xref: /petsc/src/dm/impls/plex/plexsubmesh.c (revision 6cf0e42fa0bb26eb38707ad07f4a05c512f910fe)

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

#undef __FUNCT__
#define __FUNCT__ "DMPlexMarkBoundaryFaces"
/*@
  DMPlexMarkBoundaryFaces - Mark all faces on the boundary

  Not Collective

  Input Parameter:
. dm - The original DM

  Output Parameter:
. label - The DMLabel marking boundary faces with value 1

  Level: developer

.seealso: DMLabelCreate(), DMPlexCreateLabel()
@*/
PetscErrorCode DMPlexMarkBoundaryFaces(DM dm, DMLabel label)
{
  PetscInt       fStart, fEnd, f;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
  for (f = fStart; f < fEnd; ++f) {
    PetscInt supportSize;

    ierr = DMPlexGetSupportSize(dm, f, &supportSize);CHKERRQ(ierr);
    if (supportSize == 1) {
      ierr = DMLabelSetValue(label, f, 1);CHKERRQ(ierr);
    }
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexLabelComplete"
/*@
  DMPlexLabelComplete - Starting with a label marking points on a surface, we add the transitive closure to the surface

  Input Parameters:
+ dm - The DM
- label - A DMLabel marking the surface points

  Output Parameter:
. label - A DMLabel marking all surface points in the transitive closure

  Level: developer

.seealso: DMPlexLabelCohesiveComplete()
@*/
PetscErrorCode DMPlexLabelComplete(DM dm, DMLabel label)
{
  IS              valueIS;
  const PetscInt *values;
  PetscInt        numValues, v;
  PetscErrorCode  ierr;

  PetscFunctionBegin;
  ierr = DMLabelGetNumValues(label, &numValues);CHKERRQ(ierr);
  ierr = DMLabelGetValueIS(label, &valueIS);CHKERRQ(ierr);
  ierr = ISGetIndices(valueIS, &values);CHKERRQ(ierr);
  for (v = 0; v < numValues; ++v) {
    IS              pointIS;
    const PetscInt *points;
    PetscInt        numPoints, p;

    ierr = DMLabelGetStratumSize(label, values[v], &numPoints);CHKERRQ(ierr);
    ierr = DMLabelGetStratumIS(label, values[v], &pointIS);CHKERRQ(ierr);
    ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
    for (p = 0; p < numPoints; ++p) {
      PetscInt *closure = NULL;
      PetscInt  closureSize, c;

      ierr = DMPlexGetTransitiveClosure(dm, points[p], PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
      for (c = 0; c < closureSize*2; c += 2) {
        ierr = DMLabelSetValue(label, closure[c], values[v]);CHKERRQ(ierr);
      }
      ierr = DMPlexRestoreTransitiveClosure(dm, points[p], PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
    }
    ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
    ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
  }
  ierr = ISRestoreIndices(valueIS, &values);CHKERRQ(ierr);
  ierr = ISDestroy(&valueIS);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexLabelAddCells"
/*@
  DMPlexLabelAddCells - Starting with a label marking faces on a surface, we add a cell for each face

  Input Parameters:
+ dm - The DM
- label - A DMLabel marking the surface points

  Output Parameter:
. label - A DMLabel incorporating cells

  Level: developer

  Note: The cells allow FEM boundary conditions to be applied using the cell geometry

.seealso: DMPlexLabelComplete(), DMPlexLabelCohesiveComplete()
@*/
PetscErrorCode DMPlexLabelAddCells(DM dm, DMLabel label)
{
  IS              valueIS;
  const PetscInt *values;
  PetscInt        numValues, v, cStart, cEnd;
  PetscErrorCode  ierr;

  PetscFunctionBegin;
  ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
  ierr = DMLabelGetNumValues(label, &numValues);CHKERRQ(ierr);
  ierr = DMLabelGetValueIS(label, &valueIS);CHKERRQ(ierr);
  ierr = ISGetIndices(valueIS, &values);CHKERRQ(ierr);
  for (v = 0; v < numValues; ++v) {
    IS              pointIS;
    const PetscInt *points;
    PetscInt        numPoints, p;

    ierr = DMLabelGetStratumSize(label, values[v], &numPoints);CHKERRQ(ierr);
    ierr = DMLabelGetStratumIS(label, values[v], &pointIS);CHKERRQ(ierr);
    ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
    for (p = 0; p < numPoints; ++p) {
      PetscInt *closure = NULL;
      PetscInt  closureSize, point;

      ierr = DMPlexGetTransitiveClosure(dm, points[p], PETSC_FALSE, &closureSize, &closure);CHKERRQ(ierr);
      point = closure[(closureSize-1)*2];
      if ((point >= cStart) && (point < cEnd)) {ierr = DMLabelSetValue(label, point, values[v]);CHKERRQ(ierr);}
      ierr = DMPlexRestoreTransitiveClosure(dm, points[p], PETSC_FALSE, &closureSize, &closure);CHKERRQ(ierr);
    }
    ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
    ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
  }
  ierr = ISRestoreIndices(valueIS, &values);CHKERRQ(ierr);
  ierr = ISDestroy(&valueIS);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexShiftPoint_Internal"
PETSC_STATIC_INLINE PetscInt DMPlexShiftPoint_Internal(PetscInt p, PetscInt depth, PetscInt depthMax[], PetscInt depthEnd[], PetscInt depthShift[])
{
  if (depth < 0) return p;
  /* Normal Cells                 */ if (p < depthMax[depth])                return p;
  /* Hybrid Cells+Normal Vertices */ if (p < depthMax[0])                    return p + depthShift[depth];
  /* Hybrid Vertices+Normal Faces */ if (depth < 2 || p < depthMax[depth-1]) return p + depthShift[depth] + depthShift[0];
  /* Hybrid Faces+Normal Edges    */ if (depth < 3 || p < depthMax[depth-2]) return p + depthShift[depth] + depthShift[0] + depthShift[depth-1];
  /* Hybrid Edges                 */                                         return p + depthShift[depth] + depthShift[0] + depthShift[depth-1] + depthShift[depth-2];
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexShiftSizes_Internal"
static PetscErrorCode DMPlexShiftSizes_Internal(DM dm, PetscInt depthShift[], DM dmNew)
{
  PetscInt      *depthMax, *depthEnd;
  PetscInt       depth = 0, d, pStart, pEnd, p;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
  if (depth < 0) PetscFunctionReturn(0);
  ierr = PetscMalloc2(depth+1,&depthMax,depth+1,&depthEnd);CHKERRQ(ierr);
  /* Step 1: Expand chart */
  ierr = DMPlexGetChart(dm, &pStart, &pEnd);CHKERRQ(ierr);
  ierr = DMPlexGetHybridBounds(dm, &depthMax[depth], depth > 0 ? &depthMax[depth-1] : NULL, &depthMax[1], &depthMax[0]);CHKERRQ(ierr);
  for (d = 0; d <= depth; ++d) {
    pEnd += depthShift[d];
    ierr  = DMPlexGetDepthStratum(dm, d, NULL, &depthEnd[d]);CHKERRQ(ierr);
    depthMax[d] = depthMax[d] < 0 ? depthEnd[d] : depthMax[d];
  }
  ierr = DMPlexSetChart(dmNew, pStart, pEnd);CHKERRQ(ierr);
  /* Step 2: Set cone and support sizes */
  for (d = 0; d <= depth; ++d) {
    ierr = DMPlexGetDepthStratum(dm, d, &pStart, &pEnd);CHKERRQ(ierr);
    for (p = pStart; p < pEnd; ++p) {
      PetscInt newp = DMPlexShiftPoint_Internal(p, depth, depthMax, depthEnd, depthShift);
      PetscInt size;

      ierr = DMPlexGetConeSize(dm, p, &size);CHKERRQ(ierr);
      ierr = DMPlexSetConeSize(dmNew, newp, size);CHKERRQ(ierr);
      ierr = DMPlexGetSupportSize(dm, p, &size);CHKERRQ(ierr);
      ierr = DMPlexSetSupportSize(dmNew, newp, size);CHKERRQ(ierr);
    }
  }
  ierr = PetscFree2(depthMax,depthEnd);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexShiftPoints_Internal"
static PetscErrorCode DMPlexShiftPoints_Internal(DM dm, PetscInt depthShift[], DM dmNew)
{
  PetscInt      *depthEnd, *depthMax, *newpoints;
  PetscInt       depth = 0, d, maxConeSize, maxSupportSize, maxConeSizeNew, maxSupportSizeNew, pStart, pEnd, p;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
  if (depth < 0) PetscFunctionReturn(0);
  ierr = DMPlexGetMaxSizes(dm, &maxConeSize, &maxSupportSize);CHKERRQ(ierr);
  ierr = DMPlexGetMaxSizes(dmNew, &maxConeSizeNew, &maxSupportSizeNew);CHKERRQ(ierr);
  ierr = PetscMalloc3(depth+1,&depthEnd,depth+1,&depthMax,PetscMax(PetscMax(maxConeSize, maxSupportSize), PetscMax(maxConeSizeNew, maxSupportSizeNew)),&newpoints);CHKERRQ(ierr);
  ierr = DMPlexGetHybridBounds(dm, &depthMax[depth], depth > 0 ? &depthMax[depth-1] : NULL, &depthMax[1], &depthMax[0]);CHKERRQ(ierr);
  for (d = 0; d <= depth; ++d) {
    ierr = DMPlexGetDepthStratum(dm, d, NULL, &depthEnd[d]);CHKERRQ(ierr);
    depthMax[d] = depthMax[d] < 0 ? depthEnd[d] : depthMax[d];
  }
  /* Step 5: Set cones and supports */
  ierr = DMPlexGetChart(dm, &pStart, &pEnd);CHKERRQ(ierr);
  for (p = pStart; p < pEnd; ++p) {
    const PetscInt *points = NULL, *orientations = NULL;
    PetscInt        size,sizeNew, i, newp = DMPlexShiftPoint_Internal(p, depth, depthMax, depthEnd, depthShift);

    ierr = DMPlexGetConeSize(dm, p, &size);CHKERRQ(ierr);
    ierr = DMPlexGetCone(dm, p, &points);CHKERRQ(ierr);
    ierr = DMPlexGetConeOrientation(dm, p, &orientations);CHKERRQ(ierr);
    for (i = 0; i < size; ++i) {
      newpoints[i] = DMPlexShiftPoint_Internal(points[i], depth, depthMax, depthEnd, depthShift);
    }
    ierr = DMPlexSetCone(dmNew, newp, newpoints);CHKERRQ(ierr);
    ierr = DMPlexSetConeOrientation(dmNew, newp, orientations);CHKERRQ(ierr);
    ierr = DMPlexGetSupportSize(dm, p, &size);CHKERRQ(ierr);
    ierr = DMPlexGetSupportSize(dmNew, newp, &sizeNew);CHKERRQ(ierr);
    ierr = DMPlexGetSupport(dm, p, &points);CHKERRQ(ierr);
    for (i = 0; i < size; ++i) {
      newpoints[i] = DMPlexShiftPoint_Internal(points[i], depth, depthMax, depthEnd, depthShift);
    }
    for (i = size; i < sizeNew; ++i) newpoints[i] = 0;
    ierr = DMPlexSetSupport(dmNew, newp, newpoints);CHKERRQ(ierr);
  }
  ierr = PetscFree3(depthEnd,depthMax,newpoints);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexShiftCoordinates_Internal"
static PetscErrorCode DMPlexShiftCoordinates_Internal(DM dm, PetscInt depthShift[], DM dmNew)
{
  PetscSection   coordSection, newCoordSection;
  Vec            coordinates, newCoordinates;
  PetscScalar   *coords, *newCoords;
  PetscInt      *depthEnd, coordSize;
  PetscInt       dim, depth = 0, d, vStart, vEnd, vStartNew, vEndNew, v;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
  ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
  ierr = PetscMalloc1((depth+1), &depthEnd);CHKERRQ(ierr);
  for (d = 0; d <= depth; ++d) {
    ierr = DMPlexGetDepthStratum(dm, d, NULL, &depthEnd[d]);CHKERRQ(ierr);
  }
  /* Step 8: Convert coordinates */
  ierr = DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);CHKERRQ(ierr);
  ierr = DMPlexGetDepthStratum(dmNew, 0, &vStartNew, &vEndNew);CHKERRQ(ierr);
  ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
  ierr = PetscSectionCreate(PetscObjectComm((PetscObject)dm), &newCoordSection);CHKERRQ(ierr);
  ierr = PetscSectionSetNumFields(newCoordSection, 1);CHKERRQ(ierr);
  ierr = PetscSectionSetFieldComponents(newCoordSection, 0, dim);CHKERRQ(ierr);
  ierr = PetscSectionSetChart(newCoordSection, vStartNew, vEndNew);CHKERRQ(ierr);
  for (v = vStartNew; v < vEndNew; ++v) {
    ierr = PetscSectionSetDof(newCoordSection, v, dim);CHKERRQ(ierr);
    ierr = PetscSectionSetFieldDof(newCoordSection, v, 0, dim);CHKERRQ(ierr);
  }
  ierr = PetscSectionSetUp(newCoordSection);CHKERRQ(ierr);
  ierr = DMSetCoordinateSection(dmNew, newCoordSection);CHKERRQ(ierr);
  ierr = PetscSectionGetStorageSize(newCoordSection, &coordSize);CHKERRQ(ierr);
  ierr = VecCreate(PetscObjectComm((PetscObject)dm), &newCoordinates);CHKERRQ(ierr);
  ierr = PetscObjectSetName((PetscObject) newCoordinates, "coordinates");CHKERRQ(ierr);
  ierr = VecSetSizes(newCoordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
  ierr = VecSetType(newCoordinates,VECSTANDARD);CHKERRQ(ierr);
  ierr = DMSetCoordinatesLocal(dmNew, newCoordinates);CHKERRQ(ierr);
  ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
  ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
  ierr = VecGetArray(newCoordinates, &newCoords);CHKERRQ(ierr);
  for (v = vStart; v < vEnd; ++v) {
    PetscInt dof, off, noff, d;

    ierr = PetscSectionGetDof(coordSection, v, &dof);CHKERRQ(ierr);
    ierr = PetscSectionGetOffset(coordSection, v, &off);CHKERRQ(ierr);
    ierr = PetscSectionGetOffset(newCoordSection, DMPlexShiftPoint_Internal(v, depth, depthEnd, depthEnd, depthShift), &noff);CHKERRQ(ierr);
    for (d = 0; d < dof; ++d) {
      newCoords[noff+d] = coords[off+d];
    }
  }
  ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
  ierr = VecRestoreArray(newCoordinates, &newCoords);CHKERRQ(ierr);
  ierr = VecDestroy(&newCoordinates);CHKERRQ(ierr);
  ierr = PetscSectionDestroy(&newCoordSection);CHKERRQ(ierr);
  ierr = PetscFree(depthEnd);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexShiftSF_Internal"
static PetscErrorCode DMPlexShiftSF_Internal(DM dm, PetscInt depthShift[], DM dmNew)
{
  PetscInt          *depthMax, *depthEnd;
  PetscInt           depth = 0, d;
  PetscSF            sfPoint, sfPointNew;
  const PetscSFNode *remotePoints;
  PetscSFNode       *gremotePoints;
  const PetscInt    *localPoints;
  PetscInt          *glocalPoints, *newLocation, *newRemoteLocation;
  PetscInt           numRoots, numLeaves, l, pStart, pEnd, totShift = 0;
  PetscErrorCode     ierr;

  PetscFunctionBegin;
  ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
  ierr = PetscMalloc2(depth+1,&depthMax,depth+1,&depthEnd);CHKERRQ(ierr);
  ierr = DMPlexGetHybridBounds(dm, depth >= 0 ? &depthMax[depth] : NULL, depth>1 ? &depthMax[depth-1] : NULL, depth>2 ? &depthMax[1] : NULL, depth >= 0 ? &depthMax[0] : NULL);CHKERRQ(ierr);
  for (d = 0; d <= depth; ++d) {
    totShift += depthShift[d];
    ierr      = DMPlexGetDepthStratum(dm, d, NULL, &depthEnd[d]);CHKERRQ(ierr);
    depthMax[d] = depthMax[d] < 0 ? depthEnd[d] : depthMax[d];
  }
  /* Step 9: Convert pointSF */
  ierr = DMGetPointSF(dm, &sfPoint);CHKERRQ(ierr);
  ierr = DMGetPointSF(dmNew, &sfPointNew);CHKERRQ(ierr);
  ierr = DMPlexGetChart(dm, &pStart, &pEnd);CHKERRQ(ierr);
  ierr = PetscSFGetGraph(sfPoint, &numRoots, &numLeaves, &localPoints, &remotePoints);CHKERRQ(ierr);
  if (numRoots >= 0) {
    ierr = PetscMalloc2(numRoots,&newLocation,pEnd-pStart,&newRemoteLocation);CHKERRQ(ierr);
    for (l=0; l<numRoots; l++) newLocation[l] = DMPlexShiftPoint_Internal(l, depth, depthMax, depthEnd, depthShift);
    ierr = PetscSFBcastBegin(sfPoint, MPIU_INT, newLocation, newRemoteLocation);CHKERRQ(ierr);
    ierr = PetscSFBcastEnd(sfPoint, MPIU_INT, newLocation, newRemoteLocation);CHKERRQ(ierr);
    ierr = PetscMalloc1(numLeaves,    &glocalPoints);CHKERRQ(ierr);
    ierr = PetscMalloc1(numLeaves, &gremotePoints);CHKERRQ(ierr);
    for (l = 0; l < numLeaves; ++l) {
      glocalPoints[l]        = DMPlexShiftPoint_Internal(localPoints[l], depth, depthMax, depthEnd, depthShift);
      gremotePoints[l].rank  = remotePoints[l].rank;
      gremotePoints[l].index = newRemoteLocation[localPoints[l]];
    }
    ierr = PetscFree2(newLocation,newRemoteLocation);CHKERRQ(ierr);
    ierr = PetscSFSetGraph(sfPointNew, numRoots + totShift, numLeaves, glocalPoints, PETSC_OWN_POINTER, gremotePoints, PETSC_OWN_POINTER);CHKERRQ(ierr);
  }
  ierr = PetscFree2(depthMax,depthEnd);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexShiftLabels_Internal"
static PetscErrorCode DMPlexShiftLabels_Internal(DM dm, PetscInt depthShift[], DM dmNew)
{
  PetscSF            sfPoint;
  DMLabel            vtkLabel, ghostLabel;
  PetscInt          *depthMax, *depthEnd;
  const PetscSFNode *leafRemote;
  const PetscInt    *leafLocal;
  PetscInt           depth = 0, d, numLeaves, numLabels, l, cStart, cEnd, c, fStart, fEnd, f;
  PetscMPIInt        rank;
  PetscErrorCode     ierr;

  PetscFunctionBegin;
  ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
  ierr = PetscMalloc2(depth+1,&depthMax,depth+1,&depthEnd);CHKERRQ(ierr);
  ierr = DMPlexGetHybridBounds(dm, depth >= 0 ? &depthMax[depth] : NULL, depth>1 ? &depthMax[depth-1] : NULL, depth>2 ? &depthMax[1] : NULL, depth >= 0 ? &depthMax[0] : NULL);CHKERRQ(ierr);
  for (d = 0; d <= depth; ++d) {
    ierr = DMPlexGetDepthStratum(dm, d, NULL, &depthEnd[d]);CHKERRQ(ierr);
    depthMax[d] = depthMax[d] < 0 ? depthEnd[d] : depthMax[d];
  }
  /* Step 10: Convert labels */
  ierr = DMPlexGetNumLabels(dm, &numLabels);CHKERRQ(ierr);
  for (l = 0; l < numLabels; ++l) {
    DMLabel         label, newlabel;
    const char     *lname;
    PetscBool       isDepth;
    IS              valueIS;
    const PetscInt *values;
    PetscInt        numValues, val;

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

      ierr = DMLabelGetStratumIS(label, values[val], &pointIS);CHKERRQ(ierr);
      ierr = ISGetLocalSize(pointIS, &numPoints);CHKERRQ(ierr);
      ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
      for (p = 0; p < numPoints; ++p) {
        const PetscInt newpoint = DMPlexShiftPoint_Internal(points[p], depth, depthMax, depthEnd, depthShift);

        ierr = DMLabelSetValue(newlabel, newpoint, values[val]);CHKERRQ(ierr);
      }
      ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
      ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
    }
    ierr = ISRestoreIndices(valueIS, &values);CHKERRQ(ierr);
    ierr = ISDestroy(&valueIS);CHKERRQ(ierr);
  }
  ierr = PetscFree2(depthMax,depthEnd);CHKERRQ(ierr);
  /* Step 11: Make label for output (vtk) and to mark ghost points (ghost) */
  ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);CHKERRQ(ierr);
  ierr = DMGetPointSF(dm, &sfPoint);CHKERRQ(ierr);
  ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
  ierr = PetscSFGetGraph(sfPoint, NULL, &numLeaves, &leafLocal, &leafRemote);CHKERRQ(ierr);
  ierr = DMPlexCreateLabel(dmNew, "vtk");CHKERRQ(ierr);
  ierr = DMPlexCreateLabel(dmNew, "ghost");CHKERRQ(ierr);
  ierr = DMPlexGetLabel(dmNew, "vtk", &vtkLabel);CHKERRQ(ierr);
  ierr = DMPlexGetLabel(dmNew, "ghost", &ghostLabel);CHKERRQ(ierr);
  for (l = 0, c = cStart; l < numLeaves && c < cEnd; ++l, ++c) {
    for (; c < leafLocal[l] && c < cEnd; ++c) {
      ierr = DMLabelSetValue(vtkLabel, c, 1);CHKERRQ(ierr);
    }
    if (leafLocal[l] >= cEnd) break;
    if (leafRemote[l].rank == rank) {
      ierr = DMLabelSetValue(vtkLabel, c, 1);CHKERRQ(ierr);
    } else {
      ierr = DMLabelSetValue(ghostLabel, c, 2);CHKERRQ(ierr);
    }
  }
  for (; c < cEnd; ++c) {
    ierr = DMLabelSetValue(vtkLabel, c, 1);CHKERRQ(ierr);
  }
  if (0) {
    ierr = PetscViewerASCIISynchronizedAllow(PETSC_VIEWER_STDOUT_WORLD, PETSC_TRUE);CHKERRQ(ierr);
    ierr = DMLabelView(vtkLabel, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
    ierr = PetscViewerFlush(PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
  }
  ierr = DMPlexGetHeightStratum(dmNew, 1, &fStart, &fEnd);CHKERRQ(ierr);
  for (f = fStart; f < fEnd; ++f) {
    PetscInt numCells;

    ierr = DMPlexGetSupportSize(dmNew, f, &numCells);CHKERRQ(ierr);
    if (numCells < 2) {
      ierr = DMLabelSetValue(ghostLabel, f, 1);CHKERRQ(ierr);
    } else {
      const PetscInt *cells = NULL;
      PetscInt        vA, vB;

      ierr = DMPlexGetSupport(dmNew, f, &cells);CHKERRQ(ierr);
      ierr = DMLabelGetValue(vtkLabel, cells[0], &vA);CHKERRQ(ierr);
      ierr = DMLabelGetValue(vtkLabel, cells[1], &vB);CHKERRQ(ierr);
      if (!vA && !vB) {ierr = DMLabelSetValue(ghostLabel, f, 1);CHKERRQ(ierr);}
    }
  }
  if (0) {
    ierr = PetscViewerASCIISynchronizedAllow(PETSC_VIEWER_STDOUT_WORLD, PETSC_TRUE);CHKERRQ(ierr);
    ierr = DMLabelView(ghostLabel, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
    ierr = PetscViewerFlush(PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexConstructGhostCells_Internal"
static PetscErrorCode DMPlexConstructGhostCells_Internal(DM dm, DMLabel label, PetscInt *numGhostCells, DM gdm)
{
  IS              valueIS;
  const PetscInt *values;
  PetscInt       *depthShift;
  PetscInt        depth = 0, numFS, fs, fStart, fEnd, ghostCell, cEnd, c;
  PetscErrorCode  ierr;

