xref: /petsc/src/dm/impls/plex/plexcreate.c (revision 12a889988b2e29092297f51a8d842de3d83d35e3)
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;
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   if (degree >= 0) {
224     DMPolytopeType ct = DM_POLYTOPE_UNKNOWN;
225     PetscInt       cStart, cEnd, gct;
226 
227     PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
228     if (cEnd > cStart) PetscCall(DMPlexGetCellType(dm, cStart, &ct));
229     gct = (PetscInt)ct;
230     PetscCall(MPIU_Allreduce(MPI_IN_PLACE, &gct, 1, MPIU_INT, MPI_MIN, PetscObjectComm((PetscObject)dm)));
231     ct = (DMPolytopeType)gct;
232     // Work around current bug in PetscDualSpaceSetUp_Lagrange()
233     //   Can be seen in plex_tutorials-ex10_1
234     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));
235   }
236   PetscCall(DMSetCoordinateDisc(dm, fe, project));
237   PetscCall(PetscFEDestroy(&fe));
238   mesh->coordFunc = coordFunc;
239   PetscFunctionReturn(PETSC_SUCCESS);
240 }
241 
242 /*@
243   DMPlexCreateDoublet - Creates a mesh of two cells of the specified type, optionally with later refinement.
244 
245   Collective
246 
247   Input Parameters:
248 + comm            - The communicator for the `DM` object
249 . dim             - The spatial dimension
250 . simplex         - Flag for simplicial cells, otherwise they are tensor product cells
251 . interpolate     - Flag to create intermediate mesh pieces (edges, faces)
252 - refinementLimit - A nonzero number indicates the largest admissible volume for a refined cell
253 
254   Output Parameter:
255 . newdm - The `DM` object
256 
257   Level: beginner
258 
259 .seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMSetType()`, `DMCreate()`
260 @*/
261 PetscErrorCode DMPlexCreateDoublet(MPI_Comm comm, PetscInt dim, PetscBool simplex, PetscBool interpolate, PetscReal refinementLimit, DM *newdm)
262 {
263   DM          dm;
264   PetscMPIInt rank;
265 
266   PetscFunctionBegin;
267   PetscCall(DMCreate(comm, &dm));
268   PetscCall(DMSetType(dm, DMPLEX));
269   PetscCall(DMSetDimension(dm, dim));
270   PetscCall(PetscLogEventBegin(DMPLEX_Generate, dm, 0, 0, 0));
271   PetscCallMPI(MPI_Comm_rank(comm, &rank));
272   switch (dim) {
273   case 2:
274     if (simplex) PetscCall(PetscObjectSetName((PetscObject)dm, "triangular"));
275     else PetscCall(PetscObjectSetName((PetscObject)dm, "quadrilateral"));
276     break;
277   case 3:
278     if (simplex) PetscCall(PetscObjectSetName((PetscObject)dm, "tetrahedral"));
279     else PetscCall(PetscObjectSetName((PetscObject)dm, "hexahedral"));
280     break;
281   default:
282     SETERRQ(comm, PETSC_ERR_ARG_OUTOFRANGE, "Cannot make meshes for dimension %" PetscInt_FMT, dim);
283   }
284   if (rank) {
285     PetscInt numPoints[2] = {0, 0};
286     PetscCall(DMPlexCreateFromDAG(dm, 1, numPoints, NULL, NULL, NULL, NULL));
287   } else {
288     switch (dim) {
289     case 2:
290       if (simplex) {
291         PetscInt    numPoints[2]        = {4, 2};
292         PetscInt    coneSize[6]         = {3, 3, 0, 0, 0, 0};
293         PetscInt    cones[6]            = {2, 3, 4, 5, 4, 3};
294         PetscInt    coneOrientations[6] = {0, 0, 0, 0, 0, 0};
295         PetscScalar vertexCoords[8]     = {-0.5, 0.5, 0.0, 0.0, 0.0, 1.0, 0.5, 0.5};
296 
297         PetscCall(DMPlexCreateFromDAG(dm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords));
298       } else {
299         PetscInt    numPoints[2]        = {6, 2};
300         PetscInt    coneSize[8]         = {4, 4, 0, 0, 0, 0, 0, 0};
301         PetscInt    cones[8]            = {2, 3, 4, 5, 3, 6, 7, 4};
302         PetscInt    coneOrientations[8] = {0, 0, 0, 0, 0, 0, 0, 0};
303         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};
304 
305         PetscCall(DMPlexCreateFromDAG(dm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords));
306       }
307       break;
308     case 3:
309       if (simplex) {
310         PetscInt    numPoints[2]        = {5, 2};
311         PetscInt    coneSize[7]         = {4, 4, 0, 0, 0, 0, 0};
312         PetscInt    cones[8]            = {4, 3, 5, 2, 5, 3, 4, 6};
313         PetscInt    coneOrientations[8] = {0, 0, 0, 0, 0, 0, 0, 0};
314         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};
315 
316         PetscCall(DMPlexCreateFromDAG(dm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords));
317       } else {
318         PetscInt    numPoints[2]         = {12, 2};
319         PetscInt    coneSize[14]         = {8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0};
320         PetscInt    cones[16]            = {2, 3, 4, 5, 6, 7, 8, 9, 5, 4, 10, 11, 7, 12, 13, 8};
321         PetscInt    coneOrientations[16] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0};
322         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};
323 
324         PetscCall(DMPlexCreateFromDAG(dm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords));
325       }
326       break;
327     default:
328       SETERRQ(comm, PETSC_ERR_ARG_OUTOFRANGE, "Cannot make meshes for dimension %" PetscInt_FMT, dim);
329     }
330   }
331   PetscCall(PetscLogEventEnd(DMPLEX_Generate, dm, 0, 0, 0));
332   *newdm = dm;
333   if (refinementLimit > 0.0) {
334     DM          rdm;
335     const char *name;
336 
337     PetscCall(DMPlexSetRefinementUniform(*newdm, PETSC_FALSE));
338     PetscCall(DMPlexSetRefinementLimit(*newdm, refinementLimit));
339     PetscCall(DMRefine(*newdm, comm, &rdm));
340     PetscCall(PetscObjectGetName((PetscObject)*newdm, &name));
341     PetscCall(PetscObjectSetName((PetscObject)rdm, name));
342     PetscCall(DMDestroy(newdm));
343     *newdm = rdm;
344   }
345   if (interpolate) {
346     DM idm;
347 
348     PetscCall(DMPlexInterpolate(*newdm, &idm));
349     PetscCall(DMDestroy(newdm));
350     *newdm = idm;
351   }
352   PetscFunctionReturn(PETSC_SUCCESS);
353 }
354 
355 static PetscErrorCode DMPlexCreateBoxSurfaceMesh_Tensor_1D_Internal(DM dm, const PetscReal lower[], const PetscReal upper[], const PetscInt edges[])
356 {
357   const PetscInt numVertices    = 2;
358   PetscInt       markerRight    = 1;
359   PetscInt       markerLeft     = 1;
360   PetscBool      markerSeparate = PETSC_FALSE;
361   Vec            coordinates;
362   PetscSection   coordSection;
363   PetscScalar   *coords;
364   PetscInt       coordSize;
365   PetscMPIInt    rank;
366   PetscInt       cdim = 1, v;
367 
368   PetscFunctionBegin;
369   PetscCall(PetscOptionsGetBool(((PetscObject)dm)->options, ((PetscObject)dm)->prefix, "-dm_plex_separate_marker", &markerSeparate, NULL));
370   if (markerSeparate) {
371     markerRight = 2;
372     markerLeft  = 1;
373   }
374   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank));
375   if (rank == 0) {
376     PetscCall(DMPlexSetChart(dm, 0, numVertices));
377     PetscCall(DMSetUp(dm)); /* Allocate space for cones */
378     PetscCall(DMSetLabelValue(dm, "marker", 0, markerLeft));
379     PetscCall(DMSetLabelValue(dm, "marker", 1, markerRight));
380   }
381   PetscCall(DMPlexSymmetrize(dm));
382   PetscCall(DMPlexStratify(dm));
383   /* Build coordinates */
384   PetscCall(DMSetCoordinateDim(dm, cdim));
385   PetscCall(DMGetCoordinateSection(dm, &coordSection));
386   PetscCall(PetscSectionSetNumFields(coordSection, 1));
387   PetscCall(PetscSectionSetChart(coordSection, 0, numVertices));
388   PetscCall(PetscSectionSetFieldComponents(coordSection, 0, cdim));
389   for (v = 0; v < numVertices; ++v) {
390     PetscCall(PetscSectionSetDof(coordSection, v, cdim));
391     PetscCall(PetscSectionSetFieldDof(coordSection, v, 0, cdim));
392   }
393   PetscCall(PetscSectionSetUp(coordSection));
394   PetscCall(PetscSectionGetStorageSize(coordSection, &coordSize));
395   PetscCall(VecCreate(PETSC_COMM_SELF, &coordinates));
396   PetscCall(PetscObjectSetName((PetscObject)coordinates, "coordinates"));
397   PetscCall(VecSetSizes(coordinates, coordSize, PETSC_DETERMINE));
398   PetscCall(VecSetBlockSize(coordinates, cdim));
399   PetscCall(VecSetType(coordinates, VECSTANDARD));
400   PetscCall(VecGetArray(coordinates, &coords));
401   coords[0] = lower[0];
402   coords[1] = upper[0];
403   PetscCall(VecRestoreArray(coordinates, &coords));
404   PetscCall(DMSetCoordinatesLocal(dm, coordinates));
405   PetscCall(VecDestroy(&coordinates));
406   PetscFunctionReturn(PETSC_SUCCESS);
407 }
408 
409 static PetscErrorCode DMPlexCreateBoxSurfaceMesh_Tensor_2D_Internal(DM dm, const PetscReal lower[], const PetscReal upper[], const PetscInt edges[])
410 {
411   const PetscInt numVertices    = (edges[0] + 1) * (edges[1] + 1);
412   const PetscInt numEdges       = edges[0] * (edges[1] + 1) + (edges[0] + 1) * edges[1];
413   PetscInt       markerTop      = 1;
414   PetscInt       markerBottom   = 1;
415   PetscInt       markerRight    = 1;
416   PetscInt       markerLeft     = 1;
417   PetscBool      markerSeparate = PETSC_FALSE;
418   Vec            coordinates;
419   PetscSection   coordSection;
420   PetscScalar   *coords;
421   PetscInt       coordSize;
422   PetscMPIInt    rank;
423   PetscInt       v, vx, vy;
424 
425   PetscFunctionBegin;
426   PetscCall(PetscOptionsGetBool(((PetscObject)dm)->options, ((PetscObject)dm)->prefix, "-dm_plex_separate_marker", &markerSeparate, NULL));
427   if (markerSeparate) {
428     markerTop    = 3;
429     markerBottom = 1;
430     markerRight  = 2;
431     markerLeft   = 4;
432   }
433   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank));
434   if (rank == 0) {
435     PetscInt e, ex, ey;
436 
437     PetscCall(DMPlexSetChart(dm, 0, numEdges + numVertices));
438     for (e = 0; e < numEdges; ++e) PetscCall(DMPlexSetConeSize(dm, e, 2));
439     PetscCall(DMSetUp(dm)); /* Allocate space for cones */
440     for (vx = 0; vx <= edges[0]; vx++) {
441       for (ey = 0; ey < edges[1]; ey++) {
442         PetscInt edge   = vx * edges[1] + ey + edges[0] * (edges[1] + 1);
443         PetscInt vertex = ey * (edges[0] + 1) + vx + numEdges;
444         PetscInt cone[2];
445 
446         cone[0] = vertex;
447         cone[1] = vertex + edges[0] + 1;
448         PetscCall(DMPlexSetCone(dm, edge, cone));
449         if (vx == edges[0]) {
450           PetscCall(DMSetLabelValue(dm, "marker", edge, markerRight));
451           PetscCall(DMSetLabelValue(dm, "marker", cone[0], markerRight));
452           if (ey == edges[1] - 1) {
453             PetscCall(DMSetLabelValue(dm, "marker", cone[1], markerRight));
454             PetscCall(DMSetLabelValue(dm, "Face Sets", cone[1], markerRight));
455           }
456         } else if (vx == 0) {
457           PetscCall(DMSetLabelValue(dm, "marker", edge, markerLeft));
458           PetscCall(DMSetLabelValue(dm, "marker", cone[0], markerLeft));
459           if (ey == edges[1] - 1) {
460             PetscCall(DMSetLabelValue(dm, "marker", cone[1], markerLeft));
461             PetscCall(DMSetLabelValue(dm, "Face Sets", cone[1], markerLeft));
462           }
463         }
464       }
465     }
466     for (vy = 0; vy <= edges[1]; vy++) {
467       for (ex = 0; ex < edges[0]; ex++) {
468         PetscInt edge   = vy * edges[0] + ex;
469         PetscInt vertex = vy * (edges[0] + 1) + ex + numEdges;
470         PetscInt cone[2];
471 
472         cone[0] = vertex;
473         cone[1] = vertex + 1;
474         PetscCall(DMPlexSetCone(dm, edge, cone));
475         if (vy == edges[1]) {
476           PetscCall(DMSetLabelValue(dm, "marker", edge, markerTop));
477           PetscCall(DMSetLabelValue(dm, "marker", cone[0], markerTop));
478           if (ex == edges[0] - 1) {
479             PetscCall(DMSetLabelValue(dm, "marker", cone[1], markerTop));
480             PetscCall(DMSetLabelValue(dm, "Face Sets", cone[1], markerTop));
481           }
482         } else if (vy == 0) {
483           PetscCall(DMSetLabelValue(dm, "marker", edge, markerBottom));
484           PetscCall(DMSetLabelValue(dm, "marker", cone[0], markerBottom));
485           if (ex == edges[0] - 1) {
486             PetscCall(DMSetLabelValue(dm, "marker", cone[1], markerBottom));
487             PetscCall(DMSetLabelValue(dm, "Face Sets", cone[1], markerBottom));
488           }
489         }
490       }
491     }
492   }
493   PetscCall(DMPlexSymmetrize(dm));
494   PetscCall(DMPlexStratify(dm));
495   /* Build coordinates */
496   PetscCall(DMSetCoordinateDim(dm, 2));
497   PetscCall(DMGetCoordinateSection(dm, &coordSection));
498   PetscCall(PetscSectionSetNumFields(coordSection, 1));
499   PetscCall(PetscSectionSetChart(coordSection, numEdges, numEdges + numVertices));
500   PetscCall(PetscSectionSetFieldComponents(coordSection, 0, 2));
501   for (v = numEdges; v < numEdges + numVertices; ++v) {
502     PetscCall(PetscSectionSetDof(coordSection, v, 2));
503     PetscCall(PetscSectionSetFieldDof(coordSection, v, 0, 2));
504   }
505   PetscCall(PetscSectionSetUp(coordSection));
506   PetscCall(PetscSectionGetStorageSize(coordSection, &coordSize));
507   PetscCall(VecCreate(PETSC_COMM_SELF, &coordinates));
508   PetscCall(PetscObjectSetName((PetscObject)coordinates, "coordinates"));
509   PetscCall(VecSetSizes(coordinates, coordSize, PETSC_DETERMINE));
510   PetscCall(VecSetBlockSize(coordinates, 2));
511   PetscCall(VecSetType(coordinates, VECSTANDARD));
512   PetscCall(VecGetArray(coordinates, &coords));
513   for (vy = 0; vy <= edges[1]; ++vy) {
514     for (vx = 0; vx <= edges[0]; ++vx) {
515       coords[(vy * (edges[0] + 1) + vx) * 2 + 0] = lower[0] + ((upper[0] - lower[0]) / edges[0]) * vx;
516       coords[(vy * (edges[0] + 1) + vx) * 2 + 1] = lower[1] + ((upper[1] - lower[1]) / edges[1]) * vy;
517     }
518   }
519   PetscCall(VecRestoreArray(coordinates, &coords));
520   PetscCall(DMSetCoordinatesLocal(dm, coordinates));
521   PetscCall(VecDestroy(&coordinates));
522   PetscFunctionReturn(PETSC_SUCCESS);
523 }
524 
525 static PetscErrorCode DMPlexCreateBoxSurfaceMesh_Tensor_3D_Internal(DM dm, const PetscReal lower[], const PetscReal upper[], const PetscInt faces[])
526 {
527   PetscInt     vertices[3], numVertices;
528   PetscInt     numFaces       = 2 * faces[0] * faces[1] + 2 * faces[1] * faces[2] + 2 * faces[0] * faces[2];
529   PetscInt     markerTop      = 1;
530   PetscInt     markerBottom   = 1;
531   PetscInt     markerFront    = 1;
532   PetscInt     markerBack     = 1;
533   PetscInt     markerRight    = 1;
534   PetscInt     markerLeft     = 1;
535   PetscBool    markerSeparate = PETSC_FALSE;
536   Vec          coordinates;
537   PetscSection coordSection;
538   PetscScalar *coords;
539   PetscInt     coordSize;
540   PetscMPIInt  rank;
541   PetscInt     v, vx, vy, vz;
542   PetscInt     voffset, iface = 0, cone[4];
543 
544   PetscFunctionBegin;
545   PetscCheck(faces[0] >= 1 && faces[1] >= 1 && faces[2] >= 1, PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Must have at least 1 face per side");
546   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank));
547   PetscCall(PetscOptionsGetBool(((PetscObject)dm)->options, ((PetscObject)dm)->prefix, "-dm_plex_separate_marker", &markerSeparate, NULL));
548   if (markerSeparate) {
549     markerBottom = 1;
550     markerTop    = 2;
551     markerFront  = 3;
552     markerBack   = 4;
553     markerRight  = 5;
554     markerLeft   = 6;
555   }
556   vertices[0] = faces[0] + 1;
557   vertices[1] = faces[1] + 1;
558   vertices[2] = faces[2] + 1;
559   numVertices = vertices[0] * vertices[1] * vertices[2];
560   if (rank == 0) {
561     PetscInt f;
562 
563     PetscCall(DMPlexSetChart(dm, 0, numFaces + numVertices));
564     for (f = 0; f < numFaces; ++f) PetscCall(DMPlexSetConeSize(dm, f, 4));
565     PetscCall(DMSetUp(dm)); /* Allocate space for cones */
566 
567     /* Side 0 (Top) */
568     for (vy = 0; vy < faces[1]; vy++) {
569       for (vx = 0; vx < faces[0]; vx++) {
570         voffset = numFaces + vertices[0] * vertices[1] * (vertices[2] - 1) + vy * vertices[0] + vx;
571         cone[0] = voffset;
572         cone[1] = voffset + 1;
573         cone[2] = voffset + vertices[0] + 1;
574         cone[3] = voffset + vertices[0];
575         PetscCall(DMPlexSetCone(dm, iface, cone));
576         PetscCall(DMSetLabelValue(dm, "marker", iface, markerTop));
577         PetscCall(DMSetLabelValue(dm, "marker", voffset + 0, markerTop));
578         PetscCall(DMSetLabelValue(dm, "marker", voffset + 1, markerTop));
579         PetscCall(DMSetLabelValue(dm, "marker", voffset + vertices[0] + 0, markerTop));
580         PetscCall(DMSetLabelValue(dm, "marker", voffset + vertices[0] + 1, markerTop));
581         iface++;
582       }
583     }
584 
585     /* Side 1 (Bottom) */
586     for (vy = 0; vy < faces[1]; vy++) {
587       for (vx = 0; vx < faces[0]; vx++) {
588         voffset = numFaces + vy * (faces[0] + 1) + vx;
589         cone[0] = voffset + 1;
590         cone[1] = voffset;
591         cone[2] = voffset + vertices[0];
592         cone[3] = voffset + vertices[0] + 1;
593         PetscCall(DMPlexSetCone(dm, iface, cone));
594         PetscCall(DMSetLabelValue(dm, "marker", iface, markerBottom));
595         PetscCall(DMSetLabelValue(dm, "marker", voffset + 0, markerBottom));
596         PetscCall(DMSetLabelValue(dm, "marker", voffset + 1, markerBottom));
597         PetscCall(DMSetLabelValue(dm, "marker", voffset + vertices[0] + 0, markerBottom));
598         PetscCall(DMSetLabelValue(dm, "marker", voffset + vertices[0] + 1, markerBottom));
599         iface++;
600       }
601     }
602 
603     /* Side 2 (Front) */
604     for (vz = 0; vz < faces[2]; vz++) {
605       for (vx = 0; vx < faces[0]; vx++) {
606         voffset = numFaces + vz * vertices[0] * vertices[1] + vx;
607         cone[0] = voffset;
608         cone[1] = voffset + 1;
609         cone[2] = voffset + vertices[0] * vertices[1] + 1;
610         cone[3] = voffset + vertices[0] * vertices[1];
611         PetscCall(DMPlexSetCone(dm, iface, cone));
612         PetscCall(DMSetLabelValue(dm, "marker", iface, markerFront));
613         PetscCall(DMSetLabelValue(dm, "marker", voffset + 0, markerFront));
614         PetscCall(DMSetLabelValue(dm, "marker", voffset + 1, markerFront));
615         PetscCall(DMSetLabelValue(dm, "marker", voffset + vertices[0] * vertices[1] + 0, markerFront));
616         PetscCall(DMSetLabelValue(dm, "marker", voffset + vertices[0] * vertices[1] + 1, markerFront));
617         iface++;
618       }
619     }
620 
621     /* Side 3 (Back) */
622     for (vz = 0; vz < faces[2]; vz++) {
623       for (vx = 0; vx < faces[0]; vx++) {
624         voffset = numFaces + vz * vertices[0] * vertices[1] + vertices[0] * (vertices[1] - 1) + vx;
625         cone[0] = voffset + vertices[0] * vertices[1];
626         cone[1] = voffset + vertices[0] * vertices[1] + 1;
627         cone[2] = voffset + 1;
628         cone[3] = voffset;
629         PetscCall(DMPlexSetCone(dm, iface, cone));
630         PetscCall(DMSetLabelValue(dm, "marker", iface, markerBack));
631         PetscCall(DMSetLabelValue(dm, "marker", voffset + 0, markerBack));
632         PetscCall(DMSetLabelValue(dm, "marker", voffset + 1, markerBack));
633         PetscCall(DMSetLabelValue(dm, "marker", voffset + vertices[0] * vertices[1] + 0, markerBack));
634         PetscCall(DMSetLabelValue(dm, "marker", voffset + vertices[0] * vertices[1] + 1, markerBack));
635         iface++;
636       }
637     }
638 
639     /* Side 4 (Left) */
640     for (vz = 0; vz < faces[2]; vz++) {
641       for (vy = 0; vy < faces[1]; vy++) {
642         voffset = numFaces + vz * vertices[0] * vertices[1] + vy * vertices[0];
643         cone[0] = voffset;
644         cone[1] = voffset + vertices[0] * vertices[1];
645         cone[2] = voffset + vertices[0] * vertices[1] + vertices[0];
646         cone[3] = voffset + vertices[0];
647         PetscCall(DMPlexSetCone(dm, iface, cone));
648         PetscCall(DMSetLabelValue(dm, "marker", iface, markerLeft));
649         PetscCall(DMSetLabelValue(dm, "marker", voffset + 0, markerLeft));
650         PetscCall(DMSetLabelValue(dm, "marker", voffset + vertices[0] + 0, markerLeft));
651         PetscCall(DMSetLabelValue(dm, "marker", voffset + vertices[1] + 0, markerLeft));
652         PetscCall(DMSetLabelValue(dm, "marker", voffset + vertices[0] * vertices[1] + vertices[0], markerLeft));
653         iface++;
654       }
655     }
656 
657     /* Side 5 (Right) */
658     for (vz = 0; vz < faces[2]; vz++) {
659       for (vy = 0; vy < faces[1]; vy++) {
660         voffset = numFaces + vz * vertices[0] * vertices[1] + vy * vertices[0] + faces[0];
661         cone[0] = voffset + vertices[0] * vertices[1];
662         cone[1] = voffset;
663         cone[2] = voffset + vertices[0];
664         cone[3] = voffset + vertices[0] * vertices[1] + vertices[0];
665         PetscCall(DMPlexSetCone(dm, iface, cone));
666         PetscCall(DMSetLabelValue(dm, "marker", iface, markerRight));
667         PetscCall(DMSetLabelValue(dm, "marker", voffset + 0, markerRight));
668         PetscCall(DMSetLabelValue(dm, "marker", voffset + vertices[0] + 0, markerRight));
669         PetscCall(DMSetLabelValue(dm, "marker", voffset + vertices[0] * vertices[1] + 0, markerRight));
670         PetscCall(DMSetLabelValue(dm, "marker", voffset + vertices[0] * vertices[1] + vertices[0], markerRight));
671         iface++;
672       }
673     }
674   }
675   PetscCall(DMPlexSymmetrize(dm));
676   PetscCall(DMPlexStratify(dm));
677   /* Build coordinates */
678   PetscCall(DMSetCoordinateDim(dm, 3));
679   PetscCall(DMGetCoordinateSection(dm, &coordSection));
680   PetscCall(PetscSectionSetNumFields(coordSection, 1));
681   PetscCall(PetscSectionSetChart(coordSection, numFaces, numFaces + numVertices));
682   PetscCall(PetscSectionSetFieldComponents(coordSection, 0, 3));
683   for (v = numFaces; v < numFaces + numVertices; ++v) {
684     PetscCall(PetscSectionSetDof(coordSection, v, 3));
685     PetscCall(PetscSectionSetFieldDof(coordSection, v, 0, 3));
686   }
687   PetscCall(PetscSectionSetUp(coordSection));
688   PetscCall(PetscSectionGetStorageSize(coordSection, &coordSize));
689   PetscCall(VecCreate(PETSC_COMM_SELF, &coordinates));
690   PetscCall(PetscObjectSetName((PetscObject)coordinates, "coordinates"));
691   PetscCall(VecSetSizes(coordinates, coordSize, PETSC_DETERMINE));
692   PetscCall(VecSetBlockSize(coordinates, 3));
693   PetscCall(VecSetType(coordinates, VECSTANDARD));
694   PetscCall(VecGetArray(coordinates, &coords));
695   for (vz = 0; vz <= faces[2]; ++vz) {
696     for (vy = 0; vy <= faces[1]; ++vy) {
697       for (vx = 0; vx <= faces[0]; ++vx) {
698         coords[((vz * (faces[1] + 1) + vy) * (faces[0] + 1) + vx) * 3 + 0] = lower[0] + ((upper[0] - lower[0]) / faces[0]) * vx;
699         coords[((vz * (faces[1] + 1) + vy) * (faces[0] + 1) + vx) * 3 + 1] = lower[1] + ((upper[1] - lower[1]) / faces[1]) * vy;
700         coords[((vz * (faces[1] + 1) + vy) * (faces[0] + 1) + vx) * 3 + 2] = lower[2] + ((upper[2] - lower[2]) / faces[2]) * vz;
701       }
702     }
703   }
704   PetscCall(VecRestoreArray(coordinates, &coords));
705   PetscCall(DMSetCoordinatesLocal(dm, coordinates));
706   PetscCall(VecDestroy(&coordinates));
707   PetscFunctionReturn(PETSC_SUCCESS);
708 }
709 
710 static PetscErrorCode DMPlexCreateBoxSurfaceMesh_Internal(DM dm, PetscInt dim, const PetscInt faces[], const PetscReal lower[], const PetscReal upper[], PetscBool interpolate)
711 {
712   PetscFunctionBegin;
713   PetscValidLogicalCollectiveInt(dm, dim, 2);
714   PetscCall(PetscLogEventBegin(DMPLEX_Generate, dm, 0, 0, 0));
715   PetscCall(DMSetDimension(dm, dim - 1));
716   PetscCall(DMSetCoordinateDim(dm, dim));
717   switch (dim) {
718   case 1:
719     PetscCall(DMPlexCreateBoxSurfaceMesh_Tensor_1D_Internal(dm, lower, upper, faces));
720     break;
721   case 2:
722     PetscCall(DMPlexCreateBoxSurfaceMesh_Tensor_2D_Internal(dm, lower, upper, faces));
723     break;
724   case 3:
725     PetscCall(DMPlexCreateBoxSurfaceMesh_Tensor_3D_Internal(dm, lower, upper, faces));
726     break;
727   default:
728     SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Dimension not supported: %" PetscInt_FMT, dim);
729   }
730   PetscCall(PetscLogEventEnd(DMPLEX_Generate, dm, 0, 0, 0));
731   if (interpolate) PetscCall(DMPlexInterpolateInPlace_Internal(dm));
732   PetscFunctionReturn(PETSC_SUCCESS);
733 }
734 
735 /*@C
736   DMPlexCreateBoxSurfaceMesh - Creates a mesh on the surface of the tensor product of unit intervals (box) using tensor cells (hexahedra).
