xref: /petsc/src/dm/impls/plex/plexcreate.c (revision b2f36b75b482ff5d6fb826dd2b9be57b9ad8cf37)
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 
6 PetscLogEvent DMPLEX_CreateFromFile, DMPLEX_BuildFromCellList, DMPLEX_BuildCoordinatesFromCellList;
7 
8 /* External function declarations here */
9 static PetscErrorCode DMInitialize_Plex(DM dm);
10 
11 /* Replace dm with the contents of ndm, and then destroy ndm
12    - Share the DM_Plex structure
13    - Share the coordinates
14    - Share the SF
15 */
16 static PetscErrorCode DMPlexReplace_Static(DM dm, DM *ndm)
17 {
18   PetscSF               sf;
19   DM                    dmNew = *ndm, coordDM, coarseDM;
20   Vec                   coords;
21   PetscBool             isper;
22   const PetscReal      *maxCell, *L;
23   const DMBoundaryType *bd;
24   PetscInt              dim, cdim;
25   PetscErrorCode        ierr;
26 
27   PetscFunctionBegin;
28   if (dm == dmNew) {
29     ierr = DMDestroy(ndm);CHKERRQ(ierr);
30     PetscFunctionReturn(0);
31   }
32   dm->setupcalled = dmNew->setupcalled;
33   ierr = DMGetDimension(dmNew, &dim);CHKERRQ(ierr);
34   ierr = DMSetDimension(dm, dim);CHKERRQ(ierr);
35   ierr = DMGetCoordinateDim(dmNew, &cdim);CHKERRQ(ierr);
36   ierr = DMSetCoordinateDim(dm, cdim);CHKERRQ(ierr);
37   ierr = DMGetPointSF(dmNew, &sf);CHKERRQ(ierr);
38   ierr = DMSetPointSF(dm, sf);CHKERRQ(ierr);
39   ierr = DMGetCoordinateDM(dmNew, &coordDM);CHKERRQ(ierr);
40   ierr = DMGetCoordinatesLocal(dmNew, &coords);CHKERRQ(ierr);
41   ierr = DMSetCoordinateDM(dm, coordDM);CHKERRQ(ierr);
42   ierr = DMSetCoordinatesLocal(dm, coords);CHKERRQ(ierr);
43   /* Do not want to create the coordinate field if it does not already exist, so do not call DMGetCoordinateField() */
44   ierr = DMFieldDestroy(&dm->coordinateField);CHKERRQ(ierr);
45   dm->coordinateField = dmNew->coordinateField;
46   ((DM_Plex *) dmNew->data)->coordFunc = ((DM_Plex *) dm->data)->coordFunc;
47   ierr = DMGetPeriodicity(dmNew, &isper, &maxCell, &L, &bd);CHKERRQ(ierr);
48   ierr = DMSetPeriodicity(dm, isper, maxCell, L, bd);CHKERRQ(ierr);
49   ierr = DMDestroy_Plex(dm);CHKERRQ(ierr);
50   ierr = DMInitialize_Plex(dm);CHKERRQ(ierr);
51   dm->data = dmNew->data;
52   ((DM_Plex *) dmNew->data)->refct++;
53   ierr = DMDestroyLabelLinkList_Internal(dm);CHKERRQ(ierr);
54   ierr = DMCopyLabels(dmNew, dm, PETSC_OWN_POINTER, PETSC_TRUE, DM_COPY_LABELS_FAIL);CHKERRQ(ierr);
55   ierr = DMGetCoarseDM(dmNew,&coarseDM);CHKERRQ(ierr);
56   ierr = DMSetCoarseDM(dm,coarseDM);CHKERRQ(ierr);
57   ierr = DMDestroy(ndm);CHKERRQ(ierr);
58   PetscFunctionReturn(0);
59 }
60 
61 /* Swap dm with the contents of dmNew
62    - Swap the DM_Plex structure
63    - Swap the coordinates
64    - Swap the point PetscSF
65 */
66 static PetscErrorCode DMPlexSwap_Static(DM dmA, DM dmB)
67 {
68   DM              coordDMA, coordDMB;
69   Vec             coordsA,  coordsB;
70   PetscSF         sfA,      sfB;
71   DMField         fieldTmp;
72   void            *tmp;
73   DMLabelLink     listTmp;
74   DMLabel         depthTmp;
75   PetscInt        tmpI;
76   PetscErrorCode  ierr;
77 
78   PetscFunctionBegin;
79   if (dmA == dmB) PetscFunctionReturn(0);
80   ierr = DMGetPointSF(dmA, &sfA);CHKERRQ(ierr);
81   ierr = DMGetPointSF(dmB, &sfB);CHKERRQ(ierr);
82   ierr = PetscObjectReference((PetscObject) sfA);CHKERRQ(ierr);
83   ierr = DMSetPointSF(dmA, sfB);CHKERRQ(ierr);
84   ierr = DMSetPointSF(dmB, sfA);CHKERRQ(ierr);
85   ierr = PetscObjectDereference((PetscObject) sfA);CHKERRQ(ierr);
86 
87   ierr = DMGetCoordinateDM(dmA, &coordDMA);CHKERRQ(ierr);
88   ierr = DMGetCoordinateDM(dmB, &coordDMB);CHKERRQ(ierr);
89   ierr = PetscObjectReference((PetscObject) coordDMA);CHKERRQ(ierr);
90   ierr = DMSetCoordinateDM(dmA, coordDMB);CHKERRQ(ierr);
91   ierr = DMSetCoordinateDM(dmB, coordDMA);CHKERRQ(ierr);
92   ierr = PetscObjectDereference((PetscObject) coordDMA);CHKERRQ(ierr);
93 
94   ierr = DMGetCoordinatesLocal(dmA, &coordsA);CHKERRQ(ierr);
95   ierr = DMGetCoordinatesLocal(dmB, &coordsB);CHKERRQ(ierr);
96   ierr = PetscObjectReference((PetscObject) coordsA);CHKERRQ(ierr);
97   ierr = DMSetCoordinatesLocal(dmA, coordsB);CHKERRQ(ierr);
98   ierr = DMSetCoordinatesLocal(dmB, coordsA);CHKERRQ(ierr);
99   ierr = PetscObjectDereference((PetscObject) coordsA);CHKERRQ(ierr);
100 
101   fieldTmp             = dmA->coordinateField;
102   dmA->coordinateField = dmB->coordinateField;
103   dmB->coordinateField = fieldTmp;
104   tmp       = dmA->data;
105   dmA->data = dmB->data;
106   dmB->data = tmp;
107   listTmp   = dmA->labels;
108   dmA->labels = dmB->labels;
109   dmB->labels = listTmp;
110   depthTmp  = dmA->depthLabel;
111   dmA->depthLabel = dmB->depthLabel;
112   dmB->depthLabel = depthTmp;
113   depthTmp  = dmA->celltypeLabel;
114   dmA->celltypeLabel = dmB->celltypeLabel;
115   dmB->celltypeLabel = depthTmp;
116   tmpI         = dmA->levelup;
117   dmA->levelup = dmB->levelup;
118   dmB->levelup = tmpI;
119   PetscFunctionReturn(0);
120 }
121 
122 static PetscErrorCode DMPlexInterpolateInPlace_Internal(DM dm)
123 {
124   DM             idm;
125   PetscErrorCode ierr;
126 
127   PetscFunctionBegin;
128   ierr = DMPlexInterpolate(dm, &idm);CHKERRQ(ierr);
129   ierr = DMPlexCopyCoordinates(dm, idm);CHKERRQ(ierr);
130   ierr = DMPlexReplace_Static(dm, &idm);CHKERRQ(ierr);
131   PetscFunctionReturn(0);
132 }
133 
134 /*@C
135   DMPlexCreateCoordinateSpace - Creates a finite element space for the coordinates
136 
137   Collective
138 
139   Input Parameters:
140 + DM        - The DM
141 . degree    - The degree of the finite element
142 - coordFunc - An optional function to map new points from refinement to the surface
143 
144   Level: advanced
145 
146 .seealso: PetscFECreateLagrange(), DMGetCoordinateDM()
147 @*/
148 PetscErrorCode DMPlexCreateCoordinateSpace(DM dm, PetscInt degree, PetscPointFunc coordFunc)
149 {
150   DM_Plex       *mesh = (DM_Plex *) dm->data;
151   DM             cdm;
152   PetscDS        cds;
153   PetscFE        fe;
154   PetscClassId   id;
155   PetscErrorCode ierr;
156 
157   PetscFunctionBegin;
158   ierr = DMGetCoordinateDM(dm, &cdm);CHKERRQ(ierr);
159   ierr = DMGetDS(cdm, &cds);CHKERRQ(ierr);
160   ierr = PetscDSGetDiscretization(cds, 0, (PetscObject *) &fe);CHKERRQ(ierr);
161   ierr = PetscObjectGetClassId((PetscObject) fe, &id);CHKERRQ(ierr);
162   if (id != PETSCFE_CLASSID) {
163     PetscBool simplex;
164     PetscInt  dim, dE, qorder;
165 
166     ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
167     ierr = DMGetCoordinateDim(dm, &dE);CHKERRQ(ierr);
168     ierr = DMPlexIsSimplex(dm, &simplex);CHKERRQ(ierr);
169     qorder = degree;
170     ierr = PetscObjectOptionsBegin((PetscObject) cdm);CHKERRQ(ierr);
171     ierr = PetscOptionsBoundedInt("-coord_dm_default_quadrature_order", "Quadrature order is one less than quadrature points per edge", "DMPlexCreateCoordinateSpace", qorder, &qorder, NULL, 0);CHKERRQ(ierr);
172     ierr = PetscOptionsEnd();CHKERRQ(ierr);
173     ierr = PetscFECreateLagrange(PETSC_COMM_SELF, dim, dE, simplex, degree, qorder, &fe);CHKERRQ(ierr);
174     ierr = DMSetField(cdm, 0, NULL, (PetscObject) fe);CHKERRQ(ierr);
175     ierr = DMCreateDS(cdm);CHKERRQ(ierr);
176     ierr = DMProjectCoordinates(dm, fe);CHKERRQ(ierr);
177     ierr = PetscFEDestroy(&fe);CHKERRQ(ierr);
178   }
179   mesh->coordFunc = coordFunc;
180   PetscFunctionReturn(0);
181 }
182 
183 /*@
184   DMPlexCreateDoublet - Creates a mesh of two cells of the specified type, optionally with later refinement.
185 
186   Collective
187 
188   Input Parameters:
189 + comm - The communicator for the DM object
190 . dim - The spatial dimension
191 . simplex - Flag for simplicial cells, otherwise they are tensor product cells
192 . interpolate - Flag to create intermediate mesh pieces (edges, faces)
193 - refinementLimit - A nonzero number indicates the largest admissible volume for a refined cell
194 
195   Output Parameter:
196 . dm - The DM object
197 
198   Level: beginner
199 
200 .seealso: DMSetType(), DMCreate()
201 @*/
202 PetscErrorCode DMPlexCreateDoublet(MPI_Comm comm, PetscInt dim, PetscBool simplex, PetscBool interpolate, PetscReal refinementLimit, DM *newdm)
203 {
204   DM             dm;
205   PetscMPIInt    rank;
206   PetscErrorCode ierr;
207 
208   PetscFunctionBegin;
209   ierr = DMCreate(comm, &dm);CHKERRQ(ierr);
210   ierr = DMSetType(dm, DMPLEX);CHKERRQ(ierr);
211   ierr = DMSetDimension(dm, dim);CHKERRQ(ierr);
212   ierr = MPI_Comm_rank(comm, &rank);CHKERRMPI(ierr);
213   switch (dim) {
214   case 2:
215     if (simplex) {ierr = PetscObjectSetName((PetscObject) dm, "triangular");CHKERRQ(ierr);}
216     else         {ierr = PetscObjectSetName((PetscObject) dm, "quadrilateral");CHKERRQ(ierr);}
217     break;
218   case 3:
219     if (simplex) {ierr = PetscObjectSetName((PetscObject) dm, "tetrahedral");CHKERRQ(ierr);}
220     else         {ierr = PetscObjectSetName((PetscObject) dm, "hexahedral");CHKERRQ(ierr);}
221     break;
222   default:
223     SETERRQ1(comm, PETSC_ERR_ARG_OUTOFRANGE, "Cannot make meshes for dimension %D", dim);
224   }
225   if (rank) {
226     PetscInt numPoints[2] = {0, 0};
227     ierr = DMPlexCreateFromDAG(dm, 1, numPoints, NULL, NULL, NULL, NULL);CHKERRQ(ierr);
228   } else {
229     switch (dim) {
230     case 2:
231       if (simplex) {
232         PetscInt    numPoints[2]        = {4, 2};
233         PetscInt    coneSize[6]         = {3, 3, 0, 0, 0, 0};
234         PetscInt    cones[6]            = {2, 3, 4,  5, 4, 3};
235         PetscInt    coneOrientations[6] = {0, 0, 0,  0, 0, 0};
236         PetscScalar vertexCoords[8]     = {-0.5, 0.5, 0.0, 0.0, 0.0, 1.0, 0.5, 0.5};
237 
238         ierr = DMPlexCreateFromDAG(dm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
239       } else {
240         PetscInt    numPoints[2]        = {6, 2};
241         PetscInt    coneSize[8]         = {4, 4, 0, 0, 0, 0, 0, 0};
242         PetscInt    cones[8]            = {2, 3, 4, 5,  3, 6, 7, 4};
243         PetscInt    coneOrientations[8] = {0, 0, 0, 0,  0, 0, 0, 0};
244         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};
245 
246         ierr = DMPlexCreateFromDAG(dm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
247       }
248       break;
249     case 3:
250       if (simplex) {
251         PetscInt    numPoints[2]        = {5, 2};
252         PetscInt    coneSize[7]         = {4, 4, 0, 0, 0, 0, 0};
253         PetscInt    cones[8]            = {4, 3, 5, 2,  5, 3, 4, 6};
254         PetscInt    coneOrientations[8] = {0, 0, 0, 0,  0, 0, 0, 0};
255         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};
256 
257         ierr = DMPlexCreateFromDAG(dm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
258       } else {
259         PetscInt    numPoints[2]         = {12, 2};
260         PetscInt    coneSize[14]         = {8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0};
261         PetscInt    cones[16]            = {2, 3, 4, 5, 6, 7, 8, 9,  5, 4, 10, 11, 7, 12, 13, 8};
262         PetscInt    coneOrientations[16] = {0, 0, 0, 0, 0, 0, 0, 0,  0, 0,  0,  0, 0,  0,  0, 0};
263         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,
264                                             -1.0, -0.5,  0.5,   0.0, -0.5,  0.5,  0.0,  0.5,  0.5,  -1.0,  0.5,  0.5,
265                                              1.0,  0.5, -0.5,   1.0, -0.5, -0.5,  1.0, -0.5,  0.5,   1.0,  0.5,  0.5};
266 
267         ierr = DMPlexCreateFromDAG(dm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
268       }
269       break;
270     default:
271       SETERRQ1(comm, PETSC_ERR_ARG_OUTOFRANGE, "Cannot make meshes for dimension %D", dim);
272     }
273   }
274   *newdm = dm;
275   if (refinementLimit > 0.0) {
276     DM rdm;
277     const char *name;
278 
279     ierr = DMPlexSetRefinementUniform(*newdm, PETSC_FALSE);CHKERRQ(ierr);
280     ierr = DMPlexSetRefinementLimit(*newdm, refinementLimit);CHKERRQ(ierr);
281     ierr = DMRefine(*newdm, comm, &rdm);CHKERRQ(ierr);
282     ierr = PetscObjectGetName((PetscObject) *newdm, &name);CHKERRQ(ierr);
283     ierr = PetscObjectSetName((PetscObject)    rdm,  name);CHKERRQ(ierr);
284     ierr = DMDestroy(newdm);CHKERRQ(ierr);
285     *newdm = rdm;
286   }
287   if (interpolate) {
288     DM idm;
289 
290     ierr = DMPlexInterpolate(*newdm, &idm);CHKERRQ(ierr);
291     ierr = DMDestroy(newdm);CHKERRQ(ierr);
292     *newdm = idm;
293   }
294   PetscFunctionReturn(0);
295 }
296 
297 static PetscErrorCode DMPlexCreateBoxSurfaceMesh_Tensor_1D_Internal(DM dm, const PetscReal lower[], const PetscReal upper[], const PetscInt edges[])
298 {
299   const PetscInt numVertices    = 2;
300   PetscInt       markerRight    = 1;
301   PetscInt       markerLeft     = 1;
302   PetscBool      markerSeparate = PETSC_FALSE;
303   Vec            coordinates;
304   PetscSection   coordSection;
305   PetscScalar   *coords;
306   PetscInt       coordSize;
307   PetscMPIInt    rank;
308   PetscInt       cdim = 1, v;
309   PetscErrorCode ierr;
310 
311   PetscFunctionBegin;
312   ierr = PetscOptionsGetBool(((PetscObject) dm)->options,((PetscObject) dm)->prefix, "-dm_plex_separate_marker", &markerSeparate, NULL);CHKERRQ(ierr);
313   if (markerSeparate) {
314     markerRight  = 2;
315     markerLeft   = 1;
316   }
317   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);CHKERRMPI(ierr);
318   if (!rank) {
319     ierr = DMPlexSetChart(dm, 0, numVertices);CHKERRQ(ierr);
320     ierr = DMSetUp(dm);CHKERRQ(ierr); /* Allocate space for cones */
321     ierr = DMSetLabelValue(dm, "marker", 0, markerLeft);CHKERRQ(ierr);
322     ierr = DMSetLabelValue(dm, "marker", 1, markerRight);CHKERRQ(ierr);
323   }
324   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
325   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
326   /* Build coordinates */
327   ierr = DMSetCoordinateDim(dm, cdim);CHKERRQ(ierr);
328   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
329   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
330   ierr = PetscSectionSetChart(coordSection, 0, numVertices);CHKERRQ(ierr);
331   ierr = PetscSectionSetFieldComponents(coordSection, 0, cdim);CHKERRQ(ierr);
332   for (v = 0; v < numVertices; ++v) {
333     ierr = PetscSectionSetDof(coordSection, v, cdim);CHKERRQ(ierr);
334     ierr = PetscSectionSetFieldDof(coordSection, v, 0, cdim);CHKERRQ(ierr);
335   }
336   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
337   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
338   ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
339   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
340   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
341   ierr = VecSetBlockSize(coordinates, cdim);CHKERRQ(ierr);
342   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
343   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
344   coords[0] = lower[0];
345   coords[1] = upper[0];
346   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
347   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
348   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
349   PetscFunctionReturn(0);
350 }
351 
