xref: /petsc/src/dm/impls/plex/plexsfc.c (revision 75155f4810bbdad9dc5d1c7fa5006c4f40d2d440)
1 #include <petsc/private/dmpleximpl.h> /*I   "petscdmplex.h"   I*/
2 #include <petscsf.h>
3 #include <petsc/private/hashset.h>
4 
5 typedef uint64_t ZCode;
6 
7 PETSC_HASH_SET(ZSet, ZCode, PetscHash_UInt64, PetscHashEqual)
8 
9 typedef struct {
10   PetscInt i, j, k;
11 } Ijk;
12 
13 typedef struct {
14   Ijk         eextent;
15   Ijk         vextent;
16   PetscMPIInt comm_size;
17   ZCode      *zstarts;
18 } ZLayout;
19 
20 // ***** Overview of ZCode *******
21 // The SFC uses integer indexing for each dimension and encodes them into a single integer by interleaving the bits of each index.
22 // This is known as Morton encoding, and is refered to as ZCode in this code.
23 // So for index i having bits [i2,i1,i0], and similar for indexes j and k, the ZCode (Morton number) would be:
24 //    [k2,j2,i2,k1,j1,i1,k0,j0,i0]
25 // This encoding allows for easier traversal of the SFC structure (see https://en.wikipedia.org/wiki/Z-order_curve and `ZStepOct()`).
26 // `ZEncode()` is used to go from indices to ZCode, while `ZCodeSplit()` goes from ZCode back to indices.
27 
28 // Decodes the leading interleaved index from a ZCode
29 // e.g. [k2,j2,i2,k1,j1,i1,k0,j0,i0] -> [i2,i1,i0]
30 // Magic numbers taken from https://stackoverflow.com/a/18528775/7564988 (translated to octal)
31 static unsigned ZCodeSplit1(ZCode z)
32 {
33   z &= 0111111111111111111111;
34   z = (z | z >> 2) & 0103030303030303030303;
35   z = (z | z >> 4) & 0100170017001700170017;
36   z = (z | z >> 8) & 0370000037700000377;
37   z = (z | z >> 16) & 0370000000000177777;
38   z = (z | z >> 32) & 07777777;
39   return (unsigned)z;
40 }
41 
42 // Encodes the leading interleaved index from a ZCode
43 // e.g. [i2,i1,i0] -> [0,0,i2,0,0,i1,0,0,i0]
44 static ZCode ZEncode1(unsigned t)
45 {
46   ZCode z = t;
47   z &= 07777777;
48   z = (z | z << 32) & 0370000000000177777;
49   z = (z | z << 16) & 0370000037700000377;
50   z = (z | z << 8) & 0100170017001700170017;
51   z = (z | z << 4) & 0103030303030303030303;
52   z = (z | z << 2) & 0111111111111111111111;
53   return z;
54 }
55 
56 // Decodes i j k indices from a ZCode.
57 // Uses `ZCodeSplit1()` by shifting ZCode so that the leading index is the desired one to decode
58 static Ijk ZCodeSplit(ZCode z)
59 {
60   Ijk c;
61   c.i = ZCodeSplit1(z >> 2);
62   c.j = ZCodeSplit1(z >> 1);
63   c.k = ZCodeSplit1(z >> 0);
64   return c;
65 }
66 
67 // Encodes i j k indices to a ZCode.
68 // Uses `ZCodeEncode1()` by shifting resulting ZCode to the appropriate bit placement
69 static ZCode ZEncode(Ijk c)
70 {
71   ZCode z = (ZEncode1((unsigned int)c.i) << 2) | (ZEncode1((unsigned int)c.j) << 1) | ZEncode1((unsigned int)c.k);
72   return z;
73 }
74 
75 static PetscBool IjkActive(Ijk extent, Ijk l)
76 {
77   if (l.i < extent.i && l.j < extent.j && l.k < extent.k) return PETSC_TRUE;
78   return PETSC_FALSE;
79 }
80 
81 // If z is not the base of an octet (last 3 bits 0), return 0.
82 //
83 // If z is the base of an octet, we recursively grow to the biggest structured octet. This is typically useful when a z
84 // is outside the domain and we wish to skip a (possibly recursively large) octet to find our next interesting point.
85 static ZCode ZStepOct(ZCode z)
86 {
87   if (PetscUnlikely(z == 0)) return 0; // Infinite loop below if z == 0
88   ZCode step = 07;
89   for (; (z & step) == 0; step = (step << 3) | 07) { }
90   return step >> 3;
91 }
92 
93 // Since element/vertex box extents are typically not equal powers of 2, Z codes that lie within the domain are not contiguous.
94 static PetscErrorCode ZLayoutCreate(PetscMPIInt size, const PetscInt eextent[3], const PetscInt vextent[3], ZLayout *layout)
95 {
96   PetscFunctionBegin;
97   layout->eextent.i = eextent[0];
98   layout->eextent.j = eextent[1];
99   layout->eextent.k = eextent[2];
100   layout->vextent.i = vextent[0];
101   layout->vextent.j = vextent[1];
102   layout->vextent.k = vextent[2];
103   layout->comm_size = size;
104   layout->zstarts   = NULL;
105   PetscCall(PetscMalloc1(size + 1, &layout->zstarts));
106 
107   PetscInt total_elems = eextent[0] * eextent[1] * eextent[2];
108   ZCode    z           = 0;
109   layout->zstarts[0]   = 0;
110   // This loop traverses all vertices in the global domain, so is worth making fast. We use ZStepBound
111   for (PetscMPIInt r = 0; r < size; r++) {
112     PetscInt elems_needed = (total_elems / size) + (total_elems % size > r), count;
113     for (count = 0; count < elems_needed; z++) {
114       ZCode skip = ZStepOct(z); // optimistically attempt a longer step
115       for (ZCode s = skip;; s >>= 3) {
116         Ijk trial = ZCodeSplit(z + s);
117         if (IjkActive(layout->eextent, trial)) {
118           while (count + s + 1 > (ZCode)elems_needed) s >>= 3; // Shrink the octet
119           count += s + 1;
120           z += s;
121           break;
122         }
123         if (s == 0) { // the whole skip octet is inactive
124           z += skip;
125           break;
126         }
127       }
128     }
129     // Pick up any extra vertices in the Z ordering before the next rank's first owned element.
130     //
131     // This leads to poorly balanced vertices when eextent is a power of 2, since all the fringe vertices end up
132     // on the last rank. A possible solution is to balance the Z-order vertices independently from the cells, which will
133     // result in a lot of element closures being remote. We could finish marking boundary conditions, then do a round of
134     // vertex ownership smoothing (which would reorder and redistribute vertices without touching element distribution).
135     // Another would be to have an analytic ownership criteria for vertices in the fringe veextent - eextent. This would
136     // complicate the job of identifying an owner and its offset.
137     //
138     // The current recommended approach is to let `-dm_distribute 1` (default) resolve vertex ownership. This is
139     // *mandatory* with isoperiodicity (except in special cases) to remove standed vertices from local spaces. Here's
140     // the issue:
141     //
142     // Consider this partition on rank 0 (left) and rank 1.
143     //
144     //    4 --------  5 -- 14 --10 -- 21 --11
145     //                |          |          |
146     // 7 -- 16 --  8  |          |          |
147     // |           |  3 -------  7 -------  9
148     // |           |             |          |
149     // 4 --------  6 ------ 10   |          |
150     // |           |         |   6 -- 16 -- 8
151     // |           |         |
152     // 3 ---11---  5 --18--  9
153     //
154     // The periodic face SF looks like
155     // [0] Number of roots=21, leaves=1, remote ranks=1
156     // [0] 16 <- (0,11)
157     // [1] Number of roots=22, leaves=2, remote ranks=2
158     // [1] 14 <- (0,18)
159     // [1] 21 <- (1,16)
160     //
161     // 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
162     // the point SF links to (1,4) and (1,5). Rank 1 learns about the periodic mapping of (1,5) while handling face
163     // (1,14), but never learns that vertex (1,4) has been mapped to (0,3) by face (0,16).
164     //
165     // We can relatively easily inform vertex (1,4) of this mapping, but it stays in rank 1's local space despite not
166     // being in the closure and thus not being contributed to. This would be mostly harmless except that some viewer
167     // routines expect all local points to be somehow significant. It is not easy to analytically remove the (1,4)
168     // vertex because the point SF and isoperiodic face SF would need to be updated to account for removal of the
169     // stranded vertices.
170     for (; z <= ZEncode(layout->vextent); z++) {
171       Ijk loc = ZCodeSplit(z);
172       if (IjkActive(layout->eextent, loc)) break;
173       z += ZStepOct(z);
174     }
175     layout->zstarts[r + 1] = z;
176   }
177   layout->zstarts[size] = ZEncode(layout->vextent);
178   PetscFunctionReturn(PETSC_SUCCESS);
179 }
180 
181 static PetscInt ZLayoutElementsOnRank(const ZLayout *layout, PetscMPIInt rank)
182 {
183   PetscInt remote_elem = 0;
184   for (ZCode rz = layout->zstarts[rank]; rz < layout->zstarts[rank + 1]; rz++) {
185     Ijk loc = ZCodeSplit(rz);
186     if (IjkActive(layout->eextent, loc)) remote_elem++;
187     else rz += ZStepOct(rz);
188   }
189   return remote_elem;
190 }
191 
192 static PetscInt ZCodeFind(ZCode key, PetscInt n, const ZCode X[])
193 {
194   PetscInt lo = 0, hi = n;
195 
196   if (n == 0) return -1;
197   while (hi - lo > 1) {
198     PetscInt mid = lo + (hi - lo) / 2;
199     if (key < X[mid]) hi = mid;
200     else lo = mid;
201   }
202   return key == X[lo] ? lo : -(lo + (key > X[lo]) + 1);
203 }
204 
205 static inline PetscBool IsPointInsideStratum(PetscInt point, PetscInt pStart, PetscInt pEnd)
206 {
207   return (point >= pStart && point < pEnd) ? PETSC_TRUE : PETSC_FALSE;
208 }
209 
210 static PetscErrorCode DMPlexCreateBoxMesh_Tensor_SFC_Periodicity_Private(DM dm, const ZLayout *layout, const ZCode *vert_z, PetscSegBuffer per_faces[3], const PetscReal *lower, const PetscReal *upper, const DMBoundaryType *periodicity, PetscSegBuffer donor_face_closure[3], PetscSegBuffer my_donor_faces[3])
211 {
212   MPI_Comm    comm;
213   PetscInt    dim, vStart, vEnd;
214   PetscMPIInt size;
215   PetscSF     face_sfs[3];
216   PetscScalar transforms[3][4][4] = {{{0}}};
217 
218   PetscFunctionBegin;
219   PetscCall(PetscObjectGetComm((PetscObject)dm, &comm));
220   PetscCallMPI(MPI_Comm_size(comm, &size));
221   PetscCall(DMGetDimension(dm, &dim));
222   const PetscInt csize = PetscPowInt(2, dim - 1);
223   PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
224 
225   PetscInt num_directions = 0;
226   for (PetscInt direction = 0; direction < dim; direction++) {
227     PetscCount   num_faces;
228     PetscInt    *faces;
229     ZCode       *donor_verts, *donor_minz;
230     PetscSFNode *leaf;
231     PetscCount   num_multiroots = 0;
232     PetscInt     pStart, pEnd;
233     PetscBool    sorted;
234     PetscInt     inum_faces;
235 
236     if (periodicity[direction] != DM_BOUNDARY_PERIODIC) continue;
237     PetscCall(PetscSegBufferGetSize(per_faces[direction], &num_faces));
238     PetscCall(PetscSegBufferExtractInPlace(per_faces[direction], &faces));
239     PetscCall(PetscSegBufferExtractInPlace(donor_face_closure[direction], &donor_verts));
240     PetscCall(PetscMalloc1(num_faces, &donor_minz));
241     PetscCall(PetscMalloc1(num_faces, &leaf));
242     for (PetscCount i = 0; i < num_faces; i++) {
243       ZCode minz = donor_verts[i * csize];
244 
245       for (PetscInt j = 1; j < csize; j++) minz = PetscMin(minz, donor_verts[i * csize + j]);
246       donor_minz[i] = minz;
247     }
248     PetscCall(PetscIntCast(num_faces, &inum_faces));
249     PetscCall(PetscSortedInt64(inum_faces, (const PetscInt64 *)donor_minz, &sorted));
250     // If a donor vertex were chosen to broker multiple faces, we would have a logic error.
