xref: /petsc/src/dm/impls/plex/plexdistribute.c (revision 4a54e0719ac9dff749f865efc3bd2d4c156b2fce)

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

#undef __FUNCT__
#define __FUNCT__ "DMPlexSetAdjacencyUseCone"
/*@
  DMPlexSetAdjacencyUseCone - Define adjacency in the mesh using either the cone or the support first

  Input Parameters:
+ dm      - The DM object
- useCone - Flag to use the cone first

  Level: intermediate

  Notes:
$     FEM:   Two points p and q are adjacent if q \in closure(star(p)),   useCone = PETSC_FALSE, useClosure = PETSC_TRUE
$     FVM:   Two points p and q are adjacent if q \in support(p+cone(p)), useCone = PETSC_TRUE,  useClosure = PETSC_FALSE
$     FVM++: Two points p and q are adjacent if q \in star(closure(p)),   useCone = PETSC_TRUE,  useClosure = PETSC_TRUE

.seealso: DMPlexGetAdjacencyUseCone(), DMPlexSetAdjacencyUseClosure(), DMPlexGetAdjacencyUseClosure(), DMPlexDistribute(), DMPlexPreallocateOperator()
@*/
PetscErrorCode DMPlexSetAdjacencyUseCone(DM dm, PetscBool useCone)
{
  DM_Plex *mesh = (DM_Plex *) dm->data;

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

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetAdjacencyUseCone"
/*@
  DMPlexGetAdjacencyUseCone - Query whether adjacency in the mesh uses the cone or the support first

  Input Parameter:
. dm      - The DM object

  Output Parameter:
. useCone - Flag to use the cone first

  Level: intermediate

  Notes:
$     FEM:   Two points p and q are adjacent if q \in closure(star(p)),   useCone = PETSC_FALSE, useClosure = PETSC_TRUE
$     FVM:   Two points p and q are adjacent if q \in support(p+cone(p)), useCone = PETSC_TRUE,  useClosure = PETSC_FALSE
$     FVM++: Two points p and q are adjacent if q \in star(closure(p)),   useCone = PETSC_TRUE,  useClosure = PETSC_TRUE

.seealso: DMPlexSetAdjacencyUseCone(), DMPlexSetAdjacencyUseClosure(), DMPlexGetAdjacencyUseClosure(), DMPlexDistribute(), DMPlexPreallocateOperator()
@*/
PetscErrorCode DMPlexGetAdjacencyUseCone(DM dm, PetscBool *useCone)
{
  DM_Plex *mesh = (DM_Plex *) dm->data;

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

#undef __FUNCT__
#define __FUNCT__ "DMPlexSetAdjacencyUseClosure"
/*@
  DMPlexSetAdjacencyUseClosure - Define adjacency in the mesh using the transitive closure

  Input Parameters:
+ dm      - The DM object
- useClosure - Flag to use the closure

  Level: intermediate

  Notes:
$     FEM:   Two points p and q are adjacent if q \in closure(star(p)),   useCone = PETSC_FALSE, useClosure = PETSC_TRUE
$     FVM:   Two points p and q are adjacent if q \in support(p+cone(p)), useCone = PETSC_TRUE,  useClosure = PETSC_FALSE
$     FVM++: Two points p and q are adjacent if q \in star(closure(p)),   useCone = PETSC_TRUE,  useClosure = PETSC_TRUE

.seealso: DMPlexGetAdjacencyUseClosure(), DMPlexSetAdjacencyUseCone(), DMPlexGetAdjacencyUseCone(), DMPlexDistribute(), DMPlexPreallocateOperator()
@*/
PetscErrorCode DMPlexSetAdjacencyUseClosure(DM dm, PetscBool useClosure)
{
  DM_Plex *mesh = (DM_Plex *) dm->data;

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

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetAdjacencyUseClosure"
/*@
  DMPlexGetAdjacencyUseClosure - Query whether adjacency in the mesh uses the transitive closure

  Input Parameter:
. dm      - The DM object

  Output Parameter:
. useClosure - Flag to use the closure

  Level: intermediate

  Notes:
$     FEM:   Two points p and q are adjacent if q \in closure(star(p)),   useCone = PETSC_FALSE, useClosure = PETSC_TRUE
$     FVM:   Two points p and q are adjacent if q \in support(p+cone(p)), useCone = PETSC_TRUE,  useClosure = PETSC_FALSE
$     FVM++: Two points p and q are adjacent if q \in star(closure(p)),   useCone = PETSC_TRUE,  useClosure = PETSC_TRUE

.seealso: DMPlexSetAdjacencyUseClosure(), DMPlexSetAdjacencyUseCone(), DMPlexGetAdjacencyUseCone(), DMPlexDistribute(), DMPlexPreallocateOperator()
@*/
PetscErrorCode DMPlexGetAdjacencyUseClosure(DM dm, PetscBool *useClosure)
{
  DM_Plex *mesh = (DM_Plex *) dm->data;

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

#undef __FUNCT__
#define __FUNCT__ "DMPlexSetAdjacencyUseAnchors"
/*@
  DMPlexSetAdjacencyUseAnchors - Define adjacency in the mesh using the point-to-point constraints.

  Input Parameters:
+ dm      - The DM object
- useAnchors - Flag to use the constraints.  If PETSC_TRUE, then constrained points are omitted from DMPlexGetAdjacency(), and their anchor points appear in their place.

  Level: intermediate

.seealso: DMPlexGetAdjacencyUseClosure(), DMPlexSetAdjacencyUseCone(), DMPlexGetAdjacencyUseCone(), DMPlexDistribute(), DMPlexPreallocateOperator(), DMPlexSetAnchors()
@*/
PetscErrorCode DMPlexSetAdjacencyUseAnchors(DM dm, PetscBool useAnchors)
{
  DM_Plex *mesh = (DM_Plex *) dm->data;

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

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetAdjacencyUseAnchors"
/*@
  DMPlexGetAdjacencyUseAnchors - Query whether adjacency in the mesh uses the point-to-point constraints.

  Input Parameter:
. dm      - The DM object

  Output Parameter:
. useAnchors - Flag to use the closure.  If PETSC_TRUE, then constrained points are omitted from DMPlexGetAdjacency(), and their anchor points appear in their place.

  Level: intermediate

.seealso: DMPlexSetAdjacencyUseAnchors(), DMPlexSetAdjacencyUseCone(), DMPlexGetAdjacencyUseCone(), DMPlexDistribute(), DMPlexPreallocateOperator(), DMPlexSetAnchors()
@*/
PetscErrorCode DMPlexGetAdjacencyUseAnchors(DM dm, PetscBool *useAnchors)
{
  DM_Plex *mesh = (DM_Plex *) dm->data;

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

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetAdjacency_Cone_Internal"
static PetscErrorCode DMPlexGetAdjacency_Cone_Internal(DM dm, PetscInt p, PetscInt *adjSize, PetscInt adj[])
{
  const PetscInt *cone = NULL;
  PetscInt        numAdj = 0, maxAdjSize = *adjSize, coneSize, c;
  PetscErrorCode  ierr;

  PetscFunctionBeginHot;
  ierr = DMPlexGetConeSize(dm, p, &coneSize);CHKERRQ(ierr);
  ierr = DMPlexGetCone(dm, p, &cone);CHKERRQ(ierr);
  for (c = 0; c <= coneSize; ++c) {
    const PetscInt  point   = !c ? p : cone[c-1];
    const PetscInt *support = NULL;
    PetscInt        supportSize, s, q;

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

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

  PetscFunctionBeginHot;
  ierr = DMPlexGetSupportSize(dm, p, &supportSize);CHKERRQ(ierr);
  ierr = DMPlexGetSupport(dm, p, &support);CHKERRQ(ierr);
  for (s = 0; s <= supportSize; ++s) {
    const PetscInt  point = !s ? p : support[s-1];
    const PetscInt *cone  = NULL;
    PetscInt        coneSize, c, q;

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

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

  PetscFunctionBeginHot;
  ierr = DMPlexGetTransitiveClosure(dm, p, useClosure, &starSize, &star);CHKERRQ(ierr);
  for (s = 0; s < starSize*2; s += 2) {
    const PetscInt *closure = NULL;
    PetscInt        closureSize, c, q;

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

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetAdjacency_Internal"
PetscErrorCode DMPlexGetAdjacency_Internal(DM dm, PetscInt p, PetscBool useCone, PetscBool useTransitiveClosure, PetscBool useAnchors, PetscInt *adjSize, PetscInt *adj[])
{
  static PetscInt asiz = 0;
  PetscInt maxAnchors = 1;
  PetscInt aStart = -1, aEnd = -1;
  PetscInt maxAdjSize;
  PetscSection aSec = NULL;
  IS aIS = NULL;
  const PetscInt *anchors;
  PetscErrorCode  ierr;

  PetscFunctionBeginHot;
  if (useAnchors) {
    ierr = DMPlexGetAnchors(dm,&aSec,&aIS);CHKERRQ(ierr);
    if (aSec) {
      ierr = PetscSectionGetMaxDof(aSec,&maxAnchors);CHKERRQ(ierr);
      maxAnchors = PetscMax(1,maxAnchors);
      ierr = PetscSectionGetChart(aSec,&aStart,&aEnd);CHKERRQ(ierr);
      ierr = ISGetIndices(aIS,&anchors);CHKERRQ(ierr);
    }
  }
  if (!*adj) {
    PetscInt depth, coneSeries, supportSeries, maxC, maxS, pStart, pEnd;

    ierr  = DMPlexGetChart(dm, &pStart,&pEnd);CHKERRQ(ierr);
    ierr  = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
    ierr  = DMPlexGetMaxSizes(dm, &maxC, &maxS);CHKERRQ(ierr);
    coneSeries    = (maxC > 1) ? ((PetscPowInt(maxC,depth+1)-1)/(maxC-1)) : depth+1;
    supportSeries = (maxS > 1) ? ((PetscPowInt(maxS,depth+1)-1)/(maxS-1)) : depth+1;
    asiz  = PetscMax(PetscPowInt(maxS,depth)*coneSeries,PetscPowInt(maxC,depth)*supportSeries);
    asiz *= maxAnchors;
    asiz  = PetscMin(asiz,pEnd-pStart);
    ierr  = PetscMalloc1(asiz,adj);CHKERRQ(ierr);
  }
  if (*adjSize < 0) *adjSize = asiz;
  maxAdjSize = *adjSize;
  if (useTransitiveClosure) {
    ierr = DMPlexGetAdjacency_Transitive_Internal(dm, p, useCone, adjSize, *adj);CHKERRQ(ierr);
  } else if (useCone) {
    ierr = DMPlexGetAdjacency_Cone_Internal(dm, p, adjSize, *adj);CHKERRQ(ierr);
  } else {
    ierr = DMPlexGetAdjacency_Support_Internal(dm, p, adjSize, *adj);CHKERRQ(ierr);
  }
  if (useAnchors && aSec) {
    PetscInt origSize = *adjSize;
    PetscInt numAdj = origSize;
    PetscInt i = 0, j;
    PetscInt *orig = *adj;

    while (i < origSize) {
      PetscInt p = orig[i];
      PetscInt aDof = 0;

      if (p >= aStart && p < aEnd) {
        ierr = PetscSectionGetDof(aSec,p,&aDof);CHKERRQ(ierr);
      }
      if (aDof) {
        PetscInt aOff;
        PetscInt s, q;

        for (j = i + 1; j < numAdj; j++) {
          orig[j - 1] = orig[j];
        }
        origSize--;
        numAdj--;
        ierr = PetscSectionGetOffset(aSec,p,&aOff);CHKERRQ(ierr);
        for (s = 0; s < aDof; ++s) {
          for (q = 0; q < numAdj || (orig[numAdj++] = anchors[aOff+s],0); ++q) {
            if (anchors[aOff+s] == orig[q]) break;
          }
          if (numAdj > maxAdjSize) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid mesh exceeded adjacency allocation (%D)", maxAdjSize);
        }
      }
      else {
        i++;
      }
    }
    *adjSize = numAdj;
    ierr = ISRestoreIndices(aIS,&anchors);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetAdjacency"
/*@
  DMPlexGetAdjacency - Return all points adjacent to the given point

