xref: /petsc/src/dm/impls/plex/plexcreate.c (revision 1df12153c015c3bd9652822fec3328bd993d376b)
1 #define PETSCDM_DLL
2 #include <petsc/private/dmpleximpl.h> /*I   "petscdmplex.h"   I*/
3 #include <petsc/private/hashseti.h>   /*I   "petscdmplex.h"   I*/
4 #include <petscsf.h>
5 #include <petscdmplextransform.h>
6 #include <petscdmlabelephemeral.h>
7 #include <petsc/private/kernels/blockmatmult.h>
8 #include <petsc/private/kernels/blockinvert.h>
9 
10 PetscLogEvent DMPLEX_CreateFromFile, DMPLEX_CreateFromOptions, DMPLEX_BuildFromCellList, DMPLEX_BuildCoordinatesFromCellList;
11 
12 /* External function declarations here */
13 static PetscErrorCode DMInitialize_Plex(DM dm);
14 
15 /* This copies internal things in the Plex structure that we generally want when making a new, related Plex */
16 PetscErrorCode DMPlexCopy_Internal(DM dmin, PetscBool copyPeriodicity, PetscBool copyOverlap, DM dmout)
17 {
18   const PetscReal         *maxCell, *Lstart, *L;
19   VecType                  vecType;
20   MatType                  matType;
21   PetscBool                dist, useCeed;
22   DMPlexReorderDefaultFlag reorder;
23 
24   PetscFunctionBegin;
25   PetscCall(DMGetVecType(dmin, &vecType));
26   PetscCall(DMSetVecType(dmout, vecType));
27   PetscCall(DMGetMatType(dmin, &matType));
28   PetscCall(DMSetMatType(dmout, matType));
29   if (copyPeriodicity) {
30     PetscCall(DMGetPeriodicity(dmin, &maxCell, &Lstart, &L));
31     PetscCall(DMSetPeriodicity(dmout, maxCell, Lstart, L));
32   }
33   PetscCall(DMPlexDistributeGetDefault(dmin, &dist));
34   PetscCall(DMPlexDistributeSetDefault(dmout, dist));
35   PetscCall(DMPlexReorderGetDefault(dmin, &reorder));
36   PetscCall(DMPlexReorderSetDefault(dmout, reorder));
37   PetscCall(DMPlexGetUseCeed(dmin, &useCeed));
38   PetscCall(DMPlexSetUseCeed(dmout, useCeed));
39   ((DM_Plex *)dmout->data)->useHashLocation = ((DM_Plex *)dmin->data)->useHashLocation;
40   ((DM_Plex *)dmout->data)->printSetValues  = ((DM_Plex *)dmin->data)->printSetValues;
41   ((DM_Plex *)dmout->data)->printFEM        = ((DM_Plex *)dmin->data)->printFEM;
42   ((DM_Plex *)dmout->data)->printFVM        = ((DM_Plex *)dmin->data)->printFVM;
43   ((DM_Plex *)dmout->data)->printL2         = ((DM_Plex *)dmin->data)->printL2;
44   ((DM_Plex *)dmout->data)->printLocate     = ((DM_Plex *)dmin->data)->printLocate;
45   ((DM_Plex *)dmout->data)->printTol        = ((DM_Plex *)dmin->data)->printTol;
46   if (copyOverlap) PetscCall(DMPlexSetOverlap_Plex(dmout, dmin, 0));
47   PetscFunctionReturn(PETSC_SUCCESS);
48 }
49 
50 /* Replace dm with the contents of ndm, and then destroy ndm
51    - Share the DM_Plex structure
52    - Share the coordinates
53    - Share the SF
54 */
55 PetscErrorCode DMPlexReplace_Internal(DM dm, DM *ndm)
56 {
57   PetscSF          sf;
58   DM               dmNew = *ndm, coordDM, coarseDM;
59   Vec              coords;
60   const PetscReal *maxCell, *Lstart, *L;
61   PetscInt         dim, cdim;
62 
63   PetscFunctionBegin;
64   if (dm == dmNew) {
65     PetscCall(DMDestroy(ndm));
66     PetscFunctionReturn(PETSC_SUCCESS);
67   }
68   dm->setupcalled = dmNew->setupcalled;
69   PetscCall(DMGetDimension(dmNew, &dim));
70   PetscCall(DMSetDimension(dm, dim));
71   PetscCall(DMGetCoordinateDim(dmNew, &cdim));
72   PetscCall(DMSetCoordinateDim(dm, cdim));
73   PetscCall(DMGetPointSF(dmNew, &sf));
74   PetscCall(DMSetPointSF(dm, sf));
75   PetscCall(DMGetCoordinateDM(dmNew, &coordDM));
76   PetscCall(DMGetCoordinatesLocal(dmNew, &coords));
77   PetscCall(DMSetCoordinateDM(dm, coordDM));
78   PetscCall(DMSetCoordinatesLocal(dm, coords));
79   PetscCall(DMGetCellCoordinateDM(dmNew, &coordDM));
80   PetscCall(DMGetCellCoordinatesLocal(dmNew, &coords));
81   PetscCall(DMSetCellCoordinateDM(dm, coordDM));
82   PetscCall(DMSetCellCoordinatesLocal(dm, coords));
83   /* Do not want to create the coordinate field if it does not already exist, so do not call DMGetCoordinateField() */
84   PetscCall(DMFieldDestroy(&dm->coordinates[0].field));
85   dm->coordinates[0].field            = dmNew->coordinates[0].field;
86   ((DM_Plex *)dmNew->data)->coordFunc = ((DM_Plex *)dm->data)->coordFunc;
87   PetscCall(DMGetPeriodicity(dmNew, &maxCell, &Lstart, &L));
88   PetscCall(DMSetPeriodicity(dm, maxCell, Lstart, L));
89   PetscCall(DMPlexGetGlobalToNaturalSF(dmNew, &sf));
90   PetscCall(DMPlexSetGlobalToNaturalSF(dm, sf));
91   PetscCall(DMDestroy_Plex(dm));
92   PetscCall(DMInitialize_Plex(dm));
93   dm->data = dmNew->data;
94   ((DM_Plex *)dmNew->data)->refct++;
95   PetscCall(DMPlexGetIsoperiodicFaceSF(dm, &sf));
96   PetscCall(DMPlexSetIsoperiodicFaceSF(dm, sf)); // for the compose function effect on dm
97   PetscCall(DMDestroyLabelLinkList_Internal(dm));
98   PetscCall(DMCopyLabels(dmNew, dm, PETSC_OWN_POINTER, PETSC_TRUE, DM_COPY_LABELS_FAIL));
99   PetscCall(DMGetCoarseDM(dmNew, &coarseDM));
100   PetscCall(DMSetCoarseDM(dm, coarseDM));
101   PetscCall(DMDestroy(ndm));
102   PetscFunctionReturn(PETSC_SUCCESS);
103 }
104 
105 /* Swap dm with the contents of dmNew
106    - Swap the DM_Plex structure
107    - Swap the coordinates
108    - Swap the point PetscSF
109 */
110 static PetscErrorCode DMPlexSwap_Static(DM dmA, DM dmB)
111 {
112   DM          coordDMA, coordDMB;
113   Vec         coordsA, coordsB;
114   PetscSF     sfA, sfB;
115   DMField     fieldTmp;
116   void       *tmp;
117   DMLabelLink listTmp;
118   DMLabel     depthTmp;
119   PetscInt    tmpI;
120 
121   PetscFunctionBegin;
122   if (dmA == dmB) PetscFunctionReturn(PETSC_SUCCESS);
123   PetscCall(DMGetPointSF(dmA, &sfA));
124   PetscCall(DMGetPointSF(dmB, &sfB));
125   PetscCall(PetscObjectReference((PetscObject)sfA));
126   PetscCall(DMSetPointSF(dmA, sfB));
127   PetscCall(DMSetPointSF(dmB, sfA));
128   PetscCall(PetscObjectDereference((PetscObject)sfA));
129 
130   PetscCall(DMGetCoordinateDM(dmA, &coordDMA));
131   PetscCall(DMGetCoordinateDM(dmB, &coordDMB));
132   PetscCall(PetscObjectReference((PetscObject)coordDMA));
133   PetscCall(DMSetCoordinateDM(dmA, coordDMB));
134   PetscCall(DMSetCoordinateDM(dmB, coordDMA));
135   PetscCall(PetscObjectDereference((PetscObject)coordDMA));
136 
137   PetscCall(DMGetCoordinatesLocal(dmA, &coordsA));
138   PetscCall(DMGetCoordinatesLocal(dmB, &coordsB));
139   PetscCall(PetscObjectReference((PetscObject)coordsA));
140   PetscCall(DMSetCoordinatesLocal(dmA, coordsB));
141   PetscCall(DMSetCoordinatesLocal(dmB, coordsA));
142   PetscCall(PetscObjectDereference((PetscObject)coordsA));
143 
144   PetscCall(DMGetCellCoordinateDM(dmA, &coordDMA));
145   PetscCall(DMGetCellCoordinateDM(dmB, &coordDMB));
146   PetscCall(PetscObjectReference((PetscObject)coordDMA));
147   PetscCall(DMSetCellCoordinateDM(dmA, coordDMB));
148   PetscCall(DMSetCellCoordinateDM(dmB, coordDMA));
149   PetscCall(PetscObjectDereference((PetscObject)coordDMA));
150 
151   PetscCall(DMGetCellCoordinatesLocal(dmA, &coordsA));
152   PetscCall(DMGetCellCoordinatesLocal(dmB, &coordsB));
153   PetscCall(PetscObjectReference((PetscObject)coordsA));
154   PetscCall(DMSetCellCoordinatesLocal(dmA, coordsB));
155   PetscCall(DMSetCellCoordinatesLocal(dmB, coordsA));
156   PetscCall(PetscObjectDereference((PetscObject)coordsA));
157 
158   fieldTmp                  = dmA->coordinates[0].field;
159   dmA->coordinates[0].field = dmB->coordinates[0].field;
160   dmB->coordinates[0].field = fieldTmp;
161   fieldTmp                  = dmA->coordinates[1].field;
162   dmA->coordinates[1].field = dmB->coordinates[1].field;
163   dmB->coordinates[1].field = fieldTmp;
164   tmp                       = dmA->data;
165   dmA->data                 = dmB->data;
166   dmB->data                 = tmp;
167   listTmp                   = dmA->labels;
168   dmA->labels               = dmB->labels;
169   dmB->labels               = listTmp;
170   depthTmp                  = dmA->depthLabel;
171   dmA->depthLabel           = dmB->depthLabel;
172   dmB->depthLabel           = depthTmp;
173   depthTmp                  = dmA->celltypeLabel;
174   dmA->celltypeLabel        = dmB->celltypeLabel;
175   dmB->celltypeLabel        = depthTmp;
176   tmpI                      = dmA->levelup;
177   dmA->levelup              = dmB->levelup;
178   dmB->levelup              = tmpI;
179   PetscFunctionReturn(PETSC_SUCCESS);
180 }
181 
182 PetscErrorCode DMPlexInterpolateInPlace_Internal(DM dm)
183 {
184   DM idm;
185 
186   PetscFunctionBegin;
187   PetscCall(DMPlexInterpolate(dm, &idm));
188   PetscCall(DMPlexCopyCoordinates(dm, idm));
189   PetscCall(DMPlexReplace_Internal(dm, &idm));
190   PetscFunctionReturn(PETSC_SUCCESS);
191 }
192 
193 /*@C
194   DMPlexCreateCoordinateSpace - Creates a finite element space for the coordinates
195 
196   Collective
197 
198   Input Parameters:
199 + dm        - The `DMPLEX`
200 . degree    - The degree of the finite element or `PETSC_DECIDE`
201 . project   - Flag to project current coordinates into the space
202 - coordFunc - An optional function to map new points from refinement to the surface
203 
204   Level: advanced
205 
206 .seealso: [](ch_unstructured), `DM`, `DMPLEX`, `PetscPointFunc`, `PetscFECreateLagrange()`, `DMGetCoordinateDM()`
207 @*/
208 PetscErrorCode DMPlexCreateCoordinateSpace(DM dm, PetscInt degree, PetscBool project, PetscPointFunc coordFunc)
209 {
210   DM_Plex *mesh = (DM_Plex *)dm->data;
211   PetscFE  fe   = NULL;
212   DM       cdm;
213   PetscInt dim, dE, qorder, height;
214 
215   PetscFunctionBegin;
216   PetscCall(DMGetDimension(dm, &dim));
217   PetscCall(DMGetCoordinateDim(dm, &dE));
218   qorder = degree;
219   PetscCall(DMGetCoordinateDM(dm, &cdm));
220   PetscObjectOptionsBegin((PetscObject)cdm);
221   PetscCall(PetscOptionsBoundedInt("-default_quadrature_order", "Quadrature order is one less than quadrature points per edge", "DMPlexCreateCoordinateSpace", qorder, &qorder, NULL, 0));
222   PetscOptionsEnd();
223   PetscCall(DMPlexGetVTKCellHeight(dm, &height));
224   if (degree >= 0) {
225     DMPolytopeType ct = DM_POLYTOPE_UNKNOWN;
226     PetscInt       cStart, cEnd, gct;
227 
228     PetscCall(DMPlexGetHeightStratum(dm, height, &cStart, &cEnd));
229     if (cEnd > cStart) PetscCall(DMPlexGetCellType(dm, cStart, &ct));
230     gct = (PetscInt)ct;
231     PetscCall(MPIU_Allreduce(MPI_IN_PLACE, &gct, 1, MPIU_INT, MPI_MIN, PetscObjectComm((PetscObject)dm)));
232     ct = (DMPolytopeType)gct;
233     // Work around current bug in PetscDualSpaceSetUp_Lagrange()
234     //   Can be seen in plex_tutorials-ex10_1
235     if (ct != DM_POLYTOPE_SEG_PRISM_TENSOR && ct != DM_POLYTOPE_TRI_PRISM_TENSOR && ct != DM_POLYTOPE_QUAD_PRISM_TENSOR) PetscCall(PetscFECreateLagrangeByCell(PETSC_COMM_SELF, dim, dE, ct, degree, qorder, &fe));
236   }
237   PetscCall(DMSetCoordinateDisc(dm, fe, project));
238   PetscCall(PetscFEDestroy(&fe));
239   mesh->coordFunc = coordFunc;
240   PetscFunctionReturn(PETSC_SUCCESS);
241 }
242 
243 /*@
244   DMPlexCreateDoublet - Creates a mesh of two cells of the specified type, optionally with later refinement.
245 
246   Collective
247 
248   Input Parameters:
249 + comm            - The communicator for the `DM` object
250 . dim             - The spatial dimension
251 . simplex         - Flag for simplicial cells, otherwise they are tensor product cells
252 . interpolate     - Flag to create intermediate mesh pieces (edges, faces)
253 - refinementLimit - A nonzero number indicates the largest admissible volume for a refined cell
254 
255   Output Parameter:
256 . newdm - The `DM` object
257 
258   Level: beginner
259 
260 .seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMSetType()`, `DMCreate()`
261 @*/
262 PetscErrorCode DMPlexCreateDoublet(MPI_Comm comm, PetscInt dim, PetscBool simplex, PetscBool interpolate, PetscReal refinementLimit, DM *newdm)
263 {
264   DM          dm;
265   PetscMPIInt rank;
266 
267   PetscFunctionBegin;
268   PetscCall(DMCreate(comm, &dm));
269   PetscCall(DMSetType(dm, DMPLEX));
270   PetscCall(DMSetDimension(dm, dim));
271   PetscCall(PetscLogEventBegin(DMPLEX_Generate, dm, 0, 0, 0));
272   PetscCallMPI(MPI_Comm_rank(comm, &rank));
273   switch (dim) {
274   case 2:
275     if (simplex) PetscCall(PetscObjectSetName((PetscObject)dm, "triangular"));
276     else PetscCall(PetscObjectSetName((PetscObject)dm, "quadrilateral"));
277     break;
278   case 3:
279     if (simplex) PetscCall(PetscObjectSetName((PetscObject)dm, "tetrahedral"));
280     else PetscCall(PetscObjectSetName((PetscObject)dm, "hexahedral"));
281     break;
282   default:
283     SETERRQ(comm, PETSC_ERR_ARG_OUTOFRANGE, "Cannot make meshes for dimension %" PetscInt_FMT, dim);
284   }
285   if (rank) {
286     PetscInt numPoints[2] = {0, 0};
287     PetscCall(DMPlexCreateFromDAG(dm, 1, numPoints, NULL, NULL, NULL, NULL));
288   } else {
289     switch (dim) {
290     case 2:
291       if (simplex) {
292         PetscInt    numPoints[2]        = {4, 2};
293         PetscInt    coneSize[6]         = {3, 3, 0, 0, 0, 0};
294         PetscInt    cones[6]            = {2, 3, 4, 5, 4, 3};
295         PetscInt    coneOrientations[6] = {0, 0, 0, 0, 0, 0};
296         PetscScalar vertexCoords[8]     = {-0.5, 0.5, 0.0, 0.0, 0.0, 1.0, 0.5, 0.5};
297 
298         PetscCall(DMPlexCreateFromDAG(dm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords));
299       } else {
300         PetscInt    numPoints[2]        = {6, 2};
301         PetscInt    coneSize[8]         = {4, 4, 0, 0, 0, 0, 0, 0};
302         PetscInt    cones[8]            = {2, 3, 4, 5, 3, 6, 7, 4};
303         PetscInt    coneOrientations[8] = {0, 0, 0, 0, 0, 0, 0, 0};
304         PetscScalar vertexCoords[12]    = {-1.0, -0.5, 0.0, -0.5, 0.0, 0.5, -1.0, 0.5, 1.0, -0.5, 1.0, 0.5};
305 
306         PetscCall(DMPlexCreateFromDAG(dm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords));
307       }
308       break;
309     case 3:
310       if (simplex) {
311         PetscInt    numPoints[2]        = {5, 2};
312         PetscInt    coneSize[7]         = {4, 4, 0, 0, 0, 0, 0};
313         PetscInt    cones[8]            = {4, 3, 5, 2, 5, 3, 4, 6};
314         PetscInt    coneOrientations[8] = {0, 0, 0, 0, 0, 0, 0, 0};
315         PetscScalar vertexCoords[15]    = {-1.0, 0.0, 0.0, 0.0, -1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 1.0, 0.0, 1.0, 0.0, 0.0};
316 
317         PetscCall(DMPlexCreateFromDAG(dm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords));
318       } else {
319         PetscInt    numPoints[2]         = {12, 2};
320         PetscInt    coneSize[14]         = {8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0};
321         PetscInt    cones[16]            = {2, 3, 4, 5, 6, 7, 8, 9, 5, 4, 10, 11, 7, 12, 13, 8};
322         PetscInt    coneOrientations[16] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0};
323         PetscScalar vertexCoords[36]     = {-1.0, -0.5, -0.5, -1.0, 0.5, -0.5, 0.0, 0.5, -0.5, 0.0, -0.5, -0.5, -1.0, -0.5, 0.5, 0.0, -0.5, 0.5, 0.0, 0.5, 0.5, -1.0, 0.5, 0.5, 1.0, 0.5, -0.5, 1.0, -0.5, -0.5, 1.0, -0.5, 0.5, 1.0, 0.5, 0.5};
324 
325         PetscCall(DMPlexCreateFromDAG(dm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords));
326       }
327       break;
328     default:
329       SETERRQ(comm, PETSC_ERR_ARG_OUTOFRANGE, "Cannot make meshes for dimension %" PetscInt_FMT, dim);
330     }
331   }
332   PetscCall(PetscLogEventEnd(DMPLEX_Generate, dm, 0, 0, 0));
333   *newdm = dm;
334   if (refinementLimit > 0.0) {
335     DM          rdm;
336     const char *name;
337 
338     PetscCall(DMPlexSetRefinementUniform(*newdm, PETSC_FALSE));
339     PetscCall(DMPlexSetRefinementLimit(*newdm, refinementLimit));
340     PetscCall(DMRefine(*newdm, comm, &rdm));
341     PetscCall(PetscObjectGetName((PetscObject)*newdm, &name));
342     PetscCall(PetscObjectSetName((PetscObject)rdm, name));
343     PetscCall(DMDestroy(newdm));
344     *newdm = rdm;
345   }
346   if (interpolate) {
347     DM idm;
348 
349     PetscCall(DMPlexInterpolate(*newdm, &idm));
350     PetscCall(DMDestroy(newdm));
351     *newdm = idm;
352   }
353   PetscFunctionReturn(PETSC_SUCCESS);
354 }
355 
356 static PetscErrorCode DMPlexCreateBoxSurfaceMesh_Tensor_1D_Internal(DM dm, const PetscReal lower[], const PetscReal upper[], const PetscInt edges[])
357 {
358   const PetscInt numVertices    = 2;
359   PetscInt       markerRight    = 1;
360   PetscInt       markerLeft     = 1;
361   PetscBool      markerSeparate = PETSC_FALSE;
362   Vec            coordinates;
363   PetscSection   coordSection;
364   PetscScalar   *coords;
365   PetscInt       coordSize;
366   PetscMPIInt    rank;
367   PetscInt       cdim = 1, v;
368 
369   PetscFunctionBegin;
370   PetscCall(PetscOptionsGetBool(((PetscObject)dm)->options, ((PetscObject)dm)->prefix, "-dm_plex_separate_marker", &markerSeparate, NULL));
371   if (markerSeparate) {
372     markerRight = 2;
373     markerLeft  = 1;
374   }
375   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank));
376   if (rank == 0) {
377     PetscCall(DMPlexSetChart(dm, 0, numVertices));
378     PetscCall(DMSetUp(dm)); /* Allocate space for cones */
379     PetscCall(DMSetLabelValue(dm, "marker", 0, markerLeft));
380     PetscCall(DMSetLabelValue(dm, "marker", 1, markerRight));
381   }
382   PetscCall(DMPlexSymmetrize(dm));
383   PetscCall(DMPlexStratify(dm));
384   /* Build coordinates */
385   PetscCall(DMSetCoordinateDim(dm, cdim));
386   PetscCall(DMGetCoordinateSection(dm, &coordSection));
387   PetscCall(PetscSectionSetNumFields(coordSection, 1));
388   PetscCall(PetscSectionSetChart(coordSection, 0, numVertices));
389   PetscCall(PetscSectionSetFieldComponents(coordSection, 0, cdim));
390   for (v = 0; v < numVertices; ++v) {
391     PetscCall(PetscSectionSetDof(coordSection, v, cdim));
392     PetscCall(PetscSectionSetFieldDof(coordSection, v, 0, cdim));
393   }
394   PetscCall(PetscSectionSetUp(coordSection));
395   PetscCall(PetscSectionGetStorageSize(coordSection, &coordSize));
396   PetscCall(VecCreate(PETSC_COMM_SELF, &coordinates));
397   PetscCall(PetscObjectSetName((PetscObject)coordinates, "coordinates"));
398   PetscCall(VecSetSizes(coordinates, coordSize, PETSC_DETERMINE));
399   PetscCall(VecSetBlockSize(coordinates, cdim));
400   PetscCall(VecSetType(coordinates, VECSTANDARD));
401   PetscCall(VecGetArray(coordinates, &coords));
402   coords[0] = lower[0];
403   coords[1] = upper[0];
404   PetscCall(VecRestoreArray(coordinates, &coords));
405   PetscCall(DMSetCoordinatesLocal(dm, coordinates));
406   PetscCall(VecDestroy(&coordinates));
407   PetscFunctionReturn(PETSC_SUCCESS);
408 }
409 
410 static PetscErrorCode DMPlexCreateBoxSurfaceMesh_Tensor_2D_Internal(DM dm, const PetscReal lower[], const PetscReal upper[], const PetscInt edges[])
411 {
412   const PetscInt numVertices    = (edges[0] + 1) * (edges[1] + 1);
413   const PetscInt numEdges       = edges[0] * (edges[1] + 1) + (edges[0] + 1) * edges[1];
414   PetscInt       markerTop      = 1;
415   PetscInt       markerBottom   = 1;
416   PetscInt       markerRight    = 1;
417   PetscInt       markerLeft     = 1;
418   PetscBool      markerSeparate = PETSC_FALSE;
419   Vec            coordinates;
420   PetscSection   coordSection;
421   PetscScalar   *coords;
422   PetscInt       coordSize;
423   PetscMPIInt    rank;
424   PetscInt       v, vx, vy;
425 
426   PetscFunctionBegin;
427   PetscCall(PetscOptionsGetBool(((PetscObject)dm)->options, ((PetscObject)dm)->prefix, "-dm_plex_separate_marker", &markerSeparate, NULL));
428   if (markerSeparate) {
429     markerTop    = 3;
430     markerBottom = 1;
431     markerRight  = 2;
432     markerLeft   = 4;
433   }
434   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank));
435   if (rank == 0) {
436     PetscInt e, ex, ey;
437 
438     PetscCall(DMPlexSetChart(dm, 0, numEdges + numVertices));
439     for (e = 0; e < numEdges; ++e) PetscCall(DMPlexSetConeSize(dm, e, 2));
440     PetscCall(DMSetUp(dm)); /* Allocate space for cones */
441     for (vx = 0; vx <= edges[0]; vx++) {
442       for (ey = 0; ey < edges[1]; ey++) {
443         PetscInt edge   = vx * edges[1] + ey + edges[0] * (edges[1] + 1);
444         PetscInt vertex = ey * (edges[0] + 1) + vx + numEdges;
445         PetscInt cone[2];
446 
447         cone[0] = vertex;
448         cone[1] = vertex + edges[0] + 1;
449         PetscCall(DMPlexSetCone(dm, edge, cone));
450         if (vx == edges[0]) {
451           PetscCall(DMSetLabelValue(dm, "marker", edge, markerRight));
452           PetscCall(DMSetLabelValue(dm, "marker", cone[0], markerRight));
453           if (ey == edges[1] - 1) {
454             PetscCall(DMSetLabelValue(dm, "marker", cone[1], markerRight));
455             PetscCall(DMSetLabelValue(dm, "Face Sets", cone[1], markerRight));
456           }
457         } else if (vx == 0) {
458           PetscCall(DMSetLabelValue(dm, "marker", edge, markerLeft));
459           PetscCall(DMSetLabelValue(dm, "marker", cone[0], markerLeft));
460           if (ey == edges[1] - 1) {
461             PetscCall(DMSetLabelValue(dm, "marker", cone[1], markerLeft));
462             PetscCall(DMSetLabelValue(dm, "Face Sets", cone[1], markerLeft));
463           }
464         }
465       }
466     }
467     for (vy = 0; vy <= edges[1]; vy++) {
468       for (ex = 0; ex < edges[0]; ex++) {
469         PetscInt edge   = vy * edges[0] + ex;
470         PetscInt vertex = vy * (edges[0] + 1) + ex + numEdges;
471         PetscInt cone[2];
472 
473         cone[0] = vertex;
474         cone[1] = vertex + 1;
475         PetscCall(DMPlexSetCone(dm, edge, cone));
476         if (vy == edges[1]) {
477           PetscCall(DMSetLabelValue(dm, "marker", edge, markerTop));
478           PetscCall(DMSetLabelValue(dm, "marker", cone[0], markerTop));
479           if (ex == edges[0] - 1) {
480             PetscCall(DMSetLabelValue(dm, "marker", cone[1], markerTop));
481             PetscCall(DMSetLabelValue(dm, "Face Sets", cone[1], markerTop));
482           }
483         } else if (vy == 0) {
484           PetscCall(DMSetLabelValue(dm, "marker", edge, markerBottom));
485           PetscCall(DMSetLabelValue(dm, "marker", cone[0], markerBottom));
486           if (ex == edges[0] - 1) {
487             PetscCall(DMSetLabelValue(dm, "marker", cone[1], markerBottom));
488             PetscCall(DMSetLabelValue(dm, "Face Sets", cone[1], markerBottom));
489           }
490         }
491       }
492     }
493   }
494   PetscCall(DMPlexSymmetrize(dm));
495   PetscCall(DMPlexStratify(dm));
496   /* Build coordinates */
497   PetscCall(DMSetCoordinateDim(dm, 2));
498   PetscCall(DMGetCoordinateSection(dm, &coordSection));
499   PetscCall(PetscSectionSetNumFields(coordSection, 1));
500   PetscCall(PetscSectionSetChart(coordSection, numEdges, numEdges + numVertices));
501   PetscCall(PetscSectionSetFieldComponents(coordSection, 0, 2));
502   for (v = numEdges; v < numEdges + numVertices; ++v) {
503     PetscCall(PetscSectionSetDof(coordSection, v, 2));
504     PetscCall(PetscSectionSetFieldDof(coordSection, v, 0, 2));
505   }
506   PetscCall(PetscSectionSetUp(coordSection));
507   PetscCall(PetscSectionGetStorageSize(coordSection, &coordSize));
508   PetscCall(VecCreate(PETSC_COMM_SELF, &coordinates));
509   PetscCall(PetscObjectSetName((PetscObject)coordinates, "coordinates"));
510   PetscCall(VecSetSizes(coordinates, coordSize, PETSC_DETERMINE));
511   PetscCall(VecSetBlockSize(coordinates, 2));
512   PetscCall(VecSetType(coordinates, VECSTANDARD));
513   PetscCall(VecGetArray(coordinates, &coords));
514   for (vy = 0; vy <= edges[1]; ++vy) {
515     for (vx = 0; vx <= edges[0]; ++vx) {
516       coords[(vy * (edges[0] + 1) + vx) * 2 + 0] = lower[0] + ((upper[0] - lower[0]) / edges[0]) * vx;
517       coords[(vy * (edges[0] + 1) + vx) * 2 + 1] = lower[1] + ((upper[1] - lower[1]) / edges[1]) * vy;
518     }
519   }
520   PetscCall(VecRestoreArray(coordinates, &coords));
521   PetscCall(DMSetCoordinatesLocal(dm, coordinates));
522   PetscCall(VecDestroy(&coordinates));
523   PetscFunctionReturn(PETSC_SUCCESS);
524 }
525 
526 static PetscErrorCode DMPlexCreateBoxSurfaceMesh_Tensor_3D_Internal(DM dm, const PetscReal lower[], const PetscReal upper[], const PetscInt faces[])
527 {
528   PetscInt     vertices[3], numVertices;
529   PetscInt     numFaces       = 2 * faces[0] * faces[1] + 2 * faces[1] * faces[2] + 2 * faces[0] * faces[2];
530   PetscInt     markerTop      = 1;
531   PetscInt     markerBottom   = 1;
532   PetscInt     markerFront    = 1;
533   PetscInt     markerBack     = 1;
534   PetscInt     markerRight    = 1;
535   PetscInt     markerLeft     = 1;
536   PetscBool    markerSeparate = PETSC_FALSE;
537   Vec          coordinates;
538   PetscSection coordSection;
539   PetscScalar *coords;
540   PetscInt     coordSize;
541   PetscMPIInt  rank;
542   PetscInt     v, vx, vy, vz;
543   PetscInt     voffset, iface = 0, cone[4];
544 
545   PetscFunctionBegin;
546   PetscCheck(faces[0] >= 1 && faces[1] >= 1 && faces[2] >= 1, PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Must have at least 1 face per side");
547   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank));
548   PetscCall(PetscOptionsGetBool(((PetscObject)dm)->options, ((PetscObject)dm)->prefix, "-dm_plex_separate_marker", &markerSeparate, NULL));
549   if (markerSeparate) {
550     markerBottom = 1;
551     markerTop    = 2;
552     markerFront  = 3;
553     markerBack   = 4;
554     markerRight  = 5;
555     markerLeft   = 6;
556   }
557   vertices[0] = faces[0] + 1;
558   vertices[1] = faces[1] + 1;
559   vertices[2] = faces[2] + 1;
560   numVertices = vertices[0] * vertices[1] * vertices[2];
561   if (rank == 0) {
562     PetscInt f;
563 
564     PetscCall(DMPlexSetChart(dm, 0, numFaces + numVertices));
565     for (f = 0; f < numFaces; ++f) PetscCall(DMPlexSetConeSize(dm, f, 4));
566     PetscCall(DMSetUp(dm)); /* Allocate space for cones */
567 
568     /* Side 0 (Top) */
569     for (vy = 0; vy < faces[1]; vy++) {
570       for (vx = 0; vx < faces[0]; vx++) {
571         voffset = numFaces + vertices[0] * vertices[1] * (vertices[2] - 1) + vy * vertices[0] + vx;
572         cone[0] = voffset;
573         cone[1] = voffset + 1;
574         cone[2] = voffset + vertices[0] + 1;
575         cone[3] = voffset + vertices[0];
576         PetscCall(DMPlexSetCone(dm, iface, cone));
577         PetscCall(DMSetLabelValue(dm, "marker", iface, markerTop));
578         PetscCall(DMSetLabelValue(dm, "marker", voffset + 0, markerTop));
579         PetscCall(DMSetLabelValue(dm, "marker", voffset + 1, markerTop));
580         PetscCall(DMSetLabelValue(dm, "marker", voffset + vertices[0] + 0, markerTop));
581         PetscCall(DMSetLabelValue(dm, "marker", voffset + vertices[0] + 1, markerTop));
582         iface++;
583       }
584     }
585 
586     /* Side 1 (Bottom) */
587     for (vy = 0; vy < faces[1]; vy++) {
588       for (vx = 0; vx < faces[0]; vx++) {
589         voffset = numFaces + vy * (faces[0] + 1) + vx;
590         cone[0] = voffset + 1;
591         cone[1] = voffset;
592         cone[2] = voffset + vertices[0];
593         cone[3] = voffset + vertices[0] + 1;
594         PetscCall(DMPlexSetCone(dm, iface, cone));
595         PetscCall(DMSetLabelValue(dm, "marker", iface, markerBottom));
596         PetscCall(DMSetLabelValue(dm, "marker", voffset + 0, markerBottom));
597         PetscCall(DMSetLabelValue(dm, "marker", voffset + 1, markerBottom));
598         PetscCall(DMSetLabelValue(dm, "marker", voffset + vertices[0] + 0, markerBottom));
599         PetscCall(DMSetLabelValue(dm, "marker", voffset + vertices[0] + 1, markerBottom));
600         iface++;
601       }
602     }
603 
604     /* Side 2 (Front) */
605     for (vz = 0; vz < faces[2]; vz++) {
606       for (vx = 0; vx < faces[0]; vx++) {
607         voffset = numFaces + vz * vertices[0] * vertices[1] + vx;
608         cone[0] = voffset;
609         cone[1] = voffset + 1;
610         cone[2] = voffset + vertices[0] * vertices[1] + 1;
611         cone[3] = voffset + vertices[0] * vertices[1];
612         PetscCall(DMPlexSetCone(dm, iface, cone));
613         PetscCall(DMSetLabelValue(dm, "marker", iface, markerFront));
614         PetscCall(DMSetLabelValue(dm, "marker", voffset + 0, markerFront));
615         PetscCall(DMSetLabelValue(dm, "marker", voffset + 1, markerFront));
616         PetscCall(DMSetLabelValue(dm, "marker", voffset + vertices[0] * vertices[1] + 0, markerFront));
617         PetscCall(DMSetLabelValue(dm, "marker", voffset + vertices[0] * vertices[1] + 1, markerFront));
618         iface++;
619       }
620     }
621 
622     /* Side 3 (Back) */
623     for (vz = 0; vz < faces[2]; vz++) {
624       for (vx = 0; vx < faces[0]; vx++) {
625         voffset = numFaces + vz * vertices[0] * vertices[1] + vertices[0] * (vertices[1] - 1) + vx;
626         cone[0] = voffset + vertices[0] * vertices[1];
627         cone[1] = voffset + vertices[0] * vertices[1] + 1;
628         cone[2] = voffset + 1;
629         cone[3] = voffset;
630         PetscCall(DMPlexSetCone(dm, iface, cone));
631         PetscCall(DMSetLabelValue(dm, "marker", iface, markerBack));
632         PetscCall(DMSetLabelValue(dm, "marker", voffset + 0, markerBack));
633         PetscCall(DMSetLabelValue(dm, "marker", voffset + 1, markerBack));
634         PetscCall(DMSetLabelValue(dm, "marker", voffset + vertices[0] * vertices[1] + 0, markerBack));
635         PetscCall(DMSetLabelValue(dm, "marker", voffset + vertices[0] * vertices[1] + 1, markerBack));
636         iface++;
637       }
638     }
639 
640     /* Side 4 (Left) */
641     for (vz = 0; vz < faces[2]; vz++) {
642       for (vy = 0; vy < faces[1]; vy++) {
643         voffset = numFaces + vz * vertices[0] * vertices[1] + vy * vertices[0];
644         cone[0] = voffset;
645         cone[1] = voffset + vertices[0] * vertices[1];
646         cone[2] = voffset + vertices[0] * vertices[1] + vertices[0];
647         cone[3] = voffset + vertices[0];
648         PetscCall(DMPlexSetCone(dm, iface, cone));
649         PetscCall(DMSetLabelValue(dm, "marker", iface, markerLeft));
650         PetscCall(DMSetLabelValue(dm, "marker", voffset + 0, markerLeft));
651         PetscCall(DMSetLabelValue(dm, "marker", voffset + vertices[0] + 0, markerLeft));
652         PetscCall(DMSetLabelValue(dm, "marker", voffset + vertices[1] + 0, markerLeft));
653         PetscCall(DMSetLabelValue(dm, "marker", voffset + vertices[0] * vertices[1] + vertices[0], markerLeft));
654         iface++;
655       }
656     }
657 
658     /* Side 5 (Right) */
659     for (vz = 0; vz < faces[2]; vz++) {
660       for (vy = 0; vy < faces[1]; vy++) {
661         voffset = numFaces + vz * vertices[0] * vertices[1] + vy * vertices[0] + faces[0];
662         cone[0] = voffset + vertices[0] * vertices[1];
663         cone[1] = voffset;
664         cone[2] = voffset + vertices[0];
665         cone[3] = voffset + vertices[0] * vertices[1] + vertices[0];
666         PetscCall(DMPlexSetCone(dm, iface, cone));
667         PetscCall(DMSetLabelValue(dm, "marker", iface, markerRight));
668         PetscCall(DMSetLabelValue(dm, "marker", voffset + 0, markerRight));
669         PetscCall(DMSetLabelValue(dm, "marker", voffset + vertices[0] + 0, markerRight));
670         PetscCall(DMSetLabelValue(dm, "marker", voffset + vertices[0] * vertices[1] + 0, markerRight));
671         PetscCall(DMSetLabelValue(dm, "marker", voffset + vertices[0] * vertices[1] + vertices[0], markerRight));
672         iface++;
673       }
674     }
675   }
676   PetscCall(DMPlexSymmetrize(dm));
677   PetscCall(DMPlexStratify(dm));
678   /* Build coordinates */
679   PetscCall(DMSetCoordinateDim(dm, 3));
680   PetscCall(DMGetCoordinateSection(dm, &coordSection));
681   PetscCall(PetscSectionSetNumFields(coordSection, 1));
682   PetscCall(PetscSectionSetChart(coordSection, numFaces, numFaces + numVertices));
683   PetscCall(PetscSectionSetFieldComponents(coordSection, 0, 3));
684   for (v = numFaces; v < numFaces + numVertices; ++v) {
685     PetscCall(PetscSectionSetDof(coordSection, v, 3));
686     PetscCall(PetscSectionSetFieldDof(coordSection, v, 0, 3));
687   }
688   PetscCall(PetscSectionSetUp(coordSection));
689   PetscCall(PetscSectionGetStorageSize(coordSection, &coordSize));
690   PetscCall(VecCreate(PETSC_COMM_SELF, &coordinates));
691   PetscCall(PetscObjectSetName((PetscObject)coordinates, "coordinates"));
692   PetscCall(VecSetSizes(coordinates, coordSize, PETSC_DETERMINE));
693   PetscCall(VecSetBlockSize(coordinates, 3));
694   PetscCall(VecSetType(coordinates, VECSTANDARD));
695   PetscCall(VecGetArray(coordinates, &coords));
696   for (vz = 0; vz <= faces[2]; ++vz) {
697     for (vy = 0; vy <= faces[1]; ++vy) {
698       for (vx = 0; vx <= faces[0]; ++vx) {
699         coords[((vz * (faces[1] + 1) + vy) * (faces[0] + 1) + vx) * 3 + 0] = lower[0] + ((upper[0] - lower[0]) / faces[0]) * vx;
700         coords[((vz * (faces[1] + 1) + vy) * (faces[0] + 1) + vx) * 3 + 1] = lower[1] + ((upper[1] - lower[1]) / faces[1]) * vy;
701         coords[((vz * (faces[1] + 1) + vy) * (faces[0] + 1) + vx) * 3 + 2] = lower[2] + ((upper[2] - lower[2]) / faces[2]) * vz;
702       }
703     }
704   }
705   PetscCall(VecRestoreArray(coordinates, &coords));
706   PetscCall(DMSetCoordinatesLocal(dm, coordinates));
707   PetscCall(VecDestroy(&coordinates));
708   PetscFunctionReturn(PETSC_SUCCESS);
709 }
710 
711 static PetscErrorCode DMPlexCreateBoxSurfaceMesh_Internal(DM dm, PetscInt dim, const PetscInt faces[], const PetscReal lower[], const PetscReal upper[], PetscBool interpolate)
712 {
713   PetscFunctionBegin;
714   PetscValidLogicalCollectiveInt(dm, dim, 2);
715   PetscCall(PetscLogEventBegin(DMPLEX_Generate, dm, 0, 0, 0));
716   PetscCall(DMSetDimension(dm, dim - 1));
717   PetscCall(DMSetCoordinateDim(dm, dim));
718   switch (dim) {
719   case 1:
720     PetscCall(DMPlexCreateBoxSurfaceMesh_Tensor_1D_Internal(dm, lower, upper, faces));
721     break;
722   case 2:
723     PetscCall(DMPlexCreateBoxSurfaceMesh_Tensor_2D_Internal(dm, lower, upper, faces));
724     break;
725   case 3:
726     PetscCall(DMPlexCreateBoxSurfaceMesh_Tensor_3D_Internal(dm, lower, upper, faces));
727     break;
728   default:
729     SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Dimension not supported: %" PetscInt_FMT, dim);
730   }
731   PetscCall(PetscLogEventEnd(DMPLEX_Generate, dm, 0, 0, 0));
732   if (interpolate) PetscCall(DMPlexInterpolateInPlace_Internal(dm));
733   PetscFunctionReturn(PETSC_SUCCESS);
734 }
735 
736 /*@C
737   DMPlexCreateBoxSurfaceMesh - Creates a mesh on the surface of the tensor product of unit intervals (box) using tensor cells (hexahedra).