737 
738   Collective
739 
740   Input Parameters:
741 + comm        - The communicator for the `DM` object
742 . dim         - The spatial dimension of the box, so the resulting mesh is has dimension `dim`-1
743 . faces       - Number of faces per dimension, or `NULL` for (1,) in 1D and (2, 2) in 2D and (1, 1, 1) in 3D
744 . lower       - The lower left corner, or `NULL` for (0, 0, 0)
745 . upper       - The upper right corner, or `NULL` for (1, 1, 1)
746 - interpolate - Flag to create intermediate mesh pieces (edges, faces)
747 
748   Output Parameter:
749 . dm - The `DM` object
750 
751   Level: beginner
752 
753 .seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMSetFromOptions()`, `DMPlexCreateBoxMesh()`, `DMPlexCreateFromFile()`, `DMSetType()`, `DMCreate()`
754 @*/
755 PetscErrorCode DMPlexCreateBoxSurfaceMesh(MPI_Comm comm, PetscInt dim, const PetscInt faces[], const PetscReal lower[], const PetscReal upper[], PetscBool interpolate, DM *dm)
756 {
757   PetscInt  fac[3] = {1, 1, 1};
758   PetscReal low[3] = {0, 0, 0};
759   PetscReal upp[3] = {1, 1, 1};
760 
761   PetscFunctionBegin;
762   PetscCall(DMCreate(comm, dm));
763   PetscCall(DMSetType(*dm, DMPLEX));
764   PetscCall(DMPlexCreateBoxSurfaceMesh_Internal(*dm, dim, faces ? faces : fac, lower ? lower : low, upper ? upper : upp, interpolate));
765   PetscFunctionReturn(PETSC_SUCCESS);
766 }
767 
768 static PetscErrorCode DMPlexCreateLineMesh_Internal(DM dm, PetscInt segments, PetscReal lower, PetscReal upper, DMBoundaryType bd)
769 {
770   PetscInt     i, fStart, fEnd, numCells = 0, numVerts = 0;
771   PetscInt     numPoints[2], *coneSize, *cones, *coneOrientations;
772   PetscScalar *vertexCoords;
773   PetscReal    L, maxCell;
774   PetscBool    markerSeparate = PETSC_FALSE;
775   PetscInt     markerLeft = 1, faceMarkerLeft = 1;
776   PetscInt     markerRight = 1, faceMarkerRight = 2;
777   PetscBool    wrap = (bd == DM_BOUNDARY_PERIODIC || bd == DM_BOUNDARY_TWIST) ? PETSC_TRUE : PETSC_FALSE;
778   PetscMPIInt  rank;
779 
780   PetscFunctionBegin;
781   PetscAssertPointer(dm, 1);
782 
783   PetscCall(DMSetDimension(dm, 1));
784   PetscCall(DMCreateLabel(dm, "marker"));
785   PetscCall(DMCreateLabel(dm, "Face Sets"));
786 
787   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank));
788   if (rank == 0) numCells = segments;
789   if (rank == 0) numVerts = segments + (wrap ? 0 : 1);
790 
791   numPoints[0] = numVerts;
792   numPoints[1] = numCells;
793   PetscCall(PetscMalloc4(numCells + numVerts, &coneSize, numCells * 2, &cones, numCells + numVerts, &coneOrientations, numVerts, &vertexCoords));
794   PetscCall(PetscArrayzero(coneOrientations, numCells + numVerts));
795   for (i = 0; i < numCells; ++i) coneSize[i] = 2;
796   for (i = 0; i < numVerts; ++i) coneSize[numCells + i] = 0;
797   for (i = 0; i < numCells; ++i) {
798     cones[2 * i]     = numCells + i % numVerts;
799     cones[2 * i + 1] = numCells + (i + 1) % numVerts;
800   }
801   for (i = 0; i < numVerts; ++i) vertexCoords[i] = lower + (upper - lower) * ((PetscReal)i / (PetscReal)numCells);
802   PetscCall(DMPlexCreateFromDAG(dm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords));
803   PetscCall(PetscFree4(coneSize, cones, coneOrientations, vertexCoords));
804 
805   PetscCall(PetscOptionsGetBool(((PetscObject)dm)->options, ((PetscObject)dm)->prefix, "-dm_plex_separate_marker", &markerSeparate, NULL));
806   if (markerSeparate) {
807     markerLeft  = faceMarkerLeft;
808     markerRight = faceMarkerRight;
809   }
810   if (!wrap && rank == 0) {
811     PetscCall(DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd));
812     PetscCall(DMSetLabelValue(dm, "marker", fStart, markerLeft));
813     PetscCall(DMSetLabelValue(dm, "marker", fEnd - 1, markerRight));
814     PetscCall(DMSetLabelValue(dm, "Face Sets", fStart, faceMarkerLeft));
815     PetscCall(DMSetLabelValue(dm, "Face Sets", fEnd - 1, faceMarkerRight));
816   }
817   if (wrap) {
818     L       = upper - lower;
819     maxCell = (PetscReal)1.1 * (L / (PetscReal)PetscMax(1, segments));
820     PetscCall(DMSetPeriodicity(dm, &maxCell, &lower, &L));
821   }
822   PetscCall(DMPlexSetRefinementUniform(dm, PETSC_TRUE));
823   PetscFunctionReturn(PETSC_SUCCESS);
824 }
825 
826 static PetscErrorCode DMPlexCreateBoxMesh_Simplex_Internal(DM dm, PetscInt dim, const PetscInt faces[], const PetscReal lower[], const PetscReal upper[], const DMBoundaryType periodicity[], PetscBool interpolate)
827 {
828   DM      boundary, vol;
829   DMLabel bdlabel;
830 
831   PetscFunctionBegin;
832   PetscAssertPointer(dm, 1);
833   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");
834   PetscCall(DMCreate(PetscObjectComm((PetscObject)dm), &boundary));
835   PetscCall(DMSetType(boundary, DMPLEX));
836   PetscCall(DMPlexCreateBoxSurfaceMesh_Internal(boundary, dim, faces, lower, upper, PETSC_FALSE));
837   PetscCall(DMPlexGenerate(boundary, NULL, interpolate, &vol));
838   PetscCall(DMGetLabel(vol, "marker", &bdlabel));
839   if (bdlabel) PetscCall(DMPlexLabelComplete(vol, bdlabel));
840   PetscCall(DMPlexCopy_Internal(dm, PETSC_TRUE, PETSC_FALSE, vol));
841   PetscCall(DMPlexReplace_Internal(dm, &vol));
842   PetscCall(DMDestroy(&boundary));
843   PetscFunctionReturn(PETSC_SUCCESS);
844 }
845 
846 static PetscErrorCode DMPlexCreateCubeMesh_Internal(DM dm, const PetscReal lower[], const PetscReal upper[], const PetscInt edges[], DMBoundaryType bdX, DMBoundaryType bdY, DMBoundaryType bdZ)
847 {
848   DMLabel     cutLabel  = NULL;
849   PetscInt    markerTop = 1, faceMarkerTop = 1;
850   PetscInt    markerBottom = 1, faceMarkerBottom = 1;
851   PetscInt    markerFront = 1, faceMarkerFront = 1;
852   PetscInt    markerBack = 1, faceMarkerBack = 1;
853   PetscInt    markerRight = 1, faceMarkerRight = 1;
854   PetscInt    markerLeft = 1, faceMarkerLeft = 1;
855   PetscInt    dim;
856   PetscBool   markerSeparate = PETSC_FALSE, cutMarker = PETSC_FALSE;
857   PetscMPIInt rank;
858 
859   PetscFunctionBegin;
860   PetscCall(DMGetDimension(dm, &dim));
861   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank));
862   PetscCall(DMCreateLabel(dm, "marker"));
863   PetscCall(DMCreateLabel(dm, "Face Sets"));
864   PetscCall(PetscOptionsGetBool(((PetscObject)dm)->options, ((PetscObject)dm)->prefix, "-dm_plex_periodic_cut", &cutMarker, NULL));
865   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) {
866     if (cutMarker) {
867       PetscCall(DMCreateLabel(dm, "periodic_cut"));
868       PetscCall(DMGetLabel(dm, "periodic_cut", &cutLabel));
869     }
870   }
871   switch (dim) {
872   case 2:
873     faceMarkerTop    = 3;
874     faceMarkerBottom = 1;
875     faceMarkerRight  = 2;
876     faceMarkerLeft   = 4;
877     break;
878   case 3:
879     faceMarkerBottom = 1;
880     faceMarkerTop    = 2;
881     faceMarkerFront  = 3;
882     faceMarkerBack   = 4;
883     faceMarkerRight  = 5;
884     faceMarkerLeft   = 6;
885     break;
886   default:
887     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Dimension %" PetscInt_FMT " not supported", dim);
888   }
889   PetscCall(PetscOptionsGetBool(((PetscObject)dm)->options, ((PetscObject)dm)->prefix, "-dm_plex_separate_marker", &markerSeparate, NULL));
890   if (markerSeparate) {
891     markerBottom = faceMarkerBottom;
892     markerTop    = faceMarkerTop;
893     markerFront  = faceMarkerFront;
894     markerBack   = faceMarkerBack;
895     markerRight  = faceMarkerRight;
896     markerLeft   = faceMarkerLeft;
897   }
898   {
899     const PetscInt numXEdges    = rank == 0 ? edges[0] : 0;
900     const PetscInt numYEdges    = rank == 0 ? edges[1] : 0;
901     const PetscInt numZEdges    = rank == 0 ? edges[2] : 0;
902     const PetscInt numXVertices = rank == 0 ? (bdX == DM_BOUNDARY_PERIODIC || bdX == DM_BOUNDARY_TWIST ? edges[0] : edges[0] + 1) : 0;
903     const PetscInt numYVertices = rank == 0 ? (bdY == DM_BOUNDARY_PERIODIC || bdY == DM_BOUNDARY_TWIST ? edges[1] : edges[1] + 1) : 0;
904     const PetscInt numZVertices = rank == 0 ? (bdZ == DM_BOUNDARY_PERIODIC || bdZ == DM_BOUNDARY_TWIST ? edges[2] : edges[2] + 1) : 0;
905     const PetscInt numCells     = numXEdges * numYEdges * numZEdges;
906     const PetscInt numXFaces    = numYEdges * numZEdges;
907     const PetscInt numYFaces    = numXEdges * numZEdges;
908     const PetscInt numZFaces    = numXEdges * numYEdges;
909     const PetscInt numTotXFaces = numXVertices * numXFaces;
910     const PetscInt numTotYFaces = numYVertices * numYFaces;
911     const PetscInt numTotZFaces = numZVertices * numZFaces;
912     const PetscInt numFaces     = numTotXFaces + numTotYFaces + numTotZFaces;
913     const PetscInt numTotXEdges = numXEdges * numYVertices * numZVertices;
914     const PetscInt numTotYEdges = numYEdges * numXVertices * numZVertices;
915     const PetscInt numTotZEdges = numZEdges * numXVertices * numYVertices;
916     const PetscInt numVertices  = numXVertices * numYVertices * numZVertices;
917     const PetscInt numEdges     = numTotXEdges + numTotYEdges + numTotZEdges;
918     const PetscInt firstVertex  = (dim == 2) ? numFaces : numCells;
919     const PetscInt firstXFace   = (dim == 2) ? 0 : numCells + numVertices;
920     const PetscInt firstYFace   = firstXFace + numTotXFaces;
921     const PetscInt firstZFace   = firstYFace + numTotYFaces;
922     const PetscInt firstXEdge   = numCells + numFaces + numVertices;
923     const PetscInt firstYEdge   = firstXEdge + numTotXEdges;
924     const PetscInt firstZEdge   = firstYEdge + numTotYEdges;
925     Vec            coordinates;
926     PetscSection   coordSection;
927     PetscScalar   *coords;
928     PetscInt       coordSize;
929     PetscInt       v, vx, vy, vz;
930     PetscInt       c, f, fx, fy, fz, e, ex, ey, ez;
931 
932     PetscCall(DMPlexSetChart(dm, 0, numCells + numFaces + numEdges + numVertices));
933     for (c = 0; c < numCells; c++) PetscCall(DMPlexSetConeSize(dm, c, 6));
934     for (f = firstXFace; f < firstXFace + numFaces; ++f) PetscCall(DMPlexSetConeSize(dm, f, 4));
935     for (e = firstXEdge; e < firstXEdge + numEdges; ++e) PetscCall(DMPlexSetConeSize(dm, e, 2));
936     PetscCall(DMSetUp(dm)); /* Allocate space for cones */
937     /* Build cells */
938     for (fz = 0; fz < numZEdges; ++fz) {
939       for (fy = 0; fy < numYEdges; ++fy) {
940         for (fx = 0; fx < numXEdges; ++fx) {
941           PetscInt cell  = (fz * numYEdges + fy) * numXEdges + fx;
942           PetscInt faceB = firstZFace + (fy * numXEdges + fx) * numZVertices + fz;
943           PetscInt faceT = firstZFace + (fy * numXEdges + fx) * numZVertices + ((fz + 1) % numZVertices);
944           PetscInt faceF = firstYFace + (fz * numXEdges + fx) * numYVertices + fy;
945           PetscInt faceK = firstYFace + (fz * numXEdges + fx) * numYVertices + ((fy + 1) % numYVertices);
946           PetscInt faceL = firstXFace + (fz * numYEdges + fy) * numXVertices + fx;
947           PetscInt faceR = firstXFace + (fz * numYEdges + fy) * numXVertices + ((fx + 1) % numXVertices);
948           /* B,  T,  F,  K,  R,  L */
949           PetscInt ornt[6] = {-2, 0, 0, -3, 0, -2}; /* ??? */
950           PetscInt cone[6];
951 
952           /* no boundary twisting in 3D */
953           cone[0] = faceB;
954           cone[1] = faceT;
955           cone[2] = faceF;
956           cone[3] = faceK;
957           cone[4] = faceR;
958           cone[5] = faceL;
959           PetscCall(DMPlexSetCone(dm, cell, cone));
960           PetscCall(DMPlexSetConeOrientation(dm, cell, ornt));
961           if (bdX != DM_BOUNDARY_NONE && fx == numXEdges - 1 && cutLabel) PetscCall(DMLabelSetValue(cutLabel, cell, 2));
962           if (bdY != DM_BOUNDARY_NONE && fy == numYEdges - 1 && cutLabel) PetscCall(DMLabelSetValue(cutLabel, cell, 2));
963           if (bdZ != DM_BOUNDARY_NONE && fz == numZEdges - 1 && cutLabel) PetscCall(DMLabelSetValue(cutLabel, cell, 2));
964         }
965       }
966     }
967     /* Build x faces */
968     for (fz = 0; fz < numZEdges; ++fz) {
969       for (fy = 0; fy < numYEdges; ++fy) {
970         for (fx = 0; fx < numXVertices; ++fx) {
971           PetscInt face    = firstXFace + (fz * numYEdges + fy) * numXVertices + fx;
972           PetscInt edgeL   = firstZEdge + (fy * numXVertices + fx) * numZEdges + fz;
973           PetscInt edgeR   = firstZEdge + (((fy + 1) % numYVertices) * numXVertices + fx) * numZEdges + fz;
974           PetscInt edgeB   = firstYEdge + (fz * numXVertices + fx) * numYEdges + fy;
975           PetscInt edgeT   = firstYEdge + (((fz + 1) % numZVertices) * numXVertices + fx) * numYEdges + fy;
976           PetscInt ornt[4] = {0, 0, -1, -1};
977           PetscInt cone[4];
978 
979           if (dim == 3) {
980             /* markers */
981             if (bdX != DM_BOUNDARY_PERIODIC) {
982               if (fx == numXVertices - 1) {
983                 PetscCall(DMSetLabelValue(dm, "Face Sets", face, faceMarkerRight));
984                 PetscCall(DMSetLabelValue(dm, "marker", face, markerRight));
985               } else if (fx == 0) {
986                 PetscCall(DMSetLabelValue(dm, "Face Sets", face, faceMarkerLeft));
987                 PetscCall(DMSetLabelValue(dm, "marker", face, markerLeft));
988               }
989             }
990           }
991           cone[0] = edgeB;
992           cone[1] = edgeR;
993           cone[2] = edgeT;
994           cone[3] = edgeL;
995           PetscCall(DMPlexSetCone(dm, face, cone));
996           PetscCall(DMPlexSetConeOrientation(dm, face, ornt));
997         }
998       }
999     }
1000     /* Build y faces */
1001     for (fz = 0; fz < numZEdges; ++fz) {
1002       for (fx = 0; fx < numXEdges; ++fx) {
1003         for (fy = 0; fy < numYVertices; ++fy) {
1004           PetscInt face    = firstYFace + (fz * numXEdges + fx) * numYVertices + fy;
1005           PetscInt edgeL   = firstZEdge + (fy * numXVertices + fx) * numZEdges + fz;
1006           PetscInt edgeR   = firstZEdge + (fy * numXVertices + ((fx + 1) % numXVertices)) * numZEdges + fz;
1007           PetscInt edgeB   = firstXEdge + (fz * numYVertices + fy) * numXEdges + fx;
1008           PetscInt edgeT   = firstXEdge + (((fz + 1) % numZVertices) * numYVertices + fy) * numXEdges + fx;
1009           PetscInt ornt[4] = {0, 0, -1, -1};
1010           PetscInt cone[4];
1011 
1012           if (dim == 3) {
1013             /* markers */
1014             if (bdY != DM_BOUNDARY_PERIODIC) {
1015               if (fy == numYVertices - 1) {
1016                 PetscCall(DMSetLabelValue(dm, "Face Sets", face, faceMarkerBack));
1017                 PetscCall(DMSetLabelValue(dm, "marker", face, markerBack));
1018               } else if (fy == 0) {
1019                 PetscCall(DMSetLabelValue(dm, "Face Sets", face, faceMarkerFront));
1020                 PetscCall(DMSetLabelValue(dm, "marker", face, markerFront));
1021               }
1022             }
1023           }
1024           cone[0] = edgeB;
1025           cone[1] = edgeR;
1026           cone[2] = edgeT;
1027           cone[3] = edgeL;
1028           PetscCall(DMPlexSetCone(dm, face, cone));
1029           PetscCall(DMPlexSetConeOrientation(dm, face, ornt));
1030         }
1031       }
1032     }
1033     /* Build z faces */
1034     for (fy = 0; fy < numYEdges; ++fy) {
1035       for (fx = 0; fx < numXEdges; ++fx) {
1036         for (fz = 0; fz < numZVertices; fz++) {
1037           PetscInt face    = firstZFace + (fy * numXEdges + fx) * numZVertices + fz;
1038           PetscInt edgeL   = firstYEdge + (fz * numXVertices + fx) * numYEdges + fy;
1039           PetscInt edgeR   = firstYEdge + (fz * numXVertices + ((fx + 1) % numXVertices)) * numYEdges + fy;
1040           PetscInt edgeB   = firstXEdge + (fz * numYVertices + fy) * numXEdges + fx;
1041           PetscInt edgeT   = firstXEdge + (fz * numYVertices + ((fy + 1) % numYVertices)) * numXEdges + fx;
1042           PetscInt ornt[4] = {0, 0, -1, -1};
1043           PetscInt cone[4];
1044 
1045           if (dim == 2) {
1046             if (bdX == DM_BOUNDARY_TWIST && fx == numXEdges - 1) {
1047               edgeR += numYEdges - 1 - 2 * fy;
1048               ornt[1] = -1;
1049             }
1050             if (bdY == DM_BOUNDARY_TWIST && fy == numYEdges - 1) {
1051               edgeT += numXEdges - 1 - 2 * fx;
1052               ornt[2] = 0;
1053             }
1054             if (bdX != DM_BOUNDARY_NONE && fx == numXEdges - 1 && cutLabel) PetscCall(DMLabelSetValue(cutLabel, face, 2));
1055             if (bdY != DM_BOUNDARY_NONE && fy == numYEdges - 1 && cutLabel) PetscCall(DMLabelSetValue(cutLabel, face, 2));
1056           } else {
1057             /* markers */
1058             if (bdZ != DM_BOUNDARY_PERIODIC) {
1059               if (fz == numZVertices - 1) {
1060                 PetscCall(DMSetLabelValue(dm, "Face Sets", face, faceMarkerTop));
1061                 PetscCall(DMSetLabelValue(dm, "marker", face, markerTop));
1062               } else if (fz == 0) {
1063                 PetscCall(DMSetLabelValue(dm, "Face Sets", face, faceMarkerBottom));
1064                 PetscCall(DMSetLabelValue(dm, "marker", face, markerBottom));
1065               }
1066             }
1067           }
1068           cone[0] = edgeB;
1069           cone[1] = edgeR;
1070           cone[2] = edgeT;
1071           cone[3] = edgeL;
1072           PetscCall(DMPlexSetCone(dm, face, cone));
1073           PetscCall(DMPlexSetConeOrientation(dm, face, ornt));
1074         }
1075       }
1076     }
1077     /* Build Z edges*/
1078     for (vy = 0; vy < numYVertices; vy++) {
1079       for (vx = 0; vx < numXVertices; vx++) {
1080         for (ez = 0; ez < numZEdges; ez++) {
1081           const PetscInt edge    = firstZEdge + (vy * numXVertices + vx) * numZEdges + ez;
1082           const PetscInt vertexB = firstVertex + (ez * numYVertices + vy) * numXVertices + vx;
1083           const PetscInt vertexT = firstVertex + (((ez + 1) % numZVertices) * numYVertices + vy) * numXVertices + vx;
1084           PetscInt       cone[2];
1085 
1086           cone[0] = vertexB;
1087           cone[1] = vertexT;
1088           PetscCall(DMPlexSetCone(dm, edge, cone));
1089           if (dim == 3) {
1090             if (bdX != DM_BOUNDARY_PERIODIC) {
1091               if (vx == numXVertices - 1) {
1092                 PetscCall(DMSetLabelValue(dm, "marker", edge, markerRight));
1093                 PetscCall(DMSetLabelValue(dm, "marker", cone[0], markerRight));
1094                 if (ez == numZEdges - 1) PetscCall(DMSetLabelValue(dm, "marker", cone[1], markerRight));
1095               } else if (vx == 0) {
1096                 PetscCall(DMSetLabelValue(dm, "marker", edge, markerLeft));
1097                 PetscCall(DMSetLabelValue(dm, "marker", cone[0], markerLeft));
1098                 if (ez == numZEdges - 1) PetscCall(DMSetLabelValue(dm, "marker", cone[1], markerLeft));
1099               }
1100             }
1101             if (bdY != DM_BOUNDARY_PERIODIC) {
1102               if (vy == numYVertices - 1) {
1103                 PetscCall(DMSetLabelValue(dm, "marker", edge, markerBack));
1104                 PetscCall(DMSetLabelValue(dm, "marker", cone[0], markerBack));
1105                 if (ez == numZEdges - 1) PetscCall(DMSetLabelValue(dm, "marker", cone[1], markerBack));
1106               } else if (vy == 0) {
1107                 PetscCall(DMSetLabelValue(dm, "marker", edge, markerFront));
1108                 PetscCall(DMSetLabelValue(dm, "marker", cone[0], markerFront));
1109                 if (ez == numZEdges - 1) PetscCall(DMSetLabelValue(dm, "marker", cone[1], markerFront));
1110               }
1111             }
1112           }
1113         }
1114       }
1115     }
1116     /* Build Y edges*/
1117     for (vz = 0; vz < numZVertices; vz++) {
1118       for (vx = 0; vx < numXVertices; vx++) {
1119         for (ey = 0; ey < numYEdges; ey++) {
1120           const PetscInt nextv   = (dim == 2 && bdY == DM_BOUNDARY_TWIST && ey == numYEdges - 1) ? (numXVertices - vx - 1) : (vz * numYVertices + ((ey + 1) % numYVertices)) * numXVertices + vx;
1121           const PetscInt edge    = firstYEdge + (vz * numXVertices + vx) * numYEdges + ey;
1122           const PetscInt vertexF = firstVertex + (vz * numYVertices + ey) * numXVertices + vx;
1123           const PetscInt vertexK = firstVertex + nextv;
1124           PetscInt       cone[2];
1125 
1126           cone[0] = vertexF;
1127           cone[1] = vertexK;
1128           PetscCall(DMPlexSetCone(dm, edge, cone));
1129           if (dim == 2) {
1130             if ((bdX != DM_BOUNDARY_PERIODIC) && (bdX != DM_BOUNDARY_TWIST)) {
1131               if (vx == numXVertices - 1) {
1132                 PetscCall(DMSetLabelValue(dm, "Face Sets", edge, faceMarkerRight));
1133                 PetscCall(DMSetLabelValue(dm, "marker", edge, markerRight));
1134                 PetscCall(DMSetLabelValue(dm, "marker", cone[0], markerRight));
1135                 if (ey == numYEdges - 1) PetscCall(DMSetLabelValue(dm, "marker", cone[1], markerRight));
1136               } else if (vx == 0) {
1137                 PetscCall(DMSetLabelValue(dm, "Face Sets", edge, faceMarkerLeft));
1138                 PetscCall(DMSetLabelValue(dm, "marker", edge, markerLeft));
1139                 PetscCall(DMSetLabelValue(dm, "marker", cone[0], markerLeft));
1140                 if (ey == numYEdges - 1) PetscCall(DMSetLabelValue(dm, "marker", cone[1], markerLeft));
1141               }
1142             } else {
1143               if (vx == 0 && cutLabel) {
1144                 PetscCall(DMLabelSetValue(cutLabel, edge, 1));
1145                 PetscCall(DMLabelSetValue(cutLabel, cone[0], 1));
1146                 if (ey == numYEdges - 1) PetscCall(DMLabelSetValue(cutLabel, cone[1], 1));
1147               }
1148             }
1149           } else {
1150             if (bdX != DM_BOUNDARY_PERIODIC) {
1151               if (vx == numXVertices - 1) {
1152                 PetscCall(DMSetLabelValue(dm, "marker", edge, markerRight));
1153                 PetscCall(DMSetLabelValue(dm, "marker", cone[0], markerRight));
1154                 if (ey == numYEdges - 1) PetscCall(DMSetLabelValue(dm, "marker", cone[1], markerRight));
1155               } else if (vx == 0) {
1156                 PetscCall(DMSetLabelValue(dm, "marker", edge, markerLeft));
1157                 PetscCall(DMSetLabelValue(dm, "marker", cone[0], markerLeft));
1158                 if (ey == numYEdges - 1) PetscCall(DMSetLabelValue(dm, "marker", cone[1], markerLeft));
1159               }
1160             }
1161             if (bdZ != DM_BOUNDARY_PERIODIC) {
1162               if (vz == numZVertices - 1) {
1163                 PetscCall(DMSetLabelValue(dm, "marker", edge, markerTop));
1164                 PetscCall(DMSetLabelValue(dm, "marker", cone[0], markerTop));
1165                 if (ey == numYEdges - 1) PetscCall(DMSetLabelValue(dm, "marker", cone[1], markerTop));
1166               } else if (vz == 0) {
1167                 PetscCall(DMSetLabelValue(dm, "marker", edge, markerBottom));
1168                 PetscCall(DMSetLabelValue(dm, "marker", cone[0], markerBottom));
1169                 if (ey == numYEdges - 1) PetscCall(DMSetLabelValue(dm, "marker", cone[1], markerBottom));
1170               }
1171             }
1172           }
1173         }
1174       }
1175     }
1176     /* Build X edges*/
1177     for (vz = 0; vz < numZVertices; vz++) {
1178       for (vy = 0; vy < numYVertices; vy++) {
1179         for (ex = 0; ex < numXEdges; ex++) {
1180           const PetscInt nextv   = (dim == 2 && bdX == DM_BOUNDARY_TWIST && ex == numXEdges - 1) ? (numYVertices - vy - 1) * numXVertices : (vz * numYVertices + vy) * numXVertices + (ex + 1) % numXVertices;
1181           const PetscInt edge    = firstXEdge + (vz * numYVertices + vy) * numXEdges + ex;
1182           const PetscInt vertexL = firstVertex + (vz * numYVertices + vy) * numXVertices + ex;
1183           const PetscInt vertexR = firstVertex + nextv;
1184           PetscInt       cone[2];
1185 
1186           cone[0] = vertexL;
1187           cone[1] = vertexR;
1188           PetscCall(DMPlexSetCone(dm, edge, cone));
1189           if (dim == 2) {
1190             if ((bdY != DM_BOUNDARY_PERIODIC) && (bdY != DM_BOUNDARY_TWIST)) {
1191               if (vy == numYVertices - 1) {
1192                 PetscCall(DMSetLabelValue(dm, "Face Sets", edge, faceMarkerTop));
1193                 PetscCall(DMSetLabelValue(dm, "marker", edge, markerTop));
1194                 PetscCall(DMSetLabelValue(dm, "marker", cone[0], markerTop));
1195                 if (ex == numXEdges - 1) PetscCall(DMSetLabelValue(dm, "marker", cone[1], markerTop));
1196               } else if (vy == 0) {
1197                 PetscCall(DMSetLabelValue(dm, "Face Sets", edge, faceMarkerBottom));
1198                 PetscCall(DMSetLabelValue(dm, "marker", edge, markerBottom));
1199                 PetscCall(DMSetLabelValue(dm, "marker", cone[0], markerBottom));
1200                 if (ex == numXEdges - 1) PetscCall(DMSetLabelValue(dm, "marker", cone[1], markerBottom));
1201               }
1202             } else {
1203               if (vy == 0 && cutLabel) {
1204                 PetscCall(DMLabelSetValue(cutLabel, edge, 1));
1205                 PetscCall(DMLabelSetValue(cutLabel, cone[0], 1));
1206                 if (ex == numXEdges - 1) PetscCall(DMLabelSetValue(cutLabel, cone[1], 1));
1207               }
1208             }
1209           } else {
1210             if (bdY != DM_BOUNDARY_PERIODIC) {
1211               if (vy == numYVertices - 1) {
1212                 PetscCall(DMSetLabelValue(dm, "marker", edge, markerBack));
1213                 PetscCall(DMSetLabelValue(dm, "marker", cone[0], markerBack));
1214                 if (ex == numXEdges - 1) PetscCall(DMSetLabelValue(dm, "marker", cone[1], markerBack));
1215               } else if (vy == 0) {
1216                 PetscCall(DMSetLabelValue(dm, "marker", edge, markerFront));
1217                 PetscCall(DMSetLabelValue(dm, "marker", cone[0], markerFront));
1218                 if (ex == numXEdges - 1) PetscCall(DMSetLabelValue(dm, "marker", cone[1], markerFront));
1219               }
1220             }
1221             if (bdZ != DM_BOUNDARY_PERIODIC) {
1222               if (vz == numZVertices - 1) {
1223                 PetscCall(DMSetLabelValue(dm, "marker", edge, markerTop));
1224                 PetscCall(DMSetLabelValue(dm, "marker", cone[0], markerTop));
1225                 if (ex == numXEdges - 1) PetscCall(DMSetLabelValue(dm, "marker", cone[1], markerTop));
1226               } else if (vz == 0) {
1227                 PetscCall(DMSetLabelValue(dm, "marker", edge, markerBottom));
1228                 PetscCall(DMSetLabelValue(dm, "marker", cone[0], markerBottom));
1229                 if (ex == numXEdges - 1) PetscCall(DMSetLabelValue(dm, "marker", cone[1], markerBottom));
1230               }
1231             }
1232           }
1233         }
1234       }
1235     }
1236     PetscCall(DMPlexSymmetrize(dm));
1237     PetscCall(DMPlexStratify(dm));
1238     /* Build coordinates */
1239     PetscCall(DMGetCoordinateSection(dm, &coordSection));
1240     PetscCall(PetscSectionSetNumFields(coordSection, 1));
1241     PetscCall(PetscSectionSetFieldComponents(coordSection, 0, dim));
1242     PetscCall(PetscSectionSetChart(coordSection, firstVertex, firstVertex + numVertices));
1243     for (v = firstVertex; v < firstVertex + numVertices; ++v) {
1244       PetscCall(PetscSectionSetDof(coordSection, v, dim));
1245       PetscCall(PetscSectionSetFieldDof(coordSection, v, 0, dim));
1246     }
1247     PetscCall(PetscSectionSetUp(coordSection));
1248     PetscCall(PetscSectionGetStorageSize(coordSection, &coordSize));
1249     PetscCall(VecCreate(PETSC_COMM_SELF, &coordinates));
1250     PetscCall(PetscObjectSetName((PetscObject)coordinates, "coordinates"));
1251     PetscCall(VecSetSizes(coordinates, coordSize, PETSC_DETERMINE));
1252     PetscCall(VecSetBlockSize(coordinates, dim));
1253     PetscCall(VecSetType(coordinates, VECSTANDARD));
1254     PetscCall(VecGetArray(coordinates, &coords));
1255     for (vz = 0; vz < numZVertices; ++vz) {
1256       for (vy = 0; vy < numYVertices; ++vy) {
1257         for (vx = 0; vx < numXVertices; ++vx) {
1258           coords[((vz * numYVertices + vy) * numXVertices + vx) * dim + 0] = lower[0] + ((upper[0] - lower[0]) / numXEdges) * vx;
1259           coords[((vz * numYVertices + vy) * numXVertices + vx) * dim + 1] = lower[1] + ((upper[1] - lower[1]) / numYEdges) * vy;
1260           if (dim == 3) coords[((vz * numYVertices + vy) * numXVertices + vx) * dim + 2] = lower[2] + ((upper[2] - lower[2]) / numZEdges) * vz;
1261         }
1262       }
1263     }
1264     PetscCall(VecRestoreArray(coordinates, &coords));
1265     PetscCall(DMSetCoordinatesLocal(dm, coordinates));
1266     PetscCall(VecDestroy(&coordinates));
1267   }
1268   PetscFunctionReturn(PETSC_SUCCESS);
1269 }
1270 
1271 static PetscErrorCode DMPlexCreateBoxMesh_Tensor_Internal(DM dm, PetscInt dim, const PetscInt faces[], const PetscReal lower[], const PetscReal upper[], const DMBoundaryType periodicity[])
1272 {
1273   DMBoundaryType bdt[3] = {DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE};
1274   PetscInt       fac[3] = {0, 0, 0}, d;
1275 
1276   PetscFunctionBegin;
1277   PetscAssertPointer(dm, 1);
1278   PetscValidLogicalCollectiveInt(dm, dim, 2);
1279   PetscCall(DMSetDimension(dm, dim));
1280   for (d = 0; d < dim; ++d) {
1281     fac[d] = faces[d];
1282     bdt[d] = periodicity[d];
1283   }
1284   PetscCall(DMPlexCreateCubeMesh_Internal(dm, lower, upper, fac, bdt[0], bdt[1], bdt[2]));
1285   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))) {
1286     PetscReal L[3]       = {-1., -1., 0.};
1287     PetscReal maxCell[3] = {-1., -1., 0.};
1288 
1289     for (d = 0; d < dim; ++d) {
1290       if (periodicity[d] != DM_BOUNDARY_NONE) {
1291         L[d]       = upper[d] - lower[d];
1292         maxCell[d] = 1.1 * (L[d] / PetscMax(1, faces[d]));
1293       }
1294     }
1295     PetscCall(DMSetPeriodicity(dm, maxCell, lower, L));
1296   }
1297   PetscCall(DMPlexSetRefinementUniform(dm, PETSC_TRUE));
1298   PetscFunctionReturn(PETSC_SUCCESS);
1299 }
1300 
1301 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)
1302 {
1303   PetscFunctionBegin;
1304   PetscCall(PetscLogEventBegin(DMPLEX_Generate, dm, 0, 0, 0));
1305   if (shape == DM_SHAPE_ZBOX) PetscCall(DMPlexCreateBoxMesh_Tensor_SFC_Internal(dm, dim, faces, lower, upper, periodicity, interpolate));
1306   else if (dim == 1) PetscCall(DMPlexCreateLineMesh_Internal(dm, faces[0], lower[0], upper[0], periodicity[0]));
1307   else if (simplex) PetscCall(DMPlexCreateBoxMesh_Simplex_Internal(dm, dim, faces, lower, upper, periodicity, interpolate));
1308   else PetscCall(DMPlexCreateBoxMesh_Tensor_Internal(dm, dim, faces, lower, upper, periodicity));
1309   if (!interpolate && dim > 1 && !simplex) {
1310     DM udm;
1311 
1312     PetscCall(DMPlexUninterpolate(dm, &udm));
1313     PetscCall(DMPlexCopyCoordinates(dm, udm));
1314     PetscCall(DMPlexReplace_Internal(dm, &udm));
1315   }
1316   PetscCall(PetscLogEventEnd(DMPLEX_Generate, dm, 0, 0, 0));
1317   PetscFunctionReturn(PETSC_SUCCESS);
1318 }
1319 
1320 /*@C
1321   DMPlexCreateBoxMesh - Creates a mesh on the tensor product of unit intervals (box) using simplices or tensor cells (hexahedra).
1322 
1323   Collective
1324 
1325   Input Parameters:
1326 + comm        - The communicator for the `DM` object
1327 . dim         - The spatial dimension
1328 . simplex     - `PETSC_TRUE` for simplices, `PETSC_FALSE` for tensor cells
1329 . faces       - Number of faces per dimension, or `NULL` for (1,) in 1D and (2, 2) in 2D and (1, 1, 1) in 3D
1330 . lower       - The lower left corner, or `NULL` for (0, 0, 0)
1331 . upper       - The upper right corner, or `NULL` for (1, 1, 1)
1332 . periodicity - The boundary type for the X,Y,Z direction, or `NULL` for `DM_BOUNDARY_NONE`
1333 - interpolate - Flag to create intermediate mesh pieces (edges, faces)
1334 
1335   Output Parameter:
1336 . dm - The `DM` object
1337 
1338   Level: beginner
1339 
1340   Note:
1341   To customize this mesh using options, use
1342 .vb
1343   DMCreate(comm, &dm);
1344   DMSetType(dm, DMPLEX);
1345   DMSetFromOptions(dm);
1346 .ve
1347   and use the options in `DMSetFromOptions()`.
1348 
1349   Here is the numbering returned for 2 faces in each direction for tensor cells\:
1350 .vb
1351  10---17---11---18----12
1352   |         |         |
1353   |         |         |
1354  20    2   22    3    24
1355   |         |         |
1356   |         |         |
1357   7---15----8---16----9
1358   |         |         |
1359   |         |         |
1360  19    0   21    1   23
1361   |         |         |
1362   |         |         |
1363   4---13----5---14----6
1364 .ve
1365   and for simplicial cells
1366 .vb
1367  14----8---15----9----16
1368   |\     5  |\      7 |
1369   | \       | \       |
1370  13   2    14    3    15
1371   | 4   \   | 6   \   |
1372   |       \ |       \ |
1373  11----6---12----7----13
1374   |\        |\        |
1375   | \    1  | \     3 |
1376  10   0    11    1    12
1377   | 0   \   | 2   \   |
1378   |       \ |       \ |
1379   8----4----9----5----10
1380 .ve
1381 
1382 .seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMSetFromOptions()`, `DMPlexCreateFromFile()`, `DMPlexCreateHexCylinderMesh()`, `DMSetType()`, `DMCreate()`
1383 @*/
1384 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)
1385 {
1386   PetscInt       fac[3] = {1, 1, 1};
1387   PetscReal      low[3] = {0, 0, 0};
1388   PetscReal      upp[3] = {1, 1, 1};
1389   DMBoundaryType bdt[3] = {DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE};
1390 
1391   PetscFunctionBegin;
1392   PetscCall(DMCreate(comm, dm));
1393   PetscCall(DMSetType(*dm, DMPLEX));
1394   PetscCall(DMPlexCreateBoxMesh_Internal(*dm, DM_SHAPE_BOX, dim, simplex, faces ? faces : fac, lower ? lower : low, upper ? upper : upp, periodicity ? periodicity : bdt, interpolate));
1395   if (periodicity) PetscCall(DMLocalizeCoordinates(*dm));
1396   PetscFunctionReturn(PETSC_SUCCESS);
1397 }
1398 
1399 static PetscErrorCode DMPlexCreateWedgeBoxMesh_Internal(DM dm, const PetscInt faces[], const PetscReal lower[], const PetscReal upper[], const DMBoundaryType periodicity[])
1400 {
1401   DM       bdm, vol;
1402   PetscInt i;
1403 
1404   PetscFunctionBegin;
1405   // TODO Now we can support periodicity
1406   for (i = 0; i < 3; ++i) PetscCheck(periodicity[i] == DM_BOUNDARY_NONE, PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Periodicity not yet supported");
1407   PetscCall(DMCreate(PetscObjectComm((PetscObject)dm), &bdm));
1408   PetscCall(DMSetType(bdm, DMPLEX));
1409   PetscCall(DMSetDimension(bdm, 2));
1410   PetscCall(PetscLogEventBegin(DMPLEX_Generate, bdm, 0, 0, 0));
1411   PetscCall(DMPlexCreateBoxMesh_Simplex_Internal(bdm, 2, faces, lower, upper, periodicity, PETSC_TRUE));
1412   PetscCall(DMPlexExtrude(bdm, faces[2], upper[2] - lower[2], PETSC_TRUE, PETSC_FALSE, PETSC_FALSE, NULL, NULL, &vol));
1413   PetscCall(PetscLogEventEnd(DMPLEX_Generate, bdm, 0, 0, 0));
1414   PetscCall(DMDestroy(&bdm));
1415   PetscCall(DMPlexReplace_Internal(dm, &vol));
1416   if (lower[2] != 0.0) {
1417     Vec          v;
1418     PetscScalar *x;
1419     PetscInt     cDim, n;
1420 
1421     PetscCall(DMGetCoordinatesLocal(dm, &v));
1422     PetscCall(VecGetBlockSize(v, &cDim));
1423     PetscCall(VecGetLocalSize(v, &n));
1424     PetscCall(VecGetArray(v, &x));
1425     x += cDim;
1426     for (i = 0; i < n; i += cDim) x[i] += lower[2];
1427     PetscCall(VecRestoreArray(v, &x));
1428     PetscCall(DMSetCoordinatesLocal(dm, v));
1429   }
1430   PetscFunctionReturn(PETSC_SUCCESS);
1431 }
1432 
1433 /*@
1434   DMPlexCreateWedgeBoxMesh - Creates a 3-D mesh tesselating the (x,y) plane and extruding in the third direction using wedge cells.
1435 
1436   Collective
1437 
1438   Input Parameters:
1439 + comm        - The communicator for the `DM` object
1440 . faces       - Number of faces per dimension, or `NULL` for (1, 1, 1)
1441 . lower       - The lower left corner, or `NULL` for (0, 0, 0)
1442 . upper       - The upper right corner, or `NULL` for (1, 1, 1)
1443 . periodicity - The boundary type for the X,Y,Z direction, or `NULL` for `DM_BOUNDARY_NONE`
1444 . orderHeight - If `PETSC_TRUE`, orders the extruded cells in the height first. Otherwise, orders the cell on the layers first
1445 - interpolate - Flag to create intermediate mesh pieces (edges, faces)
1446 
1447   Output Parameter:
1448 . dm - The `DM` object
1449 
1450   Level: beginner
1451 
1452 .seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexCreateHexCylinderMesh()`, `DMPlexCreateWedgeCylinderMesh()`, `DMExtrude()`, `DMPlexCreateBoxMesh()`, `DMSetType()`, `DMCreate()`
1453 @*/
1454 PetscErrorCode DMPlexCreateWedgeBoxMesh(MPI_Comm comm, const PetscInt faces[], const PetscReal lower[], const PetscReal upper[], const DMBoundaryType periodicity[], PetscBool orderHeight, PetscBool interpolate, DM *dm)
1455 {
1456   PetscInt       fac[3] = {1, 1, 1};
1457   PetscReal      low[3] = {0, 0, 0};
1458   PetscReal      upp[3] = {1, 1, 1};
1459   DMBoundaryType bdt[3] = {DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE};
1460 
1461   PetscFunctionBegin;
1462   PetscCall(DMCreate(comm, dm));
1463   PetscCall(DMSetType(*dm, DMPLEX));
1464   PetscCall(DMPlexCreateWedgeBoxMesh_Internal(*dm, faces ? faces : fac, lower ? lower : low, upper ? upper : upp, periodicity ? periodicity : bdt));
1465   if (!interpolate) {
1466     DM udm;
1467 
1468     PetscCall(DMPlexUninterpolate(*dm, &udm));
1469     PetscCall(DMPlexReplace_Internal(*dm, &udm));
1470   }
1471   if (periodicity) PetscCall(DMLocalizeCoordinates(*dm));
1472   PetscFunctionReturn(PETSC_SUCCESS);
1473 }
1474 
1475 /*
1476   DMPlexTensorPointLexicographic_Private - Returns all tuples of size 'len' with nonnegative integers that are all less than or equal to 'max' for that dimension.
1477 
1478   Input Parameters:
1479 + len - The length of the tuple
1480 . max - The maximum for each dimension, so values are in [0, max)
1481 - tup - A tuple of length len+1: tup[len] > 0 indicates a stopping condition
1482 
1483   Output Parameter:
1484 . tup - A tuple of `len` integers whose entries are at most `max`
1485 
1486   Level: developer
1487 
1488   Note:
1489   Ordering is lexicographic with lowest index as least significant in ordering.
1490   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}.
