xref: /petsc/src/dm/impls/plex/plexsfc.c (revision 5f06a3dd92e34bdfe6112242961ce57bf1b830e2)

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

typedef uint64_t ZCode;

PETSC_HASH_SET(ZSet, ZCode, PetscHash_UInt64, PetscHashEqual)

typedef struct {
  PetscInt i, j, k;
} Ijk;

typedef struct {
  Ijk         eextent;
  Ijk         vextent;
  PetscMPIInt comm_size;
  ZCode      *zstarts;
} ZLayout;

static unsigned ZCodeSplit1(ZCode z)
{
  z = ((z & 01001001001001001) | ((z >> 2) & 02002002002002002) | ((z >> 4) & 04004004004004004));
  z = (z | (z >> 6) | (z >> 12)) & 0000000777000000777;
  z = (z | (z >> 18)) & 0777777;
  return (unsigned)z;
}

static ZCode ZEncode1(unsigned t)
{
  ZCode z = t;
  z       = (z | (z << 18)) & 0777000000777;
  z       = (z | (z << 6) | (z << 12)) & 07007007007007007;
  z       = (z | (z << 2) | (z << 4)) & 0111111111111111111;
  return z;
}

static Ijk ZCodeSplit(ZCode z)
{
  Ijk c;
  c.i = ZCodeSplit1(z >> 2);
  c.j = ZCodeSplit1(z >> 1);
  c.k = ZCodeSplit1(z >> 0);
  return c;
}

static ZCode ZEncode(Ijk c)
{
  ZCode z = (ZEncode1(c.i) << 2) | (ZEncode1(c.j) << 1) | ZEncode1(c.k);
  return z;
}

static PetscBool IjkActive(Ijk extent, Ijk l)
{
  if (l.i < extent.i && l.j < extent.j && l.k < extent.k) return PETSC_TRUE;
  return PETSC_FALSE;
}

// Since element/vertex box extents are typically not equal powers of 2, Z codes that lie within the domain are not contiguous.
static PetscErrorCode ZLayoutCreate(PetscMPIInt size, const PetscInt eextent[3], const PetscInt vextent[3], ZLayout *layout)
{
  PetscFunctionBegin;
  layout->eextent.i = eextent[0];
  layout->eextent.j = eextent[1];
  layout->eextent.k = eextent[2];
  layout->vextent.i = vextent[0];
  layout->vextent.j = vextent[1];
  layout->vextent.k = vextent[2];
  layout->comm_size = size;
  layout->zstarts   = NULL;
  PetscCall(PetscMalloc1(size + 1, &layout->zstarts));

  PetscInt total_elems = eextent[0] * eextent[1] * eextent[2];
  ZCode    z           = 0;
  layout->zstarts[0]   = 0;
  for (PetscMPIInt r = 0; r < size; r++) {
    PetscInt elems_needed = (total_elems / size) + (total_elems % size > r), count;
    for (count = 0; count < elems_needed; z++) {
      Ijk loc = ZCodeSplit(z);
      if (IjkActive(layout->eextent, loc)) count++;
    }
    // Pick up any extra vertices in the Z ordering before the next rank's first owned element.
    //
    // This leads to poorly balanced vertices when eextent is a power of 2, since all the fringe vertices end up
    // on the last rank. A possible solution is to balance the Z-order vertices independently from the cells, which will
    // result in a lot of element closures being remote. We could finish marking boundary conditions, then do a round of
    // vertex ownership smoothing (which would reorder and redistribute vertices without touching element distribution).
    // Another would be to have an analytic ownership criteria for vertices in the fringe veextent - eextent. This would
    // complicate the job of identifying an owner and its offset.
    //
    // The current recommended approach is to let `-dm_distribute 1` (default) resolve vertex ownership. This is
    // *mandatory* with isoperiodicity (except in special cases) to remove standed vertices from local spaces. Here's
    // the issue:
    //
    // Consider this partition on rank 0 (left) and rank 1.
    //
    //    4 --------  5 -- 14 --10 -- 21 --11
    //                |          |          |
    // 7 -- 16 --  8  |          |          |
    // |           |  3 -------  7 -------  9
    // |           |             |          |
    // 4 --------  6 ------ 10   |          |
    // |           |         |   6 -- 16 -- 8
    // |           |         |
    // 3 ---11---  5 --18--  9
    //
    // The periodic face SF looks like
    // [0] Number of roots=21, leaves=1, remote ranks=1
    // [0] 16 <- (0,11)
    // [1] Number of roots=22, leaves=2, remote ranks=2
    // [1] 14 <- (0,18)
    // [1] 21 <- (1,16)
    //
    // In handling face (0,16), rank 0 learns that (0,7) and (0,8) map to (0,3) and (0,5) respectively, thus we won't use
    // the point SF links to (1,4) and (1,5). Rank 1 learns about the periodic mapping of (1,5) while handling face
    // (1,14), but never learns that vertex (1,4) has been mapped to (0,3) by face (0,16).
    //
    // We can relatively easily inform vertex (1,4) of this mapping, but it stays in rank 1's local space despite not
    // being in the closure and thus not being contributed to. This would be mostly harmless except that some viewer
    // routines expect all local points to be somehow significant. It is not easy to analytically remove the (1,4)
    // vertex because the point SF and isoperiodic face SF would need to be updated to account for removal of the
    // stranded vertices.
    for (; z <= ZEncode(layout->vextent); z++) {
      Ijk loc = ZCodeSplit(z);
      if (IjkActive(layout->eextent, loc)) break;
    }
    layout->zstarts[r + 1] = z;
  }
  PetscFunctionReturn(0);
}

static PetscInt ZLayoutElementsOnRank(const ZLayout *layout, PetscMPIInt rank)
{
  PetscInt remote_elem = 0;
  for (ZCode rz = layout->zstarts[rank]; rz < layout->zstarts[rank + 1]; rz++) {
    Ijk loc = ZCodeSplit(rz);
    if (IjkActive(layout->eextent, loc)) remote_elem++;
  }
  return remote_elem;
}