738 
739   Collective
740 
741   Input Parameters:
742 + comm        - The communicator for the `DM` object
743 . dim         - The spatial dimension of the box, so the resulting mesh is has dimension `dim`-1
744 . faces       - Number of faces per dimension, or `NULL` for (1,) in 1D and (2, 2) in 2D and (1, 1, 1) in 3D
745 . lower       - The lower left corner, or `NULL` for (0, 0, 0)
746 . upper       - The upper right corner, or `NULL` for (1, 1, 1)
747 - interpolate - Flag to create intermediate mesh pieces (edges, faces)
748 
749   Output Parameter:
750 . dm - The `DM` object
751 
752   Level: beginner
753 
754 .seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMSetFromOptions()`, `DMPlexCreateBoxMesh()`, `DMPlexCreateFromFile()`, `DMSetType()`, `DMCreate()`
755 @*/
756 PetscErrorCode DMPlexCreateBoxSurfaceMesh(MPI_Comm comm, PetscInt dim, const PetscInt faces[], const PetscReal lower[], const PetscReal upper[], PetscBool interpolate, DM *dm)
757 {
758   PetscInt  fac[3] = {1, 1, 1};
759   PetscReal low[3] = {0, 0, 0};
760   PetscReal upp[3] = {1, 1, 1};
761 
762   PetscFunctionBegin;
763   PetscCall(DMCreate(comm, dm));
764   PetscCall(DMSetType(*dm, DMPLEX));
765   PetscCall(DMPlexCreateBoxSurfaceMesh_Internal(*dm, dim, faces ? faces : fac, lower ? lower : low, upper ? upper : upp, interpolate));
766   PetscFunctionReturn(PETSC_SUCCESS);
767 }
768 
769 static PetscErrorCode DMPlexCreateLineMesh_Internal(DM dm, PetscInt segments, PetscReal lower, PetscReal upper, DMBoundaryType bd)
770 {
771   PetscInt     i, fStart, fEnd, numCells = 0, numVerts = 0;
772   PetscInt     numPoints[2], *coneSize, *cones, *coneOrientations;
773   PetscScalar *vertexCoords;
774   PetscReal    L, maxCell;
775   PetscBool    markerSeparate = PETSC_FALSE;
776   PetscInt     markerLeft = 1, faceMarkerLeft = 1;
777   PetscInt     markerRight = 1, faceMarkerRight = 2;
778   PetscBool    wrap = (bd == DM_BOUNDARY_PERIODIC || bd == DM_BOUNDARY_TWIST) ? PETSC_TRUE : PETSC_FALSE;
779   PetscMPIInt  rank;
780 
781   PetscFunctionBegin;
782   PetscAssertPointer(dm, 1);
783 
784   PetscCall(DMSetDimension(dm, 1));
785   PetscCall(DMCreateLabel(dm, "marker"));
786   PetscCall(DMCreateLabel(dm, "Face Sets"));
787 
788   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank));
789   if (rank == 0) numCells = segments;
790   if (rank == 0) numVerts = segments + (wrap ? 0 : 1);
791 
792   numPoints[0] = numVerts;
793   numPoints[1] = numCells;
794   PetscCall(PetscMalloc4(numCells + numVerts, &coneSize, numCells * 2, &cones, numCells + numVerts, &coneOrientations, numVerts, &vertexCoords));
795   PetscCall(PetscArrayzero(coneOrientations, numCells + numVerts));
796   for (i = 0; i < numCells; ++i) coneSize[i] = 2;
797   for (i = 0; i < numVerts; ++i) coneSize[numCells + i] = 0;
798   for (i = 0; i < numCells; ++i) {
799     cones[2 * i]     = numCells + i % numVerts;
800     cones[2 * i + 1] = numCells + (i + 1) % numVerts;
801   }
802   for (i = 0; i < numVerts; ++i) vertexCoords[i] = lower + (upper - lower) * ((PetscReal)i / (PetscReal)numCells);
803   PetscCall(DMPlexCreateFromDAG(dm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords));
804   PetscCall(PetscFree4(coneSize, cones, coneOrientations, vertexCoords));
805 
806   PetscCall(PetscOptionsGetBool(((PetscObject)dm)->options, ((PetscObject)dm)->prefix, "-dm_plex_separate_marker", &markerSeparate, NULL));
807   if (markerSeparate) {
808     markerLeft  = faceMarkerLeft;
809     markerRight = faceMarkerRight;
810   }
811   if (!wrap && rank == 0) {
812     PetscCall(DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd));
813     PetscCall(DMSetLabelValue(dm, "marker", fStart, markerLeft));
814     PetscCall(DMSetLabelValue(dm, "marker", fEnd - 1, markerRight));
815     PetscCall(DMSetLabelValue(dm, "Face Sets", fStart, faceMarkerLeft));
816     PetscCall(DMSetLabelValue(dm, "Face Sets", fEnd - 1, faceMarkerRight));
817   }
818   if (wrap) {
819     L       = upper - lower;
820     maxCell = (PetscReal)1.1 * (L / (PetscReal)PetscMax(1, segments));
821     PetscCall(DMSetPeriodicity(dm, &maxCell, &lower, &L));
822   }
823   PetscCall(DMPlexSetRefinementUniform(dm, PETSC_TRUE));
824   PetscFunctionReturn(PETSC_SUCCESS);
825 }
826 
827 static PetscErrorCode DMPlexCreateBoxMesh_Simplex_Internal(DM dm, PetscInt dim, const PetscInt faces[], const PetscReal lower[], const PetscReal upper[], const DMBoundaryType periodicity[], PetscBool interpolate)
828 {
829   DM      boundary, vol;
830   DMLabel bdlabel;
831 
832   PetscFunctionBegin;
833   PetscAssertPointer(dm, 1);
834   for (PetscInt i = 0; i < dim; ++i) PetscCheck(periodicity[i] == DM_BOUNDARY_NONE, PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Periodicity is not supported for simplex meshes");
835   PetscCall(DMCreate(PetscObjectComm((PetscObject)dm), &boundary));
836   PetscCall(DMSetType(boundary, DMPLEX));
837   PetscCall(DMPlexCreateBoxSurfaceMesh_Internal(boundary, dim, faces, lower, upper, PETSC_FALSE));
838   PetscCall(DMPlexGenerate(boundary, NULL, interpolate, &vol));
839   PetscCall(DMGetLabel(vol, "marker", &bdlabel));
840   if (bdlabel) PetscCall(DMPlexLabelComplete(vol, bdlabel));
841   PetscCall(DMPlexCopy_Internal(dm, PETSC_TRUE, PETSC_FALSE, vol));
842   PetscCall(DMPlexReplace_Internal(dm, &vol));
843   PetscCall(DMDestroy(&boundary));
844   PetscFunctionReturn(PETSC_SUCCESS);
845 }
846 
847 static PetscErrorCode DMPlexCreateCubeMesh_Internal(DM dm, const PetscReal lower[], const PetscReal upper[], const PetscInt edges[], DMBoundaryType bdX, DMBoundaryType bdY, DMBoundaryType bdZ)
848 {
849   DMLabel     cutLabel  = NULL;
850   PetscInt    markerTop = 1, faceMarkerTop = 1;
851   PetscInt    markerBottom = 1, faceMarkerBottom = 1;
852   PetscInt    markerFront = 1, faceMarkerFront = 1;
853   PetscInt    markerBack = 1, faceMarkerBack = 1;
854   PetscInt    markerRight = 1, faceMarkerRight = 1;
855   PetscInt    markerLeft = 1, faceMarkerLeft = 1;
856   PetscInt    dim;
857   PetscBool   markerSeparate = PETSC_FALSE, cutMarker = PETSC_FALSE;
858   PetscMPIInt rank;
859 
860   PetscFunctionBegin;
861   PetscCall(DMGetDimension(dm, &dim));
862   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank));
863   PetscCall(DMCreateLabel(dm, "marker"));
864   PetscCall(DMCreateLabel(dm, "Face Sets"));
865   PetscCall(PetscOptionsGetBool(((PetscObject)dm)->options, ((PetscObject)dm)->prefix, "-dm_plex_periodic_cut", &cutMarker, NULL));
866   if (bdX == DM_BOUNDARY_PERIODIC || bdX == DM_BOUNDARY_TWIST || bdY == DM_BOUNDARY_PERIODIC || bdY == DM_BOUNDARY_TWIST || bdZ == DM_BOUNDARY_PERIODIC || bdZ == DM_BOUNDARY_TWIST) {
867     if (cutMarker) {
868       PetscCall(DMCreateLabel(dm, "periodic_cut"));
869       PetscCall(DMGetLabel(dm, "periodic_cut", &cutLabel));
870     }
871   }
872   switch (dim) {
873   case 2:
874     faceMarkerTop    = 3;
875     faceMarkerBottom = 1;
876     faceMarkerRight  = 2;
877     faceMarkerLeft   = 4;
878     break;
879   case 3:
880     faceMarkerBottom = 1;
881     faceMarkerTop    = 2;
882     faceMarkerFront  = 3;
883     faceMarkerBack   = 4;
884     faceMarkerRight  = 5;
885     faceMarkerLeft   = 6;
886     break;
887   default:
888     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Dimension %" PetscInt_FMT " not supported", dim);
889   }
890   PetscCall(PetscOptionsGetBool(((PetscObject)dm)->options, ((PetscObject)dm)->prefix, "-dm_plex_separate_marker", &markerSeparate, NULL));
891   if (markerSeparate) {
892     markerBottom = faceMarkerBottom;
893     markerTop    = faceMarkerTop;
894     markerFront  = faceMarkerFront;
895     markerBack   = faceMarkerBack;
896     markerRight  = faceMarkerRight;
897     markerLeft   = faceMarkerLeft;
898   }
899   {
900     const PetscInt numXEdges    = rank == 0 ? edges[0] : 0;
901     const PetscInt numYEdges    = rank == 0 ? edges[1] : 0;
902     const PetscInt numZEdges    = rank == 0 ? edges[2] : 0;
903     const PetscInt numXVertices = rank == 0 ? (bdX == DM_BOUNDARY_PERIODIC || bdX == DM_BOUNDARY_TWIST ? edges[0] : edges[0] + 1) : 0;
904     const PetscInt numYVertices = rank == 0 ? (bdY == DM_BOUNDARY_PERIODIC || bdY == DM_BOUNDARY_TWIST ? edges[1] : edges[1] + 1) : 0;
905     const PetscInt numZVertices = rank == 0 ? (bdZ == DM_BOUNDARY_PERIODIC || bdZ == DM_BOUNDARY_TWIST ? edges[2] : edges[2] + 1) : 0;
906     const PetscInt numCells     = numXEdges * numYEdges * numZEdges;
907     const PetscInt numXFaces    = numYEdges * numZEdges;
908     const PetscInt numYFaces    = numXEdges * numZEdges;
909     const PetscInt numZFaces    = numXEdges * numYEdges;
910     const PetscInt numTotXFaces = numXVertices * numXFaces;
911     const PetscInt numTotYFaces = numYVertices * numYFaces;
912     const PetscInt numTotZFaces = numZVertices * numZFaces;
913     const PetscInt numFaces     = numTotXFaces + numTotYFaces + numTotZFaces;
914     const PetscInt numTotXEdges = numXEdges * numYVertices * numZVertices;
915     const PetscInt numTotYEdges = numYEdges * numXVertices * numZVertices;
916     const PetscInt numTotZEdges = numZEdges * numXVertices * numYVertices;
917     const PetscInt numVertices  = numXVertices * numYVertices * numZVertices;
918     const PetscInt numEdges     = numTotXEdges + numTotYEdges + numTotZEdges;
919     const PetscInt firstVertex  = (dim == 2) ? numFaces : numCells;
920     const PetscInt firstXFace   = (dim == 2) ? 0 : numCells + numVertices;
921     const PetscInt firstYFace   = firstXFace + numTotXFaces;
922     const PetscInt firstZFace   = firstYFace + numTotYFaces;
923     const PetscInt firstXEdge   = numCells + numFaces + numVertices;
924     const PetscInt firstYEdge   = firstXEdge + numTotXEdges;
925     const PetscInt firstZEdge   = firstYEdge + numTotYEdges;
926     Vec            coordinates;
927     PetscSection   coordSection;
928     PetscScalar   *coords;
929     PetscInt       coordSize;
930     PetscInt       v, vx, vy, vz;
931     PetscInt       c, f, fx, fy, fz, e, ex, ey, ez;
932 
933     PetscCall(DMPlexSetChart(dm, 0, numCells + numFaces + numEdges + numVertices));
934     for (c = 0; c < numCells; c++) PetscCall(DMPlexSetConeSize(dm, c, 6));
935     for (f = firstXFace; f < firstXFace + numFaces; ++f) PetscCall(DMPlexSetConeSize(dm, f, 4));
936     for (e = firstXEdge; e < firstXEdge + numEdges; ++e) PetscCall(DMPlexSetConeSize(dm, e, 2));
937     PetscCall(DMSetUp(dm)); /* Allocate space for cones */
938     /* Build cells */
939     for (fz = 0; fz < numZEdges; ++fz) {
940       for (fy = 0; fy < numYEdges; ++fy) {
941         for (fx = 0; fx < numXEdges; ++fx) {
942           PetscInt cell  = (fz * numYEdges + fy) * numXEdges + fx;
943           PetscInt faceB = firstZFace + (fy * numXEdges + fx) * numZVertices + fz;
944           PetscInt faceT = firstZFace + (fy * numXEdges + fx) * numZVertices + ((fz + 1) % numZVertices);
945           PetscInt faceF = firstYFace + (fz * numXEdges + fx) * numYVertices + fy;
946           PetscInt faceK = firstYFace + (fz * numXEdges + fx) * numYVertices + ((fy + 1) % numYVertices);
947           PetscInt faceL = firstXFace + (fz * numYEdges + fy) * numXVertices + fx;
948           PetscInt faceR = firstXFace + (fz * numYEdges + fy) * numXVertices + ((fx + 1) % numXVertices);
949           /* B,  T,  F,  K,  R,  L */
950           PetscInt ornt[6] = {-2, 0, 0, -3, 0, -2}; /* ??? */
951           PetscInt cone[6];
952 
953           /* no boundary twisting in 3D */
954           cone[0] = faceB;
955           cone[1] = faceT;
956           cone[2] = faceF;
957           cone[3] = faceK;
958           cone[4] = faceR;
959           cone[5] = faceL;
960           PetscCall(DMPlexSetCone(dm, cell, cone));
961           PetscCall(DMPlexSetConeOrientation(dm, cell, ornt));
962           if (bdX != DM_BOUNDARY_NONE && fx == numXEdges - 1 && cutLabel) PetscCall(DMLabelSetValue(cutLabel, cell, 2));
963           if (bdY != DM_BOUNDARY_NONE && fy == numYEdges - 1 && cutLabel) PetscCall(DMLabelSetValue(cutLabel, cell, 2));
964           if (bdZ != DM_BOUNDARY_NONE && fz == numZEdges - 1 && cutLabel) PetscCall(DMLabelSetValue(cutLabel, cell, 2));
965         }
966       }
967     }
968     /* Build x faces */
969     for (fz = 0; fz < numZEdges; ++fz) {
970       for (fy = 0; fy < numYEdges; ++fy) {
971         for (fx = 0; fx < numXVertices; ++fx) {
972           PetscInt face    = firstXFace + (fz * numYEdges + fy) * numXVertices + fx;
973           PetscInt edgeL   = firstZEdge + (fy * numXVertices + fx) * numZEdges + fz;
974           PetscInt edgeR   = firstZEdge + (((fy + 1) % numYVertices) * numXVertices + fx) * numZEdges + fz;
975           PetscInt edgeB   = firstYEdge + (fz * numXVertices + fx) * numYEdges + fy;
976           PetscInt edgeT   = firstYEdge + (((fz + 1) % numZVertices) * numXVertices + fx) * numYEdges + fy;
977           PetscInt ornt[4] = {0, 0, -1, -1};
978           PetscInt cone[4];
979 
980           if (dim == 3) {
981             /* markers */
982             if (bdX != DM_BOUNDARY_PERIODIC) {
983               if (fx == numXVertices - 1) {
984                 PetscCall(DMSetLabelValue(dm, "Face Sets", face, faceMarkerRight));
985                 PetscCall(DMSetLabelValue(dm, "marker", face, markerRight));
986               } else if (fx == 0) {
987                 PetscCall(DMSetLabelValue(dm, "Face Sets", face, faceMarkerLeft));
988                 PetscCall(DMSetLabelValue(dm, "marker", face, markerLeft));
989               }
990             }
991           }
992           cone[0] = edgeB;
993           cone[1] = edgeR;
994           cone[2] = edgeT;
995           cone[3] = edgeL;
996           PetscCall(DMPlexSetCone(dm, face, cone));
997           PetscCall(DMPlexSetConeOrientation(dm, face, ornt));
998         }
999       }
1000     }
1001     /* Build y faces */
1002     for (fz = 0; fz < numZEdges; ++fz) {
1003       for (fx = 0; fx < numXEdges; ++fx) {
1004         for (fy = 0; fy < numYVertices; ++fy) {
1005           PetscInt face    = firstYFace + (fz * numXEdges + fx) * numYVertices + fy;
1006           PetscInt edgeL   = firstZEdge + (fy * numXVertices + fx) * numZEdges + fz;
1007           PetscInt edgeR   = firstZEdge + (fy * numXVertices + ((fx + 1) % numXVertices)) * numZEdges + fz;
1008           PetscInt edgeB   = firstXEdge + (fz * numYVertices + fy) * numXEdges + fx;
1009           PetscInt edgeT   = firstXEdge + (((fz + 1) % numZVertices) * numYVertices + fy) * numXEdges + fx;
1010           PetscInt ornt[4] = {0, 0, -1, -1};
1011           PetscInt cone[4];
1012 
1013           if (dim == 3) {
1014             /* markers */
1015             if (bdY != DM_BOUNDARY_PERIODIC) {
1016               if (fy == numYVertices - 1) {
1017                 PetscCall(DMSetLabelValue(dm, "Face Sets", face, faceMarkerBack));
1018                 PetscCall(DMSetLabelValue(dm, "marker", face, markerBack));
1019               } else if (fy == 0) {
1020                 PetscCall(DMSetLabelValue(dm, "Face Sets", face, faceMarkerFront));
1021                 PetscCall(DMSetLabelValue(dm, "marker", face, markerFront));
1022               }
1023             }
1024           }
1025           cone[0] = edgeB;
1026           cone[1] = edgeR;
1027           cone[2] = edgeT;
1028           cone[3] = edgeL;
1029           PetscCall(DMPlexSetCone(dm, face, cone));
1030           PetscCall(DMPlexSetConeOrientation(dm, face, ornt));
1031         }
1032       }
1033     }
1034     /* Build z faces */
1035     for (fy = 0; fy < numYEdges; ++fy) {
1036       for (fx = 0; fx < numXEdges; ++fx) {
1037         for (fz = 0; fz < numZVertices; fz++) {
1038           PetscInt face    = firstZFace + (fy * numXEdges + fx) * numZVertices + fz;
1039           PetscInt edgeL   = firstYEdge + (fz * numXVertices + fx) * numYEdges + fy;
1040           PetscInt edgeR   = firstYEdge + (fz * numXVertices + ((fx + 1) % numXVertices)) * numYEdges + fy;
1041           PetscInt edgeB   = firstXEdge + (fz * numYVertices + fy) * numXEdges + fx;
1042           PetscInt edgeT   = firstXEdge + (fz * numYVertices + ((fy + 1) % numYVertices)) * numXEdges + fx;
1043           PetscInt ornt[4] = {0, 0, -1, -1};
1044           PetscInt cone[4];
1045 
1046           if (dim == 2) {
1047             if (bdX == DM_BOUNDARY_TWIST && fx == numXEdges - 1) {
1048               edgeR += numYEdges - 1 - 2 * fy;
1049               ornt[1] = -1;
1050             }
1051             if (bdY == DM_BOUNDARY_TWIST && fy == numYEdges - 1) {
1052               edgeT += numXEdges - 1 - 2 * fx;
1053               ornt[2] = 0;
1054             }
1055             if (bdX != DM_BOUNDARY_NONE && fx == numXEdges - 1 && cutLabel) PetscCall(DMLabelSetValue(cutLabel, face, 2));
1056             if (bdY != DM_BOUNDARY_NONE && fy == numYEdges - 1 && cutLabel) PetscCall(DMLabelSetValue(cutLabel, face, 2));
1057           } else {
1058             /* markers */
1059             if (bdZ != DM_BOUNDARY_PERIODIC) {
1060               if (fz == numZVertices - 1) {
1061                 PetscCall(DMSetLabelValue(dm, "Face Sets", face, faceMarkerTop));
1062                 PetscCall(DMSetLabelValue(dm, "marker", face, markerTop));
1063               } else if (fz == 0) {
1064                 PetscCall(DMSetLabelValue(dm, "Face Sets", face, faceMarkerBottom));
1065                 PetscCall(DMSetLabelValue(dm, "marker", face, markerBottom));
1066               }
1067             }
1068           }
1069           cone[0] = edgeB;
1070           cone[1] = edgeR;
1071           cone[2] = edgeT;
1072           cone[3] = edgeL;
1073           PetscCall(DMPlexSetCone(dm, face, cone));
1074           PetscCall(DMPlexSetConeOrientation(dm, face, ornt));
1075         }
1076       }
1077     }
1078     /* Build Z edges*/
1079     for (vy = 0; vy < numYVertices; vy++) {
1080       for (vx = 0; vx < numXVertices; vx++) {
1081         for (ez = 0; ez < numZEdges; ez++) {
1082           const PetscInt edge    = firstZEdge + (vy * numXVertices + vx) * numZEdges + ez;
1083           const PetscInt vertexB = firstVertex + (ez * numYVertices + vy) * numXVertices + vx;
1084           const PetscInt vertexT = firstVertex + (((ez + 1) % numZVertices) * numYVertices + vy) * numXVertices + vx;
1085           PetscInt       cone[2];
1086 
1087           cone[0] = vertexB;
1088           cone[1] = vertexT;
1089           PetscCall(DMPlexSetCone(dm, edge, cone));
1090           if (dim == 3) {
1091             if (bdX != DM_BOUNDARY_PERIODIC) {
1092               if (vx == numXVertices - 1) {
1093                 PetscCall(DMSetLabelValue(dm, "marker", edge, markerRight));
1094                 PetscCall(DMSetLabelValue(dm, "marker", cone[0], markerRight));
1095                 if (ez == numZEdges - 1) PetscCall(DMSetLabelValue(dm, "marker", cone[1], markerRight));
1096               } else if (vx == 0) {
1097                 PetscCall(DMSetLabelValue(dm, "marker", edge, markerLeft));
1098                 PetscCall(DMSetLabelValue(dm, "marker", cone[0], markerLeft));
1099                 if (ez == numZEdges - 1) PetscCall(DMSetLabelValue(dm, "marker", cone[1], markerLeft));
1100               }
1101             }
1102             if (bdY != DM_BOUNDARY_PERIODIC) {
1103               if (vy == numYVertices - 1) {
1104                 PetscCall(DMSetLabelValue(dm, "marker", edge, markerBack));
1105                 PetscCall(DMSetLabelValue(dm, "marker", cone[0], markerBack));
1106                 if (ez == numZEdges - 1) PetscCall(DMSetLabelValue(dm, "marker", cone[1], markerBack));
1107               } else if (vy == 0) {
1108                 PetscCall(DMSetLabelValue(dm, "marker", edge, markerFront));
1109                 PetscCall(DMSetLabelValue(dm, "marker", cone[0], markerFront));
1110                 if (ez == numZEdges - 1) PetscCall(DMSetLabelValue(dm, "marker", cone[1], markerFront));
1111               }
1112             }
1113           }
1114         }
1115       }
1116     }
1117     /* Build Y edges*/
1118     for (vz = 0; vz < numZVertices; vz++) {
1119       for (vx = 0; vx < numXVertices; vx++) {
1120         for (ey = 0; ey < numYEdges; ey++) {
1121           const PetscInt nextv   = (dim == 2 && bdY == DM_BOUNDARY_TWIST && ey == numYEdges - 1) ? (numXVertices - vx - 1) : (vz * numYVertices + ((ey + 1) % numYVertices)) * numXVertices + vx;
1122           const PetscInt edge    = firstYEdge + (vz * numXVertices + vx) * numYEdges + ey;
1123           const PetscInt vertexF = firstVertex + (vz * numYVertices + ey) * numXVertices + vx;
1124           const PetscInt vertexK = firstVertex + nextv;
1125           PetscInt       cone[2];
1126 
1127           cone[0] = vertexF;
1128           cone[1] = vertexK;
1129           PetscCall(DMPlexSetCone(dm, edge, cone));
1130           if (dim == 2) {
1131             if ((bdX != DM_BOUNDARY_PERIODIC) && (bdX != DM_BOUNDARY_TWIST)) {
1132               if (vx == numXVertices - 1) {
1133                 PetscCall(DMSetLabelValue(dm, "Face Sets", edge, faceMarkerRight));
1134                 PetscCall(DMSetLabelValue(dm, "marker", edge, markerRight));
1135                 PetscCall(DMSetLabelValue(dm, "marker", cone[0], markerRight));
1136                 if (ey == numYEdges - 1) PetscCall(DMSetLabelValue(dm, "marker", cone[1], markerRight));
1137               } else if (vx == 0) {
1138                 PetscCall(DMSetLabelValue(dm, "Face Sets", edge, faceMarkerLeft));
1139                 PetscCall(DMSetLabelValue(dm, "marker", edge, markerLeft));
1140                 PetscCall(DMSetLabelValue(dm, "marker", cone[0], markerLeft));
1141                 if (ey == numYEdges - 1) PetscCall(DMSetLabelValue(dm, "marker", cone[1], markerLeft));
1142               }
1143             } else {
1144               if (vx == 0 && cutLabel) {
1145                 PetscCall(DMLabelSetValue(cutLabel, edge, 1));
1146                 PetscCall(DMLabelSetValue(cutLabel, cone[0], 1));
1147                 if (ey == numYEdges - 1) PetscCall(DMLabelSetValue(cutLabel, cone[1], 1));
1148               }
1149             }
1150           } else {
1151             if (bdX != DM_BOUNDARY_PERIODIC) {
1152               if (vx == numXVertices - 1) {
1153                 PetscCall(DMSetLabelValue(dm, "marker", edge, markerRight));
1154                 PetscCall(DMSetLabelValue(dm, "marker", cone[0], markerRight));
1155                 if (ey == numYEdges - 1) PetscCall(DMSetLabelValue(dm, "marker", cone[1], markerRight));
1156               } else if (vx == 0) {
1157                 PetscCall(DMSetLabelValue(dm, "marker", edge, markerLeft));
1158                 PetscCall(DMSetLabelValue(dm, "marker", cone[0], markerLeft));
1159                 if (ey == numYEdges - 1) PetscCall(DMSetLabelValue(dm, "marker", cone[1], markerLeft));
1160               }
1161             }
1162             if (bdZ != DM_BOUNDARY_PERIODIC) {
1163               if (vz == numZVertices - 1) {
1164                 PetscCall(DMSetLabelValue(dm, "marker", edge, markerTop));
1165                 PetscCall(DMSetLabelValue(dm, "marker", cone[0], markerTop));
1166                 if (ey == numYEdges - 1) PetscCall(DMSetLabelValue(dm, "marker", cone[1], markerTop));
1167               } else if (vz == 0) {
1168                 PetscCall(DMSetLabelValue(dm, "marker", edge, markerBottom));
1169                 PetscCall(DMSetLabelValue(dm, "marker", cone[0], markerBottom));
1170                 if (ey == numYEdges - 1) PetscCall(DMSetLabelValue(dm, "marker", cone[1], markerBottom));
1171               }
1172             }
1173           }
1174         }
1175       }
1176     }
1177     /* Build X edges*/
1178     for (vz = 0; vz < numZVertices; vz++) {
1179       for (vy = 0; vy < numYVertices; vy++) {
1180         for (ex = 0; ex < numXEdges; ex++) {
1181           const PetscInt nextv   = (dim == 2 && bdX == DM_BOUNDARY_TWIST && ex == numXEdges - 1) ? (numYVertices - vy - 1) * numXVertices : (vz * numYVertices + vy) * numXVertices + (ex + 1) % numXVertices;
1182           const PetscInt edge    = firstXEdge + (vz * numYVertices + vy) * numXEdges + ex;
1183           const PetscInt vertexL = firstVertex + (vz * numYVertices + vy) * numXVertices + ex;
1184           const PetscInt vertexR = firstVertex + nextv;
1185           PetscInt       cone[2];
1186 
1187           cone[0] = vertexL;
1188           cone[1] = vertexR;
1189           PetscCall(DMPlexSetCone(dm, edge, cone));
1190           if (dim == 2) {
1191             if ((bdY != DM_BOUNDARY_PERIODIC) && (bdY != DM_BOUNDARY_TWIST)) {
1192               if (vy == numYVertices - 1) {
1193                 PetscCall(DMSetLabelValue(dm, "Face Sets", edge, faceMarkerTop));
1194                 PetscCall(DMSetLabelValue(dm, "marker", edge, markerTop));
1195                 PetscCall(DMSetLabelValue(dm, "marker", cone[0], markerTop));
1196                 if (ex == numXEdges - 1) PetscCall(DMSetLabelValue(dm, "marker", cone[1], markerTop));
1197               } else if (vy == 0) {
1198                 PetscCall(DMSetLabelValue(dm, "Face Sets", edge, faceMarkerBottom));
1199                 PetscCall(DMSetLabelValue(dm, "marker", edge, markerBottom));
1200                 PetscCall(DMSetLabelValue(dm, "marker", cone[0], markerBottom));
1201                 if (ex == numXEdges - 1) PetscCall(DMSetLabelValue(dm, "marker", cone[1], markerBottom));
1202               }
1203             } else {
1204               if (vy == 0 && cutLabel) {
1205                 PetscCall(DMLabelSetValue(cutLabel, edge, 1));
1206                 PetscCall(DMLabelSetValue(cutLabel, cone[0], 1));
1207                 if (ex == numXEdges - 1) PetscCall(DMLabelSetValue(cutLabel, cone[1], 1));
1208               }
1209             }
1210           } else {
1211             if (bdY != DM_BOUNDARY_PERIODIC) {
1212               if (vy == numYVertices - 1) {
1213                 PetscCall(DMSetLabelValue(dm, "marker", edge, markerBack));
1214                 PetscCall(DMSetLabelValue(dm, "marker", cone[0], markerBack));
1215                 if (ex == numXEdges - 1) PetscCall(DMSetLabelValue(dm, "marker", cone[1], markerBack));
1216               } else if (vy == 0) {
1217                 PetscCall(DMSetLabelValue(dm, "marker", edge, markerFront));
1218                 PetscCall(DMSetLabelValue(dm, "marker", cone[0], markerFront));
1219                 if (ex == numXEdges - 1) PetscCall(DMSetLabelValue(dm, "marker", cone[1], markerFront));
1220               }
1221             }
1222             if (bdZ != DM_BOUNDARY_PERIODIC) {
1223               if (vz == numZVertices - 1) {
1224                 PetscCall(DMSetLabelValue(dm, "marker", edge, markerTop));
1225                 PetscCall(DMSetLabelValue(dm, "marker", cone[0], markerTop));
1226                 if (ex == numXEdges - 1) PetscCall(DMSetLabelValue(dm, "marker", cone[1], markerTop));
1227               } else if (vz == 0) {
1228                 PetscCall(DMSetLabelValue(dm, "marker", edge, markerBottom));
1229                 PetscCall(DMSetLabelValue(dm, "marker", cone[0], markerBottom));
1230                 if (ex == numXEdges - 1) PetscCall(DMSetLabelValue(dm, "marker", cone[1], markerBottom));
1231               }
1232             }
1233           }
1234         }
1235       }
1236     }
1237     PetscCall(DMPlexSymmetrize(dm));
1238     PetscCall(DMPlexStratify(dm));
1239     /* Build coordinates */
1240     PetscCall(DMGetCoordinateSection(dm, &coordSection));
1241     PetscCall(PetscSectionSetNumFields(coordSection, 1));
1242     PetscCall(PetscSectionSetFieldComponents(coordSection, 0, dim));
1243     PetscCall(PetscSectionSetChart(coordSection, firstVertex, firstVertex + numVertices));
1244     for (v = firstVertex; v < firstVertex + numVertices; ++v) {
1245       PetscCall(PetscSectionSetDof(coordSection, v, dim));
1246       PetscCall(PetscSectionSetFieldDof(coordSection, v, 0, dim));
1247     }
1248     PetscCall(PetscSectionSetUp(coordSection));
1249     PetscCall(PetscSectionGetStorageSize(coordSection, &coordSize));
1250     PetscCall(VecCreate(PETSC_COMM_SELF, &coordinates));
1251     PetscCall(PetscObjectSetName((PetscObject)coordinates, "coordinates"));
1252     PetscCall(VecSetSizes(coordinates, coordSize, PETSC_DETERMINE));
1253     PetscCall(VecSetBlockSize(coordinates, dim));
1254     PetscCall(VecSetType(coordinates, VECSTANDARD));
1255     PetscCall(VecGetArray(coordinates, &coords));
1256     for (vz = 0; vz < numZVertices; ++vz) {
1257       for (vy = 0; vy < numYVertices; ++vy) {
1258         for (vx = 0; vx < numXVertices; ++vx) {
1259           coords[((vz * numYVertices + vy) * numXVertices + vx) * dim + 0] = lower[0] + ((upper[0] - lower[0]) / numXEdges) * vx;
1260           coords[((vz * numYVertices + vy) * numXVertices + vx) * dim + 1] = lower[1] + ((upper[1] - lower[1]) / numYEdges) * vy;
1261           if (dim == 3) coords[((vz * numYVertices + vy) * numXVertices + vx) * dim + 2] = lower[2] + ((upper[2] - lower[2]) / numZEdges) * vz;
1262         }
1263       }
1264     }
1265     PetscCall(VecRestoreArray(coordinates, &coords));
1266     PetscCall(DMSetCoordinatesLocal(dm, coordinates));
1267     PetscCall(VecDestroy(&coordinates));
1268   }
1269   PetscFunctionReturn(PETSC_SUCCESS);
1270 }
1271 
1272 static PetscErrorCode DMPlexCreateBoxMesh_Tensor_Internal(DM dm, PetscInt dim, const PetscInt faces[], const PetscReal lower[], const PetscReal upper[], const DMBoundaryType periodicity[])
1273 {
1274   DMBoundaryType bdt[3] = {DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE};
1275   PetscInt       fac[3] = {0, 0, 0}, d;
1276 
1277   PetscFunctionBegin;
1278   PetscAssertPointer(dm, 1);
1279   PetscValidLogicalCollectiveInt(dm, dim, 2);
1280   PetscCall(DMSetDimension(dm, dim));
1281   for (d = 0; d < dim; ++d) {
1282     fac[d] = faces[d];
1283     bdt[d] = periodicity[d];
1284   }
1285   PetscCall(DMPlexCreateCubeMesh_Internal(dm, lower, upper, fac, bdt[0], bdt[1], bdt[2]));
1286   if (periodicity[0] == DM_BOUNDARY_PERIODIC || periodicity[0] == DM_BOUNDARY_TWIST || periodicity[1] == DM_BOUNDARY_PERIODIC || periodicity[1] == DM_BOUNDARY_TWIST || (dim > 2 && (periodicity[2] == DM_BOUNDARY_PERIODIC || periodicity[2] == DM_BOUNDARY_TWIST))) {
1287     PetscReal L[3]       = {-1., -1., 0.};
1288     PetscReal maxCell[3] = {-1., -1., 0.};
1289 
1290     for (d = 0; d < dim; ++d) {
1291       if (periodicity[d] != DM_BOUNDARY_NONE) {
1292         L[d]       = upper[d] - lower[d];
1293         maxCell[d] = 1.1 * (L[d] / PetscMax(1, faces[d]));
1294       }
1295     }
1296     PetscCall(DMSetPeriodicity(dm, maxCell, lower, L));
1297   }
1298   PetscCall(DMPlexSetRefinementUniform(dm, PETSC_TRUE));
1299   PetscFunctionReturn(PETSC_SUCCESS);
1300 }
1301 
1302 static PetscErrorCode DMPlexCreateBoxMesh_Internal(DM dm, DMPlexShape shape, PetscInt dim, PetscBool simplex, const PetscInt faces[], const PetscReal lower[], const PetscReal upper[], const DMBoundaryType periodicity[], PetscBool interpolate)
1303 {
1304   PetscFunctionBegin;
1305   PetscCall(PetscLogEventBegin(DMPLEX_Generate, dm, 0, 0, 0));
1306   if (shape == DM_SHAPE_ZBOX) PetscCall(DMPlexCreateBoxMesh_Tensor_SFC_Internal(dm, dim, faces, lower, upper, periodicity, interpolate));
1307   else if (dim == 1) PetscCall(DMPlexCreateLineMesh_Internal(dm, faces[0], lower[0], upper[0], periodicity[0]));
1308   else if (simplex) PetscCall(DMPlexCreateBoxMesh_Simplex_Internal(dm, dim, faces, lower, upper, periodicity, interpolate));
1309   else PetscCall(DMPlexCreateBoxMesh_Tensor_Internal(dm, dim, faces, lower, upper, periodicity));
1310   if (!interpolate && dim > 1 && !simplex) {
1311     DM udm;
1312 
1313     PetscCall(DMPlexUninterpolate(dm, &udm));
1314     PetscCall(DMPlexCopyCoordinates(dm, udm));
1315     PetscCall(DMPlexReplace_Internal(dm, &udm));
1316   }
1317   PetscCall(PetscLogEventEnd(DMPLEX_Generate, dm, 0, 0, 0));
1318   PetscFunctionReturn(PETSC_SUCCESS);
1319 }
1320 
1321 /*@C
1322   DMPlexCreateBoxMesh - Creates a mesh on the tensor product of unit intervals (box) using simplices or tensor cells (hexahedra).
1323 
1324   Collective
1325 
1326   Input Parameters:
1327 + comm        - The communicator for the `DM` object
1328 . dim         - The spatial dimension
1329 . simplex     - `PETSC_TRUE` for simplices, `PETSC_FALSE` for tensor cells
1330 . faces       - Number of faces per dimension, or `NULL` for (1,) in 1D and (2, 2) in 2D and (1, 1, 1) in 3D
1331 . lower       - The lower left corner, or `NULL` for (0, 0, 0)
1332 . upper       - The upper right corner, or `NULL` for (1, 1, 1)
1333 . periodicity - The boundary type for the X,Y,Z direction, or `NULL` for `DM_BOUNDARY_NONE`
1334 - interpolate - Flag to create intermediate mesh pieces (edges, faces)
1335 
1336   Output Parameter:
1337 . dm - The `DM` object
1338 
1339   Level: beginner
1340 
1341   Note:
1342   To customize this mesh using options, use
1343 .vb
1344   DMCreate(comm, &dm);
1345   DMSetType(dm, DMPLEX);
1346   DMSetFromOptions(dm);
1347 .ve
1348   and use the options in `DMSetFromOptions()`.
