impls/plex/plex.c

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

/* Logging support */
PetscLogEvent DMPLEX_Interpolate, DMPLEX_Partition, DMPLEX_Distribute, DMPLEX_DistributeCones, DMPLEX_DistributeLabels, DMPLEX_DistributeSF, DMPLEX_DistributeField, DMPLEX_DistributeData, DMPLEX_Stratify, DMPLEX_Preallocate, DMPLEX_ResidualFEM, DMPLEX_JacobianFEM, DMPLEX_InterpolatorFEM, DMPLEX_InjectorFEM;

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

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetFieldType_Internal"
PetscErrorCode DMPlexGetFieldType_Internal(DM dm, PetscSection section, PetscInt field, PetscInt *sStart, PetscInt *sEnd, PetscViewerVTKFieldType *ft)
{
  PetscInt       dim, pStart, pEnd, vStart, vEnd, cStart, cEnd, vdof = 0, cdof = 0;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  *ft  = PETSC_VTK_POINT_FIELD;
  ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
  ierr = DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);CHKERRQ(ierr);
  ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
  ierr = PetscSectionGetChart(section, &pStart, &pEnd);CHKERRQ(ierr);
  if (field >= 0) {
    if ((vStart >= pStart) && (vStart < pEnd)) {ierr = PetscSectionGetFieldDof(section, vStart, field, &vdof);CHKERRQ(ierr);}
    if ((cStart >= pStart) && (cStart < pEnd)) {ierr = PetscSectionGetFieldDof(section, cStart, field, &cdof);CHKERRQ(ierr);}
  } else {
    if ((vStart >= pStart) && (vStart < pEnd)) {ierr = PetscSectionGetDof(section, vStart, &vdof);CHKERRQ(ierr);}
    if ((cStart >= pStart) && (cStart < pEnd)) {ierr = PetscSectionGetDof(section, cStart, &cdof);CHKERRQ(ierr);}
  }
  if (vdof) {
    *sStart = vStart;
    *sEnd   = vEnd;
    if (vdof == dim) *ft = PETSC_VTK_POINT_VECTOR_FIELD;
    else             *ft = PETSC_VTK_POINT_FIELD;
  } else if (cdof) {
    *sStart = cStart;
    *sEnd   = cEnd;
    if (cdof == dim) *ft = PETSC_VTK_CELL_VECTOR_FIELD;
    else             *ft = PETSC_VTK_CELL_FIELD;
  } else SETERRQ(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_WRONG, "Could not classify input Vec for VTK");
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "VecView_Plex_Local"
PetscErrorCode VecView_Plex_Local(Vec v, PetscViewer viewer)
{
  DM             dm;
  PetscBool      isvtk, ishdf5, isseq;
  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);
  ierr = PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERHDF5, &ishdf5);CHKERRQ(ierr);
  ierr = PetscObjectTypeCompare((PetscObject) v, VECSEQ, &isseq);CHKERRQ(ierr);
  if (isvtk || ishdf5) {
    PetscInt  numFields;
    PetscBool fem = PETSC_FALSE;

    ierr = DMGetNumFields(dm, &numFields);CHKERRQ(ierr);
    if (numFields) {
      PetscObject fe;

      ierr = DMGetField(dm, 0, &fe);CHKERRQ(ierr);
      if (fe->classid == PETSCFE_CLASSID) fem = PETSC_TRUE;
    }
    if (fem) {ierr = DMPlexInsertBoundaryValuesFEM(dm, v);CHKERRQ(ierr);}
  }
  if (isvtk) {
    PetscSection            section;
    PetscViewerVTKFieldType ft;
    PetscInt                pStart, pEnd;

    ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);
    ierr = DMPlexGetFieldType_Internal(dm, section, PETSC_DETERMINE, &pStart, &pEnd, &ft);CHKERRQ(ierr);
    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 if (ishdf5) {
#if defined(PETSC_HAVE_HDF5)
    ierr = VecView_Plex_Local_HDF5(v, viewer);CHKERRQ(ierr);
#else
    SETERRQ(PetscObjectComm((PetscObject) dm), PETSC_ERR_SUP, "HDF5 not supported in this build.\nPlease reconfigure using --download-hdf5");
#endif
  } else {
    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, ishdf5, isseq;
  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);
  ierr = PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERHDF5, &ishdf5);CHKERRQ(ierr);
  ierr = PetscObjectTypeCompare((PetscObject) v, VECSEQ, &isseq);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 if (ishdf5) {
#if defined(PETSC_HAVE_HDF5)
    ierr = VecView_Plex_HDF5(v, viewer);CHKERRQ(ierr);
#else
    SETERRQ(PetscObjectComm((PetscObject) dm), PETSC_ERR_SUP, "HDF5 not supported in this build.\nPlease reconfigure using --download-hdf5");
#endif
  } else {
    if (isseq) {ierr = VecView_Seq(v, viewer);CHKERRQ(ierr);}
    else       {ierr = VecView_MPI(v, viewer);CHKERRQ(ierr);}
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "VecLoad_Plex_Local"
PetscErrorCode VecLoad_Plex_Local(Vec v, PetscViewer viewer)
{
  DM             dm;
  PetscBool      ishdf5;
  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, PETSCVIEWERHDF5, &ishdf5);CHKERRQ(ierr);
  if (ishdf5) {
    DM          dmBC;
    Vec         gv;
    const char *name;

    ierr = DMGetOutputDM(dm, &dmBC);CHKERRQ(ierr);
    ierr = DMGetGlobalVector(dmBC, &gv);CHKERRQ(ierr);
    ierr = PetscObjectGetName((PetscObject) v, &name);CHKERRQ(ierr);
    ierr = PetscObjectSetName((PetscObject) gv, name);CHKERRQ(ierr);
    ierr = VecLoad_Default(gv, viewer);CHKERRQ(ierr);
    ierr = DMGlobalToLocalBegin(dmBC, gv, INSERT_VALUES, v);CHKERRQ(ierr);
    ierr = DMGlobalToLocalEnd(dmBC, gv, INSERT_VALUES, v);CHKERRQ(ierr);
    ierr = DMRestoreGlobalVector(dmBC, &gv);CHKERRQ(ierr);
  } else {
    ierr = VecLoad_Default(v, viewer);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "VecLoad_Plex"
PetscErrorCode VecLoad_Plex(Vec v, PetscViewer viewer)
{
  DM             dm;
  PetscBool      ishdf5;
  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, PETSCVIEWERHDF5, &ishdf5);CHKERRQ(ierr);
  if (ishdf5) {
#if defined(PETSC_HAVE_HDF5)
    ierr = VecLoad_Plex_HDF5(v, viewer);CHKERRQ(ierr);
#else
    SETERRQ(PetscObjectComm((PetscObject) dm), PETSC_ERR_SUP, "HDF5 not supported in this build.\nPlease reconfigure using --download-hdf5");
#endif
  } else {
    ierr = VecLoad_Default(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", (double)(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", (double)(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, *hybsizes;
    PetscInt    locDepth, depth, dim, d, pMax[4];
    PetscInt    pStart, pEnd, p;
    PetscInt    numLabels, l;
    const char *name;
    PetscMPIInt size;

    ierr = PetscObjectGetComm((PetscObject)dm,&comm);CHKERRQ(ierr);
    ierr = MPI_Comm_size(comm, &size);CHKERRQ(ierr);
    ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
    ierr = PetscObjectGetName((PetscObject) dm, &name);CHKERRQ(ierr);
    if (name) {ierr = PetscViewerASCIIPrintf(viewer, "%s in %D dimensions:\n", name, dim);CHKERRQ(ierr);}
    else      {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 = DMPlexGetHybridBounds(dm, &pMax[depth], depth > 0 ? &pMax[depth-1] : NULL, &pMax[1], &pMax[0]);CHKERRQ(ierr);
    ierr = PetscMalloc2(size,&sizes,size,&hybsizes);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    -= pStart;
        pMax[d] -= pStart;
        ierr = MPI_Gather(&pEnd, 1, MPIU_INT, sizes, 1, MPIU_INT, 0, comm);CHKERRQ(ierr);
        ierr = MPI_Gather(&pMax[d], 1, MPIU_INT, hybsizes, 1, MPIU_INT, 0, comm);CHKERRQ(ierr);
        ierr = PetscViewerASCIIPrintf(viewer, "  %D-cells:", d);CHKERRQ(ierr);
        for (p = 0; p < size; ++p) {
          if (hybsizes[p] >= 0) {ierr = PetscViewerASCIIPrintf(viewer, " %D (%D)", sizes[p], sizes[p] - hybsizes[p]);CHKERRQ(ierr);}
          else                  {ierr = PetscViewerASCIIPrintf(viewer, " %D", sizes[p]);CHKERRQ(ierr);}
        }
        ierr = PetscViewerASCIIPrintf(viewer, "\n");CHKERRQ(ierr);
      }
    }
    ierr = PetscFree2(sizes,hybsizes);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);
      ierr = ISDestroy(&valueIS);CHKERRQ(ierr);
    }
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMView_Plex"
PetscErrorCode DMView_Plex(DM dm, PetscViewer viewer)
{
  PetscBool      iascii, ishdf5, isvtk;
  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, PETSCVIEWERVTK,   &isvtk);CHKERRQ(ierr);
  ierr = PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERHDF5,  &ishdf5);CHKERRQ(ierr);
  if (iascii) {
    ierr = DMPlexView_Ascii(dm, viewer);CHKERRQ(ierr);
  } else if (ishdf5) {
#if defined(PETSC_HAVE_HDF5)
    ierr = PetscViewerPushFormat(viewer, PETSC_VIEWER_HDF5_VIZ);CHKERRQ(ierr);
    ierr = DMPlexView_HDF5(dm, viewer);CHKERRQ(ierr);
    ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);
#else
    SETERRQ(PetscObjectComm((PetscObject) dm), PETSC_ERR_SUP, "HDF5 not supported in this build.\nPlease reconfigure using --download-hdf5");
#endif
  }
  else if (isvtk) {
    ierr = DMPlexVTKWriteAll((PetscObject) dm,viewer);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMLoad_Plex"
PetscErrorCode DMLoad_Plex(DM dm, PetscViewer viewer)
{
  PetscBool      isbinary, ishdf5;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidHeaderSpecific(viewer, PETSC_VIEWER_CLASSID, 2);
  ierr = PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERBINARY, &isbinary);CHKERRQ(ierr);
  ierr = PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERHDF5,   &ishdf5);CHKERRQ(ierr);
  if (isbinary) {SETERRQ(PetscObjectComm((PetscObject) dm), PETSC_ERR_SUP, "Do not yet support binary viewers");}
  else if (ishdf5) {
#if defined(PETSC_HAVE_HDF5)
    ierr = DMPlexLoad_HDF5(dm, viewer);CHKERRQ(ierr);
#else
    SETERRQ(PetscObjectComm((PetscObject) dm), PETSC_ERR_SUP, "HDF5 not supported in this build.\nPlease reconfigure using --download-hdf5");
#endif
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "BoundaryDestroy"
static PetscErrorCode BoundaryDestroy(DMBoundary *boundary)
{
  DMBoundary     b, next;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if (!boundary) PetscFunctionReturn(0);
  b = *boundary;
  *boundary = NULL;
  for (; b; b = next) {
    next = b->next;
    ierr = PetscFree(b->ids);CHKERRQ(ierr);
    ierr = PetscFree(b->name);CHKERRQ(ierr);
    ierr = PetscFree(b->labelname);CHKERRQ(ierr);
    ierr = PetscFree(b);CHKERRQ(ierr);
  }
  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 = DMDestroy(&mesh->coarseMesh);CHKERRQ(ierr);
  ierr = DMLabelDestroy(&mesh->subpointMap);CHKERRQ(ierr);
  ierr = ISDestroy(&mesh->globalVertexNumbers);CHKERRQ(ierr);
  ierr = ISDestroy(&mesh->globalCellNumbers);CHKERRQ(ierr);
  ierr = BoundaryDestroy(&mesh->boundary);CHKERRQ(ierr);
  ierr = PetscSectionDestroy(&mesh->anchorSection);CHKERRQ(ierr);
  ierr = ISDestroy(&mesh->anchorIS);CHKERRQ(ierr);
  ierr = PetscSectionDestroy(&mesh->constraintSection);CHKERRQ(ierr);
  ierr = MatDestroy(&mesh->constraintMat);CHKERRQ(ierr);
  ierr = DMDestroy(&mesh->referenceTree);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__ "DMCreateMatrix_Plex"
PetscErrorCode DMCreateMatrix_Plex(DM dm, Mat *J)
{
  PetscSection   section, sectionGlobal;
  PetscInt       bs = -1;
  PetscInt       localSize;
  PetscBool      isShell, isBlock, isSeqBlock, isMPIBlock, isSymBlock, isSymSeqBlock, isSymMPIBlock;
  PetscErrorCode ierr;
  MatType        mtype;

  PetscFunctionBegin;
  ierr = MatInitializePackage();CHKERRQ(ierr);
  mtype = dm->mattype;
  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);
  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 = PetscCalloc4(localSize/bs, &dnz, localSize/bs, &onz, localSize/bs, &dnzu, localSize/bs, &onzu);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__ "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__ "DMPlexAddConeSize"
/*@
  DMPlexAddConeSize - Add the given number of in-edges to 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 additional cone size for point p

  Output Parameter:

  Note:
  This should be called after DMPlexSetChart().

  Level: beginner

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

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  ierr = PetscSectionAddDof(mesh->coneSection, p, size);CHKERRQ(ierr);
  ierr = PetscSectionGetDof(mesh->coneSection, p, &csize);CHKERRQ(ierr);

  mesh->maxConeSize = PetscMax(mesh->maxConeSize, csize);
  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

  Fortran Notes:
  Since it returns an array, this routine is only available in Fortran 90, and you must
  include petsc.h90 in your code.

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

.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

  Fortran Notes:
  Since it returns an array, this routine is only available in Fortran 90, and you must
  include petsc.h90 in your code.

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

.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

  Fortran Notes:
  Since it returns an array, this routine is only available in Fortran 90, and you must
  include petsc.h90 in your code.

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

.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.

  Fortran Notes:
  Since it returns an array, this routine is only available in Fortran 90, and you must
  include petsc.h90 in your code.

  The numPoints argument is not present in the Fortran 90 binding since it is internal to the array.

  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);
  /* 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);
  }
  if (depth == 1) {
    if (*points) {
      closure = *points;
    } else {
      maxSize = 2*(PetscMax(mesh->maxConeSize, mesh->maxSupportSize)+1);
      ierr = DMGetWorkArray(dm, maxSize, PETSC_INT, &closure);CHKERRQ(ierr);
    }
    closure[0] = p; closure[1] = 0;
    for (t = 0; t < tmpSize; ++t, closureSize += 2) {
      closure[closureSize]   = tmp[t];
      closure[closureSize+1] = tmpO ? tmpO[t] : 0;
    }
    if (numPoints) *numPoints = closureSize/2;
    if (points)    *points    = closure;
    PetscFunctionReturn(0);
  }
  {
    PetscInt c, coneSeries, s,supportSeries;

    c = mesh->maxConeSize;
    coneSeries = (c > 1) ? ((PetscPowInt(c,depth+1)-1)/(c-1)) : depth+1;
    s = mesh->maxSupportSize;
    supportSeries = (s > 1) ? ((PetscPowInt(s,depth+1)-1)/(s-1)) : depth+1;
    maxSize = 2*PetscMax(coneSeries,supportSeries);
  }
  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;
  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;
  }
  /* Should kick out early when depth is reached, rather than checking all vertices for empty cones */
  while (fifoSize - fifoStart) {
    const PetscInt q   = fifo[fifoStart];
    const PetscInt o   = fifo[fifoStart+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: When we reverse orientation, we both reverse the direction of iteration and start at the other end of the chain. */
      /* HACK: It is worse to get the size here, than to change the interpretation of -(*+1)
       const PetscInt co = tmpO ? (rev ? -(tmpO[i]+1) : tmpO[i]) : 0; */
      PetscInt       co = tmpO ? tmpO[i] : 0;
      PetscInt       c;

      if (rev) {
        PetscInt childSize, coff;
        ierr = DMPlexGetConeSize(dm, cp, &childSize);CHKERRQ(ierr);
        coff = tmpO[i] < 0 ? -(tmpO[i]+1) : tmpO[i];
        co   = childSize ? -(((coff+childSize-1)%childSize)+1) : 0;
      }
      /* 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__ "DMPlexGetTransitiveClosure_Internal"
/*@C
  DMPlexGetTransitiveClosure_Internal - Return the points on the transitive closure of the in-edges or out-edges for this point in the Sieve DAG with a specified initial orientation

  Not collective

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

  Fortran Notes:
  Since it returns an array, this routine is only available in Fortran 90, and you must
  include petsc.h90 in your code.

  The numPoints argument is not present in the Fortran 90 binding since it is internal to the array.

  Level: beginner

.seealso: DMPlexRestoreTransitiveClosure(), DMPlexCreate(), DMPlexSetCone(), DMPlexSetChart(), DMPlexGetCone()
@*/
PetscErrorCode DMPlexGetTransitiveClosure_Internal(DM dm, PetscInt p, PetscInt ornt, 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);
  /* 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);
  }
  if (depth == 1) {
    if (*points) {
      closure = *points;
    } else {
      maxSize = 2*(PetscMax(mesh->maxConeSize, mesh->maxSupportSize)+1);
      ierr = DMGetWorkArray(dm, maxSize, PETSC_INT, &closure);CHKERRQ(ierr);
    }
    closure[0] = p; closure[1] = ornt;
    for (t = 0; t < tmpSize; ++t, closureSize += 2) {
      const PetscInt i = ornt >= 0 ? (t+ornt)%tmpSize : (-(ornt+1) + tmpSize-t)%tmpSize;
      closure[closureSize]   = tmp[i];
      closure[closureSize+1] = tmpO ? tmpO[i] : 0;
    }
    if (numPoints) *numPoints = closureSize/2;
    if (points)    *points    = closure;
    PetscFunctionReturn(0);
  }
  {
    PetscInt c, coneSeries, s,supportSeries;

    c = mesh->maxConeSize;
    coneSeries = (c > 1) ? ((PetscPowInt(c,depth+1)-1)/(c-1)) : depth+1;
    s = mesh->maxSupportSize;
    supportSeries = (s > 1) ? ((PetscPowInt(s,depth+1)-1)/(s-1)) : depth+1;
    maxSize = 2*PetscMax(coneSeries,supportSeries);
  }
  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] = ornt;
  for (t = 0; t < tmpSize; ++t, closureSize += 2, fifoSize += 2) {
    const PetscInt i  = ornt >= 0 ? (t+ornt)%tmpSize : (-(ornt+1) + tmpSize-t)%tmpSize;
    const PetscInt cp = tmp[i];
    PetscInt       co = tmpO ? tmpO[i] : 0;

    if (ornt < 0) {
      PetscInt childSize, coff;
      ierr = DMPlexGetConeSize(dm, cp, &childSize);CHKERRQ(ierr);
      coff = tmpO[i] < 0 ? -(tmpO[i]+1) : tmpO[i];
      co   = childSize ? -(((coff+childSize-1)%childSize)+1) : 0;
    }
    closure[closureSize]   = cp;
    closure[closureSize+1] = co;
    fifo[fifoSize]         = cp;
    fifo[fifoSize+1]       = co;
  }
  /* Should kick out early when depth is reached, rather than checking all vertices for empty cones */
  while (fifoSize - fifoStart) {
    const PetscInt q   = fifo[fifoStart];
    const PetscInt o   = fifo[fifoStart+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: When we reverse orientation, we both reverse the direction of iteration and start at the other end of the chain. */
      /* HACK: It is worse to get the size here, than to change the interpretation of -(*+1)
       const PetscInt co = tmpO ? (rev ? -(tmpO[i]+1) : tmpO[i]) : 0; */
      PetscInt       co = tmpO ? tmpO[i] : 0;
      PetscInt       c;

      if (rev) {
        PetscInt childSize, coff;
        ierr = DMPlexGetConeSize(dm, cp, &childSize);CHKERRQ(ierr);
        coff = tmpO[i] < 0 ? -(tmpO[i]+1) : tmpO[i];
        co   = childSize ? -(((coff+childSize-1)%childSize)+1) : 0;
      }
      /* 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
. numPoints - The number of points in the closure, so points[] is of size 2*numPoints, zeroed on exit
- points - The points and point orientations, interleaved as pairs [p0, o0, p1, o1, ...], zeroed on exit

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

  Fortran Notes:
  Since it returns an array, this routine is only available in Fortran 90, and you must
  include petsc.h90 in your code.

  The numPoints argument is not present in the Fortran 90 binding since it is internal to the array.

  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);
  if (numPoints) PetscValidIntPointer(numPoints,4);
  if (points) PetscValidPointer(points,5);
  ierr = DMRestoreWorkArray(dm, 0, PETSC_INT, points);CHKERRQ(ierr);
  if (numPoints) *numPoints = 0;
  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 = PetscMalloc1(size, &mesh->cones);CHKERRQ(ierr);
  ierr = PetscCalloc1(size, &mesh->coneOrientations);CHKERRQ(ierr);
  if (mesh->maxSupportSize) {
    ierr = PetscSectionSetUp(mesh->supportSection);CHKERRQ(ierr);
    ierr = PetscSectionGetStorageSize(mesh->supportSection, &size);CHKERRQ(ierr);
    ierr = PetscMalloc1(size, &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)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if (subdm) {ierr = DMClone(dm, subdm);CHKERRQ(ierr);}
  ierr = DMCreateSubDM_Section_Private(dm, numFields, fields, is, subdm);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 = PetscMalloc1(supportSize, &mesh->supports);CHKERRQ(ierr);
  ierr = PetscCalloc1(pEnd - pStart, &offsets);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__ "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:
  Concretely, DMPlexStratify() creates a new label named "depth" containing the dimension of each element: 0 for vertices,
  1 for edges, and so on.  The depth label can be accessed through DMPlexGetDepthLabel() or DMPlexGetDepthStratum(), or
  manually via DMPlexGetLabel().  The height is defined implicitly by height = maxDimension - depth, and can be accessed
  via DMPlexGetHeightStratum().  For example, cells have height 0 and faces have height 1.