1491 
1492 .seealso: PetscDualSpaceTensorPointLexicographic_Internal(), PetscDualSpaceLatticePointLexicographic_Internal()
1493 */
1494 static PetscErrorCode DMPlexTensorPointLexicographic_Private(PetscInt len, const PetscInt max[], PetscInt tup[])
1495 {
1496   PetscInt i;
1497 
1498   PetscFunctionBegin;
1499   for (i = 0; i < len; ++i) {
1500     if (tup[i] < max[i] - 1) {
1501       break;
1502     } else {
1503       tup[i] = 0;
1504     }
1505   }
1506   if (i == len) tup[i - 1] = max[i - 1];
1507   else ++tup[i];
1508   PetscFunctionReturn(PETSC_SUCCESS);
1509 }
1510 
1511 static PetscInt TupleToIndex_Private(PetscInt len, const PetscInt max[], const PetscInt tup[])
1512 {
1513   PetscInt i, idx = tup[len - 1];
1514 
1515   for (i = len - 2; i >= 0; --i) {
1516     idx *= max[i];
1517     idx += tup[i];
1518   }
1519   return idx;
1520 }
1521 
1522 static PetscErrorCode DestroyExtent_Private(void *extent)
1523 {
1524   return PetscFree(extent);
1525 }
1526 
1527 static PetscErrorCode DMPlexCreateHypercubicMesh_Internal(DM dm, PetscInt dim, const PetscReal lower[], const PetscReal upper[], const PetscInt edges[], const DMBoundaryType bd[])
1528 {
1529   Vec          coordinates;
1530   PetscSection coordSection;
1531   DMLabel      cutLabel    = NULL;
1532   PetscBool    cutMarker   = PETSC_FALSE;
1533   PetscBool    periodic    = PETSC_FALSE;
1534   PetscInt     numCells    = 1, c;
1535   PetscInt     numVertices = 1, v;
1536   PetscScalar *coords;
1537   PetscInt    *vertices, *vert, *vtmp, *supp, cone[2];
1538   PetscInt     d, e, cell = 0, coordSize;
1539   PetscMPIInt  rank;
1540 
1541   PetscFunctionBegin;
1542   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank));
1543   PetscCall(DMSetDimension(dm, dim));
1544   PetscCall(PetscCalloc4(dim, &vertices, dim, &vert, dim, &vtmp, 2 * dim, &supp));
1545   PetscCall(DMCreateLabel(dm, "marker"));
1546   PetscCall(PetscOptionsGetBool(((PetscObject)dm)->options, ((PetscObject)dm)->prefix, "-dm_plex_periodic_cut", &cutMarker, NULL));
1547   for (d = 0; d < dim; ++d) periodic = (periodic || bd[d] == DM_BOUNDARY_PERIODIC) ? PETSC_TRUE : PETSC_FALSE;
1548   if (periodic && cutMarker) {
1549     PetscCall(DMCreateLabel(dm, "periodic_cut"));
1550     PetscCall(DMGetLabel(dm, "periodic_cut", &cutLabel));
1551   }
1552   for (d = 0; d < dim; ++d) PetscCheck(bd[d] == DM_BOUNDARY_PERIODIC, PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Hypercubic mesh must be periodic now");
1553   for (d = 0; d < dim; ++d) {
1554     vertices[d] = edges[d];
1555     numVertices *= vertices[d];
1556   }
1557   numCells = numVertices * dim;
1558   PetscCall(DMPlexSetChart(dm, 0, numCells + numVertices));
1559   for (c = 0; c < numCells; ++c) PetscCall(DMPlexSetConeSize(dm, c, 2));
1560   for (v = numCells; v < numCells + numVertices; ++v) PetscCall(DMPlexSetSupportSize(dm, v, 2 * dim));
1561   /* TODO Loop over boundary and reset support sizes */
1562   PetscCall(DMSetUp(dm)); /* Allocate space for cones and supports */
1563   /* Build cell cones and vertex supports */
1564   PetscCall(DMCreateLabel(dm, "celltype"));
1565   while (vert[dim - 1] < vertices[dim - 1]) {
1566     const PetscInt vertex = TupleToIndex_Private(dim, vertices, vert) + numCells;
1567     PetscInt       s      = 0;
1568 
1569     PetscCall(PetscPrintf(PETSC_COMM_SELF, "Vertex %" PetscInt_FMT ":", vertex));
1570     for (d = 0; d < dim; ++d) PetscCall(PetscPrintf(PETSC_COMM_SELF, " %" PetscInt_FMT, vert[d]));
1571     PetscCall(PetscPrintf(PETSC_COMM_SELF, "\n"));
1572     PetscCall(DMPlexSetCellType(dm, vertex, DM_POLYTOPE_POINT));
1573     for (d = 0; d < dim; ++d) {
1574       for (e = 0; e < dim; ++e) vtmp[e] = vert[e];
1575       vtmp[d] = (vert[d] + 1) % vertices[d];
1576       cone[0] = vertex;
1577       cone[1] = TupleToIndex_Private(dim, vertices, vtmp) + numCells;
1578       PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Vertex %" PetscInt_FMT ":", cone[1]));
1579       for (e = 0; e < dim; ++e) PetscCall(PetscPrintf(PETSC_COMM_SELF, " %" PetscInt_FMT, vtmp[e]));
1580       PetscCall(PetscPrintf(PETSC_COMM_SELF, "\n"));
1581       PetscCall(DMPlexSetCone(dm, cell, cone));
1582       PetscCall(DMPlexSetCellType(dm, cell, DM_POLYTOPE_SEGMENT));
1583       PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Edge %" PetscInt_FMT " (%" PetscInt_FMT " %" PetscInt_FMT ")\n", cell, cone[0], cone[1]));
1584       ++cell;
1585     }
1586     for (d = 0; d < dim; ++d) {
1587       for (e = 0; e < dim; ++e) vtmp[e] = vert[e];
1588       vtmp[d]   = (vert[d] + vertices[d] - 1) % vertices[d];
1589       supp[s++] = TupleToIndex_Private(dim, vertices, vtmp) * dim + d;
1590       supp[s++] = (vertex - numCells) * dim + d;
1591       PetscCall(DMPlexSetSupport(dm, vertex, supp));
1592     }
1593     PetscCall(DMPlexTensorPointLexicographic_Private(dim, vertices, vert));
1594   }
1595   PetscCall(DMPlexStratify(dm));
1596   /* Build coordinates */
1597   PetscCall(DMGetCoordinateSection(dm, &coordSection));
1598   PetscCall(PetscSectionSetNumFields(coordSection, 1));
1599   PetscCall(PetscSectionSetFieldComponents(coordSection, 0, dim));
1600   PetscCall(PetscSectionSetChart(coordSection, numCells, numCells + numVertices));
1601   for (v = numCells; v < numCells + numVertices; ++v) {
1602     PetscCall(PetscSectionSetDof(coordSection, v, dim));
1603     PetscCall(PetscSectionSetFieldDof(coordSection, v, 0, dim));
1604   }
1605   PetscCall(PetscSectionSetUp(coordSection));
1606   PetscCall(PetscSectionGetStorageSize(coordSection, &coordSize));
1607   PetscCall(VecCreate(PETSC_COMM_SELF, &coordinates));
1608   PetscCall(PetscObjectSetName((PetscObject)coordinates, "coordinates"));
1609   PetscCall(VecSetSizes(coordinates, coordSize, PETSC_DETERMINE));
1610   PetscCall(VecSetBlockSize(coordinates, dim));
1611   PetscCall(VecSetType(coordinates, VECSTANDARD));
1612   PetscCall(VecGetArray(coordinates, &coords));
1613   for (d = 0; d < dim; ++d) vert[d] = 0;
1614   while (vert[dim - 1] < vertices[dim - 1]) {
1615     const PetscInt vertex = TupleToIndex_Private(dim, vertices, vert);
1616 
1617     for (d = 0; d < dim; ++d) coords[vertex * dim + d] = lower[d] + ((upper[d] - lower[d]) / vertices[d]) * vert[d];
1618     PetscCall(PetscPrintf(PETSC_COMM_SELF, "Vertex %" PetscInt_FMT ":", vertex));
1619     for (d = 0; d < dim; ++d) PetscCall(PetscPrintf(PETSC_COMM_SELF, " %" PetscInt_FMT, vert[d]));
1620     for (d = 0; d < dim; ++d) PetscCall(PetscPrintf(PETSC_COMM_SELF, " %g", (double)PetscRealPart(coords[vertex * dim + d])));
1621     PetscCall(PetscPrintf(PETSC_COMM_SELF, "\n"));
1622     PetscCall(DMPlexTensorPointLexicographic_Private(dim, vertices, vert));
1623   }
1624   PetscCall(VecRestoreArray(coordinates, &coords));
1625   PetscCall(DMSetCoordinatesLocal(dm, coordinates));
1626   PetscCall(VecDestroy(&coordinates));
1627   PetscCall(PetscFree4(vertices, vert, vtmp, supp));
1628   //PetscCall(DMSetPeriodicity(dm, NULL, lower, upper));
1629   // Attach the extent
1630   {
1631     PetscContainer c;
1632     PetscInt      *extent;
1633 
1634     PetscCall(PetscMalloc1(dim, &extent));
1635     for (PetscInt d = 0; d < dim; ++d) extent[d] = edges[d];
1636     PetscCall(PetscContainerCreate(PETSC_COMM_SELF, &c));
1637     PetscCall(PetscContainerSetUserDestroy(c, DestroyExtent_Private));
1638     PetscCall(PetscContainerSetPointer(c, extent));
1639     PetscCall(PetscObjectCompose((PetscObject)dm, "_extent", (PetscObject)c));
1640     PetscCall(PetscContainerDestroy(&c));
1641   }
1642   PetscFunctionReturn(PETSC_SUCCESS);
1643 }
1644 
1645 /*@C
1646   DMPlexCreateHypercubicMesh - Creates a periodic mesh on the tensor product of unit intervals using only vertices and edges.
1647 
1648   Collective
1649 
1650   Input Parameters:
1651 + comm  - The communicator for the DM object
1652 . dim   - The spatial dimension
1653 . edges - Number of edges per dimension, or `NULL` for (1,) in 1D and (2, 2) in 2D and (1, 1, 1) in 3D
1654 . lower - The lower left corner, or `NULL` for (0, 0, 0)
1655 - upper - The upper right corner, or `NULL` for (1, 1, 1)
1656 
1657   Output Parameter:
1658 . dm - The DM object
1659 
1660   Level: beginner
1661 
1662   Note:
1663   If you want to customize this mesh using options, you just need to
1664 .vb
1665   DMCreate(comm, &dm);
1666   DMSetType(dm, DMPLEX);
1667   DMSetFromOptions(dm);
1668 .ve
1669   and use the options on the `DMSetFromOptions()` page.
1670 
1671   The vertices are numbered is lexicographic order, and the dim edges exiting a vertex in the positive orthant are number consecutively,
1672 .vb
1673  18--0-19--2-20--4-18
1674   |     |     |     |
1675  13    15    17    13
1676   |     |     |     |
1677  24-12-25-14-26-16-24
1678   |     |     |     |
1679   7     9    11     7
1680   |     |     |     |
1681  21--6-22--8-23-10-21
1682   |     |     |     |
1683   1     3     5     1
1684   |     |     |     |
1685  18--0-19--2-20--4-18
1686 .ve
1687 
1688 .seealso: `DMSetFromOptions()`, `DMPlexCreateFromFile()`, `DMPlexCreateHexCylinderMesh()`, `DMSetType()`, `DMCreate()`
1689 @*/
1690 PetscErrorCode DMPlexCreateHypercubicMesh(MPI_Comm comm, PetscInt dim, const PetscInt edges[], const PetscReal lower[], const PetscReal upper[], DM *dm)
1691 {
1692   PetscInt       *edg;
1693   PetscReal      *low, *upp;
1694   DMBoundaryType *bdt;
1695   PetscInt        d;
1696 
1697   PetscFunctionBegin;
1698   PetscCall(DMCreate(comm, dm));
1699   PetscCall(DMSetType(*dm, DMPLEX));
1700   PetscCall(PetscMalloc4(dim, &edg, dim, &low, dim, &upp, dim, &bdt));
1701   for (d = 0; d < dim; ++d) {
1702     edg[d] = edges ? edges[d] : 1;
1703     low[d] = lower ? lower[d] : 0.;
1704     upp[d] = upper ? upper[d] : 1.;
1705     bdt[d] = DM_BOUNDARY_PERIODIC;
1706   }
1707   PetscCall(DMPlexCreateHypercubicMesh_Internal(*dm, dim, low, upp, edg, bdt));
1708   PetscCall(PetscFree4(edg, low, upp, bdt));
1709   PetscFunctionReturn(PETSC_SUCCESS);
1710 }
1711 
1712 /*@C
1713   DMPlexSetOptionsPrefix - Sets the prefix used for searching for all `DM` options in the database.
1714 
1715   Logically Collective
1716 
1717   Input Parameters:
1718 + dm     - the `DM` context
1719 - prefix - the prefix to prepend to all option names
1720 
1721   Level: advanced
1722 
1723   Note:
1724   A hyphen (-) must NOT be given at the beginning of the prefix name.
1725   The first character of all runtime options is AUTOMATICALLY the hyphen.
1726 
1727 .seealso: [](ch_unstructured), `DM`, `DMPLEX`, `SNESSetFromOptions()`
1728 @*/
1729 PetscErrorCode DMPlexSetOptionsPrefix(DM dm, const char prefix[])
1730 {
1731   DM_Plex *mesh = (DM_Plex *)dm->data;
1732 
1733   PetscFunctionBegin;
1734   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1735   PetscCall(PetscObjectSetOptionsPrefix((PetscObject)dm, prefix));
1736   PetscCall(PetscObjectSetOptionsPrefix((PetscObject)mesh->partitioner, prefix));
1737   PetscFunctionReturn(PETSC_SUCCESS);
1738 }
1739 
1740 /* Remap geometry to cylinder
1741    TODO: This only works for a single refinement, then it is broken
1742 
1743      Interior square: Linear interpolation is correct
1744      The other cells all have vertices on rays from the origin. We want to uniformly expand the spacing
1745      such that the last vertex is on the unit circle. So the closest and farthest vertices are at distance
1746 
1747        phi     = arctan(y/x)
1748        d_close = sqrt(1/8 + 1/4 sin^2(phi))
1749        d_far   = sqrt(1/2 + sin^2(phi))
1750 
1751      so we remap them using
1752 
1753        x_new = x_close + (x - x_close) (1 - d_close) / (d_far - d_close)
1754        y_new = y_close + (y - y_close) (1 - d_close) / (d_far - d_close)
1755 
1756      If pi/4 < phi < 3pi/4 or -3pi/4 < phi < -pi/4, then we switch x and y.
1757 */
1758 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[])
1759 {
1760   const PetscReal dis = 1.0 / PetscSqrtReal(2.0);
1761   const PetscReal ds2 = 0.5 * dis;
1762 
1763   if ((PetscAbsScalar(u[0]) <= ds2) && (PetscAbsScalar(u[1]) <= ds2)) {
1764     f0[0] = u[0];
1765     f0[1] = u[1];
1766   } else {
1767     PetscReal phi, sinp, cosp, dc, df, x, y, xc, yc;
1768 
1769     x    = PetscRealPart(u[0]);
1770     y    = PetscRealPart(u[1]);
1771     phi  = PetscAtan2Real(y, x);
1772     sinp = PetscSinReal(phi);
1773     cosp = PetscCosReal(phi);
1774     if ((PetscAbsReal(phi) > PETSC_PI / 4.0) && (PetscAbsReal(phi) < 3.0 * PETSC_PI / 4.0)) {
1775       dc = PetscAbsReal(ds2 / sinp);
1776       df = PetscAbsReal(dis / sinp);
1777       xc = ds2 * x / PetscAbsReal(y);
1778       yc = ds2 * PetscSignReal(y);
1779     } else {
1780       dc = PetscAbsReal(ds2 / cosp);
1781       df = PetscAbsReal(dis / cosp);
1782       xc = ds2 * PetscSignReal(x);
1783       yc = ds2 * y / PetscAbsReal(x);
1784     }
1785     f0[0] = xc + (u[0] - xc) * (1.0 - dc) / (df - dc);
1786     f0[1] = yc + (u[1] - yc) * (1.0 - dc) / (df - dc);
1787   }
1788   f0[2] = u[2];
1789 }
1790 
1791 static PetscErrorCode DMPlexCreateHexCylinderMesh_Internal(DM dm, DMBoundaryType periodicZ)
1792 {
1793   const PetscInt dim = 3;
1794   PetscInt       numCells, numVertices;
1795   PetscMPIInt    rank;
1796 
1797   PetscFunctionBegin;
1798   PetscCall(PetscLogEventBegin(DMPLEX_Generate, dm, 0, 0, 0));
1799   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank));
1800   PetscCall(DMSetDimension(dm, dim));
1801   /* Create topology */
1802   {
1803     PetscInt cone[8], c;
1804 
1805     numCells    = rank == 0 ? 5 : 0;
1806     numVertices = rank == 0 ? 16 : 0;
1807     if (periodicZ == DM_BOUNDARY_PERIODIC) {
1808       numCells *= 3;
1809       numVertices = rank == 0 ? 24 : 0;
1810     }
1811     PetscCall(DMPlexSetChart(dm, 0, numCells + numVertices));
1812     for (c = 0; c < numCells; c++) PetscCall(DMPlexSetConeSize(dm, c, 8));
1813     PetscCall(DMSetUp(dm));
1814     if (rank == 0) {
1815       if (periodicZ == DM_BOUNDARY_PERIODIC) {
1816         cone[0] = 15;
1817         cone[1] = 18;
1818         cone[2] = 17;
1819         cone[3] = 16;
1820         cone[4] = 31;
1821         cone[5] = 32;
1822         cone[6] = 33;
1823         cone[7] = 34;
1824         PetscCall(DMPlexSetCone(dm, 0, cone));
1825         cone[0] = 16;
1826         cone[1] = 17;
1827         cone[2] = 24;
1828         cone[3] = 23;
1829         cone[4] = 32;
1830         cone[5] = 36;
1831         cone[6] = 37;
1832         cone[7] = 33; /* 22 25 26 21 */
1833         PetscCall(DMPlexSetCone(dm, 1, cone));
1834         cone[0] = 18;
1835         cone[1] = 27;
1836         cone[2] = 24;
1837         cone[3] = 17;
1838         cone[4] = 34;
1839         cone[5] = 33;
1840         cone[6] = 37;
1841         cone[7] = 38;
1842         PetscCall(DMPlexSetCone(dm, 2, cone));
1843         cone[0] = 29;
1844         cone[1] = 27;
1845         cone[2] = 18;
1846         cone[3] = 15;
1847         cone[4] = 35;
1848         cone[5] = 31;
1849         cone[6] = 34;
1850         cone[7] = 38;
1851         PetscCall(DMPlexSetCone(dm, 3, cone));
1852         cone[0] = 29;
1853         cone[1] = 15;
1854         cone[2] = 16;
1855         cone[3] = 23;
1856         cone[4] = 35;
1857         cone[5] = 36;
1858         cone[6] = 32;
1859         cone[7] = 31;
1860         PetscCall(DMPlexSetCone(dm, 4, cone));
1861 
1862         cone[0] = 31;
1863         cone[1] = 34;
1864         cone[2] = 33;
1865         cone[3] = 32;
1866         cone[4] = 19;
1867         cone[5] = 22;
1868         cone[6] = 21;
1869         cone[7] = 20;
1870         PetscCall(DMPlexSetCone(dm, 5, cone));
1871         cone[0] = 32;
1872         cone[1] = 33;
1873         cone[2] = 37;
1874         cone[3] = 36;
1875         cone[4] = 22;
1876         cone[5] = 25;
1877         cone[6] = 26;
1878         cone[7] = 21;
1879         PetscCall(DMPlexSetCone(dm, 6, cone));
1880         cone[0] = 34;
1881         cone[1] = 38;
1882         cone[2] = 37;
1883         cone[3] = 33;
1884         cone[4] = 20;
1885         cone[5] = 21;
1886         cone[6] = 26;
1887         cone[7] = 28;
1888         PetscCall(DMPlexSetCone(dm, 7, cone));
1889         cone[0] = 35;
1890         cone[1] = 38;
1891         cone[2] = 34;
1892         cone[3] = 31;
1893         cone[4] = 30;
1894         cone[5] = 19;
1895         cone[6] = 20;
1896         cone[7] = 28;
1897         PetscCall(DMPlexSetCone(dm, 8, cone));
1898         cone[0] = 35;
1899         cone[1] = 31;
1900         cone[2] = 32;
1901         cone[3] = 36;
1902         cone[4] = 30;
1903         cone[5] = 25;
1904         cone[6] = 22;
1905         cone[7] = 19;
1906         PetscCall(DMPlexSetCone(dm, 9, cone));
1907 
1908         cone[0] = 19;
1909         cone[1] = 20;
1910         cone[2] = 21;
1911         cone[3] = 22;
1912         cone[4] = 15;
1913         cone[5] = 16;
1914         cone[6] = 17;
1915         cone[7] = 18;
1916         PetscCall(DMPlexSetCone(dm, 10, cone));
1917         cone[0] = 22;
1918         cone[1] = 21;
1919         cone[2] = 26;
1920         cone[3] = 25;
1921         cone[4] = 16;
1922         cone[5] = 23;
1923         cone[6] = 24;
1924         cone[7] = 17;
1925         PetscCall(DMPlexSetCone(dm, 11, cone));
1926         cone[0] = 20;
1927         cone[1] = 28;
1928         cone[2] = 26;
1929         cone[3] = 21;
1930         cone[4] = 18;
1931         cone[5] = 17;
1932         cone[6] = 24;
1933         cone[7] = 27;
1934         PetscCall(DMPlexSetCone(dm, 12, cone));
1935         cone[0] = 30;
1936         cone[1] = 28;
1937         cone[2] = 20;
1938         cone[3] = 19;
1939         cone[4] = 29;
1940         cone[5] = 15;
1941         cone[6] = 18;
1942         cone[7] = 27;
1943         PetscCall(DMPlexSetCone(dm, 13, cone));
1944         cone[0] = 30;
1945         cone[1] = 19;
1946         cone[2] = 22;
1947         cone[3] = 25;
1948         cone[4] = 29;
1949         cone[5] = 23;
1950         cone[6] = 16;
1951         cone[7] = 15;
1952         PetscCall(DMPlexSetCone(dm, 14, cone));
1953       } else {
1954         cone[0] = 5;
1955         cone[1] = 8;
1956         cone[2] = 7;
1957         cone[3] = 6;
1958         cone[4] = 9;
1959         cone[5] = 12;
1960         cone[6] = 11;
1961         cone[7] = 10;
1962         PetscCall(DMPlexSetCone(dm, 0, cone));
1963         cone[0] = 6;
1964         cone[1] = 7;
1965         cone[2] = 14;
1966         cone[3] = 13;
1967         cone[4] = 12;
1968         cone[5] = 15;
1969         cone[6] = 16;
1970         cone[7] = 11;
1971         PetscCall(DMPlexSetCone(dm, 1, cone));
1972         cone[0] = 8;
1973         cone[1] = 17;
1974         cone[2] = 14;
1975         cone[3] = 7;
1976         cone[4] = 10;
1977         cone[5] = 11;
1978         cone[6] = 16;
1979         cone[7] = 18;
1980         PetscCall(DMPlexSetCone(dm, 2, cone));
1981         cone[0] = 19;
1982         cone[1] = 17;
1983         cone[2] = 8;
1984         cone[3] = 5;
1985         cone[4] = 20;
1986         cone[5] = 9;
1987         cone[6] = 10;
1988         cone[7] = 18;
1989         PetscCall(DMPlexSetCone(dm, 3, cone));
1990         cone[0] = 19;
1991         cone[1] = 5;
1992         cone[2] = 6;
1993         cone[3] = 13;
1994         cone[4] = 20;
1995         cone[5] = 15;
1996         cone[6] = 12;
1997         cone[7] = 9;
1998         PetscCall(DMPlexSetCone(dm, 4, cone));
1999       }
2000     }
2001     PetscCall(DMPlexSymmetrize(dm));
2002     PetscCall(DMPlexStratify(dm));
2003   }
2004   /* Create cube geometry */
2005   {
2006     Vec             coordinates;
2007     PetscSection    coordSection;
2008     PetscScalar    *coords;
2009     PetscInt        coordSize, v;
2010     const PetscReal dis = 1.0 / PetscSqrtReal(2.0);
2011     const PetscReal ds2 = dis / 2.0;
2012 
2013     /* Build coordinates */
2014     PetscCall(DMGetCoordinateSection(dm, &coordSection));
2015     PetscCall(PetscSectionSetNumFields(coordSection, 1));
2016     PetscCall(PetscSectionSetFieldComponents(coordSection, 0, dim));
2017     PetscCall(PetscSectionSetChart(coordSection, numCells, numCells + numVertices));
2018     for (v = numCells; v < numCells + numVertices; ++v) {
2019       PetscCall(PetscSectionSetDof(coordSection, v, dim));
2020       PetscCall(PetscSectionSetFieldDof(coordSection, v, 0, dim));
2021     }
2022     PetscCall(PetscSectionSetUp(coordSection));
2023     PetscCall(PetscSectionGetStorageSize(coordSection, &coordSize));
2024     PetscCall(VecCreate(PETSC_COMM_SELF, &coordinates));
2025     PetscCall(PetscObjectSetName((PetscObject)coordinates, "coordinates"));
2026     PetscCall(VecSetSizes(coordinates, coordSize, PETSC_DETERMINE));
2027     PetscCall(VecSetBlockSize(coordinates, dim));
2028     PetscCall(VecSetType(coordinates, VECSTANDARD));
2029     PetscCall(VecGetArray(coordinates, &coords));
2030     if (rank == 0) {
2031       coords[0 * dim + 0]  = -ds2;
2032       coords[0 * dim + 1]  = -ds2;
2033       coords[0 * dim + 2]  = 0.0;
2034       coords[1 * dim + 0]  = ds2;
2035       coords[1 * dim + 1]  = -ds2;
2036       coords[1 * dim + 2]  = 0.0;
2037       coords[2 * dim + 0]  = ds2;
2038       coords[2 * dim + 1]  = ds2;
2039       coords[2 * dim + 2]  = 0.0;
2040       coords[3 * dim + 0]  = -ds2;
2041       coords[3 * dim + 1]  = ds2;
2042       coords[3 * dim + 2]  = 0.0;
2043       coords[4 * dim + 0]  = -ds2;
2044       coords[4 * dim + 1]  = -ds2;
2045       coords[4 * dim + 2]  = 1.0;
2046       coords[5 * dim + 0]  = -ds2;
2047       coords[5 * dim + 1]  = ds2;
2048       coords[5 * dim + 2]  = 1.0;
2049       coords[6 * dim + 0]  = ds2;
2050       coords[6 * dim + 1]  = ds2;
2051       coords[6 * dim + 2]  = 1.0;
2052       coords[7 * dim + 0]  = ds2;
2053       coords[7 * dim + 1]  = -ds2;
2054       coords[7 * dim + 2]  = 1.0;
2055       coords[8 * dim + 0]  = dis;
2056       coords[8 * dim + 1]  = -dis;
2057       coords[8 * dim + 2]  = 0.0;
2058       coords[9 * dim + 0]  = dis;
2059       coords[9 * dim + 1]  = dis;
2060       coords[9 * dim + 2]  = 0.0;
2061       coords[10 * dim + 0] = dis;
2062       coords[10 * dim + 1] = -dis;
2063       coords[10 * dim + 2] = 1.0;
2064       coords[11 * dim + 0] = dis;
2065       coords[11 * dim + 1] = dis;
2066       coords[11 * dim + 2] = 1.0;
2067       coords[12 * dim + 0] = -dis;
2068       coords[12 * dim + 1] = dis;
2069       coords[12 * dim + 2] = 0.0;
2070       coords[13 * dim + 0] = -dis;
2071       coords[13 * dim + 1] = dis;
2072       coords[13 * dim + 2] = 1.0;
2073       coords[14 * dim + 0] = -dis;
2074       coords[14 * dim + 1] = -dis;
2075       coords[14 * dim + 2] = 0.0;
2076       coords[15 * dim + 0] = -dis;
2077       coords[15 * dim + 1] = -dis;
2078       coords[15 * dim + 2] = 1.0;
2079       if (periodicZ == DM_BOUNDARY_PERIODIC) {
2080         /* 15 31 19 */ coords[16 * dim + 0] = -ds2;
2081         coords[16 * dim + 1]                = -ds2;
2082         coords[16 * dim + 2]                = 0.5;
2083         /* 16 32 22 */ coords[17 * dim + 0] = ds2;
2084         coords[17 * dim + 1]                = -ds2;
2085         coords[17 * dim + 2]                = 0.5;
2086         /* 17 33 21 */ coords[18 * dim + 0] = ds2;
2087         coords[18 * dim + 1]                = ds2;
2088         coords[18 * dim + 2]                = 0.5;
2089         /* 18 34 20 */ coords[19 * dim + 0] = -ds2;
2090         coords[19 * dim + 1]                = ds2;
2091         coords[19 * dim + 2]                = 0.5;
2092         /* 29 35 30 */ coords[20 * dim + 0] = -dis;
2093         coords[20 * dim + 1]                = -dis;
2094         coords[20 * dim + 2]                = 0.5;
2095         /* 23 36 25 */ coords[21 * dim + 0] = dis;
2096         coords[21 * dim + 1]                = -dis;
2097         coords[21 * dim + 2]                = 0.5;
2098         /* 24 37 26 */ coords[22 * dim + 0] = dis;
2099         coords[22 * dim + 1]                = dis;
2100         coords[22 * dim + 2]                = 0.5;
2101         /* 27 38 28 */ coords[23 * dim + 0] = -dis;
2102         coords[23 * dim + 1]                = dis;
2103         coords[23 * dim + 2]                = 0.5;
2104       }
2105     }
2106     PetscCall(VecRestoreArray(coordinates, &coords));
2107     PetscCall(DMSetCoordinatesLocal(dm, coordinates));
2108     PetscCall(VecDestroy(&coordinates));
2109   }
2110   /* Create periodicity */
2111   if (periodicZ == DM_BOUNDARY_PERIODIC || periodicZ == DM_BOUNDARY_TWIST) {
2112     PetscReal L[3]       = {-1., -1., 0.};
2113     PetscReal maxCell[3] = {-1., -1., 0.};
2114     PetscReal lower[3]   = {0.0, 0.0, 0.0};
2115     PetscReal upper[3]   = {1.0, 1.0, 1.5};
2116     PetscInt  numZCells  = 3;
2117 
2118     L[2]       = upper[2] - lower[2];
2119     maxCell[2] = 1.1 * (L[2] / numZCells);
2120     PetscCall(DMSetPeriodicity(dm, maxCell, lower, L));
2121   }
2122   {
2123     DM          cdm;
2124     PetscDS     cds;
2125     PetscScalar c[2] = {1.0, 1.0};
2126 
2127     PetscCall(DMPlexCreateCoordinateSpace(dm, 1, PETSC_TRUE, snapToCylinder));
2128     PetscCall(DMGetCoordinateDM(dm, &cdm));
2129     PetscCall(DMGetDS(cdm, &cds));
2130     PetscCall(PetscDSSetConstants(cds, 2, c));
2131   }
2132   PetscCall(PetscLogEventEnd(DMPLEX_Generate, dm, 0, 0, 0));
2133 
2134   /* Wait for coordinate creation before doing in-place modification */
2135   PetscCall(DMPlexInterpolateInPlace_Internal(dm));
2136   PetscFunctionReturn(PETSC_SUCCESS);
2137 }
2138 
2139 /*@
2140   DMPlexCreateHexCylinderMesh - Creates a mesh on the tensor product of the unit interval with the circle (cylinder) using hexahedra.
2141 
2142   Collective
2143 
2144   Input Parameters:
2145 + comm      - The communicator for the `DM` object
2146 - periodicZ - The boundary type for the Z direction
2147 
2148   Output Parameter:
2149 . dm - The `DM` object
2150 
2151   Level: beginner
2152 
2153   Note:
2154   Here is the output numbering looking from the bottom of the cylinder\:
2155 .vb
2156        17-----14
2157         |     |
2158         |  2  |
2159         |     |
2160  17-----8-----7-----14
2161   |     |     |     |
2162   |  3  |  0  |  1  |
2163   |     |     |     |
2164  19-----5-----6-----13
2165         |     |
2166         |  4  |
2167         |     |
2168        19-----13
2169 
2170  and up through the top
2171 
2172        18-----16
2173         |     |
2174         |  2  |
2175         |     |
2176  18----10----11-----16
2177   |     |     |     |
2178   |  3  |  0  |  1  |
2179   |     |     |     |
2180  20-----9----12-----15
2181         |     |
2182         |  4  |
2183         |     |
2184        20-----15
2185 .ve
2186 
2187 .seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexCreateBoxMesh()`, `DMSetType()`, `DMCreate()`
2188 @*/
2189 PetscErrorCode DMPlexCreateHexCylinderMesh(MPI_Comm comm, DMBoundaryType periodicZ, DM *dm)
2190 {
2191   PetscFunctionBegin;
2192   PetscAssertPointer(dm, 3);
2193   PetscCall(DMCreate(comm, dm));
2194   PetscCall(DMSetType(*dm, DMPLEX));
2195   PetscCall(DMPlexCreateHexCylinderMesh_Internal(*dm, periodicZ));
2196   PetscFunctionReturn(PETSC_SUCCESS);
2197 }
2198 
2199 static PetscErrorCode DMPlexCreateWedgeCylinderMesh_Internal(DM dm, PetscInt n, PetscBool interpolate)
2200 {
2201   const PetscInt dim = 3;
2202   PetscInt       numCells, numVertices, v;
2203   PetscMPIInt    rank;
2204 
2205   PetscFunctionBegin;
2206   PetscCheck(n >= 0, PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "Number of wedges %" PetscInt_FMT " cannot be negative", n);
2207   PetscCall(PetscLogEventBegin(DMPLEX_Generate, dm, 0, 0, 0));
2208   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank));
2209   PetscCall(DMSetDimension(dm, dim));
2210   /* Must create the celltype label here so that we do not automatically try to compute the types */
2211   PetscCall(DMCreateLabel(dm, "celltype"));
2212   /* Create topology */
2213   {
2214     PetscInt cone[6], c;
2215 
2216     numCells    = rank == 0 ? n : 0;
2217     numVertices = rank == 0 ? 2 * (n + 1) : 0;
2218     PetscCall(DMPlexSetChart(dm, 0, numCells + numVertices));
2219     for (c = 0; c < numCells; c++) PetscCall(DMPlexSetConeSize(dm, c, 6));
2220     PetscCall(DMSetUp(dm));
2221     for (c = 0; c < numCells; c++) {
2222       cone[0] = c + n * 1;
2223       cone[1] = (c + 1) % n + n * 1;
2224       cone[2] = 0 + 3 * n;
2225       cone[3] = c + n * 2;
2226       cone[4] = (c + 1) % n + n * 2;
2227       cone[5] = 1 + 3 * n;
2228       PetscCall(DMPlexSetCone(dm, c, cone));
2229       PetscCall(DMPlexSetCellType(dm, c, DM_POLYTOPE_TRI_PRISM_TENSOR));
2230     }
2231     PetscCall(DMPlexSymmetrize(dm));
2232     PetscCall(DMPlexStratify(dm));
2233   }
2234   for (v = numCells; v < numCells + numVertices; ++v) PetscCall(DMPlexSetCellType(dm, v, DM_POLYTOPE_POINT));
2235   /* Create cylinder geometry */
2236   {
2237     Vec          coordinates;
2238     PetscSection coordSection;
2239     PetscScalar *coords;
2240     PetscInt     coordSize, c;
2241 
2242     /* Build coordinates */
2243     PetscCall(DMGetCoordinateSection(dm, &coordSection));
2244     PetscCall(PetscSectionSetNumFields(coordSection, 1));
2245     PetscCall(PetscSectionSetFieldComponents(coordSection, 0, dim));
2246     PetscCall(PetscSectionSetChart(coordSection, numCells, numCells + numVertices));
2247     for (v = numCells; v < numCells + numVertices; ++v) {
2248       PetscCall(PetscSectionSetDof(coordSection, v, dim));
2249       PetscCall(PetscSectionSetFieldDof(coordSection, v, 0, dim));
2250     }
2251     PetscCall(PetscSectionSetUp(coordSection));
2252     PetscCall(PetscSectionGetStorageSize(coordSection, &coordSize));
2253     PetscCall(VecCreate(PETSC_COMM_SELF, &coordinates));
2254     PetscCall(PetscObjectSetName((PetscObject)coordinates, "coordinates"));
2255     PetscCall(VecSetSizes(coordinates, coordSize, PETSC_DETERMINE));
2256     PetscCall(VecSetBlockSize(coordinates, dim));
2257     PetscCall(VecSetType(coordinates, VECSTANDARD));
2258     PetscCall(VecGetArray(coordinates, &coords));
2259     for (c = 0; c < numCells; c++) {
2260       coords[(c + 0 * n) * dim + 0] = PetscCosReal(2.0 * c * PETSC_PI / n);
2261       coords[(c + 0 * n) * dim + 1] = PetscSinReal(2.0 * c * PETSC_PI / n);
2262       coords[(c + 0 * n) * dim + 2] = 1.0;
2263       coords[(c + 1 * n) * dim + 0] = PetscCosReal(2.0 * c * PETSC_PI / n);
2264       coords[(c + 1 * n) * dim + 1] = PetscSinReal(2.0 * c * PETSC_PI / n);
2265       coords[(c + 1 * n) * dim + 2] = 0.0;
2266     }
2267     if (rank == 0) {
2268       coords[(2 * n + 0) * dim + 0] = 0.0;
2269       coords[(2 * n + 0) * dim + 1] = 0.0;
2270       coords[(2 * n + 0) * dim + 2] = 1.0;
2271       coords[(2 * n + 1) * dim + 0] = 0.0;
2272       coords[(2 * n + 1) * dim + 1] = 0.0;
2273       coords[(2 * n + 1) * dim + 2] = 0.0;
2274     }
2275     PetscCall(VecRestoreArray(coordinates, &coords));
2276     PetscCall(DMSetCoordinatesLocal(dm, coordinates));
2277     PetscCall(VecDestroy(&coordinates));
2278   }
2279   PetscCall(PetscLogEventEnd(DMPLEX_Generate, dm, 0, 0, 0));
2280   /* Interpolate */
2281   if (interpolate) PetscCall(DMPlexInterpolateInPlace_Internal(dm));
2282   PetscFunctionReturn(PETSC_SUCCESS);
2283 }
2284 
2285 /*@
2286   DMPlexCreateWedgeCylinderMesh - Creates a mesh on the tensor product of the unit interval with the circle (cylinder) using wedges.