1349 
1350   Here is the numbering returned for 2 faces in each direction for tensor cells\:
1351 .vb
1352  10---17---11---18----12
1353   |         |         |
1354   |         |         |
1355  20    2   22    3    24
1356   |         |         |
1357   |         |         |
1358   7---15----8---16----9
1359   |         |         |
1360   |         |         |
1361  19    0   21    1   23
1362   |         |         |
1363   |         |         |
1364   4---13----5---14----6
1365 .ve
1366   and for simplicial cells
1367 .vb
1368  14----8---15----9----16
1369   |\     5  |\      7 |
1370   | \       | \       |
1371  13   2    14    3    15
1372   | 4   \   | 6   \   |
1373   |       \ |       \ |
1374  11----6---12----7----13
1375   |\        |\        |
1376   | \    1  | \     3 |
1377  10   0    11    1    12
1378   | 0   \   | 2   \   |
1379   |       \ |       \ |
1380   8----4----9----5----10
1381 .ve
1382 
1383 .seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMSetFromOptions()`, `DMPlexCreateFromFile()`, `DMPlexCreateHexCylinderMesh()`, `DMSetType()`, `DMCreate()`
1384 @*/
1385 PetscErrorCode DMPlexCreateBoxMesh(MPI_Comm comm, PetscInt dim, PetscBool simplex, const PetscInt faces[], const PetscReal lower[], const PetscReal upper[], const DMBoundaryType periodicity[], PetscBool interpolate, DM *dm)
1386 {
1387   PetscInt       fac[3] = {1, 1, 1};
1388   PetscReal      low[3] = {0, 0, 0};
1389   PetscReal      upp[3] = {1, 1, 1};
1390   DMBoundaryType bdt[3] = {DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE};
1391 
1392   PetscFunctionBegin;
1393   PetscCall(DMCreate(comm, dm));
1394   PetscCall(DMSetType(*dm, DMPLEX));
1395   PetscCall(DMPlexCreateBoxMesh_Internal(*dm, DM_SHAPE_BOX, dim, simplex, faces ? faces : fac, lower ? lower : low, upper ? upper : upp, periodicity ? periodicity : bdt, interpolate));
1396   if (periodicity) PetscCall(DMLocalizeCoordinates(*dm));
1397   PetscFunctionReturn(PETSC_SUCCESS);
1398 }
1399 
1400 static PetscErrorCode DMPlexCreateWedgeBoxMesh_Internal(DM dm, const PetscInt faces[], const PetscReal lower[], const PetscReal upper[], const DMBoundaryType periodicity[])
1401 {
1402   DM       bdm, vol;
1403   PetscInt i;
1404 
1405   PetscFunctionBegin;
1406   // TODO Now we can support periodicity
1407   for (i = 0; i < 3; ++i) PetscCheck(periodicity[i] == DM_BOUNDARY_NONE, PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Periodicity not yet supported");
1408   PetscCall(DMCreate(PetscObjectComm((PetscObject)dm), &bdm));
1409   PetscCall(DMSetType(bdm, DMPLEX));
1410   PetscCall(DMSetDimension(bdm, 2));
1411   PetscCall(PetscLogEventBegin(DMPLEX_Generate, bdm, 0, 0, 0));
1412   PetscCall(DMPlexCreateBoxMesh_Simplex_Internal(bdm, 2, faces, lower, upper, periodicity, PETSC_TRUE));
1413   PetscCall(DMPlexExtrude(bdm, faces[2], upper[2] - lower[2], PETSC_TRUE, PETSC_FALSE, PETSC_FALSE, NULL, NULL, &vol));
1414   PetscCall(PetscLogEventEnd(DMPLEX_Generate, bdm, 0, 0, 0));
1415   PetscCall(DMDestroy(&bdm));
1416   PetscCall(DMPlexReplace_Internal(dm, &vol));
1417   if (lower[2] != 0.0) {
1418     Vec          v;
1419     PetscScalar *x;
1420     PetscInt     cDim, n;
1421 
1422     PetscCall(DMGetCoordinatesLocal(dm, &v));
1423     PetscCall(VecGetBlockSize(v, &cDim));
1424     PetscCall(VecGetLocalSize(v, &n));
1425     PetscCall(VecGetArray(v, &x));
1426     x += cDim;
1427     for (i = 0; i < n; i += cDim) x[i] += lower[2];
1428     PetscCall(VecRestoreArray(v, &x));
1429     PetscCall(DMSetCoordinatesLocal(dm, v));
1430   }
1431   PetscFunctionReturn(PETSC_SUCCESS);
1432 }
1433 
1434 /*@
1435   DMPlexCreateWedgeBoxMesh - Creates a 3-D mesh tesselating the (x,y) plane and extruding in the third direction using wedge cells.
1436 
1437   Collective
1438 
1439   Input Parameters:
1440 + comm        - The communicator for the `DM` object
1441 . faces       - Number of faces per dimension, or `NULL` for (1, 1, 1)
1442 . lower       - The lower left corner, or `NULL` for (0, 0, 0)
1443 . upper       - The upper right corner, or `NULL` for (1, 1, 1)
1444 . periodicity - The boundary type for the X,Y,Z direction, or `NULL` for `DM_BOUNDARY_NONE`
1445 . orderHeight - If `PETSC_TRUE`, orders the extruded cells in the height first. Otherwise, orders the cell on the layers first
1446 - interpolate - Flag to create intermediate mesh pieces (edges, faces)
1447 
1448   Output Parameter:
1449 . dm - The `DM` object
1450 
1451   Level: beginner
1452 
1453 .seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexCreateHexCylinderMesh()`, `DMPlexCreateWedgeCylinderMesh()`, `DMExtrude()`, `DMPlexCreateBoxMesh()`, `DMSetType()`, `DMCreate()`
1454 @*/
1455 PetscErrorCode DMPlexCreateWedgeBoxMesh(MPI_Comm comm, const PetscInt faces[], const PetscReal lower[], const PetscReal upper[], const DMBoundaryType periodicity[], PetscBool orderHeight, PetscBool interpolate, DM *dm)
1456 {
1457   PetscInt       fac[3] = {1, 1, 1};
1458   PetscReal      low[3] = {0, 0, 0};
1459   PetscReal      upp[3] = {1, 1, 1};
1460   DMBoundaryType bdt[3] = {DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE};
1461 
1462   PetscFunctionBegin;
1463   PetscCall(DMCreate(comm, dm));
1464   PetscCall(DMSetType(*dm, DMPLEX));
1465   PetscCall(DMPlexCreateWedgeBoxMesh_Internal(*dm, faces ? faces : fac, lower ? lower : low, upper ? upper : upp, periodicity ? periodicity : bdt));
1466   if (!interpolate) {
1467     DM udm;
1468 
1469     PetscCall(DMPlexUninterpolate(*dm, &udm));
1470     PetscCall(DMPlexReplace_Internal(*dm, &udm));
1471   }
1472   if (periodicity) PetscCall(DMLocalizeCoordinates(*dm));
1473   PetscFunctionReturn(PETSC_SUCCESS);
1474 }
1475 
1476 /*
1477   DMPlexTensorPointLexicographic_Private - Returns all tuples of size 'len' with nonnegative integers that are all less than or equal to 'max' for that dimension.
1478 
1479   Input Parameters:
1480 + len - The length of the tuple
1481 . max - The maximum for each dimension, so values are in [0, max)
1482 - tup - A tuple of length len+1: tup[len] > 0 indicates a stopping condition
1483 
1484   Output Parameter:
1485 . tup - A tuple of `len` integers whose entries are at most `max`
1486 
1487   Level: developer
1488 
1489   Note:
1490   Ordering is lexicographic with lowest index as least significant in ordering.
1491   e.g. for len == 2 and max == 2, this will return, in order, {0,0}, {1,0}, {2,0}, {0,1}, {1,1}, {2,1}, {0,2}, {1,2}, {2,2}.
1492 
1493 .seealso: PetscDualSpaceTensorPointLexicographic_Internal(), PetscDualSpaceLatticePointLexicographic_Internal()
1494 */
1495 static PetscErrorCode DMPlexTensorPointLexicographic_Private(PetscInt len, const PetscInt max[], PetscInt tup[])
1496 {
1497   PetscInt i;
1498 
1499   PetscFunctionBegin;
1500   for (i = 0; i < len; ++i) {
1501     if (tup[i] < max[i] - 1) {
1502       break;
1503     } else {
1504       tup[i] = 0;
1505     }
1506   }
1507   if (i == len) tup[i - 1] = max[i - 1];
1508   else ++tup[i];
1509   PetscFunctionReturn(PETSC_SUCCESS);
1510 }
1511 
1512 static PetscInt TupleToIndex_Private(PetscInt len, const PetscInt max[], const PetscInt tup[])
1513 {
1514   PetscInt i, idx = tup[len - 1];
1515 
1516   for (i = len - 2; i >= 0; --i) {
1517     idx *= max[i];
1518     idx += tup[i];
1519   }
1520   return idx;
1521 }
1522 
1523 static PetscErrorCode DestroyExtent_Private(void *extent)
1524 {
1525   return PetscFree(extent);
1526 }
1527 
1528 static PetscErrorCode DMPlexCreateHypercubicMesh_Internal(DM dm, PetscInt dim, const PetscReal lower[], const PetscReal upper[], const PetscInt edges[], const DMBoundaryType bd[])
1529 {
1530   Vec          coordinates;
1531   PetscSection coordSection;
1532   DMLabel      cutLabel    = NULL;
1533   PetscBool    cutMarker   = PETSC_FALSE;
1534   PetscBool    periodic    = PETSC_FALSE;
1535   PetscInt     numCells    = 1, c;
1536   PetscInt     numVertices = 1, v;
1537   PetscScalar *coords;
1538   PetscInt    *vertices, *vert, *vtmp, *supp, cone[2];
1539   PetscInt     d, e, cell = 0, coordSize;
1540   PetscMPIInt  rank;
1541 
1542   PetscFunctionBegin;
1543   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank));
1544   PetscCall(DMSetDimension(dm, dim));
1545   PetscCall(PetscCalloc4(dim, &vertices, dim, &vert, dim, &vtmp, 2 * dim, &supp));
1546   PetscCall(DMCreateLabel(dm, "marker"));
1547   PetscCall(PetscOptionsGetBool(((PetscObject)dm)->options, ((PetscObject)dm)->prefix, "-dm_plex_periodic_cut", &cutMarker, NULL));
1548   for (d = 0; d < dim; ++d) periodic = (periodic || bd[d] == DM_BOUNDARY_PERIODIC) ? PETSC_TRUE : PETSC_FALSE;
1549   if (periodic && cutMarker) {
1550     PetscCall(DMCreateLabel(dm, "periodic_cut"));
1551     PetscCall(DMGetLabel(dm, "periodic_cut", &cutLabel));
1552   }
1553   for (d = 0; d < dim; ++d) PetscCheck(bd[d] == DM_BOUNDARY_PERIODIC, PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Hypercubic mesh must be periodic now");
1554   for (d = 0; d < dim; ++d) {
1555     vertices[d] = edges[d];
1556     numVertices *= vertices[d];
1557   }
1558   numCells = numVertices * dim;
1559   PetscCall(DMPlexSetChart(dm, 0, numCells + numVertices));
1560   for (c = 0; c < numCells; ++c) PetscCall(DMPlexSetConeSize(dm, c, 2));
1561   for (v = numCells; v < numCells + numVertices; ++v) PetscCall(DMPlexSetSupportSize(dm, v, 2 * dim));
1562   /* TODO Loop over boundary and reset support sizes */
1563   PetscCall(DMSetUp(dm)); /* Allocate space for cones and supports */
1564   /* Build cell cones and vertex supports */
1565   PetscCall(DMCreateLabel(dm, "celltype"));
1566   while (vert[dim - 1] < vertices[dim - 1]) {
1567     const PetscInt vertex = TupleToIndex_Private(dim, vertices, vert) + numCells;
1568     PetscInt       s      = 0;
1569 
1570     PetscCall(PetscPrintf(PETSC_COMM_SELF, "Vertex %" PetscInt_FMT ":", vertex));
1571     for (d = 0; d < dim; ++d) PetscCall(PetscPrintf(PETSC_COMM_SELF, " %" PetscInt_FMT, vert[d]));
1572     PetscCall(PetscPrintf(PETSC_COMM_SELF, "\n"));
1573     PetscCall(DMPlexSetCellType(dm, vertex, DM_POLYTOPE_POINT));
1574     for (d = 0; d < dim; ++d) {
1575       for (e = 0; e < dim; ++e) vtmp[e] = vert[e];
1576       vtmp[d] = (vert[d] + 1) % vertices[d];
1577       cone[0] = vertex;
1578       cone[1] = TupleToIndex_Private(dim, vertices, vtmp) + numCells;
1579       PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Vertex %" PetscInt_FMT ":", cone[1]));
1580       for (e = 0; e < dim; ++e) PetscCall(PetscPrintf(PETSC_COMM_SELF, " %" PetscInt_FMT, vtmp[e]));
1581       PetscCall(PetscPrintf(PETSC_COMM_SELF, "\n"));
1582       PetscCall(DMPlexSetCone(dm, cell, cone));
1583       PetscCall(DMPlexSetCellType(dm, cell, DM_POLYTOPE_SEGMENT));
1584       PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Edge %" PetscInt_FMT " (%" PetscInt_FMT " %" PetscInt_FMT ")\n", cell, cone[0], cone[1]));
1585       ++cell;
1586     }
1587     for (d = 0; d < dim; ++d) {
1588       for (e = 0; e < dim; ++e) vtmp[e] = vert[e];
1589       vtmp[d]   = (vert[d] + vertices[d] - 1) % vertices[d];
1590       supp[s++] = TupleToIndex_Private(dim, vertices, vtmp) * dim + d;
1591       supp[s++] = (vertex - numCells) * dim + d;
1592       PetscCall(DMPlexSetSupport(dm, vertex, supp));
1593     }
1594     PetscCall(DMPlexTensorPointLexicographic_Private(dim, vertices, vert));
1595   }
1596   PetscCall(DMPlexStratify(dm));
1597   /* Build coordinates */
1598   PetscCall(DMGetCoordinateSection(dm, &coordSection));
1599   PetscCall(PetscSectionSetNumFields(coordSection, 1));
1600   PetscCall(PetscSectionSetFieldComponents(coordSection, 0, dim));
1601   PetscCall(PetscSectionSetChart(coordSection, numCells, numCells + numVertices));
1602   for (v = numCells; v < numCells + numVertices; ++v) {
1603     PetscCall(PetscSectionSetDof(coordSection, v, dim));
1604     PetscCall(PetscSectionSetFieldDof(coordSection, v, 0, dim));
1605   }
1606   PetscCall(PetscSectionSetUp(coordSection));
1607   PetscCall(PetscSectionGetStorageSize(coordSection, &coordSize));
1608   PetscCall(VecCreate(PETSC_COMM_SELF, &coordinates));
1609   PetscCall(PetscObjectSetName((PetscObject)coordinates, "coordinates"));
1610   PetscCall(VecSetSizes(coordinates, coordSize, PETSC_DETERMINE));
1611   PetscCall(VecSetBlockSize(coordinates, dim));
1612   PetscCall(VecSetType(coordinates, VECSTANDARD));
1613   PetscCall(VecGetArray(coordinates, &coords));
1614   for (d = 0; d < dim; ++d) vert[d] = 0;
1615   while (vert[dim - 1] < vertices[dim - 1]) {
1616     const PetscInt vertex = TupleToIndex_Private(dim, vertices, vert);
1617 
1618     for (d = 0; d < dim; ++d) coords[vertex * dim + d] = lower[d] + ((upper[d] - lower[d]) / vertices[d]) * vert[d];
1619     PetscCall(PetscPrintf(PETSC_COMM_SELF, "Vertex %" PetscInt_FMT ":", vertex));
1620     for (d = 0; d < dim; ++d) PetscCall(PetscPrintf(PETSC_COMM_SELF, " %" PetscInt_FMT, vert[d]));
1621     for (d = 0; d < dim; ++d) PetscCall(PetscPrintf(PETSC_COMM_SELF, " %g", (double)PetscRealPart(coords[vertex * dim + d])));
1622     PetscCall(PetscPrintf(PETSC_COMM_SELF, "\n"));
1623     PetscCall(DMPlexTensorPointLexicographic_Private(dim, vertices, vert));
1624   }
1625   PetscCall(VecRestoreArray(coordinates, &coords));
1626   PetscCall(DMSetCoordinatesLocal(dm, coordinates));
1627   PetscCall(VecDestroy(&coordinates));
1628   PetscCall(PetscFree4(vertices, vert, vtmp, supp));
1629   //PetscCall(DMSetPeriodicity(dm, NULL, lower, upper));
1630   // Attach the extent
1631   {
1632     PetscContainer c;
1633     PetscInt      *extent;
1634 
1635     PetscCall(PetscMalloc1(dim, &extent));
1636     for (PetscInt d = 0; d < dim; ++d) extent[d] = edges[d];
1637     PetscCall(PetscContainerCreate(PETSC_COMM_SELF, &c));
1638     PetscCall(PetscContainerSetUserDestroy(c, DestroyExtent_Private));
1639     PetscCall(PetscContainerSetPointer(c, extent));
1640     PetscCall(PetscObjectCompose((PetscObject)dm, "_extent", (PetscObject)c));
1641     PetscCall(PetscContainerDestroy(&c));
1642   }
1643   PetscFunctionReturn(PETSC_SUCCESS);
1644 }
1645 
1646 /*@C
1647   DMPlexCreateHypercubicMesh - Creates a periodic mesh on the tensor product of unit intervals using only vertices and edges.
1648 
1649   Collective
1650 
1651   Input Parameters:
1652 + comm  - The communicator for the DM object
1653 . dim   - The spatial dimension
1654 . edges - Number of edges per dimension, or `NULL` for (1,) in 1D and (2, 2) in 2D and (1, 1, 1) in 3D
1655 . lower - The lower left corner, or `NULL` for (0, 0, 0)
1656 - upper - The upper right corner, or `NULL` for (1, 1, 1)
1657 
1658   Output Parameter:
1659 . dm - The DM object
1660 
1661   Level: beginner
1662 
1663   Note:
1664   If you want to customize this mesh using options, you just need to
1665 .vb
1666   DMCreate(comm, &dm);
1667   DMSetType(dm, DMPLEX);
1668   DMSetFromOptions(dm);
1669 .ve
1670   and use the options on the `DMSetFromOptions()` page.
1671 
1672   The vertices are numbered is lexicographic order, and the dim edges exiting a vertex in the positive orthant are number consecutively,
1673 .vb
1674  18--0-19--2-20--4-18
1675   |     |     |     |
1676  13    15    17    13
1677   |     |     |     |
1678  24-12-25-14-26-16-24
1679   |     |     |     |
1680   7     9    11     7
1681   |     |     |     |
1682  21--6-22--8-23-10-21
1683   |     |     |     |
1684   1     3     5     1
1685   |     |     |     |
1686  18--0-19--2-20--4-18
1687 .ve
1688 
1689 .seealso: `DMSetFromOptions()`, `DMPlexCreateFromFile()`, `DMPlexCreateHexCylinderMesh()`, `DMSetType()`, `DMCreate()`
1690 @*/
1691 PetscErrorCode DMPlexCreateHypercubicMesh(MPI_Comm comm, PetscInt dim, const PetscInt edges[], const PetscReal lower[], const PetscReal upper[], DM *dm)
1692 {
1693   PetscInt       *edg;
1694   PetscReal      *low, *upp;
1695   DMBoundaryType *bdt;
1696   PetscInt        d;
1697 
1698   PetscFunctionBegin;
1699   PetscCall(DMCreate(comm, dm));
1700   PetscCall(DMSetType(*dm, DMPLEX));
1701   PetscCall(PetscMalloc4(dim, &edg, dim, &low, dim, &upp, dim, &bdt));
1702   for (d = 0; d < dim; ++d) {
1703     edg[d] = edges ? edges[d] : 1;
1704     low[d] = lower ? lower[d] : 0.;
1705     upp[d] = upper ? upper[d] : 1.;
1706     bdt[d] = DM_BOUNDARY_PERIODIC;
1707   }
1708   PetscCall(DMPlexCreateHypercubicMesh_Internal(*dm, dim, low, upp, edg, bdt));
1709   PetscCall(PetscFree4(edg, low, upp, bdt));
1710   PetscFunctionReturn(PETSC_SUCCESS);
1711 }
1712 
1713 /*@C
1714   DMPlexSetOptionsPrefix - Sets the prefix used for searching for all `DM` options in the database.
1715 
1716   Logically Collective
1717 
1718   Input Parameters:
1719 + dm     - the `DM` context
1720 - prefix - the prefix to prepend to all option names
1721 
1722   Level: advanced
1723 
1724   Note:
1725   A hyphen (-) must NOT be given at the beginning of the prefix name.
1726   The first character of all runtime options is AUTOMATICALLY the hyphen.
1727 
1728 .seealso: [](ch_unstructured), `DM`, `DMPLEX`, `SNESSetFromOptions()`
1729 @*/
1730 PetscErrorCode DMPlexSetOptionsPrefix(DM dm, const char prefix[])
1731 {
1732   DM_Plex *mesh = (DM_Plex *)dm->data;
1733 
1734   PetscFunctionBegin;
1735   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1736   PetscCall(PetscObjectSetOptionsPrefix((PetscObject)dm, prefix));
1737   PetscCall(PetscObjectSetOptionsPrefix((PetscObject)mesh->partitioner, prefix));
1738   PetscFunctionReturn(PETSC_SUCCESS);
1739 }
1740 
1741 /* Remap geometry to cylinder
1742    TODO: This only works for a single refinement, then it is broken
1743 
1744      Interior square: Linear interpolation is correct
1745      The other cells all have vertices on rays from the origin. We want to uniformly expand the spacing
1746      such that the last vertex is on the unit circle. So the closest and farthest vertices are at distance
1747 
1748        phi     = arctan(y/x)
1749        d_close = sqrt(1/8 + 1/4 sin^2(phi))
1750        d_far   = sqrt(1/2 + sin^2(phi))
1751 
1752      so we remap them using
1753 
1754        x_new = x_close + (x - x_close) (1 - d_close) / (d_far - d_close)
1755        y_new = y_close + (y - y_close) (1 - d_close) / (d_far - d_close)
1756 
1757      If pi/4 < phi < 3pi/4 or -3pi/4 < phi < -pi/4, then we switch x and y.
1758 */
1759 static void snapToCylinder(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
1760 {
1761   const PetscReal dis = 1.0 / PetscSqrtReal(2.0);
1762   const PetscReal ds2 = 0.5 * dis;
1763 
1764   if ((PetscAbsScalar(u[0]) <= ds2) && (PetscAbsScalar(u[1]) <= ds2)) {
1765     f0[0] = u[0];
1766     f0[1] = u[1];
1767   } else {
1768     PetscReal phi, sinp, cosp, dc, df, x, y, xc, yc;
1769 
1770     x    = PetscRealPart(u[0]);
1771     y    = PetscRealPart(u[1]);
1772     phi  = PetscAtan2Real(y, x);
1773     sinp = PetscSinReal(phi);
1774     cosp = PetscCosReal(phi);
1775     if ((PetscAbsReal(phi) > PETSC_PI / 4.0) && (PetscAbsReal(phi) < 3.0 * PETSC_PI / 4.0)) {
1776       dc = PetscAbsReal(ds2 / sinp);
1777       df = PetscAbsReal(dis / sinp);
1778       xc = ds2 * x / PetscAbsReal(y);
1779       yc = ds2 * PetscSignReal(y);
1780     } else {
1781       dc = PetscAbsReal(ds2 / cosp);
1782       df = PetscAbsReal(dis / cosp);
1783       xc = ds2 * PetscSignReal(x);
1784       yc = ds2 * y / PetscAbsReal(x);
1785     }
1786     f0[0] = xc + (u[0] - xc) * (1.0 - dc) / (df - dc);
1787     f0[1] = yc + (u[1] - yc) * (1.0 - dc) / (df - dc);
1788   }
1789   f0[2] = u[2];
1790 }
1791 
1792 static PetscErrorCode DMPlexCreateHexCylinderMesh_Internal(DM dm, DMBoundaryType periodicZ)
1793 {
1794   const PetscInt dim = 3;
1795   PetscInt       numCells, numVertices;
1796   PetscMPIInt    rank;
1797 
1798   PetscFunctionBegin;
1799   PetscCall(PetscLogEventBegin(DMPLEX_Generate, dm, 0, 0, 0));
1800   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank));
1801   PetscCall(DMSetDimension(dm, dim));
1802   /* Create topology */
1803   {
1804     PetscInt cone[8], c;
1805 
1806     numCells    = rank == 0 ? 5 : 0;
1807     numVertices = rank == 0 ? 16 : 0;
1808     if (periodicZ == DM_BOUNDARY_PERIODIC) {
1809       numCells *= 3;
1810       numVertices = rank == 0 ? 24 : 0;
1811     }
1812     PetscCall(DMPlexSetChart(dm, 0, numCells + numVertices));
1813     for (c = 0; c < numCells; c++) PetscCall(DMPlexSetConeSize(dm, c, 8));
1814     PetscCall(DMSetUp(dm));
1815     if (rank == 0) {
1816       if (periodicZ == DM_BOUNDARY_PERIODIC) {
1817         cone[0] = 15;
1818         cone[1] = 18;
1819         cone[2] = 17;
1820         cone[3] = 16;
1821         cone[4] = 31;
1822         cone[5] = 32;
1823         cone[6] = 33;
1824         cone[7] = 34;
1825         PetscCall(DMPlexSetCone(dm, 0, cone));
1826         cone[0] = 16;
1827         cone[1] = 17;
1828         cone[2] = 24;
1829         cone[3] = 23;
1830         cone[4] = 32;
1831         cone[5] = 36;
1832         cone[6] = 37;
1833         cone[7] = 33; /* 22 25 26 21 */
1834         PetscCall(DMPlexSetCone(dm, 1, cone));
1835         cone[0] = 18;
1836         cone[1] = 27;
1837         cone[2] = 24;
1838         cone[3] = 17;
1839         cone[4] = 34;
1840         cone[5] = 33;
1841         cone[6] = 37;
1842         cone[7] = 38;
1843         PetscCall(DMPlexSetCone(dm, 2, cone));
1844         cone[0] = 29;
1845         cone[1] = 27;
1846         cone[2] = 18;
1847         cone[3] = 15;
1848         cone[4] = 35;
1849         cone[5] = 31;
1850         cone[6] = 34;
1851         cone[7] = 38;
1852         PetscCall(DMPlexSetCone(dm, 3, cone));
1853         cone[0] = 29;
1854         cone[1] = 15;
1855         cone[2] = 16;
1856         cone[3] = 23;
1857         cone[4] = 35;
1858         cone[5] = 36;
1859         cone[6] = 32;
1860         cone[7] = 31;
1861         PetscCall(DMPlexSetCone(dm, 4, cone));
1862 
1863         cone[0] = 31;
1864         cone[1] = 34;
1865         cone[2] = 33;
1866         cone[3] = 32;
1867         cone[4] = 19;
1868         cone[5] = 22;
1869         cone[6] = 21;
1870         cone[7] = 20;
1871         PetscCall(DMPlexSetCone(dm, 5, cone));
1872         cone[0] = 32;
1873         cone[1] = 33;
1874         cone[2] = 37;
1875         cone[3] = 36;
1876         cone[4] = 22;
1877         cone[5] = 25;
1878         cone[6] = 26;
1879         cone[7] = 21;
1880         PetscCall(DMPlexSetCone(dm, 6, cone));
1881         cone[0] = 34;
1882         cone[1] = 38;
1883         cone[2] = 37;
1884         cone[3] = 33;
1885         cone[4] = 20;
1886         cone[5] = 21;
1887         cone[6] = 26;
1888         cone[7] = 28;
1889         PetscCall(DMPlexSetCone(dm, 7, cone));
1890         cone[0] = 35;
1891         cone[1] = 38;
1892         cone[2] = 34;
1893         cone[3] = 31;
1894         cone[4] = 30;
1895         cone[5] = 19;
1896         cone[6] = 20;
1897         cone[7] = 28;
1898         PetscCall(DMPlexSetCone(dm, 8, cone));
1899         cone[0] = 35;
1900         cone[1] = 31;
1901         cone[2] = 32;
1902         cone[3] = 36;
1903         cone[4] = 30;
1904         cone[5] = 25;
1905         cone[6] = 22;
1906         cone[7] = 19;
1907         PetscCall(DMPlexSetCone(dm, 9, cone));
1908 
1909         cone[0] = 19;
1910         cone[1] = 20;
1911         cone[2] = 21;
1912         cone[3] = 22;
1913         cone[4] = 15;
1914         cone[5] = 16;
1915         cone[6] = 17;
1916         cone[7] = 18;
1917         PetscCall(DMPlexSetCone(dm, 10, cone));
1918         cone[0] = 22;
1919         cone[1] = 21;
1920         cone[2] = 26;
1921         cone[3] = 25;
1922         cone[4] = 16;
1923         cone[5] = 23;
1924         cone[6] = 24;
1925         cone[7] = 17;
1926         PetscCall(DMPlexSetCone(dm, 11, cone));
1927         cone[0] = 20;
1928         cone[1] = 28;
1929         cone[2] = 26;
1930         cone[3] = 21;
1931         cone[4] = 18;
1932         cone[5] = 17;
1933         cone[6] = 24;
1934         cone[7] = 27;
1935         PetscCall(DMPlexSetCone(dm, 12, cone));
1936         cone[0] = 30;
1937         cone[1] = 28;
1938         cone[2] = 20;
1939         cone[3] = 19;
1940         cone[4] = 29;
1941         cone[5] = 15;
1942         cone[6] = 18;
1943         cone[7] = 27;
1944         PetscCall(DMPlexSetCone(dm, 13, cone));
1945         cone[0] = 30;
1946         cone[1] = 19;
1947         cone[2] = 22;
1948         cone[3] = 25;
1949         cone[4] = 29;
1950         cone[5] = 23;
1951         cone[6] = 16;
1952         cone[7] = 15;
1953         PetscCall(DMPlexSetCone(dm, 14, cone));
1954       } else {
1955         cone[0] = 5;
1956         cone[1] = 8;
1957         cone[2] = 7;
1958         cone[3] = 6;
1959         cone[4] = 9;
1960         cone[5] = 12;
1961         cone[6] = 11;
1962         cone[7] = 10;
1963         PetscCall(DMPlexSetCone(dm, 0, cone));
1964         cone[0] = 6;
1965         cone[1] = 7;
1966         cone[2] = 14;
1967         cone[3] = 13;
1968         cone[4] = 12;
1969         cone[5] = 15;
1970         cone[6] = 16;
1971         cone[7] = 11;
1972         PetscCall(DMPlexSetCone(dm, 1, cone));
1973         cone[0] = 8;
1974         cone[1] = 17;
1975         cone[2] = 14;
1976         cone[3] = 7;
1977         cone[4] = 10;
1978         cone[5] = 11;
1979         cone[6] = 16;
1980         cone[7] = 18;
1981         PetscCall(DMPlexSetCone(dm, 2, cone));
1982         cone[0] = 19;
1983         cone[1] = 17;
1984         cone[2] = 8;
1985         cone[3] = 5;
1986         cone[4] = 20;
1987         cone[5] = 9;
1988         cone[6] = 10;
1989         cone[7] = 18;
1990         PetscCall(DMPlexSetCone(dm, 3, cone));
1991         cone[0] = 19;
1992         cone[1] = 5;
1993         cone[2] = 6;
1994         cone[3] = 13;
1995         cone[4] = 20;
1996         cone[5] = 15;
1997         cone[6] = 12;
1998         cone[7] = 9;
1999         PetscCall(DMPlexSetCone(dm, 4, cone));
2000       }
2001     }
2002     PetscCall(DMPlexSymmetrize(dm));
2003     PetscCall(DMPlexStratify(dm));
2004   }
2005   /* Create cube geometry */
2006   {
2007     Vec             coordinates;
2008     PetscSection    coordSection;
2009     PetscScalar    *coords;
2010     PetscInt        coordSize, v;
2011     const PetscReal dis = 1.0 / PetscSqrtReal(2.0);
2012     const PetscReal ds2 = dis / 2.0;
2013 
2014     /* Build coordinates */
2015     PetscCall(DMGetCoordinateSection(dm, &coordSection));
2016     PetscCall(PetscSectionSetNumFields(coordSection, 1));
2017     PetscCall(PetscSectionSetFieldComponents(coordSection, 0, dim));
2018     PetscCall(PetscSectionSetChart(coordSection, numCells, numCells + numVertices));
2019     for (v = numCells; v < numCells + numVertices; ++v) {
2020       PetscCall(PetscSectionSetDof(coordSection, v, dim));
2021       PetscCall(PetscSectionSetFieldDof(coordSection, v, 0, dim));
2022     }
2023     PetscCall(PetscSectionSetUp(coordSection));
2024     PetscCall(PetscSectionGetStorageSize(coordSection, &coordSize));
2025     PetscCall(VecCreate(PETSC_COMM_SELF, &coordinates));
2026     PetscCall(PetscObjectSetName((PetscObject)coordinates, "coordinates"));
2027     PetscCall(VecSetSizes(coordinates, coordSize, PETSC_DETERMINE));
2028     PetscCall(VecSetBlockSize(coordinates, dim));
2029     PetscCall(VecSetType(coordinates, VECSTANDARD));
2030     PetscCall(VecGetArray(coordinates, &coords));
2031     if (rank == 0) {
2032       coords[0 * dim + 0]  = -ds2;
2033       coords[0 * dim + 1]  = -ds2;
2034       coords[0 * dim + 2]  = 0.0;
2035       coords[1 * dim + 0]  = ds2;
2036       coords[1 * dim + 1]  = -ds2;
2037       coords[1 * dim + 2]  = 0.0;
2038       coords[2 * dim + 0]  = ds2;
2039       coords[2 * dim + 1]  = ds2;
2040       coords[2 * dim + 2]  = 0.0;
2041       coords[3 * dim + 0]  = -ds2;
2042       coords[3 * dim + 1]  = ds2;
2043       coords[3 * dim + 2]  = 0.0;
2044       coords[4 * dim + 0]  = -ds2;
2045       coords[4 * dim + 1]  = -ds2;
2046       coords[4 * dim + 2]  = 1.0;
2047       coords[5 * dim + 0]  = -ds2;
2048       coords[5 * dim + 1]  = ds2;
2049       coords[5 * dim + 2]  = 1.0;
2050       coords[6 * dim + 0]  = ds2;
2051       coords[6 * dim + 1]  = ds2;
2052       coords[6 * dim + 2]  = 1.0;
2053       coords[7 * dim + 0]  = ds2;
2054       coords[7 * dim + 1]  = -ds2;
2055       coords[7 * dim + 2]  = 1.0;
2056       coords[8 * dim + 0]  = dis;
2057       coords[8 * dim + 1]  = -dis;
2058       coords[8 * dim + 2]  = 0.0;
2059       coords[9 * dim + 0]  = dis;
2060       coords[9 * dim + 1]  = dis;
2061       coords[9 * dim + 2]  = 0.0;
2062       coords[10 * dim + 0] = dis;
2063       coords[10 * dim + 1] = -dis;
2064       coords[10 * dim + 2] = 1.0;
2065       coords[11 * dim + 0] = dis;
2066       coords[11 * dim + 1] = dis;
2067       coords[11 * dim + 2] = 1.0;
2068       coords[12 * dim + 0] = -dis;
2069       coords[12 * dim + 1] = dis;
2070       coords[12 * dim + 2] = 0.0;
2071       coords[13 * dim + 0] = -dis;
2072       coords[13 * dim + 1] = dis;
2073       coords[13 * dim + 2] = 1.0;
2074       coords[14 * dim + 0] = -dis;
2075       coords[14 * dim + 1] = -dis;
2076       coords[14 * dim + 2] = 0.0;
2077       coords[15 * dim + 0] = -dis;
2078       coords[15 * dim + 1] = -dis;
2079       coords[15 * dim + 2] = 1.0;
2080       if (periodicZ == DM_BOUNDARY_PERIODIC) {
2081         /* 15 31 19 */ coords[16 * dim + 0] = -ds2;
2082         coords[16 * dim + 1]                = -ds2;
2083         coords[16 * dim + 2]                = 0.5;
2084         /* 16 32 22 */ coords[17 * dim + 0] = ds2;
2085         coords[17 * dim + 1]                = -ds2;
2086         coords[17 * dim + 2]                = 0.5;
2087         /* 17 33 21 */ coords[18 * dim + 0] = ds2;
2088         coords[18 * dim + 1]                = ds2;
2089         coords[18 * dim + 2]                = 0.5;
2090         /* 18 34 20 */ coords[19 * dim + 0] = -ds2;
2091         coords[19 * dim + 1]                = ds2;
2092         coords[19 * dim + 2]                = 0.5;
2093         /* 29 35 30 */ coords[20 * dim + 0] = -dis;
2094         coords[20 * dim + 1]                = -dis;
2095         coords[20 * dim + 2]                = 0.5;
2096         /* 23 36 25 */ coords[21 * dim + 0] = dis;
2097         coords[21 * dim + 1]                = -dis;
2098         coords[21 * dim + 2]                = 0.5;
2099         /* 24 37 26 */ coords[22 * dim + 0] = dis;
2100         coords[22 * dim + 1]                = dis;
2101         coords[22 * dim + 2]                = 0.5;
2102         /* 27 38 28 */ coords[23 * dim + 0] = -dis;
2103         coords[23 * dim + 1]                = dis;
2104         coords[23 * dim + 2]                = 0.5;
2105       }
2106     }
2107     PetscCall(VecRestoreArray(coordinates, &coords));
2108     PetscCall(DMSetCoordinatesLocal(dm, coordinates));
2109     PetscCall(VecDestroy(&coordinates));
2110   }
2111   /* Create periodicity */
2112   if (periodicZ == DM_BOUNDARY_PERIODIC || periodicZ == DM_BOUNDARY_TWIST) {
2113     PetscReal L[3]       = {-1., -1., 0.};
2114     PetscReal maxCell[3] = {-1., -1., 0.};
2115     PetscReal lower[3]   = {0.0, 0.0, 0.0};
2116     PetscReal upper[3]   = {1.0, 1.0, 1.5};
2117     PetscInt  numZCells  = 3;
2118 
2119     L[2]       = upper[2] - lower[2];
2120     maxCell[2] = 1.1 * (L[2] / numZCells);
2121     PetscCall(DMSetPeriodicity(dm, maxCell, lower, L));
2122   }
2123   {
2124     DM          cdm;
2125     PetscDS     cds;
2126     PetscScalar c[2] = {1.0, 1.0};
2127 
2128     PetscCall(DMPlexCreateCoordinateSpace(dm, 1, PETSC_TRUE, snapToCylinder));
2129     PetscCall(DMGetCoordinateDM(dm, &cdm));
2130     PetscCall(DMGetDS(cdm, &cds));
2131     PetscCall(PetscDSSetConstants(cds, 2, c));
2132   }
2133   PetscCall(PetscLogEventEnd(DMPLEX_Generate, dm, 0, 0, 0));
2134 
2135   /* Wait for coordinate creation before doing in-place modification */
2136   PetscCall(DMPlexInterpolateInPlace_Internal(dm));
2137   PetscFunctionReturn(PETSC_SUCCESS);
2138 }
2139 
2140 /*@
2141   DMPlexCreateHexCylinderMesh - Creates a mesh on the tensor product of the unit interval with the circle (cylinder) using hexahedra.
2142 
2143   Collective
2144 
2145   Input Parameters:
2146 + comm      - The communicator for the `DM` object
2147 - periodicZ - The boundary type for the Z direction
2148 
2149   Output Parameter:
2150 . dm - The `DM` object
2151 
2152   Level: beginner
2153 
2154   Note:
2155   Here is the output numbering looking from the bottom of the cylinder\:
2156 .vb
2157        17-----14
2158         |     |
2159         |  2  |
2160         |     |
2161  17-----8-----7-----14
2162   |     |     |     |
2163   |  3  |  0  |  1  |
2164   |     |     |     |
2165  19-----5-----6-----13
2166         |     |
2167         |  4  |
2168         |     |
2169        19-----13
2170 
2171  and up through the top
2172 
2173        18-----16
2174         |     |
2175         |  2  |
2176         |     |
2177  18----10----11-----16
2178   |     |     |     |
2179   |  3  |  0  |  1  |
2180   |     |     |     |
2181  20-----9----12-----15
2182         |     |
2183         |  4  |
2184         |     |
2185        20-----15
2186 .ve
2187 
2188 .seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexCreateBoxMesh()`, `DMSetType()`, `DMCreate()`
2189 @*/
2190 PetscErrorCode DMPlexCreateHexCylinderMesh(MPI_Comm comm, DMBoundaryType periodicZ, DM *dm)
2191 {
2192   PetscFunctionBegin;
2193   PetscAssertPointer(dm, 3);
2194   PetscCall(DMCreate(comm, dm));
2195   PetscCall(DMSetType(*dm, DMPLEX));
2196   PetscCall(DMPlexCreateHexCylinderMesh_Internal(*dm, periodicZ));
2197   PetscFunctionReturn(PETSC_SUCCESS);
2198 }
2199 
2200 static PetscErrorCode DMPlexCreateWedgeCylinderMesh_Internal(DM dm, PetscInt n, PetscBool interpolate)
2201 {
2202   const PetscInt dim = 3;
2203   PetscInt       numCells, numVertices, v;
2204   PetscMPIInt    rank;
2205 
2206   PetscFunctionBegin;
2207   PetscCheck(n >= 0, PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "Number of wedges %" PetscInt_FMT " cannot be negative", n);
2208   PetscCall(PetscLogEventBegin(DMPLEX_Generate, dm, 0, 0, 0));
2209   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank));
2210   PetscCall(DMSetDimension(dm, dim));
2211   /* Must create the celltype label here so that we do not automatically try to compute the types */
2212   PetscCall(DMCreateLabel(dm, "celltype"));
2213   /* Create topology */
2214   {
2215     PetscInt cone[6], c;
2216 
2217     numCells    = rank == 0 ? n : 0;
2218     numVertices = rank == 0 ? 2 * (n + 1) : 0;
2219     PetscCall(DMPlexSetChart(dm, 0, numCells + numVertices));
2220     for (c = 0; c < numCells; c++) PetscCall(DMPlexSetConeSize(dm, c, 6));
2221     PetscCall(DMSetUp(dm));
2222     for (c = 0; c < numCells; c++) {
2223       cone[0] = c + n * 1;
2224       cone[1] = (c + 1) % n + n * 1;
2225       cone[2] = 0 + 3 * n;
2226       cone[3] = c + n * 2;
2227       cone[4] = (c + 1) % n + n * 2;
2228       cone[5] = 1 + 3 * n;
2229       PetscCall(DMPlexSetCone(dm, c, cone));
2230       PetscCall(DMPlexSetCellType(dm, c, DM_POLYTOPE_TRI_PRISM_TENSOR));
2231     }
2232     PetscCall(DMPlexSymmetrize(dm));
2233     PetscCall(DMPlexStratify(dm));
2234   }
2235   for (v = numCells; v < numCells + numVertices; ++v) PetscCall(DMPlexSetCellType(dm, v, DM_POLYTOPE_POINT));
2236   /* Create cylinder geometry */
2237   {
2238     Vec          coordinates;
2239     PetscSection coordSection;
2240     PetscScalar *coords;
2241     PetscInt     coordSize, c;
2242 
2243     /* Build coordinates */
2244     PetscCall(DMGetCoordinateSection(dm, &coordSection));
2245     PetscCall(PetscSectionSetNumFields(coordSection, 1));
2246     PetscCall(PetscSectionSetFieldComponents(coordSection, 0, dim));
2247     PetscCall(PetscSectionSetChart(coordSection, numCells, numCells + numVertices));
2248     for (v = numCells; v < numCells + numVertices; ++v) {
2249       PetscCall(PetscSectionSetDof(coordSection, v, dim));
2250       PetscCall(PetscSectionSetFieldDof(coordSection, v, 0, dim));
2251     }
2252     PetscCall(PetscSectionSetUp(coordSection));
2253     PetscCall(PetscSectionGetStorageSize(coordSection, &coordSize));
2254     PetscCall(VecCreate(PETSC_COMM_SELF, &coordinates));
2255     PetscCall(PetscObjectSetName((PetscObject)coordinates, "coordinates"));
2256     PetscCall(VecSetSizes(coordinates, coordSize, PETSC_DETERMINE));
2257     PetscCall(VecSetBlockSize(coordinates, dim));
2258     PetscCall(VecSetType(coordinates, VECSTANDARD));
2259     PetscCall(VecGetArray(coordinates, &coords));
2260     for (c = 0; c < numCells; c++) {
2261       coords[(c + 0 * n) * dim + 0] = PetscCosReal(2.0 * c * PETSC_PI / n);
2262       coords[(c + 0 * n) * dim + 1] = PetscSinReal(2.0 * c * PETSC_PI / n);
2263       coords[(c + 0 * n) * dim + 2] = 1.0;
2264       coords[(c + 1 * n) * dim + 0] = PetscCosReal(2.0 * c * PETSC_PI / n);
2265       coords[(c + 1 * n) * dim + 1] = PetscSinReal(2.0 * c * PETSC_PI / n);
2266       coords[(c + 1 * n) * dim + 2] = 0.0;
2267     }
2268     if (rank == 0) {
2269       coords[(2 * n + 0) * dim + 0] = 0.0;
2270       coords[(2 * n + 0) * dim + 1] = 0.0;
2271       coords[(2 * n + 0) * dim + 2] = 1.0;
2272       coords[(2 * n + 1) * dim + 0] = 0.0;
2273       coords[(2 * n + 1) * dim + 1] = 0.0;
2274       coords[(2 * n + 1) * dim + 2] = 0.0;
2275     }
2276     PetscCall(VecRestoreArray(coordinates, &coords));
2277     PetscCall(DMSetCoordinatesLocal(dm, coordinates));
2278     PetscCall(VecDestroy(&coordinates));
2279   }
2280   PetscCall(PetscLogEventEnd(DMPLEX_Generate, dm, 0, 0, 0));
2281   /* Interpolate */
2282   if (interpolate) PetscCall(DMPlexInterpolateInPlace_Internal(dm));
2283   PetscFunctionReturn(PETSC_SUCCESS);
2284 }
2285 
2286 /*@
2287   DMPlexCreateWedgeCylinderMesh - Creates a mesh on the tensor product of the unit interval with the circle (cylinder) using wedges.