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

  Level: beginner

.seealso: DMPlexCreate(), DMPlexSymmetrize()
@*/
PetscErrorCode DMPlexStratify(DM dm)
{
  DMLabel        label;
  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 = DMPlexGetChart(dm, &pStart, &pEnd);CHKERRQ(ierr);
  ierr = DMPlexCreateLabel(dm, "depth");CHKERRQ(ierr);
  ierr = DMPlexGetDepthLabel(dm, &label);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 = DMLabelSetValue(label, p, 0);CHKERRQ(ierr);
    } else if (!supportSize && coneSize) {
      ++numLeaves;
    } else if (!supportSize && !coneSize) {
      /* Isolated points */
      ierr = DMLabelSetValue(label, 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 = DMLabelSetValue(label, p, 1);CHKERRQ(ierr);
      }
    }
  } else {
    IS       pointIS;
    PetscInt numPoints = 0, level = 0;

    ierr = DMLabelGetStratumIS(label, level, &pointIS);CHKERRQ(ierr);
    if (pointIS) {ierr = ISGetLocalSize(pointIS, &numPoints);CHKERRQ(ierr);}
    while (numPoints) {
      const PetscInt *points;
      const PetscInt  newLevel = level+1;

      ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
      for (p = 0; p < numPoints; ++p) {
        const PetscInt  point = points[p];
        const PetscInt *support;
        PetscInt        supportSize, s;

        ierr = DMPlexGetSupportSize(dm, point, &supportSize);CHKERRQ(ierr);
        ierr = DMPlexGetSupport(dm, point, &support);CHKERRQ(ierr);
        for (s = 0; s < supportSize; ++s) {
          ierr = DMLabelSetValue(label, support[s], newLevel);CHKERRQ(ierr);
        }
      }
      ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
      ++level;
      ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
      ierr = DMLabelGetStratumIS(label, level, &pointIS);CHKERRQ(ierr);
      if (pointIS) {ierr = ISGetLocalSize(pointIS, &numPoints);CHKERRQ(ierr);}
      else         {numPoints = 0;}
    }
    ierr = ISDestroy(&pointIS);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

  Fortran Notes:
  Since it returns an array, this routine is only available in Fortran 90, and you must
  include petsc.h90 in your code.

  The numCoveredPoints argument is not present in the Fortran 90 binding since it is internal to the array.

.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

  Fortran Notes:
  Since it returns an array, this routine is only available in Fortran 90, and you must
  include petsc.h90 in your code.

  The numCoveredPoints argument is not present in the Fortran 90 binding since it is internal to the array.

  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);
  if (points) PetscValidIntPointer(points,3);
  if (numCoveredPoints) PetscValidIntPointer(numCoveredPoints,4);
  PetscValidPointer(coveredPoints, 5);
  ierr = DMRestoreWorkArray(dm, 0, PETSC_INT, (void*) coveredPoints);CHKERRQ(ierr);
  if (numCoveredPoints) *numCoveredPoints = 0;
  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

  Fortran Notes:
  Since it returns an array, this routine is only available in Fortran 90, and you must
  include petsc.h90 in your code.

  The numCoveredPoints argument is not present in the Fortran 90 binding since it is internal to the array.

  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, ms;
  PetscErrorCode ierr;

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

  ierr    = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
  ierr    = PetscCalloc1(numPoints, &closures);CHKERRQ(ierr);
  ierr    = DMGetWorkArray(dm, numPoints*(depth+2), PETSC_INT, &offsets);CHKERRQ(ierr);
  ms      = mesh->maxSupportSize;
  maxSize = (ms > 1) ? ((PetscPowInt(ms,depth+1)-1)/(ms-1)) : depth + 1;
  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

  Fortran Notes:
  Since it returns an array, this routine is only available in Fortran 90, and you must
  include petsc.h90 in your code.

  The numCoveredPoints argument is not present in the Fortran 90 binding since it is internal to the array.

.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

  Fortran Notes:
  Since it returns an array, this routine is only available in Fortran 90, and you must
  include petsc.h90 in your code.

  The numCoveredPoints argument is not present in the Fortran 90 binding since it is internal to the array.

.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);
  if (points) PetscValidIntPointer(points,3);
  if (numCoveredPoints) PetscValidIntPointer(numCoveredPoints,4);
  PetscValidPointer(coveredPoints,5);
  ierr = DMRestoreWorkArray(dm, 0, PETSC_INT, (void*) coveredPoints);CHKERRQ(ierr);
  if (numCoveredPoints) *numCoveredPoints = 0;
  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

  Fortran Notes:
  Since it returns an array, this routine is only available in Fortran 90, and you must
  include petsc.h90 in your code.

  The numCoveredPoints argument is not present in the Fortran 90 binding since it is internal to the array.

.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, mc;
  PetscErrorCode ierr;

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

  ierr    = DMPlexGetDepth(dm, &height);CHKERRQ(ierr);
  ierr    = PetscMalloc1(numPoints, &closures);CHKERRQ(ierr);
  ierr    = DMGetWorkArray(dm, numPoints*(height+2), PETSC_INT, &offsets);CHKERRQ(ierr);
  mc      = mesh->maxConeSize;
  maxSize = (mc > 1) ? ((PetscPowInt(mc,height+1)-1)/(mc-1)) : height + 1;
  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__ "DMPlexEqual"
/*@C
  DMPlexEqual - Determine if two DMs have the same topology

  Not Collective

  Input Parameters:
+ dmA - A DMPlex object
- dmB - A DMPlex object

  Output Parameters:
. equal - PETSC_TRUE if the topologies are identical

  Level: intermediate

  Notes:
  We are not solving graph isomorphism, so we do not permutation.

.keywords: mesh
.seealso: DMPlexGetCone()
@*/
PetscErrorCode DMPlexEqual(DM dmA, DM dmB, PetscBool *equal)
{
  PetscInt       depth, depthB, pStart, pEnd, pStartB, pEndB, p;
  PetscErrorCode ierr;

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

  *equal = PETSC_FALSE;
  ierr = DMPlexGetDepth(dmA, &depth);CHKERRQ(ierr);
  ierr = DMPlexGetDepth(dmB, &depthB);CHKERRQ(ierr);
  if (depth != depthB) PetscFunctionReturn(0);
  ierr = DMPlexGetChart(dmA, &pStart,  &pEnd);CHKERRQ(ierr);
  ierr = DMPlexGetChart(dmB, &pStartB, &pEndB);CHKERRQ(ierr);
  if ((pStart != pStartB) || (pEnd != pEndB)) PetscFunctionReturn(0);
  for (p = pStart; p < pEnd; ++p) {
    const PetscInt *cone, *coneB, *ornt, *orntB, *support, *supportB;
    PetscInt        coneSize, coneSizeB, c, supportSize, supportSizeB, s;

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

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetNumFaceVertices"
PetscErrorCode DMPlexGetNumFaceVertices(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__ "DMPlexOrient"
/* Trys to give the mesh a consistent orientation */
PetscErrorCode DMPlexOrient(DM dm)
{
  PetscBT        seenCells, flippedCells, seenFaces;
  PetscInt      *faceFIFO, fTop, fBottom;
  PetscInt       dim, h, cStart, cEnd, c, fStart, fEnd, face, maxConeSize, *revcone, *revconeO;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  /* Truth Table
     mismatch    flips   do action   mismatch   flipA ^ flipB   action
         F       0 flips     no         F             F           F
         F       1 flip      yes        F             T           T
         F       2 flips     no         T             F           T
         T       0 flips     yes        T             T           F
         T       1 flip      no
         T       2 flips     yes
  */
  ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
  ierr = DMPlexGetVTKCellHeight(dm, &h);CHKERRQ(ierr);
  ierr = DMPlexGetHeightStratum(dm, h,   &cStart, &cEnd);CHKERRQ(ierr);
  ierr = DMPlexGetHeightStratum(dm, h+1, &fStart, &fEnd);CHKERRQ(ierr);
  ierr = PetscBTCreate(cEnd - cStart, &seenCells);CHKERRQ(ierr);
  ierr = PetscBTMemzero(cEnd - cStart, seenCells);CHKERRQ(ierr);
  ierr = PetscBTCreate(cEnd - cStart, &flippedCells);CHKERRQ(ierr);
  ierr = PetscBTMemzero(cEnd - cStart, flippedCells);CHKERRQ(ierr);
  ierr = PetscBTCreate(fEnd - fStart, &seenFaces);CHKERRQ(ierr);
  ierr = PetscBTMemzero(fEnd - fStart, seenFaces);CHKERRQ(ierr);
  ierr = PetscMalloc1((fEnd - fStart), &faceFIFO);CHKERRQ(ierr);
  fTop = fBottom = 0;
  /* Initialize FIFO with first cell */
  if (cEnd > cStart) {
    const PetscInt *cone;
    PetscInt        coneSize;

    ierr = DMPlexGetConeSize(dm, cStart, &coneSize);CHKERRQ(ierr);
    ierr = DMPlexGetCone(dm, cStart, &cone);CHKERRQ(ierr);
    for (c = 0; c < coneSize; ++c) {
      faceFIFO[fBottom++] = cone[c];
      ierr = PetscBTSet(seenFaces, cone[c]-fStart);CHKERRQ(ierr);
    }
  }
  /* Consider each face in FIFO */
  while (fTop < fBottom) {
    const PetscInt *support, *coneA, *coneB, *coneOA, *coneOB;
    PetscInt        supportSize, coneSizeA, coneSizeB, posA = -1, posB = -1;
    PetscInt        seenA, flippedA, seenB, flippedB, mismatch;

    face = faceFIFO[fTop++];
    ierr = DMPlexGetSupportSize(dm, face, &supportSize);CHKERRQ(ierr);
    ierr = DMPlexGetSupport(dm, face, &support);CHKERRQ(ierr);
    if (supportSize < 2) continue;
    if (supportSize != 2) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Faces should separate only two cells, not %d", supportSize);
    seenA    = PetscBTLookup(seenCells,    support[0]-cStart);
    flippedA = PetscBTLookup(flippedCells, support[0]-cStart) ? 1 : 0;
    seenB    = PetscBTLookup(seenCells,    support[1]-cStart);
    flippedB = PetscBTLookup(flippedCells, support[1]-cStart) ? 1 : 0;

    ierr = DMPlexGetConeSize(dm, support[0], &coneSizeA);CHKERRQ(ierr);
    ierr = DMPlexGetConeSize(dm, support[1], &coneSizeB);CHKERRQ(ierr);
    ierr = DMPlexGetCone(dm, support[0], &coneA);CHKERRQ(ierr);
    ierr = DMPlexGetCone(dm, support[1], &coneB);CHKERRQ(ierr);
    ierr = DMPlexGetConeOrientation(dm, support[0], &coneOA);CHKERRQ(ierr);
    ierr = DMPlexGetConeOrientation(dm, support[1], &coneOB);CHKERRQ(ierr);
    for (c = 0; c < coneSizeA; ++c) {
      if (!PetscBTLookup(seenFaces, coneA[c]-fStart)) {
        faceFIFO[fBottom++] = coneA[c];
        ierr = PetscBTSet(seenFaces, coneA[c]-fStart);CHKERRQ(ierr);
      }
      if (coneA[c] == face) posA = c;
      if (fBottom > fEnd-fStart) SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Face %d was pushed exceeding capacity %d > %d", coneA[c], fBottom, fEnd-fStart);
    }
    if (posA < 0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Face %d could not be located in cell %d", face, support[0]);
    for (c = 0; c < coneSizeB; ++c) {
      if (!PetscBTLookup(seenFaces, coneB[c]-fStart)) {
        faceFIFO[fBottom++] = coneB[c];
        ierr = PetscBTSet(seenFaces, coneB[c]-fStart);CHKERRQ(ierr);
      }
      if (coneB[c] == face) posB = c;
      if (fBottom > fEnd-fStart) SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Face %d was pushed exceeding capacity %d > %d", coneA[c], fBottom, fEnd-fStart);
    }
    if (posB < 0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Face %d could not be located in cell %d", face, support[1]);

    if (dim == 1) {
      mismatch = posA == posB;
    } else {
      mismatch = coneOA[posA] == coneOB[posB];
    }

    if (mismatch ^ (flippedA ^ flippedB)) {
      if (seenA && seenB) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Previously seen cells %d and %d do not match: Fault mesh is non-orientable", support[0], support[1]);
      if (!seenA && !flippedA) {
        ierr = PetscBTSet(flippedCells, support[0]-cStart);CHKERRQ(ierr);
      } else if (!seenB && !flippedB) {
        ierr = PetscBTSet(flippedCells, support[1]-cStart);CHKERRQ(ierr);
      } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Inconsistent mesh orientation: Fault mesh is non-orientable");
    } else if (mismatch && flippedA && flippedB) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Attempt to flip already flipped cell: Fault mesh is non-orientable");
    ierr = PetscBTSet(seenCells, support[0]-cStart);CHKERRQ(ierr);
    ierr = PetscBTSet(seenCells, support[1]-cStart);CHKERRQ(ierr);
  }
  /* Now all subdomains are oriented, but we need a consistent parallel orientation */
  {
    /* Find a representative face (edge) separating pairs of procs */
    PetscSF            sf;
    const PetscInt    *lpoints;
    const PetscSFNode *rpoints;
    PetscInt          *neighbors, *nranks;
    PetscInt           numLeaves, numRoots, numNeighbors = 0, l, n;

    ierr = DMGetPointSF(dm, &sf);CHKERRQ(ierr);
    ierr = PetscSFGetGraph(sf, &numRoots, &numLeaves, &lpoints, &rpoints);CHKERRQ(ierr);
    if (numLeaves >= 0) {
      const PetscInt *cone, *ornt, *support;
      PetscInt        coneSize, supportSize;
      int            *rornt, *lornt; /* PetscSF cannot handle smaller than int */
      PetscBool      *match, flipped = PETSC_FALSE;

      ierr = PetscMalloc1(numLeaves,&neighbors);CHKERRQ(ierr);
      /* I know this is p^2 time in general, but for bounded degree its alright */
      for (l = 0; l < numLeaves; ++l) {
        const PetscInt face = lpoints[l];
        if ((face >= fStart) && (face < fEnd)) {
          const PetscInt rank = rpoints[l].rank;
          for (n = 0; n < numNeighbors; ++n) if (rank == rpoints[neighbors[n]].rank) break;
          if (n >= numNeighbors) {
            PetscInt supportSize;
            ierr = DMPlexGetSupportSize(dm, face, &supportSize);CHKERRQ(ierr);
            if (supportSize != 1) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Boundary faces should see one cell, not %d", supportSize);
            neighbors[numNeighbors++] = l;
          }
        }
      }
      ierr = PetscCalloc4(numNeighbors,&match,numNeighbors,&nranks,numRoots,&rornt,numRoots,&lornt);CHKERRQ(ierr);
      for (face = fStart; face < fEnd; ++face) {
        ierr = DMPlexGetSupportSize(dm, face, &supportSize);CHKERRQ(ierr);
        if (supportSize != 1) continue;
        ierr = DMPlexGetSupport(dm, face, &support);CHKERRQ(ierr);

        ierr = DMPlexGetCone(dm, support[0], &cone);CHKERRQ(ierr);
        ierr = DMPlexGetConeSize(dm, support[0], &coneSize);CHKERRQ(ierr);
        ierr = DMPlexGetConeOrientation(dm, support[0], &ornt);CHKERRQ(ierr);
        for (c = 0; c < coneSize; ++c) if (cone[c] == face) break;
        if (dim == 1) {
          /* Use cone position instead, shifted to -1 or 1 */
          rornt[face] = c*2-1;
        } else {
          if (PetscBTLookup(flippedCells, support[0]-cStart)) rornt[face] = ornt[c] < 0 ? -1 :  1;
          else                                                rornt[face] = ornt[c] < 0 ?  1 : -1;
        }
      }
      /* Mark each edge with match or nomatch */
      ierr = PetscSFBcastBegin(sf, MPI_INT, rornt, lornt);CHKERRQ(ierr);
      ierr = PetscSFBcastEnd(sf, MPI_INT, rornt, lornt);CHKERRQ(ierr);
      for (n = 0; n < numNeighbors; ++n) {
        const PetscInt face = lpoints[neighbors[n]];

        if (rornt[face]*lornt[face] < 0) match[n] = PETSC_TRUE;
        else                             match[n] = PETSC_FALSE;
        nranks[n] = rpoints[neighbors[n]].rank;
      }
      /* Collect the graph on 0 */
      {
        MPI_Comm     comm = PetscObjectComm((PetscObject) sf);
        Mat          G;
        PetscBT      seenProcs, flippedProcs;
        PetscInt    *procFIFO, pTop, pBottom;
        PetscInt    *adj = NULL;
        PetscBool   *val = NULL;
        PetscMPIInt *recvcounts = NULL, *displs = NULL, p;
        PetscMPIInt  N = numNeighbors, numProcs = 0, rank;
        PetscInt     debug = 0;

        ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
        if (!rank) {ierr = MPI_Comm_size(comm, &numProcs);CHKERRQ(ierr);}
        ierr = PetscCalloc2(numProcs,&recvcounts,numProcs+1,&displs);CHKERRQ(ierr);
        ierr = MPI_Gather(&N, 1, MPI_INT, recvcounts, 1, MPI_INT, 0, comm);CHKERRQ(ierr);
        for (p = 0; p < numProcs; ++p) {
          displs[p+1] = displs[p] + recvcounts[p];
        }
        if (!rank) {ierr = PetscMalloc2(displs[numProcs],&adj,displs[numProcs],&val);CHKERRQ(ierr);}
        ierr = MPI_Gatherv(nranks, numNeighbors, MPIU_INT, adj, recvcounts, displs, MPIU_INT, 0, comm);CHKERRQ(ierr);
        ierr = MPI_Gatherv(match, numNeighbors, MPIU_BOOL, val, recvcounts, displs, MPIU_BOOL, 0, comm);CHKERRQ(ierr);
        if (debug) {
          for (p = 0; p < numProcs; ++p) {
            ierr = PetscPrintf(comm, "Proc %d:\n", p);
            for (n = 0; n < recvcounts[p]; ++n) {
              ierr = PetscPrintf(comm, "  edge %d (%d):\n", adj[displs[p]+n], val[displs[p]+n]);
            }
          }
        }
        /* Symmetrize the graph */
        ierr = MatCreate(PETSC_COMM_SELF, &G);CHKERRQ(ierr);
        ierr = MatSetSizes(G, numProcs, numProcs, numProcs, numProcs);CHKERRQ(ierr);
        ierr = MatSetUp(G);CHKERRQ(ierr);
        for (p = 0; p < numProcs; ++p) {
          for (n = 0; n < recvcounts[p]; ++n) {
            const PetscInt    r = p;
            const PetscInt    q = adj[displs[p]+n];
            const PetscScalar o = val[displs[p]+n] ? 1.0 : 0.0;

            ierr = MatSetValues(G, 1, &r, 1, &q, &o, INSERT_VALUES);CHKERRQ(ierr);
            ierr = MatSetValues(G, 1, &q, 1, &r, &o, INSERT_VALUES);CHKERRQ(ierr);
          }
        }
        ierr = MatAssemblyBegin(G, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
        ierr = MatAssemblyEnd(G, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);

        ierr = PetscBTCreate(numProcs, &seenProcs);CHKERRQ(ierr);
        ierr = PetscBTMemzero(numProcs, seenProcs);CHKERRQ(ierr);
        ierr = PetscBTCreate(numProcs, &flippedProcs);CHKERRQ(ierr);
        ierr = PetscBTMemzero(numProcs, flippedProcs);CHKERRQ(ierr);
        ierr = PetscMalloc1(numProcs,&procFIFO);CHKERRQ(ierr);
        pTop = pBottom = 0;
        for (p = 0; p < numProcs; ++p) {
          if (PetscBTLookup(seenProcs, p)) continue;
          /* Initialize FIFO with next proc */
          procFIFO[pBottom++] = p;
          ierr = PetscBTSet(seenProcs, p);CHKERRQ(ierr);
          /* Consider each proc in FIFO */
          while (pTop < pBottom) {
            const PetscScalar *ornt;
            const PetscInt    *neighbors;
            PetscInt           proc, nproc, seen, flippedA, flippedB, mismatch, numNeighbors;

            proc     = procFIFO[pTop++];
            flippedA = PetscBTLookup(flippedProcs, proc) ? 1 : 0;
            ierr = MatGetRow(G, proc, &numNeighbors, &neighbors, &ornt);CHKERRQ(ierr);
            /* Loop over neighboring procs */
            for (n = 0; n < numNeighbors; ++n) {
              nproc    = neighbors[n];
              mismatch = PetscRealPart(ornt[n]) > 0.5 ? 0 : 1;
              seen     = PetscBTLookup(seenProcs, nproc);
              flippedB = PetscBTLookup(flippedProcs, nproc) ? 1 : 0;

              if (mismatch ^ (flippedA ^ flippedB)) {
                if (seen) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Previously seen procs %d and %d do not match: Fault mesh is non-orientable", proc, nproc);
                if (!flippedB) {
                  ierr = PetscBTSet(flippedProcs, nproc);CHKERRQ(ierr);
              } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Inconsistent mesh orientation: Fault mesh is non-orientable");
              } else if (mismatch && flippedA && flippedB) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Attempt to flip already flipped cell: Fault mesh is non-orientable");
              if (!seen) {
                procFIFO[pBottom++] = nproc;
                ierr = PetscBTSet(seenProcs, nproc);CHKERRQ(ierr);
              }
            }
          }
        }
        ierr = PetscFree(procFIFO);CHKERRQ(ierr);
        ierr = MatDestroy(&G);CHKERRQ(ierr);

        ierr = PetscFree2(recvcounts,displs);CHKERRQ(ierr);
        ierr = PetscFree2(adj,val);CHKERRQ(ierr);
        {
          PetscBool *flips;

          ierr = PetscMalloc1(numProcs,&flips);CHKERRQ(ierr);
          for (p = 0; p < numProcs; ++p) {
            flips[p] = PetscBTLookup(flippedProcs, p) ? PETSC_TRUE : PETSC_FALSE;
            if (debug && flips[p]) {ierr = PetscPrintf(comm, "Flipping Proc %d:\n", p);}
          }
          ierr = MPI_Scatter(flips, 1, MPIU_BOOL, &flipped, 1, MPIU_BOOL, 0, comm);CHKERRQ(ierr);
          ierr = PetscFree(flips);CHKERRQ(ierr);
        }
        ierr = PetscBTDestroy(&seenProcs);CHKERRQ(ierr);
        ierr = PetscBTDestroy(&flippedProcs);CHKERRQ(ierr);
      }
      ierr = PetscFree4(match,nranks,rornt,lornt);CHKERRQ(ierr);
      ierr = PetscFree(neighbors);CHKERRQ(ierr);
      if (flipped) {for (c = cStart; c < cEnd; ++c) {ierr = PetscBTNegate(flippedCells, c-cStart);CHKERRQ(ierr);}}
    }
  }
  /* Reverse flipped cells in the mesh */
  ierr = DMPlexGetMaxSizes(dm, &maxConeSize, NULL);CHKERRQ(ierr);
  ierr = DMGetWorkArray(dm, maxConeSize, PETSC_INT, &revcone);CHKERRQ(ierr);
  ierr = DMGetWorkArray(dm, maxConeSize, PETSC_INT, &revconeO);CHKERRQ(ierr);
  for (c = cStart; c < cEnd; ++c) {
    const PetscInt *cone, *coneO, *support;
    PetscInt        coneSize, supportSize, faceSize, cp, sp;

    if (!PetscBTLookup(flippedCells, c-cStart)) continue;
    ierr = DMPlexGetConeSize(dm, c, &coneSize);CHKERRQ(ierr);
    ierr = DMPlexGetCone(dm, c, &cone);CHKERRQ(ierr);
    ierr = DMPlexGetConeOrientation(dm, c, &coneO);CHKERRQ(ierr);
    for (cp = 0; cp < coneSize; ++cp) {
      const PetscInt rcp = coneSize-cp-1;

      ierr = DMPlexGetConeSize(dm, cone[rcp], &faceSize);CHKERRQ(ierr);
      revcone[cp]  = cone[rcp];
      revconeO[cp] = coneO[rcp] >= 0 ? -(faceSize-coneO[rcp]) : faceSize+coneO[rcp];
    }
    ierr = DMPlexSetCone(dm, c, revcone);CHKERRQ(ierr);
    ierr = DMPlexSetConeOrientation(dm, c, revconeO);CHKERRQ(ierr);
    /* Reverse orientations of support */
    faceSize = coneSize;
    ierr = DMPlexGetSupportSize(dm, c, &supportSize);CHKERRQ(ierr);
    ierr = DMPlexGetSupport(dm, c, &support);CHKERRQ(ierr);
    for (sp = 0; sp < supportSize; ++sp) {
      ierr = DMPlexGetConeSize(dm, support[sp], &coneSize);CHKERRQ(ierr);
      ierr = DMPlexGetCone(dm, support[sp], &cone);CHKERRQ(ierr);
      ierr = DMPlexGetConeOrientation(dm, support[sp], &coneO);CHKERRQ(ierr);
      for (cp = 0; cp < coneSize; ++cp) {
        if (cone[cp] != c) continue;
        ierr = DMPlexInsertConeOrientation(dm, support[sp], cp, coneO[cp] >= 0 ? -(faceSize-coneO[cp]) : faceSize+coneO[cp]);CHKERRQ(ierr);
      }
    }
  }
  ierr = DMRestoreWorkArray(dm, maxConeSize, PETSC_INT, &revcone);CHKERRQ(ierr);
  ierr = DMRestoreWorkArray(dm, maxConeSize, PETSC_INT, &revconeO);CHKERRQ(ierr);
  ierr = PetscBTDestroy(&seenCells);CHKERRQ(ierr);
  ierr = PetscBTDestroy(&flippedCells);CHKERRQ(ierr);
  ierr = PetscBTDestroy(&seenFaces);CHKERRQ(ierr);
  ierr = PetscFree(faceFIFO);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexInvertCell_Internal"
PetscErrorCode DMPlexInvertCell_Internal(PetscInt dim, PetscInt numCorners, PetscInt cone[])
{
  int tmpc;