2287 
2288   Collective
2289 
2290   Input Parameters:
2291 + comm        - The communicator for the `DM` object
2292 . n           - The number of wedges around the origin
2293 - interpolate - Create edges and faces
2294 
2295   Output Parameter:
2296 . dm - The `DM` object
2297 
2298   Level: beginner
2299 
2300 .seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexCreateHexCylinderMesh()`, `DMPlexCreateBoxMesh()`, `DMSetType()`, `DMCreate()`
2301 @*/
2302 PetscErrorCode DMPlexCreateWedgeCylinderMesh(MPI_Comm comm, PetscInt n, PetscBool interpolate, DM *dm)
2303 {
2304   PetscFunctionBegin;
2305   PetscAssertPointer(dm, 4);
2306   PetscCall(DMCreate(comm, dm));
2307   PetscCall(DMSetType(*dm, DMPLEX));
2308   PetscCall(DMPlexCreateWedgeCylinderMesh_Internal(*dm, n, interpolate));
2309   PetscFunctionReturn(PETSC_SUCCESS);
2310 }
2311 
2312 static inline PetscReal DiffNormReal(PetscInt dim, const PetscReal x[], const PetscReal y[])
2313 {
2314   PetscReal prod = 0.0;
2315   PetscInt  i;
2316   for (i = 0; i < dim; ++i) prod += PetscSqr(x[i] - y[i]);
2317   return PetscSqrtReal(prod);
2318 }
2319 static inline PetscReal DotReal(PetscInt dim, const PetscReal x[], const PetscReal y[])
2320 {
2321   PetscReal prod = 0.0;
2322   PetscInt  i;
2323   for (i = 0; i < dim; ++i) prod += x[i] * y[i];
2324   return prod;
2325 }
2326 
2327 /* The first constant is the sphere radius */
2328 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[])
2329 {
2330   PetscReal r     = PetscRealPart(constants[0]);
2331   PetscReal norm2 = 0.0, fac;
2332   PetscInt  n     = uOff[1] - uOff[0], d;
2333 
2334   for (d = 0; d < n; ++d) norm2 += PetscSqr(PetscRealPart(u[d]));
2335   fac = r / PetscSqrtReal(norm2);
2336   for (d = 0; d < n; ++d) f0[d] = u[d] * fac;
2337 }
2338 
2339 static PetscErrorCode DMPlexCreateSphereMesh_Internal(DM dm, PetscInt dim, PetscBool simplex, PetscReal R)
2340 {
2341   const PetscInt embedDim = dim + 1;
2342   PetscSection   coordSection;
2343   Vec            coordinates;
2344   PetscScalar   *coords;
2345   PetscReal     *coordsIn;
2346   PetscInt       numCells, numEdges, numVerts = 0, firstVertex = 0, v, firstEdge, coordSize, d, c, e;
2347   PetscMPIInt    rank;
2348 
2349   PetscFunctionBegin;
2350   PetscValidLogicalCollectiveBool(dm, simplex, 3);
2351   PetscCall(PetscLogEventBegin(DMPLEX_Generate, dm, 0, 0, 0));
2352   PetscCall(DMSetDimension(dm, dim));
2353   PetscCall(DMSetCoordinateDim(dm, dim + 1));
2354   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank));
2355   switch (dim) {
2356   case 1:
2357     numCells = 16;
2358     numVerts = numCells;
2359 
2360     // Build Topology
2361     PetscCall(DMPlexSetChart(dm, 0, numCells + numVerts));
2362     for (PetscInt c = 0; c < numCells; c++) PetscCall(DMPlexSetConeSize(dm, c, embedDim));
2363     PetscCall(DMSetUp(dm));
2364     for (PetscInt c = 0; c < numCells; ++c) {
2365       PetscInt cone[2];
2366 
2367       cone[0] = c + numCells;
2368       cone[1] = (c + 1) % numVerts + numCells;
2369       PetscCall(DMPlexSetCone(dm, c, cone));
2370     }
2371     PetscCall(DMPlexSymmetrize(dm));
2372     PetscCall(DMPlexStratify(dm));
2373     PetscCall(PetscMalloc1(numVerts * embedDim, &coordsIn));
2374     for (PetscInt v = 0; v < numVerts; ++v) {
2375       const PetscReal rad = 2. * PETSC_PI * v / numVerts;
2376 
2377       coordsIn[v * embedDim + 0] = PetscCosReal(rad);
2378       coordsIn[v * embedDim + 1] = PetscSinReal(rad);
2379     }
2380     break;
2381   case 2:
2382     if (simplex) {
2383       const PetscReal radius    = PetscSqrtReal(1 + PETSC_PHI * PETSC_PHI) / (1.0 + PETSC_PHI);
2384       const PetscReal edgeLen   = 2.0 / (1.0 + PETSC_PHI) * (R / radius);
2385       const PetscInt  degree    = 5;
2386       PetscReal       vertex[3] = {0.0, 1.0 / (1.0 + PETSC_PHI), PETSC_PHI / (1.0 + PETSC_PHI)};
2387       PetscInt        s[3]      = {1, 1, 1};
2388       PetscInt        cone[3];
2389       PetscInt       *graph, p, i, j, k;
2390 
2391       vertex[0] *= R / radius;
2392       vertex[1] *= R / radius;
2393       vertex[2] *= R / radius;
2394       numCells    = rank == 0 ? 20 : 0;
2395       numVerts    = rank == 0 ? 12 : 0;
2396       firstVertex = numCells;
2397       /* Use icosahedron, which for a R-sphere has coordinates which are all cyclic permutations of
2398 
2399            (0, \pm 1/\phi+1, \pm \phi/\phi+1)
2400 
2401          where \phi^2 - \phi - 1 = 0, meaning \phi is the golden ratio \frac{1 + \sqrt{5}}{2}. The edge
2402          length is then given by 2/(1+\phi) = 2 * 0.38197 = 0.76393.
2403       */
2404       /* Construct vertices */
2405       PetscCall(PetscCalloc1(numVerts * embedDim, &coordsIn));
2406       if (rank == 0) {
2407         for (p = 0, i = 0; p < embedDim; ++p) {
2408           for (s[1] = -1; s[1] < 2; s[1] += 2) {
2409             for (s[2] = -1; s[2] < 2; s[2] += 2) {
2410               for (d = 0; d < embedDim; ++d) coordsIn[i * embedDim + d] = s[(d + p) % embedDim] * vertex[(d + p) % embedDim];
2411               ++i;
2412             }
2413           }
2414         }
2415       }
2416       /* Construct graph */
2417       PetscCall(PetscCalloc1(numVerts * numVerts, &graph));
2418       for (i = 0; i < numVerts; ++i) {
2419         for (j = 0, k = 0; j < numVerts; ++j) {
2420           if (PetscAbsReal(DiffNormReal(embedDim, &coordsIn[i * embedDim], &coordsIn[j * embedDim]) - edgeLen) < PETSC_SMALL) {
2421             graph[i * numVerts + j] = 1;
2422             ++k;
2423           }
2424         }
2425         PetscCheck(k == degree, PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Invalid icosahedron, vertex %" PetscInt_FMT " degree %" PetscInt_FMT " != %" PetscInt_FMT, i, k, degree);
2426       }
2427       /* Build Topology */
2428       PetscCall(DMPlexSetChart(dm, 0, numCells + numVerts));
2429       for (c = 0; c < numCells; c++) PetscCall(DMPlexSetConeSize(dm, c, embedDim));
2430       PetscCall(DMSetUp(dm)); /* Allocate space for cones */
2431       /* Cells */
2432       for (i = 0, c = 0; i < numVerts; ++i) {
2433         for (j = 0; j < i; ++j) {
2434           for (k = 0; k < j; ++k) {
2435             if (graph[i * numVerts + j] && graph[j * numVerts + k] && graph[k * numVerts + i]) {
2436               cone[0] = firstVertex + i;
2437               cone[1] = firstVertex + j;
2438               cone[2] = firstVertex + k;
2439               /* Check orientation */
2440               {
2441                 const PetscInt epsilon[3][3][3] = {
2442                   {{0, 0, 0},  {0, 0, 1},  {0, -1, 0}},
2443                   {{0, 0, -1}, {0, 0, 0},  {1, 0, 0} },
2444                   {{0, 1, 0},  {-1, 0, 0}, {0, 0, 0} }
2445                 };
2446                 PetscReal normal[3];
2447                 PetscInt  e, f;
2448 
2449                 for (d = 0; d < embedDim; ++d) {
2450                   normal[d] = 0.0;
2451                   for (e = 0; e < embedDim; ++e) {
2452                     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]);
2453                   }
2454                 }
2455                 if (DotReal(embedDim, normal, &coordsIn[i * embedDim]) < 0) {
2456                   PetscInt tmp = cone[1];
2457                   cone[1]      = cone[2];
2458                   cone[2]      = tmp;
2459                 }
2460               }
2461               PetscCall(DMPlexSetCone(dm, c++, cone));
2462             }
2463           }
2464         }
2465       }
2466       PetscCall(DMPlexSymmetrize(dm));
2467       PetscCall(DMPlexStratify(dm));
2468       PetscCall(PetscFree(graph));
2469     } else {
2470       /*
2471         12-21--13
2472          |     |
2473         25  4  24
2474          |     |
2475   12-25--9-16--8-24--13
2476    |     |     |     |
2477   23  5 17  0 15  3  22
2478    |     |     |     |
2479   10-20--6-14--7-19--11
2480          |     |
2481         20  1  19
2482          |     |
2483         10-18--11
2484          |     |
2485         23  2  22
2486          |     |
2487         12-21--13
2488        */
2489       PetscInt cone[4], ornt[4];
2490 
2491       numCells    = rank == 0 ? 6 : 0;
2492       numEdges    = rank == 0 ? 12 : 0;
2493       numVerts    = rank == 0 ? 8 : 0;
2494       firstVertex = numCells;
2495       firstEdge   = numCells + numVerts;
2496       /* Build Topology */
2497       PetscCall(DMPlexSetChart(dm, 0, numCells + numEdges + numVerts));
2498       for (c = 0; c < numCells; c++) PetscCall(DMPlexSetConeSize(dm, c, 4));
2499       for (e = firstEdge; e < firstEdge + numEdges; ++e) PetscCall(DMPlexSetConeSize(dm, e, 2));
2500       PetscCall(DMSetUp(dm)); /* Allocate space for cones */
2501       if (rank == 0) {
2502         /* Cell 0 */
2503         cone[0] = 14;
2504         cone[1] = 15;
2505         cone[2] = 16;
2506         cone[3] = 17;
2507         PetscCall(DMPlexSetCone(dm, 0, cone));
2508         ornt[0] = 0;
2509         ornt[1] = 0;
2510         ornt[2] = 0;
2511         ornt[3] = 0;
2512         PetscCall(DMPlexSetConeOrientation(dm, 0, ornt));
2513         /* Cell 1 */
2514         cone[0] = 18;
2515         cone[1] = 19;
2516         cone[2] = 14;
2517         cone[3] = 20;
2518         PetscCall(DMPlexSetCone(dm, 1, cone));
2519         ornt[0] = 0;
2520         ornt[1] = 0;
2521         ornt[2] = -1;
2522         ornt[3] = 0;
2523         PetscCall(DMPlexSetConeOrientation(dm, 1, ornt));
2524         /* Cell 2 */
2525         cone[0] = 21;
2526         cone[1] = 22;
2527         cone[2] = 18;
2528         cone[3] = 23;
2529         PetscCall(DMPlexSetCone(dm, 2, cone));
2530         ornt[0] = 0;
2531         ornt[1] = 0;
2532         ornt[2] = -1;
2533         ornt[3] = 0;
2534         PetscCall(DMPlexSetConeOrientation(dm, 2, ornt));
2535         /* Cell 3 */
2536         cone[0] = 19;
2537         cone[1] = 22;
2538         cone[2] = 24;
2539         cone[3] = 15;
2540         PetscCall(DMPlexSetCone(dm, 3, cone));
2541         ornt[0] = -1;
2542         ornt[1] = -1;
2543         ornt[2] = 0;
2544         ornt[3] = -1;
2545         PetscCall(DMPlexSetConeOrientation(dm, 3, ornt));
2546         /* Cell 4 */
2547         cone[0] = 16;
2548         cone[1] = 24;
2549         cone[2] = 21;
2550         cone[3] = 25;
2551         PetscCall(DMPlexSetCone(dm, 4, cone));
2552         ornt[0] = -1;
2553         ornt[1] = -1;
2554         ornt[2] = -1;
2555         ornt[3] = 0;
2556         PetscCall(DMPlexSetConeOrientation(dm, 4, ornt));
2557         /* Cell 5 */
2558         cone[0] = 20;
2559         cone[1] = 17;
2560         cone[2] = 25;
2561         cone[3] = 23;
2562         PetscCall(DMPlexSetCone(dm, 5, cone));
2563         ornt[0] = -1;
2564         ornt[1] = -1;
2565         ornt[2] = -1;
2566         ornt[3] = -1;
2567         PetscCall(DMPlexSetConeOrientation(dm, 5, ornt));
2568         /* Edges */
2569         cone[0] = 6;
2570         cone[1] = 7;
2571         PetscCall(DMPlexSetCone(dm, 14, cone));
2572         cone[0] = 7;
2573         cone[1] = 8;
2574         PetscCall(DMPlexSetCone(dm, 15, cone));
2575         cone[0] = 8;
2576         cone[1] = 9;
2577         PetscCall(DMPlexSetCone(dm, 16, cone));
2578         cone[0] = 9;
2579         cone[1] = 6;
2580         PetscCall(DMPlexSetCone(dm, 17, cone));
2581         cone[0] = 10;
2582         cone[1] = 11;
2583         PetscCall(DMPlexSetCone(dm, 18, cone));
2584         cone[0] = 11;
2585         cone[1] = 7;
2586         PetscCall(DMPlexSetCone(dm, 19, cone));
2587         cone[0] = 6;
2588         cone[1] = 10;
2589         PetscCall(DMPlexSetCone(dm, 20, cone));
2590         cone[0] = 12;
2591         cone[1] = 13;
2592         PetscCall(DMPlexSetCone(dm, 21, cone));
2593         cone[0] = 13;
2594         cone[1] = 11;
2595         PetscCall(DMPlexSetCone(dm, 22, cone));
2596         cone[0] = 10;
2597         cone[1] = 12;
2598         PetscCall(DMPlexSetCone(dm, 23, cone));
2599         cone[0] = 13;
2600         cone[1] = 8;
2601         PetscCall(DMPlexSetCone(dm, 24, cone));
2602         cone[0] = 12;
2603         cone[1] = 9;
2604         PetscCall(DMPlexSetCone(dm, 25, cone));
2605       }
2606       PetscCall(DMPlexSymmetrize(dm));
2607       PetscCall(DMPlexStratify(dm));
2608       /* Build coordinates */
2609       PetscCall(PetscCalloc1(numVerts * embedDim, &coordsIn));
2610       if (rank == 0) {
2611         coordsIn[0 * embedDim + 0] = -R;
2612         coordsIn[0 * embedDim + 1] = R;
2613         coordsIn[0 * embedDim + 2] = -R;
2614         coordsIn[1 * embedDim + 0] = R;
2615         coordsIn[1 * embedDim + 1] = R;
2616         coordsIn[1 * embedDim + 2] = -R;
2617         coordsIn[2 * embedDim + 0] = R;
2618         coordsIn[2 * embedDim + 1] = -R;
2619         coordsIn[2 * embedDim + 2] = -R;
2620         coordsIn[3 * embedDim + 0] = -R;
2621         coordsIn[3 * embedDim + 1] = -R;
2622         coordsIn[3 * embedDim + 2] = -R;
2623         coordsIn[4 * embedDim + 0] = -R;
2624         coordsIn[4 * embedDim + 1] = R;
2625         coordsIn[4 * embedDim + 2] = R;
2626         coordsIn[5 * embedDim + 0] = R;
2627         coordsIn[5 * embedDim + 1] = R;
2628         coordsIn[5 * embedDim + 2] = R;
2629         coordsIn[6 * embedDim + 0] = -R;
2630         coordsIn[6 * embedDim + 1] = -R;
2631         coordsIn[6 * embedDim + 2] = R;
2632         coordsIn[7 * embedDim + 0] = R;
2633         coordsIn[7 * embedDim + 1] = -R;
2634         coordsIn[7 * embedDim + 2] = R;
2635       }
2636     }
2637     break;
2638   case 3:
2639     if (simplex) {
2640       const PetscReal edgeLen         = 1.0 / PETSC_PHI;
2641       PetscReal       vertexA[4]      = {0.5, 0.5, 0.5, 0.5};
2642       PetscReal       vertexB[4]      = {1.0, 0.0, 0.0, 0.0};
2643       PetscReal       vertexC[4]      = {0.5, 0.5 * PETSC_PHI, 0.5 / PETSC_PHI, 0.0};
2644       const PetscInt  degree          = 12;
2645       PetscInt        s[4]            = {1, 1, 1};
2646       PetscInt        evenPerm[12][4] = {
2647         {0, 1, 2, 3},
2648         {0, 2, 3, 1},
2649         {0, 3, 1, 2},
2650         {1, 0, 3, 2},
2651         {1, 2, 0, 3},
2652         {1, 3, 2, 0},
2653         {2, 0, 1, 3},
2654         {2, 1, 3, 0},
2655         {2, 3, 0, 1},
2656         {3, 0, 2, 1},
2657         {3, 1, 0, 2},
2658         {3, 2, 1, 0}
2659       };
2660       PetscInt  cone[4];
2661       PetscInt *graph, p, i, j, k, l;
2662 
2663       vertexA[0] *= R;
2664       vertexA[1] *= R;
2665       vertexA[2] *= R;
2666       vertexA[3] *= R;
2667       vertexB[0] *= R;
2668       vertexB[1] *= R;
2669       vertexB[2] *= R;
2670       vertexB[3] *= R;
2671       vertexC[0] *= R;
2672       vertexC[1] *= R;
2673       vertexC[2] *= R;
2674       vertexC[3] *= R;
2675       numCells    = rank == 0 ? 600 : 0;
2676       numVerts    = rank == 0 ? 120 : 0;
2677       firstVertex = numCells;
2678       /* Use the 600-cell, which for a unit sphere has coordinates which are
2679 
2680            1/2 (\pm 1, \pm 1,    \pm 1, \pm 1)                          16
2681                (\pm 1,    0,       0,      0)  all cyclic permutations   8
2682            1/2 (\pm 1, \pm phi, \pm 1/phi, 0)  all even permutations    96
2683 
2684          where \phi^2 - \phi - 1 = 0, meaning \phi is the golden ratio \frac{1 + \sqrt{5}}{2}. The edge
2685          length is then given by 1/\phi = 0.61803.
2686 
2687          http://buzzard.pugetsound.edu/sage-practice/ch03s03.html
2688          http://mathworld.wolfram.com/600-Cell.html
2689       */
2690       /* Construct vertices */
2691       PetscCall(PetscCalloc1(numVerts * embedDim, &coordsIn));
2692       i = 0;
2693       if (rank == 0) {
2694         for (s[0] = -1; s[0] < 2; s[0] += 2) {
2695           for (s[1] = -1; s[1] < 2; s[1] += 2) {
2696             for (s[2] = -1; s[2] < 2; s[2] += 2) {
2697               for (s[3] = -1; s[3] < 2; s[3] += 2) {
2698                 for (d = 0; d < embedDim; ++d) coordsIn[i * embedDim + d] = s[d] * vertexA[d];
2699                 ++i;
2700               }
2701             }
2702           }
2703         }
2704         for (p = 0; p < embedDim; ++p) {
2705           s[1] = s[2] = s[3] = 1;
2706           for (s[0] = -1; s[0] < 2; s[0] += 2) {
2707             for (d = 0; d < embedDim; ++d) coordsIn[i * embedDim + d] = s[(d + p) % embedDim] * vertexB[(d + p) % embedDim];
2708             ++i;
2709           }
2710         }
2711         for (p = 0; p < 12; ++p) {
2712           s[3] = 1;
2713           for (s[0] = -1; s[0] < 2; s[0] += 2) {
2714             for (s[1] = -1; s[1] < 2; s[1] += 2) {
2715               for (s[2] = -1; s[2] < 2; s[2] += 2) {
2716                 for (d = 0; d < embedDim; ++d) coordsIn[i * embedDim + d] = s[evenPerm[p][d]] * vertexC[evenPerm[p][d]];
2717                 ++i;
2718               }
2719             }
2720           }
2721         }
2722       }
2723       PetscCheck(i == numVerts, PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Invalid 600-cell, vertices %" PetscInt_FMT " != %" PetscInt_FMT, i, numVerts);
2724       /* Construct graph */
2725       PetscCall(PetscCalloc1(numVerts * numVerts, &graph));
2726       for (i = 0; i < numVerts; ++i) {
2727         for (j = 0, k = 0; j < numVerts; ++j) {
2728           if (PetscAbsReal(DiffNormReal(embedDim, &coordsIn[i * embedDim], &coordsIn[j * embedDim]) - edgeLen) < PETSC_SMALL) {
2729             graph[i * numVerts + j] = 1;
2730             ++k;
2731           }
2732         }
2733         PetscCheck(k == degree, PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Invalid 600-cell, vertex %" PetscInt_FMT " degree %" PetscInt_FMT " != %" PetscInt_FMT, i, k, degree);
2734       }
2735       /* Build Topology */
2736       PetscCall(DMPlexSetChart(dm, 0, numCells + numVerts));
2737       for (c = 0; c < numCells; c++) PetscCall(DMPlexSetConeSize(dm, c, embedDim));
2738       PetscCall(DMSetUp(dm)); /* Allocate space for cones */
2739       /* Cells */
2740       if (rank == 0) {
2741         for (i = 0, c = 0; i < numVerts; ++i) {
2742           for (j = 0; j < i; ++j) {
2743             for (k = 0; k < j; ++k) {
2744               for (l = 0; l < k; ++l) {
2745                 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]) {
2746                   cone[0] = firstVertex + i;
2747                   cone[1] = firstVertex + j;
2748                   cone[2] = firstVertex + k;
2749                   cone[3] = firstVertex + l;
2750                   /* Check orientation: https://ef.gy/linear-algebra:normal-vectors-in-higher-dimensional-spaces */
2751                   {
2752                     const PetscInt epsilon[4][4][4][4] = {
2753                       {{{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}}},
2754 
2755                       {{{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}}},
2756 
2757                       {{{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}}},
2758 
2759                       {{{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}} }
2760                     };
2761                     PetscReal normal[4];
2762                     PetscInt  e, f, g;
2763 
2764                     for (d = 0; d < embedDim; ++d) {
2765                       normal[d] = 0.0;
2766                       for (e = 0; e < embedDim; ++e) {
2767                         for (f = 0; f < embedDim; ++f) {
2768                           for (g = 0; g < embedDim; ++g) {
2769                             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]);
2770                           }
2771                         }
2772                       }
2773                     }
2774                     if (DotReal(embedDim, normal, &coordsIn[i * embedDim]) < 0) {
2775                       PetscInt tmp = cone[1];
2776                       cone[1]      = cone[2];
2777                       cone[2]      = tmp;
2778                     }
2779                   }
2780                   PetscCall(DMPlexSetCone(dm, c++, cone));
2781                 }
2782               }
2783             }
2784           }
2785         }
2786       }
2787       PetscCall(DMPlexSymmetrize(dm));
2788       PetscCall(DMPlexStratify(dm));
2789       PetscCall(PetscFree(graph));
2790     }
2791     break;
2792   default:
2793     SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported dimension for sphere: %" PetscInt_FMT, dim);
2794   }
2795   /* Create coordinates */
2796   PetscCall(DMGetCoordinateSection(dm, &coordSection));
2797   PetscCall(PetscSectionSetNumFields(coordSection, 1));
2798   PetscCall(PetscSectionSetFieldComponents(coordSection, 0, embedDim));
2799   PetscCall(PetscSectionSetChart(coordSection, firstVertex, firstVertex + numVerts));
2800   for (v = firstVertex; v < firstVertex + numVerts; ++v) {
2801     PetscCall(PetscSectionSetDof(coordSection, v, embedDim));
2802     PetscCall(PetscSectionSetFieldDof(coordSection, v, 0, embedDim));
2803   }
2804   PetscCall(PetscSectionSetUp(coordSection));
2805   PetscCall(PetscSectionGetStorageSize(coordSection, &coordSize));
2806   PetscCall(VecCreate(PETSC_COMM_SELF, &coordinates));
2807   PetscCall(VecSetBlockSize(coordinates, embedDim));
2808   PetscCall(PetscObjectSetName((PetscObject)coordinates, "coordinates"));
2809   PetscCall(VecSetSizes(coordinates, coordSize, PETSC_DETERMINE));
2810   PetscCall(VecSetType(coordinates, VECSTANDARD));
2811   PetscCall(VecGetArray(coordinates, &coords));
2812   for (v = 0; v < numVerts; ++v)
2813     for (d = 0; d < embedDim; ++d) coords[v * embedDim + d] = coordsIn[v * embedDim + d];
2814   PetscCall(VecRestoreArray(coordinates, &coords));
2815   PetscCall(DMSetCoordinatesLocal(dm, coordinates));
2816   PetscCall(VecDestroy(&coordinates));
2817   PetscCall(PetscFree(coordsIn));
2818   {
2819     DM          cdm;
2820     PetscDS     cds;
2821     PetscScalar c = R;
2822 
2823     PetscCall(DMPlexCreateCoordinateSpace(dm, 1, PETSC_TRUE, snapToSphere));
2824     PetscCall(DMGetCoordinateDM(dm, &cdm));
2825     PetscCall(DMGetDS(cdm, &cds));
2826     PetscCall(PetscDSSetConstants(cds, 1, &c));
2827   }
2828   PetscCall(PetscLogEventEnd(DMPLEX_Generate, dm, 0, 0, 0));
2829   /* Wait for coordinate creation before doing in-place modification */
2830   if (simplex) PetscCall(DMPlexInterpolateInPlace_Internal(dm));
2831   PetscFunctionReturn(PETSC_SUCCESS);
2832 }
2833 
2834 typedef void (*TPSEvaluateFunc)(const PetscReal[], PetscReal *, PetscReal[], PetscReal (*)[3]);
2835 
2836 /*
2837  The Schwarz P implicit surface is
2838 
2839      f(x) = cos(x0) + cos(x1) + cos(x2) = 0
2840 */
2841 static void TPSEvaluate_SchwarzP(const PetscReal y[3], PetscReal *f, PetscReal grad[], PetscReal (*hess)[3])
2842 {
2843   PetscReal c[3] = {PetscCosReal(y[0] * PETSC_PI), PetscCosReal(y[1] * PETSC_PI), PetscCosReal(y[2] * PETSC_PI)};
2844   PetscReal g[3] = {-PetscSinReal(y[0] * PETSC_PI), -PetscSinReal(y[1] * PETSC_PI), -PetscSinReal(y[2] * PETSC_PI)};
2845   f[0]           = c[0] + c[1] + c[2];
2846   for (PetscInt i = 0; i < 3; i++) {
2847     grad[i] = PETSC_PI * g[i];
2848     for (PetscInt j = 0; j < 3; j++) hess[i][j] = (i == j) ? -PetscSqr(PETSC_PI) * c[i] : 0.;
2849   }
2850 }
2851 
2852 // u[] is a tentative normal on input. Replace with the implicit function gradient in the same direction
2853 static PetscErrorCode TPSExtrudeNormalFunc_SchwarzP(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt r, PetscScalar u[], void *ctx)
2854 {
2855   for (PetscInt i = 0; i < 3; i++) u[i] = -PETSC_PI * PetscSinReal(x[i] * PETSC_PI);
2856   return PETSC_SUCCESS;
2857 }
2858 
2859 /*
2860  The Gyroid implicit surface is
2861 
2862  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)
2863 
2864 */
2865 static void TPSEvaluate_Gyroid(const PetscReal y[3], PetscReal *f, PetscReal grad[], PetscReal (*hess)[3])
2866 {
2867   PetscReal s[3] = {PetscSinReal(PETSC_PI * y[0]), PetscSinReal(PETSC_PI * (y[1] + .5)), PetscSinReal(PETSC_PI * (y[2] + .25))};
2868   PetscReal c[3] = {PetscCosReal(PETSC_PI * y[0]), PetscCosReal(PETSC_PI * (y[1] + .5)), PetscCosReal(PETSC_PI * (y[2] + .25))};
2869   f[0]           = s[0] * c[1] + s[1] * c[2] + s[2] * c[0];
2870   grad[0]        = PETSC_PI * (c[0] * c[1] - s[2] * s[0]);
2871   grad[1]        = PETSC_PI * (c[1] * c[2] - s[0] * s[1]);
2872   grad[2]        = PETSC_PI * (c[2] * c[0] - s[1] * s[2]);
2873   hess[0][0]     = -PetscSqr(PETSC_PI) * (s[0] * c[1] + s[2] * c[0]);
2874   hess[0][1]     = -PetscSqr(PETSC_PI) * (c[0] * s[1]);
2875   hess[0][2]     = -PetscSqr(PETSC_PI) * (c[2] * s[0]);
2876   hess[1][0]     = -PetscSqr(PETSC_PI) * (s[1] * c[2] + s[0] * c[1]);
2877   hess[1][1]     = -PetscSqr(PETSC_PI) * (c[1] * s[2]);
2878   hess[2][2]     = -PetscSqr(PETSC_PI) * (c[0] * s[1]);
2879   hess[2][0]     = -PetscSqr(PETSC_PI) * (s[2] * c[0] + s[1] * c[2]);
2880   hess[2][1]     = -PetscSqr(PETSC_PI) * (c[2] * s[0]);
2881   hess[2][2]     = -PetscSqr(PETSC_PI) * (c[1] * s[2]);
2882 }
2883 
2884 // u[] is a tentative normal on input. Replace with the implicit function gradient in the same direction
2885 static PetscErrorCode TPSExtrudeNormalFunc_Gyroid(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt r, PetscScalar u[], void *ctx)
2886 {
2887   PetscReal s[3] = {PetscSinReal(PETSC_PI * x[0]), PetscSinReal(PETSC_PI * (x[1] + .5)), PetscSinReal(PETSC_PI * (x[2] + .25))};
2888   PetscReal c[3] = {PetscCosReal(PETSC_PI * x[0]), PetscCosReal(PETSC_PI * (x[1] + .5)), PetscCosReal(PETSC_PI * (x[2] + .25))};
2889   u[0]           = PETSC_PI * (c[0] * c[1] - s[2] * s[0]);
2890   u[1]           = PETSC_PI * (c[1] * c[2] - s[0] * s[1]);
2891   u[2]           = PETSC_PI * (c[2] * c[0] - s[1] * s[2]);
2892   return PETSC_SUCCESS;
2893 }
2894 
2895 /*
2896    We wish to solve
2897 
2898          min_y || y - x ||^2  subject to f(y) = 0
2899 
2900    Let g(y) = grad(f).  The minimization problem is equivalent to asking to satisfy
2901    f(y) = 0 and (y-x) is parallel to g(y).  We do this by using Householder QR to obtain a basis for the
2902    tangent space and ask for both components in the tangent space to be zero.
2903 
2904    Take g to be a column vector and compute the "full QR" factorization Q R = g,
2905    where Q = I - 2 n n^T is a symmetric orthogonal matrix.
2906    The first column of Q is parallel to g so the remaining two columns span the null space.
2907    Let Qn = Q[:,1:] be those remaining columns.  Then Qn Qn^T is an orthogonal projector into the tangent space.
2908    Since Q is symmetric, this is equivalent to multiplying by Q and taking the last two entries.
2909    In total, we have a system of 3 equations in 3 unknowns:
2910 
2911      f(y) = 0                       1 equation
2912      Qn^T (y - x) = 0               2 equations
2913 
2914    Here, we compute the residual and Jacobian of this system.
2915 */
2916 static void TPSNearestPointResJac(TPSEvaluateFunc feval, const PetscScalar x[], const PetscScalar y[], PetscScalar res[], PetscScalar J[])
2917 {
2918   PetscReal yreal[3] = {PetscRealPart(y[0]), PetscRealPart(y[1]), PetscRealPart(y[2])};
2919   PetscReal d[3]     = {PetscRealPart(y[0] - x[0]), PetscRealPart(y[1] - x[1]), PetscRealPart(y[2] - x[2])};
2920   PetscReal f, grad[3], n[3], norm, norm_y[3], nd, nd_y[3], sign;
2921   PetscReal n_y[3][3] = {
2922     {0, 0, 0},
2923     {0, 0, 0},
2924     {0, 0, 0}
2925   };
2926 
2927   feval(yreal, &f, grad, n_y);
2928 
2929   for (PetscInt i = 0; i < 3; i++) n[i] = grad[i];
2930   norm = PetscSqrtReal(PetscSqr(n[0]) + PetscSqr(n[1]) + PetscSqr(n[2]));
2931   for (PetscInt i = 0; i < 3; i++) norm_y[i] = 1. / norm * n[i] * n_y[i][i];
2932 
2933   // Define the Householder reflector
2934   sign = n[0] >= 0 ? 1. : -1.;
2935   n[0] += norm * sign;
2936   for (PetscInt i = 0; i < 3; i++) n_y[0][i] += norm_y[i] * sign;
2937 
2938   norm      = PetscSqrtReal(PetscSqr(n[0]) + PetscSqr(n[1]) + PetscSqr(n[2]));
2939   norm_y[0] = 1. / norm * (n[0] * n_y[0][0]);
2940   norm_y[1] = 1. / norm * (n[0] * n_y[0][1] + n[1] * n_y[1][1]);
2941   norm_y[2] = 1. / norm * (n[0] * n_y[0][2] + n[2] * n_y[2][2]);
2942 
2943   for (PetscInt i = 0; i < 3; i++) {
2944     n[i] /= norm;
2945     for (PetscInt j = 0; j < 3; j++) {
2946       // note that n[i] is n_old[i]/norm when executing the code below
2947       n_y[i][j] = n_y[i][j] / norm - n[i] / norm * norm_y[j];
2948     }
2949   }
2950 
2951   nd = n[0] * d[0] + n[1] * d[1] + n[2] * d[2];
2952   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];
2953 
2954   res[0] = f;
2955   res[1] = d[1] - 2 * n[1] * nd;
2956   res[2] = d[2] - 2 * n[2] * nd;
2957   // J[j][i] is J_{ij} (column major)
2958   for (PetscInt j = 0; j < 3; j++) {
2959     J[0 + j * 3] = grad[j];
2960     J[1 + j * 3] = (j == 1) * 1. - 2 * (n_y[1][j] * nd + n[1] * nd_y[j]);
2961     J[2 + j * 3] = (j == 2) * 1. - 2 * (n_y[2][j] * nd + n[2] * nd_y[j]);
2962   }
2963 }
2964 
2965 /*
2966    Project x to the nearest point on the implicit surface using Newton's method.
2967 */
2968 static PetscErrorCode TPSNearestPoint(TPSEvaluateFunc feval, PetscScalar x[])
2969 {
2970   PetscScalar y[3] = {x[0], x[1], x[2]}; // Initial guess
2971 
2972   PetscFunctionBegin;
2973   for (PetscInt iter = 0; iter < 10; iter++) {
2974     PetscScalar res[3], J[9];
2975     PetscReal   resnorm;
2976     TPSNearestPointResJac(feval, x, y, res, J);
2977     resnorm = PetscSqrtReal(PetscSqr(PetscRealPart(res[0])) + PetscSqr(PetscRealPart(res[1])) + PetscSqr(PetscRealPart(res[2])));
2978     if (0) { // Turn on this monitor if you need to confirm quadratic convergence
2979       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])));
2980     }
2981     if (resnorm < PETSC_SMALL) break;
2982 
2983     // Take the Newton step
2984     PetscCall(PetscKernel_A_gets_inverse_A_3(J, 0., PETSC_FALSE, NULL));
2985     PetscKernel_v_gets_v_minus_A_times_w_3(y, J, res);
2986   }
2987   for (PetscInt i = 0; i < 3; i++) x[i] = y[i];
2988   PetscFunctionReturn(PETSC_SUCCESS);
2989 }
2990 
2991 const char *const DMPlexTPSTypes[] = {"SCHWARZ_P", "GYROID", "DMPlexTPSType", "DMPLEX_TPS_", NULL};
2992 
2993 static PetscErrorCode DMPlexCreateTPSMesh_Internal(DM dm, DMPlexTPSType tpstype, const PetscInt extent[], const DMBoundaryType periodic[], PetscBool tps_distribute, PetscInt refinements, PetscInt layers, PetscReal thickness)
2994 {
2995   PetscMPIInt rank;
2996   PetscInt    topoDim = 2, spaceDim = 3, numFaces = 0, numVertices = 0, numEdges = 0;
2997   PetscInt(*edges)[2] = NULL, *edgeSets = NULL;
2998   PetscInt            *cells_flat = NULL;
2999   PetscReal           *vtxCoords  = NULL;
3000   TPSEvaluateFunc      evalFunc   = NULL;
3001   PetscSimplePointFunc normalFunc = NULL;
3002   DMLabel              label;
3003 
3004   PetscFunctionBegin;
3005   PetscCall(PetscLogEventBegin(DMPLEX_Generate, dm, 0, 0, 0));
3006   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank));
3007   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);
3008   switch (tpstype) {
3009   case DMPLEX_TPS_SCHWARZ_P:
3010     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");
3011     if (rank == 0) {
3012       PetscInt(*cells)[6][4][4] = NULL; // [junction, junction-face, cell, conn]
3013       PetscInt  Njunctions = 0, Ncuts = 0, Npipes[3], vcount;
3014       PetscReal L = 1;
3015 
3016       Npipes[0]   = (extent[0] + 1) * extent[1] * extent[2];
3017       Npipes[1]   = extent[0] * (extent[1] + 1) * extent[2];
3018       Npipes[2]   = extent[0] * extent[1] * (extent[2] + 1);
3019       Njunctions  = extent[0] * extent[1] * extent[2];
3020       Ncuts       = 2 * (extent[0] * extent[1] + extent[1] * extent[2] + extent[2] * extent[0]);
3021       numVertices = 4 * (Npipes[0] + Npipes[1] + Npipes[2]) + 8 * Njunctions;
3022       PetscCall(PetscMalloc1(3 * numVertices, &vtxCoords));
3023       PetscCall(PetscMalloc1(Njunctions, &cells));
3024       PetscCall(PetscMalloc1(Ncuts * 4, &edges));
3025       PetscCall(PetscMalloc1(Ncuts * 4, &edgeSets));
3026       // x-normal pipes
3027       vcount = 0;
3028       for (PetscInt i = 0; i < extent[0] + 1; i++) {
3029         for (PetscInt j = 0; j < extent[1]; j++) {
3030           for (PetscInt k = 0; k < extent[2]; k++) {
3031             for (PetscInt l = 0; l < 4; l++) {
3032               vtxCoords[vcount++] = (2 * i - 1) * L;
3033               vtxCoords[vcount++] = 2 * j * L + PetscCosReal((2 * l + 1) * PETSC_PI / 4) * L / 2;
3034               vtxCoords[vcount++] = 2 * k * L + PetscSinReal((2 * l + 1) * PETSC_PI / 4) * L / 2;
3035             }
3036           }
3037         }
3038       }
3039       // y-normal pipes
3040       for (PetscInt i = 0; i < extent[0]; i++) {
3041         for (PetscInt j = 0; j < extent[1] + 1; j++) {
3042           for (PetscInt k = 0; k < extent[2]; k++) {
3043             for (PetscInt l = 0; l < 4; l++) {
3044               vtxCoords[vcount++] = 2 * i * L + PetscSinReal((2 * l + 1) * PETSC_PI / 4) * L / 2;
3045               vtxCoords[vcount++] = (2 * j - 1) * L;
3046               vtxCoords[vcount++] = 2 * k * L + PetscCosReal((2 * l + 1) * PETSC_PI / 4) * L / 2;
3047             }
3048           }
3049         }
3050       }
3051       // z-normal pipes
3052       for (PetscInt i = 0; i < extent[0]; i++) {
3053         for (PetscInt j = 0; j < extent[1]; j++) {
3054           for (PetscInt k = 0; k < extent[2] + 1; k++) {
3055             for (PetscInt l = 0; l < 4; l++) {
3056               vtxCoords[vcount++] = 2 * i * L + PetscCosReal((2 * l + 1) * PETSC_PI / 4) * L / 2;
3057               vtxCoords[vcount++] = 2 * j * L + PetscSinReal((2 * l + 1) * PETSC_PI / 4) * L / 2;
3058               vtxCoords[vcount++] = (2 * k - 1) * L;
3059             }
3060           }
3061         }
3062       }
3063       // junctions
3064       for (PetscInt i = 0; i < extent[0]; i++) {
3065         for (PetscInt j = 0; j < extent[1]; j++) {
3066           for (PetscInt k = 0; k < extent[2]; k++) {
3067             const PetscInt J = (i * extent[1] + j) * extent[2] + k, Jvoff = (Npipes[0] + Npipes[1] + Npipes[2]) * 4 + J * 8;
3068             PetscCheck(vcount / 3 == Jvoff, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Unexpected vertex count");
3069             for (PetscInt ii = 0; ii < 2; ii++) {
3070               for (PetscInt jj = 0; jj < 2; jj++) {
3071                 for (PetscInt kk = 0; kk < 2; kk++) {
3072                   double Ls           = (1 - sqrt(2) / 4) * L;
3073                   vtxCoords[vcount++] = 2 * i * L + (2 * ii - 1) * Ls;
3074                   vtxCoords[vcount++] = 2 * j * L + (2 * jj - 1) * Ls;
3075                   vtxCoords[vcount++] = 2 * k * L + (2 * kk - 1) * Ls;
3076                 }
3077               }
3078             }
3079             const PetscInt jfaces[3][2][4] = {
3080               {{3, 1, 0, 2}, {7, 5, 4, 6}}, // x-aligned
3081               {{5, 4, 0, 1}, {7, 6, 2, 3}}, // y-aligned
3082               {{6, 2, 0, 4}, {7, 3, 1, 5}}  // z-aligned
3083             };
3084             const PetscInt pipe_lo[3] = {// vertex numbers of pipes
3085                                          ((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};
3086             const PetscInt pipe_hi[3] = {// vertex numbers of pipes
3087                                          (((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};
3088             for (PetscInt dir = 0; dir < 3; dir++) { // x,y,z
3089               const PetscInt ijk[3] = {i, j, k};
3090               for (PetscInt l = 0; l < 4; l++) { // rotations
3091                 cells[J][dir * 2 + 0][l][0] = pipe_lo[dir] + l;
3092                 cells[J][dir * 2 + 0][l][1] = Jvoff + jfaces[dir][0][l];
3093                 cells[J][dir * 2 + 0][l][2] = Jvoff + jfaces[dir][0][(l - 1 + 4) % 4];
3094                 cells[J][dir * 2 + 0][l][3] = pipe_lo[dir] + (l - 1 + 4) % 4;
3095                 cells[J][dir * 2 + 1][l][0] = Jvoff + jfaces[dir][1][l];
3096                 cells[J][dir * 2 + 1][l][1] = pipe_hi[dir] + l;
3097                 cells[J][dir * 2 + 1][l][2] = pipe_hi[dir] + (l - 1 + 4) % 4;
3098                 cells[J][dir * 2 + 1][l][3] = Jvoff + jfaces[dir][1][(l - 1 + 4) % 4];
3099                 if (ijk[dir] == 0) {
3100                   edges[numEdges][0] = pipe_lo[dir] + l;
3101                   edges[numEdges][1] = pipe_lo[dir] + (l + 1) % 4;
3102                   edgeSets[numEdges] = dir * 2 + 1;
3103                   numEdges++;
3104                 }
3105                 if (ijk[dir] + 1 == extent[dir]) {
3106                   edges[numEdges][0] = pipe_hi[dir] + l;
3107                   edges[numEdges][1] = pipe_hi[dir] + (l + 1) % 4;
3108                   edgeSets[numEdges] = dir * 2 + 2;
3109                   numEdges++;
3110                 }
3111               }
3112             }
3113           }
3114         }
3115       }
3116       PetscCheck(numEdges == Ncuts * 4, PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Edge count %" PetscInt_FMT " incompatible with number of cuts %" PetscInt_FMT, numEdges, Ncuts);
3117       numFaces   = 24 * Njunctions;
3118       cells_flat = cells[0][0][0];
3119     }
3120     evalFunc   = TPSEvaluate_SchwarzP;
3121     normalFunc = TPSExtrudeNormalFunc_SchwarzP;
3122     break;
3123   case DMPLEX_TPS_GYROID:
3124     if (rank == 0) {
3125       // This is a coarse mesh approximation of the gyroid shifted to being the zero of the level set
3126       //
3127       //     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)
3128       //
3129       // on the cell [0,2]^3.