PetscInt ZCodeFind(ZCode key, PetscInt n, const ZCode X[])
{
  PetscInt lo = 0, hi = n;

  if (n == 0) return -1;
  while (hi - lo > 1) {
    PetscInt mid = lo + (hi - lo) / 2;
    if (key < X[mid]) hi = mid;
    else lo = mid;
  }
  return key == X[lo] ? lo : -(lo + (key > X[lo]) + 1);
}

static PetscErrorCode DMPlexCreateBoxMesh_Tensor_SFC_Periodicity_Private(DM dm, const ZLayout *layout, const ZCode *vert_z, PetscSegBuffer per_faces, const PetscReal *lower, const PetscReal *upper, const DMBoundaryType *periodicity, PetscSegBuffer donor_face_closure, PetscSegBuffer my_donor_faces)
{
  MPI_Comm     comm;
  size_t       num_faces;
  PetscInt     dim, *faces, vStart, vEnd;
  PetscMPIInt  size;
  ZCode       *donor_verts, *donor_minz;
  PetscSFNode *leaf;

  PetscFunctionBegin;
  PetscCall(PetscObjectGetComm((PetscObject)dm, &comm));
  PetscCallMPI(MPI_Comm_size(comm, &size));
  PetscCall(DMGetDimension(dm, &dim));
  const PetscInt csize = PetscPowInt(2, dim - 1);
  PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
  PetscCall(PetscSegBufferGetSize(per_faces, &num_faces));
  PetscCall(PetscSegBufferExtractInPlace(per_faces, &faces));
  PetscCall(PetscSegBufferExtractInPlace(donor_face_closure, &donor_verts));
  PetscCall(PetscMalloc1(num_faces, &donor_minz));
  PetscCall(PetscMalloc1(num_faces, &leaf));
  for (PetscInt i = 0; i < (PetscInt)num_faces; i++) {
    ZCode minz = donor_verts[i * csize];
    for (PetscInt j = 1; j < csize; j++) minz = PetscMin(minz, donor_verts[i * csize + j]);
    donor_minz[i] = minz;
  }
  {
    PetscBool sorted;
    PetscCall(PetscSortedInt64(num_faces, (const PetscInt64 *)donor_minz, &sorted));
    PetscCheck(sorted, PETSC_COMM_SELF, PETSC_ERR_PLIB, "minz not sorted; periodicity in multiple dimensions not yet supported");
  }
  for (PetscInt i = 0; i < (PetscInt)num_faces;) {
    ZCode    z           = donor_minz[i];
    PetscInt remote_rank = ZCodeFind(z, size + 1, layout->zstarts), remote_count = 0;
    if (remote_rank < 0) remote_rank = -(remote_rank + 1) - 1;
    // Process all the vertices on this rank
    for (ZCode rz = layout->zstarts[remote_rank]; rz < layout->zstarts[remote_rank + 1]; rz++) {
      Ijk loc = ZCodeSplit(rz);
      if (rz == z) {
        leaf[i].rank  = remote_rank;
        leaf[i].index = remote_count;
        i++;
        if (i == (PetscInt)num_faces) break;
        z = donor_minz[i];
      }
      if (IjkActive(layout->vextent, loc)) remote_count++;
    }
  }
  PetscCall(PetscFree(donor_minz));
  PetscSF sfper;
  PetscCall(PetscSFCreate(PetscObjectComm((PetscObject)dm), &sfper));
  PetscCall(PetscSFSetGraph(sfper, vEnd - vStart, num_faces, PETSC_NULL, PETSC_USE_POINTER, leaf, PETSC_USE_POINTER));
  const PetscInt *my_donor_degree;
  PetscCall(PetscSFComputeDegreeBegin(sfper, &my_donor_degree));
  PetscCall(PetscSFComputeDegreeEnd(sfper, &my_donor_degree));
  PetscInt num_multiroots = 0;
  for (PetscInt i = 0; i < vEnd - vStart; i++) {
    num_multiroots += my_donor_degree[i];
    if (my_donor_degree[i] == 0) continue;
    PetscAssert(my_donor_degree[i] == 1, PETSC_COMM_SELF, PETSC_ERR_SUP, "Local vertex has multiple faces");
  }
  PetscInt *my_donors, *donor_indices, *my_donor_indices;
  size_t    num_my_donors;
  PetscCall(PetscSegBufferGetSize(my_donor_faces, &num_my_donors));
  PetscCheck((PetscInt)num_my_donors == num_multiroots, PETSC_COMM_SELF, PETSC_ERR_SUP, "Donor request does not match expected donors");
  PetscCall(PetscSegBufferExtractInPlace(my_donor_faces, &my_donors));
  PetscCall(PetscMalloc1(vEnd - vStart, &my_donor_indices));
  for (PetscInt i = 0; i < (PetscInt)num_my_donors; i++) {
    PetscInt f = my_donors[i];
    PetscInt num_points, *points = NULL, minv = PETSC_MAX_INT;
    PetscCall(DMPlexGetTransitiveClosure(dm, f, PETSC_TRUE, &num_points, &points));
    for (PetscInt j = 0; j < num_points; j++) {
      PetscInt p = points[2 * j];
      if (p < vStart || vEnd <= p) continue;
      minv = PetscMin(minv, p);
    }
    PetscCall(DMPlexRestoreTransitiveClosure(dm, f, PETSC_TRUE, &num_points, &points));
    PetscAssert(my_donor_degree[minv - vStart] == 1, PETSC_COMM_SELF, PETSC_ERR_SUP, "Local vertex not requested");
    my_donor_indices[minv - vStart] = f;
  }
  PetscCall(PetscMalloc1(num_faces, &donor_indices));
  PetscCall(PetscSFBcastBegin(sfper, MPIU_INT, my_donor_indices, donor_indices, MPI_REPLACE));
  PetscCall(PetscSFBcastEnd(sfper, MPIU_INT, my_donor_indices, donor_indices, MPI_REPLACE));
  PetscCall(PetscFree(my_donor_indices));
  // Modify our leafs so they point to donor faces instead of donor minz. Additionally, give them indices as faces.
  for (PetscInt i = 0; i < (PetscInt)num_faces; i++) leaf[i].index = donor_indices[i];
  PetscCall(PetscFree(donor_indices));
  PetscInt pStart, pEnd;
  PetscCall(DMPlexGetChart(dm, &pStart, &pEnd));
  PetscCall(PetscSFSetGraph(sfper, pEnd - pStart, num_faces, faces, PETSC_COPY_VALUES, leaf, PETSC_OWN_POINTER));
  PetscCall(PetscObjectSetName((PetscObject)sfper, "Z-order Isoperiodic Faces"));