  PetscFunctionBegin;
  if (dim != 3) PetscFunctionReturn(0);
  switch (numCorners) {
  case 4:
    tmpc    = cone[0];
    cone[0] = cone[1];
    cone[1] = tmpc;
    break;
  case 8:
    tmpc    = cone[1];
    cone[1] = cone[3];
    cone[3] = tmpc;
    break;
  default: break;
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexInvertCell"
/*@C
  DMPlexInvertCell - This flips tetrahedron and hexahedron orientation since Plex stores them internally with outward normals. Other cells are left untouched.

  Input Parameters:
+ numCorners - The number of vertices in a cell
- cone - The incoming cone

  Output Parameter:
. cone - The inverted cone (in-place)

  Level: developer

.seealso: DMPlexGenerate()
@*/
PetscErrorCode DMPlexInvertCell(PetscInt dim, PetscInt numCorners, int cone[])
{
  int tmpc;

  PetscFunctionBegin;
  if (dim != 3) PetscFunctionReturn(0);
  switch (numCorners) {
  case 4:
    tmpc    = cone[0];
    cone[0] = cone[1];
    cone[1] = tmpc;
    break;
  case 8:
    tmpc    = cone[1];
    cone[1] = cone[3];
    cone[3] = tmpc;
    break;
  default: break;
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexInvertCells_Internal"
/* This is to fix the tetrahedron orientation from TetGen */
PETSC_UNUSED static PetscErrorCode DMPlexInvertCells_Internal(PetscInt dim, PetscInt numCells, PetscInt numCorners, int cells[])
{
  PetscInt       bound = numCells*numCorners, coff;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  for (coff = 0; coff < bound; coff += numCorners) {
    ierr = DMPlexInvertCell(dim, numCorners, &cells[coff]);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->pointlist);
  free(outputCtx->pointmarkerlist);
  free(outputCtx->segmentlist);
  free(outputCtx->segmentmarkerlist);
  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 = PetscMalloc1(in.numberofpoints*dim, &in.pointlist);CHKERRQ(ierr);
    ierr = PetscMalloc1(in.numberofpoints, &in.pointmarkerlist);CHKERRQ(ierr);
    ierr = DMGetCoordinatesLocal(boundary, &coordinates);CHKERRQ(ierr);
    ierr = DMGetCoordinateSection(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 = PetscMalloc1(in.numberofsegments*2, &in.segmentlist);CHKERRQ(ierr);
    ierr = PetscMalloc1(in.numberofsegments, &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 = PetscMalloc1(in.numberofholes*dim, &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 = PetscMalloc1(in.numberofpoints*dim, &in.pointlist);CHKERRQ(ierr);
    ierr = PetscMalloc1(in.numberofpoints, &in.pointmarkerlist);CHKERRQ(ierr);
    ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
    ierr = DMGetCoordinateSection(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 = PetscMalloc1(in.numberoftriangles*in.numberofcorners, &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 = PetscMalloc1(in.numberofholes*dim, &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 = DMGetCoordinateSection(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, &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 double   *meshCoords = out.pointlist;
    int            *cells      = out.tetrahedronlist;

    ierr = DMPlexInvertCells_Internal(dim, numCells, numCorners, cells);CHKERRQ(ierr);
    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 = DMGetCoordinateSection(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       = 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 double   *meshCoords = out.pointlist;
    int            *cells      = out.tetrahedronlist;

    PetscBool      interpolate = depthGlobal > 1 ? PETSC_TRUE : PETSC_FALSE;

    ierr = DMPlexInvertCells_Internal(dim, numCells, numCorners, cells);CHKERRQ(ierr);
    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 = PetscMalloc1(in->numberofpoints*dim, &in->pointlist);CHKERRQ(ierr);
    ierr = PetscMalloc1(in->numberofpoints,       &in->pointmarkerlist);CHKERRQ(ierr);
    ierr = DMGetCoordinatesLocal(boundary, &coordinates);CHKERRQ(ierr);
    ierr = DMGetCoordinateSection(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 = PetscMalloc1(in->numberoffacets, &in->facetlist);CHKERRQ(ierr);
    ierr = PetscMalloc1(in->numberoffacets,   &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 = PetscMalloc1(in->facetlist[idx].numberofpolygons, &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                   = PetscMalloc1(poly->numberofvertices, &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 double   *meshCoords = out->pointlist;
    int            *cells      = out->tetrahedronlist;

    ierr = DMPlexInvertCells_Internal(dim, numCells, numCorners, cells);CHKERRQ(ierr);
    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 = PetscMalloc1(in->numberofpoints*dim, &in->pointlist);CHKERRQ(ierr);
    ierr = PetscMalloc1(in->numberofpoints,       &in->pointmarkerlist);CHKERRQ(ierr);
    ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
    ierr = DMGetCoordinateSection(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 = PetscMalloc1(in->numberoftetrahedra*in->numberofcorners, &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 double   *meshCoords = out->pointlist;
    int            *cells      = out->tetrahedronlist;
    PetscBool      interpolate = depthGlobal > 1 ? PETSC_TRUE : PETSC_FALSE;

    ierr = DMPlexInvertCells_Internal(dim, numCells, numCorners, cells);CHKERRQ(ierr);
    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 = DMGetDimension(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);
}

#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_Internal(dm, &cellRefiner);CHKERRQ(ierr);
    ierr = DMPlexRefineUniform_Internal(dm, cellRefiner, dmRefined);CHKERRQ(ierr);
    ierr = DMPlexCopyBoundary(dm, *dmRefined);CHKERRQ(ierr);
    PetscFunctionReturn(0);
  }
  ierr = DMPlexGetRefinementLimit(dm, &refinementLimit);CHKERRQ(ierr);
  if (refinementLimit == 0.0) PetscFunctionReturn(0);
  ierr = DMGetDimension(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 = PetscMalloc1((cEnd - cStart), &maxVolumes);CHKERRQ(ierr);
      for (c = 0; c < cEnd-cStart; ++c) maxVolumes[c] = refinementLimit;
      ierr = DMPlexRefine_Triangle(dm, maxVolumes, dmRefined);CHKERRQ(ierr);
      ierr = PetscFree(maxVolumes);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 = PetscMalloc1((cEnd - cStart), &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 = PetscMalloc1((cEnd - cStart), &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);
  }
  ierr = DMPlexCopyBoundary(dm, *dmRefined);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMRefineHierarchy_Plex"
PetscErrorCode DMRefineHierarchy_Plex(DM dm, PetscInt nlevels, DM dmRefined[])
{
  DM             cdm = dm;
  PetscInt       r;
  PetscBool      isUniform;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = DMPlexGetRefinementUniform(dm, &isUniform);CHKERRQ(ierr);
  if (!isUniform) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Non-uniform refinement is incompatible with the hierarchy");
  for (r = 0; r < nlevels; ++r) {
    CellRefiner cellRefiner;

    ierr = DMPlexGetCellRefiner_Internal(cdm, &cellRefiner);CHKERRQ(ierr);
    ierr = DMPlexRefineUniform_Internal(cdm, cellRefiner, &dmRefined[r]);CHKERRQ(ierr);
    ierr = DMPlexSetCoarseDM(dmRefined[r], cdm);CHKERRQ(ierr);
    cdm  = dmRefined[r];
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMCoarsen_Plex"
PetscErrorCode DMCoarsen_Plex(DM dm, MPI_Comm comm, DM *dmCoarsened)
{
  DM_Plex       *mesh = (DM_Plex*) dm->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscObjectReference((PetscObject) mesh->coarseMesh);CHKERRQ(ierr);
  *dmCoarsened = mesh->coarseMesh;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexLocalizeCoordinate_Internal"
PetscErrorCode DMPlexLocalizeCoordinate_Internal(DM dm, PetscInt dim, const PetscScalar anchor[], const PetscScalar in[], PetscScalar out[])
{
  PetscInt d;

  PetscFunctionBegin;
  if (!dm->maxCell) {
    for (d = 0; d < dim; ++d) out[d] = in[d];
  } else {
    for (d = 0; d < dim; ++d) {
      if (PetscAbsScalar(anchor[d] - in[d]) > dm->maxCell[d]) {
        out[d] = PetscRealPart(anchor[d]) > PetscRealPart(in[d]) ? dm->L[d] + in[d] : in[d] - dm->L[d];
      } else {
        out[d] = in[d];
      }
    }
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexLocalizeAddCoordinate_Internal"
PetscErrorCode DMPlexLocalizeAddCoordinate_Internal(DM dm, PetscInt dim, const PetscScalar anchor[], const PetscScalar in[], PetscScalar out[])
{
  PetscInt d;

  PetscFunctionBegin;
  if (!dm->maxCell) {
    for (d = 0; d < dim; ++d) out[d] += in[d];
  } else {
    for (d = 0; d < dim; ++d) {
      if (PetscAbsScalar(anchor[d] - in[d]) > dm->maxCell[d]) {
        out[d] += PetscRealPart(anchor[d]) > PetscRealPart(in[d]) ? dm->L[d] + in[d] : in[d] - dm->L[d];
      } else {
        out[d] += in[d];
      }
    }
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexLocalizeCoordinates"
PetscErrorCode DMPlexLocalizeCoordinates(DM dm)
{
  PetscSection   coordSection, cSection;
  Vec            coordinates,  cVec;
  PetscScalar   *coords, *coords2, *anchor;
  PetscInt       Nc, cStart, cEnd, c, vStart, vEnd, v, dof, d, off, off2, bs, coordSize;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (!dm->maxCell) PetscFunctionReturn(0);
  ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
  ierr = DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);CHKERRQ(ierr);
  ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
  ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
  ierr = PetscSectionCreate(PetscObjectComm((PetscObject) dm), &cSection);CHKERRQ(ierr);
  ierr = PetscSectionSetNumFields(cSection, 1);CHKERRQ(ierr);
  ierr = PetscSectionGetFieldComponents(coordSection, 0, &Nc);CHKERRQ(ierr);
  ierr = PetscSectionSetFieldComponents(cSection, 0, Nc);CHKERRQ(ierr);
  ierr = PetscSectionSetChart(cSection, cStart, vEnd);CHKERRQ(ierr);
  for (v = vStart; v < vEnd; ++v) {
    ierr = PetscSectionGetDof(coordSection, v, &dof);CHKERRQ(ierr);
    ierr = PetscSectionSetDof(cSection,     v,  dof);CHKERRQ(ierr);
    ierr = PetscSectionSetFieldDof(cSection, v, 0, dof);CHKERRQ(ierr);
  }
  for (c = cStart; c < cEnd; ++c) {
    ierr = DMPlexVecGetClosure(dm, coordSection, coordinates, c, &dof, NULL);CHKERRQ(ierr);
    ierr = PetscSectionSetDof(cSection, c, dof);CHKERRQ(ierr);
    ierr = PetscSectionSetFieldDof(cSection, c, 0, dof);CHKERRQ(ierr);
  }
  ierr = PetscSectionSetUp(cSection);CHKERRQ(ierr);
  ierr = PetscSectionGetStorageSize(cSection, &coordSize);CHKERRQ(ierr);
  ierr = VecCreate(PetscObjectComm((PetscObject) dm), &cVec);CHKERRQ(ierr);
  ierr = VecGetBlockSize(coordinates, &bs);CHKERRQ(ierr);
  ierr = VecSetBlockSize(cVec,         bs);CHKERRQ(ierr);
  ierr = VecSetSizes(cVec, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
  ierr = VecSetType(cVec,VECSTANDARD);CHKERRQ(ierr);
  ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
  ierr = VecGetArray(cVec,        &coords2);CHKERRQ(ierr);
  for (v = vStart; v < vEnd; ++v) {
    ierr = PetscSectionGetDof(coordSection, v, &dof);CHKERRQ(ierr);
    ierr = PetscSectionGetOffset(coordSection, v, &off);CHKERRQ(ierr);
    ierr = PetscSectionGetOffset(cSection,     v, &off2);CHKERRQ(ierr);
    for (d = 0; d < dof; ++d) coords2[off2+d] = coords[off+d];
  }
  ierr = DMGetWorkArray(dm, 3, PETSC_SCALAR, &anchor);CHKERRQ(ierr);
  for (c = cStart; c < cEnd; ++c) {
    PetscScalar *cellCoords = NULL;
    PetscInt     b;

    ierr = DMPlexVecGetClosure(dm, coordSection, coordinates, c, &dof, &cellCoords);CHKERRQ(ierr);
    ierr = PetscSectionGetOffset(cSection, c, &off2);CHKERRQ(ierr);
    for (b = 0; b < bs; ++b) anchor[b] = cellCoords[b];
    for (d = 0; d < dof/bs; ++d) {ierr = DMPlexLocalizeCoordinate_Internal(dm, bs, anchor, &cellCoords[d*bs], &coords2[off2+d*bs]);CHKERRQ(ierr);}
    ierr = DMPlexVecRestoreClosure(dm, coordSection, coordinates, c, &dof, &cellCoords);CHKERRQ(ierr);
  }
  ierr = DMRestoreWorkArray(dm, 3, PETSC_SCALAR, &anchor);CHKERRQ(ierr);
  ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
  ierr = VecRestoreArray(cVec,        &coords2);CHKERRQ(ierr);
  ierr = DMSetCoordinateSection(dm, PETSC_DETERMINE, cSection);CHKERRQ(ierr);
  ierr = DMSetCoordinatesLocal(dm, cVec);CHKERRQ(ierr);
  ierr = VecDestroy(&cVec);CHKERRQ(ierr);
  ierr = PetscSectionDestroy(&cSection);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetDepthLabel"
/*@
  DMPlexGetDepthLabel - Get the DMLabel recording the depth of each point

  Not Collective

  Input Parameter:
. dm    - The DMPlex object

  Output Parameter:
. depthLabel - The DMLabel recording point depth

  Level: developer

.keywords: mesh, points
.seealso: DMPlexGetDepth(), DMPlexGetHeightStratum(), DMPlexGetDepthStratum()
@*/
PetscErrorCode DMPlexGetDepthLabel(DM dm, DMLabel *depthLabel)
{
  DM_Plex       *mesh = (DM_Plex*) dm->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidPointer(depthLabel, 2);
  if (!mesh->depthLabel) {ierr = DMPlexGetLabel(dm, "depth", &mesh->depthLabel);CHKERRQ(ierr);}
  *depthLabel = mesh->depthLabel;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetDepth"
/*@
  DMPlexGetDepth - Get the depth of the DAG representing this mesh

  Not Collective

  Input Parameter:
. dm    - The DMPlex object

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

  Level: developer

.keywords: mesh, points
.seealso: DMPlexGetDepthLabel(), DMPlexGetHeightStratum(), DMPlexGetDepthStratum()
@*/
PetscErrorCode DMPlexGetDepth(DM dm, PetscInt *depth)
{
  DMLabel        label;
  PetscInt       d = 0;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidPointer(depth, 2);
  ierr = DMPlexGetDepthLabel(dm, &label);CHKERRQ(ierr);
  if (label) {ierr = DMLabelGetNumValues(label, &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)
{
  DMLabel        label;
  PetscInt       pStart, pEnd;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (start) {PetscValidPointer(start, 3); *start = 0;}
  if (end)   {PetscValidPointer(end,   4); *end   = 0;}
  ierr = DMPlexGetChart(dm, &pStart, &pEnd);CHKERRQ(ierr);
  if (pStart == pEnd) PetscFunctionReturn(0);
  if (stratumValue < 0) {
    if (start) *start = pStart;
    if (end)   *end   = pEnd;
    PetscFunctionReturn(0);
  }
  ierr = DMPlexGetDepthLabel(dm, &label);CHKERRQ(ierr);
  if (!label) SETERRQ(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_WRONG, "No label named depth was found");
  ierr = DMLabelGetStratumBounds(label, stratumValue, start, end);CHKERRQ(ierr);
  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)
{
  DMLabel        label;
  PetscInt       depth, pStart, pEnd;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (start) {PetscValidPointer(start, 3); *start = 0;}
  if (end)   {PetscValidPointer(end,   4); *end   = 0;}
  ierr = DMPlexGetChart(dm, &pStart, &pEnd);CHKERRQ(ierr);
  if (pStart == pEnd) PetscFunctionReturn(0);
  if (stratumValue < 0) {
    if (start) *start = pStart;
    if (end)   *end   = pEnd;
    PetscFunctionReturn(0);
  }
  ierr = DMPlexGetDepthLabel(dm, &label);CHKERRQ(ierr);
  if (!label) SETERRQ(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_WRONG, "No label named depth was found");CHKERRQ(ierr);
  ierr = DMLabelGetNumValues(label, &depth);CHKERRQ(ierr);
  ierr = DMLabelGetStratumBounds(label, depth-1-stratumValue, start, end);CHKERRQ(ierr);
  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       depth, pStart = 0, pEnd = 0;
  PetscInt       p, d, dep, f;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscMalloc1((dim+1), &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);
  ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
  for (dep = 0; dep <= depth; ++dep) {
    d    = dim == depth ? dep : (!dep ? 0 : dim);
    ierr = DMPlexGetDepthStratum(dm, dep, &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;
  PetscSection   aSec;
  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);
  }
  ierr = DMPlexGetConstraints(dm, &aSec, NULL);CHKERRQ(ierr);
  if (aSec) {
    PetscInt aStart, aEnd, a;

    ierr = PetscSectionGetChart(aSec, &aStart, &aEnd);CHKERRQ(ierr);
    for (a = aStart; a < aEnd; a++) {
      PetscInt dof;

      ierr = PetscSectionGetDof(aSec, a, &dof);CHKERRQ(ierr);
      if (dof) {
        /* if there are point-to-point constraints, then all dofs are constrained */
        ierr = PetscSectionGetDof(section, a, &dof);CHKERRQ(ierr);
        ierr = PetscSectionSetConstraintDof(section, a, dof);CHKERRQ(ierr);
        if (numFields) {
          PetscInt f;

          for (f = 0; f < numFields; f++) {
            ierr = PetscSectionGetFieldDof(section, a, f, &dof);CHKERRQ(ierr);
            ierr = PetscSectionSetFieldConstraintDof(section, a, f, dof);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 = PetscMalloc1((numFields+1), &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 = PetscMalloc1(maxConstraints[numFields], &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 = PetscMalloc1(maxDof, &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 = PetscMalloc1(maxDof, &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
- perm      - Optional permutation of the chart, or NULL

  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
  number of dof for field 0 on each edge.