251     // Checking for sorting is a cheap check that there are no duplicates.
252     PetscCheck(sorted, PETSC_COMM_SELF, PETSC_ERR_PLIB, "minz not sorted; possible duplicates not checked");
253     for (PetscCount i = 0; i < num_faces;) {
254       ZCode       z = donor_minz[i];
255       PetscMPIInt remote_rank, remote_count = 0;
256 
257       PetscCall(PetscMPIIntCast(ZCodeFind(z, size + 1, layout->zstarts), &remote_rank));
258       if (remote_rank < 0) remote_rank = -(remote_rank + 1) - 1;
259       // Process all the vertices on this rank
260       for (ZCode rz = layout->zstarts[remote_rank]; rz < layout->zstarts[remote_rank + 1]; rz++) {
261         Ijk loc = ZCodeSplit(rz);
262 
263         if (rz == z) {
264           leaf[i].rank  = remote_rank;
265           leaf[i].index = remote_count;
266           i++;
267           if (i == num_faces) break;
268           z = donor_minz[i];
269         }
270         if (IjkActive(layout->vextent, loc)) remote_count++;
271       }
272     }
273     PetscCall(PetscFree(donor_minz));
274     PetscCall(PetscSFCreate(PetscObjectComm((PetscObject)dm), &face_sfs[num_directions]));
275     PetscCall(PetscSFSetGraph(face_sfs[num_directions], vEnd - vStart, inum_faces, NULL, PETSC_USE_POINTER, leaf, PETSC_USE_POINTER));
276     const PetscInt *my_donor_degree;
277     PetscCall(PetscSFComputeDegreeBegin(face_sfs[num_directions], &my_donor_degree));
278     PetscCall(PetscSFComputeDegreeEnd(face_sfs[num_directions], &my_donor_degree));
279 
280     for (PetscInt i = 0; i < vEnd - vStart; i++) {
281       num_multiroots += my_donor_degree[i];
282       if (my_donor_degree[i] == 0) continue;
283       PetscAssert(my_donor_degree[i] == 1, PETSC_COMM_SELF, PETSC_ERR_SUP, "Local vertex has multiple faces");
284     }
285     PetscInt  *my_donors, *donor_indices, *my_donor_indices;
286     PetscCount num_my_donors;
287 
288     PetscCall(PetscSegBufferGetSize(my_donor_faces[direction], &num_my_donors));
289     PetscCheck(num_my_donors == num_multiroots, PETSC_COMM_SELF, PETSC_ERR_SUP, "Donor request (%" PetscCount_FMT ") does not match expected donors (%" PetscCount_FMT ")", num_my_donors, num_multiroots);
290     PetscCall(PetscSegBufferExtractInPlace(my_donor_faces[direction], &my_donors));
291     PetscCall(PetscMalloc1(vEnd - vStart, &my_donor_indices));
292     for (PetscCount i = 0; i < num_my_donors; i++) {
293       PetscInt f = my_donors[i];
294       PetscInt num_points, *points = NULL, minv = PETSC_INT_MAX;
295 
296       PetscCall(DMPlexGetTransitiveClosure(dm, f, PETSC_TRUE, &num_points, &points));
297       for (PetscInt j = 0; j < num_points; j++) {
298         PetscInt p = points[2 * j];
299         if (!IsPointInsideStratum(p, vStart, vEnd)) continue;
300         minv = PetscMin(minv, p);
301       }
302       PetscCall(DMPlexRestoreTransitiveClosure(dm, f, PETSC_TRUE, &num_points, &points));
303       PetscAssert(my_donor_degree[minv - vStart] == 1, PETSC_COMM_SELF, PETSC_ERR_SUP, "Local vertex not requested");
304       my_donor_indices[minv - vStart] = f;
305     }
306     PetscCall(PetscMalloc1(num_faces, &donor_indices));
307     PetscCall(PetscSFBcastBegin(face_sfs[num_directions], MPIU_INT, my_donor_indices, donor_indices, MPI_REPLACE));
308     PetscCall(PetscSFBcastEnd(face_sfs[num_directions], MPIU_INT, my_donor_indices, donor_indices, MPI_REPLACE));
309     PetscCall(PetscFree(my_donor_indices));
310     // Modify our leafs so they point to donor faces instead of donor minz. Additionally, give them indices as faces.
311     for (PetscCount i = 0; i < num_faces; i++) leaf[i].index = donor_indices[i];
312     PetscCall(PetscFree(donor_indices));
313     PetscCall(DMPlexGetChart(dm, &pStart, &pEnd));
314     PetscCall(PetscSFSetGraph(face_sfs[num_directions], pEnd - pStart, inum_faces, faces, PETSC_COPY_VALUES, leaf, PETSC_OWN_POINTER));
315     {
316       char face_sf_name[PETSC_MAX_PATH_LEN];
317       PetscCall(PetscSNPrintf(face_sf_name, sizeof face_sf_name, "Z-order Isoperiodic Faces #%" PetscInt_FMT, num_directions));
318       PetscCall(PetscObjectSetName((PetscObject)face_sfs[num_directions], face_sf_name));
319     }
320 
321     transforms[num_directions][0][0]         = 1;
322     transforms[num_directions][1][1]         = 1;
323     transforms[num_directions][2][2]         = 1;
324     transforms[num_directions][3][3]         = 1;
325     transforms[num_directions][direction][3] = upper[direction] - lower[direction];
326     num_directions++;
327   }
328 
329   PetscCall(DMPlexSetIsoperiodicFaceSF(dm, num_directions, face_sfs));
330   PetscCall(DMPlexSetIsoperiodicFaceTransform(dm, num_directions, (PetscScalar *)transforms));
331 
332   for (PetscInt i = 0; i < num_directions; i++) PetscCall(PetscSFDestroy(&face_sfs[i]));
333   PetscFunctionReturn(PETSC_SUCCESS);
334 }
335 
336 // This is a DMGlobalToLocalHook that applies the affine offsets. When extended for rotated periodicity, it'll need to
337 // apply a rotatonal transform and similar operations will be needed for fields (e.g., to rotate a velocity vector).
338 // We use this crude approach here so we don't have to write new GPU kernels yet.
339 static PetscErrorCode DMCoordAddPeriodicOffsets_Private(DM dm, Vec g, InsertMode mode, Vec l, void *ctx)
340 {
341   PetscFunctionBegin;
342   // These `VecScatter`s should be merged to improve efficiency; the scatters cannot be overlapped.