  PetscCall(DMPlexSetIsoperiodicFaceSF(dm, sfper));

  PetscScalar t[4][4] = {{0}};
  t[0][0]             = 1;
  t[1][1]             = 1;
  t[2][2]             = 1;
  t[3][3]             = 1;
  for (PetscInt i = 0; i < dim; i++)
    if (periodicity[i] == DM_BOUNDARY_PERIODIC) t[i][3] = upper[i] - lower[i];
  PetscCall(DMPlexSetIsoperiodicFaceTransform(dm, &t[0][0]));
  PetscCall(PetscSFDestroy(&sfper));
  PetscFunctionReturn(0);
}

// This is a DMGlobalToLocalHook that applies the affine offsets. When extended for rotated periodicity, it'll need to
// apply a rotatonal transform and similar operations will be needed for fields (e.g., to rotate a velocity vector).
// We use this crude approach here so we don't have to write new GPU kernels yet.
static PetscErrorCode DMCoordAddPeriodicOffsets_Private(DM dm, Vec g, InsertMode mode, Vec l, void *ctx)
{
  PetscFunctionBegin;
  PetscCall(VecScatterBegin(dm->periodic.affine_to_local, dm->periodic.affine, l, ADD_VALUES, SCATTER_FORWARD));
  PetscCall(VecScatterEnd(dm->periodic.affine_to_local, dm->periodic.affine, l, ADD_VALUES, SCATTER_FORWARD));
  PetscFunctionReturn(0);
}

// Start with an SF for a positive depth (e.g., faces) and create a new SF for matched closure. The caller must ensure
// that both the donor (root) face and the periodic (leaf) face have consistent orientation, meaning that their closures
// are isomorphic. It may be useful/necessary for this restriction to be loosened.
//
// Output Arguments:
//
// + closure_sf - augmented point SF (see `DMGetPointSF()`) that includes the faces and all points in its closure. This
//   can be used to create a global section and section SF.
// - is_points - index set for just the points in the closure of `face_sf`. These may be used to apply an affine
//   transformation to periodic dofs; see DMPeriodicCoordinateSetUp_Internal().
//
static PetscErrorCode DMPlexCreateIsoperiodicPointSF_Private(DM dm, PetscSF face_sf, PetscSF *closure_sf, IS *is_points)
{
  MPI_Comm           comm;
  PetscInt           nroots, nleaves, npoints;
  const PetscInt    *filocal, *pilocal;
  const PetscSFNode *firemote, *piremote;
  PetscMPIInt        rank;
  PetscSF            point_sf;

  PetscFunctionBegin;
  PetscCall(PetscObjectGetComm((PetscObject)dm, &comm));
  PetscCallMPI(MPI_Comm_rank(comm, &rank));
  PetscCall(PetscSFGetGraph(face_sf, &nroots, &nleaves, &filocal, &firemote));
  PetscCall(DMGetPointSF(dm, &point_sf)); // Point SF has remote points
  PetscCall(PetscSFGetGraph(point_sf, NULL, &npoints, &pilocal, &piremote));
  PetscInt *rootdata, *leafdata;
  PetscCall(PetscCalloc2(2 * nroots, &rootdata, 2 * nroots, &leafdata));
  for (PetscInt i = 0; i < nleaves; i++) {
    PetscInt point = filocal[i], cl_size, *closure = NULL;
    PetscCall(DMPlexGetTransitiveClosure(dm, point, PETSC_TRUE, &cl_size, &closure));
    leafdata[point] = cl_size - 1;
    PetscCall(DMPlexRestoreTransitiveClosure(dm, point, PETSC_TRUE, &cl_size, &closure));
  }
  PetscCall(PetscSFReduceBegin(face_sf, MPIU_INT, leafdata, rootdata + nroots, MPIU_SUM));
  PetscCall(PetscSFReduceEnd(face_sf, MPIU_INT, leafdata, rootdata + nroots, MPIU_SUM));

  PetscInt root_offset = 0;
  for (PetscInt p = 0; p < nroots; p++) {
    const PetscInt *donor_dof = rootdata + nroots;
    if (donor_dof[p] == 0) {
      rootdata[2 * p]     = -1;
      rootdata[2 * p + 1] = -1;
      continue;
    }
    PetscInt  cl_size;
    PetscInt *closure = NULL;
    PetscCall(DMPlexGetTransitiveClosure(dm, p, PETSC_TRUE, &cl_size, &closure));
    // cl_size - 1 = points not including self
    PetscAssert(donor_dof[p] == cl_size - 1, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Reduced leaf cone sizes do not match root cone sizes");
    rootdata[2 * p]     = root_offset;
    rootdata[2 * p + 1] = cl_size - 1;
    root_offset += cl_size - 1;
    PetscCall(DMPlexRestoreTransitiveClosure(dm, p, PETSC_TRUE, &cl_size, &closure));
  }
  PetscCall(PetscSFBcastBegin(face_sf, MPIU_2INT, rootdata, leafdata, MPI_REPLACE));
  PetscCall(PetscSFBcastEnd(face_sf, MPIU_2INT, rootdata, leafdata, MPI_REPLACE));
  // Count how many leaves we need to communicate the closures
  PetscInt leaf_offset = 0;
  for (PetscInt i = 0; i < nleaves; i++) {
    PetscInt point = filocal[i];
    if (leafdata[2 * point + 1] < 0) continue;
    leaf_offset += leafdata[2 * point + 1];
  }

  PetscSFNode *closure_leaf;
  PetscCall(PetscMalloc1(leaf_offset, &closure_leaf));
  leaf_offset = 0;
  for (PetscInt i = 0; i < nleaves; i++) {
    PetscInt point   = filocal[i];
    PetscInt cl_size = leafdata[2 * point + 1];
    if (cl_size < 0) continue;
    for (PetscInt j = 0; j < cl_size; j++) {
      closure_leaf[leaf_offset].rank  = firemote[i].rank;
      closure_leaf[leaf_offset].index = leafdata[2 * point] + j;
      leaf_offset++;
    }
  }

  PetscSF sf_closure;
  PetscCall(PetscSFCreate(comm, &sf_closure));
  PetscCall(PetscSFSetGraph(sf_closure, root_offset, leaf_offset, NULL, PETSC_USE_POINTER, closure_leaf, PETSC_OWN_POINTER));