  Input Parameters:
+ dm - The DM object
. p  - The point
. adjSize - The maximum size of adj if it is non-NULL, or PETSC_DETERMINE
- adj - Either NULL so that the array is allocated, or an existing array with size adjSize

  Output Parameters:
+ adjSize - The number of adjacent points
- adj - The adjacent points

  Level: advanced

  Notes: The user must PetscFree the adj array if it was not passed in.

.seealso: DMPlexSetAdjacencyUseCone(), DMPlexSetAdjacencyUseClosure(), DMPlexDistribute(), DMCreateMatrix(), DMPlexPreallocateOperator()
@*/
PetscErrorCode DMPlexGetAdjacency(DM dm, PetscInt p, PetscInt *adjSize, PetscInt *adj[])
{
  DM_Plex       *mesh = (DM_Plex *) dm->data;
  PetscErrorCode ierr;

  PetscFunctionBeginHot;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidPointer(adjSize,3);
  PetscValidPointer(adj,4);
  ierr = DMPlexGetAdjacency_Internal(dm, p, mesh->useCone, mesh->useClosure, mesh->useAnchors, adjSize, adj);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}
#undef __FUNCT__
#define __FUNCT__ "DMPlexCreateTwoSidedProcessSF"
/*@
  DMPlexCreateTwoSidedProcessSF - Create an SF which just has process connectivity

  Collective on DM

  Input Parameters:
+ dm      - The DM
- sfPoint - The PetscSF which encodes point connectivity

  Output Parameters:
+ processRanks - A list of process neighbors, or NULL
- sfProcess    - An SF encoding the two-sided process connectivity, or NULL

  Level: developer

.seealso: PetscSFCreate(), DMPlexCreateProcessSF()
@*/
PetscErrorCode DMPlexCreateTwoSidedProcessSF(DM dm, PetscSF sfPoint, PetscSection rootRankSection, IS rootRanks, PetscSection leafRankSection, IS leafRanks, IS *processRanks, PetscSF *sfProcess)
{
  const PetscSFNode *remotePoints;
  PetscInt          *localPointsNew;
  PetscSFNode       *remotePointsNew;
  const PetscInt    *nranks;
  PetscInt          *ranksNew;
  PetscBT            neighbors;
  PetscInt           pStart, pEnd, p, numLeaves, l, numNeighbors, n;
  PetscMPIInt        numProcs, proc, rank;
  PetscErrorCode     ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidHeaderSpecific(sfPoint, PETSCSF_CLASSID, 2);
  if (processRanks) {PetscValidPointer(processRanks, 3);}
  if (sfProcess)    {PetscValidPointer(sfProcess, 4);}
  ierr = MPI_Comm_size(PetscObjectComm((PetscObject) dm), &numProcs);CHKERRQ(ierr);
  ierr = MPI_Comm_rank(PetscObjectComm((PetscObject) dm), &rank);CHKERRQ(ierr);
  ierr = PetscSFGetGraph(sfPoint, NULL, &numLeaves, NULL, &remotePoints);CHKERRQ(ierr);
  ierr = PetscBTCreate(numProcs, &neighbors);CHKERRQ(ierr);
  ierr = PetscBTMemzero(numProcs, neighbors);CHKERRQ(ierr);
  /* Compute root-to-leaf process connectivity */
  ierr = PetscSectionGetChart(rootRankSection, &pStart, &pEnd);CHKERRQ(ierr);
  ierr = ISGetIndices(rootRanks, &nranks);CHKERRQ(ierr);
  for (p = pStart; p < pEnd; ++p) {
    PetscInt ndof, noff, n;

    ierr = PetscSectionGetDof(rootRankSection, p, &ndof);CHKERRQ(ierr);
    ierr = PetscSectionGetOffset(rootRankSection, p, &noff);CHKERRQ(ierr);
    for (n = 0; n < ndof; ++n) {ierr = PetscBTSet(neighbors, nranks[noff+n]);}
  }
  ierr = ISRestoreIndices(rootRanks, &nranks);CHKERRQ(ierr);
  /* Compute leaf-to-neighbor process connectivity */
  ierr = PetscSectionGetChart(leafRankSection, &pStart, &pEnd);CHKERRQ(ierr);
  ierr = ISGetIndices(leafRanks, &nranks);CHKERRQ(ierr);
  for (p = pStart; p < pEnd; ++p) {
    PetscInt ndof, noff, n;

    ierr = PetscSectionGetDof(leafRankSection, p, &ndof);CHKERRQ(ierr);
    ierr = PetscSectionGetOffset(leafRankSection, p, &noff);CHKERRQ(ierr);
    for (n = 0; n < ndof; ++n) {ierr = PetscBTSet(neighbors, nranks[noff+n]);}
  }
  ierr = ISRestoreIndices(leafRanks, &nranks);CHKERRQ(ierr);
  /* Compute leaf-to-root process connectivity */
  for (l = 0; l < numLeaves; ++l) {PetscBTSet(neighbors, remotePoints[l].rank);}
  /* Calculate edges */
  PetscBTClear(neighbors, rank);
  for(proc = 0, numNeighbors = 0; proc < numProcs; ++proc) {if (PetscBTLookup(neighbors, proc)) ++numNeighbors;}
  ierr = PetscMalloc1(numNeighbors, &ranksNew);CHKERRQ(ierr);
  ierr = PetscMalloc1(numNeighbors, &localPointsNew);CHKERRQ(ierr);
  ierr = PetscMalloc1(numNeighbors, &remotePointsNew);CHKERRQ(ierr);
  for(proc = 0, n = 0; proc < numProcs; ++proc) {
    if (PetscBTLookup(neighbors, proc)) {
      ranksNew[n]              = proc;
      localPointsNew[n]        = proc;
      remotePointsNew[n].index = rank;
      remotePointsNew[n].rank  = proc;
      ++n;
    }
  }
  ierr = PetscBTDestroy(&neighbors);CHKERRQ(ierr);
  if (processRanks) {ierr = ISCreateGeneral(PetscObjectComm((PetscObject)dm), numNeighbors, ranksNew, PETSC_OWN_POINTER, processRanks);CHKERRQ(ierr);}
  else              {ierr = PetscFree(ranksNew);CHKERRQ(ierr);}
  if (sfProcess) {
    ierr = PetscSFCreate(PetscObjectComm((PetscObject)dm), sfProcess);CHKERRQ(ierr);
    ierr = PetscObjectSetName((PetscObject) *sfProcess, "Two-Sided Process SF");CHKERRQ(ierr);
    ierr = PetscSFSetFromOptions(*sfProcess);CHKERRQ(ierr);
    ierr = PetscSFSetGraph(*sfProcess, numProcs, numNeighbors, localPointsNew, PETSC_OWN_POINTER, remotePointsNew, PETSC_OWN_POINTER);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexDistributeOwnership"
/*@
  DMPlexDistributeOwnership - Compute owner information for shared points. This basically gets two-sided for an SF.

  Collective on DM

  Input Parameter:
. dm - The DM

  Output Parameters:
+ rootSection - The number of leaves for a given root point
. rootrank    - The rank of each edge into the root point
. leafSection - The number of processes sharing a given leaf point
- leafrank    - The rank of each process sharing a leaf point

  Level: developer

.seealso: DMPlexCreateOverlap()
@*/
PetscErrorCode DMPlexDistributeOwnership(DM dm, PetscSection rootSection, IS *rootrank, PetscSection leafSection, IS *leafrank)
{
  MPI_Comm        comm;
  PetscSF         sfPoint;
  const PetscInt *rootdegree;
  PetscInt       *myrank, *remoterank;
  PetscInt        pStart, pEnd, p, nedges;
  PetscMPIInt     rank;
  PetscErrorCode  ierr;

  PetscFunctionBegin;
  ierr = PetscObjectGetComm((PetscObject) dm, &comm);CHKERRQ(ierr);
  ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
  ierr = DMPlexGetChart(dm, &pStart, &pEnd);CHKERRQ(ierr);
  ierr = DMGetPointSF(dm, &sfPoint);CHKERRQ(ierr);
  /* Compute number of leaves for each root */
  ierr = PetscObjectSetName((PetscObject) rootSection, "Root Section");CHKERRQ(ierr);
  ierr = PetscSectionSetChart(rootSection, pStart, pEnd);CHKERRQ(ierr);
  ierr = PetscSFComputeDegreeBegin(sfPoint, &rootdegree);CHKERRQ(ierr);
  ierr = PetscSFComputeDegreeEnd(sfPoint, &rootdegree);CHKERRQ(ierr);
  for (p = pStart; p < pEnd; ++p) {ierr = PetscSectionSetDof(rootSection, p, rootdegree[p-pStart]);CHKERRQ(ierr);}
  ierr = PetscSectionSetUp(rootSection);CHKERRQ(ierr);
  /* Gather rank of each leaf to root */
  ierr = PetscSectionGetStorageSize(rootSection, &nedges);CHKERRQ(ierr);
  ierr = PetscMalloc1(pEnd-pStart, &myrank);CHKERRQ(ierr);
  ierr = PetscMalloc1(nedges,  &remoterank);CHKERRQ(ierr);
  for (p = 0; p < pEnd-pStart; ++p) myrank[p] = rank;
  ierr = PetscSFGatherBegin(sfPoint, MPIU_INT, myrank, remoterank);CHKERRQ(ierr);
  ierr = PetscSFGatherEnd(sfPoint, MPIU_INT, myrank, remoterank);CHKERRQ(ierr);
  ierr = PetscFree(myrank);CHKERRQ(ierr);
  ierr = ISCreateGeneral(comm, nedges, remoterank, PETSC_OWN_POINTER, rootrank);CHKERRQ(ierr);
  /* Distribute remote ranks to leaves */
  ierr = PetscObjectSetName((PetscObject) leafSection, "Leaf Section");CHKERRQ(ierr);
  ierr = DMPlexDistributeFieldIS(dm, sfPoint, rootSection, *rootrank, leafSection, leafrank);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexCreateOverlap"
/*@C
  DMPlexCreateOverlap - Compute owner information for shared points. This basically gets two-sided for an SF.