343   for (PetscInt i = 0; i < dm->periodic.num_affines; i++) {
344     PetscCall(VecScatterBegin(dm->periodic.affine_to_local[i], dm->periodic.affine[i], l, ADD_VALUES, SCATTER_FORWARD));
345     PetscCall(VecScatterEnd(dm->periodic.affine_to_local[i], dm->periodic.affine[i], l, ADD_VALUES, SCATTER_FORWARD));
346   }
347   PetscFunctionReturn(PETSC_SUCCESS);
348 }
349 
350 // Modify Vec based on the transformation of `point` for the given section and field
351 static PetscErrorCode DMPlexOrientFieldPointVec(DM dm, PetscSection section, PetscInt field, Vec V, PetscInt point, PetscInt orientation)
352 {
353   PetscScalar        *copy, *V_arr;
354   PetscInt            dof, off, point_ornt[2] = {point, orientation};
355   const PetscInt    **perms;
356   const PetscScalar **rots;
357 
358   PetscFunctionBeginUser;
359   PetscCall(PetscSectionGetDof(section, point, &dof));
360   PetscCall(PetscSectionGetOffset(section, point, &off));
361   PetscCall(VecGetArray(V, &V_arr));
362   PetscCall(DMGetWorkArray(dm, dof, MPIU_SCALAR, &copy));
363   PetscArraycpy(copy, &V_arr[off], dof);
364 
365   PetscCall(PetscSectionGetFieldPointSyms(section, field, 1, point_ornt, &perms, &rots));
366   for (PetscInt i = 0; i < dof; i++) {
367     if (perms[0]) V_arr[off + perms[0][i]] = copy[i];
368     if (rots[0]) V_arr[off + perms[0][i]] *= rots[0][i];
369   }
370 
371   PetscCall(PetscSectionRestoreFieldPointSyms(section, field, 1, point_ornt, &perms, &rots));
372   PetscCall(DMRestoreWorkArray(dm, dof, MPIU_SCALAR, &copy));
373   PetscCall(VecRestoreArray(V, &V_arr));
374   PetscFunctionReturn(PETSC_SUCCESS);
375 }
376 
377 // Reorient the point in the DMPlex while also applying necessary corrections to other structures (e.g. coordinates)
378 static PetscErrorCode DMPlexOrientPointWithCorrections(DM dm, PetscInt point, PetscInt ornt)
379 {
380   // TODO: Potential speed up if we early exit for ornt == 0 (i.e. if ornt is identity, we don't need to do anything)
381   PetscFunctionBeginUser;
382   PetscCall(DMPlexOrientPoint(dm, point, ornt));
383 
384   { // Correct coordinates based on new cone ordering
385     DM           cdm;
386     PetscSection csection;
387     Vec          coordinates;
388     PetscInt     pStart, pEnd;
389 
390     PetscCall(DMGetCoordinatesLocal(dm, &coordinates));
391     PetscCall(DMGetCoordinateDM(dm, &cdm));
392     PetscCall(DMGetLocalSection(cdm, &csection));
393     PetscCall(PetscSectionGetChart(csection, &pStart, &pEnd));
394     if (IsPointInsideStratum(point, pStart, pEnd)) PetscCall(DMPlexOrientFieldPointVec(cdm, csection, 0, coordinates, point, ornt));
395   }
396   // TODO: Correct sfNatural
397   PetscFunctionReturn(PETSC_SUCCESS);
398 }
399 
400 // Creates SF to communicate data from donor to periodic faces. The data can be different sizes per donor-periodic pair and is given in `point_sizes[]`
401 static PetscErrorCode CreateDonorToPeriodicSF(DM dm, PetscSF face_sf, PetscInt pStart, PetscInt pEnd, const PetscInt point_sizes[], PetscInt *rootbuffersize, PetscInt *leafbuffersize, PetscBT *rootbt, PetscSF *sf_closure)
402 {
403   MPI_Comm           comm;
404   PetscMPIInt        rank;
405   PetscInt           nroots, nleaves;
406   PetscInt          *rootdata, *leafdata;
407   const PetscInt    *filocal;
408   const PetscSFNode *firemote;
409 
410   PetscFunctionBeginUser;
411   PetscCall(PetscObjectGetComm((PetscObject)dm, &comm));
412   PetscCallMPI(MPI_Comm_rank(comm, &rank));
413 
414   PetscCall(PetscSFGetGraph(face_sf, &nroots, &nleaves, &filocal, &firemote));
415   PetscCall(PetscCalloc2(2 * nroots, &rootdata, 2 * nroots, &leafdata));
416   for (PetscInt i = 0; i < nleaves; i++) {
417     PetscInt point = filocal[i];
418     PetscCheck(IsPointInsideStratum(point, pStart, pEnd), PETSC_COMM_SELF, PETSC_ERR_PLIB, "Point %" PetscInt_FMT " in leaves exists outside of stratum [%" PetscInt_FMT ", %" PetscInt_FMT ")", point, pStart, pEnd);
419     leafdata[point] = point_sizes[point - pStart];
420   }
421   PetscCall(PetscSFReduceBegin(face_sf, MPIU_INT, leafdata, rootdata + nroots, MPIU_SUM));
422   PetscCall(PetscSFReduceEnd(face_sf, MPIU_INT, leafdata, rootdata + nroots, MPIU_SUM));
423 
424   PetscInt root_offset = 0;
425   PetscCall(PetscBTCreate(nroots, rootbt));
426   for (PetscInt p = 0; p < nroots; p++) {
427     const PetscInt *donor_dof = rootdata + nroots;
428     if (donor_dof[p] == 0) {
429       rootdata[2 * p]     = -1;
430       rootdata[2 * p + 1] = -1;
431       continue;
432     }
433     PetscCall(PetscBTSet(*rootbt, p));
434     PetscCheck(IsPointInsideStratum(p, pStart, pEnd), PETSC_COMM_SELF, PETSC_ERR_PLIB, "Point %" PetscInt_FMT " in roots exists outside of stratum [%" PetscInt_FMT ", %" PetscInt_FMT ")", p, pStart, pEnd);
435     PetscInt p_size = point_sizes[p - pStart];
436     PetscCheck(donor_dof[p] == p_size, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Reduced leaf data size (%" PetscInt_FMT ") does not match root data size (%" PetscInt_FMT ")", donor_dof[p], p_size);
437     rootdata[2 * p]     = root_offset;
438     rootdata[2 * p + 1] = p_size;
439     root_offset += p_size;
440   }
441   PetscCall(PetscSFBcastBegin(face_sf, MPIU_2INT, rootdata, leafdata, MPI_REPLACE));
442   PetscCall(PetscSFBcastEnd(face_sf, MPIU_2INT, rootdata, leafdata, MPI_REPLACE));
443   // Count how many leaves we need to communicate the closures
444   PetscInt leaf_offset = 0;
445   for (PetscInt i = 0; i < nleaves; i++) {
446     PetscInt point = filocal[i];
447     if (leafdata[2 * point + 1] < 0) continue;
448     leaf_offset += leafdata[2 * point + 1];
449   }
450 
451   PetscSFNode *closure_leaf;
452   PetscCall(PetscMalloc1(leaf_offset, &closure_leaf));
453   leaf_offset = 0;
454   for (PetscInt i = 0; i < nleaves; i++) {
455     PetscInt point   = filocal[i];
456     PetscInt cl_size = leafdata[2 * point + 1];
457     if (cl_size < 0) continue;
458     for (PetscInt j = 0; j < cl_size; j++) {
459       closure_leaf[leaf_offset].rank  = firemote[i].rank;
460       closure_leaf[leaf_offset].index = leafdata[2 * point] + j;
461       leaf_offset++;
462     }
463   }
464 
465   PetscCall(PetscSFCreate(comm, sf_closure));
466   PetscCall(PetscSFSetGraph(*sf_closure, root_offset, leaf_offset, NULL, PETSC_USE_POINTER, closure_leaf, PETSC_OWN_POINTER));
467   *rootbuffersize = root_offset;
468   *leafbuffersize = leaf_offset;
469   PetscCall(PetscFree2(rootdata, leafdata));
470   PetscFunctionReturn(PETSC_SUCCESS);
471 }
472 
473 // Determine if `key` is in `array`. `array` does NOT need to be sorted
474 static inline PetscBool SearchIntArray(PetscInt key, PetscInt array_size, const PetscInt array[])
475 {
476   for (PetscInt i = 0; i < array_size; i++)
477     if (array[i] == key) return PETSC_TRUE;
478   return PETSC_FALSE;
479 }
480 
481 // Translate a cone in periodic points to the cone in donor points based on the `periodic2donor` array
482 static inline PetscErrorCode TranslateConeP2D(const PetscInt periodic_cone[], PetscInt cone_size, const PetscInt periodic2donor[], PetscInt p2d_count, PetscInt p2d_cone[])
483 {
484   PetscFunctionBeginUser;
485   for (PetscInt p = 0; p < cone_size; p++) {
486     PetscInt p2d_index = -1;
487     for (PetscInt p2d = 0; p2d < p2d_count; p2d++) {
488       if (periodic2donor[p2d * 2] == periodic_cone[p]) p2d_index = p2d;
489     }
490     PetscCheck(p2d_index >= 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Could not find periodic point in periodic-to-donor array");
491     p2d_cone[p] = periodic2donor[2 * p2d_index + 1];
492   }
493   PetscFunctionReturn(PETSC_SUCCESS);
494 }
495 
496 // Corrects the cone order of periodic faces (and their transitive closure's cones) to match their donor face pair.
497 //
498 // This is done by:
499 // 1. Communicating the donor's vertex coordinates and recursive cones (i.e. its own cone and those of it's constituent edges) to it's periodic pairs
500 //    - The donor vertices have the isoperiodic transform applied to them such that they should match exactly
501 // 2. Translating the periodic vertices into the donor vertices point IDs
502 // 3. Translating the cone of each periodic point into the donor point IDs
503 // 4. Comparing the periodic-to-donor cone to the donor cone for each point
504 // 5. Apply the necessary transformation to the periodic cone to make it match the donor cone
505 static PetscErrorCode DMPlexCorrectOrientationForIsoperiodic(DM dm)
506 {
507   MPI_Comm        comm;
508   DM_Plex        *plex = (DM_Plex *)dm->data;
509   PetscInt        nroots, nleaves;
510   const PetscInt *filocal;
511   DM              cdm;
512   PetscSection    csection;
513   Vec             coordinates;
514   PetscInt        coords_field_id = 0;
515   PetscBool       debug_printing  = PETSC_FALSE;
516 
517   PetscFunctionBeginUser;
518   PetscCall(PetscObjectGetComm((PetscObject)dm, &comm));
519   PetscCall(DMGetCoordinatesLocal(dm, &coordinates));
520   PetscCheck(coordinates, comm, PETSC_ERR_ARG_WRONGSTATE, "DM must have coordinates to setup isoperiodic");
521   PetscCall(DMGetCoordinateDM(dm, &cdm));
522   PetscCall(DMGetLocalSection(cdm, &csection));
523 
524   for (PetscInt f = 0; f < plex->periodic.num_face_sfs; f++) {
525     PetscSF face_sf                  = plex->periodic.face_sfs[f];
526     const PetscScalar(*transform)[4] = (const PetscScalar(*)[4])plex->periodic.transform[f];
527     PetscInt *face_vertices_size, *face_cones_size;
528     PetscInt  fStart, fEnd, vStart, vEnd, rootnumvert, leafnumvert, rootconesize, leafconesize, dim;
529     PetscSF   sf_vert_coords, sf_face_cones;
530     PetscBT   rootbt;
531 
532     PetscCall(DMGetCoordinateDim(dm, &dim));
533     PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
534     PetscCall(DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd));
535     PetscCall(PetscCalloc2(fEnd - fStart, &face_vertices_size, fEnd - fStart, &face_cones_size));
536 
537     // Create SFs to communicate donor vertices and donor cones to periodic faces
538     for (PetscInt f = fStart, index = 0; f < fEnd; f++, index++) {
539       PetscInt cl_size, *closure = NULL, num_vertices = 0;
540       PetscCall(DMPlexGetTransitiveClosure(dm, f, PETSC_TRUE, &cl_size, &closure));
541       for (PetscInt p = 0; p < cl_size; p++) {
542         PetscInt cl_point = closure[2 * p];
543         if (IsPointInsideStratum(cl_point, vStart, vEnd)) num_vertices++;
544         else {