  // Pack root buffer with owner for every point in the root cones
  PetscSFNode *donor_closure;
  PetscCall(PetscCalloc1(root_offset, &donor_closure));
  root_offset = 0;
  for (PetscInt p = 0; p < nroots; p++) {
    if (rootdata[2 * p] < 0) continue;
    PetscInt  cl_size;
    PetscInt *closure = NULL;
    PetscCall(DMPlexGetTransitiveClosure(dm, p, PETSC_TRUE, &cl_size, &closure));
    for (PetscInt j = 1; j < cl_size; j++) {
      PetscInt c = closure[2 * j];
      if (pilocal) {
        PetscInt found = -1;
        if (npoints > 0) PetscCall(PetscFindInt(c, npoints, pilocal, &found));
        if (found >= 0) {
          donor_closure[root_offset++] = piremote[found];
          continue;
        }
      }
      // we own c
      donor_closure[root_offset].rank  = rank;
      donor_closure[root_offset].index = c;
      root_offset++;
    }
    PetscCall(DMPlexRestoreTransitiveClosure(dm, p, PETSC_TRUE, &cl_size, &closure));
  }

  PetscSFNode *leaf_donor_closure;
  PetscCall(PetscMalloc1(leaf_offset, &leaf_donor_closure));
  PetscCall(PetscSFBcastBegin(sf_closure, MPIU_2INT, donor_closure, leaf_donor_closure, MPI_REPLACE));
  PetscCall(PetscSFBcastEnd(sf_closure, MPIU_2INT, donor_closure, leaf_donor_closure, MPI_REPLACE));
  PetscCall(PetscSFDestroy(&sf_closure));
  PetscCall(PetscFree(donor_closure));

  PetscSFNode *new_iremote;
  PetscCall(PetscCalloc1(nroots, &new_iremote));
  for (PetscInt i = 0; i < nroots; i++) new_iremote[i].rank = -1;
  // Walk leaves and match vertices
  leaf_offset = 0;
  for (PetscInt i = 0; i < nleaves; i++) {
    PetscInt  point   = filocal[i], cl_size;
    PetscInt *closure = NULL;
    PetscCall(DMPlexGetTransitiveClosure(dm, point, PETSC_TRUE, &cl_size, &closure));
    for (PetscInt j = 1; j < cl_size; j++) { // TODO: should we send donor edge orientations so we can flip for consistency?
      PetscInt    c  = closure[2 * j];
      PetscSFNode lc = leaf_donor_closure[leaf_offset];
      // printf("[%d] face %d.%d: %d ?-- (%d,%d)\n", rank, point, j, c, lc.rank, lc.index);
      if (new_iremote[c].rank == -1) {
        new_iremote[c] = lc;
      } else PetscCheck(new_iremote[c].rank == lc.rank && new_iremote[c].index == lc.index, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Mismatched cone ordering between faces");
      leaf_offset++;
    }
    PetscCall(DMPlexRestoreTransitiveClosure(dm, point, PETSC_TRUE, &cl_size, &closure));
  }
  PetscCall(PetscFree(leaf_donor_closure));

  // Include face points in closure SF
  for (PetscInt i = 0; i < nleaves; i++) new_iremote[filocal[i]] = firemote[i];
  // consolidate leaves
  PetscInt num_new_leaves = 0;
  for (PetscInt i = 0; i < nroots; i++) {
    if (new_iremote[i].rank == -1) continue;
    new_iremote[num_new_leaves] = new_iremote[i];
    leafdata[num_new_leaves]    = i;
    num_new_leaves++;
  }
  PetscCall(ISCreateGeneral(PETSC_COMM_SELF, num_new_leaves, leafdata, PETSC_COPY_VALUES, is_points));

  PetscSF csf;
  PetscCall(PetscSFCreate(comm, &csf));
  PetscCall(PetscSFSetGraph(csf, nroots, num_new_leaves, leafdata, PETSC_COPY_VALUES, new_iremote, PETSC_COPY_VALUES));
  PetscCall(PetscFree(new_iremote)); // copy and delete because new_iremote is longer than it needs to be
  PetscCall(PetscFree2(rootdata, leafdata));

  if (npoints < 0) { // empty point_sf
    *closure_sf = csf;
  } else {
    PetscCall(PetscSFMerge(point_sf, csf, closure_sf));
    PetscCall(PetscSFDestroy(&csf));
  }
  PetscCall(PetscObjectSetName((PetscObject)*closure_sf, "Composed Periodic Points"));
  PetscFunctionReturn(0);
}

static PetscErrorCode DMGetIsoperiodicPointSF_Plex(DM dm, PetscSF *sf)
{
  DM_Plex *plex = (DM_Plex *)dm->data;

  PetscFunctionBegin;
  if (!plex->periodic.composed_sf) {
    PetscSF face_sf = plex->periodic.face_sf;

    PetscCall(DMPlexCreateIsoperiodicPointSF_Private(dm, face_sf, &plex->periodic.composed_sf, &plex->periodic.periodic_points));
  }
  if (sf) *sf = plex->periodic.composed_sf;
  PetscFunctionReturn(0);
}

PetscErrorCode DMPlexMigrateIsoperiodicFaceSF_Internal(DM old_dm, DM dm, PetscSF sf_migration)
{
  DM_Plex    *plex = (DM_Plex *)old_dm->data;
  PetscSF     sf_point;
  PetscMPIInt rank;

  PetscFunctionBegin;
  if (!plex->periodic.face_sf) PetscFunctionReturn(0);
  PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank));
  PetscCall(DMGetPointSF(dm, &sf_point));
  PetscInt           old_npoints, new_npoints, old_nleaf, new_nleaf, point_nleaf;
  PetscSFNode       *new_leafdata, *rootdata, *leafdata;
  const PetscInt    *old_local, *point_local;
  const PetscSFNode *old_remote, *point_remote;
  PetscCall(PetscSFGetGraph(plex->periodic.face_sf, &old_npoints, &old_nleaf, &old_local, &old_remote));
  PetscCall(PetscSFGetGraph(sf_migration, NULL, &new_nleaf, NULL, NULL));
  PetscCall(PetscSFGetGraph(sf_point, &new_npoints, &point_nleaf, &point_local, &point_remote));
  PetscAssert(new_nleaf == new_npoints, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Expected migration leaf space to match new point root space");
  PetscCall(PetscMalloc3(old_npoints, &rootdata, old_npoints, &leafdata, new_npoints, &new_leafdata));