  Collective on DM

  Input Parameters:
+ dm          - The DM
. levels      - Number of overlap levels
. rootSection - The number of leaves for a given root point
. rootrank    - The rank of each edge into the root point
. leafSection - The number of processes sharing a given leaf point
- leafrank    - The rank of each process sharing a leaf point

  Output Parameters:
+ ovLabel     - DMLabel containing remote overlap contributions as point/rank pairings

  Level: developer

.seealso: DMPlexDistributeOwnership(), DMPlexDistribute()
@*/
PetscErrorCode DMPlexCreateOverlap(DM dm, PetscInt levels, PetscSection rootSection, IS rootrank, PetscSection leafSection, IS leafrank, DMLabel *ovLabel)
{
  MPI_Comm           comm;
  DMLabel            ovAdjByRank; /* A DMLabel containing all points adjacent to shared points, separated by rank (value in label) */
  PetscSF            sfPoint, sfProc;
  const PetscSFNode *remote;
  const PetscInt    *local;
  const PetscInt    *nrank, *rrank;
  PetscInt          *adj = NULL;
  PetscInt           pStart, pEnd, p, sStart, sEnd, nleaves, l;
  PetscMPIInt        rank, numProcs;
  PetscBool          useCone, useClosure, flg;
  PetscErrorCode     ierr;

  PetscFunctionBegin;
  ierr = PetscObjectGetComm((PetscObject) dm, &comm);CHKERRQ(ierr);
  ierr = MPI_Comm_size(comm, &numProcs);CHKERRQ(ierr);
  ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
  ierr = DMGetPointSF(dm, &sfPoint);CHKERRQ(ierr);
  ierr = DMPlexGetChart(dm, &pStart, &pEnd);CHKERRQ(ierr);
  ierr = PetscSectionGetChart(leafSection, &sStart, &sEnd);CHKERRQ(ierr);
  ierr = PetscSFGetGraph(sfPoint, NULL, &nleaves, &local, &remote);CHKERRQ(ierr);
  ierr = DMLabelCreate("Overlap adjacency", &ovAdjByRank);CHKERRQ(ierr);
  /* Handle leaves: shared with the root point */
  for (l = 0; l < nleaves; ++l) {
    PetscInt adjSize = PETSC_DETERMINE, a;

    ierr = DMPlexGetAdjacency(dm, local[l], &adjSize, &adj);CHKERRQ(ierr);
    for (a = 0; a < adjSize; ++a) {ierr = DMLabelSetValue(ovAdjByRank, adj[a], remote[l].rank);CHKERRQ(ierr);}
  }
  ierr = ISGetIndices(rootrank, &rrank);CHKERRQ(ierr);
  ierr = ISGetIndices(leafrank, &nrank);CHKERRQ(ierr);
  /* Handle roots */
  for (p = pStart; p < pEnd; ++p) {
    PetscInt adjSize = PETSC_DETERMINE, neighbors = 0, noff, n, a;

    if ((p >= sStart) && (p < sEnd)) {
      /* Some leaves share a root with other leaves on different processes */
      ierr = PetscSectionGetDof(leafSection, p, &neighbors);CHKERRQ(ierr);
      if (neighbors) {
        ierr = PetscSectionGetOffset(leafSection, p, &noff);CHKERRQ(ierr);
        ierr = DMPlexGetAdjacency(dm, p, &adjSize, &adj);CHKERRQ(ierr);
        for (n = 0; n < neighbors; ++n) {
          const PetscInt remoteRank = nrank[noff+n];

          if (remoteRank == rank) continue;
          for (a = 0; a < adjSize; ++a) {ierr = DMLabelSetValue(ovAdjByRank, adj[a], remoteRank);CHKERRQ(ierr);}
        }
      }
    }
    /* Roots are shared with leaves */
    ierr = PetscSectionGetDof(rootSection, p, &neighbors);CHKERRQ(ierr);
    if (!neighbors) continue;
    ierr = PetscSectionGetOffset(rootSection, p, &noff);CHKERRQ(ierr);
    ierr = DMPlexGetAdjacency(dm, p, &adjSize, &adj);CHKERRQ(ierr);
    for (n = 0; n < neighbors; ++n) {
      const PetscInt remoteRank = rrank[noff+n];

      if (remoteRank == rank) continue;
      for (a = 0; a < adjSize; ++a) {ierr = DMLabelSetValue(ovAdjByRank, adj[a], remoteRank);CHKERRQ(ierr);}
    }
  }
  ierr = PetscFree(adj);CHKERRQ(ierr);
  ierr = ISRestoreIndices(rootrank, &rrank);CHKERRQ(ierr);
  ierr = ISRestoreIndices(leafrank, &nrank);CHKERRQ(ierr);
  /* Add additional overlap levels */
  for (l = 1; l < levels; l++) {ierr = DMPlexPartitionLabelAdjacency(dm, ovAdjByRank);CHKERRQ(ierr);}
  /* We require the closure in the overlap */
  ierr = DMPlexGetAdjacencyUseCone(dm, &useCone);CHKERRQ(ierr);
  ierr = DMPlexGetAdjacencyUseClosure(dm, &useClosure);CHKERRQ(ierr);
  if (useCone || !useClosure) {
    ierr = DMPlexPartitionLabelClosure(dm, ovAdjByRank);CHKERRQ(ierr);
  }
  ierr = PetscOptionsHasName(((PetscObject) dm)->prefix, "-overlap_view", &flg);CHKERRQ(ierr);
  if (flg) {
    ierr = PetscViewerASCIISynchronizedAllow(PETSC_VIEWER_STDOUT_WORLD, PETSC_TRUE);CHKERRQ(ierr);
    ierr = DMLabelView(ovAdjByRank, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
  }
  /* Make process SF and invert sender to receiver label */
  ierr = DMPlexCreateTwoSidedProcessSF(dm, sfPoint, rootSection, rootrank, leafSection, leafrank, NULL, &sfProc);CHKERRQ(ierr);
  ierr = DMLabelCreate("Overlap label", ovLabel);CHKERRQ(ierr);
  ierr = DMPlexPartitionLabelInvert(dm, ovAdjByRank, sfProc, *ovLabel);CHKERRQ(ierr);
  /* Add owned points, except for shared local points */
  for (p = pStart; p < pEnd; ++p) {ierr = DMLabelSetValue(*ovLabel, p, rank);CHKERRQ(ierr);}
  for (l = 0; l < nleaves; ++l) {
    ierr = DMLabelClearValue(*ovLabel, local[l], rank);CHKERRQ(ierr);
    ierr = DMLabelSetValue(*ovLabel, remote[l].index, remote[l].rank);CHKERRQ(ierr);
  }
  /* Clean up */
  ierr = DMLabelDestroy(&ovAdjByRank);CHKERRQ(ierr);
  ierr = PetscSFDestroy(&sfProc);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexCreateOverlapMigrationSF"
PetscErrorCode DMPlexCreateOverlapMigrationSF(DM dm, PetscSF overlapSF, PetscSF *migrationSF)
{
  MPI_Comm           comm;
  PetscMPIInt        rank, numProcs;
  PetscInt           d, dim, p, pStart, pEnd, nroots, nleaves, newLeaves, point, numSharedPoints;
  PetscInt          *pointDepths, *remoteDepths, *ilocal;
  PetscInt          *depthRecv, *depthShift, *depthIdx;
  PetscSFNode       *iremote;
  PetscSF            pointSF;
  const PetscInt    *sharedLocal;
  const PetscSFNode *overlapRemote, *sharedRemote;
  PetscErrorCode     ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  ierr = PetscObjectGetComm((PetscObject)dm, &comm);CHKERRQ(ierr);
  ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
  ierr = MPI_Comm_size(comm, &numProcs);CHKERRQ(ierr);
  ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);

  /* Before building the migration SF we need to know the new stratum offsets */
  ierr = PetscSFGetGraph(overlapSF, &nroots, &nleaves, NULL, &overlapRemote);CHKERRQ(ierr);
  ierr = PetscMalloc2(nroots, &pointDepths, nleaves, &remoteDepths);CHKERRQ(ierr);
  for (d=0; d<dim+1; d++) {
    ierr = DMPlexGetDepthStratum(dm, d, &pStart, &pEnd);CHKERRQ(ierr);
    for (p=pStart; p<pEnd; p++) pointDepths[p] = d;
  }
  for (p=0; p<nleaves; p++) remoteDepths[p] = -1;
  ierr = PetscSFBcastBegin(overlapSF, MPIU_INT, pointDepths, remoteDepths);CHKERRQ(ierr);
  ierr = PetscSFBcastEnd(overlapSF, MPIU_INT, pointDepths, remoteDepths);CHKERRQ(ierr);

  /* Count recevied points in each stratum and compute the internal strata shift */
  ierr = PetscMalloc3(dim+1, &depthRecv, dim+1, &depthShift, dim+1, &depthIdx);CHKERRQ(ierr);
  for (d=0; d<dim+1; d++) depthRecv[d]=0;
  for (p=0; p<nleaves; p++) depthRecv[remoteDepths[p]]++;
  depthShift[dim] = 0;
  for (d=0; d<dim; d++) depthShift[d] = depthRecv[dim];
  for (d=1; d<dim; d++) depthShift[d] += depthRecv[0];
  for (d=dim-2; d>0; d--) depthShift[d] += depthRecv[d+1];
  for (d=0; d<dim+1; d++) {
    ierr = DMPlexGetDepthStratum(dm, d, &pStart, &pEnd);CHKERRQ(ierr);
    depthIdx[d] = pStart + depthShift[d];
  }

  /* Form the overlap SF build an SF that describes the full overlap migration SF */
  ierr = DMPlexGetChart(dm, &pStart, &pEnd);CHKERRQ(ierr);
  newLeaves = pEnd - pStart + nleaves;
  ierr = PetscMalloc1(newLeaves, &ilocal);CHKERRQ(ierr);
  ierr = PetscMalloc1(newLeaves, &iremote);CHKERRQ(ierr);
  /* First map local points to themselves */
  for (d=0; d<dim+1; d++) {
    ierr = DMPlexGetDepthStratum(dm, d, &pStart, &pEnd);CHKERRQ(ierr);
    for (p=pStart; p<pEnd; p++) {
      point = p + depthShift[d];
      ilocal[point] = point;
      iremote[point].index = p;
      iremote[point].rank = rank;
      depthIdx[d]++;
    }
  }