545           PetscInt cone_size;
546           PetscCall(DMPlexGetConeSize(dm, cl_point, &cone_size));
547           face_cones_size[index] += cone_size + 2;
548         }
549       }
550       face_vertices_size[index] = num_vertices;
551       face_cones_size[index] += num_vertices;
552       PetscCall(DMPlexRestoreTransitiveClosure(dm, f, PETSC_TRUE, &cl_size, &closure));
553     }
554     PetscCall(CreateDonorToPeriodicSF(dm, face_sf, fStart, fEnd, face_vertices_size, &rootnumvert, &leafnumvert, &rootbt, &sf_vert_coords));
555     PetscCall(PetscBTDestroy(&rootbt));
556     PetscCall(CreateDonorToPeriodicSF(dm, face_sf, fStart, fEnd, face_cones_size, &rootconesize, &leafconesize, &rootbt, &sf_face_cones));
557 
558     PetscCall(PetscSFGetGraph(face_sf, &nroots, &nleaves, &filocal, NULL));
559 
560     PetscReal *leaf_donor_coords;
561     PetscInt  *leaf_donor_cones;
562 
563     { // Communicate donor coords and cones to the periodic faces
564       PetscReal         *mydonor_vertices;
565       PetscInt          *mydonor_cones;
566       const PetscScalar *coords_arr;
567 
568       PetscCall(PetscCalloc2(rootnumvert * dim, &mydonor_vertices, rootconesize, &mydonor_cones));
569       PetscCall(VecGetArrayRead(coordinates, &coords_arr));
570       for (PetscInt donor_face = 0, donor_vert_offset = 0, donor_cone_offset = 0; donor_face < nroots; donor_face++) {
571         if (!PetscBTLookup(rootbt, donor_face)) continue;
572         PetscInt cl_size, *closure = NULL;
573 
574         PetscCall(DMPlexGetTransitiveClosure(dm, donor_face, PETSC_TRUE, &cl_size, &closure));
575         // Pack vertex coordinates
576         for (PetscInt p = 0; p < cl_size; p++) {
577           PetscInt cl_point = closure[2 * p], dof, offset;
578           if (!IsPointInsideStratum(cl_point, vStart, vEnd)) continue;
579           mydonor_cones[donor_cone_offset++] = cl_point;
580           PetscCall(PetscSectionGetFieldDof(csection, cl_point, coords_field_id, &dof));
581           PetscCall(PetscSectionGetFieldOffset(csection, cl_point, coords_field_id, &offset));
582           PetscAssert(dof == dim, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Point %" PetscInt_FMT " has dof size %" PetscInt_FMT ", but should match dimension size %" PetscInt_FMT, cl_point, dof, dim);
583           // Apply isoperiodic transform to donor vertices such that corresponding periodic vertices should match exactly
584           for (PetscInt d = 0; d < dof; d++) mydonor_vertices[donor_vert_offset * dim + d] = PetscRealPart(coords_arr[offset + d]) + PetscRealPart(transform[d][3]);
585           donor_vert_offset++;
586         }
587         // Pack cones of face points (including face itself)
588         for (PetscInt p = 0; p < cl_size; p++) {
589           PetscInt        cl_point = closure[2 * p], cone_size, depth;
590           const PetscInt *cone;
591 
592           PetscCall(DMPlexGetConeSize(dm, cl_point, &cone_size));
593           PetscCall(DMPlexGetCone(dm, cl_point, &cone));
594           PetscCall(DMPlexGetPointDepth(dm, cl_point, &depth));
595           if (depth == 0) continue; // don't include vertex depth
596           mydonor_cones[donor_cone_offset++] = cone_size;
597           mydonor_cones[donor_cone_offset++] = cl_point;
598           PetscArraycpy(&mydonor_cones[donor_cone_offset], cone, cone_size);
599           donor_cone_offset += cone_size;
600         }
601         PetscCall(DMPlexRestoreTransitiveClosure(dm, donor_face, PETSC_TRUE, &cl_size, &closure));
602       }
603       PetscCall(VecRestoreArrayRead(coordinates, &coords_arr));
604       PetscCall(PetscBTDestroy(&rootbt));
605 
606       MPI_Datatype vertex_unit;
607       PetscMPIInt  n;
608       PetscCall(PetscMPIIntCast(dim, &n));
609       PetscCallMPI(MPI_Type_contiguous(n, MPIU_REAL, &vertex_unit));
610       PetscCallMPI(MPI_Type_commit(&vertex_unit));
611       PetscCall(PetscMalloc2(leafnumvert * 3, &leaf_donor_coords, leafconesize, &leaf_donor_cones));
612       PetscCall(PetscSFBcastBegin(sf_vert_coords, vertex_unit, mydonor_vertices, leaf_donor_coords, MPI_REPLACE));
613       PetscCall(PetscSFBcastBegin(sf_face_cones, MPIU_INT, mydonor_cones, leaf_donor_cones, MPI_REPLACE));
614       PetscCall(PetscSFBcastEnd(sf_vert_coords, vertex_unit, mydonor_vertices, leaf_donor_coords, MPI_REPLACE));
615       PetscCall(PetscSFBcastEnd(sf_face_cones, MPIU_INT, mydonor_cones, leaf_donor_cones, MPI_REPLACE));
616       PetscCall(PetscSFDestroy(&sf_vert_coords));
617       PetscCall(PetscSFDestroy(&sf_face_cones));
618       PetscCallMPI(MPI_Type_free(&vertex_unit));
619       PetscCall(PetscFree2(mydonor_vertices, mydonor_cones));
620     }
621 
622     { // Determine periodic orientation w/rt donor vertices and reorient
623       PetscReal tol = PetscSqr(PETSC_MACHINE_EPSILON * 1e3);
624       PetscInt *periodic2donor, dm_depth, maxConeSize;
625       PetscInt  coords_offset = 0, cones_offset = 0;
626 
627       PetscCall(DMPlexGetDepth(dm, &dm_depth));
628       PetscCall(DMPlexGetMaxSizes(dm, &maxConeSize, NULL));
629       PetscCall(DMGetWorkArray(dm, 2 * PetscPowInt(maxConeSize, dm_depth - 1), MPIU_INT, &periodic2donor));
630 
631       // Translate the periodic face vertices into the donor vertices
632       // Translation stored in periodic2donor
633       for (PetscInt i = 0; i < nleaves; i++) {
634         PetscInt  periodic_face = filocal[i], cl_size, num_verts = face_vertices_size[periodic_face - fStart];
635         PetscInt  cones_size = face_cones_size[periodic_face - fStart], p2d_count = 0;
636         PetscInt *closure = NULL;
637 
638         PetscCall(DMPlexGetTransitiveClosure(dm, periodic_face, PETSC_TRUE, &cl_size, &closure));
639         for (PetscInt p = 0; p < cl_size; p++) {
640           PetscInt     cl_point = closure[2 * p], coords_size, donor_vertex = -1;
641           PetscScalar *coords = NULL;
642 
643           if (!IsPointInsideStratum(cl_point, vStart, vEnd)) continue;
644           PetscCall(DMPlexVecGetClosure(dm, csection, coordinates, cl_point, &coords_size, &coords));
645           PetscAssert(coords_size == dim, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Point %" PetscInt_FMT " has dof size %" PetscInt_FMT ", but should match dimension size %" PetscInt_FMT, cl_point, coords_size, dim);
646 
647           for (PetscInt v = 0; v < num_verts; v++) {
648             PetscReal dist_sqr = 0;
649             for (PetscInt d = 0; d < coords_size; d++) dist_sqr += PetscSqr(PetscRealPart(coords[d]) - leaf_donor_coords[(v + coords_offset) * dim + d]);
650             if (dist_sqr < tol) {
651               donor_vertex = leaf_donor_cones[cones_offset + v];
652               break;
653             }
654           }
655           PetscCheck(donor_vertex >= 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Periodic face %" PetscInt_FMT " could not find matching donor vertex for vertex %" PetscInt_FMT, periodic_face, cl_point);
656           if (PetscDefined(USE_DEBUG)) {
657             for (PetscInt c = 0; c < p2d_count; c++) PetscCheck(periodic2donor[2 * c + 1] != donor_vertex, comm, PETSC_ERR_PLIB, "Found repeated cone_point in periodic_ordering");
658           }
659 
660           periodic2donor[2 * p2d_count + 0] = cl_point;
661           periodic2donor[2 * p2d_count + 1] = donor_vertex;
662           p2d_count++;
663           PetscCall(DMPlexVecRestoreClosure(dm, csection, coordinates, cl_point, &coords_size, &coords));
664         }
665         coords_offset += num_verts;
666         PetscCall(DMPlexRestoreTransitiveClosure(dm, periodic_face, PETSC_TRUE, &cl_size, &closure));
667 
668         { // Determine periodic orientation w/rt donor vertices and reorient
669           PetscInt      depth, *p2d_cone, face_is_array[1] = {periodic_face};
670           IS           *is_arrays, face_is;
671           PetscSection *section_arrays;
672           PetscInt     *donor_cone_array = &leaf_donor_cones[cones_offset + num_verts];
673 
674           PetscCall(ISCreateGeneral(PETSC_COMM_SELF, 1, face_is_array, PETSC_USE_POINTER, &face_is));
675           PetscCall(DMPlexGetConeRecursive(dm, face_is, &depth, &is_arrays, &section_arrays));
676           PetscCall(ISDestroy(&face_is));
677           PetscCall(DMGetWorkArray(dm, maxConeSize, MPIU_INT, &p2d_cone));
678           for (PetscInt d = 0; d < depth - 1; d++) {
679             PetscInt        pStart, pEnd;
680             PetscSection    section = section_arrays[d];
681             const PetscInt *periodic_cone_arrays, *periodic_point_arrays;
682 
683             PetscCall(ISGetIndices(is_arrays[d], &periodic_cone_arrays));
684             PetscCall(ISGetIndices(is_arrays[d + 1], &periodic_point_arrays)); // Points at d+1 correspond to the cones at d
685             PetscCall(PetscSectionGetChart(section_arrays[d], &pStart, &pEnd));
686             for (PetscInt p = pStart; p < pEnd; p++) {
687               PetscInt periodic_cone_size, periodic_cone_offset, periodic_point = periodic_point_arrays[p];
688 
689               PetscCall(PetscSectionGetDof(section, p, &periodic_cone_size));
690               PetscCall(PetscSectionGetOffset(section, p, &periodic_cone_offset));
691               const PetscInt *periodic_cone = &periodic_cone_arrays[periodic_cone_offset];
692               PetscCall(TranslateConeP2D(periodic_cone, periodic_cone_size, periodic2donor, p2d_count, p2d_cone));
693 
694               // Find the donor cone that matches the periodic point's cone
695               PetscInt  donor_cone_offset = 0, donor_point = -1, *donor_cone = NULL;
696               PetscBool cone_matches = PETSC_FALSE;
697               while (donor_cone_offset < cones_size - num_verts) {
698                 PetscInt donor_cone_size = donor_cone_array[donor_cone_offset];
699                 donor_point              = donor_cone_array[donor_cone_offset + 1];
700                 donor_cone               = &donor_cone_array[donor_cone_offset + 2];
701 
702                 if (donor_cone_size != periodic_cone_size) goto next_cone;
703                 for (PetscInt c = 0; c < periodic_cone_size; c++) {
704                   cone_matches = SearchIntArray(donor_cone[c], periodic_cone_size, p2d_cone);
705                   if (!cone_matches) goto next_cone;
706                 }
707                 // Save the found donor cone's point to the translation array. These will be used for higher depth points.