  // Fill new_leafdata with new owners of all points
  for (PetscInt i = 0; i < new_npoints; i++) {
    new_leafdata[i].rank  = rank;
    new_leafdata[i].index = i;
  }
  for (PetscInt i = 0; i < point_nleaf; i++) {
    PetscInt j      = point_local[i];
    new_leafdata[j] = point_remote[i];
  }
  // REPLACE is okay because every leaf agrees about the new owners
  PetscCall(PetscSFReduceBegin(sf_migration, MPIU_2INT, new_leafdata, rootdata, MPI_REPLACE));
  PetscCall(PetscSFReduceEnd(sf_migration, MPIU_2INT, new_leafdata, rootdata, MPI_REPLACE));
  // rootdata now contains the new owners

  // Send to leaves of old space
  for (PetscInt i = 0; i < old_npoints; i++) {
    leafdata[i].rank  = -1;
    leafdata[i].index = -1;
  }
  PetscCall(PetscSFBcastBegin(plex->periodic.face_sf, MPIU_2INT, rootdata, leafdata, MPI_REPLACE));
  PetscCall(PetscSFBcastEnd(plex->periodic.face_sf, MPIU_2INT, rootdata, leafdata, MPI_REPLACE));

  // Send to new leaf space
  PetscCall(PetscSFBcastBegin(sf_migration, MPIU_2INT, leafdata, new_leafdata, MPI_REPLACE));
  PetscCall(PetscSFBcastEnd(sf_migration, MPIU_2INT, leafdata, new_leafdata, MPI_REPLACE));

  PetscInt     nface = 0, *new_local;
  PetscSFNode *new_remote;
  for (PetscInt i = 0; i < new_npoints; i++) nface += (new_leafdata[i].rank >= 0);
  PetscCall(PetscMalloc1(nface, &new_local));
  PetscCall(PetscMalloc1(nface, &new_remote));
  nface = 0;
  for (PetscInt i = 0; i < new_npoints; i++) {
    if (new_leafdata[i].rank == -1) continue;
    new_local[nface]  = i;
    new_remote[nface] = new_leafdata[i];
    nface++;
  }
  PetscCall(PetscFree3(rootdata, leafdata, new_leafdata));
  PetscSF sf_face;
  PetscCall(PetscSFCreate(PetscObjectComm((PetscObject)dm), &sf_face));
  PetscCall(PetscSFSetGraph(sf_face, new_npoints, nface, new_local, PETSC_OWN_POINTER, new_remote, PETSC_OWN_POINTER));
  PetscCall(PetscObjectSetName((PetscObject)sf_face, "Migrated Isoperiodic Faces"));
  PetscCall(DMPlexSetIsoperiodicFaceSF(dm, sf_face));
  PetscCall(DMPlexSetIsoperiodicFaceTransform(dm, &plex->periodic.transform[0][0]));
  PetscCall(PetscSFDestroy(&sf_face));
  PetscFunctionReturn(0);
}

PetscErrorCode DMPeriodicCoordinateSetUp_Internal(DM dm)
{
  DM_Plex *plex = (DM_Plex *)dm->data;
  PetscFunctionBegin;
  if (!plex->periodic.face_sf) PetscFunctionReturn(0);
  PetscCall(DMGetIsoperiodicPointSF_Plex(dm, NULL));
  PetscCall(PetscObjectComposeFunction((PetscObject)dm, "DMGetIsoperiodicPointSF_C", DMGetIsoperiodicPointSF_Plex));

  PetscInt dim;
  PetscCall(DMGetDimension(dm, &dim));
  size_t count;
  IS     isdof;
  {
    PetscInt        npoints;
    const PetscInt *points;
    IS              is = plex->periodic.periodic_points;
    PetscSegBuffer  seg;
    PetscSection    section;
    PetscCall(DMGetLocalSection(dm, &section));
    PetscCall(PetscSegBufferCreate(sizeof(PetscInt), 32, &seg));
    PetscCall(ISGetSize(is, &npoints));
    PetscCall(ISGetIndices(is, &points));
    for (PetscInt i = 0; i < npoints; i++) {
      PetscInt point = points[i], off, dof;
      PetscCall(PetscSectionGetOffset(section, point, &off));
      PetscCall(PetscSectionGetDof(section, point, &dof));
      PetscAssert(dof % dim == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Unexpected dof %" PetscInt_FMT " not divisible by dimension %" PetscInt_FMT, dof, dim);
      for (PetscInt j = 0; j < dof / dim; j++) {
        PetscInt *slot;
        PetscCall(PetscSegBufferGetInts(seg, 1, &slot));
        *slot = off / dim;
      }
    }
    PetscInt *ind;
    PetscCall(PetscSegBufferGetSize(seg, &count));
    PetscCall(PetscSegBufferExtractAlloc(seg, &ind));
    PetscCall(PetscSegBufferDestroy(&seg));
    PetscCall(ISCreateBlock(PETSC_COMM_SELF, dim, count, ind, PETSC_OWN_POINTER, &isdof));
  }
  Vec        L, P;
  VecType    vec_type;
  VecScatter scatter;
  PetscCall(DMGetLocalVector(dm, &L));
  PetscCall(VecCreate(PETSC_COMM_SELF, &P));
  PetscCall(VecSetSizes(P, count * dim, count * dim));
  PetscCall(VecGetType(L, &vec_type));
  PetscCall(VecSetType(P, vec_type));
  PetscCall(VecScatterCreate(P, NULL, L, isdof, &scatter));
  PetscCall(DMRestoreLocalVector(dm, &L));
  PetscCall(ISDestroy(&isdof));

  {
    PetscScalar *x;
    PetscCall(VecGetArrayWrite(P, &x));
    for (PetscInt i = 0; i < (PetscInt)count; i++) {
      for (PetscInt j = 0; j < dim; j++) x[i * dim + j] = plex->periodic.transform[j][3];
    }
    PetscCall(VecRestoreArrayWrite(P, &x));
  }

  dm->periodic.affine_to_local = scatter;
  dm->periodic.affine          = P;
  PetscCall(DMGlobalToLocalHookAdd(dm, NULL, DMCoordAddPeriodicOffsets_Private, NULL));
  PetscFunctionReturn(0);
}