  The chart permutation is the same one set using PetscSectionSetPermutation()

  Level: developer

  Fortran Notes:
  A Fortran 90 version is available as DMPlexCreateSectionF90()

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

  PetscFunctionBegin;
  ierr = DMPlexCreateSectionInitial(dm, dim, numFields, numComp, numDof, section);CHKERRQ(ierr);
  ierr = DMPlexCreateSectionBCDof(dm, numBC, bcField, bcPoints, PETSC_DETERMINE, *section);CHKERRQ(ierr);
  if (perm) {ierr = PetscSectionSetPermutation(*section, perm);CHKERRQ(ierr);}
  ierr = PetscSectionSetUp(*section);CHKERRQ(ierr);
  ierr = DMPlexGetConstraints(dm,&aSec,NULL);CHKERRQ(ierr);
  if (numBC || aSec) {ierr = DMPlexCreateSectionBCIndicesAll(dm, *section);CHKERRQ(ierr);}
  ierr = PetscSectionViewFromOptions(*section,NULL,"-section_view");CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

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

  PetscFunctionBegin;
  ierr = DMClone(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__ "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__ "DMPlexGetSupportSection"
PetscErrorCode DMPlexGetSupportSection(DM dm, PetscSection *section)
{
  DM_Plex *mesh = (DM_Plex*) dm->data;

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

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

#undef __FUNCT__
#define __FUNCT__ "DMPlexVecGetClosure_Depth1_Static"
PETSC_STATIC_INLINE PetscErrorCode DMPlexVecGetClosure_Depth1_Static(DM dm, PetscSection section, Vec v, PetscInt point, PetscInt *csize, PetscScalar *values[])
{
  PetscScalar    *array, *vArray;
  const PetscInt *cone, *coneO;
  PetscInt        pStart, pEnd, p, numPoints, size = 0, offset = 0;
  PetscErrorCode  ierr;

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

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

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

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

    if ((cp < pStart) || (cp >= pEnd)) continue;
    ierr = PetscSectionGetDof(section, cp, &dof);CHKERRQ(ierr);
    ierr = PetscSectionGetOffset(section, cp, &off);CHKERRQ(ierr);
    varr = &vArray[off];
    if (o >= 0) {
      for (d = 0; d < dof; ++d, ++offset) {
        array[offset] = varr[d];
      }
    } else {
      for (d = dof-1; d >= 0; --d, ++offset) {
        array[offset] = varr[d];
      }
    }
    size += dof;
  }
  ierr = VecRestoreArray(v, &vArray);CHKERRQ(ierr);
  if (!*values) {
    if (csize) *csize = size;
    *values = array;
  } else {
    if (size > *csize) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Size of input array %d < actual size %d", *csize, size);
    *csize = size;
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexVecGetClosure_Static"
PETSC_STATIC_INLINE PetscErrorCode DMPlexVecGetClosure_Static(PetscSection section, PetscInt numPoints, const PetscInt points[], const PetscScalar vArray[], PetscInt *size, PetscScalar array[])
{
  PetscInt       offset = 0, p;
  PetscErrorCode ierr;

  PetscFunctionBeginHot;
  *size = 0;
  for (p = 0; p < numPoints*2; p += 2) {
    const PetscInt point = points[p];
    const PetscInt o     = points[p+1];
    PetscInt       dof, off, d;
    const PetscScalar *varr;

    ierr = PetscSectionGetDof(section, point, &dof);CHKERRQ(ierr);
    ierr = PetscSectionGetOffset(section, point, &off);CHKERRQ(ierr);
    varr = &vArray[off];
    if (o >= 0) {
      for (d = 0; d < dof; ++d, ++offset)    array[offset] = varr[d];
    } else {
      for (d = dof-1; d >= 0; --d, ++offset) array[offset] = varr[d];
    }
  }
  *size = offset;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexVecGetClosure_Fields_Static"
PETSC_STATIC_INLINE PetscErrorCode DMPlexVecGetClosure_Fields_Static(PetscSection section, PetscInt numPoints, const PetscInt points[], PetscInt numFields, const PetscScalar vArray[], PetscInt *size, PetscScalar array[])
{
  PetscInt       offset = 0, f;
  PetscErrorCode ierr;

  PetscFunctionBeginHot;
  *size = 0;
  for (f = 0; f < numFields; ++f) {
    PetscInt fcomp, p;

    ierr = PetscSectionGetFieldComponents(section, f, &fcomp);CHKERRQ(ierr);
    for (p = 0; p < numPoints*2; p += 2) {
      const PetscInt point = points[p];
      const PetscInt o     = points[p+1];
      PetscInt       fdof, foff, d, c;
      const PetscScalar *varr;

      ierr = PetscSectionGetFieldDof(section, point, f, &fdof);CHKERRQ(ierr);
      ierr = PetscSectionGetFieldOffset(section, point, f, &foff);CHKERRQ(ierr);
      varr = &vArray[foff];
      if (o >= 0) {
        for (d = 0; d < fdof; ++d, ++offset) array[offset] = varr[d];
      } else {
        for (d = fdof/fcomp-1; d >= 0; --d) {
          for (c = 0; c < fcomp; ++c, ++offset) {
            array[offset] = varr[d*fcomp+c];
          }
        }
      }
    }
  }
  *size = offset;
  PetscFunctionReturn(0);
}

#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

  Fortran Notes:
  Since it returns an array, this routine is only available in Fortran 90, and you must
  include petsc.h90 in your code.

  The csize argument is not present in the Fortran 90 binding since it is internal to the array.

  Level: intermediate

.seealso DMPlexVecRestoreClosure(), DMPlexVecSetClosure(), DMPlexMatSetClosure()
@*/
PetscErrorCode DMPlexVecGetClosure(DM dm, PetscSection section, Vec v, PetscInt point, PetscInt *csize, PetscScalar *values[])
{
  PetscSection    clSection;
  IS              clPoints;
  PetscScalar    *array, *vArray;
  PetscInt       *points = NULL;
  const PetscInt *clp;
  PetscInt        depth, numFields, numPoints, size;
  PetscErrorCode  ierr;

  PetscFunctionBeginHot;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (!section) {ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);}
  PetscValidHeaderSpecific(section, PETSC_SECTION_CLASSID, 2);
  PetscValidHeaderSpecific(v, VEC_CLASSID, 3);
  ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
  ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
  if (depth == 1 && numFields < 2) {
    ierr = DMPlexVecGetClosure_Depth1_Static(dm, section, v, point, csize, values);CHKERRQ(ierr);
    PetscFunctionReturn(0);
  }
  /* Get points */
  ierr = PetscSectionGetClosureIndex(section, (PetscObject) dm, &clSection, &clPoints);CHKERRQ(ierr);
  if (!clPoints) {
    PetscInt pStart, pEnd, p, q;

    ierr = PetscSectionGetChart(section, &pStart, &pEnd);CHKERRQ(ierr);
    ierr = DMPlexGetTransitiveClosure(dm, point, PETSC_TRUE, &numPoints, &points);CHKERRQ(ierr);
    /* Compress out points not in the section */
    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;
  } else {
    PetscInt dof, off;

    ierr = PetscSectionGetDof(clSection, point, &dof);CHKERRQ(ierr);
    ierr = PetscSectionGetOffset(clSection, point, &off);CHKERRQ(ierr);
    ierr = ISGetIndices(clPoints, &clp);CHKERRQ(ierr);
    numPoints = dof/2;
    points    = (PetscInt *) &clp[off];
  }
  /* Get array */
  if (!values || !*values) {
    PetscInt asize = 0, dof, p;

    for (p = 0; p < numPoints*2; p += 2) {
      ierr = PetscSectionGetDof(section, points[p], &dof);CHKERRQ(ierr);
      asize += dof;
    }
    if (!values) {
      if (!clPoints) {ierr = DMPlexRestoreTransitiveClosure(dm, point, PETSC_TRUE, &numPoints, &points);CHKERRQ(ierr);}
      else           {ierr = ISRestoreIndices(clPoints, &clp);CHKERRQ(ierr);}
      if (csize) *csize = asize;
      PetscFunctionReturn(0);
    }
    ierr = DMGetWorkArray(dm, asize, PETSC_SCALAR, &array);CHKERRQ(ierr);
  } else {
    array = *values;
  }
  ierr = VecGetArray(v, &vArray);CHKERRQ(ierr);
  /* Get values */
  if (numFields > 0) {ierr = DMPlexVecGetClosure_Fields_Static(section, numPoints, points, numFields, vArray, &size, array);CHKERRQ(ierr);}
  else               {ierr = DMPlexVecGetClosure_Static(section, numPoints, points, vArray, &size, array);CHKERRQ(ierr);}
  /* Cleanup points */
  if (!clPoints) {ierr = DMPlexRestoreTransitiveClosure(dm, point, PETSC_TRUE, &numPoints, &points);CHKERRQ(ierr);}
  else           {ierr = ISRestoreIndices(clPoints, &clp);CHKERRQ(ierr);}
  /* Cleanup array */
  ierr = VecRestoreArray(v, &vArray);CHKERRQ(ierr);
  if (!*values) {
    if (csize) *csize = size;
    *values = array;
  } else {
    if (size > *csize) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Size of input array %d < actual size %d", *csize, size);
    *csize = size;
  }
  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

  Fortran Notes:
  Since it returns an array, this routine is only available in Fortran 90, and you must
  include petsc.h90 in your code.

  The csize argument is not present in the Fortran 90 binding since it is internal to the array.

  Level: intermediate

.seealso DMPlexVecGetClosure(), DMPlexVecSetClosure(), DMPlexMatSetClosure()
@*/
PetscErrorCode DMPlexVecRestoreClosure(DM dm, PetscSection section, Vec v, PetscInt point, PetscInt *csize, 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"
PETSC_STATIC_INLINE 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__ "updatePointBC_private"
PETSC_STATIC_INLINE PetscErrorCode updatePointBC_private(PetscSection section, PetscInt point, PetscInt dof, void (*fuse)(PetscScalar*, PetscScalar), 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) {
    ierr = PetscSectionGetConstraintIndices(section, point, &cdofs);CHKERRQ(ierr);
    if (orientation >= 0) {
      for (k = 0; k < dof; ++k) {
        if ((cind < cdof) && (k == cdofs[cind])) {
          fuse(&a[k], values[k]);
          ++cind;
        }
      }
    } else {
      for (k = 0; k < dof; ++k) {
        if ((cind < cdof) && (k == cdofs[cind])) {
          fuse(&a[k], values[dof-k-1]);
          ++cind;
        }
      }
    }
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "updatePointFields_private"
PETSC_STATIC_INLINE PetscErrorCode updatePointFields_private(PetscSection section, PetscInt point, PetscInt o, PetscInt f, PetscInt fcomp, void (*fuse)(PetscScalar*, PetscScalar), PetscBool setBC, const PetscScalar values[], PetscInt *offset, PetscScalar array[])
{
  PetscScalar    *a;
  PetscInt        fdof, foff, fcdof, foffset = *offset;
  const PetscInt *fcdofs; /* The indices of the constrained dofs for field f on this point */
  PetscInt        cind = 0, k, c;
  PetscErrorCode  ierr;

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

#undef __FUNCT__
#define __FUNCT__ "updatePointFieldsBC_private"
PETSC_STATIC_INLINE PetscErrorCode updatePointFieldsBC_private(PetscSection section, PetscInt point, PetscInt o, PetscInt f, PetscInt fcomp, void (*fuse)(PetscScalar*, PetscScalar), const PetscScalar values[], PetscInt *offset, PetscScalar array[])
{
  PetscScalar    *a;
  PetscInt        fdof, foff, fcdof, foffset = *offset;
  const PetscInt *fcdofs; /* The indices of the constrained dofs for field f on this point */
  PetscInt        cind = 0, k, c;
  PetscErrorCode  ierr;

  PetscFunctionBegin;
  ierr = PetscSectionGetFieldDof(section, point, f, &fdof);CHKERRQ(ierr);
  ierr = PetscSectionGetFieldConstraintDof(section, point, f, &fcdof);CHKERRQ(ierr);
  ierr = PetscSectionGetFieldOffset(section, point, f, &foff);CHKERRQ(ierr);
  a    = &array[foff];
  if (fcdof) {
    ierr = PetscSectionGetFieldConstraintIndices(section, point, f, &fcdofs);CHKERRQ(ierr);
    if (o >= 0) {
      for (k = 0; k < fdof; ++k) {
        if ((cind < fcdof) && (k == fcdofs[cind])) {
          fuse(&a[k], values[foffset+k]);
          ++cind;
        }
      }
    } else {
      for (k = fdof/fcomp-1; k >= 0; --k) {
        for (c = 0; c < fcomp; ++c) {
          if ((cind < fcdof) && (k*fcomp+c == fcdofs[cind])) {
            fuse(&a[(fdof/fcomp-1-k)*fcomp+c], values[foffset+k*fcomp+c]);
            ++cind;
          }
        }
      }
    }
  }
  *offset += fdof;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexVecSetClosure_Static"
PETSC_STATIC_INLINE PetscErrorCode DMPlexVecSetClosure_Static(DM dm, PetscSection section, Vec v, PetscInt point, const PetscScalar values[], InsertMode mode)
{
  PetscScalar    *array;
  const PetscInt *cone, *coneO;
  PetscInt        pStart, pEnd, p, numPoints, off, dof;
  PetscErrorCode  ierr;

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

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

      ierr = PetscSectionGetConstraintDof(section, cp, &cdof);CHKERRQ(ierr);
      ierr = PetscSectionGetOffset(section, cp, &coff);CHKERRQ(ierr);
      a    = &array[coff];
      if (!cdof) {
        if (o >= 0) {
          for (k = 0; k < dof; ++k) {
            a[k] += values[off+k];
          }
        } else {
          for (k = 0; k < dof; ++k) {
            a[k] += values[off+dof-k-1];
          }
        }
      } else {
        ierr = PetscSectionGetConstraintIndices(section, cp, &cdofs);CHKERRQ(ierr);
        if (o >= 0) {
          for (k = 0; k < dof; ++k) {
            if ((cind < cdof) && (k == cdofs[cind])) {++cind; continue;}
            a[k] += values[off+k];
          }
        } else {
          for (k = 0; k < dof; ++k) {
            if ((cind < cdof) && (k == cdofs[cind])) {++cind; continue;}
            a[k] += values[off+dof-k-1];
          }
        }
      }
    }
  }
  ierr = VecRestoreArray(v, &array);CHKERRQ(ierr);
  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 section
. v - The local vector
. point - The sieve point in the DM
. values - The array of values
- mode - The insert mode, where INSERT_ALL_VALUES and ADD_ALL_VALUES also overwrite boundary conditions

  Fortran Notes:
  This routine is only available in Fortran 90, and you must include petsc.h90 in your code.

  Level: intermediate

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

  PetscFunctionBeginHot;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (!section) {ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);}
  PetscValidHeaderSpecific(section, PETSC_SECTION_CLASSID, 2);
  PetscValidHeaderSpecific(v, VEC_CLASSID, 3);
  ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
  ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
  if (depth == 1 && numFields < 2 && mode == ADD_VALUES) {
    ierr = DMPlexVecSetClosure_Static(dm, section, v, point, values, mode);CHKERRQ(ierr);
    PetscFunctionReturn(0);
  }
  /* Get points */
  ierr = PetscSectionGetClosureIndex(section, (PetscObject) dm, &clSection, &clPoints);CHKERRQ(ierr);
  if (!clPoints) {
    PetscInt pStart, pEnd, q;

    ierr = PetscSectionGetChart(section, &pStart, &pEnd);CHKERRQ(ierr);
    ierr = DMPlexGetTransitiveClosure(dm, point, PETSC_TRUE, &numPoints, &points);CHKERRQ(ierr);
    /* Compress out points not in the section */
    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;
  } else {
    PetscInt dof, off;

    ierr = PetscSectionGetDof(clSection, point, &dof);CHKERRQ(ierr);
    ierr = PetscSectionGetOffset(clSection, point, &off);CHKERRQ(ierr);
    ierr = ISGetIndices(clPoints, &clp);CHKERRQ(ierr);
    numPoints = dof/2;
    points    = (PetscInt *) &clp[off];
  }
  /* Get array */
  ierr = VecGetArray(v, &array);CHKERRQ(ierr);
  /* Get values */
  if (numFields > 0) {
    PetscInt offset = 0, fcomp, f;
    for (f = 0; f < numFields; ++f) {
      ierr = PetscSectionGetFieldComponents(section, f, &fcomp);CHKERRQ(ierr);
      switch (mode) {
      case INSERT_VALUES:
        for (p = 0; p < numPoints*2; p += 2) {
          const PetscInt point = points[p];
          const PetscInt o     = points[p+1];
          updatePointFields_private(section, point, o, f, fcomp, insert, PETSC_FALSE, values, &offset, array);
        } break;
      case INSERT_ALL_VALUES:
        for (p = 0; p < numPoints*2; p += 2) {
          const PetscInt point = points[p];
          const PetscInt o     = points[p+1];
          updatePointFields_private(section, point, o, f, fcomp, insert, PETSC_TRUE, values, &offset, array);
        } break;
      case INSERT_BC_VALUES:
        for (p = 0; p < numPoints*2; p += 2) {
          const PetscInt point = points[p];
          const PetscInt o     = points[p+1];
          updatePointFieldsBC_private(section, point, o, f, fcomp, insert, values, &offset, array);
        } break;
      case ADD_VALUES:
        for (p = 0; p < numPoints*2; p += 2) {
          const PetscInt point = points[p];
          const PetscInt o     = points[p+1];
          updatePointFields_private(section, point, o, f, fcomp, add, PETSC_FALSE, values, &offset, array);
        } break;
      case ADD_ALL_VALUES:
        for (p = 0; p < numPoints*2; p += 2) {
          const PetscInt point = points[p];
          const PetscInt o     = points[p+1];
          updatePointFields_private(section, point, o, f, fcomp, add, PETSC_TRUE, values, &offset, array);
        } break;
      default:
        SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "Invalid insert mode %D", mode);
      }
    }
  } else {
    PetscInt dof, off;

    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 INSERT_BC_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);
        updatePointBC_private(section, points[p], dof, insert,  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);
    }
  }
  /* Cleanup points */
  if (!clPoints) {ierr = DMPlexRestoreTransitiveClosure(dm, point, PETSC_TRUE, &numPoints, &points);CHKERRQ(ierr);}
  else           {ierr = ISRestoreIndices(clPoints, &clp);CHKERRQ(ierr);}
  /* Cleanup array */
  ierr = VecRestoreArray(v, &array);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexVecSetFieldClosure_Internal"
PetscErrorCode DMPlexVecSetFieldClosure_Internal(DM dm, PetscSection section, Vec v, PetscBool fieldActive[], PetscInt point, const PetscScalar values[], InsertMode mode)
{
  PetscSection    clSection;
  IS              clPoints;
  PetscScalar    *array;
  PetscInt       *points = NULL;
  const PetscInt *clp;
  PetscInt        numFields, numPoints, p;
  PetscInt        offset = 0, fcomp, f;
  PetscErrorCode  ierr;

  PetscFunctionBeginHot;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (!section) {ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);}
  PetscValidHeaderSpecific(section, PETSC_SECTION_CLASSID, 2);
  PetscValidHeaderSpecific(v, VEC_CLASSID, 3);
  ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);
  /* Get points */
  ierr = PetscSectionGetClosureIndex(section, (PetscObject) dm, &clSection, &clPoints);CHKERRQ(ierr);
  if (!clPoints) {
    PetscInt pStart, pEnd, q;

    ierr = PetscSectionGetChart(section, &pStart, &pEnd);CHKERRQ(ierr);
    ierr = DMPlexGetTransitiveClosure(dm, point, PETSC_TRUE, &numPoints, &points);CHKERRQ(ierr);
    /* Compress out points not in the section */
    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;
  } else {
    PetscInt dof, off;

    ierr = PetscSectionGetDof(clSection, point, &dof);CHKERRQ(ierr);
    ierr = PetscSectionGetOffset(clSection, point, &off);CHKERRQ(ierr);
    ierr = ISGetIndices(clPoints, &clp);CHKERRQ(ierr);
    numPoints = dof/2;
    points    = (PetscInt *) &clp[off];
  }
  /* Get array */
  ierr = VecGetArray(v, &array);CHKERRQ(ierr);
  /* Get values */
  for (f = 0; f < numFields; ++f) {
    ierr = PetscSectionGetFieldComponents(section, f, &fcomp);CHKERRQ(ierr);
    if (!fieldActive[f]) {
      for (p = 0; p < numPoints*2; p += 2) {
        PetscInt fdof;
        ierr = PetscSectionGetFieldDof(section, points[p], f, &fdof);CHKERRQ(ierr);
        offset += fdof;
      }
      continue;
    }
    switch (mode) {
    case INSERT_VALUES:
      for (p = 0; p < numPoints*2; p += 2) {
        const PetscInt point = points[p];
        const PetscInt o     = points[p+1];
        updatePointFields_private(section, point, o, f, fcomp, insert, PETSC_FALSE, values, &offset, array);
      } break;
    case INSERT_ALL_VALUES:
      for (p = 0; p < numPoints*2; p += 2) {
        const PetscInt point = points[p];
        const PetscInt o     = points[p+1];
        updatePointFields_private(section, point, o, f, fcomp, insert, PETSC_TRUE, values, &offset, array);
        } break;
    case INSERT_BC_VALUES:
      for (p = 0; p < numPoints*2; p += 2) {
        const PetscInt point = points[p];
        const PetscInt o     = points[p+1];
        updatePointFieldsBC_private(section, point, o, f, fcomp, insert, values, &offset, array);
      } break;
    case ADD_VALUES:
      for (p = 0; p < numPoints*2; p += 2) {
        const PetscInt point = points[p];
        const PetscInt o     = points[p+1];
        updatePointFields_private(section, point, o, f, fcomp, add, PETSC_FALSE, values, &offset, array);
      } break;
    case ADD_ALL_VALUES:
      for (p = 0; p < numPoints*2; p += 2) {
        const PetscInt point = points[p];
        const PetscInt o     = points[p+1];
        updatePointFields_private(section, point, o, f, fcomp, add, PETSC_TRUE, values, &offset, array);
      } break;
    default:
      SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "Invalid insert mode %D", mode);
    }
  }
  /* Cleanup points */
  if (!clPoints) {ierr = DMPlexRestoreTransitiveClosure(dm, point, PETSC_TRUE, &numPoints, &points);CHKERRQ(ierr);}
  else           {ierr = ISRestoreIndices(clPoints, &clp);CHKERRQ(ierr);}
  /* Cleanup array */
  ierr = VecRestoreArray(v, &array);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexPrintMatSetValues"
PetscErrorCode DMPlexPrintMatSetValues(PetscViewer viewer, Mat A, PetscInt point, PetscInt numRIndices, const PetscInt rindices[], PetscInt numCIndices, const PetscInt cindices[], const PetscScalar values[])
{
  PetscMPIInt    rank;
  PetscInt       i, j;
  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 < numRIndices; i++) {ierr = PetscViewerASCIIPrintf(viewer, "[%D]mat row indices[%D] = %D\n", rank, i, rindices[i]);CHKERRQ(ierr);}
  for (i = 0; i < numCIndices; i++) {ierr = PetscViewerASCIIPrintf(viewer, "[%D]mat col indices[%D] = %D\n", rank, i, cindices[i]);CHKERRQ(ierr);}
  numCIndices = numCIndices ? numCIndices : numRIndices;
  for (i = 0; i < numRIndices; i++) {
    ierr = PetscViewerASCIIPrintf(viewer, "[%D]", rank);CHKERRQ(ierr);
    for (j = 0; j < numCIndices; j++) {
#if defined(PETSC_USE_COMPLEX)
      ierr = PetscViewerASCIIPrintf(viewer, " (%g,%g)", (double)PetscRealPart(values[i*numCIndices+j]), (double)PetscImaginaryPart(values[i*numCIndices+j]));CHKERRQ(ierr);
#else
      ierr = PetscViewerASCIIPrintf(viewer, " %g", (double)values[i*numCIndices+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__ "DMPlexConstraintsModifyMat"
static PetscErrorCode DMPlexConstraintsModifyMat(DM dm, PetscSection section, PetscInt numPoints, PetscInt numIndices, const PetscInt points[], const PetscScalar values[], PetscInt *outNumPoints, PetscInt *outNumIndices, PetscInt *outPoints[], PetscScalar *outValues[], PetscInt offsets[])
{
  Mat             cMat;
  PetscSection    aSec, cSec;
  IS              aIS;
  PetscInt        aStart = -1, aEnd = -1;
  const PetscInt  *anchors;
  PetscInt        numFields, f, p, q, newP;
  PetscInt        newNumPoints = 0, newNumIndices = 0;
  PetscInt        *newPoints, *indices, *newIndices;
  PetscInt        maxAnchor, maxDof;
  PetscInt        newOffsets[32];
  PetscInt        *pointMatOffsets[32];
  PetscInt        *newPointOffsets[32];
  PetscScalar     *pointMat[32];
  PetscScalar     *newValues,*tmpValues;
  PetscBool       anyConstrained = PETSC_FALSE;
  PetscErrorCode  ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidHeaderSpecific(section, PETSC_SECTION_CLASSID, 2);
  ierr = PetscSectionGetNumFields(section, &numFields);CHKERRQ(ierr);

