfProcess, depthType, depthSizeOld, rdepthSizeOld);CHKERRQ(ierr);
  for (n = 0; n < numNeighbors; ++n) {
    ierr = GetDepthStart_Private(depth, &rdepthSizeOld[n*(depth+1)], &rcStart[n], &rfStart[n], &reStart[n], &rvStart[n]);CHKERRQ(ierr);
  }
  ierr = MPI_Type_free(&depthType);CHKERRQ(ierr);
  ierr = PetscSFDestroy(&sfProcess);CHKERRQ(ierr);
  /* Calculate new point SF */
  ierr = PetscMalloc(numLeavesNew * sizeof(PetscInt),    &localPointsNew);CHKERRQ(ierr);
  ierr = PetscMalloc(numLeavesNew * sizeof(PetscSFNode), &remotePointsNew);CHKERRQ(ierr);
  ierr = ISGetIndices(processRanks, &neighbors);CHKERRQ(ierr);
  for (l = 0, m = 0; l < numLeaves; ++l) {
    PetscInt    p     = localPoints[l];
    PetscInt    rp    = remotePoints[l].index, n;
    PetscMPIInt rrank = remotePoints[l].rank;

    ierr = PetscFindInt(rrank, numNeighbors, neighbors, &n);CHKERRQ(ierr);
    if (n < 0) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Could not locate remote rank %d", rrank);
    switch (refiner) {
    case 1:
      /* Simplicial 2D */
      if ((p >= vStart) && (p < vEnd)) {
        /* Old vertices stay the same */
        localPointsNew[m]        = vStartNew     + (p  - vStart);
        remotePointsNew[m].index = rvStartNew[n] + (rp - rvStart[n]);
        remotePointsNew[m].rank  = rrank;
        ++m;
      } else if ((p >= fStart) && (p < fEnd)) {
        /* Old faces add new faces and vertex */
        localPointsNew[m]        = vStartNew     + (vEnd - vStart)              + (p  - fStart);
        remotePointsNew[m].index = rvStartNew[n] + rdepthSizeOld[n*(depth+1)+0] + (rp - rfStart[n]);
        remotePointsNew[m].rank  = rrank;
        ++m;
        for (r = 0; r < 2; ++r, ++m) {
          localPointsNew[m]        = fStartNew     + (p  - fStart)*2     + r;
          remotePointsNew[m].index = rfStartNew[n] + (rp - rfStart[n])*2 + r;
          remotePointsNew[m].rank  = rrank;
        }
      } else if ((p >= cStart) && (p < cEnd)) {
        /* Old cells add new cells and interior faces */
        for (r = 0; r < 4; ++r, ++m) {
          localPointsNew[m]        = cStartNew     + (p  - cStart)*4     + r;
          remotePointsNew[m].index = rcStartNew[n] + (rp - rcStart[n])*4 + r;
          remotePointsNew[m].rank  = rrank;
        }
        for (r = 0; r < 3; ++r, ++m) {
          localPointsNew[m]        = fStartNew     + (fEnd - fStart)*2                    + (p  - cStart)*3     + r;
          remotePointsNew[m].index = rfStartNew[n] + rdepthSizeOld[n*(depth+1)+depth-1]*2 + (rp - rcStart[n])*3 + r;
          remotePointsNew[m].rank  = rrank;
        }
      }
      break;
    case 2:
      /* Hex 2D */
      if ((p >= vStart) && (p < vEnd)) {
        /* Old vertices stay the same */
        localPointsNew[m]        = vStartNew     + (p  - vStart);
        remotePointsNew[m].index = rvStartNew[n] + (rp - rvStart[n]);
        remotePointsNew[m].rank  = rrank;
        ++m;
      } else if ((p >= fStart) && (p < fEnd)) {
        /* Old faces add new faces and vertex */
        localPointsNew[m]        = vStartNew     + (vEnd - vStart)              + (p  - fStart);
        remotePointsNew[m].index = rvStartNew[n] + rdepthSizeOld[n*(depth+1)+0] + (rp - rfStart[n]);
        remotePointsNew[m].rank  = rrank;
        ++m;
        for (r = 0; r < 2; ++r, ++m) {
          localPointsNew[m]        = fStartNew     + (p  - fStart)*2     + r;
          remotePointsNew[m].index = rfStartNew[n] + (rp - rfStart[n])*2 + r;
          remotePointsNew[m].rank  = rrank;
        }
      } else if ((p >= cStart) && (p < cEnd)) {
        /* Old cells add new cells and interior faces */
        for (r = 0; r < 4; ++r, ++m) {
          localPointsNew[m]        = cStartNew     + (p  - cStart)*4     + r;
          remotePointsNew[m].index = rcStartNew[n] + (rp - rcStart[n])*4 + r;
          remotePointsNew[m].rank  = rrank;
        }
        for (r = 0; r < 4; ++r, ++m) {
          localPointsNew[m]        = fStartNew     + (fEnd - fStart)*2                    + (p  - cStart)*4     + r;
          remotePointsNew[m].index = rfStartNew[n] + rdepthSizeOld[n*(depth+1)+depth-1]*2 + (rp - rcStart[n])*4 + r;
          remotePointsNew[m].rank  = rrank;
        }
      }
      break;
    case 3:
      /* Hybrid simplicial 2D */
      if ((p >= vStart) && (p < vEnd)) {
        /* Old vertices stay the same */
        localPointsNew[m]        = vStartNew     + (p  - vStart);
        remotePointsNew[m].index = rvStartNew[n] + (rp - rvStart[n]);
        remotePointsNew[m].rank  = rrank;
        ++m;
      } else if ((p >= fStart) && (p < fMax)) {
        /* Old interior faces add new faces and vertex */
        localPointsNew[m]        = vStartNew     + (vEnd - vStart)              + (p  - fStart);
        remotePointsNew[m].index = rvStartNew[n] + rdepthSizeOld[n*(depth+1)+0] + (rp - rfStart[n]);
        remotePointsNew[m].rank  = rrank;
        ++m;
        for (r = 0; r < 2; ++r, ++m) {
          localPointsNew[m]        = fStartNew     + (p  - fStart)*2     + r;
          remotePointsNew[m].index = rfStartNew[n] + (rp - rfStart[n])*2 + r;
          remotePointsNew[m].rank  = rrank;
        }
      } else if ((p >= fMax) && (p < fEnd)) {
        /* Old hybrid faces stay the same */
        localPointsNew[m]        = fStartNew     + (fMax                              - fStart)*2     + (p  - fMax);
        remotePointsNew[m].index = rfStartNew[n] + (rdepthMaxOld[n*(depth+1)+depth-1] - rfStart[n])*2 + (rp - rdepthMaxOld[n*(depth+1)+depth-1]);
        remotePointsNew[m].rank  = rrank;
        ++m;
      } else if ((p >= cStart) && (p < cMax)) {
        /* Old interior cells add new cells and interior faces */
        for (r = 0; r < 4; ++r, ++m) {
          localPointsNew[m]        = cStartNew     + (p  - cStart)*4     + r;
          remotePointsNew[m].index = rcStartNew[n] + (rp - rcStart[n])*4 + r;
          remotePointsNew[m].rank  = rrank;
        }
        for (r = 0; r < 3; ++r, ++m) {
          localPointsNew[m]        = fStartNew     + (fMax                              - fStart)*2     + (p  - cStart)*3     + r;
          remotePointsNew[m].index = rfStartNew[n] + (rdepthMaxOld[n*(depth+1)+depth-1] - rfStart[n])*2 + (rp - rcStart[n])*3 + r;
          remotePointsNew[m].rank  = rrank;
        }
      } else if ((p >= cStart) && (p < cMax)) {
        /* Old hybrid cells add new cells and hybrid face */
        for (r = 0; r < 2; ++r, ++m) {
          localPointsNew[m]        = cStartNew     + (p  - cStart)*4     + r;
          remotePointsNew[m].index = rcStartNew[n] + (rp - rcStart[n])*4 + r;
          remotePointsNew[m].rank  = rrank;
        }
        localPointsNew[m]        = fStartNew     + (fMax                              - fStart)*2     + (cMax                            - cStart)*3     + (p  - cMax);
        remotePointsNew[m].index = rfStartNew[n] + (rdepthMaxOld[n*(depth+1)+depth-1] - rfStart[n])*2 + (rdepthMaxOld[n*(depth+1)+depth] - rcStart[n])*3 + (rp - rdepthMaxOld[n*(depth+1)+depth]);
        remotePointsNew[m].rank  = rrank;
        ++m;
      }
      break;
    default:
      SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unknown cell refiner %d", refiner);
    }
  }
  ierr = ISRestoreIndices(processRanks, &neighbors);CHKERRQ(ierr);
  ierr = ISDestroy(&processRanks);CHKERRQ(ierr);
  ierr = PetscSFSetGraph(sfNew, pEndNew-pStartNew, numLeavesNew, localPointsNew, PETSC_OWN_POINTER, remotePointsNew, PETSC_OWN_POINTER);CHKERRQ(ierr);
  ierr = PetscFree5(rdepthSize,rvStartNew,reStartNew,rfStartNew,rcStartNew);CHKERRQ(ierr);
  ierr = PetscFree6(depthSizeOld,rdepthSizeOld,rvStart,reStart,rfStart,rcStart);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "CellRefinerCreateLabels"
PetscErrorCode CellRefinerCreateLabels(CellRefiner refiner, DM dm, PetscInt depthSize[], DM rdm)
{
  PetscInt       numLabels, l;
  PetscInt       newp, cStart, cStartNew, cEnd, cMax, vStart, vStartNew, vEnd, vMax, fStart, fStartNew, fEnd, fMax, eStart, eEnd, eMax, r;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);CHKERRQ(ierr);
  ierr = DMPlexGetDepthStratum(dm, 1, &eStart, &eEnd);CHKERRQ(ierr);
  ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
  ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);

  cStartNew = 0;
  vStartNew = depthSize[2];
  fStartNew = depthSize[2] + depthSize[0];

  ierr = DMPlexGetNumLabels(dm, &numLabels);CHKERRQ(ierr);
  ierr = DMPlexGetHybridBounds(dm, &cMax, &fMax, &eMax, &vMax);CHKERRQ(ierr);
  switch (refiner) {
  case 3:
    if (cMax < 0) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "No cell maximum specified in hybrid mesh");
    cMax = PetscMin(cEnd, cMax);
    if (fMax < 0) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "No face maximum specified in hybrid mesh");
    fMax = PetscMin(fEnd, fMax);
  }
  for (l = 0; l < numLabels; ++l) {
    DMLabel         label, labelNew;
    const char     *lname;
    PetscBool       isDepth;
    IS              valueIS;
    const PetscInt *values;
    PetscInt        numValues, val;

    ierr = DMPlexGetLabelName(dm, l, &lname);CHKERRQ(ierr);
    ierr = PetscStrcmp(lname, "depth", &isDepth);CHKERRQ(ierr);
    if (isDepth) continue;
    ierr = DMPlexCreateLabel(rdm, lname);CHKERRQ(ierr);
    ierr = DMPlexGetLabel(dm, lname, &label);CHKERRQ(ierr);
    ierr = DMPlexGetLabel(rdm, lname, &labelNew);CHKERRQ(ierr);
    ierr = DMLabelGetValueIS(label, &valueIS);CHKERRQ(ierr);
    ierr = ISGetLocalSize(valueIS, &numValues);CHKERRQ(ierr);
    ierr = ISGetIndices(valueIS, &values);CHKERRQ(ierr);
    for (val = 0; val < numValues; ++val) {
      IS              pointIS;
      const PetscInt *points;
      PetscInt        numPoints, n;

      ierr = DMLabelGetStratumIS(label, values[val], &pointIS);CHKERRQ(ierr);
      ierr = ISGetLocalSize(pointIS, &numPoints);CHKERRQ(ierr);
      ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
      for (n = 0; n < numPoints; ++n) {
        const PetscInt p = points[n];
        switch (refiner) {
        case 1:
          /* Simplicial 2D */
          if ((p >= vStart) && (p < vEnd)) {
            /* Old vertices stay the same */
            newp = vStartNew + (p - vStart);
            ierr = DMLabelSetValue(labelNew, newp, values[val]);CHKERRQ(ierr);
          } else if ((p >= fStart) && (p < fEnd)) {
            /* Old faces add new faces and vertex */
            newp = vStartNew + (vEnd - vStart) + (p - fStart);
            ierr = DMLabelSetValue(labelNew, newp, values[val]);CHKERRQ(ierr);
            for (r = 0; r < 2; ++r) {
              newp = fStartNew + (p - fStart)*2 + r;
              ierr = DMLabelSetValue(labelNew, newp, values[val]);CHKERRQ(ierr);
            }
          } else if ((p >= cStart) && (p < cEnd)) {
            /* Old cells add new cells and interior faces */
            for (r = 0; r < 4; ++r) {
              newp = cStartNew + (p - cStart)*4 + r;
              ierr = DMLabelSetValue(labelNew, newp, values[val]);CHKERRQ(ierr);
            }
            for (r = 0; r < 3; ++r) {
              newp = fStartNew + (fEnd - fStart)*2 + (p - cStart)*3 + r;
              ierr = DMLabelSetValue(labelNew, newp, values[val]);CHKERRQ(ierr);
            }
          }
          break;
        case 2:
          /* Hex 2D */
          if ((p >= vStart) && (p < vEnd)) {
            /* Old vertices stay the same */
            newp = vStartNew + (p - vStart);
            ierr = DMLabelSetValue(labelNew, newp, values[val]);CHKERRQ(ierr);
          } else if ((p >= fStart) && (p < fEnd)) {
            /* Old faces add new faces and vertex */
            newp = vStartNew + (vEnd - vStart) + (p - fStart);
            ierr = DMLabelSetValue(labelNew, newp, values[val]);CHKERRQ(ierr);
            for (r = 0; r < 2; ++r) {
              newp = fStartNew + (p - fStart)*2 + r;
              ierr = DMLabelSetValue(labelNew, newp, values[val]);CHKERRQ(ierr);
            }
          } else if ((p >= cStart) && (p < cEnd)) {
            /* Old cells add new cells and interior faces and vertex */
            for (r = 0; r < 4; ++r) {
              newp = cStartNew + (p - cStart)*4 + r;
              ierr = DMLabelSetValue(labelNew, newp, values[val]);CHKERRQ(ierr);
            }
            for (r = 0; r < 4; ++r) {
              newp = fStartNew + (fEnd - fStart)*2 + (p - cStart)*4 + r;
              ierr = DMLabelSetValue(labelNew, newp, values[val]);CHKERRQ(ierr);
            }
            newp = vStartNew + (vEnd - vStart) + (fEnd - fStart) + (p - cStart);
            ierr = DMLabelSetValue(labelNew, newp, values[val]);CHKERRQ(ierr);
          }
          break;
        case 3:
          /* Hybrid simplicial 2D */
          if ((p >= vStart) && (p < vEnd)) {
            /* Old vertices stay the same */
            newp = vStartNew + (p - vStart);
            ierr = DMLabelSetValue(labelNew, newp, values[val]);CHKERRQ(ierr);
          } else if ((p >= fStart) && (p < fMax)) {
            /* Old interior faces add new faces and vertex */
            newp = vStartNew + (vEnd - vStart) + (p - fStart);
            ierr = DMLabelSetValue(labelNew, newp, values[val]);CHKERRQ(ierr);
            for (r = 0; r < 2; ++r) {
              newp = fStartNew + (p - fStart)*2 + r;
              ierr = DMLabelSetValue(labelNew, newp, values[val]);CHKERRQ(ierr);
            }
          } else if ((p >= fMax) && (p < fEnd)) {
            /* Old hybrid faces stay the same */
            newp = fStartNew + (fMax - fStart)*2 + (p - fMax);
            ierr = DMLabelSetValue(labelNew, newp, values[val]);CHKERRQ(ierr);
          } else if ((p >= cStart) && (p < cMax)) {
            /* Old interior cells add new cells and interior faces */
            for (r = 0; r < 4; ++r) {
              newp = cStartNew + (p - cStart)*4 + r;
              ierr = DMLabelSetValue(labelNew, newp, values[val]);CHKERRQ(ierr);
            }
            for (r = 0; r < 3; ++r) {
              newp = fStartNew + (fEnd - fStart)*2 + (p - cStart)*3 + r;
              ierr = DMLabelSetValue(labelNew, newp, values[val]);CHKERRQ(ierr);
            }
          } else if ((p >= cMax) && (p < cEnd)) {
            /* Old hybrid cells add new cells and hybrid face */
            for (r = 0; r < 2; ++r) {
              newp = cStartNew + (cMax - cStart)*4 + (p - cMax)*2 + r;
              ierr = DMLabelSetValue(labelNew, newp, values[val]);CHKERRQ(ierr);
            }
            newp = fStartNew + (fMax - fStart)*2 + (cMax - cStart)*3 + (p - cMax);
            ierr = DMLabelSetValue(labelNew, newp, values[val]);CHKERRQ(ierr);
          }
          break;
        default:
          SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unknown cell refiner %d", refiner);
        }
      }
      ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
      ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
    }
    ierr = ISRestoreIndices(valueIS, &values);CHKERRQ(ierr);
    ierr = ISDestroy(&valueIS);CHKERRQ(ierr);
    if (0) {
      ierr = PetscViewerASCIISynchronizedAllow(PETSC_VIEWER_STDOUT_WORLD, PETSC_TRUE);CHKERRQ(ierr);
      ierr = DMLabelView(labelNew, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
      ierr = PetscViewerFlush(PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
    }
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexRefine_Uniform"
/* This will only work for interpolated meshes */
PetscErrorCode DMPlexRefine_Uniform(DM dm, CellRefiner cellRefiner, DM *dmRefined)
{
  DM             rdm;
  PetscInt      *depthSize;
  PetscInt       dim, depth = 0, d, pStart = 0, pEnd = 0;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = DMCreate(PetscObjectComm((PetscObject)dm), &rdm);CHKERRQ(ierr);
  ierr = DMSetType(rdm, DMPLEX);CHKERRQ(ierr);
  ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
  ierr = DMPlexSetDimension(rdm, dim);CHKERRQ(ierr);
  /* Calculate number of new points of each depth */
  ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
  ierr = PetscMalloc((depth+1) * sizeof(PetscInt), &depthSize);CHKERRQ(ierr);
  ierr = PetscMemzero(depthSize, (depth+1) * sizeof(PetscInt));CHKERRQ(ierr);
  ierr = CellRefinerGetSizes(cellRefiner, dm, depthSize);CHKERRQ(ierr);
  /* Step 1: Set chart */
  for (d = 0; d <= depth; ++d) pEnd += depthSize[d];
  ierr = DMPlexSetChart(rdm, pStart, pEnd);CHKERRQ(ierr);
  /* Step 2: Set cone/support sizes */
  ierr = CellRefinerSetConeSizes(cellRefiner, dm, depthSize, rdm);CHKERRQ(ierr);
  /* Step 3: Setup refined DM */
  ierr = DMSetUp(rdm);CHKERRQ(ierr);
  /* Step 4: Set cones and supports */
  ierr = CellRefinerSetCones(cellRefiner, dm, depthSize, rdm);CHKERRQ(ierr);
  /* Step 5: Stratify */
  ierr = DMPlexStratify(rdm);CHKERRQ(ierr);
  /* Step 6: Set coordinates for vertices */
  ierr = CellRefinerSetCoordinates(cellRefiner, dm, depthSize, rdm);CHKERRQ(ierr);
  /* Step 7: Create pointSF */
  ierr = CellRefinerCreateSF(cellRefiner, dm, depthSize, rdm);CHKERRQ(ierr);
  /* Step 8: Create labels */
  ierr = CellRefinerCreateLabels(cellRefiner, dm, depthSize, rdm);CHKERRQ(ierr);
  ierr = PetscFree(depthSize);CHKERRQ(ierr);