708                 // i.e. we save the edge translations for when we look for face cones
709                 periodic2donor[2 * p2d_count + 0] = periodic_point;
710                 periodic2donor[2 * p2d_count + 1] = donor_point;
711                 p2d_count++;
712                 break;
713 
714               next_cone:
715                 donor_cone_offset += donor_cone_size + 2;
716               }
717               PetscCheck(donor_cone_offset < cones_size - num_verts, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Could not find donor cone equivalent to cone of periodic point %" PetscInt_FMT, periodic_point);
718 
719               { // Compare the donor cone with the translated periodic cone and reorient
720                 PetscInt       ornt;
721                 DMPolytopeType cell_type;
722                 PetscBool      found;
723                 PetscCall(DMPlexGetCellType(dm, periodic_point, &cell_type));
724                 PetscCall(DMPolytopeMatchOrientation(cell_type, donor_cone, p2d_cone, &ornt, &found));
725                 PetscCheck(found, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Could not find transformation between donor (%" PetscInt_FMT ") and periodic (%" PetscInt_FMT ") cone's", periodic_point, donor_point);
726                 if (debug_printing) PetscCall(PetscPrintf(PETSC_COMM_SELF, "Reorienting point %" PetscInt_FMT " by %" PetscInt_FMT "\n", periodic_point, ornt));
727                 PetscCall(DMPlexOrientPointWithCorrections(dm, periodic_point, ornt));
728               }
729             }
730             PetscCall(ISRestoreIndices(is_arrays[d], &periodic_cone_arrays));
731             PetscCall(ISRestoreIndices(is_arrays[d + 1], &periodic_point_arrays));
732           }
733           PetscCall(DMRestoreWorkArray(dm, maxConeSize, MPIU_INT, &p2d_cone));
734           PetscCall(DMPlexRestoreConeRecursive(dm, face_is, &depth, &is_arrays, &section_arrays));
735         }
736 
737         PetscCall(DMPlexRestoreTransitiveClosure(dm, periodic_face, PETSC_TRUE, &cl_size, &closure));
738         cones_offset += cones_size;
739       }
740       PetscCall(DMRestoreWorkArray(dm, 2 * PetscPowInt(maxConeSize, dm_depth - 1), MPIU_INT, &periodic2donor));
741     }
742 
743     PetscCall(PetscFree2(leaf_donor_coords, leaf_donor_cones));
744     PetscCall(PetscFree2(face_vertices_size, face_cones_size));
745   }
746   PetscFunctionReturn(PETSC_SUCCESS);
747 }
748 
749 // Start with an SF for a positive depth (e.g., faces) and create a new SF for matched closure.
750 //
751 // Output Arguments:
752 //
753 // + closure_sf - augmented point SF (see `DMGetPointSF()`) that includes the faces and all points in its closure. This
754 //   can be used to create a global section and section SF.
755 // - is_points - array of index sets for just the points in the closure of `face_sf`. These may be used to apply an affine
756 //   transformation to periodic dofs; see DMPeriodicCoordinateSetUp_Internal().
757 //
758 static PetscErrorCode DMPlexCreateIsoperiodicPointSF_Private(DM dm, PetscInt num_face_sfs, PetscSF *face_sfs, PetscSF *closure_sf, IS **is_points)
759 {
760   MPI_Comm           comm;
761   PetscMPIInt        rank;
762   PetscSF            point_sf;
763   PetscInt           nroots, nleaves;
764   const PetscInt    *filocal;
765   const PetscSFNode *firemote;
766 
767   PetscFunctionBegin;
768   PetscCall(PetscObjectGetComm((PetscObject)dm, &comm));
769   PetscCallMPI(MPI_Comm_rank(comm, &rank));
770   PetscCall(DMGetPointSF(dm, &point_sf)); // Point SF has remote points
771   PetscCall(PetscMalloc1(num_face_sfs, is_points));
772 
773   PetscCall(DMPlexCorrectOrientationForIsoperiodic(dm));
774 
775   for (PetscInt f = 0; f < num_face_sfs; f++) {
776     PetscSF   face_sf = face_sfs[f];
777     PetscInt *cl_sizes;
778     PetscInt  fStart, fEnd, rootbuffersize, leafbuffersize;
779     PetscSF   sf_closure;
780     PetscBT   rootbt;
781 
782     PetscCall(DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd));
783     PetscCall(PetscMalloc1(fEnd - fStart, &cl_sizes));
784     for (PetscInt f = fStart, index = 0; f < fEnd; f++, index++) {
785       PetscInt cl_size, *closure = NULL;
786       PetscCall(DMPlexGetTransitiveClosure(dm, f, PETSC_TRUE, &cl_size, &closure));
787       cl_sizes[index] = cl_size - 1;
788       PetscCall(DMPlexRestoreTransitiveClosure(dm, f, PETSC_TRUE, &cl_size, &closure));
789     }
790 
791     PetscCall(CreateDonorToPeriodicSF(dm, face_sf, fStart, fEnd, cl_sizes, &rootbuffersize, &leafbuffersize, &rootbt, &sf_closure));
792     PetscCall(PetscFree(cl_sizes));
793     PetscCall(PetscSFGetGraph(face_sf, &nroots, &nleaves, &filocal, &firemote));
794 
795     PetscSFNode *leaf_donor_closure;
796     { // Pack root buffer with owner for every point in the root cones
797       PetscSFNode       *donor_closure;
798       const PetscInt    *pilocal;
799       const PetscSFNode *piremote;
800       PetscInt           npoints;
801 
802       PetscCall(PetscSFGetGraph(point_sf, NULL, &npoints, &pilocal, &piremote));
803       PetscCall(PetscCalloc1(rootbuffersize, &donor_closure));
804       for (PetscInt p = 0, root_offset = 0; p < nroots; p++) {
805         if (!PetscBTLookup(rootbt, p)) continue;
806         PetscInt cl_size, *closure = NULL;
807         PetscCall(DMPlexGetTransitiveClosure(dm, p, PETSC_TRUE, &cl_size, &closure));
808         for (PetscInt j = 1; j < cl_size; j++) {
809           PetscInt c = closure[2 * j];
810           if (pilocal) {
811             PetscInt found = -1;
812             if (npoints > 0) PetscCall(PetscFindInt(c, npoints, pilocal, &found));
813             if (found >= 0) {
814               donor_closure[root_offset++] = piremote[found];
815               continue;
816             }
817           }
818           // we own c
819           donor_closure[root_offset].rank  = rank;
820           donor_closure[root_offset].index = c;
821           root_offset++;
822         }
823         PetscCall(DMPlexRestoreTransitiveClosure(dm, p, PETSC_TRUE, &cl_size, &closure));
824       }
825 
826       PetscCall(PetscMalloc1(leafbuffersize, &leaf_donor_closure));
827       PetscCall(PetscSFBcastBegin(sf_closure, MPIU_SF_NODE, donor_closure, leaf_donor_closure, MPI_REPLACE));
828       PetscCall(PetscSFBcastEnd(sf_closure, MPIU_SF_NODE, donor_closure, leaf_donor_closure, MPI_REPLACE));
829       PetscCall(PetscSFDestroy(&sf_closure));
830       PetscCall(PetscFree(donor_closure));
831     }
832 
833     PetscSFNode *new_iremote;
834     PetscCall(PetscCalloc1(nroots, &new_iremote));
835     for (PetscInt i = 0; i < nroots; i++) new_iremote[i].rank = -1;
836     // Walk leaves and match vertices
837     for (PetscInt i = 0, leaf_offset = 0; i < nleaves; i++) {
838       PetscInt  point   = filocal[i], cl_size;
839       PetscInt *closure = NULL;
840       PetscCall(DMPlexGetTransitiveClosure(dm, point, PETSC_TRUE, &cl_size, &closure));
841       for (PetscInt j = 1; j < cl_size; j++) {
842         PetscInt    c  = closure[2 * j];
843         PetscSFNode lc = leaf_donor_closure[leaf_offset];
844         // printf("[%d] face %d.%d: %d ?-- (%d,%d)\n", rank, point, j, c, lc.rank, lc.index);
845         if (new_iremote[c].rank == -1) {
846           new_iremote[c] = lc;
847         } 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");
848         leaf_offset++;
849       }
850       PetscCall(DMPlexRestoreTransitiveClosure(dm, point, PETSC_TRUE, &cl_size, &closure));
851     }
852     PetscCall(PetscFree(leaf_donor_closure));
853 
854     // Include face points in closure SF
855     for (PetscInt i = 0; i < nleaves; i++) new_iremote[filocal[i]] = firemote[i];
856     // consolidate leaves
857     PetscInt *leafdata;
858     PetscCall(PetscMalloc1(nroots, &leafdata));
859     PetscInt num_new_leaves = 0;
860     for (PetscInt i = 0; i < nroots; i++) {
861       if (new_iremote[i].rank == -1) continue;
862       new_iremote[num_new_leaves] = new_iremote[i];
863       leafdata[num_new_leaves]    = i;
864       num_new_leaves++;
865     }
866     PetscCall(ISCreateGeneral(PETSC_COMM_SELF, num_new_leaves, leafdata, PETSC_COPY_VALUES, &(*is_points)[f]));
867 
868     PetscSF csf;
869     PetscCall(PetscSFCreate(comm, &csf));
870     PetscCall(PetscSFSetGraph(csf, nroots, num_new_leaves, leafdata, PETSC_COPY_VALUES, new_iremote, PETSC_COPY_VALUES));
871     PetscCall(PetscFree(new_iremote)); // copy and delete because new_iremote is longer than it needs to be
872     PetscCall(PetscFree(leafdata));
873     PetscCall(PetscBTDestroy(&rootbt));
874 
875     PetscInt npoints;
876     PetscCall(PetscSFGetGraph(point_sf, NULL, &npoints, NULL, NULL));
877     if (npoints < 0) { // empty point_sf
878       *closure_sf = csf;
879     } else {
880       PetscCall(PetscSFMerge(point_sf, csf, closure_sf));
881       PetscCall(PetscSFDestroy(&csf));
882     }
883     if (f > 0) PetscCall(PetscSFDestroy(&point_sf)); // Only destroy if point_sf is from previous calls to PetscSFMerge
884     point_sf = *closure_sf;                          // Use combined point + isoperiodic SF to define point ownership for further face_sf
885   }
886   PetscCall(PetscObjectSetName((PetscObject)*closure_sf, "Composed Periodic Points"));
887   PetscFunctionReturn(PETSC_SUCCESS);
888 }
889 