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

      if (b >= aStart && b < aEnd) {
        ierr = PetscSectionGetDof(aSec,b,&bDof);CHKERRQ(ierr);
      }
      if (bDof) {
        /* this point is constrained */
        /* it is going to be replaced by its anchors */
        PetscInt bOff, q;

        anyConstrained = PETSC_TRUE;
        newNumPoints  += bDof;
        ierr = PetscSectionGetOffset(aSec,b,&bOff);CHKERRQ(ierr);
        for (q = 0; q < bDof; q++) {
          PetscInt a = anchors[bOff + q];
          PetscInt aDof;

          ierr           = PetscSectionGetDof(section,a,&aDof);CHKERRQ(ierr);
          newNumIndices += aDof;
          for (f = 0; f < numFields; ++f) {
            PetscInt fDof;

            ierr             = PetscSectionGetFieldDof(section, a, f, &fDof);CHKERRQ(ierr);
            newOffsets[f+1] += fDof;
          }
        }
      }
      else {
        /* this point is not constrained */
        newNumPoints++;
        ierr           = PetscSectionGetDof(section,b,&bDof);CHKERRQ(ierr);
        newNumIndices += bDof;
        for (f = 0; f < numFields; ++f) {
          PetscInt fDof;

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

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

  if (numFields && newOffsets[numFields] != newNumIndices) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid size for closure %d should be %d", newOffsets[numFields], newNumIndices);

  ierr = DMPlexGetConstraintSection(dm, &cSec);CHKERRQ(ierr);
  ierr = DMPlexGetConstraintMatrix(dm, &cMat);CHKERRQ(ierr);

  /* output arrays */
  ierr = DMGetWorkArray(dm,2*newNumPoints,PETSC_INT,&newPoints);CHKERRQ(ierr);
  ierr = DMGetWorkArray(dm,newNumIndices*newNumIndices,PETSC_SCALAR,&newValues);CHKERRQ(ierr);

  /* workspaces */
  ierr = DMGetWorkArray(dm,newNumIndices*numIndices,PETSC_SCALAR,&tmpValues);CHKERRQ(ierr);
  if (numFields) {
    for (f = 0; f < numFields; f++) {
      ierr = DMGetWorkArray(dm,numPoints+1,PETSC_INT,&pointMatOffsets[f]);CHKERRQ(ierr);
      ierr = DMGetWorkArray(dm,numPoints+1,PETSC_INT,&newPointOffsets[f]);CHKERRQ(ierr);
    }
  }
  else {
    ierr = DMGetWorkArray(dm,numPoints+1,PETSC_INT,&pointMatOffsets[0]);CHKERRQ(ierr);
    ierr = DMGetWorkArray(dm,numPoints,PETSC_INT,&newPointOffsets[0]);CHKERRQ(ierr);
  }

  /* get workspaces for the point-to-point matrices */
  if (numFields) {
    for (p = 0; p < numPoints; p++) {
      PetscInt b    = points[2*p];
      PetscInt bDof = 0;

      if (b >= aStart && b < aEnd) {
        ierr = PetscSectionGetDof(aSec, b, &bDof);CHKERRQ(ierr);
      }
      if (bDof) {
        for (f = 0; f < numFields; f++) {
          PetscInt fDof, q, bOff, allFDof = 0;

          ierr = PetscSectionGetFieldDof(section, b, f, &fDof);CHKERRQ(ierr);
          ierr = PetscSectionGetOffset(aSec, b, &bOff);CHKERRQ(ierr);
          for (q = 0; q < bDof; q++) {
            PetscInt a = anchors[bOff + q];
            PetscInt aFDof;

            ierr     = PetscSectionGetFieldDof(section, a, f, &aFDof);CHKERRQ(ierr);
            allFDof += aFDof;
          }
          newPointOffsets[f][p+1] = allFDof;
          pointMatOffsets[f][p+1] = fDof * allFDof;
        }
      }
      else {
        for (f = 0; f < numFields; f++) {
          PetscInt fDof;

          ierr = PetscSectionGetFieldDof(section, b, f, &fDof);CHKERRQ(ierr);
          newPointOffsets[f][p+1] = fDof;
          pointMatOffsets[f][p+1] = 0;
        }
      }
    }
    for (f = 0; f < numFields; f++) {
      newPointOffsets[f][0] = 0;
      pointMatOffsets[f][0] = 0;
      for (p = 0; p < numPoints; p++) {
        newPointOffsets[f][p+1] += newPointOffsets[f][p];
        pointMatOffsets[f][p+1] += pointMatOffsets[f][p];
      }
      ierr = DMGetWorkArray(dm,pointMatOffsets[f][numPoints],PETSC_SCALAR,&pointMat[f]);CHKERRQ(ierr);
    }
  }
  else {
    for (p = 0; p < numPoints; p++) {
      PetscInt b    = points[2*p];
      PetscInt bDof = 0;

      if (b >= aStart && b < aEnd) {
        ierr = PetscSectionGetDof(aSec, b, &bDof);CHKERRQ(ierr);
      }
      if (bDof) {
        PetscInt dof, bOff, q, allDof = 0;

        ierr = PetscSectionGetDof(section, b, &dof);CHKERRQ(ierr);
        ierr = PetscSectionGetOffset(aSec, b, &bOff);CHKERRQ(ierr);
        for (q = 0; q < bDof; q++) {
          PetscInt a = anchors[bOff + q], aDof;

          ierr    = PetscSectionGetDof(section, a, &aDof);CHKERRQ(ierr);
          allDof += aDof;
        }
        newPointOffsets[0][p+1] = allDof;
        pointMatOffsets[0][p+1] = dof * allDof;
      }
      else {
        PetscInt dof;

        ierr = PetscSectionGetDof(section, b, &dof);CHKERRQ(ierr);
        newPointOffsets[0][p+1] = dof;
        pointMatOffsets[0][p+1] = 0;
      }
    }
    newPointOffsets[0][0] = 0;
    pointMatOffsets[0][0] = 0;
    for (p = 0; p < numPoints; p++) {
      newPointOffsets[0][p+1] += newPointOffsets[0][p];
      pointMatOffsets[0][p+1] += pointMatOffsets[0][p];
    }
    ierr = DMGetWorkArray(dm,pointMatOffsets[0][numPoints],PETSC_SCALAR,&pointMat[0]);CHKERRQ(ierr);
  }

  /* get the point-to-point matrices; construct newPoints */
  ierr = PetscSectionGetMaxDof(aSec, &maxAnchor);CHKERRQ(ierr);
  ierr = PetscSectionGetMaxDof(section, &maxDof);CHKERRQ(ierr);
  ierr = DMGetWorkArray(dm,maxDof,PETSC_INT,&indices);CHKERRQ(ierr);
  ierr = DMGetWorkArray(dm,maxAnchor*maxDof,PETSC_INT,&newIndices);CHKERRQ(ierr);
  if (numFields) {
    for (p = 0, newP = 0; p < numPoints; p++) {
      PetscInt b    = points[2*p];
      PetscInt o    = points[2*p+1];
      PetscInt bDof = 0;

      if (b >= aStart && b < aEnd) {
        ierr = PetscSectionGetDof(aSec, b, &bDof);CHKERRQ(ierr);
      }
      if (bDof) {
        PetscInt fStart[32], fEnd[32], fAnchorStart[32], fAnchorEnd[32], bOff, q;

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

          ierr        = PetscSectionGetFieldDof(cSec, b, f, &fDof);CHKERRQ(ierr);
          fStart[f+1] = fStart[f] + fDof;
          fEnd[f+1]   = fStart[f+1];
        }
        ierr = PetscSectionGetOffset(cSec, b, &bOff);CHKERRQ(ierr);
        ierr = indicesPointFields_private(cSec, b, bOff, fEnd, PETSC_TRUE, o, indices);CHKERRQ(ierr);

        fAnchorStart[0] = 0;
        fAnchorEnd[0]   = 0;
        for (f = 0; f < numFields; f++) {
          PetscInt fDof = newPointOffsets[f][p + 1] - newPointOffsets[f][p];

          fAnchorStart[f+1] = fAnchorStart[f] + fDof;
          fAnchorEnd[f+1]   = fAnchorStart[f + 1];
        }
        ierr = PetscSectionGetOffset (aSec, b, &bOff);CHKERRQ(ierr);
        for (q = 0; q < bDof; q++) {
          PetscInt a = anchors[bOff + q], aOff;

          /* we take the orientation of ap into account in the order that we constructed the indices above: the newly added points have no orientation */
          newPoints[2*(newP + q)]     = a;
          newPoints[2*(newP + q) + 1] = 0;
          ierr = PetscSectionGetOffset(section, a, &aOff);
          ierr = indicesPointFields_private(section, a, aOff, fAnchorEnd, PETSC_TRUE, 0, newIndices);CHKERRQ(ierr);
        }
        newP += bDof;

        /* get the point-to-point submatrix */
        for (f = 0; f < numFields; f++) {
          ierr = MatGetValues(cMat,fEnd[f]-fStart[f],indices + fStart[f],fAnchorEnd[f] - fAnchorStart[f],newIndices + fAnchorStart[f],pointMat[f] + pointMatOffsets[f][p]);CHKERRQ(ierr);
        }
      }
      else {
        newPoints[2 * newP]     = b;
        newPoints[2 * newP + 1] = o;
        newP++;
      }
    }
  } else {
    for (p = 0; p < numPoints; p++) {
      PetscInt b    = points[2*p];
      PetscInt o    = points[2*p+1];
      PetscInt bDof = 0;

      if (b >= aStart && b < aEnd) {
        ierr = PetscSectionGetDof(aSec, b, &bDof);CHKERRQ(ierr);
      }
      if (bDof) {
        PetscInt bEnd = 0, bAnchorEnd = 0, bOff;

        ierr = PetscSectionGetOffset(cSec, b, &bOff);CHKERRQ(ierr);
        ierr = indicesPoint_private(cSec, b, bOff, &bEnd, PETSC_TRUE, o, indices);CHKERRQ(ierr);

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

          /* we take the orientation of ap into account in the order that we constructed the indices above: the newly added points have no orientation */

          newPoints[2*(newP + q)]     = a;
          newPoints[2*(newP + q) + 1] = 0;
          ierr = PetscSectionGetOffset(section, a, &aOff);
          ierr = indicesPoint_private(section, a, aOff, &bAnchorEnd, PETSC_TRUE, 0, newIndices);CHKERRQ(ierr);
        }
        newP += bDof;

        /* get the point-to-point submatrix */
        ierr = MatGetValues(cMat,bEnd,indices,bAnchorEnd,newIndices,pointMat[0] + pointMatOffsets[0][p]);CHKERRQ(ierr);
      }
      else {
        newPoints[2 * newP]     = b;
        newPoints[2 * newP + 1] = o;
        newP++;
      }
    }
  }

  ierr = PetscMemzero(tmpValues,newNumIndices*numIndices*sizeof(*tmpValues));CHKERRQ(ierr);
  /* multiply constraints on the right */
  if (numFields) {
    for (f = 0; f < numFields; f++) {
      PetscInt oldOff = offsets[f];

      for (p = 0; p < numPoints; p++) {
        PetscInt cStart = newPointOffsets[f][p];
        PetscInt b      = points[2 * p];
        PetscInt c, r, k;
        PetscInt dof;

        ierr = PetscSectionGetFieldDof(section,b,f,&dof);CHKERRQ(ierr);
        if (pointMatOffsets[f][p] < pointMatOffsets[f][p + 1]) {
          PetscInt nCols         = newPointOffsets[f][p+1]-cStart;
          const PetscScalar *mat = pointMat[f] + pointMatOffsets[f][p];

          for (r = 0; r < numIndices; r++) {
            for (c = 0; c < nCols; c++) {
              for (k = 0; k < dof; k++) {
                tmpValues[r * newNumIndices + cStart + c] += mat[k * nCols + c] * values[r * numIndices + oldOff + k];
              }
            }
          }
        }
        else {
          /* copy this column as is */
          for (r = 0; r < numIndices; r++) {
            for (c = 0; c < dof; c++) {
              tmpValues[r * newNumIndices + cStart + c] = values[r * numIndices + oldOff + c];
            }
          }
        }
        oldOff += dof;
      }
    }
  }
  else {
    PetscInt oldOff = 0;
    for (p = 0; p < numPoints; p++) {
      PetscInt cStart = newPointOffsets[0][p];
      PetscInt b      = points[2 * p];
      PetscInt c, r, k;
      PetscInt dof;

      ierr = PetscSectionGetDof(section,b,&dof);CHKERRQ(ierr);
      if (pointMatOffsets[0][p] < pointMatOffsets[0][p + 1]) {
        PetscInt nCols         = newPointOffsets[0][p+1]-cStart;
        const PetscScalar *mat = pointMat[0] + pointMatOffsets[0][p];

        for (r = 0; r < numIndices; r++) {
          for (c = 0; c < nCols; c++) {
            for (k = 0; k < dof; k++) {
              tmpValues[r * newNumIndices + cStart + c] += mat[k * nCols + c] * values[r * numIndices + oldOff + k];
            }
          }
        }
      }
      else {
        /* copy this column as is */
        for (r = 0; r < numIndices; r++) {
          for (c = 0; c < dof; c++) {
            tmpValues[r * newNumIndices + cStart + c] = values[r * numIndices + oldOff + c];
          }
        }
      }
      oldOff += dof;
    }
  }

  ierr = PetscMemzero(newValues,newNumIndices*newNumIndices*sizeof(*newValues));CHKERRQ(ierr);
  /* multiply constraints transpose on the left */
  if (numFields) {
    for (f = 0; f < numFields; f++) {
      PetscInt oldOff = offsets[f];

      for (p = 0; p < numPoints; p++) {
        PetscInt rStart = newPointOffsets[f][p];
        PetscInt b      = points[2 * p];
        PetscInt c, r, k;
        PetscInt dof;

        ierr = PetscSectionGetFieldDof(section,b,f,&dof);CHKERRQ(ierr);
        if (pointMatOffsets[f][p] < pointMatOffsets[f][p + 1]) {
          PetscInt nRows                        = newPointOffsets[f][p+1]-rStart;
          const PetscScalar *PETSC_RESTRICT mat = pointMat[f] + pointMatOffsets[f][p];

          for (r = 0; r < nRows; r++) {
            for (c = 0; c < newNumIndices; c++) {
              for (k = 0; k < dof; k++) {
                newValues[(rStart + r) * newNumIndices + c] += mat[k * nRows + r] * tmpValues[(oldOff + k) * newNumIndices + c];
              }
            }
          }
        }
        else {
          /* copy this row as is */
          for (r = 0; r < dof; r++) {
            for (c = 0; c < newNumIndices; c++) {
              newValues[(rStart + r) * newNumIndices + c] = tmpValues[(oldOff + r) * newNumIndices + c];
            }
          }
        }
        oldOff += dof;
      }
    }
  }
  else {
    PetscInt oldOff = 0;

    for (p = 0; p < numPoints; p++) {
      PetscInt rStart = newPointOffsets[0][p];
      PetscInt b      = points[2 * p];
      PetscInt c, r, k;
      PetscInt dof;

      ierr = PetscSectionGetDof(section,b,&dof);CHKERRQ(ierr);
      if (pointMatOffsets[0][p] < pointMatOffsets[0][p + 1]) {
        PetscInt nRows                        = newPointOffsets[0][p+1]-rStart;
        const PetscScalar *PETSC_RESTRICT mat = pointMat[0] + pointMatOffsets[0][p];

        for (r = 0; r < nRows; r++) {
          for (c = 0; c < newNumIndices; c++) {
            for (k = 0; k < dof; k++) {
              newValues[(rStart + r) * newNumIndices + c] += mat[k * nRows + r] * tmpValues[(oldOff + k) * newNumIndices + c];
            }
          }
        }
      }
      else {
        /* copy this row as is */
        for (r = 0; r < dof; c++) {
          for (c = 0; c < newNumIndices; c++) {
            newValues[(rStart + r) * newNumIndices + c] = tmpValues[(oldOff + r) * newNumIndices + c];
          }
        }
      }
      oldOff += dof;
    }
  }

  /* clean up */
  ierr = DMRestoreWorkArray(dm,maxDof,PETSC_INT,&indices);CHKERRQ(ierr);
  ierr = DMRestoreWorkArray(dm,maxAnchor*maxDof,PETSC_INT,&newIndices);CHKERRQ(ierr);
  if (numFields) {
    for (f = 0; f < numFields; f++) {
      ierr = DMRestoreWorkArray(dm,pointMatOffsets[f][numPoints],PETSC_SCALAR,&pointMat[f]);CHKERRQ(ierr);
      ierr = DMRestoreWorkArray(dm,numPoints+1,PETSC_INT,&pointMatOffsets[f]);CHKERRQ(ierr);
      ierr = DMRestoreWorkArray(dm,numPoints+1,PETSC_INT,&newPointOffsets[f]);CHKERRQ(ierr);
    }
  }
  else {
    ierr = DMRestoreWorkArray(dm,pointMatOffsets[0][numPoints],PETSC_SCALAR,&pointMat[0]);CHKERRQ(ierr);
    ierr = DMRestoreWorkArray(dm,numPoints+1,PETSC_INT,&pointMatOffsets[0]);CHKERRQ(ierr);
    ierr = DMRestoreWorkArray(dm,numPoints+1,PETSC_INT,&newPointOffsets[0]);CHKERRQ(ierr);
  }
  ierr = DMRestoreWorkArray(dm,newNumIndices*numIndices,PETSC_SCALAR,&tmpValues);CHKERRQ(ierr);
  ierr = ISRestoreIndices(aIS,&anchors);CHKERRQ(ierr);

  /* output */
  *outNumPoints  = newNumPoints;
  *outNumIndices = newNumIndices;
  *outPoints     = newPoints;
  *outValues     = newValues;
  for (f = 0; f < numFields; f++) {
    offsets[f] = newOffsets[f];
  }
  PetscFunctionReturn(0);
}

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

  Not collective

  Input Parameters:
+ dm - The DM
. section - The section describing the layout in v, or NULL to use the default section
. globalSection - The section describing the layout in v, or NULL to use the default global section
. A - The matrix
. point - The sieve point in the DM
. values - The array of values
- mode - The insert mode, where INSERT_ALL_VALUES and ADD_ALL_VALUES also overwrite boundary conditions

  Fortran Notes:
  This routine is only available in Fortran 90, and you must include petsc.h90 in your code.