352 static PetscErrorCode DMPlexCreateBoxSurfaceMesh_Tensor_2D_Internal(DM dm, const PetscReal lower[], const PetscReal upper[], const PetscInt edges[])
353 {
354   const PetscInt numVertices    = (edges[0]+1)*(edges[1]+1);
355   const PetscInt numEdges       = edges[0]*(edges[1]+1) + (edges[0]+1)*edges[1];
356   PetscInt       markerTop      = 1;
357   PetscInt       markerBottom   = 1;
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       v, vx, vy;
367   PetscErrorCode ierr;
368 
369   PetscFunctionBegin;
370   ierr = PetscOptionsGetBool(((PetscObject) dm)->options,((PetscObject) dm)->prefix, "-dm_plex_separate_marker", &markerSeparate, NULL);CHKERRQ(ierr);
371   if (markerSeparate) {
372     markerTop    = 3;
373     markerBottom = 1;
374     markerRight  = 2;
375     markerLeft   = 4;
376   }
377   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);CHKERRMPI(ierr);
378   if (rank == 0) {
379     PetscInt e, ex, ey;
380 
381     ierr = DMPlexSetChart(dm, 0, numEdges+numVertices);CHKERRQ(ierr);
382     for (e = 0; e < numEdges; ++e) {
383       ierr = DMPlexSetConeSize(dm, e, 2);CHKERRQ(ierr);
384     }
385     ierr = DMSetUp(dm);CHKERRQ(ierr); /* Allocate space for cones */
386     for (vx = 0; vx <= edges[0]; vx++) {
387       for (ey = 0; ey < edges[1]; ey++) {
388         PetscInt edge   = vx*edges[1] + ey + edges[0]*(edges[1]+1);
389         PetscInt vertex = ey*(edges[0]+1) + vx + numEdges;
390         PetscInt cone[2];
391 
392         cone[0] = vertex; cone[1] = vertex+edges[0]+1;
393         ierr    = DMPlexSetCone(dm, edge, cone);CHKERRQ(ierr);
394         if (vx == edges[0]) {
395           ierr = DMSetLabelValue(dm, "marker", edge,    markerRight);CHKERRQ(ierr);
396           ierr = DMSetLabelValue(dm, "marker", cone[0], markerRight);CHKERRQ(ierr);
397           if (ey == edges[1]-1) {
398             ierr = DMSetLabelValue(dm, "marker", cone[1], markerRight);CHKERRQ(ierr);
399             ierr = DMSetLabelValue(dm, "Face Sets", cone[1], markerRight);CHKERRQ(ierr);
400           }
401         } else if (vx == 0) {
402           ierr = DMSetLabelValue(dm, "marker", edge,    markerLeft);CHKERRQ(ierr);
403           ierr = DMSetLabelValue(dm, "marker", cone[0], markerLeft);CHKERRQ(ierr);
404           if (ey == edges[1]-1) {
405             ierr = DMSetLabelValue(dm, "marker", cone[1], markerLeft);CHKERRQ(ierr);
406             ierr = DMSetLabelValue(dm, "Face Sets", cone[1], markerLeft);CHKERRQ(ierr);
407           }
408         }
409       }
410     }
411     for (vy = 0; vy <= edges[1]; vy++) {
412       for (ex = 0; ex < edges[0]; ex++) {
413         PetscInt edge   = vy*edges[0]     + ex;
414         PetscInt vertex = vy*(edges[0]+1) + ex + numEdges;
415         PetscInt cone[2];
416 
417         cone[0] = vertex; cone[1] = vertex+1;
418         ierr    = DMPlexSetCone(dm, edge, cone);CHKERRQ(ierr);
419         if (vy == edges[1]) {
420           ierr = DMSetLabelValue(dm, "marker", edge,    markerTop);CHKERRQ(ierr);
421           ierr = DMSetLabelValue(dm, "marker", cone[0], markerTop);CHKERRQ(ierr);
422           if (ex == edges[0]-1) {
423             ierr = DMSetLabelValue(dm, "marker", cone[1], markerTop);CHKERRQ(ierr);
424             ierr = DMSetLabelValue(dm, "Face Sets", cone[1], markerTop);CHKERRQ(ierr);
425           }
426         } else if (vy == 0) {
427           ierr = DMSetLabelValue(dm, "marker", edge,    markerBottom);CHKERRQ(ierr);
428           ierr = DMSetLabelValue(dm, "marker", cone[0], markerBottom);CHKERRQ(ierr);
429           if (ex == edges[0]-1) {
430             ierr = DMSetLabelValue(dm, "marker", cone[1], markerBottom);CHKERRQ(ierr);
431             ierr = DMSetLabelValue(dm, "Face Sets", cone[1], markerBottom);CHKERRQ(ierr);
432           }
433         }
434       }
435     }
436   }
437   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
438   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
439   /* Build coordinates */
440   ierr = DMSetCoordinateDim(dm, 2);CHKERRQ(ierr);
441   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
442   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
443   ierr = PetscSectionSetChart(coordSection, numEdges, numEdges + numVertices);CHKERRQ(ierr);
444   ierr = PetscSectionSetFieldComponents(coordSection, 0, 2);CHKERRQ(ierr);
445   for (v = numEdges; v < numEdges+numVertices; ++v) {
446     ierr = PetscSectionSetDof(coordSection, v, 2);CHKERRQ(ierr);
447     ierr = PetscSectionSetFieldDof(coordSection, v, 0, 2);CHKERRQ(ierr);
448   }
449   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
450   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
451   ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
452   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
453   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
454   ierr = VecSetBlockSize(coordinates, 2);CHKERRQ(ierr);
455   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
456   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
457   for (vy = 0; vy <= edges[1]; ++vy) {
458     for (vx = 0; vx <= edges[0]; ++vx) {
459       coords[(vy*(edges[0]+1)+vx)*2+0] = lower[0] + ((upper[0] - lower[0])/edges[0])*vx;
460       coords[(vy*(edges[0]+1)+vx)*2+1] = lower[1] + ((upper[1] - lower[1])/edges[1])*vy;
461     }
462   }
463   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
464   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
465   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
466   PetscFunctionReturn(0);
467 }
468 
469 static PetscErrorCode DMPlexCreateBoxSurfaceMesh_Tensor_3D_Internal(DM dm, const PetscReal lower[], const PetscReal upper[], const PetscInt faces[])
470 {
471   PetscInt       vertices[3], numVertices;
472   PetscInt       numFaces    = 2*faces[0]*faces[1] + 2*faces[1]*faces[2] + 2*faces[0]*faces[2];
473   Vec            coordinates;
474   PetscSection   coordSection;
475   PetscScalar    *coords;
476   PetscInt       coordSize;
477   PetscMPIInt    rank;
478   PetscInt       v, vx, vy, vz;
479   PetscInt       voffset, iface=0, cone[4];
480   PetscErrorCode ierr;
481 
482   PetscFunctionBegin;
483   if ((faces[0] < 1) || (faces[1] < 1) || (faces[2] < 1)) SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Must have at least 1 face per side");
484   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);CHKERRMPI(ierr);
485   vertices[0] = faces[0]+1; vertices[1] = faces[1]+1; vertices[2] = faces[2]+1;
486   numVertices = vertices[0]*vertices[1]*vertices[2];
487   if (rank == 0) {
488     PetscInt f;
489 
490     ierr = DMPlexSetChart(dm, 0, numFaces+numVertices);CHKERRQ(ierr);
491     for (f = 0; f < numFaces; ++f) {
492       ierr = DMPlexSetConeSize(dm, f, 4);CHKERRQ(ierr);
493     }
494     ierr = DMSetUp(dm);CHKERRQ(ierr); /* Allocate space for cones */
495 
496     /* Side 0 (Top) */
497     for (vy = 0; vy < faces[1]; vy++) {
498       for (vx = 0; vx < faces[0]; vx++) {
499         voffset = numFaces + vertices[0]*vertices[1]*(vertices[2]-1) + vy*vertices[0] + vx;
500         cone[0] = voffset; cone[1] = voffset+1; cone[2] = voffset+vertices[0]+1; cone[3] = voffset+vertices[0];
501         ierr    = DMPlexSetCone(dm, iface, cone);CHKERRQ(ierr);
502         ierr    = DMSetLabelValue(dm, "marker", iface, 1);CHKERRQ(ierr);
503         ierr    = DMSetLabelValue(dm, "marker", voffset+0, 1);CHKERRQ(ierr);
504         ierr    = DMSetLabelValue(dm, "marker", voffset+1, 1);CHKERRQ(ierr);
505         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[0]+0, 1);CHKERRQ(ierr);
506         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[0]+1, 1);CHKERRQ(ierr);
507         iface++;
508       }
509     }
510 
511     /* Side 1 (Bottom) */
512     for (vy = 0; vy < faces[1]; vy++) {
513       for (vx = 0; vx < faces[0]; vx++) {
514         voffset = numFaces + vy*(faces[0]+1) + vx;
515         cone[0] = voffset+1; cone[1] = voffset; cone[2] = voffset+vertices[0]; cone[3] = voffset+vertices[0]+1;
516         ierr    = DMPlexSetCone(dm, iface, cone);CHKERRQ(ierr);
517         ierr    = DMSetLabelValue(dm, "marker", iface, 1);CHKERRQ(ierr);
518         ierr    = DMSetLabelValue(dm, "marker", voffset+0, 1);CHKERRQ(ierr);
519         ierr    = DMSetLabelValue(dm, "marker", voffset+1, 1);CHKERRQ(ierr);
520         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[0]+0, 1);CHKERRQ(ierr);
521         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[0]+1, 1);CHKERRQ(ierr);
522         iface++;
523       }
524     }
525 
526     /* Side 2 (Front) */
527     for (vz = 0; vz < faces[2]; vz++) {
528       for (vx = 0; vx < faces[0]; vx++) {
529         voffset = numFaces + vz*vertices[0]*vertices[1] + vx;
530         cone[0] = voffset; cone[1] = voffset+1; cone[2] = voffset+vertices[0]*vertices[1]+1; cone[3] = voffset+vertices[0]*vertices[1];
531         ierr    = DMPlexSetCone(dm, iface, cone);CHKERRQ(ierr);
532         ierr    = DMSetLabelValue(dm, "marker", iface, 1);CHKERRQ(ierr);
533         ierr    = DMSetLabelValue(dm, "marker", voffset+0, 1);CHKERRQ(ierr);
534         ierr    = DMSetLabelValue(dm, "marker", voffset+1, 1);CHKERRQ(ierr);
535         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[0]*vertices[1]+0, 1);CHKERRQ(ierr);
536         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[0]*vertices[1]+1, 1);CHKERRQ(ierr);
537         iface++;
538       }
539     }
540 
541     /* Side 3 (Back) */
542     for (vz = 0; vz < faces[2]; vz++) {
543       for (vx = 0; vx < faces[0]; vx++) {
544         voffset = numFaces + vz*vertices[0]*vertices[1] + vertices[0]*(vertices[1]-1) + vx;
545         cone[0] = voffset+vertices[0]*vertices[1]; cone[1] = voffset+vertices[0]*vertices[1]+1;
546         cone[2] = voffset+1; cone[3] = voffset;
547         ierr    = DMPlexSetCone(dm, iface, cone);CHKERRQ(ierr);
548         ierr    = DMSetLabelValue(dm, "marker", iface, 1);CHKERRQ(ierr);
549         ierr    = DMSetLabelValue(dm, "marker", voffset+0, 1);CHKERRQ(ierr);
550         ierr    = DMSetLabelValue(dm, "marker", voffset+1, 1);CHKERRQ(ierr);
551         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[0]*vertices[1]+0, 1);CHKERRQ(ierr);
552         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[0]*vertices[1]+1, 1);CHKERRQ(ierr);
553         iface++;
554       }
555     }
556 
557     /* Side 4 (Left) */
558     for (vz = 0; vz < faces[2]; vz++) {
559       for (vy = 0; vy < faces[1]; vy++) {
560         voffset = numFaces + vz*vertices[0]*vertices[1] + vy*vertices[0];
561         cone[0] = voffset; cone[1] = voffset+vertices[0]*vertices[1];
562         cone[2] = voffset+vertices[0]*vertices[1]+vertices[0]; cone[3] = voffset+vertices[0];
563         ierr    = DMPlexSetCone(dm, iface, cone);CHKERRQ(ierr);
564         ierr    = DMSetLabelValue(dm, "marker", iface, 1);CHKERRQ(ierr);
565         ierr    = DMSetLabelValue(dm, "marker", voffset+0, 1);CHKERRQ(ierr);
566         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[0]+0, 1);CHKERRQ(ierr);
567         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[1]+0, 1);CHKERRQ(ierr);
568         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[0]*vertices[1]+vertices[0], 1);CHKERRQ(ierr);
569         iface++;
570       }
571     }
572 
573     /* Side 5 (Right) */
574     for (vz = 0; vz < faces[2]; vz++) {
575       for (vy = 0; vy < faces[1]; vy++) {
576         voffset = numFaces + vz*vertices[0]*vertices[1] + vy*vertices[0] + faces[0];
577         cone[0] = voffset+vertices[0]*vertices[1]; cone[1] = voffset;
578         cone[2] = voffset+vertices[0]; cone[3] = voffset+vertices[0]*vertices[1]+vertices[0];
579         ierr    = DMPlexSetCone(dm, iface, cone);CHKERRQ(ierr);
580         ierr    = DMSetLabelValue(dm, "marker", iface, 1);CHKERRQ(ierr);
581         ierr    = DMSetLabelValue(dm, "marker", voffset+0, 1);CHKERRQ(ierr);
582         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[0]+0, 1);CHKERRQ(ierr);
583         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[0]*vertices[1]+0, 1);CHKERRQ(ierr);
584         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[0]*vertices[1]+vertices[0], 1);CHKERRQ(ierr);
585         iface++;
586       }
587     }
588   }
589   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
590   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
591   /* Build coordinates */
592   ierr = DMSetCoordinateDim(dm, 3);CHKERRQ(ierr);
593   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
594   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
595   ierr = PetscSectionSetChart(coordSection, numFaces, numFaces + numVertices);CHKERRQ(ierr);
596   ierr = PetscSectionSetFieldComponents(coordSection, 0, 3);CHKERRQ(ierr);
597   for (v = numFaces; v < numFaces+numVertices; ++v) {
598     ierr = PetscSectionSetDof(coordSection, v, 3);CHKERRQ(ierr);
599     ierr = PetscSectionSetFieldDof(coordSection, v, 0, 3);CHKERRQ(ierr);
600   }
601   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
602   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
603   ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
604   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
605   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
606   ierr = VecSetBlockSize(coordinates, 3);CHKERRQ(ierr);
607   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
608   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
609   for (vz = 0; vz <= faces[2]; ++vz) {
610     for (vy = 0; vy <= faces[1]; ++vy) {
611       for (vx = 0; vx <= faces[0]; ++vx) {
612         coords[((vz*(faces[1]+1)+vy)*(faces[0]+1)+vx)*3+0] = lower[0] + ((upper[0] - lower[0])/faces[0])*vx;
613         coords[((vz*(faces[1]+1)+vy)*(faces[0]+1)+vx)*3+1] = lower[1] + ((upper[1] - lower[1])/faces[1])*vy;
614         coords[((vz*(faces[1]+1)+vy)*(faces[0]+1)+vx)*3+2] = lower[2] + ((upper[2] - lower[2])/faces[2])*vz;
615       }
616     }
617   }
618   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
619   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
620   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
621   PetscFunctionReturn(0);
622 }
623 
624 static PetscErrorCode DMPlexCreateBoxSurfaceMesh_Internal(DM dm, PetscInt dim, const PetscInt faces[], const PetscReal lower[], const PetscReal upper[], PetscBool interpolate)
625 {
626   PetscErrorCode ierr;
627 
628   PetscFunctionBegin;
629   PetscValidLogicalCollectiveInt(dm, dim, 2);
630   ierr = DMSetDimension(dm, dim-1);CHKERRQ(ierr);
631   ierr = DMSetCoordinateDim(dm, dim);CHKERRQ(ierr);
632   switch (dim) {
633     case 1: ierr = DMPlexCreateBoxSurfaceMesh_Tensor_1D_Internal(dm, lower, upper, faces);CHKERRQ(ierr);break;
634     case 2: ierr = DMPlexCreateBoxSurfaceMesh_Tensor_2D_Internal(dm, lower, upper, faces);CHKERRQ(ierr);break;
635     case 3: ierr = DMPlexCreateBoxSurfaceMesh_Tensor_3D_Internal(dm, lower, upper, faces);CHKERRQ(ierr);break;
636     default: SETERRQ1(PetscObjectComm((PetscObject) dm), PETSC_ERR_SUP, "Dimension not supported: %D", dim);
637   }
638   if (interpolate) {ierr = DMPlexInterpolateInPlace_Internal(dm);CHKERRQ(ierr);}
639   PetscFunctionReturn(0);
640 }
641 
642 /*@C
643   DMPlexCreateBoxSurfaceMesh - Creates a mesh on the surface of the tensor product of unit intervals (box) using tensor cells (hexahedra).