2288 
2289   Collective
2290 
2291   Input Parameters:
2292 + comm        - The communicator for the `DM` object
2293 . n           - The number of wedges around the origin
2294 - interpolate - Create edges and faces
2295 
2296   Output Parameter:
2297 . dm - The `DM` object
2298 
2299   Level: beginner
2300 
2301 .seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexCreateHexCylinderMesh()`, `DMPlexCreateBoxMesh()`, `DMSetType()`, `DMCreate()`
2302 @*/
2303 PetscErrorCode DMPlexCreateWedgeCylinderMesh(MPI_Comm comm, PetscInt n, PetscBool interpolate, DM *dm)
2304 {
2305   PetscFunctionBegin;
2306   PetscAssertPointer(dm, 4);
2307   PetscCall(DMCreate(comm, dm));
2308   PetscCall(DMSetType(*dm, DMPLEX));
2309   PetscCall(DMPlexCreateWedgeCylinderMesh_Internal(*dm, n, interpolate));
2310   PetscFunctionReturn(PETSC_SUCCESS);
2311 }
2312 
2313 static inline PetscReal DiffNormReal(PetscInt dim, const PetscReal x[], const PetscReal y[])
2314 {
2315   PetscReal prod = 0.0;
2316   PetscInt  i;
2317   for (i = 0; i < dim; ++i) prod += PetscSqr(x[i] - y[i]);
2318   return PetscSqrtReal(prod);
2319 }
2320 static inline PetscReal DotReal(PetscInt dim, const PetscReal x[], const PetscReal y[])
2321 {
2322   PetscReal prod = 0.0;
2323   PetscInt  i;
2324   for (i = 0; i < dim; ++i) prod += x[i] * y[i];
2325   return prod;
2326 }
2327 
2328 /* The first constant is the sphere radius */
2329 static void snapToSphere(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
2330 {
2331   PetscReal r     = PetscRealPart(constants[0]);
2332   PetscReal norm2 = 0.0, fac;
2333   PetscInt  n     = uOff[1] - uOff[0], d;
2334 
2335   for (d = 0; d < n; ++d) norm2 += PetscSqr(PetscRealPart(u[d]));
2336   fac = r / PetscSqrtReal(norm2);
2337   for (d = 0; d < n; ++d) f0[d] = u[d] * fac;
2338 }
2339 
2340 static PetscErrorCode DMPlexCreateSphereMesh_Internal(DM dm, PetscInt dim, PetscBool simplex, PetscReal R)
2341 {
2342   const PetscInt embedDim = dim + 1;
2343   PetscSection   coordSection;
2344   Vec            coordinates;
2345   PetscScalar   *coords;
2346   PetscReal     *coordsIn;
2347   PetscInt       numCells, numEdges, numVerts = 0, firstVertex = 0, v, firstEdge, coordSize, d, e;
2348   PetscMPIInt    rank;
2349 
2350   PetscFunctionBegin;
2351   PetscValidLogicalCollectiveBool(dm, simplex, 3);
2352   PetscCall(PetscLogEventBegin(DMPLEX_Generate, dm, 0, 0, 0));
2353   PetscCall(DMSetDimension(dm, dim));
2354   PetscCall(DMSetCoordinateDim(dm, dim + 1));
2355   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank));
2356   switch (dim) {
2357   case 1:
2358     numCells = 16;
2359     numVerts = numCells;
2360 
2361     // Build Topology
2362     PetscCall(DMPlexSetChart(dm, 0, numCells + numVerts));
2363     for (PetscInt c = 0; c < numCells; c++) PetscCall(DMPlexSetConeSize(dm, c, embedDim));
2364     PetscCall(DMSetUp(dm));
2365     for (PetscInt c = 0; c < numCells; ++c) {
2366       PetscInt cone[2];
2367 
2368       cone[0] = c + numCells;
2369       cone[1] = (c + 1) % numVerts + numCells;
2370       PetscCall(DMPlexSetCone(dm, c, cone));
2371     }
2372     PetscCall(DMPlexSymmetrize(dm));
2373     PetscCall(DMPlexStratify(dm));
2374     PetscCall(PetscMalloc1(numVerts * embedDim, &coordsIn));
2375     for (PetscInt v = 0; v < numVerts; ++v) {
2376       const PetscReal rad = 2. * PETSC_PI * v / numVerts;
2377 
2378       coordsIn[v * embedDim + 0] = PetscCosReal(rad);
2379       coordsIn[v * embedDim + 1] = PetscSinReal(rad);
2380     }
2381     break;
2382   case 2:
2383     if (simplex) {
2384       const PetscReal radius    = PetscSqrtReal(1 + PETSC_PHI * PETSC_PHI) / (1.0 + PETSC_PHI);
2385       const PetscReal edgeLen   = 2.0 / (1.0 + PETSC_PHI) * (R / radius);
2386       const PetscInt  degree    = 5;
2387       PetscReal       vertex[3] = {0.0, 1.0 / (1.0 + PETSC_PHI), PETSC_PHI / (1.0 + PETSC_PHI)};
2388       PetscInt        s[3]      = {1, 1, 1};
2389       PetscInt        cone[3];
2390       PetscInt       *graph;
2391 
2392       vertex[0] *= R / radius;
2393       vertex[1] *= R / radius;
2394       vertex[2] *= R / radius;
2395       numCells    = rank == 0 ? 20 : 0;
2396       numVerts    = rank == 0 ? 12 : 0;
2397       firstVertex = numCells;
2398       /* Use icosahedron, which for a R-sphere has coordinates which are all cyclic permutations of
2399 
2400            (0, \pm 1/\phi+1, \pm \phi/\phi+1)
2401 
2402          where \phi^2 - \phi - 1 = 0, meaning \phi is the golden ratio \frac{1 + \sqrt{5}}{2}. The edge
2403          length is then given by 2/(1+\phi) = 2 * 0.38197 = 0.76393.
2404       */
2405       /* Construct vertices */
2406       PetscCall(PetscCalloc1(numVerts * embedDim, &coordsIn));
2407       if (rank == 0) {
2408         for (PetscInt p = 0, i = 0; p < embedDim; ++p) {
2409           for (s[1] = -1; s[1] < 2; s[1] += 2) {
2410             for (s[2] = -1; s[2] < 2; s[2] += 2) {
2411               for (d = 0; d < embedDim; ++d) coordsIn[i * embedDim + d] = s[(d + p) % embedDim] * vertex[(d + p) % embedDim];
2412               ++i;
2413             }
2414           }
2415         }
2416       }
2417       /* Construct graph */
2418       PetscCall(PetscCalloc1(numVerts * numVerts, &graph));
2419       for (PetscInt i = 0; i < numVerts; ++i) {
2420         PetscInt k = 0;
2421         for (PetscInt j = 0; j < numVerts; ++j) {
2422           if (PetscAbsReal(DiffNormReal(embedDim, &coordsIn[i * embedDim], &coordsIn[j * embedDim]) - edgeLen) < PETSC_SMALL) {
2423             graph[i * numVerts + j] = 1;
2424             ++k;
2425           }
2426         }
2427         PetscCheck(k == degree, PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Invalid icosahedron, vertex %" PetscInt_FMT " degree %" PetscInt_FMT " != %" PetscInt_FMT, i, k, degree);
2428       }
2429       /* Build Topology */
2430       PetscCall(DMPlexSetChart(dm, 0, numCells + numVerts));
2431       for (PetscInt c = 0; c < numCells; c++) PetscCall(DMPlexSetConeSize(dm, c, embedDim));
2432       PetscCall(DMSetUp(dm)); /* Allocate space for cones */
2433       /* Cells */
2434       for (PetscInt i = 0, c = 0; i < numVerts; ++i) {
2435         for (PetscInt j = 0; j < i; ++j) {
2436           for (PetscInt k = 0; k < j; ++k) {
2437             if (graph[i * numVerts + j] && graph[j * numVerts + k] && graph[k * numVerts + i]) {
2438               cone[0] = firstVertex + i;
2439               cone[1] = firstVertex + j;
2440               cone[2] = firstVertex + k;
2441               /* Check orientation */
2442               {
2443                 const PetscInt epsilon[3][3][3] = {
2444                   {{0, 0, 0},  {0, 0, 1},  {0, -1, 0}},
2445                   {{0, 0, -1}, {0, 0, 0},  {1, 0, 0} },
2446                   {{0, 1, 0},  {-1, 0, 0}, {0, 0, 0} }
2447                 };
2448                 PetscReal normal[3];
2449                 PetscInt  e, f;
2450 
2451                 for (d = 0; d < embedDim; ++d) {
2452                   normal[d] = 0.0;
2453                   for (e = 0; e < embedDim; ++e) {
2454                     for (f = 0; f < embedDim; ++f) normal[d] += epsilon[d][e][f] * (coordsIn[j * embedDim + e] - coordsIn[i * embedDim + e]) * (coordsIn[k * embedDim + f] - coordsIn[i * embedDim + f]);
2455                   }
2456                 }
2457                 if (DotReal(embedDim, normal, &coordsIn[i * embedDim]) < 0) {
2458                   PetscInt tmp = cone[1];
2459                   cone[1]      = cone[2];
2460                   cone[2]      = tmp;
2461                 }
2462               }
2463               PetscCall(DMPlexSetCone(dm, c++, cone));
2464             }
2465           }
2466         }
2467       }
2468       PetscCall(DMPlexSymmetrize(dm));
2469       PetscCall(DMPlexStratify(dm));
2470       PetscCall(PetscFree(graph));
2471     } else {
2472       /*
2473         12-21--13
2474          |     |
2475         25  4  24
2476          |     |
2477   12-25--9-16--8-24--13
2478    |     |     |     |
2479   23  5 17  0 15  3  22
2480    |     |     |     |
2481   10-20--6-14--7-19--11
2482          |     |
2483         20  1  19
2484          |     |
2485         10-18--11
2486          |     |
2487         23  2  22
2488          |     |
2489         12-21--13
2490        */
2491       PetscInt cone[4], ornt[4];
2492 
2493       numCells    = rank == 0 ? 6 : 0;
2494       numEdges    = rank == 0 ? 12 : 0;
2495       numVerts    = rank == 0 ? 8 : 0;
2496       firstVertex = numCells;
2497       firstEdge   = numCells + numVerts;
2498       /* Build Topology */
2499       PetscCall(DMPlexSetChart(dm, 0, numCells + numEdges + numVerts));
2500       for (PetscInt c = 0; c < numCells; c++) PetscCall(DMPlexSetConeSize(dm, c, 4));
2501       for (e = firstEdge; e < firstEdge + numEdges; ++e) PetscCall(DMPlexSetConeSize(dm, e, 2));
2502       PetscCall(DMSetUp(dm)); /* Allocate space for cones */
2503       if (rank == 0) {
2504         /* Cell 0 */
2505         cone[0] = 14;
2506         cone[1] = 15;
2507         cone[2] = 16;
2508         cone[3] = 17;
2509         PetscCall(DMPlexSetCone(dm, 0, cone));
2510         ornt[0] = 0;
2511         ornt[1] = 0;
2512         ornt[2] = 0;
2513         ornt[3] = 0;
2514         PetscCall(DMPlexSetConeOrientation(dm, 0, ornt));
2515         /* Cell 1 */
2516         cone[0] = 18;
2517         cone[1] = 19;
2518         cone[2] = 14;
2519         cone[3] = 20;
2520         PetscCall(DMPlexSetCone(dm, 1, cone));
2521         ornt[0] = 0;
2522         ornt[1] = 0;
2523         ornt[2] = -1;
2524         ornt[3] = 0;
2525         PetscCall(DMPlexSetConeOrientation(dm, 1, ornt));
2526         /* Cell 2 */
2527         cone[0] = 21;
2528         cone[1] = 22;
2529         cone[2] = 18;
2530         cone[3] = 23;
2531         PetscCall(DMPlexSetCone(dm, 2, cone));
2532         ornt[0] = 0;
2533         ornt[1] = 0;
2534         ornt[2] = -1;
2535         ornt[3] = 0;
2536         PetscCall(DMPlexSetConeOrientation(dm, 2, ornt));
2537         /* Cell 3 */
2538         cone[0] = 19;
2539         cone[1] = 22;
2540         cone[2] = 24;
2541         cone[3] = 15;
2542         PetscCall(DMPlexSetCone(dm, 3, cone));
2543         ornt[0] = -1;
2544         ornt[1] = -1;
2545         ornt[2] = 0;
2546         ornt[3] = -1;
2547         PetscCall(DMPlexSetConeOrientation(dm, 3, ornt));
2548         /* Cell 4 */
2549         cone[0] = 16;
2550         cone[1] = 24;
2551         cone[2] = 21;
2552         cone[3] = 25;
2553         PetscCall(DMPlexSetCone(dm, 4, cone));
2554         ornt[0] = -1;
2555         ornt[1] = -1;
2556         ornt[2] = -1;
2557         ornt[3] = 0;
2558         PetscCall(DMPlexSetConeOrientation(dm, 4, ornt));
2559         /* Cell 5 */
2560         cone[0] = 20;
2561         cone[1] = 17;
2562         cone[2] = 25;
2563         cone[3] = 23;
2564         PetscCall(DMPlexSetCone(dm, 5, cone));
2565         ornt[0] = -1;
2566         ornt[1] = -1;
2567         ornt[2] = -1;
2568         ornt[3] = -1;
2569         PetscCall(DMPlexSetConeOrientation(dm, 5, ornt));
2570         /* Edges */
2571         cone[0] = 6;
2572         cone[1] = 7;
2573         PetscCall(DMPlexSetCone(dm, 14, cone));
2574         cone[0] = 7;
2575         cone[1] = 8;
2576         PetscCall(DMPlexSetCone(dm, 15, cone));
2577         cone[0] = 8;
2578         cone[1] = 9;
2579         PetscCall(DMPlexSetCone(dm, 16, cone));
2580         cone[0] = 9;
2581         cone[1] = 6;
2582         PetscCall(DMPlexSetCone(dm, 17, cone));
2583         cone[0] = 10;
2584         cone[1] = 11;
2585         PetscCall(DMPlexSetCone(dm, 18, cone));
2586         cone[0] = 11;
2587         cone[1] = 7;
2588         PetscCall(DMPlexSetCone(dm, 19, cone));
2589         cone[0] = 6;
2590         cone[1] = 10;
2591         PetscCall(DMPlexSetCone(dm, 20, cone));
2592         cone[0] = 12;
2593         cone[1] = 13;
2594         PetscCall(DMPlexSetCone(dm, 21, cone));
2595         cone[0] = 13;
2596         cone[1] = 11;
2597         PetscCall(DMPlexSetCone(dm, 22, cone));
2598         cone[0] = 10;
2599         cone[1] = 12;
2600         PetscCall(DMPlexSetCone(dm, 23, cone));
2601         cone[0] = 13;
2602         cone[1] = 8;
2603         PetscCall(DMPlexSetCone(dm, 24, cone));
2604         cone[0] = 12;
2605         cone[1] = 9;
2606         PetscCall(DMPlexSetCone(dm, 25, cone));
2607       }
2608       PetscCall(DMPlexSymmetrize(dm));
2609       PetscCall(DMPlexStratify(dm));
2610       /* Build coordinates */
2611       PetscCall(PetscCalloc1(numVerts * embedDim, &coordsIn));
2612       if (rank == 0) {
2613         coordsIn[0 * embedDim + 0] = -R;
2614         coordsIn[0 * embedDim + 1] = R;
2615         coordsIn[0 * embedDim + 2] = -R;
2616         coordsIn[1 * embedDim + 0] = R;
2617         coordsIn[1 * embedDim + 1] = R;
2618         coordsIn[1 * embedDim + 2] = -R;
2619         coordsIn[2 * embedDim + 0] = R;
2620         coordsIn[2 * embedDim + 1] = -R;
2621         coordsIn[2 * embedDim + 2] = -R;
2622         coordsIn[3 * embedDim + 0] = -R;
2623         coordsIn[3 * embedDim + 1] = -R;
2624         coordsIn[3 * embedDim + 2] = -R;
2625         coordsIn[4 * embedDim + 0] = -R;
2626         coordsIn[4 * embedDim + 1] = R;
2627         coordsIn[4 * embedDim + 2] = R;
2628         coordsIn[5 * embedDim + 0] = R;
2629         coordsIn[5 * embedDim + 1] = R;
2630         coordsIn[5 * embedDim + 2] = R;
2631         coordsIn[6 * embedDim + 0] = -R;
2632         coordsIn[6 * embedDim + 1] = -R;
2633         coordsIn[6 * embedDim + 2] = R;
2634         coordsIn[7 * embedDim + 0] = R;
2635         coordsIn[7 * embedDim + 1] = -R;
2636         coordsIn[7 * embedDim + 2] = R;
2637       }
2638     }
2639     break;
2640   case 3:
2641     if (simplex) {
2642       const PetscReal edgeLen         = 1.0 / PETSC_PHI;
2643       PetscReal       vertexA[4]      = {0.5, 0.5, 0.5, 0.5};
2644       PetscReal       vertexB[4]      = {1.0, 0.0, 0.0, 0.0};
2645       PetscReal       vertexC[4]      = {0.5, 0.5 * PETSC_PHI, 0.5 / PETSC_PHI, 0.0};
2646       const PetscInt  degree          = 12;
2647       PetscInt        s[4]            = {1, 1, 1};
2648       PetscInt        evenPerm[12][4] = {
2649         {0, 1, 2, 3},
2650         {0, 2, 3, 1},
2651         {0, 3, 1, 2},
2652         {1, 0, 3, 2},
2653         {1, 2, 0, 3},
2654         {1, 3, 2, 0},
2655         {2, 0, 1, 3},
2656         {2, 1, 3, 0},
2657         {2, 3, 0, 1},
2658         {3, 0, 2, 1},
2659         {3, 1, 0, 2},
2660         {3, 2, 1, 0}
2661       };
2662       PetscInt  cone[4];
2663       PetscInt *graph, p, i, j, k, l;
2664 
2665       vertexA[0] *= R;
2666       vertexA[1] *= R;
2667       vertexA[2] *= R;
2668       vertexA[3] *= R;
2669       vertexB[0] *= R;
2670       vertexB[1] *= R;
2671       vertexB[2] *= R;
2672       vertexB[3] *= R;
2673       vertexC[0] *= R;
2674       vertexC[1] *= R;
2675       vertexC[2] *= R;
2676       vertexC[3] *= R;
2677       numCells    = rank == 0 ? 600 : 0;
2678       numVerts    = rank == 0 ? 120 : 0;
2679       firstVertex = numCells;
2680       /* Use the 600-cell, which for a unit sphere has coordinates which are
2681 
2682            1/2 (\pm 1, \pm 1,    \pm 1, \pm 1)                          16
2683                (\pm 1,    0,       0,      0)  all cyclic permutations   8
2684            1/2 (\pm 1, \pm phi, \pm 1/phi, 0)  all even permutations    96
2685 
2686          where \phi^2 - \phi - 1 = 0, meaning \phi is the golden ratio \frac{1 + \sqrt{5}}{2}. The edge
2687          length is then given by 1/\phi = 0.61803.
2688 
2689          http://buzzard.pugetsound.edu/sage-practice/ch03s03.html
2690          http://mathworld.wolfram.com/600-Cell.html
2691       */
2692       /* Construct vertices */
2693       PetscCall(PetscCalloc1(numVerts * embedDim, &coordsIn));
2694       i = 0;
2695       if (rank == 0) {
2696         for (s[0] = -1; s[0] < 2; s[0] += 2) {
2697           for (s[1] = -1; s[1] < 2; s[1] += 2) {
2698             for (s[2] = -1; s[2] < 2; s[2] += 2) {
2699               for (s[3] = -1; s[3] < 2; s[3] += 2) {
2700                 for (d = 0; d < embedDim; ++d) coordsIn[i * embedDim + d] = s[d] * vertexA[d];
2701                 ++i;
2702               }
2703             }
2704           }
2705         }
2706         for (p = 0; p < embedDim; ++p) {
2707           s[1] = s[2] = s[3] = 1;
2708           for (s[0] = -1; s[0] < 2; s[0] += 2) {
2709             for (d = 0; d < embedDim; ++d) coordsIn[i * embedDim + d] = s[(d + p) % embedDim] * vertexB[(d + p) % embedDim];
2710             ++i;
2711           }
2712         }
2713         for (p = 0; p < 12; ++p) {
2714           s[3] = 1;
2715           for (s[0] = -1; s[0] < 2; s[0] += 2) {
2716             for (s[1] = -1; s[1] < 2; s[1] += 2) {
2717               for (s[2] = -1; s[2] < 2; s[2] += 2) {
2718                 for (d = 0; d < embedDim; ++d) coordsIn[i * embedDim + d] = s[evenPerm[p][d]] * vertexC[evenPerm[p][d]];
2719                 ++i;
2720               }
2721             }
2722           }
2723         }
2724       }
2725       PetscCheck(i == numVerts, PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Invalid 600-cell, vertices %" PetscInt_FMT " != %" PetscInt_FMT, i, numVerts);
2726       /* Construct graph */
2727       PetscCall(PetscCalloc1(numVerts * numVerts, &graph));
2728       for (i = 0; i < numVerts; ++i) {
2729         for (j = 0, k = 0; j < numVerts; ++j) {
2730           if (PetscAbsReal(DiffNormReal(embedDim, &coordsIn[i * embedDim], &coordsIn[j * embedDim]) - edgeLen) < PETSC_SMALL) {
2731             graph[i * numVerts + j] = 1;
2732             ++k;
2733           }
2734         }
2735         PetscCheck(k == degree, PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Invalid 600-cell, vertex %" PetscInt_FMT " degree %" PetscInt_FMT " != %" PetscInt_FMT, i, k, degree);
2736       }
2737       /* Build Topology */
2738       PetscCall(DMPlexSetChart(dm, 0, numCells + numVerts));
2739       for (PetscInt c = 0; c < numCells; c++) PetscCall(DMPlexSetConeSize(dm, c, embedDim));
2740       PetscCall(DMSetUp(dm)); /* Allocate space for cones */
2741       /* Cells */
2742       if (rank == 0) {
2743         for (PetscInt i = 0, c = 0; i < numVerts; ++i) {
2744           for (j = 0; j < i; ++j) {
2745             for (k = 0; k < j; ++k) {
2746               for (l = 0; l < k; ++l) {
2747                 if (graph[i * numVerts + j] && graph[j * numVerts + k] && graph[k * numVerts + i] && graph[l * numVerts + i] && graph[l * numVerts + j] && graph[l * numVerts + k]) {
2748                   cone[0] = firstVertex + i;
2749                   cone[1] = firstVertex + j;
2750                   cone[2] = firstVertex + k;
2751                   cone[3] = firstVertex + l;
2752                   /* Check orientation: https://ef.gy/linear-algebra:normal-vectors-in-higher-dimensional-spaces */
2753                   {
2754                     const PetscInt epsilon[4][4][4][4] = {
2755                       {{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},  {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 1}, {0, 0, -1, 0}}, {{0, 0, 0, 0}, {0, 0, 0, -1}, {0, 0, 0, 0}, {0, 1, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 1, 0}, {0, -1, 0, 0}, {0, 0, 0, 0}}},
2756 
2757                       {{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, -1}, {0, 0, 1, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},  {{0, 0, 0, 1}, {0, 0, 0, 0}, {0, 0, 0, 0}, {-1, 0, 0, 0}}, {{0, 0, -1, 0}, {0, 0, 0, 0}, {1, 0, 0, 0}, {0, 0, 0, 0}}},
2758 
2759                       {{{0, 0, 0, 0}, {0, 0, 0, 1}, {0, 0, 0, 0}, {0, -1, 0, 0}}, {{0, 0, 0, -1}, {0, 0, 0, 0}, {0, 0, 0, 0}, {1, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},  {{0, 1, 0, 0}, {-1, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}},
2760 
2761                       {{{0, 0, 0, 0}, {0, 0, -1, 0}, {0, 1, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 1, 0}, {0, 0, 0, 0}, {-1, 0, 0, 0}, {0, 0, 0, 0}}, {{0, -1, 0, 0}, {1, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}, {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}} }
2762                     };
2763                     PetscReal normal[4];
2764                     PetscInt  e, f, g;
2765 
2766                     for (d = 0; d < embedDim; ++d) {
2767                       normal[d] = 0.0;
2768                       for (e = 0; e < embedDim; ++e) {
2769                         for (f = 0; f < embedDim; ++f) {
2770                           for (g = 0; g < embedDim; ++g) {
2771                             normal[d] += epsilon[d][e][f][g] * (coordsIn[j * embedDim + e] - coordsIn[i * embedDim + e]) * (coordsIn[k * embedDim + f] - coordsIn[i * embedDim + f]) * (coordsIn[l * embedDim + f] - coordsIn[i * embedDim + f]);
2772                           }
2773                         }
2774                       }
2775                     }
2776                     if (DotReal(embedDim, normal, &coordsIn[i * embedDim]) < 0) {
2777                       PetscInt tmp = cone[1];
2778                       cone[1]      = cone[2];
2779                       cone[2]      = tmp;
2780                     }
2781                   }
2782                   PetscCall(DMPlexSetCone(dm, c++, cone));
2783                 }
2784               }
2785             }
2786           }
2787         }
2788       }
2789       PetscCall(DMPlexSymmetrize(dm));
2790       PetscCall(DMPlexStratify(dm));
2791       PetscCall(PetscFree(graph));
2792     }
2793     break;
2794   default:
2795     SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported dimension for sphere: %" PetscInt_FMT, dim);
2796   }
2797   /* Create coordinates */
2798   PetscCall(DMGetCoordinateSection(dm, &coordSection));
2799   PetscCall(PetscSectionSetNumFields(coordSection, 1));
2800   PetscCall(PetscSectionSetFieldComponents(coordSection, 0, embedDim));
2801   PetscCall(PetscSectionSetChart(coordSection, firstVertex, firstVertex + numVerts));
2802   for (v = firstVertex; v < firstVertex + numVerts; ++v) {
2803     PetscCall(PetscSectionSetDof(coordSection, v, embedDim));
2804     PetscCall(PetscSectionSetFieldDof(coordSection, v, 0, embedDim));
2805   }
2806   PetscCall(PetscSectionSetUp(coordSection));
2807   PetscCall(PetscSectionGetStorageSize(coordSection, &coordSize));
2808   PetscCall(VecCreate(PETSC_COMM_SELF, &coordinates));
2809   PetscCall(VecSetBlockSize(coordinates, embedDim));
2810   PetscCall(PetscObjectSetName((PetscObject)coordinates, "coordinates"));
2811   PetscCall(VecSetSizes(coordinates, coordSize, PETSC_DETERMINE));
2812   PetscCall(VecSetType(coordinates, VECSTANDARD));
2813   PetscCall(VecGetArray(coordinates, &coords));
2814   for (v = 0; v < numVerts; ++v)
2815     for (d = 0; d < embedDim; ++d) coords[v * embedDim + d] = coordsIn[v * embedDim + d];
2816   PetscCall(VecRestoreArray(coordinates, &coords));
2817   PetscCall(DMSetCoordinatesLocal(dm, coordinates));
2818   PetscCall(VecDestroy(&coordinates));
2819   PetscCall(PetscFree(coordsIn));
2820   {
2821     DM          cdm;
2822     PetscDS     cds;
2823     PetscScalar c = R;
2824 
2825     PetscCall(DMPlexCreateCoordinateSpace(dm, 1, PETSC_TRUE, snapToSphere));
2826     PetscCall(DMGetCoordinateDM(dm, &cdm));
2827     PetscCall(DMGetDS(cdm, &cds));
2828     PetscCall(PetscDSSetConstants(cds, 1, &c));
2829   }
2830   PetscCall(PetscLogEventEnd(DMPLEX_Generate, dm, 0, 0, 0));
2831   /* Wait for coordinate creation before doing in-place modification */
2832   if (simplex) PetscCall(DMPlexInterpolateInPlace_Internal(dm));
2833   PetscFunctionReturn(PETSC_SUCCESS);
2834 }
2835 
2836 typedef void (*TPSEvaluateFunc)(const PetscReal[], PetscReal *, PetscReal[], PetscReal (*)[3]);
2837 
2838 /*
2839  The Schwarz P implicit surface is
2840 
2841      f(x) = cos(x0) + cos(x1) + cos(x2) = 0
2842 */
2843 static void TPSEvaluate_SchwarzP(const PetscReal y[3], PetscReal *f, PetscReal grad[], PetscReal (*hess)[3])
2844 {
2845   PetscReal c[3] = {PetscCosReal(y[0] * PETSC_PI), PetscCosReal(y[1] * PETSC_PI), PetscCosReal(y[2] * PETSC_PI)};
2846   PetscReal g[3] = {-PetscSinReal(y[0] * PETSC_PI), -PetscSinReal(y[1] * PETSC_PI), -PetscSinReal(y[2] * PETSC_PI)};
2847   f[0]           = c[0] + c[1] + c[2];
2848   for (PetscInt i = 0; i < 3; i++) {
2849     grad[i] = PETSC_PI * g[i];
2850     for (PetscInt j = 0; j < 3; j++) hess[i][j] = (i == j) ? -PetscSqr(PETSC_PI) * c[i] : 0.;
2851   }
2852 }
2853 
2854 // u[] is a tentative normal on input. Replace with the implicit function gradient in the same direction
2855 static PetscErrorCode TPSExtrudeNormalFunc_SchwarzP(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt r, PetscScalar u[], void *ctx)
2856 {
2857   for (PetscInt i = 0; i < 3; i++) u[i] = -PETSC_PI * PetscSinReal(x[i] * PETSC_PI);
2858   return PETSC_SUCCESS;
2859 }
2860 
2861 /*
2862  The Gyroid implicit surface is
2863 
2864  f(x,y,z) = sin(pi * x) * cos (pi * (y + 1/2))  + sin(pi * (y + 1/2)) * cos(pi * (z + 1/4)) + sin(pi * (z + 1/4)) * cos(pi * x)
2865 
2866 */
2867 static void TPSEvaluate_Gyroid(const PetscReal y[3], PetscReal *f, PetscReal grad[], PetscReal (*hess)[3])
2868 {
2869   PetscReal s[3] = {PetscSinReal(PETSC_PI * y[0]), PetscSinReal(PETSC_PI * (y[1] + .5)), PetscSinReal(PETSC_PI * (y[2] + .25))};
2870   PetscReal c[3] = {PetscCosReal(PETSC_PI * y[0]), PetscCosReal(PETSC_PI * (y[1] + .5)), PetscCosReal(PETSC_PI * (y[2] + .25))};
2871   f[0]           = s[0] * c[1] + s[1] * c[2] + s[2] * c[0];
2872   grad[0]        = PETSC_PI * (c[0] * c[1] - s[2] * s[0]);
2873   grad[1]        = PETSC_PI * (c[1] * c[2] - s[0] * s[1]);
2874   grad[2]        = PETSC_PI * (c[2] * c[0] - s[1] * s[2]);
2875   hess[0][0]     = -PetscSqr(PETSC_PI) * (s[0] * c[1] + s[2] * c[0]);
2876   hess[0][1]     = -PetscSqr(PETSC_PI) * (c[0] * s[1]);
2877   hess[0][2]     = -PetscSqr(PETSC_PI) * (c[2] * s[0]);
2878   hess[1][0]     = -PetscSqr(PETSC_PI) * (s[1] * c[2] + s[0] * c[1]);
2879   hess[1][1]     = -PetscSqr(PETSC_PI) * (c[1] * s[2]);
2880   hess[2][2]     = -PetscSqr(PETSC_PI) * (c[0] * s[1]);
2881   hess[2][0]     = -PetscSqr(PETSC_PI) * (s[2] * c[0] + s[1] * c[2]);
2882   hess[2][1]     = -PetscSqr(PETSC_PI) * (c[2] * s[0]);
2883   hess[2][2]     = -PetscSqr(PETSC_PI) * (c[1] * s[2]);
2884 }
2885 
2886 // u[] is a tentative normal on input. Replace with the implicit function gradient in the same direction
2887 static PetscErrorCode TPSExtrudeNormalFunc_Gyroid(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt r, PetscScalar u[], void *ctx)
2888 {
2889   PetscReal s[3] = {PetscSinReal(PETSC_PI * x[0]), PetscSinReal(PETSC_PI * (x[1] + .5)), PetscSinReal(PETSC_PI * (x[2] + .25))};
2890   PetscReal c[3] = {PetscCosReal(PETSC_PI * x[0]), PetscCosReal(PETSC_PI * (x[1] + .5)), PetscCosReal(PETSC_PI * (x[2] + .25))};
2891   u[0]           = PETSC_PI * (c[0] * c[1] - s[2] * s[0]);
2892   u[1]           = PETSC_PI * (c[1] * c[2] - s[0] * s[1]);
2893   u[2]           = PETSC_PI * (c[2] * c[0] - s[1] * s[2]);
2894   return PETSC_SUCCESS;
2895 }
2896 
2897 /*
2898    We wish to solve
2899 
2900          min_y || y - x ||^2  subject to f(y) = 0
2901 
2902    Let g(y) = grad(f).  The minimization problem is equivalent to asking to satisfy
2903    f(y) = 0 and (y-x) is parallel to g(y).  We do this by using Householder QR to obtain a basis for the
2904    tangent space and ask for both components in the tangent space to be zero.
2905 
2906    Take g to be a column vector and compute the "full QR" factorization Q R = g,
2907    where Q = I - 2 n n^T is a symmetric orthogonal matrix.