  Level: intermediate

.seealso DMPlexVecGetClosure(), DMPlexVecSetClosure()
@*/
PetscErrorCode DMPlexMatSetClosure(DM dm, PetscSection section, PetscSection globalSection, Mat A, PetscInt point, const PetscScalar values[], InsertMode mode)
{
  DM_Plex        *mesh   = (DM_Plex*) dm->data;
  PetscSection    clSection;
  IS              clPoints;
  PetscInt       *points = NULL, *newPoints;
  const PetscInt *clp;
  PetscInt       *indices;
  PetscInt        offsets[32];
  PetscInt        numFields, numPoints, newNumPoints, numIndices, newNumIndices, dof, off, globalOff, pStart, pEnd, p, q, f;
  PetscScalar    *newValues;
  PetscErrorCode  ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (!section) {ierr = DMGetDefaultSection(dm, &section);CHKERRQ(ierr);}
  PetscValidHeaderSpecific(section, PETSC_SECTION_CLASSID, 2);
  if (!globalSection) {ierr = DMGetDefaultGlobalSection(dm, &globalSection);CHKERRQ(ierr);}
  PetscValidHeaderSpecific(globalSection, PETSC_SECTION_CLASSID, 3);
  PetscValidHeaderSpecific(A, MAT_CLASSID, 4);
  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 = PetscSectionGetClosureIndex(section, (PetscObject) dm, &clSection, &clPoints);CHKERRQ(ierr);
  if (!clPoints) {
    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;
  } else {
    PetscInt dof, off;

    ierr = PetscSectionGetDof(clSection, point, &dof);CHKERRQ(ierr);
    numPoints = dof/2;
    ierr = PetscSectionGetOffset(clSection, point, &off);CHKERRQ(ierr);
    ierr = ISGetIndices(clPoints, &clp);CHKERRQ(ierr);
    points = (PetscInt *) &clp[off];
  }
  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 = DMPlexConstraintsModifyMat(dm,section,numPoints,numIndices,points,values,&newNumPoints,&newNumIndices,&newPoints,&newValues,offsets);CHKERRQ(ierr);
  if (newNumPoints) {
    if (!clPoints) {
      ierr = DMPlexRestoreTransitiveClosure(dm, point, PETSC_TRUE, &numPoints, &points);CHKERRQ(ierr);
    } else {
      ierr = ISRestoreIndices(clPoints, &clp);CHKERRQ(ierr);
    }
    numPoints  = newNumPoints;
    numIndices = newNumIndices;
    points     = newPoints;
    values     = newValues;
  }
  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 (mesh->printSetValues) {ierr = DMPlexPrintMatSetValues(PETSC_VIEWER_STDOUT_SELF, A, point, numIndices, indices, 0, NULL, 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, 0, NULL, values);CHKERRQ(ierr2);
    ierr2 = DMRestoreWorkArray(dm, numIndices, PETSC_INT, &indices);CHKERRQ(ierr2);
    CHKERRQ(ierr);
  }
  if (newNumPoints) {
    ierr = DMRestoreWorkArray(dm,newNumIndices*newNumIndices,PETSC_SCALAR,&newValues);CHKERRQ(ierr);
    ierr = DMRestoreWorkArray(dm,2*newNumPoints,PETSC_INT,&newPoints);CHKERRQ(ierr);
  }
  else {
    if (!clPoints) {
      ierr = DMPlexRestoreTransitiveClosure(dm, point, PETSC_TRUE, &numPoints, &points);CHKERRQ(ierr);
    } else {
      ierr = ISRestoreIndices(clPoints, &clp);CHKERRQ(ierr);
    }
  }
  ierr = DMRestoreWorkArray(dm, numIndices, PETSC_INT, &indices);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexMatSetClosureRefined"
PetscErrorCode DMPlexMatSetClosureRefined(DM dmf, PetscSection fsection, PetscSection globalFSection, DM dmc, PetscSection csection, PetscSection globalCSection, Mat A, PetscInt point, const PetscScalar values[], InsertMode mode)
{
  DM_Plex        *mesh   = (DM_Plex*) dmf->data;
  PetscInt       *fpoints = NULL, *ftotpoints = NULL;
  PetscInt       *cpoints = NULL;
  PetscInt       *findices, *cindices;
  PetscInt        foffsets[32], coffsets[32];
  CellRefiner     cellRefiner;
  PetscInt        numFields, numSubcells, maxFPoints, numFPoints, numCPoints, numFIndices, numCIndices, dof, off, globalOff, pStart, pEnd, p, q, r, s, f;
  PetscErrorCode  ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dmf, DM_CLASSID, 1);
  PetscValidHeaderSpecific(dmc, DM_CLASSID, 4);
  if (!fsection) {ierr = DMGetDefaultSection(dmf, &fsection);CHKERRQ(ierr);}
  PetscValidHeaderSpecific(fsection, PETSC_SECTION_CLASSID, 2);
  if (!csection) {ierr = DMGetDefaultSection(dmc, &csection);CHKERRQ(ierr);}
  PetscValidHeaderSpecific(csection, PETSC_SECTION_CLASSID, 5);
  if (!globalFSection) {ierr = DMGetDefaultGlobalSection(dmf, &globalFSection);CHKERRQ(ierr);}
  PetscValidHeaderSpecific(globalFSection, PETSC_SECTION_CLASSID, 3);
  if (!globalCSection) {ierr = DMGetDefaultGlobalSection(dmc, &globalCSection);CHKERRQ(ierr);}
  PetscValidHeaderSpecific(globalCSection, PETSC_SECTION_CLASSID, 6);
  PetscValidHeaderSpecific(A, MAT_CLASSID, 7);
  ierr = PetscSectionGetNumFields(fsection, &numFields);CHKERRQ(ierr);
  if (numFields > 31) SETERRQ1(PetscObjectComm((PetscObject)dmf), PETSC_ERR_ARG_OUTOFRANGE, "Number of fields %D limited to 31", numFields);
  ierr = PetscMemzero(foffsets, 32 * sizeof(PetscInt));CHKERRQ(ierr);
  ierr = PetscMemzero(coffsets, 32 * sizeof(PetscInt));CHKERRQ(ierr);
  /* Column indices */
  ierr = DMPlexGetTransitiveClosure(dmc, point, PETSC_TRUE, &numCPoints, &cpoints);CHKERRQ(ierr);
  maxFPoints = numCPoints;
  /* Compress out points not in the section */
  /*   TODO: Squeeze out points with 0 dof as well */
  ierr = PetscSectionGetChart(csection, &pStart, &pEnd);CHKERRQ(ierr);
  for (p = 0, q = 0; p < numCPoints*2; p += 2) {
    if ((cpoints[p] >= pStart) && (cpoints[p] < pEnd)) {
      cpoints[q*2]   = cpoints[p];
      cpoints[q*2+1] = cpoints[p+1];
      ++q;
    }
  }
  numCPoints = q;
  for (p = 0, numCIndices = 0; p < numCPoints*2; p += 2) {
    PetscInt fdof;

    ierr = PetscSectionGetDof(csection, cpoints[p], &dof);CHKERRQ(ierr);
    if (!dof) continue;
    for (f = 0; f < numFields; ++f) {
      ierr           = PetscSectionGetFieldDof(csection, cpoints[p], f, &fdof);CHKERRQ(ierr);
      coffsets[f+1] += fdof;
    }
    numCIndices += dof;
  }
  for (f = 1; f < numFields; ++f) coffsets[f+1] += coffsets[f];
  /* Row indices */
  ierr = DMPlexGetCellRefiner_Internal(dmc, &cellRefiner);CHKERRQ(ierr);
  ierr = CellRefinerGetAffineTransforms_Internal(cellRefiner, &numSubcells, NULL, NULL, NULL);CHKERRQ(ierr);
  ierr = DMGetWorkArray(dmf, maxFPoints*2*numSubcells, PETSC_INT, &ftotpoints);CHKERRQ(ierr);
  for (r = 0, q = 0; r < numSubcells; ++r) {
    /* TODO Map from coarse to fine cells */
    ierr = DMPlexGetTransitiveClosure(dmf, point*numSubcells + r, PETSC_TRUE, &numFPoints, &fpoints);CHKERRQ(ierr);
    /* Compress out points not in the section */
    ierr = PetscSectionGetChart(fsection, &pStart, &pEnd);CHKERRQ(ierr);
    for (p = 0; p < numFPoints*2; p += 2) {
      if ((fpoints[p] >= pStart) && (fpoints[p] < pEnd)) {
        ierr = PetscSectionGetDof(fsection, fpoints[p], &dof);CHKERRQ(ierr);
        if (!dof) continue;
        for (s = 0; s < q; ++s) if (fpoints[p] == ftotpoints[s*2]) break;
        if (s < q) continue;
        ftotpoints[q*2]   = fpoints[p];
        ftotpoints[q*2+1] = fpoints[p+1];
        ++q;
      }
    }
    ierr = DMPlexRestoreTransitiveClosure(dmf, point, PETSC_TRUE, &numFPoints, &fpoints);CHKERRQ(ierr);
  }
  numFPoints = q;
  for (p = 0, numFIndices = 0; p < numFPoints*2; p += 2) {
    PetscInt fdof;

    ierr = PetscSectionGetDof(fsection, ftotpoints[p], &dof);CHKERRQ(ierr);
    if (!dof) continue;
    for (f = 0; f < numFields; ++f) {
      ierr           = PetscSectionGetFieldDof(fsection, ftotpoints[p], f, &fdof);CHKERRQ(ierr);
      foffsets[f+1] += fdof;
    }
    numFIndices += dof;
  }
  for (f = 1; f < numFields; ++f) foffsets[f+1] += foffsets[f];

  if (numFields && foffsets[numFields] != numFIndices) SETERRQ2(PetscObjectComm((PetscObject)dmf), PETSC_ERR_PLIB, "Invalid size for closure %d should be %d", foffsets[numFields], numFIndices);
  if (numFields && coffsets[numFields] != numCIndices) SETERRQ2(PetscObjectComm((PetscObject)dmc), PETSC_ERR_PLIB, "Invalid size for closure %d should be %d", coffsets[numFields], numCIndices);
  ierr = DMGetWorkArray(dmf, numFIndices, PETSC_INT, &findices);CHKERRQ(ierr);
  ierr = DMGetWorkArray(dmc, numCIndices, PETSC_INT, &cindices);CHKERRQ(ierr);
  if (numFields) {
    for (p = 0; p < numFPoints*2; p += 2) {
      PetscInt o = ftotpoints[p+1];
      ierr = PetscSectionGetOffset(globalFSection, ftotpoints[p], &globalOff);CHKERRQ(ierr);
      indicesPointFields_private(fsection, ftotpoints[p], globalOff < 0 ? -(globalOff+1) : globalOff, foffsets, PETSC_FALSE, o, findices);
    }
    for (p = 0; p < numCPoints*2; p += 2) {
      PetscInt o = cpoints[p+1];
      ierr = PetscSectionGetOffset(globalCSection, cpoints[p], &globalOff);CHKERRQ(ierr);
      indicesPointFields_private(csection, cpoints[p], globalOff < 0 ? -(globalOff+1) : globalOff, coffsets, PETSC_FALSE, o, cindices);
    }
  } else {
    for (p = 0, off = 0; p < numFPoints*2; p += 2) {
      PetscInt o = ftotpoints[p+1];
      ierr = PetscSectionGetOffset(globalFSection, ftotpoints[p], &globalOff);CHKERRQ(ierr);
      indicesPoint_private(fsection, ftotpoints[p], globalOff < 0 ? -(globalOff+1) : globalOff, &off, PETSC_FALSE, o, findices);
    }
    for (p = 0, off = 0; p < numCPoints*2; p += 2) {
      PetscInt o = cpoints[p+1];
      ierr = PetscSectionGetOffset(globalCSection, cpoints[p], &globalOff);CHKERRQ(ierr);
      indicesPoint_private(csection, cpoints[p], globalOff < 0 ? -(globalOff+1) : globalOff, &off, PETSC_FALSE, o, cindices);
    }
  }
  if (mesh->printSetValues) {ierr = DMPlexPrintMatSetValues(PETSC_VIEWER_STDOUT_SELF, A, point, numFIndices, findices, numCIndices, cindices, values);CHKERRQ(ierr);}
  ierr = MatSetValues(A, numFIndices, findices, numCIndices, cindices, 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, numFIndices, findices, numCIndices, cindices, values);CHKERRQ(ierr2);
    ierr2 = DMRestoreWorkArray(dmf, numFIndices, PETSC_INT, &findices);CHKERRQ(ierr2);
    ierr2 = DMRestoreWorkArray(dmc, numCIndices, PETSC_INT, &cindices);CHKERRQ(ierr2);
    CHKERRQ(ierr);
  }
  ierr = DMRestoreWorkArray(dmf, numCPoints*2*4, PETSC_INT, &ftotpoints);CHKERRQ(ierr);
  ierr = DMPlexRestoreTransitiveClosure(dmc, point, PETSC_TRUE, &numCPoints, &cpoints);CHKERRQ(ierr);
  ierr = DMRestoreWorkArray(dmf, numFIndices, PETSC_INT, &findices);CHKERRQ(ierr);
  ierr = DMRestoreWorkArray(dmc, numCIndices, PETSC_INT, &cindices);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexMatGetClosureIndicesRefined"
PetscErrorCode DMPlexMatGetClosureIndicesRefined(DM dmf, PetscSection fsection, PetscSection globalFSection, DM dmc, PetscSection csection, PetscSection globalCSection, PetscInt point, PetscInt cindices[], PetscInt findices[])
{
  PetscInt      *fpoints = NULL, *ftotpoints = NULL;
  PetscInt      *cpoints = NULL;
  PetscInt       foffsets[32], coffsets[32];
  CellRefiner    cellRefiner;
  PetscInt       numFields, numSubcells, maxFPoints, numFPoints, numCPoints, numFIndices, numCIndices, dof, off, globalOff, pStart, pEnd, p, q, r, s, f;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dmf, DM_CLASSID, 1);
  PetscValidHeaderSpecific(dmc, DM_CLASSID, 4);
  if (!fsection) {ierr = DMGetDefaultSection(dmf, &fsection);CHKERRQ(ierr);}
  PetscValidHeaderSpecific(fsection, PETSC_SECTION_CLASSID, 2);
  if (!csection) {ierr = DMGetDefaultSection(dmc, &csection);CHKERRQ(ierr);}
  PetscValidHeaderSpecific(csection, PETSC_SECTION_CLASSID, 5);
  if (!globalFSection) {ierr = DMGetDefaultGlobalSection(dmf, &globalFSection);CHKERRQ(ierr);}
  PetscValidHeaderSpecific(globalFSection, PETSC_SECTION_CLASSID, 3);
  if (!globalCSection) {ierr = DMGetDefaultGlobalSection(dmc, &globalCSection);CHKERRQ(ierr);}
  PetscValidHeaderSpecific(globalCSection, PETSC_SECTION_CLASSID, 6);
  ierr = PetscSectionGetNumFields(fsection, &numFields);CHKERRQ(ierr);
  if (numFields > 31) SETERRQ1(PetscObjectComm((PetscObject)dmf), PETSC_ERR_ARG_OUTOFRANGE, "Number of fields %D limited to 31", numFields);
  ierr = PetscMemzero(foffsets, 32 * sizeof(PetscInt));CHKERRQ(ierr);
  ierr = PetscMemzero(coffsets, 32 * sizeof(PetscInt));CHKERRQ(ierr);
  /* Column indices */
  ierr = DMPlexGetTransitiveClosure(dmc, point, PETSC_TRUE, &numCPoints, &cpoints);CHKERRQ(ierr);
  maxFPoints = numCPoints;
  /* Compress out points not in the section */
  /*   TODO: Squeeze out points with 0 dof as well */
  ierr = PetscSectionGetChart(csection, &pStart, &pEnd);CHKERRQ(ierr);
  for (p = 0, q = 0; p < numCPoints*2; p += 2) {
    if ((cpoints[p] >= pStart) && (cpoints[p] < pEnd)) {
      cpoints[q*2]   = cpoints[p];
      cpoints[q*2+1] = cpoints[p+1];
      ++q;
    }
  }
  numCPoints = q;
  for (p = 0, numCIndices = 0; p < numCPoints*2; p += 2) {
    PetscInt fdof;

    ierr = PetscSectionGetDof(csection, cpoints[p], &dof);CHKERRQ(ierr);
    if (!dof) continue;
    for (f = 0; f < numFields; ++f) {
      ierr           = PetscSectionGetFieldDof(csection, cpoints[p], f, &fdof);CHKERRQ(ierr);
      coffsets[f+1] += fdof;
    }
    numCIndices += dof;
  }
  for (f = 1; f < numFields; ++f) coffsets[f+1] += coffsets[f];
  /* Row indices */
  ierr = DMPlexGetCellRefiner_Internal(dmc, &cellRefiner);CHKERRQ(ierr);
  ierr = CellRefinerGetAffineTransforms_Internal(cellRefiner, &numSubcells, NULL, NULL, NULL);CHKERRQ(ierr);
  ierr = DMGetWorkArray(dmf, maxFPoints*2*numSubcells, PETSC_INT, &ftotpoints);CHKERRQ(ierr);
  for (r = 0, q = 0; r < numSubcells; ++r) {
    /* TODO Map from coarse to fine cells */
    ierr = DMPlexGetTransitiveClosure(dmf, point*numSubcells + r, PETSC_TRUE, &numFPoints, &fpoints);CHKERRQ(ierr);
    /* Compress out points not in the section */
    ierr = PetscSectionGetChart(fsection, &pStart, &pEnd);CHKERRQ(ierr);
    for (p = 0; p < numFPoints*2; p += 2) {
      if ((fpoints[p] >= pStart) && (fpoints[p] < pEnd)) {
        ierr = PetscSectionGetDof(fsection, fpoints[p], &dof);CHKERRQ(ierr);
        if (!dof) continue;
        for (s = 0; s < q; ++s) if (fpoints[p] == ftotpoints[s*2]) break;
        if (s < q) continue;
        ftotpoints[q*2]   = fpoints[p];
        ftotpoints[q*2+1] = fpoints[p+1];
        ++q;
      }
    }
    ierr = DMPlexRestoreTransitiveClosure(dmf, point, PETSC_TRUE, &numFPoints, &fpoints);CHKERRQ(ierr);
  }
  numFPoints = q;
  for (p = 0, numFIndices = 0; p < numFPoints*2; p += 2) {
    PetscInt fdof;

    ierr = PetscSectionGetDof(fsection, ftotpoints[p], &dof);CHKERRQ(ierr);
    if (!dof) continue;
    for (f = 0; f < numFields; ++f) {
      ierr           = PetscSectionGetFieldDof(fsection, ftotpoints[p], f, &fdof);CHKERRQ(ierr);
      foffsets[f+1] += fdof;
    }
    numFIndices += dof;
  }
  for (f = 1; f < numFields; ++f) foffsets[f+1] += foffsets[f];

  if (numFields && foffsets[numFields] != numFIndices) SETERRQ2(PetscObjectComm((PetscObject)dmf), PETSC_ERR_PLIB, "Invalid size for closure %d should be %d", foffsets[numFields], numFIndices);
  if (numFields && coffsets[numFields] != numCIndices) SETERRQ2(PetscObjectComm((PetscObject)dmc), PETSC_ERR_PLIB, "Invalid size for closure %d should be %d", coffsets[numFields], numCIndices);
  if (numFields) {
    for (p = 0; p < numFPoints*2; p += 2) {
      PetscInt o = ftotpoints[p+1];
      ierr = PetscSectionGetOffset(globalFSection, ftotpoints[p], &globalOff);CHKERRQ(ierr);
      indicesPointFields_private(fsection, ftotpoints[p], globalOff < 0 ? -(globalOff+1) : globalOff, foffsets, PETSC_FALSE, o, findices);
    }
    for (p = 0; p < numCPoints*2; p += 2) {
      PetscInt o = cpoints[p+1];
      ierr = PetscSectionGetOffset(globalCSection, cpoints[p], &globalOff);CHKERRQ(ierr);
      indicesPointFields_private(csection, cpoints[p], globalOff < 0 ? -(globalOff+1) : globalOff, coffsets, PETSC_FALSE, o, cindices);
    }
  } else {
    for (p = 0, off = 0; p < numFPoints*2; p += 2) {
      PetscInt o = ftotpoints[p+1];
      ierr = PetscSectionGetOffset(globalFSection, ftotpoints[p], &globalOff);CHKERRQ(ierr);
      indicesPoint_private(fsection, ftotpoints[p], globalOff < 0 ? -(globalOff+1) : globalOff, &off, PETSC_FALSE, o, findices);
    }
    for (p = 0, off = 0; p < numCPoints*2; p += 2) {
      PetscInt o = cpoints[p+1];
      ierr = PetscSectionGetOffset(globalCSection, cpoints[p], &globalOff);CHKERRQ(ierr);
      indicesPoint_private(csection, cpoints[p], globalOff < 0 ? -(globalOff+1) : globalOff, &off, PETSC_FALSE, o, cindices);
    }
  }
  ierr = DMRestoreWorkArray(dmf, numCPoints*2*4, PETSC_INT, &ftotpoints);CHKERRQ(ierr);
  ierr = DMPlexRestoreTransitiveClosure(dmc, point, PETSC_TRUE, &numCPoints, &cpoints);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetHybridBounds"
/*@
  DMPlexGetHybridBounds - Get the first mesh point of each dimension which is a hybrid

  Input Parameter:
. dm - The DMPlex object

  Output Parameters:
+ cMax - The first hybrid cell
. fMax - The first hybrid face
. eMax - The first hybrid edge
- vMax - The first hybrid vertex

  Level: developer

.seealso DMPlexCreateHybridMesh(), DMPlexSetHybridBounds()
@*/
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 = DMGetDimension(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"
/*@
  DMPlexSetHybridBounds - Set the first mesh point of each dimension which is a hybrid

  Input Parameters:
. dm   - The DMPlex object
. cMax - The first hybrid cell
. fMax - The first hybrid face
. eMax - The first hybrid edge
- vMax - The first hybrid vertex

  Level: developer

.seealso DMPlexCreateHybridMesh(), DMPlexGetHybridBounds()
@*/
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 = DMGetDimension(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 */
static PetscErrorCode DMPlexCreateNumbering_Private(DM dm, PetscInt pStart, PetscInt pEnd, PetscInt shift, PetscInt *globalSize, 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 = PetscMalloc1((pEnd - pStart), &numbers);CHKERRQ(ierr);
  for (p = pStart; p < pEnd; ++p) {
    ierr = PetscSectionGetOffset(globalSection, p, &numbers[p-pStart]);CHKERRQ(ierr);
    if (numbers[p-pStart] < 0) numbers[p-pStart] -= shift;
    else                       numbers[p-pStart] += shift;
  }
  ierr = ISCreateGeneral(PetscObjectComm((PetscObject) dm), pEnd - pStart, numbers, PETSC_OWN_POINTER, numbering);CHKERRQ(ierr);
  if (globalSize) {
    PetscLayout layout;
    ierr = PetscSectionGetPointLayout(PetscObjectComm((PetscObject) dm), globalSection, &layout);CHKERRQ(ierr);
    ierr = PetscLayoutGetSize(layout, globalSize);CHKERRQ(ierr);
    ierr = PetscLayoutDestroy(&layout);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, 0, NULL, 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, 0, NULL, dm->sf, &mesh->globalVertexNumbers);CHKERRQ(ierr);
  }
  *globalVertexNumbers = mesh->globalVertexNumbers;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexCreatePointNumbering"
PetscErrorCode DMPlexCreatePointNumbering(DM dm, IS *globalPointNumbers)
{
  IS             nums[4];
  PetscInt       depths[4];
  PetscInt       depth, d, shift = 0;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
  depths[0] = depth; depths[1] = 0;
  for (d = 2; d <= depth; ++d) depths[d] = depth-d+1;
  for (d = 0; d <= depth; ++d) {
    PetscInt pStart, pEnd, gsize;

    ierr = DMPlexGetDepthStratum(dm, depths[d], &pStart, &pEnd);CHKERRQ(ierr);
    ierr = DMPlexCreateNumbering_Private(dm, pStart, pEnd, shift, &gsize, dm->sf, &nums[d]);CHKERRQ(ierr);
    shift += gsize;
  }
  ierr = ISConcatenate(PetscObjectComm((PetscObject) dm), depth+1, nums, globalPointNumbers);
  for (d = 0; d <= depth; ++d) {ierr = ISDestroy(&nums[d]);CHKERRQ(ierr);}
  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 = NULL, *tmpOff = NULL;
  PetscInt       pStart, pEnd, p, dof, cdof, off, globalOff = 0, nroots;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscSectionCreate(PetscObjectComm((PetscObject) s), gsection);CHKERRQ(ierr);
  ierr = PetscSectionGetChart(s, &pStart, &pEnd);CHKERRQ(ierr);
  ierr = PetscSectionSetChart(*gsection, pStart, pEnd);CHKERRQ(ierr);
  ierr = PetscSFGetGraph(sf, &nroots, NULL, NULL, NULL);CHKERRQ(ierr);
  if (nroots >= 0) {
    if (nroots < pEnd-pStart) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "PetscSF nroots %d < %d section size", nroots, pEnd-pStart);
    ierr = PetscCalloc1(nroots, &neg);CHKERRQ(ierr);
    if (nroots > pEnd-pStart) {
      ierr = PetscCalloc1(nroots, &tmpOff);CHKERRQ(ierr);
    } else {
      tmpOff = &(*gsection)->atlasDof[-pStart];
    }
  }
  /* 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);}
    if (neg) neg[p] = -(dof+1);
  }
  ierr = PetscSectionSetUpBC(*gsection);CHKERRQ(ierr);
  if (nroots >= 0) {
    ierr = PetscSFBcastBegin(sf, MPIU_INT, neg, tmpOff);CHKERRQ(ierr);
    ierr = PetscSFBcastEnd(sf, MPIU_INT, neg, tmpOff);CHKERRQ(ierr);
    if (nroots > pEnd-pStart) {
      for (p = pStart; p < pEnd; ++p) {if (tmpOff[p] < 0) (*gsection)->atlasDof[p-pStart] = tmpOff[p];}
    }
  }
  /* 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, PetscObjectComm((PetscObject) s));CHKERRQ(ierr);
  globalOff -= off;
  for (p = 0, off = 0; p < pEnd-pStart; ++p) {
    (*gsection)->atlasOff[p] += globalOff;
    if (neg) neg[p] = -((*gsection)->atlasOff[p]+1);
  }
  /* Put in negative offsets for ghost points */
  if (nroots >= 0) {
    ierr = PetscSFBcastBegin(sf, MPIU_INT, neg, tmpOff);CHKERRQ(ierr);
    ierr = PetscSFBcastEnd(sf, MPIU_INT, neg, tmpOff);CHKERRQ(ierr);
    if (nroots > pEnd-pStart) {
      for (p = pStart; p < pEnd; ++p) {if (tmpOff[p] < 0) (*gsection)->atlasOff[p-pStart] = tmpOff[p];}
    }
  }
  if (nroots >= 0 && nroots > pEnd-pStart) {ierr = PetscFree(tmpOff);CHKERRQ(ierr);}
  ierr = PetscFree(neg);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexCheckSymmetry"
/*@
  DMPlexCheckSymmetry - Check that the adjacency information in the mesh is symmetric.