  PetscFunctionBegin;
  ierr = DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);CHKERRQ(ierr);
  /* Count ghost cells */
  ierr = DMLabelGetValueIS(label, &valueIS);CHKERRQ(ierr);
  ierr = ISGetLocalSize(valueIS, &numFS);CHKERRQ(ierr);
  ierr = ISGetIndices(valueIS, &values);CHKERRQ(ierr);
  *numGhostCells = 0;
  for (fs = 0; fs < numFS; ++fs) {
    IS              faceIS;
    const PetscInt *faces;
    PetscInt        numFaces, f, numBdFaces = 0;

    ierr = DMLabelGetStratumIS(label, values[fs], &faceIS);CHKERRQ(ierr);
    ierr = ISGetLocalSize(faceIS, &numFaces);CHKERRQ(ierr);
    ierr = ISGetIndices(faceIS, &faces);CHKERRQ(ierr);
    for (f = 0; f < numFaces; ++f) {
      if ((faces[f] >= fStart) && (faces[f] < fEnd)) ++numBdFaces;
    }
    *numGhostCells += numBdFaces;
    ierr = ISDestroy(&faceIS);CHKERRQ(ierr);
  }
  ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
  ierr = PetscMalloc1((depth+1), &depthShift);CHKERRQ(ierr);
  ierr = PetscMemzero(depthShift, (depth+1) * sizeof(PetscInt));CHKERRQ(ierr);
  if (depth >= 0) depthShift[depth] = *numGhostCells;
  ierr = DMPlexShiftSizes_Internal(dm, depthShift, gdm);CHKERRQ(ierr);
  /* Step 3: Set cone/support sizes for new points */
  ierr = DMPlexGetHeightStratum(dm, 0, NULL, &cEnd);CHKERRQ(ierr);
  for (c = cEnd; c < cEnd + *numGhostCells; ++c) {
    ierr = DMPlexSetConeSize(gdm, c, 1);CHKERRQ(ierr);
  }
  for (fs = 0; fs < numFS; ++fs) {
    IS              faceIS;
    const PetscInt *faces;
    PetscInt        numFaces, f;

    ierr = DMLabelGetStratumIS(label, values[fs], &faceIS);CHKERRQ(ierr);
    ierr = ISGetLocalSize(faceIS, &numFaces);CHKERRQ(ierr);
    ierr = ISGetIndices(faceIS, &faces);CHKERRQ(ierr);
    for (f = 0; f < numFaces; ++f) {
      PetscInt size;

      if ((faces[f] < fStart) || (faces[f] >= fEnd)) continue;
      ierr = DMPlexGetSupportSize(dm, faces[f], &size);CHKERRQ(ierr);
      if (size != 1) SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "DM has boundary face %d with %d support cells", faces[f], size);
      ierr = DMPlexSetSupportSize(gdm, faces[f] + *numGhostCells, 2);CHKERRQ(ierr);
    }
    ierr = ISRestoreIndices(faceIS, &faces);CHKERRQ(ierr);
    ierr = ISDestroy(&faceIS);CHKERRQ(ierr);
  }
  /* Step 4: Setup ghosted DM */
  ierr = DMSetUp(gdm);CHKERRQ(ierr);
  ierr = DMPlexShiftPoints_Internal(dm, depthShift, gdm);CHKERRQ(ierr);
  /* Step 6: Set cones and supports for new points */
  ghostCell = cEnd;
  for (fs = 0; fs < numFS; ++fs) {
    IS              faceIS;
    const PetscInt *faces;
    PetscInt        numFaces, f;

    ierr = DMLabelGetStratumIS(label, values[fs], &faceIS);CHKERRQ(ierr);
    ierr = ISGetLocalSize(faceIS, &numFaces);CHKERRQ(ierr);
    ierr = ISGetIndices(faceIS, &faces);CHKERRQ(ierr);
    for (f = 0; f < numFaces; ++f) {
      PetscInt newFace = faces[f] + *numGhostCells;

      if ((faces[f] < fStart) || (faces[f] >= fEnd)) continue;
      ierr = DMPlexSetCone(gdm, ghostCell, &newFace);CHKERRQ(ierr);
      ierr = DMPlexInsertSupport(gdm, newFace, 1, ghostCell);CHKERRQ(ierr);
      ++ghostCell;
    }
    ierr = ISRestoreIndices(faceIS, &faces);CHKERRQ(ierr);
    ierr = ISDestroy(&faceIS);CHKERRQ(ierr);
  }
  ierr = ISRestoreIndices(valueIS, &values);CHKERRQ(ierr);
  ierr = ISDestroy(&valueIS);CHKERRQ(ierr);
  /* Step 7: Stratify */
  ierr = DMPlexStratify(gdm);CHKERRQ(ierr);
  ierr = DMPlexShiftCoordinates_Internal(dm, depthShift, gdm);CHKERRQ(ierr);
  ierr = DMPlexShiftSF_Internal(dm, depthShift, gdm);CHKERRQ(ierr);
  ierr = DMPlexShiftLabels_Internal(dm, depthShift, gdm);CHKERRQ(ierr);
  ierr = PetscFree(depthShift);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexConstructGhostCells"
/*@C
  DMPlexConstructGhostCells - Construct ghost cells which connect to every boundary face

  Collective on dm

  Input Parameters:
+ dm - The original DM
- labelName - The label specifying the boundary faces, or "Face Sets" if this is NULL

  Output Parameters:
+ numGhostCells - The number of ghost cells added to the DM
- dmGhosted - The new DM

  Note: If no label exists of that name, one will be created marking all boundary faces

  Level: developer

.seealso: DMCreate()
@*/
PetscErrorCode DMPlexConstructGhostCells(DM dm, const char labelName[], PetscInt *numGhostCells, DM *dmGhosted)
{
  DM             gdm;
  DMLabel        label;
  const char    *name = labelName ? labelName : "Face Sets";
  PetscInt       dim;
  PetscBool      flag;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidPointer(numGhostCells, 3);
  PetscValidPointer(dmGhosted, 4);
  ierr = DMCreate(PetscObjectComm((PetscObject)dm), &gdm);CHKERRQ(ierr);
  ierr = DMSetType(gdm, DMPLEX);CHKERRQ(ierr);
  ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
  ierr = DMPlexSetDimension(gdm, dim);CHKERRQ(ierr);
  ierr = DMPlexGetAdjacencyUseCone(dm, &flag);CHKERRQ(ierr);
  ierr = DMPlexSetAdjacencyUseCone(gdm, flag);CHKERRQ(ierr);
  ierr = DMPlexGetAdjacencyUseClosure(dm, &flag);CHKERRQ(ierr);
  ierr = DMPlexSetAdjacencyUseClosure(gdm, flag);CHKERRQ(ierr);
  ierr = DMPlexGetLabel(dm, name, &label);CHKERRQ(ierr);
  if (!label) {
    /* Get label for boundary faces */
    ierr = DMPlexCreateLabel(dm, name);CHKERRQ(ierr);
    ierr = DMPlexGetLabel(dm, name, &label);CHKERRQ(ierr);
    ierr = DMPlexMarkBoundaryFaces(dm, label);CHKERRQ(ierr);
  }
  ierr = DMPlexConstructGhostCells_Internal(dm, label, numGhostCells, gdm);CHKERRQ(ierr);
  ierr = DMSetFromOptions(gdm);CHKERRQ(ierr);
  *dmGhosted = gdm;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexConstructCohesiveCells_Internal"
/*
  We are adding three kinds of points here:
    Replicated:     Copies of points which exist in the mesh, such as vertices identified across a fault
    Non-replicated: Points which exist on the fault, but are not replicated
    Hybrid:         Entirely new points, such as cohesive cells

  When creating subsequent cohesive cells, we shift the old hybrid cells to the end of the numbering at
  each depth so that the new split/hybrid points can be inserted as a block.
*/
static PetscErrorCode DMPlexConstructCohesiveCells_Internal(DM dm, DMLabel label, DM sdm)
{
  MPI_Comm         comm;
  IS               valueIS;
  PetscInt         numSP = 0;       /* The number of depths for which we have replicated points */
  const PetscInt  *values;          /* List of depths for which we have replicated points */
  IS              *splitIS;
  IS              *unsplitIS;
  PetscInt        *numSplitPoints;     /* The number of replicated points at each depth */
  PetscInt        *numUnsplitPoints;   /* The number of non-replicated points at each depth which still give rise to hybrid points */
  PetscInt        *numHybridPoints;    /* The number of new hybrid points at each depth */
  PetscInt        *numHybridPointsOld; /* The number of existing hybrid points at each depth */
  const PetscInt **splitPoints;        /* Replicated points for each depth */
  const PetscInt **unsplitPoints;      /* Non-replicated points for each depth */
  PetscSection     coordSection;
  Vec              coordinates;
  PetscScalar     *coords;
  PetscInt         depths[4];          /* Depths in the order that plex points are numbered */
  PetscInt        *depthMax;           /* The first hybrid point at each depth in the original mesh */
  PetscInt        *depthEnd;           /* The point limit at each depth in the original mesh */
  PetscInt        *depthShift;         /* Number of replicated+hybrid points at each depth */
  PetscInt        *depthOffset;        /* Prefix sums of depthShift */
  PetscInt        *pMaxNew;            /* The first replicated point at each depth in the new mesh, hybrids come after this */
  PetscInt        *coneNew, *coneONew, *supportNew;
  PetscInt         shift = 100, shift2 = 200, depth = 0, dep, dim, d, sp, maxConeSize, maxSupportSize, maxConeSizeNew, maxSupportSizeNew, numLabels, vStart, vEnd, pEnd, p, v;
  PetscErrorCode   ierr;

  PetscFunctionBegin;
  ierr = PetscObjectGetComm((PetscObject)dm,&comm);CHKERRQ(ierr);
  ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
  ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
  ierr = DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);CHKERRQ(ierr);
  depths[0] = depth;
  depths[1] = 0;
  depths[2] = depth-1;
  depths[3] = 1;
  /* Count split points and add cohesive cells */
  ierr = DMPlexGetMaxSizes(dm, &maxConeSize, &maxSupportSize);CHKERRQ(ierr);
  ierr = PetscMalloc6(depth+1,&depthMax,depth+1,&depthEnd,depth+1,&depthShift,depth+1,&depthOffset,depth+1,&pMaxNew,depth+1,&numHybridPointsOld);CHKERRQ(ierr);
  ierr = PetscMalloc7(depth+1,&splitIS,depth+1,&unsplitIS,depth+1,&numSplitPoints,depth+1,&numUnsplitPoints,depth+1,&numHybridPoints,depth+1,&splitPoints,depth+1,&unsplitPoints);CHKERRQ(ierr);
  ierr = PetscMemzero(depthShift,  (depth+1) * sizeof(PetscInt));CHKERRQ(ierr);
  ierr = PetscMemzero(depthOffset, (depth+1) * sizeof(PetscInt));CHKERRQ(ierr);
  ierr = DMPlexGetHybridBounds(dm, depth >= 0 ? &depthMax[depth] : NULL, depth>1 ? &depthMax[depth-1] : NULL, depth>2 ? &depthMax[1] : NULL, depth >= 0 ? &depthMax[0] : NULL);CHKERRQ(ierr);
  for (d = 0; d <= depth; ++d) {
    ierr = DMPlexGetDepthStratum(dm, d, NULL, &pMaxNew[d]);CHKERRQ(ierr);
    depthEnd[d]           = pMaxNew[d];
    depthMax[d]           = depthMax[d] < 0 ? depthEnd[d] : depthMax[d];
    numSplitPoints[d]     = 0;
    numUnsplitPoints[d]   = 0;
    numHybridPoints[d]    = 0;
    numHybridPointsOld[d] = depthMax[d] < 0 ? 0 : depthEnd[d] - depthMax[d];
    splitPoints[d]        = NULL;
    unsplitPoints[d]      = NULL;
    splitIS[d]            = NULL;
    unsplitIS[d]          = NULL;
  }
  if (label) {
    ierr = DMLabelGetValueIS(label, &valueIS);CHKERRQ(ierr);
    ierr = ISGetLocalSize(valueIS, &numSP);CHKERRQ(ierr);
    ierr = ISGetIndices(valueIS, &values);CHKERRQ(ierr);
  }
  for (sp = 0; sp < numSP; ++sp) {
    const PetscInt dep = values[sp];

    if ((dep < 0) || (dep > depth)) continue;
    ierr = DMLabelGetStratumIS(label, dep, &splitIS[dep]);CHKERRQ(ierr);
    if (splitIS[dep]) {
      ierr = ISGetLocalSize(splitIS[dep], &numSplitPoints[dep]);CHKERRQ(ierr);
      ierr = ISGetIndices(splitIS[dep], &splitPoints[dep]);CHKERRQ(ierr);
    }
    ierr = DMLabelGetStratumIS(label, shift2+dep, &unsplitIS[dep]);CHKERRQ(ierr);
    if (unsplitIS[dep]) {
      ierr = ISGetLocalSize(unsplitIS[dep], &numUnsplitPoints[dep]);CHKERRQ(ierr);
      ierr = ISGetIndices(unsplitIS[dep], &unsplitPoints[dep]);CHKERRQ(ierr);
    }
  }
  /* Calculate number of hybrid points */
  for (d = 1; d <= depth; ++d) numHybridPoints[d]     = numSplitPoints[d-1] + numUnsplitPoints[d-1]; /* There is a hybrid cell/face/edge for every split face/edge/vertex   */
  for (d = 0; d <= depth; ++d) depthShift[d]          = numSplitPoints[d] + numHybridPoints[d];
  for (d = 1; d <= depth; ++d) depthOffset[depths[d]] = depthOffset[depths[d-1]] + depthShift[depths[d-1]];
  for (d = 0; d <= depth; ++d) pMaxNew[d]            += depthOffset[d] - numHybridPointsOld[d];
  ierr = DMPlexShiftSizes_Internal(dm, depthShift, sdm);CHKERRQ(ierr);
  /* Step 3: Set cone/support sizes for new points */
  for (dep = 0; dep <= depth; ++dep) {
    for (p = 0; p < numSplitPoints[dep]; ++p) {
      const PetscInt  oldp   = splitPoints[dep][p];
      const PetscInt  newp   = DMPlexShiftPoint_Internal(oldp, depth, depthMax, depthEnd, depthShift) /*oldp + depthOffset[dep]*/;
      const PetscInt  splitp = p    + pMaxNew[dep];
      const PetscInt *support;
      PetscInt        coneSize, supportSize, qf, qn, qp, e;

      ierr = DMPlexGetConeSize(dm, oldp, &coneSize);CHKERRQ(ierr);
      ierr = DMPlexSetConeSize(sdm, splitp, coneSize);CHKERRQ(ierr);
      ierr = DMPlexGetSupportSize(dm, oldp, &supportSize);CHKERRQ(ierr);
      ierr = DMPlexSetSupportSize(sdm, splitp, supportSize);CHKERRQ(ierr);
      if (dep == depth-1) {
        const PetscInt hybcell = p + pMaxNew[dep+1] + numSplitPoints[dep+1];

        /* Add cohesive cells, they are prisms */
        ierr = DMPlexSetConeSize(sdm, hybcell, 2 + coneSize);CHKERRQ(ierr);
      } else if (dep == 0) {
        const PetscInt hybedge = p + pMaxNew[dep+1] + numSplitPoints[dep+1];

        ierr = DMPlexGetSupport(dm, oldp, &support);CHKERRQ(ierr);
        for (e = 0, qn = 0, qp = 0, qf = 0; e < supportSize; ++e) {
          PetscInt val;

          ierr = DMLabelGetValue(label, support[e], &val);CHKERRQ(ierr);
          if (val == 1) ++qf;
          if ((val == 1) || (val ==  (shift + 1))) ++qn;
          if ((val == 1) || (val == -(shift + 1))) ++qp;
        }
        /* Split old vertex: Edges into original vertex and new cohesive edge */
        ierr = DMPlexSetSupportSize(sdm, newp, qn+1);CHKERRQ(ierr);
        /* Split new vertex: Edges into split vertex and new cohesive edge */
        ierr = DMPlexSetSupportSize(sdm, splitp, qp+1);CHKERRQ(ierr);
        /* Add hybrid edge */
        ierr = DMPlexSetConeSize(sdm, hybedge, 2);CHKERRQ(ierr);
        ierr = DMPlexSetSupportSize(sdm, hybedge, qf);CHKERRQ(ierr);
      } else if (dep == dim-2) {
        const PetscInt hybface = p + pMaxNew[dep+1] + numSplitPoints[dep+1];

        ierr = DMPlexGetSupport(dm, oldp, &support);CHKERRQ(ierr);
        for (e = 0, qn = 0, qp = 0, qf = 0; e < supportSize; ++e) {
          PetscInt val;

          ierr = DMLabelGetValue(label, support[e], &val);CHKERRQ(ierr);
          if (val == dim-1) ++qf;
          if ((val == dim-1) || (val ==  (shift + dim-1))) ++qn;
          if ((val == dim-1) || (val == -(shift + dim-1))) ++qp;
        }
        /* Split old edge: Faces into original edge and cohesive face (positive side?) */
        ierr = DMPlexSetSupportSize(sdm, newp, qn+1);CHKERRQ(ierr);
        /* Split new edge: Faces into split edge and cohesive face (negative side?) */
        ierr = DMPlexSetSupportSize(sdm, splitp, qp+1);CHKERRQ(ierr);
        /* Add hybrid face */
        ierr = DMPlexSetConeSize(sdm, hybface, 4);CHKERRQ(ierr);
        ierr = DMPlexSetSupportSize(sdm, hybface, qf);CHKERRQ(ierr);
      }
    }
  }
  for (dep = 0; dep <= depth; ++dep) {
    for (p = 0; p < numUnsplitPoints[dep]; ++p) {
      const PetscInt  oldp   = unsplitPoints[dep][p];
      const PetscInt  newp   = DMPlexShiftPoint_Internal(oldp, depth, depthMax, depthEnd, depthShift) /*oldp + depthOffset[dep]*/;
      const PetscInt *support;
      PetscInt        coneSize, supportSize, qf, e, s;

      ierr = DMPlexGetConeSize(dm, oldp, &coneSize);CHKERRQ(ierr);
      ierr = DMPlexGetSupportSize(dm, oldp, &supportSize);CHKERRQ(ierr);
      ierr = DMPlexGetSupport(dm, oldp, &support);CHKERRQ(ierr);
      if (dep == 0) {
        const PetscInt hybedge = p + pMaxNew[dep+1] + numSplitPoints[dep+1] + numSplitPoints[dep];

        /* Unsplit vertex: Edges into original vertex, split edges, and new cohesive edge twice */
        for (s = 0, qf = 0; s < supportSize; ++s, ++qf) {
          ierr = PetscFindInt(support[s], numSplitPoints[dep+1], splitPoints[dep+1], &e);CHKERRQ(ierr);
          if (e >= 0) ++qf;
        }
        ierr = DMPlexSetSupportSize(sdm, newp, qf+2);CHKERRQ(ierr);
        /* Add hybrid edge */
        ierr = DMPlexSetConeSize(sdm, hybedge, 2);CHKERRQ(ierr);
        for (e = 0, qf = 0; e < supportSize; ++e) {
          PetscInt val;

          ierr = DMLabelGetValue(label, support[e], &val);CHKERRQ(ierr);
          /* Split and unsplit edges produce hybrid faces */
          if (val == 1) ++qf;
          if (val == (shift2 + 1)) ++qf;
        }
        ierr = DMPlexSetSupportSize(sdm, hybedge, qf);CHKERRQ(ierr);
      } else if (dep == dim-2) {
        const PetscInt hybface = p + pMaxNew[dep+1] + numSplitPoints[dep+1] + numSplitPoints[dep];
        PetscInt       val;

        for (e = 0, qf = 0; e < supportSize; ++e) {
          ierr = DMLabelGetValue(label, support[e], &val);CHKERRQ(ierr);
          if (val == dim-1) qf += 2;
          else              ++qf;
        }
        /* Unsplit edge: Faces into original edge, split face, and cohesive face twice */
        ierr = DMPlexSetSupportSize(sdm, newp, qf+2);CHKERRQ(ierr);
        /* Add hybrid face */
        for (e = 0, qf = 0; e < supportSize; ++e) {
          ierr = DMLabelGetValue(label, support[e], &val);CHKERRQ(ierr);
          if (val == dim-1) ++qf;
        }
        ierr = DMPlexSetConeSize(sdm, hybface, 4);CHKERRQ(ierr);
        ierr = DMPlexSetSupportSize(sdm, hybface, qf);CHKERRQ(ierr);
      }
    }
  }
  /* Step 4: Setup split DM */
  ierr = DMSetUp(sdm);CHKERRQ(ierr);
  ierr = DMPlexShiftPoints_Internal(dm, depthShift, sdm);CHKERRQ(ierr);
  ierr = DMPlexGetMaxSizes(sdm, &maxConeSizeNew, &maxSupportSizeNew);CHKERRQ(ierr);
  ierr = PetscMalloc3(PetscMax(maxConeSize, maxConeSizeNew)*3,&coneNew,PetscMax(maxConeSize, maxConeSizeNew)*3,&coneONew,PetscMax(maxSupportSize, maxSupportSizeNew),&supportNew);CHKERRQ(ierr);
  /* Step 6: Set cones and supports for new points */
  for (dep = 0; dep <= depth; ++dep) {
    for (p = 0; p < numSplitPoints[dep]; ++p) {
      const PetscInt  oldp   = splitPoints[dep][p];
      const PetscInt  newp   = DMPlexShiftPoint_Internal(oldp, depth, depthMax, depthEnd, depthShift) /*oldp + depthOffset[dep]*/;
      const PetscInt  splitp = p    + pMaxNew[dep];
      const PetscInt *cone, *support, *ornt;
      PetscInt        coneSize, supportSize, q, qf, qn, qp, v, e, s;

      ierr = DMPlexGetConeSize(dm, oldp, &coneSize);CHKERRQ(ierr);
      ierr = DMPlexGetCone(dm, oldp, &cone);CHKERRQ(ierr);
      ierr = DMPlexGetConeOrientation(dm, oldp, &ornt);CHKERRQ(ierr);
      ierr = DMPlexGetSupportSize(dm, oldp, &supportSize);CHKERRQ(ierr);
      ierr = DMPlexGetSupport(dm, oldp, &support);CHKERRQ(ierr);
      if (dep == depth-1) {
        PetscBool       hasUnsplit = PETSC_FALSE;
        const PetscInt  hybcell    = p + pMaxNew[dep+1] + numSplitPoints[dep+1];
        const PetscInt *supportF;