2908    The first column of Q is parallel to g so the remaining two columns span the null space.
2909    Let Qn = Q[:,1:] be those remaining columns.  Then Qn Qn^T is an orthogonal projector into the tangent space.
2910    Since Q is symmetric, this is equivalent to multiplying by Q and taking the last two entries.
2911    In total, we have a system of 3 equations in 3 unknowns:
2912 
2913      f(y) = 0                       1 equation
2914      Qn^T (y - x) = 0               2 equations
2915 
2916    Here, we compute the residual and Jacobian of this system.
2917 */
2918 static void TPSNearestPointResJac(TPSEvaluateFunc feval, const PetscScalar x[], const PetscScalar y[], PetscScalar res[], PetscScalar J[])
2919 {
2920   PetscReal yreal[3] = {PetscRealPart(y[0]), PetscRealPart(y[1]), PetscRealPart(y[2])};
2921   PetscReal d[3]     = {PetscRealPart(y[0] - x[0]), PetscRealPart(y[1] - x[1]), PetscRealPart(y[2] - x[2])};
2922   PetscReal f, grad[3], n[3], norm, norm_y[3], nd, nd_y[3], sign;
2923   PetscReal n_y[3][3] = {
2924     {0, 0, 0},
2925     {0, 0, 0},
2926     {0, 0, 0}
2927   };
2928 
2929   feval(yreal, &f, grad, n_y);
2930 
2931   for (PetscInt i = 0; i < 3; i++) n[i] = grad[i];
2932   norm = PetscSqrtReal(PetscSqr(n[0]) + PetscSqr(n[1]) + PetscSqr(n[2]));
2933   for (PetscInt i = 0; i < 3; i++) norm_y[i] = 1. / norm * n[i] * n_y[i][i];
2934 
2935   // Define the Householder reflector
2936   sign = n[0] >= 0 ? 1. : -1.;
2937   n[0] += norm * sign;
2938   for (PetscInt i = 0; i < 3; i++) n_y[0][i] += norm_y[i] * sign;
2939 
2940   norm      = PetscSqrtReal(PetscSqr(n[0]) + PetscSqr(n[1]) + PetscSqr(n[2]));
2941   norm_y[0] = 1. / norm * (n[0] * n_y[0][0]);
2942   norm_y[1] = 1. / norm * (n[0] * n_y[0][1] + n[1] * n_y[1][1]);
2943   norm_y[2] = 1. / norm * (n[0] * n_y[0][2] + n[2] * n_y[2][2]);
2944 
2945   for (PetscInt i = 0; i < 3; i++) {
2946     n[i] /= norm;
2947     for (PetscInt j = 0; j < 3; j++) {
2948       // note that n[i] is n_old[i]/norm when executing the code below
2949       n_y[i][j] = n_y[i][j] / norm - n[i] / norm * norm_y[j];
2950     }
2951   }
2952 
2953   nd = n[0] * d[0] + n[1] * d[1] + n[2] * d[2];
2954   for (PetscInt i = 0; i < 3; i++) nd_y[i] = n[i] + n_y[0][i] * d[0] + n_y[1][i] * d[1] + n_y[2][i] * d[2];
2955 
2956   res[0] = f;
2957   res[1] = d[1] - 2 * n[1] * nd;
2958   res[2] = d[2] - 2 * n[2] * nd;
2959   // J[j][i] is J_{ij} (column major)
2960   for (PetscInt j = 0; j < 3; j++) {
2961     J[0 + j * 3] = grad[j];
2962     J[1 + j * 3] = (j == 1) * 1. - 2 * (n_y[1][j] * nd + n[1] * nd_y[j]);
2963     J[2 + j * 3] = (j == 2) * 1. - 2 * (n_y[2][j] * nd + n[2] * nd_y[j]);
2964   }
2965 }
2966 
2967 /*
2968    Project x to the nearest point on the implicit surface using Newton's method.
2969 */
2970 static PetscErrorCode TPSNearestPoint(TPSEvaluateFunc feval, PetscScalar x[])
2971 {
2972   PetscScalar y[3] = {x[0], x[1], x[2]}; // Initial guess
2973 
2974   PetscFunctionBegin;
2975   for (PetscInt iter = 0; iter < 10; iter++) {
2976     PetscScalar res[3], J[9];
2977     PetscReal   resnorm;
2978     TPSNearestPointResJac(feval, x, y, res, J);
2979     resnorm = PetscSqrtReal(PetscSqr(PetscRealPart(res[0])) + PetscSqr(PetscRealPart(res[1])) + PetscSqr(PetscRealPart(res[2])));
2980     if (0) { // Turn on this monitor if you need to confirm quadratic convergence
2981       PetscCall(PetscPrintf(PETSC_COMM_SELF, "[%" PetscInt_FMT "] res [%g %g %g]\n", iter, (double)PetscRealPart(res[0]), (double)PetscRealPart(res[1]), (double)PetscRealPart(res[2])));
2982     }
2983     if (resnorm < PETSC_SMALL) break;
2984 
2985     // Take the Newton step
2986     PetscCall(PetscKernel_A_gets_inverse_A_3(J, 0., PETSC_FALSE, NULL));
2987     PetscKernel_v_gets_v_minus_A_times_w_3(y, J, res);
2988   }
2989   for (PetscInt i = 0; i < 3; i++) x[i] = y[i];
2990   PetscFunctionReturn(PETSC_SUCCESS);
2991 }
2992 
2993 const char *const DMPlexTPSTypes[] = {"SCHWARZ_P", "GYROID", "DMPlexTPSType", "DMPLEX_TPS_", NULL};
2994 
2995 static PetscErrorCode DMPlexCreateTPSMesh_Internal(DM dm, DMPlexTPSType tpstype, const PetscInt extent[], const DMBoundaryType periodic[], PetscBool tps_distribute, PetscInt refinements, PetscInt layers, PetscReal thickness)
2996 {
2997   PetscMPIInt rank;
2998   PetscInt    topoDim = 2, spaceDim = 3, numFaces = 0, numVertices = 0, numEdges = 0;
2999   PetscInt(*edges)[2] = NULL, *edgeSets = NULL;
3000   PetscInt            *cells_flat = NULL;
3001   PetscReal           *vtxCoords  = NULL;
3002   TPSEvaluateFunc      evalFunc   = NULL;
3003   PetscSimplePointFunc normalFunc = NULL;
3004   DMLabel              label;
3005 
3006   PetscFunctionBegin;
3007   PetscCall(PetscLogEventBegin(DMPLEX_Generate, dm, 0, 0, 0));
3008   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank));
3009   PetscCheck((layers != 0) ^ (thickness == 0.), PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_INCOMP, "Layers %" PetscInt_FMT " must be nonzero iff thickness %g is nonzero", layers, (double)thickness);
3010   switch (tpstype) {
3011   case DMPLEX_TPS_SCHWARZ_P:
3012     PetscCheck(!periodic || (periodic[0] == DM_BOUNDARY_NONE && periodic[1] == DM_BOUNDARY_NONE && periodic[2] == DM_BOUNDARY_NONE), PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Schwarz P does not support periodic meshes");
3013     if (rank == 0) {
3014       PetscInt(*cells)[6][4][4] = NULL; // [junction, junction-face, cell, conn]
3015       PetscInt  Njunctions = 0, Ncuts = 0, Npipes[3], vcount;
3016       PetscReal L = 1;
3017 
3018       Npipes[0]   = (extent[0] + 1) * extent[1] * extent[2];
3019       Npipes[1]   = extent[0] * (extent[1] + 1) * extent[2];
3020       Npipes[2]   = extent[0] * extent[1] * (extent[2] + 1);
3021       Njunctions  = extent[0] * extent[1] * extent[2];
3022       Ncuts       = 2 * (extent[0] * extent[1] + extent[1] * extent[2] + extent[2] * extent[0]);
3023       numVertices = 4 * (Npipes[0] + Npipes[1] + Npipes[2]) + 8 * Njunctions;
3024       PetscCall(PetscMalloc1(3 * numVertices, &vtxCoords));
3025       PetscCall(PetscMalloc1(Njunctions, &cells));
3026       PetscCall(PetscMalloc1(Ncuts * 4, &edges));
3027       PetscCall(PetscMalloc1(Ncuts * 4, &edgeSets));
3028       // x-normal pipes
3029       vcount = 0;
3030       for (PetscInt i = 0; i < extent[0] + 1; i++) {
3031         for (PetscInt j = 0; j < extent[1]; j++) {
3032           for (PetscInt k = 0; k < extent[2]; k++) {
3033             for (PetscInt l = 0; l < 4; l++) {
3034               vtxCoords[vcount++] = (2 * i - 1) * L;
3035               vtxCoords[vcount++] = 2 * j * L + PetscCosReal((2 * l + 1) * PETSC_PI / 4) * L / 2;
3036               vtxCoords[vcount++] = 2 * k * L + PetscSinReal((2 * l + 1) * PETSC_PI / 4) * L / 2;
3037             }
3038           }
3039         }
3040       }
3041       // y-normal pipes
3042       for (PetscInt i = 0; i < extent[0]; i++) {
3043         for (PetscInt j = 0; j < extent[1] + 1; j++) {
3044           for (PetscInt k = 0; k < extent[2]; k++) {
3045             for (PetscInt l = 0; l < 4; l++) {
3046               vtxCoords[vcount++] = 2 * i * L + PetscSinReal((2 * l + 1) * PETSC_PI / 4) * L / 2;
3047               vtxCoords[vcount++] = (2 * j - 1) * L;
3048               vtxCoords[vcount++] = 2 * k * L + PetscCosReal((2 * l + 1) * PETSC_PI / 4) * L / 2;
3049             }
3050           }
3051         }
3052       }
3053       // z-normal pipes
3054       for (PetscInt i = 0; i < extent[0]; i++) {
3055         for (PetscInt j = 0; j < extent[1]; j++) {
3056           for (PetscInt k = 0; k < extent[2] + 1; k++) {
3057             for (PetscInt l = 0; l < 4; l++) {
3058               vtxCoords[vcount++] = 2 * i * L + PetscCosReal((2 * l + 1) * PETSC_PI / 4) * L / 2;
3059               vtxCoords[vcount++] = 2 * j * L + PetscSinReal((2 * l + 1) * PETSC_PI / 4) * L / 2;
3060               vtxCoords[vcount++] = (2 * k - 1) * L;
3061             }
3062           }
3063         }
3064       }
3065       // junctions
3066       for (PetscInt i = 0; i < extent[0]; i++) {
3067         for (PetscInt j = 0; j < extent[1]; j++) {
3068           for (PetscInt k = 0; k < extent[2]; k++) {
3069             const PetscInt J = (i * extent[1] + j) * extent[2] + k, Jvoff = (Npipes[0] + Npipes[1] + Npipes[2]) * 4 + J * 8;
3070             PetscCheck(vcount / 3 == Jvoff, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Unexpected vertex count");
3071             for (PetscInt ii = 0; ii < 2; ii++) {
3072               for (PetscInt jj = 0; jj < 2; jj++) {
3073                 for (PetscInt kk = 0; kk < 2; kk++) {
3074                   double Ls           = (1 - sqrt(2) / 4) * L;
3075                   vtxCoords[vcount++] = 2 * i * L + (2 * ii - 1) * Ls;
3076                   vtxCoords[vcount++] = 2 * j * L + (2 * jj - 1) * Ls;
3077                   vtxCoords[vcount++] = 2 * k * L + (2 * kk - 1) * Ls;
3078                 }
3079               }
3080             }
3081             const PetscInt jfaces[3][2][4] = {
3082               {{3, 1, 0, 2}, {7, 5, 4, 6}}, // x-aligned
3083               {{5, 4, 0, 1}, {7, 6, 2, 3}}, // y-aligned
3084               {{6, 2, 0, 4}, {7, 3, 1, 5}}  // z-aligned
3085             };
3086             const PetscInt pipe_lo[3] = {// vertex numbers of pipes
3087                                          ((i * extent[1] + j) * extent[2] + k) * 4, ((i * (extent[1] + 1) + j) * extent[2] + k + Npipes[0]) * 4, ((i * extent[1] + j) * (extent[2] + 1) + k + Npipes[0] + Npipes[1]) * 4};
3088             const PetscInt pipe_hi[3] = {// vertex numbers of pipes
3089                                          (((i + 1) * extent[1] + j) * extent[2] + k) * 4, ((i * (extent[1] + 1) + j + 1) * extent[2] + k + Npipes[0]) * 4, ((i * extent[1] + j) * (extent[2] + 1) + k + 1 + Npipes[0] + Npipes[1]) * 4};
3090             for (PetscInt dir = 0; dir < 3; dir++) { // x,y,z
3091               const PetscInt ijk[3] = {i, j, k};
3092               for (PetscInt l = 0; l < 4; l++) { // rotations
3093                 cells[J][dir * 2 + 0][l][0] = pipe_lo[dir] + l;
3094                 cells[J][dir * 2 + 0][l][1] = Jvoff + jfaces[dir][0][l];
3095                 cells[J][dir * 2 + 0][l][2] = Jvoff + jfaces[dir][0][(l - 1 + 4) % 4];
3096                 cells[J][dir * 2 + 0][l][3] = pipe_lo[dir] + (l - 1 + 4) % 4;
3097                 cells[J][dir * 2 + 1][l][0] = Jvoff + jfaces[dir][1][l];
3098                 cells[J][dir * 2 + 1][l][1] = pipe_hi[dir] + l;
3099                 cells[J][dir * 2 + 1][l][2] = pipe_hi[dir] + (l - 1 + 4) % 4;
3100                 cells[J][dir * 2 + 1][l][3] = Jvoff + jfaces[dir][1][(l - 1 + 4) % 4];
3101                 if (ijk[dir] == 0) {
3102                   edges[numEdges][0] = pipe_lo[dir] + l;
3103                   edges[numEdges][1] = pipe_lo[dir] + (l + 1) % 4;
3104                   edgeSets[numEdges] = dir * 2 + 1;
3105                   numEdges++;
3106                 }
3107                 if (ijk[dir] + 1 == extent[dir]) {
3108                   edges[numEdges][0] = pipe_hi[dir] + l;
3109                   edges[numEdges][1] = pipe_hi[dir] + (l + 1) % 4;
3110                   edgeSets[numEdges] = dir * 2 + 2;
3111                   numEdges++;
3112                 }
3113               }
3114             }
3115           }
3116         }
3117       }
3118       PetscCheck(numEdges == Ncuts * 4, PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Edge count %" PetscInt_FMT " incompatible with number of cuts %" PetscInt_FMT, numEdges, Ncuts);
3119       numFaces   = 24 * Njunctions;
3120       cells_flat = cells[0][0][0];
3121     }
3122     evalFunc   = TPSEvaluate_SchwarzP;
3123     normalFunc = TPSExtrudeNormalFunc_SchwarzP;
3124     break;
3125   case DMPLEX_TPS_GYROID:
3126     if (rank == 0) {
3127       // This is a coarse mesh approximation of the gyroid shifted to being the zero of the level set
3128       //
3129       //     sin(pi*x)*cos(pi*(y+1/2)) + sin(pi*(y+1/2))*cos(pi*(z+1/4)) + sin(pi*(z+1/4))*cos(x)
3130       //
3131       // on the cell [0,2]^3.
3132       //
3133       // Think about dividing that cell into four columns, and focus on the column [0,1]x[0,1]x[0,2].
3134       // If you looked at the gyroid in that column at different slices of z you would see that it kind of spins
3135       // like a boomerang:
3136       //
3137       //     z = 0          z = 1/4        z = 1/2        z = 3/4     //
3138       //     -----          -------        -------        -------     //
3139       //                                                              //
3140       //     +       +      +       +      +       +      +   \   +   //
3141       //      \                                   /            \      //
3142       //       \            `-_   _-'            /              }     //
3143       //        *-_            `-'            _-'              /      //
3144       //     +     `-+      +       +      +-'     +      +   /   +   //
3145       //                                                              //
3146       //                                                              //
3147       //     z = 1          z = 5/4        z = 3/2        z = 7/4     //
3148       //     -----          -------        -------        -------     //
3149       //                                                              //
3150       //     +-_     +      +       +      +     _-+      +   /   +   //
3151       //        `-_            _-_            _-`            /        //
3152       //           \        _-'   `-_        /              {         //
3153       //            \                       /                \        //
3154       //     +       +      +       +      +       +      +   \   +   //
3155       //
3156       //
3157       // This course mesh approximates each of these slices by two line segments,
3158       // and then connects the segments in consecutive layers with quadrilateral faces.
3159       // All of the end points of the segments are multiples of 1/4 except for the
3160       // point * in the picture for z = 0 above and the similar points in other layers.
3161       // That point is at (gamma, gamma, 0), where gamma is calculated below.
3162       //
3163       // The column  [1,2]x[1,2]x[0,2] looks the same as this column;
3164       // The columns [1,2]x[0,1]x[0,2] and [0,1]x[1,2]x[0,2] are mirror images.
3165       //
3166       // As for how this method turned into the names given to the vertices:
3167       // that was not systematic, it was just the way it worked out in my handwritten notes.
3168 
3169       PetscInt facesPerBlock = 64;
3170       PetscInt vertsPerBlock = 56;
3171       PetscInt extentPlus[3];
3172       PetscInt numBlocks, numBlocksPlus;
3173       const PetscInt A = 0, B = 1, C = 2, D = 3, E = 4, F = 5, G = 6, H = 7, II = 8, J = 9, K = 10, L = 11, M = 12, N = 13, O = 14, P = 15, Q = 16, R = 17, S = 18, T = 19, U = 20, V = 21, W = 22, X = 23, Y = 24, Z = 25, Ap = 26, Bp = 27, Cp = 28, Dp = 29, Ep = 30, Fp = 31, Gp = 32, Hp = 33, Ip = 34, Jp = 35, Kp = 36, Lp = 37, Mp = 38, Np = 39, Op = 40, Pp = 41, Qp = 42, Rp = 43, Sp = 44, Tp = 45, Up = 46, Vp = 47, Wp = 48, Xp = 49, Yp = 50, Zp = 51, Aq = 52, Bq = 53, Cq = 54, Dq = 55;
3174       const PetscInt pattern[64][4] = {
3175   /* face to vertex within the coarse discretization of a single gyroid block */
3176   /* layer 0 */
3177         {A,           C,           K,           G          },
3178         {C,           B,           II,          K          },
3179         {D,           A,           H,           L          },
3180         {B + 56 * 1,  D,           L,           J          },
3181         {E,           B + 56 * 1,  J,           N          },
3182         {A + 56 * 2,  E,           N,           H + 56 * 2 },
3183         {F,           A + 56 * 2,  G + 56 * 2,  M          },
3184         {B,           F,           M,           II         },
3185  /* layer 1 */
3186         {G,           K,           Q,           O          },
3187         {K,           II,          P,           Q          },
3188         {L,           H,           O + 56 * 1,  R          },
3189         {J,           L,           R,           P          },
3190         {N,           J,           P,           S          },
3191         {H + 56 * 2,  N,           S,           O + 56 * 3 },
3192         {M,           G + 56 * 2,  O + 56 * 2,  T          },
3193         {II,          M,           T,           P          },
3194  /* layer 2 */
3195         {O,           Q,           Y,           U          },
3196         {Q,           P,           W,           Y          },
3197         {R,           O + 56 * 1,  U + 56 * 1,  Ap         },
3198         {P,           R,           Ap,          W          },
3199         {S,           P,           X,           Bp         },
3200         {O + 56 * 3,  S,           Bp,          V + 56 * 1 },
3201         {T,           O + 56 * 2,  V,           Z          },
3202         {P,           T,           Z,           X          },
3203  /* layer 3 */
3204         {U,           Y,           Ep,          Dp         },
3205         {Y,           W,           Cp,          Ep         },
3206         {Ap,          U + 56 * 1,  Dp + 56 * 1, Gp         },
3207         {W,           Ap,          Gp,          Cp         },
3208         {Bp,          X,           Cp + 56 * 2, Fp         },
3209         {V + 56 * 1,  Bp,          Fp,          Dp + 56 * 1},
3210         {Z,           V,           Dp,          Hp         },
3211         {X,           Z,           Hp,          Cp + 56 * 2},
3212  /* layer 4 */
3213         {Dp,          Ep,          Mp,          Kp         },
3214         {Ep,          Cp,          Ip,          Mp         },
3215         {Gp,          Dp + 56 * 1, Lp,          Np         },
3216         {Cp,          Gp,          Np,          Jp         },
3217         {Fp,          Cp + 56 * 2, Jp + 56 * 2, Pp         },
3218         {Dp + 56 * 1, Fp,          Pp,          Lp         },
3219         {Hp,          Dp,          Kp,          Op         },
3220         {Cp + 56 * 2, Hp,          Op,          Ip + 56 * 2},
3221  /* layer 5 */
3222         {Kp,          Mp,          Sp,          Rp         },
3223         {Mp,          Ip,          Qp,          Sp         },
3224         {Np,          Lp,          Rp,          Tp         },
3225         {Jp,          Np,          Tp,          Qp + 56 * 1},
3226         {Pp,          Jp + 56 * 2, Qp + 56 * 3, Up         },
3227         {Lp,          Pp,          Up,          Rp         },
3228         {Op,          Kp,          Rp,          Vp         },
3229         {Ip + 56 * 2, Op,          Vp,          Qp + 56 * 2},
3230  /* layer 6 */
3231         {Rp,          Sp,          Aq,          Yp         },
3232         {Sp,          Qp,          Wp,          Aq         },
3233         {Tp,          Rp,          Yp,          Cq         },
3234         {Qp + 56 * 1, Tp,          Cq,          Wp + 56 * 1},
3235         {Up,          Qp + 56 * 3, Xp + 56 * 1, Dq         },
3236         {Rp,          Up,          Dq,          Zp         },
3237         {Vp,          Rp,          Zp,          Bq         },
3238         {Qp + 56 * 2, Vp,          Bq,          Xp         },
3239  /* layer 7 (the top is the periodic image of the bottom of layer 0) */
3240         {Yp,          Aq,          C + 56 * 4,  A + 56 * 4 },
3241         {Aq,          Wp,          B + 56 * 4,  C + 56 * 4 },
3242         {Cq,          Yp,          A + 56 * 4,  D + 56 * 4 },
3243         {Wp + 56 * 1, Cq,          D + 56 * 4,  B + 56 * 5 },
3244         {Dq,          Xp + 56 * 1, B + 56 * 5,  E + 56 * 4 },
3245         {Zp,          Dq,          E + 56 * 4,  A + 56 * 6 },
3246         {Bq,          Zp,          A + 56 * 6,  F + 56 * 4 },
3247         {Xp,          Bq,          F + 56 * 4,  B + 56 * 4 }
3248       };
3249       const PetscReal gamma                = PetscAcosReal((PetscSqrtReal(3.) - 1.) / PetscSqrtReal(2.)) / PETSC_PI;
3250       const PetscReal patternCoords[56][3] = {
3251         {1.,        0.,        0.  }, /* A  */
3252         {0.,        1.,        0.  }, /* B  */
3253         {gamma,     gamma,     0.  }, /* C  */
3254         {1 + gamma, 1 - gamma, 0.  }, /* D  */
3255         {2 - gamma, 2 - gamma, 0.  }, /* E  */
3256         {1 - gamma, 1 + gamma, 0.  }, /* F  */
3257 
3258         {.5,        0,         .25 }, /* G  */
3259         {1.5,       0.,        .25 }, /* H  */
3260         {.5,        1.,        .25 }, /* II */
3261         {1.5,       1.,        .25 }, /* J  */
3262         {.25,       .5,        .25 }, /* K  */
3263         {1.25,      .5,        .25 }, /* L  */
3264         {.75,       1.5,       .25 }, /* M  */
3265         {1.75,      1.5,       .25 }, /* N  */
3266 
3267         {0.,        0.,        .5  }, /* O  */
3268         {1.,        1.,        .5  }, /* P  */
3269         {gamma,     1 - gamma, .5  }, /* Q  */
3270         {1 + gamma, gamma,     .5  }, /* R  */
3271         {2 - gamma, 1 + gamma, .5  }, /* S  */
3272         {1 - gamma, 2 - gamma, .5  }, /* T  */
3273 
3274         {0.,        .5,        .75 }, /* U  */
3275         {0.,        1.5,       .75 }, /* V  */
3276         {1.,        .5,        .75 }, /* W  */
3277         {1.,        1.5,       .75 }, /* X  */
3278         {.5,        .75,       .75 }, /* Y  */
3279         {.5,        1.75,      .75 }, /* Z  */
3280         {1.5,       .25,       .75 }, /* Ap */
3281         {1.5,       1.25,      .75 }, /* Bp */
3282 
3283         {1.,        0.,        1.  }, /* Cp */
3284         {0.,        1.,        1.  }, /* Dp */
3285         {1 - gamma, 1 - gamma, 1.  }, /* Ep */
3286         {1 + gamma, 1 + gamma, 1.  }, /* Fp */
3287         {2 - gamma, gamma,     1.  }, /* Gp */
3288         {gamma,     2 - gamma, 1.  }, /* Hp */
3289 
3290         {.5,        0.,        1.25}, /* Ip */
3291         {1.5,       0.,        1.25}, /* Jp */
3292         {.5,        1.,        1.25}, /* Kp */
3293         {1.5,       1.,        1.25}, /* Lp */
3294         {.75,       .5,        1.25}, /* Mp */
3295         {1.75,      .5,        1.25}, /* Np */
3296         {.25,       1.5,       1.25}, /* Op */
3297         {1.25,      1.5,       1.25}, /* Pp */
3298 
3299         {0.,        0.,        1.5 }, /* Qp */
3300         {1.,        1.,        1.5 }, /* Rp */
3301         {1 - gamma, gamma,     1.5 }, /* Sp */
3302         {2 - gamma, 1 - gamma, 1.5 }, /* Tp */
3303         {1 + gamma, 2 - gamma, 1.5 }, /* Up */
3304         {gamma,     1 + gamma, 1.5 }, /* Vp */
3305 
3306         {0.,        .5,        1.75}, /* Wp */
3307         {0.,        1.5,       1.75}, /* Xp */
3308         {1.,        .5,        1.75}, /* Yp */
3309         {1.,        1.5,       1.75}, /* Zp */
3310         {.5,        .25,       1.75}, /* Aq */
3311         {.5,        1.25,      1.75}, /* Bq */
3312         {1.5,       .75,       1.75}, /* Cq */
3313         {1.5,       1.75,      1.75}, /* Dq */
3314       };
3315       PetscInt(*cells)[64][4] = NULL;
3316       PetscBool *seen;
3317       PetscInt  *vertToTrueVert;
3318       PetscInt   count;
3319 
3320       for (PetscInt i = 0; i < 3; i++) extentPlus[i] = extent[i] + 1;
3321       numBlocks = 1;
3322       for (PetscInt i = 0; i < 3; i++) numBlocks *= extent[i];
3323       numBlocksPlus = 1;
3324       for (PetscInt i = 0; i < 3; i++) numBlocksPlus *= extentPlus[i];
3325       numFaces = numBlocks * facesPerBlock;
3326       PetscCall(PetscMalloc1(numBlocks, &cells));
3327       PetscCall(PetscCalloc1(numBlocksPlus * vertsPerBlock, &seen));
3328       for (PetscInt k = 0; k < extent[2]; k++) {
3329         for (PetscInt j = 0; j < extent[1]; j++) {
3330           for (PetscInt i = 0; i < extent[0]; i++) {
3331             for (PetscInt f = 0; f < facesPerBlock; f++) {
3332               for (PetscInt v = 0; v < 4; v++) {
3333                 PetscInt vertRaw     = pattern[f][v];
3334                 PetscInt blockidx    = vertRaw / 56;
3335                 PetscInt patternvert = vertRaw % 56;
3336                 PetscInt xplus       = (blockidx & 1);
3337                 PetscInt yplus       = (blockidx & 2) >> 1;
3338                 PetscInt zplus       = (blockidx & 4) >> 2;
3339                 PetscInt zcoord      = (periodic && periodic[2] == DM_BOUNDARY_PERIODIC) ? ((k + zplus) % extent[2]) : (k + zplus);
3340                 PetscInt ycoord      = (periodic && periodic[1] == DM_BOUNDARY_PERIODIC) ? ((j + yplus) % extent[1]) : (j + yplus);
3341                 PetscInt xcoord      = (periodic && periodic[0] == DM_BOUNDARY_PERIODIC) ? ((i + xplus) % extent[0]) : (i + xplus);
3342                 PetscInt vert        = ((zcoord * extentPlus[1] + ycoord) * extentPlus[0] + xcoord) * 56 + patternvert;
3343 
3344                 cells[(k * extent[1] + j) * extent[0] + i][f][v] = vert;
3345                 seen[vert]                                       = PETSC_TRUE;
3346               }
3347             }
3348           }
3349         }
3350       }
3351       for (PetscInt i = 0; i < numBlocksPlus * vertsPerBlock; i++)
3352         if (seen[i]) numVertices++;
3353       count = 0;
3354       PetscCall(PetscMalloc1(numBlocksPlus * vertsPerBlock, &vertToTrueVert));
3355       PetscCall(PetscMalloc1(numVertices * 3, &vtxCoords));
3356       for (PetscInt i = 0; i < numBlocksPlus * vertsPerBlock; i++) vertToTrueVert[i] = -1;
3357       for (PetscInt k = 0; k < extentPlus[2]; k++) {
3358         for (PetscInt j = 0; j < extentPlus[1]; j++) {
3359           for (PetscInt i = 0; i < extentPlus[0]; i++) {
3360             for (PetscInt v = 0; v < vertsPerBlock; v++) {
3361               PetscInt vIdx = ((k * extentPlus[1] + j) * extentPlus[0] + i) * vertsPerBlock + v;
3362 
3363               if (seen[vIdx]) {
3364                 PetscInt thisVert;
3365 
3366                 vertToTrueVert[vIdx] = thisVert = count++;
3367 
3368                 for (PetscInt d = 0; d < 3; d++) vtxCoords[3 * thisVert + d] = patternCoords[v][d];
3369                 vtxCoords[3 * thisVert + 0] += i * 2;
3370                 vtxCoords[3 * thisVert + 1] += j * 2;
3371                 vtxCoords[3 * thisVert + 2] += k * 2;
3372               }
3373             }
3374           }
3375         }
3376       }
3377       for (PetscInt i = 0; i < numBlocks; i++) {
3378         for (PetscInt f = 0; f < facesPerBlock; f++) {
3379           for (PetscInt v = 0; v < 4; v++) cells[i][f][v] = vertToTrueVert[cells[i][f][v]];
3380         }
3381       }
3382       PetscCall(PetscFree(vertToTrueVert));
3383       PetscCall(PetscFree(seen));
3384       cells_flat = cells[0][0];
3385       numEdges   = 0;
3386       for (PetscInt i = 0; i < numFaces; i++) {
3387         for (PetscInt e = 0; e < 4; e++) {
3388           PetscInt         ev[]       = {cells_flat[i * 4 + e], cells_flat[i * 4 + ((e + 1) % 4)]};
3389           const PetscReal *evCoords[] = {&vtxCoords[3 * ev[0]], &vtxCoords[3 * ev[1]]};
3390 
3391           for (PetscInt d = 0; d < 3; d++) {
3392             if (!periodic || periodic[0] != DM_BOUNDARY_PERIODIC) {
3393               if (evCoords[0][d] == 0. && evCoords[1][d] == 0.) numEdges++;
3394               if (evCoords[0][d] == 2. * extent[d] && evCoords[1][d] == 2. * extent[d]) numEdges++;
3395             }
3396           }
3397         }
3398       }
3399       PetscCall(PetscMalloc1(numEdges, &edges));
3400       PetscCall(PetscMalloc1(numEdges, &edgeSets));
3401       for (PetscInt edge = 0, i = 0; i < numFaces; i++) {
3402         for (PetscInt e = 0; e < 4; e++) {
3403           PetscInt         ev[]       = {cells_flat[i * 4 + e], cells_flat[i * 4 + ((e + 1) % 4)]};
3404           const PetscReal *evCoords[] = {&vtxCoords[3 * ev[0]], &vtxCoords[3 * ev[1]]};
3405 
3406           for (PetscInt d = 0; d < 3; d++) {
3407             if (!periodic || periodic[d] != DM_BOUNDARY_PERIODIC) {
3408               if (evCoords[0][d] == 0. && evCoords[1][d] == 0.) {
3409                 edges[edge][0]   = ev[0];
3410                 edges[edge][1]   = ev[1];
3411                 edgeSets[edge++] = 2 * d;
3412               }
3413               if (evCoords[0][d] == 2. * extent[d] && evCoords[1][d] == 2. * extent[d]) {
3414                 edges[edge][0]   = ev[0];
3415                 edges[edge][1]   = ev[1];
3416                 edgeSets[edge++] = 2 * d + 1;
3417               }
3418             }
3419           }
3420         }
3421       }
3422     }
3423     evalFunc   = TPSEvaluate_Gyroid;
3424     normalFunc = TPSExtrudeNormalFunc_Gyroid;
3425     break;
3426   }
3427 
3428   PetscCall(DMSetDimension(dm, topoDim));
3429   if (rank == 0) PetscCall(DMPlexBuildFromCellList(dm, numFaces, numVertices, 4, cells_flat));
3430   else PetscCall(DMPlexBuildFromCellList(dm, 0, 0, 0, NULL));
3431   PetscCall(PetscFree(cells_flat));
3432   {
3433     DM idm;
3434     PetscCall(DMPlexInterpolate(dm, &idm));
3435     PetscCall(DMPlexReplace_Internal(dm, &idm));
3436   }
3437   if (rank == 0) PetscCall(DMPlexBuildCoordinatesFromCellList(dm, spaceDim, vtxCoords));
3438   else PetscCall(DMPlexBuildCoordinatesFromCellList(dm, spaceDim, NULL));
3439   PetscCall(PetscFree(vtxCoords));
3440 
3441   PetscCall(DMCreateLabel(dm, "Face Sets"));
3442   PetscCall(DMGetLabel(dm, "Face Sets", &label));
3443   for (PetscInt e = 0; e < numEdges; e++) {
3444     PetscInt        njoin;
3445     const PetscInt *join, verts[] = {numFaces + edges[e][0], numFaces + edges[e][1]};
3446     PetscCall(DMPlexGetJoin(dm, 2, verts, &njoin, &join));
3447     PetscCheck(njoin == 1, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Expected unique join of vertices %" PetscInt_FMT " and %" PetscInt_FMT, edges[e][0], edges[e][1]);
3448     PetscCall(DMLabelSetValue(label, join[0], edgeSets[e]));
3449     PetscCall(DMPlexRestoreJoin(dm, 2, verts, &njoin, &join));
3450   }
3451   PetscCall(PetscFree(edges));
3452   PetscCall(PetscFree(edgeSets));
3453   if (tps_distribute) {
3454     DM               pdm = NULL;
3455     PetscPartitioner part;
3456 
3457     PetscCall(DMPlexGetPartitioner(dm, &part));
3458     PetscCall(PetscPartitionerSetFromOptions(part));
3459     PetscCall(DMPlexDistribute(dm, 0, NULL, &pdm));
3460     if (pdm) PetscCall(DMPlexReplace_Internal(dm, &pdm));
3461     // Do not auto-distribute again
3462     PetscCall(DMPlexDistributeSetDefault(dm, PETSC_FALSE));
3463   }
3464 
3465   PetscCall(DMPlexSetRefinementUniform(dm, PETSC_TRUE));
3466   for (PetscInt refine = 0; refine < refinements; refine++) {
3467     PetscInt     m;
3468     DM           dmf;
3469     Vec          X;
3470     PetscScalar *x;
3471     PetscCall(DMRefine(dm, MPI_COMM_NULL, &dmf));
3472     PetscCall(DMPlexReplace_Internal(dm, &dmf));
3473 
3474     PetscCall(DMGetCoordinatesLocal(dm, &X));
3475     PetscCall(VecGetLocalSize(X, &m));
3476     PetscCall(VecGetArray(X, &x));
3477     for (PetscInt i = 0; i < m; i += 3) PetscCall(TPSNearestPoint(evalFunc, &x[i]));
3478     PetscCall(VecRestoreArray(X, &x));
3479   }
3480 
3481   // Face Sets has already been propagated to new vertices during refinement; this propagates to the initial vertices.
3482   PetscCall(DMGetLabel(dm, "Face Sets", &label));
3483   PetscCall(DMPlexLabelComplete(dm, label));
3484 
3485   PetscCall(PetscLogEventEnd(DMPLEX_Generate, dm, 0, 0, 0));
3486 
3487   if (thickness > 0) {
3488     DM              edm, cdm, ecdm;
3489     DMPlexTransform tr;
3490     const char     *prefix;
3491     PetscOptions    options;
3492     // Code from DMPlexExtrude
3493     PetscCall(DMPlexTransformCreate(PetscObjectComm((PetscObject)dm), &tr));
3494     PetscCall(DMPlexTransformSetDM(tr, dm));
3495     PetscCall(DMPlexTransformSetType(tr, DMPLEXEXTRUDE));
3496     PetscCall(PetscObjectGetOptionsPrefix((PetscObject)dm, &prefix));
3497     PetscCall(PetscObjectSetOptionsPrefix((PetscObject)tr, prefix));
3498     PetscCall(PetscObjectGetOptions((PetscObject)dm, &options));
3499     PetscCall(PetscObjectSetOptions((PetscObject)tr, options));
3500     PetscCall(DMPlexTransformExtrudeSetLayers(tr, layers));
3501     PetscCall(DMPlexTransformExtrudeSetThickness(tr, thickness));
3502     PetscCall(DMPlexTransformExtrudeSetTensor(tr, PETSC_FALSE));
3503     PetscCall(DMPlexTransformExtrudeSetSymmetric(tr, PETSC_TRUE));
3504     PetscCall(DMPlexTransformExtrudeSetNormalFunction(tr, normalFunc));
3505     PetscCall(DMPlexTransformSetFromOptions(tr));
3506     PetscCall(PetscObjectSetOptions((PetscObject)tr, NULL));
3507     PetscCall(DMPlexTransformSetUp(tr));
3508     PetscCall(PetscObjectViewFromOptions((PetscObject)tr, NULL, "-dm_plex_tps_transform_view"));
3509     PetscCall(DMPlexTransformApply(tr, dm, &edm));
3510     PetscCall(DMCopyDisc(dm, edm));
3511     PetscCall(DMGetCoordinateDM(dm, &cdm));
3512     PetscCall(DMGetCoordinateDM(edm, &ecdm));
3513     PetscCall(DMCopyDisc(cdm, ecdm));
3514     PetscCall(DMPlexTransformCreateDiscLabels(tr, edm));
3515     PetscCall(DMPlexTransformDestroy(&tr));
3516     if (edm) {
3517       ((DM_Plex *)edm->data)->printFEM    = ((DM_Plex *)dm->data)->printFEM;
3518       ((DM_Plex *)edm->data)->printL2     = ((DM_Plex *)dm->data)->printL2;
3519       ((DM_Plex *)edm->data)->printLocate = ((DM_Plex *)dm->data)->printLocate;
3520     }
3521     PetscCall(DMPlexReplace_Internal(dm, &edm));
3522   }
3523   PetscFunctionReturn(PETSC_SUCCESS);
3524 }
3525 
3526 /*@
3527   DMPlexCreateTPSMesh - Create a distributed, interpolated mesh of a triply-periodic surface
3528 
3529   Collective
3530 
3531   Input Parameters:
3532 + comm           - The communicator for the `DM` object
3533 . tpstype        - Type of triply-periodic surface
3534 . extent         - Array of length 3 containing number of periods in each direction
3535 . periodic       - array of length 3 with periodicity, or `NULL` for non-periodic
3536 . tps_distribute - Distribute 2D manifold mesh prior to refinement and extrusion (more scalable)
3537 . refinements    - Number of factor-of-2 refinements of 2D manifold mesh
3538 . layers         - Number of cell layers extruded in normal direction
3539 - thickness      - Thickness in normal direction
3540 
3541   Output Parameter:
3542 . dm - The `DM` object
3543 
3544   Level: beginner
3545 
3546   Notes:
3547   This meshes the surface of the Schwarz P or Gyroid surfaces.  Schwarz P is is the simplest member of the triply-periodic minimal surfaces.
3548   <https://en.wikipedia.org/wiki/Schwarz_minimal_surface#Schwarz_P_(%22Primitive%22)> and can be cut with "clean" boundaries.
3549   The Gyroid <https://en.wikipedia.org/wiki/Gyroid> is another triply-periodic minimal surface with applications in additive manufacturing; it is much more difficult to "cut" since there are no planes of symmetry.
3550   Our implementation creates a very coarse mesh of the surface and refines (by 4-way splitting) as many times as requested.
3551   On each refinement, all vertices are projected to their nearest point on the surface.
3552   This projection could readily be extended to related surfaces.
3553 
3554   See {cite}`maskery2018insights`
3555 
3556   The face (edge) sets for the Schwarz P surface are numbered $1(-x), 2(+x), 3(-y), 4(+y), 5(-z), 6(+z)$.
3557   When the mesh is refined, "Face Sets" contain the new vertices (created during refinement).
3558   Use `DMPlexLabelComplete()` to propagate to coarse-level vertices.
3559 
3560   Developer Notes:
3561   The Gyroid mesh does not currently mark boundary sets.
3562 
3563 .seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexCreateSphereMesh()`, `DMSetType()`, `DMCreate()`
3564 @*/
3565 PetscErrorCode DMPlexCreateTPSMesh(MPI_Comm comm, DMPlexTPSType tpstype, const PetscInt extent[], const DMBoundaryType periodic[], PetscBool tps_distribute, PetscInt refinements, PetscInt layers, PetscReal thickness, DM *dm)
3566 {
3567   PetscFunctionBegin;
3568   PetscCall(DMCreate(comm, dm));
3569   PetscCall(DMSetType(*dm, DMPLEX));
3570   PetscCall(DMPlexCreateTPSMesh_Internal(*dm, tpstype, extent, periodic, tps_distribute, refinements, layers, thickness));
3571   PetscFunctionReturn(PETSC_SUCCESS);
3572 }
3573 
3574 /*@
3575   DMPlexCreateSphereMesh - Creates a mesh on the d-dimensional sphere, S^d.
3576 
3577   Collective
3578 
3579   Input Parameters:
3580 + comm    - The communicator for the `DM` object
3581 . dim     - The dimension
3582 . simplex - Use simplices, or tensor product cells
3583 - R       - The radius
3584 
3585   Output Parameter:
3586 . dm - The `DM` object
3587 
3588   Level: beginner
3589 
3590 .seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexCreateBallMesh()`, `DMPlexCreateBoxMesh()`, `DMSetType()`, `DMCreate()`
3591 @*/
3592 PetscErrorCode DMPlexCreateSphereMesh(MPI_Comm comm, PetscInt dim, PetscBool simplex, PetscReal R, DM *dm)
3593 {
3594   PetscFunctionBegin;
3595   PetscAssertPointer(dm, 5);
3596   PetscCall(DMCreate(comm, dm));
3597   PetscCall(DMSetType(*dm, DMPLEX));
3598   PetscCall(DMPlexCreateSphereMesh_Internal(*dm, dim, simplex, R));
3599   PetscFunctionReturn(PETSC_SUCCESS);
3600 }
3601 
3602 static PetscErrorCode DMPlexCreateBallMesh_Internal(DM dm, PetscInt dim, PetscReal R)