3130       //
3131       // Think about dividing that cell into four columns, and focus on the column [0,1]x[0,1]x[0,2].
3132       // If you looked at the gyroid in that column at different slices of z you would see that it kind of spins
3133       // like a boomerang:
3134       //
3135       //     z = 0          z = 1/4        z = 1/2        z = 3/4     //
3136       //     -----          -------        -------        -------     //
3137       //                                                              //
3138       //     +       +      +       +      +       +      +   \   +   //
3139       //      \                                   /            \      //
3140       //       \            `-_   _-'            /              }     //
3141       //        *-_            `-'            _-'              /      //
3142       //     +     `-+      +       +      +-'     +      +   /   +   //
3143       //                                                              //
3144       //                                                              //
3145       //     z = 1          z = 5/4        z = 3/2        z = 7/4     //
3146       //     -----          -------        -------        -------     //
3147       //                                                              //
3148       //     +-_     +      +       +      +     _-+      +   /   +   //
3149       //        `-_            _-_            _-`            /        //
3150       //           \        _-'   `-_        /              {         //
3151       //            \                       /                \        //
3152       //     +       +      +       +      +       +      +   \   +   //
3153       //
3154       //
3155       // This course mesh approximates each of these slices by two line segments,
3156       // and then connects the segments in consecutive layers with quadrilateral faces.
3157       // All of the end points of the segments are multiples of 1/4 except for the
3158       // point * in the picture for z = 0 above and the similar points in other layers.
3159       // That point is at (gamma, gamma, 0), where gamma is calculated below.
3160       //
3161       // The column  [1,2]x[1,2]x[0,2] looks the same as this column;
3162       // The columns [1,2]x[0,1]x[0,2] and [0,1]x[1,2]x[0,2] are mirror images.
3163       //
3164       // As for how this method turned into the names given to the vertices:
3165       // that was not systematic, it was just the way it worked out in my handwritten notes.
3166 
3167       PetscInt facesPerBlock = 64;
3168       PetscInt vertsPerBlock = 56;
3169       PetscInt extentPlus[3];
3170       PetscInt numBlocks, numBlocksPlus;
3171       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;
3172       const PetscInt pattern[64][4] = {
3173   /* face to vertex within the coarse discretization of a single gyroid block */
3174   /* layer 0 */
3175         {A,           C,           K,           G          },
3176         {C,           B,           II,          K          },
3177         {D,           A,           H,           L          },
3178         {B + 56 * 1,  D,           L,           J          },
3179         {E,           B + 56 * 1,  J,           N          },
3180         {A + 56 * 2,  E,           N,           H + 56 * 2 },
3181         {F,           A + 56 * 2,  G + 56 * 2,  M          },
3182         {B,           F,           M,           II         },
3183  /* layer 1 */
3184         {G,           K,           Q,           O          },
3185         {K,           II,          P,           Q          },
3186         {L,           H,           O + 56 * 1,  R          },
3187         {J,           L,           R,           P          },
3188         {N,           J,           P,           S          },
3189         {H + 56 * 2,  N,           S,           O + 56 * 3 },
3190         {M,           G + 56 * 2,  O + 56 * 2,  T          },
3191         {II,          M,           T,           P          },
3192  /* layer 2 */
3193         {O,           Q,           Y,           U          },
3194         {Q,           P,           W,           Y          },
3195         {R,           O + 56 * 1,  U + 56 * 1,  Ap         },
3196         {P,           R,           Ap,          W          },
3197         {S,           P,           X,           Bp         },
3198         {O + 56 * 3,  S,           Bp,          V + 56 * 1 },
3199         {T,           O + 56 * 2,  V,           Z          },
3200         {P,           T,           Z,           X          },
3201  /* layer 3 */
3202         {U,           Y,           Ep,          Dp         },
3203         {Y,           W,           Cp,          Ep         },
3204         {Ap,          U + 56 * 1,  Dp + 56 * 1, Gp         },
3205         {W,           Ap,          Gp,          Cp         },
3206         {Bp,          X,           Cp + 56 * 2, Fp         },
3207         {V + 56 * 1,  Bp,          Fp,          Dp + 56 * 1},
3208         {Z,           V,           Dp,          Hp         },
3209         {X,           Z,           Hp,          Cp + 56 * 2},
3210  /* layer 4 */
3211         {Dp,          Ep,          Mp,          Kp         },
3212         {Ep,          Cp,          Ip,          Mp         },
3213         {Gp,          Dp + 56 * 1, Lp,          Np         },
3214         {Cp,          Gp,          Np,          Jp         },
3215         {Fp,          Cp + 56 * 2, Jp + 56 * 2, Pp         },
3216         {Dp + 56 * 1, Fp,          Pp,          Lp         },
3217         {Hp,          Dp,          Kp,          Op         },
3218         {Cp + 56 * 2, Hp,          Op,          Ip + 56 * 2},
3219  /* layer 5 */
3220         {Kp,          Mp,          Sp,          Rp         },
3221         {Mp,          Ip,          Qp,          Sp         },
3222         {Np,          Lp,          Rp,          Tp         },
3223         {Jp,          Np,          Tp,          Qp + 56 * 1},
3224         {Pp,          Jp + 56 * 2, Qp + 56 * 3, Up         },
3225         {Lp,          Pp,          Up,          Rp         },
3226         {Op,          Kp,          Rp,          Vp         },
3227         {Ip + 56 * 2, Op,          Vp,          Qp + 56 * 2},
3228  /* layer 6 */
3229         {Rp,          Sp,          Aq,          Yp         },
3230         {Sp,          Qp,          Wp,          Aq         },
3231         {Tp,          Rp,          Yp,          Cq         },
3232         {Qp + 56 * 1, Tp,          Cq,          Wp + 56 * 1},
3233         {Up,          Qp + 56 * 3, Xp + 56 * 1, Dq         },
3234         {Rp,          Up,          Dq,          Zp         },
3235         {Vp,          Rp,          Zp,          Bq         },
3236         {Qp + 56 * 2, Vp,          Bq,          Xp         },
3237  /* layer 7 (the top is the periodic image of the bottom of layer 0) */
3238         {Yp,          Aq,          C + 56 * 4,  A + 56 * 4 },
3239         {Aq,          Wp,          B + 56 * 4,  C + 56 * 4 },
3240         {Cq,          Yp,          A + 56 * 4,  D + 56 * 4 },
3241         {Wp + 56 * 1, Cq,          D + 56 * 4,  B + 56 * 5 },
3242         {Dq,          Xp + 56 * 1, B + 56 * 5,  E + 56 * 4 },
3243         {Zp,          Dq,          E + 56 * 4,  A + 56 * 6 },
3244         {Bq,          Zp,          A + 56 * 6,  F + 56 * 4 },
3245         {Xp,          Bq,          F + 56 * 4,  B + 56 * 4 }
3246       };
3247       const PetscReal gamma                = PetscAcosReal((PetscSqrtReal(3.) - 1.) / PetscSqrtReal(2.)) / PETSC_PI;
3248       const PetscReal patternCoords[56][3] = {
3249         {1.,        0.,        0.  }, /* A  */
3250         {0.,        1.,        0.  }, /* B  */
3251         {gamma,     gamma,     0.  }, /* C  */
3252         {1 + gamma, 1 - gamma, 0.  }, /* D  */
3253         {2 - gamma, 2 - gamma, 0.  }, /* E  */
3254         {1 - gamma, 1 + gamma, 0.  }, /* F  */
3255 
3256         {.5,        0,         .25 }, /* G  */
3257         {1.5,       0.,        .25 }, /* H  */
3258         {.5,        1.,        .25 }, /* II */
3259         {1.5,       1.,        .25 }, /* J  */
3260         {.25,       .5,        .25 }, /* K  */
3261         {1.25,      .5,        .25 }, /* L  */
3262         {.75,       1.5,       .25 }, /* M  */
3263         {1.75,      1.5,       .25 }, /* N  */
3264 
3265         {0.,        0.,        .5  }, /* O  */
3266         {1.,        1.,        .5  }, /* P  */
3267         {gamma,     1 - gamma, .5  }, /* Q  */
3268         {1 + gamma, gamma,     .5  }, /* R  */
3269         {2 - gamma, 1 + gamma, .5  }, /* S  */
3270         {1 - gamma, 2 - gamma, .5  }, /* T  */
3271 
3272         {0.,        .5,        .75 }, /* U  */
3273         {0.,        1.5,       .75 }, /* V  */
3274         {1.,        .5,        .75 }, /* W  */
3275         {1.,        1.5,       .75 }, /* X  */
3276         {.5,        .75,       .75 }, /* Y  */
3277         {.5,        1.75,      .75 }, /* Z  */
3278         {1.5,       .25,       .75 }, /* Ap */
3279         {1.5,       1.25,      .75 }, /* Bp */
3280 
3281         {1.,        0.,        1.  }, /* Cp */
3282         {0.,        1.,        1.  }, /* Dp */
3283         {1 - gamma, 1 - gamma, 1.  }, /* Ep */
3284         {1 + gamma, 1 + gamma, 1.  }, /* Fp */
3285         {2 - gamma, gamma,     1.  }, /* Gp */
3286         {gamma,     2 - gamma, 1.  }, /* Hp */
3287 
3288         {.5,        0.,        1.25}, /* Ip */
3289         {1.5,       0.,        1.25}, /* Jp */
3290         {.5,        1.,        1.25}, /* Kp */
3291         {1.5,       1.,        1.25}, /* Lp */
3292         {.75,       .5,        1.25}, /* Mp */
3293         {1.75,      .5,        1.25}, /* Np */
3294         {.25,       1.5,       1.25}, /* Op */
3295         {1.25,      1.5,       1.25}, /* Pp */
3296 
3297         {0.,        0.,        1.5 }, /* Qp */
3298         {1.,        1.,        1.5 }, /* Rp */
3299         {1 - gamma, gamma,     1.5 }, /* Sp */
3300         {2 - gamma, 1 - gamma, 1.5 }, /* Tp */
3301         {1 + gamma, 2 - gamma, 1.5 }, /* Up */
3302         {gamma,     1 + gamma, 1.5 }, /* Vp */
3303 
3304         {0.,        .5,        1.75}, /* Wp */
3305         {0.,        1.5,       1.75}, /* Xp */
3306         {1.,        .5,        1.75}, /* Yp */
3307         {1.,        1.5,       1.75}, /* Zp */
3308         {.5,        .25,       1.75}, /* Aq */
3309         {.5,        1.25,      1.75}, /* Bq */
3310         {1.5,       .75,       1.75}, /* Cq */
3311         {1.5,       1.75,      1.75}, /* Dq */
3312       };
3313       PetscInt(*cells)[64][4] = NULL;
3314       PetscBool *seen;
3315       PetscInt  *vertToTrueVert;
3316       PetscInt   count;
3317 
3318       for (PetscInt i = 0; i < 3; i++) extentPlus[i] = extent[i] + 1;
3319       numBlocks = 1;
3320       for (PetscInt i = 0; i < 3; i++) numBlocks *= extent[i];
3321       numBlocksPlus = 1;
3322       for (PetscInt i = 0; i < 3; i++) numBlocksPlus *= extentPlus[i];
3323       numFaces = numBlocks * facesPerBlock;
3324       PetscCall(PetscMalloc1(numBlocks, &cells));
3325       PetscCall(PetscCalloc1(numBlocksPlus * vertsPerBlock, &seen));
3326       for (PetscInt k = 0; k < extent[2]; k++) {
3327         for (PetscInt j = 0; j < extent[1]; j++) {
3328           for (PetscInt i = 0; i < extent[0]; i++) {
3329             for (PetscInt f = 0; f < facesPerBlock; f++) {
3330               for (PetscInt v = 0; v < 4; v++) {
3331                 PetscInt vertRaw     = pattern[f][v];
3332                 PetscInt blockidx    = vertRaw / 56;
3333                 PetscInt patternvert = vertRaw % 56;
3334                 PetscInt xplus       = (blockidx & 1);
3335                 PetscInt yplus       = (blockidx & 2) >> 1;
3336                 PetscInt zplus       = (blockidx & 4) >> 2;
3337                 PetscInt zcoord      = (periodic && periodic[2] == DM_BOUNDARY_PERIODIC) ? ((k + zplus) % extent[2]) : (k + zplus);
3338                 PetscInt ycoord      = (periodic && periodic[1] == DM_BOUNDARY_PERIODIC) ? ((j + yplus) % extent[1]) : (j + yplus);
3339                 PetscInt xcoord      = (periodic && periodic[0] == DM_BOUNDARY_PERIODIC) ? ((i + xplus) % extent[0]) : (i + xplus);
3340                 PetscInt vert        = ((zcoord * extentPlus[1] + ycoord) * extentPlus[0] + xcoord) * 56 + patternvert;
3341 
3342                 cells[(k * extent[1] + j) * extent[0] + i][f][v] = vert;
3343                 seen[vert]                                       = PETSC_TRUE;
3344               }
3345             }
3346           }
3347         }
3348       }
3349       for (PetscInt i = 0; i < numBlocksPlus * vertsPerBlock; i++)
3350         if (seen[i]) numVertices++;
3351       count = 0;
3352       PetscCall(PetscMalloc1(numBlocksPlus * vertsPerBlock, &vertToTrueVert));
3353       PetscCall(PetscMalloc1(numVertices * 3, &vtxCoords));
3354       for (PetscInt i = 0; i < numBlocksPlus * vertsPerBlock; i++) vertToTrueVert[i] = -1;
3355       for (PetscInt k = 0; k < extentPlus[2]; k++) {
3356         for (PetscInt j = 0; j < extentPlus[1]; j++) {
3357           for (PetscInt i = 0; i < extentPlus[0]; i++) {
3358             for (PetscInt v = 0; v < vertsPerBlock; v++) {
3359               PetscInt vIdx = ((k * extentPlus[1] + j) * extentPlus[0] + i) * vertsPerBlock + v;
3360 
3361               if (seen[vIdx]) {
3362                 PetscInt thisVert;
3363 
3364                 vertToTrueVert[vIdx] = thisVert = count++;
3365 
3366                 for (PetscInt d = 0; d < 3; d++) vtxCoords[3 * thisVert + d] = patternCoords[v][d];
3367                 vtxCoords[3 * thisVert + 0] += i * 2;
3368                 vtxCoords[3 * thisVert + 1] += j * 2;
3369                 vtxCoords[3 * thisVert + 2] += k * 2;
3370               }
3371             }
3372           }
3373         }
3374       }
3375       for (PetscInt i = 0; i < numBlocks; i++) {
3376         for (PetscInt f = 0; f < facesPerBlock; f++) {
3377           for (PetscInt v = 0; v < 4; v++) cells[i][f][v] = vertToTrueVert[cells[i][f][v]];
3378         }
3379       }
3380       PetscCall(PetscFree(vertToTrueVert));
3381       PetscCall(PetscFree(seen));
3382       cells_flat = cells[0][0];
3383       numEdges   = 0;
3384       for (PetscInt i = 0; i < numFaces; i++) {
3385         for (PetscInt e = 0; e < 4; e++) {
3386           PetscInt         ev[]       = {cells_flat[i * 4 + e], cells_flat[i * 4 + ((e + 1) % 4)]};
3387           const PetscReal *evCoords[] = {&vtxCoords[3 * ev[0]], &vtxCoords[3 * ev[1]]};
3388 
3389           for (PetscInt d = 0; d < 3; d++) {
3390             if (!periodic || periodic[0] != DM_BOUNDARY_PERIODIC) {
3391               if (evCoords[0][d] == 0. && evCoords[1][d] == 0.) numEdges++;
3392               if (evCoords[0][d] == 2. * extent[d] && evCoords[1][d] == 2. * extent[d]) numEdges++;
3393             }
3394           }
3395         }
3396       }
3397       PetscCall(PetscMalloc1(numEdges, &edges));
3398       PetscCall(PetscMalloc1(numEdges, &edgeSets));
3399       for (PetscInt edge = 0, i = 0; i < numFaces; i++) {
3400         for (PetscInt e = 0; e < 4; e++) {
3401           PetscInt         ev[]       = {cells_flat[i * 4 + e], cells_flat[i * 4 + ((e + 1) % 4)]};
3402           const PetscReal *evCoords[] = {&vtxCoords[3 * ev[0]], &vtxCoords[3 * ev[1]]};
3403 
3404           for (PetscInt d = 0; d < 3; d++) {
3405             if (!periodic || periodic[d] != DM_BOUNDARY_PERIODIC) {
3406               if (evCoords[0][d] == 0. && evCoords[1][d] == 0.) {
3407                 edges[edge][0]   = ev[0];
3408                 edges[edge][1]   = ev[1];
3409                 edgeSets[edge++] = 2 * d;
3410               }
3411               if (evCoords[0][d] == 2. * extent[d] && evCoords[1][d] == 2. * extent[d]) {
3412                 edges[edge][0]   = ev[0];
3413                 edges[edge][1]   = ev[1];
3414                 edgeSets[edge++] = 2 * d + 1;
3415               }
3416             }
3417           }
3418         }
3419       }
3420     }
3421     evalFunc   = TPSEvaluate_Gyroid;
3422     normalFunc = TPSExtrudeNormalFunc_Gyroid;
3423     break;
3424   }
3425 
3426   PetscCall(DMSetDimension(dm, topoDim));
3427   if (rank == 0) PetscCall(DMPlexBuildFromCellList(dm, numFaces, numVertices, 4, cells_flat));
3428   else PetscCall(DMPlexBuildFromCellList(dm, 0, 0, 0, NULL));
3429   PetscCall(PetscFree(cells_flat));
3430   {
3431     DM idm;
3432     PetscCall(DMPlexInterpolate(dm, &idm));
3433     PetscCall(DMPlexReplace_Internal(dm, &idm));
3434   }
3435   if (rank == 0) PetscCall(DMPlexBuildCoordinatesFromCellList(dm, spaceDim, vtxCoords));
3436   else PetscCall(DMPlexBuildCoordinatesFromCellList(dm, spaceDim, NULL));
3437   PetscCall(PetscFree(vtxCoords));
3438 
3439   PetscCall(DMCreateLabel(dm, "Face Sets"));
3440   PetscCall(DMGetLabel(dm, "Face Sets", &label));
3441   for (PetscInt e = 0; e < numEdges; e++) {
3442     PetscInt        njoin;
3443     const PetscInt *join, verts[] = {numFaces + edges[e][0], numFaces + edges[e][1]};
3444     PetscCall(DMPlexGetJoin(dm, 2, verts, &njoin, &join));
3445     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]);
3446     PetscCall(DMLabelSetValue(label, join[0], edgeSets[e]));
3447     PetscCall(DMPlexRestoreJoin(dm, 2, verts, &njoin, &join));
3448   }
3449   PetscCall(PetscFree(edges));
3450   PetscCall(PetscFree(edgeSets));
3451   if (tps_distribute) {
3452     DM               pdm = NULL;
3453     PetscPartitioner part;
3454 
3455     PetscCall(DMPlexGetPartitioner(dm, &part));
3456     PetscCall(PetscPartitionerSetFromOptions(part));
3457     PetscCall(DMPlexDistribute(dm, 0, NULL, &pdm));
3458     if (pdm) PetscCall(DMPlexReplace_Internal(dm, &pdm));
3459     // Do not auto-distribute again
3460     PetscCall(DMPlexDistributeSetDefault(dm, PETSC_FALSE));
3461   }
3462 
3463   PetscCall(DMPlexSetRefinementUniform(dm, PETSC_TRUE));
3464   for (PetscInt refine = 0; refine < refinements; refine++) {
3465     PetscInt     m;
3466     DM           dmf;
3467     Vec          X;
3468     PetscScalar *x;
3469     PetscCall(DMRefine(dm, MPI_COMM_NULL, &dmf));
3470     PetscCall(DMPlexReplace_Internal(dm, &dmf));
3471 
3472     PetscCall(DMGetCoordinatesLocal(dm, &X));
3473     PetscCall(VecGetLocalSize(X, &m));
3474     PetscCall(VecGetArray(X, &x));
3475     for (PetscInt i = 0; i < m; i += 3) PetscCall(TPSNearestPoint(evalFunc, &x[i]));
3476     PetscCall(VecRestoreArray(X, &x));
3477   }
3478 
3479   // Face Sets has already been propagated to new vertices during refinement; this propagates to the initial vertices.
3480   PetscCall(DMGetLabel(dm, "Face Sets", &label));
3481   PetscCall(DMPlexLabelComplete(dm, label));
3482 
3483   PetscCall(PetscLogEventEnd(DMPLEX_Generate, dm, 0, 0, 0));
3484 
3485   if (thickness > 0) {
3486     DM              edm, cdm, ecdm;
3487     DMPlexTransform tr;
3488     const char     *prefix;
3489     PetscOptions    options;
3490     // Code from DMPlexExtrude
3491     PetscCall(DMPlexTransformCreate(PetscObjectComm((PetscObject)dm), &tr));
3492     PetscCall(DMPlexTransformSetDM(tr, dm));
3493     PetscCall(DMPlexTransformSetType(tr, DMPLEXEXTRUDE));
3494     PetscCall(PetscObjectGetOptionsPrefix((PetscObject)dm, &prefix));
3495     PetscCall(PetscObjectSetOptionsPrefix((PetscObject)tr, prefix));
3496     PetscCall(PetscObjectGetOptions((PetscObject)dm, &options));
3497     PetscCall(PetscObjectSetOptions((PetscObject)tr, options));
3498     PetscCall(DMPlexTransformExtrudeSetLayers(tr, layers));
3499     PetscCall(DMPlexTransformExtrudeSetThickness(tr, thickness));
3500     PetscCall(DMPlexTransformExtrudeSetTensor(tr, PETSC_FALSE));
3501     PetscCall(DMPlexTransformExtrudeSetSymmetric(tr, PETSC_TRUE));
3502     PetscCall(DMPlexTransformExtrudeSetNormalFunction(tr, normalFunc));
3503     PetscCall(DMPlexTransformSetFromOptions(tr));
3504     PetscCall(PetscObjectSetOptions((PetscObject)tr, NULL));
3505     PetscCall(DMPlexTransformSetUp(tr));
3506     PetscCall(PetscObjectViewFromOptions((PetscObject)tr, NULL, "-dm_plex_tps_transform_view"));
3507     PetscCall(DMPlexTransformApply(tr, dm, &edm));
3508     PetscCall(DMCopyDisc(dm, edm));
3509     PetscCall(DMGetCoordinateDM(dm, &cdm));
3510     PetscCall(DMGetCoordinateDM(edm, &ecdm));
3511     PetscCall(DMCopyDisc(cdm, ecdm));
3512     PetscCall(DMPlexTransformCreateDiscLabels(tr, edm));
3513     PetscCall(DMPlexTransformDestroy(&tr));
3514     if (edm) {
3515       ((DM_Plex *)edm->data)->printFEM    = ((DM_Plex *)dm->data)->printFEM;
3516       ((DM_Plex *)edm->data)->printL2     = ((DM_Plex *)dm->data)->printL2;
3517       ((DM_Plex *)edm->data)->printLocate = ((DM_Plex *)dm->data)->printLocate;
3518     }
3519     PetscCall(DMPlexReplace_Internal(dm, &edm));
3520   }
3521   PetscFunctionReturn(PETSC_SUCCESS);
3522 }
3523 
3524 /*@
3525   DMPlexCreateTPSMesh - Create a distributed, interpolated mesh of a triply-periodic surface
3526 
3527   Collective
3528 
3529   Input Parameters:
3530 + comm           - The communicator for the `DM` object
3531 . tpstype        - Type of triply-periodic surface
3532 . extent         - Array of length 3 containing number of periods in each direction
3533 . periodic       - array of length 3 with periodicity, or `NULL` for non-periodic
3534 . tps_distribute - Distribute 2D manifold mesh prior to refinement and extrusion (more scalable)
3535 . refinements    - Number of factor-of-2 refinements of 2D manifold mesh
3536 . layers         - Number of cell layers extruded in normal direction
3537 - thickness      - Thickness in normal direction
3538 
3539   Output Parameter:
3540 . dm - The `DM` object
3541 
3542   Level: beginner
3543 
3544   Notes:
3545   This meshes the surface of the Schwarz P or Gyroid surfaces.  Schwarz P is is the simplest member of the triply-periodic minimal surfaces.
3546   https://en.wikipedia.org/wiki/Schwarz_minimal_surface#Schwarz_P_(%22Primitive%22) and can be cut with "clean" boundaries.
3547   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.
3548   Our implementation creates a very coarse mesh of the surface and refines (by 4-way splitting) as many times as requested.
3549   On each refinement, all vertices are projected to their nearest point on the surface.
3550   This projection could readily be extended to related surfaces.
3551 
3552   The face (edge) sets for the Schwarz P surface are numbered 1(-x), 2(+x), 3(-y), 4(+y), 5(-z), 6(+z).
3553   When the mesh is refined, "Face Sets" contain the new vertices (created during refinement).  Use `DMPlexLabelComplete()` to propagate to coarse-level vertices.
3554 
3555   Developer Notes:
3556   The Gyroid mesh does not currently mark boundary sets.
3557 
3558   References:
3559 . * - Maskery et al, Insights into the mechanical properties of several triply periodic minimal surface lattice structures made by polymer additive manufacturing, 2017.
3560   https://doi.org/10.1016/j.polymer.2017.11.049
3561 
3562 .seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexCreateSphereMesh()`, `DMSetType()`, `DMCreate()`
3563 @*/
3564 PetscErrorCode DMPlexCreateTPSMesh(MPI_Comm comm, DMPlexTPSType tpstype, const PetscInt extent[], const DMBoundaryType periodic[], PetscBool tps_distribute, PetscInt refinements, PetscInt layers, PetscReal thickness, DM *dm)
3565 {
3566   PetscFunctionBegin;
3567   PetscCall(DMCreate(comm, dm));
3568   PetscCall(DMSetType(*dm, DMPLEX));
3569   PetscCall(DMPlexCreateTPSMesh_Internal(*dm, tpstype, extent, periodic, tps_distribute, refinements, layers, thickness));
3570   PetscFunctionReturn(PETSC_SUCCESS);
3571 }
3572 
3573 /*@
3574   DMPlexCreateSphereMesh - Creates a mesh on the d-dimensional sphere, S^d.
3575 
3576   Collective
3577 
3578   Input Parameters:
3579 + comm    - The communicator for the `DM` object
3580 . dim     - The dimension
3581 . simplex - Use simplices, or tensor product cells
3582 - R       - The radius
3583 
3584   Output Parameter:
3585 . dm - The `DM` object
3586 
3587   Level: beginner
3588 
3589 .seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexCreateBallMesh()`, `DMPlexCreateBoxMesh()`, `DMSetType()`, `DMCreate()`
3590 @*/
3591 PetscErrorCode DMPlexCreateSphereMesh(MPI_Comm comm, PetscInt dim, PetscBool simplex, PetscReal R, DM *dm)
3592 {
3593   PetscFunctionBegin;
3594   PetscAssertPointer(dm, 5);
3595   PetscCall(DMCreate(comm, dm));
3596   PetscCall(DMSetType(*dm, DMPLEX));
3597   PetscCall(DMPlexCreateSphereMesh_Internal(*dm, dim, simplex, R));
3598   PetscFunctionReturn(PETSC_SUCCESS);
3599 }
3600 
3601 static PetscErrorCode DMPlexCreateBallMesh_Internal(DM dm, PetscInt dim, PetscReal R)
3602 {
3603   DM      sdm, vol;
3604   DMLabel bdlabel;
3605 
3606   PetscFunctionBegin;
3607   PetscCall(DMCreate(PetscObjectComm((PetscObject)dm), &sdm));
3608   PetscCall(DMSetType(sdm, DMPLEX));
3609   PetscCall(PetscObjectSetOptionsPrefix((PetscObject)sdm, "bd_"));
3610   PetscCall(DMPlexCreateSphereMesh_Internal(sdm, dim - 1, PETSC_TRUE, R));
3611   PetscCall(DMSetFromOptions(sdm));
3612   PetscCall(DMViewFromOptions(sdm, NULL, "-dm_view"));
3613   PetscCall(DMPlexGenerate(sdm, NULL, PETSC_TRUE, &vol));
3614   PetscCall(DMDestroy(&sdm));
3615   PetscCall(DMPlexReplace_Internal(dm, &vol));
3616   PetscCall(DMCreateLabel(dm, "marker"));
3617   PetscCall(DMGetLabel(dm, "marker", &bdlabel));
3618   PetscCall(DMPlexMarkBoundaryFaces(dm, PETSC_DETERMINE, bdlabel));
3619   PetscCall(DMPlexLabelComplete(dm, bdlabel));
3620   PetscFunctionReturn(PETSC_SUCCESS);
3621 }
3622 
3623 /*@
3624   DMPlexCreateBallMesh - Creates a simplex mesh on the d-dimensional ball, B^d.
3625 
3626   Collective
3627 
3628   Input Parameters:
3629 + comm - The communicator for the `DM` object
3630 . dim  - The dimension
3631 - R    - The radius
3632 
3633   Output Parameter:
3634 . dm - The `DM` object
3635 
3636   Options Database Key:
3637 . bd_dm_refine - This will refine the surface mesh preserving the sphere geometry
3638 
3639   Level: beginner
3640 
3641 .seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexCreateSphereMesh()`, `DMPlexCreateBoxMesh()`, `DMSetType()`, `DMCreate()`
3642 @*/
3643 PetscErrorCode DMPlexCreateBallMesh(MPI_Comm comm, PetscInt dim, PetscReal R, DM *dm)
3644 {
3645   PetscFunctionBegin;
3646   PetscCall(DMCreate(comm, dm));
3647   PetscCall(DMSetType(*dm, DMPLEX));
3648   PetscCall(DMPlexCreateBallMesh_Internal(*dm, dim, R));
3649   PetscFunctionReturn(PETSC_SUCCESS);
3650 }
3651 
3652 static PetscErrorCode DMPlexCreateReferenceCell_Internal(DM rdm, DMPolytopeType ct)
3653 {
3654   PetscFunctionBegin;
3655   switch (ct) {
3656   case DM_POLYTOPE_POINT: {
3657     PetscInt    numPoints[1]        = {1};
3658     PetscInt    coneSize[1]         = {0};
3659     PetscInt    cones[1]            = {0};
3660     PetscInt    coneOrientations[1] = {0};
3661     PetscScalar vertexCoords[1]     = {0.0};
3662 
3663     PetscCall(DMSetDimension(rdm, 0));
3664     PetscCall(DMPlexCreateFromDAG(rdm, 0, numPoints, coneSize, cones, coneOrientations, vertexCoords));
3665   } break;
3666   case DM_POLYTOPE_SEGMENT: {
3667     PetscInt    numPoints[2]        = {2, 1};
3668     PetscInt    coneSize[3]         = {2, 0, 0};
3669     PetscInt    cones[2]            = {1, 2};
3670     PetscInt    coneOrientations[2] = {0, 0};
3671     PetscScalar vertexCoords[2]     = {-1.0, 1.0};
3672 
3673     PetscCall(DMSetDimension(rdm, 1));
3674     PetscCall(DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords));
3675   } break;
3676   case DM_POLYTOPE_POINT_PRISM_TENSOR: {
3677     PetscInt    numPoints[2]        = {2, 1};
3678     PetscInt    coneSize[3]         = {2, 0, 0};
3679     PetscInt    cones[2]            = {1, 2};
3680     PetscInt    coneOrientations[2] = {0, 0};
3681     PetscScalar vertexCoords[2]     = {-1.0, 1.0};
3682 
3683     PetscCall(DMSetDimension(rdm, 1));
3684     PetscCall(DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords));
3685   } break;
3686   case DM_POLYTOPE_TRIANGLE: {
3687     PetscInt    numPoints[2]        = {3, 1};
3688     PetscInt    coneSize[4]         = {3, 0, 0, 0};
3689     PetscInt    cones[3]            = {1, 2, 3};
3690     PetscInt    coneOrientations[3] = {0, 0, 0};
3691     PetscScalar vertexCoords[6]     = {-1.0, -1.0, 1.0, -1.0, -1.0, 1.0};
3692 
3693     PetscCall(DMSetDimension(rdm, 2));
3694     PetscCall(DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords));
3695   } break;
3696   case DM_POLYTOPE_QUADRILATERAL: {
3697     PetscInt    numPoints[2]        = {4, 1};
3698     PetscInt    coneSize[5]         = {4, 0, 0, 0, 0};
3699     PetscInt    cones[4]            = {1, 2, 3, 4};
3700     PetscInt    coneOrientations[4] = {0, 0, 0, 0};
3701     PetscScalar vertexCoords[8]     = {-1.0, -1.0, 1.0, -1.0, 1.0, 1.0, -1.0, 1.0};
3702 
3703     PetscCall(DMSetDimension(rdm, 2));
3704     PetscCall(DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords));
3705   } break;
3706   case DM_POLYTOPE_SEG_PRISM_TENSOR: {
3707     PetscInt    numPoints[2]        = {4, 1};
3708     PetscInt    coneSize[5]         = {4, 0, 0, 0, 0};
3709     PetscInt    cones[4]            = {1, 2, 3, 4};
3710     PetscInt    coneOrientations[4] = {0, 0, 0, 0};
3711     PetscScalar vertexCoords[8]     = {-1.0, -1.0, 1.0, -1.0, -1.0, 1.0, 1.0, 1.0};
3712 
3713     PetscCall(DMSetDimension(rdm, 2));
3714     PetscCall(DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords));
3715   } break;
3716   case DM_POLYTOPE_TETRAHEDRON: {
3717     PetscInt    numPoints[2]        = {4, 1};
3718     PetscInt    coneSize[5]         = {4, 0, 0, 0, 0};
3719     PetscInt    cones[4]            = {1, 2, 3, 4};
3720     PetscInt    coneOrientations[4] = {0, 0, 0, 0};
3721     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};
3722 
3723     PetscCall(DMSetDimension(rdm, 3));
3724     PetscCall(DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords));
3725   } break;
3726   case DM_POLYTOPE_HEXAHEDRON: {
3727     PetscInt    numPoints[2]        = {8, 1};
3728     PetscInt    coneSize[9]         = {8, 0, 0, 0, 0, 0, 0, 0, 0};
3729     PetscInt    cones[8]            = {1, 2, 3, 4, 5, 6, 7, 8};
3730     PetscInt    coneOrientations[8] = {0, 0, 0, 0, 0, 0, 0, 0};
3731     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};
3732 
3733     PetscCall(DMSetDimension(rdm, 3));
3734     PetscCall(DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords));
3735   } break;
3736   case DM_POLYTOPE_TRI_PRISM: {
3737     PetscInt    numPoints[2]        = {6, 1};
3738     PetscInt    coneSize[7]         = {6, 0, 0, 0, 0, 0, 0};
3739     PetscInt    cones[6]            = {1, 2, 3, 4, 5, 6};
3740     PetscInt    coneOrientations[6] = {0, 0, 0, 0, 0, 0};
3741     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};
3742 
3743     PetscCall(DMSetDimension(rdm, 3));
3744     PetscCall(DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords));
3745   } break;
3746   case DM_POLYTOPE_TRI_PRISM_TENSOR: {
3747     PetscInt    numPoints[2]        = {6, 1};
3748     PetscInt    coneSize[7]         = {6, 0, 0, 0, 0, 0, 0};
3749     PetscInt    cones[6]            = {1, 2, 3, 4, 5, 6};
3750     PetscInt    coneOrientations[6] = {0, 0, 0, 0, 0, 0};
3751     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};
3752 
3753     PetscCall(DMSetDimension(rdm, 3));
3754     PetscCall(DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords));
3755   } break;
3756   case DM_POLYTOPE_QUAD_PRISM_TENSOR: {
3757     PetscInt    numPoints[2]        = {8, 1};
3758     PetscInt    coneSize[9]         = {8, 0, 0, 0, 0, 0, 0, 0, 0};
3759     PetscInt    cones[8]            = {1, 2, 3, 4, 5, 6, 7, 8};
3760     PetscInt    coneOrientations[8] = {0, 0, 0, 0, 0, 0, 0, 0};
3761     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};
3762 
3763     PetscCall(DMSetDimension(rdm, 3));
3764     PetscCall(DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords));
3765   } break;
3766   case DM_POLYTOPE_PYRAMID: {
3767     PetscInt    numPoints[2]        = {5, 1};
3768     PetscInt    coneSize[6]         = {5, 0, 0, 0, 0, 0};
3769     PetscInt    cones[5]            = {1, 2, 3, 4, 5};
3770     PetscInt    coneOrientations[8] = {0, 0, 0, 0, 0, 0, 0, 0};
3771     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};
3772 
3773     PetscCall(DMSetDimension(rdm, 3));
3774     PetscCall(DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords));
3775   } break;
3776   default:
3777     SETERRQ(PetscObjectComm((PetscObject)rdm), PETSC_ERR_ARG_WRONG, "Cannot create reference cell for cell type %s", DMPolytopeTypes[ct]);
3778   }
3779   {
3780     PetscInt Nv, v;
3781 
3782     /* Must create the celltype label here so that we do not automatically try to compute the types */
3783     PetscCall(DMCreateLabel(rdm, "celltype"));
3784     PetscCall(DMPlexSetCellType(rdm, 0, ct));
3785     PetscCall(DMPlexGetChart(rdm, NULL, &Nv));
3786     for (v = 1; v < Nv; ++v) PetscCall(DMPlexSetCellType(rdm, v, DM_POLYTOPE_POINT));
3787   }
3788   PetscCall(DMPlexInterpolateInPlace_Internal(rdm));
3789   PetscCall(PetscObjectSetName((PetscObject)rdm, DMPolytopeTypes[ct]));
3790   PetscFunctionReturn(PETSC_SUCCESS);
3791 }
3792 
3793 /*@
3794   DMPlexCreateReferenceCell - Create a `DMPLEX` with the appropriate FEM reference cell
3795 
3796   Collective
3797 
3798   Input Parameters:
3799 + comm - The communicator
3800 - ct   - The cell type of the reference cell
3801 
3802   Output Parameter:
3803 . refdm - The reference cell
3804 
3805   Level: intermediate
3806 
3807 .seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexCreateBoxMesh()`
3808 @*/
3809 PetscErrorCode DMPlexCreateReferenceCell(MPI_Comm comm, DMPolytopeType ct, DM *refdm)
3810 {
3811   PetscFunctionBegin;
3812   PetscCall(DMCreate(comm, refdm));
3813   PetscCall(DMSetType(*refdm, DMPLEX));
3814   PetscCall(DMPlexCreateReferenceCell_Internal(*refdm, ct));
3815   PetscFunctionReturn(PETSC_SUCCESS);
3816 }
3817 
3818 static PetscErrorCode DMPlexCreateBoundaryLabel_Private(DM dm, const char name[])
3819 {
3820   DM        plex;
3821   DMLabel   label;
3822   PetscBool hasLabel;
3823 
3824   PetscFunctionBegin;
3825   PetscCall(DMHasLabel(dm, name, &hasLabel));
3826   if (hasLabel) PetscFunctionReturn(PETSC_SUCCESS);
3827   PetscCall(DMCreateLabel(dm, name));
3828   PetscCall(DMGetLabel(dm, name, &label));
3829   PetscCall(DMConvert(dm, DMPLEX, &plex));
3830   PetscCall(DMPlexMarkBoundaryFaces(plex, 1, label));
3831   PetscCall(DMPlexLabelComplete(plex, label));
3832   PetscCall(DMDestroy(&plex));
3833   PetscFunctionReturn(PETSC_SUCCESS);
3834 }
3835 
3836 /*
3837   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.