644 
645   Collective
646 
647   Input Parameters:
648 + comm        - The communicator for the DM object
649 . dim         - The spatial dimension of the box, so the resulting mesh is has dimension dim-1
650 . faces       - Number of faces per dimension, or NULL for (1,) in 1D and (2, 2) in 2D and (1, 1, 1) in 3D
651 . lower       - The lower left corner, or NULL for (0, 0, 0)
652 . upper       - The upper right corner, or NULL for (1, 1, 1)
653 - interpolate - Flag to create intermediate mesh pieces (edges, faces)
654 
655   Output Parameter:
656 . dm  - The DM object
657 
658   Level: beginner
659 
660 .seealso: DMSetFromOptions(), DMPlexCreateBoxMesh(), DMPlexCreateFromFile(), DMSetType(), DMCreate()
661 @*/
662 PetscErrorCode DMPlexCreateBoxSurfaceMesh(MPI_Comm comm, PetscInt dim, const PetscInt faces[], const PetscReal lower[], const PetscReal upper[], PetscBool interpolate, DM *dm)
663 {
664   PetscInt       fac[3] = {1, 1, 1};
665   PetscReal      low[3] = {0, 0, 0};
666   PetscReal      upp[3] = {1, 1, 1};
667   PetscErrorCode ierr;
668 
669   PetscFunctionBegin;
670   ierr = DMCreate(comm,dm);CHKERRQ(ierr);
671   ierr = DMSetType(*dm,DMPLEX);CHKERRQ(ierr);
672   ierr = DMPlexCreateBoxSurfaceMesh_Internal(*dm, dim, faces ? faces : fac, lower ? lower : low, upper ? upper : upp, interpolate);CHKERRQ(ierr);
673   PetscFunctionReturn(0);
674 }
675 
676 static PetscErrorCode DMPlexCreateLineMesh_Internal(DM dm,PetscInt segments,PetscReal lower,PetscReal upper,DMBoundaryType bd)
677 {
678   PetscInt       i,fStart,fEnd,numCells = 0,numVerts = 0;
679   PetscInt       numPoints[2],*coneSize,*cones,*coneOrientations;
680   PetscScalar    *vertexCoords;
681   PetscReal      L,maxCell;
682   PetscBool      markerSeparate = PETSC_FALSE;
683   PetscInt       markerLeft  = 1, faceMarkerLeft  = 1;
684   PetscInt       markerRight = 1, faceMarkerRight = 2;
685   PetscBool      wrap = (bd == DM_BOUNDARY_PERIODIC || bd == DM_BOUNDARY_TWIST) ? PETSC_TRUE : PETSC_FALSE;
686   PetscMPIInt    rank;
687   PetscErrorCode ierr;
688 
689   PetscFunctionBegin;
690   PetscValidPointer(dm,1);
691 
692   ierr = DMSetDimension(dm,1);CHKERRQ(ierr);
693   ierr = DMCreateLabel(dm,"marker");CHKERRQ(ierr);
694   ierr = DMCreateLabel(dm,"Face Sets");CHKERRQ(ierr);
695 
696   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject) dm),&rank);CHKERRMPI(ierr);
697   if (rank == 0) numCells = segments;
698   if (rank == 0) numVerts = segments + (wrap ? 0 : 1);
699 
700   numPoints[0] = numVerts ; numPoints[1] = numCells;
701   ierr = PetscMalloc4(numCells+numVerts,&coneSize,numCells*2,&cones,numCells+numVerts,&coneOrientations,numVerts,&vertexCoords);CHKERRQ(ierr);
702   ierr = PetscArrayzero(coneOrientations,numCells+numVerts);CHKERRQ(ierr);
703   for (i = 0; i < numCells; ++i) { coneSize[i] = 2; }
704   for (i = 0; i < numVerts; ++i) { coneSize[numCells+i] = 0; }
705   for (i = 0; i < numCells; ++i) { cones[2*i] = numCells + i%numVerts; cones[2*i+1] = numCells + (i+1)%numVerts; }
706   for (i = 0; i < numVerts; ++i) { vertexCoords[i] = lower + (upper-lower)*((PetscReal)i/(PetscReal)numCells); }
707   ierr = DMPlexCreateFromDAG(dm,1,numPoints,coneSize,cones,coneOrientations,vertexCoords);CHKERRQ(ierr);
708   ierr = PetscFree4(coneSize,cones,coneOrientations,vertexCoords);CHKERRQ(ierr);
709 
710   ierr = PetscOptionsGetBool(((PetscObject)dm)->options,((PetscObject)dm)->prefix,"-dm_plex_separate_marker",&markerSeparate,NULL);CHKERRQ(ierr);
711   if (markerSeparate) { markerLeft = faceMarkerLeft; markerRight = faceMarkerRight;}
712   if (!wrap && rank == 0) {
713     ierr = DMPlexGetHeightStratum(dm,1,&fStart,&fEnd);CHKERRQ(ierr);
714     ierr = DMSetLabelValue(dm,"marker",fStart,markerLeft);CHKERRQ(ierr);
715     ierr = DMSetLabelValue(dm,"marker",fEnd-1,markerRight);CHKERRQ(ierr);
716     ierr = DMSetLabelValue(dm,"Face Sets",fStart,faceMarkerLeft);CHKERRQ(ierr);
717     ierr = DMSetLabelValue(dm,"Face Sets",fEnd-1,faceMarkerRight);CHKERRQ(ierr);
718   }
719   if (wrap) {
720     L       = upper - lower;
721     maxCell = (PetscReal)1.1*(L/(PetscReal)PetscMax(1,segments));
722     ierr = DMSetPeriodicity(dm,PETSC_TRUE,&maxCell,&L,&bd);CHKERRQ(ierr);
723   }
724   ierr = DMPlexSetRefinementUniform(dm, PETSC_TRUE);CHKERRQ(ierr);
725   PetscFunctionReturn(0);
726 }
727 
728 static PetscErrorCode DMPlexCreateBoxMesh_Simplex_Internal(DM dm, PetscInt dim, const PetscInt faces[], const PetscReal lower[], const PetscReal upper[], const DMBoundaryType periodicity[], PetscBool interpolate)
729 {
730   DM             boundary, vol;
731   PetscInt       i;
732   PetscErrorCode ierr;
733 
734   PetscFunctionBegin;
735   PetscValidPointer(dm, 1);
736   for (i = 0; i < dim; ++i) if (periodicity[i] != DM_BOUNDARY_NONE) SETERRQ(PetscObjectComm((PetscObject) dm), PETSC_ERR_SUP, "Periodicity is not supported for simplex meshes");
737   ierr = DMCreate(PetscObjectComm((PetscObject) dm), &boundary);CHKERRQ(ierr);
738   ierr = DMSetType(boundary, DMPLEX);CHKERRQ(ierr);
739   ierr = DMPlexCreateBoxSurfaceMesh_Internal(boundary, dim, faces, lower, upper, PETSC_FALSE);CHKERRQ(ierr);
740   ierr = DMPlexGenerate(boundary, NULL, interpolate, &vol);CHKERRQ(ierr);
741   ierr = DMPlexReplace_Static(dm, &vol);CHKERRQ(ierr);
742   ierr = DMDestroy(&boundary);CHKERRQ(ierr);
743   PetscFunctionReturn(0);
744 }
745 
746 static PetscErrorCode DMPlexCreateCubeMesh_Internal(DM dm, const PetscReal lower[], const PetscReal upper[], const PetscInt edges[], DMBoundaryType bdX, DMBoundaryType bdY, DMBoundaryType bdZ)
747 {
748   DMLabel        cutLabel = NULL;
749   PetscInt       markerTop      = 1, faceMarkerTop      = 1;
750   PetscInt       markerBottom   = 1, faceMarkerBottom   = 1;
751   PetscInt       markerFront    = 1, faceMarkerFront    = 1;
752   PetscInt       markerBack     = 1, faceMarkerBack     = 1;
753   PetscInt       markerRight    = 1, faceMarkerRight    = 1;
754   PetscInt       markerLeft     = 1, faceMarkerLeft     = 1;
755   PetscInt       dim;
756   PetscBool      markerSeparate = PETSC_FALSE, cutMarker = PETSC_FALSE;
757   PetscMPIInt    rank;
758   PetscErrorCode ierr;
759 
760   PetscFunctionBegin;
761   ierr = DMGetDimension(dm,&dim);CHKERRQ(ierr);
762   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);CHKERRMPI(ierr);
763   ierr = DMCreateLabel(dm,"marker");CHKERRQ(ierr);
764   ierr = DMCreateLabel(dm,"Face Sets");CHKERRQ(ierr);
765   ierr = PetscOptionsGetBool(((PetscObject) dm)->options,((PetscObject) dm)->prefix, "-dm_plex_periodic_cut", &cutMarker, NULL);CHKERRQ(ierr);
766   if (bdX == DM_BOUNDARY_PERIODIC || bdX == DM_BOUNDARY_TWIST ||
767       bdY == DM_BOUNDARY_PERIODIC || bdY == DM_BOUNDARY_TWIST ||
768       bdZ == DM_BOUNDARY_PERIODIC || bdZ == DM_BOUNDARY_TWIST) {
769 
770     if (cutMarker) {ierr = DMCreateLabel(dm, "periodic_cut");CHKERRQ(ierr); ierr = DMGetLabel(dm, "periodic_cut", &cutLabel);CHKERRQ(ierr);}
771   }
772   switch (dim) {
773   case 2:
774     faceMarkerTop    = 3;
775     faceMarkerBottom = 1;
776     faceMarkerRight  = 2;
777     faceMarkerLeft   = 4;
778     break;
779   case 3:
780     faceMarkerBottom = 1;
781     faceMarkerTop    = 2;
782     faceMarkerFront  = 3;
783     faceMarkerBack   = 4;
784     faceMarkerRight  = 5;
785     faceMarkerLeft   = 6;
786     break;
787   default:
788     SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Dimension %D not supported",dim);
789   }
790   ierr = PetscOptionsGetBool(((PetscObject) dm)->options,((PetscObject) dm)->prefix, "-dm_plex_separate_marker", &markerSeparate, NULL);CHKERRQ(ierr);
791   if (markerSeparate) {
792     markerBottom = faceMarkerBottom;
793     markerTop    = faceMarkerTop;
794     markerFront  = faceMarkerFront;
795     markerBack   = faceMarkerBack;
796     markerRight  = faceMarkerRight;
797     markerLeft   = faceMarkerLeft;
798   }
799   {
800     const PetscInt numXEdges    = rank == 0 ? edges[0] : 0;
801     const PetscInt numYEdges    = rank == 0 ? edges[1] : 0;
802     const PetscInt numZEdges    = rank == 0 ? edges[2] : 0;
803     const PetscInt numXVertices = rank == 0 ? (bdX == DM_BOUNDARY_PERIODIC || bdX == DM_BOUNDARY_TWIST ? edges[0] : edges[0]+1) : 0;
804     const PetscInt numYVertices = rank == 0 ? (bdY == DM_BOUNDARY_PERIODIC || bdY == DM_BOUNDARY_TWIST ? edges[1] : edges[1]+1) : 0;
805     const PetscInt numZVertices = rank == 0 ? (bdZ == DM_BOUNDARY_PERIODIC || bdZ == DM_BOUNDARY_TWIST ? edges[2] : edges[2]+1) : 0;
806     const PetscInt numCells     = numXEdges*numYEdges*numZEdges;
807     const PetscInt numXFaces    = numYEdges*numZEdges;
808     const PetscInt numYFaces    = numXEdges*numZEdges;
809     const PetscInt numZFaces    = numXEdges*numYEdges;
810     const PetscInt numTotXFaces = numXVertices*numXFaces;
811     const PetscInt numTotYFaces = numYVertices*numYFaces;
812     const PetscInt numTotZFaces = numZVertices*numZFaces;
813     const PetscInt numFaces     = numTotXFaces + numTotYFaces + numTotZFaces;
814     const PetscInt numTotXEdges = numXEdges*numYVertices*numZVertices;
815     const PetscInt numTotYEdges = numYEdges*numXVertices*numZVertices;
816     const PetscInt numTotZEdges = numZEdges*numXVertices*numYVertices;
817     const PetscInt numVertices  = numXVertices*numYVertices*numZVertices;
818     const PetscInt numEdges     = numTotXEdges + numTotYEdges + numTotZEdges;
819     const PetscInt firstVertex  = (dim == 2) ? numFaces : numCells;
820     const PetscInt firstXFace   = (dim == 2) ? 0 : numCells + numVertices;
821     const PetscInt firstYFace   = firstXFace + numTotXFaces;
822     const PetscInt firstZFace   = firstYFace + numTotYFaces;
823     const PetscInt firstXEdge   = numCells + numFaces + numVertices;
824     const PetscInt firstYEdge   = firstXEdge + numTotXEdges;
825     const PetscInt firstZEdge   = firstYEdge + numTotYEdges;
826     Vec            coordinates;
827     PetscSection   coordSection;
828     PetscScalar   *coords;
829     PetscInt       coordSize;
830     PetscInt       v, vx, vy, vz;
831     PetscInt       c, f, fx, fy, fz, e, ex, ey, ez;
832 
833     ierr = DMPlexSetChart(dm, 0, numCells+numFaces+numEdges+numVertices);CHKERRQ(ierr);
834     for (c = 0; c < numCells; c++) {
835       ierr = DMPlexSetConeSize(dm, c, 6);CHKERRQ(ierr);
836     }
837     for (f = firstXFace; f < firstXFace+numFaces; ++f) {
838       ierr = DMPlexSetConeSize(dm, f, 4);CHKERRQ(ierr);
839     }
840     for (e = firstXEdge; e < firstXEdge+numEdges; ++e) {
841       ierr = DMPlexSetConeSize(dm, e, 2);CHKERRQ(ierr);
842     }
843     ierr = DMSetUp(dm);CHKERRQ(ierr); /* Allocate space for cones */
844     /* Build cells */
845     for (fz = 0; fz < numZEdges; ++fz) {
846       for (fy = 0; fy < numYEdges; ++fy) {
847         for (fx = 0; fx < numXEdges; ++fx) {
848           PetscInt cell    = (fz*numYEdges + fy)*numXEdges + fx;
849           PetscInt faceB   = firstZFace + (fy*numXEdges+fx)*numZVertices +   fz;
850           PetscInt faceT   = firstZFace + (fy*numXEdges+fx)*numZVertices + ((fz+1)%numZVertices);
851           PetscInt faceF   = firstYFace + (fz*numXEdges+fx)*numYVertices +   fy;
852           PetscInt faceK   = firstYFace + (fz*numXEdges+fx)*numYVertices + ((fy+1)%numYVertices);
853           PetscInt faceL   = firstXFace + (fz*numYEdges+fy)*numXVertices +   fx;
854           PetscInt faceR   = firstXFace + (fz*numYEdges+fy)*numXVertices + ((fx+1)%numXVertices);
855                             /* B,  T,  F,  K,  R,  L */
856           PetscInt ornt[6] = {-2,  0,  0, -3,  0, -2}; /* ??? */
857           PetscInt cone[6];
858 
859           /* no boundary twisting in 3D */
860           cone[0] = faceB; cone[1] = faceT; cone[2] = faceF; cone[3] = faceK; cone[4] = faceR; cone[5] = faceL;
861           ierr    = DMPlexSetCone(dm, cell, cone);CHKERRQ(ierr);
862           ierr    = DMPlexSetConeOrientation(dm, cell, ornt);CHKERRQ(ierr);
863           if (bdX != DM_BOUNDARY_NONE && fx == numXEdges-1 && cutLabel) {ierr = DMLabelSetValue(cutLabel, cell, 2);CHKERRQ(ierr);}
864           if (bdY != DM_BOUNDARY_NONE && fy == numYEdges-1 && cutLabel) {ierr = DMLabelSetValue(cutLabel, cell, 2);CHKERRQ(ierr);}
865           if (bdZ != DM_BOUNDARY_NONE && fz == numZEdges-1 && cutLabel) {ierr = DMLabelSetValue(cutLabel, cell, 2);CHKERRQ(ierr);}
866         }
867       }
868     }
869     /* Build x faces */
870     for (fz = 0; fz < numZEdges; ++fz) {
871       for (fy = 0; fy < numYEdges; ++fy) {
872         for (fx = 0; fx < numXVertices; ++fx) {
873           PetscInt face    = firstXFace + (fz*numYEdges+fy)     *numXVertices+fx;
874           PetscInt edgeL   = firstZEdge + (fy                   *numXVertices+fx)*numZEdges + fz;
875           PetscInt edgeR   = firstZEdge + (((fy+1)%numYVertices)*numXVertices+fx)*numZEdges + fz;
876           PetscInt edgeB   = firstYEdge + (fz                   *numXVertices+fx)*numYEdges + fy;
877           PetscInt edgeT   = firstYEdge + (((fz+1)%numZVertices)*numXVertices+fx)*numYEdges + fy;
878           PetscInt ornt[4] = {0, 0, -1, -1};
879           PetscInt cone[4];
880 
881           if (dim == 3) {
882             /* markers */
883             if (bdX != DM_BOUNDARY_PERIODIC) {
884               if (fx == numXVertices-1) {
885                 ierr = DMSetLabelValue(dm, "Face Sets", face, faceMarkerRight);CHKERRQ(ierr);
886                 ierr = DMSetLabelValue(dm, "marker", face, markerRight);CHKERRQ(ierr);
887               }
888               else if (fx == 0) {
889                 ierr = DMSetLabelValue(dm, "Face Sets", face, faceMarkerLeft);CHKERRQ(ierr);
890                 ierr = DMSetLabelValue(dm, "marker", face, markerLeft);CHKERRQ(ierr);
891               }
892             }
893           }
894           cone[0] = edgeB; cone[1] = edgeR; cone[2] = edgeT; cone[3] = edgeL;
895           ierr    = DMPlexSetCone(dm, face, cone);CHKERRQ(ierr);
896           ierr    = DMPlexSetConeOrientation(dm, face, ornt);CHKERRQ(ierr);
897         }
898       }
899     }
900     /* Build y faces */
901     for (fz = 0; fz < numZEdges; ++fz) {
902       for (fx = 0; fx < numXEdges; ++fx) {
903         for (fy = 0; fy < numYVertices; ++fy) {
904           PetscInt face    = firstYFace + (fz*numXEdges+fx)*numYVertices + fy;
905           PetscInt edgeL   = firstZEdge + (fy*numXVertices+  fx)*numZEdges + fz;
906           PetscInt edgeR   = firstZEdge + (fy*numXVertices+((fx+1)%numXVertices))*numZEdges + fz;
907           PetscInt edgeB   = firstXEdge + (fz                   *numYVertices+fy)*numXEdges + fx;
908           PetscInt edgeT   = firstXEdge + (((fz+1)%numZVertices)*numYVertices+fy)*numXEdges + fx;
909           PetscInt ornt[4] = {0, 0, -1, -1};
910           PetscInt cone[4];
911 
912           if (dim == 3) {
913             /* markers */
914             if (bdY != DM_BOUNDARY_PERIODIC) {
915               if (fy == numYVertices-1) {
916                 ierr = DMSetLabelValue(dm, "Face Sets", face, faceMarkerBack);CHKERRQ(ierr);
917                 ierr = DMSetLabelValue(dm, "marker", face, markerBack);CHKERRQ(ierr);
918               }
919               else if (fy == 0) {
920                 ierr = DMSetLabelValue(dm, "Face Sets", face, faceMarkerFront);CHKERRQ(ierr);
921                 ierr = DMSetLabelValue(dm, "marker", face, markerFront);CHKERRQ(ierr);
922               }
923             }
924           }
925           cone[0] = edgeB; cone[1] = edgeR; cone[2] = edgeT; cone[3] = edgeL;
926           ierr    = DMPlexSetCone(dm, face, cone);CHKERRQ(ierr);
927           ierr    = DMPlexSetConeOrientation(dm, face, ornt);CHKERRQ(ierr);
928         }
929       }
930     }
931     /* Build z faces */
932     for (fy = 0; fy < numYEdges; ++fy) {
933       for (fx = 0; fx < numXEdges; ++fx) {
934         for (fz = 0; fz < numZVertices; fz++) {
935           PetscInt face    = firstZFace + (fy*numXEdges+fx)*numZVertices + fz;
936           PetscInt edgeL   = firstYEdge + (fz*numXVertices+  fx)*numYEdges + fy;
937           PetscInt edgeR   = firstYEdge + (fz*numXVertices+((fx+1)%numXVertices))*numYEdges + fy;
938           PetscInt edgeB   = firstXEdge + (fz*numYVertices+  fy)*numXEdges + fx;
939           PetscInt edgeT   = firstXEdge + (fz*numYVertices+((fy+1)%numYVertices))*numXEdges + fx;
940           PetscInt ornt[4] = {0, 0, -1, -1};
941           PetscInt cone[4];
942 
943           if (dim == 2) {
944             if (bdX == DM_BOUNDARY_TWIST && fx == numXEdges-1) {edgeR += numYEdges-1-2*fy; ornt[1] = -1;}
945             if (bdY == DM_BOUNDARY_TWIST && fy == numYEdges-1) {edgeT += numXEdges-1-2*fx; ornt[2] =  0;}
946             if (bdX != DM_BOUNDARY_NONE && fx == numXEdges-1 && cutLabel) {ierr = DMLabelSetValue(cutLabel, face, 2);CHKERRQ(ierr);}
947             if (bdY != DM_BOUNDARY_NONE && fy == numYEdges-1 && cutLabel) {ierr = DMLabelSetValue(cutLabel, face, 2);CHKERRQ(ierr);}
948           } else {
949             /* markers */
950             if (bdZ != DM_BOUNDARY_PERIODIC) {
951               if (fz == numZVertices-1) {
952                 ierr = DMSetLabelValue(dm, "Face Sets", face, faceMarkerTop);CHKERRQ(ierr);
953                 ierr = DMSetLabelValue(dm, "marker", face, markerTop);CHKERRQ(ierr);
954               }
955               else if (fz == 0) {