  *dmRefined = rdm;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexSetRefinementUniform"
PetscErrorCode DMPlexSetRefinementUniform(DM dm, PetscBool refinementUniform)
{
  DM_Plex *mesh = (DM_Plex*) dm->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  mesh->refinementUniform = refinementUniform;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetRefinementUniform"
PetscErrorCode DMPlexGetRefinementUniform(DM dm, PetscBool *refinementUniform)
{
  DM_Plex *mesh = (DM_Plex*) dm->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidPointer(refinementUniform,  2);
  *refinementUniform = mesh->refinementUniform;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexSetRefinementLimit"
PetscErrorCode DMPlexSetRefinementLimit(DM dm, PetscReal refinementLimit)
{
  DM_Plex *mesh = (DM_Plex*) dm->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  mesh->refinementLimit = refinementLimit;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetRefinementLimit"
PetscErrorCode DMPlexGetRefinementLimit(DM dm, PetscReal *refinementLimit)
{
  DM_Plex *mesh = (DM_Plex*) dm->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidPointer(refinementLimit,  2);
  /* if (mesh->refinementLimit < 0) = getMaxVolume()/2.0; */
  *refinementLimit = mesh->refinementLimit;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetCellRefiner_Private"
PetscErrorCode DMPlexGetCellRefiner_Private(DM dm, CellRefiner *cellRefiner)
{
  PetscInt       dim, cStart, coneSize, cMax;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
  ierr = DMPlexGetHeightStratum(dm, 0, &cStart, NULL);CHKERRQ(ierr);
  ierr = DMPlexGetConeSize(dm, cStart, &coneSize);CHKERRQ(ierr);
  ierr = DMPlexGetHybridBounds(dm, &cMax, NULL, NULL, NULL);CHKERRQ(ierr);
  switch (dim) {
  case 2:
    switch (coneSize) {
    case 3:
      if (cMax >= 0) *cellRefiner = 3; /* Hybrid */
      else *cellRefiner = 1; /* Triangular */
      break;
    case 4:
      if (cMax >= 0) *cellRefiner = 4; /* Hybrid */
      else *cellRefiner = 2; /* Quadrilateral */
      break;
    default:
      SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unknown coneSize %d in dimension %d for cell refiner", coneSize, dim);
    }
    break;
  default:
    SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unknown dimension %d for cell refiner", dim);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMRefine_Plex"
PetscErrorCode DMRefine_Plex(DM dm, MPI_Comm comm, DM *dmRefined)
{
  PetscReal      refinementLimit;
  PetscInt       dim, cStart, cEnd;
  char           genname[1024], *name = NULL;
  PetscBool      isUniform, isTriangle = PETSC_FALSE, isTetgen = PETSC_FALSE, isCTetgen = PETSC_FALSE, flg;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = DMPlexGetRefinementUniform(dm, &isUniform);CHKERRQ(ierr);
  if (isUniform) {
    CellRefiner cellRefiner;

    ierr = DMPlexGetCellRefiner_Private(dm, &cellRefiner);CHKERRQ(ierr);
    ierr = DMPlexRefine_Uniform(dm, cellRefiner, dmRefined);CHKERRQ(ierr);
    PetscFunctionReturn(0);
  }
  ierr = DMPlexGetRefinementLimit(dm, &refinementLimit);CHKERRQ(ierr);
  if (refinementLimit == 0.0) PetscFunctionReturn(0);
  ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
  ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
  ierr = PetscOptionsGetString(((PetscObject) dm)->prefix, "-dm_plex_generator", genname, 1024, &flg);CHKERRQ(ierr);
  if (flg) name = genname;
  if (name) {
    ierr = PetscStrcmp(name, "triangle", &isTriangle);CHKERRQ(ierr);
    ierr = PetscStrcmp(name, "tetgen",   &isTetgen);CHKERRQ(ierr);
    ierr = PetscStrcmp(name, "ctetgen",  &isCTetgen);CHKERRQ(ierr);
  }
  switch (dim) {
  case 2:
    if (!name || isTriangle) {
#if defined(PETSC_HAVE_TRIANGLE)
      double  *maxVolumes;
      PetscInt c;

      ierr = PetscMalloc((cEnd - cStart) * sizeof(double), &maxVolumes);CHKERRQ(ierr);
      for (c = 0; c < cEnd-cStart; ++c) maxVolumes[c] = refinementLimit;
      ierr = DMPlexRefine_Triangle(dm, maxVolumes, dmRefined);CHKERRQ(ierr);
#else
      SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Mesh refinement needs external package support.\nPlease reconfigure with --download-triangle.");
#endif
    } else SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unknown 2D mesh generation package %s", name);
    break;
  case 3:
    if (!name || isCTetgen) {
#if defined(PETSC_HAVE_CTETGEN)
      PetscReal *maxVolumes;
      PetscInt   c;

      ierr = PetscMalloc((cEnd - cStart) * sizeof(PetscReal), &maxVolumes);CHKERRQ(ierr);
      for (c = 0; c < cEnd-cStart; ++c) maxVolumes[c] = refinementLimit;
      ierr = DMPlexRefine_CTetgen(dm, maxVolumes, dmRefined);CHKERRQ(ierr);
#else
      SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "CTetgen needs external package support.\nPlease reconfigure with --download-ctetgen.");
#endif
    } else if (isTetgen) {
#if defined(PETSC_HAVE_TETGEN)
      double  *maxVolumes;
      PetscInt c;

      ierr = PetscMalloc((cEnd - cStart) * sizeof(double), &maxVolumes);CHKERRQ(ierr);
      for (c = 0; c < cEnd-cStart; ++c) maxVolumes[c] = refinementLimit;
      ierr = DMPlexRefine_Tetgen(dm, maxVolumes, dmRefined);CHKERRQ(ierr);
#else
      SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Tetgen needs external package support.\nPlease reconfigure with --with-c-language=cxx --download-tetgen.");
#endif
    } else SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unknown 3D mesh generation package %s", name);
    break;
  default:
    SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Mesh refinement in dimension %d is not supported.", dim);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetDepth"
/*@
  DMPlexGetDepth - get the number of strata

  Not Collective

  Input Parameters:
. dm           - The DMPlex object

  Output Parameters:
. depth - number of strata

  Level: developer

  Notes:
  DMPlexGetHeightStratum(dm,0,..) should return the same points as DMPlexGetDepthStratum(dm,depth,..).

.keywords: mesh, points
.seealso: DMPlexGetHeightStratum(), DMPlexGetDepthStratum()
@*/
PetscErrorCode DMPlexGetDepth(DM dm, PetscInt *depth)
{
  PetscInt       d;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidPointer(depth, 2);
  ierr   = DMPlexGetLabelSize(dm, "depth", &d);CHKERRQ(ierr);
  *depth = d-1;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetDepthStratum"
/*@
  DMPlexGetDepthStratum - Get the bounds [start, end) for all points at a certain depth.

  Not Collective

  Input Parameters:
+ dm           - The DMPlex object
- stratumValue - The requested depth

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

  Level: developer

.keywords: mesh, points
.seealso: DMPlexGetHeightStratum(), DMPlexGetDepth()
@*/
PetscErrorCode DMPlexGetDepthStratum(DM dm, PetscInt stratumValue, PetscInt *start, PetscInt *end)
{
  DM_Plex       *mesh = (DM_Plex*) dm->data;
  DMLabel        next  = mesh->labels;
  PetscBool      flg   = PETSC_FALSE;
  PetscInt       depth;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (stratumValue < 0) {
    ierr = DMPlexGetChart(dm, start, end);CHKERRQ(ierr);
    PetscFunctionReturn(0);
  } else {
    PetscInt pStart, pEnd;

    if (start) *start = 0;
    if (end)   *end   = 0;
    ierr = DMPlexGetChart(dm, &pStart, &pEnd);CHKERRQ(ierr);
    if (pStart == pEnd) PetscFunctionReturn(0);
  }
  ierr = DMPlexHasLabel(dm, "depth", &flg);CHKERRQ(ierr);
  if (!flg) SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "No label named depth was found");CHKERRQ(ierr);
  /* We should have a generic GetLabel() and a Label class */
  while (next) {
    ierr = PetscStrcmp("depth", next->name, &flg);CHKERRQ(ierr);
    if (flg) break;
    next = next->next;
  }
  /* Strata are sorted and contiguous -- In addition, depth/height is either full or 1-level */
  depth = stratumValue;
  if ((depth < 0) || (depth >= next->numStrata)) {
    if (start) *start = 0;
    if (end)   *end   = 0;
  } else {
    if (start) *start = next->points[next->stratumOffsets[depth]];
    if (end)   *end   = next->points[next->stratumOffsets[depth]+next->stratumSizes[depth]-1]+1;
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetHeightStratum"
/*@
  DMPlexGetHeightStratum - Get the bounds [start, end) for all points at a certain height.

  Not Collective

  Input Parameters:
+ dm           - The DMPlex object
- stratumValue - The requested height

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

  Level: developer

.keywords: mesh, points
.seealso: DMPlexGetDepthStratum(), DMPlexGetDepth()
@*/
PetscErrorCode DMPlexGetHeightStratum(DM dm, PetscInt stratumValue, PetscInt *start, PetscInt *end)
{
  DM_Plex       *mesh = (DM_Plex*) dm->data;
  DMLabel        next  = mesh->labels;
  PetscBool      flg   = PETSC_FALSE;
  PetscInt       depth;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (stratumValue < 0) {
    ierr = DMPlexGetChart(dm, start, end);CHKERRQ(ierr);
  } else {
    PetscInt pStart, pEnd;

    if (start) *start = 0;
    if (end)   *end   = 0;
    ierr = DMPlexGetChart(dm, &pStart, &pEnd);CHKERRQ(ierr);
    if (pStart == pEnd) PetscFunctionReturn(0);
  }
  ierr = DMPlexHasLabel(dm, "depth", &flg);CHKERRQ(ierr);
  if (!flg) SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "No label named depth was found");CHKERRQ(ierr);
  /* We should have a generic GetLabel() and a Label class */
  while (next) {
    ierr = PetscStrcmp("depth", next->name, &flg);CHKERRQ(ierr);
    if (flg) break;
    next = next->next;
  }
  /* Strata are sorted and contiguous -- In addition, depth/height is either full or 1-level */
  depth = next->stratumValues[next->numStrata-1] - stratumValue;
  if ((depth < 0) || (depth >= next->numStrata)) {
    if (start) *start = 0;
    if (end)   *end   = 0;
  } else {
    if (start) *start = next->points[next->stratumOffsets[depth]];
    if (end)   *end   = next->points[next->stratumOffsets[depth]+next->stratumSizes[depth]-1]+1;
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexCreateSectionInitial"
/* Set the number of dof on each point and separate by fields */
PetscErrorCode DMPlexCreateSectionInitial(DM dm, PetscInt dim, PetscInt numFields,const PetscInt numComp[],const PetscInt numDof[], PetscSection *section)
{
  PetscInt      *numDofTot;
  PetscInt       pStart = 0, pEnd = 0;
  PetscInt       p, d, f;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscMalloc((dim+1) * sizeof(PetscInt), &numDofTot);CHKERRQ(ierr);
  for (d = 0; d <= dim; ++d) {
    numDofTot[d] = 0;
    for (f = 0; f < numFields; ++f) numDofTot[d] += numDof[f*(dim+1)+d];
  }
  ierr = PetscSectionCreate(PetscObjectComm((PetscObject)dm), section);CHKERRQ(ierr);
  if (numFields > 0) {
    ierr = PetscSectionSetNumFields(*section, numFields);CHKERRQ(ierr);
    if (numComp) {
      for (f = 0; f < numFields; ++f) {
        ierr = PetscSectionSetFieldComponents(*section, f, numComp[f]);CHKERRQ(ierr);
      }
    }
  }
  ierr = DMPlexGetChart(dm, &pStart, &pEnd);CHKERRQ(ierr);
  ierr = PetscSectionSetChart(*section, pStart, pEnd);CHKERRQ(ierr);
  for (d = 0; d <= dim; ++d) {
    ierr = DMPlexGetDepthStratum(dm, d, &pStart, &pEnd);CHKERRQ(ierr);
    for (p = pStart; p < pEnd; ++p) {
      for (f = 0; f < numFields; ++f) {
        ierr = PetscSectionSetFieldDof(*section, p, f, numDof[f*(dim+1)+d]);CHKERRQ(ierr);
      }
      ierr = PetscSectionSetDof(*section, p, numDofTot[d]);CHKERRQ(ierr);
    }
  }
  ierr = PetscFree(numDofTot);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexCreateSectionBCDof"
/* Set the number of dof on each point and separate by fields
   If constDof is PETSC_DETERMINE, constrain every dof on the point
*/
PetscErrorCode DMPlexCreateSectionBCDof(DM dm, PetscInt numBC,const PetscInt bcField[],const IS bcPoints[], PetscInt constDof, PetscSection section)
{
  PetscInt       numFields;
  PetscInt       bc;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
  for (bc = 0; bc < numBC; ++bc) {
    PetscInt        field = 0;
    const PetscInt *idx;
    PetscInt        n, i;

    if (numFields) field = bcField[bc];
    ierr = ISGetLocalSize(bcPoints[bc], &n);CHKERRQ(ierr);
    ierr = ISGetIndices(bcPoints[bc], &idx);CHKERRQ(ierr);
    for (i = 0; i < n; ++i) {
      const PetscInt p        = idx[i];
      PetscInt       numConst = constDof;