        /* Split face:       copy in old face to new face to start */
        ierr = DMPlexGetSupport(sdm, newp,  &supportF);CHKERRQ(ierr);
        ierr = DMPlexSetSupport(sdm, splitp, supportF);CHKERRQ(ierr);
        /* Split old face:   old vertices/edges in cone so no change */
        /* Split new face:   new vertices/edges in cone */
        for (q = 0; q < coneSize; ++q) {
          ierr = PetscFindInt(cone[q], numSplitPoints[dep-1], splitPoints[dep-1], &v);CHKERRQ(ierr);
          if (v < 0) {
            ierr = PetscFindInt(cone[q], numUnsplitPoints[dep-1], unsplitPoints[dep-1], &v);CHKERRQ(ierr);
            if (v < 0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Could not locate point %d in split or unsplit points of depth %d", cone[q], dep-1);
            coneNew[2+q] = DMPlexShiftPoint_Internal(cone[q], depth, depthMax, depthEnd, depthShift) /*cone[q] + depthOffset[dep-1]*/;
            hasUnsplit   = PETSC_TRUE;
          } else {
            coneNew[2+q] = v + pMaxNew[dep-1];
            if (dep > 1) {
              const PetscInt *econe;
              PetscInt        econeSize, r, vs, vu;

              ierr = DMPlexGetConeSize(dm, cone[q], &econeSize);CHKERRQ(ierr);
              ierr = DMPlexGetCone(dm, cone[q], &econe);CHKERRQ(ierr);
              for (r = 0; r < econeSize; ++r) {
                ierr = PetscFindInt(econe[r], numSplitPoints[dep-2],   splitPoints[dep-2],   &vs);CHKERRQ(ierr);
                ierr = PetscFindInt(econe[r], numUnsplitPoints[dep-2], unsplitPoints[dep-2], &vu);CHKERRQ(ierr);
                if (vs >= 0) continue;
                if (vu < 0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Could not locate point %d in split or unsplit points of depth %d", econe[r], dep-2);
                hasUnsplit   = PETSC_TRUE;
              }
            }
          }
        }
        ierr = DMPlexSetCone(sdm, splitp, &coneNew[2]);CHKERRQ(ierr);
        ierr = DMPlexSetConeOrientation(sdm, splitp, ornt);CHKERRQ(ierr);
        /* Face support */
        for (s = 0; s < supportSize; ++s) {
          PetscInt val;

          ierr = DMLabelGetValue(label, support[s], &val);CHKERRQ(ierr);
          if (val < 0) {
            /* Split old face:   Replace negative side cell with cohesive cell */
             ierr = DMPlexInsertSupport(sdm, newp, s, hybcell);CHKERRQ(ierr);
          } else {
            /* Split new face:   Replace positive side cell with cohesive cell */
            ierr = DMPlexInsertSupport(sdm, splitp, s, hybcell);CHKERRQ(ierr);
            /* Get orientation for cohesive face */
            {
              const PetscInt *ncone, *nconeO;
              PetscInt        nconeSize, nc;

              ierr = DMPlexGetConeSize(dm, support[s], &nconeSize);CHKERRQ(ierr);
              ierr = DMPlexGetCone(dm, support[s], &ncone);CHKERRQ(ierr);
              ierr = DMPlexGetConeOrientation(dm, support[s], &nconeO);CHKERRQ(ierr);
              for (nc = 0; nc < nconeSize; ++nc) {
                if (ncone[nc] == oldp) {
                  coneONew[0] = nconeO[nc];
                  break;
                }
              }
              if (nc >= nconeSize) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Could not locate face %d in neighboring cell %d", oldp, support[s]);
            }
          }
        }
        /* Cohesive cell:    Old and new split face, then new cohesive faces */
        coneNew[0]  = newp;   /* Extracted negative side orientation above */
        coneNew[1]  = splitp;
        coneONew[1] = coneONew[0];
        for (q = 0; q < coneSize; ++q) {
          ierr = PetscFindInt(cone[q], numSplitPoints[dep-1], splitPoints[dep-1], &v);CHKERRQ(ierr);
          if (v < 0) {
            ierr = PetscFindInt(cone[q], numUnsplitPoints[dep-1], unsplitPoints[dep-1], &v);CHKERRQ(ierr);
            coneNew[2+q]  = v + pMaxNew[dep] + numSplitPoints[dep] + numSplitPoints[dep-1];
            coneONew[2+q] = 0;
          } else {
            coneNew[2+q]  = v + pMaxNew[dep] + numSplitPoints[dep];
          }
          coneONew[2+q] = 0;
        }
        ierr = DMPlexSetCone(sdm, hybcell, coneNew);CHKERRQ(ierr);
        ierr = DMPlexSetConeOrientation(sdm, hybcell, coneONew);CHKERRQ(ierr);
        /* Label the hybrid cells on the boundary of the split */
        if (hasUnsplit) {ierr = DMLabelSetValue(label, -hybcell, dim);CHKERRQ(ierr);}
      } else if (dep == 0) {
        const PetscInt hybedge = p + pMaxNew[dep+1] + numSplitPoints[dep+1];

        /* Split old vertex: Edges in old split faces and new cohesive edge */
        for (e = 0, qn = 0; e < supportSize; ++e) {
          PetscInt val;

          ierr = DMLabelGetValue(label, support[e], &val);CHKERRQ(ierr);
          if ((val == 1) || (val == (shift + 1))) {
            supportNew[qn++] = DMPlexShiftPoint_Internal(support[e], depth, depthMax, depthEnd, depthShift) /*support[e] + depthOffset[dep+1]*/;
          }
        }
        supportNew[qn] = hybedge;
        ierr = DMPlexSetSupport(sdm, newp, supportNew);CHKERRQ(ierr);
        /* Split new vertex: Edges in new split faces and new cohesive edge */
        for (e = 0, qp = 0; e < supportSize; ++e) {
          PetscInt val, edge;

          ierr = DMLabelGetValue(label, support[e], &val);CHKERRQ(ierr);
          if (val == 1) {
            ierr = PetscFindInt(support[e], numSplitPoints[dep+1], splitPoints[dep+1], &edge);CHKERRQ(ierr);
            if (edge < 0) SETERRQ1(comm, PETSC_ERR_ARG_WRONG, "Edge %d is not a split edge", support[e]);
            supportNew[qp++] = edge + pMaxNew[dep+1];
          } else if (val == -(shift + 1)) {
            supportNew[qp++] = DMPlexShiftPoint_Internal(support[e], depth, depthMax, depthEnd, depthShift) /*support[e] + depthOffset[dep+1]*/;
          }
        }
        supportNew[qp] = hybedge;
        ierr = DMPlexSetSupport(sdm, splitp, supportNew);CHKERRQ(ierr);
        /* Hybrid edge:    Old and new split vertex */
        coneNew[0] = newp;
        coneNew[1] = splitp;
        ierr = DMPlexSetCone(sdm, hybedge, coneNew);CHKERRQ(ierr);
        for (e = 0, qf = 0; e < supportSize; ++e) {
          PetscInt val, edge;

          ierr = DMLabelGetValue(label, support[e], &val);CHKERRQ(ierr);
          if (val == 1) {
            ierr = PetscFindInt(support[e], numSplitPoints[dep+1], splitPoints[dep+1], &edge);CHKERRQ(ierr);
            if (edge < 0) SETERRQ1(comm, PETSC_ERR_ARG_WRONG, "Edge %d is not a split edge", support[e]);
            supportNew[qf++] = edge + pMaxNew[dep+2] + numSplitPoints[dep+2];
          }
        }
        ierr = DMPlexSetSupport(sdm, hybedge, supportNew);CHKERRQ(ierr);
      } else if (dep == dim-2) {
        const PetscInt hybface = p + pMaxNew[dep+1] + numSplitPoints[dep+1];

        /* Split old edge:   old vertices in cone so no change */
        /* Split new edge:   new vertices in cone */
        for (q = 0; q < coneSize; ++q) {
          ierr = PetscFindInt(cone[q], numSplitPoints[dep-1], splitPoints[dep-1], &v);CHKERRQ(ierr);
          if (v < 0) {
            ierr = PetscFindInt(cone[q], numUnsplitPoints[dep-1], unsplitPoints[dep-1], &v);CHKERRQ(ierr);
            if (v < 0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Could not locate point %d in split or unsplit points of depth %d", cone[q], dep-1);
            coneNew[q] = DMPlexShiftPoint_Internal(cone[q], depth, depthMax, depthEnd, depthShift) /*cone[q] + depthOffset[dep-1]*/;
          } else {
            coneNew[q] = v + pMaxNew[dep-1];
          }
        }
        ierr = DMPlexSetCone(sdm, splitp, coneNew);CHKERRQ(ierr);
        /* Split old edge: Faces in positive side cells and old split faces */
        for (e = 0, q = 0; e < supportSize; ++e) {
          PetscInt val;

          ierr = DMLabelGetValue(label, support[e], &val);CHKERRQ(ierr);
          if (val == dim-1) {
            supportNew[q++] = DMPlexShiftPoint_Internal(support[e], depth, depthMax, depthEnd, depthShift) /*support[e] + depthOffset[dep+1]*/;
          } else if (val == (shift + dim-1)) {
            supportNew[q++] = DMPlexShiftPoint_Internal(support[e], depth, depthMax, depthEnd, depthShift) /*support[e] + depthOffset[dep+1]*/;
          }
        }
        supportNew[q++] = p + pMaxNew[dep+1] + numSplitPoints[dep+1];
        ierr = DMPlexSetSupport(sdm, newp, supportNew);CHKERRQ(ierr);
        /* Split new edge: Faces in negative side cells and new split faces */
        for (e = 0, q = 0; e < supportSize; ++e) {
          PetscInt val, face;

          ierr = DMLabelGetValue(label, support[e], &val);CHKERRQ(ierr);
          if (val == dim-1) {
            ierr = PetscFindInt(support[e], numSplitPoints[dep+1], splitPoints[dep+1], &face);CHKERRQ(ierr);
            if (face < 0) SETERRQ1(comm, PETSC_ERR_ARG_WRONG, "Face %d is not a split face", support[e]);
            supportNew[q++] = face + pMaxNew[dep+1];
          } else if (val == -(shift + dim-1)) {
            supportNew[q++] = DMPlexShiftPoint_Internal(support[e], depth, depthMax, depthEnd, depthShift) /*support[e] + depthOffset[dep+1]*/;
          }
        }
        supportNew[q++] = p + pMaxNew[dep+1] + numSplitPoints[dep+1];
        ierr = DMPlexSetSupport(sdm, splitp, supportNew);CHKERRQ(ierr);
        /* Hybrid face */
        coneNew[0] = newp;
        coneNew[1] = splitp;
        for (v = 0; v < coneSize; ++v) {
          PetscInt vertex;
          ierr = PetscFindInt(cone[v], numSplitPoints[dep-1], splitPoints[dep-1], &vertex);CHKERRQ(ierr);
          if (vertex < 0) {
            ierr = PetscFindInt(cone[v], numUnsplitPoints[dep-1], unsplitPoints[dep-1], &vertex);CHKERRQ(ierr);
            if (vertex < 0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Could not locate point %d in split or unsplit points of depth %d", cone[v], dep-1);
            coneNew[2+v] = vertex + pMaxNew[dep] + numSplitPoints[dep] + numSplitPoints[dep-1];
          } else {
            coneNew[2+v] = vertex + pMaxNew[dep] + numSplitPoints[dep];
          }
        }
        ierr = DMPlexSetCone(sdm, hybface, coneNew);CHKERRQ(ierr);
        for (e = 0, qf = 0; e < supportSize; ++e) {
          PetscInt val, face;

          ierr = DMLabelGetValue(label, support[e], &val);CHKERRQ(ierr);
          if (val == dim-1) {
            ierr = PetscFindInt(support[e], numSplitPoints[dep+1], splitPoints[dep+1], &face);CHKERRQ(ierr);
            if (face < 0) SETERRQ1(comm, PETSC_ERR_ARG_WRONG, "Face %d is not a split face", support[e]);
            supportNew[qf++] = face + pMaxNew[dep+2] + numSplitPoints[dep+2];
          }
        }
        ierr = DMPlexSetSupport(sdm, hybface, supportNew);CHKERRQ(ierr);
      }
    }
  }
  for (dep = 0; dep <= depth; ++dep) {
    for (p = 0; p < numUnsplitPoints[dep]; ++p) {
      const PetscInt  oldp   = unsplitPoints[dep][p];
      const PetscInt  newp   = DMPlexShiftPoint_Internal(oldp, depth, depthMax, depthEnd, depthShift) /*oldp + depthOffset[dep]*/;
      const PetscInt *cone, *support, *ornt;
      PetscInt        coneSize, supportSize, supportSizeNew, q, qf, e, f, s;

      ierr = DMPlexGetConeSize(dm, oldp, &coneSize);CHKERRQ(ierr);
      ierr = DMPlexGetCone(dm, oldp, &cone);CHKERRQ(ierr);
      ierr = DMPlexGetConeOrientation(dm, oldp, &ornt);CHKERRQ(ierr);
      ierr = DMPlexGetSupportSize(dm, oldp, &supportSize);CHKERRQ(ierr);
      ierr = DMPlexGetSupport(dm, oldp, &support);CHKERRQ(ierr);
      if (dep == 0) {
        const PetscInt hybedge = p + pMaxNew[dep+1] + numSplitPoints[dep+1] + numSplitPoints[dep];

        /* Unsplit vertex */
        ierr = DMPlexGetSupportSize(sdm, newp, &supportSizeNew);CHKERRQ(ierr);
        for (s = 0, q = 0; s < supportSize; ++s) {
          supportNew[q++] = DMPlexShiftPoint_Internal(support[s], depth, depthMax, depthEnd, depthShift) /*support[s] + depthOffset[dep+1]*/;
          ierr = PetscFindInt(support[s], numSplitPoints[dep+1], splitPoints[dep+1], &e);CHKERRQ(ierr);
          if (e >= 0) {
            supportNew[q++] = e + pMaxNew[dep+1];
          }
        }
        supportNew[q++] = hybedge;
        supportNew[q++] = hybedge;
        if (q != supportSizeNew) SETERRQ3(comm, PETSC_ERR_ARG_WRONG, "Support size %d != %d for vertex %d", q, supportSizeNew, newp);
        ierr = DMPlexSetSupport(sdm, newp, supportNew);CHKERRQ(ierr);
        /* Hybrid edge */
        coneNew[0] = newp;
        coneNew[1] = newp;
        ierr = DMPlexSetCone(sdm, hybedge, coneNew);CHKERRQ(ierr);
        for (e = 0, qf = 0; e < supportSize; ++e) {
          PetscInt val, edge;

          ierr = DMLabelGetValue(label, support[e], &val);CHKERRQ(ierr);
          if (val == 1) {
            ierr = PetscFindInt(support[e], numSplitPoints[dep+1], splitPoints[dep+1], &edge);CHKERRQ(ierr);
            if (edge < 0) SETERRQ1(comm, PETSC_ERR_ARG_WRONG, "Edge %d is not a split edge", support[e]);
            supportNew[qf++] = edge + pMaxNew[dep+2] + numSplitPoints[dep+2];
          } else if  (val ==  (shift2 + 1)) {
            ierr = PetscFindInt(support[e], numUnsplitPoints[dep+1], unsplitPoints[dep+1], &edge);CHKERRQ(ierr);
            if (edge < 0) SETERRQ1(comm, PETSC_ERR_ARG_WRONG, "Edge %d is not a unsplit edge", support[e]);
            supportNew[qf++] = edge + pMaxNew[dep+2] + numSplitPoints[dep+2] + numSplitPoints[dep+1];
          }
        }
        ierr = DMPlexSetSupport(sdm, hybedge, supportNew);CHKERRQ(ierr);
      } else if (dep == dim-2) {
        const PetscInt hybface = p + pMaxNew[dep+1] + numSplitPoints[dep+1] + numSplitPoints[dep];

        /* Unsplit edge: Faces into original edge, split face, and hybrid face twice */
        for (f = 0, qf = 0; f < supportSize; ++f) {
          PetscInt val, face;

          ierr = DMLabelGetValue(label, support[f], &val);CHKERRQ(ierr);
          if (val == dim-1) {
            ierr = PetscFindInt(support[f], numSplitPoints[dep+1], splitPoints[dep+1], &face);CHKERRQ(ierr);
            if (face < 0) SETERRQ1(comm, PETSC_ERR_ARG_WRONG, "Face %d is not a split face", support[f]);
            supportNew[qf++] = DMPlexShiftPoint_Internal(support[f], depth, depthMax, depthEnd, depthShift) /*support[f] + depthOffset[dep+1]*/;
            supportNew[qf++] = face + pMaxNew[dep+1];
          } else {
            supportNew[qf++] = DMPlexShiftPoint_Internal(support[f], depth, depthMax, depthEnd, depthShift) /*support[f] + depthOffset[dep+1]*/;
          }
        }
        supportNew[qf++] = hybface;
        supportNew[qf++] = hybface;
        ierr = DMPlexGetSupportSize(sdm, newp, &supportSizeNew);CHKERRQ(ierr);
        if (qf != supportSizeNew) SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Support size for unsplit edge %d is %d != %d\n", newp, qf, supportSizeNew);
        ierr = DMPlexSetSupport(sdm, newp, supportNew);CHKERRQ(ierr);
        /* Add hybrid face */
        coneNew[0] = newp;
        coneNew[1] = newp;
        ierr = PetscFindInt(cone[0], numUnsplitPoints[dep-1], unsplitPoints[dep-1], &v);CHKERRQ(ierr);
        if (v < 0) SETERRQ1(comm, PETSC_ERR_ARG_WRONG, "Vertex %d is not an unsplit vertex", cone[0]);
        coneNew[2] = v + pMaxNew[dep] + numSplitPoints[dep] + numSplitPoints[dep-1];
        ierr = PetscFindInt(cone[1], numUnsplitPoints[dep-1], unsplitPoints[dep-1], &v);CHKERRQ(ierr);
        if (v < 0) SETERRQ1(comm, PETSC_ERR_ARG_WRONG, "Vertex %d is not an unsplit vertex", cone[1]);
        coneNew[3] = v + pMaxNew[dep] + numSplitPoints[dep] + numSplitPoints[dep-1];
        ierr = DMPlexSetCone(sdm, hybface, coneNew);CHKERRQ(ierr);
        for (f = 0, qf = 0; f < supportSize; ++f) {
          PetscInt val, face;

          ierr = DMLabelGetValue(label, support[f], &val);CHKERRQ(ierr);
          if (val == dim-1) {
            ierr = PetscFindInt(support[f], numSplitPoints[dep+1], splitPoints[dep+1], &face);CHKERRQ(ierr);
            supportNew[qf++] = face + pMaxNew[dep+2] + numSplitPoints[dep+2];
          }
        }
        ierr = DMPlexGetSupportSize(sdm, hybface, &supportSizeNew);CHKERRQ(ierr);
        if (qf != supportSizeNew) SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Support size for hybrid face %d is %d != %d\n", hybface, qf, supportSizeNew);
        ierr = DMPlexSetSupport(sdm, hybface, supportNew);CHKERRQ(ierr);
      }
    }
  }
  /* Step 6b: Replace split points in negative side cones */
  for (sp = 0; sp < numSP; ++sp) {
    PetscInt        dep = values[sp];
    IS              pIS;
    PetscInt        numPoints;
    const PetscInt *points;

    if (dep >= 0) continue;
    ierr = DMLabelGetStratumIS(label, dep, &pIS);CHKERRQ(ierr);
    if (!pIS) continue;
    dep  = -dep - shift;
    ierr = ISGetLocalSize(pIS, &numPoints);CHKERRQ(ierr);
    ierr = ISGetIndices(pIS, &points);CHKERRQ(ierr);
    for (p = 0; p < numPoints; ++p) {
      const PetscInt  oldp = points[p];
      const PetscInt  newp = DMPlexShiftPoint_Internal(oldp, depth, depthMax, depthEnd, depthShift) /*depthOffset[dep] + oldp*/;
      const PetscInt *cone;
      PetscInt        coneSize, c;
      /* PetscBool       replaced = PETSC_FALSE; */