956                 ierr = DMSetLabelValue(dm, "Face Sets", face, faceMarkerBottom);CHKERRQ(ierr);
957                 ierr = DMSetLabelValue(dm, "marker", face, markerBottom);CHKERRQ(ierr);
958               }
959             }
960           }
961           cone[0] = edgeB; cone[1] = edgeR; cone[2] = edgeT; cone[3] = edgeL;
962           ierr    = DMPlexSetCone(dm, face, cone);CHKERRQ(ierr);
963           ierr    = DMPlexSetConeOrientation(dm, face, ornt);CHKERRQ(ierr);
964         }
965       }
966     }
967     /* Build Z edges*/
968     for (vy = 0; vy < numYVertices; vy++) {
969       for (vx = 0; vx < numXVertices; vx++) {
970         for (ez = 0; ez < numZEdges; ez++) {
971           const PetscInt edge    = firstZEdge  + (vy*numXVertices+vx)*numZEdges + ez;
972           const PetscInt vertexB = firstVertex + (ez                   *numYVertices+vy)*numXVertices + vx;
973           const PetscInt vertexT = firstVertex + (((ez+1)%numZVertices)*numYVertices+vy)*numXVertices + vx;
974           PetscInt       cone[2];
975 
976           if (dim == 3) {
977             if (bdX != DM_BOUNDARY_PERIODIC) {
978               if (vx == numXVertices-1) {
979                 ierr = DMSetLabelValue(dm, "marker", edge, markerRight);CHKERRQ(ierr);
980               }
981               else if (vx == 0) {
982                 ierr = DMSetLabelValue(dm, "marker", edge, markerLeft);CHKERRQ(ierr);
983               }
984             }
985             if (bdY != DM_BOUNDARY_PERIODIC) {
986               if (vy == numYVertices-1) {
987                 ierr = DMSetLabelValue(dm, "marker", edge, markerBack);CHKERRQ(ierr);
988               }
989               else if (vy == 0) {
990                 ierr = DMSetLabelValue(dm, "marker", edge, markerFront);CHKERRQ(ierr);
991               }
992             }
993           }
994           cone[0] = vertexB; cone[1] = vertexT;
995           ierr = DMPlexSetCone(dm, edge, cone);CHKERRQ(ierr);
996         }
997       }
998     }
999     /* Build Y edges*/
1000     for (vz = 0; vz < numZVertices; vz++) {
1001       for (vx = 0; vx < numXVertices; vx++) {
1002         for (ey = 0; ey < numYEdges; ey++) {
1003           const PetscInt nextv   = (dim == 2 && bdY == DM_BOUNDARY_TWIST && ey == numYEdges-1) ? (numXVertices-vx-1) : (vz*numYVertices+((ey+1)%numYVertices))*numXVertices + vx;
1004           const PetscInt edge    = firstYEdge  + (vz*numXVertices+vx)*numYEdges + ey;
1005           const PetscInt vertexF = firstVertex + (vz*numYVertices+ey)*numXVertices + vx;
1006           const PetscInt vertexK = firstVertex + nextv;
1007           PetscInt       cone[2];
1008 
1009           cone[0] = vertexF; cone[1] = vertexK;
1010           ierr = DMPlexSetCone(dm, edge, cone);CHKERRQ(ierr);
1011           if (dim == 2) {
1012             if ((bdX != DM_BOUNDARY_PERIODIC) && (bdX != DM_BOUNDARY_TWIST)) {
1013               if (vx == numXVertices-1) {
1014                 ierr = DMSetLabelValue(dm, "Face Sets", edge, faceMarkerRight);CHKERRQ(ierr);
1015                 ierr = DMSetLabelValue(dm, "marker", edge,    markerRight);CHKERRQ(ierr);
1016                 ierr = DMSetLabelValue(dm, "marker", cone[0], markerRight);CHKERRQ(ierr);
1017                 if (ey == numYEdges-1) {
1018                   ierr = DMSetLabelValue(dm, "marker", cone[1], markerRight);CHKERRQ(ierr);
1019                 }
1020               } else if (vx == 0) {
1021                 ierr = DMSetLabelValue(dm, "Face Sets", edge, faceMarkerLeft);CHKERRQ(ierr);
1022                 ierr = DMSetLabelValue(dm, "marker", edge,    markerLeft);CHKERRQ(ierr);
1023                 ierr = DMSetLabelValue(dm, "marker", cone[0], markerLeft);CHKERRQ(ierr);
1024                 if (ey == numYEdges-1) {
1025                   ierr = DMSetLabelValue(dm, "marker", cone[1], markerLeft);CHKERRQ(ierr);
1026                 }
1027               }
1028             } else {
1029               if (vx == 0 && cutLabel) {
1030                 ierr = DMLabelSetValue(cutLabel, edge,    1);CHKERRQ(ierr);
1031                 ierr = DMLabelSetValue(cutLabel, cone[0], 1);CHKERRQ(ierr);
1032                 if (ey == numYEdges-1) {
1033                   ierr = DMLabelSetValue(cutLabel, cone[1], 1);CHKERRQ(ierr);
1034                 }
1035               }
1036             }
1037           } else {
1038             if (bdX != DM_BOUNDARY_PERIODIC) {
1039               if (vx == numXVertices-1) {
1040                 ierr = DMSetLabelValue(dm, "marker", edge, markerRight);CHKERRQ(ierr);
1041               } else if (vx == 0) {
1042                 ierr = DMSetLabelValue(dm, "marker", edge, markerLeft);CHKERRQ(ierr);
1043               }
1044             }
1045             if (bdZ != DM_BOUNDARY_PERIODIC) {
1046               if (vz == numZVertices-1) {
1047                 ierr = DMSetLabelValue(dm, "marker", edge, markerTop);CHKERRQ(ierr);
1048               } else if (vz == 0) {
1049                 ierr = DMSetLabelValue(dm, "marker", edge, markerBottom);CHKERRQ(ierr);
1050               }
1051             }
1052           }
1053         }
1054       }
1055     }
1056     /* Build X edges*/
1057     for (vz = 0; vz < numZVertices; vz++) {
1058       for (vy = 0; vy < numYVertices; vy++) {
1059         for (ex = 0; ex < numXEdges; ex++) {
1060           const PetscInt nextv   = (dim == 2 && bdX == DM_BOUNDARY_TWIST && ex == numXEdges-1) ? (numYVertices-vy-1)*numXVertices : (vz*numYVertices+vy)*numXVertices + (ex+1)%numXVertices;
1061           const PetscInt edge    = firstXEdge  + (vz*numYVertices+vy)*numXEdges + ex;
1062           const PetscInt vertexL = firstVertex + (vz*numYVertices+vy)*numXVertices + ex;
1063           const PetscInt vertexR = firstVertex + nextv;
1064           PetscInt       cone[2];
1065 
1066           cone[0] = vertexL; cone[1] = vertexR;
1067           ierr = DMPlexSetCone(dm, edge, cone);CHKERRQ(ierr);
1068           if (dim == 2) {
1069             if ((bdY != DM_BOUNDARY_PERIODIC) && (bdY != DM_BOUNDARY_TWIST)) {
1070               if (vy == numYVertices-1) {
1071                 ierr = DMSetLabelValue(dm, "Face Sets", edge, faceMarkerTop);CHKERRQ(ierr);
1072                 ierr = DMSetLabelValue(dm, "marker", edge,    markerTop);CHKERRQ(ierr);
1073                 ierr = DMSetLabelValue(dm, "marker", cone[0], markerTop);CHKERRQ(ierr);
1074                 if (ex == numXEdges-1) {
1075                   ierr = DMSetLabelValue(dm, "marker", cone[1], markerTop);CHKERRQ(ierr);
1076                 }
1077               } else if (vy == 0) {
1078                 ierr = DMSetLabelValue(dm, "Face Sets", edge, faceMarkerBottom);CHKERRQ(ierr);
1079                 ierr = DMSetLabelValue(dm, "marker", edge,    markerBottom);CHKERRQ(ierr);
1080                 ierr = DMSetLabelValue(dm, "marker", cone[0], markerBottom);CHKERRQ(ierr);
1081                 if (ex == numXEdges-1) {
1082                   ierr = DMSetLabelValue(dm, "marker", cone[1], markerBottom);CHKERRQ(ierr);
1083                 }
1084               }
1085             } else {
1086               if (vy == 0 && cutLabel) {
1087                 ierr = DMLabelSetValue(cutLabel, edge,    1);CHKERRQ(ierr);
1088                 ierr = DMLabelSetValue(cutLabel, cone[0], 1);CHKERRQ(ierr);
1089                 if (ex == numXEdges-1) {
1090                   ierr = DMLabelSetValue(cutLabel, cone[1], 1);CHKERRQ(ierr);
1091                 }
1092               }
1093             }
1094           } else {
1095             if (bdY != DM_BOUNDARY_PERIODIC) {
1096               if (vy == numYVertices-1) {
1097                 ierr = DMSetLabelValue(dm, "marker", edge, markerBack);CHKERRQ(ierr);
1098               }
1099               else if (vy == 0) {
1100                 ierr = DMSetLabelValue(dm, "marker", edge, markerFront);CHKERRQ(ierr);
1101               }
1102             }
1103             if (bdZ != DM_BOUNDARY_PERIODIC) {
1104               if (vz == numZVertices-1) {
1105                 ierr = DMSetLabelValue(dm, "marker", edge, markerTop);CHKERRQ(ierr);
1106               }
1107               else if (vz == 0) {
1108                 ierr = DMSetLabelValue(dm, "marker", edge, markerBottom);CHKERRQ(ierr);
1109               }
1110             }
1111           }
1112         }
1113       }
1114     }
1115     ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
1116     ierr = DMPlexStratify(dm);CHKERRQ(ierr);
1117     /* Build coordinates */
1118     ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
1119     ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
1120     ierr = PetscSectionSetFieldComponents(coordSection, 0, dim);CHKERRQ(ierr);
1121     ierr = PetscSectionSetChart(coordSection, firstVertex, firstVertex+numVertices);CHKERRQ(ierr);
1122     for (v = firstVertex; v < firstVertex+numVertices; ++v) {
1123       ierr = PetscSectionSetDof(coordSection, v, dim);CHKERRQ(ierr);
1124       ierr = PetscSectionSetFieldDof(coordSection, v, 0, dim);CHKERRQ(ierr);
1125     }
1126     ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
1127     ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
1128     ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
1129     ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
1130     ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
1131     ierr = VecSetBlockSize(coordinates, dim);CHKERRQ(ierr);
1132     ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
1133     ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
1134     for (vz = 0; vz < numZVertices; ++vz) {
1135       for (vy = 0; vy < numYVertices; ++vy) {
1136         for (vx = 0; vx < numXVertices; ++vx) {
1137           coords[((vz*numYVertices+vy)*numXVertices+vx)*dim+0] = lower[0] + ((upper[0] - lower[0])/numXEdges)*vx;
1138           coords[((vz*numYVertices+vy)*numXVertices+vx)*dim+1] = lower[1] + ((upper[1] - lower[1])/numYEdges)*vy;
1139           if (dim == 3) {
1140             coords[((vz*numYVertices+vy)*numXVertices+vx)*dim+2] = lower[2] + ((upper[2] - lower[2])/numZEdges)*vz;
1141           }
1142         }
1143       }
1144     }
1145     ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
1146     ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
1147     ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
1148   }
1149   PetscFunctionReturn(0);
1150 }
1151 
1152 static PetscErrorCode DMPlexCreateBoxMesh_Tensor_Internal(DM dm, PetscInt dim, const PetscInt faces[], const PetscReal lower[], const PetscReal upper[], const DMBoundaryType periodicity[])
1153 {
1154   DMBoundaryType bdt[3] = {DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE};
1155   PetscInt       fac[3] = {0, 0, 0}, d;
1156   PetscErrorCode ierr;
1157 
1158   PetscFunctionBegin;
1159   PetscValidPointer(dm, 1);
1160   PetscValidLogicalCollectiveInt(dm, dim, 2);
1161   ierr = DMSetDimension(dm, dim);CHKERRQ(ierr);
1162   for (d = 0; d < dim; ++d) {fac[d] = faces[d]; bdt[d] = periodicity[d];}
1163   ierr = DMPlexCreateCubeMesh_Internal(dm, lower, upper, fac, bdt[0], bdt[1], bdt[2]);CHKERRQ(ierr);
1164   if (periodicity[0] == DM_BOUNDARY_PERIODIC || periodicity[0] == DM_BOUNDARY_TWIST ||
1165       periodicity[1] == DM_BOUNDARY_PERIODIC || periodicity[1] == DM_BOUNDARY_TWIST ||
1166       (dim > 2 && (periodicity[2] == DM_BOUNDARY_PERIODIC || periodicity[2] == DM_BOUNDARY_TWIST))) {
1167     PetscReal L[3];
1168     PetscReal maxCell[3];
1169 
1170     for (d = 0; d < dim; ++d) {
1171       L[d]       = upper[d] - lower[d];
1172       maxCell[d] = 1.1 * (L[d] / PetscMax(1, faces[d]));
1173     }
1174     ierr = DMSetPeriodicity(dm, PETSC_TRUE, maxCell, L, periodicity);CHKERRQ(ierr);
1175   }
1176   ierr = DMPlexSetRefinementUniform(dm, PETSC_TRUE);CHKERRQ(ierr);
1177   PetscFunctionReturn(0);
1178 }
1179 
1180 static PetscErrorCode DMPlexCreateBoxMesh_Internal(DM dm, PetscInt dim, PetscBool simplex, const PetscInt faces[], const PetscReal lower[], const PetscReal upper[], const DMBoundaryType periodicity[], PetscBool interpolate)
1181 {
1182   PetscErrorCode ierr;
1183 
1184   PetscFunctionBegin;
1185   if (dim == 1)      {ierr = DMPlexCreateLineMesh_Internal(dm, faces[0], lower[0], upper[0], periodicity[0]);CHKERRQ(ierr);}
1186   else if (simplex)  {ierr = DMPlexCreateBoxMesh_Simplex_Internal(dm, dim, faces, lower, upper, periodicity, interpolate);CHKERRQ(ierr);}
1187   else               {ierr = DMPlexCreateBoxMesh_Tensor_Internal(dm, dim, faces, lower, upper, periodicity);CHKERRQ(ierr);}
1188   if (!interpolate && dim > 1 && !simplex) {
1189     DM udm;
1190 
1191     ierr = DMPlexUninterpolate(dm, &udm);CHKERRQ(ierr);
1192     ierr = DMPlexCopyCoordinates(dm, udm);CHKERRQ(ierr);
1193     ierr = DMPlexReplace_Static(dm, &udm);CHKERRQ(ierr);
1194   }
1195   PetscFunctionReturn(0);
1196 }
1197 
1198 /*@C
1199   DMPlexCreateBoxMesh - Creates a mesh on the tensor product of unit intervals (box) using simplices or tensor cells (hexahedra).
1200 
1201   Collective
1202 
1203   Input Parameters:
1204 + comm        - The communicator for the DM object
1205 . dim         - The spatial dimension
1206 . simplex     - PETSC_TRUE for simplices, PETSC_FALSE for tensor cells
1207 . faces       - Number of faces per dimension, or NULL for (1,) in 1D and (2, 2) in 2D and (1, 1, 1) in 3D
1208 . lower       - The lower left corner, or NULL for (0, 0, 0)
1209 . upper       - The upper right corner, or NULL for (1, 1, 1)
1210 . periodicity - The boundary type for the X,Y,Z direction, or NULL for DM_BOUNDARY_NONE
1211 - interpolate - Flag to create intermediate mesh pieces (edges, faces)
1212 
1213   Output Parameter:
1214 . dm  - The DM object
1215 
1216   Note: If you want to customize this mesh using options, you just need to
1217 $  DMCreate(comm, &dm);
1218 $  DMSetType(dm, DMPLEX);
1219 $  DMSetFromOptions(dm);
1220 and use the options on the DMSetFromOptions() page.
1221 
1222   Here is the numbering returned for 2 faces in each direction for tensor cells:
1223 $ 10---17---11---18----12
1224 $  |         |         |
1225 $  |         |         |
1226 $ 20    2   22    3    24
1227 $  |         |         |
1228 $  |         |         |
1229 $  7---15----8---16----9
1230 $  |         |         |
1231 $  |         |         |
1232 $ 19    0   21    1   23
1233 $  |         |         |
1234 $  |         |         |
1235 $  4---13----5---14----6
1236 
1237 and for simplicial cells
1238 
1239 $ 14----8---15----9----16
1240 $  |\     5  |\      7 |
1241 $  | \       | \       |
1242 $ 13   2    14    3    15
1243 $  | 4   \   | 6   \   |
1244 $  |       \ |       \ |
1245 $ 11----6---12----7----13
1246 $  |\        |\        |
1247 $  | \    1  | \     3 |
1248 $ 10   0    11    1    12
1249 $  | 0   \   | 2   \   |
1250 $  |       \ |       \ |
1251 $  8----4----9----5----10
1252 
1253   Level: beginner
1254 
1255 .seealso: DMSetFromOptions(), DMPlexCreateFromFile(), DMPlexCreateHexCylinderMesh(), DMSetType(), DMCreate()
1256 @*/
1257 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)
1258 {
1259   PetscInt       fac[3] = {1, 1, 1};
1260   PetscReal      low[3] = {0, 0, 0};
1261   PetscReal      upp[3] = {1, 1, 1};
1262   DMBoundaryType bdt[3] = {DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE};
1263   PetscErrorCode ierr;
1264 
1265   PetscFunctionBegin;
1266   ierr = DMCreate(comm,dm);CHKERRQ(ierr);
1267   ierr = DMSetType(*dm,DMPLEX);CHKERRQ(ierr);
1268   ierr = DMPlexCreateBoxMesh_Internal(*dm, dim, simplex, faces ? faces : fac, lower ? lower : low, upper ? upper : upp, periodicity ? periodicity : bdt, interpolate);CHKERRQ(ierr);
1269   PetscFunctionReturn(0);
1270 }
1271 
1272 static PetscErrorCode DMPlexCreateWedgeBoxMesh_Internal(DM dm, const PetscInt faces[], const PetscReal lower[], const PetscReal upper[], const DMBoundaryType periodicity[])
1273 {
1274   DM             bdm, vol;
1275   PetscInt       i;
1276   PetscErrorCode ierr;
1277 
1278   PetscFunctionBegin;
1279   for (i = 0; i < 3; ++i) if (periodicity[i] != DM_BOUNDARY_NONE) SETERRQ(PetscObjectComm((PetscObject) dm), PETSC_ERR_SUP, "Periodicity not yet supported");
1280   ierr = DMCreate(PetscObjectComm((PetscObject) dm), &bdm);CHKERRQ(ierr);
1281   ierr = DMSetType(bdm, DMPLEX);CHKERRQ(ierr);
1282   ierr = DMSetDimension(bdm, 2);CHKERRQ(ierr);
1283   ierr = DMPlexCreateBoxMesh_Simplex_Internal(bdm, 2, faces, lower, upper, periodicity, PETSC_TRUE);CHKERRQ(ierr);
1284   ierr = DMPlexExtrude(bdm, faces[2], upper[2] - lower[2], PETSC_TRUE, PETSC_FALSE, NULL, NULL, &vol);CHKERRQ(ierr);
1285   ierr = DMDestroy(&bdm);CHKERRQ(ierr);
1286   ierr = DMPlexReplace_Static(dm, &vol);CHKERRQ(ierr);
1287   if (lower[2] != 0.0) {
1288     Vec          v;
1289     PetscScalar *x;
1290     PetscInt     cDim, n;
1291 
1292     ierr = DMGetCoordinatesLocal(dm, &v);CHKERRQ(ierr);
1293     ierr = VecGetBlockSize(v, &cDim);CHKERRQ(ierr);
1294     ierr = VecGetLocalSize(v, &n);CHKERRQ(ierr);
1295     ierr = VecGetArray(v, &x);CHKERRQ(ierr);
1296     x   += cDim;
1297     for (i = 0; i < n; i += cDim) x[i] += lower[2];
1298     ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
1299     ierr = DMSetCoordinatesLocal(dm, v);CHKERRQ(ierr);
1300   }
1301   PetscFunctionReturn(0);
1302 }
1303 
1304 /*@
1305   DMPlexCreateWedgeBoxMesh - Creates a 3-D mesh tesselating the (x,y) plane and extruding in the third direction using wedge cells.