  /* Add in the remote roots for currently shared points */
  ierr = DMGetPointSF(dm, &pointSF);CHKERRQ(ierr);
  ierr = PetscSFGetGraph(pointSF, NULL, &numSharedPoints, &sharedLocal, &sharedRemote);CHKERRQ(ierr);
  for (d=0; d<dim+1; d++) {
    ierr = DMPlexGetDepthStratum(dm, d, &pStart, &pEnd);CHKERRQ(ierr);
    for (p=0; p<numSharedPoints; p++) {
      if (pStart <= sharedLocal[p] && sharedLocal[p] < pEnd) {
        point = sharedLocal[p] + depthShift[d];
        iremote[point].index = sharedRemote[p].index;
        iremote[point].rank = sharedRemote[p].rank;
      }
    }
  }

  /* Now add the incoming overlap points */
  for (p=0; p<nleaves; p++) {
    point = depthIdx[remoteDepths[p]];
    ilocal[point] = point;
    iremote[point].index = overlapRemote[p].index;
    iremote[point].rank = overlapRemote[p].rank;
    depthIdx[remoteDepths[p]]++;
  }
  ierr = PetscFree2(pointDepths,remoteDepths);CHKERRQ(ierr);

  ierr = PetscSFCreate(comm, migrationSF);CHKERRQ(ierr);
  ierr = PetscObjectSetName((PetscObject) *migrationSF, "Overlap Migration SF");CHKERRQ(ierr);
  ierr = PetscSFSetFromOptions(*migrationSF);CHKERRQ(ierr);
  ierr = DMPlexGetChart(dm, &pStart, &pEnd);CHKERRQ(ierr);
  ierr = PetscSFSetGraph(*migrationSF, pEnd-pStart, newLeaves, ilocal, PETSC_OWN_POINTER, iremote, PETSC_OWN_POINTER);CHKERRQ(ierr);

  ierr = PetscFree3(depthRecv, depthShift, depthIdx);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexStratifyMigrationSF"
/*@
  DMPlexStratifyMigrationSF - Add partition overlap to a distributed non-overlapping DM.

  Input Parameter:
+ dm          - The DM
- sf          - A star forest with non-ordered leaves, usually defining a DM point migration

  Output Parameter:
. migrationSF - A star forest with added leaf indirection that ensures the resulting DM is stratified

  Level: developer

.seealso: DMPlexPartitionLabelCreateSF(), DMPlexDistribute(), DMPlexDistributeOverlap()
@*/
PetscErrorCode DMPlexStratifyMigrationSF(DM dm, PetscSF sf, PetscSF *migrationSF)
{
  MPI_Comm           comm;
  PetscMPIInt        rank, numProcs;
  PetscInt           d, ldepth, depth, p, pStart, pEnd, nroots, nleaves;
  PetscInt          *pointDepths, *remoteDepths, *ilocal;
  PetscInt          *depthRecv, *depthShift, *depthIdx;
  const PetscSFNode *iremote;
  PetscErrorCode     ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  ierr = PetscObjectGetComm((PetscObject) dm, &comm);CHKERRQ(ierr);
  ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
  ierr = MPI_Comm_size(comm, &numProcs);CHKERRQ(ierr);
  ierr = DMPlexGetDepth(dm, &ldepth);CHKERRQ(ierr);
  ierr = MPI_Allreduce(&ldepth, &depth, 1, MPIU_INT, MPI_MAX, comm);CHKERRQ(ierr);
  if ((ldepth >= 0) && (depth != ldepth)) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Inconsistent Plex depth %d != %d", ldepth, depth);

  /* Before building the migration SF we need to know the new stratum offsets */
  ierr = PetscSFGetGraph(sf, &nroots, &nleaves, NULL, &iremote);CHKERRQ(ierr);
  ierr = PetscMalloc2(nroots, &pointDepths, nleaves, &remoteDepths);CHKERRQ(ierr);
  for (d = 0; d < depth+1; ++d) {
    ierr = DMPlexGetDepthStratum(dm, d, &pStart, &pEnd);CHKERRQ(ierr);
    for (p = pStart; p < pEnd; ++p) pointDepths[p] = d;
  }
  for (p = 0; p < nleaves; ++p) remoteDepths[p] = -1;
  ierr = PetscSFBcastBegin(sf, MPIU_INT, pointDepths, remoteDepths);CHKERRQ(ierr);
  ierr = PetscSFBcastEnd(sf, MPIU_INT, pointDepths, remoteDepths);CHKERRQ(ierr);
  /* Count recevied points in each stratum and compute the internal strata shift */
  ierr = PetscMalloc3(depth+1, &depthRecv, depth+1, &depthShift, depth+1, &depthIdx);CHKERRQ(ierr);
  for (d = 0; d < depth+1; ++d) depthRecv[d] = 0;
  for (p = 0; p < nleaves; ++p) depthRecv[remoteDepths[p]]++;
  depthShift[depth] = 0;
  for (d = 0; d < depth; ++d) depthShift[d] = depthRecv[depth];
  for (d = 1; d < depth; ++d) depthShift[d] += depthRecv[0];
  for (d = depth-2; d > 0; --d) depthShift[d] += depthRecv[d+1];
  for (d = 0; d < depth+1; ++d) {depthIdx[d] = 0;}
  /* Derive a new local permutation based on stratified indices */
  ierr = PetscMalloc1(nleaves, &ilocal);CHKERRQ(ierr);
  for (p = 0; p < nleaves; ++p) {
    const PetscInt dep = remoteDepths[p];

    ilocal[p] = depthShift[dep] + depthIdx[dep];
    depthIdx[dep]++;
  }
  ierr = PetscSFCreate(comm, migrationSF);CHKERRQ(ierr);
  ierr = PetscObjectSetName((PetscObject) *migrationSF, "Migration SF");CHKERRQ(ierr);
  ierr = PetscSFSetGraph(*migrationSF, nroots, nleaves, ilocal, PETSC_OWN_POINTER, iremote, PETSC_COPY_VALUES);CHKERRQ(ierr);
  ierr = PetscFree2(pointDepths,remoteDepths);CHKERRQ(ierr);
  ierr = PetscFree3(depthRecv, depthShift, depthIdx);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexDistributeField"
/*@
  DMPlexDistributeField - Distribute field data to match a given PetscSF, usually the SF from mesh distribution

  Collective on DM

  Input Parameters:
+ dm - The DMPlex object
. pointSF - The PetscSF describing the communication pattern
. originalSection - The PetscSection for existing data layout
- originalVec - The existing data

  Output Parameters:
+ newSection - The PetscSF describing the new data layout
- newVec - The new data

  Level: developer

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

  PetscFunctionBegin;
  ierr = PetscLogEventBegin(DMPLEX_DistributeField,dm,0,0,0);CHKERRQ(ierr);
  ierr = PetscSFDistributeSection(pointSF, originalSection, &remoteOffsets, newSection);CHKERRQ(ierr);

  ierr = PetscSectionGetStorageSize(newSection, &fieldSize);CHKERRQ(ierr);
  ierr = VecSetSizes(newVec, fieldSize, PETSC_DETERMINE);CHKERRQ(ierr);
  ierr = VecSetType(newVec,dm->vectype);CHKERRQ(ierr);

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

#undef __FUNCT__
#define __FUNCT__ "DMPlexDistributeFieldIS"
/*@
  DMPlexDistributeFieldIS - Distribute field data to match a given PetscSF, usually the SF from mesh distribution

  Collective on DM

  Input Parameters:
+ dm - The DMPlex object
. pointSF - The PetscSF describing the communication pattern
. originalSection - The PetscSection for existing data layout
- originalIS - The existing data

  Output Parameters:
+ newSection - The PetscSF describing the new data layout
- newIS - The new data

  Level: developer

.seealso: DMPlexDistribute(), DMPlexDistributeField(), DMPlexDistributeData()
@*/
PetscErrorCode DMPlexDistributeFieldIS(DM dm, PetscSF pointSF, PetscSection originalSection, IS originalIS, PetscSection newSection, IS *newIS)
{
  PetscSF         fieldSF;
  PetscInt       *newValues, *remoteOffsets, fieldSize;
  const PetscInt *originalValues;
  PetscErrorCode  ierr;

  PetscFunctionBegin;
  ierr = PetscLogEventBegin(DMPLEX_DistributeField,dm,0,0,0);CHKERRQ(ierr);
  ierr = PetscSFDistributeSection(pointSF, originalSection, &remoteOffsets, newSection);CHKERRQ(ierr);

  ierr = PetscSectionGetStorageSize(newSection, &fieldSize);CHKERRQ(ierr);
  ierr = PetscMalloc1(fieldSize, &newValues);CHKERRQ(ierr);

  ierr = ISGetIndices(originalIS, &originalValues);CHKERRQ(ierr);
  ierr = PetscSFCreateSectionSF(pointSF, originalSection, remoteOffsets, newSection, &fieldSF);CHKERRQ(ierr);
  ierr = PetscSFBcastBegin(fieldSF, MPIU_INT, (PetscInt *) originalValues, newValues);CHKERRQ(ierr);
  ierr = PetscSFBcastEnd(fieldSF, MPIU_INT, (PetscInt *) originalValues, newValues);CHKERRQ(ierr);
  ierr = PetscSFDestroy(&fieldSF);CHKERRQ(ierr);
  ierr = ISRestoreIndices(originalIS, &originalValues);CHKERRQ(ierr);
  ierr = ISCreateGeneral(PetscObjectComm((PetscObject) pointSF), fieldSize, newValues, PETSC_OWN_POINTER, newIS);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(DMPLEX_DistributeField,dm,0,0,0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexDistributeData"
/*@
  DMPlexDistributeData - Distribute field data to match a given PetscSF, usually the SF from mesh distribution

  Collective on DM

  Input Parameters:
+ dm - The DMPlex object
. pointSF - The PetscSF describing the communication pattern
. originalSection - The PetscSection for existing data layout
. datatype - The type of data
- originalData - The existing data

  Output Parameters:
+ newSection - The PetscSection describing the new data layout
- newData - The new data