3838 
3839     (x, y) -> (r, theta) = (x[1], (x[0] - lower[0]) * 2\pi/(upper[0] - lower[0]))
3840 */
3841 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[])
3842 {
3843   const PetscReal low = PetscRealPart(constants[0]);
3844   const PetscReal upp = PetscRealPart(constants[1]);
3845   const PetscReal r   = PetscRealPart(u[1]);
3846   const PetscReal th  = 2. * PETSC_PI * (PetscRealPart(u[0]) - low) / (upp - low);
3847 
3848   f0[0] = r * PetscCosReal(th);
3849   f0[1] = r * PetscSinReal(th);
3850 }
3851 
3852 const char *const DMPlexShapes[] = {"box", "box_surface", "ball", "sphere", "cylinder", "schwarz_p", "gyroid", "doublet", "annulus", "hypercubic", "zbox", "unknown", "DMPlexShape", "DM_SHAPE_", NULL};
3853 
3854 static PetscErrorCode DMPlexCreateFromOptions_Internal(PetscOptionItems *PetscOptionsObject, PetscBool *useCoordSpace, DM dm)
3855 {
3856   DMPlexShape    shape   = DM_SHAPE_BOX;
3857   DMPolytopeType cell    = DM_POLYTOPE_TRIANGLE;
3858   PetscInt       dim     = 2;
3859   PetscBool      simplex = PETSC_TRUE, interpolate = PETSC_TRUE, adjCone = PETSC_FALSE, adjClosure = PETSC_TRUE, refDomain = PETSC_FALSE;
3860   PetscBool      flg, flg2, fflg, bdfflg, nameflg;
3861   MPI_Comm       comm;
3862   char           filename[PETSC_MAX_PATH_LEN]   = "<unspecified>";
3863   char           bdFilename[PETSC_MAX_PATH_LEN] = "<unspecified>";
3864   char           plexname[PETSC_MAX_PATH_LEN]   = "";
3865 
3866   PetscFunctionBegin;
3867   PetscCall(PetscLogEventBegin(DMPLEX_CreateFromOptions, dm, 0, 0, 0));
3868   PetscCall(PetscObjectGetComm((PetscObject)dm, &comm));
3869   /* TODO Turn this into a registration interface */
3870   PetscCall(PetscOptionsString("-dm_plex_filename", "File containing a mesh", "DMPlexCreateFromFile", filename, filename, sizeof(filename), &fflg));
3871   PetscCall(PetscOptionsString("-dm_plex_boundary_filename", "File containing a mesh boundary", "DMPlexCreateFromFile", bdFilename, bdFilename, sizeof(bdFilename), &bdfflg));
3872   PetscCall(PetscOptionsString("-dm_plex_name", "Name of the mesh in the file", "DMPlexCreateFromFile", plexname, plexname, sizeof(plexname), &nameflg));
3873   PetscCall(PetscOptionsEnum("-dm_plex_cell", "Cell shape", "", DMPolytopeTypes, (PetscEnum)cell, (PetscEnum *)&cell, NULL));
3874   PetscCall(PetscOptionsBool("-dm_plex_reference_cell_domain", "Use a reference cell domain", "", refDomain, &refDomain, NULL));
3875   PetscCall(PetscOptionsEnum("-dm_plex_shape", "Shape for built-in mesh", "", DMPlexShapes, (PetscEnum)shape, (PetscEnum *)&shape, &flg));
3876   PetscCall(PetscOptionsBoundedInt("-dm_plex_dim", "Topological dimension of the mesh", "DMGetDimension", dim, &dim, &flg, 0));
3877   PetscCheck(dim >= 0, comm, PETSC_ERR_ARG_OUTOFRANGE, "Dimension %" PetscInt_FMT " should be in [0, infinity)", dim);
3878   PetscCall(PetscOptionsBool("-dm_plex_simplex", "Mesh cell shape", "", simplex, &simplex, &flg));
3879   PetscCall(PetscOptionsBool("-dm_plex_interpolate", "Flag to create edges and faces automatically", "", interpolate, &interpolate, &flg));
3880   PetscCall(PetscOptionsBool("-dm_plex_adj_cone", "Set adjacency direction", "DMSetBasicAdjacency", adjCone, &adjCone, &flg));
3881   PetscCall(PetscOptionsBool("-dm_plex_adj_closure", "Set adjacency size", "DMSetBasicAdjacency", adjClosure, &adjClosure, &flg2));
3882   if (flg || flg2) PetscCall(DMSetBasicAdjacency(dm, adjCone, adjClosure));
3883 
3884   switch (cell) {
3885   case DM_POLYTOPE_POINT:
3886   case DM_POLYTOPE_SEGMENT:
3887   case DM_POLYTOPE_POINT_PRISM_TENSOR:
3888   case DM_POLYTOPE_TRIANGLE:
3889   case DM_POLYTOPE_QUADRILATERAL:
3890   case DM_POLYTOPE_TETRAHEDRON:
3891   case DM_POLYTOPE_HEXAHEDRON:
3892     *useCoordSpace = PETSC_TRUE;
3893     break;
3894   default:
3895     *useCoordSpace = PETSC_FALSE;
3896     break;
3897   }
3898 
3899   if (fflg) {
3900     DM dmnew;
3901 
3902     PetscCall(DMPlexCreateFromFile(PetscObjectComm((PetscObject)dm), filename, plexname, interpolate, &dmnew));
3903     PetscCall(DMPlexCopy_Internal(dm, PETSC_FALSE, PETSC_FALSE, dmnew));
3904     PetscCall(DMPlexReplace_Internal(dm, &dmnew));
3905   } else if (refDomain) {
3906     PetscCall(DMPlexCreateReferenceCell_Internal(dm, cell));
3907   } else if (bdfflg) {
3908     DM bdm, dmnew;
3909 
3910     PetscCall(DMPlexCreateFromFile(PetscObjectComm((PetscObject)dm), bdFilename, plexname, interpolate, &bdm));
3911     PetscCall(PetscObjectSetOptionsPrefix((PetscObject)bdm, "bd_"));
3912     PetscCall(DMSetFromOptions(bdm));
3913     PetscCall(DMPlexGenerate(bdm, NULL, interpolate, &dmnew));
3914     PetscCall(DMDestroy(&bdm));
3915     PetscCall(DMPlexCopy_Internal(dm, PETSC_FALSE, PETSC_FALSE, dmnew));
3916     PetscCall(DMPlexReplace_Internal(dm, &dmnew));
3917   } else {
3918     PetscCall(PetscObjectSetName((PetscObject)dm, DMPlexShapes[shape]));
3919     switch (shape) {
3920     case DM_SHAPE_BOX:
3921     case DM_SHAPE_ZBOX:
3922     case DM_SHAPE_ANNULUS: {
3923       PetscInt       faces[3]  = {0, 0, 0};
3924       PetscReal      lower[3]  = {0, 0, 0};
3925       PetscReal      upper[3]  = {1, 1, 1};
3926       DMBoundaryType bdt[3]    = {DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE};
3927       PetscBool      isAnnular = shape == DM_SHAPE_ANNULUS ? PETSC_TRUE : PETSC_FALSE;
3928       PetscInt       i, n;
3929 
3930       n = dim;
3931       for (i = 0; i < dim; ++i) faces[i] = (dim == 1 ? 1 : 4 - dim);
3932       PetscCall(PetscOptionsIntArray("-dm_plex_box_faces", "Number of faces along each dimension", "", faces, &n, &flg));
3933       n = 3;
3934       PetscCall(PetscOptionsRealArray("-dm_plex_box_lower", "Lower left corner of box", "", lower, &n, &flg));
3935       PetscCheck(!flg || !(n != dim), comm, PETSC_ERR_ARG_SIZ, "Lower box point had %" PetscInt_FMT " values, should have been %" PetscInt_FMT, n, dim);
3936       n = 3;
3937       PetscCall(PetscOptionsRealArray("-dm_plex_box_upper", "Upper right corner of box", "", upper, &n, &flg));
3938       PetscCheck(!flg || !(n != dim), comm, PETSC_ERR_ARG_SIZ, "Upper box point had %" PetscInt_FMT " values, should have been %" PetscInt_FMT, n, dim);
3939       n = 3;
3940       PetscCall(PetscOptionsEnumArray("-dm_plex_box_bd", "Boundary type for each dimension", "", DMBoundaryTypes, (PetscEnum *)bdt, &n, &flg));
3941       PetscCheck(!flg || !(n != dim), comm, PETSC_ERR_ARG_SIZ, "Box boundary types had %" PetscInt_FMT " values, should have been %" PetscInt_FMT, n, dim);
3942 
3943       PetscCheck(!isAnnular || dim == 2, comm, PETSC_ERR_ARG_OUTOFRANGE, "Only two dimensional annuli have been implemented");
3944       if (isAnnular)
3945         for (i = 0; i < dim - 1; ++i) bdt[i] = DM_BOUNDARY_PERIODIC;
3946 
3947       switch (cell) {
3948       case DM_POLYTOPE_TRI_PRISM_TENSOR:
3949         PetscCall(DMPlexCreateWedgeBoxMesh_Internal(dm, faces, lower, upper, bdt));
3950         if (!interpolate) {
3951           DM udm;
3952 
3953           PetscCall(DMPlexUninterpolate(dm, &udm));
3954           PetscCall(DMPlexReplace_Internal(dm, &udm));
3955         }
3956         break;
3957       default:
3958         PetscCall(DMPlexCreateBoxMesh_Internal(dm, shape, dim, simplex, faces, lower, upper, bdt, interpolate));
3959         break;
3960       }
3961       if (isAnnular) {
3962         DM          cdm;
3963         PetscDS     cds;
3964         PetscScalar bounds[2] = {lower[0], upper[0]};
3965 
3966         // Fix coordinates for annular region
3967         PetscCall(DMSetPeriodicity(dm, NULL, NULL, NULL));
3968         PetscCall(DMSetCellCoordinatesLocal(dm, NULL));
3969         PetscCall(DMSetCellCoordinates(dm, NULL));
3970         PetscCall(DMPlexCreateCoordinateSpace(dm, 1, PETSC_TRUE, NULL));
3971         PetscCall(DMGetCoordinateDM(dm, &cdm));
3972         PetscCall(DMGetDS(cdm, &cds));
3973         PetscCall(PetscDSSetConstants(cds, 2, bounds));
3974         PetscCall(DMPlexRemapGeometry(dm, 0.0, boxToAnnulus));
3975       }
3976     } break;
3977     case DM_SHAPE_BOX_SURFACE: {
3978       PetscInt  faces[3] = {0, 0, 0};
3979       PetscReal lower[3] = {0, 0, 0};
3980       PetscReal upper[3] = {1, 1, 1};
3981       PetscInt  i, n;
3982 
3983       n = dim + 1;
3984       for (i = 0; i < dim + 1; ++i) faces[i] = (dim + 1 == 1 ? 1 : 4 - (dim + 1));
3985       PetscCall(PetscOptionsIntArray("-dm_plex_box_faces", "Number of faces along each dimension", "", faces, &n, &flg));
3986       n = 3;
3987       PetscCall(PetscOptionsRealArray("-dm_plex_box_lower", "Lower left corner of box", "", lower, &n, &flg));
3988       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);
3989       n = 3;
3990       PetscCall(PetscOptionsRealArray("-dm_plex_box_upper", "Upper right corner of box", "", upper, &n, &flg));
3991       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);
3992       PetscCall(DMPlexCreateBoxSurfaceMesh_Internal(dm, dim + 1, faces, lower, upper, interpolate));
3993     } break;
3994     case DM_SHAPE_SPHERE: {
3995       PetscReal R = 1.0;
3996 
3997       PetscCall(PetscOptionsReal("-dm_plex_sphere_radius", "Radius of the sphere", "", R, &R, &flg));
3998       PetscCall(DMPlexCreateSphereMesh_Internal(dm, dim, simplex, R));
3999     } break;
4000     case DM_SHAPE_BALL: {
4001       PetscReal R = 1.0;
4002 
4003       PetscCall(PetscOptionsReal("-dm_plex_ball_radius", "Radius of the ball", "", R, &R, &flg));
4004       PetscCall(DMPlexCreateBallMesh_Internal(dm, dim, R));
4005     } break;
4006     case DM_SHAPE_CYLINDER: {
4007       DMBoundaryType bdt = DM_BOUNDARY_NONE;
4008       PetscInt       Nw  = 6;
4009 
4010       PetscCall(PetscOptionsEnum("-dm_plex_cylinder_bd", "Boundary type in the z direction", "", DMBoundaryTypes, (PetscEnum)bdt, (PetscEnum *)&bdt, NULL));
4011       PetscCall(PetscOptionsInt("-dm_plex_cylinder_num_wedges", "Number of wedges around the cylinder", "", Nw, &Nw, NULL));
4012       switch (cell) {
4013       case DM_POLYTOPE_TRI_PRISM_TENSOR:
4014         PetscCall(DMPlexCreateWedgeCylinderMesh_Internal(dm, Nw, interpolate));
4015         break;
4016       default:
4017         PetscCall(DMPlexCreateHexCylinderMesh_Internal(dm, bdt));
4018         break;
4019       }
4020     } break;
4021     case DM_SHAPE_SCHWARZ_P: // fallthrough
4022     case DM_SHAPE_GYROID: {
4023       PetscInt       extent[3] = {1, 1, 1}, refine = 0, layers = 0, three;
4024       PetscReal      thickness   = 0.;
4025       DMBoundaryType periodic[3] = {DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE};
4026       DMPlexTPSType  tps_type    = shape == DM_SHAPE_SCHWARZ_P ? DMPLEX_TPS_SCHWARZ_P : DMPLEX_TPS_GYROID;
4027       PetscBool      tps_distribute;
4028       PetscCall(PetscOptionsIntArray("-dm_plex_tps_extent", "Number of replicas for each of three dimensions", NULL, extent, (three = 3, &three), NULL));
4029       PetscCall(PetscOptionsInt("-dm_plex_tps_refine", "Number of refinements", NULL, refine, &refine, NULL));
4030       PetscCall(PetscOptionsEnumArray("-dm_plex_tps_periodic", "Periodicity in each of three dimensions", NULL, DMBoundaryTypes, (PetscEnum *)periodic, (three = 3, &three), NULL));
4031       PetscCall(PetscOptionsInt("-dm_plex_tps_layers", "Number of layers in volumetric extrusion (or zero to not extrude)", NULL, layers, &layers, NULL));
4032       PetscCall(PetscOptionsReal("-dm_plex_tps_thickness", "Thickness of volumetric extrusion", NULL, thickness, &thickness, NULL));
4033       PetscCall(DMPlexDistributeGetDefault(dm, &tps_distribute));
4034       PetscCall(PetscOptionsBool("-dm_plex_tps_distribute", "Distribute the 2D mesh prior to refinement and extrusion", NULL, tps_distribute, &tps_distribute, NULL));
4035       PetscCall(DMPlexCreateTPSMesh_Internal(dm, tps_type, extent, periodic, tps_distribute, refine, layers, thickness));
4036     } break;
4037     case DM_SHAPE_DOUBLET: {
4038       DM        dmnew;
4039       PetscReal rl = 0.0;
4040 
4041       PetscCall(PetscOptionsReal("-dm_plex_doublet_refinementlimit", "Refinement limit", NULL, rl, &rl, NULL));
4042       PetscCall(DMPlexCreateDoublet(PetscObjectComm((PetscObject)dm), dim, simplex, interpolate, rl, &dmnew));
4043       PetscCall(DMPlexCopy_Internal(dm, PETSC_FALSE, PETSC_FALSE, dmnew));
4044       PetscCall(DMPlexReplace_Internal(dm, &dmnew));
4045     } break;
4046     case DM_SHAPE_HYPERCUBIC: {
4047       PetscInt       *edges;
4048       PetscReal      *lower, *upper;
4049       DMBoundaryType *bdt;
4050       PetscInt        n, d;
4051 
4052       *useCoordSpace = PETSC_FALSE;
4053       PetscCall(PetscMalloc4(dim, &edges, dim, &lower, dim, &upper, dim, &bdt));
4054       for (d = 0; d < dim; ++d) {
4055         edges[d] = 1;
4056         lower[d] = 0.;
4057         upper[d] = 1.;
4058         bdt[d]   = DM_BOUNDARY_PERIODIC;
4059       }
4060       n = dim;
4061       PetscCall(PetscOptionsIntArray("-dm_plex_box_faces", "Number of faces along each dimension", "", edges, &n, &flg));
4062       n = dim;
4063       PetscCall(PetscOptionsRealArray("-dm_plex_box_lower", "Lower left corner of box", "", lower, &n, &flg));
4064       PetscCheck(!flg || n == dim, comm, PETSC_ERR_ARG_SIZ, "Lower box point had %" PetscInt_FMT " values, should have been %" PetscInt_FMT, n, dim);
4065       n = dim;
4066       PetscCall(PetscOptionsRealArray("-dm_plex_box_upper", "Upper right corner of box", "", upper, &n, &flg));
4067       PetscCheck(!flg || n == dim, comm, PETSC_ERR_ARG_SIZ, "Upper box point had %" PetscInt_FMT " values, should have been %" PetscInt_FMT, n, dim);
4068       n = dim;
4069       PetscCall(PetscOptionsEnumArray("-dm_plex_box_bd", "Boundary type for each dimension", "", DMBoundaryTypes, (PetscEnum *)bdt, &n, &flg));
4070       PetscCheck(!flg || n == dim, comm, PETSC_ERR_ARG_SIZ, "Box boundary types had %" PetscInt_FMT " values, should have been %" PetscInt_FMT, n, dim);
4071       PetscCall(DMPlexCreateHypercubicMesh_Internal(dm, dim, lower, upper, edges, bdt));
4072       PetscCall(PetscFree4(edges, lower, upper, bdt));
4073     } break;
4074     default:
4075       SETERRQ(comm, PETSC_ERR_SUP, "Domain shape %s is unsupported", DMPlexShapes[shape]);
4076     }
4077   }
4078   PetscCall(DMPlexSetRefinementUniform(dm, PETSC_TRUE));
4079   if (!((PetscObject)dm)->name && nameflg) PetscCall(PetscObjectSetName((PetscObject)dm, plexname));
4080   PetscCall(PetscLogEventEnd(DMPLEX_CreateFromOptions, dm, 0, 0, 0));
4081   PetscFunctionReturn(PETSC_SUCCESS);
4082 }
4083 
4084 PetscErrorCode DMSetFromOptions_NonRefinement_Plex(DM dm, PetscOptionItems *PetscOptionsObject)
4085 {
4086   DM_Plex  *mesh = (DM_Plex *)dm->data;
4087   PetscBool flg, flg2;
4088   char      bdLabel[PETSC_MAX_PATH_LEN];
4089 
4090   PetscFunctionBegin;
4091   /* Handle viewing */
4092   PetscCall(PetscOptionsBool("-dm_plex_print_set_values", "Output all set values info", "DMPlexMatSetClosure", PETSC_FALSE, &mesh->printSetValues, NULL));
4093   PetscCall(PetscOptionsBoundedInt("-dm_plex_print_fem", "Debug output level for all fem computations", "DMPlexSNESComputeResidualFEM", 0, &mesh->printFEM, NULL, 0));
4094   PetscCall(PetscOptionsBoundedInt("-dm_plex_print_fvm", "Debug output level for all fvm computations", "DMPlexSNESComputeResidualFVM", 0, &mesh->printFVM, NULL, 0));
4095   PetscCall(PetscOptionsReal("-dm_plex_print_tol", "Tolerance for FEM output", "DMPlexSNESComputeResidualFEM", mesh->printTol, &mesh->printTol, NULL));
4096   PetscCall(PetscOptionsBoundedInt("-dm_plex_print_l2", "Debug output level all L2 diff computations", "DMComputeL2Diff", 0, &mesh->printL2, NULL, 0));
4097   PetscCall(PetscOptionsBoundedInt("-dm_plex_print_locate", "Debug output level all point location computations", "DMLocatePoints", 0, &mesh->printLocate, NULL, 0));
4098   PetscCall(DMMonitorSetFromOptions(dm, "-dm_plex_monitor_throughput", "Monitor the simulation throughput", "DMPlexMonitorThroughput", DMPlexMonitorThroughput, NULL, &flg));
4099   if (flg) PetscCall(PetscLogDefaultBegin());
4100   /* Labeling */
4101   PetscCall(PetscOptionsString("-dm_plex_boundary_label", "Label to mark the mesh boundary", "", bdLabel, bdLabel, sizeof(bdLabel), &flg));
4102   if (flg) PetscCall(DMPlexCreateBoundaryLabel_Private(dm, bdLabel));
4103   /* Point Location */
4104   PetscCall(PetscOptionsBool("-dm_plex_hash_location", "Use grid hashing for point location", "DMInterpolate", PETSC_FALSE, &mesh->useHashLocation, NULL));
4105   /* Partitioning and distribution */
4106   PetscCall(PetscOptionsBool("-dm_plex_partition_balance", "Attempt to evenly divide points on partition boundary between processes", "DMPlexSetPartitionBalance", PETSC_FALSE, &mesh->partitionBalance, NULL));
4107   /* Generation and remeshing */
4108   PetscCall(PetscOptionsBool("-dm_plex_remesh_bd", "Allow changes to the boundary on remeshing", "DMAdapt", PETSC_FALSE, &mesh->remeshBd, NULL));
4109   /* Projection behavior */
4110   PetscCall(PetscOptionsBoundedInt("-dm_plex_max_projection_height", "Maximum mesh point height used to project locally", "DMPlexSetMaxProjectionHeight", 0, &mesh->maxProjectionHeight, NULL, 0));
4111   PetscCall(PetscOptionsBool("-dm_plex_regular_refinement", "Use special nested projection algorithm for regular refinement", "DMPlexSetRegularRefinement", mesh->regularRefinement, &mesh->regularRefinement, NULL));
4112   /* Checking structure */
4113   {
4114     PetscBool all = PETSC_FALSE;
4115 
4116     PetscCall(PetscOptionsBool("-dm_plex_check_all", "Perform all basic checks", "DMPlexCheck", PETSC_FALSE, &all, NULL));
4117     if (all) {
4118       PetscCall(DMPlexCheck(dm));
4119     } else {
4120       PetscCall(PetscOptionsBool("-dm_plex_check_symmetry", "Check that the adjacency information in the mesh is symmetric", "DMPlexCheckSymmetry", PETSC_FALSE, &flg, &flg2));
4121       if (flg && flg2) PetscCall(DMPlexCheckSymmetry(dm));
4122       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));
4123       if (flg && flg2) PetscCall(DMPlexCheckSkeleton(dm, 0));
4124       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));
4125       if (flg && flg2) PetscCall(DMPlexCheckFaces(dm, 0));
4126       PetscCall(PetscOptionsBool("-dm_plex_check_geometry", "Check that cells have positive volume", "DMPlexCheckGeometry", PETSC_FALSE, &flg, &flg2));
4127       if (flg && flg2) PetscCall(DMPlexCheckGeometry(dm));
4128       PetscCall(PetscOptionsBool("-dm_plex_check_pointsf", "Check some necessary conditions for PointSF", "DMPlexCheckPointSF", PETSC_FALSE, &flg, &flg2));
4129       if (flg && flg2) PetscCall(DMPlexCheckPointSF(dm, NULL, PETSC_FALSE));
4130       PetscCall(PetscOptionsBool("-dm_plex_check_interface_cones", "Check points on inter-partition interfaces have conforming order of cone points", "DMPlexCheckInterfaceCones", PETSC_FALSE, &flg, &flg2));
4131       if (flg && flg2) PetscCall(DMPlexCheckInterfaceCones(dm));
4132     }
4133     PetscCall(PetscOptionsBool("-dm_plex_check_cell_shape", "Check cell shape", "DMPlexCheckCellShape", PETSC_FALSE, &flg, &flg2));
4134     if (flg && flg2) PetscCall(DMPlexCheckCellShape(dm, PETSC_TRUE, PETSC_DETERMINE));
4135   }
4136   {
4137     PetscReal scale = 1.0;
4138 
4139     PetscCall(PetscOptionsReal("-dm_plex_scale", "Scale factor for mesh coordinates", "DMPlexScale", scale, &scale, &flg));
4140     if (flg) {
4141       Vec coordinates, coordinatesLocal;
4142 
4143       PetscCall(DMGetCoordinates(dm, &coordinates));
4144       PetscCall(DMGetCoordinatesLocal(dm, &coordinatesLocal));
4145       PetscCall(VecScale(coordinates, scale));
4146       PetscCall(VecScale(coordinatesLocal, scale));
4147     }
4148   }
4149   PetscCall(PetscPartitionerSetFromOptions(mesh->partitioner));
4150   PetscFunctionReturn(PETSC_SUCCESS);
4151 }
4152 
4153 PetscErrorCode DMSetFromOptions_Overlap_Plex(DM dm, PetscOptionItems *PetscOptionsObject, PetscInt *overlap)
4154 {
4155   PetscInt  numOvLabels = 16, numOvExLabels = 16;
4156   char     *ovLabelNames[16], *ovExLabelNames[16];
4157   PetscInt  numOvValues = 16, numOvExValues = 16, l;
4158   PetscBool flg;
4159 
4160   PetscFunctionBegin;
4161   PetscCall(PetscOptionsBoundedInt("-dm_distribute_overlap", "The size of the overlap halo", "DMPlexDistribute", *overlap, overlap, NULL, 0));
4162   PetscCall(PetscOptionsStringArray("-dm_distribute_overlap_labels", "List of overlap label names", "DMPlexDistribute", ovLabelNames, &numOvLabels, &flg));
4163   if (!flg) numOvLabels = 0;
4164   if (numOvLabels) {
4165     ((DM_Plex *)dm->data)->numOvLabels = numOvLabels;
4166     for (l = 0; l < numOvLabels; ++l) {
4167       PetscCall(DMGetLabel(dm, ovLabelNames[l], &((DM_Plex *)dm->data)->ovLabels[l]));
4168       PetscCheck(((DM_Plex *)dm->data)->ovLabels[l], PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Invalid label name %s", ovLabelNames[l]);
4169       PetscCall(PetscFree(ovLabelNames[l]));
4170     }
4171     PetscCall(PetscOptionsIntArray("-dm_distribute_overlap_values", "List of overlap label values", "DMPlexDistribute", ((DM_Plex *)dm->data)->ovValues, &numOvValues, &flg));
4172     if (!flg) numOvValues = 0;
4173     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);
4174 
4175     PetscCall(PetscOptionsStringArray("-dm_distribute_overlap_exclude_labels", "List of overlap exclude label names", "DMPlexDistribute", ovExLabelNames, &numOvExLabels, &flg));
4176     if (!flg) numOvExLabels = 0;
4177     ((DM_Plex *)dm->data)->numOvExLabels = numOvExLabels;
4178     for (l = 0; l < numOvExLabels; ++l) {
4179       PetscCall(DMGetLabel(dm, ovExLabelNames[l], &((DM_Plex *)dm->data)->ovExLabels[l]));
4180       PetscCheck(((DM_Plex *)dm->data)->ovExLabels[l], PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Invalid label name %s", ovExLabelNames[l]);
4181       PetscCall(PetscFree(ovExLabelNames[l]));
4182     }
4183     PetscCall(PetscOptionsIntArray("-dm_distribute_overlap_exclude_values", "List of overlap exclude label values", "DMPlexDistribute", ((DM_Plex *)dm->data)->ovExValues, &numOvExValues, &flg));
4184     if (!flg) numOvExValues = 0;
4185     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);
4186   }
4187   PetscFunctionReturn(PETSC_SUCCESS);
4188 }
4189 
4190 static PetscErrorCode DMSetFromOptions_Plex(DM dm, PetscOptionItems *PetscOptionsObject)
4191 {
4192   PetscFunctionList        ordlist;
4193   char                     oname[256];
4194   DMPlexReorderDefaultFlag reorder;
4195   PetscReal                volume    = -1.0;
4196   PetscInt                 prerefine = 0, refine = 0, r, coarsen = 0, overlap = 0, extLayers = 0, dim;
4197   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;
4198 
4199   PetscFunctionBegin;
4200   PetscOptionsHeadBegin(PetscOptionsObject, "DMPlex Options");
4201   if (dm->cloneOpts) goto non_refine;
4202   /* Handle automatic creation */
4203   PetscCall(DMGetDimension(dm, &dim));
4204   if (dim < 0) {
4205     PetscCall(DMPlexCreateFromOptions_Internal(PetscOptionsObject, &coordSpace, dm));
4206     created = PETSC_TRUE;
4207   }
4208   PetscCall(DMGetDimension(dm, &dim));
4209   /* Handle interpolation before distribution */
4210   PetscCall(PetscOptionsBool("-dm_plex_interpolate_pre", "Flag to interpolate mesh before distribution", "", interpolate, &interpolate, &flg));
4211   if (flg) {
4212     DMPlexInterpolatedFlag interpolated;
4213 
4214     PetscCall(DMPlexIsInterpolated(dm, &interpolated));
4215     if (interpolated == DMPLEX_INTERPOLATED_FULL && !interpolate) {
4216       DM udm;
4217 
4218       PetscCall(DMPlexUninterpolate(dm, &udm));
4219       PetscCall(DMPlexReplace_Internal(dm, &udm));
4220     } else if (interpolated != DMPLEX_INTERPOLATED_FULL && interpolate) {
4221       DM idm;
4222 
4223       PetscCall(DMPlexInterpolate(dm, &idm));
4224       PetscCall(DMPlexReplace_Internal(dm, &idm));
4225     }
4226   }
4227   /* Handle DMPlex refinement before distribution */
4228   PetscCall(PetscOptionsBool("-dm_refine_ignore_model", "Flag to ignore the geometry model when refining", "DMCreate", ignoreModel, &ignoreModel, &flg));
4229   if (flg) ((DM_Plex *)dm->data)->ignoreModel = ignoreModel;
4230   PetscCall(DMPlexGetRefinementUniform(dm, &uniformOrig));
4231   PetscCall(PetscOptionsBoundedInt("-dm_refine_pre", "The number of refinements before distribution", "DMCreate", prerefine, &prerefine, NULL, 0));
4232   PetscCall(PetscOptionsBool("-dm_refine_remap_pre", "Flag to control coordinate remapping", "DMCreate", remap, &remap, NULL));
4233   PetscCall(PetscOptionsBool("-dm_refine_uniform_pre", "Flag for uniform refinement before distribution", "DMCreate", uniform, &uniform, &flg));
4234   if (flg) PetscCall(DMPlexSetRefinementUniform(dm, uniform));
4235   PetscCall(PetscOptionsReal("-dm_refine_volume_limit_pre", "The maximum cell volume after refinement before distribution", "DMCreate", volume, &volume, &flg));
4236   if (flg) {
4237     PetscCall(DMPlexSetRefinementUniform(dm, PETSC_FALSE));
4238     PetscCall(DMPlexSetRefinementLimit(dm, volume));
4239     prerefine = PetscMax(prerefine, 1);
4240   }
4241   for (r = 0; r < prerefine; ++r) {
4242     DM             rdm;
4243     PetscPointFunc coordFunc = ((DM_Plex *)dm->data)->coordFunc;
4244 
4245     PetscCall(DMSetFromOptions_NonRefinement_Plex(dm, PetscOptionsObject));
4246     PetscCall(DMRefine(dm, PetscObjectComm((PetscObject)dm), &rdm));
4247     PetscCall(DMPlexReplace_Internal(dm, &rdm));
4248     PetscCall(DMSetFromOptions_NonRefinement_Plex(dm, PetscOptionsObject));
4249     if (coordFunc && remap) {
4250       PetscCall(DMPlexRemapGeometry(dm, 0.0, coordFunc));
4251       ((DM_Plex *)dm->data)->coordFunc = coordFunc;
4252     }
4253   }
4254   PetscCall(DMPlexSetRefinementUniform(dm, uniformOrig));
4255   /* Handle DMPlex extrusion before distribution */
4256   PetscCall(PetscOptionsBoundedInt("-dm_extrude", "The number of layers to extrude", "", extLayers, &extLayers, NULL, 0));
4257   if (extLayers) {
4258     DM edm;
4259 
4260     PetscCall(DMExtrude(dm, extLayers, &edm));
4261     PetscCall(DMPlexReplace_Internal(dm, &edm));
4262     ((DM_Plex *)dm->data)->coordFunc = NULL;
4263     PetscCall(DMSetFromOptions_NonRefinement_Plex(dm, PetscOptionsObject));
4264     extLayers = 0;
4265     PetscCall(DMGetDimension(dm, &dim));
4266   }
4267   /* Handle DMPlex reordering before distribution */
4268   PetscCall(DMPlexReorderGetDefault(dm, &reorder));
4269   PetscCall(MatGetOrderingList(&ordlist));
4270   PetscCall(PetscStrncpy(oname, MATORDERINGNATURAL, sizeof(oname)));
4271   PetscCall(PetscOptionsFList("-dm_plex_reorder", "Set mesh reordering type", "DMPlexGetOrdering", ordlist, MATORDERINGNATURAL, oname, sizeof(oname), &flg));
4272   if (reorder == DMPLEX_REORDER_DEFAULT_TRUE || flg) {
4273     DM pdm;
4274     IS perm;
4275 
4276     PetscCall(DMPlexGetOrdering(dm, oname, NULL, &perm));
4277     PetscCall(DMPlexPermute(dm, perm, &pdm));
4278     PetscCall(ISDestroy(&perm));
4279     PetscCall(DMPlexReplace_Internal(dm, &pdm));
4280     PetscCall(DMSetFromOptions_NonRefinement_Plex(dm, PetscOptionsObject));
4281   }
4282   /* Handle DMPlex distribution */
4283   PetscCall(DMPlexDistributeGetDefault(dm, &distribute));
4284   PetscCall(PetscOptionsBool("-dm_distribute", "Flag to redistribute a mesh among processes", "DMPlexDistribute", distribute, &distribute, NULL));
4285   PetscCall(PetscOptionsBool("-dm_distribute_save_sf", "Flag to save the migration SF", "DMPlexSetMigrationSF", saveSF, &saveSF, NULL));
4286   PetscCall(DMSetFromOptions_Overlap_Plex(dm, PetscOptionsObject, &overlap));
4287   if (distribute) {
4288     DM               pdm = NULL;
4289     PetscPartitioner part;
4290     PetscSF          sfMigration;
4291 
4292     PetscCall(DMPlexGetPartitioner(dm, &part));
4293     PetscCall(PetscPartitionerSetFromOptions(part));
4294     PetscCall(DMPlexDistribute(dm, overlap, &sfMigration, &pdm));
4295     if (pdm) PetscCall(DMPlexReplace_Internal(dm, &pdm));
4296     if (saveSF) PetscCall(DMPlexSetMigrationSF(dm, sfMigration));
4297     PetscCall(PetscSFDestroy(&sfMigration));
4298   }
4299   /* Must check CEED options before creating function space for coordinates */
4300   {
4301     PetscBool useCeed = PETSC_FALSE, flg;
4302 
4303     PetscCall(PetscOptionsBool("-dm_plex_use_ceed", "Use LibCEED as the FEM backend", "DMPlexSetUseCeed", useCeed, &useCeed, &flg));
4304     if (flg) PetscCall(DMPlexSetUseCeed(dm, useCeed));
4305   }
4306   /* Create coordinate space */
4307   if (created) {
4308     DM_Plex  *mesh   = (DM_Plex *)dm->data;
4309     PetscInt  degree = 1, deg;
4310     PetscInt  height = 0;
4311     DM        cdm;
4312     PetscBool flg;
4313 
4314     PetscCall(PetscOptionsBool("-dm_coord_space", "Use an FEM space for coordinates", "", coordSpace, &coordSpace, &flg));
4315     PetscCall(PetscOptionsInt("-dm_coord_petscspace_degree", "FEM degree for coordinate space", "", degree, &degree, NULL));
4316     PetscCall(DMGetCoordinateDegree_Internal(dm, &deg));
4317     if (coordSpace && deg <= 1) PetscCall(DMPlexCreateCoordinateSpace(dm, degree, PETSC_TRUE, mesh->coordFunc));
4318     PetscCall(DMGetCoordinateDM(dm, &cdm));
4319     if (flg && !coordSpace) {
4320       PetscDS      cds;
4321       PetscObject  obj;
4322       PetscClassId id;
4323 
4324       PetscCall(DMGetDS(cdm, &cds));
4325       PetscCall(PetscDSGetDiscretization(cds, 0, &obj));
4326       PetscCall(PetscObjectGetClassId(obj, &id));
4327       if (id == PETSCFE_CLASSID) {
4328         PetscContainer dummy;
4329 
4330         PetscCall(PetscContainerCreate(PETSC_COMM_SELF, &dummy));
4331         PetscCall(PetscObjectSetName((PetscObject)dummy, "coordinates"));
4332         PetscCall(DMSetField(cdm, 0, NULL, (PetscObject)dummy));
4333         PetscCall(PetscContainerDestroy(&dummy));
4334         PetscCall(DMClearDS(cdm));
4335       }
4336       mesh->coordFunc = NULL;
4337     }
4338     PetscCall(PetscOptionsBool("-dm_sparse_localize", "Localize only necessary cells", "", dm->sparseLocalize, &dm->sparseLocalize, &flg));
4339     PetscCall(PetscOptionsInt("-dm_localize_height", "Localize edges and faces in addition to cells", "", height, &height, &flg));
4340     if (flg) PetscCall(DMPlexSetMaxProjectionHeight(cdm, height));
4341     PetscCall(DMLocalizeCoordinates(dm));
4342   }
4343   /* Handle DMPlex refinement */
4344   remap = PETSC_TRUE;