      /* Negative edge: replace split vertex */
      /* Negative cell: replace split face */
      ierr = DMPlexGetConeSize(sdm, newp, &coneSize);CHKERRQ(ierr);
      ierr = DMPlexGetCone(sdm, newp, &cone);CHKERRQ(ierr);
      for (c = 0; c < coneSize; ++c) {
        const PetscInt coldp = cone[c] - depthOffset[dep-1];
        PetscInt       csplitp, cp, val;

        ierr = DMLabelGetValue(label, coldp, &val);CHKERRQ(ierr);
        if (val == dep-1) {
          ierr = PetscFindInt(coldp, numSplitPoints[dep-1], splitPoints[dep-1], &cp);CHKERRQ(ierr);
          if (cp < 0) SETERRQ2(comm, PETSC_ERR_ARG_WRONG, "Point %d is not a split point of dimension %d", oldp, dep-1);
          csplitp  = pMaxNew[dep-1] + cp;
          ierr     = DMPlexInsertCone(sdm, newp, c, csplitp);CHKERRQ(ierr);
          /* replaced = PETSC_TRUE; */
        }
      }
      /* Cells with only a vertex or edge on the submesh have no replacement */
      /* if (!replaced) SETERRQ1(comm, PETSC_ERR_ARG_WRONG, "The cone of point %d does not contain split points", oldp); */
    }
    ierr = ISRestoreIndices(pIS, &points);CHKERRQ(ierr);
    ierr = ISDestroy(&pIS);CHKERRQ(ierr);
  }
  /* Step 7: Stratify */
  ierr = DMPlexStratify(sdm);CHKERRQ(ierr);
  /* Step 8: Coordinates */
  ierr = DMPlexShiftCoordinates_Internal(dm, depthShift, sdm);CHKERRQ(ierr);
  ierr = DMGetCoordinateSection(sdm, &coordSection);CHKERRQ(ierr);
  ierr = DMGetCoordinatesLocal(sdm, &coordinates);CHKERRQ(ierr);
  ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
  for (v = 0; v < (numSplitPoints ? numSplitPoints[0] : 0); ++v) {
    const PetscInt newp   = DMPlexShiftPoint_Internal(splitPoints[0][v], depth, depthMax, depthEnd, depthShift) /*depthOffset[0] + splitPoints[0][v]*/;
    const PetscInt splitp = pMaxNew[0] + v;
    PetscInt       dof, off, soff, d;

    ierr = PetscSectionGetDof(coordSection, newp, &dof);CHKERRQ(ierr);
    ierr = PetscSectionGetOffset(coordSection, newp, &off);CHKERRQ(ierr);
    ierr = PetscSectionGetOffset(coordSection, splitp, &soff);CHKERRQ(ierr);
    for (d = 0; d < dof; ++d) coords[soff+d] = coords[off+d];
  }
  ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
  /* Step 9: SF, if I can figure this out we can split the mesh in parallel */
  ierr = DMPlexShiftSF_Internal(dm, depthShift, sdm);CHKERRQ(ierr);
  /* Step 10: Labels */
  ierr = DMPlexShiftLabels_Internal(dm, depthShift, sdm);CHKERRQ(ierr);
  ierr = DMPlexGetNumLabels(sdm, &numLabels);CHKERRQ(ierr);
  for (dep = 0; dep <= depth; ++dep) {
    for (p = 0; p < numSplitPoints[dep]; ++p) {
      const PetscInt newp   = DMPlexShiftPoint_Internal(splitPoints[dep][p], depth, depthMax, depthEnd, depthShift) /*depthOffset[dep] + splitPoints[dep][p]*/;
      const PetscInt splitp = pMaxNew[dep] + p;
      PetscInt       l;

      for (l = 0; l < numLabels; ++l) {
        DMLabel     mlabel;
        const char *lname;
        PetscInt    val;
        PetscBool   isDepth;

        ierr = DMPlexGetLabelName(sdm, l, &lname);CHKERRQ(ierr);
        ierr = PetscStrcmp(lname, "depth", &isDepth);CHKERRQ(ierr);
        if (isDepth) continue;
        ierr = DMPlexGetLabel(sdm, lname, &mlabel);CHKERRQ(ierr);
        ierr = DMLabelGetValue(mlabel, newp, &val);CHKERRQ(ierr);
        if (val >= 0) {
          ierr = DMLabelSetValue(mlabel, splitp, val);CHKERRQ(ierr);
#if 0
          /* Do not put cohesive edges into the label */
          if (dep == 0) {
            const PetscInt cedge = p + pMaxNew[dep+1] + numSplitPoints[dep+1];
            ierr = DMLabelSetValue(mlabel, cedge, val);CHKERRQ(ierr);
          } else if (dep == dim-2) {
            const PetscInt cface = p + pMaxNew[dep+1] + numSplitPoints[dep+1];
            ierr = DMLabelSetValue(mlabel, cface, val);CHKERRQ(ierr);
          }
          /* Do not put cohesive faces into the label */
#endif
        }
      }
    }
  }
  for (sp = 0; sp < numSP; ++sp) {
    const PetscInt dep = values[sp];

    if ((dep < 0) || (dep > depth)) continue;
    if (splitIS[dep]) {ierr = ISRestoreIndices(splitIS[dep], &splitPoints[dep]);CHKERRQ(ierr);}
    ierr = ISDestroy(&splitIS[dep]);CHKERRQ(ierr);
    if (unsplitIS[dep]) {ierr = ISRestoreIndices(unsplitIS[dep], &unsplitPoints[dep]);CHKERRQ(ierr);}
    ierr = ISDestroy(&unsplitIS[dep]);CHKERRQ(ierr);
  }
  if (label) {
    ierr = ISRestoreIndices(valueIS, &values);CHKERRQ(ierr);
    ierr = ISDestroy(&valueIS);CHKERRQ(ierr);
  }
  for (d = 0; d <= depth; ++d) {
    ierr = DMPlexGetDepthStratum(sdm, d, NULL, &pEnd);CHKERRQ(ierr);
    pMaxNew[d] = pEnd - numHybridPoints[d] - numHybridPointsOld[d];
  }
  ierr = DMPlexSetHybridBounds(sdm, depth >= 0 ? pMaxNew[depth] : PETSC_DETERMINE, depth>1 ? pMaxNew[depth-1] : PETSC_DETERMINE, depth>2 ? pMaxNew[1] : PETSC_DETERMINE, depth >= 0 ? pMaxNew[0] : PETSC_DETERMINE);CHKERRQ(ierr);
  ierr = PetscFree3(coneNew, coneONew, supportNew);CHKERRQ(ierr);
  ierr = PetscFree6(depthMax, depthEnd, depthShift, depthOffset, pMaxNew, numHybridPointsOld);CHKERRQ(ierr);
  ierr = PetscFree7(splitIS, unsplitIS, numSplitPoints, numUnsplitPoints, numHybridPoints, splitPoints, unsplitPoints);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexConstructCohesiveCells"
/*@C
  DMPlexConstructCohesiveCells - Construct cohesive cells which split the face along an internal interface

  Collective on dm

  Input Parameters:
+ dm - The original DM
- label - The label specifying the boundary faces (this could be auto-generated)

  Output Parameters:
- dmSplit - The new DM

  Level: developer

.seealso: DMCreate(), DMPlexLabelCohesiveComplete()
@*/
PetscErrorCode DMPlexConstructCohesiveCells(DM dm, DMLabel label, DM *dmSplit)
{
  DM             sdm;
  PetscInt       dim;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidPointer(dmSplit, 3);
  ierr = DMCreate(PetscObjectComm((PetscObject)dm), &sdm);CHKERRQ(ierr);
  ierr = DMSetType(sdm, DMPLEX);CHKERRQ(ierr);
  ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
  ierr = DMPlexSetDimension(sdm, dim);CHKERRQ(ierr);
  switch (dim) {
  case 2:
  case 3:
    ierr = DMPlexConstructCohesiveCells_Internal(dm, label, sdm);CHKERRQ(ierr);
    break;
  default:
    SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "Cannot construct cohesive cells for dimension %d", dim);
  }
  *dmSplit = sdm;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexLabelCohesiveComplete"
/*@
  DMPlexLabelCohesiveComplete - Starting with a label marking vertices on an internal surface, we add all other mesh pieces
  to complete the surface

  Input Parameters:
+ dm - The DM
. label - A DMLabel marking the surface vertices
. flip  - Flag to flip the submesh normal and replace points on the other side
- subdm - The subDM associated with the label, or NULL

  Output Parameter:
. label - A DMLabel marking all surface points

  Level: developer

.seealso: DMPlexConstructCohesiveCells(), DMPlexLabelComplete()
@*/
PetscErrorCode DMPlexLabelCohesiveComplete(DM dm, DMLabel label, PetscBool flip, DM subdm)
{
  DMLabel         depthLabel;
  IS              dimIS, subpointIS, facePosIS, faceNegIS;
  const PetscInt *points, *subpoints;
  const PetscInt  rev   = flip ? -1 : 1;
  PetscInt        shift = 100, shift2 = 200, dim, dep, cStart, cEnd, numPoints, numSubpoints, p, val;
  PetscErrorCode  ierr;

  PetscFunctionBegin;
  ierr = DMPlexGetDepthLabel(dm, &depthLabel);CHKERRQ(ierr);
  ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
  if (subdm) {
    ierr = DMPlexCreateSubpointIS(subdm, &subpointIS);CHKERRQ(ierr);
    if (subpointIS) {
      ierr = ISGetLocalSize(subpointIS, &numSubpoints);CHKERRQ(ierr);
      ierr = ISGetIndices(subpointIS, &subpoints);CHKERRQ(ierr);
    }
  }
  /* Mark cell on the fault, and its faces which touch the fault: cell orientation for face gives the side of the fault */
  ierr = DMLabelGetStratumIS(label, dim-1, &dimIS);CHKERRQ(ierr);
  if (!dimIS) PetscFunctionReturn(0);
  ierr = ISGetLocalSize(dimIS, &numPoints);CHKERRQ(ierr);
  ierr = ISGetIndices(dimIS, &points);CHKERRQ(ierr);
  for (p = 0; p < numPoints; ++p) { /* Loop over fault faces */
    const PetscInt *support;
    PetscInt        supportSize, s;

    ierr = DMPlexGetSupportSize(dm, points[p], &supportSize);CHKERRQ(ierr);
    if (supportSize != 2) SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Split face %d has %d != 2 supports", points[p], supportSize);
    ierr = DMPlexGetSupport(dm, points[p], &support);CHKERRQ(ierr);
    for (s = 0; s < supportSize; ++s) {
      const PetscInt *cone, *ornt;
      PetscInt        coneSize, c;
      PetscBool       pos = PETSC_TRUE;

      ierr = DMPlexGetConeSize(dm, support[s], &coneSize);CHKERRQ(ierr);
      ierr = DMPlexGetCone(dm, support[s], &cone);CHKERRQ(ierr);
      ierr = DMPlexGetConeOrientation(dm, support[s], &ornt);CHKERRQ(ierr);
      for (c = 0; c < coneSize; ++c) {
        if (cone[c] == points[p]) {
          PetscInt o = ornt[c];

          if (subdm) {
            const PetscInt *subcone, *subornt;
            PetscInt        subpoint, subface, subconeSize, sc;

            ierr = PetscFindInt(support[s], numSubpoints, subpoints, &subpoint);CHKERRQ(ierr);
            ierr = PetscFindInt(points[p],  numSubpoints, subpoints, &subface);CHKERRQ(ierr);
            ierr = DMPlexGetConeSize(subdm, subpoint, &subconeSize);CHKERRQ(ierr);
            ierr = DMPlexGetCone(subdm, subpoint, &subcone);CHKERRQ(ierr);
            ierr = DMPlexGetConeOrientation(subdm, subpoint, &subornt);CHKERRQ(ierr);
            for (sc = 0; sc < subconeSize; ++sc) {
              if (subcone[sc] == subface) {
                o = subornt[0];
                break;
              }
            }
            if (sc >= subconeSize) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Could not find point %d in cone for subpoint %d", points[p], subpoint);
          }
          if (o >= 0) {
            ierr = DMLabelSetValue(label, support[s],  rev*(shift+dim));CHKERRQ(ierr);
            pos  = rev > 0 ? PETSC_TRUE : PETSC_FALSE;
          } else {
            ierr = DMLabelSetValue(label, support[s], -rev*(shift+dim));CHKERRQ(ierr);
            pos  = rev > 0 ? PETSC_FALSE : PETSC_TRUE;
          }
          break;
        }
      }
      if (c == coneSize) SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Cell split face %d support does not have it in the cone", points[p]);
      /* Put faces touching the fault in the label */
      for (c = 0; c < coneSize; ++c) {
        const PetscInt point = cone[c];

        ierr = DMLabelGetValue(label, point, &val);CHKERRQ(ierr);
        if (val == -1) {
          PetscInt *closure = NULL;
          PetscInt  closureSize, cl;

          ierr = DMPlexGetTransitiveClosure(dm, point, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
          for (cl = 0; cl < closureSize*2; cl += 2) {
            const PetscInt clp = closure[cl];

            ierr = DMLabelGetValue(label, clp, &val);CHKERRQ(ierr);
            if ((val >= 0) && (val < dim-1)) {
              ierr = DMLabelSetValue(label, point, pos == PETSC_TRUE ? shift+dim-1 : -(shift+dim-1));CHKERRQ(ierr);
              break;
            }
          }
          ierr = DMPlexRestoreTransitiveClosure(dm, point, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
        }
      }
    }
  }
  if (subdm) {
    if (subpointIS) {ierr = ISRestoreIndices(subpointIS, &subpoints);CHKERRQ(ierr);}
    ierr = ISDestroy(&subpointIS);CHKERRQ(ierr);
  }
  ierr = ISRestoreIndices(dimIS, &points);CHKERRQ(ierr);
  ierr = ISDestroy(&dimIS);CHKERRQ(ierr);
  /* Search for other cells/faces/edges connected to the fault by a vertex */
  ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
  ierr = DMLabelGetStratumIS(label, 0, &dimIS);CHKERRQ(ierr);
  if (!dimIS) PetscFunctionReturn(0);
  ierr = ISGetLocalSize(dimIS, &numPoints);CHKERRQ(ierr);
  ierr = ISGetIndices(dimIS, &points);CHKERRQ(ierr);
  for (p = 0; p < numPoints; ++p) { /* Loop over fault vertices */
    PetscInt *star = NULL;
    PetscInt  starSize, s;
    PetscInt  again = 1;  /* 0: Finished 1: Keep iterating after a change 2: No change */

    /* All points connected to the fault are inside a cell, so at the top level we will only check cells */
    ierr = DMPlexGetTransitiveClosure(dm, points[p], PETSC_FALSE, &starSize, &star);CHKERRQ(ierr);
    while (again) {
      if (again > 1) SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Could not classify all cells connected to the fault");
      again = 0;
      for (s = 0; s < starSize*2; s += 2) {
        const PetscInt  point = star[s];
        const PetscInt *cone;
        PetscInt        coneSize, c;

        if ((point < cStart) || (point >= cEnd)) continue;
        ierr = DMLabelGetValue(label, point, &val);CHKERRQ(ierr);
        if (val != -1) continue;
        again = again == 1 ? 1 : 2;
        ierr  = DMPlexGetConeSize(dm, point, &coneSize);CHKERRQ(ierr);
        ierr  = DMPlexGetCone(dm, point, &cone);CHKERRQ(ierr);
        for (c = 0; c < coneSize; ++c) {
          ierr = DMLabelGetValue(label, cone[c], &val);CHKERRQ(ierr);
          if (val != -1) {
            const PetscInt *ccone;
            PetscInt        cconeSize, cc, side;

            if (abs(val) < shift) SETERRQ3(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Face %d on cell %d has an invalid label %d", cone[c], point, val);
            if (val > 0) side =  1;
            else         side = -1;
            ierr = DMLabelSetValue(label, point, side*(shift+dim));CHKERRQ(ierr);
            /* Mark cell faces which touch the fault */
            ierr = DMPlexGetConeSize(dm, point, &cconeSize);CHKERRQ(ierr);
            ierr = DMPlexGetCone(dm, point, &ccone);CHKERRQ(ierr);
            for (cc = 0; cc < cconeSize; ++cc) {
              PetscInt *closure = NULL;
              PetscInt  closureSize, cl;

              ierr = DMLabelGetValue(label, ccone[cc], &val);CHKERRQ(ierr);
              if (val != -1) continue;
              ierr = DMPlexGetTransitiveClosure(dm, ccone[cc], PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
              for (cl = 0; cl < closureSize*2; cl += 2) {
                const PetscInt clp = closure[cl];

                ierr = DMLabelGetValue(label, clp, &val);CHKERRQ(ierr);
                if (val == -1) continue;
                ierr = DMLabelSetValue(label, ccone[cc], side*(shift+dim-1));CHKERRQ(ierr);
                break;
              }
              ierr = DMPlexRestoreTransitiveClosure(dm, ccone[cc], PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
            }
            again = 1;
            break;
          }
        }
      }
    }
    /* Classify the rest by cell membership */
    for (s = 0; s < starSize*2; s += 2) {
      const PetscInt point = star[s];

      ierr = DMLabelGetValue(label, point, &val);CHKERRQ(ierr);
      if (val == -1) {
        PetscInt  *sstar = NULL;
        PetscInt   sstarSize, ss;
        PetscBool  marked = PETSC_FALSE;

        ierr = DMPlexGetTransitiveClosure(dm, point, PETSC_FALSE, &sstarSize, &sstar);CHKERRQ(ierr);
        for (ss = 0; ss < sstarSize*2; ss += 2) {
          const PetscInt spoint = sstar[ss];

          if ((spoint < cStart) || (spoint >= cEnd)) continue;
          ierr = DMLabelGetValue(label, spoint, &val);CHKERRQ(ierr);
          if (val == -1) SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Cell %d in star of %d does not have a valid label", spoint, point);
          ierr = DMLabelGetValue(depthLabel, point, &dep);CHKERRQ(ierr);
          if (val > 0) {
            ierr = DMLabelSetValue(label, point,   shift+dep);CHKERRQ(ierr);
          } else {
            ierr = DMLabelSetValue(label, point, -(shift+dep));CHKERRQ(ierr);
          }
          marked = PETSC_TRUE;
          break;
        }
        ierr = DMPlexRestoreTransitiveClosure(dm, point, PETSC_FALSE, &sstarSize, &sstar);CHKERRQ(ierr);
        if (!marked) SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Point %d could not be classified", point);
      }
    }
    ierr = DMPlexRestoreTransitiveClosure(dm, points[p], PETSC_FALSE, &starSize, &star);CHKERRQ(ierr);
  }
  ierr = ISRestoreIndices(dimIS, &points);CHKERRQ(ierr);
  ierr = ISDestroy(&dimIS);CHKERRQ(ierr);
  /* If any faces touching the fault divide cells on either side, split them */
  ierr = DMLabelGetStratumIS(label,   shift+dim-1,  &facePosIS);CHKERRQ(ierr);
  ierr = DMLabelGetStratumIS(label, -(shift+dim-1), &faceNegIS);CHKERRQ(ierr);
  ierr = ISExpand(facePosIS, faceNegIS, &dimIS);CHKERRQ(ierr);
  ierr = ISDestroy(&facePosIS);CHKERRQ(ierr);
  ierr = ISDestroy(&faceNegIS);CHKERRQ(ierr);
  ierr = ISGetLocalSize(dimIS, &numPoints);CHKERRQ(ierr);
  ierr = ISGetIndices(dimIS, &points);CHKERRQ(ierr);
  for (p = 0; p < numPoints; ++p) {
    const PetscInt  point = points[p];
    const PetscInt *support;
    PetscInt        supportSize, valA, valB;

    ierr = DMPlexGetSupportSize(dm, point, &supportSize);CHKERRQ(ierr);
    if (supportSize != 2) continue;
    ierr = DMPlexGetSupport(dm, point, &support);CHKERRQ(ierr);
    ierr = DMLabelGetValue(label, support[0], &valA);CHKERRQ(ierr);
    ierr = DMLabelGetValue(label, support[1], &valB);CHKERRQ(ierr);
    if ((valA == -1) || (valB == -1)) continue;
    if (valA*valB > 0) continue;
    /* Split the face */
    ierr = DMLabelGetValue(label, point, &valA);CHKERRQ(ierr);
    ierr = DMLabelClearValue(label, point, valA);CHKERRQ(ierr);
    ierr = DMLabelSetValue(label, point, dim-1);CHKERRQ(ierr);
    /* Label its closure:
      unmarked: label as unsplit
      incident: relabel as split
      split:    do nothing
    */
    {
      PetscInt *closure = NULL;
      PetscInt  closureSize, cl;

      ierr = DMPlexGetTransitiveClosure(dm, point, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
      for (cl = 0; cl < closureSize*2; cl += 2) {
        ierr = DMLabelGetValue(label, closure[cl], &valA);CHKERRQ(ierr);
        if (valA == -1) { /* Mark as unsplit */
          ierr = DMLabelGetValue(depthLabel, closure[cl], &dep);CHKERRQ(ierr);
          ierr = DMLabelSetValue(label, closure[cl], shift2+dep);CHKERRQ(ierr);
        } else if (((valA >= shift) && (valA < shift2)) || ((valA <= -shift) && (valA > -shift2))) {
          ierr = DMLabelGetValue(depthLabel, closure[cl], &dep);CHKERRQ(ierr);
          ierr = DMLabelClearValue(label, closure[cl], valA);CHKERRQ(ierr);
          ierr = DMLabelSetValue(label, closure[cl], dep);CHKERRQ(ierr);
        }
      }
      ierr = DMPlexRestoreTransitiveClosure(dm, point, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
    }
  }
  ierr = ISRestoreIndices(dimIS, &points);CHKERRQ(ierr);
  ierr = ISDestroy(&dimIS);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexCreateHybridMesh"
/*@C
  DMPlexCreateHybridMesh - Create a mesh with hybrid cells along an internal interface

  Collective on dm

  Input Parameters:
+ dm - The original DM
- labelName - The label specifying the interface vertices

  Output Parameters:
+ hybridLabel - The label fully marking the interface
- dmHybrid - The new DM

  Level: developer

.seealso: DMPlexConstructCohesiveCells(), DMPlexLabelCohesiveComplete(), DMCreate()
@*/
PetscErrorCode DMPlexCreateHybridMesh(DM dm, DMLabel label, DMLabel *hybridLabel, DM *dmHybrid)
{
  DM             idm;
  DMLabel        subpointMap, hlabel;
  PetscInt       dim;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (hybridLabel) PetscValidPointer(hybridLabel, 3);
  PetscValidPointer(dmHybrid, 4);
  ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
  ierr = DMPlexCreateSubmesh(dm, label, 1, &idm);CHKERRQ(ierr);
  ierr = DMPlexOrient(idm);CHKERRQ(ierr);
  ierr = DMPlexGetSubpointMap(idm, &subpointMap);CHKERRQ(ierr);
  ierr = DMLabelDuplicate(subpointMap, &hlabel);CHKERRQ(ierr);
  ierr = DMLabelClearStratum(hlabel, dim);CHKERRQ(ierr);
  ierr = DMPlexLabelCohesiveComplete(dm, hlabel, PETSC_FALSE, idm);CHKERRQ(ierr);
  ierr = DMDestroy(&idm);CHKERRQ(ierr);
  ierr = DMPlexConstructCohesiveCells(dm, hlabel, dmHybrid);CHKERRQ(ierr);
  if (hybridLabel) *hybridLabel = hlabel;
  else             {ierr = DMLabelDestroy(&hlabel);CHKERRQ(ierr);}
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexMarkSubmesh_Uninterpolated"
/* Here we need the explicit assumption that:

     For any marked cell, the marked vertices constitute a single face
*/
static PetscErrorCode DMPlexMarkSubmesh_Uninterpolated(DM dm, DMLabel vertexLabel, PetscInt value, DMLabel subpointMap, PetscInt *numFaces, PetscInt *nFV, DM subdm)
{
  IS               subvertexIS = NULL;
  const PetscInt  *subvertices;
  PetscInt        *pStart, *pEnd, *pMax, pSize;
  PetscInt         depth, dim, d, numSubVerticesInitial = 0, v;
  PetscErrorCode   ierr;

  PetscFunctionBegin;
  *numFaces = 0;
  *nFV      = 0;
  ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
  ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
  pSize = PetscMax(depth, dim) + 1;
  ierr = PetscMalloc3(pSize,&pStart,pSize,&pEnd,pSize,&pMax);CHKERRQ(ierr);
  ierr = DMPlexGetHybridBounds(dm, depth >= 0 ? &pMax[depth] : NULL, depth>1 ? &pMax[depth-1] : NULL, depth>2 ? &pMax[1] : NULL, &pMax[0]);CHKERRQ(ierr);
  for (d = 0; d <= depth; ++d) {
    ierr = DMPlexGetDepthStratum(dm, d, &pStart[d], &pEnd[d]);CHKERRQ(ierr);
    if (pMax[d] >= 0) pEnd[d] = PetscMin(pEnd[d], pMax[d]);
  }
  /* Loop over initial vertices and mark all faces in the collective star() */
  if (vertexLabel) {ierr = DMLabelGetStratumIS(vertexLabel, value, &subvertexIS);CHKERRQ(ierr);}
  if (subvertexIS) {
    ierr = ISGetSize(subvertexIS, &numSubVerticesInitial);CHKERRQ(ierr);
    ierr = ISGetIndices(subvertexIS, &subvertices);CHKERRQ(ierr);
  }
  for (v = 0; v < numSubVerticesInitial; ++v) {
    const PetscInt vertex = subvertices[v];
    PetscInt      *star   = NULL;
    PetscInt       starSize, s, numCells = 0, c;

    ierr = DMPlexGetTransitiveClosure(dm, vertex, PETSC_FALSE, &starSize, &star);CHKERRQ(ierr);
    for (s = 0; s < starSize*2; s += 2) {
      const PetscInt point = star[s];
      if ((point >= pStart[depth]) && (point < pEnd[depth])) star[numCells++] = point;
    }
    for (c = 0; c < numCells; ++c) {
      const PetscInt cell    = star[c];
      PetscInt      *closure = NULL;
      PetscInt       closureSize, cl;
      PetscInt       cellLoc, numCorners = 0, faceSize = 0;

      ierr = DMLabelGetValue(subpointMap, cell, &cellLoc);CHKERRQ(ierr);
      if (cellLoc == 2) continue;
      if (cellLoc >= 0) SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Cell %d has dimension %d in the surface label", cell, cellLoc);
      ierr = DMPlexGetTransitiveClosure(dm, cell, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
      for (cl = 0; cl < closureSize*2; cl += 2) {
        const PetscInt point = closure[cl];
        PetscInt       vertexLoc;

        if ((point >= pStart[0]) && (point < pEnd[0])) {
          ++numCorners;
          ierr = DMLabelGetValue(vertexLabel, point, &vertexLoc);CHKERRQ(ierr);
          if (vertexLoc == value) closure[faceSize++] = point;
        }
      }
      if (!(*nFV)) {ierr = DMPlexGetNumFaceVertices(dm, dim, numCorners, nFV);CHKERRQ(ierr);}
      if (faceSize > *nFV) SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Invalid submesh: Too many vertices %d of an element on the surface", faceSize);
      if (faceSize == *nFV) {
        const PetscInt *cells = NULL;
        PetscInt        numCells, nc;

        ++(*numFaces);
        for (cl = 0; cl < faceSize; ++cl) {
          ierr = DMLabelSetValue(subpointMap, closure[cl], 0);CHKERRQ(ierr);
        }
        ierr = DMPlexGetJoin(dm, faceSize, closure, &numCells, &cells);CHKERRQ(ierr);
        for (nc = 0; nc < numCells; ++nc) {
          ierr = DMLabelSetValue(subpointMap, cells[nc], 2);CHKERRQ(ierr);
        }
        ierr = DMPlexRestoreJoin(dm, faceSize, closure, &numCells, &cells);CHKERRQ(ierr);
      }
      ierr = DMPlexRestoreTransitiveClosure(dm, cell, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
    }
    ierr = DMPlexRestoreTransitiveClosure(dm, vertex, PETSC_FALSE, &starSize, &star);CHKERRQ(ierr);
  }
  if (subvertexIS) {
    ierr = ISRestoreIndices(subvertexIS, &subvertices);CHKERRQ(ierr);
  }
  ierr = ISDestroy(&subvertexIS);CHKERRQ(ierr);
  ierr = PetscFree3(pStart,pEnd,pMax);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexMarkSubmesh_Interpolated"
static PetscErrorCode DMPlexMarkSubmesh_Interpolated(DM dm, DMLabel vertexLabel, PetscInt value, DMLabel subpointMap, DM subdm)
{
  IS               subvertexIS;
  const PetscInt  *subvertices;
  PetscInt        *pStart, *pEnd, *pMax;
  PetscInt         dim, d, numSubVerticesInitial = 0, v;
  PetscErrorCode   ierr;

  PetscFunctionBegin;
  ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
  ierr = PetscMalloc3(dim+1,&pStart,dim+1,&pEnd,dim+1,&pMax);CHKERRQ(ierr);
  ierr = DMPlexGetHybridBounds(dm, &pMax[dim], dim>1 ? &pMax[dim-1] : NULL, dim > 2 ? &pMax[1] : NULL, &pMax[0]);CHKERRQ(ierr);
  for (d = 0; d <= dim; ++d) {
    ierr = DMPlexGetDepthStratum(dm, d, &pStart[d], &pEnd[d]);CHKERRQ(ierr);
    if (pMax[d] >= 0) pEnd[d] = PetscMin(pEnd[d], pMax[d]);
  }
  /* Loop over initial vertices and mark all faces in the collective star() */
  ierr = DMLabelGetStratumIS(vertexLabel, value, &subvertexIS);CHKERRQ(ierr);
  if (subvertexIS) {
    ierr = ISGetSize(subvertexIS, &numSubVerticesInitial);CHKERRQ(ierr);
    ierr = ISGetIndices(subvertexIS, &subvertices);CHKERRQ(ierr);
  }
  for (v = 0; v < numSubVerticesInitial; ++v) {
    const PetscInt vertex = subvertices[v];
    PetscInt      *star   = NULL;
    PetscInt       starSize, s, numFaces = 0, f;

    ierr = DMPlexGetTransitiveClosure(dm, vertex, PETSC_FALSE, &starSize, &star);CHKERRQ(ierr);
    for (s = 0; s < starSize*2; s += 2) {
      const PetscInt point = star[s];
      if ((point >= pStart[dim-1]) && (point < pEnd[dim-1])) star[numFaces++] = point;
    }
    for (f = 0; f < numFaces; ++f) {
      const PetscInt face    = star[f];
      PetscInt      *closure = NULL;
      PetscInt       closureSize, c;
      PetscInt       faceLoc;

      ierr = DMLabelGetValue(subpointMap, face, &faceLoc);CHKERRQ(ierr);
      if (faceLoc == dim-1) continue;
      if (faceLoc >= 0) SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Face %d has dimension %d in the surface label", face, faceLoc);
      ierr = DMPlexGetTransitiveClosure(dm, face, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
      for (c = 0; c < closureSize*2; c += 2) {
        const PetscInt point = closure[c];
        PetscInt       vertexLoc;

        if ((point >= pStart[0]) && (point < pEnd[0])) {
          ierr = DMLabelGetValue(vertexLabel, point, &vertexLoc);CHKERRQ(ierr);
          if (vertexLoc != value) break;
        }
      }
      if (c == closureSize*2) {
        const PetscInt *support;
        PetscInt        supportSize, s;

        for (c = 0; c < closureSize*2; c += 2) {
          const PetscInt point = closure[c];

          for (d = 0; d < dim; ++d) {
            if ((point >= pStart[d]) && (point < pEnd[d])) {
              ierr = DMLabelSetValue(subpointMap, point, d);CHKERRQ(ierr);
              break;
            }
          }
        }
        ierr = DMPlexGetSupportSize(dm, face, &supportSize);CHKERRQ(ierr);
        ierr = DMPlexGetSupport(dm, face, &support);CHKERRQ(ierr);
        for (s = 0; s < supportSize; ++s) {
          ierr = DMLabelSetValue(subpointMap, support[s], dim);CHKERRQ(ierr);
        }
      }
      ierr = DMPlexRestoreTransitiveClosure(dm, face, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
    }
    ierr = DMPlexRestoreTransitiveClosure(dm, vertex, PETSC_FALSE, &starSize, &star);CHKERRQ(ierr);
  }
  if (subvertexIS) {
    ierr = ISRestoreIndices(subvertexIS, &subvertices);CHKERRQ(ierr);
  }
  ierr = ISDestroy(&subvertexIS);CHKERRQ(ierr);
  ierr = PetscFree3(pStart,pEnd,pMax);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexMarkCohesiveSubmesh_Uninterpolated"
static PetscErrorCode DMPlexMarkCohesiveSubmesh_Uninterpolated(DM dm, PetscBool hasLagrange, const char labelname[], PetscInt value, DMLabel subpointMap, PetscInt *numFaces, PetscInt *nFV, PetscInt *subCells[], DM subdm)
{
  DMLabel         label = NULL;
  const PetscInt *cone;
  PetscInt        dim, cMax, cEnd, c, subc = 0, p, coneSize;
  PetscErrorCode  ierr;

  PetscFunctionBegin;
  *numFaces = 0;
  *nFV = 0;
  if (labelname) {ierr = DMPlexGetLabel(dm, labelname, &label);CHKERRQ(ierr);}
  *subCells = NULL;
  ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
  ierr = DMPlexGetHeightStratum(dm, 0, NULL, &cEnd);CHKERRQ(ierr);
  ierr = DMPlexGetHybridBounds(dm, &cMax, NULL, NULL, NULL);CHKERRQ(ierr);
  if (cMax < 0) PetscFunctionReturn(0);
  if (label) {
    for (c = cMax; c < cEnd; ++c) {
      PetscInt val;

      ierr = DMLabelGetValue(label, c, &val);CHKERRQ(ierr);
      if (val == value) {
        ++(*numFaces);
        ierr = DMPlexGetConeSize(dm, c, &coneSize);CHKERRQ(ierr);
      }
    }
  } else {
    *numFaces = cEnd - cMax;
    ierr = DMPlexGetConeSize(dm, cMax, &coneSize);CHKERRQ(ierr);
  }
  *nFV = hasLagrange ? coneSize/3 : coneSize/2;
  ierr = PetscMalloc1(*numFaces *2, subCells);CHKERRQ(ierr);
  for (c = cMax; c < cEnd; ++c) {
    const PetscInt *cells;
    PetscInt        numCells;

    if (label) {
      PetscInt val;

      ierr = DMLabelGetValue(label, c, &val);CHKERRQ(ierr);
      if (val != value) continue;
    }
    ierr = DMPlexGetCone(dm, c, &cone);CHKERRQ(ierr);
    for (p = 0; p < *nFV; ++p) {
      ierr = DMLabelSetValue(subpointMap, cone[p], 0);CHKERRQ(ierr);
    }
    /* Negative face */
    ierr = DMPlexGetJoin(dm, *nFV, cone, &numCells, &cells);CHKERRQ(ierr);
    /* Not true in parallel
    if (numCells != 2) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cohesive cells should separate two cells"); */
    for (p = 0; p < numCells; ++p) {
      ierr = DMLabelSetValue(subpointMap, cells[p], 2);CHKERRQ(ierr);
      (*subCells)[subc++] = cells[p];
    }
    ierr = DMPlexRestoreJoin(dm, *nFV, cone, &numCells, &cells);CHKERRQ(ierr);
    /* Positive face is not included */
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexMarkCohesiveSubmesh_Interpolated"
static PetscErrorCode DMPlexMarkCohesiveSubmesh_Interpolated(DM dm, const char labelname[], PetscInt value, DMLabel subpointMap, DM subdm)
{
  DMLabel        label = NULL;
  PetscInt      *pStart, *pEnd;
  PetscInt       dim, cMax, cEnd, c, d;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if (labelname) {ierr = DMPlexGetLabel(dm, labelname, &label);CHKERRQ(ierr);}
  ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
  ierr = DMPlexGetHeightStratum(dm, 0, NULL, &cEnd);CHKERRQ(ierr);
  ierr = DMPlexGetHybridBounds(dm, &cMax, NULL, NULL, NULL);CHKERRQ(ierr);
  if (cMax < 0) PetscFunctionReturn(0);
  ierr = PetscMalloc2(dim+1,&pStart,dim+1,&pEnd);CHKERRQ(ierr);
  for (d = 0; d <= dim; ++d) {ierr = DMPlexGetDepthStratum(dm, d, &pStart[d], &pEnd[d]);CHKERRQ(ierr);}
  for (c = cMax; c < cEnd; ++c) {
    const PetscInt *cone;
    PetscInt       *closure = NULL;
    PetscInt        fconeSize, coneSize, closureSize, cl, val;

    if (label) {
      ierr = DMLabelGetValue(label, c, &val);CHKERRQ(ierr);
      if (val != value) continue;
    }
    ierr = DMPlexGetConeSize(dm, c, &coneSize);CHKERRQ(ierr);
    ierr = DMPlexGetCone(dm, c, &cone);CHKERRQ(ierr);
    ierr = DMPlexGetConeSize(dm, cone[0], &fconeSize);CHKERRQ(ierr);
    if (coneSize != (fconeSize ? fconeSize : 1) + 2) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cohesive cells should separate two cells");
    /* Negative face */
    ierr = DMPlexGetTransitiveClosure(dm, cone[0], PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
    for (cl = 0; cl < closureSize*2; cl += 2) {
      const PetscInt point = closure[cl];

      for (d = 0; d <= dim; ++d) {
        if ((point >= pStart[d]) && (point < pEnd[d])) {
          ierr = DMLabelSetValue(subpointMap, point, d);CHKERRQ(ierr);
          break;
        }
      }
    }
    ierr = DMPlexRestoreTransitiveClosure(dm, cone[0], PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
    /* Cells -- positive face is not included */
    for (cl = 0; cl < 1; ++cl) {
      const PetscInt *support;
      PetscInt        supportSize, s;

      ierr = DMPlexGetSupportSize(dm, cone[cl], &supportSize);CHKERRQ(ierr);
      /* if (supportSize != 2) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cohesive faces should separate two cells"); */
      ierr = DMPlexGetSupport(dm, cone[cl], &support);CHKERRQ(ierr);
      for (s = 0; s < supportSize; ++s) {
        ierr = DMLabelSetValue(subpointMap, support[s], dim);CHKERRQ(ierr);
      }
    }
  }
  ierr = PetscFree2(pStart, pEnd);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetFaceOrientation"
PetscErrorCode DMPlexGetFaceOrientation(DM dm, PetscInt cell, PetscInt numCorners, PetscInt indices[], PetscInt oppositeVertex, PetscInt origVertices[], PetscInt faceVertices[], PetscBool *posOriented)
{
  MPI_Comm       comm;
  PetscBool      posOrient = PETSC_FALSE;
  const PetscInt debug     = 0;
  PetscInt       cellDim, faceSize, f;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscObjectGetComm((PetscObject)dm,&comm);CHKERRQ(ierr);
  ierr = DMPlexGetDimension(dm, &cellDim);CHKERRQ(ierr);
  if (debug) {PetscPrintf(comm, "cellDim: %d numCorners: %d\n", cellDim, numCorners);CHKERRQ(ierr);}

  if (cellDim == 1 && numCorners == 2) {
    /* Triangle */
    faceSize  = numCorners-1;
    posOrient = !(oppositeVertex%2) ? PETSC_TRUE : PETSC_FALSE;
  } else if (cellDim == 2 && numCorners == 3) {
    /* Triangle */
    faceSize  = numCorners-1;
    posOrient = !(oppositeVertex%2) ? PETSC_TRUE : PETSC_FALSE;
  } else if (cellDim == 3 && numCorners == 4) {
    /* Tetrahedron */
    faceSize  = numCorners-1;
    posOrient = (oppositeVertex%2) ? PETSC_TRUE : PETSC_FALSE;
  } else if (cellDim == 1 && numCorners == 3) {
    /* Quadratic line */
    faceSize  = 1;
    posOrient = PETSC_TRUE;
  } else if (cellDim == 2 && numCorners == 4) {
    /* Quads */
    faceSize = 2;
    if ((indices[1] > indices[0]) && (indices[1] - indices[0] == 1)) {
      posOrient = PETSC_TRUE;
    } else if ((indices[0] == 3) && (indices[1] == 0)) {
      posOrient = PETSC_TRUE;
    } else {
      if (((indices[0] > indices[1]) && (indices[0] - indices[1] == 1)) || ((indices[0] == 0) && (indices[1] == 3))) {
        posOrient = PETSC_FALSE;
      } else SETERRQ(comm, PETSC_ERR_ARG_WRONG, "Invalid quad crossedge");
    }
  } else if (cellDim == 2 && numCorners == 6) {
    /* Quadratic triangle (I hate this) */
    /* Edges are determined by the first 2 vertices (corners of edges) */
    const PetscInt faceSizeTri = 3;
    PetscInt       sortedIndices[3], i, iFace;
    PetscBool      found                    = PETSC_FALSE;
    PetscInt       faceVerticesTriSorted[9] = {
      0, 3,  4, /* bottom */
      1, 4,  5, /* right */
      2, 3,  5, /* left */
    };
    PetscInt       faceVerticesTri[9] = {
      0, 3,  4, /* bottom */
      1, 4,  5, /* right */
      2, 5,  3, /* left */
    };

    faceSize = faceSizeTri;
    for (i = 0; i < faceSizeTri; ++i) sortedIndices[i] = indices[i];
    ierr = PetscSortInt(faceSizeTri, sortedIndices);CHKERRQ(ierr);
    for (iFace = 0; iFace < 3; ++iFace) {
      const PetscInt ii = iFace*faceSizeTri;
      PetscInt       fVertex, cVertex;

      if ((sortedIndices[0] == faceVerticesTriSorted[ii+0]) &&
          (sortedIndices[1] == faceVerticesTriSorted[ii+1])) {
        for (fVertex = 0; fVertex < faceSizeTri; ++fVertex) {
          for (cVertex = 0; cVertex < faceSizeTri; ++cVertex) {
            if (indices[cVertex] == faceVerticesTri[ii+fVertex]) {
              faceVertices[fVertex] = origVertices[cVertex];
              break;
            }
          }
        }
        found = PETSC_TRUE;
        break;
      }
    }
    if (!found) SETERRQ(comm, PETSC_ERR_ARG_WRONG, "Invalid tri crossface");
    if (posOriented) *posOriented = PETSC_TRUE;
    PetscFunctionReturn(0);
  } else if (cellDim == 2 && numCorners == 9) {
    /* Quadratic quad (I hate this) */
    /* Edges are determined by the first 2 vertices (corners of edges) */
    const PetscInt faceSizeQuad = 3;
    PetscInt       sortedIndices[3], i, iFace;
    PetscBool      found                      = PETSC_FALSE;
    PetscInt       faceVerticesQuadSorted[12] = {
      0, 1,  4, /* bottom */
      1, 2,  5, /* right */
      2, 3,  6, /* top */
      0, 3,  7, /* left */
    };
    PetscInt       faceVerticesQuad[12] = {
      0, 1,  4, /* bottom */
      1, 2,  5, /* right */
      2, 3,  6, /* top */
      3, 0,  7, /* left */
    };

    faceSize = faceSizeQuad;
    for (i = 0; i < faceSizeQuad; ++i) sortedIndices[i] = indices[i];
    ierr = PetscSortInt(faceSizeQuad, sortedIndices);CHKERRQ(ierr);
    for (iFace = 0; iFace < 4; ++iFace) {
      const PetscInt ii = iFace*faceSizeQuad;
      PetscInt       fVertex, cVertex;

      if ((sortedIndices[0] == faceVerticesQuadSorted[ii+0]) &&
          (sortedIndices[1] == faceVerticesQuadSorted[ii+1])) {
        for (fVertex = 0; fVertex < faceSizeQuad; ++fVertex) {
          for (cVertex = 0; cVertex < faceSizeQuad; ++cVertex) {
            if (indices[cVertex] == faceVerticesQuad[ii+fVertex]) {
              faceVertices[fVertex] = origVertices[cVertex];
              break;
            }
          }
        }
        found = PETSC_TRUE;
        break;
      }
    }
    if (!found) SETERRQ(comm, PETSC_ERR_ARG_WRONG, "Invalid quad crossface");
    if (posOriented) *posOriented = PETSC_TRUE;
    PetscFunctionReturn(0);
  } else if (cellDim == 3 && numCorners == 8) {
    /* Hexes
       A hex is two oriented quads with the normal of the first
       pointing up at the second.