      /* Constrain every dof on the point */
      if (numConst < 0) {
        if (numFields) {
          ierr = PetscSectionGetFieldDof(section, p, field, &numConst);CHKERRQ(ierr);
        } else {
          ierr = PetscSectionGetDof(section, p, &numConst);CHKERRQ(ierr);
        }
      }
      if (numFields) {
        ierr = PetscSectionAddFieldConstraintDof(section, p, field, numConst);CHKERRQ(ierr);
      }
      ierr = PetscSectionAddConstraintDof(section, p, numConst);CHKERRQ(ierr);
    }
    ierr = ISRestoreIndices(bcPoints[bc], &idx);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexCreateSectionBCIndicesAll"
/* Set the constrained indices on each point and separate by fields */
PetscErrorCode DMPlexCreateSectionBCIndicesAll(DM dm, PetscSection section)
{
  PetscInt      *maxConstraints;
  PetscInt       numFields, f, pStart = 0, pEnd = 0, p;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
  ierr = PetscSectionGetChart(section, &pStart, &pEnd);CHKERRQ(ierr);
  ierr = PetscMalloc((numFields+1) * sizeof(PetscInt), &maxConstraints);CHKERRQ(ierr);
  for (f = 0; f <= numFields; ++f) maxConstraints[f] = 0;
  for (p = pStart; p < pEnd; ++p) {
    PetscInt cdof;

    if (numFields) {
      for (f = 0; f < numFields; ++f) {
        ierr              = PetscSectionGetFieldConstraintDof(section, p, f, &cdof);CHKERRQ(ierr);
        maxConstraints[f] = PetscMax(maxConstraints[f], cdof);
      }
    } else {
      ierr              = PetscSectionGetConstraintDof(section, p, &cdof);CHKERRQ(ierr);
      maxConstraints[0] = PetscMax(maxConstraints[0], cdof);
    }
  }
  for (f = 0; f < numFields; ++f) {
    maxConstraints[numFields] += maxConstraints[f];
  }
  if (maxConstraints[numFields]) {
    PetscInt *indices;

    ierr = PetscMalloc(maxConstraints[numFields] * sizeof(PetscInt), &indices);CHKERRQ(ierr);
    for (p = pStart; p < pEnd; ++p) {
      PetscInt cdof, d;

      ierr = PetscSectionGetConstraintDof(section, p, &cdof);CHKERRQ(ierr);
      if (cdof) {
        if (cdof > maxConstraints[numFields]) SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_LIB, "Likely memory corruption, point %D cDof %D > maxConstraints %D", p, cdof, maxConstraints[numFields]);
        if (numFields) {
          PetscInt numConst = 0, foff = 0;

          for (f = 0; f < numFields; ++f) {
            PetscInt cfdof, fdof;

            ierr = PetscSectionGetFieldDof(section, p, f, &fdof);CHKERRQ(ierr);
            ierr = PetscSectionGetFieldConstraintDof(section, p, f, &cfdof);CHKERRQ(ierr);
            /* Change constraint numbering from absolute local dof number to field relative local dof number */
            for (d = 0; d < cfdof; ++d) indices[numConst+d] = d;
            ierr = PetscSectionSetFieldConstraintIndices(section, p, f, &indices[numConst]);CHKERRQ(ierr);
            for (d = 0; d < cfdof; ++d) indices[numConst+d] += foff;
            numConst += cfdof;
            foff     += fdof;
          }
          if (cdof != numConst) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_LIB, "Total number of field constraints %D should be %D", numConst, cdof);
        } else {
          for (d = 0; d < cdof; ++d) indices[d] = d;
        }
        ierr = PetscSectionSetConstraintIndices(section, p, indices);CHKERRQ(ierr);
      }
    }
    ierr = PetscFree(indices);CHKERRQ(ierr);
  }
  ierr = PetscFree(maxConstraints);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexCreateSectionBCIndicesField"
/* Set the constrained field indices on each point */
PetscErrorCode DMPlexCreateSectionBCIndicesField(DM dm, PetscInt field, IS bcPoints, IS constraintIndices, PetscSection section)
{
  const PetscInt *points, *indices;
  PetscInt        numFields, maxDof, numPoints, p, numConstraints;
  PetscErrorCode  ierr;

  PetscFunctionBegin;
  ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
  if ((field < 0) || (field >= numFields)) SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Section field %d should be in [%d, %d)", field, 0, numFields);

  ierr = ISGetLocalSize(bcPoints, &numPoints);CHKERRQ(ierr);
  ierr = ISGetIndices(bcPoints, &points);CHKERRQ(ierr);
  if (!constraintIndices) {
    PetscInt *idx, i;

    ierr = PetscSectionGetMaxDof(section, &maxDof);CHKERRQ(ierr);
    ierr = PetscMalloc(maxDof * sizeof(PetscInt), &idx);CHKERRQ(ierr);
    for (i = 0; i < maxDof; ++i) idx[i] = i;
    for (p = 0; p < numPoints; ++p) {
      ierr = PetscSectionSetFieldConstraintIndices(section, points[p], field, idx);CHKERRQ(ierr);
    }
    ierr = PetscFree(idx);CHKERRQ(ierr);
  } else {
    ierr = ISGetLocalSize(constraintIndices, &numConstraints);CHKERRQ(ierr);
    ierr = ISGetIndices(constraintIndices, &indices);CHKERRQ(ierr);
    for (p = 0; p < numPoints; ++p) {
      PetscInt fcdof;

      ierr = PetscSectionGetFieldConstraintDof(section, points[p], field, &fcdof);CHKERRQ(ierr);
      if (fcdof != numConstraints) SETERRQ4(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Section point %d field %d has %d constraints, but yo ugave %d indices", p, field, fcdof, numConstraints);
      ierr = PetscSectionSetFieldConstraintIndices(section, points[p], field, indices);CHKERRQ(ierr);
    }
    ierr = ISRestoreIndices(constraintIndices, &indices);CHKERRQ(ierr);
  }
  ierr = ISRestoreIndices(bcPoints, &points);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexCreateSectionBCIndices"
/* Set the constrained indices on each point and separate by fields */
PetscErrorCode DMPlexCreateSectionBCIndices(DM dm, PetscSection section)
{
  PetscInt      *indices;
  PetscInt       numFields, maxDof, f, pStart = 0, pEnd = 0, p;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscSectionGetMaxDof(section, &maxDof);CHKERRQ(ierr);
  ierr = PetscMalloc(maxDof * sizeof(PetscInt), &indices);CHKERRQ(ierr);
  ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
  if (!numFields) SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "This function only works after users have set field constraint indices.");
  ierr = PetscSectionGetChart(section, &pStart, &pEnd);CHKERRQ(ierr);
  for (p = pStart; p < pEnd; ++p) {
    PetscInt cdof, d;

    ierr = PetscSectionGetConstraintDof(section, p, &cdof);CHKERRQ(ierr);
    if (cdof) {
      PetscInt numConst = 0, foff = 0;

      for (f = 0; f < numFields; ++f) {
        const PetscInt *fcind;
        PetscInt        fdof, fcdof;

        ierr = PetscSectionGetFieldDof(section, p, f, &fdof);CHKERRQ(ierr);
        ierr = PetscSectionGetFieldConstraintDof(section, p, f, &fcdof);CHKERRQ(ierr);
        if (fcdof) {ierr = PetscSectionGetFieldConstraintIndices(section, p, f, &fcind);CHKERRQ(ierr);}
        /* Change constraint numbering from field relative local dof number to absolute local dof number */
        for (d = 0; d < fcdof; ++d) indices[numConst+d] = fcind[d]+foff;
        foff     += fdof;
        numConst += fcdof;
      }
      if (cdof != numConst) SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_LIB, "Total number of field constraints %D should be %D", numConst, cdof);
      ierr = PetscSectionSetConstraintIndices(section, p, indices);CHKERRQ(ierr);
    }
  }
  ierr = PetscFree(indices);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexCreateSection"
/*@C
  DMPlexCreateSection - Create a PetscSection based upon the dof layout specification provided.

  Not Collective

  Input Parameters:
+ dm        - The DMPlex object
. dim       - The spatial dimension of the problem
. numFields - The number of fields in the problem
. numComp   - An array of size numFields that holds the number of components for each field
. numDof    - An array of size numFields*(dim+1) which holds the number of dof for each field on a mesh piece of dimension d
. numBC     - The number of boundary conditions
. bcField   - An array of size numBC giving the field number for each boundry condition
- bcPoints  - An array of size numBC giving an IS holding the sieve points to which each boundary condition applies

  Output Parameter:
. section - The PetscSection object

  Notes: numDof[f*(dim+1)+d] gives the number of dof for field f on sieve points of dimension d. For instance, numDof[1] is the
  nubmer of dof for field 0 on each edge.

  Level: developer

.keywords: mesh, elements
.seealso: DMPlexCreate(), PetscSectionCreate()
@*/
PetscErrorCode DMPlexCreateSection(DM dm, PetscInt dim, PetscInt numFields,const PetscInt numComp[],const PetscInt numDof[], PetscInt numBC,const PetscInt bcField[],const IS bcPoints[], PetscSection *section)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = DMPlexCreateSectionInitial(dm, dim, numFields, numComp, numDof, section);CHKERRQ(ierr);
  ierr = DMPlexCreateSectionBCDof(dm, numBC, bcField, bcPoints, PETSC_DETERMINE, *section);CHKERRQ(ierr);
  ierr = PetscSectionSetUp(*section);CHKERRQ(ierr);
  if (numBC) {ierr = DMPlexCreateSectionBCIndicesAll(dm, *section);CHKERRQ(ierr);}
  {
    PetscBool view = PETSC_FALSE;

    ierr = PetscOptionsHasName(((PetscObject) dm)->prefix, "-section_view", &view);CHKERRQ(ierr);
    if (view) {ierr = PetscSectionView(*section, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);}
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMCreateCoordinateDM_Plex"
PetscErrorCode DMCreateCoordinateDM_Plex(DM dm, DM *cdm)
{
  PetscSection   section;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = DMPlexClone(dm, cdm);CHKERRQ(ierr);
  ierr = PetscSectionCreate(PetscObjectComm((PetscObject)dm), &section);CHKERRQ(ierr);
  ierr = DMSetDefaultSection(*cdm, section);CHKERRQ(ierr);
  ierr = PetscSectionDestroy(&section);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetCoordinateSection"
/*@
  DMPlexGetCoordinateSection - Retrieve the layout of coordinate values over the mesh.

  Not Collective

  Input Parameter:
. dm - The DMPlex object

  Output Parameter:
. section - The PetscSection object

  Level: intermediate

.keywords: mesh, coordinates
.seealso: DMGetCoordinateDM(), DMPlexGetDefaultSection(), DMPlexSetDefaultSection()
@*/
PetscErrorCode DMPlexGetCoordinateSection(DM dm, PetscSection *section)
{
  DM             cdm;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidPointer(section, 2);
  ierr = DMGetCoordinateDM(dm, &cdm);CHKERRQ(ierr);
  ierr = DMGetDefaultSection(cdm, section);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexSetCoordinateSection"
/*@
  DMPlexSetCoordinateSection - Set the layout of coordinate values over the mesh.

  Not Collective

  Input Parameters:
+ dm      - The DMPlex object
- section - The PetscSection object

  Level: intermediate

.keywords: mesh, coordinates
.seealso: DMPlexGetCoordinateSection(), DMPlexGetDefaultSection(), DMPlexSetDefaultSection()
@*/
PetscErrorCode DMPlexSetCoordinateSection(DM dm, PetscSection section)
{
  DM             cdm;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm,DM_CLASSID,1);
  PetscValidHeaderSpecific(section,PETSC_SECTION_CLASSID,2);
  ierr = DMGetCoordinateDM(dm, &cdm);CHKERRQ(ierr);
  ierr = DMSetDefaultSection(cdm, section);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetConeSection"
PetscErrorCode DMPlexGetConeSection(DM dm, PetscSection *section)
{
  DM_Plex *mesh = (DM_Plex*) dm->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (section) *section = mesh->coneSection;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetCones"
PetscErrorCode DMPlexGetCones(DM dm, PetscInt *cones[])
{
  DM_Plex *mesh = (DM_Plex*) dm->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (cones) *cones = mesh->cones;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetConeOrientations"
PetscErrorCode DMPlexGetConeOrientations(DM dm, PetscInt *coneOrientations[])
{
  DM_Plex *mesh = (DM_Plex*) dm->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (coneOrientations) *coneOrientations = mesh->coneOrientations;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexLocatePoint_Simplex_2D"
PetscErrorCode DMPlexLocatePoint_Simplex_2D(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
{
  const PetscInt embedDim = 2;
  PetscReal      x        = PetscRealPart(point[0]);
  PetscReal      y        = PetscRealPart(point[1]);
  PetscReal      v0[2], J[4], invJ[4], detJ;
  PetscReal      xi, eta;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = DMPlexComputeCellGeometry(dm, c, v0, J, invJ, &detJ);CHKERRQ(ierr);
  xi  = invJ[0*embedDim+0]*(x - v0[0]) + invJ[0*embedDim+1]*(y - v0[1]);
  eta = invJ[1*embedDim+0]*(x - v0[0]) + invJ[1*embedDim+1]*(y - v0[1]);

  if ((xi >= 0.0) && (eta >= 0.0) && (xi + eta <= 2.0)) *cell = c;
  else *cell = -1;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexLocatePoint_General_2D"
PetscErrorCode DMPlexLocatePoint_General_2D(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
{
  PetscSection       coordSection;
  Vec                coordsLocal;
  const PetscScalar *coords;
  const PetscInt     faces[8]  = {0, 1, 1, 2, 2, 3, 3, 0};
  PetscReal          x         = PetscRealPart(point[0]);
  PetscReal          y         = PetscRealPart(point[1]);
  PetscInt           crossings = 0, f;
  PetscErrorCode     ierr;

  PetscFunctionBegin;
  ierr = DMGetCoordinatesLocal(dm, &coordsLocal);CHKERRQ(ierr);
  ierr = DMPlexGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
  ierr = DMPlexVecGetClosure(dm, coordSection, coordsLocal, c, NULL, &coords);CHKERRQ(ierr);
  for (f = 0; f < 4; ++f) {
    PetscReal x_i   = PetscRealPart(coords[faces[2*f+0]*2+0]);
    PetscReal y_i   = PetscRealPart(coords[faces[2*f+0]*2+1]);
    PetscReal x_j   = PetscRealPart(coords[faces[2*f+1]*2+0]);
    PetscReal y_j   = PetscRealPart(coords[faces[2*f+1]*2+1]);
    PetscReal slope = (y_j - y_i) / (x_j - x_i);
    PetscBool cond1 = (x_i <= x) && (x < x_j) ? PETSC_TRUE : PETSC_FALSE;
    PetscBool cond2 = (x_j <= x) && (x < x_i) ? PETSC_TRUE : PETSC_FALSE;
    PetscBool above = (y < slope * (x - x_i) + y_i) ? PETSC_TRUE : PETSC_FALSE;
    if ((cond1 || cond2)  && above) ++crossings;
  }
  if (crossings % 2) *cell = c;
  else *cell = -1;
  ierr = DMPlexVecRestoreClosure(dm, coordSection, coordsLocal, c, NULL, &coords);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexLocatePoint_Simplex_3D"
PetscErrorCode DMPlexLocatePoint_Simplex_3D(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
{
  const PetscInt embedDim = 3;
  PetscReal      v0[3], J[9], invJ[9], detJ;
  PetscReal      x = PetscRealPart(point[0]);
  PetscReal      y = PetscRealPart(point[1]);
  PetscReal      z = PetscRealPart(point[2]);
  PetscReal      xi, eta, zeta;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = DMPlexComputeCellGeometry(dm, c, v0, J, invJ, &detJ);CHKERRQ(ierr);
  xi   = invJ[0*embedDim+0]*(x - v0[0]) + invJ[0*embedDim+1]*(y - v0[1]) + invJ[0*embedDim+2]*(z - v0[2]);
  eta  = invJ[1*embedDim+0]*(x - v0[0]) + invJ[1*embedDim+1]*(y - v0[1]) + invJ[1*embedDim+2]*(z - v0[2]);
  zeta = invJ[2*embedDim+0]*(x - v0[0]) + invJ[2*embedDim+1]*(y - v0[1]) + invJ[2*embedDim+2]*(z - v0[2]);

  if ((xi >= 0.0) && (eta >= 0.0) && (zeta >= 0.0) && (xi + eta + zeta <= 2.0)) *cell = c;
  else *cell = -1;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexLocatePoint_General_3D"
PetscErrorCode DMPlexLocatePoint_General_3D(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
{
  PetscSection       coordSection;
  Vec                coordsLocal;
  const PetscScalar *coords;
  const PetscInt     faces[24] = {0, 1, 2, 3,  5, 4, 7, 6,  1, 0, 4, 5,
                                  3, 2, 6, 7,  1, 5, 6, 2,  0, 3, 7, 4};
  PetscBool          found = PETSC_TRUE;
  PetscInt           f;
  PetscErrorCode     ierr;