3603 {
3604   DM      sdm, vol;
3605   DMLabel bdlabel;
3606 
3607   PetscFunctionBegin;
3608   PetscCall(DMCreate(PetscObjectComm((PetscObject)dm), &sdm));
3609   PetscCall(DMSetType(sdm, DMPLEX));
3610   PetscCall(PetscObjectSetOptionsPrefix((PetscObject)sdm, "bd_"));
3611   PetscCall(DMPlexCreateSphereMesh_Internal(sdm, dim - 1, PETSC_TRUE, R));
3612   PetscCall(DMSetFromOptions(sdm));
3613   PetscCall(DMViewFromOptions(sdm, NULL, "-dm_view"));
3614   PetscCall(DMPlexGenerate(sdm, NULL, PETSC_TRUE, &vol));
3615   PetscCall(DMDestroy(&sdm));
3616   PetscCall(DMPlexReplace_Internal(dm, &vol));
3617   PetscCall(DMCreateLabel(dm, "marker"));
3618   PetscCall(DMGetLabel(dm, "marker", &bdlabel));
3619   PetscCall(DMPlexMarkBoundaryFaces(dm, PETSC_DETERMINE, bdlabel));
3620   PetscCall(DMPlexLabelComplete(dm, bdlabel));
3621   PetscFunctionReturn(PETSC_SUCCESS);
3622 }
3623 
3624 /*@
3625   DMPlexCreateBallMesh - Creates a simplex mesh on the d-dimensional ball, B^d.
3626 
3627   Collective
3628 
3629   Input Parameters:
3630 + comm - The communicator for the `DM` object
3631 . dim  - The dimension
3632 - R    - The radius
3633 
3634   Output Parameter:
3635 . dm - The `DM` object
3636 
3637   Options Database Key:
3638 . bd_dm_refine - This will refine the surface mesh preserving the sphere geometry
3639 
3640   Level: beginner
3641 
3642 .seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexCreateSphereMesh()`, `DMPlexCreateBoxMesh()`, `DMSetType()`, `DMCreate()`
3643 @*/
3644 PetscErrorCode DMPlexCreateBallMesh(MPI_Comm comm, PetscInt dim, PetscReal R, DM *dm)
3645 {
3646   PetscFunctionBegin;
3647   PetscCall(DMCreate(comm, dm));
3648   PetscCall(DMSetType(*dm, DMPLEX));
3649   PetscCall(DMPlexCreateBallMesh_Internal(*dm, dim, R));
3650   PetscFunctionReturn(PETSC_SUCCESS);
3651 }
3652 
3653 static PetscErrorCode DMPlexCreateReferenceCell_Internal(DM rdm, DMPolytopeType ct)
3654 {
3655   PetscFunctionBegin;
3656   switch (ct) {
3657   case DM_POLYTOPE_POINT: {
3658     PetscInt    numPoints[1]        = {1};
3659     PetscInt    coneSize[1]         = {0};
3660     PetscInt    cones[1]            = {0};
3661     PetscInt    coneOrientations[1] = {0};
3662     PetscScalar vertexCoords[1]     = {0.0};
3663 
3664     PetscCall(DMSetDimension(rdm, 0));
3665     PetscCall(DMPlexCreateFromDAG(rdm, 0, numPoints, coneSize, cones, coneOrientations, vertexCoords));
3666   } break;
3667   case DM_POLYTOPE_SEGMENT: {
3668     PetscInt    numPoints[2]        = {2, 1};
3669     PetscInt    coneSize[3]         = {2, 0, 0};
3670     PetscInt    cones[2]            = {1, 2};
3671     PetscInt    coneOrientations[2] = {0, 0};
3672     PetscScalar vertexCoords[2]     = {-1.0, 1.0};
3673 
3674     PetscCall(DMSetDimension(rdm, 1));
3675     PetscCall(DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords));
3676   } break;
3677   case DM_POLYTOPE_POINT_PRISM_TENSOR: {
3678     PetscInt    numPoints[2]        = {2, 1};
3679     PetscInt    coneSize[3]         = {2, 0, 0};
3680     PetscInt    cones[2]            = {1, 2};
3681     PetscInt    coneOrientations[2] = {0, 0};
3682     PetscScalar vertexCoords[2]     = {-1.0, 1.0};
3683 
3684     PetscCall(DMSetDimension(rdm, 1));
3685     PetscCall(DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords));
3686   } break;
3687   case DM_POLYTOPE_TRIANGLE: {
3688     PetscInt    numPoints[2]        = {3, 1};
3689     PetscInt    coneSize[4]         = {3, 0, 0, 0};
3690     PetscInt    cones[3]            = {1, 2, 3};
3691     PetscInt    coneOrientations[3] = {0, 0, 0};
3692     PetscScalar vertexCoords[6]     = {-1.0, -1.0, 1.0, -1.0, -1.0, 1.0};
3693 
3694     PetscCall(DMSetDimension(rdm, 2));
3695     PetscCall(DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords));
3696   } break;
3697   case DM_POLYTOPE_QUADRILATERAL: {
3698     PetscInt    numPoints[2]        = {4, 1};
3699     PetscInt    coneSize[5]         = {4, 0, 0, 0, 0};
3700     PetscInt    cones[4]            = {1, 2, 3, 4};
3701     PetscInt    coneOrientations[4] = {0, 0, 0, 0};
3702     PetscScalar vertexCoords[8]     = {-1.0, -1.0, 1.0, -1.0, 1.0, 1.0, -1.0, 1.0};
3703 
3704     PetscCall(DMSetDimension(rdm, 2));
3705     PetscCall(DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords));
3706   } break;
3707   case DM_POLYTOPE_SEG_PRISM_TENSOR: {
3708     PetscInt    numPoints[2]        = {4, 1};
3709     PetscInt    coneSize[5]         = {4, 0, 0, 0, 0};
3710     PetscInt    cones[4]            = {1, 2, 3, 4};
3711     PetscInt    coneOrientations[4] = {0, 0, 0, 0};
3712     PetscScalar vertexCoords[8]     = {-1.0, -1.0, 1.0, -1.0, -1.0, 1.0, 1.0, 1.0};
3713 
3714     PetscCall(DMSetDimension(rdm, 2));
3715     PetscCall(DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords));
3716   } break;
3717   case DM_POLYTOPE_TETRAHEDRON: {
3718     PetscInt    numPoints[2]        = {4, 1};
3719     PetscInt    coneSize[5]         = {4, 0, 0, 0, 0};
3720     PetscInt    cones[4]            = {1, 2, 3, 4};
3721     PetscInt    coneOrientations[4] = {0, 0, 0, 0};
3722     PetscScalar vertexCoords[12]    = {-1.0, -1.0, -1.0, -1.0, 1.0, -1.0, 1.0, -1.0, -1.0, -1.0, -1.0, 1.0};
3723 
3724     PetscCall(DMSetDimension(rdm, 3));
3725     PetscCall(DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords));
3726   } break;
3727   case DM_POLYTOPE_HEXAHEDRON: {
3728     PetscInt    numPoints[2]        = {8, 1};
3729     PetscInt    coneSize[9]         = {8, 0, 0, 0, 0, 0, 0, 0, 0};
3730     PetscInt    cones[8]            = {1, 2, 3, 4, 5, 6, 7, 8};
3731     PetscInt    coneOrientations[8] = {0, 0, 0, 0, 0, 0, 0, 0};
3732     PetscScalar vertexCoords[24]    = {-1.0, -1.0, -1.0, -1.0, 1.0, -1.0, 1.0, 1.0, -1.0, 1.0, -1.0, -1.0, -1.0, -1.0, 1.0, 1.0, -1.0, 1.0, 1.0, 1.0, 1.0, -1.0, 1.0, 1.0};
3733 
3734     PetscCall(DMSetDimension(rdm, 3));
3735     PetscCall(DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords));
3736   } break;
3737   case DM_POLYTOPE_TRI_PRISM: {
3738     PetscInt    numPoints[2]        = {6, 1};
3739     PetscInt    coneSize[7]         = {6, 0, 0, 0, 0, 0, 0};
3740     PetscInt    cones[6]            = {1, 2, 3, 4, 5, 6};
3741     PetscInt    coneOrientations[6] = {0, 0, 0, 0, 0, 0};
3742     PetscScalar vertexCoords[18]    = {-1.0, -1.0, -1.0, -1.0, 1.0, -1.0, 1.0, -1.0, -1.0, -1.0, -1.0, 1.0, 1.0, -1.0, 1.0, -1.0, 1.0, 1.0};
3743 
3744     PetscCall(DMSetDimension(rdm, 3));
3745     PetscCall(DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords));
3746   } break;
3747   case DM_POLYTOPE_TRI_PRISM_TENSOR: {
3748     PetscInt    numPoints[2]        = {6, 1};
3749     PetscInt    coneSize[7]         = {6, 0, 0, 0, 0, 0, 0};
3750     PetscInt    cones[6]            = {1, 2, 3, 4, 5, 6};
3751     PetscInt    coneOrientations[6] = {0, 0, 0, 0, 0, 0};
3752     PetscScalar vertexCoords[18]    = {-1.0, -1.0, -1.0, 1.0, -1.0, -1.0, -1.0, 1.0, -1.0, -1.0, -1.0, 1.0, 1.0, -1.0, 1.0, -1.0, 1.0, 1.0};
3753 
3754     PetscCall(DMSetDimension(rdm, 3));
3755     PetscCall(DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords));
3756   } break;
3757   case DM_POLYTOPE_QUAD_PRISM_TENSOR: {
3758     PetscInt    numPoints[2]        = {8, 1};
3759     PetscInt    coneSize[9]         = {8, 0, 0, 0, 0, 0, 0, 0, 0};
3760     PetscInt    cones[8]            = {1, 2, 3, 4, 5, 6, 7, 8};
3761     PetscInt    coneOrientations[8] = {0, 0, 0, 0, 0, 0, 0, 0};
3762     PetscScalar vertexCoords[24]    = {-1.0, -1.0, -1.0, 1.0, -1.0, -1.0, 1.0, 1.0, -1.0, -1.0, 1.0, -1.0, -1.0, -1.0, 1.0, 1.0, -1.0, 1.0, 1.0, 1.0, 1.0, -1.0, 1.0, 1.0};
3763 
3764     PetscCall(DMSetDimension(rdm, 3));
3765     PetscCall(DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords));
3766   } break;
3767   case DM_POLYTOPE_PYRAMID: {
3768     PetscInt    numPoints[2]        = {5, 1};
3769     PetscInt    coneSize[6]         = {5, 0, 0, 0, 0, 0};
3770     PetscInt    cones[5]            = {1, 2, 3, 4, 5};
3771     PetscInt    coneOrientations[8] = {0, 0, 0, 0, 0, 0, 0, 0};
3772     PetscScalar vertexCoords[24]    = {-1.0, -1.0, -1.0, -1.0, 1.0, -1.0, 1.0, 1.0, -1.0, 1.0, -1.0, -1.0, 0.0, 0.0, 1.0};
3773 
3774     PetscCall(DMSetDimension(rdm, 3));
3775     PetscCall(DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords));
3776   } break;
3777   default:
3778     SETERRQ(PetscObjectComm((PetscObject)rdm), PETSC_ERR_ARG_WRONG, "Cannot create reference cell for cell type %s", DMPolytopeTypes[ct]);
3779   }
3780   {
3781     PetscInt Nv, v;
3782 
3783     /* Must create the celltype label here so that we do not automatically try to compute the types */
3784     PetscCall(DMCreateLabel(rdm, "celltype"));
3785     PetscCall(DMPlexSetCellType(rdm, 0, ct));
3786     PetscCall(DMPlexGetChart(rdm, NULL, &Nv));
3787     for (v = 1; v < Nv; ++v) PetscCall(DMPlexSetCellType(rdm, v, DM_POLYTOPE_POINT));
3788   }
3789   PetscCall(DMPlexInterpolateInPlace_Internal(rdm));
3790   PetscCall(PetscObjectSetName((PetscObject)rdm, DMPolytopeTypes[ct]));
3791   PetscFunctionReturn(PETSC_SUCCESS);
3792 }
3793 
3794 /*@
3795   DMPlexCreateReferenceCell - Create a `DMPLEX` with the appropriate FEM reference cell
3796 
3797   Collective
3798 
3799   Input Parameters:
3800 + comm - The communicator
3801 - ct   - The cell type of the reference cell
3802 
3803   Output Parameter:
3804 . refdm - The reference cell
3805 
3806   Level: intermediate
3807 
3808 .seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexCreateBoxMesh()`
3809 @*/
3810 PetscErrorCode DMPlexCreateReferenceCell(MPI_Comm comm, DMPolytopeType ct, DM *refdm)
3811 {
3812   PetscFunctionBegin;
3813   PetscCall(DMCreate(comm, refdm));
3814   PetscCall(DMSetType(*refdm, DMPLEX));
3815   PetscCall(DMPlexCreateReferenceCell_Internal(*refdm, ct));
3816   PetscFunctionReturn(PETSC_SUCCESS);
3817 }
3818 
3819 static PetscErrorCode DMPlexCreateBoundaryLabel_Private(DM dm, const char name[])
3820 {
3821   DM        plex;
3822   DMLabel   label;
3823   PetscBool hasLabel;
3824 
3825   PetscFunctionBegin;
3826   PetscCall(DMHasLabel(dm, name, &hasLabel));
3827   if (hasLabel) PetscFunctionReturn(PETSC_SUCCESS);
3828   PetscCall(DMCreateLabel(dm, name));
3829   PetscCall(DMGetLabel(dm, name, &label));
3830   PetscCall(DMConvert(dm, DMPLEX, &plex));
3831   PetscCall(DMPlexMarkBoundaryFaces(plex, 1, label));
3832   PetscCall(DMPlexLabelComplete(plex, label));
3833   PetscCall(DMDestroy(&plex));
3834   PetscFunctionReturn(PETSC_SUCCESS);
3835 }
3836 
3837 /*
3838   We use the last coordinate as the radius, the inner radius is lower[dim-1] and the outer radius is upper[dim-1]. Then we map the first coordinate around the circle.
3839 
3840     (x, y) -> (r, theta) = (x[1], (x[0] - lower[0]) * 2\pi/(upper[0] - lower[0]))
3841 */
3842 static void boxToAnnulus(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
3843 {
3844   const PetscReal low = PetscRealPart(constants[0]);
3845   const PetscReal upp = PetscRealPart(constants[1]);
3846   const PetscReal r   = PetscRealPart(u[1]);
3847   const PetscReal th  = 2. * PETSC_PI * (PetscRealPart(u[0]) - low) / (upp - low);
3848 
3849   f0[0] = r * PetscCosReal(th);
3850   f0[1] = r * PetscSinReal(th);
3851 }
3852 
3853 const char *const DMPlexShapes[] = {"box", "box_surface", "ball", "sphere", "cylinder", "schwarz_p", "gyroid", "doublet", "annulus", "hypercubic", "zbox", "unknown", "DMPlexShape", "DM_SHAPE_", NULL};
3854 
3855 static PetscErrorCode DMPlexCreateFromOptions_Internal(PetscOptionItems *PetscOptionsObject, PetscBool *useCoordSpace, DM dm)
3856 {
3857   DMPlexShape    shape   = DM_SHAPE_BOX;
3858   DMPolytopeType cell    = DM_POLYTOPE_TRIANGLE;
3859   PetscInt       dim     = 2;
3860   PetscBool      simplex = PETSC_TRUE, interpolate = PETSC_TRUE, adjCone = PETSC_FALSE, adjClosure = PETSC_TRUE, refDomain = PETSC_FALSE;
3861   PetscBool      flg, flg2, fflg, bdfflg, nameflg;
3862   MPI_Comm       comm;
3863   char           filename[PETSC_MAX_PATH_LEN]   = "<unspecified>";
3864   char           bdFilename[PETSC_MAX_PATH_LEN] = "<unspecified>";
3865   char           plexname[PETSC_MAX_PATH_LEN]   = "";
3866 
3867   PetscFunctionBegin;
3868   PetscCall(PetscLogEventBegin(DMPLEX_CreateFromOptions, dm, 0, 0, 0));
3869   PetscCall(PetscObjectGetComm((PetscObject)dm, &comm));
3870   /* TODO Turn this into a registration interface */
3871   PetscCall(PetscOptionsString("-dm_plex_filename", "File containing a mesh", "DMPlexCreateFromFile", filename, filename, sizeof(filename), &fflg));
3872   PetscCall(PetscOptionsString("-dm_plex_boundary_filename", "File containing a mesh boundary", "DMPlexCreateFromFile", bdFilename, bdFilename, sizeof(bdFilename), &bdfflg));
3873   PetscCall(PetscOptionsString("-dm_plex_name", "Name of the mesh in the file", "DMPlexCreateFromFile", plexname, plexname, sizeof(plexname), &nameflg));
3874   PetscCall(PetscOptionsEnum("-dm_plex_cell", "Cell shape", "", DMPolytopeTypes, (PetscEnum)cell, (PetscEnum *)&cell, NULL));
3875   PetscCall(PetscOptionsBool("-dm_plex_reference_cell_domain", "Use a reference cell domain", "", refDomain, &refDomain, NULL));
3876   PetscCall(PetscOptionsEnum("-dm_plex_shape", "Shape for built-in mesh", "", DMPlexShapes, (PetscEnum)shape, (PetscEnum *)&shape, &flg));
3877   PetscCall(PetscOptionsBoundedInt("-dm_plex_dim", "Topological dimension of the mesh", "DMGetDimension", dim, &dim, &flg, 0));
3878   PetscCheck(dim >= 0, comm, PETSC_ERR_ARG_OUTOFRANGE, "Dimension %" PetscInt_FMT " should be in [0, infinity)", dim);
3879   PetscCall(PetscOptionsBool("-dm_plex_simplex", "Mesh cell shape", "", simplex, &simplex, &flg));
3880   PetscCall(PetscOptionsBool("-dm_plex_interpolate", "Flag to create edges and faces automatically", "", interpolate, &interpolate, &flg));
3881   PetscCall(PetscOptionsBool("-dm_plex_adj_cone", "Set adjacency direction", "DMSetBasicAdjacency", adjCone, &adjCone, &flg));
3882   PetscCall(PetscOptionsBool("-dm_plex_adj_closure", "Set adjacency size", "DMSetBasicAdjacency", adjClosure, &adjClosure, &flg2));
3883   if (flg || flg2) PetscCall(DMSetBasicAdjacency(dm, adjCone, adjClosure));
3884 
3885   switch (cell) {
3886   case DM_POLYTOPE_POINT:
3887   case DM_POLYTOPE_SEGMENT:
3888   case DM_POLYTOPE_POINT_PRISM_TENSOR:
3889   case DM_POLYTOPE_TRIANGLE:
3890   case DM_POLYTOPE_QUADRILATERAL:
3891   case DM_POLYTOPE_TETRAHEDRON:
3892   case DM_POLYTOPE_HEXAHEDRON:
3893     *useCoordSpace = PETSC_TRUE;
3894     break;
3895   default:
3896     *useCoordSpace = PETSC_FALSE;
3897     break;
3898   }
3899 
3900   if (fflg) {
3901     DM dmnew;
3902 
3903     PetscCall(DMPlexCreateFromFile(PetscObjectComm((PetscObject)dm), filename, plexname, interpolate, &dmnew));
3904     PetscCall(DMPlexCopy_Internal(dm, PETSC_FALSE, PETSC_FALSE, dmnew));
3905     PetscCall(DMPlexReplace_Internal(dm, &dmnew));
3906   } else if (refDomain) {
3907     PetscCall(DMPlexCreateReferenceCell_Internal(dm, cell));
3908   } else if (bdfflg) {
3909     DM bdm, dmnew;
3910 
3911     PetscCall(DMPlexCreateFromFile(PetscObjectComm((PetscObject)dm), bdFilename, plexname, interpolate, &bdm));
3912     PetscCall(PetscObjectSetOptionsPrefix((PetscObject)bdm, "bd_"));
3913     PetscCall(DMSetFromOptions(bdm));
3914     PetscCall(DMPlexGenerate(bdm, NULL, interpolate, &dmnew));
3915     PetscCall(DMDestroy(&bdm));
3916     PetscCall(DMPlexCopy_Internal(dm, PETSC_FALSE, PETSC_FALSE, dmnew));
3917     PetscCall(DMPlexReplace_Internal(dm, &dmnew));
3918   } else {
3919     PetscCall(PetscObjectSetName((PetscObject)dm, DMPlexShapes[shape]));
3920     switch (shape) {
3921     case DM_SHAPE_BOX:
3922     case DM_SHAPE_ZBOX:
3923     case DM_SHAPE_ANNULUS: {
3924       PetscInt       faces[3]  = {0, 0, 0};
3925       PetscReal      lower[3]  = {0, 0, 0};
3926       PetscReal      upper[3]  = {1, 1, 1};
3927       DMBoundaryType bdt[3]    = {DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE};
3928       PetscBool      isAnnular = shape == DM_SHAPE_ANNULUS ? PETSC_TRUE : PETSC_FALSE;
3929       PetscInt       i, n;
3930 
3931       n = dim;
3932       for (i = 0; i < dim; ++i) faces[i] = (dim == 1 ? 1 : 4 - dim);
3933       PetscCall(PetscOptionsIntArray("-dm_plex_box_faces", "Number of faces along each dimension", "", faces, &n, &flg));
3934       n = 3;
3935       PetscCall(PetscOptionsRealArray("-dm_plex_box_lower", "Lower left corner of box", "", lower, &n, &flg));
3936       PetscCheck(!flg || !(n != dim), comm, PETSC_ERR_ARG_SIZ, "Lower box point had %" PetscInt_FMT " values, should have been %" PetscInt_FMT, n, dim);
3937       n = 3;
3938       PetscCall(PetscOptionsRealArray("-dm_plex_box_upper", "Upper right corner of box", "", upper, &n, &flg));
3939       PetscCheck(!flg || !(n != dim), comm, PETSC_ERR_ARG_SIZ, "Upper box point had %" PetscInt_FMT " values, should have been %" PetscInt_FMT, n, dim);
3940       n = 3;
3941       PetscCall(PetscOptionsEnumArray("-dm_plex_box_bd", "Boundary type for each dimension", "", DMBoundaryTypes, (PetscEnum *)bdt, &n, &flg));
3942       PetscCheck(!flg || !(n != dim), comm, PETSC_ERR_ARG_SIZ, "Box boundary types had %" PetscInt_FMT " values, should have been %" PetscInt_FMT, n, dim);
3943 
3944       PetscCheck(!isAnnular || dim == 2, comm, PETSC_ERR_ARG_OUTOFRANGE, "Only two dimensional annuli have been implemented");
3945       if (isAnnular)
3946         for (i = 0; i < dim - 1; ++i) bdt[i] = DM_BOUNDARY_PERIODIC;
3947 
3948       switch (cell) {
3949       case DM_POLYTOPE_TRI_PRISM_TENSOR:
3950         PetscCall(DMPlexCreateWedgeBoxMesh_Internal(dm, faces, lower, upper, bdt));
3951         if (!interpolate) {
3952           DM udm;
3953 
3954           PetscCall(DMPlexUninterpolate(dm, &udm));
3955           PetscCall(DMPlexReplace_Internal(dm, &udm));
3956         }
3957         break;
3958       default:
3959         PetscCall(DMPlexCreateBoxMesh_Internal(dm, shape, dim, simplex, faces, lower, upper, bdt, interpolate));
3960         break;
3961       }
3962       if (isAnnular) {
3963         DM          cdm;
3964         PetscDS     cds;
3965         PetscScalar bounds[2] = {lower[0], upper[0]};
3966 
3967         // Fix coordinates for annular region
3968         PetscCall(DMSetPeriodicity(dm, NULL, NULL, NULL));
3969         PetscCall(DMSetCellCoordinatesLocal(dm, NULL));
3970         PetscCall(DMSetCellCoordinates(dm, NULL));
3971         PetscCall(DMPlexCreateCoordinateSpace(dm, 1, PETSC_TRUE, NULL));
3972         PetscCall(DMGetCoordinateDM(dm, &cdm));
3973         PetscCall(DMGetDS(cdm, &cds));
3974         PetscCall(PetscDSSetConstants(cds, 2, bounds));
3975         PetscCall(DMPlexRemapGeometry(dm, 0.0, boxToAnnulus));
3976       }
3977     } break;
3978     case DM_SHAPE_BOX_SURFACE: {
3979       PetscInt  faces[3] = {0, 0, 0};
3980       PetscReal lower[3] = {0, 0, 0};
3981       PetscReal upper[3] = {1, 1, 1};
3982       PetscInt  i, n;
3983 
3984       n = dim + 1;
3985       for (i = 0; i < dim + 1; ++i) faces[i] = (dim + 1 == 1 ? 1 : 4 - (dim + 1));
3986       PetscCall(PetscOptionsIntArray("-dm_plex_box_faces", "Number of faces along each dimension", "", faces, &n, &flg));
3987       n = 3;
3988       PetscCall(PetscOptionsRealArray("-dm_plex_box_lower", "Lower left corner of box", "", lower, &n, &flg));
3989       PetscCheck(!flg || !(n != dim + 1), comm, PETSC_ERR_ARG_SIZ, "Lower box point had %" PetscInt_FMT " values, should have been %" PetscInt_FMT, n, dim + 1);
3990       n = 3;
3991       PetscCall(PetscOptionsRealArray("-dm_plex_box_upper", "Upper right corner of box", "", upper, &n, &flg));
3992       PetscCheck(!flg || !(n != dim + 1), comm, PETSC_ERR_ARG_SIZ, "Upper box point had %" PetscInt_FMT " values, should have been %" PetscInt_FMT, n, dim + 1);
3993       PetscCall(DMPlexCreateBoxSurfaceMesh_Internal(dm, dim + 1, faces, lower, upper, interpolate));
3994     } break;
3995     case DM_SHAPE_SPHERE: {
3996       PetscReal R = 1.0;
3997 
3998       PetscCall(PetscOptionsReal("-dm_plex_sphere_radius", "Radius of the sphere", "", R, &R, &flg));
3999       PetscCall(DMPlexCreateSphereMesh_Internal(dm, dim, simplex, R));
4000     } break;
4001     case DM_SHAPE_BALL: {
4002       PetscReal R = 1.0;
4003 
4004       PetscCall(PetscOptionsReal("-dm_plex_ball_radius", "Radius of the ball", "", R, &R, &flg));
4005       PetscCall(DMPlexCreateBallMesh_Internal(dm, dim, R));
4006     } break;
4007     case DM_SHAPE_CYLINDER: {
4008       DMBoundaryType bdt = DM_BOUNDARY_NONE;
4009       PetscInt       Nw  = 6;
4010 
4011       PetscCall(PetscOptionsEnum("-dm_plex_cylinder_bd", "Boundary type in the z direction", "", DMBoundaryTypes, (PetscEnum)bdt, (PetscEnum *)&bdt, NULL));
4012       PetscCall(PetscOptionsInt("-dm_plex_cylinder_num_wedges", "Number of wedges around the cylinder", "", Nw, &Nw, NULL));
4013       switch (cell) {
4014       case DM_POLYTOPE_TRI_PRISM_TENSOR:
4015         PetscCall(DMPlexCreateWedgeCylinderMesh_Internal(dm, Nw, interpolate));
4016         break;
4017       default:
4018         PetscCall(DMPlexCreateHexCylinderMesh_Internal(dm, bdt));
4019         break;
4020       }
4021     } break;
4022     case DM_SHAPE_SCHWARZ_P: // fallthrough
4023     case DM_SHAPE_GYROID: {
4024       PetscInt       extent[3] = {1, 1, 1}, refine = 0, layers = 0, three;
4025       PetscReal      thickness   = 0.;
4026       DMBoundaryType periodic[3] = {DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE};
4027       DMPlexTPSType  tps_type    = shape == DM_SHAPE_SCHWARZ_P ? DMPLEX_TPS_SCHWARZ_P : DMPLEX_TPS_GYROID;
4028       PetscBool      tps_distribute;
4029       PetscCall(PetscOptionsIntArray("-dm_plex_tps_extent", "Number of replicas for each of three dimensions", NULL, extent, (three = 3, &three), NULL));
4030       PetscCall(PetscOptionsInt("-dm_plex_tps_refine", "Number of refinements", NULL, refine, &refine, NULL));
4031       PetscCall(PetscOptionsEnumArray("-dm_plex_tps_periodic", "Periodicity in each of three dimensions", NULL, DMBoundaryTypes, (PetscEnum *)periodic, (three = 3, &three), NULL));
4032       PetscCall(PetscOptionsInt("-dm_plex_tps_layers", "Number of layers in volumetric extrusion (or zero to not extrude)", NULL, layers, &layers, NULL));
4033       PetscCall(PetscOptionsReal("-dm_plex_tps_thickness", "Thickness of volumetric extrusion", NULL, thickness, &thickness, NULL));
4034       PetscCall(DMPlexDistributeGetDefault(dm, &tps_distribute));
4035       PetscCall(PetscOptionsBool("-dm_plex_tps_distribute", "Distribute the 2D mesh prior to refinement and extrusion", NULL, tps_distribute, &tps_distribute, NULL));
4036       PetscCall(DMPlexCreateTPSMesh_Internal(dm, tps_type, extent, periodic, tps_distribute, refine, layers, thickness));
4037     } break;
4038     case DM_SHAPE_DOUBLET: {
4039       DM        dmnew;
4040       PetscReal rl = 0.0;
4041 
4042       PetscCall(PetscOptionsReal("-dm_plex_doublet_refinementlimit", "Refinement limit", NULL, rl, &rl, NULL));
4043       PetscCall(DMPlexCreateDoublet(PetscObjectComm((PetscObject)dm), dim, simplex, interpolate, rl, &dmnew));
4044       PetscCall(DMPlexCopy_Internal(dm, PETSC_FALSE, PETSC_FALSE, dmnew));
4045       PetscCall(DMPlexReplace_Internal(dm, &dmnew));
4046     } break;
4047     case DM_SHAPE_HYPERCUBIC: {
4048       PetscInt       *edges;
4049       PetscReal      *lower, *upper;
4050       DMBoundaryType *bdt;
4051       PetscInt        n, d;
4052 
4053       *useCoordSpace = PETSC_FALSE;
4054       PetscCall(PetscMalloc4(dim, &edges, dim, &lower, dim, &upper, dim, &bdt));
4055       for (d = 0; d < dim; ++d) {
4056         edges[d] = 1;
4057         lower[d] = 0.;
4058         upper[d] = 1.;
4059         bdt[d]   = DM_BOUNDARY_PERIODIC;
4060       }
4061       n = dim;
4062       PetscCall(PetscOptionsIntArray("-dm_plex_box_faces", "Number of faces along each dimension", "", edges, &n, &flg));
4063       n = dim;
4064       PetscCall(PetscOptionsRealArray("-dm_plex_box_lower", "Lower left corner of box", "", lower, &n, &flg));
4065       PetscCheck(!flg || n == dim, comm, PETSC_ERR_ARG_SIZ, "Lower box point had %" PetscInt_FMT " values, should have been %" PetscInt_FMT, n, dim);
4066       n = dim;
4067       PetscCall(PetscOptionsRealArray("-dm_plex_box_upper", "Upper right corner of box", "", upper, &n, &flg));
4068       PetscCheck(!flg || n == dim, comm, PETSC_ERR_ARG_SIZ, "Upper box point had %" PetscInt_FMT " values, should have been %" PetscInt_FMT, n, dim);
4069       n = dim;
4070       PetscCall(PetscOptionsEnumArray("-dm_plex_box_bd", "Boundary type for each dimension", "", DMBoundaryTypes, (PetscEnum *)bdt, &n, &flg));
4071       PetscCheck(!flg || n == dim, comm, PETSC_ERR_ARG_SIZ, "Box boundary types had %" PetscInt_FMT " values, should have been %" PetscInt_FMT, n, dim);
4072       PetscCall(DMPlexCreateHypercubicMesh_Internal(dm, dim, lower, upper, edges, bdt));
4073       PetscCall(PetscFree4(edges, lower, upper, bdt));
4074     } break;
4075     default:
4076       SETERRQ(comm, PETSC_ERR_SUP, "Domain shape %s is unsupported", DMPlexShapes[shape]);
4077     }
4078   }
4079   PetscCall(DMPlexSetRefinementUniform(dm, PETSC_TRUE));
4080   if (!((PetscObject)dm)->name && nameflg) PetscCall(PetscObjectSetName((PetscObject)dm, plexname));
4081   PetscCall(PetscLogEventEnd(DMPLEX_CreateFromOptions, dm, 0, 0, 0));
4082   PetscFunctionReturn(PETSC_SUCCESS);
4083 }
4084 
4085 PetscErrorCode DMSetFromOptions_NonRefinement_Plex(DM dm, PetscOptionItems *PetscOptionsObject)
4086 {
4087   DM_Plex  *mesh = (DM_Plex *)dm->data;
4088   PetscBool flg, flg2;
4089   char      bdLabel[PETSC_MAX_PATH_LEN];
4090 
4091   PetscFunctionBegin;
4092   /* Handle viewing */
4093   PetscCall(PetscOptionsBool("-dm_plex_print_set_values", "Output all set values info", "DMPlexMatSetClosure", PETSC_FALSE, &mesh->printSetValues, NULL));
4094   PetscCall(PetscOptionsBoundedInt("-dm_plex_print_fem", "Debug output level for all fem computations", "DMPlexSNESComputeResidualFEM", 0, &mesh->printFEM, NULL, 0));
4095   PetscCall(PetscOptionsBoundedInt("-dm_plex_print_fvm", "Debug output level for all fvm computations", "DMPlexSNESComputeResidualFVM", 0, &mesh->printFVM, NULL, 0));
4096   PetscCall(PetscOptionsReal("-dm_plex_print_tol", "Tolerance for FEM output", "DMPlexSNESComputeResidualFEM", mesh->printTol, &mesh->printTol, NULL));
4097   PetscCall(PetscOptionsBoundedInt("-dm_plex_print_l2", "Debug output level all L2 diff computations", "DMComputeL2Diff", 0, &mesh->printL2, NULL, 0));
4098   PetscCall(PetscOptionsBoundedInt("-dm_plex_print_locate", "Debug output level all point location computations", "DMLocatePoints", 0, &mesh->printLocate, NULL, 0));
4099   PetscCall(DMMonitorSetFromOptions(dm, "-dm_plex_monitor_throughput", "Monitor the simulation throughput", "DMPlexMonitorThroughput", DMPlexMonitorThroughput, NULL, &flg));
4100   if (flg) PetscCall(PetscLogDefaultBegin());
4101   /* Labeling */
4102   PetscCall(PetscOptionsString("-dm_plex_boundary_label", "Label to mark the mesh boundary", "", bdLabel, bdLabel, sizeof(bdLabel), &flg));
4103   if (flg) PetscCall(DMPlexCreateBoundaryLabel_Private(dm, bdLabel));
4104   /* Point Location */
4105   PetscCall(PetscOptionsBool("-dm_plex_hash_location", "Use grid hashing for point location", "DMInterpolate", PETSC_FALSE, &mesh->useHashLocation, NULL));
4106   /* Partitioning and distribution */
4107   PetscCall(PetscOptionsBool("-dm_plex_partition_balance", "Attempt to evenly divide points on partition boundary between processes", "DMPlexSetPartitionBalance", PETSC_FALSE, &mesh->partitionBalance, NULL));
4108   /* Generation and remeshing */
4109   PetscCall(PetscOptionsBool("-dm_plex_remesh_bd", "Allow changes to the boundary on remeshing", "DMAdapt", PETSC_FALSE, &mesh->remeshBd, NULL));
4110   /* Projection behavior */
4111   PetscCall(PetscOptionsBoundedInt("-dm_plex_max_projection_height", "Maximum mesh point height used to project locally", "DMPlexSetMaxProjectionHeight", 0, &mesh->maxProjectionHeight, NULL, 0));
4112   PetscCall(PetscOptionsBool("-dm_plex_regular_refinement", "Use special nested projection algorithm for regular refinement", "DMPlexSetRegularRefinement", mesh->regularRefinement, &mesh->regularRefinement, NULL));
4113   /* Checking structure */
4114   {
4115     PetscBool all = PETSC_FALSE;
4116 
4117     PetscCall(PetscOptionsBool("-dm_plex_check_all", "Perform all basic checks", "DMPlexCheck", PETSC_FALSE, &all, NULL));
4118     if (all) {
4119       PetscCall(DMPlexCheck(dm));
4120     } else {
4121       PetscCall(PetscOptionsBool("-dm_plex_check_symmetry", "Check that the adjacency information in the mesh is symmetric", "DMPlexCheckSymmetry", PETSC_FALSE, &flg, &flg2));
4122       if (flg && flg2) PetscCall(DMPlexCheckSymmetry(dm));
4123       PetscCall(PetscOptionsBool("-dm_plex_check_skeleton", "Check that each cell has the correct number of vertices (only for homogeneous simplex or tensor meshes)", "DMPlexCheckSkeleton", PETSC_FALSE, &flg, &flg2));
4124       if (flg && flg2) PetscCall(DMPlexCheckSkeleton(dm, 0));
4125       PetscCall(PetscOptionsBool("-dm_plex_check_faces", "Check that the faces of each cell give a vertex order this is consistent with what we expect from the cell type", "DMPlexCheckFaces", PETSC_FALSE, &flg, &flg2));
4126       if (flg && flg2) PetscCall(DMPlexCheckFaces(dm, 0));
4127       PetscCall(PetscOptionsBool("-dm_plex_check_geometry", "Check that cells have positive volume", "DMPlexCheckGeometry", PETSC_FALSE, &flg, &flg2));
4128       if (flg && flg2) PetscCall(DMPlexCheckGeometry(dm));
4129       PetscCall(PetscOptionsBool("-dm_plex_check_pointsf", "Check some necessary conditions for PointSF", "DMPlexCheckPointSF", PETSC_FALSE, &flg, &flg2));
4130       if (flg && flg2) PetscCall(DMPlexCheckPointSF(dm, NULL, PETSC_FALSE));
4131       PetscCall(PetscOptionsBool("-dm_plex_check_interface_cones", "Check points on inter-partition interfaces have conforming order of cone points", "DMPlexCheckInterfaceCones", PETSC_FALSE, &flg, &flg2));
4132       if (flg && flg2) PetscCall(DMPlexCheckInterfaceCones(dm));
4133     }
4134     PetscCall(PetscOptionsBool("-dm_plex_check_cell_shape", "Check cell shape", "DMPlexCheckCellShape", PETSC_FALSE, &flg, &flg2));
4135     if (flg && flg2) PetscCall(DMPlexCheckCellShape(dm, PETSC_TRUE, PETSC_DETERMINE));
4136   }
4137   {
4138     PetscReal scale = 1.0;
4139 
4140     PetscCall(PetscOptionsReal("-dm_plex_scale", "Scale factor for mesh coordinates", "DMPlexScale", scale, &scale, &flg));
4141     if (flg) {
4142       Vec coordinates, coordinatesLocal;
4143 
4144       PetscCall(DMGetCoordinates(dm, &coordinates));
4145       PetscCall(DMGetCoordinatesLocal(dm, &coordinatesLocal));
4146       PetscCall(VecScale(coordinates, scale));
4147       PetscCall(VecScale(coordinatesLocal, scale));
4148     }
4149   }
4150   PetscCall(PetscPartitionerSetFromOptions(mesh->partitioner));
4151   PetscFunctionReturn(PETSC_SUCCESS);
4152 }
4153 
4154 PetscErrorCode DMSetFromOptions_Overlap_Plex(DM dm, PetscOptionItems *PetscOptionsObject, PetscInt *overlap)
4155 {
4156   PetscInt  numOvLabels = 16, numOvExLabels = 16;
4157   char     *ovLabelNames[16], *ovExLabelNames[16];
4158   PetscInt  numOvValues = 16, numOvExValues = 16, l;
4159   PetscBool flg;
4160 
4161   PetscFunctionBegin;
4162   PetscCall(PetscOptionsBoundedInt("-dm_distribute_overlap", "The size of the overlap halo", "DMPlexDistribute", *overlap, overlap, NULL, 0));
4163   PetscCall(PetscOptionsStringArray("-dm_distribute_overlap_labels", "List of overlap label names", "DMPlexDistribute", ovLabelNames, &numOvLabels, &flg));
4164   if (!flg) numOvLabels = 0;
4165   if (numOvLabels) {
4166     ((DM_Plex *)dm->data)->numOvLabels = numOvLabels;
4167     for (l = 0; l < numOvLabels; ++l) {
4168       PetscCall(DMGetLabel(dm, ovLabelNames[l], &((DM_Plex *)dm->data)->ovLabels[l]));
4169       PetscCheck(((DM_Plex *)dm->data)->ovLabels[l], PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Invalid label name %s", ovLabelNames[l]);
4170       PetscCall(PetscFree(ovLabelNames[l]));
4171     }
4172     PetscCall(PetscOptionsIntArray("-dm_distribute_overlap_values", "List of overlap label values", "DMPlexDistribute", ((DM_Plex *)dm->data)->ovValues, &numOvValues, &flg));
4173     if (!flg) numOvValues = 0;
4174     PetscCheck(numOvLabels == numOvValues, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "The number of labels %" PetscInt_FMT " must match the number of values %" PetscInt_FMT, numOvLabels, numOvValues);
4175 
4176     PetscCall(PetscOptionsStringArray("-dm_distribute_overlap_exclude_labels", "List of overlap exclude label names", "DMPlexDistribute", ovExLabelNames, &numOvExLabels, &flg));
4177     if (!flg) numOvExLabels = 0;
4178     ((DM_Plex *)dm->data)->numOvExLabels = numOvExLabels;
4179     for (l = 0; l < numOvExLabels; ++l) {
4180       PetscCall(DMGetLabel(dm, ovExLabelNames[l], &((DM_Plex *)dm->data)->ovExLabels[l]));
4181       PetscCheck(((DM_Plex *)dm->data)->ovExLabels[l], PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Invalid label name %s", ovExLabelNames[l]);
4182       PetscCall(PetscFree(ovExLabelNames[l]));
4183     }
4184     PetscCall(PetscOptionsIntArray("-dm_distribute_overlap_exclude_values", "List of overlap exclude label values", "DMPlexDistribute", ((DM_Plex *)dm->data)->ovExValues, &numOvExValues, &flg));
4185     if (!flg) numOvExValues = 0;
4186     PetscCheck(numOvExLabels == numOvExValues, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "The number of exclude labels %" PetscInt_FMT " must match the number of values %" PetscInt_FMT, numOvExLabels, numOvExValues);
4187   }
4188   PetscFunctionReturn(PETSC_SUCCESS);
4189 }
4190 
4191 static PetscErrorCode DMSetFromOptions_Plex(DM dm, PetscOptionItems *PetscOptionsObject)
4192 {
4193   PetscFunctionList        ordlist;
4194   char                     oname[256];
4195   DMPlexReorderDefaultFlag reorder;
4196   PetscReal                volume    = -1.0;
4197   PetscInt                 prerefine = 0, refine = 0, r, coarsen = 0, overlap = 0, extLayers = 0, dim;
4198   PetscBool uniformOrig = PETSC_FALSE, created = PETSC_FALSE, uniform = PETSC_TRUE, distribute, saveSF = PETSC_FALSE, interpolate = PETSC_TRUE, coordSpace = PETSC_TRUE, remap = PETSC_TRUE, ghostCells = PETSC_FALSE, isHierarchy, ignoreModel = PETSC_FALSE, flg;
4199 
4200   PetscFunctionBegin;
4201   PetscOptionsHeadBegin(PetscOptionsObject, "DMPlex Options");
4202   if (dm->cloneOpts) goto non_refine;
4203   /* Handle automatic creation */
4204   PetscCall(DMGetDimension(dm, &dim));
4205   if (dim < 0) {
4206     PetscCall(DMPlexCreateFromOptions_Internal(PetscOptionsObject, &coordSpace, dm));
4207     created = PETSC_TRUE;
4208   }
4209   PetscCall(DMGetDimension(dm, &dim));
4210   /* Handle interpolation before distribution */
4211   PetscCall(PetscOptionsBool("-dm_plex_interpolate_pre", "Flag to interpolate mesh before distribution", "", interpolate, &interpolate, &flg));
4212   if (flg) {
4213     DMPlexInterpolatedFlag interpolated;
4214 
4215     PetscCall(DMPlexIsInterpolated(dm, &interpolated));
4216     if (interpolated == DMPLEX_INTERPOLATED_FULL && !interpolate) {
4217       DM udm;
4218 
4219       PetscCall(DMPlexUninterpolate(dm, &udm));
4220       PetscCall(DMPlexReplace_Internal(dm, &udm));
4221     } else if (interpolated != DMPLEX_INTERPOLATED_FULL && interpolate) {
4222       DM idm;
4223 
4224       PetscCall(DMPlexInterpolate(dm, &idm));
4225       PetscCall(DMPlexReplace_Internal(dm, &idm));
4226     }
4227   }
4228   /* Handle DMPlex refinement before distribution */
4229   PetscCall(PetscOptionsBool("-dm_refine_ignore_model", "Flag to ignore the geometry model when refining", "DMCreate", ignoreModel, &ignoreModel, &flg));
4230   if (flg) ((DM_Plex *)dm->data)->ignoreModel = ignoreModel;
4231   PetscCall(DMPlexGetRefinementUniform(dm, &uniformOrig));
4232   PetscCall(PetscOptionsBoundedInt("-dm_refine_pre", "The number of refinements before distribution", "DMCreate", prerefine, &prerefine, NULL, 0));
4233   PetscCall(PetscOptionsBool("-dm_refine_remap_pre", "Flag to control coordinate remapping", "DMCreate", remap, &remap, NULL));
4234   PetscCall(PetscOptionsBool("-dm_refine_uniform_pre", "Flag for uniform refinement before distribution", "DMCreate", uniform, &uniform, &flg));
4235   if (flg) PetscCall(DMPlexSetRefinementUniform(dm, uniform));
4236   PetscCall(PetscOptionsReal("-dm_refine_volume_limit_pre", "The maximum cell volume after refinement before distribution", "DMCreate", volume, &volume, &flg));