          7---6
         /|  /|
        4---5 |
        | 1-|-2
        |/  |/
        0---3

        Faces are determined by the first 4 vertices (corners of faces) */
    const PetscInt faceSizeHex = 4;
    PetscInt       sortedIndices[4], i, iFace;
    PetscBool      found                     = PETSC_FALSE;
    PetscInt       faceVerticesHexSorted[24] = {
      0, 1, 2, 3,  /* bottom */
      4, 5, 6, 7,  /* top */
      0, 3, 4, 5,  /* front */
      2, 3, 5, 6,  /* right */
      1, 2, 6, 7,  /* back */
      0, 1, 4, 7,  /* left */
    };
    PetscInt       faceVerticesHex[24] = {
      1, 2, 3, 0,  /* bottom */
      4, 5, 6, 7,  /* top */
      0, 3, 5, 4,  /* front */
      3, 2, 6, 5,  /* right */
      2, 1, 7, 6,  /* back */
      1, 0, 4, 7,  /* left */
    };

    faceSize = faceSizeHex;
    for (i = 0; i < faceSizeHex; ++i) sortedIndices[i] = indices[i];
    ierr = PetscSortInt(faceSizeHex, sortedIndices);CHKERRQ(ierr);
    for (iFace = 0; iFace < 6; ++iFace) {
      const PetscInt ii = iFace*faceSizeHex;
      PetscInt       fVertex, cVertex;

      if ((sortedIndices[0] == faceVerticesHexSorted[ii+0]) &&
          (sortedIndices[1] == faceVerticesHexSorted[ii+1]) &&
          (sortedIndices[2] == faceVerticesHexSorted[ii+2]) &&
          (sortedIndices[3] == faceVerticesHexSorted[ii+3])) {
        for (fVertex = 0; fVertex < faceSizeHex; ++fVertex) {
          for (cVertex = 0; cVertex < faceSizeHex; ++cVertex) {
            if (indices[cVertex] == faceVerticesHex[ii+fVertex]) {
              faceVertices[fVertex] = origVertices[cVertex];
              break;
            }
          }
        }
        found = PETSC_TRUE;
        break;
      }
    }
    if (!found) SETERRQ(comm, PETSC_ERR_ARG_WRONG, "Invalid hex crossface");
    if (posOriented) *posOriented = PETSC_TRUE;
    PetscFunctionReturn(0);
  } else if (cellDim == 3 && numCorners == 10) {
    /* Quadratic tet */
    /* Faces are determined by the first 3 vertices (corners of faces) */
    const PetscInt faceSizeTet = 6;
    PetscInt       sortedIndices[6], i, iFace;
    PetscBool      found                     = PETSC_FALSE;
    PetscInt       faceVerticesTetSorted[24] = {
      0, 1, 2,  6, 7, 8, /* bottom */
      0, 3, 4,  6, 7, 9,  /* front */
      1, 4, 5,  7, 8, 9,  /* right */
      2, 3, 5,  6, 8, 9,  /* left */
    };
    PetscInt       faceVerticesTet[24] = {
      0, 1, 2,  6, 7, 8, /* bottom */
      0, 4, 3,  6, 7, 9,  /* front */
      1, 5, 4,  7, 8, 9,  /* right */
      2, 3, 5,  8, 6, 9,  /* left */
    };

    faceSize = faceSizeTet;
    for (i = 0; i < faceSizeTet; ++i) sortedIndices[i] = indices[i];
    ierr = PetscSortInt(faceSizeTet, sortedIndices);CHKERRQ(ierr);
    for (iFace=0; iFace < 4; ++iFace) {
      const PetscInt ii = iFace*faceSizeTet;
      PetscInt       fVertex, cVertex;

      if ((sortedIndices[0] == faceVerticesTetSorted[ii+0]) &&
          (sortedIndices[1] == faceVerticesTetSorted[ii+1]) &&
          (sortedIndices[2] == faceVerticesTetSorted[ii+2]) &&
          (sortedIndices[3] == faceVerticesTetSorted[ii+3])) {
        for (fVertex = 0; fVertex < faceSizeTet; ++fVertex) {
          for (cVertex = 0; cVertex < faceSizeTet; ++cVertex) {
            if (indices[cVertex] == faceVerticesTet[ii+fVertex]) {
              faceVertices[fVertex] = origVertices[cVertex];
              break;
            }
          }
        }
        found = PETSC_TRUE;
        break;
      }
    }
    if (!found) SETERRQ(comm, PETSC_ERR_ARG_WRONG, "Invalid tet crossface");
    if (posOriented) *posOriented = PETSC_TRUE;
    PetscFunctionReturn(0);
  } else if (cellDim == 3 && numCorners == 27) {
    /* Quadratic hexes (I hate this)
       A hex is two oriented quads with the normal of the first
       pointing up at the second.

         7---6
        /|  /|
       4---5 |
       | 3-|-2
       |/  |/
       0---1

       Faces are determined by the first 4 vertices (corners of faces) */
    const PetscInt faceSizeQuadHex = 9;
    PetscInt       sortedIndices[9], i, iFace;
    PetscBool      found                         = PETSC_FALSE;
    PetscInt       faceVerticesQuadHexSorted[54] = {
      0, 1, 2, 3,  8, 9, 10, 11,  24, /* bottom */
      4, 5, 6, 7,  12, 13, 14, 15,  25, /* top */
      0, 1, 4, 5,  8, 12, 16, 17,  22, /* front */
      1, 2, 5, 6,  9, 13, 17, 18,  21, /* right */
      2, 3, 6, 7,  10, 14, 18, 19,  23, /* back */
      0, 3, 4, 7,  11, 15, 16, 19,  20, /* left */
    };
    PetscInt       faceVerticesQuadHex[54] = {
      3, 2, 1, 0,  10, 9, 8, 11,  24, /* bottom */
      4, 5, 6, 7,  12, 13, 14, 15,  25, /* top */
      0, 1, 5, 4,  8, 17, 12, 16,  22, /* front */
      1, 2, 6, 5,  9, 18, 13, 17,  21, /* right */
      2, 3, 7, 6,  10, 19, 14, 18,  23, /* back */
      3, 0, 4, 7,  11, 16, 15, 19,  20 /* left */
    };

    faceSize = faceSizeQuadHex;
    for (i = 0; i < faceSizeQuadHex; ++i) sortedIndices[i] = indices[i];
    ierr = PetscSortInt(faceSizeQuadHex, sortedIndices);CHKERRQ(ierr);
    for (iFace = 0; iFace < 6; ++iFace) {
      const PetscInt ii = iFace*faceSizeQuadHex;
      PetscInt       fVertex, cVertex;

      if ((sortedIndices[0] == faceVerticesQuadHexSorted[ii+0]) &&
          (sortedIndices[1] == faceVerticesQuadHexSorted[ii+1]) &&
          (sortedIndices[2] == faceVerticesQuadHexSorted[ii+2]) &&
          (sortedIndices[3] == faceVerticesQuadHexSorted[ii+3])) {
        for (fVertex = 0; fVertex < faceSizeQuadHex; ++fVertex) {
          for (cVertex = 0; cVertex < faceSizeQuadHex; ++cVertex) {
            if (indices[cVertex] == faceVerticesQuadHex[ii+fVertex]) {
              faceVertices[fVertex] = origVertices[cVertex];
              break;
            }
          }
        }
        found = PETSC_TRUE;
        break;
      }
    }
    if (!found) SETERRQ(comm, PETSC_ERR_ARG_WRONG, "Invalid hex crossface");
    if (posOriented) *posOriented = PETSC_TRUE;
    PetscFunctionReturn(0);
  } else SETERRQ(comm, PETSC_ERR_ARG_WRONG, "Unknown cell type for faceOrientation().");
  if (!posOrient) {
    if (debug) {ierr = PetscPrintf(comm, "  Reversing initial face orientation\n");CHKERRQ(ierr);}
    for (f = 0; f < faceSize; ++f) faceVertices[f] = origVertices[faceSize-1 - f];
  } else {
    if (debug) {ierr = PetscPrintf(comm, "  Keeping initial face orientation\n");CHKERRQ(ierr);}
    for (f = 0; f < faceSize; ++f) faceVertices[f] = origVertices[f];
  }
  if (posOriented) *posOriented = posOrient;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetOrientedFace"
/*
    Given a cell and a face, as a set of vertices,
      return the oriented face, as a set of vertices, in faceVertices
    The orientation is such that the face normal points out of the cell
*/
PetscErrorCode DMPlexGetOrientedFace(DM dm, PetscInt cell, PetscInt faceSize, const PetscInt face[], PetscInt numCorners, PetscInt indices[], PetscInt origVertices[], PetscInt faceVertices[], PetscBool *posOriented)
{
  const PetscInt *cone = NULL;
  PetscInt        coneSize, v, f, v2;
  PetscInt        oppositeVertex = -1;
  PetscErrorCode  ierr;

  PetscFunctionBegin;
  ierr = DMPlexGetConeSize(dm, cell, &coneSize);CHKERRQ(ierr);
  ierr = DMPlexGetCone(dm, cell, &cone);CHKERRQ(ierr);
  for (v = 0, v2 = 0; v < coneSize; ++v) {
    PetscBool found = PETSC_FALSE;

    for (f = 0; f < faceSize; ++f) {
      if (face[f] == cone[v]) {
        found = PETSC_TRUE; break;
      }
    }
    if (found) {
      indices[v2]      = v;
      origVertices[v2] = cone[v];
      ++v2;
    } else {
      oppositeVertex = v;
    }
  }
  ierr = DMPlexGetFaceOrientation(dm, cell, numCorners, indices, oppositeVertex, origVertices, faceVertices, posOriented);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexInsertFace_Internal"
/*
  DMPlexInsertFace_Internal - Puts a face into the mesh

  Not collective

  Input Parameters:
  + dm              - The DMPlex
  . numFaceVertex   - The number of vertices in the face
  . faceVertices    - The vertices in the face for dm
  . subfaceVertices - The vertices in the face for subdm
  . numCorners      - The number of vertices in the cell
  . cell            - A cell in dm containing the face
  . subcell         - A cell in subdm containing the face
  . firstFace       - First face in the mesh
  - newFacePoint    - Next face in the mesh

  Output Parameters:
  . newFacePoint - Contains next face point number on input, updated on output

  Level: developer
*/
static PetscErrorCode DMPlexInsertFace_Internal(DM dm, DM subdm, PetscInt numFaceVertices, const PetscInt faceVertices[], const PetscInt subfaceVertices[], PetscInt numCorners, PetscInt cell, PetscInt subcell, PetscInt firstFace, PetscInt *newFacePoint)
{
  MPI_Comm        comm;
  DM_Plex        *submesh = (DM_Plex*) subdm->data;
  const PetscInt *faces;
  PetscInt        numFaces, coneSize;
  PetscErrorCode  ierr;

  PetscFunctionBegin;
  ierr = PetscObjectGetComm((PetscObject)dm,&comm);CHKERRQ(ierr);
  ierr = DMPlexGetConeSize(subdm, subcell, &coneSize);CHKERRQ(ierr);
  if (coneSize != 1) SETERRQ2(comm, PETSC_ERR_ARG_OUTOFRANGE, "Cone size of cell %d is %d != 1", cell, coneSize);
#if 0
  /* Cannot use this because support() has not been constructed yet */
  ierr = DMPlexGetJoin(subdm, numFaceVertices, subfaceVertices, &numFaces, &faces);CHKERRQ(ierr);
#else
  {
    PetscInt f;

    numFaces = 0;
    ierr     = DMGetWorkArray(subdm, 1, PETSC_INT, (void **) &faces);CHKERRQ(ierr);
    for (f = firstFace; f < *newFacePoint; ++f) {
      PetscInt dof, off, d;

      ierr = PetscSectionGetDof(submesh->coneSection, f, &dof);CHKERRQ(ierr);
      ierr = PetscSectionGetOffset(submesh->coneSection, f, &off);CHKERRQ(ierr);
      /* Yes, I know this is quadratic, but I expect the sizes to be <5 */
      for (d = 0; d < dof; ++d) {
        const PetscInt p = submesh->cones[off+d];
        PetscInt       v;

        for (v = 0; v < numFaceVertices; ++v) {
          if (subfaceVertices[v] == p) break;
        }
        if (v == numFaceVertices) break;
      }
      if (d == dof) {
        numFaces               = 1;
        ((PetscInt*) faces)[0] = f;
      }
    }
  }
#endif
  if (numFaces > 1) SETERRQ1(comm, PETSC_ERR_ARG_WRONG, "Vertex set had %d faces, not one", numFaces);
  else if (numFaces == 1) {
    /* Add the other cell neighbor for this face */
    ierr = DMPlexSetCone(subdm, subcell, faces);CHKERRQ(ierr);
  } else {
    PetscInt *indices, *origVertices, *orientedVertices, *orientedSubVertices, v, ov;
    PetscBool posOriented;

    ierr                = DMGetWorkArray(subdm, 4*numFaceVertices * sizeof(PetscInt), PETSC_INT, &orientedVertices);CHKERRQ(ierr);
    origVertices        = &orientedVertices[numFaceVertices];
    indices             = &orientedVertices[numFaceVertices*2];
    orientedSubVertices = &orientedVertices[numFaceVertices*3];
    ierr                = DMPlexGetOrientedFace(dm, cell, numFaceVertices, faceVertices, numCorners, indices, origVertices, orientedVertices, &posOriented);CHKERRQ(ierr);
    /* TODO: I know that routine should return a permutation, not the indices */
    for (v = 0; v < numFaceVertices; ++v) {
      const PetscInt vertex = faceVertices[v], subvertex = subfaceVertices[v];
      for (ov = 0; ov < numFaceVertices; ++ov) {
        if (orientedVertices[ov] == vertex) {
          orientedSubVertices[ov] = subvertex;
          break;
        }
      }
      if (ov == numFaceVertices) SETERRQ1(comm, PETSC_ERR_PLIB, "Could not find face vertex %d in orientated set", vertex);
    }
    ierr = DMPlexSetCone(subdm, *newFacePoint, orientedSubVertices);CHKERRQ(ierr);
    ierr = DMPlexSetCone(subdm, subcell, newFacePoint);CHKERRQ(ierr);
    ierr = DMRestoreWorkArray(subdm, 4*numFaceVertices * sizeof(PetscInt), PETSC_INT, &orientedVertices);CHKERRQ(ierr);
    ++(*newFacePoint);
  }
#if 0
  ierr = DMPlexRestoreJoin(subdm, numFaceVertices, subfaceVertices, &numFaces, &faces);CHKERRQ(ierr);
#else
  ierr = DMRestoreWorkArray(subdm, 1, PETSC_INT, (void **) &faces);CHKERRQ(ierr);
#endif
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexCreateSubmesh_Uninterpolated"
static PetscErrorCode DMPlexCreateSubmesh_Uninterpolated(DM dm, DMLabel vertexLabel, PetscInt value, DM subdm)
{
  MPI_Comm        comm;
  DMLabel         subpointMap;
  IS              subvertexIS,  subcellIS;
  const PetscInt *subVertices, *subCells;
  PetscInt        numSubVertices, firstSubVertex, numSubCells;
  PetscInt       *subface, maxConeSize, numSubFaces = 0, firstSubFace, newFacePoint, nFV = 0;
  PetscInt        vStart, vEnd, c, f;
  PetscErrorCode  ierr;

  PetscFunctionBegin;
  ierr = PetscObjectGetComm((PetscObject)dm,&comm);CHKERRQ(ierr);
  /* Create subpointMap which marks the submesh */
  ierr = DMLabelCreate("subpoint_map", &subpointMap);CHKERRQ(ierr);
  ierr = DMPlexSetSubpointMap(subdm, subpointMap);CHKERRQ(ierr);
  ierr = DMLabelDestroy(&subpointMap);CHKERRQ(ierr);
  if (vertexLabel) {ierr = DMPlexMarkSubmesh_Uninterpolated(dm, vertexLabel, value, subpointMap, &numSubFaces, &nFV, subdm);CHKERRQ(ierr);}
  /* Setup chart */
  ierr = DMLabelGetStratumSize(subpointMap, 0, &numSubVertices);CHKERRQ(ierr);
  ierr = DMLabelGetStratumSize(subpointMap, 2, &numSubCells);CHKERRQ(ierr);
  ierr = DMPlexSetChart(subdm, 0, numSubCells+numSubFaces+numSubVertices);CHKERRQ(ierr);
  ierr = DMPlexSetVTKCellHeight(subdm, 1);CHKERRQ(ierr);
  /* Set cone sizes */
  firstSubVertex = numSubCells;
  firstSubFace   = numSubCells+numSubVertices;
  newFacePoint   = firstSubFace;
  ierr = DMLabelGetStratumIS(subpointMap, 0, &subvertexIS);CHKERRQ(ierr);
  if (subvertexIS) {ierr = ISGetIndices(subvertexIS, &subVertices);CHKERRQ(ierr);}
  ierr = DMLabelGetStratumIS(subpointMap, 2, &subcellIS);CHKERRQ(ierr);
  if (subcellIS) {ierr = ISGetIndices(subcellIS, &subCells);CHKERRQ(ierr);}
  for (c = 0; c < numSubCells; ++c) {
    ierr = DMPlexSetConeSize(subdm, c, 1);CHKERRQ(ierr);
  }
  for (f = firstSubFace; f < firstSubFace+numSubFaces; ++f) {
    ierr = DMPlexSetConeSize(subdm, f, nFV);CHKERRQ(ierr);
  }
  ierr = DMSetUp(subdm);CHKERRQ(ierr);
  /* Create face cones */
  ierr = DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);CHKERRQ(ierr);
  ierr = DMPlexGetMaxSizes(dm, &maxConeSize, NULL);CHKERRQ(ierr);
  ierr = DMGetWorkArray(subdm, maxConeSize, PETSC_INT, (void**) &subface);CHKERRQ(ierr);
  for (c = 0; c < numSubCells; ++c) {
    const PetscInt cell    = subCells[c];
    const PetscInt subcell = c;
    PetscInt      *closure = NULL;
    PetscInt       closureSize, cl, numCorners = 0, faceSize = 0;

    ierr = DMPlexGetTransitiveClosure(dm, cell, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
    for (cl = 0; cl < closureSize*2; cl += 2) {
      const PetscInt point = closure[cl];
      PetscInt       subVertex;

      if ((point >= vStart) && (point < vEnd)) {
        ++numCorners;
        ierr = PetscFindInt(point, numSubVertices, subVertices, &subVertex);CHKERRQ(ierr);
        if (subVertex >= 0) {
          closure[faceSize] = point;
          subface[faceSize] = firstSubVertex+subVertex;
          ++faceSize;
        }
      }
    }
    if (faceSize > nFV) SETERRQ1(comm, PETSC_ERR_ARG_WRONG, "Invalid submesh: Too many vertices %d of an element on the surface", faceSize);
    if (faceSize == nFV) {
      ierr = DMPlexInsertFace_Internal(dm, subdm, faceSize, closure, subface, numCorners, cell, subcell, firstSubFace, &newFacePoint);CHKERRQ(ierr);
    }
    ierr = DMPlexRestoreTransitiveClosure(dm, cell, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
  }
  ierr = DMRestoreWorkArray(subdm, maxConeSize, PETSC_INT, (void**) &subface);CHKERRQ(ierr);
  ierr = DMPlexSymmetrize(subdm);CHKERRQ(ierr);
  ierr = DMPlexStratify(subdm);CHKERRQ(ierr);
  /* Build coordinates */
  {
    PetscSection coordSection, subCoordSection;
    Vec          coordinates, subCoordinates;
    PetscScalar *coords, *subCoords;
    PetscInt     numComp, coordSize, v;

    ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
    ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
    ierr = DMGetCoordinateSection(subdm, &subCoordSection);CHKERRQ(ierr);
    ierr = PetscSectionSetNumFields(subCoordSection, 1);CHKERRQ(ierr);
    ierr = PetscSectionGetFieldComponents(coordSection, 0, &numComp);CHKERRQ(ierr);
    ierr = PetscSectionSetFieldComponents(subCoordSection, 0, numComp);CHKERRQ(ierr);
    ierr = PetscSectionSetChart(subCoordSection, firstSubVertex, firstSubVertex+numSubVertices);CHKERRQ(ierr);
    for (v = 0; v < numSubVertices; ++v) {
      const PetscInt vertex    = subVertices[v];
      const PetscInt subvertex = firstSubVertex+v;
      PetscInt       dof;

      ierr = PetscSectionGetDof(coordSection, vertex, &dof);CHKERRQ(ierr);
      ierr = PetscSectionSetDof(subCoordSection, subvertex, dof);CHKERRQ(ierr);
      ierr = PetscSectionSetFieldDof(subCoordSection, subvertex, 0, dof);CHKERRQ(ierr);
    }
    ierr = PetscSectionSetUp(subCoordSection);CHKERRQ(ierr);
    ierr = PetscSectionGetStorageSize(subCoordSection, &coordSize);CHKERRQ(ierr);
    ierr = VecCreate(comm, &subCoordinates);CHKERRQ(ierr);
    ierr = VecSetSizes(subCoordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
    ierr = VecSetType(subCoordinates,VECSTANDARD);CHKERRQ(ierr);
    if (coordSize) {
      ierr = VecGetArray(coordinates,    &coords);CHKERRQ(ierr);
      ierr = VecGetArray(subCoordinates, &subCoords);CHKERRQ(ierr);
      for (v = 0; v < numSubVertices; ++v) {
        const PetscInt vertex    = subVertices[v];
        const PetscInt subvertex = firstSubVertex+v;
        PetscInt       dof, off, sdof, soff, d;

        ierr = PetscSectionGetDof(coordSection, vertex, &dof);CHKERRQ(ierr);
        ierr = PetscSectionGetOffset(coordSection, vertex, &off);CHKERRQ(ierr);
        ierr = PetscSectionGetDof(subCoordSection, subvertex, &sdof);CHKERRQ(ierr);
        ierr = PetscSectionGetOffset(subCoordSection, subvertex, &soff);CHKERRQ(ierr);
        if (dof != sdof) SETERRQ4(comm, PETSC_ERR_PLIB, "Coordinate dimension %d on subvertex %d, vertex %d should be %d", sdof, subvertex, vertex, dof);
        for (d = 0; d < dof; ++d) subCoords[soff+d] = coords[off+d];
      }
      ierr = VecRestoreArray(coordinates,    &coords);CHKERRQ(ierr);
      ierr = VecRestoreArray(subCoordinates, &subCoords);CHKERRQ(ierr);
    }
    ierr = DMSetCoordinatesLocal(subdm, subCoordinates);CHKERRQ(ierr);
    ierr = VecDestroy(&subCoordinates);CHKERRQ(ierr);
  }
  /* Cleanup */
  if (subvertexIS) {ierr = ISRestoreIndices(subvertexIS, &subVertices);CHKERRQ(ierr);}
  ierr = ISDestroy(&subvertexIS);CHKERRQ(ierr);
  if (subcellIS) {ierr = ISRestoreIndices(subcellIS, &subCells);CHKERRQ(ierr);}
  ierr = ISDestroy(&subcellIS);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexCreateSubmesh_Interpolated"
static PetscErrorCode DMPlexCreateSubmesh_Interpolated(DM dm, DMLabel vertexLabel, PetscInt value, DM subdm)
{
  MPI_Comm         comm;
  DMLabel          subpointMap;
  IS              *subpointIS;
  const PetscInt **subpoints;
  PetscInt        *numSubPoints, *firstSubPoint, *coneNew, *coneONew;
  PetscInt         totSubPoints = 0, maxConeSize, dim, p, d, v;
  PetscErrorCode   ierr;