  PetscFunctionBegin;
  ierr = DMGetCoordinatesLocal(dm, &coordsLocal);CHKERRQ(ierr);
  ierr = DMPlexGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
  ierr = DMPlexVecGetClosure(dm, coordSection, coordsLocal, c, NULL, &coords);CHKERRQ(ierr);
  for (f = 0; f < 6; ++f) {
    /* Check the point is under plane */
    /*   Get face normal */
    PetscReal v_i[3];
    PetscReal v_j[3];
    PetscReal normal[3];
    PetscReal pp[3];
    PetscReal dot;

    v_i[0]    = PetscRealPart(coords[faces[f*4+3]*3+0]-coords[faces[f*4+0]*3+0]);
    v_i[1]    = PetscRealPart(coords[faces[f*4+3]*3+1]-coords[faces[f*4+0]*3+1]);
    v_i[2]    = PetscRealPart(coords[faces[f*4+3]*3+2]-coords[faces[f*4+0]*3+2]);
    v_j[0]    = PetscRealPart(coords[faces[f*4+1]*3+0]-coords[faces[f*4+0]*3+0]);
    v_j[1]    = PetscRealPart(coords[faces[f*4+1]*3+1]-coords[faces[f*4+0]*3+1]);
    v_j[2]    = PetscRealPart(coords[faces[f*4+1]*3+2]-coords[faces[f*4+0]*3+2]);
    normal[0] = v_i[1]*v_j[2] - v_i[2]*v_j[1];
    normal[1] = v_i[2]*v_j[0] - v_i[0]*v_j[2];
    normal[2] = v_i[0]*v_j[1] - v_i[1]*v_j[0];
    pp[0]     = PetscRealPart(coords[faces[f*4+0]*3+0] - point[0]);
    pp[1]     = PetscRealPart(coords[faces[f*4+0]*3+1] - point[1]);
    pp[2]     = PetscRealPart(coords[faces[f*4+0]*3+2] - point[2]);
    dot       = normal[0]*pp[0] + normal[1]*pp[1] + normal[2]*pp[2];

    /* Check that projected point is in face (2D location problem) */
    if (dot < 0.0) {
      found = PETSC_FALSE;
      break;
    }
  }
  if (found) *cell = c;
  else *cell = -1;
  ierr = DMPlexVecRestoreClosure(dm, coordSection, coordsLocal, c, NULL, &coords);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMLocatePoints_Plex"
/*
 Need to implement using the guess
*/
PetscErrorCode DMLocatePoints_Plex(DM dm, Vec v, IS *cellIS)
{
  PetscInt       cell = -1 /*, guess = -1*/;
  PetscInt       bs, numPoints, p;
  PetscInt       dim, cStart, cEnd, cMax, c, coneSize;
  PetscInt      *cells;
  PetscScalar   *a;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
  ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
  ierr = DMPlexGetHybridBounds(dm, &cMax, NULL, NULL, NULL);CHKERRQ(ierr);
  if (cMax >= 0) cEnd = PetscMin(cEnd, cMax);
  ierr = VecGetLocalSize(v, &numPoints);CHKERRQ(ierr);
  ierr = VecGetBlockSize(v, &bs);CHKERRQ(ierr);
  ierr = VecGetArray(v, &a);CHKERRQ(ierr);
  if (bs != dim) SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Block size for point vector %d must be the mesh coordinate dimension %d", bs, dim);
  numPoints /= bs;
  ierr       = PetscMalloc(numPoints * sizeof(PetscInt), &cells);CHKERRQ(ierr);
  for (p = 0; p < numPoints; ++p) {
    const PetscScalar *point = &a[p*bs];

    switch (dim) {
    case 2:
      for (c = cStart; c < cEnd; ++c) {
        ierr = DMPlexGetConeSize(dm, c, &coneSize);CHKERRQ(ierr);
        switch (coneSize) {
        case 3:
          ierr = DMPlexLocatePoint_Simplex_2D(dm, point, c, &cell);CHKERRQ(ierr);
          break;
        case 4:
          ierr = DMPlexLocatePoint_General_2D(dm, point, c, &cell);CHKERRQ(ierr);
          break;
        default:
          SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No point location for cell with cone size %d", coneSize);
        }
        if (cell >= 0) break;
      }
      break;
    case 3:
      for (c = cStart; c < cEnd; ++c) {
        ierr = DMPlexGetConeSize(dm, c, &coneSize);CHKERRQ(ierr);
        switch (coneSize) {
        case 4:
          ierr = DMPlexLocatePoint_Simplex_3D(dm, point, c, &cell);CHKERRQ(ierr);
          break;
        case 8:
          ierr = DMPlexLocatePoint_General_3D(dm, point, c, &cell);CHKERRQ(ierr);
          break;
        default:
          SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No point location for cell with cone size %d", coneSize);
        }
        if (cell >= 0) break;
      }
      break;
    default:
      SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No point location for mesh dimension %d", dim);
    }
    cells[p] = cell;
  }
  ierr = VecRestoreArray(v, &a);CHKERRQ(ierr);
  ierr = ISCreateGeneral(PETSC_COMM_SELF, numPoints, cells, PETSC_OWN_POINTER, cellIS);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/******************************** FEM Support **********************************/

#undef __FUNCT__
#define __FUNCT__ "DMPlexVecGetClosure"
/*@C
  DMPlexVecGetClosure - Get an array of the values on the closure of 'point'

  Not collective

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

  Output Parameters:
+ csize - The number of values in the closure, or NULL
- values - The array of values, which is a borrowed array and should not be freed

  Level: intermediate

.seealso DMPlexVecRestoreClosure(), DMPlexVecSetClosure(), DMPlexMatSetClosure()
@*/
PetscErrorCode DMPlexVecGetClosure(DM dm, PetscSection section, Vec v, PetscInt point, PetscInt *csize, const PetscScalar *values[])
{
  PetscScalar   *array, *vArray;
  PetscInt      *points = NULL;
  PetscInt       offsets[32];
  PetscInt       numFields, size, numPoints, pStart, pEnd, p, q, f;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidHeaderSpecific(v, VEC_CLASSID, 3);
  if (!section) {
    ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
  }
  ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
  if (numFields > 31) SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "Number of fields %D limited to 31", numFields);
  ierr = PetscMemzero(offsets, 32 * sizeof(PetscInt));CHKERRQ(ierr);
  ierr = DMPlexGetTransitiveClosure(dm, point, PETSC_TRUE, &numPoints, &points);CHKERRQ(ierr);
  /* Compress out points not in the section */
  ierr = PetscSectionGetChart(section, &pStart, &pEnd);CHKERRQ(ierr);
  for (p = 0, q = 0; p < numPoints*2; p += 2) {
    if ((points[p] >= pStart) && (points[p] < pEnd)) {
      points[q*2]   = points[p];
      points[q*2+1] = points[p+1];
      ++q;
    }
  }
  numPoints = q;
  for (p = 0, size = 0; p < numPoints*2; p += 2) {
    PetscInt dof, fdof;

    ierr = PetscSectionGetDof(section, points[p], &dof);CHKERRQ(ierr);
    for (f = 0; f < numFields; ++f) {
      ierr          = PetscSectionGetFieldDof(section, points[p], f, &fdof);CHKERRQ(ierr);
      offsets[f+1] += fdof;
    }
    size += dof;
  }
  for (f = 1; f < numFields; ++f) offsets[f+1] += offsets[f];
  if (numFields && offsets[numFields] != size) SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Invalid size for closure %d should be %d", offsets[numFields], size);
  ierr = DMGetWorkArray(dm, size, PETSC_SCALAR, &array);CHKERRQ(ierr);
  ierr = VecGetArray(v, &vArray);CHKERRQ(ierr);
  for (p = 0; p < numPoints*2; p += 2) {
    PetscInt     o = points[p+1];
    PetscInt     dof, off, d;
    PetscScalar *varr;

    ierr = PetscSectionGetDof(section, points[p], &dof);CHKERRQ(ierr);
    ierr = PetscSectionGetOffset(section, points[p], &off);CHKERRQ(ierr);
    varr = &vArray[off];
    if (numFields) {
      PetscInt fdof, foff, fcomp, f, c;

      for (f = 0, foff = 0; f < numFields; ++f) {
        ierr = PetscSectionGetFieldDof(section, points[p], f, &fdof);CHKERRQ(ierr);
        if (o >= 0) {
          for (d = 0; d < fdof; ++d, ++offsets[f]) {
            array[offsets[f]] = varr[foff+d];
          }
        } else {
          ierr = PetscSectionGetFieldComponents(section, f, &fcomp);CHKERRQ(ierr);
          for (d = fdof/fcomp-1; d >= 0; --d) {
            for (c = 0; c < fcomp; ++c, ++offsets[f]) {
              array[offsets[f]] = varr[foff+d*fcomp+c];
            }
          }
        }
        foff += fdof;
      }
    } else {
      if (o >= 0) {
        for (d = 0; d < dof; ++d, ++offsets[0]) {
          array[offsets[0]] = varr[d];
        }
      } else {
        for (d = dof-1; d >= 0; --d, ++offsets[0]) {
          array[offsets[0]] = varr[d];
        }
      }
    }
  }
  ierr = DMPlexRestoreTransitiveClosure(dm, point, PETSC_TRUE, &numPoints, &points);CHKERRQ(ierr);
  ierr = VecRestoreArray(v, &vArray);CHKERRQ(ierr);
  if (csize) *csize = size;
  *values = array;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexVecRestoreClosure"
/*@C
  DMPlexVecRestoreClosure - Restore the array of the values on the closure of 'point'

  Not collective

  Input Parameters:
+ dm - The DM
. section - The section describing the layout in v, or NULL to use the default section
. v - The local vector
. point - The sieve point in the DM
. csize - The number of values in the closure, or NULL
- values - The array of values, which is a borrowed array and should not be freed

  Level: intermediate

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

  PetscFunctionBegin;
  /* Should work without recalculating size */
  ierr = DMRestoreWorkArray(dm, size, PETSC_SCALAR, (void*) values);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

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

#undef __FUNCT__
#define __FUNCT__ "updatePoint_private"
PetscErrorCode updatePoint_private(PetscSection section, PetscInt point, PetscInt dof, void (*fuse)(PetscScalar*, PetscScalar), PetscBool setBC, PetscInt orientation, const PetscScalar values[], PetscScalar array[])
{
  PetscInt        cdof;   /* The number of constraints on this point */
  const PetscInt *cdofs; /* The indices of the constrained dofs on this point */
  PetscScalar    *a;
  PetscInt        off, cind = 0, k;
  PetscErrorCode  ierr;

  PetscFunctionBegin;
  ierr = PetscSectionGetConstraintDof(section, point, &cdof);CHKERRQ(ierr);
  ierr = PetscSectionGetOffset(section, point, &off);CHKERRQ(ierr);
  a    = &array[off];
  if (!cdof || setBC) {
    if (orientation >= 0) {
      for (k = 0; k < dof; ++k) {
        fuse(&a[k], values[k]);
      }
    } else {
      for (k = 0; k < dof; ++k) {
        fuse(&a[k], values[dof-k-1]);
      }
    }
  } else {
    ierr = PetscSectionGetConstraintIndices(section, point, &cdofs);CHKERRQ(ierr);
    if (orientation >= 0) {
      for (k = 0; k < dof; ++k) {
        if ((cind < cdof) && (k == cdofs[cind])) {++cind; continue;}
        fuse(&a[k], values[k]);
      }
    } else {
      for (k = 0; k < dof; ++k) {
        if ((cind < cdof) && (k == cdofs[cind])) {++cind; continue;}
        fuse(&a[k], values[dof-k-1]);
      }
    }
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "updatePointFields_private"
PetscErrorCode updatePointFields_private(PetscSection section, PetscInt point, PetscInt foffs[], void (*fuse)(PetscScalar*, PetscScalar), PetscBool setBC, PetscInt orientation, const PetscScalar values[], PetscScalar array[])
{
  PetscScalar   *a;
  PetscInt       numFields, off, foff, f;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
  ierr = PetscSectionGetOffset(section, point, &off);CHKERRQ(ierr);
  a    = &array[off];
  for (f = 0, foff = 0; f < numFields; ++f) {
    PetscInt        fdof, fcomp, fcdof;
    const PetscInt *fcdofs; /* The indices of the constrained dofs for field f on this point */
    PetscInt        cind = 0, k, c;

    ierr = PetscSectionGetFieldComponents(section, f, &fcomp);CHKERRQ(ierr);
    ierr = PetscSectionGetFieldDof(section, point, f, &fdof);CHKERRQ(ierr);
    ierr = PetscSectionGetFieldConstraintDof(section, point, f, &fcdof);CHKERRQ(ierr);
    if (!fcdof || setBC) {
      if (orientation >= 0) {
        for (k = 0; k < fdof; ++k) {
          fuse(&a[foff+k], values[foffs[f]+k]);
        }
      } else {
        for (k = fdof/fcomp-1; k >= 0; --k) {
          for (c = 0; c < fcomp; ++c) {
            fuse(&a[foff+(fdof/fcomp-1-k)*fcomp+c], values[foffs[f]+k*fcomp+c]);
          }
        }
      }
    } else {
      ierr = PetscSectionGetFieldConstraintIndices(section, point, f, &fcdofs);CHKERRQ(ierr);
      if (orientation >= 0) {
        for (k = 0; k < fdof; ++k) {
          if ((cind < fcdof) && (k == fcdofs[cind])) {++cind; continue;}
          fuse(&a[foff+k], values[foffs[f]+k]);
        }
      } else {
        for (k = fdof/fcomp-1; k >= 0; --k) {
          for (c = 0; c < fcomp; ++c) {
            if ((cind < fcdof) && (k*fcomp+c == fcdofs[cind])) {++cind; continue;}
            fuse(&a[foff+(fdof/fcomp-1-k)*fcomp+c], values[foffs[f]+k*fcomp+c]);
          }
        }
      }
    }
    foff     += fdof;
    foffs[f] += fdof;
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexVecSetClosure"
/*@C
  DMPlexVecSetClosure - Set an array of the values on the closure of 'point'

  Not collective

  Input Parameters:
+ dm - The DM
. section - The section describing the layout in v, or NULL to use the default sectionw
. v - The local vector
. point - The sieve point in the DM
. values - The array of values, which is a borrowed array and should not be freed
- mode - The insert mode, where INSERT_ALL_VALUES and ADD_ALL_VALUES also overwrite boundary conditions

  Level: intermediate

.seealso DMPlexVecGetClosure(), DMPlexMatSetClosure()
@*/
PetscErrorCode DMPlexVecSetClosure(DM dm, PetscSection section, Vec v, PetscInt point, const PetscScalar values[], InsertMode mode)
{
  PetscScalar   *array;
  PetscInt      *points = NULL;
  PetscInt       offsets[32];
  PetscInt       numFields, numPoints, off, dof, pStart, pEnd, p, q, f;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidHeaderSpecific(v, VEC_CLASSID, 3);
  if (!section) {
    ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
  }
  ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
  if (numFields > 31) SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "Number of fields %D limited to 31", numFields);
  ierr = PetscMemzero(offsets, 32 * sizeof(PetscInt));CHKERRQ(ierr);
  ierr = DMPlexGetTransitiveClosure(dm, point, PETSC_TRUE, &numPoints, &points);CHKERRQ(ierr);
  /* Compress out points not in the section */
  ierr = PetscSectionGetChart(section, &pStart, &pEnd);CHKERRQ(ierr);
  for (p = 0, q = 0; p < numPoints*2; p += 2) {
    if ((points[p] >= pStart) && (points[p] < pEnd)) {
      points[q*2]   = points[p];
      points[q*2+1] = points[p+1];
      ++q;
    }
  }
  numPoints = q;
  for (p = 0; p < numPoints*2; p += 2) {
    PetscInt fdof;