  Level: developer

.seealso: DMPlexDistribute(), DMPlexDistributeField()
@*/
PetscErrorCode DMPlexDistributeData(DM dm, PetscSF pointSF, PetscSection originalSection, MPI_Datatype datatype, void *originalData, PetscSection newSection, void **newData)
{
  PetscSF        fieldSF;
  PetscInt      *remoteOffsets, fieldSize;
  PetscMPIInt    dataSize;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscLogEventBegin(DMPLEX_DistributeData,dm,0,0,0);CHKERRQ(ierr);
  ierr = PetscSFDistributeSection(pointSF, originalSection, &remoteOffsets, newSection);CHKERRQ(ierr);

  ierr = PetscSectionGetStorageSize(newSection, &fieldSize);CHKERRQ(ierr);
  ierr = MPI_Type_size(datatype, &dataSize);CHKERRQ(ierr);
  ierr = PetscMalloc(fieldSize * dataSize, newData);CHKERRQ(ierr);

  ierr = PetscSFCreateSectionSF(pointSF, originalSection, remoteOffsets, newSection, &fieldSF);CHKERRQ(ierr);
  ierr = PetscSFBcastBegin(fieldSF, datatype, originalData, *newData);CHKERRQ(ierr);
  ierr = PetscSFBcastEnd(fieldSF, datatype, originalData, *newData);CHKERRQ(ierr);
  ierr = PetscSFDestroy(&fieldSF);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(DMPLEX_DistributeData,dm,0,0,0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexDistributeCones"
PetscErrorCode DMPlexDistributeCones(DM dm, PetscSF migrationSF, ISLocalToGlobalMapping renumbering, DM dmParallel)
{
  DM_Plex               *mesh  = (DM_Plex*) dm->data;
  DM_Plex               *pmesh = (DM_Plex*) (dmParallel)->data;
  MPI_Comm               comm;
  PetscSF                coneSF;
  PetscSection           originalConeSection, newConeSection;
  PetscInt              *remoteOffsets, *cones, *newCones, newConesSize;
  PetscBool              flg;
  PetscErrorCode         ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidPointer(dmParallel,4);
  ierr = PetscLogEventBegin(DMPLEX_DistributeCones,dm,0,0,0);CHKERRQ(ierr);

  /* Distribute cone section */
  ierr = PetscObjectGetComm((PetscObject)dm, &comm);CHKERRQ(ierr);
  ierr = DMPlexGetConeSection(dm, &originalConeSection);CHKERRQ(ierr);
  ierr = DMPlexGetConeSection(dmParallel, &newConeSection);CHKERRQ(ierr);
  ierr = PetscSFDistributeSection(migrationSF, originalConeSection, &remoteOffsets, newConeSection);CHKERRQ(ierr);
  ierr = DMSetUp(dmParallel);CHKERRQ(ierr);
  {
    PetscInt pStart, pEnd, p;

    ierr = PetscSectionGetChart(newConeSection, &pStart, &pEnd);CHKERRQ(ierr);
    for (p = pStart; p < pEnd; ++p) {
      PetscInt coneSize;
      ierr               = PetscSectionGetDof(newConeSection, p, &coneSize);CHKERRQ(ierr);
      pmesh->maxConeSize = PetscMax(pmesh->maxConeSize, coneSize);
    }
  }
  /* Communicate and renumber cones */
  ierr = PetscSFCreateSectionSF(migrationSF, originalConeSection, remoteOffsets, newConeSection, &coneSF);CHKERRQ(ierr);
  ierr = DMPlexGetCones(dm, &cones);CHKERRQ(ierr);
  ierr = DMPlexGetCones(dmParallel, &newCones);CHKERRQ(ierr);
  ierr = PetscSFBcastBegin(coneSF, MPIU_INT, cones, newCones);CHKERRQ(ierr);
  ierr = PetscSFBcastEnd(coneSF, MPIU_INT, cones, newCones);CHKERRQ(ierr);
  ierr = PetscSectionGetStorageSize(newConeSection, &newConesSize);CHKERRQ(ierr);
  ierr = ISGlobalToLocalMappingApplyBlock(renumbering, IS_GTOLM_MASK, newConesSize, newCones, NULL, newCones);CHKERRQ(ierr);
#if PETSC_USE_DEBUG
  {
    PetscInt  p;
    PetscBool valid = PETSC_TRUE;
    for (p = 0; p < newConesSize; ++p) {
      if (newCones[p] < 0) {valid = PETSC_FALSE; ierr = PetscPrintf(PETSC_COMM_SELF, "Point %d not in overlap SF\n", p);CHKERRQ(ierr);}
    }
    if (!valid) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid global to local map");
  }
#endif
  ierr = PetscOptionsHasName(((PetscObject) dm)->prefix, "-cones_view", &flg);CHKERRQ(ierr);
  if (flg) {
    ierr = PetscPrintf(comm, "Serial Cone Section:\n");CHKERRQ(ierr);
    ierr = PetscSectionView(originalConeSection, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
    ierr = PetscPrintf(comm, "Parallel Cone Section:\n");CHKERRQ(ierr);
    ierr = PetscSectionView(newConeSection, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
    ierr = PetscSFView(coneSF, NULL);CHKERRQ(ierr);
  }
  ierr = DMPlexGetConeOrientations(dm, &cones);CHKERRQ(ierr);
  ierr = DMPlexGetConeOrientations(dmParallel, &newCones);CHKERRQ(ierr);
  ierr = PetscSFBcastBegin(coneSF, MPIU_INT, cones, newCones);CHKERRQ(ierr);
  ierr = PetscSFBcastEnd(coneSF, MPIU_INT, cones, newCones);CHKERRQ(ierr);
  ierr = PetscSFDestroy(&coneSF);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(DMPLEX_DistributeCones,dm,0,0,0);CHKERRQ(ierr);
  /* Create supports and stratify sieve */
  {
    PetscInt pStart, pEnd;

    ierr = PetscSectionGetChart(pmesh->coneSection, &pStart, &pEnd);CHKERRQ(ierr);
    ierr = PetscSectionSetChart(pmesh->supportSection, pStart, pEnd);CHKERRQ(ierr);
  }
  ierr = DMPlexSymmetrize(dmParallel);CHKERRQ(ierr);
  ierr = DMPlexStratify(dmParallel);CHKERRQ(ierr);
  pmesh->useCone    = mesh->useCone;
  pmesh->useClosure = mesh->useClosure;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexDistributeCoordinates"
PetscErrorCode DMPlexDistributeCoordinates(DM dm, PetscSF migrationSF, DM dmParallel)
{
  MPI_Comm         comm;
  PetscSection     originalCoordSection, newCoordSection;
  Vec              originalCoordinates, newCoordinates;
  PetscInt         bs;
  const char      *name;
  const PetscReal *maxCell, *L;
  PetscErrorCode   ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidPointer(dmParallel, 3);

  ierr = PetscObjectGetComm((PetscObject)dm, &comm);CHKERRQ(ierr);
  ierr = DMGetCoordinateSection(dm, &originalCoordSection);CHKERRQ(ierr);
  ierr = DMGetCoordinateSection(dmParallel, &newCoordSection);CHKERRQ(ierr);
  ierr = DMGetCoordinatesLocal(dm, &originalCoordinates);CHKERRQ(ierr);
  if (originalCoordinates) {
    ierr = VecCreate(comm, &newCoordinates);CHKERRQ(ierr);
    ierr = PetscObjectGetName((PetscObject) originalCoordinates, &name);CHKERRQ(ierr);
    ierr = PetscObjectSetName((PetscObject) newCoordinates, name);CHKERRQ(ierr);

    ierr = DMPlexDistributeField(dm, migrationSF, originalCoordSection, originalCoordinates, newCoordSection, newCoordinates);CHKERRQ(ierr);
    ierr = DMSetCoordinatesLocal(dmParallel, newCoordinates);CHKERRQ(ierr);
    ierr = VecGetBlockSize(originalCoordinates, &bs);CHKERRQ(ierr);
    ierr = VecSetBlockSize(newCoordinates, bs);CHKERRQ(ierr);
    ierr = VecDestroy(&newCoordinates);CHKERRQ(ierr);
  }
  ierr = DMGetPeriodicity(dm, &maxCell, &L);CHKERRQ(ierr);
  if (L) {ierr = DMSetPeriodicity(dmParallel, maxCell, L);CHKERRQ(ierr);}
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexDistributeLabels"
/* Here we are assuming that process 0 always has everything */
PetscErrorCode DMPlexDistributeLabels(DM dm, PetscSF migrationSF, DM dmParallel)
{
  MPI_Comm       comm;
  PetscMPIInt    rank;
  PetscInt       numLabels, numLocalLabels, l;
  PetscBool      hasLabels = PETSC_FALSE;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidHeaderSpecific(dm, DM_CLASSID, 3);
  ierr = PetscLogEventBegin(DMPLEX_DistributeLabels,dm,0,0,0);CHKERRQ(ierr);
  ierr = PetscObjectGetComm((PetscObject)dm, &comm);CHKERRQ(ierr);
  ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);

  /* Everyone must have either the same number of labels, or none */
  ierr = DMPlexGetNumLabels(dm, &numLocalLabels);CHKERRQ(ierr);
  numLabels = numLocalLabels;
  ierr = MPI_Bcast(&numLabels, 1, MPIU_INT, 0, comm);CHKERRQ(ierr);
  if (numLabels == numLocalLabels) hasLabels = PETSC_TRUE;
  for (l = numLabels-1; l >= 0; --l) {
    DMLabel     label = NULL, labelNew = NULL;
    PetscBool   isdepth;

    if (hasLabels) {
      ierr = DMPlexGetLabelByNum(dm, l, &label);CHKERRQ(ierr);
      /* Skip "depth" because it is recreated */
      ierr = PetscStrcmp(label->name, "depth", &isdepth);CHKERRQ(ierr);
    }
    ierr = MPI_Bcast(&isdepth, 1, MPIU_BOOL, 0, comm);CHKERRQ(ierr);
    if (isdepth) continue;
    ierr = DMLabelDistribute(label, migrationSF, &labelNew);CHKERRQ(ierr);
    ierr = DMPlexAddLabel(dmParallel, labelNew);CHKERRQ(ierr);
  }
  ierr = PetscLogEventEnd(DMPLEX_DistributeLabels,dm,0,0,0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexDistributeSetupHybrid"
PetscErrorCode DMPlexDistributeSetupHybrid(DM dm, PetscSF migrationSF, ISLocalToGlobalMapping renumbering, DM dmParallel)
{
  DM_Plex        *mesh  = (DM_Plex*) dm->data;
  DM_Plex        *pmesh = (DM_Plex*) (dmParallel)->data;
  MPI_Comm        comm;
  const PetscInt *gpoints;
  PetscInt        dim, depth, n, d;
  PetscErrorCode  ierr;

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

  ierr = PetscObjectGetComm((PetscObject)dm, &comm);CHKERRQ(ierr);
  ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);