  PetscFunctionBegin;
  ierr = PetscObjectGetComm((PetscObject)dm,&comm);CHKERRQ(ierr);
  /* Create subpointMap which marks the submesh */
  ierr = DMLabelCreate("subpoint_map", &subpointMap);CHKERRQ(ierr);
  ierr = DMPlexSetSubpointMap(subdm, subpointMap);CHKERRQ(ierr);
  ierr = DMLabelDestroy(&subpointMap);CHKERRQ(ierr);
  if (vertexLabel) {ierr = DMPlexMarkSubmesh_Interpolated(dm, vertexLabel, value, subpointMap, subdm);CHKERRQ(ierr);}
  /* Setup chart */
  ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
  ierr = PetscMalloc4(dim+1,&numSubPoints,dim+1,&firstSubPoint,dim+1,&subpointIS,dim+1,&subpoints);CHKERRQ(ierr);
  for (d = 0; d <= dim; ++d) {
    ierr = DMLabelGetStratumSize(subpointMap, d, &numSubPoints[d]);CHKERRQ(ierr);
    totSubPoints += numSubPoints[d];
  }
  ierr = DMPlexSetChart(subdm, 0, totSubPoints);CHKERRQ(ierr);
  ierr = DMPlexSetVTKCellHeight(subdm, 1);CHKERRQ(ierr);
  /* Set cone sizes */
  firstSubPoint[dim] = 0;
  firstSubPoint[0]   = firstSubPoint[dim] + numSubPoints[dim];
  if (dim > 1) {firstSubPoint[dim-1] = firstSubPoint[0]     + numSubPoints[0];}
  if (dim > 2) {firstSubPoint[dim-2] = firstSubPoint[dim-1] + numSubPoints[dim-1];}
  for (d = 0; d <= dim; ++d) {
    ierr = DMLabelGetStratumIS(subpointMap, d, &subpointIS[d]);CHKERRQ(ierr);
    if (subpointIS[d]) {ierr = ISGetIndices(subpointIS[d], &subpoints[d]);CHKERRQ(ierr);}
  }
  for (d = 0; d <= dim; ++d) {
    for (p = 0; p < numSubPoints[d]; ++p) {
      const PetscInt  point    = subpoints[d][p];
      const PetscInt  subpoint = firstSubPoint[d] + p;
      const PetscInt *cone;
      PetscInt        coneSize, coneSizeNew, c, val;

      ierr = DMPlexGetConeSize(dm, point, &coneSize);CHKERRQ(ierr);
      ierr = DMPlexSetConeSize(subdm, subpoint, coneSize);CHKERRQ(ierr);
      if (d == dim) {
        ierr = DMPlexGetCone(dm, point, &cone);CHKERRQ(ierr);
        for (c = 0, coneSizeNew = 0; c < coneSize; ++c) {
          ierr = DMLabelGetValue(subpointMap, cone[c], &val);CHKERRQ(ierr);
          if (val >= 0) coneSizeNew++;
        }
        ierr = DMPlexSetConeSize(subdm, subpoint, coneSizeNew);CHKERRQ(ierr);
      }
    }
  }
  ierr = DMSetUp(subdm);CHKERRQ(ierr);
  /* Set cones */
  ierr = DMPlexGetMaxSizes(dm, &maxConeSize, NULL);CHKERRQ(ierr);
  ierr = PetscMalloc2(maxConeSize,&coneNew,maxConeSize,&coneONew);CHKERRQ(ierr);
  for (d = 0; d <= dim; ++d) {
    for (p = 0; p < numSubPoints[d]; ++p) {
      const PetscInt  point    = subpoints[d][p];
      const PetscInt  subpoint = firstSubPoint[d] + p;
      const PetscInt *cone, *ornt;
      PetscInt        coneSize, subconeSize, coneSizeNew, c, subc;

      ierr = DMPlexGetConeSize(dm, point, &coneSize);CHKERRQ(ierr);
      ierr = DMPlexGetConeSize(subdm, subpoint, &subconeSize);CHKERRQ(ierr);
      ierr = DMPlexGetCone(dm, point, &cone);CHKERRQ(ierr);
      ierr = DMPlexGetConeOrientation(dm, point, &ornt);CHKERRQ(ierr);
      for (c = 0, coneSizeNew = 0; c < coneSize; ++c) {
        ierr = PetscFindInt(cone[c], numSubPoints[d-1], subpoints[d-1], &subc);CHKERRQ(ierr);
        if (subc >= 0) {
          coneNew[coneSizeNew]  = firstSubPoint[d-1] + subc;
          coneONew[coneSizeNew] = ornt[c];
          ++coneSizeNew;
        }
      }
      if (coneSizeNew != subconeSize) SETERRQ2(comm, PETSC_ERR_PLIB, "Number of cone points located %d does not match subcone size %d", coneSizeNew, subconeSize);
      ierr = DMPlexSetCone(subdm, subpoint, coneNew);CHKERRQ(ierr);
      ierr = DMPlexSetConeOrientation(subdm, subpoint, coneONew);CHKERRQ(ierr);
    }
  }
  ierr = PetscFree2(coneNew,coneONew);CHKERRQ(ierr);
  ierr = DMPlexSymmetrize(subdm);CHKERRQ(ierr);
  ierr = DMPlexStratify(subdm);CHKERRQ(ierr);
  /* Build coordinates */
  {
    PetscSection coordSection, subCoordSection;
    Vec          coordinates, subCoordinates;
    PetscScalar *coords, *subCoords;
    PetscInt     numComp, coordSize;

    ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
    ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
    ierr = DMGetCoordinateSection(subdm, &subCoordSection);CHKERRQ(ierr);
    ierr = PetscSectionSetNumFields(subCoordSection, 1);CHKERRQ(ierr);
    ierr = PetscSectionGetFieldComponents(coordSection, 0, &numComp);CHKERRQ(ierr);
    ierr = PetscSectionSetFieldComponents(subCoordSection, 0, numComp);CHKERRQ(ierr);
    ierr = PetscSectionSetChart(subCoordSection, firstSubPoint[0], firstSubPoint[0]+numSubPoints[0]);CHKERRQ(ierr);
    for (v = 0; v < numSubPoints[0]; ++v) {
      const PetscInt vertex    = subpoints[0][v];
      const PetscInt subvertex = firstSubPoint[0]+v;
      PetscInt       dof;

      ierr = PetscSectionGetDof(coordSection, vertex, &dof);CHKERRQ(ierr);
      ierr = PetscSectionSetDof(subCoordSection, subvertex, dof);CHKERRQ(ierr);
      ierr = PetscSectionSetFieldDof(subCoordSection, subvertex, 0, dof);CHKERRQ(ierr);
    }
    ierr = PetscSectionSetUp(subCoordSection);CHKERRQ(ierr);
    ierr = PetscSectionGetStorageSize(subCoordSection, &coordSize);CHKERRQ(ierr);
    ierr = VecCreate(comm, &subCoordinates);CHKERRQ(ierr);
    ierr = VecSetSizes(subCoordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
    ierr = VecSetType(subCoordinates,VECSTANDARD);CHKERRQ(ierr);
    ierr = VecGetArray(coordinates,    &coords);CHKERRQ(ierr);
    ierr = VecGetArray(subCoordinates, &subCoords);CHKERRQ(ierr);
    for (v = 0; v < numSubPoints[0]; ++v) {
      const PetscInt vertex    = subpoints[0][v];
      const PetscInt subvertex = firstSubPoint[0]+v;
      PetscInt dof, off, sdof, soff, d;

      ierr = PetscSectionGetDof(coordSection, vertex, &dof);CHKERRQ(ierr);
      ierr = PetscSectionGetOffset(coordSection, vertex, &off);CHKERRQ(ierr);
      ierr = PetscSectionGetDof(subCoordSection, subvertex, &sdof);CHKERRQ(ierr);
      ierr = PetscSectionGetOffset(subCoordSection, subvertex, &soff);CHKERRQ(ierr);
      if (dof != sdof) SETERRQ4(comm, PETSC_ERR_PLIB, "Coordinate dimension %d on subvertex %d, vertex %d should be %d", sdof, subvertex, vertex, dof);
      for (d = 0; d < dof; ++d) subCoords[soff+d] = coords[off+d];
    }
    ierr = VecRestoreArray(coordinates,    &coords);CHKERRQ(ierr);
    ierr = VecRestoreArray(subCoordinates, &subCoords);CHKERRQ(ierr);
    ierr = DMSetCoordinatesLocal(subdm, subCoordinates);CHKERRQ(ierr);
    ierr = VecDestroy(&subCoordinates);CHKERRQ(ierr);
  }
  /* Cleanup */
  for (d = 0; d <= dim; ++d) {
    if (subpointIS[d]) {ierr = ISRestoreIndices(subpointIS[d], &subpoints[d]);CHKERRQ(ierr);}
    ierr = ISDestroy(&subpointIS[d]);CHKERRQ(ierr);
  }
  ierr = PetscFree4(numSubPoints,firstSubPoint,subpointIS,subpoints);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexCreateSubmesh"
/*@
  DMPlexCreateSubmesh - Extract a hypersurface from the mesh using vertices defined by a label

  Input Parameters:
+ dm           - The original mesh
. vertexLabel  - The DMLabel marking vertices contained in the surface
- value        - The label value to use

  Output Parameter:
. subdm - The surface mesh

  Note: This function produces a DMLabel mapping original points in the submesh to their depth. This can be obtained using DMPlexGetSubpointMap().

  Level: developer

.seealso: DMPlexGetSubpointMap(), DMPlexGetLabel(), DMLabelSetValue()
@*/
PetscErrorCode DMPlexCreateSubmesh(DM dm, DMLabel vertexLabel, PetscInt value, DM *subdm)
{
  PetscInt       dim, depth;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidPointer(subdm, 3);
  ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
  ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
  ierr = DMCreate(PetscObjectComm((PetscObject)dm), subdm);CHKERRQ(ierr);
  ierr = DMSetType(*subdm, DMPLEX);CHKERRQ(ierr);
  ierr = DMPlexSetDimension(*subdm, dim-1);CHKERRQ(ierr);
  if (depth == dim) {
    ierr = DMPlexCreateSubmesh_Interpolated(dm, vertexLabel, value, *subdm);CHKERRQ(ierr);
  } else {
    ierr = DMPlexCreateSubmesh_Uninterpolated(dm, vertexLabel, value, *subdm);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexFilterPoint_Internal"
PETSC_STATIC_INLINE PetscInt DMPlexFilterPoint_Internal(PetscInt point, PetscInt firstSubPoint, PetscInt numSubPoints, const PetscInt subPoints[])
{
  PetscInt       subPoint;
  PetscErrorCode ierr;

  ierr = PetscFindInt(point, numSubPoints, subPoints, &subPoint); if (ierr < 0) return ierr;
  return subPoint < 0 ? subPoint : firstSubPoint+subPoint;
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexCreateCohesiveSubmesh_Uninterpolated"
static PetscErrorCode DMPlexCreateCohesiveSubmesh_Uninterpolated(DM dm, PetscBool hasLagrange, const char label[], PetscInt value, DM subdm)
{
  MPI_Comm        comm;
  DMLabel         subpointMap;
  IS              subvertexIS;
  const PetscInt *subVertices;
  PetscInt        numSubVertices, firstSubVertex, numSubCells, *subCells = NULL;
  PetscInt       *subface, maxConeSize, numSubFaces, firstSubFace, newFacePoint, nFV;
  PetscInt        cMax, c, f;
  PetscErrorCode  ierr;

  PetscFunctionBegin;
  ierr = PetscObjectGetComm((PetscObject)dm, &comm);CHKERRQ(ierr);
  /* Create subpointMap which marks the submesh */
  ierr = DMLabelCreate("subpoint_map", &subpointMap);CHKERRQ(ierr);
  ierr = DMPlexSetSubpointMap(subdm, subpointMap);CHKERRQ(ierr);
  ierr = DMLabelDestroy(&subpointMap);CHKERRQ(ierr);
  ierr = DMPlexMarkCohesiveSubmesh_Uninterpolated(dm, hasLagrange, label, value, subpointMap, &numSubFaces, &nFV, &subCells, subdm);CHKERRQ(ierr);
  /* Setup chart */
  ierr = DMLabelGetStratumSize(subpointMap, 0, &numSubVertices);CHKERRQ(ierr);
  ierr = DMLabelGetStratumSize(subpointMap, 2, &numSubCells);CHKERRQ(ierr);
  ierr = DMPlexSetChart(subdm, 0, numSubCells+numSubFaces+numSubVertices);CHKERRQ(ierr);
  ierr = DMPlexSetVTKCellHeight(subdm, 1);CHKERRQ(ierr);
  /* Set cone sizes */
  firstSubVertex = numSubCells;
  firstSubFace   = numSubCells+numSubVertices;
  newFacePoint   = firstSubFace;
  ierr = DMLabelGetStratumIS(subpointMap, 0, &subvertexIS);CHKERRQ(ierr);
  if (subvertexIS) {ierr = ISGetIndices(subvertexIS, &subVertices);CHKERRQ(ierr);}
  for (c = 0; c < numSubCells; ++c) {
    ierr = DMPlexSetConeSize(subdm, c, 1);CHKERRQ(ierr);
  }
  for (f = firstSubFace; f < firstSubFace+numSubFaces; ++f) {
    ierr = DMPlexSetConeSize(subdm, f, nFV);CHKERRQ(ierr);
  }
  ierr = DMSetUp(subdm);CHKERRQ(ierr);
  /* Create face cones */
  ierr = DMPlexGetMaxSizes(dm, &maxConeSize, NULL);CHKERRQ(ierr);
  ierr = DMPlexGetHybridBounds(dm, &cMax, NULL, NULL, NULL);CHKERRQ(ierr);
  ierr = DMGetWorkArray(subdm, maxConeSize, PETSC_INT, (void**) &subface);CHKERRQ(ierr);
  for (c = 0; c < numSubCells; ++c) {
    const PetscInt  cell    = subCells[c];
    const PetscInt  subcell = c;
    const PetscInt *cone, *cells;
    PetscInt        numCells, subVertex, p, v;

    if (cell < cMax) continue;
    ierr = DMPlexGetCone(dm, cell, &cone);CHKERRQ(ierr);
    for (v = 0; v < nFV; ++v) {
      ierr = PetscFindInt(cone[v], numSubVertices, subVertices, &subVertex);CHKERRQ(ierr);
      subface[v] = firstSubVertex+subVertex;
    }
    ierr = DMPlexSetCone(subdm, newFacePoint, subface);CHKERRQ(ierr);
    ierr = DMPlexSetCone(subdm, subcell, &newFacePoint);CHKERRQ(ierr);
    ierr = DMPlexGetJoin(dm, nFV, cone, &numCells, &cells);CHKERRQ(ierr);
    /* Not true in parallel
    if (numCells != 2) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cohesive cells should separate two cells"); */
    for (p = 0; p < numCells; ++p) {
      PetscInt negsubcell;

      if (cells[p] >= cMax) continue;
      /* I know this is a crap search */
      for (negsubcell = 0; negsubcell < numSubCells; ++negsubcell) {
        if (subCells[negsubcell] == cells[p]) break;
      }
      if (negsubcell == numSubCells) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Could not find negative face neighbor for cohesive cell %d", cell);
      ierr = DMPlexSetCone(subdm, negsubcell, &newFacePoint);CHKERRQ(ierr);
    }
    ierr = DMPlexRestoreJoin(dm, nFV, cone, &numCells, &cells);CHKERRQ(ierr);
    ++newFacePoint;
  }
  ierr = DMRestoreWorkArray(subdm, maxConeSize, PETSC_INT, (void**) &subface);CHKERRQ(ierr);
  ierr = DMPlexSymmetrize(subdm);CHKERRQ(ierr);
  ierr = DMPlexStratify(subdm);CHKERRQ(ierr);
  /* Build coordinates */
  {
    PetscSection coordSection, subCoordSection;
    Vec          coordinates, subCoordinates;
    PetscScalar *coords, *subCoords;
    PetscInt     numComp, coordSize, v;

    ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
    ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
    ierr = DMGetCoordinateSection(subdm, &subCoordSection);CHKERRQ(ierr);
    ierr = PetscSectionSetNumFields(subCoordSection, 1);CHKERRQ(ierr);
    ierr = PetscSectionGetFieldComponents(coordSection, 0, &numComp);CHKERRQ(ierr);
    ierr = PetscSectionSetFieldComponents(subCoordSection, 0, numComp);CHKERRQ(ierr);
    ierr = PetscSectionSetChart(subCoordSection, firstSubVertex, firstSubVertex+numSubVertices);CHKERRQ(ierr);
    for (v = 0; v < numSubVertices; ++v) {
      const PetscInt vertex    = subVertices[v];
      const PetscInt subvertex = firstSubVertex+v;
      PetscInt       dof;

      ierr = PetscSectionGetDof(coordSection, vertex, &dof);CHKERRQ(ierr);
      ierr = PetscSectionSetDof(subCoordSection, subvertex, dof);CHKERRQ(ierr);
      ierr = PetscSectionSetFieldDof(subCoordSection, subvertex, 0, dof);CHKERRQ(ierr);
    }
    ierr = PetscSectionSetUp(subCoordSection);CHKERRQ(ierr);
    ierr = PetscSectionGetStorageSize(subCoordSection, &coordSize);CHKERRQ(ierr);
    ierr = VecCreate(comm, &subCoordinates);CHKERRQ(ierr);
    ierr = VecSetSizes(subCoordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
    ierr = VecSetType(subCoordinates,VECSTANDARD);CHKERRQ(ierr);
    ierr = VecGetArray(coordinates,    &coords);CHKERRQ(ierr);
    ierr = VecGetArray(subCoordinates, &subCoords);CHKERRQ(ierr);
    for (v = 0; v < numSubVertices; ++v) {
      const PetscInt vertex    = subVertices[v];
      const PetscInt subvertex = firstSubVertex+v;
      PetscInt       dof, off, sdof, soff, d;

      ierr = PetscSectionGetDof(coordSection, vertex, &dof);CHKERRQ(ierr);
      ierr = PetscSectionGetOffset(coordSection, vertex, &off);CHKERRQ(ierr);
      ierr = PetscSectionGetDof(subCoordSection, subvertex, &sdof);CHKERRQ(ierr);
      ierr = PetscSectionGetOffset(subCoordSection, subvertex, &soff);CHKERRQ(ierr);
      if (dof != sdof) SETERRQ4(comm, PETSC_ERR_PLIB, "Coordinate dimension %d on subvertex %d, vertex %d should be %d", sdof, subvertex, vertex, dof);
      for (d = 0; d < dof; ++d) subCoords[soff+d] = coords[off+d];
    }
    ierr = VecRestoreArray(coordinates,    &coords);CHKERRQ(ierr);
    ierr = VecRestoreArray(subCoordinates, &subCoords);CHKERRQ(ierr);
    ierr = DMSetCoordinatesLocal(subdm, subCoordinates);CHKERRQ(ierr);
    ierr = VecDestroy(&subCoordinates);CHKERRQ(ierr);
  }
  /* Build SF */
  CHKMEMQ;
  {
    PetscSF            sfPoint, sfPointSub;
    const PetscSFNode *remotePoints;
    PetscSFNode       *sremotePoints, *newLocalPoints, *newOwners;
    const PetscInt    *localPoints;
    PetscInt          *slocalPoints;
    PetscInt           numRoots, numLeaves, numSubRoots = numSubCells+numSubFaces+numSubVertices, numSubLeaves = 0, l, sl, ll, pStart, pEnd, p, vStart, vEnd;
    PetscMPIInt        rank;

    ierr = MPI_Comm_rank(PetscObjectComm((PetscObject) dm), &rank);CHKERRQ(ierr);
    ierr = DMGetPointSF(dm, &sfPoint);CHKERRQ(ierr);
    ierr = DMGetPointSF(subdm, &sfPointSub);CHKERRQ(ierr);
    ierr = DMPlexGetChart(dm, &pStart, &pEnd);CHKERRQ(ierr);
    ierr = DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);CHKERRQ(ierr);
    ierr = PetscSFGetGraph(sfPoint, &numRoots, &numLeaves, &localPoints, &remotePoints);CHKERRQ(ierr);
    if (numRoots >= 0) {
      /* Only vertices should be shared */
      ierr = PetscMalloc2(pEnd-pStart,&newLocalPoints,numRoots,&newOwners);CHKERRQ(ierr);
      for (p = 0; p < pEnd-pStart; ++p) {
        newLocalPoints[p].rank  = -2;
        newLocalPoints[p].index = -2;
      }
      /* Set subleaves */
      for (l = 0; l < numLeaves; ++l) {
        const PetscInt point    = localPoints[l];
        const PetscInt subPoint = DMPlexFilterPoint_Internal(point, firstSubVertex, numSubVertices, subVertices);

        if ((point < vStart) && (point >= vEnd)) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Should not be mapping anything but vertices, %d", point);
        if (subPoint < 0) continue;
        newLocalPoints[point-pStart].rank  = rank;
        newLocalPoints[point-pStart].index = subPoint;
        ++numSubLeaves;
      }
      /* Must put in owned subpoints */
      for (p = pStart; p < pEnd; ++p) {
        const PetscInt subPoint = DMPlexFilterPoint_Internal(p, firstSubVertex, numSubVertices, subVertices);

        if (subPoint < 0) {
          newOwners[p-pStart].rank  = -3;
          newOwners[p-pStart].index = -3;
        } else {
          newOwners[p-pStart].rank  = rank;
          newOwners[p-pStart].index = subPoint;
        }
      }
      ierr = PetscSFReduceBegin(sfPoint, MPIU_2INT, newLocalPoints, newOwners, MPI_MAXLOC);CHKERRQ(ierr);
      ierr = PetscSFReduceEnd(sfPoint, MPIU_2INT, newLocalPoints, newOwners, MPI_MAXLOC);CHKERRQ(ierr);
      ierr = PetscSFBcastBegin(sfPoint, MPIU_2INT, newOwners, newLocalPoints);CHKERRQ(ierr);
      ierr = PetscSFBcastEnd(sfPoint, MPIU_2INT, newOwners, newLocalPoints);CHKERRQ(ierr);
      ierr = PetscMalloc1(numSubLeaves,    &slocalPoints);CHKERRQ(ierr);
      ierr = PetscMalloc1(numSubLeaves, &sremotePoints);CHKERRQ(ierr);
      for (l = 0, sl = 0, ll = 0; l < numLeaves; ++l) {
        const PetscInt point    = localPoints[l];
        const PetscInt subPoint = DMPlexFilterPoint_Internal(point, firstSubVertex, numSubVertices, subVertices);

        if (subPoint < 0) continue;
        if (newLocalPoints[point].rank == rank) {++ll; continue;}
        slocalPoints[sl]        = subPoint;
        sremotePoints[sl].rank  = newLocalPoints[point].rank;
        sremotePoints[sl].index = newLocalPoints[point].index;
        if (sremotePoints[sl].rank  < 0) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid remote rank for local point %d", point);
        if (sremotePoints[sl].index < 0) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid remote subpoint for local point %d", point);
        ++sl;
      }
      ierr = PetscFree2(newLocalPoints,newOwners);CHKERRQ(ierr);
      if (sl + ll != numSubLeaves) SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Mismatch in number of subleaves %d + %d != %d", sl, ll, numSubLeaves);
      ierr = PetscSFSetGraph(sfPointSub, numSubRoots, sl, slocalPoints, PETSC_OWN_POINTER, sremotePoints, PETSC_OWN_POINTER);CHKERRQ(ierr);
    }
  }
  CHKMEMQ;
  /* Cleanup */
  if (subvertexIS) {ierr = ISRestoreIndices(subvertexIS, &subVertices);CHKERRQ(ierr);}
  ierr = ISDestroy(&subvertexIS);CHKERRQ(ierr);
  ierr = PetscFree(subCells);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexCreateCohesiveSubmesh_Interpolated"
static PetscErrorCode DMPlexCreateCohesiveSubmesh_Interpolated(DM dm, const char label[], PetscInt value, DM subdm)
{
  MPI_Comm         comm;
  DMLabel          subpointMap;
  IS              *subpointIS;
  const PetscInt **subpoints;
  PetscInt        *numSubPoints, *firstSubPoint, *coneNew, *orntNew;
  PetscInt         totSubPoints = 0, maxConeSize, dim, p, d, v;
  PetscErrorCode   ierr;