1306 
1307   Collective
1308 
1309   Input Parameters:
1310 + comm        - The communicator for the DM object
1311 . faces       - Number of faces per dimension, or NULL for (1, 1, 1)
1312 . lower       - The lower left corner, or NULL for (0, 0, 0)
1313 . upper       - The upper right corner, or NULL for (1, 1, 1)
1314 . periodicity - The boundary type for the X,Y,Z direction, or NULL for DM_BOUNDARY_NONE
1315 . orderHeight - If PETSC_TRUE, orders the extruded cells in the height first. Otherwise, orders the cell on the layers first
1316 - interpolate - Flag to create intermediate mesh pieces (edges, faces)
1317 
1318   Output Parameter:
1319 . dm  - The DM object
1320 
1321   Level: beginner
1322 
1323 .seealso: DMPlexCreateHexCylinderMesh(), DMPlexCreateWedgeCylinderMesh(), DMExtrude(), DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
1324 @*/
1325 PetscErrorCode DMPlexCreateWedgeBoxMesh(MPI_Comm comm, const PetscInt faces[], const PetscReal lower[], const PetscReal upper[], const DMBoundaryType periodicity[], PetscBool orderHeight, PetscBool interpolate, DM *dm)
1326 {
1327   PetscInt       fac[3] = {1, 1, 1};
1328   PetscReal      low[3] = {0, 0, 0};
1329   PetscReal      upp[3] = {1, 1, 1};
1330   DMBoundaryType bdt[3] = {DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE};
1331   PetscErrorCode ierr;
1332 
1333   PetscFunctionBegin;
1334   ierr = DMCreate(comm,dm);CHKERRQ(ierr);
1335   ierr = DMSetType(*dm,DMPLEX);CHKERRQ(ierr);
1336   ierr = DMPlexCreateWedgeBoxMesh_Internal(*dm, faces ? faces : fac, lower ? lower : low, upper ? upper : upp, periodicity ? periodicity : bdt);CHKERRQ(ierr);
1337   if (!interpolate) {
1338     DM udm;
1339 
1340     ierr = DMPlexUninterpolate(*dm, &udm);CHKERRQ(ierr);
1341     ierr = DMPlexReplace_Static(*dm, &udm);CHKERRQ(ierr);
1342   }
1343   PetscFunctionReturn(0);
1344 }
1345 
1346 /*@C
1347   DMPlexSetOptionsPrefix - Sets the prefix used for searching for all DM options in the database.
1348 
1349   Logically Collective on dm
1350 
1351   Input Parameters:
1352 + dm - the DM context
1353 - prefix - the prefix to prepend to all option names
1354 
1355   Notes:
1356   A hyphen (-) must NOT be given at the beginning of the prefix name.
1357   The first character of all runtime options is AUTOMATICALLY the hyphen.
1358 
1359   Level: advanced
1360 
1361 .seealso: SNESSetFromOptions()
1362 @*/
1363 PetscErrorCode DMPlexSetOptionsPrefix(DM dm, const char prefix[])
1364 {
1365   DM_Plex       *mesh = (DM_Plex *) dm->data;
1366   PetscErrorCode ierr;
1367 
1368   PetscFunctionBegin;
1369   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1370   ierr = PetscObjectSetOptionsPrefix((PetscObject) dm, prefix);CHKERRQ(ierr);
1371   ierr = PetscObjectSetOptionsPrefix((PetscObject) mesh->partitioner, prefix);CHKERRQ(ierr);
1372   PetscFunctionReturn(0);
1373 }
1374 
1375 /* Remap geometry to cylinder
1376    TODO: This only works for a single refinement, then it is broken
1377 
1378      Interior square: Linear interpolation is correct
1379      The other cells all have vertices on rays from the origin. We want to uniformly expand the spacing
1380      such that the last vertex is on the unit circle. So the closest and farthest vertices are at distance
1381 
1382        phi     = arctan(y/x)
1383        d_close = sqrt(1/8 + 1/4 sin^2(phi))
1384        d_far   = sqrt(1/2 + sin^2(phi))
1385 
1386      so we remap them using
1387 
1388        x_new = x_close + (x - x_close) (1 - d_close) / (d_far - d_close)
1389        y_new = y_close + (y - y_close) (1 - d_close) / (d_far - d_close)
1390 
1391      If pi/4 < phi < 3pi/4 or -3pi/4 < phi < -pi/4, then we switch x and y.
1392 */
1393 static void snapToCylinder(PetscInt dim, PetscInt Nf, PetscInt NfAux,
1394                            const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
1395                            const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
1396                            PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
1397 {
1398   const PetscReal dis = 1.0/PetscSqrtReal(2.0);
1399   const PetscReal ds2 = 0.5*dis;
1400 
1401   if ((PetscAbsScalar(u[0]) <= ds2) && (PetscAbsScalar(u[1]) <= ds2)) {
1402     f0[0] = u[0];
1403     f0[1] = u[1];
1404   } else {
1405     PetscReal phi, sinp, cosp, dc, df, x, y, xc, yc;
1406 
1407     x    = PetscRealPart(u[0]);
1408     y    = PetscRealPart(u[1]);
1409     phi  = PetscAtan2Real(y, x);
1410     sinp = PetscSinReal(phi);
1411     cosp = PetscCosReal(phi);
1412     if ((PetscAbsReal(phi) > PETSC_PI/4.0) && (PetscAbsReal(phi) < 3.0*PETSC_PI/4.0)) {
1413       dc = PetscAbsReal(ds2/sinp);
1414       df = PetscAbsReal(dis/sinp);
1415       xc = ds2*x/PetscAbsReal(y);
1416       yc = ds2*PetscSignReal(y);
1417     } else {
1418       dc = PetscAbsReal(ds2/cosp);
1419       df = PetscAbsReal(dis/cosp);
1420       xc = ds2*PetscSignReal(x);
1421       yc = ds2*y/PetscAbsReal(x);
1422     }
1423     f0[0] = xc + (u[0] - xc)*(1.0 - dc)/(df - dc);
1424     f0[1] = yc + (u[1] - yc)*(1.0 - dc)/(df - dc);
1425   }
1426   f0[2] = u[2];
1427 }
1428 
1429 static PetscErrorCode DMPlexCreateHexCylinderMesh_Internal(DM dm, DMBoundaryType periodicZ)
1430 {
1431   const PetscInt dim = 3;
1432   PetscInt       numCells, numVertices;
1433   PetscMPIInt    rank;
1434   PetscErrorCode ierr;
1435 
1436   PetscFunctionBegin;
1437   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject) dm), &rank);CHKERRMPI(ierr);
1438   ierr = DMSetDimension(dm, dim);CHKERRQ(ierr);
1439   /* Create topology */
1440   {
1441     PetscInt cone[8], c;
1442 
1443     numCells    = rank == 0 ?  5 : 0;
1444     numVertices = rank == 0 ? 16 : 0;
1445     if (periodicZ == DM_BOUNDARY_PERIODIC) {
1446       numCells   *= 3;
1447       numVertices = rank == 0 ? 24 : 0;
1448     }
1449     ierr = DMPlexSetChart(dm, 0, numCells+numVertices);CHKERRQ(ierr);
1450     for (c = 0; c < numCells; c++) {ierr = DMPlexSetConeSize(dm, c, 8);CHKERRQ(ierr);}
1451     ierr = DMSetUp(dm);CHKERRQ(ierr);
1452     if (rank == 0) {
1453       if (periodicZ == DM_BOUNDARY_PERIODIC) {
1454         cone[0] = 15; cone[1] = 18; cone[2] = 17; cone[3] = 16;
1455         cone[4] = 31; cone[5] = 32; cone[6] = 33; cone[7] = 34;
1456         ierr = DMPlexSetCone(dm, 0, cone);CHKERRQ(ierr);
1457         cone[0] = 16; cone[1] = 17; cone[2] = 24; cone[3] = 23;
1458         cone[4] = 32; cone[5] = 36; cone[6] = 37; cone[7] = 33; /* 22 25 26 21 */
1459         ierr = DMPlexSetCone(dm, 1, cone);CHKERRQ(ierr);
1460         cone[0] = 18; cone[1] = 27; cone[2] = 24; cone[3] = 17;
1461         cone[4] = 34; cone[5] = 33; cone[6] = 37; cone[7] = 38;
1462         ierr = DMPlexSetCone(dm, 2, cone);CHKERRQ(ierr);
1463         cone[0] = 29; cone[1] = 27; cone[2] = 18; cone[3] = 15;
1464         cone[4] = 35; cone[5] = 31; cone[6] = 34; cone[7] = 38;
1465         ierr = DMPlexSetCone(dm, 3, cone);CHKERRQ(ierr);
1466         cone[0] = 29; cone[1] = 15; cone[2] = 16; cone[3] = 23;
1467         cone[4] = 35; cone[5] = 36; cone[6] = 32; cone[7] = 31;
1468         ierr = DMPlexSetCone(dm, 4, cone);CHKERRQ(ierr);
1469 
1470         cone[0] = 31; cone[1] = 34; cone[2] = 33; cone[3] = 32;
1471         cone[4] = 19; cone[5] = 22; cone[6] = 21; cone[7] = 20;
1472         ierr = DMPlexSetCone(dm, 5, cone);CHKERRQ(ierr);
1473         cone[0] = 32; cone[1] = 33; cone[2] = 37; cone[3] = 36;
1474         cone[4] = 22; cone[5] = 25; cone[6] = 26; cone[7] = 21;
1475         ierr = DMPlexSetCone(dm, 6, cone);CHKERRQ(ierr);
1476         cone[0] = 34; cone[1] = 38; cone[2] = 37; cone[3] = 33;
1477         cone[4] = 20; cone[5] = 21; cone[6] = 26; cone[7] = 28;
1478         ierr = DMPlexSetCone(dm, 7, cone);CHKERRQ(ierr);
1479         cone[0] = 35; cone[1] = 38; cone[2] = 34; cone[3] = 31;
1480         cone[4] = 30; cone[5] = 19; cone[6] = 20; cone[7] = 28;
1481         ierr = DMPlexSetCone(dm, 8, cone);CHKERRQ(ierr);
1482         cone[0] = 35; cone[1] = 31; cone[2] = 32; cone[3] = 36;
1483         cone[4] = 30; cone[5] = 25; cone[6] = 22; cone[7] = 19;
1484         ierr = DMPlexSetCone(dm, 9, cone);CHKERRQ(ierr);
1485 
1486         cone[0] = 19; cone[1] = 20; cone[2] = 21; cone[3] = 22;
1487         cone[4] = 15; cone[5] = 16; cone[6] = 17; cone[7] = 18;
1488         ierr = DMPlexSetCone(dm, 10, cone);CHKERRQ(ierr);
1489         cone[0] = 22; cone[1] = 21; cone[2] = 26; cone[3] = 25;
1490         cone[4] = 16; cone[5] = 23; cone[6] = 24; cone[7] = 17;
1491         ierr = DMPlexSetCone(dm, 11, cone);CHKERRQ(ierr);
1492         cone[0] = 20; cone[1] = 28; cone[2] = 26; cone[3] = 21;
1493         cone[4] = 18; cone[5] = 17; cone[6] = 24; cone[7] = 27;
1494         ierr = DMPlexSetCone(dm, 12, cone);CHKERRQ(ierr);
1495         cone[0] = 30; cone[1] = 28; cone[2] = 20; cone[3] = 19;
1496         cone[4] = 29; cone[5] = 15; cone[6] = 18; cone[7] = 27;
1497         ierr = DMPlexSetCone(dm, 13, cone);CHKERRQ(ierr);
1498         cone[0] = 30; cone[1] = 19; cone[2] = 22; cone[3] = 25;
1499         cone[4] = 29; cone[5] = 23; cone[6] = 16; cone[7] = 15;
1500         ierr = DMPlexSetCone(dm, 14, cone);CHKERRQ(ierr);
1501       } else {
1502         cone[0] =  5; cone[1] =  8; cone[2] =  7; cone[3] =  6;
1503         cone[4] =  9; cone[5] = 12; cone[6] = 11; cone[7] = 10;
1504         ierr = DMPlexSetCone(dm, 0, cone);CHKERRQ(ierr);
1505         cone[0] =  6; cone[1] =  7; cone[2] = 14; cone[3] = 13;
1506         cone[4] = 12; cone[5] = 15; cone[6] = 16; cone[7] = 11;
1507         ierr = DMPlexSetCone(dm, 1, cone);CHKERRQ(ierr);
1508         cone[0] =  8; cone[1] = 17; cone[2] = 14; cone[3] =  7;
1509         cone[4] = 10; cone[5] = 11; cone[6] = 16; cone[7] = 18;
1510         ierr = DMPlexSetCone(dm, 2, cone);CHKERRQ(ierr);
1511         cone[0] = 19; cone[1] = 17; cone[2] =  8; cone[3] =  5;
1512         cone[4] = 20; cone[5] =  9; cone[6] = 10; cone[7] = 18;
1513         ierr = DMPlexSetCone(dm, 3, cone);CHKERRQ(ierr);
1514         cone[0] = 19; cone[1] =  5; cone[2] =  6; cone[3] = 13;
1515         cone[4] = 20; cone[5] = 15; cone[6] = 12; cone[7] =  9;
1516         ierr = DMPlexSetCone(dm, 4, cone);CHKERRQ(ierr);
1517       }
1518     }
1519     ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
1520     ierr = DMPlexStratify(dm);CHKERRQ(ierr);
1521   }
1522   /* Create cube geometry */
1523   {
1524     Vec             coordinates;
1525     PetscSection    coordSection;
1526     PetscScalar    *coords;
1527     PetscInt        coordSize, v;
1528     const PetscReal dis = 1.0/PetscSqrtReal(2.0);
1529     const PetscReal ds2 = dis/2.0;
1530 
1531     /* Build coordinates */
1532     ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
1533     ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
1534     ierr = PetscSectionSetFieldComponents(coordSection, 0, dim);CHKERRQ(ierr);
1535     ierr = PetscSectionSetChart(coordSection, numCells, numCells+numVertices);CHKERRQ(ierr);
1536     for (v = numCells; v < numCells+numVertices; ++v) {
1537       ierr = PetscSectionSetDof(coordSection, v, dim);CHKERRQ(ierr);
1538       ierr = PetscSectionSetFieldDof(coordSection, v, 0, dim);CHKERRQ(ierr);
1539     }
1540     ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
1541     ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
1542     ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
1543     ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
1544     ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
1545     ierr = VecSetBlockSize(coordinates, dim);CHKERRQ(ierr);
1546     ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
1547     ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
1548     if (rank == 0) {
1549       coords[0*dim+0] = -ds2; coords[0*dim+1] = -ds2; coords[0*dim+2] = 0.0;
1550       coords[1*dim+0] =  ds2; coords[1*dim+1] = -ds2; coords[1*dim+2] = 0.0;
1551       coords[2*dim+0] =  ds2; coords[2*dim+1] =  ds2; coords[2*dim+2] = 0.0;
1552       coords[3*dim+0] = -ds2; coords[3*dim+1] =  ds2; coords[3*dim+2] = 0.0;
1553       coords[4*dim+0] = -ds2; coords[4*dim+1] = -ds2; coords[4*dim+2] = 1.0;
1554       coords[5*dim+0] = -ds2; coords[5*dim+1] =  ds2; coords[5*dim+2] = 1.0;
1555       coords[6*dim+0] =  ds2; coords[6*dim+1] =  ds2; coords[6*dim+2] = 1.0;
1556       coords[7*dim+0] =  ds2; coords[7*dim+1] = -ds2; coords[7*dim+2] = 1.0;
1557       coords[ 8*dim+0] =  dis; coords[ 8*dim+1] = -dis; coords[ 8*dim+2] = 0.0;
1558       coords[ 9*dim+0] =  dis; coords[ 9*dim+1] =  dis; coords[ 9*dim+2] = 0.0;
1559       coords[10*dim+0] =  dis; coords[10*dim+1] = -dis; coords[10*dim+2] = 1.0;
1560       coords[11*dim+0] =  dis; coords[11*dim+1] =  dis; coords[11*dim+2] = 1.0;
1561       coords[12*dim+0] = -dis; coords[12*dim+1] =  dis; coords[12*dim+2] = 0.0;
1562       coords[13*dim+0] = -dis; coords[13*dim+1] =  dis; coords[13*dim+2] = 1.0;
1563       coords[14*dim+0] = -dis; coords[14*dim+1] = -dis; coords[14*dim+2] = 0.0;
1564       coords[15*dim+0] = -dis; coords[15*dim+1] = -dis; coords[15*dim+2] = 1.0;
1565       if (periodicZ == DM_BOUNDARY_PERIODIC) {
1566         /* 15 31 19 */ coords[16*dim+0] = -ds2; coords[16*dim+1] = -ds2; coords[16*dim+2] = 0.5;
1567         /* 16 32 22 */ coords[17*dim+0] =  ds2; coords[17*dim+1] = -ds2; coords[17*dim+2] = 0.5;
1568         /* 17 33 21 */ coords[18*dim+0] =  ds2; coords[18*dim+1] =  ds2; coords[18*dim+2] = 0.5;
1569         /* 18 34 20 */ coords[19*dim+0] = -ds2; coords[19*dim+1] =  ds2; coords[19*dim+2] = 0.5;
1570         /* 29 35 30 */ coords[20*dim+0] = -dis; coords[20*dim+1] = -dis; coords[20*dim+2] = 0.5;
1571         /* 23 36 25 */ coords[21*dim+0] =  dis; coords[21*dim+1] = -dis; coords[21*dim+2] = 0.5;
1572         /* 24 37 26 */ coords[22*dim+0] =  dis; coords[22*dim+1] =  dis; coords[22*dim+2] = 0.5;
1573         /* 27 38 28 */ coords[23*dim+0] = -dis; coords[23*dim+1] =  dis; coords[23*dim+2] = 0.5;
1574       }
1575     }
1576     ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
1577     ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
1578     ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
1579   }
1580   /* Create periodicity */
1581   if (periodicZ == DM_BOUNDARY_PERIODIC || periodicZ == DM_BOUNDARY_TWIST) {
1582     PetscReal      L[3];
1583     PetscReal      maxCell[3];
1584     DMBoundaryType bdType[3];
1585     PetscReal      lower[3] = {0.0, 0.0, 0.0};
1586     PetscReal      upper[3] = {1.0, 1.0, 1.5};
1587     PetscInt       i, numZCells = 3;
1588 
1589     bdType[0] = DM_BOUNDARY_NONE;
1590     bdType[1] = DM_BOUNDARY_NONE;
1591     bdType[2] = periodicZ;
1592     for (i = 0; i < dim; i++) {
1593       L[i]       = upper[i] - lower[i];
1594       maxCell[i] = 1.1 * (L[i] / numZCells);
1595     }
1596     ierr = DMSetPeriodicity(dm, PETSC_TRUE, maxCell, L, bdType);CHKERRQ(ierr);
1597   }
1598   {
1599     DM          cdm;
1600     PetscDS     cds;
1601     PetscScalar c[2] = {1.0, 1.0};
1602 
1603     ierr = DMPlexCreateCoordinateSpace(dm, 1, snapToCylinder);CHKERRQ(ierr);
1604     ierr = DMGetCoordinateDM(dm, &cdm);CHKERRQ(ierr);
1605     ierr = DMGetDS(cdm, &cds);CHKERRQ(ierr);
1606     ierr = PetscDSSetConstants(cds, 2, c);CHKERRQ(ierr);
1607   }
1608   /* Wait for coordinate creation before doing in-place modification */
1609   ierr = DMPlexInterpolateInPlace_Internal(dm);CHKERRQ(ierr);
1610   PetscFunctionReturn(0);
1611 }
1612 
1613 /*@
1614   DMPlexCreateHexCylinderMesh - Creates a mesh on the tensor product of the unit interval with the circle (cylinder) using hexahedra.