  /* Setup hybrid structure */
  for (d = 0; d <= dim; ++d) {pmesh->hybridPointMax[d] = mesh->hybridPointMax[d];}
  ierr = MPI_Bcast(pmesh->hybridPointMax, dim+1, MPIU_INT, 0, comm);CHKERRQ(ierr);
  ierr = ISLocalToGlobalMappingGetSize(renumbering, &n);CHKERRQ(ierr);
  ierr = ISLocalToGlobalMappingGetIndices(renumbering, &gpoints);CHKERRQ(ierr);
  ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
  for (d = 0; d <= dim; ++d) {
    PetscInt pmax = pmesh->hybridPointMax[d], newmax = 0, pEnd, stratum[2], p;

    if (pmax < 0) continue;
    ierr = DMPlexGetDepthStratum(dm, d > depth ? depth : d, &stratum[0], &stratum[1]);CHKERRQ(ierr);
    ierr = DMPlexGetDepthStratum(dmParallel, d, NULL, &pEnd);CHKERRQ(ierr);
    ierr = MPI_Bcast(stratum, 2, MPIU_INT, 0, comm);CHKERRQ(ierr);
    for (p = 0; p < n; ++p) {
      const PetscInt point = gpoints[p];

      if ((point >= stratum[0]) && (point < stratum[1]) && (point >= pmax)) ++newmax;
    }
    if (newmax > 0) pmesh->hybridPointMax[d] = pEnd - newmax;
    else            pmesh->hybridPointMax[d] = -1;
  }
  ierr = ISLocalToGlobalMappingRestoreIndices(renumbering, &gpoints);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexDistributeSetupTree"
PetscErrorCode DMPlexDistributeSetupTree(DM dm, PetscSF migrationSF, ISLocalToGlobalMapping renumbering, DM dmParallel)
{
  DM_Plex        *mesh  = (DM_Plex*) dm->data;
  DM_Plex        *pmesh = (DM_Plex*) (dmParallel)->data;
  MPI_Comm        comm;
  DM              refTree;
  PetscSection    origParentSection, newParentSection;
  PetscInt        *origParents, *origChildIDs;
  PetscBool       flg;
  PetscErrorCode  ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidHeaderSpecific(dm, DM_CLASSID, 4);
  ierr = PetscObjectGetComm((PetscObject)dm, &comm);CHKERRQ(ierr);

  /* Set up tree */
  ierr = DMPlexGetReferenceTree(dm,&refTree);CHKERRQ(ierr);
  ierr = DMPlexSetReferenceTree(dmParallel,refTree);CHKERRQ(ierr);
  ierr = DMPlexGetTree(dm,&origParentSection,&origParents,&origChildIDs,NULL,NULL);CHKERRQ(ierr);
  if (origParentSection) {
    PetscInt        pStart, pEnd;
    PetscInt        *newParents, *newChildIDs;
    PetscInt        *remoteOffsetsParents, newParentSize;
    PetscSF         parentSF;

    ierr = DMPlexGetChart(dmParallel, &pStart, &pEnd);CHKERRQ(ierr);
    ierr = PetscSectionCreate(PetscObjectComm((PetscObject)dmParallel),&newParentSection);CHKERRQ(ierr);
    ierr = PetscSectionSetChart(newParentSection,pStart,pEnd);CHKERRQ(ierr);
    ierr = PetscSFDistributeSection(migrationSF, origParentSection, &remoteOffsetsParents, newParentSection);CHKERRQ(ierr);
    ierr = PetscSFCreateSectionSF(migrationSF, origParentSection, remoteOffsetsParents, newParentSection, &parentSF);CHKERRQ(ierr);
    ierr = PetscSectionGetStorageSize(newParentSection,&newParentSize);CHKERRQ(ierr);
    ierr = PetscMalloc2(newParentSize,&newParents,newParentSize,&newChildIDs);CHKERRQ(ierr);
    ierr = PetscSFBcastBegin(parentSF, MPIU_INT, origParents, newParents);CHKERRQ(ierr);
    ierr = PetscSFBcastEnd(parentSF, MPIU_INT, origParents, newParents);CHKERRQ(ierr);
    ierr = PetscSFBcastBegin(parentSF, MPIU_INT, origChildIDs, newChildIDs);CHKERRQ(ierr);
    ierr = PetscSFBcastEnd(parentSF, MPIU_INT, origChildIDs, newChildIDs);CHKERRQ(ierr);
    ierr = ISGlobalToLocalMappingApplyBlock(renumbering,IS_GTOLM_MASK, newParentSize, newParents, NULL, newParents);CHKERRQ(ierr);
#if PETSC_USE_DEBUG
    {
      PetscInt  p;
      PetscBool valid = PETSC_TRUE;
      for (p = 0; p < newParentSize; ++p) {
        if (newParents[p] < 0) {valid = PETSC_FALSE; ierr = PetscPrintf(PETSC_COMM_SELF, "Point %d not in overlap SF\n", p);CHKERRQ(ierr);}
      }
      if (!valid) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid global to local map");
    }
#endif
    ierr = PetscOptionsHasName(((PetscObject) dm)->prefix, "-parents_view", &flg);CHKERRQ(ierr);
    if (flg) {
      ierr = PetscPrintf(comm, "Serial Parent Section: \n");CHKERRQ(ierr);
      ierr = PetscSectionView(origParentSection, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
      ierr = PetscPrintf(comm, "Parallel Parent Section: \n");CHKERRQ(ierr);
      ierr = PetscSectionView(newParentSection, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
      ierr = PetscSFView(parentSF, NULL);CHKERRQ(ierr);
    }
    ierr = DMPlexSetTree(dmParallel,newParentSection,newParents,newChildIDs);CHKERRQ(ierr);
    ierr = PetscSectionDestroy(&newParentSection);CHKERRQ(ierr);
    ierr = PetscFree2(newParents,newChildIDs);CHKERRQ(ierr);
    ierr = PetscSFDestroy(&parentSF);CHKERRQ(ierr);
  }
  pmesh->useAnchors = mesh->useAnchors;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexDistributeSF"
PetscErrorCode DMPlexDistributeSF(DM dm, PetscSF migrationSF, DM dmParallel)
{
  DM_Plex               *mesh  = (DM_Plex*) dm->data;
  DM_Plex               *pmesh = (DM_Plex*) (dmParallel)->data;
  PetscMPIInt            rank, numProcs;
  MPI_Comm               comm;
  PetscErrorCode         ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidPointer(dmParallel,7);

  /* Create point SF for parallel mesh */
  ierr = PetscLogEventBegin(DMPLEX_DistributeSF,dm,0,0,0);CHKERRQ(ierr);
  ierr = PetscObjectGetComm((PetscObject)dm, &comm);CHKERRQ(ierr);
  ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
  ierr = MPI_Comm_size(comm, &numProcs);CHKERRQ(ierr);
  {
    const PetscInt *leaves;
    PetscSFNode    *remotePoints, *rowners, *lowners;
    PetscInt        numRoots, numLeaves, numGhostPoints = 0, p, gp, *ghostPoints;
    PetscInt        pStart, pEnd;

    ierr = DMPlexGetChart(dmParallel, &pStart, &pEnd);CHKERRQ(ierr);
    ierr = PetscSFGetGraph(migrationSF, &numRoots, &numLeaves, &leaves, NULL);CHKERRQ(ierr);
    ierr = PetscMalloc2(numRoots,&rowners,numLeaves,&lowners);CHKERRQ(ierr);
    for (p=0; p<numRoots; p++) {
      rowners[p].rank  = -1;
      rowners[p].index = -1;
    }
    ierr = PetscSFBcastBegin(migrationSF, MPIU_2INT, rowners, lowners);CHKERRQ(ierr);
    ierr = PetscSFBcastEnd(migrationSF, MPIU_2INT, rowners, lowners);CHKERRQ(ierr);
    for (p = 0; p < numLeaves; ++p) {
      if (lowners[p].rank < 0 || lowners[p].rank == rank) { /* Either put in a bid or we know we own it */
        lowners[p].rank  = rank;
        lowners[p].index = leaves ? leaves[p] : p;
      } else if (lowners[p].rank >= 0) { /* Point already claimed so flag so that MAXLOC does not listen to us */
        lowners[p].rank  = -2;
        lowners[p].index = -2;
      }
    }
    for (p=0; p<numRoots; p++) { /* Root must not participate in the rediction, flag so that MAXLOC does not use */
      rowners[p].rank  = -3;
      rowners[p].index = -3;
    }
    ierr = PetscSFReduceBegin(migrationSF, MPIU_2INT, lowners, rowners, MPI_MAXLOC);CHKERRQ(ierr);
    ierr = PetscSFReduceEnd(migrationSF, MPIU_2INT, lowners, rowners, MPI_MAXLOC);CHKERRQ(ierr);
    ierr = PetscSFBcastBegin(migrationSF, MPIU_2INT, rowners, lowners);CHKERRQ(ierr);
    ierr = PetscSFBcastEnd(migrationSF, MPIU_2INT, rowners, lowners);CHKERRQ(ierr);
    for (p = 0; p < numLeaves; ++p) {
      if (lowners[p].rank < 0 || lowners[p].index < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Cell partition corrupt: point not claimed");
      if (lowners[p].rank != rank) ++numGhostPoints;
    }
    ierr = PetscMalloc1(numGhostPoints, &ghostPoints);CHKERRQ(ierr);
    ierr = PetscMalloc1(numGhostPoints, &remotePoints);CHKERRQ(ierr);
    for (p = 0, gp = 0; p < numLeaves; ++p) {
      if (lowners[p].rank != rank) {
        ghostPoints[gp]        = leaves ? leaves[p] : p;
        remotePoints[gp].rank  = lowners[p].rank;
        remotePoints[gp].index = lowners[p].index;
        ++gp;
      }
    }
    ierr = PetscFree2(rowners,lowners);CHKERRQ(ierr);
    ierr = PetscSFSetGraph((dmParallel)->sf, pEnd - pStart, numGhostPoints, ghostPoints, PETSC_OWN_POINTER, remotePoints, PETSC_OWN_POINTER);CHKERRQ(ierr);
    ierr = PetscSFSetFromOptions((dmParallel)->sf);CHKERRQ(ierr);
  }
  pmesh->useCone    = mesh->useCone;
  pmesh->useClosure = mesh->useClosure;
  ierr = PetscLogEventEnd(DMPLEX_DistributeSF,dm,0,0,0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexCreatePointSF"
/*@C
  DMPlexDerivePointSF - Build a point SF from an SF describing a point migration

  Input Parameter:
+ dm          - The source DMPlex object
. migrationSF - The star forest that describes the parallel point remapping
. ownership   - Flag causing a vote to determine point ownership

  Output Parameter:
- pointSF     - The star forest describing the point overlap in the remapped DM