4237   if (flg) {
4238     PetscCall(DMPlexSetRefinementUniform(dm, PETSC_FALSE));
4239     PetscCall(DMPlexSetRefinementLimit(dm, volume));
4240     prerefine = PetscMax(prerefine, 1);
4241   }
4242   for (r = 0; r < prerefine; ++r) {
4243     DM             rdm;
4244     PetscPointFunc coordFunc = ((DM_Plex *)dm->data)->coordFunc;
4245 
4246     PetscCall(DMSetFromOptions_NonRefinement_Plex(dm, PetscOptionsObject));
4247     PetscCall(DMRefine(dm, PetscObjectComm((PetscObject)dm), &rdm));
4248     PetscCall(DMPlexReplace_Internal(dm, &rdm));
4249     PetscCall(DMSetFromOptions_NonRefinement_Plex(dm, PetscOptionsObject));
4250     if (coordFunc && remap) {
4251       PetscCall(DMPlexRemapGeometry(dm, 0.0, coordFunc));
4252       ((DM_Plex *)dm->data)->coordFunc = coordFunc;
4253     }
4254   }
4255   PetscCall(DMPlexSetRefinementUniform(dm, uniformOrig));
4256   /* Handle DMPlex extrusion before distribution */
4257   PetscCall(PetscOptionsBoundedInt("-dm_extrude", "The number of layers to extrude", "", extLayers, &extLayers, NULL, 0));
4258   if (extLayers) {
4259     DM edm;
4260 
4261     PetscCall(DMExtrude(dm, extLayers, &edm));
4262     PetscCall(DMPlexReplace_Internal(dm, &edm));
4263     ((DM_Plex *)dm->data)->coordFunc = NULL;
4264     PetscCall(DMSetFromOptions_NonRefinement_Plex(dm, PetscOptionsObject));
4265     extLayers = 0;
4266     PetscCall(DMGetDimension(dm, &dim));
4267   }
4268   /* Handle DMPlex reordering before distribution */
4269   PetscCall(DMPlexReorderGetDefault(dm, &reorder));
4270   PetscCall(MatGetOrderingList(&ordlist));
4271   PetscCall(PetscStrncpy(oname, MATORDERINGNATURAL, sizeof(oname)));
4272   PetscCall(PetscOptionsFList("-dm_plex_reorder", "Set mesh reordering type", "DMPlexGetOrdering", ordlist, MATORDERINGNATURAL, oname, sizeof(oname), &flg));
4273   if (reorder == DMPLEX_REORDER_DEFAULT_TRUE || flg) {
4274     DM pdm;
4275     IS perm;
4276 
4277     PetscCall(DMPlexGetOrdering(dm, oname, NULL, &perm));
4278     PetscCall(DMPlexPermute(dm, perm, &pdm));
4279     PetscCall(ISDestroy(&perm));
4280     PetscCall(DMPlexReplace_Internal(dm, &pdm));
4281     PetscCall(DMSetFromOptions_NonRefinement_Plex(dm, PetscOptionsObject));
4282   }
4283   /* Handle DMPlex distribution */
4284   PetscCall(DMPlexDistributeGetDefault(dm, &distribute));
4285   PetscCall(PetscOptionsBool("-dm_distribute", "Flag to redistribute a mesh among processes", "DMPlexDistribute", distribute, &distribute, NULL));
4286   PetscCall(PetscOptionsBool("-dm_distribute_save_sf", "Flag to save the migration SF", "DMPlexSetMigrationSF", saveSF, &saveSF, NULL));
4287   PetscCall(DMSetFromOptions_Overlap_Plex(dm, PetscOptionsObject, &overlap));
4288   if (distribute) {
4289     DM               pdm = NULL;
4290     PetscPartitioner part;
4291     PetscSF          sfMigration;
4292 
4293     PetscCall(DMPlexGetPartitioner(dm, &part));
4294     PetscCall(PetscPartitionerSetFromOptions(part));
4295     PetscCall(DMPlexDistribute(dm, overlap, &sfMigration, &pdm));
4296     if (pdm) PetscCall(DMPlexReplace_Internal(dm, &pdm));
4297     if (saveSF) PetscCall(DMPlexSetMigrationSF(dm, sfMigration));
4298     PetscCall(PetscSFDestroy(&sfMigration));
4299   }
4300   /* Must check CEED options before creating function space for coordinates */
4301   {
4302     PetscBool useCeed = PETSC_FALSE, flg;
4303 
4304     PetscCall(PetscOptionsBool("-dm_plex_use_ceed", "Use LibCEED as the FEM backend", "DMPlexSetUseCeed", useCeed, &useCeed, &flg));
4305     if (flg) PetscCall(DMPlexSetUseCeed(dm, useCeed));
4306   }
4307   /* Create coordinate space */
4308   if (created) {
4309     DM_Plex  *mesh   = (DM_Plex *)dm->data;
4310     PetscInt  degree = 1, deg;
4311     PetscInt  height = 0;
4312     DM        cdm;
4313     PetscBool flg;
4314 
4315     PetscCall(PetscOptionsBool("-dm_coord_space", "Use an FEM space for coordinates", "", coordSpace, &coordSpace, &flg));
4316     PetscCall(PetscOptionsInt("-dm_coord_petscspace_degree", "FEM degree for coordinate space", "", degree, &degree, NULL));
4317     PetscCall(DMGetCoordinateDegree_Internal(dm, &deg));
4318     if (coordSpace && deg <= 1) PetscCall(DMPlexCreateCoordinateSpace(dm, degree, PETSC_TRUE, mesh->coordFunc));
4319     PetscCall(DMGetCoordinateDM(dm, &cdm));
4320     if (flg && !coordSpace) {
4321       PetscDS      cds;
4322       PetscObject  obj;
4323       PetscClassId id;
4324 
4325       PetscCall(DMGetDS(cdm, &cds));
4326       PetscCall(PetscDSGetDiscretization(cds, 0, &obj));
4327       PetscCall(PetscObjectGetClassId(obj, &id));
4328       if (id == PETSCFE_CLASSID) {
4329         PetscContainer dummy;
4330 
4331         PetscCall(PetscContainerCreate(PETSC_COMM_SELF, &dummy));
4332         PetscCall(PetscObjectSetName((PetscObject)dummy, "coordinates"));
4333         PetscCall(DMSetField(cdm, 0, NULL, (PetscObject)dummy));
4334         PetscCall(PetscContainerDestroy(&dummy));
4335         PetscCall(DMClearDS(cdm));
4336       }
4337       mesh->coordFunc = NULL;
4338     }
4339     PetscCall(PetscOptionsBool("-dm_sparse_localize", "Localize only necessary cells", "", dm->sparseLocalize, &dm->sparseLocalize, &flg));
4340     PetscCall(PetscOptionsInt("-dm_localize_height", "Localize edges and faces in addition to cells", "", height, &height, &flg));
4341     if (flg) PetscCall(DMPlexSetMaxProjectionHeight(cdm, height));
4342     PetscCall(DMLocalizeCoordinates(dm));
4343   }
4344   /* Handle DMPlex refinement */
4345   remap = PETSC_TRUE;
4346   PetscCall(PetscOptionsBoundedInt("-dm_refine", "The number of uniform refinements", "DMCreate", refine, &refine, NULL, 0));
4347   PetscCall(PetscOptionsBool("-dm_refine_remap", "Flag to control coordinate remapping", "DMCreate", remap, &remap, NULL));
4348   PetscCall(PetscOptionsBoundedInt("-dm_refine_hierarchy", "The number of uniform refinements", "DMCreate", refine, &refine, &isHierarchy, 0));
4349   if (refine) PetscCall(DMPlexSetRefinementUniform(dm, PETSC_TRUE));
4350   if (refine && isHierarchy) {
4351     DM *dms, coarseDM;
4352 
4353     PetscCall(DMGetCoarseDM(dm, &coarseDM));
4354     PetscCall(PetscObjectReference((PetscObject)coarseDM));
4355     PetscCall(PetscMalloc1(refine, &dms));
4356     PetscCall(DMRefineHierarchy(dm, refine, dms));
4357     /* Total hack since we do not pass in a pointer */
4358     PetscCall(DMPlexSwap_Static(dm, dms[refine - 1]));
4359     if (refine == 1) {
4360       PetscCall(DMSetCoarseDM(dm, dms[0]));
4361       PetscCall(DMPlexSetRegularRefinement(dm, PETSC_TRUE));
4362     } else {
4363       PetscCall(DMSetCoarseDM(dm, dms[refine - 2]));
4364       PetscCall(DMPlexSetRegularRefinement(dm, PETSC_TRUE));
4365       PetscCall(DMSetCoarseDM(dms[0], dms[refine - 1]));
4366       PetscCall(DMPlexSetRegularRefinement(dms[0], PETSC_TRUE));
4367     }
4368     PetscCall(DMSetCoarseDM(dms[refine - 1], coarseDM));
4369     PetscCall(PetscObjectDereference((PetscObject)coarseDM));
4370     /* Free DMs */
4371     for (r = 0; r < refine; ++r) {
4372       PetscCall(DMSetFromOptions_NonRefinement_Plex(dms[r], PetscOptionsObject));
4373       PetscCall(DMDestroy(&dms[r]));
4374     }
4375     PetscCall(PetscFree(dms));
4376   } else {
4377     for (r = 0; r < refine; ++r) {
4378       DM             rdm;
4379       PetscPointFunc coordFunc = ((DM_Plex *)dm->data)->coordFunc;
4380 
4381       PetscCall(DMSetFromOptions_NonRefinement_Plex(dm, PetscOptionsObject));
4382       PetscCall(DMRefine(dm, PetscObjectComm((PetscObject)dm), &rdm));
4383       /* Total hack since we do not pass in a pointer */
4384       PetscCall(DMPlexReplace_Internal(dm, &rdm));
4385       PetscCall(DMSetFromOptions_NonRefinement_Plex(dm, PetscOptionsObject));
4386       if (coordFunc && remap) {
4387         PetscCall(DMPlexRemapGeometry(dm, 0.0, coordFunc));
4388         ((DM_Plex *)dm->data)->coordFunc = coordFunc;
4389       }
4390     }
4391   }
4392   /* Handle DMPlex coarsening */
4393   PetscCall(PetscOptionsBoundedInt("-dm_coarsen", "Coarsen the mesh", "DMCreate", coarsen, &coarsen, NULL, 0));
4394   PetscCall(PetscOptionsBoundedInt("-dm_coarsen_hierarchy", "The number of coarsenings", "DMCreate", coarsen, &coarsen, &isHierarchy, 0));
4395   if (coarsen && isHierarchy) {
4396     DM *dms;
4397 
4398     PetscCall(PetscMalloc1(coarsen, &dms));
4399     PetscCall(DMCoarsenHierarchy(dm, coarsen, dms));
4400     /* Free DMs */
4401     for (r = 0; r < coarsen; ++r) {
4402       PetscCall(DMSetFromOptions_NonRefinement_Plex(dms[r], PetscOptionsObject));
4403       PetscCall(DMDestroy(&dms[r]));
4404     }
4405     PetscCall(PetscFree(dms));
4406   } else {
4407     for (r = 0; r < coarsen; ++r) {
4408       DM             cdm;
4409       PetscPointFunc coordFunc = ((DM_Plex *)dm->data)->coordFunc;
4410 
4411       PetscCall(DMSetFromOptions_NonRefinement_Plex(dm, PetscOptionsObject));
4412       PetscCall(DMCoarsen(dm, PetscObjectComm((PetscObject)dm), &cdm));
4413       /* Total hack since we do not pass in a pointer */
4414       PetscCall(DMPlexReplace_Internal(dm, &cdm));
4415       PetscCall(DMSetFromOptions_NonRefinement_Plex(dm, PetscOptionsObject));
4416       if (coordFunc) {
4417         PetscCall(DMPlexRemapGeometry(dm, 0.0, coordFunc));
4418         ((DM_Plex *)dm->data)->coordFunc = coordFunc;
4419       }
4420     }
4421   }
4422   /* Handle ghost cells */
4423   PetscCall(PetscOptionsBool("-dm_plex_create_fv_ghost_cells", "Flag to create finite volume ghost cells on the boundary", "DMCreate", ghostCells, &ghostCells, NULL));
4424   if (ghostCells) {
4425     DM   gdm;
4426     char lname[PETSC_MAX_PATH_LEN];
4427 
4428     lname[0] = '\0';
4429     PetscCall(PetscOptionsString("-dm_plex_fv_ghost_cells_label", "Label name for ghost cells boundary", "DMCreate", lname, lname, sizeof(lname), &flg));
4430     PetscCall(DMPlexConstructGhostCells(dm, flg ? lname : NULL, NULL, &gdm));
4431     PetscCall(DMPlexReplace_Internal(dm, &gdm));
4432   }
4433   /* Handle 1D order */
4434   if (reorder != DMPLEX_REORDER_DEFAULT_FALSE && dim == 1) {
4435     DM           cdm, rdm;
4436     PetscDS      cds;
4437     PetscObject  obj;
4438     PetscClassId id = PETSC_OBJECT_CLASSID;
4439     IS           perm;
4440     PetscInt     Nf;
4441     PetscBool    distributed;
4442 
4443     PetscCall(DMPlexIsDistributed(dm, &distributed));
4444     PetscCall(DMGetCoordinateDM(dm, &cdm));
4445     PetscCall(DMGetDS(cdm, &cds));
4446     PetscCall(PetscDSGetNumFields(cds, &Nf));
4447     if (Nf) {
4448       PetscCall(PetscDSGetDiscretization(cds, 0, &obj));
4449       PetscCall(PetscObjectGetClassId(obj, &id));
4450     }
4451     if (!distributed && id != PETSCFE_CLASSID) {
4452       PetscCall(DMPlexGetOrdering1D(dm, &perm));
4453       PetscCall(DMPlexPermute(dm, perm, &rdm));
4454       PetscCall(DMPlexReplace_Internal(dm, &rdm));
4455       PetscCall(ISDestroy(&perm));
4456     }
4457   }
4458 /* Handle */
4459 non_refine:
4460   PetscCall(DMSetFromOptions_NonRefinement_Plex(dm, PetscOptionsObject));
4461   PetscOptionsHeadEnd();
4462   PetscFunctionReturn(PETSC_SUCCESS);
4463 }
4464 
4465 static PetscErrorCode DMCreateGlobalVector_Plex(DM dm, Vec *vec)
4466 {
4467   PetscFunctionBegin;
4468   PetscCall(DMCreateGlobalVector_Section_Private(dm, vec));
4469   /* PetscCall(VecSetOperation(*vec, VECOP_DUPLICATE, (void(*)(void)) VecDuplicate_MPI_DM)); */
4470   PetscCall(VecSetOperation(*vec, VECOP_VIEW, (void (*)(void))VecView_Plex));
4471   PetscCall(VecSetOperation(*vec, VECOP_VIEWNATIVE, (void (*)(void))VecView_Plex_Native));
4472   PetscCall(VecSetOperation(*vec, VECOP_LOAD, (void (*)(void))VecLoad_Plex));
4473   PetscCall(VecSetOperation(*vec, VECOP_LOADNATIVE, (void (*)(void))VecLoad_Plex_Native));
4474   PetscFunctionReturn(PETSC_SUCCESS);
4475 }
4476 
4477 static PetscErrorCode DMCreateLocalVector_Plex(DM dm, Vec *vec)
4478 {
4479   PetscFunctionBegin;
4480   PetscCall(DMCreateLocalVector_Section_Private(dm, vec));
4481   PetscCall(VecSetOperation(*vec, VECOP_VIEW, (void (*)(void))VecView_Plex_Local));
4482   PetscCall(VecSetOperation(*vec, VECOP_LOAD, (void (*)(void))VecLoad_Plex_Local));
4483   PetscFunctionReturn(PETSC_SUCCESS);
4484 }
4485 
4486 static PetscErrorCode DMGetDimPoints_Plex(DM dm, PetscInt dim, PetscInt *pStart, PetscInt *pEnd)
4487 {
4488   PetscInt depth, d;
4489 
4490   PetscFunctionBegin;
4491   PetscCall(DMPlexGetDepth(dm, &depth));
4492   if (depth == 1) {
4493     PetscCall(DMGetDimension(dm, &d));
4494     if (dim == 0) PetscCall(DMPlexGetDepthStratum(dm, dim, pStart, pEnd));
4495     else if (dim == d) PetscCall(DMPlexGetDepthStratum(dm, 1, pStart, pEnd));
4496     else {
4497       *pStart = 0;
4498       *pEnd   = 0;
4499     }
4500   } else {
4501     PetscCall(DMPlexGetDepthStratum(dm, dim, pStart, pEnd));
4502   }
4503   PetscFunctionReturn(PETSC_SUCCESS);
4504 }
4505 
4506 static PetscErrorCode DMGetNeighbors_Plex(DM dm, PetscInt *nranks, const PetscMPIInt *ranks[])
4507 {
4508   PetscSF            sf;
4509   PetscInt           niranks, njranks, n;
4510   const PetscMPIInt *iranks, *jranks;
4511   DM_Plex           *data = (DM_Plex *)dm->data;
4512 
4513   PetscFunctionBegin;
4514   PetscCall(DMGetPointSF(dm, &sf));
4515   if (!data->neighbors) {
4516     PetscCall(PetscSFSetUp(sf));
4517     PetscCall(PetscSFGetRootRanks(sf, &njranks, &jranks, NULL, NULL, NULL));
4518     PetscCall(PetscSFGetLeafRanks(sf, &niranks, &iranks, NULL, NULL));
4519     PetscCall(PetscMalloc1(njranks + niranks + 1, &data->neighbors));
4520     PetscCall(PetscArraycpy(data->neighbors + 1, jranks, njranks));
4521     PetscCall(PetscArraycpy(data->neighbors + njranks + 1, iranks, niranks));
4522     n = njranks + niranks;
4523     PetscCall(PetscSortRemoveDupsMPIInt(&n, data->neighbors + 1));
4524     /* The following cast should never fail: can't have more neighbors than PETSC_MPI_INT_MAX */
4525     PetscCall(PetscMPIIntCast(n, data->neighbors));
4526   }
4527   if (nranks) *nranks = data->neighbors[0];
4528   if (ranks) {
4529     if (data->neighbors[0]) *ranks = data->neighbors + 1;
4530     else *ranks = NULL;
4531   }
4532   PetscFunctionReturn(PETSC_SUCCESS);
4533 }
4534 
4535 PETSC_INTERN PetscErrorCode DMInterpolateSolution_Plex(DM, DM, Mat, Vec, Vec);
4536 
4537 static PetscErrorCode DMInitialize_Plex(DM dm)
4538 {
4539   PetscFunctionBegin;
4540   dm->ops->view                      = DMView_Plex;
4541   dm->ops->load                      = DMLoad_Plex;
4542   dm->ops->setfromoptions            = DMSetFromOptions_Plex;
4543   dm->ops->clone                     = DMClone_Plex;
4544   dm->ops->setup                     = DMSetUp_Plex;
4545   dm->ops->createlocalsection        = DMCreateLocalSection_Plex;
4546   dm->ops->createdefaultconstraints  = DMCreateDefaultConstraints_Plex;
4547   dm->ops->createglobalvector        = DMCreateGlobalVector_Plex;
4548   dm->ops->createlocalvector         = DMCreateLocalVector_Plex;
4549   dm->ops->getlocaltoglobalmapping   = NULL;
4550   dm->ops->createfieldis             = NULL;
4551   dm->ops->createcoordinatedm        = DMCreateCoordinateDM_Plex;
4552   dm->ops->createcoordinatefield     = DMCreateCoordinateField_Plex;
4553   dm->ops->getcoloring               = NULL;
4554   dm->ops->creatematrix              = DMCreateMatrix_Plex;
4555   dm->ops->createinterpolation       = DMCreateInterpolation_Plex;
4556   dm->ops->createmassmatrix          = DMCreateMassMatrix_Plex;
4557   dm->ops->createmassmatrixlumped    = DMCreateMassMatrixLumped_Plex;
4558   dm->ops->createinjection           = DMCreateInjection_Plex;
4559   dm->ops->refine                    = DMRefine_Plex;
4560   dm->ops->coarsen                   = DMCoarsen_Plex;
4561   dm->ops->refinehierarchy           = DMRefineHierarchy_Plex;
4562   dm->ops->coarsenhierarchy          = DMCoarsenHierarchy_Plex;
4563   dm->ops->extrude                   = DMExtrude_Plex;
4564   dm->ops->globaltolocalbegin        = NULL;
4565   dm->ops->globaltolocalend          = NULL;
4566   dm->ops->localtoglobalbegin        = NULL;
4567   dm->ops->localtoglobalend          = NULL;
4568   dm->ops->destroy                   = DMDestroy_Plex;
4569   dm->ops->createsubdm               = DMCreateSubDM_Plex;
4570   dm->ops->createsuperdm             = DMCreateSuperDM_Plex;
4571   dm->ops->getdimpoints              = DMGetDimPoints_Plex;
4572   dm->ops->locatepoints              = DMLocatePoints_Plex;
4573   dm->ops->projectfunctionlocal      = DMProjectFunctionLocal_Plex;
4574   dm->ops->projectfunctionlabellocal = DMProjectFunctionLabelLocal_Plex;
4575   dm->ops->projectfieldlocal         = DMProjectFieldLocal_Plex;
4576   dm->ops->projectfieldlabellocal    = DMProjectFieldLabelLocal_Plex;
4577   dm->ops->projectbdfieldlabellocal  = DMProjectBdFieldLabelLocal_Plex;
4578   dm->ops->computel2diff             = DMComputeL2Diff_Plex;
4579   dm->ops->computel2gradientdiff     = DMComputeL2GradientDiff_Plex;
4580   dm->ops->computel2fielddiff        = DMComputeL2FieldDiff_Plex;
4581   dm->ops->getneighbors              = DMGetNeighbors_Plex;
4582   dm->ops->createdomaindecomposition = DMCreateDomainDecomposition_Plex;
4583   dm->ops->createddscatters          = DMCreateDomainDecompositionScatters_Plex;
4584   PetscCall(PetscObjectComposeFunction((PetscObject)dm, "DMPlexInsertBoundaryValues_C", DMPlexInsertBoundaryValues_Plex));
4585   PetscCall(PetscObjectComposeFunction((PetscObject)dm, "DMPlexInsertTimeDerivativeBoundaryValues_C", DMPlexInsertTimeDerivativeBoundaryValues_Plex));
4586   PetscCall(PetscObjectComposeFunction((PetscObject)dm, "DMSetUpGLVisViewer_C", DMSetUpGLVisViewer_Plex));
4587   PetscCall(PetscObjectComposeFunction((PetscObject)dm, "DMCreateNeumannOverlap_C", DMCreateNeumannOverlap_Plex));
4588   PetscCall(PetscObjectComposeFunction((PetscObject)dm, "DMPlexDistributeGetDefault_C", DMPlexDistributeGetDefault_Plex));
4589   PetscCall(PetscObjectComposeFunction((PetscObject)dm, "DMPlexDistributeSetDefault_C", DMPlexDistributeSetDefault_Plex));
4590   PetscCall(PetscObjectComposeFunction((PetscObject)dm, "DMPlexReorderGetDefault_C", DMPlexReorderGetDefault_Plex));
4591   PetscCall(PetscObjectComposeFunction((PetscObject)dm, "DMPlexReorderSetDefault_C", DMPlexReorderSetDefault_Plex));
4592   PetscCall(PetscObjectComposeFunction((PetscObject)dm, "DMInterpolateSolution_C", DMInterpolateSolution_Plex));
4593   PetscCall(PetscObjectComposeFunction((PetscObject)dm, "DMPlexGetOverlap_C", DMPlexGetOverlap_Plex));
4594   PetscCall(PetscObjectComposeFunction((PetscObject)dm, "DMPlexSetOverlap_C", DMPlexSetOverlap_Plex));
4595   PetscCall(PetscObjectComposeFunction((PetscObject)dm, "DMPlexGetUseCeed_C", DMPlexGetUseCeed_Plex));
4596   PetscCall(PetscObjectComposeFunction((PetscObject)dm, "DMPlexSetUseCeed_C", DMPlexSetUseCeed_Plex));
4597   PetscFunctionReturn(PETSC_SUCCESS);
4598 }
4599 
4600 PETSC_INTERN PetscErrorCode DMClone_Plex(DM dm, DM *newdm)
4601 {
4602   DM_Plex *mesh = (DM_Plex *)dm->data;
4603   PetscSF  face_sf;
4604 
4605   PetscFunctionBegin;
4606   mesh->refct++;
4607   (*newdm)->data = mesh;
4608   PetscCall(DMPlexGetIsoperiodicFaceSF(dm, &face_sf));
4609   PetscCall(DMPlexSetIsoperiodicFaceSF(*newdm, face_sf));
4610   PetscCall(PetscObjectChangeTypeName((PetscObject)*newdm, DMPLEX));
4611   PetscCall(DMInitialize_Plex(*newdm));
4612   PetscFunctionReturn(PETSC_SUCCESS);
4613 }
4614 
4615 /*MC
4616   DMPLEX = "plex" - A `DM` object that encapsulates an unstructured mesh, or CW Complex, which can be expressed using a Hasse Diagram.
4617                     In the local representation, `Vec`s contain all unknowns in the interior and shared boundary. This is
4618                     specified by a PetscSection object. Ownership in the global representation is determined by
4619                     ownership of the underlying `DMPLEX` points. This is specified by another `PetscSection` object.
4620 
4621   Options Database Keys:
4622 + -dm_refine_pre                     - Refine mesh before distribution
4623 + -dm_refine_uniform_pre             - Choose uniform or generator-based refinement
4624 + -dm_refine_volume_limit_pre        - Cell volume limit after pre-refinement using generator
4625 . -dm_distribute                     - Distribute mesh across processes
4626 . -dm_distribute_overlap             - Number of cells to overlap for distribution
4627 . -dm_refine                         - Refine mesh after distribution
4628 . -dm_plex_hash_location             - Use grid hashing for point location
4629 . -dm_plex_hash_box_faces <n,m,p>    - The number of divisions in each direction of the grid hash
4630 . -dm_plex_partition_balance         - Attempt to evenly divide points on partition boundary between processes
4631 . -dm_plex_remesh_bd                 - Allow changes to the boundary on remeshing
4632 . -dm_plex_max_projection_height     - Maximum mesh point height used to project locally
4633 . -dm_plex_regular_refinement        - Use special nested projection algorithm for regular refinement
4634 . -dm_plex_check_all                 - Perform all checks below
4635 . -dm_plex_check_symmetry            - Check that the adjacency information in the mesh is symmetric
4636 . -dm_plex_check_skeleton <celltype> - Check that each cell has the correct number of vertices
4637 . -dm_plex_check_faces <celltype>    - Check that the faces of each cell give a vertex order this is consistent with what we expect from the cell type
4638 . -dm_plex_check_geometry            - Check that cells have positive volume
4639 . -dm_view :mesh.tex:ascii_latex     - View the mesh in LaTeX/TikZ
4640 . -dm_plex_view_scale <num>          - Scale the TikZ
4641 . -dm_plex_print_fem <num>           - View FEM assembly information, such as element vectors and matrices
4642 - -dm_plex_print_fvm <num>           - View FVM assembly information, such as flux updates
4643 
4644   Level: intermediate
4645 
4646 .seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMType`, `DMPlexCreate()`, `DMCreate()`, `DMSetType()`, `PetscSection`
4647 M*/
4648 
4649 PETSC_EXTERN PetscErrorCode DMCreate_Plex(DM dm)
4650 {
4651   DM_Plex *mesh;
4652   PetscInt unit;
4653 
4654   PetscFunctionBegin;
4655   PetscCall(PetscCitationsRegister(PlexCitation, &Plexcite));
4656   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
4657   PetscCall(PetscNew(&mesh));
4658   dm->data = mesh;
4659 
4660   mesh->refct = 1;
4661   PetscCall(PetscSectionCreate(PetscObjectComm((PetscObject)dm), &mesh->coneSection));
4662   PetscCall(PetscSectionCreate(PetscObjectComm((PetscObject)dm), &mesh->supportSection));
4663   mesh->refinementUniform      = PETSC_TRUE;
4664   mesh->refinementLimit        = -1.0;
4665   mesh->distDefault            = PETSC_TRUE;
4666   mesh->reorderDefault         = DMPLEX_REORDER_DEFAULT_NOTSET;
4667   mesh->distributionName       = NULL;
4668   mesh->interpolated           = DMPLEX_INTERPOLATED_INVALID;
4669   mesh->interpolatedCollective = DMPLEX_INTERPOLATED_INVALID;
4670 
4671   PetscCall(PetscPartitionerCreate(PetscObjectComm((PetscObject)dm), &mesh->partitioner));
4672   mesh->remeshBd = PETSC_FALSE;
4673 
4674   for (unit = 0; unit < NUM_PETSC_UNITS; ++unit) mesh->scale[unit] = 1.0;
4675 
4676   mesh->depthState    = -1;
4677   mesh->celltypeState = -1;
4678   mesh->printTol      = 1.0e-10;
4679 
4680   PetscCall(DMInitialize_Plex(dm));
4681   PetscFunctionReturn(PETSC_SUCCESS);
4682 }
4683 
4684 /*@
4685   DMPlexCreate - Creates a `DMPLEX` object, which encapsulates an unstructured mesh, or CW complex, which can be expressed using a Hasse Diagram.
4686 
4687   Collective
4688 
4689   Input Parameter:
4690 . comm - The communicator for the `DMPLEX` object
4691 
4692   Output Parameter:
4693 . mesh - The `DMPLEX` object
4694 
4695   Level: beginner
4696 
4697 .seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMType`, `DMCreate()`, `DMSetType()`
4698 @*/
4699 PetscErrorCode DMPlexCreate(MPI_Comm comm, DM *mesh)
4700 {
4701   PetscFunctionBegin;
4702   PetscAssertPointer(mesh, 2);
4703   PetscCall(DMCreate(comm, mesh));
4704   PetscCall(DMSetType(*mesh, DMPLEX));
4705   PetscFunctionReturn(PETSC_SUCCESS);
4706 }
4707 
4708 /*@C
4709   DMPlexBuildFromCellListParallel - Build distributed `DMPLEX` topology from a list of vertices for each cell (common mesh generator output)
4710 
4711   Collective; No Fortran Support
4712 
4713   Input Parameters:
4714 + dm          - The `DM`
4715 . numCells    - The number of cells owned by this process
4716 . numVertices - The number of vertices to be owned by this process, or `PETSC_DECIDE`
4717 . NVertices   - The global number of vertices, or `PETSC_DETERMINE`
4718 . numCorners  - The number of vertices for each cell
4719 - cells       - An array of numCells*numCorners numbers, the global vertex numbers for each cell
4720 
4721   Output Parameters:
4722 + vertexSF         - (Optional) `PetscSF` describing complete vertex ownership
4723 - verticesAdjSaved - (Optional) vertex adjacency array
4724 
4725   Level: advanced
4726 
4727   Notes:
4728   Two triangles sharing a face
4729 .vb
4730 
4731         2
4732       / | \
4733      /  |  \
4734     /   |   \
4735    0  0 | 1  3
4736     \   |   /
4737      \  |  /
4738       \ | /
4739         1
4740 .ve
4741   would have input
4742 .vb
4743   numCells = 2, numVertices = 4
4744   cells = [0 1 2  1 3 2]
4745 .ve
4746   which would result in the `DMPLEX`
4747 .vb
4748 
4749         4
4750       / | \
4751      /  |  \
4752     /   |   \
4753    2  0 | 1  5
4754     \   |   /
4755      \  |  /
4756       \ | /
4757         3
4758 .ve
4759 
4760   Vertices are implicitly numbered consecutively 0,...,NVertices.
4761   Each rank owns a chunk of numVertices consecutive vertices.
4762   If numVertices is `PETSC_DECIDE`, PETSc will distribute them as evenly as possible using PetscLayout.
4763   If NVertices is `PETSC_DETERMINE` and numVertices is PETSC_DECIDE, NVertices is computed by PETSc as the maximum vertex index in cells + 1.
4764   If only NVertices is `PETSC_DETERMINE`, it is computed as the sum of numVertices over all ranks.
4765 
4766   The cell distribution is arbitrary non-overlapping, independent of the vertex distribution.
4767 
4768 .seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexBuildFromCellList()`, `DMPlexCreateFromCellListParallelPetsc()`, `DMPlexBuildCoordinatesFromCellListParallel()`,
4769           `PetscSF`
4770 @*/
4771 PetscErrorCode DMPlexBuildFromCellListParallel(DM dm, PetscInt numCells, PetscInt numVertices, PetscInt NVertices, PetscInt numCorners, const PetscInt cells[], PetscSF *vertexSF, PetscInt **verticesAdjSaved)
4772 {
4773   PetscSF     sfPoint;
4774   PetscLayout layout;
4775   PetscInt    numVerticesAdj, *verticesAdj, *cones, c, p;
4776 
4777   PetscFunctionBegin;
4778   PetscValidLogicalCollectiveInt(dm, NVertices, 4);
4779   PetscCall(PetscLogEventBegin(DMPLEX_BuildFromCellList, dm, 0, 0, 0));
4780   /* Get/check global number of vertices */
4781   {
4782     PetscInt       NVerticesInCells, i;
4783     const PetscInt len = numCells * numCorners;
4784 
4785     /* NVerticesInCells = max(cells) + 1 */
4786     NVerticesInCells = PETSC_MIN_INT;
4787     for (i = 0; i < len; i++)
4788       if (cells[i] > NVerticesInCells) NVerticesInCells = cells[i];
4789     ++NVerticesInCells;
4790     PetscCall(MPIU_Allreduce(MPI_IN_PLACE, &NVerticesInCells, 1, MPIU_INT, MPI_MAX, PetscObjectComm((PetscObject)dm)));
4791 
4792     if (numVertices == PETSC_DECIDE && NVertices == PETSC_DECIDE) NVertices = NVerticesInCells;
4793     else
4794       PetscCheck(NVertices == PETSC_DECIDE || NVertices >= NVerticesInCells, PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Specified global number of vertices %" PetscInt_FMT " must be greater than or equal to the number of vertices in cells %" PetscInt_FMT, NVertices, NVerticesInCells);
4795   }
4796   /* Count locally unique vertices */
4797   {
4798     PetscHSetI vhash;
4799     PetscInt   off = 0;
4800 
4801     PetscCall(PetscHSetICreate(&vhash));
4802     for (c = 0; c < numCells; ++c) {
4803       for (p = 0; p < numCorners; ++p) PetscCall(PetscHSetIAdd(vhash, cells[c * numCorners + p]));
4804     }
4805     PetscCall(PetscHSetIGetSize(vhash, &numVerticesAdj));
4806     if (!verticesAdjSaved) PetscCall(PetscMalloc1(numVerticesAdj, &verticesAdj));
4807     else verticesAdj = *verticesAdjSaved;
4808     PetscCall(PetscHSetIGetElems(vhash, &off, verticesAdj));
4809     PetscCall(PetscHSetIDestroy(&vhash));
4810     PetscCheck(off == numVerticesAdj, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Invalid number of local vertices %" PetscInt_FMT " should be %" PetscInt_FMT, off, numVerticesAdj);
4811   }
4812   PetscCall(PetscSortInt(numVerticesAdj, verticesAdj));
4813   /* Create cones */
4814   PetscCall(DMPlexSetChart(dm, 0, numCells + numVerticesAdj));
4815   for (c = 0; c < numCells; ++c) PetscCall(DMPlexSetConeSize(dm, c, numCorners));
4816   PetscCall(DMSetUp(dm));
4817   PetscCall(DMPlexGetCones(dm, &cones));
4818   for (c = 0; c < numCells; ++c) {
4819     for (p = 0; p < numCorners; ++p) {
4820       const PetscInt gv = cells[c * numCorners + p];
4821       PetscInt       lv;
4822 
4823       /* Positions within verticesAdj form 0-based local vertex numbering;
4824          we need to shift it by numCells to get correct DAG points (cells go first) */
4825       PetscCall(PetscFindInt(gv, numVerticesAdj, verticesAdj, &lv));
4826       PetscCheck(lv >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Could not find global vertex %" PetscInt_FMT " in local connectivity", gv);
4827       cones[c * numCorners + p] = lv + numCells;
4828     }
4829   }
4830   /* Build point sf */
4831   PetscCall(PetscLayoutCreate(PetscObjectComm((PetscObject)dm), &layout));
4832   PetscCall(PetscLayoutSetSize(layout, NVertices));
4833   PetscCall(PetscLayoutSetLocalSize(layout, numVertices));
4834   PetscCall(PetscLayoutSetBlockSize(layout, 1));
4835   PetscCall(PetscSFCreateByMatchingIndices(layout, numVerticesAdj, verticesAdj, NULL, numCells, numVerticesAdj, verticesAdj, NULL, numCells, vertexSF, &sfPoint));
4836   PetscCall(PetscLayoutDestroy(&layout));
4837   if (!verticesAdjSaved) PetscCall(PetscFree(verticesAdj));
4838   PetscCall(PetscObjectSetName((PetscObject)sfPoint, "point SF"));
4839   if (dm->sf) {
4840     const char *prefix;
4841 
4842     PetscCall(PetscObjectGetOptionsPrefix((PetscObject)dm->sf, &prefix));
4843     PetscCall(PetscObjectSetOptionsPrefix((PetscObject)sfPoint, prefix));
4844   }
4845   PetscCall(DMSetPointSF(dm, sfPoint));
4846   PetscCall(PetscSFDestroy(&sfPoint));
4847   if (vertexSF) PetscCall(PetscObjectSetName((PetscObject)(*vertexSF), "Vertex Ownership SF"));
4848   /* Fill in the rest of the topology structure */
4849   PetscCall(DMPlexSymmetrize(dm));
4850   PetscCall(DMPlexStratify(dm));
4851   PetscCall(PetscLogEventEnd(DMPLEX_BuildFromCellList, dm, 0, 0, 0));
4852   PetscFunctionReturn(PETSC_SUCCESS);
4853 }
4854 
4855 /*@C
4856   DMPlexBuildCoordinatesFromCellListParallel - Build `DM` coordinates from a list of coordinates for each owned vertex (common mesh generator output)
4857 
4858   Collective; No Fortran Support
4859 
4860   Input Parameters:
4861 + dm           - The `DM`
4862 . spaceDim     - The spatial dimension used for coordinates
4863 . sfVert       - `PetscSF` describing complete vertex ownership
4864 - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex
4865 
4866   Level: advanced
4867 
4868 .seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexBuildCoordinatesFromCellList()`, `DMPlexCreateFromCellListParallelPetsc()`, `DMPlexBuildFromCellListParallel()`
4869 @*/
4870 PetscErrorCode DMPlexBuildCoordinatesFromCellListParallel(DM dm, PetscInt spaceDim, PetscSF sfVert, const PetscReal vertexCoords[])
4871 {
4872   PetscSection coordSection;
4873   Vec          coordinates;
4874   PetscScalar *coords;
4875   PetscInt     numVertices, numVerticesAdj, coordSize, v, vStart, vEnd;
4876 
4877   PetscFunctionBegin;
4878   PetscCall(PetscLogEventBegin(DMPLEX_BuildCoordinatesFromCellList, dm, 0, 0, 0));
4879   PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
4880   PetscCheck(vStart >= 0 && vEnd >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "DM is not set up properly. DMPlexBuildFromCellList() should be called first.");
4881   PetscCall(DMSetCoordinateDim(dm, spaceDim));
4882   PetscCall(PetscSFGetGraph(sfVert, &numVertices, &numVerticesAdj, NULL, NULL));
4883   PetscCheck(vEnd - vStart == numVerticesAdj, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Supplied sfVert has wrong number of leaves = %" PetscInt_FMT " != %" PetscInt_FMT " = vEnd - vStart", numVerticesAdj, vEnd - vStart);
4884   PetscCall(DMGetCoordinateSection(dm, &coordSection));
4885   PetscCall(PetscSectionSetNumFields(coordSection, 1));
4886   PetscCall(PetscSectionSetFieldComponents(coordSection, 0, spaceDim));
4887   PetscCall(PetscSectionSetChart(coordSection, vStart, vEnd));
4888   for (v = vStart; v < vEnd; ++v) {
4889     PetscCall(PetscSectionSetDof(coordSection, v, spaceDim));
4890     PetscCall(PetscSectionSetFieldDof(coordSection, v, 0, spaceDim));
4891   }
4892   PetscCall(PetscSectionSetUp(coordSection));
4893   PetscCall(PetscSectionGetStorageSize(coordSection, &coordSize));
4894   PetscCall(VecCreate(PetscObjectComm((PetscObject)dm), &coordinates));
4895   PetscCall(VecSetBlockSize(coordinates, spaceDim));
4896   PetscCall(PetscObjectSetName((PetscObject)coordinates, "coordinates"));
4897   PetscCall(VecSetSizes(coordinates, coordSize, PETSC_DETERMINE));
4898   PetscCall(VecSetType(coordinates, VECSTANDARD));
4899   PetscCall(VecGetArray(coordinates, &coords));
4900   {
4901     MPI_Datatype coordtype;
4902 
4903     /* Need a temp buffer for coords if we have complex/single */
4904     PetscCallMPI(MPI_Type_contiguous(spaceDim, MPIU_SCALAR, &coordtype));
4905     PetscCallMPI(MPI_Type_commit(&coordtype));
4906 #if defined(PETSC_USE_COMPLEX)
4907     {
4908       PetscScalar *svertexCoords;
4909       PetscInt     i;
4910       PetscCall(PetscMalloc1(numVertices * spaceDim, &svertexCoords));
4911       for (i = 0; i < numVertices * spaceDim; i++) svertexCoords[i] = vertexCoords[i];
4912       PetscCall(PetscSFBcastBegin(sfVert, coordtype, svertexCoords, coords, MPI_REPLACE));
4913       PetscCall(PetscSFBcastEnd(sfVert, coordtype, svertexCoords, coords, MPI_REPLACE));
4914       PetscCall(PetscFree(svertexCoords));
4915     }
4916 #else
4917     PetscCall(PetscSFBcastBegin(sfVert, coordtype, vertexCoords, coords, MPI_REPLACE));
4918     PetscCall(PetscSFBcastEnd(sfVert, coordtype, vertexCoords, coords, MPI_REPLACE));
4919 #endif
4920     PetscCallMPI(MPI_Type_free(&coordtype));
4921   }
4922   PetscCall(VecRestoreArray(coordinates, &coords));
4923   PetscCall(DMSetCoordinatesLocal(dm, coordinates));
4924   PetscCall(VecDestroy(&coordinates));
4925   PetscCall(PetscLogEventEnd(DMPLEX_BuildCoordinatesFromCellList, dm, 0, 0, 0));
4926   PetscFunctionReturn(PETSC_SUCCESS);
4927 }
4928 
4929 /*@
4930   DMPlexCreateFromCellListParallelPetsc - Create distributed `DMPLEX` from a list of vertices for each cell (common mesh generator output)
4931 
4932   Collective
4933 
4934   Input Parameters:
4935 + comm         - The communicator
4936 . dim          - The topological dimension of the mesh
4937 . numCells     - The number of cells owned by this process
4938 . numVertices  - The number of vertices owned by this process, or `PETSC_DECIDE`
4939 . NVertices    - The global number of vertices, or `PETSC_DECIDE`
4940 . numCorners   - The number of vertices for each cell
4941 . interpolate  - Flag indicating that intermediate mesh entities (faces, edges) should be created automatically
4942 . cells        - An array of numCells*numCorners numbers, the global vertex numbers for each cell
4943 . spaceDim     - The spatial dimension used for coordinates
4944 - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex
4945 
4946   Output Parameters:
4947 + dm          - The `DM`
4948 . vertexSF    - (Optional) `PetscSF` describing complete vertex ownership
4949 - verticesAdj - (Optional) vertex adjacency array
4950 
4951   Level: intermediate
4952 
4953   Notes:
4954   This function is just a convenient sequence of `DMCreate()`, `DMSetType()`, `DMSetDimension()`,
4955   `DMPlexBuildFromCellListParallel()`, `DMPlexInterpolate()`, `DMPlexBuildCoordinatesFromCellListParallel()`