4345   PetscCall(PetscOptionsBoundedInt("-dm_refine", "The number of uniform refinements", "DMCreate", refine, &refine, NULL, 0));
4346   PetscCall(PetscOptionsBool("-dm_refine_remap", "Flag to control coordinate remapping", "DMCreate", remap, &remap, NULL));
4347   PetscCall(PetscOptionsBoundedInt("-dm_refine_hierarchy", "The number of uniform refinements", "DMCreate", refine, &refine, &isHierarchy, 0));
4348   if (refine) PetscCall(DMPlexSetRefinementUniform(dm, PETSC_TRUE));
4349   if (refine && isHierarchy) {
4350     DM *dms, coarseDM;
4351 
4352     PetscCall(DMGetCoarseDM(dm, &coarseDM));
4353     PetscCall(PetscObjectReference((PetscObject)coarseDM));
4354     PetscCall(PetscMalloc1(refine, &dms));
4355     PetscCall(DMRefineHierarchy(dm, refine, dms));
4356     /* Total hack since we do not pass in a pointer */
4357     PetscCall(DMPlexSwap_Static(dm, dms[refine - 1]));
4358     if (refine == 1) {
4359       PetscCall(DMSetCoarseDM(dm, dms[0]));
4360       PetscCall(DMPlexSetRegularRefinement(dm, PETSC_TRUE));
4361     } else {
4362       PetscCall(DMSetCoarseDM(dm, dms[refine - 2]));
4363       PetscCall(DMPlexSetRegularRefinement(dm, PETSC_TRUE));
4364       PetscCall(DMSetCoarseDM(dms[0], dms[refine - 1]));
4365       PetscCall(DMPlexSetRegularRefinement(dms[0], PETSC_TRUE));
4366     }
4367     PetscCall(DMSetCoarseDM(dms[refine - 1], coarseDM));
4368     PetscCall(PetscObjectDereference((PetscObject)coarseDM));
4369     /* Free DMs */
4370     for (r = 0; r < refine; ++r) {
4371       PetscCall(DMSetFromOptions_NonRefinement_Plex(dms[r], PetscOptionsObject));
4372       PetscCall(DMDestroy(&dms[r]));
4373     }
4374     PetscCall(PetscFree(dms));
4375   } else {
4376     for (r = 0; r < refine; ++r) {
4377       DM             rdm;
4378       PetscPointFunc coordFunc = ((DM_Plex *)dm->data)->coordFunc;
4379 
4380       PetscCall(DMSetFromOptions_NonRefinement_Plex(dm, PetscOptionsObject));
4381       PetscCall(DMRefine(dm, PetscObjectComm((PetscObject)dm), &rdm));
4382       /* Total hack since we do not pass in a pointer */
4383       PetscCall(DMPlexReplace_Internal(dm, &rdm));
4384       PetscCall(DMSetFromOptions_NonRefinement_Plex(dm, PetscOptionsObject));
4385       if (coordFunc && remap) {
4386         PetscCall(DMPlexRemapGeometry(dm, 0.0, coordFunc));
4387         ((DM_Plex *)dm->data)->coordFunc = coordFunc;
4388       }
4389     }
4390   }
4391   /* Handle DMPlex coarsening */
4392   PetscCall(PetscOptionsBoundedInt("-dm_coarsen", "Coarsen the mesh", "DMCreate", coarsen, &coarsen, NULL, 0));
4393   PetscCall(PetscOptionsBoundedInt("-dm_coarsen_hierarchy", "The number of coarsenings", "DMCreate", coarsen, &coarsen, &isHierarchy, 0));
4394   if (coarsen && isHierarchy) {
4395     DM *dms;
4396 
4397     PetscCall(PetscMalloc1(coarsen, &dms));
4398     PetscCall(DMCoarsenHierarchy(dm, coarsen, dms));
4399     /* Free DMs */
4400     for (r = 0; r < coarsen; ++r) {
4401       PetscCall(DMSetFromOptions_NonRefinement_Plex(dms[r], PetscOptionsObject));
4402       PetscCall(DMDestroy(&dms[r]));
4403     }
4404     PetscCall(PetscFree(dms));
4405   } else {
4406     for (r = 0; r < coarsen; ++r) {
4407       DM             cdm;
4408       PetscPointFunc coordFunc = ((DM_Plex *)dm->data)->coordFunc;
4409 
4410       PetscCall(DMSetFromOptions_NonRefinement_Plex(dm, PetscOptionsObject));
4411       PetscCall(DMCoarsen(dm, PetscObjectComm((PetscObject)dm), &cdm));
4412       /* Total hack since we do not pass in a pointer */
4413       PetscCall(DMPlexReplace_Internal(dm, &cdm));
4414       PetscCall(DMSetFromOptions_NonRefinement_Plex(dm, PetscOptionsObject));
4415       if (coordFunc) {
4416         PetscCall(DMPlexRemapGeometry(dm, 0.0, coordFunc));
4417         ((DM_Plex *)dm->data)->coordFunc = coordFunc;
4418       }
4419     }
4420   }
4421   /* Handle ghost cells */
4422   PetscCall(PetscOptionsBool("-dm_plex_create_fv_ghost_cells", "Flag to create finite volume ghost cells on the boundary", "DMCreate", ghostCells, &ghostCells, NULL));
4423   if (ghostCells) {
4424     DM   gdm;
4425     char lname[PETSC_MAX_PATH_LEN];
4426 
4427     lname[0] = '\0';
4428     PetscCall(PetscOptionsString("-dm_plex_fv_ghost_cells_label", "Label name for ghost cells boundary", "DMCreate", lname, lname, sizeof(lname), &flg));
4429     PetscCall(DMPlexConstructGhostCells(dm, flg ? lname : NULL, NULL, &gdm));
4430     PetscCall(DMPlexReplace_Internal(dm, &gdm));
4431   }
4432   /* Handle 1D order */
4433   if (reorder != DMPLEX_REORDER_DEFAULT_FALSE && dim == 1) {
4434     DM           cdm, rdm;
4435     PetscDS      cds;
4436     PetscObject  obj;
4437     PetscClassId id = PETSC_OBJECT_CLASSID;
4438     IS           perm;
4439     PetscInt     Nf;
4440     PetscBool    distributed;
4441 
4442     PetscCall(DMPlexIsDistributed(dm, &distributed));
4443     PetscCall(DMGetCoordinateDM(dm, &cdm));
4444     PetscCall(DMGetDS(cdm, &cds));
4445     PetscCall(PetscDSGetNumFields(cds, &Nf));
4446     if (Nf) {
4447       PetscCall(PetscDSGetDiscretization(cds, 0, &obj));
4448       PetscCall(PetscObjectGetClassId(obj, &id));
4449     }
4450     if (!distributed && id != PETSCFE_CLASSID) {
4451       PetscCall(DMPlexGetOrdering1D(dm, &perm));
4452       PetscCall(DMPlexPermute(dm, perm, &rdm));
4453       PetscCall(DMPlexReplace_Internal(dm, &rdm));
4454       PetscCall(ISDestroy(&perm));
4455     }
4456   }
4457 /* Handle */
4458 non_refine:
4459   PetscCall(DMSetFromOptions_NonRefinement_Plex(dm, PetscOptionsObject));
4460   PetscOptionsHeadEnd();
4461   PetscFunctionReturn(PETSC_SUCCESS);
4462 }
4463 
4464 static PetscErrorCode DMCreateGlobalVector_Plex(DM dm, Vec *vec)
4465 {
4466   PetscFunctionBegin;
4467   PetscCall(DMCreateGlobalVector_Section_Private(dm, vec));
4468   /* PetscCall(VecSetOperation(*vec, VECOP_DUPLICATE, (void(*)(void)) VecDuplicate_MPI_DM)); */
4469   PetscCall(VecSetOperation(*vec, VECOP_VIEW, (void (*)(void))VecView_Plex));
4470   PetscCall(VecSetOperation(*vec, VECOP_VIEWNATIVE, (void (*)(void))VecView_Plex_Native));
4471   PetscCall(VecSetOperation(*vec, VECOP_LOAD, (void (*)(void))VecLoad_Plex));
4472   PetscCall(VecSetOperation(*vec, VECOP_LOADNATIVE, (void (*)(void))VecLoad_Plex_Native));
4473   PetscFunctionReturn(PETSC_SUCCESS);
4474 }
4475 
4476 static PetscErrorCode DMCreateLocalVector_Plex(DM dm, Vec *vec)
4477 {
4478   PetscFunctionBegin;
4479   PetscCall(DMCreateLocalVector_Section_Private(dm, vec));
4480   PetscCall(VecSetOperation(*vec, VECOP_VIEW, (void (*)(void))VecView_Plex_Local));
4481   PetscCall(VecSetOperation(*vec, VECOP_LOAD, (void (*)(void))VecLoad_Plex_Local));
4482   PetscFunctionReturn(PETSC_SUCCESS);
4483 }
4484 
4485 static PetscErrorCode DMGetDimPoints_Plex(DM dm, PetscInt dim, PetscInt *pStart, PetscInt *pEnd)
4486 {
4487   PetscInt depth, d;
4488 
4489   PetscFunctionBegin;
4490   PetscCall(DMPlexGetDepth(dm, &depth));
4491   if (depth == 1) {
4492     PetscCall(DMGetDimension(dm, &d));
4493     if (dim == 0) PetscCall(DMPlexGetDepthStratum(dm, dim, pStart, pEnd));
4494     else if (dim == d) PetscCall(DMPlexGetDepthStratum(dm, 1, pStart, pEnd));
4495     else {
4496       *pStart = 0;
4497       *pEnd   = 0;
4498     }
4499   } else {
4500     PetscCall(DMPlexGetDepthStratum(dm, dim, pStart, pEnd));
4501   }
4502   PetscFunctionReturn(PETSC_SUCCESS);
4503 }
4504 
4505 static PetscErrorCode DMGetNeighbors_Plex(DM dm, PetscInt *nranks, const PetscMPIInt *ranks[])
4506 {
4507   PetscSF            sf;
4508   PetscInt           niranks, njranks, n;
4509   const PetscMPIInt *iranks, *jranks;
4510   DM_Plex           *data = (DM_Plex *)dm->data;
4511 
4512   PetscFunctionBegin;
4513   PetscCall(DMGetPointSF(dm, &sf));
4514   if (!data->neighbors) {
4515     PetscCall(PetscSFSetUp(sf));
4516     PetscCall(PetscSFGetRootRanks(sf, &njranks, &jranks, NULL, NULL, NULL));
4517     PetscCall(PetscSFGetLeafRanks(sf, &niranks, &iranks, NULL, NULL));
4518     PetscCall(PetscMalloc1(njranks + niranks + 1, &data->neighbors));
4519     PetscCall(PetscArraycpy(data->neighbors + 1, jranks, njranks));
4520     PetscCall(PetscArraycpy(data->neighbors + njranks + 1, iranks, niranks));
4521     n = njranks + niranks;
4522     PetscCall(PetscSortRemoveDupsMPIInt(&n, data->neighbors + 1));
4523     /* The following cast should never fail: can't have more neighbors than PETSC_MPI_INT_MAX */
4524     PetscCall(PetscMPIIntCast(n, data->neighbors));
4525   }
4526   if (nranks) *nranks = data->neighbors[0];
4527   if (ranks) {
4528     if (data->neighbors[0]) *ranks = data->neighbors + 1;
4529     else *ranks = NULL;
4530   }
4531   PetscFunctionReturn(PETSC_SUCCESS);
4532 }
4533 
4534 PETSC_INTERN PetscErrorCode DMInterpolateSolution_Plex(DM, DM, Mat, Vec, Vec);
4535 
4536 static PetscErrorCode DMInitialize_Plex(DM dm)
4537 {
4538   PetscFunctionBegin;
4539   dm->ops->view                      = DMView_Plex;
4540   dm->ops->load                      = DMLoad_Plex;
4541   dm->ops->setfromoptions            = DMSetFromOptions_Plex;
4542   dm->ops->clone                     = DMClone_Plex;
4543   dm->ops->setup                     = DMSetUp_Plex;
4544   dm->ops->createlocalsection        = DMCreateLocalSection_Plex;
4545   dm->ops->createdefaultconstraints  = DMCreateDefaultConstraints_Plex;
4546   dm->ops->createglobalvector        = DMCreateGlobalVector_Plex;
4547   dm->ops->createlocalvector         = DMCreateLocalVector_Plex;
4548   dm->ops->getlocaltoglobalmapping   = NULL;
4549   dm->ops->createfieldis             = NULL;
4550   dm->ops->createcoordinatedm        = DMCreateCoordinateDM_Plex;
4551   dm->ops->createcoordinatefield     = DMCreateCoordinateField_Plex;
4552   dm->ops->getcoloring               = NULL;
4553   dm->ops->creatematrix              = DMCreateMatrix_Plex;
4554   dm->ops->createinterpolation       = DMCreateInterpolation_Plex;
4555   dm->ops->createmassmatrix          = DMCreateMassMatrix_Plex;
4556   dm->ops->createmassmatrixlumped    = DMCreateMassMatrixLumped_Plex;
4557   dm->ops->createinjection           = DMCreateInjection_Plex;
4558   dm->ops->refine                    = DMRefine_Plex;
4559   dm->ops->coarsen                   = DMCoarsen_Plex;
4560   dm->ops->refinehierarchy           = DMRefineHierarchy_Plex;
4561   dm->ops->coarsenhierarchy          = DMCoarsenHierarchy_Plex;
4562   dm->ops->extrude                   = DMExtrude_Plex;
4563   dm->ops->globaltolocalbegin        = NULL;
4564   dm->ops->globaltolocalend          = NULL;
4565   dm->ops->localtoglobalbegin        = NULL;
4566   dm->ops->localtoglobalend          = NULL;
4567   dm->ops->destroy                   = DMDestroy_Plex;
4568   dm->ops->createsubdm               = DMCreateSubDM_Plex;
4569   dm->ops->createsuperdm             = DMCreateSuperDM_Plex;
4570   dm->ops->getdimpoints              = DMGetDimPoints_Plex;
4571   dm->ops->locatepoints              = DMLocatePoints_Plex;
4572   dm->ops->projectfunctionlocal      = DMProjectFunctionLocal_Plex;
4573   dm->ops->projectfunctionlabellocal = DMProjectFunctionLabelLocal_Plex;
4574   dm->ops->projectfieldlocal         = DMProjectFieldLocal_Plex;
4575   dm->ops->projectfieldlabellocal    = DMProjectFieldLabelLocal_Plex;
4576   dm->ops->projectbdfieldlabellocal  = DMProjectBdFieldLabelLocal_Plex;
4577   dm->ops->computel2diff             = DMComputeL2Diff_Plex;
4578   dm->ops->computel2gradientdiff     = DMComputeL2GradientDiff_Plex;
4579   dm->ops->computel2fielddiff        = DMComputeL2FieldDiff_Plex;
4580   dm->ops->getneighbors              = DMGetNeighbors_Plex;
4581   PetscCall(PetscObjectComposeFunction((PetscObject)dm, "DMPlexInsertBoundaryValues_C", DMPlexInsertBoundaryValues_Plex));
4582   PetscCall(PetscObjectComposeFunction((PetscObject)dm, "DMPlexInsertTimeDerviativeBoundaryValues_C", DMPlexInsertTimeDerivativeBoundaryValues_Plex));
4583   PetscCall(PetscObjectComposeFunction((PetscObject)dm, "DMSetUpGLVisViewer_C", DMSetUpGLVisViewer_Plex));
4584   PetscCall(PetscObjectComposeFunction((PetscObject)dm, "DMCreateNeumannOverlap_C", DMCreateNeumannOverlap_Plex));
4585   PetscCall(PetscObjectComposeFunction((PetscObject)dm, "DMPlexGetOverlap_C", DMPlexGetOverlap_Plex));
4586   PetscCall(PetscObjectComposeFunction((PetscObject)dm, "DMPlexDistributeGetDefault_C", DMPlexDistributeGetDefault_Plex));
4587   PetscCall(PetscObjectComposeFunction((PetscObject)dm, "DMPlexDistributeSetDefault_C", DMPlexDistributeSetDefault_Plex));
4588   PetscCall(PetscObjectComposeFunction((PetscObject)dm, "DMPlexReorderGetDefault_C", DMPlexReorderGetDefault_Plex));
4589   PetscCall(PetscObjectComposeFunction((PetscObject)dm, "DMPlexReorderSetDefault_C", DMPlexReorderSetDefault_Plex));
4590   PetscCall(PetscObjectComposeFunction((PetscObject)dm, "DMInterpolateSolution_C", DMInterpolateSolution_Plex));
4591   PetscCall(PetscObjectComposeFunction((PetscObject)dm, "DMPlexGetOverlap_C", DMPlexGetOverlap_Plex));
4592   PetscCall(PetscObjectComposeFunction((PetscObject)dm, "DMPlexSetOverlap_C", DMPlexSetOverlap_Plex));
4593   PetscCall(PetscObjectComposeFunction((PetscObject)dm, "DMPlexGetUseCeed_C", DMPlexGetUseCeed_Plex));
4594   PetscCall(PetscObjectComposeFunction((PetscObject)dm, "DMPlexSetUseCeed_C", DMPlexSetUseCeed_Plex));
4595   PetscFunctionReturn(PETSC_SUCCESS);
4596 }
4597 
4598 PETSC_INTERN PetscErrorCode DMClone_Plex(DM dm, DM *newdm)
4599 {
4600   DM_Plex *mesh = (DM_Plex *)dm->data;
4601   PetscSF  face_sf;
4602 
4603   PetscFunctionBegin;
4604   mesh->refct++;
4605   (*newdm)->data = mesh;
4606   PetscCall(DMPlexGetIsoperiodicFaceSF(dm, &face_sf));
4607   PetscCall(DMPlexSetIsoperiodicFaceSF(*newdm, face_sf));
4608   PetscCall(PetscObjectChangeTypeName((PetscObject)*newdm, DMPLEX));
4609   PetscCall(DMInitialize_Plex(*newdm));
4610   PetscFunctionReturn(PETSC_SUCCESS);
4611 }
4612 
4613 /*MC
4614   DMPLEX = "plex" - A `DM` object that encapsulates an unstructured mesh, or CW Complex, which can be expressed using a Hasse Diagram.
4615                     In the local representation, `Vec`s contain all unknowns in the interior and shared boundary. This is
4616                     specified by a PetscSection object. Ownership in the global representation is determined by
4617                     ownership of the underlying `DMPLEX` points. This is specified by another `PetscSection` object.
4618 
4619   Options Database Keys:
4620 + -dm_refine_pre                     - Refine mesh before distribution
4621 + -dm_refine_uniform_pre             - Choose uniform or generator-based refinement
4622 + -dm_refine_volume_limit_pre        - Cell volume limit after pre-refinement using generator
4623 . -dm_distribute                     - Distribute mesh across processes
4624 . -dm_distribute_overlap             - Number of cells to overlap for distribution
4625 . -dm_refine                         - Refine mesh after distribution
4626 . -dm_plex_hash_location             - Use grid hashing for point location
4627 . -dm_plex_hash_box_faces <n,m,p>    - The number of divisions in each direction of the grid hash
4628 . -dm_plex_partition_balance         - Attempt to evenly divide points on partition boundary between processes
4629 . -dm_plex_remesh_bd                 - Allow changes to the boundary on remeshing
4630 . -dm_plex_max_projection_height     - Maximum mesh point height used to project locally
4631 . -dm_plex_regular_refinement        - Use special nested projection algorithm for regular refinement
4632 . -dm_plex_check_all                 - Perform all checks below
4633 . -dm_plex_check_symmetry            - Check that the adjacency information in the mesh is symmetric
4634 . -dm_plex_check_skeleton <celltype> - Check that each cell has the correct number of vertices
4635 . -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
4636 . -dm_plex_check_geometry            - Check that cells have positive volume
4637 . -dm_view :mesh.tex:ascii_latex     - View the mesh in LaTeX/TikZ
4638 . -dm_plex_view_scale <num>          - Scale the TikZ
4639 . -dm_plex_print_fem <num>           - View FEM assembly information, such as element vectors and matrices
4640 - -dm_plex_print_fvm <num>           - View FVM assembly information, such as flux updates
4641 
4642   Level: intermediate
4643 
4644 .seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMType`, `DMPlexCreate()`, `DMCreate()`, `DMSetType()`, `PetscSection`
4645 M*/
4646 
4647 PETSC_EXTERN PetscErrorCode DMCreate_Plex(DM dm)
4648 {
4649   DM_Plex *mesh;
4650   PetscInt unit;
4651 
4652   PetscFunctionBegin;
4653   PetscCall(PetscCitationsRegister(PlexCitation, &Plexcite));
4654   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
4655   PetscCall(PetscNew(&mesh));
4656   dm->data = mesh;
4657 
4658   mesh->refct = 1;
4659   PetscCall(PetscSectionCreate(PetscObjectComm((PetscObject)dm), &mesh->coneSection));
4660   PetscCall(PetscSectionCreate(PetscObjectComm((PetscObject)dm), &mesh->supportSection));
4661   mesh->refinementUniform      = PETSC_TRUE;
4662   mesh->refinementLimit        = -1.0;
4663   mesh->distDefault            = PETSC_TRUE;
4664   mesh->reorderDefault         = DMPLEX_REORDER_DEFAULT_NOTSET;
4665   mesh->distributionName       = NULL;
4666   mesh->interpolated           = DMPLEX_INTERPOLATED_INVALID;
4667   mesh->interpolatedCollective = DMPLEX_INTERPOLATED_INVALID;
4668 
4669   PetscCall(PetscPartitionerCreate(PetscObjectComm((PetscObject)dm), &mesh->partitioner));
4670   mesh->remeshBd = PETSC_FALSE;
4671 
4672   for (unit = 0; unit < NUM_PETSC_UNITS; ++unit) mesh->scale[unit] = 1.0;
4673 
4674   mesh->depthState    = -1;
4675   mesh->celltypeState = -1;
4676   mesh->printTol      = 1.0e-10;
4677 
4678   PetscCall(DMInitialize_Plex(dm));
4679   PetscFunctionReturn(PETSC_SUCCESS);
4680 }
4681 
4682 /*@
4683   DMPlexCreate - Creates a `DMPLEX` object, which encapsulates an unstructured mesh, or CW complex, which can be expressed using a Hasse Diagram.
4684 
4685   Collective
4686 
4687   Input Parameter:
4688 . comm - The communicator for the `DMPLEX` object
4689 
4690   Output Parameter:
4691 . mesh - The `DMPLEX` object
4692 
4693   Level: beginner
4694 
4695 .seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMType`, `DMCreate()`, `DMSetType()`
4696 @*/
4697 PetscErrorCode DMPlexCreate(MPI_Comm comm, DM *mesh)
4698 {
4699   PetscFunctionBegin;
4700   PetscAssertPointer(mesh, 2);
4701   PetscCall(DMCreate(comm, mesh));
4702   PetscCall(DMSetType(*mesh, DMPLEX));
4703   PetscFunctionReturn(PETSC_SUCCESS);
4704 }
4705 
4706 /*@C
4707   DMPlexBuildFromCellListParallel - Build distributed `DMPLEX` topology from a list of vertices for each cell (common mesh generator output)
4708 
4709   Collective; No Fortran Support
4710 
4711   Input Parameters:
4712 + dm          - The `DM`
4713 . numCells    - The number of cells owned by this process
4714 . numVertices - The number of vertices to be owned by this process, or `PETSC_DECIDE`
4715 . NVertices   - The global number of vertices, or `PETSC_DETERMINE`
4716 . numCorners  - The number of vertices for each cell
4717 - cells       - An array of numCells*numCorners numbers, the global vertex numbers for each cell
4718 
4719   Output Parameters:
4720 + vertexSF         - (Optional) `PetscSF` describing complete vertex ownership
4721 - verticesAdjSaved - (Optional) vertex adjacency array
4722 
4723   Level: advanced
4724 
4725   Notes:
4726   Two triangles sharing a face
4727 .vb
4728 
4729         2
4730       / | \
4731      /  |  \
4732     /   |   \
4733    0  0 | 1  3
4734     \   |   /
4735      \  |  /
4736       \ | /
4737         1
4738 .ve
4739   would have input
4740 .vb
4741   numCells = 2, numVertices = 4
4742   cells = [0 1 2  1 3 2]
4743 .ve
4744   which would result in the `DMPLEX`
4745 .vb
4746 
4747         4
4748       / | \
4749      /  |  \
4750     /   |   \
4751    2  0 | 1  5
4752     \   |   /
4753      \  |  /
4754       \ | /
4755         3
4756 .ve
4757 
4758   Vertices are implicitly numbered consecutively 0,...,NVertices.
4759   Each rank owns a chunk of numVertices consecutive vertices.
4760   If numVertices is `PETSC_DECIDE`, PETSc will distribute them as evenly as possible using PetscLayout.
4761   If NVertices is `PETSC_DETERMINE` and numVertices is PETSC_DECIDE, NVertices is computed by PETSc as the maximum vertex index in cells + 1.
4762   If only NVertices is `PETSC_DETERMINE`, it is computed as the sum of numVertices over all ranks.
4763 
4764   The cell distribution is arbitrary non-overlapping, independent of the vertex distribution.
4765 
4766 .seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexBuildFromCellList()`, `DMPlexCreateFromCellListParallelPetsc()`, `DMPlexBuildCoordinatesFromCellListParallel()`,
4767           `PetscSF`
4768 @*/
4769 PetscErrorCode DMPlexBuildFromCellListParallel(DM dm, PetscInt numCells, PetscInt numVertices, PetscInt NVertices, PetscInt numCorners, const PetscInt cells[], PetscSF *vertexSF, PetscInt **verticesAdjSaved)
4770 {
4771   PetscSF     sfPoint;
4772   PetscLayout layout;
4773   PetscInt    numVerticesAdj, *verticesAdj, *cones, c, p;
4774 
4775   PetscFunctionBegin;
4776   PetscValidLogicalCollectiveInt(dm, NVertices, 4);
4777   PetscCall(PetscLogEventBegin(DMPLEX_BuildFromCellList, dm, 0, 0, 0));
4778   /* Get/check global number of vertices */
4779   {
4780     PetscInt       NVerticesInCells, i;
4781     const PetscInt len = numCells * numCorners;
4782 
4783     /* NVerticesInCells = max(cells) + 1 */
4784     NVerticesInCells = PETSC_MIN_INT;
4785     for (i = 0; i < len; i++)
4786       if (cells[i] > NVerticesInCells) NVerticesInCells = cells[i];
4787     ++NVerticesInCells;
4788     PetscCall(MPIU_Allreduce(MPI_IN_PLACE, &NVerticesInCells, 1, MPIU_INT, MPI_MAX, PetscObjectComm((PetscObject)dm)));
4789 
4790     if (numVertices == PETSC_DECIDE && NVertices == PETSC_DECIDE) NVertices = NVerticesInCells;
4791     else
4792       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);
4793   }
4794   /* Count locally unique vertices */
4795   {
4796     PetscHSetI vhash;
4797     PetscInt   off = 0;
4798 
4799     PetscCall(PetscHSetICreate(&vhash));
4800     for (c = 0; c < numCells; ++c) {
4801       for (p = 0; p < numCorners; ++p) PetscCall(PetscHSetIAdd(vhash, cells[c * numCorners + p]));
4802     }
4803     PetscCall(PetscHSetIGetSize(vhash, &numVerticesAdj));
4804     if (!verticesAdjSaved) PetscCall(PetscMalloc1(numVerticesAdj, &verticesAdj));
4805     else verticesAdj = *verticesAdjSaved;
4806     PetscCall(PetscHSetIGetElems(vhash, &off, verticesAdj));
4807     PetscCall(PetscHSetIDestroy(&vhash));
4808     PetscCheck(off == numVerticesAdj, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Invalid number of local vertices %" PetscInt_FMT " should be %" PetscInt_FMT, off, numVerticesAdj);
4809   }
4810   PetscCall(PetscSortInt(numVerticesAdj, verticesAdj));
4811   /* Create cones */
4812   PetscCall(DMPlexSetChart(dm, 0, numCells + numVerticesAdj));
4813   for (c = 0; c < numCells; ++c) PetscCall(DMPlexSetConeSize(dm, c, numCorners));
4814   PetscCall(DMSetUp(dm));
4815   PetscCall(DMPlexGetCones(dm, &cones));
4816   for (c = 0; c < numCells; ++c) {
4817     for (p = 0; p < numCorners; ++p) {
4818       const PetscInt gv = cells[c * numCorners + p];
4819       PetscInt       lv;
4820 
4821       /* Positions within verticesAdj form 0-based local vertex numbering;
4822          we need to shift it by numCells to get correct DAG points (cells go first) */
4823       PetscCall(PetscFindInt(gv, numVerticesAdj, verticesAdj, &lv));
4824       PetscCheck(lv >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Could not find global vertex %" PetscInt_FMT " in local connectivity", gv);
4825       cones[c * numCorners + p] = lv + numCells;
4826     }
4827   }
4828   /* Build point sf */
4829   PetscCall(PetscLayoutCreate(PetscObjectComm((PetscObject)dm), &layout));
4830   PetscCall(PetscLayoutSetSize(layout, NVertices));
4831   PetscCall(PetscLayoutSetLocalSize(layout, numVertices));
4832   PetscCall(PetscLayoutSetBlockSize(layout, 1));
4833   PetscCall(PetscSFCreateByMatchingIndices(layout, numVerticesAdj, verticesAdj, NULL, numCells, numVerticesAdj, verticesAdj, NULL, numCells, vertexSF, &sfPoint));
4834   PetscCall(PetscLayoutDestroy(&layout));
4835   if (!verticesAdjSaved) PetscCall(PetscFree(verticesAdj));
4836   PetscCall(PetscObjectSetName((PetscObject)sfPoint, "point SF"));
4837   if (dm->sf) {
4838     const char *prefix;
4839 
4840     PetscCall(PetscObjectGetOptionsPrefix((PetscObject)dm->sf, &prefix));
4841     PetscCall(PetscObjectSetOptionsPrefix((PetscObject)sfPoint, prefix));
4842   }
4843   PetscCall(DMSetPointSF(dm, sfPoint));
4844   PetscCall(PetscSFDestroy(&sfPoint));
4845   if (vertexSF) PetscCall(PetscObjectSetName((PetscObject)(*vertexSF), "Vertex Ownership SF"));
4846   /* Fill in the rest of the topology structure */
4847   PetscCall(DMPlexSymmetrize(dm));
4848   PetscCall(DMPlexStratify(dm));
4849   PetscCall(PetscLogEventEnd(DMPLEX_BuildFromCellList, dm, 0, 0, 0));
4850   PetscFunctionReturn(PETSC_SUCCESS);
4851 }
4852 
4853 /*@C
4854   DMPlexBuildCoordinatesFromCellListParallel - Build `DM` coordinates from a list of coordinates for each owned vertex (common mesh generator output)
4855 
4856   Collective; No Fortran Support
4857 
4858   Input Parameters:
4859 + dm           - The `DM`
4860 . spaceDim     - The spatial dimension used for coordinates
4861 . sfVert       - `PetscSF` describing complete vertex ownership
4862 - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex
4863 
4864   Level: advanced
4865 
4866 .seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexBuildCoordinatesFromCellList()`, `DMPlexCreateFromCellListParallelPetsc()`, `DMPlexBuildFromCellListParallel()`
4867 @*/
4868 PetscErrorCode DMPlexBuildCoordinatesFromCellListParallel(DM dm, PetscInt spaceDim, PetscSF sfVert, const PetscReal vertexCoords[])
4869 {
4870   PetscSection coordSection;
4871   Vec          coordinates;
4872   PetscScalar *coords;
4873   PetscInt     numVertices, numVerticesAdj, coordSize, v, vStart, vEnd;
4874 
4875   PetscFunctionBegin;
4876   PetscCall(PetscLogEventBegin(DMPLEX_BuildCoordinatesFromCellList, dm, 0, 0, 0));
4877   PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
4878   PetscCheck(vStart >= 0 && vEnd >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "DM is not set up properly. DMPlexBuildFromCellList() should be called first.");
4879   PetscCall(DMSetCoordinateDim(dm, spaceDim));
4880   PetscCall(PetscSFGetGraph(sfVert, &numVertices, &numVerticesAdj, NULL, NULL));
4881   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);
4882   PetscCall(DMGetCoordinateSection(dm, &coordSection));
4883   PetscCall(PetscSectionSetNumFields(coordSection, 1));
4884   PetscCall(PetscSectionSetFieldComponents(coordSection, 0, spaceDim));
4885   PetscCall(PetscSectionSetChart(coordSection, vStart, vEnd));
4886   for (v = vStart; v < vEnd; ++v) {
4887     PetscCall(PetscSectionSetDof(coordSection, v, spaceDim));
4888     PetscCall(PetscSectionSetFieldDof(coordSection, v, 0, spaceDim));
4889   }
4890   PetscCall(PetscSectionSetUp(coordSection));
4891   PetscCall(PetscSectionGetStorageSize(coordSection, &coordSize));
4892   PetscCall(VecCreate(PetscObjectComm((PetscObject)dm), &coordinates));
4893   PetscCall(VecSetBlockSize(coordinates, spaceDim));
4894   PetscCall(PetscObjectSetName((PetscObject)coordinates, "coordinates"));
4895   PetscCall(VecSetSizes(coordinates, coordSize, PETSC_DETERMINE));
4896   PetscCall(VecSetType(coordinates, VECSTANDARD));
4897   PetscCall(VecGetArray(coordinates, &coords));
4898   {
4899     MPI_Datatype coordtype;
4900 
4901     /* Need a temp buffer for coords if we have complex/single */
4902     PetscCallMPI(MPI_Type_contiguous(spaceDim, MPIU_SCALAR, &coordtype));
4903     PetscCallMPI(MPI_Type_commit(&coordtype));
4904 #if defined(PETSC_USE_COMPLEX)
4905     {
4906       PetscScalar *svertexCoords;
4907       PetscInt     i;
4908       PetscCall(PetscMalloc1(numVertices * spaceDim, &svertexCoords));
4909       for (i = 0; i < numVertices * spaceDim; i++) svertexCoords[i] = vertexCoords[i];
4910       PetscCall(PetscSFBcastBegin(sfVert, coordtype, svertexCoords, coords, MPI_REPLACE));
4911       PetscCall(PetscSFBcastEnd(sfVert, coordtype, svertexCoords, coords, MPI_REPLACE));
4912       PetscCall(PetscFree(svertexCoords));
4913     }
4914 #else
4915     PetscCall(PetscSFBcastBegin(sfVert, coordtype, vertexCoords, coords, MPI_REPLACE));
4916     PetscCall(PetscSFBcastEnd(sfVert, coordtype, vertexCoords, coords, MPI_REPLACE));
4917 #endif
4918     PetscCallMPI(MPI_Type_free(&coordtype));
4919   }
4920   PetscCall(VecRestoreArray(coordinates, &coords));
4921   PetscCall(DMSetCoordinatesLocal(dm, coordinates));
4922   PetscCall(VecDestroy(&coordinates));
4923   PetscCall(PetscLogEventEnd(DMPLEX_BuildCoordinatesFromCellList, dm, 0, 0, 0));
4924   PetscFunctionReturn(PETSC_SUCCESS);
4925 }
4926 
4927 /*@
4928   DMPlexCreateFromCellListParallelPetsc - Create distributed `DMPLEX` from a list of vertices for each cell (common mesh generator output)
4929 
4930   Collective
4931 
4932   Input Parameters:
4933 + comm         - The communicator
4934 . dim          - The topological dimension of the mesh
4935 . numCells     - The number of cells owned by this process
4936 . numVertices  - The number of vertices owned by this process, or `PETSC_DECIDE`
4937 . NVertices    - The global number of vertices, or `PETSC_DECIDE`
4938 . numCorners   - The number of vertices for each cell
4939 . interpolate  - Flag indicating that intermediate mesh entities (faces, edges) should be created automatically
4940 . cells        - An array of numCells*numCorners numbers, the global vertex numbers for each cell
4941 . spaceDim     - The spatial dimension used for coordinates
4942 - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex
4943 
4944   Output Parameters:
4945 + dm          - The `DM`
4946 . vertexSF    - (Optional) `PetscSF` describing complete vertex ownership
4947 - verticesAdj - (Optional) vertex adjacency array
4948 
4949   Level: intermediate
4950 
4951   Notes:
4952   This function is just a convenient sequence of `DMCreate()`, `DMSetType()`, `DMSetDimension()`,
4953   `DMPlexBuildFromCellListParallel()`, `DMPlexInterpolate()`, `DMPlexBuildCoordinatesFromCellListParallel()`