  Level: developer

.seealso: DMPlexDistribute(), DMPlexDistributeOverlap()
@*/
PetscErrorCode DMPlexCreatePointSF(DM dm, PetscSF migrationSF, PetscBool ownership, PetscSF *pointSF)
{
  PetscMPIInt        rank;
  PetscInt           p, nroots, nleaves, idx, npointLeaves;
  PetscInt          *pointLocal;
  const PetscInt    *leaves;
  const PetscSFNode *roots;
  PetscSFNode       *rootNodes, *leafNodes, *pointRemote;
  PetscErrorCode     ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  ierr = MPI_Comm_rank(PetscObjectComm((PetscObject) dm), &rank);CHKERRQ(ierr);

  ierr = PetscSFGetGraph(migrationSF, &nroots, &nleaves, &leaves, &roots);CHKERRQ(ierr);
  ierr = PetscMalloc2(nroots, &rootNodes, nleaves, &leafNodes);CHKERRQ(ierr);
  if (ownership) {
    /* Point ownership vote: Process with highest rank ownes shared points */
    for (p = 0; p < nleaves; ++p) {
      /* Either put in a bid or we know we own it */
      leafNodes[p].rank  = rank;
      leafNodes[p].index = p;
    }
    for (p = 0; p < nroots; p++) {
      /* Root must not participate in the reduction, flag so that MAXLOC does not use */
      rootNodes[p].rank  = -3;
      rootNodes[p].index = -3;
    }
    ierr = PetscSFReduceBegin(migrationSF, MPIU_2INT, leafNodes, rootNodes, MPI_MAXLOC);CHKERRQ(ierr);
    ierr = PetscSFReduceEnd(migrationSF, MPIU_2INT, leafNodes, rootNodes, MPI_MAXLOC);CHKERRQ(ierr);
  } else {
    for (p = 0; p < nroots; p++) {
      rootNodes[p].index = -1;
      rootNodes[p].rank = rank;
    };
    for (p = 0; p < nleaves; p++) {
      /* Write new local id into old location */
      if (roots[p].rank == rank) {
        rootNodes[roots[p].index].index = leaves[p];
      }
    }
  }
  ierr = PetscSFBcastBegin(migrationSF, MPIU_2INT, rootNodes, leafNodes);CHKERRQ(ierr);
  ierr = PetscSFBcastEnd(migrationSF, MPIU_2INT, rootNodes, leafNodes);CHKERRQ(ierr);

  for (npointLeaves = 0, p = 0; p < nleaves; p++) {if (leafNodes[p].rank != rank) npointLeaves++;}
  ierr = PetscMalloc1(npointLeaves, &pointLocal);CHKERRQ(ierr);
  ierr = PetscMalloc1(npointLeaves, &pointRemote);CHKERRQ(ierr);
  for (idx = 0, p = 0; p < nleaves; p++) {
    if (leafNodes[p].rank != rank) {
      pointLocal[idx] = p;
      pointRemote[idx] = leafNodes[p];
      idx++;
    }
  }
  ierr = PetscSFCreate(PetscObjectComm((PetscObject) dm), pointSF);CHKERRQ(ierr);
  ierr = PetscSFSetFromOptions(*pointSF);CHKERRQ(ierr);
  ierr = PetscSFSetGraph(*pointSF, nleaves, npointLeaves, pointLocal, PETSC_OWN_POINTER, pointRemote, PETSC_OWN_POINTER);CHKERRQ(ierr);
  ierr = PetscFree2(rootNodes, leafNodes);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexMigrate"
/*@C
  DMPlexMigrate  - Migrates internal DM data over the supplied star forest

  Input Parameter:
+ dm       - The source DMPlex object
. sf       - The star forest communication context describing the migration pattern

  Output Parameter:
- targetDM - The target DMPlex object

  Level: intermediate

.seealso: DMPlexDistribute(), DMPlexDistributeOverlap()
@*/
PetscErrorCode DMPlexMigrate(DM dm, PetscSF sf, DM targetDM)
{
  MPI_Comm               comm;
  PetscInt               dim, nroots;
  PetscSF                sfPoint;
  ISLocalToGlobalMapping ltogMigration;
  PetscBool              flg;
  PetscErrorCode         ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  ierr = PetscLogEventBegin(DMPLEX_Migrate, dm, 0, 0, 0);CHKERRQ(ierr);
  ierr = PetscObjectGetComm((PetscObject) dm, &comm);CHKERRQ(ierr);
  ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
  ierr = DMSetDimension(targetDM, dim);CHKERRQ(ierr);

  /* Check for a one-to-all distribution pattern */
  ierr = DMGetPointSF(dm, &sfPoint);CHKERRQ(ierr);
  ierr = PetscSFGetGraph(sfPoint, &nroots, NULL, NULL, NULL);CHKERRQ(ierr);
  if (nroots >= 0) {
    IS                     isOriginal;
    ISLocalToGlobalMapping ltogOriginal;
    PetscInt               n, size, nleaves, conesSize;
    PetscInt              *numbering_orig, *numbering_new, *cones;
    PetscSection           coneSection;
    /* Get the original point numbering */
    ierr = DMPlexCreatePointNumbering(dm, &isOriginal);CHKERRQ(ierr);
    ierr = ISLocalToGlobalMappingCreateIS(isOriginal, &ltogOriginal);CHKERRQ(ierr);
    ierr = ISLocalToGlobalMappingGetSize(ltogOriginal, &size);CHKERRQ(ierr);
    ierr = ISLocalToGlobalMappingGetBlockIndices(ltogOriginal, (const PetscInt**)&numbering_orig);CHKERRQ(ierr);
    /* Convert to positive global numbers */
    for (n=0; n<size; n++) {if (numbering_orig[n] < 0) numbering_orig[n] = -(numbering_orig[n]+1);}
    /* Derive the new local-to-global mapping from the old one */
    ierr = PetscSFGetGraph(sf, NULL, &nleaves, NULL, NULL);CHKERRQ(ierr);
    ierr = PetscMalloc1(nleaves, &numbering_new);CHKERRQ(ierr);
    ierr = PetscSFBcastBegin(sf, MPIU_INT, (PetscInt *) numbering_orig, numbering_new);CHKERRQ(ierr);
    ierr = PetscSFBcastEnd(sf, MPIU_INT, (PetscInt *) numbering_orig, numbering_new);CHKERRQ(ierr);
    ierr = ISLocalToGlobalMappingCreate(comm, 1, nleaves, (const PetscInt*) numbering_new, PETSC_OWN_POINTER, &ltogMigration);CHKERRQ(ierr);
    ierr = ISLocalToGlobalMappingRestoreIndices(ltogOriginal, (const PetscInt**)&numbering_orig);CHKERRQ(ierr);
    /* Convert cones to global numbering before migrating them */
    ierr = DMPlexGetConeSection(dm, &coneSection);CHKERRQ(ierr);
    ierr = PetscSectionGetStorageSize(coneSection, &conesSize);CHKERRQ(ierr);
    ierr = DMPlexGetCones(dm, &cones);CHKERRQ(ierr);
    ierr = ISLocalToGlobalMappingApplyBlock(ltogOriginal, conesSize, cones, cones);CHKERRQ(ierr);
    ierr = ISDestroy(&isOriginal);CHKERRQ(ierr);
    ierr = ISLocalToGlobalMappingDestroy(&ltogOriginal);
  } else {
    /* One-to-all distribution pattern: We can derive LToG from SF */
    ierr = ISLocalToGlobalMappingCreateSF(sf, 0, &ltogMigration);CHKERRQ(ierr);
  }
  ierr = PetscOptionsHasName(((PetscObject) dm)->prefix, "-partition_view", &flg);CHKERRQ(ierr);
  if (flg) {
    ierr = PetscPrintf(comm, "Point renumbering for DM migration:\n");CHKERRQ(ierr);
    ierr = ISLocalToGlobalMappingView(ltogMigration, NULL);CHKERRQ(ierr);
  }
  /* Migrate DM data to target DM */
  ierr = DMPlexDistributeCones(dm, sf, ltogMigration, targetDM);CHKERRQ(ierr);
  ierr = DMPlexDistributeCoordinates(dm, sf, targetDM);CHKERRQ(ierr);
  ierr = DMPlexDistributeLabels(dm, sf, targetDM);CHKERRQ(ierr);
  ierr = DMPlexDistributeSetupHybrid(dm, sf, ltogMigration, targetDM);CHKERRQ(ierr);
  ierr = DMPlexDistributeSetupTree(dm, sf, ltogMigration, targetDM);CHKERRQ(ierr);
  ierr = ISLocalToGlobalMappingDestroy(&ltogMigration);
  ierr = PetscLogEventEnd(DMPLEX_Migrate, dm, 0, 0, 0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

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

  Not Collective

  Input Parameter:
+ dm  - The original DMPlex object
- overlap - The overlap of partitions, 0 is the default

  Output Parameter:
+ sf - The PetscSF used for point distribution
- parallelMesh - The distributed DMPlex object, or NULL

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

  The user can control the definition of adjacency for the mesh using DMPlexGetAdjacencyUseCone() and
  DMPlexSetAdjacencyUseClosure(). They should choose the combination appropriate for the function
  representation on the mesh.

  Level: intermediate

.keywords: mesh, elements
.seealso: DMPlexCreate(), DMPlexDistributeByFace(), DMPlexSetAdjacencyUseCone(), DMPlexSetAdjacencyUseClosure()
@*/
PetscErrorCode DMPlexDistribute(DM dm, PetscInt overlap, PetscSF *sf, DM *dmParallel)
{
  MPI_Comm               comm;
  PetscPartitioner       partitioner;
  IS                     cellPart;
  PetscSection           cellPartSection;
  DM                     dmCoord;
  DMLabel                lblPartition, lblMigration;
  PetscSF                sfProcess, sfMigration, sfStratified, sfPoint;
  PetscBool              flg;
  PetscMPIInt            rank, numProcs, p;
  PetscErrorCode         ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (sf) PetscValidPointer(sf,4);
  PetscValidPointer(dmParallel,5);