1615 
1616   Collective
1617 
1618   Input Parameters:
1619 + comm      - The communicator for the DM object
1620 - periodicZ - The boundary type for the Z direction
1621 
1622   Output Parameter:
1623 . dm  - The DM object
1624 
1625   Note:
1626   Here is the output numbering looking from the bottom of the cylinder:
1627 $       17-----14
1628 $        |     |
1629 $        |  2  |
1630 $        |     |
1631 $ 17-----8-----7-----14
1632 $  |     |     |     |
1633 $  |  3  |  0  |  1  |
1634 $  |     |     |     |
1635 $ 19-----5-----6-----13
1636 $        |     |
1637 $        |  4  |
1638 $        |     |
1639 $       19-----13
1640 $
1641 $ and up through the top
1642 $
1643 $       18-----16
1644 $        |     |
1645 $        |  2  |
1646 $        |     |
1647 $ 18----10----11-----16
1648 $  |     |     |     |
1649 $  |  3  |  0  |  1  |
1650 $  |     |     |     |
1651 $ 20-----9----12-----15
1652 $        |     |
1653 $        |  4  |
1654 $        |     |
1655 $       20-----15
1656 
1657   Level: beginner
1658 
1659 .seealso: DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
1660 @*/
1661 PetscErrorCode DMPlexCreateHexCylinderMesh(MPI_Comm comm, DMBoundaryType periodicZ, DM *dm)
1662 {
1663   PetscErrorCode ierr;
1664 
1665   PetscFunctionBegin;
1666   PetscValidPointer(dm, 3);
1667   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
1668   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
1669   ierr = DMPlexCreateHexCylinderMesh_Internal(*dm, periodicZ);CHKERRQ(ierr);
1670   PetscFunctionReturn(0);
1671 }
1672 
1673 static PetscErrorCode DMPlexCreateWedgeCylinderMesh_Internal(DM dm, PetscInt n, PetscBool interpolate)
1674 {
1675   const PetscInt dim = 3;
1676   PetscInt       numCells, numVertices, v;
1677   PetscMPIInt    rank;
1678   PetscErrorCode ierr;
1679 
1680   PetscFunctionBegin;
1681   if (n < 0) SETERRQ1(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_OUTOFRANGE, "Number of wedges %D cannot be negative", n);
1682   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject) dm), &rank);CHKERRMPI(ierr);
1683   ierr = DMSetDimension(dm, dim);CHKERRQ(ierr);
1684   /* Must create the celltype label here so that we do not automatically try to compute the types */
1685   ierr = DMCreateLabel(dm, "celltype");CHKERRQ(ierr);
1686   /* Create topology */
1687   {
1688     PetscInt cone[6], c;
1689 
1690     numCells    = rank == 0 ?        n : 0;
1691     numVertices = rank == 0 ?  2*(n+1) : 0;
1692     ierr = DMPlexSetChart(dm, 0, numCells+numVertices);CHKERRQ(ierr);
1693     for (c = 0; c < numCells; c++) {ierr = DMPlexSetConeSize(dm, c, 6);CHKERRQ(ierr);}
1694     ierr = DMSetUp(dm);CHKERRQ(ierr);
1695     for (c = 0; c < numCells; c++) {
1696       cone[0] =  c+n*1; cone[1] = (c+1)%n+n*1; cone[2] = 0+3*n;
1697       cone[3] =  c+n*2; cone[4] = (c+1)%n+n*2; cone[5] = 1+3*n;
1698       ierr = DMPlexSetCone(dm, c, cone);CHKERRQ(ierr);
1699       ierr = DMPlexSetCellType(dm, c, DM_POLYTOPE_TRI_PRISM_TENSOR);CHKERRQ(ierr);
1700     }
1701     ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
1702     ierr = DMPlexStratify(dm);CHKERRQ(ierr);
1703   }
1704   for (v = numCells; v < numCells+numVertices; ++v) {
1705     ierr = DMPlexSetCellType(dm, v, DM_POLYTOPE_POINT);CHKERRQ(ierr);
1706   }
1707   /* Create cylinder geometry */
1708   {
1709     Vec          coordinates;
1710     PetscSection coordSection;
1711     PetscScalar *coords;
1712     PetscInt     coordSize, c;
1713 
1714     /* Build coordinates */
1715     ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
1716     ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
1717     ierr = PetscSectionSetFieldComponents(coordSection, 0, dim);CHKERRQ(ierr);
1718     ierr = PetscSectionSetChart(coordSection, numCells, numCells+numVertices);CHKERRQ(ierr);
1719     for (v = numCells; v < numCells+numVertices; ++v) {
1720       ierr = PetscSectionSetDof(coordSection, v, dim);CHKERRQ(ierr);
1721       ierr = PetscSectionSetFieldDof(coordSection, v, 0, dim);CHKERRQ(ierr);
1722     }
1723     ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
1724     ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
1725     ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
1726     ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
1727     ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
1728     ierr = VecSetBlockSize(coordinates, dim);CHKERRQ(ierr);
1729     ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
1730     ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
1731     for (c = 0; c < numCells; c++) {
1732       coords[(c+0*n)*dim+0] = PetscCosReal(2.0*c*PETSC_PI/n); coords[(c+0*n)*dim+1] = PetscSinReal(2.0*c*PETSC_PI/n); coords[(c+0*n)*dim+2] = 1.0;
1733       coords[(c+1*n)*dim+0] = PetscCosReal(2.0*c*PETSC_PI/n); coords[(c+1*n)*dim+1] = PetscSinReal(2.0*c*PETSC_PI/n); coords[(c+1*n)*dim+2] = 0.0;
1734     }
1735     if (rank == 0) {
1736       coords[(2*n+0)*dim+0] = 0.0; coords[(2*n+0)*dim+1] = 0.0; coords[(2*n+0)*dim+2] = 1.0;
1737       coords[(2*n+1)*dim+0] = 0.0; coords[(2*n+1)*dim+1] = 0.0; coords[(2*n+1)*dim+2] = 0.0;
1738     }
1739     ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
1740     ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
1741     ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
1742   }
1743   /* Interpolate */
1744   if (interpolate) {ierr = DMPlexInterpolateInPlace_Internal(dm);CHKERRQ(ierr);}
1745   PetscFunctionReturn(0);
1746 }
1747 
1748 /*@
1749   DMPlexCreateWedgeCylinderMesh - Creates a mesh on the tensor product of the unit interval with the circle (cylinder) using wedges.
1750 
1751   Collective
1752 
1753   Input Parameters:
1754 + comm - The communicator for the DM object
1755 . n    - The number of wedges around the origin
1756 - interpolate - Create edges and faces
1757 
1758   Output Parameter:
1759 . dm  - The DM object
1760 
1761   Level: beginner
1762 
1763 .seealso: DMPlexCreateHexCylinderMesh(), DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
1764 @*/
1765 PetscErrorCode DMPlexCreateWedgeCylinderMesh(MPI_Comm comm, PetscInt n, PetscBool interpolate, DM *dm)
1766 {
1767   PetscErrorCode ierr;
1768 
1769   PetscFunctionBegin;
1770   PetscValidPointer(dm, 4);
1771   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
1772   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
1773   ierr = DMPlexCreateWedgeCylinderMesh_Internal(*dm, n, interpolate);CHKERRQ(ierr);
1774   PetscFunctionReturn(0);
1775 }
1776 
1777 PETSC_STATIC_INLINE PetscReal DiffNormReal(PetscInt dim, const PetscReal x[], const PetscReal y[])
1778 {
1779   PetscReal prod = 0.0;
1780   PetscInt  i;
1781   for (i = 0; i < dim; ++i) prod += PetscSqr(x[i] - y[i]);
1782   return PetscSqrtReal(prod);
1783 }
1784 PETSC_STATIC_INLINE PetscReal DotReal(PetscInt dim, const PetscReal x[], const PetscReal y[])
1785 {
1786   PetscReal prod = 0.0;
1787   PetscInt  i;
1788   for (i = 0; i < dim; ++i) prod += x[i]*y[i];
1789   return prod;
1790 }
1791 
1792 /* The first constant is the sphere radius */
1793 static void snapToSphere(PetscInt dim, PetscInt Nf, PetscInt NfAux,
1794                          const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
1795                          const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
1796                          PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
1797 {
1798   PetscReal r = PetscRealPart(constants[0]);
1799   PetscReal norm2 = 0.0, fac;
1800   PetscInt  n = uOff[1] - uOff[0], d;
1801 
1802   for (d = 0; d < n; ++d) norm2 += PetscSqr(PetscRealPart(u[d]));
1803   fac = r/PetscSqrtReal(norm2);
1804   for (d = 0; d < n; ++d) f0[d] = u[d]*fac;
1805 }
1806 
1807 static PetscErrorCode DMPlexCreateSphereMesh_Internal(DM dm, PetscInt dim, PetscBool simplex, PetscReal R)
1808 {
1809   const PetscInt  embedDim = dim+1;
1810   PetscSection    coordSection;
1811   Vec             coordinates;
1812   PetscScalar    *coords;
1813   PetscReal      *coordsIn;
1814   PetscInt        numCells, numEdges, numVerts, firstVertex, v, firstEdge, coordSize, d, c, e;
1815   PetscMPIInt     rank;
1816   PetscErrorCode  ierr;
1817 
1818   PetscFunctionBegin;
1819   PetscValidLogicalCollectiveBool(dm, simplex, 3);
1820   ierr = DMSetDimension(dm, dim);CHKERRQ(ierr);
1821   ierr = DMSetCoordinateDim(dm, dim+1);CHKERRQ(ierr);
1822   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject) dm), &rank);CHKERRMPI(ierr);
1823   switch (dim) {
1824   case 2:
1825     if (simplex) {
1826       const PetscReal radius    = PetscSqrtReal(1 + PETSC_PHI*PETSC_PHI)/(1.0 + PETSC_PHI);
1827       const PetscReal edgeLen   = 2.0/(1.0 + PETSC_PHI) * (R/radius);
1828       const PetscInt  degree    = 5;
1829       PetscReal       vertex[3] = {0.0, 1.0/(1.0 + PETSC_PHI), PETSC_PHI/(1.0 + PETSC_PHI)};
1830       PetscInt        s[3]      = {1, 1, 1};
1831       PetscInt        cone[3];
1832       PetscInt       *graph, p, i, j, k;
1833 
1834       vertex[0] *= R/radius; vertex[1] *= R/radius; vertex[2] *= R/radius;
1835       numCells    = rank == 0 ? 20 : 0;
1836       numVerts    = rank == 0 ? 12 : 0;
1837       firstVertex = numCells;
1838       /* Use icosahedron, which for a R-sphere has coordinates which are all cyclic permutations of
1839 
1840            (0, \pm 1/\phi+1, \pm \phi/\phi+1)
1841 
1842          where \phi^2 - \phi - 1 = 0, meaning \phi is the golden ratio \frac{1 + \sqrt{5}}{2}. The edge
1843          length is then given by 2/(1+\phi) = 2 * 0.38197 = 0.76393.