  PetscFunctionBegin;
  ierr = PetscObjectGetComm((PetscObject)dm,&comm);CHKERRQ(ierr);
  /* Create subpointMap which marks the submesh */
  ierr = DMLabelCreate("subpoint_map", &subpointMap);CHKERRQ(ierr);
  ierr = DMPlexSetSubpointMap(subdm, subpointMap);CHKERRQ(ierr);
  ierr = DMLabelDestroy(&subpointMap);CHKERRQ(ierr);
  ierr = DMPlexMarkCohesiveSubmesh_Interpolated(dm, label, value, subpointMap, subdm);CHKERRQ(ierr);
  /* Setup chart */
  ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
  ierr = PetscMalloc4(dim+1,&numSubPoints,dim+1,&firstSubPoint,dim+1,&subpointIS,dim+1,&subpoints);CHKERRQ(ierr);
  for (d = 0; d <= dim; ++d) {
    ierr = DMLabelGetStratumSize(subpointMap, d, &numSubPoints[d]);CHKERRQ(ierr);
    totSubPoints += numSubPoints[d];
  }
  ierr = DMPlexSetChart(subdm, 0, totSubPoints);CHKERRQ(ierr);
  ierr = DMPlexSetVTKCellHeight(subdm, 1);CHKERRQ(ierr);
  /* Set cone sizes */
  firstSubPoint[dim] = 0;
  firstSubPoint[0]   = firstSubPoint[dim] + numSubPoints[dim];
  if (dim > 1) {firstSubPoint[dim-1] = firstSubPoint[0]     + numSubPoints[0];}
  if (dim > 2) {firstSubPoint[dim-2] = firstSubPoint[dim-1] + numSubPoints[dim-1];}
  for (d = 0; d <= dim; ++d) {
    ierr = DMLabelGetStratumIS(subpointMap, d, &subpointIS[d]);CHKERRQ(ierr);
    if (subpointIS[d]) {ierr = ISGetIndices(subpointIS[d], &subpoints[d]);CHKERRQ(ierr);}
  }
  for (d = 0; d <= dim; ++d) {
    for (p = 0; p < numSubPoints[d]; ++p) {
      const PetscInt  point    = subpoints[d][p];
      const PetscInt  subpoint = firstSubPoint[d] + p;
      const PetscInt *cone;
      PetscInt        coneSize, coneSizeNew, c, val;

      ierr = DMPlexGetConeSize(dm, point, &coneSize);CHKERRQ(ierr);
      ierr = DMPlexSetConeSize(subdm, subpoint, coneSize);CHKERRQ(ierr);
      if (d == dim) {
        ierr = DMPlexGetCone(dm, point, &cone);CHKERRQ(ierr);
        for (c = 0, coneSizeNew = 0; c < coneSize; ++c) {
          ierr = DMLabelGetValue(subpointMap, cone[c], &val);CHKERRQ(ierr);
          if (val >= 0) coneSizeNew++;
        }
        ierr = DMPlexSetConeSize(subdm, subpoint, coneSizeNew);CHKERRQ(ierr);
      }
    }
  }
  ierr = DMSetUp(subdm);CHKERRQ(ierr);
  /* Set cones */
  ierr = DMPlexGetMaxSizes(dm, &maxConeSize, NULL);CHKERRQ(ierr);
  ierr = PetscMalloc2(maxConeSize,&coneNew,maxConeSize,&orntNew);CHKERRQ(ierr);
  for (d = 0; d <= dim; ++d) {
    for (p = 0; p < numSubPoints[d]; ++p) {
      const PetscInt  point    = subpoints[d][p];
      const PetscInt  subpoint = firstSubPoint[d] + p;
      const PetscInt *cone, *ornt;
      PetscInt        coneSize, subconeSize, coneSizeNew, c, subc;

      ierr = DMPlexGetConeSize(dm, point, &coneSize);CHKERRQ(ierr);
      ierr = DMPlexGetConeSize(subdm, subpoint, &subconeSize);CHKERRQ(ierr);
      ierr = DMPlexGetCone(dm, point, &cone);CHKERRQ(ierr);
      ierr = DMPlexGetConeOrientation(dm, point, &ornt);CHKERRQ(ierr);
      for (c = 0, coneSizeNew = 0; c < coneSize; ++c) {
        ierr = PetscFindInt(cone[c], numSubPoints[d-1], subpoints[d-1], &subc);CHKERRQ(ierr);
        if (subc >= 0) {
          coneNew[coneSizeNew]   = firstSubPoint[d-1] + subc;
          orntNew[coneSizeNew++] = ornt[c];
        }
      }
      if (coneSizeNew != subconeSize) SETERRQ2(comm, PETSC_ERR_PLIB, "Number of cone points located %d does not match subcone size %d", coneSizeNew, subconeSize);
      ierr = DMPlexSetCone(subdm, subpoint, coneNew);CHKERRQ(ierr);
      ierr = DMPlexSetConeOrientation(subdm, subpoint, orntNew);CHKERRQ(ierr);
    }
  }
  ierr = PetscFree2(coneNew,orntNew);CHKERRQ(ierr);
  ierr = DMPlexSymmetrize(subdm);CHKERRQ(ierr);
  ierr = DMPlexStratify(subdm);CHKERRQ(ierr);
  /* Build coordinates */
  {
    PetscSection coordSection, subCoordSection;
    Vec          coordinates, subCoordinates;
    PetscScalar *coords, *subCoords;
    PetscInt     numComp, coordSize;

    ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
    ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
    ierr = DMGetCoordinateSection(subdm, &subCoordSection);CHKERRQ(ierr);
    ierr = PetscSectionSetNumFields(subCoordSection, 1);CHKERRQ(ierr);
    ierr = PetscSectionGetFieldComponents(coordSection, 0, &numComp);CHKERRQ(ierr);
    ierr = PetscSectionSetFieldComponents(subCoordSection, 0, numComp);CHKERRQ(ierr);
    ierr = PetscSectionSetChart(subCoordSection, firstSubPoint[0], firstSubPoint[0]+numSubPoints[0]);CHKERRQ(ierr);
    for (v = 0; v < numSubPoints[0]; ++v) {
      const PetscInt vertex    = subpoints[0][v];
      const PetscInt subvertex = firstSubPoint[0]+v;
      PetscInt       dof;

      ierr = PetscSectionGetDof(coordSection, vertex, &dof);CHKERRQ(ierr);
      ierr = PetscSectionSetDof(subCoordSection, subvertex, dof);CHKERRQ(ierr);
      ierr = PetscSectionSetFieldDof(subCoordSection, subvertex, 0, dof);CHKERRQ(ierr);
    }
    ierr = PetscSectionSetUp(subCoordSection);CHKERRQ(ierr);
    ierr = PetscSectionGetStorageSize(subCoordSection, &coordSize);CHKERRQ(ierr);
    ierr = VecCreate(comm, &subCoordinates);CHKERRQ(ierr);
    ierr = VecSetSizes(subCoordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
    ierr = VecSetType(subCoordinates,VECSTANDARD);CHKERRQ(ierr);
    ierr = VecGetArray(coordinates,    &coords);CHKERRQ(ierr);
    ierr = VecGetArray(subCoordinates, &subCoords);CHKERRQ(ierr);
    for (v = 0; v < numSubPoints[0]; ++v) {
      const PetscInt vertex    = subpoints[0][v];
      const PetscInt subvertex = firstSubPoint[0]+v;
      PetscInt dof, off, sdof, soff, d;

      ierr = PetscSectionGetDof(coordSection, vertex, &dof);CHKERRQ(ierr);
      ierr = PetscSectionGetOffset(coordSection, vertex, &off);CHKERRQ(ierr);
      ierr = PetscSectionGetDof(subCoordSection, subvertex, &sdof);CHKERRQ(ierr);
      ierr = PetscSectionGetOffset(subCoordSection, subvertex, &soff);CHKERRQ(ierr);
      if (dof != sdof) SETERRQ4(comm, PETSC_ERR_PLIB, "Coordinate dimension %d on subvertex %d, vertex %d should be %d", sdof, subvertex, vertex, dof);
      for (d = 0; d < dof; ++d) subCoords[soff+d] = coords[off+d];
    }
    ierr = VecRestoreArray(coordinates,    &coords);CHKERRQ(ierr);
    ierr = VecRestoreArray(subCoordinates, &subCoords);CHKERRQ(ierr);
    ierr = DMSetCoordinatesLocal(subdm, subCoordinates);CHKERRQ(ierr);
    ierr = VecDestroy(&subCoordinates);CHKERRQ(ierr);
  }
  /* Build SF: We need this complexity because subpoints might not be selected on the owning process */
  {
    PetscSF            sfPoint, sfPointSub;
    IS                 subpIS;
    const PetscSFNode *remotePoints;
    PetscSFNode       *sremotePoints, *newLocalPoints, *newOwners;
    const PetscInt    *localPoints, *subpoints;
    PetscInt          *slocalPoints;
    PetscInt           numRoots, numLeaves, numSubpoints = 0, numSubroots, numSubleaves = 0, l, sl, ll, pStart, pEnd, p;
    PetscMPIInt        rank;

    ierr = MPI_Comm_rank(PetscObjectComm((PetscObject) dm), &rank);CHKERRQ(ierr);
    ierr = DMGetPointSF(dm, &sfPoint);CHKERRQ(ierr);
    ierr = DMGetPointSF(subdm, &sfPointSub);CHKERRQ(ierr);
    ierr = DMPlexGetChart(dm, &pStart, &pEnd);CHKERRQ(ierr);
    ierr = DMPlexGetChart(subdm, NULL, &numSubroots);CHKERRQ(ierr);
    ierr = DMPlexCreateSubpointIS(subdm, &subpIS);CHKERRQ(ierr);
    if (subpIS) {
      ierr = ISGetIndices(subpIS, &subpoints);CHKERRQ(ierr);
      ierr = ISGetLocalSize(subpIS, &numSubpoints);CHKERRQ(ierr);
    }
    ierr = PetscSFGetGraph(sfPoint, &numRoots, &numLeaves, &localPoints, &remotePoints);CHKERRQ(ierr);
    if (numRoots >= 0) {
      ierr = PetscMalloc2(pEnd-pStart,&newLocalPoints,numRoots,&newOwners);CHKERRQ(ierr);
      for (p = 0; p < pEnd-pStart; ++p) {
        newLocalPoints[p].rank  = -2;
        newLocalPoints[p].index = -2;
      }
      /* Set subleaves */
      for (l = 0; l < numLeaves; ++l) {
        const PetscInt point    = localPoints[l];
        const PetscInt subpoint = DMPlexFilterPoint_Internal(point, 0, numSubpoints, subpoints);

        if (subpoint < 0) continue;
        newLocalPoints[point-pStart].rank  = rank;
        newLocalPoints[point-pStart].index = subpoint;
        ++numSubleaves;
      }
      /* Must put in owned subpoints */
      for (p = pStart; p < pEnd; ++p) {
        const PetscInt subpoint = DMPlexFilterPoint_Internal(p, 0, numSubpoints, subpoints);

        if (subpoint < 0) {
          newOwners[p-pStart].rank  = -3;
          newOwners[p-pStart].index = -3;
        } else {
          newOwners[p-pStart].rank  = rank;
          newOwners[p-pStart].index = subpoint;
        }
      }
      ierr = PetscSFReduceBegin(sfPoint, MPIU_2INT, newLocalPoints, newOwners, MPI_MAXLOC);CHKERRQ(ierr);
      ierr = PetscSFReduceEnd(sfPoint, MPIU_2INT, newLocalPoints, newOwners, MPI_MAXLOC);CHKERRQ(ierr);
      ierr = PetscSFBcastBegin(sfPoint, MPIU_2INT, newOwners, newLocalPoints);CHKERRQ(ierr);
      ierr = PetscSFBcastEnd(sfPoint, MPIU_2INT, newOwners, newLocalPoints);CHKERRQ(ierr);
      ierr = PetscMalloc(numSubleaves * sizeof(PetscInt),    &slocalPoints);CHKERRQ(ierr);
      ierr = PetscMalloc(numSubleaves * sizeof(PetscSFNode), &sremotePoints);CHKERRQ(ierr);
      for (l = 0, sl = 0, ll = 0; l < numLeaves; ++l) {
        const PetscInt point    = localPoints[l];
        const PetscInt subpoint = DMPlexFilterPoint_Internal(point, 0, numSubpoints, subpoints);

        if (subpoint < 0) continue;
        if (newLocalPoints[point].rank == rank) {++ll; continue;}
        slocalPoints[sl]        = subpoint;
        sremotePoints[sl].rank  = newLocalPoints[point].rank;
        sremotePoints[sl].index = newLocalPoints[point].index;
        if (sremotePoints[sl].rank  < 0) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid remote rank for local point %d", point);
        if (sremotePoints[sl].index < 0) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid remote subpoint for local point %d", point);
        ++sl;
      }
      if (sl + ll != numSubleaves) SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Mismatch in number of subleaves %d + %d != %d", sl, ll, numSubleaves);
      ierr = PetscFree2(newLocalPoints,newOwners);CHKERRQ(ierr);
      ierr = PetscSFSetGraph(sfPointSub, numSubroots, sl, slocalPoints, PETSC_OWN_POINTER, sremotePoints, PETSC_OWN_POINTER);CHKERRQ(ierr);
    }
    if (subpIS) {
      ierr = ISRestoreIndices(subpIS, &subpoints);CHKERRQ(ierr);
      ierr = ISDestroy(&subpIS);CHKERRQ(ierr);
    }
  }
  /* Cleanup */
  for (d = 0; d <= dim; ++d) {
    if (subpointIS[d]) {ierr = ISRestoreIndices(subpointIS[d], &subpoints[d]);CHKERRQ(ierr);}
    ierr = ISDestroy(&subpointIS[d]);CHKERRQ(ierr);
  }
  ierr = PetscFree4(numSubPoints,firstSubPoint,subpointIS,subpoints);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexCreateCohesiveSubmesh"
/*
  DMPlexCreateCohesiveSubmesh - Extract from a mesh with cohesive cells the hypersurface defined by one face of the cells. Optionally, a Label an be given to restrict the cells.

  Input Parameters:
+ dm          - The original mesh
. hasLagrange - The mesh has Lagrange unknowns in the cohesive cells
. label       - A label name, or NULL
- value  - A label value

  Output Parameter:
. subdm - The surface mesh

  Note: This function produces a DMLabel mapping original points in the submesh to their depth. This can be obtained using DMPlexGetSubpointMap().

  Level: developer

.seealso: DMPlexGetSubpointMap(), DMPlexCreateSubmesh()
*/
PetscErrorCode DMPlexCreateCohesiveSubmesh(DM dm, PetscBool hasLagrange, const char label[], PetscInt value, DM *subdm)
{
  PetscInt       dim, depth;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidPointer(subdm, 5);
  ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
  ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
  ierr = DMCreate(PetscObjectComm((PetscObject)dm), subdm);CHKERRQ(ierr);
  ierr = DMSetType(*subdm, DMPLEX);CHKERRQ(ierr);
  ierr = DMPlexSetDimension(*subdm, dim-1);CHKERRQ(ierr);
  if (depth == dim) {
    ierr = DMPlexCreateCohesiveSubmesh_Interpolated(dm, label, value, *subdm);CHKERRQ(ierr);
  } else {
    ierr = DMPlexCreateCohesiveSubmesh_Uninterpolated(dm, hasLagrange, label, value, *subdm);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetSubpointMap"
/*@
  DMPlexGetSubpointMap - Returns a DMLabel with point dimension as values

  Input Parameter:
. dm - The submesh DM

  Output Parameter:
. subpointMap - The DMLabel of all the points from the original mesh in this submesh, or NULL if this is not a submesh

  Level: developer

.seealso: DMPlexCreateSubmesh(), DMPlexCreateSubpointIS()
@*/
PetscErrorCode DMPlexGetSubpointMap(DM dm, DMLabel *subpointMap)
{
  DM_Plex *mesh = (DM_Plex*) dm->data;

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

#undef __FUNCT__
#define __FUNCT__ "DMPlexSetSubpointMap"
/* Note: Should normally not be called by the user, since it is set in DMPlexCreateSubmesh() */
PetscErrorCode DMPlexSetSubpointMap(DM dm, DMLabel subpointMap)
{
  DM_Plex       *mesh = (DM_Plex *) dm->data;
  DMLabel        tmp;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  tmp  = mesh->subpointMap;
  mesh->subpointMap = subpointMap;
  ++mesh->subpointMap->refct;
  ierr = DMLabelDestroy(&tmp);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexCreateSubpointIS"
/*@
  DMPlexCreateSubpointIS - Creates an IS covering the entire subdm chart with the original points as data

  Input Parameter:
. dm - The submesh DM

  Output Parameter:
. subpointIS - The IS of all the points from the original mesh in this submesh, or NULL if this is not a submesh

  Note: This is IS is guaranteed to be sorted by the construction of the submesh

  Level: developer

.seealso: DMPlexCreateSubmesh(), DMPlexGetSubpointMap()
@*/
PetscErrorCode DMPlexCreateSubpointIS(DM dm, IS *subpointIS)
{
  MPI_Comm        comm;
  DMLabel         subpointMap;
  IS              is;
  const PetscInt *opoints;
  PetscInt       *points, *depths;
  PetscInt        depth, depStart, depEnd, d, pStart, pEnd, p, n, off;
  PetscErrorCode  ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidPointer(subpointIS, 2);
  ierr = PetscObjectGetComm((PetscObject)dm,&comm);CHKERRQ(ierr);
  *subpointIS = NULL;
  ierr = DMPlexGetSubpointMap(dm, &subpointMap);CHKERRQ(ierr);
  ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
  if (subpointMap && depth >= 0) {
    ierr = DMPlexGetChart(dm, &pStart, &pEnd);CHKERRQ(ierr);
    if (pStart) SETERRQ1(comm, PETSC_ERR_ARG_WRONG, "Submeshes must start the point numbering at 0, not %d", pStart);
    ierr = DMGetWorkArray(dm, depth+1, PETSC_INT, &depths);CHKERRQ(ierr);
    depths[0] = depth;
    depths[1] = 0;
    for(d = 2; d <= depth; ++d) {depths[d] = depth+1 - d;}
    ierr = PetscMalloc1(pEnd, &points);CHKERRQ(ierr);
    for(d = 0, off = 0; d <= depth; ++d) {
      const PetscInt dep = depths[d];

      ierr = DMPlexGetDepthStratum(dm, dep, &depStart, &depEnd);CHKERRQ(ierr);
      ierr = DMLabelGetStratumSize(subpointMap, dep, &n);CHKERRQ(ierr);
      if (((d < 2) && (depth > 1)) || (d == 1)) { /* Only check vertices and cells for now since the map is broken for others */
        if (n != depEnd-depStart) SETERRQ3(comm, PETSC_ERR_ARG_WRONG, "The number of mapped submesh points %d at depth %d should be %d", n, dep, depEnd-depStart);
      } else {
        if (!n) {
          if (d == 0) {
            /* Missing cells */
            for(p = 0; p < depEnd-depStart; ++p, ++off) points[off] = -1;
          } else {
            /* Missing faces */
            for(p = 0; p < depEnd-depStart; ++p, ++off) points[off] = PETSC_MAX_INT;
          }
        }
      }
      if (n) {
        ierr = DMLabelGetStratumIS(subpointMap, dep, &is);CHKERRQ(ierr);
        ierr = ISGetIndices(is, &opoints);CHKERRQ(ierr);
        for(p = 0; p < n; ++p, ++off) points[off] = opoints[p];
        ierr = ISRestoreIndices(is, &opoints);CHKERRQ(ierr);
        ierr = ISDestroy(&is);CHKERRQ(ierr);
      }
    }
    ierr = DMRestoreWorkArray(dm, depth+1, PETSC_INT, &depths);CHKERRQ(ierr);
    if (off != pEnd) SETERRQ2(comm, PETSC_ERR_ARG_WRONG, "The number of mapped submesh points %d should be %d", off, pEnd);
    ierr = ISCreateGeneral(PETSC_COMM_SELF, pEnd, points, PETSC_OWN_POINTER, subpointIS);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}