    for (f = 0; f < numFields; ++f) {
      ierr          = PetscSectionGetFieldDof(section, points[p], f, &fdof);CHKERRQ(ierr);
      offsets[f+1] += fdof;
    }
  }
  for (f = 1; f < numFields; ++f) offsets[f+1] += offsets[f];
  ierr = VecGetArray(v, &array);CHKERRQ(ierr);
  if (numFields) {
    switch (mode) {
    case INSERT_VALUES:
      for (p = 0; p < numPoints*2; p += 2) {
        PetscInt o = points[p+1];
        updatePointFields_private(section, points[p], offsets, insert, PETSC_FALSE, o, values, array);
      } break;
    case INSERT_ALL_VALUES:
      for (p = 0; p < numPoints*2; p += 2) {
        PetscInt o = points[p+1];
        updatePointFields_private(section, points[p], offsets, insert, PETSC_TRUE,  o, values, array);
      } break;
    case ADD_VALUES:
      for (p = 0; p < numPoints*2; p += 2) {
        PetscInt o = points[p+1];
        updatePointFields_private(section, points[p], offsets, add,    PETSC_FALSE, o, values, array);
      } break;
    case ADD_ALL_VALUES:
      for (p = 0; p < numPoints*2; p += 2) {
        PetscInt o = points[p+1];
        updatePointFields_private(section, points[p], offsets, add,    PETSC_TRUE,  o, values, array);
      } break;
    default:
      SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "Invalid insert mode %D", mode);
    }
  } else {
    switch (mode) {
    case INSERT_VALUES:
      for (p = 0, off = 0; p < numPoints*2; p += 2, off += dof) {
        PetscInt o = points[p+1];
        ierr = PetscSectionGetDof(section, points[p], &dof);CHKERRQ(ierr);
        updatePoint_private(section, points[p], dof, insert, PETSC_FALSE, o, &values[off], array);
      } break;
    case INSERT_ALL_VALUES:
      for (p = 0, off = 0; p < numPoints*2; p += 2, off += dof) {
        PetscInt o = points[p+1];
        ierr = PetscSectionGetDof(section, points[p], &dof);CHKERRQ(ierr);
        updatePoint_private(section, points[p], dof, insert, PETSC_TRUE,  o, &values[off], array);
      } break;
    case ADD_VALUES:
      for (p = 0, off = 0; p < numPoints*2; p += 2, off += dof) {
        PetscInt o = points[p+1];
        ierr = PetscSectionGetDof(section, points[p], &dof);CHKERRQ(ierr);
        updatePoint_private(section, points[p], dof, add,    PETSC_FALSE, o, &values[off], array);
      } break;
    case ADD_ALL_VALUES:
      for (p = 0, off = 0; p < numPoints*2; p += 2, off += dof) {
        PetscInt o = points[p+1];
        ierr = PetscSectionGetDof(section, points[p], &dof);CHKERRQ(ierr);
        updatePoint_private(section, points[p], dof, add,    PETSC_TRUE,  o, &values[off], array);
      } break;
    default:
      SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "Invalid insert mode %D", mode);
    }
  }
  ierr = DMPlexRestoreTransitiveClosure(dm, point, PETSC_TRUE, &numPoints, &points);CHKERRQ(ierr);
  ierr = VecRestoreArray(v, &array);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexPrintMatSetValues"
PetscErrorCode DMPlexPrintMatSetValues(PetscViewer viewer, Mat A, PetscInt point, PetscInt numIndices, const PetscInt indices[], PetscScalar values[])
{
  PetscMPIInt    rank;
  PetscInt       i, j;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)A), &rank);CHKERRQ(ierr);
  ierr = PetscViewerASCIIPrintf(viewer, "[%D]mat for sieve point %D\n", rank, point);CHKERRQ(ierr);
  for (i = 0; i < numIndices; i++) {
    ierr = PetscViewerASCIIPrintf(viewer, "[%D]mat indices[%D] = %D\n", rank, i, indices[i]);CHKERRQ(ierr);
  }
  for (i = 0; i < numIndices; i++) {
    ierr = PetscViewerASCIIPrintf(viewer, "[%D]", rank);CHKERRQ(ierr);
    for (j = 0; j < numIndices; j++) {
#if defined(PETSC_USE_COMPLEX)
      ierr = PetscViewerASCIIPrintf(viewer, " (%G,%G)", PetscRealPart(values[i*numIndices+j]), PetscImaginaryPart(values[i*numIndices+j]));CHKERRQ(ierr);
#else
      ierr = PetscViewerASCIIPrintf(viewer, " %G", values[i*numIndices+j]);CHKERRQ(ierr);
#endif
    }
    ierr = PetscViewerASCIIPrintf(viewer, "\n");CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "indicesPoint_private"
/* . off - The global offset of this point */
PetscErrorCode indicesPoint_private(PetscSection section, PetscInt point, PetscInt off, PetscInt *loff, PetscBool setBC, PetscInt orientation, PetscInt indices[])
{
  PetscInt        dof;    /* The number of unknowns on this point */
  PetscInt        cdof;   /* The number of constraints on this point */
  const PetscInt *cdofs; /* The indices of the constrained dofs on this point */
  PetscInt        cind = 0, k;
  PetscErrorCode  ierr;

  PetscFunctionBegin;
  ierr = PetscSectionGetDof(section, point, &dof);CHKERRQ(ierr);
  ierr = PetscSectionGetConstraintDof(section, point, &cdof);CHKERRQ(ierr);
  if (!cdof || setBC) {
    if (orientation >= 0) {
      for (k = 0; k < dof; ++k) indices[*loff+k] = off+k;
    } else {
      for (k = 0; k < dof; ++k) indices[*loff+dof-k-1] = off+k;
    }
  } else {
    ierr = PetscSectionGetConstraintIndices(section, point, &cdofs);CHKERRQ(ierr);
    if (orientation >= 0) {
      for (k = 0; k < dof; ++k) {
        if ((cind < cdof) && (k == cdofs[cind])) {
          /* Insert check for returning constrained indices */
          indices[*loff+k] = -(off+k+1);
          ++cind;
        } else {
          indices[*loff+k] = off+k-cind;
        }
      }
    } else {
      for (k = 0; k < dof; ++k) {
        if ((cind < cdof) && (k == cdofs[cind])) {
          /* Insert check for returning constrained indices */
          indices[*loff+dof-k-1] = -(off+k+1);
          ++cind;
        } else {
          indices[*loff+dof-k-1] = off+k-cind;
        }
      }
    }
  }
  *loff += dof;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "indicesPointFields_private"
/* . off - The global offset of this point */
PetscErrorCode indicesPointFields_private(PetscSection section, PetscInt point, PetscInt off, PetscInt foffs[], PetscBool setBC, PetscInt orientation, PetscInt indices[])
{
  PetscInt       numFields, foff, f;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
  for (f = 0, foff = 0; f < numFields; ++f) {
    PetscInt        fdof, fcomp, cfdof;
    const PetscInt *fcdofs; /* The indices of the constrained dofs for field f on this point */
    PetscInt        cind = 0, k, c;

    ierr = PetscSectionGetFieldComponents(section, f, &fcomp);CHKERRQ(ierr);
    ierr = PetscSectionGetFieldDof(section, point, f, &fdof);CHKERRQ(ierr);
    ierr = PetscSectionGetFieldConstraintDof(section, point, f, &cfdof);CHKERRQ(ierr);
    if (!cfdof || setBC) {
      if (orientation >= 0) {
        for (k = 0; k < fdof; ++k) indices[foffs[f]+k] = off+foff+k;
      } else {
        for (k = fdof/fcomp-1; k >= 0; --k) {
          for (c = 0; c < fcomp; ++c) {
            indices[foffs[f]+k*fcomp+c] = off+foff+(fdof/fcomp-1-k)*fcomp+c;
          }
        }
      }
    } else {
      ierr = PetscSectionGetFieldConstraintIndices(section, point, f, &fcdofs);CHKERRQ(ierr);
      if (orientation >= 0) {
        for (k = 0; k < fdof; ++k) {
          if ((cind < cfdof) && (k == fcdofs[cind])) {
            indices[foffs[f]+k] = -(off+foff+k+1);
            ++cind;
          } else {
            indices[foffs[f]+k] = off+foff+k-cind;
          }
        }
      } else {
        for (k = fdof/fcomp-1; k >= 0; --k) {
          for (c = 0; c < fcomp; ++c) {
            if ((cind < cfdof) && ((fdof/fcomp-1-k)*fcomp+c == fcdofs[cind])) {
              indices[foffs[f]+k*fcomp+c] = -(off+foff+(fdof/fcomp-1-k)*fcomp+c+1);
              ++cind;
            } else {
              indices[foffs[f]+k*fcomp+c] = off+foff+(fdof/fcomp-1-k)*fcomp+c-cind;
            }
          }
        }
      }
    }
    foff     += fdof - cfdof;
    foffs[f] += fdof;
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexMatSetClosure"
PetscErrorCode DMPlexMatSetClosure(DM dm, PetscSection section, PetscSection globalSection, Mat A, PetscInt point, PetscScalar values[], InsertMode mode)
{
  DM_Plex       *mesh   = (DM_Plex*) dm->data;
  PetscInt      *points = NULL;
  PetscInt      *indices;
  PetscInt       offsets[32];
  PetscInt       numFields, numPoints, numIndices, dof, off, globalOff, pStart, pEnd, p, q, f;
  PetscBool      useDefault       =       !section ? PETSC_TRUE : PETSC_FALSE;
  PetscBool      useGlobalDefault = !globalSection ? PETSC_TRUE : PETSC_FALSE;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidHeaderSpecific(A, MAT_CLASSID, 3);
  if (useDefault) {
    ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
  }
  if (useGlobalDefault) {
    if (useDefault) {
      ierr = DMGetDefaultGlobalSection(dm, &globalSection);CHKERRQ(ierr);
    } else {
      ierr = PetscSectionCreateGlobalSection(section, dm->sf, PETSC_FALSE, &globalSection);CHKERRQ(ierr);
    }
  }
  ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
  if (numFields > 31) SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "Number of fields %D limited to 31", numFields);
  ierr = PetscMemzero(offsets, 32 * sizeof(PetscInt));CHKERRQ(ierr);
  ierr = DMPlexGetTransitiveClosure(dm, point, PETSC_TRUE, &numPoints, &points);CHKERRQ(ierr);
  /* Compress out points not in the section */
  ierr = PetscSectionGetChart(section, &pStart, &pEnd);CHKERRQ(ierr);
  for (p = 0, q = 0; p < numPoints*2; p += 2) {
    if ((points[p] >= pStart) && (points[p] < pEnd)) {
      points[q*2]   = points[p];
      points[q*2+1] = points[p+1];
      ++q;
    }
  }
  numPoints = q;
  for (p = 0, numIndices = 0; p < numPoints*2; p += 2) {
    PetscInt fdof;

    ierr = PetscSectionGetDof(section, points[p], &dof);CHKERRQ(ierr);
    for (f = 0; f < numFields; ++f) {
      ierr          = PetscSectionGetFieldDof(section, points[p], f, &fdof);CHKERRQ(ierr);
      offsets[f+1] += fdof;
    }
    numIndices += dof;
  }
  for (f = 1; f < numFields; ++f) offsets[f+1] += offsets[f];

  if (numFields && offsets[numFields] != numIndices) SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Invalid size for closure %d should be %d", offsets[numFields], numIndices);
  ierr = DMGetWorkArray(dm, numIndices, PETSC_INT, &indices);CHKERRQ(ierr);
  if (numFields) {
    for (p = 0; p < numPoints*2; p += 2) {
      PetscInt o = points[p+1];
      ierr = PetscSectionGetOffset(globalSection, points[p], &globalOff);CHKERRQ(ierr);
      indicesPointFields_private(section, points[p], globalOff < 0 ? -(globalOff+1) : globalOff, offsets, PETSC_FALSE, o, indices);
    }
  } else {
    for (p = 0, off = 0; p < numPoints*2; p += 2) {
      PetscInt o = points[p+1];
      ierr = PetscSectionGetOffset(globalSection, points[p], &globalOff);CHKERRQ(ierr);
      indicesPoint_private(section, points[p], globalOff < 0 ? -(globalOff+1) : globalOff, &off, PETSC_FALSE, o, indices);
    }
  }
  if (useGlobalDefault && !useDefault) {
    ierr = PetscSectionDestroy(&globalSection);CHKERRQ(ierr);
  }
  if (mesh->printSetValues) {ierr = DMPlexPrintMatSetValues(PETSC_VIEWER_STDOUT_SELF, A, point, numIndices, indices, values);CHKERRQ(ierr);}
  ierr = MatSetValues(A, numIndices, indices, numIndices, indices, values, mode);
  if (ierr) {
    PetscMPIInt    rank;
    PetscErrorCode ierr2;

    ierr2 = MPI_Comm_rank(PetscObjectComm((PetscObject)A), &rank);CHKERRQ(ierr2);
    ierr2 = (*PetscErrorPrintf)("[%D]ERROR in DMPlexMatSetClosure\n", rank);CHKERRQ(ierr2);
    ierr2 = DMPlexPrintMatSetValues(PETSC_VIEWER_STDERR_SELF, A, point, numIndices, indices, values);CHKERRQ(ierr2);
    ierr2 = DMRestoreWorkArray(dm, numIndices, PETSC_INT, &indices);CHKERRQ(ierr2);
    CHKERRQ(ierr);
  }
  ierr = DMPlexRestoreTransitiveClosure(dm, point, PETSC_TRUE, &numPoints, &points);CHKERRQ(ierr);
  ierr = DMRestoreWorkArray(dm, numIndices, PETSC_INT, &indices);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexComputeTriangleGeometry_private"
PetscErrorCode DMPlexComputeTriangleGeometry_private(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
{
  PetscSection       coordSection;
  Vec                coordinates;
  const PetscScalar *coords;
  const PetscInt     dim = 2;
  PetscInt           d, f;
  PetscErrorCode     ierr;

  PetscFunctionBegin;
  ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
  ierr = DMPlexGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
  ierr = DMPlexVecGetClosure(dm, coordSection, coordinates, e, NULL, &coords);CHKERRQ(ierr);
  if (v0) {
    for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
  }
  if (J) {
    for (d = 0; d < dim; d++) {
      for (f = 0; f < dim; f++) {
        J[d*dim+f] = 0.5*(PetscRealPart(coords[(f+1)*dim+d]) - PetscRealPart(coords[0*dim+d]));
      }
    }
    *detJ = J[0]*J[3] - J[1]*J[2];
#if 0
    if (detJ < 0.0) {
      const PetscReal xLength = mesh->periodicity[0];

      if (xLength != 0.0) {
        PetscReal v0x = coords[0*dim+0];

        if (v0x == 0.0) v0x = v0[0] = xLength;
        for (f = 0; f < dim; f++) {
          const PetscReal px = coords[(f+1)*dim+0] == 0.0 ? xLength : coords[(f+1)*dim+0];

          J[0*dim+f] = 0.5*(px - v0x);
        }
      }
      detJ = J[0]*J[3] - J[1]*J[2];
    }
#endif
    PetscLogFlops(8.0 + 3.0);
  }
  if (invJ) {
    const PetscReal invDet = 1.0/(*detJ);

    invJ[0] =  invDet*J[3];
    invJ[1] = -invDet*J[1];
    invJ[2] = -invDet*J[2];
    invJ[3] =  invDet*J[0];
    PetscLogFlops(5.0);
  }
  ierr = DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, NULL, &coords);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexComputeRectangleGeometry_private"
PetscErrorCode DMPlexComputeRectangleGeometry_private(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
{
  PetscSection       coordSection;
  Vec                coordinates;
  const PetscScalar *coords;
  const PetscInt     dim = 2;
  PetscInt           d, f;
  PetscErrorCode     ierr;

  PetscFunctionBegin;
  ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
  ierr = DMPlexGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
  ierr = DMPlexVecGetClosure(dm, coordSection, coordinates, e, NULL, &coords);CHKERRQ(ierr);
  if (v0) {
    for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
  }
  if (J) {
    for (d = 0; d < dim; d++) {
      for (f = 0; f < dim; f++) {
        J[d*dim+f] = 0.5*(PetscRealPart(coords[(f*2+1)*dim+d]) - PetscRealPart(coords[0*dim+d]));
      }
    }
    *detJ = J[0]*J[3] - J[1]*J[2];
    PetscLogFlops(8.0 + 3.0);
  }
  if (invJ) {
    const PetscReal invDet = 1.0/(*detJ);

    invJ[0] =  invDet*J[3];
    invJ[1] = -invDet*J[1];
    invJ[2] = -invDet*J[2];
    invJ[3] =  invDet*J[0];
    PetscLogFlops(5.0);
  }
  ierr = DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, NULL, &coords);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexComputeTetrahedronGeometry_private"
PetscErrorCode DMPlexComputeTetrahedronGeometry_private(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
{
  PetscSection       coordSection;
  Vec                coordinates;
  const PetscScalar *coords;
  const PetscInt     dim = 3;
  PetscInt           d, f;
  PetscErrorCode     ierr;

  PetscFunctionBegin;
  ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
  ierr = DMPlexGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
  ierr = DMPlexVecGetClosure(dm, coordSection, coordinates, e, NULL, &coords);CHKERRQ(ierr);
  if (v0) {
    for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
  }
  if (J) {
    for (d = 0; d < dim; d++) {
      for (f = 0; f < dim; f++) {
        J[d*dim+f] = 0.5*(PetscRealPart(coords[(f+1)*dim+d]) - PetscRealPart(coords[0*dim+d]));
      }
    }
    /* ??? This does not work with CTetGen: The minus sign is here since I orient the first face to get the outward normal */
    *detJ = (J[0*3+0]*(J[1*3+1]*J[2*3+2] - J[1*3+2]*J[2*3+1]) +
             J[0*3+1]*(J[1*3+2]*J[2*3+0] - J[1*3+0]*J[2*3+2]) +
             J[0*3+2]*(J[1*3+0]*J[2*3+1] - J[1*3+1]*J[2*3+0]));
    PetscLogFlops(18.0 + 12.0);
  }
  if (invJ) {
    const PetscReal invDet = 1.0/(*detJ);

    invJ[0*3+0] = invDet*(J[1*3+1]*J[2*3+2] - J[1*3+2]*J[2*3+1]);
    invJ[0*3+1] = invDet*(J[0*3+2]*J[2*3+1] - J[0*3+1]*J[2*3+2]);
    invJ[0*3+2] = invDet*(J[0*3+1]*J[1*3+2] - J[0*3+2]*J[1*3+1]);
    invJ[1*3+0] = invDet*(J[1*3+2]*J[2*3+0] - J[1*3+0]*J[2*3+2]);
    invJ[1*3+1] = invDet*(J[0*3+0]*J[2*3+2] - J[0*3+2]*J[2*3+0]);
    invJ[1*3+2] = invDet*(J[0*3+2]*J[1*3+0] - J[0*3+0]*J[1*3+2]);
    invJ[2*3+0] = invDet*(J[1*3+0]*J[2*3+1] - J[1*3+1]*J[2*3+0]);
    invJ[2*3+1] = invDet*(J[0*3+1]*J[2*3+0] - J[0*3+0]*J[2*3+1]);
    invJ[2*3+2] = invDet*(J[0*3+0]*J[1*3+1] - J[0*3+1]*J[1*3+0]);
    PetscLogFlops(37.0);
  }
  ierr = DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, NULL, &coords);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexComputeHexahedronGeometry_private"
PetscErrorCode DMPlexComputeHexahedronGeometry_private(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
{
  PetscSection       coordSection;
  Vec                coordinates;
  const PetscScalar *coords;
  const PetscInt     dim = 3;
  PetscInt           d;
  PetscErrorCode     ierr;