  Input Parameters:
  + dm - The DMPlex object

  Note: This is a useful diagnostic when creating meshes programmatically.

  Level: developer

.seealso: DMCreate(), DMCheckSkeleton(), DMCheckFaces()
@*/
PetscErrorCode DMPlexCheckSymmetry(DM dm)
{
  PetscSection    coneSection, supportSection;
  const PetscInt *cone, *support;
  PetscInt        coneSize, c, supportSize, s;
  PetscInt        pStart, pEnd, p, csize, ssize;
  PetscErrorCode  ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  ierr = DMPlexGetConeSection(dm, &coneSection);CHKERRQ(ierr);
  ierr = DMPlexGetSupportSection(dm, &supportSection);CHKERRQ(ierr);
  /* Check that point p is found in the support of its cone points, and vice versa */
  ierr = DMPlexGetChart(dm, &pStart, &pEnd);CHKERRQ(ierr);
  for (p = pStart; p < pEnd; ++p) {
    ierr = DMPlexGetConeSize(dm, p, &coneSize);CHKERRQ(ierr);
    ierr = DMPlexGetCone(dm, p, &cone);CHKERRQ(ierr);
    for (c = 0; c < coneSize; ++c) {
      PetscBool dup = PETSC_FALSE;
      PetscInt  d;
      for (d = c-1; d >= 0; --d) {
        if (cone[c] == cone[d]) {dup = PETSC_TRUE; break;}
      }
      ierr = DMPlexGetSupportSize(dm, cone[c], &supportSize);CHKERRQ(ierr);
      ierr = DMPlexGetSupport(dm, cone[c], &support);CHKERRQ(ierr);
      for (s = 0; s < supportSize; ++s) {
        if (support[s] == p) break;
      }
      if ((s >= supportSize) || (dup && (support[s+1] != p))) {
        ierr = PetscPrintf(PETSC_COMM_SELF, "p: %d cone: ", p);
        for (s = 0; s < coneSize; ++s) {
          ierr = PetscPrintf(PETSC_COMM_SELF, "%d, ", cone[s]);
        }
        ierr = PetscPrintf(PETSC_COMM_SELF, "\n");
        ierr = PetscPrintf(PETSC_COMM_SELF, "p: %d support: ", cone[c]);
        for (s = 0; s < supportSize; ++s) {
          ierr = PetscPrintf(PETSC_COMM_SELF, "%d, ", support[s]);
        }
        ierr = PetscPrintf(PETSC_COMM_SELF, "\n");
        if (dup) {
          SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Point %d not repeatedly found in support of repeated cone point %d", p, cone[c]);
        } else {
          SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Point %d not found in support of cone point %d", p, cone[c]);
        }
      }
    }
    ierr = DMPlexGetSupportSize(dm, p, &supportSize);CHKERRQ(ierr);
    ierr = DMPlexGetSupport(dm, p, &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] == p) break;
      }
      if (c >= coneSize) {
        ierr = PetscPrintf(PETSC_COMM_SELF, "p: %d support: ", p);
        for (c = 0; c < supportSize; ++c) {
          ierr = PetscPrintf(PETSC_COMM_SELF, "%d, ", support[c]);
        }
        ierr = PetscPrintf(PETSC_COMM_SELF, "\n");
        ierr = PetscPrintf(PETSC_COMM_SELF, "p: %d cone: ", support[s]);
        for (c = 0; c < coneSize; ++c) {
          ierr = PetscPrintf(PETSC_COMM_SELF, "%d, ", cone[c]);
        }
        ierr = PetscPrintf(PETSC_COMM_SELF, "\n");
        SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Point %d not found in cone of support point %d", p, support[s]);
      }
    }
  }
  ierr = PetscSectionGetStorageSize(coneSection, &csize);CHKERRQ(ierr);
  ierr = PetscSectionGetStorageSize(supportSection, &ssize);CHKERRQ(ierr);
  if (csize != ssize) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Total cone size %d != Total support size %d", csize, ssize);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexCheckSkeleton"
/*@
  DMPlexCheckSkeleton - Check that each cell has the correct number of vertices

  Input Parameters:
+ dm - The DMPlex object
. isSimplex - Are the cells simplices or tensor products
- cellHeight - Normally 0

  Note: This is a useful diagnostic when creating meshes programmatically.

  Level: developer

.seealso: DMCreate(), DMCheckSymmetry(), DMCheckFaces()
@*/
PetscErrorCode DMPlexCheckSkeleton(DM dm, PetscBool isSimplex, PetscInt cellHeight)
{
  PetscInt       dim, numCorners, numHybridCorners, vStart, vEnd, cStart, cEnd, cMax, c;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
  switch (dim) {
  case 1: numCorners = isSimplex ? 2 : 2; numHybridCorners = isSimplex ? 2 : 2; break;
  case 2: numCorners = isSimplex ? 3 : 4; numHybridCorners = isSimplex ? 4 : 4; break;
  case 3: numCorners = isSimplex ? 4 : 8; numHybridCorners = isSimplex ? 6 : 8; break;
  default:
    SETERRQ1(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_OUTOFRANGE, "Cannot handle meshes of dimension %d", dim);
  }
  ierr = DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);CHKERRQ(ierr);
  ierr = DMPlexGetHeightStratum(dm, cellHeight, &cStart, &cEnd);CHKERRQ(ierr);
  ierr = DMPlexGetHybridBounds(dm, &cMax, NULL, NULL, NULL);CHKERRQ(ierr);
  cMax = cMax >= 0 ? cMax : cEnd;
  for (c = cStart; c < cMax; ++c) {
    PetscInt *closure = NULL, closureSize, cl, coneSize = 0;

    ierr = DMPlexGetTransitiveClosure(dm, c, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
    for (cl = 0; cl < closureSize*2; cl += 2) {
      const PetscInt p = closure[cl];
      if ((p >= vStart) && (p < vEnd)) ++coneSize;
    }
    ierr = DMPlexRestoreTransitiveClosure(dm, c, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
    if (coneSize != numCorners) SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cell %d has  %d vertices != %d", c, coneSize, numCorners);
  }
  for (c = cMax; c < cEnd; ++c) {
    PetscInt *closure = NULL, closureSize, cl, coneSize = 0;

    ierr = DMPlexGetTransitiveClosure(dm, c, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
    for (cl = 0; cl < closureSize*2; cl += 2) {
      const PetscInt p = closure[cl];
      if ((p >= vStart) && (p < vEnd)) ++coneSize;
    }
    ierr = DMPlexRestoreTransitiveClosure(dm, c, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
    if (coneSize > numHybridCorners) SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Hybrid cell %d has  %d vertices > %d", c, coneSize, numHybridCorners);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexCheckFaces"
/*@
  DMPlexCheckFaces - Check that the faces of each cell give a vertex order this is consistent with what we expect from the cell type

  Input Parameters:
+ dm - The DMPlex object
. isSimplex - Are the cells simplices or tensor products
- cellHeight - Normally 0

  Note: This is a useful diagnostic when creating meshes programmatically.

  Level: developer

.seealso: DMCreate(), DMCheckSymmetry(), DMCheckSkeleton()
@*/
PetscErrorCode DMPlexCheckFaces(DM dm, PetscBool isSimplex, PetscInt cellHeight)
{
  PetscInt       pMax[4];
  PetscInt       dim, vStart, vEnd, cStart, cEnd, c, h;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
  ierr = DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);CHKERRQ(ierr);
  ierr = DMPlexGetHybridBounds(dm, &pMax[dim], &pMax[dim-1], &pMax[1], &pMax[0]);CHKERRQ(ierr);
  for (h = cellHeight; h < dim; ++h) {
    ierr = DMPlexGetHeightStratum(dm, h, &cStart, &cEnd);CHKERRQ(ierr);
    for (c = cStart; c < cEnd; ++c) {
      const PetscInt *cone, *ornt, *faces;
      PetscInt        numFaces, faceSize, coneSize,f;
      PetscInt       *closure = NULL, closureSize, cl, numCorners = 0;

      if (pMax[dim-h] >= 0 && c >= pMax[dim-h]) continue;
      ierr = DMPlexGetConeSize(dm, c, &coneSize);CHKERRQ(ierr);
      ierr = DMPlexGetCone(dm, c, &cone);CHKERRQ(ierr);
      ierr = DMPlexGetConeOrientation(dm, c, &ornt);CHKERRQ(ierr);
      ierr = DMPlexGetTransitiveClosure(dm, c, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
      for (cl = 0; cl < closureSize*2; cl += 2) {
        const PetscInt p = closure[cl];
        if ((p >= vStart) && (p < vEnd)) closure[numCorners++] = p;
      }
      ierr = DMPlexGetRawFaces_Internal(dm, dim-h, numCorners, closure, &numFaces, &faceSize, &faces);CHKERRQ(ierr);
      if (coneSize != numFaces) SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cell %d has %d faces but should have %d", c, coneSize, numFaces);
      for (f = 0; f < numFaces; ++f) {
        PetscInt *fclosure = NULL, fclosureSize, cl, fnumCorners = 0, v;

        ierr = DMPlexGetTransitiveClosure_Internal(dm, cone[f], ornt[f], PETSC_TRUE, &fclosureSize, &fclosure);CHKERRQ(ierr);
        for (cl = 0; cl < fclosureSize*2; cl += 2) {
          const PetscInt p = fclosure[cl];
          if ((p >= vStart) && (p < vEnd)) fclosure[fnumCorners++] = p;
        }
        if (fnumCorners != faceSize) SETERRQ5(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Face %d (%d) of cell %d has %d vertices but should have %d", cone[f], f, c, fnumCorners, faceSize);
        for (v = 0; v < fnumCorners; ++v) {
          if (fclosure[v] != faces[f*faceSize+v]) SETERRQ6(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Face %d (%d) of cell %d vertex %d, %d != %d", cone[f], f, c, v, fclosure[v], faces[f*faceSize+v]);
        }
        ierr = DMPlexRestoreTransitiveClosure(dm, cone[f], PETSC_TRUE, &fclosureSize, &fclosure);CHKERRQ(ierr);
      }
      ierr = DMPlexRestoreFaces_Internal(dm, dim, c, &numFaces, &faceSize, &faces);CHKERRQ(ierr);
      ierr = DMPlexRestoreTransitiveClosure(dm, c, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
    }
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMCreateInterpolation_Plex"
/* Pointwise interpolation
     Just code FEM for now
     u^f = I u^c
     sum_k u^f_k phi^f_k = I sum_j u^c_j phi^c_j
     u^f_i = sum_j psi^f_i I phi^c_j u^c_j
     I_{ij} = psi^f_i phi^c_j
*/
PetscErrorCode DMCreateInterpolation_Plex(DM dmCoarse, DM dmFine, Mat *interpolation, Vec *scaling)
{
  PetscSection   gsc, gsf;
  PetscInt       m, n;
  void          *ctx;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  /*
  Loop over coarse cells
    Loop over coarse basis functions
      Loop over fine cells in coarse cell
        Loop over fine dual basis functions
          Evaluate coarse basis on fine dual basis quad points
          Sum
          Update local element matrix
    Accumulate to interpolation matrix

   Can extend PetscFEIntegrateJacobian_Basic() to do a specialized cell loop
  */
  ierr = DMGetDefaultGlobalSection(dmFine, &gsf);CHKERRQ(ierr);
  ierr = PetscSectionGetConstrainedStorageSize(gsf, &m);CHKERRQ(ierr);
  ierr = DMGetDefaultGlobalSection(dmCoarse, &gsc);CHKERRQ(ierr);
  ierr = PetscSectionGetConstrainedStorageSize(gsc, &n);CHKERRQ(ierr);
  /* We need to preallocate properly */
  ierr = MatCreate(PetscObjectComm((PetscObject) dmCoarse), interpolation);CHKERRQ(ierr);
  ierr = MatSetSizes(*interpolation, m, n, PETSC_DETERMINE, PETSC_DETERMINE);CHKERRQ(ierr);
  ierr = MatSetType(*interpolation, dmCoarse->mattype);CHKERRQ(ierr);
  ierr = DMGetApplicationContext(dmFine, &ctx);CHKERRQ(ierr);
  ierr = DMPlexComputeInterpolatorFEM(dmCoarse, dmFine, *interpolation, ctx);CHKERRQ(ierr);
  /* Use naive scaling */
  ierr = DMCreateInterpolationScale(dmCoarse, dmFine, *interpolation, scaling);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMCreateInjection_Plex"
PetscErrorCode DMCreateInjection_Plex(DM dmCoarse, DM dmFine, VecScatter *ctx)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = DMPlexComputeInjectorFEM(dmCoarse, dmFine, ctx, NULL);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMCreateDefaultSection_Plex"
/* Pointwise interpolation
     Just code FEM for now
     u^f = I u^c
     sum_k u^f_k phi^f_k = I sum_l u^c_l phi^c_l
     u^f_i = sum_l int psi^f_i I phi^c_l u^c_l
     I_{ij} = int psi^f_i phi^c_j
*/
PetscErrorCode DMCreateDefaultSection_Plex(DM dm)
{
  PetscSection   section;
  IS            *bcPoints;
  PetscInt      *bcFields, *numComp, *numDof;
  PetscInt       depth, dim, numBd, numBC = 0, numFields, bd, bc, f;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  /* Handle boundary conditions */
  ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
  ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
  ierr = DMPlexGetNumBoundary(dm, &numBd);CHKERRQ(ierr);
  for (bd = 0; bd < numBd; ++bd) {
    PetscBool isEssential;
    ierr = DMPlexGetBoundary(dm, bd, &isEssential, NULL, NULL, NULL, NULL, NULL, NULL, NULL);CHKERRQ(ierr);
    if (isEssential) ++numBC;
  }
  ierr = PetscMalloc2(numBC,&bcFields,numBC,&bcPoints);CHKERRQ(ierr);
  for (bd = 0, bc = 0; bd < numBd; ++bd) {
    const char     *bdLabel;
    DMLabel         label;
    const PetscInt *values;
    PetscInt        bd2, field, numValues;
    PetscBool       isEssential, duplicate = PETSC_FALSE;

    ierr = DMPlexGetBoundary(dm, bd, &isEssential, NULL, &bdLabel, &field, NULL, &numValues, &values, NULL);CHKERRQ(ierr);
    if (numValues != 1) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Bug me and I will fix this");
    ierr = DMPlexGetLabel(dm, bdLabel, &label);CHKERRQ(ierr);
    /* Only want to do this for FEM, and only once */
    for (bd2 = 0; bd2 < bd; ++bd2) {
      const char *bdname;
      ierr = DMPlexGetBoundary(dm, bd2, NULL, NULL, &bdname, NULL, NULL, NULL, NULL, NULL);CHKERRQ(ierr);
      ierr = PetscStrcmp(bdname, bdLabel, &duplicate);CHKERRQ(ierr);
      if (duplicate) break;
    }
    if (!duplicate) {
      ierr = DMPlexLabelComplete(dm, label);CHKERRQ(ierr);
      ierr = DMPlexLabelAddCells(dm, label);CHKERRQ(ierr);
    }
    /* Filter out cells, if you actually want to constraint cells you need to do things by hand right now */
    if (isEssential) {
      IS              tmp;
      PetscInt       *newidx;
      const PetscInt *idx;
      PetscInt        cStart, cEnd, n, p, newn = 0;

      bcFields[bc] = field;
      ierr = DMPlexGetStratumIS(dm, bdLabel, values[0], &tmp);CHKERRQ(ierr);
      ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
      ierr = ISGetLocalSize(tmp, &n);CHKERRQ(ierr);
      ierr = ISGetIndices(tmp, &idx);CHKERRQ(ierr);
      for (p = 0; p < n; ++p) if ((idx[p] < cStart) || (idx[p] >= cEnd)) ++newn;
      ierr = PetscMalloc1(newn,&newidx);CHKERRQ(ierr);
      newn = 0;
      for (p = 0; p < n; ++p) if ((idx[p] < cStart) || (idx[p] >= cEnd)) newidx[newn++] = idx[p];
      ierr = ISCreateGeneral(PetscObjectComm((PetscObject) dm), newn, newidx, PETSC_OWN_POINTER, &bcPoints[bc++]);CHKERRQ(ierr);
      ierr = ISRestoreIndices(tmp, &idx);CHKERRQ(ierr);
      ierr = ISDestroy(&tmp);CHKERRQ(ierr);
    }
  }
  /* Handle discretization */
  ierr = DMGetNumFields(dm, &numFields);CHKERRQ(ierr);
  ierr = PetscMalloc2(numFields,&numComp,numFields*(dim+1),&numDof);CHKERRQ(ierr);
  for (f = 0; f < numFields; ++f) {
    PetscFE         fe;
    const PetscInt *numFieldDof;
    PetscInt        d;

    ierr = DMGetField(dm, f, (PetscObject *) &fe);CHKERRQ(ierr);
    ierr = PetscFEGetNumComponents(fe, &numComp[f]);CHKERRQ(ierr);
    ierr = PetscFEGetNumDof(fe, &numFieldDof);CHKERRQ(ierr);
    for (d = 0; d < dim+1; ++d) numDof[f*(dim+1)+d] = numFieldDof[d];
  }
  for (f = 0; f < numFields; ++f) {
    PetscInt d;
    for (d = 1; d < dim; ++d) {
      if ((numDof[f*(dim+1)+d] > 0) && (depth < dim)) SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Mesh must be interpolated when unknowns are specified on edges or faces.");
    }
  }
  ierr = DMPlexCreateSection(dm, dim, numFields, numComp, numDof, numBC, bcFields, bcPoints, NULL, &section);CHKERRQ(ierr);
  for (f = 0; f < numFields; ++f) {
    PetscFE     fe;
    const char *name;

    ierr = DMGetField(dm, f, (PetscObject *) &fe);CHKERRQ(ierr);
    ierr = PetscObjectGetName((PetscObject) fe, &name);CHKERRQ(ierr);
    ierr = PetscSectionSetFieldName(section, f, name);CHKERRQ(ierr);
  }
  ierr = DMSetDefaultSection(dm, section);CHKERRQ(ierr);
  ierr = PetscSectionDestroy(&section);CHKERRQ(ierr);
  for (bc = 0; bc < numBC; ++bc) {ierr = ISDestroy(&bcPoints[bc]);CHKERRQ(ierr);}
  ierr = PetscFree2(bcFields,bcPoints);CHKERRQ(ierr);
  ierr = PetscFree2(numComp,numDof);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetCoarseDM"
/*@
  DMPlexGetCoarseDM - Get the coarse mesh from which this was obtained by refinement

  Input Parameter:
. dm - The DMPlex object

  Output Parameter:
. cdm - The coarse DM

  Level: intermediate

.seealso: DMPlexSetCoarseDM()
@*/
PetscErrorCode DMPlexGetCoarseDM(DM dm, DM *cdm)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidPointer(cdm, 2);
  *cdm = ((DM_Plex *) dm->data)->coarseMesh;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexSetCoarseDM"
/*@
  DMPlexSetCoarseDM - Set the coarse mesh from which this was obtained by refinement

  Input Parameters:
+ dm - The DMPlex object
- cdm - The coarse DM

  Level: intermediate

.seealso: DMPlexGetCoarseDM()
@*/
PetscErrorCode DMPlexSetCoarseDM(DM dm, DM cdm)
{
  DM_Plex       *mesh;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (cdm) PetscValidHeaderSpecific(cdm, DM_CLASSID, 2);
  mesh = (DM_Plex *) dm->data;
  ierr = DMDestroy(&mesh->coarseMesh);CHKERRQ(ierr);
  mesh->coarseMesh = cdm;
  ierr = PetscObjectReference((PetscObject) mesh->coarseMesh);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/* constraints */
#undef __FUNCT__
#define __FUNCT__ "DMPlexGetConstraints"
/*@
  DMPlexGetConstraints - Get the layout of the local point-to-point constraints

  not collective

  Input Parameters:
. dm - The DMPlex object

  Output Parameters:
+ anchorSection - If not NULL, set to the section describing which points anchor the constrained points.
- anchorIS - If not NULL, set to the list of anchors indexed by anchorSection


  Level: intermediate

.seealso: DMPlexSetConstraints(), DMPlexGetConstraintSection(), DMPlexGetConstraintMatrix(), DMPlexSetConstraintMatrix()
@*/
PetscErrorCode DMPlexGetConstraints(DM dm, PetscSection *anchorSection, IS *anchorIS)
{
  DM_Plex *plex = (DM_Plex *)dm->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (anchorSection) *anchorSection = plex->anchorSection;
  if (anchorIS) *anchorIS = plex->anchorIS;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMGlobalToLocalHook_Plex_constraints"
static PetscErrorCode DMGlobalToLocalHook_Plex_constraints(DM dm, Vec g, InsertMode mode, Vec l, void *ctx)
{
  DM_Plex *plex = (DM_Plex *)dm->data;
  Mat cMat;
  Vec cVec;
  PetscSection section, cSec;
  PetscInt pStart, pEnd, p, dof;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  cMat = plex->constraintMat;
  if (cMat && (mode == INSERT_VALUES || mode == INSERT_ALL_VALUES || mode == INSERT_BC_VALUES)) {
    ierr = DMGetDefaultSection(dm,&section);CHKERRQ(ierr);
    cSec = plex->constraintSection;
    ierr = MatGetVecs(cMat,NULL,&cVec);CHKERRQ(ierr);
    ierr = MatMult(cMat,l,cVec);CHKERRQ(ierr);
    ierr = PetscSectionGetChart(cSec,&pStart,&pEnd);CHKERRQ(ierr);
    for (p = pStart; p < pEnd; p++) {
      ierr = PetscSectionGetDof(cSec,p,&dof);CHKERRQ(ierr);
      if (dof) {
        PetscScalar *vals;
        ierr = VecGetValuesSection(cVec,cSec,p,&vals);CHKERRQ(ierr);
        ierr = VecSetValuesSection(l,section,p,vals,INSERT_ALL_VALUES);CHKERRQ(ierr);
      }
    }
    ierr = VecDestroy(&cVec);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMLocalToGlobalHook_Plex_constraints"
static PetscErrorCode DMLocalToGlobalHook_Plex_constraints(DM dm, Vec l, InsertMode mode, Vec g, void *ctx)
{
  DM_Plex *plex = (DM_Plex *)dm->data;
  Mat cMat;
  Vec cVec;
  PetscSection section, cSec;
  PetscInt pStart, pEnd, p, dof;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  cMat = plex->constraintMat;
  if (cMat && (mode == ADD_VALUES || mode == ADD_ALL_VALUES || mode == ADD_BC_VALUES)) {
    ierr = DMGetDefaultSection(dm,&section);CHKERRQ(ierr);
    cSec = plex->constraintSection;
    ierr = MatGetVecs(cMat,NULL,&cVec);CHKERRQ(ierr);
    ierr = PetscSectionGetChart(cSec,&pStart,&pEnd);CHKERRQ(ierr);
    for (p = pStart; p < pEnd; p++) {
      ierr = PetscSectionGetDof(cSec,p,&dof);CHKERRQ(ierr);
      if (dof) {
        PetscInt d;
        PetscScalar *vals;
        ierr = VecGetValuesSection(l,section,p,&vals);CHKERRQ(ierr);
        ierr = VecSetValuesSection(cVec,cSec,p,vals,mode);CHKERRQ(ierr);
        /* for this to be the true transpose, we have to zero the values that
         * we just extracted */
        for (d = 0; d < dof; d++) {
          vals[d] = 0.;
        }
      }
    }
    ierr = MatMultTransposeAdd(cMat,cVec,l,l);CHKERRQ(ierr);
    ierr = VecDestroy(&cVec);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexSetConstraints"
/*@
  DMPlexSetConstraints - Set the layout of the local point-to-point constraints.  Unlike boundary conditions, when a
  point's degrees of freedom in a section are constrained to an outside value, the point-to-point constraints set a
  point's degrees of freedom to be a linear combination of other points' degrees of freedom.