890 static PetscErrorCode DMGetIsoperiodicPointSF_Plex(DM dm, PetscSF *sf)
891 {
892   DM_Plex *plex = (DM_Plex *)dm->data;
893 
894   PetscFunctionBegin;
895   if (!plex->periodic.composed_sf) PetscCall(DMPlexCreateIsoperiodicPointSF_Private(dm, plex->periodic.num_face_sfs, plex->periodic.face_sfs, &plex->periodic.composed_sf, &plex->periodic.periodic_points));
896   if (sf) *sf = plex->periodic.composed_sf;
897   PetscFunctionReturn(PETSC_SUCCESS);
898 }
899 
900 PetscErrorCode DMPlexMigrateIsoperiodicFaceSF_Internal(DM old_dm, DM dm, PetscSF sf_migration)
901 {
902   DM_Plex    *plex = (DM_Plex *)old_dm->data;
903   PetscSF     sf_point, *new_face_sfs;
904   PetscMPIInt rank;
905 
906   PetscFunctionBegin;
907   if (!plex->periodic.face_sfs) PetscFunctionReturn(PETSC_SUCCESS);
908   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank));
909   PetscCall(DMGetPointSF(dm, &sf_point));
910   PetscCall(PetscMalloc1(plex->periodic.num_face_sfs, &new_face_sfs));
911 
912   for (PetscInt f = 0; f < plex->periodic.num_face_sfs; f++) {
913     PetscInt           old_npoints, new_npoints, old_nleaf, new_nleaf, point_nleaf;
914     PetscSFNode       *new_leafdata, *rootdata, *leafdata;
915     const PetscInt    *old_local, *point_local;
916     const PetscSFNode *old_remote, *point_remote;
917 
918     PetscCall(PetscSFGetGraph(plex->periodic.face_sfs[f], &old_npoints, &old_nleaf, &old_local, &old_remote));
919     PetscCall(PetscSFGetGraph(sf_migration, NULL, &new_nleaf, NULL, NULL));
920     PetscCall(PetscSFGetGraph(sf_point, &new_npoints, &point_nleaf, &point_local, &point_remote));
921     PetscAssert(new_nleaf == new_npoints, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Expected migration leaf space to match new point root space");
922     PetscCall(PetscMalloc3(old_npoints, &rootdata, old_npoints, &leafdata, new_npoints, &new_leafdata));
923 
924     // Fill new_leafdata with new owners of all points
925     for (PetscInt i = 0; i < new_npoints; i++) {
926       new_leafdata[i].rank  = rank;
927       new_leafdata[i].index = i;
928     }
929     for (PetscInt i = 0; i < point_nleaf; i++) {
930       PetscInt j      = point_local[i];
931       new_leafdata[j] = point_remote[i];
932     }
933     // REPLACE is okay because every leaf agrees about the new owners
934     PetscCall(PetscSFReduceBegin(sf_migration, MPIU_SF_NODE, new_leafdata, rootdata, MPI_REPLACE));
935     PetscCall(PetscSFReduceEnd(sf_migration, MPIU_SF_NODE, new_leafdata, rootdata, MPI_REPLACE));
936     // rootdata now contains the new owners
937 
938     // Send to leaves of old space
939     for (PetscInt i = 0; i < old_npoints; i++) {
940       leafdata[i].rank  = -1;
941       leafdata[i].index = -1;
942     }
943     PetscCall(PetscSFBcastBegin(plex->periodic.face_sfs[f], MPIU_SF_NODE, rootdata, leafdata, MPI_REPLACE));
944     PetscCall(PetscSFBcastEnd(plex->periodic.face_sfs[f], MPIU_SF_NODE, rootdata, leafdata, MPI_REPLACE));
945 
946     // Send to new leaf space
947     PetscCall(PetscSFBcastBegin(sf_migration, MPIU_SF_NODE, leafdata, new_leafdata, MPI_REPLACE));
948     PetscCall(PetscSFBcastEnd(sf_migration, MPIU_SF_NODE, leafdata, new_leafdata, MPI_REPLACE));
949 
950     PetscInt     nface = 0, *new_local;
951     PetscSFNode *new_remote;
952     for (PetscInt i = 0; i < new_npoints; i++) nface += (new_leafdata[i].rank >= 0);
953     PetscCall(PetscMalloc1(nface, &new_local));
954     PetscCall(PetscMalloc1(nface, &new_remote));
955     nface = 0;
956     for (PetscInt i = 0; i < new_npoints; i++) {
957       if (new_leafdata[i].rank == -1) continue;
958       new_local[nface]  = i;
959       new_remote[nface] = new_leafdata[i];
960       nface++;
961     }
962     PetscCall(PetscFree3(rootdata, leafdata, new_leafdata));
963     PetscCall(PetscSFCreate(PetscObjectComm((PetscObject)dm), &new_face_sfs[f]));
964     PetscCall(PetscSFSetGraph(new_face_sfs[f], new_npoints, nface, new_local, PETSC_OWN_POINTER, new_remote, PETSC_OWN_POINTER));
965     {
966       char new_face_sf_name[PETSC_MAX_PATH_LEN];
967       PetscCall(PetscSNPrintf(new_face_sf_name, sizeof new_face_sf_name, "Migrated Isoperiodic Faces #%" PetscInt_FMT, f));
968       PetscCall(PetscObjectSetName((PetscObject)new_face_sfs[f], new_face_sf_name));
969     }
970   }
971 
972   PetscCall(DMPlexSetIsoperiodicFaceSF(dm, plex->periodic.num_face_sfs, new_face_sfs));
973   PetscCall(DMPlexSetIsoperiodicFaceTransform(dm, plex->periodic.num_face_sfs, (PetscScalar *)plex->periodic.transform));
974   for (PetscInt f = 0; f < plex->periodic.num_face_sfs; f++) PetscCall(PetscSFDestroy(&new_face_sfs[f]));
975   PetscCall(PetscFree(new_face_sfs));
976   PetscFunctionReturn(PETSC_SUCCESS);
977 }
978 
979 PetscErrorCode DMPeriodicCoordinateSetUp_Internal(DM dm)
980 {
981   DM_Plex   *plex = (DM_Plex *)dm->data;
982   PetscCount count;
983   IS         isdof;
984   PetscInt   dim;
985 
986   PetscFunctionBegin;
987   if (!plex->periodic.face_sfs) PetscFunctionReturn(PETSC_SUCCESS);
988   PetscCheck(plex->periodic.periodic_points, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Isoperiodic PointSF must be created before this function is called");
989 
990   PetscCall(DMGetCoordinateDim(dm, &dim));
991   dm->periodic.num_affines = plex->periodic.num_face_sfs;
992   PetscCall(PetscFree2(dm->periodic.affine_to_local, dm->periodic.affine));
993   PetscCall(PetscMalloc2(dm->periodic.num_affines, &dm->periodic.affine_to_local, dm->periodic.num_affines, &dm->periodic.affine));
994 
995   for (PetscInt f = 0; f < plex->periodic.num_face_sfs; f++) {
996     PetscInt        npoints, vsize, isize;
997     const PetscInt *points;
998     IS              is = plex->periodic.periodic_points[f];
999     PetscSegBuffer  seg;
1000     PetscSection    section;
1001     PetscInt       *ind;
1002     Vec             L, P;
1003     VecType         vec_type;
1004     VecScatter      scatter;
1005     PetscScalar    *x;
1006 
1007     PetscCall(DMGetLocalSection(dm, &section));
1008     PetscCall(PetscSegBufferCreate(sizeof(PetscInt), 32, &seg));
1009     PetscCall(ISGetSize(is, &npoints));
1010     PetscCall(ISGetIndices(is, &points));
1011     for (PetscInt i = 0; i < npoints; i++) {
1012       PetscInt point = points[i], off, dof;
1013 
1014       PetscCall(PetscSectionGetOffset(section, point, &off));
1015       PetscCall(PetscSectionGetDof(section, point, &dof));
1016       PetscAssert(dof % dim == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Unexpected dof %" PetscInt_FMT " not divisible by dimension %" PetscInt_FMT, dof, dim);
1017       for (PetscInt j = 0; j < dof / dim; j++) {
1018         PetscInt *slot;
1019 
1020         PetscCall(PetscSegBufferGetInts(seg, 1, &slot));
1021         *slot = off / dim + j;
1022       }
1023     }
1024     PetscCall(PetscSegBufferGetSize(seg, &count));
1025     PetscCall(PetscSegBufferExtractAlloc(seg, &ind));
1026     PetscCall(PetscSegBufferDestroy(&seg));
1027     PetscCall(PetscIntCast(count, &isize));
1028     PetscCall(ISCreateBlock(PETSC_COMM_SELF, dim, isize, ind, PETSC_OWN_POINTER, &isdof));
1029 
1030     PetscCall(PetscIntCast(count * dim, &vsize));
1031     PetscCall(DMGetLocalVector(dm, &L));
1032     PetscCall(VecCreate(PETSC_COMM_SELF, &P));
1033     PetscCall(VecSetSizes(P, vsize, vsize));
1034     PetscCall(VecGetType(L, &vec_type));
1035     PetscCall(VecSetType(P, vec_type));
1036     PetscCall(VecScatterCreate(P, NULL, L, isdof, &scatter));
1037     PetscCall(DMRestoreLocalVector(dm, &L));
1038     PetscCall(ISDestroy(&isdof));
1039 
1040     PetscCall(VecGetArrayWrite(P, &x));
1041     for (PetscCount i = 0; i < count; i++) {
1042       for (PetscInt j = 0; j < dim; j++) x[i * dim + j] = plex->periodic.transform[f][j][3];
1043     }
1044     PetscCall(VecRestoreArrayWrite(P, &x));
1045 
1046     dm->periodic.affine_to_local[f] = scatter;
1047     dm->periodic.affine[f]          = P;
1048   }
1049   PetscCall(DMGlobalToLocalHookAdd(dm, NULL, DMCoordAddPeriodicOffsets_Private, NULL));
1050   PetscFunctionReturn(PETSC_SUCCESS);
1051 }
1052 
1053 PetscErrorCode DMPlexCreateBoxMesh_Tensor_SFC_Internal(DM dm, PetscInt dim, const PetscInt faces[], const PetscReal lower[], const PetscReal upper[], const DMBoundaryType periodicity[], PetscBool interpolate)
1054 {
1055   PetscInt  eextent[3] = {1, 1, 1}, vextent[3] = {1, 1, 1};
1056   const Ijk closure_1[] = {
1057     {0, 0, 0},
1058     {1, 0, 0},
1059   };
1060   const Ijk closure_2[] = {
1061     {0, 0, 0},
1062     {1, 0, 0},
1063     {1, 1, 0},
1064     {0, 1, 0},
1065   };
1066   const Ijk closure_3[] = {
1067     {0, 0, 0},
1068     {0, 1, 0},
1069     {1, 1, 0},
1070     {1, 0, 0},
1071     {0, 0, 1},
1072     {1, 0, 1},
1073     {1, 1, 1},
1074     {0, 1, 1},
1075   };
1076   const Ijk *const closure_dim[] = {NULL, closure_1, closure_2, closure_3};
1077   // This must be kept consistent with DMPlexCreateCubeMesh_Internal
1078   const PetscInt        face_marker_1[]   = {1, 2};
1079   const PetscInt        face_marker_2[]   = {4, 2, 1, 3};
1080   const PetscInt        face_marker_3[]   = {6, 5, 3, 4, 1, 2};
1081   const PetscInt *const face_marker_dim[] = {NULL, face_marker_1, face_marker_2, face_marker_3};
1082   // Orient faces so the normal is in the positive axis and the first vertex is the one closest to zero.