1844       */
1845       /* Construct vertices */
1846       ierr = PetscCalloc1(numVerts * embedDim, &coordsIn);CHKERRQ(ierr);
1847       if (rank == 0) {
1848         for (p = 0, i = 0; p < embedDim; ++p) {
1849           for (s[1] = -1; s[1] < 2; s[1] += 2) {
1850             for (s[2] = -1; s[2] < 2; s[2] += 2) {
1851               for (d = 0; d < embedDim; ++d) coordsIn[i*embedDim+d] = s[(d+p)%embedDim]*vertex[(d+p)%embedDim];
1852               ++i;
1853             }
1854           }
1855         }
1856       }
1857       /* Construct graph */
1858       ierr = PetscCalloc1(numVerts * numVerts, &graph);CHKERRQ(ierr);
1859       for (i = 0; i < numVerts; ++i) {
1860         for (j = 0, k = 0; j < numVerts; ++j) {
1861           if (PetscAbsReal(DiffNormReal(embedDim, &coordsIn[i*embedDim], &coordsIn[j*embedDim]) - edgeLen) < PETSC_SMALL) {graph[i*numVerts+j] = 1; ++k;}
1862         }
1863         if (k != degree) SETERRQ3(PetscObjectComm((PetscObject) dm), PETSC_ERR_PLIB, "Invalid icosahedron, vertex %D degree %D != %D", i, k, degree);
1864       }
1865       /* Build Topology */
1866       ierr = DMPlexSetChart(dm, 0, numCells+numVerts);CHKERRQ(ierr);
1867       for (c = 0; c < numCells; c++) {
1868         ierr = DMPlexSetConeSize(dm, c, embedDim);CHKERRQ(ierr);
1869       }
1870       ierr = DMSetUp(dm);CHKERRQ(ierr); /* Allocate space for cones */
1871       /* Cells */
1872       for (i = 0, c = 0; i < numVerts; ++i) {
1873         for (j = 0; j < i; ++j) {
1874           for (k = 0; k < j; ++k) {
1875             if (graph[i*numVerts+j] && graph[j*numVerts+k] && graph[k*numVerts+i]) {
1876               cone[0] = firstVertex+i; cone[1] = firstVertex+j; cone[2] = firstVertex+k;
1877               /* Check orientation */
1878               {
1879                 const PetscInt epsilon[3][3][3] = {{{0, 0, 0}, {0, 0, 1}, {0, -1, 0}}, {{0, 0, -1}, {0, 0, 0}, {1, 0, 0}}, {{0, 1, 0}, {-1, 0, 0}, {0, 0, 0}}};
1880                 PetscReal normal[3];
1881                 PetscInt  e, f;
1882 
1883                 for (d = 0; d < embedDim; ++d) {
1884                   normal[d] = 0.0;
1885                   for (e = 0; e < embedDim; ++e) {
1886                     for (f = 0; f < embedDim; ++f) {
1887                       normal[d] += epsilon[d][e][f]*(coordsIn[j*embedDim+e] - coordsIn[i*embedDim+e])*(coordsIn[k*embedDim+f] - coordsIn[i*embedDim+f]);
1888                     }
1889                   }
1890                 }
1891                 if (DotReal(embedDim, normal, &coordsIn[i*embedDim]) < 0) {PetscInt tmp = cone[1]; cone[1] = cone[2]; cone[2] = tmp;}
1892               }
1893               ierr = DMPlexSetCone(dm, c++, cone);CHKERRQ(ierr);
1894             }
1895           }
1896         }
1897       }
1898       ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
1899       ierr = DMPlexStratify(dm);CHKERRQ(ierr);
1900       ierr = PetscFree(graph);CHKERRQ(ierr);
1901     } else {
1902       /*
1903         12-21--13
1904          |     |
1905         25  4  24
1906          |     |
1907   12-25--9-16--8-24--13
1908    |     |     |     |
1909   23  5 17  0 15  3  22
1910    |     |     |     |
1911   10-20--6-14--7-19--11
1912          |     |
1913         20  1  19
1914          |     |
1915         10-18--11
1916          |     |
1917         23  2  22
1918          |     |
1919         12-21--13
1920        */
1921       PetscInt cone[4], ornt[4];
1922 
1923       numCells    = rank == 0 ?  6 : 0;
1924       numEdges    = rank == 0 ? 12 : 0;
1925       numVerts    = rank == 0 ?  8 : 0;
1926       firstVertex = numCells;
1927       firstEdge   = numCells + numVerts;
1928       /* Build Topology */
1929       ierr = DMPlexSetChart(dm, 0, numCells+numEdges+numVerts);CHKERRQ(ierr);
1930       for (c = 0; c < numCells; c++) {
1931         ierr = DMPlexSetConeSize(dm, c, 4);CHKERRQ(ierr);
1932       }
1933       for (e = firstEdge; e < firstEdge+numEdges; ++e) {
1934         ierr = DMPlexSetConeSize(dm, e, 2);CHKERRQ(ierr);
1935       }
1936       ierr = DMSetUp(dm);CHKERRQ(ierr); /* Allocate space for cones */
1937       if (rank == 0) {
1938         /* Cell 0 */
1939         cone[0] = 14; cone[1] = 15; cone[2] = 16; cone[3] = 17;
1940         ierr = DMPlexSetCone(dm, 0, cone);CHKERRQ(ierr);
1941         ornt[0] = 0; ornt[1] = 0; ornt[2] = 0; ornt[3] = 0;
1942         ierr = DMPlexSetConeOrientation(dm, 0, ornt);CHKERRQ(ierr);
1943         /* Cell 1 */
1944         cone[0] = 18; cone[1] = 19; cone[2] = 14; cone[3] = 20;
1945         ierr = DMPlexSetCone(dm, 1, cone);CHKERRQ(ierr);
1946         ornt[0] = 0; ornt[1] = 0; ornt[2] = -1; ornt[3] = 0;
1947         ierr = DMPlexSetConeOrientation(dm, 1, ornt);CHKERRQ(ierr);
1948         /* Cell 2 */
1949         cone[0] = 21; cone[1] = 22; cone[2] = 18; cone[3] = 23;
1950         ierr = DMPlexSetCone(dm, 2, cone);CHKERRQ(ierr);
1951         ornt[0] = 0; ornt[1] = 0; ornt[2] = -1; ornt[3] = 0;
1952         ierr = DMPlexSetConeOrientation(dm, 2, ornt);CHKERRQ(ierr);
1953         /* Cell 3 */
1954         cone[0] = 19; cone[1] = 22; cone[2] = 24; cone[3] = 15;
1955         ierr = DMPlexSetCone(dm, 3, cone);CHKERRQ(ierr);
1956         ornt[0] = -1; ornt[1] = -1; ornt[2] = 0; ornt[3] = -1;
1957         ierr = DMPlexSetConeOrientation(dm, 3, ornt);CHKERRQ(ierr);
1958         /* Cell 4 */
1959         cone[0] = 16; cone[1] = 24; cone[2] = 21; cone[3] = 25;
1960         ierr = DMPlexSetCone(dm, 4, cone);CHKERRQ(ierr);
1961         ornt[0] = -1; ornt[1] = -1; ornt[2] = -1; ornt[3] = 0;
1962         ierr = DMPlexSetConeOrientation(dm, 4, ornt);CHKERRQ(ierr);
1963         /* Cell 5 */
1964         cone[0] = 20; cone[1] = 17; cone[2] = 25; cone[3] = 23;
1965         ierr = DMPlexSetCone(dm, 5, cone);CHKERRQ(ierr);
1966         ornt[0] = -1; ornt[1] = -1; ornt[2] = -1; ornt[3] = -1;
1967         ierr = DMPlexSetConeOrientation(dm, 5, ornt);CHKERRQ(ierr);
1968         /* Edges */
1969         cone[0] =  6; cone[1] =  7;
1970         ierr = DMPlexSetCone(dm, 14, cone);CHKERRQ(ierr);
1971         cone[0] =  7; cone[1] =  8;
1972         ierr = DMPlexSetCone(dm, 15, cone);CHKERRQ(ierr);
1973         cone[0] =  8; cone[1] =  9;
1974         ierr = DMPlexSetCone(dm, 16, cone);CHKERRQ(ierr);
1975         cone[0] =  9; cone[1] =  6;
1976         ierr = DMPlexSetCone(dm, 17, cone);CHKERRQ(ierr);
1977         cone[0] = 10; cone[1] = 11;
1978         ierr = DMPlexSetCone(dm, 18, cone);CHKERRQ(ierr);
1979         cone[0] = 11; cone[1] =  7;
1980         ierr = DMPlexSetCone(dm, 19, cone);CHKERRQ(ierr);
1981         cone[0] =  6; cone[1] = 10;
1982         ierr = DMPlexSetCone(dm, 20, cone);CHKERRQ(ierr);
1983         cone[0] = 12; cone[1] = 13;
1984         ierr = DMPlexSetCone(dm, 21, cone);CHKERRQ(ierr);
1985         cone[0] = 13; cone[1] = 11;
1986         ierr = DMPlexSetCone(dm, 22, cone);CHKERRQ(ierr);
1987         cone[0] = 10; cone[1] = 12;
1988         ierr = DMPlexSetCone(dm, 23, cone);CHKERRQ(ierr);
1989         cone[0] = 13; cone[1] =  8;
1990         ierr = DMPlexSetCone(dm, 24, cone);CHKERRQ(ierr);
1991         cone[0] = 12; cone[1] =  9;
1992         ierr = DMPlexSetCone(dm, 25, cone);CHKERRQ(ierr);
1993       }
1994       ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
1995       ierr = DMPlexStratify(dm);CHKERRQ(ierr);
1996       /* Build coordinates */
1997       ierr = PetscCalloc1(numVerts * embedDim, &coordsIn);CHKERRQ(ierr);
1998       if (rank == 0) {
1999         coordsIn[0*embedDim+0] = -R; coordsIn[0*embedDim+1] =  R; coordsIn[0*embedDim+2] = -R;
2000         coordsIn[1*embedDim+0] =  R; coordsIn[1*embedDim+1] =  R; coordsIn[1*embedDim+2] = -R;
2001         coordsIn[2*embedDim+0] =  R; coordsIn[2*embedDim+1] = -R; coordsIn[2*embedDim+2] = -R;
2002         coordsIn[3*embedDim+0] = -R; coordsIn[3*embedDim+1] = -R; coordsIn[3*embedDim+2] = -R;
2003         coordsIn[4*embedDim+0] = -R; coordsIn[4*embedDim+1] =  R; coordsIn[4*embedDim+2] =  R;
2004         coordsIn[5*embedDim+0] =  R; coordsIn[5*embedDim+1] =  R; coordsIn[5*embedDim+2] =  R;
2005         coordsIn[6*embedDim+0] = -R; coordsIn[6*embedDim+1] = -R; coordsIn[6*embedDim+2] =  R;
2006         coordsIn[7*embedDim+0] =  R; coordsIn[7*embedDim+1] = -R; coordsIn[7*embedDim+2] =  R;
2007       }
2008     }
2009     break;
2010   case 3:
2011     if (simplex) {
2012       const PetscReal edgeLen         = 1.0/PETSC_PHI;
2013       PetscReal       vertexA[4]      = {0.5, 0.5, 0.5, 0.5};
2014       PetscReal       vertexB[4]      = {1.0, 0.0, 0.0, 0.0};
2015       PetscReal       vertexC[4]      = {0.5, 0.5*PETSC_PHI, 0.5/PETSC_PHI, 0.0};
2016       const PetscInt  degree          = 12;
2017       PetscInt        s[4]            = {1, 1, 1};
2018       PetscInt        evenPerm[12][4] = {{0, 1, 2, 3}, {0, 2, 3, 1}, {0, 3, 1, 2}, {1, 0, 3, 2}, {1, 2, 0, 3}, {1, 3, 2, 0},
2019                                          {2, 0, 1, 3}, {2, 1, 3, 0}, {2, 3, 0, 1}, {3, 0, 2, 1}, {3, 1, 0, 2}, {3, 2, 1, 0}};
2020       PetscInt        cone[4];
2021       PetscInt       *graph, p, i, j, k, l;
2022 
2023       vertexA[0] *= R; vertexA[1] *= R; vertexA[2] *= R; vertexA[3] *= R;
2024       vertexB[0] *= R; vertexB[1] *= R; vertexB[2] *= R; vertexB[3] *= R;
2025       vertexC[0] *= R; vertexC[1] *= R; vertexC[2] *= R; vertexC[3] *= R;
2026       numCells    = rank == 0 ? 600 : 0;
2027       numVerts    = rank == 0 ? 120 : 0;
2028       firstVertex = numCells;
2029       /* Use the 600-cell, which for a unit sphere has coordinates which are
2030 
2031            1/2 (\pm 1, \pm 1,    \pm 1, \pm 1)                          16
2032                (\pm 1,    0,       0,      0)  all cyclic permutations   8
2033            1/2 (\pm 1, \pm phi, \pm 1/phi, 0)  all even permutations    96
2034 
2035          where \phi^2 - \phi - 1 = 0, meaning \phi is the golden ratio \frac{1 + \sqrt{5}}{2}. The edge
2036          length is then given by 1/\phi = 0.61803.
2037 
2038          http://buzzard.pugetsound.edu/sage-practice/ch03s03.html
2039          http://mathworld.wolfram.com/600-Cell.html
2040       */
2041       /* Construct vertices */
2042       ierr = PetscCalloc1(numVerts * embedDim, &coordsIn);CHKERRQ(ierr);
2043       i    = 0;
2044       if (rank == 0) {
2045         for (s[0] = -1; s[0] < 2; s[0] += 2) {
2046           for (s[1] = -1; s[1] < 2; s[1] += 2) {
2047             for (s[2] = -1; s[2] < 2; s[2] += 2) {
2048               for (s[3] = -1; s[3] < 2; s[3] += 2) {
2049                 for (d = 0; d < embedDim; ++d) coordsIn[i*embedDim+d] = s[d]*vertexA[d];
2050                 ++i;
2051               }
2052             }
2053           }
2054         }
2055         for (p = 0; p < embedDim; ++p) {
2056           s[1] = s[2] = s[3] = 1;
2057           for (s[0] = -1; s[0] < 2; s[0] += 2) {
2058             for (d = 0; d < embedDim; ++d) coordsIn[i*embedDim+d] = s[(d+p)%embedDim]*vertexB[(d+p)%embedDim];
2059             ++i;
2060           }
2061         }
2062         for (p = 0; p < 12; ++p) {
2063           s[3] = 1;
2064           for (s[0] = -1; s[0] < 2; s[0] += 2) {
2065             for (s[1] = -1; s[1] < 2; s[1] += 2) {
2066               for (s[2] = -1; s[2] < 2; s[2] += 2) {
2067                 for (d = 0; d < embedDim; ++d) coordsIn[i*embedDim+d] = s[evenPerm[p][d]]*vertexC[evenPerm[p][d]];
2068                 ++i;
2069               }
2070             }
2071           }
2072         }
2073       }
2074       if (i != numVerts) SETERRQ2(PetscObjectComm((PetscObject) dm), PETSC_ERR_PLIB, "Invalid 600-cell, vertices %D != %D", i, numVerts);
2075       /* Construct graph */
2076       ierr = PetscCalloc1(numVerts * numVerts, &graph);CHKERRQ(ierr);
2077       for (i = 0; i < numVerts; ++i) {
2078         for (j = 0, k = 0; j < numVerts; ++j) {
2079           if (PetscAbsReal(DiffNormReal(embedDim, &coordsIn[i*embedDim], &coordsIn[j*embedDim]) - edgeLen) < PETSC_SMALL) {graph[i*numVerts+j] = 1; ++k;}
2080         }
2081         if (k != degree) SETERRQ3(PetscObjectComm((PetscObject) dm), PETSC_ERR_PLIB, "Invalid 600-cell, vertex %D degree %D != %D", i, k, degree);
2082       }
2083       /* Build Topology */
2084       ierr = DMPlexSetChart(dm, 0, numCells+numVerts);CHKERRQ(ierr);
2085       for (c = 0; c < numCells; c++) {
2086         ierr = DMPlexSetConeSize(dm, c, embedDim);CHKERRQ(ierr);
2087       }
2088       ierr = DMSetUp(dm);CHKERRQ(ierr); /* Allocate space for cones */
2089       /* Cells */
2090       if (rank == 0) {
2091         for (i = 0, c = 0; i < numVerts; ++i) {
2092           for (j = 0; j < i; ++j) {
2093             for (k = 0; k < j; ++k) {
2094               for (l = 0; l < k; ++l) {
2095                 if (graph[i*numVerts+j] && graph[j*numVerts+k] && graph[k*numVerts+i] &&
2096                     graph[l*numVerts+i] && graph[l*numVerts+j] && graph[l*numVerts+k]) {
2097                   cone[0] = firstVertex+i; cone[1] = firstVertex+j; cone[2] = firstVertex+k; cone[3] = firstVertex+l;
2098                   /* Check orientation: https://ef.gy/linear-algebra:normal-vectors-in-higher-dimensional-spaces */
2099                   {
2100                     const PetscInt epsilon[4][4][4][4] = {{{{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}},
2101                                                            {{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  1}, { 0,  0, -1, 0}},
2102                                                            {{0,  0,  0,  0}, { 0, 0,  0, -1}, { 0,  0, 0,  0}, { 0,  1,  0, 0}},
2103                                                            {{0,  0,  0,  0}, { 0, 0,  1,  0}, { 0, -1, 0,  0}, { 0,  0,  0, 0}}},
2104 
2105                                                           {{{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0, -1}, { 0,  0,  1, 0}},
2106                                                            {{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}},
2107                                                            {{0,  0,  0,  1}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, {-1,  0,  0, 0}},
2108                                                            {{0,  0, -1,  0}, { 0, 0,  0,  0}, { 1,  0, 0,  0}, { 0,  0,  0, 0}}},
2109 
2110                                                           {{{0,  0,  0,  0}, { 0, 0,  0,  1}, { 0,  0, 0,  0}, { 0, -1,  0, 0}},
2111                                                            {{0,  0,  0, -1}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 1,  0,  0, 0}},
2112                                                            {{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}},
2113                                                            {{0,  1,  0,  0}, {-1, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}}},
2114 
2115                                                           {{{0,  0,  0,  0}, { 0, 0, -1,  0}, { 0,  1, 0,  0}, { 0,  0,  0, 0}},
2116                                                            {{0,  0,  1,  0}, { 0, 0,  0,  0}, {-1,  0, 0,  0}, { 0,  0,  0, 0}},
2117                                                            {{0, -1,  0,  0}, { 1, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}},
2118                                                            {{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}}}};
2119                     PetscReal normal[4];
2120                     PetscInt  e, f, g;
2121 
2122                     for (d = 0; d < embedDim; ++d) {
2123                       normal[d] = 0.0;
2124                       for (e = 0; e < embedDim; ++e) {
2125                         for (f = 0; f < embedDim; ++f) {
2126                           for (g = 0; g < embedDim; ++g) {
2127                             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]);
2128                           }
2129                         }
2130                       }
2131                     }
2132                     if (DotReal(embedDim, normal, &coordsIn[i*embedDim]) < 0) {PetscInt tmp = cone[1]; cone[1] = cone[2]; cone[2] = tmp;}
2133                   }
2134                   ierr = DMPlexSetCone(dm, c++, cone);CHKERRQ(ierr);
2135                 }
2136               }
2137             }
2138           }
2139         }
2140       }
2141       ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
2142       ierr = DMPlexStratify(dm);CHKERRQ(ierr);
2143       ierr = PetscFree(graph);CHKERRQ(ierr);
2144       break;
2145     }
2146   default: SETERRQ1(PetscObjectComm((PetscObject) dm), PETSC_ERR_SUP, "Unsupported dimension for sphere: %D", dim);
2147   }
2148   /* Create coordinates */
2149   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
2150   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
2151   ierr = PetscSectionSetFieldComponents(coordSection, 0, embedDim);CHKERRQ(ierr);
2152   ierr = PetscSectionSetChart(coordSection, firstVertex, firstVertex+numVerts);CHKERRQ(ierr);
2153   for (v = firstVertex; v < firstVertex+numVerts; ++v) {
2154     ierr = PetscSectionSetDof(coordSection, v, embedDim);CHKERRQ(ierr);
2155     ierr = PetscSectionSetFieldDof(coordSection, v, 0, embedDim);CHKERRQ(ierr);
2156   }
2157   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
2158   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
2159   ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
2160   ierr = VecSetBlockSize(coordinates, embedDim);CHKERRQ(ierr);
2161   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
2162   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
2163   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
2164   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
2165   for (v = 0; v < numVerts; ++v) for (d = 0; d < embedDim; ++d) {coords[v*embedDim+d] = coordsIn[v*embedDim+d];}
2166   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
2167   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
2168   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
2169   ierr = PetscFree(coordsIn);CHKERRQ(ierr);
2170   {
2171     DM          cdm;
2172     PetscDS     cds;
2173     PetscScalar c = R;
2174 
2175     ierr = DMPlexCreateCoordinateSpace(dm, 1, snapToSphere);CHKERRQ(ierr);
2176     ierr = DMGetCoordinateDM(dm, &cdm);CHKERRQ(ierr);
2177     ierr = DMGetDS(cdm, &cds);CHKERRQ(ierr);
2178     ierr = PetscDSSetConstants(cds, 1, &c);CHKERRQ(ierr);
2179   }
2180   /* Wait for coordinate creation before doing in-place modification */
2181   if (simplex) {ierr = DMPlexInterpolateInPlace_Internal(dm);CHKERRQ(ierr);}
2182   PetscFunctionReturn(0);
2183 }
2184 
2185 /*@
2186   DMPlexCreateSphereMesh - Creates a mesh on the d-dimensional sphere, S^d.
2187 
2188   Collective
2189 
2190   Input Parameters:
2191 + comm    - The communicator for the DM object
2192 . dim     - The dimension
2193 . simplex - Use simplices, or tensor product cells
2194 - R       - The radius
2195 
2196   Output Parameter:
2197 . dm  - The DM object
2198 
2199   Level: beginner
2200 
2201 .seealso: DMPlexCreateBallMesh(), DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
2202 @*/
2203 PetscErrorCode DMPlexCreateSphereMesh(MPI_Comm comm, PetscInt dim, PetscBool simplex, PetscReal R, DM *dm)
2204 {
2205   PetscErrorCode ierr;
2206 
2207   PetscFunctionBegin;
2208   PetscValidPointer(dm, 5);
2209   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
2210   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
2211   ierr = DMPlexCreateSphereMesh_Internal(*dm, dim, simplex, R);CHKERRQ(ierr);
2212   PetscFunctionReturn(0);
2213 }
2214 
2215 static PetscErrorCode DMPlexCreateBallMesh_Internal(DM dm, PetscInt dim, PetscReal R)
2216 {
2217   DM             sdm, vol;
2218   DMLabel        bdlabel;
2219   PetscErrorCode ierr;
2220 
2221   PetscFunctionBegin;
2222   ierr = DMCreate(PetscObjectComm((PetscObject) dm), &sdm);CHKERRQ(ierr);
2223   ierr = DMSetType(sdm, DMPLEX);CHKERRQ(ierr);
2224   ierr = PetscObjectSetOptionsPrefix((PetscObject) sdm, "bd_");CHKERRQ(ierr);
2225   ierr = DMPlexCreateSphereMesh_Internal(sdm, dim-1, PETSC_TRUE, R);CHKERRQ(ierr);
2226   ierr = DMSetFromOptions(sdm);CHKERRQ(ierr);
2227   ierr = DMViewFromOptions(sdm, NULL, "-dm_view");CHKERRQ(ierr);
2228   ierr = DMPlexGenerate(sdm, NULL, PETSC_TRUE, &vol);CHKERRQ(ierr);
2229   ierr = DMDestroy(&sdm);CHKERRQ(ierr);
2230   ierr = DMPlexReplace_Static(dm, &vol);CHKERRQ(ierr);
2231   ierr = DMCreateLabel(dm, "marker");CHKERRQ(ierr);
2232   ierr = DMGetLabel(dm, "marker", &bdlabel);CHKERRQ(ierr);
2233   ierr = DMPlexMarkBoundaryFaces(dm, PETSC_DETERMINE, bdlabel);CHKERRQ(ierr);
2234   ierr = DMPlexLabelComplete(dm, bdlabel);CHKERRQ(ierr);