4954 
4955   See `DMPlexBuildFromCellListParallel()` for an example and details about the topology-related parameters.
4956 
4957   See `DMPlexBuildCoordinatesFromCellListParallel()` for details about the geometry-related parameters.
4958 
4959 .seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexCreateFromCellListPetsc()`, `DMPlexBuildFromCellListParallel()`, `DMPlexBuildCoordinatesFromCellListParallel()`, `DMPlexCreateFromDAG()`, `DMPlexCreate()`
4960 @*/
4961 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)
4962 {
4963   PetscSF sfVert;
4964 
4965   PetscFunctionBegin;
4966   PetscCall(DMCreate(comm, dm));
4967   PetscCall(DMSetType(*dm, DMPLEX));
4968   PetscValidLogicalCollectiveInt(*dm, dim, 2);
4969   PetscValidLogicalCollectiveInt(*dm, spaceDim, 9);
4970   PetscCall(DMSetDimension(*dm, dim));
4971   PetscCall(DMPlexBuildFromCellListParallel(*dm, numCells, numVertices, NVertices, numCorners, cells, &sfVert, verticesAdj));
4972   if (interpolate) {
4973     DM idm;
4974 
4975     PetscCall(DMPlexInterpolate(*dm, &idm));
4976     PetscCall(DMDestroy(dm));
4977     *dm = idm;
4978   }
4979   PetscCall(DMPlexBuildCoordinatesFromCellListParallel(*dm, spaceDim, sfVert, vertexCoords));
4980   if (vertexSF) *vertexSF = sfVert;
4981   else PetscCall(PetscSFDestroy(&sfVert));
4982   PetscFunctionReturn(PETSC_SUCCESS);
4983 }
4984 
4985 /*@C
4986   DMPlexBuildFromCellList - Build `DMPLEX` topology from a list of vertices for each cell (common mesh generator output)
4987 
4988   Collective; No Fortran Support
4989 
4990   Input Parameters:
4991 + dm          - The `DM`
4992 . numCells    - The number of cells owned by this process
4993 . numVertices - The number of vertices owned by this process, or `PETSC_DETERMINE`
4994 . numCorners  - The number of vertices for each cell
4995 - cells       - An array of numCells*numCorners numbers, the global vertex numbers for each cell
4996 
4997   Level: advanced
4998 
4999   Notes:
5000   Two triangles sharing a face
5001 .vb
5002 
5003         2
5004       / | \
5005      /  |  \
5006     /   |   \
5007    0  0 | 1  3
5008     \   |   /
5009      \  |  /
5010       \ | /
5011         1
5012 .ve
5013   would have input
5014 .vb
5015   numCells = 2, numVertices = 4
5016   cells = [0 1 2  1 3 2]
5017 .ve
5018   which would result in the `DMPLEX`
5019 .vb
5020 
5021         4
5022       / | \
5023      /  |  \
5024     /   |   \
5025    2  0 | 1  5
5026     \   |   /
5027      \  |  /
5028       \ | /
5029         3
5030 .ve
5031 
5032   If numVertices is `PETSC_DETERMINE`, it is computed by PETSc as the maximum vertex index in cells + 1.
5033 
5034 .seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexBuildFromCellListParallel()`, `DMPlexBuildCoordinatesFromCellList()`, `DMPlexCreateFromCellListPetsc()`
5035 @*/
5036 PetscErrorCode DMPlexBuildFromCellList(DM dm, PetscInt numCells, PetscInt numVertices, PetscInt numCorners, const PetscInt cells[])
5037 {
5038   PetscInt *cones, c, p, dim;
5039 
5040   PetscFunctionBegin;
5041   PetscCall(PetscLogEventBegin(DMPLEX_BuildFromCellList, dm, 0, 0, 0));
5042   PetscCall(DMGetDimension(dm, &dim));
5043   /* Get/check global number of vertices */
5044   {
5045     PetscInt       NVerticesInCells, i;
5046     const PetscInt len = numCells * numCorners;
5047 
5048     /* NVerticesInCells = max(cells) + 1 */
5049     NVerticesInCells = PETSC_MIN_INT;
5050     for (i = 0; i < len; i++)
5051       if (cells[i] > NVerticesInCells) NVerticesInCells = cells[i];
5052     ++NVerticesInCells;
5053 
5054     if (numVertices == PETSC_DECIDE) numVertices = NVerticesInCells;
5055     else
5056       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);
5057   }
5058   PetscCall(DMPlexSetChart(dm, 0, numCells + numVertices));
5059   for (c = 0; c < numCells; ++c) PetscCall(DMPlexSetConeSize(dm, c, numCorners));
5060   PetscCall(DMSetUp(dm));
5061   PetscCall(DMPlexGetCones(dm, &cones));
5062   for (c = 0; c < numCells; ++c) {
5063     for (p = 0; p < numCorners; ++p) cones[c * numCorners + p] = cells[c * numCorners + p] + numCells;
5064   }
5065   PetscCall(DMPlexSymmetrize(dm));
5066   PetscCall(DMPlexStratify(dm));
5067   PetscCall(PetscLogEventEnd(DMPLEX_BuildFromCellList, dm, 0, 0, 0));
5068   PetscFunctionReturn(PETSC_SUCCESS);
5069 }
5070 
5071 /*@C
5072   DMPlexBuildCoordinatesFromCellList - Build `DM` coordinates from a list of coordinates for each owned vertex (common mesh generator output)
5073 
5074   Collective; No Fortran Support
5075 
5076   Input Parameters:
5077 + dm           - The `DM`
5078 . spaceDim     - The spatial dimension used for coordinates
5079 - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex
5080 
5081   Level: advanced
5082 
5083 .seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexBuildCoordinatesFromCellListParallel()`, `DMPlexCreateFromCellListPetsc()`, `DMPlexBuildFromCellList()`
5084 @*/
5085 PetscErrorCode DMPlexBuildCoordinatesFromCellList(DM dm, PetscInt spaceDim, const PetscReal vertexCoords[])
5086 {
5087   PetscSection coordSection;
5088   Vec          coordinates;
5089   DM           cdm;
5090   PetscScalar *coords;
5091   PetscInt     v, vStart, vEnd, d;
5092 
5093   PetscFunctionBegin;
5094   PetscCall(PetscLogEventBegin(DMPLEX_BuildCoordinatesFromCellList, dm, 0, 0, 0));
5095   PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
5096   PetscCheck(vStart >= 0 && vEnd >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "DM is not set up properly. DMPlexBuildFromCellList() should be called first.");
5097   PetscCall(DMSetCoordinateDim(dm, spaceDim));
5098   PetscCall(DMGetCoordinateSection(dm, &coordSection));
5099   PetscCall(PetscSectionSetNumFields(coordSection, 1));
5100   PetscCall(PetscSectionSetFieldComponents(coordSection, 0, spaceDim));
5101   PetscCall(PetscSectionSetChart(coordSection, vStart, vEnd));
5102   for (v = vStart; v < vEnd; ++v) {
5103     PetscCall(PetscSectionSetDof(coordSection, v, spaceDim));
5104     PetscCall(PetscSectionSetFieldDof(coordSection, v, 0, spaceDim));
5105   }
5106   PetscCall(PetscSectionSetUp(coordSection));
5107 
5108   PetscCall(DMGetCoordinateDM(dm, &cdm));
5109   PetscCall(DMCreateLocalVector(cdm, &coordinates));
5110   PetscCall(VecSetBlockSize(coordinates, spaceDim));
5111   PetscCall(PetscObjectSetName((PetscObject)coordinates, "coordinates"));
5112   PetscCall(VecGetArrayWrite(coordinates, &coords));
5113   for (v = 0; v < vEnd - vStart; ++v) {
5114     for (d = 0; d < spaceDim; ++d) coords[v * spaceDim + d] = vertexCoords[v * spaceDim + d];
5115   }
5116   PetscCall(VecRestoreArrayWrite(coordinates, &coords));
5117   PetscCall(DMSetCoordinatesLocal(dm, coordinates));
5118   PetscCall(VecDestroy(&coordinates));
5119   PetscCall(PetscLogEventEnd(DMPLEX_BuildCoordinatesFromCellList, dm, 0, 0, 0));
5120   PetscFunctionReturn(PETSC_SUCCESS);
5121 }
5122 
5123 /*@
5124   DMPlexCreateFromCellListPetsc - Create `DMPLEX` from a list of vertices for each cell (common mesh generator output), but only process 0 takes in the input
5125 
5126   Collective
5127 
5128   Input Parameters:
5129 + comm         - The communicator
5130 . dim          - The topological dimension of the mesh
5131 . numCells     - The number of cells, only on process 0
5132 . numVertices  - The number of vertices owned by this process, or `PETSC_DECIDE`, only on process 0
5133 . numCorners   - The number of vertices for each cell, only on process 0
5134 . interpolate  - Flag indicating that intermediate mesh entities (faces, edges) should be created automatically
5135 . cells        - An array of numCells*numCorners numbers, the vertices for each cell, only on process 0
5136 . spaceDim     - The spatial dimension used for coordinates
5137 - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex, only on process 0
5138 
5139   Output Parameter:
5140 . dm - The `DM`, which only has points on process 0
5141 
5142   Level: intermediate
5143 
5144   Notes:
5145   This function is just a convenient sequence of `DMCreate()`, `DMSetType()`, `DMSetDimension()`, `DMPlexBuildFromCellList()`,
5146   `DMPlexInterpolate()`, `DMPlexBuildCoordinatesFromCellList()`
5147 
5148   See `DMPlexBuildFromCellList()` for an example and details about the topology-related parameters.
5149   See `DMPlexBuildCoordinatesFromCellList()` for details about the geometry-related parameters.
5150   See `DMPlexCreateFromCellListParallelPetsc()` for parallel input
5151 
5152 .seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexCreateFromCellListParallelPetsc()`, `DMPlexBuildFromCellList()`, `DMPlexBuildCoordinatesFromCellList()`, `DMPlexCreateFromDAG()`, `DMPlexCreate()`
5153 @*/
5154 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)
5155 {
5156   PetscMPIInt rank;
5157 
5158   PetscFunctionBegin;
5159   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.");
5160   PetscCallMPI(MPI_Comm_rank(comm, &rank));
5161   PetscCall(DMCreate(comm, dm));
5162   PetscCall(DMSetType(*dm, DMPLEX));
5163   PetscCall(DMSetDimension(*dm, dim));
5164   if (rank == 0) PetscCall(DMPlexBuildFromCellList(*dm, numCells, numVertices, numCorners, cells));
5165   else PetscCall(DMPlexBuildFromCellList(*dm, 0, 0, 0, NULL));
5166   if (interpolate) {
5167     DM idm;
5168 
5169     PetscCall(DMPlexInterpolate(*dm, &idm));
5170     PetscCall(DMDestroy(dm));
5171     *dm = idm;
5172   }
5173   if (rank == 0) PetscCall(DMPlexBuildCoordinatesFromCellList(*dm, spaceDim, vertexCoords));
5174   else PetscCall(DMPlexBuildCoordinatesFromCellList(*dm, spaceDim, NULL));
5175   PetscFunctionReturn(PETSC_SUCCESS);
5176 }
5177 
5178 /*@
5179   DMPlexCreateFromDAG - This takes as input the adjacency-list representation of the Directed Acyclic Graph (Hasse Diagram) encoding a mesh, and produces a `DM`
5180 
5181   Input Parameters:
5182 + dm               - The empty `DM` object, usually from `DMCreate()` and `DMSetDimension()`
5183 . depth            - The depth of the DAG
5184 . numPoints        - Array of size depth + 1 containing the number of points at each `depth`
5185 . coneSize         - The cone size of each point
5186 . cones            - The concatenation of the cone points for each point, the cone list must be oriented correctly for each point
5187 . coneOrientations - The orientation of each cone point
5188 - vertexCoords     - An array of `numPoints`[0]*spacedim numbers representing the coordinates of each vertex, with spacedim the value set via `DMSetCoordinateDim()`
5189 
5190   Output Parameter:
5191 . dm - The `DM`
5192 
5193   Level: advanced
5194 
5195   Note:
5196   Two triangles sharing a face would have input
5197 .vb
5198   depth = 1, numPoints = [4 2], coneSize = [3 3 0 0 0 0]
5199   cones = [2 3 4  3 5 4], coneOrientations = [0 0 0  0 0 0]
5200  vertexCoords = [-1.0 0.0  0.0 -1.0  0.0 1.0  1.0 0.0]
5201 .ve
5202   which would result in the DMPlex
5203 .vb
5204         4
5205       / | \
5206      /  |  \
5207     /   |   \
5208    2  0 | 1  5
5209     \   |   /
5210      \  |  /
5211       \ | /
5212         3
5213 .ve
5214   Notice that all points are numbered consecutively, unlike `DMPlexCreateFromCellListPetsc()`
5215 
5216 .seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexCreateFromCellListPetsc()`, `DMPlexCreate()`
5217 @*/
5218 PetscErrorCode DMPlexCreateFromDAG(DM dm, PetscInt depth, const PetscInt numPoints[], const PetscInt coneSize[], const PetscInt cones[], const PetscInt coneOrientations[], const PetscScalar vertexCoords[])
5219 {
5220   Vec          coordinates;
5221   PetscSection coordSection;
5222   PetscScalar *coords;
5223   PetscInt     coordSize, firstVertex = -1, pStart = 0, pEnd = 0, p, v, dim, dimEmbed, d, off;
5224 
5225   PetscFunctionBegin;
5226   PetscCall(DMGetDimension(dm, &dim));
5227   PetscCall(DMGetCoordinateDim(dm, &dimEmbed));
5228   PetscCheck(dimEmbed >= dim, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Embedding dimension %" PetscInt_FMT " cannot be less than intrinsic dimension %" PetscInt_FMT, dimEmbed, dim);
5229   for (d = 0; d <= depth; ++d) pEnd += numPoints[d];
5230   PetscCall(DMPlexSetChart(dm, pStart, pEnd));
5231   for (p = pStart; p < pEnd; ++p) {
5232     PetscCall(DMPlexSetConeSize(dm, p, coneSize[p - pStart]));
5233     if (firstVertex < 0 && !coneSize[p - pStart]) firstVertex = p - pStart;
5234   }
5235   PetscCheck(firstVertex >= 0 || !numPoints[0], PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Expected %" PetscInt_FMT " vertices but could not find any", numPoints[0]);
5236   PetscCall(DMSetUp(dm)); /* Allocate space for cones */
5237   for (p = pStart, off = 0; p < pEnd; off += coneSize[p - pStart], ++p) {
5238     PetscCall(DMPlexSetCone(dm, p, &cones[off]));
5239     PetscCall(DMPlexSetConeOrientation(dm, p, &coneOrientations[off]));
5240   }
5241   PetscCall(DMPlexSymmetrize(dm));
5242   PetscCall(DMPlexStratify(dm));
5243   /* Build coordinates */
5244   PetscCall(DMGetCoordinateSection(dm, &coordSection));
5245   PetscCall(PetscSectionSetNumFields(coordSection, 1));
5246   PetscCall(PetscSectionSetFieldComponents(coordSection, 0, dimEmbed));
5247   PetscCall(PetscSectionSetChart(coordSection, firstVertex, firstVertex + numPoints[0]));
5248   for (v = firstVertex; v < firstVertex + numPoints[0]; ++v) {
5249     PetscCall(PetscSectionSetDof(coordSection, v, dimEmbed));
5250     PetscCall(PetscSectionSetFieldDof(coordSection, v, 0, dimEmbed));
5251   }
5252   PetscCall(PetscSectionSetUp(coordSection));
5253   PetscCall(PetscSectionGetStorageSize(coordSection, &coordSize));
5254   PetscCall(VecCreate(PETSC_COMM_SELF, &coordinates));
5255   PetscCall(PetscObjectSetName((PetscObject)coordinates, "coordinates"));
5256   PetscCall(VecSetSizes(coordinates, coordSize, PETSC_DETERMINE));
5257   PetscCall(VecSetBlockSize(coordinates, dimEmbed));
5258   PetscCall(VecSetType(coordinates, VECSTANDARD));
5259   if (vertexCoords) {
5260     PetscCall(VecGetArray(coordinates, &coords));
5261     for (v = 0; v < numPoints[0]; ++v) {
5262       PetscInt off;
5263 
5264       PetscCall(PetscSectionGetOffset(coordSection, v + firstVertex, &off));
5265       for (d = 0; d < dimEmbed; ++d) coords[off + d] = vertexCoords[v * dimEmbed + d];
5266     }
5267   }
5268   PetscCall(VecRestoreArray(coordinates, &coords));
5269   PetscCall(DMSetCoordinatesLocal(dm, coordinates));
5270   PetscCall(VecDestroy(&coordinates));
5271   PetscFunctionReturn(PETSC_SUCCESS);
5272 }
5273 
5274 /*
5275   DMPlexCreateCellVertexFromFile - Create a `DMPLEX` mesh from a simple cell-vertex file.
5276 
5277   Collective
5278 
5279 + comm        - The MPI communicator
5280 . filename    - Name of the .dat file
5281 - interpolate - Create faces and edges in the mesh
5282 
5283   Output Parameter:
5284 . dm  - The `DM` object representing the mesh
5285 
5286   Level: beginner
5287 
5288   Note:
5289   The format is the simplest possible:
5290 .vb
5291   Ne
5292   v0 v1 ... vk
5293   Nv
5294   x y z marker
5295 .ve
5296 
5297   Developer Note:
5298   Should use a `PetscViewer` not a filename
5299 
5300 .seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexCreateFromFile()`, `DMPlexCreateMedFromFile()`, `DMPlexCreateGmsh()`, `DMPlexCreate()`
5301 */
5302 static PetscErrorCode DMPlexCreateCellVertexFromFile(MPI_Comm comm, const char filename[], PetscBool interpolate, DM *dm)
5303 {
5304   DMLabel      marker;
5305   PetscViewer  viewer;
5306   Vec          coordinates;
5307   PetscSection coordSection;
5308   PetscScalar *coords;
5309   char         line[PETSC_MAX_PATH_LEN];
5310   PetscInt     dim = 3, cdim = 3, coordSize, v, c, d;
5311   PetscMPIInt  rank;
5312   int          snum, Nv, Nc, Ncn, Nl;
5313 
5314   PetscFunctionBegin;
5315   PetscCallMPI(MPI_Comm_rank(comm, &rank));
5316   PetscCall(PetscViewerCreate(comm, &viewer));
5317   PetscCall(PetscViewerSetType(viewer, PETSCVIEWERASCII));
5318   PetscCall(PetscViewerFileSetMode(viewer, FILE_MODE_READ));
5319   PetscCall(PetscViewerFileSetName(viewer, filename));
5320   if (rank == 0) {
5321     PetscCall(PetscViewerRead(viewer, line, 4, NULL, PETSC_STRING));
5322     snum = sscanf(line, "%d %d %d %d", &Nc, &Nv, &Ncn, &Nl);
5323     PetscCheck(snum == 4, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unable to parse cell-vertex file: %s", line);
5324   } else {
5325     Nc = Nv = Ncn = Nl = 0;
5326   }
5327   PetscCall(DMCreate(comm, dm));
5328   PetscCall(DMSetType(*dm, DMPLEX));
5329   PetscCall(DMPlexSetChart(*dm, 0, Nc + Nv));
5330   PetscCall(DMSetDimension(*dm, dim));
5331   PetscCall(DMSetCoordinateDim(*dm, cdim));
5332   /* Read topology */
5333   if (rank == 0) {
5334     char     format[PETSC_MAX_PATH_LEN];
5335     PetscInt cone[8];
5336     int      vbuf[8], v;
5337 
5338     for (c = 0; c < Ncn; ++c) {
5339       format[c * 3 + 0] = '%';
5340       format[c * 3 + 1] = 'd';
5341       format[c * 3 + 2] = ' ';
5342     }
5343     format[Ncn * 3 - 1] = '\0';
5344     for (c = 0; c < Nc; ++c) PetscCall(DMPlexSetConeSize(*dm, c, Ncn));
5345     PetscCall(DMSetUp(*dm));
5346     for (c = 0; c < Nc; ++c) {
5347       PetscCall(PetscViewerRead(viewer, line, Ncn, NULL, PETSC_STRING));
5348       switch (Ncn) {
5349       case 2:
5350         snum = sscanf(line, format, &vbuf[0], &vbuf[1]);
5351         break;
5352       case 3:
5353         snum = sscanf(line, format, &vbuf[0], &vbuf[1], &vbuf[2]);
5354         break;
5355       case 4:
5356         snum = sscanf(line, format, &vbuf[0], &vbuf[1], &vbuf[2], &vbuf[3]);
5357         break;
5358       case 6:
5359         snum = sscanf(line, format, &vbuf[0], &vbuf[1], &vbuf[2], &vbuf[3], &vbuf[4], &vbuf[5]);
5360         break;
5361       case 8:
5362         snum = sscanf(line, format, &vbuf[0], &vbuf[1], &vbuf[2], &vbuf[3], &vbuf[4], &vbuf[5], &vbuf[6], &vbuf[7]);
5363         break;
5364       default:
5365         SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "No cell shape with %d vertices", Ncn);
5366       }
5367       PetscCheck(snum == Ncn, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unable to parse cell-vertex file: %s", line);
5368       for (v = 0; v < Ncn; ++v) cone[v] = vbuf[v] + Nc;
5369       /* Hexahedra are inverted */
5370       if (Ncn == 8) {
5371         PetscInt tmp = cone[1];
5372         cone[1]      = cone[3];
5373         cone[3]      = tmp;
5374       }
5375       PetscCall(DMPlexSetCone(*dm, c, cone));
5376     }
5377   }
5378   PetscCall(DMPlexSymmetrize(*dm));
5379   PetscCall(DMPlexStratify(*dm));
5380   /* Read coordinates */
5381   PetscCall(DMGetCoordinateSection(*dm, &coordSection));
5382   PetscCall(PetscSectionSetNumFields(coordSection, 1));
5383   PetscCall(PetscSectionSetFieldComponents(coordSection, 0, cdim));
5384   PetscCall(PetscSectionSetChart(coordSection, Nc, Nc + Nv));
5385   for (v = Nc; v < Nc + Nv; ++v) {
5386     PetscCall(PetscSectionSetDof(coordSection, v, cdim));
5387     PetscCall(PetscSectionSetFieldDof(coordSection, v, 0, cdim));
5388   }
5389   PetscCall(PetscSectionSetUp(coordSection));
5390   PetscCall(PetscSectionGetStorageSize(coordSection, &coordSize));
5391   PetscCall(VecCreate(PETSC_COMM_SELF, &coordinates));
5392   PetscCall(PetscObjectSetName((PetscObject)coordinates, "coordinates"));
5393   PetscCall(VecSetSizes(coordinates, coordSize, PETSC_DETERMINE));
5394   PetscCall(VecSetBlockSize(coordinates, cdim));
5395   PetscCall(VecSetType(coordinates, VECSTANDARD));
5396   PetscCall(VecGetArray(coordinates, &coords));
5397   if (rank == 0) {
5398     char   format[PETSC_MAX_PATH_LEN];
5399     double x[3];
5400     int    l, val[3];
5401 
5402     if (Nl) {
5403       for (l = 0; l < Nl; ++l) {
5404         format[l * 3 + 0] = '%';
5405         format[l * 3 + 1] = 'd';
5406         format[l * 3 + 2] = ' ';
5407       }
5408       format[Nl * 3 - 1] = '\0';
5409       PetscCall(DMCreateLabel(*dm, "marker"));
5410       PetscCall(DMGetLabel(*dm, "marker", &marker));
5411     }
5412     for (v = 0; v < Nv; ++v) {
5413       PetscCall(PetscViewerRead(viewer, line, 3 + Nl, NULL, PETSC_STRING));
5414       snum = sscanf(line, "%lg %lg %lg", &x[0], &x[1], &x[2]);
5415       PetscCheck(snum == 3, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unable to parse cell-vertex file: %s", line);
5416       switch (Nl) {
5417       case 0:
5418         snum = 0;
5419         break;
5420       case 1:
5421         snum = sscanf(line, format, &val[0]);
5422         break;
5423       case 2:
5424         snum = sscanf(line, format, &val[0], &val[1]);
5425         break;
5426       case 3:
5427         snum = sscanf(line, format, &val[0], &val[1], &val[2]);
5428         break;
5429       default:
5430         SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Request support for %d labels", Nl);
5431       }
5432       PetscCheck(snum == Nl, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unable to parse cell-vertex file: %s", line);
5433       for (d = 0; d < cdim; ++d) coords[v * cdim + d] = x[d];
5434       for (l = 0; l < Nl; ++l) PetscCall(DMLabelSetValue(marker, v + Nc, val[l]));
5435     }
5436   }
5437   PetscCall(VecRestoreArray(coordinates, &coords));
5438   PetscCall(DMSetCoordinatesLocal(*dm, coordinates));
5439   PetscCall(VecDestroy(&coordinates));
5440   PetscCall(PetscViewerDestroy(&viewer));
5441   if (interpolate) {
5442     DM      idm;
5443     DMLabel bdlabel;
5444 
5445     PetscCall(DMPlexInterpolate(*dm, &idm));
5446     PetscCall(DMDestroy(dm));
5447     *dm = idm;
5448 
5449     if (!Nl) {
5450       PetscCall(DMCreateLabel(*dm, "marker"));
5451       PetscCall(DMGetLabel(*dm, "marker", &bdlabel));
5452       PetscCall(DMPlexMarkBoundaryFaces(*dm, PETSC_DETERMINE, bdlabel));
5453       PetscCall(DMPlexLabelComplete(*dm, bdlabel));
5454     }
5455   }
5456   PetscFunctionReturn(PETSC_SUCCESS);
5457 }
5458 
5459 /*@C
5460   DMPlexCreateFromFile - This takes a filename and produces a `DM`
5461 
5462   Collective
5463 
5464   Input Parameters:
5465 + comm        - The communicator
5466 . filename    - A file name
5467 . plexname    - The object name of the resulting `DM`, also used for intra-datafile lookup by some formats
5468 - interpolate - Flag to create intermediate mesh pieces (edges, faces)
5469 
5470   Output Parameter:
5471 . dm - The `DM`
5472 
5473   Options Database Key:
5474 . -dm_plex_create_from_hdf5_xdmf - use the `PETSC_VIEWER_HDF5_XDMF` format for reading HDF5
5475 
5476   Use `-dm_plex_create_ prefix` to pass options to the internal `PetscViewer`, e.g.
5477 $ -dm_plex_create_viewer_hdf5_collective
5478 
5479   Level: beginner
5480 
5481   Notes:
5482   Using `PETSCVIEWERHDF5` type with `PETSC_VIEWER_HDF5_PETSC` format, one can save multiple `DMPLEX`
5483   meshes in a single HDF5 file. This in turn requires one to name the `DMPLEX` object with `PetscObjectSetName()`
5484   before saving it with `DMView()` and before loading it with `DMLoad()` for identification of the mesh object.
5485   The input parameter name is thus used to name the `DMPLEX` object when `DMPlexCreateFromFile()` internally
5486   calls `DMLoad()`. Currently, name is ignored for other viewer types and/or formats.
5487 
5488 .seealso: [](ch_unstructured), `DM`, `DMPLEX`, `DMPlexCreateFromDAG()`, `DMPlexCreateFromCellListPetsc()`, `DMPlexCreate()`, `PetscObjectSetName()`, `DMView()`, `DMLoad()`
5489 @*/
5490 PetscErrorCode DMPlexCreateFromFile(MPI_Comm comm, const char filename[], const char plexname[], PetscBool interpolate, DM *dm)
5491 {
5492   const char  extGmsh[]      = ".msh";
5493   const char  extGmsh2[]     = ".msh2";
5494   const char  extGmsh4[]     = ".msh4";
5495   const char  extCGNS[]      = ".cgns";
5496   const char  extExodus[]    = ".exo";
5497   const char  extExodus_e[]  = ".e";
5498   const char  extGenesis[]   = ".gen";
5499   const char  extFluent[]    = ".cas";
5500   const char  extHDF5[]      = ".h5";
5501   const char  extXDMFHDF5[]  = ".xdmf.h5";
5502   const char  extMed[]       = ".med";
5503   const char  extPLY[]       = ".ply";
5504   const char  extEGADSLite[] = ".egadslite";
5505   const char  extEGADS[]     = ".egads";
5506   const char  extIGES[]      = ".igs";
5507   const char  extSTEP[]      = ".stp";
5508   const char  extCV[]        = ".dat";
5509   size_t      len;
5510   PetscBool   isGmsh, isGmsh2, isGmsh4, isCGNS, isExodus, isGenesis, isFluent, isHDF5, isMed, isPLY, isEGADSLite, isEGADS, isIGES, isSTEP, isCV, isXDMFHDF5;
5511   PetscMPIInt rank;
5512 
5513   PetscFunctionBegin;
5514   PetscAssertPointer(filename, 2);
5515   if (plexname) PetscAssertPointer(plexname, 3);
5516   PetscAssertPointer(dm, 5);
5517   PetscCall(DMInitializePackage());
5518   PetscCall(PetscLogEventBegin(DMPLEX_CreateFromFile, 0, 0, 0, 0));
5519   PetscCallMPI(MPI_Comm_rank(comm, &rank));
5520   PetscCall(PetscStrlen(filename, &len));
5521   PetscCheck(len, comm, PETSC_ERR_ARG_WRONG, "Filename must be a valid path");
5522 
5523 #define CheckExtension(extension__, is_extension__) \
5524   do { \
5525     PetscAssert(sizeof(extension__), comm, PETSC_ERR_PLIB, "Zero-size extension: %s", extension__); \
5526     /* don't count the null-terminator at the end */ \
5527     const size_t ext_len = sizeof(extension__) - 1; \
5528     if (len < ext_len) { \
5529       is_extension__ = PETSC_FALSE; \
5530     } else { \
5531       PetscCall(PetscStrncmp(filename + len - ext_len, extension__, ext_len, &is_extension__)); \
5532     } \
5533   } while (0)
5534 
5535   CheckExtension(extGmsh, isGmsh);
5536   CheckExtension(extGmsh2, isGmsh2);
5537   CheckExtension(extGmsh4, isGmsh4);
5538   CheckExtension(extCGNS, isCGNS);
5539   CheckExtension(extExodus, isExodus);
5540   if (!isExodus) CheckExtension(extExodus_e, isExodus);
5541   CheckExtension(extGenesis, isGenesis);
5542   CheckExtension(extFluent, isFluent);
5543   CheckExtension(extHDF5, isHDF5);
5544   CheckExtension(extMed, isMed);
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 (isMed) {
5591     PetscCall(DMPlexCreateMedFromFile(comm, filename, interpolate, dm));
5592   } else if (isPLY) {
5593     PetscCall(DMPlexCreatePLYFromFile(comm, filename, interpolate, dm));
5594   } else if (isEGADSLite || isEGADS || isIGES || isSTEP) {
5595     if (isEGADSLite) PetscCall(DMPlexCreateEGADSLiteFromFile(comm, filename, dm));
5596     else PetscCall(DMPlexCreateEGADSFromFile(comm, filename, dm));
5597     if (!interpolate) {
5598       DM udm;
5599 
5600       PetscCall(DMPlexUninterpolate(*dm, &udm));
5601       PetscCall(DMDestroy(dm));
5602       *dm = udm;
5603     }
5604   } else if (isCV) {
5605     PetscCall(DMPlexCreateCellVertexFromFile(comm, filename, interpolate, dm));
5606   } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cannot load file %s: unrecognized extension", filename);
5607   PetscCall(PetscStrlen(plexname, &len));
5608   if (len) PetscCall(PetscObjectSetName((PetscObject)(*dm), plexname));
5609   PetscCall(PetscLogEventEnd(DMPLEX_CreateFromFile, 0, 0, 0, 0));
5610   PetscFunctionReturn(PETSC_SUCCESS);
5611 }
5612 
5613 /*@C
5614   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.
5615 
5616   Input Parameters:
5617 + tr     - The `DMPlexTransform`
5618 - prefix - An options prefix, or NULL
5619 
5620   Output Parameter:
5621 . dm - The `DM`
5622 
5623   Level: beginner
5624 
5625   Notes:
5626   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.
5627 
5628 .seealso: `DMPlexCreateFromFile`, `DMPlexCreateFromDAG()`, `DMPlexCreateFromCellListPetsc()`, `DMPlexCreate()`
5629 @*/
5630 PetscErrorCode DMPlexCreateEphemeral(DMPlexTransform tr, const char prefix[], DM *dm)
5631 {
5632   DM           bdm, bcdm, cdm;
5633   Vec          coordinates, coordinatesNew;
5634   PetscSection cs;
5635   PetscInt     dim, cdim, Nl;
5636 
5637   PetscFunctionBegin;
5638   PetscCall(DMCreate(PetscObjectComm((PetscObject)tr), dm));
5639   PetscCall(DMSetType(*dm, DMPLEX));
5640   ((DM_Plex *)(*dm)->data)->interpolated = DMPLEX_INTERPOLATED_FULL;
5641   // Handle coordinates
5642   PetscCall(DMPlexTransformGetDM(tr, &bdm));
5643   PetscCall(DMGetCoordinateDim(bdm, &cdim));
5644   PetscCall(DMSetCoordinateDim(*dm, cdim));
5645   PetscCall(DMGetDimension(bdm, &dim));
5646   PetscCall(DMSetDimension(*dm, dim));
5647   PetscCall(DMGetCoordinateDM(bdm, &bcdm));
5648   PetscCall(DMGetCoordinateDM(*dm, &cdm));
5649   PetscCall(DMCopyDisc(bcdm, cdm));
5650   PetscCall(DMGetLocalSection(cdm, &cs));
5651   PetscCall(PetscSectionSetNumFields(cs, 1));
5652   PetscCall(PetscSectionSetFieldComponents(cs, 0, cdim));
5653   PetscCall(DMGetCoordinatesLocal(bdm, &coordinates));
5654   PetscCall(VecDuplicate(coordinates, &coordinatesNew));
5655   PetscCall(VecCopy(coordinates, coordinatesNew));
5656   PetscCall(DMSetCoordinatesLocal(*dm, coordinatesNew));
5657   PetscCall(VecDestroy(&coordinatesNew));
5658 
5659   PetscCall(PetscObjectReference((PetscObject)tr));
5660   PetscCall(DMPlexTransformDestroy(&((DM_Plex *)(*dm)->data)->tr));
5661   ((DM_Plex *)(*dm)->data)->tr = tr;
5662   PetscCall(DMPlexDistributeSetDefault(*dm, PETSC_FALSE));
5663   PetscCall(PetscObjectSetOptionsPrefix((PetscObject)*dm, prefix));
5664   PetscCall(DMSetFromOptions(*dm));
5665 
5666   PetscCall(DMGetNumLabels(bdm, &Nl));
5667   for (PetscInt l = 0; l < Nl; ++l) {
5668     DMLabel     label, labelNew;
5669     const char *lname;
5670     PetscBool   isDepth, isCellType;
5671 
5672     PetscCall(DMGetLabelName(bdm, l, &lname));
5673     PetscCall(PetscStrcmp(lname, "depth", &isDepth));
5674     if (isDepth) continue;
5675     PetscCall(PetscStrcmp(lname, "celltype", &isCellType));
5676     if (isCellType) continue;
5677     PetscCall(DMCreateLabel(*dm, lname));
5678     PetscCall(DMGetLabel(bdm, lname, &label));
5679     PetscCall(DMGetLabel(*dm, lname, &labelNew));
5680     PetscCall(DMLabelSetType(labelNew, DMLABELEPHEMERAL));
5681     PetscCall(DMLabelEphemeralSetLabel(labelNew, label));
5682     PetscCall(DMLabelEphemeralSetTransform(labelNew, tr));
5683     PetscCall(DMLabelSetUp(labelNew));
5684   }
5685   PetscFunctionReturn(PETSC_SUCCESS);
5686 }
5687