  PetscFunctionBegin;
  ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
  ierr = DMPlexGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
  ierr = DMPlexVecGetClosure(dm, coordSection, coordinates, e, NULL, &coords);CHKERRQ(ierr);
  if (v0) {
    for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
  }
  if (J) {
    for (d = 0; d < dim; d++) {
      J[d*dim+0] = 0.5*(PetscRealPart(coords[(0+1)*dim+d]) - PetscRealPart(coords[0*dim+d]));
      J[d*dim+1] = 0.5*(PetscRealPart(coords[(1+1)*dim+d]) - PetscRealPart(coords[0*dim+d]));
      J[d*dim+2] = 0.5*(PetscRealPart(coords[(3+1)*dim+d]) - PetscRealPart(coords[0*dim+d]));
    }
    *detJ = (J[0*3+0]*(J[1*3+1]*J[2*3+2] - J[1*3+2]*J[2*3+1]) +
             J[0*3+1]*(J[1*3+2]*J[2*3+0] - J[1*3+0]*J[2*3+2]) +
             J[0*3+2]*(J[1*3+0]*J[2*3+1] - J[1*3+1]*J[2*3+0]));
    PetscLogFlops(18.0 + 12.0);
  }
  if (invJ) {
    const PetscReal invDet = -1.0/(*detJ);

    invJ[0*3+0] = invDet*(J[1*3+1]*J[2*3+2] - J[1*3+2]*J[2*3+1]);
    invJ[0*3+1] = invDet*(J[0*3+2]*J[2*3+1] - J[0*3+1]*J[2*3+2]);
    invJ[0*3+2] = invDet*(J[0*3+1]*J[1*3+2] - J[0*3+2]*J[1*3+1]);
    invJ[1*3+0] = invDet*(J[1*3+2]*J[2*3+0] - J[1*3+0]*J[2*3+2]);
    invJ[1*3+1] = invDet*(J[0*3+0]*J[2*3+2] - J[0*3+2]*J[2*3+0]);
    invJ[1*3+2] = invDet*(J[0*3+2]*J[1*3+0] - J[0*3+0]*J[1*3+2]);
    invJ[2*3+0] = invDet*(J[1*3+0]*J[2*3+1] - J[1*3+1]*J[2*3+0]);
    invJ[2*3+1] = invDet*(J[0*3+1]*J[2*3+0] - J[0*3+0]*J[2*3+1]);
    invJ[2*3+2] = invDet*(J[0*3+0]*J[1*3+1] - J[0*3+1]*J[1*3+0]);
    PetscLogFlops(37.0);
  }
  *detJ *= 8.0;
  ierr   = DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, NULL, &coords);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexComputeCellGeometry"
/*@C
  DMPlexComputeCellGeometry - Compute the Jacobian, inverse Jacobian, and Jacobian determinant for a given cell

  Collective on DM

  Input Arguments:
+ dm   - the DM
- cell - the cell

  Output Arguments:
+ v0   - the translation part of this affine transform
. J    - the Jacobian of the transform to the reference element
. invJ - the inverse of the Jacobian
- detJ - the Jacobian determinant

  Level: advanced

.seealso: DMPlexGetCoordinateSection(), DMPlexGetCoordinateVec()
@*/
PetscErrorCode DMPlexComputeCellGeometry(DM dm, PetscInt cell, PetscReal *v0, PetscReal *J, PetscReal *invJ, PetscReal *detJ)
{
  PetscInt       dim, coneSize;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
  ierr = DMPlexGetConeSize(dm, cell, &coneSize);CHKERRQ(ierr);
  switch (dim) {
  case 2:
    switch (coneSize) {
    case 3:
      ierr = DMPlexComputeTriangleGeometry_private(dm, cell, v0, J, invJ, detJ);CHKERRQ(ierr);
      break;
    case 4:
      ierr = DMPlexComputeRectangleGeometry_private(dm, cell, v0, J, invJ, detJ);CHKERRQ(ierr);
      break;
    default:
      SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported number of vertices %D in cell %D for element geometry computation", coneSize, cell);
    }
    break;
  case 3:
    switch (coneSize) {
    case 4:
      ierr = DMPlexComputeTetrahedronGeometry_private(dm, cell, v0, J, invJ, detJ);CHKERRQ(ierr);
      break;
    case 8:
      ierr = DMPlexComputeHexahedronGeometry_private(dm, cell, v0, J, invJ, detJ);CHKERRQ(ierr);
      break;
    default:
      SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported number of vertices %D in cell %D for element geometry computation", coneSize, cell);
    }
    break;
  default:
    SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported dimension %D for element geometry computation", dim);
  }
  PetscFunctionReturn(0);
}

PETSC_STATIC_INLINE PetscInt epsilon(PetscInt i, PetscInt j, PetscInt k)
{
  switch (i) {
  case 0:
    switch (j) {
    case 0: return 0;
    case 1:
      switch (k) {
      case 0: return 0;
      case 1: return 0;
      case 2: return 1;
      }
    case 2:
      switch (k) {
      case 0: return 0;
      case 1: return -1;
      case 2: return 0;
      }
    }
  case 1:
    switch (j) {
    case 0:
      switch (k) {
      case 0: return 0;
      case 1: return 0;
      case 2: return -1;
      }
    case 1: return 0;
    case 2:
      switch (k) {
      case 0: return 1;
      case 1: return 0;
      case 2: return 0;
      }
    }
  case 2:
    switch (j) {
    case 0:
      switch (k) {
      case 0: return 0;
      case 1: return 1;
      case 2: return 0;
      }
    case 1:
      switch (k) {
      case 0: return -1;
      case 1: return 0;
      case 2: return 0;
      }
    case 2: return 0;
    }
  }
  return 0;
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexCreateRigidBody"
/*@C
  DMPlexCreateRigidBody - create rigid body modes from coordinates

  Collective on DM

  Input Arguments:
+ dm - the DM
. section - the local section associated with the rigid field, or NULL for the default section
- globalSection - the global section associated with the rigid field, or NULL for the default section

  Output Argument:
. sp - the null space

  Note: This is necessary to take account of Dirichlet conditions on the displacements

  Level: advanced

.seealso: MatNullSpaceCreate()
@*/
PetscErrorCode DMPlexCreateRigidBody(DM dm, PetscSection section, PetscSection globalSection, MatNullSpace *sp)
{
  MPI_Comm       comm;
  Vec            coordinates, localMode, mode[6];
  PetscSection   coordSection;
  PetscScalar   *coords;
  PetscInt       dim, vStart, vEnd, v, n, m, d, i, j;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscObjectGetComm((PetscObject)dm,&comm);CHKERRQ(ierr);
  ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
  if (dim == 1) {
    ierr = MatNullSpaceCreate(comm, PETSC_TRUE, 0, NULL, sp);CHKERRQ(ierr);
    PetscFunctionReturn(0);
  }
  if (!section)       {ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);}
  if (!globalSection) {ierr = DMGetDefaultGlobalSection(dm, &globalSection);CHKERRQ(ierr);}
  ierr = PetscSectionGetConstrainedStorageSize(globalSection, &n);CHKERRQ(ierr);
  ierr = DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);CHKERRQ(ierr);
  ierr = DMPlexGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
  ierr = DMGetCoordinatesLocal(dm, &coordinates);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);}
  /* Assume P1 */
  ierr = DMGetLocalVector(dm, &localMode);CHKERRQ(ierr);
  for (d = 0; d < dim; ++d) {
    PetscScalar values[3] = {0.0, 0.0, 0.0};

    values[d] = 1.0;
    ierr      = VecSet(localMode, 0.0);CHKERRQ(ierr);
    for (v = vStart; v < vEnd; ++v) {
      ierr = DMPlexVecSetClosure(dm, section, localMode, v, values, INSERT_VALUES);CHKERRQ(ierr);
    }
    ierr = DMLocalToGlobalBegin(dm, localMode, INSERT_VALUES, mode[d]);CHKERRQ(ierr);
    ierr = DMLocalToGlobalEnd(dm, localMode, INSERT_VALUES, mode[d]);CHKERRQ(ierr);
  }
  ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
  for (d = dim; d < dim*(dim+1)/2; ++d) {
    PetscInt i, j, k = dim > 2 ? d - dim : d;

    ierr = VecSet(localMode, 0.0);CHKERRQ(ierr);
    for (v = vStart; v < vEnd; ++v) {
      PetscScalar values[3] = {0.0, 0.0, 0.0};
      PetscInt    off;

      ierr = PetscSectionGetOffset(coordSection, v, &off);CHKERRQ(ierr);
      for (i = 0; i < dim; ++i) {
        for (j = 0; j < dim; ++j) {
          values[j] += epsilon(i, j, k)*PetscRealPart(coords[off+i]);
        }
      }
      ierr = DMPlexVecSetClosure(dm, section, localMode, v, values, INSERT_VALUES);CHKERRQ(ierr);
    }
    ierr = DMLocalToGlobalBegin(dm, localMode, INSERT_VALUES, mode[d]);CHKERRQ(ierr);
    ierr = DMLocalToGlobalEnd(dm, localMode, INSERT_VALUES, mode[d]);CHKERRQ(ierr);
  }
  ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
  ierr = DMRestoreLocalVector(dm, &localMode);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);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetHybridBounds"
PetscErrorCode DMPlexGetHybridBounds(DM dm, PetscInt *cMax, PetscInt *fMax, PetscInt *eMax, PetscInt *vMax)
{
  DM_Plex       *mesh = (DM_Plex*) dm->data;
  PetscInt       dim;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
  if (cMax) *cMax = mesh->hybridPointMax[dim];
  if (fMax) *fMax = mesh->hybridPointMax[dim-1];
  if (eMax) *eMax = mesh->hybridPointMax[1];
  if (vMax) *vMax = mesh->hybridPointMax[0];
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexSetHybridBounds"
PetscErrorCode DMPlexSetHybridBounds(DM dm, PetscInt cMax, PetscInt fMax, PetscInt eMax, PetscInt vMax)
{
  DM_Plex       *mesh = (DM_Plex*) dm->data;
  PetscInt       dim;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
  if (cMax >= 0) mesh->hybridPointMax[dim]   = cMax;
  if (fMax >= 0) mesh->hybridPointMax[dim-1] = fMax;
  if (eMax >= 0) mesh->hybridPointMax[1]     = eMax;
  if (vMax >= 0) mesh->hybridPointMax[0]     = vMax;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetVTKCellHeight"
PetscErrorCode DMPlexGetVTKCellHeight(DM dm, PetscInt *cellHeight)
{
  DM_Plex *mesh = (DM_Plex*) dm->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidPointer(cellHeight, 2);
  *cellHeight = mesh->vtkCellHeight;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexSetVTKCellHeight"
PetscErrorCode DMPlexSetVTKCellHeight(DM dm, PetscInt cellHeight)
{
  DM_Plex *mesh = (DM_Plex*) dm->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  mesh->vtkCellHeight = cellHeight;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexCreateNumbering_Private"
/* We can easily have a form that takes an IS instead */
PetscErrorCode DMPlexCreateNumbering_Private(DM dm, PetscInt pStart, PetscInt pEnd, PetscSF sf, IS *numbering)
{
  PetscSection   section, globalSection;
  PetscInt      *numbers, p;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscSectionCreate(PetscObjectComm((PetscObject)dm), &section);CHKERRQ(ierr);
  ierr = PetscSectionSetChart(section, pStart, pEnd);CHKERRQ(ierr);
  for (p = pStart; p < pEnd; ++p) {
    ierr = PetscSectionSetDof(section, p, 1);CHKERRQ(ierr);
  }
  ierr = PetscSectionSetUp(section);CHKERRQ(ierr);
  ierr = PetscSectionCreateGlobalSection(section, sf, PETSC_FALSE, &globalSection);CHKERRQ(ierr);
  ierr = PetscMalloc((pEnd - pStart) * sizeof(PetscInt), &numbers);CHKERRQ(ierr);
  for (p = pStart; p < pEnd; ++p) {
    ierr = PetscSectionGetOffset(globalSection, p, &numbers[p-pStart]);CHKERRQ(ierr);
  }
  ierr = ISCreateGeneral(PetscObjectComm((PetscObject)dm), pEnd - pStart, numbers, PETSC_OWN_POINTER, numbering);CHKERRQ(ierr);
  ierr = PetscSectionDestroy(&section);CHKERRQ(ierr);
  ierr = PetscSectionDestroy(&globalSection);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetCellNumbering"
PetscErrorCode DMPlexGetCellNumbering(DM dm, IS *globalCellNumbers)
{
  DM_Plex       *mesh = (DM_Plex*) dm->data;
  PetscInt       cellHeight, cStart, cEnd, cMax;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (!mesh->globalCellNumbers) {
    ierr = DMPlexGetVTKCellHeight(dm, &cellHeight);CHKERRQ(ierr);
    ierr = DMPlexGetHeightStratum(dm, cellHeight, &cStart, &cEnd);CHKERRQ(ierr);
    ierr = DMPlexGetHybridBounds(dm, &cMax, NULL, NULL, NULL);CHKERRQ(ierr);
    if (cMax >= 0) cEnd = PetscMin(cEnd, cMax);
    ierr = DMPlexCreateNumbering_Private(dm, cStart, cEnd, dm->sf, &mesh->globalCellNumbers);CHKERRQ(ierr);
  }
  *globalCellNumbers = mesh->globalCellNumbers;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetVertexNumbering"
PetscErrorCode DMPlexGetVertexNumbering(DM dm, IS *globalVertexNumbers)
{
  DM_Plex       *mesh = (DM_Plex*) dm->data;
  PetscInt       vStart, vEnd, vMax;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (!mesh->globalVertexNumbers) {
    ierr = DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);CHKERRQ(ierr);
    ierr = DMPlexGetHybridBounds(dm, NULL, NULL, NULL, &vMax);CHKERRQ(ierr);
    if (vMax >= 0) vEnd = PetscMin(vEnd, vMax);
    ierr = DMPlexCreateNumbering_Private(dm, vStart, vEnd, dm->sf, &mesh->globalVertexNumbers);CHKERRQ(ierr);
  }
  *globalVertexNumbers = mesh->globalVertexNumbers;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetScale"
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);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexSetScale"
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);
}


/*******************************************************************************
This should be in a separate Discretization object, but I am not sure how to lay
it out yet, so I am stuffing things here while I experiment.
*******************************************************************************/
#undef __FUNCT__
#define __FUNCT__ "DMPlexSetFEMIntegration"
PetscErrorCode DMPlexSetFEMIntegration(DM dm,
                                          PetscErrorCode (*integrateResidualFEM)(PetscInt, PetscInt, PetscInt, PetscQuadrature[], const PetscScalar[],
                                                                                 const PetscReal[], const PetscReal[], const PetscReal[], const PetscReal[],
                                                                                 void (*)(const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]),
                                                                                 void (*)(const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]), PetscScalar[]),
                                          PetscErrorCode (*integrateJacobianActionFEM)(PetscInt, PetscInt, PetscInt, PetscQuadrature[], const PetscScalar[], const PetscScalar[],
                                                                                       const PetscReal[], const PetscReal[], const PetscReal[], const PetscReal[],
                                                                                       void (**)(const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]),
                                                                                       void (**)(const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]),
                                                                                       void (**)(const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]),
                                                                                       void (**)(const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]), PetscScalar[]),
                                          PetscErrorCode (*integrateJacobianFEM)(PetscInt, PetscInt, PetscInt, PetscInt, PetscQuadrature[], const PetscScalar[],
                                                                                 const PetscReal[], const PetscReal[], const PetscReal[], const PetscReal[],
                                                                                 void (*)(const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]),
                                                                                 void (*)(const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]),
                                                                                 void (*)(const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]),
                                                                                 void (*)(const PetscScalar[], const PetscScalar[], const PetscReal[], PetscScalar[]), PetscScalar[]))
{
  DM_Plex *mesh = (DM_Plex*) dm->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  mesh->integrateResidualFEM       = integrateResidualFEM;
  mesh->integrateJacobianActionFEM = integrateJacobianActionFEM;
  mesh->integrateJacobianFEM       = integrateJacobianFEM;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexProjectFunctionLocal"
PetscErrorCode DMPlexProjectFunctionLocal(DM dm, PetscInt numComp, PetscScalar (**funcs)(const PetscReal []), InsertMode mode, Vec localX)
{
  Vec            coordinates;
  PetscSection   section, cSection;
  PetscInt       dim, vStart, vEnd, v, c, d;
  PetscScalar   *values, *cArray;
  PetscReal     *coords;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);CHKERRQ(ierr);
  ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
  ierr = DMPlexGetCoordinateSection(dm, &cSection);CHKERRQ(ierr);
  ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
  ierr = PetscMalloc(numComp * sizeof(PetscScalar), &values);CHKERRQ(ierr);
  ierr = VecGetArray(coordinates, &cArray);CHKERRQ(ierr);
  ierr = PetscSectionGetDof(cSection, vStart, &dim);CHKERRQ(ierr);
  ierr = PetscMalloc(dim * sizeof(PetscReal),&coords);CHKERRQ(ierr);
  for (v = vStart; v < vEnd; ++v) {
    PetscInt dof, off;