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

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

  /* Create cell partition */
  ierr = PetscLogEventBegin(PETSCPARTITIONER_Partition,dm,0,0,0);CHKERRQ(ierr);
  ierr = PetscSectionCreate(comm, &cellPartSection);CHKERRQ(ierr);
  ierr = DMPlexGetPartitioner(dm, &partitioner);CHKERRQ(ierr);
  ierr = PetscPartitionerPartition(partitioner, dm, cellPartSection, &cellPart);CHKERRQ(ierr);
  {
    /* Convert partition to DMLabel */
    PetscInt proc, pStart, pEnd, npoints, poffset;
    const PetscInt *points;
    ierr = DMLabelCreate("Point Partition", &lblPartition);CHKERRQ(ierr);
    ierr = ISGetIndices(cellPart, &points);CHKERRQ(ierr);
    ierr = PetscSectionGetChart(cellPartSection, &pStart, &pEnd);CHKERRQ(ierr);
    for (proc = pStart; proc < pEnd; proc++) {
      ierr = PetscSectionGetDof(cellPartSection, proc, &npoints);CHKERRQ(ierr);
      ierr = PetscSectionGetOffset(cellPartSection, proc, &poffset);CHKERRQ(ierr);
      for (p = poffset; p < poffset+npoints; p++) {
        ierr = DMLabelSetValue(lblPartition, points[p], proc);CHKERRQ(ierr);
      }
    }
    ierr = ISRestoreIndices(cellPart, &points);CHKERRQ(ierr);
  }
  ierr = DMPlexPartitionLabelClosure(dm, lblPartition);CHKERRQ(ierr);
  {
    /* Build a global process SF */
    PetscSFNode *remoteProc;
    ierr = PetscMalloc1(numProcs, &remoteProc);CHKERRQ(ierr);
    for (p = 0; p < numProcs; ++p) {
      remoteProc[p].rank  = p;
      remoteProc[p].index = rank;
    }
    ierr = PetscSFCreate(comm, &sfProcess);CHKERRQ(ierr);
    ierr = PetscObjectSetName((PetscObject) sfProcess, "Process SF");CHKERRQ(ierr);
    ierr = PetscSFSetGraph(sfProcess, numProcs, numProcs, NULL, PETSC_OWN_POINTER, remoteProc, PETSC_OWN_POINTER);CHKERRQ(ierr);
  }
  ierr = DMLabelCreate("Point migration", &lblMigration);CHKERRQ(ierr);
  ierr = DMPlexPartitionLabelInvert(dm, lblPartition, sfProcess, lblMigration);CHKERRQ(ierr);
  ierr = DMPlexPartitionLabelCreateSF(dm, lblMigration, &sfMigration);
  /* Stratify the SF in case we are migrating an already parallel plex */
  ierr = DMPlexStratifyMigrationSF(dm, sfMigration, &sfStratified);CHKERRQ(ierr);
  ierr = PetscSFDestroy(&sfMigration);CHKERRQ(ierr);
  sfMigration = sfStratified;
  ierr = PetscLogEventEnd(PETSCPARTITIONER_Partition,dm,0,0,0);CHKERRQ(ierr);
  ierr = PetscOptionsHasName(((PetscObject) dm)->prefix, "-partition_view", &flg);CHKERRQ(ierr);
  if (flg) {
    ierr = PetscViewerASCIISynchronizedAllow(PETSC_VIEWER_STDOUT_WORLD, PETSC_TRUE);CHKERRQ(ierr);
    ierr = DMLabelView(lblPartition, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
    ierr = PetscSFView(sfMigration, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
  }

  /* Create non-overlapping parallel DM and migrate internal data */
  ierr = DMPlexCreate(comm, dmParallel);CHKERRQ(ierr);
  ierr = PetscObjectSetName((PetscObject) *dmParallel, "Parallel Mesh");CHKERRQ(ierr);
  ierr = DMPlexMigrate(dm, sfMigration, *dmParallel);CHKERRQ(ierr);

  /* Build the point SF without overlap */
  ierr = DMPlexCreatePointSF(*dmParallel, sfMigration, PETSC_TRUE, &sfPoint);CHKERRQ(ierr);
  ierr = DMSetPointSF(*dmParallel, sfPoint);CHKERRQ(ierr);
  ierr = DMGetCoordinateDM(*dmParallel, &dmCoord);CHKERRQ(ierr);
  if (dmCoord) {ierr = DMSetPointSF(dmCoord, sfPoint);CHKERRQ(ierr);}
  if (flg) {ierr = PetscSFView(sfPoint, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);}

  if (overlap > 0) {
    DM                 dmOverlap;
    PetscInt           nroots, nleaves;
    PetscSFNode       *newRemote;
    const PetscSFNode *oldRemote;
    PetscSF            sfOverlap, sfOverlapPoint;
    /* Add the partition overlap to the distributed DM */
    ierr = DMPlexDistributeOverlap(*dmParallel, overlap, &sfOverlap, &dmOverlap);CHKERRQ(ierr);
    ierr = DMDestroy(dmParallel);CHKERRQ(ierr);
    *dmParallel = dmOverlap;
    if (flg) {
      ierr = PetscPrintf(comm, "Overlap Migration SF:\n");CHKERRQ(ierr);
      ierr = PetscSFView(sfOverlap, NULL);CHKERRQ(ierr);
    }

    /* Re-map the migration SF to establish the full migration pattern */
    ierr = PetscSFGetGraph(sfMigration, &nroots, NULL, NULL, &oldRemote);CHKERRQ(ierr);
    ierr = PetscSFGetGraph(sfOverlap, NULL, &nleaves, NULL, NULL);CHKERRQ(ierr);
    ierr = PetscMalloc1(nleaves, &newRemote);CHKERRQ(ierr);
    ierr = PetscSFBcastBegin(sfOverlap, MPIU_2INT, oldRemote, newRemote);CHKERRQ(ierr);
    ierr = PetscSFBcastEnd(sfOverlap, MPIU_2INT, oldRemote, newRemote);CHKERRQ(ierr);
    ierr = PetscSFCreate(comm, &sfOverlapPoint);CHKERRQ(ierr);
    ierr = PetscSFSetGraph(sfOverlapPoint, nroots, nleaves, NULL, PETSC_OWN_POINTER, newRemote, PETSC_OWN_POINTER);CHKERRQ(ierr);
    ierr = PetscSFDestroy(&sfOverlap);CHKERRQ(ierr);
    ierr = PetscSFDestroy(&sfMigration);CHKERRQ(ierr);
    sfMigration = sfOverlapPoint;
  }
  /* Cleanup Partition */
  ierr = PetscSFDestroy(&sfProcess);CHKERRQ(ierr);
  ierr = DMLabelDestroy(&lblPartition);CHKERRQ(ierr);
  ierr = DMLabelDestroy(&lblMigration);CHKERRQ(ierr);
  ierr = PetscSectionDestroy(&cellPartSection);CHKERRQ(ierr);
  ierr = ISDestroy(&cellPart);CHKERRQ(ierr);
  /* Copy BC */
  ierr = DMPlexCopyBoundary(dm, *dmParallel);CHKERRQ(ierr);
  /* Cleanup */
  if (sf) {*sf = sfMigration;}
  else    {ierr = PetscSFDestroy(&sfMigration);CHKERRQ(ierr);}
  ierr = PetscSFDestroy(&sfPoint);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(DMPLEX_Distribute,dm,0,0,0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexDistributeOverlap"
/*@C
  DMPlexDistribute - Add partition overlap to a distributed non-overlapping DM.

  Not Collective

  Input Parameter:
+ dm  - The non-overlapping distrbuted DMPlex object
- overlap - The overlap of partitions, 0 is the default

  Output Parameter:
+ sf - The PetscSF used for point distribution
- dmOverlap - The overlapping distributed DMPlex object, or NULL

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

  The user can control the definition of adjacency for the mesh using DMPlexGetAdjacencyUseCone() and
  DMPlexSetAdjacencyUseClosure(). They should choose the combination appropriate for the function
  representation on the mesh.

  Level: intermediate

.keywords: mesh, elements
.seealso: DMPlexCreate(), DMPlexDistributeByFace(), DMPlexSetAdjacencyUseCone(), DMPlexSetAdjacencyUseClosure()
@*/
PetscErrorCode DMPlexDistributeOverlap(DM dm, PetscInt overlap, PetscSF *sf, DM *dmOverlap)
{
  MPI_Comm               comm;
  PetscMPIInt            rank;
  PetscSection           rootSection, leafSection;
  IS                     rootrank, leafrank;
  DM                     dmCoord;
  DMLabel                lblOverlap;
  PetscSF                sfOverlap, sfStratified, sfPoint;
  PetscErrorCode         ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (sf) PetscValidPointer(sf, 3);
  PetscValidPointer(dmOverlap, 4);

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

  /* Compute point overlap with neighbouring processes on the distributed DM */
  ierr = PetscLogEventBegin(PETSCPARTITIONER_Partition,dm,0,0,0);CHKERRQ(ierr);
  ierr = PetscSectionCreate(comm, &rootSection);CHKERRQ(ierr);
  ierr = PetscSectionCreate(comm, &leafSection);CHKERRQ(ierr);
  ierr = DMPlexDistributeOwnership(dm, rootSection, &rootrank, leafSection, &leafrank);CHKERRQ(ierr);
  ierr = DMPlexCreateOverlap(dm, overlap, rootSection, rootrank, leafSection, leafrank, &lblOverlap);CHKERRQ(ierr);
  /* Convert overlap label to stratified migration SF */
  ierr = DMPlexPartitionLabelCreateSF(dm, lblOverlap, &sfOverlap);CHKERRQ(ierr);
  ierr = DMPlexStratifyMigrationSF(dm, sfOverlap, &sfStratified);CHKERRQ(ierr);
  ierr = PetscSFDestroy(&sfOverlap);CHKERRQ(ierr);
  sfOverlap = sfStratified;
  ierr = PetscObjectSetName((PetscObject) sfOverlap, "Overlap SF");CHKERRQ(ierr);
  ierr = PetscSFSetFromOptions(sfOverlap);CHKERRQ(ierr);

  ierr = PetscSectionDestroy(&rootSection);CHKERRQ(ierr);
  ierr = PetscSectionDestroy(&leafSection);CHKERRQ(ierr);
  ierr = ISDestroy(&rootrank);CHKERRQ(ierr);
  ierr = ISDestroy(&leafrank);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(PETSCPARTITIONER_Partition,dm,0,0,0);CHKERRQ(ierr);

  /* Build the overlapping DM */
  ierr = DMPlexCreate(comm, dmOverlap);CHKERRQ(ierr);
  ierr = PetscObjectSetName((PetscObject) *dmOverlap, "Parallel Mesh");CHKERRQ(ierr);
  ierr = DMPlexMigrate(dm, sfOverlap, *dmOverlap);CHKERRQ(ierr);
  /* Build the new point SF */
  ierr = DMPlexCreatePointSF(*dmOverlap, sfOverlap, PETSC_FALSE, &sfPoint);CHKERRQ(ierr);
  ierr = DMSetPointSF(*dmOverlap, sfPoint);CHKERRQ(ierr);
  ierr = DMGetCoordinateDM(*dmOverlap, &dmCoord);CHKERRQ(ierr);
  if (dmCoord) {ierr = DMSetPointSF(dmCoord, sfPoint);CHKERRQ(ierr);}
  ierr = PetscSFDestroy(&sfPoint);CHKERRQ(ierr);
  /* Cleanup overlap partition */
  ierr = DMLabelDestroy(&lblOverlap);CHKERRQ(ierr);
  if (sf) *sf = sfOverlap;
  else    {ierr = PetscSFDestroy(&sfOverlap);CHKERRQ(ierr);}
  ierr = PetscLogEventEnd(DMPLEX_DistributeOverlap, dm, 0, 0, 0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}