  After specifying the layout of constraints with DMPlexSetConstraints(), one specifies the constraints by calling
  DMPlexGetConstraintMatrix() and filling in the entries.  This matrix will be used fill in the constrained values
  from the anchor values in local vectors in DMGlobalToLocalEnd() with mode = INSERT_VALUES, and its transpose is used
  to sum constrained values back to their anchor values in DMLocalToGlobalBegin() with mode = ADD_VALUES.

  logically collective

  Input Parameters:
+ dm - The DMPlex object
. anchorSection - The section that describes the mapping from constrained points to the anchor points listed in anchorIS.
- anchorIS - The list of all anchor points.

  The reference counts of anchorSection and anchorIS are incremented.


  Level: intermediate

.seealso: DMPlexGetConstraints(), DMPlexGetConstraintSection(), DMPlexGetConstraintMatrix(), DMPlexSetConstraintMatrix()
@*/
PetscErrorCode DMPlexSetConstraints(DM dm, PetscSection anchorSection, IS anchorIS)
{
  DM_Plex *plex = (DM_Plex *)dm->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);

  ierr = PetscObjectReference((PetscObject)anchorSection);CHKERRQ(ierr);
  ierr = PetscSectionDestroy(&plex->anchorSection);CHKERRQ(ierr);
  plex->anchorSection = anchorSection;

  ierr = PetscObjectReference((PetscObject)anchorIS);CHKERRQ(ierr);
  ierr = ISDestroy(&plex->anchorIS);CHKERRQ(ierr);
  plex->anchorIS = anchorIS;

#if defined(PETSC_USE_DEBUG)
  if (anchorIS && anchorSection) {
    PetscInt size, a, pStart, pEnd;
    const PetscInt *anchors;

    ierr = PetscSectionGetChart(anchorSection,&pStart,&pEnd);CHKERRQ(ierr);
    ierr = ISGetLocalSize(anchorIS,&size);CHKERRQ(ierr);
    ierr = ISGetIndices(anchorIS,&anchors);CHKERRQ(ierr);
    for (a = 0; a < size; a++) {
      PetscInt p;

      p = anchors[a];
      if (p >= pStart && p < pEnd) {
        PetscInt dof;

        ierr = PetscSectionGetDof(anchorSection,p,&dof);CHKERRQ(ierr);
        if (dof) {
          PetscErrorCode ierr2;

          ierr2 = ISRestoreIndices(anchorIS,&anchors);CHKERRQ(ierr2);
          SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Point %d cannot be constrained and an anchor",p);
        }
      }
    }
    ierr = ISRestoreIndices(anchorIS,&anchors);CHKERRQ(ierr);
  }
#endif

  ierr = PetscSectionDestroy(&plex->constraintSection);CHKERRQ(ierr);
  ierr = MatDestroy(&plex->constraintMat);CHKERRQ(ierr);

  if (anchorSection) {
    /* add the constraint hooks if they have not already been added */
    {
      DMGlobalToLocalHookLink link,next=NULL;
      for (link=dm->gtolhook; link; link=next) {
        next = link->next;
        if (link->endhook == DMGlobalToLocalHook_Plex_constraints) {
          break;
        }
      }
      if (!link) {
        ierr = DMGlobalToLocalHookAdd(dm,NULL,DMGlobalToLocalHook_Plex_constraints,NULL);CHKERRQ(ierr);
      }
    }
    {
      DMLocalToGlobalHookLink link,next=NULL;
      for (link=dm->ltoghook; link; link=next) {
        next = link->next;
        if (link->beginhook == DMLocalToGlobalHook_Plex_constraints) {
          break;
        }
      }
      if (!link) {
        ierr = DMLocalToGlobalHookAdd(dm,DMLocalToGlobalHook_Plex_constraints,NULL,NULL);CHKERRQ(ierr);
      }
    }
  }
  else {
    /* remove the constraint hooks if they were added before */
    {
      DMGlobalToLocalHookLink prev=NULL,link,next=NULL;
      for (link=dm->gtolhook; link; link=next) {
        next = link->next;
        if (link->endhook == DMGlobalToLocalHook_Plex_constraints) {
          break;
        }
      }
      if (link) {
        ierr = PetscFree(link);CHKERRQ(ierr);
        if (prev) {
          prev->next = next;
        }
        else {
          dm->gtolhook = next;
        }
      }
    }
    {
      DMLocalToGlobalHookLink prev=NULL,link,next=NULL;
      for (link=dm->ltoghook; link; link=next) {
        next = link->next;
        if (link->beginhook == DMLocalToGlobalHook_Plex_constraints) {
          break;
        }
      }
      if (link) {
        ierr = PetscFree(link);CHKERRQ(ierr);
        if (prev) {
          prev->next = next;
        }
        else {
          dm->ltoghook = next;
        }
      }
    }
  }

  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexCreateConstraintSection"
static PetscErrorCode DMPlexCreateConstraintSection(DM dm, PetscSection *cSec)
{
  DM_Plex *plex = (DM_Plex *)dm->data;
  PetscSection section, anchorSection;
  PetscInt pStart, pEnd, p, dof, numFields, f;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  anchorSection = plex->anchorSection;
  ierr = DMGetDefaultSection(dm,&section);CHKERRQ(ierr);
  ierr = PetscSectionCreate(PetscObjectComm((PetscObject)section),cSec);CHKERRQ(ierr);
  ierr = PetscSectionGetNumFields(section,&numFields);CHKERRQ(ierr);
  ierr = PetscSectionSetNumFields(*cSec,numFields);CHKERRQ(ierr);
  ierr = PetscSectionGetChart(anchorSection,&pStart,&pEnd);CHKERRQ(ierr);
  ierr = PetscSectionSetChart(*cSec,pStart,pEnd);CHKERRQ(ierr);
  for (p = pStart; p < pEnd; p++) {
    ierr = PetscSectionGetDof(anchorSection,p,&dof);CHKERRQ(ierr);
    if (dof) {
      ierr = PetscSectionGetDof(section,p,&dof);CHKERRQ(ierr);
      ierr = PetscSectionSetDof(*cSec,p,dof);CHKERRQ(ierr);
      for (f = 0; f < numFields; f++) {
        ierr = PetscSectionGetFieldDof(section,p,f,&dof);CHKERRQ(ierr);
        ierr = PetscSectionSetFieldDof(*cSec,p,f,dof);CHKERRQ(ierr);
      }
    }
  }
  ierr = PetscSectionSetUp(*cSec);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetConstraintSection"
/*@
  DMPlexGetConstraintSection - Get the section that maps constrained points to rows of the constraint matrix.

  The default section obtained with DMGetDefaultSection() maps points to columns of the constraint matrix.

  logically collective

  Input Parameters:
. dm - The DMPlex object

  Output Parameters:
. cSec - If not NULL, set to the section describing which points anchor the constrained points.


  Level: intermediate

.seealso: DMPlexGetConstraints(), DMPlexSetConstraints(), DMPlexGetConstraintMatrix(), DMPlexSetConstraintMatrix()
@*/
PetscErrorCode DMPlexGetConstraintSection(DM dm, PetscSection *cSec)
{
  DM_Plex *plex = (DM_Plex *)dm->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (plex->anchorSection && !plex->constraintSection) {
    ierr = DMPlexCreateConstraintSection(dm,&plex->constraintSection);CHKERRQ(ierr);
  }
  if (cSec) *cSec = plex->constraintSection;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexCreateConstraintMatrix"
static PetscErrorCode DMPlexCreateConstraintMatrix(DM dm, Mat *cMat)
{
  DM_Plex *plex = (DM_Plex *)dm->data;
  PetscSection section, aSec, cSec;
  PetscInt pStart, pEnd, p, dof, aDof, aOff, off, nnz, annz, m, n, q, a, offset, *i, *j;
  const PetscInt *anchors;
  PetscInt numFields, f;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  ierr = DMGetDefaultSection(dm,&section);CHKERRQ(ierr);
  ierr = DMPlexGetConstraintSection(dm, &cSec);CHKERRQ(ierr);
  ierr = PetscSectionGetStorageSize(cSec, &m);CHKERRQ(ierr);
  ierr = PetscSectionGetStorageSize(section, &n);CHKERRQ(ierr);
  ierr = MatCreate(PETSC_COMM_SELF,cMat);CHKERRQ(ierr);
  ierr = MatSetSizes(*cMat,m,n,m,n);CHKERRQ(ierr);
  ierr = MatSetType(*cMat,MATSEQAIJ);
  aSec = plex->anchorSection;
  ierr = ISGetIndices(plex->anchorIS,&anchors);CHKERRQ(ierr);
  ierr = PetscSectionGetChart(aSec,&pStart,&pEnd);CHKERRQ(ierr);
  ierr = PetscMalloc1(m+1,&i);CHKERRQ(ierr);
  i[0] = 0;
  ierr = PetscSectionGetNumFields(section,&numFields);CHKERRQ(ierr);
  for (p = pStart; p < pEnd; p++) {
    ierr = PetscSectionGetDof(aSec,p,&dof);CHKERRQ(ierr);
    if (!dof) continue;
    ierr = PetscSectionGetOffset(aSec,p,&off);CHKERRQ(ierr);
    if (numFields) {
      for (f = 0; f < numFields; f++) {
        annz = 0;
        for (q = 0; q < dof; q++) {
          a = anchors[off + q];
          ierr = PetscSectionGetFieldDof(section,a,f,&aDof);CHKERRQ(ierr);
          annz += aDof;
        }
        ierr = PetscSectionGetFieldDof(cSec,p,f,&dof);CHKERRQ(ierr);
        ierr = PetscSectionGetFieldOffset(cSec,p,f,&off);CHKERRQ(ierr);
        for (q = 0; q < dof; q++) {
          i[off + q + 1] = i[off + q] + annz;
        }
      }
    }
    else {
      annz = 0;
      for (q = 0; q < dof; q++) {
        a = anchors[off + q];
        ierr = PetscSectionGetDof(section,a,&aDof);CHKERRQ(ierr);
        annz += aDof;
      }
      ierr = PetscSectionGetDof(cSec,p,&dof);CHKERRQ(ierr);
      ierr = PetscSectionGetOffset(cSec,p,&off);CHKERRQ(ierr);
      for (q = 0; q < dof; q++) {
        i[off + q + 1] = i[off + q] + annz;
      }
    }
  }
  nnz = i[m];
  ierr = PetscMalloc1(nnz,&j);CHKERRQ(ierr);
  offset = 0;
  for (p = pStart; p < pEnd; p++) {
    if (numFields) {
      for (f = 0; f < numFields; f++) {
        ierr = PetscSectionGetFieldDof(cSec,p,f,&dof);CHKERRQ(ierr);
        for (q = 0; q < dof; q++) {
          PetscInt rDof, rOff, r;
          ierr = PetscSectionGetDof(aSec,p,&rDof);CHKERRQ(ierr);
          ierr = PetscSectionGetOffset(aSec,p,&rOff);CHKERRQ(ierr);
          for (r = 0; r < rDof; r++) {
            PetscInt s;

            a = anchors[rOff + r];

            ierr = PetscSectionGetFieldDof(section,a,f,&aDof);CHKERRQ(ierr);
            ierr = PetscSectionGetFieldOffset(section,a,f,&aOff);CHKERRQ(ierr);
            for (s = 0; s < aDof; s++) {
              j[offset++] = aOff + s;
            }
          }
        }
      }
    }
    else {
      ierr = PetscSectionGetDof(cSec,p,&dof);CHKERRQ(ierr);
      for (q = 0; q < dof; q++) {
        PetscInt rDof, rOff, r;
        ierr = PetscSectionGetDof(aSec,p,&rDof);CHKERRQ(ierr);
        ierr = PetscSectionGetOffset(aSec,p,&rOff);CHKERRQ(ierr);
        for (r = 0; r < rDof; r++) {
          PetscInt s;

          a = anchors[rOff + r];

          ierr = PetscSectionGetDof(section,a,&aDof);CHKERRQ(ierr);
          ierr = PetscSectionGetOffset(section,a,&aOff);CHKERRQ(ierr);
          for (s = 0; s < aDof; s++) {
            j[offset++] = aOff + s;
          }
        }
      }
    }
  }
  ierr = MatSeqAIJSetPreallocationCSR(*cMat,i,j,NULL);CHKERRQ(ierr);
  ierr = PetscFree2(i,j);CHKERRQ(ierr);
  ierr = ISRestoreIndices(plex->anchorIS,&anchors);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetConstraintMatrix"
/*@
  DMPlexGetConstraintMatrix - Get the matrix that specifies the point-to-point constraints.

  logically collective

  Input Parameters:
. dm - The DMPlex object

  Output Parameters:
. cMat - If not NULL, returns the constraint matrix.  If the constraint matrix has not been created before, then it is
         created and its nonzero structure is allocated, so that the user can insert values.


  Level: intermediate

.seealso: DMPlexGetConstraints(), DMPlexSetConstraints(), DMPlexGetConstraintSection(), DMPlexSetConstraintMatrix()
@*/
PetscErrorCode DMPlexGetConstraintMatrix(DM dm, Mat *cMat)
{
  DM_Plex *plex = (DM_Plex *)dm->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (plex->anchorSection && !plex->constraintMat) {
    ierr = DMPlexCreateConstraintMatrix(dm,&plex->constraintMat);CHKERRQ(ierr);
  }
  if (cMat) *cMat = plex->constraintMat;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexSetConstraintMatrix"
/*@
  DMPlexSetConstraintMatrix - Set the matrix that specifies the point-to-point constraints.  It should have the same
  number of rows as the layout size of the section returned by DMPlexGetConstraintSection(), and it should have the
  same number of columns as the layout size of the section returned by DMGetDefaultSection().  For the constraint
  matrix to be used when constructing a matrix in, e.g., DMPlexSNESComputeJacobianFEM(), then MatGetValues() must be
  implemented.

  logically collective

  Input Parameters:
+ dm - The DMPlex object
- cMat - The constraint matrix.

  The reference count of cMat is incremented.


  Level: advanced.

.seealso: DMPlexGetConstraints(), DMPlexSetConstraints(), DMPlexGetConstraintSection(), DMPlexGetConstraintMatrix()
@*/
PetscErrorCode DMPlexSetConstraintMatrix(DM dm, Mat cMat)
{
  DM_Plex *plex = (DM_Plex *)dm->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  ierr = PetscObjectReference((PetscObject)cMat);CHKERRQ(ierr);
  ierr = MatDestroy(&plex->constraintMat);CHKERRQ(ierr);
  plex->constraintMat = cMat;
  PetscFunctionReturn(0);
}

typedef struct _projectConstraintsCtx
{
  DM  dm;
  Vec mask;
}
projectConstraintsCtx;

#undef __FUNCT__
#define __FUNCT__ "MatMult_PlexProjectConstraintsNormal"
PetscErrorCode MatMult_PlexProjectConstraintsNormal(Mat CtC, Vec x, Vec y)
{
  DM                    dm;
  Vec                   local, mask;
  projectConstraintsCtx *ctx;
  PetscErrorCode        ierr;

  PetscFunctionBegin;
  ierr = MatShellGetContext(CtC,&ctx);CHKERRQ(ierr);
  dm   = ctx->dm;
  mask = ctx->mask;
  ierr = DMGetLocalVector(dm,&local);CHKERRQ(ierr);
  ierr = DMGlobalToLocalBegin(dm,x,INSERT_VALUES,local);CHKERRQ(ierr);
  ierr = DMGlobalToLocalEnd(dm,x,INSERT_VALUES,local);CHKERRQ(ierr);
  ierr = VecPointwiseMult(local,mask,local);CHKERRQ(ierr);
  ierr = VecSet(y,0.);CHKERRQ(ierr);
  ierr = DMLocalToGlobalBegin(dm,local,ADD_VALUES,y);CHKERRQ(ierr);
  ierr = DMLocalToGlobalEnd(dm,local,ADD_VALUES,y);CHKERRQ(ierr);
  ierr = DMRestoreLocalVector(dm,&local);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexProjectConstraints_Internal"
/* Solve the normal equation for the constraints: x is local and y is global */
PetscErrorCode DMPlexProjectConstraints_Internal(DM dm, Vec x, Vec y)
{
  Mat                   cMat, CtC;
  PetscInt              n, N, cStart, cEnd, c;
  KSP                   ksp;
  PC                    pc;
  Vec                   global, mask;
  projectConstraintsCtx ctx;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = DMPlexGetConstraintMatrix(dm,&cMat);CHKERRQ(ierr);
  if (!cMat) {
    PetscFunctionReturn(0);
  }
  ierr = DMGetLocalVector(dm,&mask);CHKERRQ(ierr);
  ierr = VecSet(mask,0.0);CHKERRQ(ierr);
  ierr = DMPlexGetHeightStratum(dm,0,&cStart,&cEnd);CHKERRQ(ierr);
  if (cEnd > cStart) {
    PetscScalar *ones;
    PetscInt numValues, i;

    ierr = DMPlexVecGetClosure(dm,NULL,mask,cStart,&numValues,NULL);CHKERRQ(ierr);
    ierr = PetscMalloc1(numValues,&ones);CHKERRQ(ierr);
    for (i = 0; i < numValues; i++) {
      ones[i] = 1.;
    }
    for (c = cStart; c < cEnd; c++) {
      ierr = DMPlexVecSetClosure(dm,NULL,mask,c,ones,INSERT_VALUES);CHKERRQ(ierr);
    }
    ierr = PetscFree(ones);CHKERRQ(ierr);
  }
  ctx.dm   = dm;
  ctx.mask = mask;
  ierr = VecGetSize(y,&N);CHKERRQ(ierr);
  ierr = VecGetLocalSize(y,&n);CHKERRQ(ierr);
  ierr = MatCreate(PetscObjectComm((PetscObject)dm),&CtC);CHKERRQ(ierr);
  ierr = MatSetSizes(CtC,n,n,N,N);CHKERRQ(ierr);
  ierr = MatSetType(CtC,MATSHELL);CHKERRQ(ierr);
  ierr = MatSetUp(CtC);CHKERRQ(ierr);
  ierr = MatShellSetContext(CtC,&ctx);CHKERRQ(ierr);
  ierr = MatShellSetOperation(CtC,MATOP_MULT,(void(*)(void))MatMult_PlexProjectConstraintsNormal);CHKERRQ(ierr);
  ierr = KSPCreate(PetscObjectComm((PetscObject)dm),&ksp);CHKERRQ(ierr);
  ierr = KSPSetOperators(ksp,CtC,CtC);CHKERRQ(ierr);
  ierr = KSPSetType(ksp,KSPCG);CHKERRQ(ierr);
  ierr = KSPGetPC(ksp,&pc);CHKERRQ(ierr);
  ierr = PCSetType(pc,PCNONE);CHKERRQ(ierr);
  ierr = KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);CHKERRQ(ierr);
  ierr = KSPSetUp(ksp);CHKERRQ(ierr);
  ierr = DMGetGlobalVector(dm,&global);CHKERRQ(ierr);
  ierr = VecSet(global,0.);CHKERRQ(ierr);
  ierr = VecPointwiseMult(x,mask,x);CHKERRQ(ierr);
  ierr = DMLocalToGlobalBegin(dm,x,ADD_VALUES,global);CHKERRQ(ierr);
  ierr = DMLocalToGlobalEnd(dm,x,ADD_VALUES,global);CHKERRQ(ierr);
  ierr = KSPSetFromOptions(ksp);CHKERRQ(ierr);
  ierr = KSPSolve(ksp,global,y);CHKERRQ(ierr);
  ierr = DMRestoreGlobalVector(dm,&global);CHKERRQ(ierr);
  /* clean up */
  ierr = DMRestoreLocalVector(dm,&mask);CHKERRQ(ierr);
  ierr = KSPDestroy(&ksp);CHKERRQ(ierr);
  ierr = MatDestroy(&CtC);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}