    ierr = PetscSectionGetDof(cSection, v, &dof);CHKERRQ(ierr);
    ierr = PetscSectionGetOffset(cSection, v, &off);CHKERRQ(ierr);
    if (dof > dim) SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Cannot have more coordinates %d then dimensions %d", dof, dim);
    for (d = 0; d < dof; ++d) coords[d] = PetscRealPart(cArray[off+d]);
    for (c = 0; c < numComp; ++c) values[c] = (*funcs[c])(coords);
    ierr = VecSetValuesSection(localX, section, v, values, mode);CHKERRQ(ierr);
  }
  ierr = VecRestoreArray(coordinates, &cArray);CHKERRQ(ierr);
  /* Temporary, must be replaced by a projection on the finite element basis */
  {
    PetscInt eStart = 0, eEnd = 0, e, depth;

    ierr = DMPlexGetLabelSize(dm, "depth", &depth);CHKERRQ(ierr);
    --depth;
    if (depth > 1) {ierr = DMPlexGetDepthStratum(dm, 1, &eStart, &eEnd);CHKERRQ(ierr);}
    for (e = eStart; e < eEnd; ++e) {
      const PetscInt *cone = NULL;
      PetscInt        coneSize, d;
      PetscScalar    *coordsA, *coordsB;

      ierr = DMPlexGetConeSize(dm, e, &coneSize);CHKERRQ(ierr);
      ierr = DMPlexGetCone(dm, e, &cone);CHKERRQ(ierr);
      if (coneSize != 2) SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_SIZ, "Cone size %d for point %d should be 2", coneSize, e);
      ierr = VecGetValuesSection(coordinates, cSection, cone[0], &coordsA);CHKERRQ(ierr);
      ierr = VecGetValuesSection(coordinates, cSection, cone[1], &coordsB);CHKERRQ(ierr);
      for (d = 0; d < dim; ++d) {
        coords[d] = 0.5*(PetscRealPart(coordsA[d]) + PetscRealPart(coordsB[d]));
      }
      for (c = 0; c < numComp; ++c) values[c] = (*funcs[c])(coords);
      ierr = VecSetValuesSection(localX, section, e, values, mode);CHKERRQ(ierr);
    }
  }

  ierr = PetscFree(coords);CHKERRQ(ierr);
  ierr = PetscFree(values);CHKERRQ(ierr);
#if 0
  const PetscInt localDof = this->_mesh->sizeWithBC(s, *cells->begin());
  PetscReal      detJ;

  ierr = PetscMalloc(localDof * sizeof(PetscScalar), &values);CHKERRQ(ierr);
  ierr = PetscMalloc2(dim,PetscReal,&v0,dim*dim,PetscReal,&J);CHKERRQ(ierr);
  ALE::ISieveVisitor::PointRetriever<PETSC_MESH_TYPE::sieve_type> pV(PetscPowInt(this->_mesh->getSieve()->getMaxConeSize(),dim+1), true);

  for (PetscInt c = cStart; c < cEnd; ++c) {
    ALE::ISieveTraversal<PETSC_MESH_TYPE::sieve_type>::orientedClosure(*this->_mesh->getSieve(), c, pV);
    const PETSC_MESH_TYPE::point_type *oPoints = pV.getPoints();
    const int                          oSize   = pV.getSize();
    int                                v       = 0;

    ierr = DMPlexComputeCellGeometry(dm, c, v0, J, NULL, &detJ);CHKERRQ(ierr);
    for (PetscInt cl = 0; cl < oSize; ++cl) {
      const PetscInt fDim;

      ierr = PetscSectionGetDof(oPoints[cl], &fDim);CHKERRQ(ierr);
      if (pointDim) {
        for (PetscInt d = 0; d < fDim; ++d, ++v) {
          values[v] = (*this->_options.integrate)(v0, J, v, initFunc);
        }
      }
    }
    ierr = DMPlexVecSetClosure(dm, NULL, localX, c, values);CHKERRQ(ierr);
    pV.clear();
  }
  ierr = PetscFree2(v0,J);CHKERRQ(ierr);
  ierr = PetscFree(values);CHKERRQ(ierr);
#endif
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexProjectFunction"
/*@C
  DMPlexProjectFunction - This projects the given function into the function space provided.

  Input Parameters:
+ dm      - The DM
. numComp - The number of components (functions)
. funcs   - The coordinate functions to evaluate
- mode    - The insertion mode for values

  Output Parameter:
. X - vector

  Level: developer

  Note:
  This currently just calls the function with the coordinates of each vertex and edge midpoint, and stores the result in a vector.
  We will eventually fix it.

,seealso: DMPlexComputeL2Diff()
*/
PetscErrorCode DMPlexProjectFunction(DM dm, PetscInt numComp, PetscScalar (**funcs)(const PetscReal []), InsertMode mode, Vec X)
{
  Vec            localX;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = DMGetLocalVector(dm, &localX);CHKERRQ(ierr);
  ierr = DMPlexProjectFunctionLocal(dm, numComp, funcs, mode, localX);CHKERRQ(ierr);
  ierr = DMLocalToGlobalBegin(dm, localX, mode, X);CHKERRQ(ierr);
  ierr = DMLocalToGlobalEnd(dm, localX, mode, X);CHKERRQ(ierr);
  ierr = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexComputeL2Diff"
/*@C
  DMPlexComputeL2Diff - This function computes the L_2 difference between a function u and an FEM interpolant solution u_h.

  Input Parameters:
+ dm    - The DM
. quad  - The PetscQuadrature object for each field
. funcs - The functions to evaluate for each field component
- X     - The coefficient vector u_h

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

  Level: developer

.seealso: DMPlexProjectFunction()
*/
PetscErrorCode DMPlexComputeL2Diff(DM dm, PetscQuadrature quad[], PetscScalar (**funcs)(const PetscReal []), Vec X, PetscReal *diff)
{
  const PetscInt debug = 0;
  PetscSection   section;
  Vec            localX;
  PetscReal     *coords, *v0, *J, *invJ, detJ;
  PetscReal      localDiff = 0.0;
  PetscInt       dim, numFields, numComponents = 0, cStart, cEnd, c, field, fieldOffset, comp;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = DMPlexGetDimension(dm, &dim);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) {
    numComponents += quad[field].numComponents;
  }
  ierr = DMPlexProjectFunctionLocal(dm, numComponents, funcs, INSERT_BC_VALUES, localX);CHKERRQ(ierr);
  ierr = PetscMalloc4(dim,PetscReal,&coords,dim,PetscReal,&v0,dim*dim,PetscReal,&J,dim*dim,PetscReal,&invJ);CHKERRQ(ierr);
  ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
  for (c = cStart; c < cEnd; ++c) {
    const PetscScalar *x;
    PetscReal          elemDiff = 0.0;

    ierr = DMPlexComputeCellGeometry(dm, c, v0, J, invJ, &detJ);CHKERRQ(ierr);
    if (detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ, c);
    ierr = DMPlexVecGetClosure(dm, NULL, localX, c, NULL, &x);CHKERRQ(ierr);

    for (field = 0, comp = 0, fieldOffset = 0; field < numFields; ++field) {
      const PetscInt   numQuadPoints = quad[field].numQuadPoints;
      const PetscReal *quadPoints    = quad[field].quadPoints;
      const PetscReal *quadWeights   = quad[field].quadWeights;
      const PetscInt   numBasisFuncs = quad[field].numBasisFuncs;
      const PetscInt   numBasisComps = quad[field].numComponents;
      const PetscReal *basis         = quad[field].basis;
      PetscInt         q, d, e, fc, f;

      if (debug) {
        char title[1024];
        ierr = PetscSNPrintf(title, 1023, "Solution for Field %d", field);CHKERRQ(ierr);
        ierr = DMPrintCellVector(c, title, numBasisFuncs*numBasisComps, &x[fieldOffset]);CHKERRQ(ierr);
      }
      for (q = 0; q < numQuadPoints; ++q) {
        for (d = 0; d < dim; d++) {
          coords[d] = v0[d];
          for (e = 0; e < dim; e++) {
            coords[d] += J[d*dim+e]*(quadPoints[q*dim+e] + 1.0);
          }
        }
        for (fc = 0; fc < numBasisComps; ++fc) {
          const PetscReal funcVal     = PetscRealPart((*funcs[comp+fc])(coords));
          PetscReal       interpolant = 0.0;
          for (f = 0; f < numBasisFuncs; ++f) {
            const PetscInt fidx = f*numBasisComps+fc;
            interpolant += PetscRealPart(x[fieldOffset+fidx])*basis[q*numBasisFuncs*numBasisComps+fidx];
          }
          if (debug) {ierr = PetscPrintf(PETSC_COMM_SELF, "    elem %d field %d diff %g\n", c, field, PetscSqr(interpolant - funcVal)*quadWeights[q]*detJ);CHKERRQ(ierr);}
          elemDiff += PetscSqr(interpolant - funcVal)*quadWeights[q]*detJ;
        }
      }
      comp        += numBasisComps;
      fieldOffset += numBasisFuncs*numBasisComps;
    }
    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  = PetscFree4(coords,v0,J,invJ);CHKERRQ(ierr);
  ierr  = DMRestoreLocalVector(dm, &localX);CHKERRQ(ierr);
  ierr  = MPI_Allreduce(&localDiff, diff, 1, MPIU_REAL, MPI_SUM, PETSC_COMM_WORLD);CHKERRQ(ierr);
  *diff = PetscSqrtReal(*diff);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexComputeResidualFEM"
/*@
  DMPlexComputeResidualFEM - Form the local residual F from the local input X using pointwise functions specified by the user

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

  Output Parameter:
. F  - Local output vector

  Note:
  The second member of the user context must be an FEMContext.

  We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
  like a GPU, or vectorize on a multicore machine.

.seealso: DMPlexComputeJacobianActionFEM()
*/
PetscErrorCode DMPlexComputeResidualFEM(DM dm, Vec X, Vec F, void *user)
{
  DM_Plex         *mesh = (DM_Plex*) dm->data;
  PetscFEM        *fem  = (PetscFEM*) &((DM*) user)[1];
  PetscQuadrature *quad = fem->quad;
  PetscSection     section;
  PetscReal       *v0, *J, *invJ, *detJ;
  PetscScalar     *elemVec, *u;
  PetscInt         dim, numFields, field, numBatchesTmp = 1, numCells, cStart, cEnd, c;
  PetscInt         cellDof = 0, numComponents = 0;
  PetscErrorCode   ierr;

  PetscFunctionBegin;
  /* ierr = PetscLogEventBegin(ResidualFEMEvent,0,0,0,0);CHKERRQ(ierr); */
  ierr     = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
  ierr     = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
  ierr     = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
  ierr     = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
  numCells = cEnd - cStart;
  for (field = 0; field < numFields; ++field) {
    cellDof       += quad[field].numBasisFuncs*quad[field].numComponents;
    numComponents += quad[field].numComponents;
  }
  ierr = DMPlexProjectFunctionLocal(dm, numComponents, fem->bcFuncs, INSERT_BC_VALUES, X);CHKERRQ(ierr);
  ierr = VecSet(F, 0.0);CHKERRQ(ierr);
  ierr = PetscMalloc6(numCells*cellDof,PetscScalar,&u,numCells*dim,PetscReal,&v0,numCells*dim*dim,PetscReal,&J,numCells*dim*dim,PetscReal,&invJ,numCells,PetscReal,&detJ,numCells*cellDof,PetscScalar,&elemVec);CHKERRQ(ierr);
  for (c = cStart; c < cEnd; ++c) {
    const PetscScalar *x;
    PetscInt           i;

    ierr = DMPlexComputeCellGeometry(dm, c, &v0[c*dim], &J[c*dim*dim], &invJ[c*dim*dim], &detJ[c]);CHKERRQ(ierr);
    if (detJ[c] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ[c], c);
    ierr = DMPlexVecGetClosure(dm, NULL, X, c, NULL, &x);CHKERRQ(ierr);

    for (i = 0; i < cellDof; ++i) u[c*cellDof+i] = x[i];
    ierr = DMPlexVecRestoreClosure(dm, NULL, X, c, NULL, &x);CHKERRQ(ierr);
  }
  for (field = 0; field < numFields; ++field) {
    const PetscInt numQuadPoints = quad[field].numQuadPoints;
    const PetscInt numBasisFuncs = quad[field].numBasisFuncs;
    void           (*f0)(const PetscScalar u[], const PetscScalar gradU[], const PetscReal x[], PetscScalar f0[]) = fem->f0Funcs[field];
    void           (*f1)(const PetscScalar u[], const PetscScalar gradU[], const PetscReal x[], PetscScalar f1[]) = fem->f1Funcs[field];
    /* Conforming batches */
    PetscInt blockSize  = numBasisFuncs*numQuadPoints;
    PetscInt numBlocks  = 1;
    PetscInt batchSize  = numBlocks * blockSize;
    PetscInt numBatches = numBatchesTmp;
    PetscInt numChunks  = numCells / (numBatches*batchSize);
    /* Remainder */
    PetscInt numRemainder = numCells % (numBatches * batchSize);
    PetscInt offset       = numCells - numRemainder;

    ierr = (*mesh->integrateResidualFEM)(numChunks*numBatches*batchSize, numFields, field, quad, u, v0, J, invJ, detJ, f0, f1, elemVec);CHKERRQ(ierr);
    ierr = (*mesh->integrateResidualFEM)(numRemainder, numFields, field, quad, &u[offset*cellDof], &v0[offset*dim], &J[offset*dim*dim], &invJ[offset*dim*dim], &detJ[offset],
                                         f0, f1, &elemVec[offset*cellDof]);CHKERRQ(ierr);
  }
  for (c = cStart; c < cEnd; ++c) {
    if (mesh->printFEM > 1) {ierr = DMPrintCellVector(c, "Residual", cellDof, &elemVec[c*cellDof]);CHKERRQ(ierr);}
    ierr = DMPlexVecSetClosure(dm, NULL, F, c, &elemVec[c*cellDof], ADD_VALUES);CHKERRQ(ierr);
  }
  ierr = PetscFree6(u,v0,J,invJ,detJ,elemVec);CHKERRQ(ierr);
  if (mesh->printFEM) {
    PetscMPIInt rank, numProcs;
    PetscInt    p;

    ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);CHKERRQ(ierr);
    ierr = MPI_Comm_size(PetscObjectComm((PetscObject)dm), &numProcs);CHKERRQ(ierr);
    ierr = PetscPrintf(PETSC_COMM_WORLD, "Residual:\n");CHKERRQ(ierr);
    for (p = 0; p < numProcs; ++p) {
      if (p == rank) {
        Vec f;

        ierr = VecDuplicate(F, &f);CHKERRQ(ierr);
        ierr = VecCopy(F, f);CHKERRQ(ierr);
        ierr = VecChop(f, 1.0e-10);CHKERRQ(ierr);
        ierr = VecView(f, PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
        ierr = VecDestroy(&f);CHKERRQ(ierr);
        ierr = PetscViewerFlush(PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
      }
      ierr = PetscBarrier((PetscObject) dm);CHKERRQ(ierr);
    }
  }
  /* ierr = PetscLogEventEnd(ResidualFEMEvent,0,0,0,0);CHKERRQ(ierr); */
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexComputeJacobianActionFEM"
/*@C
  DMPlexComputeJacobianActionFEM - Form the local action of Jacobian J(u) on the local input X using pointwise functions specified by the user

  Input Parameters:
+ dm - The mesh
. J  - The Jacobian shell matrix
. X  - Local input vector
- user - The user context

  Output Parameter:
. F  - Local output vector

  Note:
  The second member of the user context must be an FEMContext.

  We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
  like a GPU, or vectorize on a multicore machine.