1083   // These orientations can be determined by examining cones of a reference quad and hex element.
1084   const PetscInt        face_orient_1[]   = {0, 0};
1085   const PetscInt        face_orient_2[]   = {-1, 0, 0, -1};
1086   const PetscInt        face_orient_3[]   = {-2, 0, -2, 1, -2, 0};
1087   const PetscInt *const face_orient_dim[] = {NULL, face_orient_1, face_orient_2, face_orient_3};
1088 
1089   PetscFunctionBegin;
1090   PetscCall(PetscLogEventBegin(DMPLEX_CreateBoxSFC, dm, 0, 0, 0));
1091   PetscAssertPointer(dm, 1);
1092   PetscValidLogicalCollectiveInt(dm, dim, 2);
1093   PetscCall(DMSetDimension(dm, dim));
1094   PetscMPIInt rank, size;
1095   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)dm), &size));
1096   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank));
1097   for (PetscInt i = 0; i < dim; i++) {
1098     eextent[i] = faces[i];
1099     vextent[i] = faces[i] + 1;
1100   }
1101   ZLayout layout;
1102   PetscCall(ZLayoutCreate(size, eextent, vextent, &layout));
1103   PetscZSet vset; // set of all vertices in the closure of the owned elements
1104   PetscCall(PetscZSetCreate(&vset));
1105   PetscInt local_elems = 0;
1106   for (ZCode z = layout.zstarts[rank]; z < layout.zstarts[rank + 1]; z++) {
1107     Ijk loc = ZCodeSplit(z);
1108     if (IjkActive(layout.vextent, loc)) PetscCall(PetscZSetAdd(vset, z));
1109     else {
1110       z += ZStepOct(z);
1111       continue;
1112     }
1113     if (IjkActive(layout.eextent, loc)) {
1114       local_elems++;
1115       // Add all neighboring vertices to set
1116       for (PetscInt n = 0; n < PetscPowInt(2, dim); n++) {
1117         Ijk   inc  = closure_dim[dim][n];
1118         Ijk   nloc = {loc.i + inc.i, loc.j + inc.j, loc.k + inc.k};
1119         ZCode v    = ZEncode(nloc);
1120         PetscCall(PetscZSetAdd(vset, v));
1121       }
1122     }
1123   }
1124   PetscInt local_verts, off = 0;
1125   ZCode   *vert_z;
1126   PetscCall(PetscZSetGetSize(vset, &local_verts));
1127   PetscCall(PetscMalloc1(local_verts, &vert_z));
1128   PetscCall(PetscZSetGetElems(vset, &off, vert_z));
1129   PetscCall(PetscZSetDestroy(&vset));
1130   // ZCode is unsigned for bitwise convenience, but highest bit should never be set, so can interpret as signed
1131   PetscCall(PetscSortInt64(local_verts, (PetscInt64 *)vert_z));
1132 
1133   PetscCall(DMPlexSetChart(dm, 0, local_elems + local_verts));
1134   for (PetscInt e = 0; e < local_elems; e++) PetscCall(DMPlexSetConeSize(dm, e, PetscPowInt(2, dim)));
1135   PetscCall(DMSetUp(dm));
1136   {
1137     PetscInt e = 0;
1138     for (ZCode z = layout.zstarts[rank]; z < layout.zstarts[rank + 1]; z++) {
1139       Ijk loc = ZCodeSplit(z);
1140       if (!IjkActive(layout.eextent, loc)) {
1141         z += ZStepOct(z);
1142         continue;
1143       }
1144       PetscInt cone[8], orient[8] = {0};
1145       for (PetscInt n = 0; n < PetscPowInt(2, dim); n++) {
1146         Ijk      inc  = closure_dim[dim][n];
1147         Ijk      nloc = {loc.i + inc.i, loc.j + inc.j, loc.k + inc.k};
1148         ZCode    v    = ZEncode(nloc);
1149         PetscInt ci   = ZCodeFind(v, local_verts, vert_z);
1150         PetscAssert(ci >= 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Did not find neighbor vertex in set");
1151         cone[n] = local_elems + ci;
1152       }
1153       PetscCall(DMPlexSetCone(dm, e, cone));
1154       PetscCall(DMPlexSetConeOrientation(dm, e, orient));
1155       e++;
1156     }
1157   }
1158 
1159   PetscCall(DMPlexSymmetrize(dm));
1160   PetscCall(DMPlexStratify(dm));
1161 
1162   { // Create point SF
1163     PetscSF sf;
1164     PetscCall(PetscSFCreate(PetscObjectComm((PetscObject)dm), &sf));
1165     PetscInt owned_verts = ZCodeFind(layout.zstarts[rank + 1], local_verts, vert_z);
1166     if (owned_verts < 0) owned_verts = -(owned_verts + 1); // We don't care whether the key was found
1167     PetscInt     num_ghosts = local_verts - owned_verts;   // Due to sorting, owned vertices always come first
1168     PetscInt    *local_ghosts;
1169     PetscSFNode *ghosts;
1170     PetscCall(PetscMalloc1(num_ghosts, &local_ghosts));
1171     PetscCall(PetscMalloc1(num_ghosts, &ghosts));
1172     for (PetscInt i = 0; i < num_ghosts;) {
1173       ZCode       z = vert_z[owned_verts + i];
1174       PetscMPIInt remote_rank, remote_count = 0;
1175 
1176       PetscCall(PetscMPIIntCast(ZCodeFind(z, size + 1, layout.zstarts), &remote_rank));
1177       if (remote_rank < 0) remote_rank = -(remote_rank + 1) - 1;
1178       // We have a new remote rank; find all the ghost indices (which are contiguous in vert_z)
1179 
1180       // Count the elements on remote_rank
1181       PetscInt remote_elem = ZLayoutElementsOnRank(&layout, remote_rank);
1182 
1183       // Traverse vertices and make ghost links
1184       for (ZCode rz = layout.zstarts[remote_rank]; rz < layout.zstarts[remote_rank + 1]; rz++) {
1185         Ijk loc = ZCodeSplit(rz);
1186         if (rz == z) {
1187           local_ghosts[i] = local_elems + owned_verts + i;
1188           ghosts[i].rank  = remote_rank;
1189           ghosts[i].index = remote_elem + remote_count;
1190           i++;
1191           if (i == num_ghosts) break;
1192           z = vert_z[owned_verts + i];
1193         }
1194         if (IjkActive(layout.vextent, loc)) remote_count++;
1195         else rz += ZStepOct(rz);
1196       }
1197     }
1198     PetscCall(PetscSFSetGraph(sf, local_elems + local_verts, num_ghosts, local_ghosts, PETSC_OWN_POINTER, ghosts, PETSC_OWN_POINTER));
1199     PetscCall(PetscObjectSetName((PetscObject)sf, "SFC Point SF"));
1200     PetscCall(DMSetPointSF(dm, sf));
1201     PetscCall(PetscSFDestroy(&sf));
1202   }
1203   {
1204     Vec          coordinates;
1205     PetscScalar *coords;
1206     PetscSection coord_section;
1207     PetscInt     coord_size;
1208     PetscCall(DMGetCoordinateSection(dm, &coord_section));
1209     PetscCall(PetscSectionSetNumFields(coord_section, 1));
1210     PetscCall(PetscSectionSetFieldComponents(coord_section, 0, dim));
1211     PetscCall(PetscSectionSetChart(coord_section, local_elems, local_elems + local_verts));
1212     for (PetscInt v = 0; v < local_verts; v++) {
1213       PetscInt point = local_elems + v;
1214       PetscCall(PetscSectionSetDof(coord_section, point, dim));
1215       PetscCall(PetscSectionSetFieldDof(coord_section, point, 0, dim));
1216     }
1217     PetscCall(PetscSectionSetUp(coord_section));
1218     PetscCall(PetscSectionGetStorageSize(coord_section, &coord_size));
1219     PetscCall(VecCreate(PETSC_COMM_SELF, &coordinates));
1220     PetscCall(PetscObjectSetName((PetscObject)coordinates, "coordinates"));
1221     PetscCall(VecSetSizes(coordinates, coord_size, PETSC_DETERMINE));
1222     PetscCall(VecSetBlockSize(coordinates, dim));
1223     PetscCall(VecSetType(coordinates, VECSTANDARD));
1224     PetscCall(VecGetArray(coordinates, &coords));
1225     for (PetscInt v = 0; v < local_verts; v++) {
1226       Ijk loc             = ZCodeSplit(vert_z[v]);
1227       coords[v * dim + 0] = lower[0] + loc.i * (upper[0] - lower[0]) / layout.eextent.i;
1228       if (dim > 1) coords[v * dim + 1] = lower[1] + loc.j * (upper[1] - lower[1]) / layout.eextent.j;
1229       if (dim > 2) coords[v * dim + 2] = lower[2] + loc.k * (upper[2] - lower[2]) / layout.eextent.k;
1230     }
1231     PetscCall(VecRestoreArray(coordinates, &coords));
1232     PetscCall(DMSetCoordinatesLocal(dm, coordinates));
1233     PetscCall(VecDestroy(&coordinates));
1234   }
1235   if (interpolate) {
1236     PetscCall(DMPlexInterpolateInPlace_Internal(dm));
1237 
1238     DMLabel label;
1239     PetscCall(DMCreateLabel(dm, "Face Sets"));
1240     PetscCall(DMGetLabel(dm, "Face Sets", &label));
1241     PetscSegBuffer per_faces[3], donor_face_closure[3], my_donor_faces[3];
1242     for (PetscInt i = 0; i < 3; i++) {
1243       PetscCall(PetscSegBufferCreate(sizeof(PetscInt), 64, &per_faces[i]));
1244       PetscCall(PetscSegBufferCreate(sizeof(PetscInt), 64, &my_donor_faces[i]));
1245       PetscCall(PetscSegBufferCreate(sizeof(ZCode), 64 * PetscPowInt(2, dim), &donor_face_closure[i]));
1246     }
1247     PetscInt fStart, fEnd, vStart, vEnd;
1248     PetscCall(DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd));
1249     PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
1250     for (PetscInt f = fStart; f < fEnd; f++) {
1251       PetscInt npoints, *points = NULL, num_fverts = 0, fverts[8];
1252       PetscCall(DMPlexGetTransitiveClosure(dm, f, PETSC_TRUE, &npoints, &points));
1253       PetscInt bc_count[6] = {0};
1254       for (PetscInt i = 0; i < npoints; i++) {
1255         PetscInt p = points[2 * i];
1256         if (!IsPointInsideStratum(p, vStart, vEnd)) continue;
1257         fverts[num_fverts++] = p;
1258         Ijk loc              = ZCodeSplit(vert_z[p - vStart]);