// We'll just orient all the edges, though only periodic boundary edges need orientation
static PetscErrorCode DMPlexOrientPositiveEdges_Private(DM dm)
{
  PetscInt dim, eStart, eEnd;
  PetscFunctionBegin;
  PetscCall(DMGetDimension(dm, &dim));
  if (dim < 3) PetscFunctionReturn(0); // not necessary
  PetscCall(DMPlexGetDepthStratum(dm, 1, &eStart, &eEnd));
  for (PetscInt e = eStart; e < eEnd; e++) {
    const PetscInt *cone;
    PetscCall(DMPlexGetCone(dm, e, &cone));
    if (cone[0] > cone[1]) PetscCall(DMPlexOrientPoint(dm, e, -1));
  }
  PetscFunctionReturn(0);
}

PetscErrorCode DMPlexCreateBoxMesh_Tensor_SFC_Internal(DM dm, PetscInt dim, const PetscInt faces[], const PetscReal lower[], const PetscReal upper[], const DMBoundaryType periodicity[], PetscBool interpolate)
{
  PetscInt  eextent[3] = {1, 1, 1}, vextent[3] = {1, 1, 1};
  const Ijk closure_1[] = {
    {0, 0, 0},
    {1, 0, 0},
  };
  const Ijk closure_2[] = {
    {0, 0, 0},
    {1, 0, 0},
    {1, 1, 0},
    {0, 1, 0},
  };
  const Ijk closure_3[] = {
    {0, 0, 0},
    {0, 1, 0},
    {1, 1, 0},
    {1, 0, 0},
    {0, 0, 1},
    {1, 0, 1},
    {1, 1, 1},
    {0, 1, 1},
  };
  const Ijk *const closure_dim[] = {NULL, closure_1, closure_2, closure_3};
  // This must be kept consistent with DMPlexCreateCubeMesh_Internal
  const PetscInt        face_marker_1[]   = {1, 2};
  const PetscInt        face_marker_2[]   = {4, 2, 1, 3};
  const PetscInt        face_marker_3[]   = {6, 5, 3, 4, 1, 2};
  const PetscInt *const face_marker_dim[] = {NULL, face_marker_1, face_marker_2, face_marker_3};
  // Orient faces so the normal is in the positive axis and the first vertex is the one closest to zero.
  // These orientations can be determined by examining cones of a reference quad and hex element.
  const PetscInt        face_orient_1[]   = {0, 0};
  const PetscInt        face_orient_2[]   = {-1, 0, 0, -1};
  const PetscInt        face_orient_3[]   = {-2, 0, -2, 1, -2, 0};
  const PetscInt *const face_orient_dim[] = {NULL, face_orient_1, face_orient_2, face_orient_3};

  PetscFunctionBegin;
  PetscValidPointer(dm, 1);
  PetscValidLogicalCollectiveInt(dm, dim, 2);
  PetscCall(DMSetDimension(dm, dim));
  PetscMPIInt rank, size;
  PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)dm), &size));
  PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank));
  for (PetscInt i = 0; i < dim; i++) {
    eextent[i] = faces[i];
    vextent[i] = faces[i] + 1;
  }
  ZLayout layout;
  PetscCall(ZLayoutCreate(size, eextent, vextent, &layout));
  PetscZSet vset; // set of all vertices in the closure of the owned elements
  PetscCall(PetscZSetCreate(&vset));
  PetscInt local_elems = 0;
  for (ZCode z = layout.zstarts[rank]; z < layout.zstarts[rank + 1]; z++) {
    Ijk loc = ZCodeSplit(z);
    if (IjkActive(layout.vextent, loc)) PetscZSetAdd(vset, z);
    if (IjkActive(layout.eextent, loc)) {
      local_elems++;
      // Add all neighboring vertices to set
      for (PetscInt n = 0; n < PetscPowInt(2, dim); n++) {
        Ijk   inc  = closure_dim[dim][n];
        Ijk   nloc = {loc.i + inc.i, loc.j + inc.j, loc.k + inc.k};
        ZCode v    = ZEncode(nloc);
        PetscZSetAdd(vset, v);
      }
    }
  }
  PetscInt local_verts, off = 0;
  ZCode   *vert_z;
  PetscCall(PetscZSetGetSize(vset, &local_verts));
  PetscCall(PetscMalloc1(local_verts, &vert_z));
  PetscCall(PetscZSetGetElems(vset, &off, vert_z));
  PetscCall(PetscZSetDestroy(&vset));
  // ZCode is unsigned for bitwise convenience, but highest bit should never be set, so can interpret as signed
  PetscCall(PetscSortInt64(local_verts, (PetscInt64 *)vert_z));

  PetscCall(DMPlexSetChart(dm, 0, local_elems + local_verts));
  for (PetscInt e = 0; e < local_elems; e++) PetscCall(DMPlexSetConeSize(dm, e, PetscPowInt(2, dim)));
  PetscCall(DMSetUp(dm));
  {
    PetscInt e = 0;
    for (ZCode z = layout.zstarts[rank]; z < layout.zstarts[rank + 1]; z++) {
      Ijk loc = ZCodeSplit(z);
      if (!IjkActive(layout.eextent, loc)) continue;
      PetscInt cone[8], orient[8] = {0};
      for (PetscInt n = 0; n < PetscPowInt(2, dim); n++) {
        Ijk      inc  = closure_dim[dim][n];
        Ijk      nloc = {loc.i + inc.i, loc.j + inc.j, loc.k + inc.k};
        ZCode    v    = ZEncode(nloc);
        PetscInt ci   = ZCodeFind(v, local_verts, vert_z);
        PetscAssert(ci >= 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Did not find neighbor vertex in set");
        cone[n] = local_elems + ci;
      }
      PetscCall(DMPlexSetCone(dm, e, cone));
      PetscCall(DMPlexSetConeOrientation(dm, e, orient));
      e++;
    }
  }

  PetscCall(DMPlexSymmetrize(dm));
  PetscCall(DMPlexStratify(dm));