4956 
4957   See `DMPlexBuildFromCellListParallel()` for an example and details about the topology-related parameters.
4958 
4959   See `DMPlexBuildCoordinatesFromCellListParallel()` for details about the geometry-related parameters.
4960 
4961 .seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexCreateFromCellListPetsc()`, `DMPlexBuildFromCellListParallel()`, `DMPlexBuildCoordinatesFromCellListParallel()`, `DMPlexCreateFromDAG()`, `DMPlexCreate()`
4962 @*/
4963 PetscErrorCode DMPlexCreateFromCellListParallelPetsc(MPI_Comm comm, PetscInt dim, PetscInt numCells, PetscInt numVertices, PetscInt NVertices, PetscInt numCorners, PetscBool interpolate, const PetscInt cells[], PetscInt spaceDim, const PetscReal vertexCoords[], PetscSF *vertexSF, PetscInt **verticesAdj, DM *dm)
4964 {
4965   PetscSF sfVert;
4966 
4967   PetscFunctionBegin;
4968   PetscCall(DMCreate(comm, dm));
4969   PetscCall(DMSetType(*dm, DMPLEX));
4970   PetscValidLogicalCollectiveInt(*dm, dim, 2);
4971   PetscValidLogicalCollectiveInt(*dm, spaceDim, 9);
4972   PetscCall(DMSetDimension(*dm, dim));
4973   PetscCall(DMPlexBuildFromCellListParallel(*dm, numCells, numVertices, NVertices, numCorners, cells, &sfVert, verticesAdj));
4974   if (interpolate) {
4975     DM idm;
4976 
4977     PetscCall(DMPlexInterpolate(*dm, &idm));
4978     PetscCall(DMDestroy(dm));
4979     *dm = idm;
4980   }
4981   PetscCall(DMPlexBuildCoordinatesFromCellListParallel(*dm, spaceDim, sfVert, vertexCoords));
4982   if (vertexSF) *vertexSF = sfVert;
4983   else PetscCall(PetscSFDestroy(&sfVert));
4984   PetscFunctionReturn(PETSC_SUCCESS);
4985 }
4986 
4987 /*@C
4988   DMPlexBuildFromCellList - Build `DMPLEX` topology from a list of vertices for each cell (common mesh generator output)
4989 
4990   Collective; No Fortran Support
4991 
4992   Input Parameters:
4993 + dm          - The `DM`
4994 . numCells    - The number of cells owned by this process
4995 . numVertices - The number of vertices owned by this process, or `PETSC_DETERMINE`
4996 . numCorners  - The number of vertices for each cell
4997 - cells       - An array of numCells*numCorners numbers, the global vertex numbers for each cell
4998 
4999   Level: advanced
5000 
5001   Notes:
5002   Two triangles sharing a face
5003 .vb
5004 
5005         2
5006       / | \
5007      /  |  \
5008     /   |   \
5009    0  0 | 1  3
5010     \   |   /
5011      \  |  /
5012       \ | /
5013         1
5014 .ve
5015   would have input
5016 .vb
5017   numCells = 2, numVertices = 4
5018   cells = [0 1 2  1 3 2]
5019 .ve
5020   which would result in the `DMPLEX`
5021 .vb
5022 
5023         4
5024       / | \
5025      /  |  \
5026     /   |   \
5027    2  0 | 1  5
5028     \   |   /
5029      \  |  /
5030       \ | /
5031         3
5032 .ve
5033 
5034   If numVertices is `PETSC_DETERMINE`, it is computed by PETSc as the maximum vertex index in cells + 1.
5035 
5036 .seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexBuildFromCellListParallel()`, `DMPlexBuildCoordinatesFromCellList()`, `DMPlexCreateFromCellListPetsc()`
5037 @*/
5038 PetscErrorCode DMPlexBuildFromCellList(DM dm, PetscInt numCells, PetscInt numVertices, PetscInt numCorners, const PetscInt cells[])
5039 {
5040   PetscInt *cones, c, p, dim;
5041 
5042   PetscFunctionBegin;
5043   PetscCall(PetscLogEventBegin(DMPLEX_BuildFromCellList, dm, 0, 0, 0));
5044   PetscCall(DMGetDimension(dm, &dim));
5045   /* Get/check global number of vertices */
5046   {
5047     PetscInt       NVerticesInCells, i;
5048     const PetscInt len = numCells * numCorners;
5049 
5050     /* NVerticesInCells = max(cells) + 1 */
5051     NVerticesInCells = PETSC_MIN_INT;
5052     for (i = 0; i < len; i++)
5053       if (cells[i] > NVerticesInCells) NVerticesInCells = cells[i];
5054     ++NVerticesInCells;
5055 
5056     if (numVertices == PETSC_DECIDE) numVertices = NVerticesInCells;
5057     else
5058       PetscCheck(numVertices >= NVerticesInCells, PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Specified number of vertices %" PetscInt_FMT " must be greater than or equal to the number of vertices in cells %" PetscInt_FMT, numVertices, NVerticesInCells);
5059   }
5060   PetscCall(DMPlexSetChart(dm, 0, numCells + numVertices));
5061   for (c = 0; c < numCells; ++c) PetscCall(DMPlexSetConeSize(dm, c, numCorners));
5062   PetscCall(DMSetUp(dm));
5063   PetscCall(DMPlexGetCones(dm, &cones));
5064   for (c = 0; c < numCells; ++c) {
5065     for (p = 0; p < numCorners; ++p) cones[c * numCorners + p] = cells[c * numCorners + p] + numCells;
5066   }
5067   PetscCall(DMPlexSymmetrize(dm));
5068   PetscCall(DMPlexStratify(dm));
5069   PetscCall(PetscLogEventEnd(DMPLEX_BuildFromCellList, dm, 0, 0, 0));
5070   PetscFunctionReturn(PETSC_SUCCESS);
5071 }
5072 
5073 /*@C
5074   DMPlexBuildCoordinatesFromCellList - Build `DM` coordinates from a list of coordinates for each owned vertex (common mesh generator output)
5075 
5076   Collective; No Fortran Support
5077 
5078   Input Parameters:
5079 + dm           - The `DM`
5080 . spaceDim     - The spatial dimension used for coordinates
5081 - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex
5082 
5083   Level: advanced
5084 
5085 .seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexBuildCoordinatesFromCellListParallel()`, `DMPlexCreateFromCellListPetsc()`, `DMPlexBuildFromCellList()`
5086 @*/
5087 PetscErrorCode DMPlexBuildCoordinatesFromCellList(DM dm, PetscInt spaceDim, const PetscReal vertexCoords[])
5088 {
5089   PetscSection coordSection;
5090   Vec          coordinates;
5091   DM           cdm;
5092   PetscScalar *coords;
5093   PetscInt     v, vStart, vEnd, d;
5094 
5095   PetscFunctionBegin;
5096   PetscCall(PetscLogEventBegin(DMPLEX_BuildCoordinatesFromCellList, dm, 0, 0, 0));
5097   PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
5098   PetscCheck(vStart >= 0 && vEnd >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "DM is not set up properly. DMPlexBuildFromCellList() should be called first.");
5099   PetscCall(DMSetCoordinateDim(dm, spaceDim));
5100   PetscCall(DMGetCoordinateSection(dm, &coordSection));
5101   PetscCall(PetscSectionSetNumFields(coordSection, 1));
5102   PetscCall(PetscSectionSetFieldComponents(coordSection, 0, spaceDim));
5103   PetscCall(PetscSectionSetChart(coordSection, vStart, vEnd));
5104   for (v = vStart; v < vEnd; ++v) {
5105     PetscCall(PetscSectionSetDof(coordSection, v, spaceDim));
5106     PetscCall(PetscSectionSetFieldDof(coordSection, v, 0, spaceDim));
5107   }
5108   PetscCall(PetscSectionSetUp(coordSection));
5109 
5110   PetscCall(DMGetCoordinateDM(dm, &cdm));
5111   PetscCall(DMCreateLocalVector(cdm, &coordinates));
5112   PetscCall(VecSetBlockSize(coordinates, spaceDim));
5113   PetscCall(PetscObjectSetName((PetscObject)coordinates, "coordinates"));
5114   PetscCall(VecGetArrayWrite(coordinates, &coords));
5115   for (v = 0; v < vEnd - vStart; ++v) {
5116     for (d = 0; d < spaceDim; ++d) coords[v * spaceDim + d] = vertexCoords[v * spaceDim + d];
5117   }
5118   PetscCall(VecRestoreArrayWrite(coordinates, &coords));
5119   PetscCall(DMSetCoordinatesLocal(dm, coordinates));
5120   PetscCall(VecDestroy(&coordinates));
5121   PetscCall(PetscLogEventEnd(DMPLEX_BuildCoordinatesFromCellList, dm, 0, 0, 0));
5122   PetscFunctionReturn(PETSC_SUCCESS);
5123 }
5124 
5125 /*@
5126   DMPlexCreateFromCellListPetsc - Create `DMPLEX` from a list of vertices for each cell (common mesh generator output), but only process 0 takes in the input
5127 
5128   Collective
5129 
5130   Input Parameters:
5131 + comm         - The communicator
5132 . dim          - The topological dimension of the mesh
5133 . numCells     - The number of cells, only on process 0
5134 . numVertices  - The number of vertices owned by this process, or `PETSC_DECIDE`, only on process 0
5135 . numCorners   - The number of vertices for each cell, only on process 0
5136 . interpolate  - Flag indicating that intermediate mesh entities (faces, edges) should be created automatically
5137 . cells        - An array of numCells*numCorners numbers, the vertices for each cell, only on process 0
5138 . spaceDim     - The spatial dimension used for coordinates
5139 - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex, only on process 0
5140 
5141   Output Parameter:
5142 . dm - The `DM`, which only has points on process 0
5143 
5144   Level: intermediate
5145 
5146   Notes:
5147   This function is just a convenient sequence of `DMCreate()`, `DMSetType()`, `DMSetDimension()`, `DMPlexBuildFromCellList()`,
5148   `DMPlexInterpolate()`, `DMPlexBuildCoordinatesFromCellList()`
5149 
5150   See `DMPlexBuildFromCellList()` for an example and details about the topology-related parameters.
5151   See `DMPlexBuildCoordinatesFromCellList()` for details about the geometry-related parameters.
5152   See `DMPlexCreateFromCellListParallelPetsc()` for parallel input
5153 
5154 .seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexCreateFromCellListParallelPetsc()`, `DMPlexBuildFromCellList()`, `DMPlexBuildCoordinatesFromCellList()`, `DMPlexCreateFromDAG()`, `DMPlexCreate()`
5155 @*/
5156 PetscErrorCode DMPlexCreateFromCellListPetsc(MPI_Comm comm, PetscInt dim, PetscInt numCells, PetscInt numVertices, PetscInt numCorners, PetscBool interpolate, const PetscInt cells[], PetscInt spaceDim, const PetscReal vertexCoords[], DM *dm)
5157 {
5158   PetscMPIInt rank;
5159 
5160   PetscFunctionBegin;
5161   PetscCheck(dim, comm, PETSC_ERR_ARG_OUTOFRANGE, "This is not appropriate for 0-dimensional meshes. Consider either creating the DM using DMPlexCreateFromDAG(), by hand, or using DMSwarm.");
5162   PetscCallMPI(MPI_Comm_rank(comm, &rank));
5163   PetscCall(DMCreate(comm, dm));
5164   PetscCall(DMSetType(*dm, DMPLEX));
5165   PetscCall(DMSetDimension(*dm, dim));
5166   if (rank == 0) PetscCall(DMPlexBuildFromCellList(*dm, numCells, numVertices, numCorners, cells));
5167   else PetscCall(DMPlexBuildFromCellList(*dm, 0, 0, 0, NULL));
5168   if (interpolate) {
5169     DM idm;
5170 
5171     PetscCall(DMPlexInterpolate(*dm, &idm));
5172     PetscCall(DMDestroy(dm));
5173     *dm = idm;
5174   }
5175   if (rank == 0) PetscCall(DMPlexBuildCoordinatesFromCellList(*dm, spaceDim, vertexCoords));
5176   else PetscCall(DMPlexBuildCoordinatesFromCellList(*dm, spaceDim, NULL));
5177   PetscFunctionReturn(PETSC_SUCCESS);
5178 }
5179 
5180 /*@
5181   DMPlexCreateFromDAG - This takes as input the adjacency-list representation of the Directed Acyclic Graph (Hasse Diagram) encoding a mesh, and produces a `DM`
5182 
5183   Input Parameters:
5184 + dm               - The empty `DM` object, usually from `DMCreate()` and `DMSetDimension()`
5185 . depth            - The depth of the DAG
5186 . numPoints        - Array of size depth + 1 containing the number of points at each `depth`
5187 . coneSize         - The cone size of each point
5188 . cones            - The concatenation of the cone points for each point, the cone list must be oriented correctly for each point
5189 . coneOrientations - The orientation of each cone point
5190 - vertexCoords     - An array of `numPoints`[0]*spacedim numbers representing the coordinates of each vertex, with spacedim the value set via `DMSetCoordinateDim()`
5191 
5192   Output Parameter:
5193 . dm - The `DM`
5194 
5195   Level: advanced
5196 
5197   Note:
5198   Two triangles sharing a face would have input
5199 .vb
5200   depth = 1, numPoints = [4 2], coneSize = [3 3 0 0 0 0]
5201   cones = [2 3 4  3 5 4], coneOrientations = [0 0 0  0 0 0]
5202  vertexCoords = [-1.0 0.0  0.0 -1.0  0.0 1.0  1.0 0.0]
5203 .ve
5204   which would result in the DMPlex
5205 .vb
5206         4
5207       / | \
5208      /  |  \
5209     /   |   \
5210    2  0 | 1  5
5211     \   |   /
5212      \  |  /
5213       \ | /
5214         3
5215 .ve
5216   Notice that all points are numbered consecutively, unlike `DMPlexCreateFromCellListPetsc()`
5217 
5218 .seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexCreateFromCellListPetsc()`, `DMPlexCreate()`
5219 @*/
5220 PetscErrorCode DMPlexCreateFromDAG(DM dm, PetscInt depth, const PetscInt numPoints[], const PetscInt coneSize[], const PetscInt cones[], const PetscInt coneOrientations[], const PetscScalar vertexCoords[])
5221 {
5222   Vec          coordinates;
5223   PetscSection coordSection;
5224   PetscScalar *coords;
5225   PetscInt     coordSize, firstVertex = -1, pStart = 0, pEnd = 0, p, v, dim, dimEmbed, d, off;
5226 
5227   PetscFunctionBegin;
5228   PetscCall(DMGetDimension(dm, &dim));
5229   PetscCall(DMGetCoordinateDim(dm, &dimEmbed));
5230   PetscCheck(dimEmbed >= dim, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Embedding dimension %" PetscInt_FMT " cannot be less than intrinsic dimension %" PetscInt_FMT, dimEmbed, dim);
5231   for (d = 0; d <= depth; ++d) pEnd += numPoints[d];
5232   PetscCall(DMPlexSetChart(dm, pStart, pEnd));
5233   for (p = pStart; p < pEnd; ++p) {
5234     PetscCall(DMPlexSetConeSize(dm, p, coneSize[p - pStart]));
5235     if (firstVertex < 0 && !coneSize[p - pStart]) firstVertex = p - pStart;
5236   }
5237   PetscCheck(firstVertex >= 0 || !numPoints[0], PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected %" PetscInt_FMT " vertices but could not find any", numPoints[0]);
5238   PetscCall(DMSetUp(dm)); /* Allocate space for cones */
5239   for (p = pStart, off = 0; p < pEnd; off += coneSize[p - pStart], ++p) {
5240     PetscCall(DMPlexSetCone(dm, p, &cones[off]));
5241     PetscCall(DMPlexSetConeOrientation(dm, p, &coneOrientations[off]));
5242   }
5243   PetscCall(DMPlexSymmetrize(dm));
5244   PetscCall(DMPlexStratify(dm));
5245   /* Build coordinates */
5246   PetscCall(DMGetCoordinateSection(dm, &coordSection));
5247   PetscCall(PetscSectionSetNumFields(coordSection, 1));
5248   PetscCall(PetscSectionSetFieldComponents(coordSection, 0, dimEmbed));
5249   PetscCall(PetscSectionSetChart(coordSection, firstVertex, firstVertex + numPoints[0]));
5250   for (v = firstVertex; v < firstVertex + numPoints[0]; ++v) {
5251     PetscCall(PetscSectionSetDof(coordSection, v, dimEmbed));
5252     PetscCall(PetscSectionSetFieldDof(coordSection, v, 0, dimEmbed));
5253   }
5254   PetscCall(PetscSectionSetUp(coordSection));
5255   PetscCall(PetscSectionGetStorageSize(coordSection, &coordSize));
5256   PetscCall(VecCreate(PETSC_COMM_SELF, &coordinates));
5257   PetscCall(PetscObjectSetName((PetscObject)coordinates, "coordinates"));
5258   PetscCall(VecSetSizes(coordinates, coordSize, PETSC_DETERMINE));
5259   PetscCall(VecSetBlockSize(coordinates, dimEmbed));
5260   PetscCall(VecSetType(coordinates, VECSTANDARD));
5261   if (vertexCoords) {
5262     PetscCall(VecGetArray(coordinates, &coords));
5263     for (v = 0; v < numPoints[0]; ++v) {
5264       PetscInt off;
5265 
5266       PetscCall(PetscSectionGetOffset(coordSection, v + firstVertex, &off));
5267       for (d = 0; d < dimEmbed; ++d) coords[off + d] = vertexCoords[v * dimEmbed + d];
5268     }
5269   }
5270   PetscCall(VecRestoreArray(coordinates, &coords));
5271   PetscCall(DMSetCoordinatesLocal(dm, coordinates));
5272   PetscCall(VecDestroy(&coordinates));
5273   PetscFunctionReturn(PETSC_SUCCESS);
5274 }
5275 
5276 /*
5277   DMPlexCreateCellVertexFromFile - Create a `DMPLEX` mesh from a simple cell-vertex file.
5278 
5279   Collective
5280 
5281 + comm        - The MPI communicator
5282 . filename    - Name of the .dat file
5283 - interpolate - Create faces and edges in the mesh
5284 
5285   Output Parameter:
5286 . dm  - The `DM` object representing the mesh
5287 
5288   Level: beginner
5289 
5290   Note:
5291   The format is the simplest possible:
5292 .vb
5293   Ne
5294   v0 v1 ... vk
5295   Nv
5296   x y z marker
5297 .ve
5298 
5299   Developer Note:
5300   Should use a `PetscViewer` not a filename
5301 
5302 .seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexCreateFromFile()`, `DMPlexCreateGmsh()`, `DMPlexCreate()`
5303 */
5304 static PetscErrorCode DMPlexCreateCellVertexFromFile(MPI_Comm comm, const char filename[], PetscBool interpolate, DM *dm)
5305 {
5306   DMLabel      marker;
5307   PetscViewer  viewer;
5308   Vec          coordinates;
5309   PetscSection coordSection;
5310   PetscScalar *coords;
5311   char         line[PETSC_MAX_PATH_LEN];
5312   PetscInt     dim = 3, cdim = 3, coordSize, v, c, d;
5313   PetscMPIInt  rank;
5314   int          snum, Nv, Nc, Ncn, Nl;
5315 
5316   PetscFunctionBegin;
5317   PetscCallMPI(MPI_Comm_rank(comm, &rank));
5318   PetscCall(PetscViewerCreate(comm, &viewer));
5319   PetscCall(PetscViewerSetType(viewer, PETSCVIEWERASCII));
5320   PetscCall(PetscViewerFileSetMode(viewer, FILE_MODE_READ));
5321   PetscCall(PetscViewerFileSetName(viewer, filename));
5322   if (rank == 0) {
5323     PetscCall(PetscViewerRead(viewer, line, 4, NULL, PETSC_STRING));
5324     snum = sscanf(line, "%d %d %d %d", &Nc, &Nv, &Ncn, &Nl);
5325     PetscCheck(snum == 4, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unable to parse cell-vertex file: %s", line);
5326   } else {
5327     Nc = Nv = Ncn = Nl = 0;
5328   }
5329   PetscCall(DMCreate(comm, dm));
5330   PetscCall(DMSetType(*dm, DMPLEX));
5331   PetscCall(DMPlexSetChart(*dm, 0, Nc + Nv));
5332   PetscCall(DMSetDimension(*dm, dim));
5333   PetscCall(DMSetCoordinateDim(*dm, cdim));
5334   /* Read topology */
5335   if (rank == 0) {
5336     char     format[PETSC_MAX_PATH_LEN];
5337     PetscInt cone[8];
5338     int      vbuf[8], v;
5339 
5340     for (c = 0; c < Ncn; ++c) {
5341       format[c * 3 + 0] = '%';
5342       format[c * 3 + 1] = 'd';
5343       format[c * 3 + 2] = ' ';
5344     }
5345     format[Ncn * 3 - 1] = '\0';
5346     for (c = 0; c < Nc; ++c) PetscCall(DMPlexSetConeSize(*dm, c, Ncn));
5347     PetscCall(DMSetUp(*dm));
5348     for (c = 0; c < Nc; ++c) {
5349       PetscCall(PetscViewerRead(viewer, line, Ncn, NULL, PETSC_STRING));
5350       switch (Ncn) {
5351       case 2:
5352         snum = sscanf(line, format, &vbuf[0], &vbuf[1]);
5353         break;
5354       case 3:
5355         snum = sscanf(line, format, &vbuf[0], &vbuf[1], &vbuf[2]);
5356         break;
5357       case 4:
5358         snum = sscanf(line, format, &vbuf[0], &vbuf[1], &vbuf[2], &vbuf[3]);
5359         break;
5360       case 6:
5361         snum = sscanf(line, format, &vbuf[0], &vbuf[1], &vbuf[2], &vbuf[3], &vbuf[4], &vbuf[5]);
5362         break;
5363       case 8:
5364         snum = sscanf(line, format, &vbuf[0], &vbuf[1], &vbuf[2], &vbuf[3], &vbuf[4], &vbuf[5], &vbuf[6], &vbuf[7]);
5365         break;
5366       default:
5367         SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "No cell shape with %d vertices", Ncn);
5368       }
5369       PetscCheck(snum == Ncn, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unable to parse cell-vertex file: %s", line);
5370       for (v = 0; v < Ncn; ++v) cone[v] = vbuf[v] + Nc;
5371       /* Hexahedra are inverted */
5372       if (Ncn == 8) {
5373         PetscInt tmp = cone[1];
5374         cone[1]      = cone[3];
5375         cone[3]      = tmp;
5376       }
5377       PetscCall(DMPlexSetCone(*dm, c, cone));
5378     }
5379   }
5380   PetscCall(DMPlexSymmetrize(*dm));
5381   PetscCall(DMPlexStratify(*dm));
5382   /* Read coordinates */
5383   PetscCall(DMGetCoordinateSection(*dm, &coordSection));
5384   PetscCall(PetscSectionSetNumFields(coordSection, 1));
5385   PetscCall(PetscSectionSetFieldComponents(coordSection, 0, cdim));
5386   PetscCall(PetscSectionSetChart(coordSection, Nc, Nc + Nv));
5387   for (v = Nc; v < Nc + Nv; ++v) {
5388     PetscCall(PetscSectionSetDof(coordSection, v, cdim));
5389     PetscCall(PetscSectionSetFieldDof(coordSection, v, 0, cdim));
5390   }
5391   PetscCall(PetscSectionSetUp(coordSection));
5392   PetscCall(PetscSectionGetStorageSize(coordSection, &coordSize));
5393   PetscCall(VecCreate(PETSC_COMM_SELF, &coordinates));
5394   PetscCall(PetscObjectSetName((PetscObject)coordinates, "coordinates"));
5395   PetscCall(VecSetSizes(coordinates, coordSize, PETSC_DETERMINE));
5396   PetscCall(VecSetBlockSize(coordinates, cdim));
5397   PetscCall(VecSetType(coordinates, VECSTANDARD));
5398   PetscCall(VecGetArray(coordinates, &coords));
5399   if (rank == 0) {
5400     char   format[PETSC_MAX_PATH_LEN];
5401     double x[3];
5402     int    l, val[3];
5403 
5404     if (Nl) {
5405       for (l = 0; l < Nl; ++l) {
5406         format[l * 3 + 0] = '%';
5407         format[l * 3 + 1] = 'd';
5408         format[l * 3 + 2] = ' ';
5409       }
5410       format[Nl * 3 - 1] = '\0';
5411       PetscCall(DMCreateLabel(*dm, "marker"));
5412       PetscCall(DMGetLabel(*dm, "marker", &marker));
5413     }
5414     for (v = 0; v < Nv; ++v) {
5415       PetscCall(PetscViewerRead(viewer, line, 3 + Nl, NULL, PETSC_STRING));
5416       snum = sscanf(line, "%lg %lg %lg", &x[0], &x[1], &x[2]);
5417       PetscCheck(snum == 3, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unable to parse cell-vertex file: %s", line);
5418       switch (Nl) {
5419       case 0:
5420         snum = 0;
5421         break;
5422       case 1:
5423         snum = sscanf(line, format, &val[0]);
5424         break;
5425       case 2:
5426         snum = sscanf(line, format, &val[0], &val[1]);
5427         break;
5428       case 3:
5429         snum = sscanf(line, format, &val[0], &val[1], &val[2]);
5430         break;
5431       default:
5432         SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Request support for %d labels", Nl);
5433       }
5434       PetscCheck(snum == Nl, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unable to parse cell-vertex file: %s", line);
5435       for (d = 0; d < cdim; ++d) coords[v * cdim + d] = x[d];
5436       for (l = 0; l < Nl; ++l) PetscCall(DMLabelSetValue(marker, v + Nc, val[l]));
5437     }
5438   }
5439   PetscCall(VecRestoreArray(coordinates, &coords));
5440   PetscCall(DMSetCoordinatesLocal(*dm, coordinates));
5441   PetscCall(VecDestroy(&coordinates));
5442   PetscCall(PetscViewerDestroy(&viewer));
5443   if (interpolate) {
5444     DM      idm;
5445     DMLabel bdlabel;
5446 
5447     PetscCall(DMPlexInterpolate(*dm, &idm));
5448     PetscCall(DMDestroy(dm));
5449     *dm = idm;
5450 
5451     if (!Nl) {
5452       PetscCall(DMCreateLabel(*dm, "marker"));
5453       PetscCall(DMGetLabel(*dm, "marker", &bdlabel));
5454       PetscCall(DMPlexMarkBoundaryFaces(*dm, PETSC_DETERMINE, bdlabel));
5455       PetscCall(DMPlexLabelComplete(*dm, bdlabel));
5456     }
5457   }
5458   PetscFunctionReturn(PETSC_SUCCESS);
5459 }
5460 
5461 /*@C
5462   DMPlexCreateFromFile - This takes a filename and produces a `DM`
5463 
5464   Collective
5465 
5466   Input Parameters:
5467 + comm        - The communicator
5468 . filename    - A file name
5469 . plexname    - The object name of the resulting `DM`, also used for intra-datafile lookup by some formats
5470 - interpolate - Flag to create intermediate mesh pieces (edges, faces)
5471 
5472   Output Parameter:
5473 . dm - The `DM`
5474 
5475   Options Database Key:
5476 . -dm_plex_create_from_hdf5_xdmf - use the `PETSC_VIEWER_HDF5_XDMF` format for reading HDF5
5477 
5478   Use `-dm_plex_create_ prefix` to pass options to the internal `PetscViewer`, e.g.
5479 $ -dm_plex_create_viewer_hdf5_collective
5480 
5481   Level: beginner
5482 
5483   Notes:
5484   Using `PETSCVIEWERHDF5` type with `PETSC_VIEWER_HDF5_PETSC` format, one can save multiple `DMPLEX`
5485   meshes in a single HDF5 file. This in turn requires one to name the `DMPLEX` object with `PetscObjectSetName()`
5486   before saving it with `DMView()` and before loading it with `DMLoad()` for identification of the mesh object.
5487   The input parameter name is thus used to name the `DMPLEX` object when `DMPlexCreateFromFile()` internally
5488   calls `DMLoad()`. Currently, name is ignored for other viewer types and/or formats.
5489 
5490 .seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexCreateFromDAG()`, `DMPlexCreateFromCellListPetsc()`, `DMPlexCreate()`, `PetscObjectSetName()`, `DMView()`, `DMLoad()`
5491 @*/
5492 PetscErrorCode DMPlexCreateFromFile(MPI_Comm comm, const char filename[], const char plexname[], PetscBool interpolate, DM *dm)
5493 {
5494   const char  extGmsh[]      = ".msh";
5495   const char  extGmsh2[]     = ".msh2";
5496   const char  extGmsh4[]     = ".msh4";
5497   const char  extCGNS[]      = ".cgns";
5498   const char  extExodus[]    = ".exo";
5499   const char  extExodus_e[]  = ".e";
5500   const char  extGenesis[]   = ".gen";
5501   const char  extFluent[]    = ".cas";
5502   const char  extHDF5[]      = ".h5";
5503   const char  extXDMFHDF5[]  = ".xdmf.h5";
5504   const char  extPLY[]       = ".ply";
5505   const char  extEGADSLite[] = ".egadslite";
5506   const char  extEGADS[]     = ".egads";
5507   const char  extIGES[]      = ".igs";
5508   const char  extSTEP[]      = ".stp";
5509   const char  extCV[]        = ".dat";
5510   size_t      len;
5511   PetscBool   isGmsh, isGmsh2, isGmsh4, isCGNS, isExodus, isGenesis, isFluent, isHDF5, isPLY, isEGADSLite, isEGADS, isIGES, isSTEP, isCV, isXDMFHDF5;
5512   PetscMPIInt rank;
5513 
5514   PetscFunctionBegin;
5515   PetscAssertPointer(filename, 2);
5516   if (plexname) PetscAssertPointer(plexname, 3);
5517   PetscAssertPointer(dm, 5);
5518   PetscCall(DMInitializePackage());
5519   PetscCall(PetscLogEventBegin(DMPLEX_CreateFromFile, 0, 0, 0, 0));
5520   PetscCallMPI(MPI_Comm_rank(comm, &rank));
5521   PetscCall(PetscStrlen(filename, &len));
5522   PetscCheck(len, comm, PETSC_ERR_ARG_WRONG, "Filename must be a valid path");
5523 
5524 #define CheckExtension(extension__, is_extension__) \
5525   do { \
5526     PetscAssert(sizeof(extension__), comm, PETSC_ERR_PLIB, "Zero-size extension: %s", extension__); \
5527     /* don't count the null-terminator at the end */ \
5528     const size_t ext_len = sizeof(extension__) - 1; \
5529     if (len < ext_len) { \
5530       is_extension__ = PETSC_FALSE; \
5531     } else { \
5532       PetscCall(PetscStrncmp(filename + len - ext_len, extension__, ext_len, &is_extension__)); \
5533     } \
5534   } while (0)
5535 
5536   CheckExtension(extGmsh, isGmsh);
5537   CheckExtension(extGmsh2, isGmsh2);
5538   CheckExtension(extGmsh4, isGmsh4);
5539   CheckExtension(extCGNS, isCGNS);
5540   CheckExtension(extExodus, isExodus);
5541   if (!isExodus) CheckExtension(extExodus_e, isExodus);
5542   CheckExtension(extGenesis, isGenesis);
5543   CheckExtension(extFluent, isFluent);
5544   CheckExtension(extHDF5, isHDF5);
5545   CheckExtension(extPLY, isPLY);
5546   CheckExtension(extEGADSLite, isEGADSLite);
5547   CheckExtension(extEGADS, isEGADS);
5548   CheckExtension(extIGES, isIGES);
5549   CheckExtension(extSTEP, isSTEP);
5550   CheckExtension(extCV, isCV);
5551   CheckExtension(extXDMFHDF5, isXDMFHDF5);
5552 
5553 #undef CheckExtension
5554 
5555   if (isGmsh || isGmsh2 || isGmsh4) {
5556     PetscCall(DMPlexCreateGmshFromFile(comm, filename, interpolate, dm));
5557   } else if (isCGNS) {
5558     PetscCall(DMPlexCreateCGNSFromFile(comm, filename, interpolate, dm));
5559   } else if (isExodus || isGenesis) {
5560     PetscCall(DMPlexCreateExodusFromFile(comm, filename, interpolate, dm));
5561   } else if (isFluent) {
5562     PetscCall(DMPlexCreateFluentFromFile(comm, filename, interpolate, dm));
5563   } else if (isHDF5) {
5564     PetscViewer viewer;
5565 
5566     /* PETSC_VIEWER_HDF5_XDMF is used if the filename ends with .xdmf.h5, or if -dm_plex_create_from_hdf5_xdmf option is present */
5567     PetscCall(PetscOptionsGetBool(NULL, NULL, "-dm_plex_create_from_hdf5_xdmf", &isXDMFHDF5, NULL));
5568     PetscCall(PetscViewerCreate(comm, &viewer));
5569     PetscCall(PetscViewerSetType(viewer, PETSCVIEWERHDF5));
5570     PetscCall(PetscViewerSetOptionsPrefix(viewer, "dm_plex_create_"));
5571     PetscCall(PetscViewerSetFromOptions(viewer));
5572     PetscCall(PetscViewerFileSetMode(viewer, FILE_MODE_READ));
5573     PetscCall(PetscViewerFileSetName(viewer, filename));
5574 
5575     PetscCall(DMCreate(comm, dm));
5576     PetscCall(PetscObjectSetName((PetscObject)(*dm), plexname));
5577     PetscCall(DMSetType(*dm, DMPLEX));
5578     if (isXDMFHDF5) PetscCall(PetscViewerPushFormat(viewer, PETSC_VIEWER_HDF5_XDMF));
5579     PetscCall(DMLoad(*dm, viewer));
5580     if (isXDMFHDF5) PetscCall(PetscViewerPopFormat(viewer));
5581     PetscCall(PetscViewerDestroy(&viewer));
5582 
5583     if (interpolate) {
5584       DM idm;
5585 
5586       PetscCall(DMPlexInterpolate(*dm, &idm));
5587       PetscCall(DMDestroy(dm));
5588       *dm = idm;
5589     }
5590   } else if (isPLY) {
5591     PetscCall(DMPlexCreatePLYFromFile(comm, filename, interpolate, dm));
5592   } else if (isEGADSLite || isEGADS || isIGES || isSTEP) {
5593     if (isEGADSLite) PetscCall(DMPlexCreateEGADSLiteFromFile(comm, filename, dm));
5594     else PetscCall(DMPlexCreateEGADSFromFile(comm, filename, dm));
5595     if (!interpolate) {
5596       DM udm;
5597 
5598       PetscCall(DMPlexUninterpolate(*dm, &udm));
5599       PetscCall(DMDestroy(dm));
5600       *dm = udm;
5601     }
5602   } else if (isCV) {
5603     PetscCall(DMPlexCreateCellVertexFromFile(comm, filename, interpolate, dm));
5604   } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cannot load file %s: unrecognized extension", filename);
5605   PetscCall(PetscStrlen(plexname, &len));
5606   if (len) PetscCall(PetscObjectSetName((PetscObject)(*dm), plexname));
5607   PetscCall(PetscLogEventEnd(DMPLEX_CreateFromFile, 0, 0, 0, 0));
5608   PetscFunctionReturn(PETSC_SUCCESS);
5609 }
5610 
5611 /*@C
5612   DMPlexCreateEphemeral - This takes a `DMPlexTransform` and a base `DMPlex` and produces an ephemeral `DM`, meaning one that is created on the fly in response to queries.
5613 
5614   Input Parameters:
5615 + tr     - The `DMPlexTransform`
5616 - prefix - An options prefix, or NULL
5617 
5618   Output Parameter:
5619 . dm - The `DM`
5620 
5621   Level: beginner
5622 
5623   Notes:
5624   An emphemeral mesh is one that is not stored concretely, as in the default `DMPLEX` implementation, but rather is produced on the fly in response to queries, using information from the transform and the base mesh.
5625 
5626 .seealso: `DMPlexCreateFromFile`, `DMPlexCreateFromDAG()`, `DMPlexCreateFromCellListPetsc()`, `DMPlexCreate()`
5627 @*/
5628 PetscErrorCode DMPlexCreateEphemeral(DMPlexTransform tr, const char prefix[], DM *dm)
5629 {
5630   DM           bdm, bcdm, cdm;
5631   Vec          coordinates, coordinatesNew;
5632   PetscSection cs;
5633   PetscInt     dim, cdim, Nl;
5634 
5635   PetscFunctionBegin;
5636   PetscCall(DMCreate(PetscObjectComm((PetscObject)tr), dm));
5637   PetscCall(DMSetType(*dm, DMPLEX));
5638   ((DM_Plex *)(*dm)->data)->interpolated = DMPLEX_INTERPOLATED_FULL;
5639   // Handle coordinates
5640   PetscCall(DMPlexTransformGetDM(tr, &bdm));
5641   PetscCall(DMGetCoordinateDim(bdm, &cdim));
5642   PetscCall(DMSetCoordinateDim(*dm, cdim));
5643   PetscCall(DMGetDimension(bdm, &dim));
5644   PetscCall(DMSetDimension(*dm, dim));
5645   PetscCall(DMGetCoordinateDM(bdm, &bcdm));
5646   PetscCall(DMGetCoordinateDM(*dm, &cdm));
5647   PetscCall(DMCopyDisc(bcdm, cdm));
5648   PetscCall(DMGetLocalSection(cdm, &cs));
5649   PetscCall(PetscSectionSetNumFields(cs, 1));
5650   PetscCall(PetscSectionSetFieldComponents(cs, 0, cdim));
5651   PetscCall(DMGetCoordinatesLocal(bdm, &coordinates));
5652   PetscCall(VecDuplicate(coordinates, &coordinatesNew));
5653   PetscCall(VecCopy(coordinates, coordinatesNew));
5654   PetscCall(DMSetCoordinatesLocal(*dm, coordinatesNew));
5655   PetscCall(VecDestroy(&coordinatesNew));
5656 
5657   PetscCall(PetscObjectReference((PetscObject)tr));
5658   PetscCall(DMPlexTransformDestroy(&((DM_Plex *)(*dm)->data)->tr));
5659   ((DM_Plex *)(*dm)->data)->tr = tr;
5660   PetscCall(DMPlexDistributeSetDefault(*dm, PETSC_FALSE));
5661   PetscCall(PetscObjectSetOptionsPrefix((PetscObject)*dm, prefix));
5662   PetscCall(DMSetFromOptions(*dm));
5663 
5664   PetscCall(DMGetNumLabels(bdm, &Nl));
5665   for (PetscInt l = 0; l < Nl; ++l) {
5666     DMLabel     label, labelNew;
5667     const char *lname;
5668     PetscBool   isDepth, isCellType;
5669 
5670     PetscCall(DMGetLabelName(bdm, l, &lname));
5671     PetscCall(PetscStrcmp(lname, "depth", &isDepth));
5672     if (isDepth) continue;
5673     PetscCall(PetscStrcmp(lname, "celltype", &isCellType));
5674     if (isCellType) continue;
5675     PetscCall(DMCreateLabel(*dm, lname));
5676     PetscCall(DMGetLabel(bdm, lname, &label));
5677     PetscCall(DMGetLabel(*dm, lname, &labelNew));
5678     PetscCall(DMLabelSetType(labelNew, DMLABELEPHEMERAL));
5679     PetscCall(DMLabelEphemeralSetLabel(labelNew, label));
5680     PetscCall(DMLabelEphemeralSetTransform(labelNew, tr));
5681     PetscCall(DMLabelSetUp(labelNew));
5682   }
5683   PetscFunctionReturn(PETSC_SUCCESS);
5684 }
5685