1259         // Convention here matches DMPlexCreateCubeMesh_Internal
1260         bc_count[0] += loc.i == 0;
1261         bc_count[1] += loc.i == layout.vextent.i - 1;
1262         bc_count[2] += loc.j == 0;
1263         bc_count[3] += loc.j == layout.vextent.j - 1;
1264         bc_count[4] += loc.k == 0;
1265         bc_count[5] += loc.k == layout.vextent.k - 1;
1266       }
1267       PetscCall(DMPlexRestoreTransitiveClosure(dm, f, PETSC_TRUE, &npoints, &points));
1268       for (PetscInt bc = 0, bc_match = 0; bc < 2 * dim; bc++) {
1269         if (bc_count[bc] == PetscPowInt(2, dim - 1)) {
1270           PetscCall(DMPlexOrientPoint(dm, f, face_orient_dim[dim][bc]));
1271           if (periodicity[bc / 2] == DM_BOUNDARY_PERIODIC) {
1272             PetscInt *put;
1273             if (bc % 2 == 0) { // donor face; no label
1274               PetscCall(PetscSegBufferGet(my_donor_faces[bc / 2], 1, &put));
1275               *put = f;
1276             } else { // periodic face
1277               PetscCall(PetscSegBufferGet(per_faces[bc / 2], 1, &put));
1278               *put = f;
1279               ZCode *zput;
1280               PetscCall(PetscSegBufferGet(donor_face_closure[bc / 2], num_fverts, &zput));
1281               for (PetscInt i = 0; i < num_fverts; i++) {
1282                 Ijk loc = ZCodeSplit(vert_z[fverts[i] - vStart]);
1283                 switch (bc / 2) {
1284                 case 0:
1285                   loc.i = 0;
1286                   break;
1287                 case 1:
1288                   loc.j = 0;
1289                   break;
1290                 case 2:
1291                   loc.k = 0;
1292                   break;
1293                 }
1294                 *zput++ = ZEncode(loc);
1295               }
1296             }
1297             continue;
1298           }
1299           PetscAssert(bc_match == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Face matches multiple face sets");
1300           PetscCall(DMLabelSetValue(label, f, face_marker_dim[dim][bc]));
1301           bc_match++;
1302         }
1303       }
1304     }
1305     // Ensure that the Coordinate DM has our new boundary labels
1306     DM cdm;
1307     PetscCall(DMGetCoordinateDM(dm, &cdm));
1308     PetscCall(DMCopyLabels(dm, cdm, PETSC_COPY_VALUES, PETSC_FALSE, DM_COPY_LABELS_FAIL));
1309     if (periodicity[0] == DM_BOUNDARY_PERIODIC || (dim > 1 && periodicity[1] == DM_BOUNDARY_PERIODIC) || (dim > 2 && periodicity[2] == DM_BOUNDARY_PERIODIC)) {
1310       PetscCall(DMPlexCreateBoxMesh_Tensor_SFC_Periodicity_Private(dm, &layout, vert_z, per_faces, lower, upper, periodicity, donor_face_closure, my_donor_faces));
1311     }
1312     for (PetscInt i = 0; i < 3; i++) {
1313       PetscCall(PetscSegBufferDestroy(&per_faces[i]));
1314       PetscCall(PetscSegBufferDestroy(&donor_face_closure[i]));
1315       PetscCall(PetscSegBufferDestroy(&my_donor_faces[i]));
1316     }
1317   }
1318   PetscCall(PetscFree(layout.zstarts));
1319   PetscCall(PetscFree(vert_z));
1320   PetscCall(PetscLogEventEnd(DMPLEX_CreateBoxSFC, dm, 0, 0, 0));
1321   PetscFunctionReturn(PETSC_SUCCESS);
1322 }
1323 
1324 /*@
1325   DMPlexSetIsoperiodicFaceSF - Express periodicity from an existing mesh
1326 
1327   Logically Collective
1328 
1329   Input Parameters:
1330 + dm           - The `DMPLEX` on which to set periodicity
1331 . num_face_sfs - Number of `PetscSF`s in `face_sfs`
1332 - face_sfs     - Array of `PetscSF` in which roots are (owned) donor faces and leaves are faces that must be matched to a (possibly remote) donor face.
1333 
1334   Level: advanced
1335 
1336   Note:
1337   One can use `-dm_plex_shape zbox` to use this mode of periodicity, wherein the periodic points are distinct both globally
1338   and locally, but are paired when creating a global dof space.
1339 
1340 .seealso: [](ch_unstructured), `DMPLEX`, `DMGetGlobalSection()`, `DMPlexGetIsoperiodicFaceSF()`
1341 @*/
1342 PetscErrorCode DMPlexSetIsoperiodicFaceSF(DM dm, PetscInt num_face_sfs, PetscSF *face_sfs)
1343 {
1344   DM_Plex *plex = (DM_Plex *)dm->data;
1345 
1346   PetscFunctionBegin;
1347   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1348   if (num_face_sfs) PetscCall(PetscObjectComposeFunction((PetscObject)dm, "DMGetIsoperiodicPointSF_C", DMGetIsoperiodicPointSF_Plex));
1349   else PetscCall(PetscObjectComposeFunction((PetscObject)dm, "DMGetIsoperiodicPointSF_C", NULL));
1350   if (num_face_sfs == plex->periodic.num_face_sfs && (num_face_sfs == 0 || face_sfs == plex->periodic.face_sfs)) PetscFunctionReturn(PETSC_SUCCESS);
1351   PetscCall(DMSetGlobalSection(dm, NULL));
1352 
1353   for (PetscInt i = 0; i < num_face_sfs; i++) PetscCall(PetscObjectReference((PetscObject)face_sfs[i]));
1354 
1355   if (plex->periodic.num_face_sfs > 0) {
1356     for (PetscInt i = 0; i < plex->periodic.num_face_sfs; i++) PetscCall(PetscSFDestroy(&plex->periodic.face_sfs[i]));
1357     PetscCall(PetscFree(plex->periodic.face_sfs));
1358   }
1359 
1360   plex->periodic.num_face_sfs = num_face_sfs;
1361   PetscCall(PetscCalloc1(num_face_sfs, &plex->periodic.face_sfs));
1362   for (PetscInt i = 0; i < num_face_sfs; i++) plex->periodic.face_sfs[i] = face_sfs[i];
1363 
1364   DM cdm = dm->coordinates[0].dm; // Can't DMGetCoordinateDM because it automatically creates one
1365   if (cdm) {
1366     PetscCall(DMPlexSetIsoperiodicFaceSF(cdm, num_face_sfs, face_sfs));
1367     if (face_sfs) cdm->periodic.setup = DMPeriodicCoordinateSetUp_Internal;
1368   }
1369   PetscFunctionReturn(PETSC_SUCCESS);
1370 }
1371 
1372 /*@C
1373   DMPlexGetIsoperiodicFaceSF - Obtain periodicity for a mesh
1374 
1375   Logically Collective
1376 
1377   Input Parameter:
1378 . dm - The `DMPLEX` for which to obtain periodic relation
1379 
1380   Output Parameters:
1381 + num_face_sfs - Number of `PetscSF`s in the array
1382 - face_sfs     - Array of `PetscSF` in which roots are (owned) donor faces and leaves are faces that must be matched to a (possibly remote) donor face.
1383 
1384   Level: advanced
1385 
1386 .seealso: [](ch_unstructured), `DMPLEX`, `DMGetGlobalSection()`, `DMPlexSetIsoperiodicFaceSF()`
1387 @*/
1388 PetscErrorCode DMPlexGetIsoperiodicFaceSF(DM dm, PetscInt *num_face_sfs, const PetscSF **face_sfs)
1389 {
1390   DM_Plex *plex = (DM_Plex *)dm->data;
1391 
1392   PetscFunctionBegin;
1393   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1394   *face_sfs     = plex->periodic.face_sfs;
1395   *num_face_sfs = plex->periodic.num_face_sfs;
1396   PetscFunctionReturn(PETSC_SUCCESS);
1397 }
1398 
1399 /*@C
1400   DMPlexSetIsoperiodicFaceTransform - set geometric transform from donor to periodic points
1401 
1402   Logically Collective
1403 
1404   Input Parameters:
1405 + dm - `DMPLEX` that has been configured with `DMPlexSetIsoperiodicFaceSF()`
1406 . n  - Number of transforms in array
1407 - t  - Array of 4x4 affine transformation basis.
1408 
1409   Level: advanced
1410 
1411   Notes:
1412   Affine transforms are 4x4 matrices in which the leading 3x3 block expresses a rotation (or identity for no rotation),
1413   the last column contains a translation vector, and the bottom row is all zero except the last entry, which must always
1414   be 1. This representation is common in geometric modeling and allows affine transformations to be composed using
1415   simple matrix multiplication.
1416 
1417   Although the interface accepts a general affine transform, only affine translation is supported at present.
1418 
1419   Developer Notes:
1420   This interface should be replaced by making BasisTransform public, expanding it to support affine representations, and
1421   adding GPU implementations to apply the G2L/L2G transforms.
1422 
1423 .seealso: [](ch_unstructured), `DMPLEX`, `DMGetGlobalSection()`, `DMPlexSetIsoperiodicFaceSF()`
1424 @*/
1425 PetscErrorCode DMPlexSetIsoperiodicFaceTransform(DM dm, PetscInt n, const PetscScalar t[])
1426 {
1427   DM_Plex *plex = (DM_Plex *)dm->data;
1428 
1429   PetscFunctionBegin;
1430   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1431   PetscCheck(n == plex->periodic.num_face_sfs, PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "Number of transforms (%" PetscInt_FMT ") must equal number of isoperiodc face SFs (%" PetscInt_FMT ")", n, plex->periodic.num_face_sfs);
1432 
1433   PetscCall(PetscFree(plex->periodic.transform));
1434   PetscCall(PetscMalloc1(n, &plex->periodic.transform));
1435   for (PetscInt i = 0; i < n; i++) {
1436     for (PetscInt j = 0; j < 4; j++) {
1437       for (PetscInt k = 0; k < 4; k++) {
1438         PetscCheck(j != k || t[i * 16 + j * 4 + k] == 1., PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Rotated transforms not supported");
1439         plex->periodic.transform[i][j][k] = t[i * 16 + j * 4 + k];
1440       }
1441     }
1442   }
1443   PetscFunctionReturn(PETSC_SUCCESS);
1444 }
1445