  { // Create point SF
    PetscSF sf;
    PetscSFCreate(PetscObjectComm((PetscObject)dm), &sf);
    PetscInt owned_verts = ZCodeFind(layout.zstarts[rank + 1], local_verts, vert_z);
    if (owned_verts < 0) owned_verts = -(owned_verts + 1); // We don't care whether the key was found
    PetscInt     num_ghosts = local_verts - owned_verts;   // Due to sorting, owned vertices always come first
    PetscInt    *local_ghosts;
    PetscSFNode *ghosts;
    PetscCall(PetscMalloc1(num_ghosts, &local_ghosts));
    PetscCall(PetscMalloc1(num_ghosts, &ghosts));
    for (PetscInt i = 0; i < num_ghosts;) {
      ZCode    z           = vert_z[owned_verts + i];
      PetscInt remote_rank = ZCodeFind(z, size + 1, layout.zstarts), remote_count = 0;
      if (remote_rank < 0) remote_rank = -(remote_rank + 1) - 1;
      // We have a new remote rank; find all the ghost indices (which are contiguous in vert_z)

      // Count the elements on remote_rank
      PetscInt remote_elem = ZLayoutElementsOnRank(&layout, remote_rank);

      // Traverse vertices and make ghost links
      for (ZCode rz = layout.zstarts[remote_rank]; rz < layout.zstarts[remote_rank + 1]; rz++) {
        Ijk loc = ZCodeSplit(rz);
        if (rz == z) {
          local_ghosts[i] = local_elems + owned_verts + i;
          ghosts[i].rank  = remote_rank;
          ghosts[i].index = remote_elem + remote_count;
          i++;
          if (i == num_ghosts) break;
          z = vert_z[owned_verts + i];
        }
        if (IjkActive(layout.vextent, loc)) remote_count++;
      }
    }
    PetscCall(PetscSFSetGraph(sf, local_elems + local_verts, num_ghosts, local_ghosts, PETSC_OWN_POINTER, ghosts, PETSC_OWN_POINTER));
    PetscCall(PetscObjectSetName((PetscObject)sf, "SFC Point SF"));
    PetscCall(DMSetPointSF(dm, sf));
    PetscCall(PetscSFDestroy(&sf));
  }
  {
    Vec          coordinates;
    PetscScalar *coords;
    PetscSection coord_section;
    PetscInt     coord_size;
    PetscCall(DMGetCoordinateSection(dm, &coord_section));
    PetscCall(PetscSectionSetNumFields(coord_section, 1));
    PetscCall(PetscSectionSetFieldComponents(coord_section, 0, dim));
    PetscCall(PetscSectionSetChart(coord_section, local_elems, local_elems + local_verts));
    for (PetscInt v = 0; v < local_verts; v++) {
      PetscInt point = local_elems + v;
      PetscCall(PetscSectionSetDof(coord_section, point, dim));
      PetscCall(PetscSectionSetFieldDof(coord_section, point, 0, dim));
    }
    PetscCall(PetscSectionSetUp(coord_section));
    PetscCall(PetscSectionGetStorageSize(coord_section, &coord_size));
    PetscCall(VecCreate(PETSC_COMM_SELF, &coordinates));
    PetscCall(PetscObjectSetName((PetscObject)coordinates, "coordinates"));
    PetscCall(VecSetSizes(coordinates, coord_size, PETSC_DETERMINE));
    PetscCall(VecSetBlockSize(coordinates, dim));
    PetscCall(VecSetType(coordinates, VECSTANDARD));
    PetscCall(VecGetArray(coordinates, &coords));
    for (PetscInt v = 0; v < local_verts; v++) {
      Ijk loc             = ZCodeSplit(vert_z[v]);
      coords[v * dim + 0] = lower[0] + loc.i * (upper[0] - lower[0]) / layout.eextent.i;
      if (dim > 1) coords[v * dim + 1] = lower[1] + loc.j * (upper[1] - lower[1]) / layout.eextent.j;
      if (dim > 2) coords[v * dim + 2] = lower[2] + loc.k * (upper[2] - lower[2]) / layout.eextent.k;
    }
    PetscCall(VecRestoreArray(coordinates, &coords));
    PetscCall(DMSetCoordinatesLocal(dm, coordinates));
    PetscCall(VecDestroy(&coordinates));
  }
  if (interpolate) {
    PetscCall(DMPlexInterpolateInPlace_Internal(dm));
    // It's currently necessary to orient the donor and periodic edges consistently. An easy way to ensure that is ot
    // give all edges positive orientation. Since vertices are created in Z-order, all ranks will agree about the
    // ordering cone[0] < cone[1]. This is overkill and it would be nice to remove this preparation and make
    // DMPlexCreateIsoperiodicClosureSF_Private() more resilient, so it fixes any inconsistent orientations. That might
    // be needed in a general CGNS reader, for example.
    PetscCall(DMPlexOrientPositiveEdges_Private(dm));