.seealso: DMPlexComputeResidualFEM()
*/
PetscErrorCode DMPlexComputeJacobianActionFEM(DM dm, Mat Jac, Vec X, Vec F, void *user)
{
  DM_Plex         *mesh = (DM_Plex*) dm->data;
  PetscFEM        *fem  = (PetscFEM*) &((DM*) user)[1];
  PetscQuadrature *quad = fem->quad;
  PetscSection     section;
  JacActionCtx    *jctx;
  PetscReal       *v0, *J, *invJ, *detJ;
  PetscScalar     *elemVec, *u, *a;
  PetscInt         dim, numFields, field, numBatchesTmp = 1, numCells, cStart, cEnd, c;
  PetscInt         cellDof = 0;
  PetscErrorCode   ierr;

  PetscFunctionBegin;
  /* ierr = PetscLogEventBegin(JacobianActionFEMEvent,0,0,0,0);CHKERRQ(ierr); */
  ierr     = MatShellGetContext(Jac, &jctx);CHKERRQ(ierr);
  ierr     = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
  ierr     = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
  ierr     = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
  ierr     = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
  numCells = cEnd - cStart;
  for (field = 0; field < numFields; ++field) {
    cellDof += quad[field].numBasisFuncs*quad[field].numComponents;
  }
  ierr = VecSet(F, 0.0);CHKERRQ(ierr);
  ierr = PetscMalloc7(numCells*cellDof,PetscScalar,&u,numCells*cellDof,PetscScalar,&a,numCells*dim,PetscReal,&v0,numCells*dim*dim,PetscReal,&J,numCells*dim*dim,PetscReal,&invJ,numCells,PetscReal,&detJ,numCells*cellDof,PetscScalar,&elemVec);CHKERRQ(ierr);
  for (c = cStart; c < cEnd; ++c) {
    const PetscScalar *x;
    PetscInt           i;

    ierr = DMPlexComputeCellGeometry(dm, c, &v0[c*dim], &J[c*dim*dim], &invJ[c*dim*dim], &detJ[c]);CHKERRQ(ierr);
    if (detJ[c] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ[c], c);
    ierr = DMPlexVecGetClosure(dm, NULL, jctx->u, c, NULL, &x);CHKERRQ(ierr);
    for (i = 0; i < cellDof; ++i) u[c*cellDof+i] = x[i];
    ierr = DMPlexVecRestoreClosure(dm, NULL, jctx->u, c, NULL, &x);CHKERRQ(ierr);
    ierr = DMPlexVecGetClosure(dm, NULL, X, c, NULL, &x);CHKERRQ(ierr);
    for (i = 0; i < cellDof; ++i) a[c*cellDof+i] = x[i];
    ierr = DMPlexVecRestoreClosure(dm, NULL, X, c, NULL, &x);CHKERRQ(ierr);
  }
  for (field = 0; field < numFields; ++field) {
    const PetscInt numQuadPoints = quad[field].numQuadPoints;
    const PetscInt numBasisFuncs = quad[field].numBasisFuncs;
    /* Conforming batches */
    PetscInt blockSize  = numBasisFuncs*numQuadPoints;
    PetscInt numBlocks  = 1;
    PetscInt batchSize  = numBlocks * blockSize;
    PetscInt numBatches = numBatchesTmp;
    PetscInt numChunks  = numCells / (numBatches*batchSize);
    /* Remainder */
    PetscInt numRemainder = numCells % (numBatches * batchSize);
    PetscInt offset       = numCells - numRemainder;

    ierr = (*mesh->integrateJacobianActionFEM)(numChunks*numBatches*batchSize, numFields, field, quad, u, a, v0, J, invJ, detJ, fem->g0Funcs, fem->g1Funcs, fem->g2Funcs, fem->g3Funcs, elemVec);CHKERRQ(ierr);
    ierr = (*mesh->integrateJacobianActionFEM)(numRemainder, numFields, field, quad, &u[offset*cellDof], &a[offset*cellDof], &v0[offset*dim], &J[offset*dim*dim], &invJ[offset*dim*dim], &detJ[offset],
                                               fem->g0Funcs, fem->g1Funcs, fem->g2Funcs, fem->g3Funcs, &elemVec[offset*cellDof]);CHKERRQ(ierr);
  }
  for (c = cStart; c < cEnd; ++c) {
    if (mesh->printFEM > 1) {ierr = DMPrintCellVector(c, "Jacobian Action", cellDof, &elemVec[c*cellDof]);CHKERRQ(ierr);}
    ierr = DMPlexVecSetClosure(dm, NULL, F, c, &elemVec[c*cellDof], ADD_VALUES);CHKERRQ(ierr);
  }
  ierr = PetscFree7(u,a,v0,J,invJ,detJ,elemVec);CHKERRQ(ierr);
  if (mesh->printFEM) {
    PetscMPIInt rank, numProcs;
    PetscInt    p;

    ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);CHKERRQ(ierr);
    ierr = MPI_Comm_size(PetscObjectComm((PetscObject)dm), &numProcs);CHKERRQ(ierr);
    ierr = PetscPrintf(PETSC_COMM_WORLD, "Jacobian Action:\n");CHKERRQ(ierr);
    for (p = 0; p < numProcs; ++p) {
      if (p == rank) {ierr = VecView(F, PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);}
      ierr = PetscBarrier((PetscObject) dm);CHKERRQ(ierr);
    }
  }
  /* ierr = PetscLogEventEnd(JacobianActionFEMEvent,0,0,0,0);CHKERRQ(ierr); */
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexComputeJacobianFEM"
/*@
  DMPlexComputeJacobianFEM - Form the local portion of the Jacobian matrix J at the local solution X using pointwise functions specified by the user.

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

  Output Parameter:
. Jac  - Jacobian matrix

  Note:
  The second member of the user context must be an FEMContext.

  We form the residual one batch of elements at a time. This allows us to offload work onto an accelerator,
  like a GPU, or vectorize on a multicore machine.

.seealso: FormFunctionLocal()
*/
PetscErrorCode DMPlexComputeJacobianFEM(DM dm, Vec X, Mat Jac, Mat JacP, MatStructure *str,void *user)
{
  DM_Plex         *mesh = (DM_Plex*) dm->data;
  PetscFEM        *fem  = (PetscFEM*) &((DM*) user)[1];
  PetscQuadrature *quad = fem->quad;
  PetscSection     section;
  PetscReal       *v0, *J, *invJ, *detJ;
  PetscScalar     *elemMat, *u;
  PetscInt         dim, numFields, field, fieldI, numBatchesTmp = 1, numCells, cStart, cEnd, c;
  PetscInt         cellDof = 0, numComponents = 0;
  PetscBool        isShell;
  PetscErrorCode   ierr;

  PetscFunctionBegin;
  /* ierr = PetscLogEventBegin(JacobianFEMEvent,0,0,0,0);CHKERRQ(ierr); */
  ierr     = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
  ierr     = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
  ierr     = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
  ierr     = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
  numCells = cEnd - cStart;
  for (field = 0; field < numFields; ++field) {
    cellDof       += quad[field].numBasisFuncs*quad[field].numComponents;
    numComponents += quad[field].numComponents;
  }
  ierr = DMPlexProjectFunctionLocal(dm, numComponents, fem->bcFuncs, INSERT_BC_VALUES, X);CHKERRQ(ierr);
  ierr = MatZeroEntries(JacP);CHKERRQ(ierr);
  ierr = PetscMalloc6(numCells*cellDof,PetscScalar,&u,numCells*dim,PetscReal,&v0,numCells*dim*dim,PetscReal,&J,numCells*dim*dim,PetscReal,&invJ,numCells,PetscReal,&detJ,numCells*cellDof*cellDof,PetscScalar,&elemMat);CHKERRQ(ierr);
  for (c = cStart; c < cEnd; ++c) {
    const PetscScalar *x;
    PetscInt           i;

    ierr = DMPlexComputeCellGeometry(dm, c, &v0[c*dim], &J[c*dim*dim], &invJ[c*dim*dim], &detJ[c]);CHKERRQ(ierr);
    if (detJ[c] <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ[c], c);
    ierr = DMPlexVecGetClosure(dm, NULL, X, c, NULL, &x);CHKERRQ(ierr);

    for (i = 0; i < cellDof; ++i) u[c*cellDof+i] = x[i];
    ierr = DMPlexVecRestoreClosure(dm, NULL, X, c, NULL, &x);CHKERRQ(ierr);
  }
  ierr = PetscMemzero(elemMat, numCells*cellDof*cellDof * sizeof(PetscScalar));CHKERRQ(ierr);
  for (fieldI = 0; fieldI < numFields; ++fieldI) {
    const PetscInt numQuadPoints = quad[fieldI].numQuadPoints;
    const PetscInt numBasisFuncs = quad[fieldI].numBasisFuncs;
    PetscInt       fieldJ;

    for (fieldJ = 0; fieldJ < numFields; ++fieldJ) {
      void (*g0)(const PetscScalar u[], const PetscScalar gradU[], const PetscReal x[], PetscScalar g0[]) = fem->g0Funcs[fieldI*numFields+fieldJ];
      void (*g1)(const PetscScalar u[], const PetscScalar gradU[], const PetscReal x[], PetscScalar g1[]) = fem->g1Funcs[fieldI*numFields+fieldJ];
      void (*g2)(const PetscScalar u[], const PetscScalar gradU[], const PetscReal x[], PetscScalar g2[]) = fem->g2Funcs[fieldI*numFields+fieldJ];
      void (*g3)(const PetscScalar u[], const PetscScalar gradU[], const PetscReal x[], PetscScalar g3[]) = fem->g3Funcs[fieldI*numFields+fieldJ];
      /* Conforming batches */
      PetscInt blockSize  = numBasisFuncs*numQuadPoints;
      PetscInt numBlocks  = 1;
      PetscInt batchSize  = numBlocks * blockSize;
      PetscInt numBatches = numBatchesTmp;
      PetscInt numChunks  = numCells / (numBatches*batchSize);
      /* Remainder */
      PetscInt numRemainder = numCells % (numBatches * batchSize);
      PetscInt offset       = numCells - numRemainder;

      ierr = (*mesh->integrateJacobianFEM)(numChunks*numBatches*batchSize, numFields, fieldI, fieldJ, quad, u, v0, J, invJ, detJ, g0, g1, g2, g3, elemMat);CHKERRQ(ierr);
      ierr = (*mesh->integrateJacobianFEM)(numRemainder, numFields, fieldI, fieldJ, quad, &u[offset*cellDof], &v0[offset*dim], &J[offset*dim*dim], &invJ[offset*dim*dim], &detJ[offset],
                                           g0, g1, g2, g3, &elemMat[offset*cellDof*cellDof]);CHKERRQ(ierr);
    }
  }
  for (c = cStart; c < cEnd; ++c) {
    if (mesh->printFEM > 1) {ierr = DMPrintCellMatrix(c, "Jacobian", cellDof, cellDof, &elemMat[c*cellDof*cellDof]);CHKERRQ(ierr);}
    ierr = DMPlexMatSetClosure(dm, NULL, NULL, JacP, c, &elemMat[c*cellDof*cellDof], ADD_VALUES);CHKERRQ(ierr);
  }
  ierr = PetscFree6(u,v0,J,invJ,detJ,elemMat);CHKERRQ(ierr);

  /* Assemble matrix, using the 2-step process:
       MatAssemblyBegin(), MatAssemblyEnd(). */
  ierr = MatAssemblyBegin(JacP, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(JacP, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);

  if (mesh->printFEM) {
    ierr = PetscPrintf(PETSC_COMM_WORLD, "Jacobian:\n");CHKERRQ(ierr);
    ierr = MatChop(JacP, 1.0e-10);CHKERRQ(ierr);
    ierr = MatView(JacP, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
  }
  /* ierr = PetscLogEventEnd(JacobianFEMEvent,0,0,0,0);CHKERRQ(ierr); */
  ierr = PetscObjectTypeCompare((PetscObject)Jac, MATSHELL, &isShell);CHKERRQ(ierr);
  if (isShell) {
    JacActionCtx *jctx;

    ierr = MatShellGetContext(Jac, &jctx);CHKERRQ(ierr);
    ierr = VecCopy(X, jctx->u);CHKERRQ(ierr);
  }
  *str = SAME_NONZERO_PATTERN;
  PetscFunctionReturn(0);
}


#undef __FUNCT__
#define __FUNCT__ "PetscSectionCreateGlobalSectionLabel"
/*@C
  PetscSectionCreateGlobalSectionLabel - Create a section describing the global field layout using
  the local section and an SF describing the section point overlap.

  Input Parameters:
  + s - The PetscSection for the local field layout
  . sf - The SF describing parallel layout of the section points
  . includeConstraints - By default this is PETSC_FALSE, meaning that the global field vector will not possess constrained dofs
  . label - The label specifying the points
  - labelValue - The label stratum specifying the points

  Output Parameter:
  . gsection - The PetscSection for the global field layout

  Note: This gives negative sizes and offsets to points not owned by this process

  Level: developer

.seealso: PetscSectionCreate()
@*/
PetscErrorCode PetscSectionCreateGlobalSectionLabel(PetscSection s, PetscSF sf, PetscBool includeConstraints, DMLabel label, PetscInt labelValue, PetscSection *gsection)
{
  PetscInt      *neg;
  PetscInt       pStart, pEnd, p, dof, cdof, off, globalOff = 0, nroots;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscSectionCreate(s->atlasLayout.comm, gsection);CHKERRQ(ierr);
  ierr = PetscSectionGetChart(s, &pStart, &pEnd);CHKERRQ(ierr);
  ierr = PetscSectionSetChart(*gsection, pStart, pEnd);CHKERRQ(ierr);
  ierr = PetscMalloc((pEnd - pStart) * sizeof(PetscInt), &neg);CHKERRQ(ierr);
  /* Mark ghost points with negative dof */
  for (p = pStart; p < pEnd; ++p) {
    PetscInt value;

    ierr = DMLabelGetValue(label, p, &value);CHKERRQ(ierr);
    if (value != labelValue) continue;
    ierr = PetscSectionGetDof(s, p, &dof);CHKERRQ(ierr);
    ierr = PetscSectionSetDof(*gsection, p, dof);CHKERRQ(ierr);
    ierr = PetscSectionGetConstraintDof(s, p, &cdof);CHKERRQ(ierr);
    if (!includeConstraints && cdof > 0) {ierr = PetscSectionSetConstraintDof(*gsection, p, cdof);CHKERRQ(ierr);}
    neg[p-pStart] = -(dof+1);
  }
  ierr = PetscSectionSetUpBC(*gsection);CHKERRQ(ierr);
  ierr = PetscSFGetGraph(sf, &nroots, NULL, NULL, NULL);CHKERRQ(ierr);
  if (nroots >= 0) {
    if (nroots > pEnd - pStart) {
      PetscInt *tmpDof;
      /* Help Jed: HAVE TO MAKE A BUFFER HERE THE SIZE OF THE COMPLETE SPACE AND THEN COPY INTO THE atlasDof FOR THIS SECTION */
      ierr = PetscMalloc(nroots * sizeof(PetscInt), &tmpDof);CHKERRQ(ierr);
      ierr = PetscSFBcastBegin(sf, MPIU_INT, &neg[-pStart], tmpDof);CHKERRQ(ierr);
      ierr = PetscSFBcastEnd(sf, MPIU_INT, &neg[-pStart], tmpDof);CHKERRQ(ierr);
      for (p = pStart; p < pEnd; ++p) {
        if (tmpDof[p] < 0) (*gsection)->atlasDof[p-pStart] = tmpDof[p];
      }
      ierr = PetscFree(tmpDof);CHKERRQ(ierr);
    } else {
      ierr = PetscSFBcastBegin(sf, MPIU_INT, &neg[-pStart], &(*gsection)->atlasDof[-pStart]);CHKERRQ(ierr);
      ierr = PetscSFBcastEnd(sf, MPIU_INT, &neg[-pStart], &(*gsection)->atlasDof[-pStart]);CHKERRQ(ierr);
    }
  }
  /* Calculate new sizes, get proccess offset, and calculate point offsets */
  for (p = 0, off = 0; p < pEnd-pStart; ++p) {
    cdof = (!includeConstraints && s->bc) ? s->bc->atlasDof[p] : 0;

    (*gsection)->atlasOff[p] = off;

    off += (*gsection)->atlasDof[p] > 0 ? (*gsection)->atlasDof[p]-cdof : 0;
  }
  ierr       = MPI_Scan(&off, &globalOff, 1, MPIU_INT, MPI_SUM, s->atlasLayout.comm);CHKERRQ(ierr);
  globalOff -= off;
  for (p = 0, off = 0; p < pEnd-pStart; ++p) {
    (*gsection)->atlasOff[p] += globalOff;

    neg[p] = -((*gsection)->atlasOff[p]+1);
  }
  /* Put in negative offsets for ghost points */
  if (nroots >= 0) {
    if (nroots > pEnd - pStart) {
      PetscInt *tmpOff;
      /* Help Jed: HAVE TO MAKE A BUFFER HERE THE SIZE OF THE COMPLETE SPACE AND THEN COPY INTO THE atlasDof FOR THIS SECTION */
      ierr = PetscMalloc(nroots * sizeof(PetscInt), &tmpOff);CHKERRQ(ierr);
      ierr = PetscSFBcastBegin(sf, MPIU_INT, &neg[-pStart], tmpOff);CHKERRQ(ierr);
      ierr = PetscSFBcastEnd(sf, MPIU_INT, &neg[-pStart], tmpOff);CHKERRQ(ierr);
      for (p = pStart; p < pEnd; ++p) {
        if (tmpOff[p] < 0) (*gsection)->atlasOff[p-pStart] = tmpOff[p];
      }
      ierr = PetscFree(tmpOff);CHKERRQ(ierr);
    } else {
      ierr = PetscSFBcastBegin(sf, MPIU_INT, &neg[-pStart], &(*gsection)->atlasOff[-pStart]);CHKERRQ(ierr);
      ierr = PetscSFBcastEnd(sf, MPIU_INT, &neg[-pStart], &(*gsection)->atlasOff[-pStart]);CHKERRQ(ierr);
    }
  }
  ierr = PetscFree(neg);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}