    DMLabel label;
    PetscCall(DMCreateLabel(dm, "Face Sets"));
    PetscCall(DMGetLabel(dm, "Face Sets", &label));
    PetscSegBuffer per_faces, donor_face_closure, my_donor_faces;
    PetscCall(PetscSegBufferCreate(sizeof(PetscInt), 64, &per_faces));
    PetscCall(PetscSegBufferCreate(sizeof(PetscInt), 64, &my_donor_faces));
    PetscCall(PetscSegBufferCreate(sizeof(ZCode), 64 * PetscPowInt(2, dim), &donor_face_closure));
    PetscInt fStart, fEnd, vStart, vEnd;
    PetscCall(DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd));
    PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
    for (PetscInt f = fStart; f < fEnd; f++) {
      PetscInt npoints, *points = NULL, num_fverts = 0, fverts[8];
      PetscCall(DMPlexGetTransitiveClosure(dm, f, PETSC_TRUE, &npoints, &points));
      PetscInt bc_count[6] = {0};
      for (PetscInt i = 0; i < npoints; i++) {
        PetscInt p = points[2 * i];
        if (p < vStart || vEnd <= p) continue;
        fverts[num_fverts++] = p;
        Ijk loc              = ZCodeSplit(vert_z[p - vStart]);
        // Convention here matches DMPlexCreateCubeMesh_Internal
        bc_count[0] += loc.i == 0;
        bc_count[1] += loc.i == layout.vextent.i - 1;
        bc_count[2] += loc.j == 0;
        bc_count[3] += loc.j == layout.vextent.j - 1;
        bc_count[4] += loc.k == 0;
        bc_count[5] += loc.k == layout.vextent.k - 1;
      }
      PetscCall(DMPlexRestoreTransitiveClosure(dm, f, PETSC_TRUE, &npoints, &points));
      for (PetscInt bc = 0, bc_match = 0; bc < 2 * dim; bc++) {
        if (bc_count[bc] == PetscPowInt(2, dim - 1)) {
          PetscCall(DMPlexOrientPoint(dm, f, face_orient_dim[dim][bc]));
          if (periodicity[bc / 2] == DM_BOUNDARY_PERIODIC) {
            PetscInt *put;
            if (bc % 2 == 0) { // donor face; no label
              PetscCall(PetscSegBufferGet(my_donor_faces, 1, &put));
              *put = f;
            } else { // periodic face
              PetscCall(PetscSegBufferGet(per_faces, 1, &put));
              *put = f;
              ZCode *zput;
              PetscCall(PetscSegBufferGet(donor_face_closure, num_fverts, &zput));
              for (PetscInt i = 0; i < num_fverts; i++) {
                Ijk loc = ZCodeSplit(vert_z[fverts[i] - vStart]);
                switch (bc / 2) {
                case 0:
                  loc.i = 0;
                  break;
                case 1:
                  loc.j = 0;
                  break;
                case 2:
                  loc.k = 0;
                  break;
                }
                *zput++ = ZEncode(loc);
              }
            }
            continue;
          }
          PetscAssert(bc_match == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Face matches multiple face sets");
          PetscCall(DMLabelSetValue(label, f, face_marker_dim[dim][bc]));
          bc_match++;
        }
      }
    }
    // Ensure that the Coordinate DM has our new boundary labels
    DM cdm;
    PetscCall(DMGetCoordinateDM(dm, &cdm));
    PetscCall(DMCopyLabels(dm, cdm, PETSC_COPY_VALUES, PETSC_FALSE, DM_COPY_LABELS_FAIL));
    if (periodicity[0] == DM_BOUNDARY_PERIODIC || (dim > 1 && periodicity[1] == DM_BOUNDARY_PERIODIC) || (dim > 2 && periodicity[2] == DM_BOUNDARY_PERIODIC)) {
      PetscCall(DMPlexCreateBoxMesh_Tensor_SFC_Periodicity_Private(dm, &layout, vert_z, per_faces, lower, upper, periodicity, donor_face_closure, my_donor_faces));
    }
    PetscCall(PetscSegBufferDestroy(&per_faces));
    PetscCall(PetscSegBufferDestroy(&donor_face_closure));
    PetscCall(PetscSegBufferDestroy(&my_donor_faces));
  }
  PetscCall(PetscFree(layout.zstarts));
  PetscCall(PetscFree(vert_z));
  PetscFunctionReturn(0);
}

/*@
  DMPlexSetIsoperiodicFaceSF - Express periodicity from an existing mesh

  Logically collective

  Input Parameters:
+ dm - The `DMPLEX` on which to set periodicity
- face_sf - SF in which roots are (owned) donor faces and leaves are faces that must be matched to a (possibly remote) donor face.

  Level: advanced

  Notes:

  One can use `-dm_plex_box_sfc` to use this mode of periodicity, wherein the periodic points are distinct both globally
  and locally, but are paired when creating a global dof space.

.seealso: [](chapter_unstructured), `DMPLEX`, `DMGetGlobalSection()`, `DMPlexGetIsoperiodicFaceSF()`
@*/
PetscErrorCode DMPlexSetIsoperiodicFaceSF(DM dm, PetscSF face_sf)
{
  DM_Plex *plex = (DM_Plex *)dm->data;
  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscCall(PetscObjectReference((PetscObject)face_sf));
  PetscCall(PetscSFDestroy(&plex->periodic.face_sf));
  plex->periodic.face_sf = face_sf;
  if (face_sf) PetscCall(PetscObjectComposeFunction((PetscObject)dm, "DMGetIsoperiodicPointSF_C", DMGetIsoperiodicPointSF_Plex));

  DM cdm = dm->coordinates[0].dm; // Can't DMGetCoordinateDM because it automatically creates one
  if (cdm) {
    PetscCall(DMPlexSetIsoperiodicFaceSF(cdm, face_sf));
    if (face_sf) cdm->periodic.setup = DMPeriodicCoordinateSetUp_Internal;
  }
  PetscFunctionReturn(0);
}

/*@
  DMPlexGetIsoperiodicFaceSF - Obtain periodicity for a mesh

  Logically collective

  Input Parameters:
. dm - The `DMPLEX` for which to obtain periodic relation

  Output Parameters:
. face_sf - SF in which roots are (owned) donor faces and leaves are faces that must be matched to a (possibly remote) donor face.

  Level: advanced

.seealso: [](chapter_unstructured), `DMPLEX`, `DMGetGlobalSection()`, `DMPlexSetIsoperiodicFaceSF()`
@*/
PetscErrorCode DMPlexGetIsoperiodicFaceSF(DM dm, PetscSF *face_sf)
{
  DM_Plex *plex = (DM_Plex *)dm->data;
  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  *face_sf = plex->periodic.face_sf;
  PetscFunctionReturn(0);
}

/*@C
  DMPlexSetIsoperiodicFaceTransform - set geometric transform from donor to periodic points

  Logically Collective

  Input Arguments:
+ dm - `DMPlex` that has been configured with `DMPlexSetIsoperiodicFaceSF()`
- t - 4x4 affine transformation basis.

  Notes:
  Affine transforms are 4x4 matrices in which the leading 3x3 block expresses a rotation (or identity for no rotation),
  the last column contains a translation vector, and the bottom row is all zero except the last entry, which must always
  be 1. This representation is common in geometric modeling and allows affine transformations to be composed using
  simple matrix mulitplication.

  Although the interface accepts a general affine transform, only affine translation is supported at present.

  Developer Notes:
  This interface should be replaced by making BasisTransform public, expanding it to support affine representations, and
  adding GPU implementations to apply the G2L/L2G transforms.
@*/
PetscErrorCode DMPlexSetIsoperiodicFaceTransform(DM dm, const PetscScalar t[])
{
  DM_Plex *plex = (DM_Plex *)dm->data;
  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  for (PetscInt i = 0; i < 4; i++) {
    for (PetscInt j = 0; j < 4; j++) {
      PetscCheck(i != j || t[i * 4 + j] == 1., PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Rotated transforms not supported");
      plex->periodic.transform[i][j] = t[i * 4 + j];
    }
  }
  PetscFunctionReturn(0);
}