2235   PetscFunctionReturn(0);
2236 }
2237 
2238 /*@
2239   DMPlexCreateBallMesh - Creates a simplex mesh on the d-dimensional ball, B^d.
2240 
2241   Collective
2242 
2243   Input Parameters:
2244 + comm  - The communicator for the DM object
2245 . dim   - The dimension
2246 - R     - The radius
2247 
2248   Output Parameter:
2249 . dm  - The DM object
2250 
2251   Options Database Keys:
2252 - bd_dm_refine - This will refine the surface mesh preserving the sphere geometry
2253 
2254   Level: beginner
2255 
2256 .seealso: DMPlexCreateSphereMesh(), DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
2257 @*/
2258 PetscErrorCode DMPlexCreateBallMesh(MPI_Comm comm, PetscInt dim, PetscReal R, DM *dm)
2259 {
2260   PetscErrorCode ierr;
2261 
2262   PetscFunctionBegin;
2263   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
2264   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
2265   ierr = DMPlexCreateBallMesh_Internal(*dm, dim, R);CHKERRQ(ierr);
2266   PetscFunctionReturn(0);
2267 }
2268 
2269 static PetscErrorCode DMPlexCreateReferenceCell_Internal(DM rdm, DMPolytopeType ct)
2270 {
2271   PetscErrorCode ierr;
2272 
2273   PetscFunctionBegin;
2274   switch (ct) {
2275     case DM_POLYTOPE_POINT:
2276     {
2277       PetscInt    numPoints[1]        = {1};
2278       PetscInt    coneSize[1]         = {0};
2279       PetscInt    cones[1]            = {0};
2280       PetscInt    coneOrientations[1] = {0};
2281       PetscScalar vertexCoords[1]     = {0.0};
2282 
2283       ierr = DMSetDimension(rdm, 0);CHKERRQ(ierr);
2284       ierr = DMPlexCreateFromDAG(rdm, 0, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2285     }
2286     break;
2287     case DM_POLYTOPE_SEGMENT:
2288     {
2289       PetscInt    numPoints[2]        = {2, 1};
2290       PetscInt    coneSize[3]         = {2, 0, 0};
2291       PetscInt    cones[2]            = {1, 2};
2292       PetscInt    coneOrientations[2] = {0, 0};
2293       PetscScalar vertexCoords[2]     = {-1.0,  1.0};
2294 
2295       ierr = DMSetDimension(rdm, 1);CHKERRQ(ierr);
2296       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2297     }
2298     break;
2299     case DM_POLYTOPE_POINT_PRISM_TENSOR:
2300     {
2301       PetscInt    numPoints[2]        = {2, 1};
2302       PetscInt    coneSize[3]         = {2, 0, 0};
2303       PetscInt    cones[2]            = {1, 2};
2304       PetscInt    coneOrientations[2] = {0, 0};
2305       PetscScalar vertexCoords[2]     = {-1.0,  1.0};
2306 
2307       ierr = DMSetDimension(rdm, 1);CHKERRQ(ierr);
2308       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2309     }
2310     break;
2311     case DM_POLYTOPE_TRIANGLE:
2312     {
2313       PetscInt    numPoints[2]        = {3, 1};
2314       PetscInt    coneSize[4]         = {3, 0, 0, 0};
2315       PetscInt    cones[3]            = {1, 2, 3};
2316       PetscInt    coneOrientations[3] = {0, 0, 0};
2317       PetscScalar vertexCoords[6]     = {-1.0, -1.0,  1.0, -1.0,  -1.0, 1.0};
2318 
2319       ierr = DMSetDimension(rdm, 2);CHKERRQ(ierr);
2320       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2321     }
2322     break;
2323     case DM_POLYTOPE_QUADRILATERAL:
2324     {
2325       PetscInt    numPoints[2]        = {4, 1};
2326       PetscInt    coneSize[5]         = {4, 0, 0, 0, 0};
2327       PetscInt    cones[4]            = {1, 2, 3, 4};
2328       PetscInt    coneOrientations[4] = {0, 0, 0, 0};
2329       PetscScalar vertexCoords[8]     = {-1.0, -1.0,  1.0, -1.0,  1.0, 1.0,  -1.0, 1.0};
2330 
2331       ierr = DMSetDimension(rdm, 2);CHKERRQ(ierr);
2332       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2333     }
2334     break;
2335     case DM_POLYTOPE_SEG_PRISM_TENSOR:
2336     {
2337       PetscInt    numPoints[2]        = {4, 1};
2338       PetscInt    coneSize[5]         = {4, 0, 0, 0, 0};
2339       PetscInt    cones[4]            = {1, 2, 3, 4};
2340       PetscInt    coneOrientations[4] = {0, 0, 0, 0};
2341       PetscScalar vertexCoords[8]     = {-1.0, -1.0,  1.0, -1.0,  -1.0, 1.0,  1.0, 1.0};
2342 
2343       ierr = DMSetDimension(rdm, 2);CHKERRQ(ierr);
2344       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2345     }
2346     break;
2347     case DM_POLYTOPE_TETRAHEDRON:
2348     {
2349       PetscInt    numPoints[2]        = {4, 1};
2350       PetscInt    coneSize[5]         = {4, 0, 0, 0, 0};
2351       PetscInt    cones[4]            = {1, 2, 3, 4};
2352       PetscInt    coneOrientations[4] = {0, 0, 0, 0};
2353       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};
2354 
2355       ierr = DMSetDimension(rdm, 3);CHKERRQ(ierr);
2356       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2357     }
2358     break;
2359     case DM_POLYTOPE_HEXAHEDRON:
2360     {
2361       PetscInt    numPoints[2]        = {8, 1};
2362       PetscInt    coneSize[9]         = {8, 0, 0, 0, 0, 0, 0, 0, 0};
2363       PetscInt    cones[8]            = {1, 2, 3, 4, 5, 6, 7, 8};
2364       PetscInt    coneOrientations[8] = {0, 0, 0, 0, 0, 0, 0, 0};
2365       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,
2366                                          -1.0, -1.0,  1.0,   1.0, -1.0,  1.0,  1.0, 1.0,  1.0,  -1.0,  1.0,  1.0};
2367 
2368       ierr = DMSetDimension(rdm, 3);CHKERRQ(ierr);
2369       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2370     }
2371     break;
2372     case DM_POLYTOPE_TRI_PRISM:
2373     {
2374       PetscInt    numPoints[2]        = {6, 1};
2375       PetscInt    coneSize[7]         = {6, 0, 0, 0, 0, 0, 0};
2376       PetscInt    cones[6]            = {1, 2, 3, 4, 5, 6};
2377       PetscInt    coneOrientations[6] = {0, 0, 0, 0, 0, 0};
2378       PetscScalar vertexCoords[18]    = {-1.0, -1.0, -1.0, -1.0,  1.0, -1.0,   1.0, -1.0, -1.0,
2379                                          -1.0, -1.0,  1.0,  1.0, -1.0,  1.0,  -1.0,  1.0,  1.0};
2380 
2381       ierr = DMSetDimension(rdm, 3);CHKERRQ(ierr);
2382       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2383     }
2384     break;
2385     case DM_POLYTOPE_TRI_PRISM_TENSOR:
2386     {
2387       PetscInt    numPoints[2]        = {6, 1};
2388       PetscInt    coneSize[7]         = {6, 0, 0, 0, 0, 0, 0};
2389       PetscInt    cones[6]            = {1, 2, 3, 4, 5, 6};
2390       PetscInt    coneOrientations[6] = {0, 0, 0, 0, 0, 0};
2391       PetscScalar vertexCoords[18]    = {-1.0, -1.0, -1.0,  1.0, -1.0, -1.0,  -1.0, 1.0, -1.0,
2392                                          -1.0, -1.0,  1.0,  1.0, -1.0,  1.0,  -1.0, 1.0,  1.0};
2393 
2394       ierr = DMSetDimension(rdm, 3);CHKERRQ(ierr);
2395       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2396     }
2397     break;
2398     case DM_POLYTOPE_QUAD_PRISM_TENSOR:
2399     {
2400       PetscInt    numPoints[2]        = {8, 1};
2401       PetscInt    coneSize[9]         = {8, 0, 0, 0, 0, 0, 0, 0, 0};
2402       PetscInt    cones[8]            = {1, 2, 3, 4, 5, 6, 7, 8};
2403       PetscInt    coneOrientations[8] = {0, 0, 0, 0, 0, 0, 0, 0};
2404       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,
2405                                          -1.0, -1.0,  1.0,  1.0, -1.0,  1.0,  1.0, 1.0,  1.0,  -1.0, 1.0,  1.0};
2406 
2407       ierr = DMSetDimension(rdm, 3);CHKERRQ(ierr);
2408       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2409     }
2410     break;
2411     case DM_POLYTOPE_PYRAMID:
2412     {
2413       PetscInt    numPoints[2]        = {5, 1};
2414       PetscInt    coneSize[6]         = {5, 0, 0, 0, 0, 0};
2415       PetscInt    cones[5]            = {1, 2, 3, 4, 5};
2416       PetscInt    coneOrientations[8] = {0, 0, 0, 0, 0, 0, 0, 0};
2417       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,
2418                                           0.0,  0.0,  1.0};
2419 
2420       ierr = DMSetDimension(rdm, 3);CHKERRQ(ierr);
2421       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2422     }
2423     break;
2424     default: SETERRQ1(PetscObjectComm((PetscObject) rdm), PETSC_ERR_ARG_WRONG, "Cannot create reference cell for cell type %s", DMPolytopeTypes[ct]);
2425   }
2426   {
2427     PetscInt Nv, v;
2428 
2429     /* Must create the celltype label here so that we do not automatically try to compute the types */
2430     ierr = DMCreateLabel(rdm, "celltype");CHKERRQ(ierr);
2431     ierr = DMPlexSetCellType(rdm, 0, ct);CHKERRQ(ierr);
2432     ierr = DMPlexGetChart(rdm, NULL, &Nv);CHKERRQ(ierr);
2433     for (v = 1; v < Nv; ++v) {ierr = DMPlexSetCellType(rdm, v, DM_POLYTOPE_POINT);CHKERRQ(ierr);}
2434   }
2435   ierr = DMPlexInterpolateInPlace_Internal(rdm);CHKERRQ(ierr);
2436   ierr = PetscObjectSetName((PetscObject) rdm, DMPolytopeTypes[ct]);CHKERRQ(ierr);
2437   PetscFunctionReturn(0);
2438 }
2439 
2440 /*@
2441   DMPlexCreateReferenceCell - Create a DMPLEX with the appropriate FEM reference cell
2442 
2443   Collective
2444 
2445   Input Parameters:
2446 + comm - The communicator
2447 - ct   - The cell type of the reference cell
2448 
2449   Output Parameter:
2450 . refdm - The reference cell
2451 
2452   Level: intermediate
2453 
2454 .seealso: DMPlexCreateReferenceCell(), DMPlexCreateBoxMesh()
2455 @*/
2456 PetscErrorCode DMPlexCreateReferenceCell(MPI_Comm comm, DMPolytopeType ct, DM *refdm)
2457 {
2458   PetscErrorCode ierr;
2459 
2460   PetscFunctionBegin;
2461   ierr = DMCreate(comm, refdm);CHKERRQ(ierr);
2462   ierr = DMSetType(*refdm, DMPLEX);CHKERRQ(ierr);
2463   ierr = DMPlexCreateReferenceCell_Internal(*refdm, ct);CHKERRQ(ierr);
2464   PetscFunctionReturn(0);
2465 }
2466 
2467 static PetscErrorCode DMPlexCreateBoundaryLabel_Private(DM dm, const char name[])
2468 {
2469   DM             plex;
2470   DMLabel        label;
2471   PetscBool      hasLabel;
2472   PetscErrorCode ierr;
2473 
2474   PetscFunctionBeginUser;
2475   ierr = DMHasLabel(dm, name, &hasLabel);CHKERRQ(ierr);
2476   if (hasLabel) PetscFunctionReturn(0);
2477   ierr = DMCreateLabel(dm, name);CHKERRQ(ierr);
2478   ierr = DMGetLabel(dm, name, &label);CHKERRQ(ierr);
2479   ierr = DMConvert(dm, DMPLEX, &plex);CHKERRQ(ierr);
2480   ierr = DMPlexMarkBoundaryFaces(plex, 1, label);CHKERRQ(ierr);
2481   ierr = DMDestroy(&plex);CHKERRQ(ierr);
2482   PetscFunctionReturn(0);
2483 }
2484 
2485 const char * const DMPlexShapes[] = {"box", "box_surface", "ball", "sphere", "cylinder", "unknown", "DMPlexShape", "DM_SHAPE_", NULL};
2486 
2487 static PetscErrorCode DMPlexCreateFromOptions_Internal(PetscOptionItems *PetscOptionsObject, PetscBool *useCoordSpace, DM dm)
2488 {
2489   DMPlexShape    shape = DM_SHAPE_BOX;
2490   DMPolytopeType cell  = DM_POLYTOPE_TRIANGLE;
2491   PetscInt       dim   = 2;
2492   PetscBool      simplex = PETSC_TRUE, interpolate = PETSC_TRUE, adjCone = PETSC_FALSE, adjClosure = PETSC_TRUE, refDomain = PETSC_FALSE;
2493   PetscBool      flg, flg2, fflg, bdfflg;
2494   MPI_Comm       comm;
2495   char           filename[PETSC_MAX_PATH_LEN], bdFilename[PETSC_MAX_PATH_LEN];
2496   PetscErrorCode ierr;
2497 
2498   PetscFunctionBegin;
2499   ierr = PetscObjectGetComm((PetscObject) dm, &comm);CHKERRQ(ierr);
2500   /* TODO Turn this into a registration interface */
2501   ierr = PetscOptionsString("-dm_plex_filename", "File containing a mesh", "DMPlexCreateFromFile", filename, filename, sizeof(filename), &fflg);CHKERRQ(ierr);
2502   ierr = PetscOptionsString("-dm_plex_boundary_filename", "File containing a mesh boundary", "DMPlexCreateFromFile", bdFilename, bdFilename, sizeof(bdFilename), &bdfflg);CHKERRQ(ierr);
2503   ierr = PetscOptionsEnum("-dm_plex_cell", "Cell shape", "", DMPolytopeTypes, (PetscEnum) cell, (PetscEnum *) &cell, NULL);CHKERRQ(ierr);
2504   ierr = PetscOptionsBool("-dm_plex_reference_cell_domain", "Use a reference cell domain", "", refDomain, &refDomain, NULL);CHKERRQ(ierr);
2505   ierr = PetscOptionsEnum("-dm_plex_shape", "Shape for built-in mesh", "", DMPlexShapes, (PetscEnum) shape, (PetscEnum *) &shape, &flg);CHKERRQ(ierr);
2506   ierr = PetscOptionsBoundedInt("-dm_plex_dim", "Topological dimension of the mesh", "DMGetDimension", dim, &dim, &flg, 0);CHKERRQ(ierr);
2507   if ((dim < 0) || (dim > 3)) SETERRQ1(comm, PETSC_ERR_ARG_OUTOFRANGE, "Dimension %D should be in [1, 3]", dim);
2508   ierr = PetscOptionsBool("-dm_plex_simplex", "Mesh cell shape", "", simplex,  &simplex, &flg);CHKERRQ(ierr);
2509   ierr = PetscOptionsBool("-dm_plex_interpolate", "Flag to create edges and faces automatically", "", interpolate, &interpolate, &flg);CHKERRQ(ierr);
2510   ierr = PetscOptionsBool("-dm_plex_adj_cone", "Set adjacency direction", "DMSetBasicAdjacency", adjCone,  &adjCone, &flg);CHKERRQ(ierr);
2511   ierr = PetscOptionsBool("-dm_plex_adj_closure", "Set adjacency size", "DMSetBasicAdjacency", adjClosure,  &adjClosure, &flg2);CHKERRQ(ierr);
2512   if (flg || flg2) {ierr = DMSetBasicAdjacency(dm, adjCone, adjClosure);CHKERRQ(ierr);}
2513 
2514   switch (cell) {
2515     case DM_POLYTOPE_POINT:
2516     case DM_POLYTOPE_SEGMENT:
2517     case DM_POLYTOPE_POINT_PRISM_TENSOR:
2518     case DM_POLYTOPE_TRIANGLE:
2519     case DM_POLYTOPE_QUADRILATERAL:
2520     case DM_POLYTOPE_TETRAHEDRON:
2521     case DM_POLYTOPE_HEXAHEDRON:
2522       *useCoordSpace = PETSC_TRUE;break;
2523     default: *useCoordSpace = PETSC_FALSE;break;
2524   }
2525 
2526   if (fflg) {
2527     DM dmnew;
2528 
2529     ierr = DMPlexCreateFromFile(PetscObjectComm((PetscObject) dm), filename, interpolate, &dmnew);CHKERRQ(ierr);
2530     ierr = DMPlexReplace_Static(dm, &dmnew);CHKERRQ(ierr);
2531   } else if (refDomain) {
2532     ierr = DMPlexCreateReferenceCell_Internal(dm, cell);CHKERRQ(ierr);
2533   } else if (bdfflg) {
2534     DM bdm, dmnew;
2535 
2536     ierr = DMPlexCreateFromFile(PetscObjectComm((PetscObject) dm), bdFilename, interpolate, &bdm);CHKERRQ(ierr);
2537     ierr = PetscObjectSetOptionsPrefix((PetscObject) bdm, "bd_");CHKERRQ(ierr);
2538     ierr = DMSetFromOptions(bdm);CHKERRQ(ierr);
2539     ierr = DMPlexGenerate(bdm, NULL, interpolate, &dmnew);CHKERRQ(ierr);
2540     ierr = DMDestroy(&bdm);CHKERRQ(ierr);
2541     ierr = DMPlexReplace_Static(dm, &dmnew);CHKERRQ(ierr);
2542   } else {
2543     ierr = PetscObjectSetName((PetscObject) dm, DMPlexShapes[shape]);CHKERRQ(ierr);
2544     switch (shape) {
2545       case DM_SHAPE_BOX:
2546       {
2547         PetscInt       faces[3] = {0, 0, 0};
2548         PetscReal      lower[3] = {0, 0, 0};
2549         PetscReal      upper[3] = {1, 1, 1};
2550         DMBoundaryType bdt[3]   = {DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE};
2551         PetscInt       i, n;
2552 
2553         n    = dim;
2554         for (i = 0; i < dim; ++i) faces[i] = (dim == 1 ? 1 : 4-dim);
2555         ierr = PetscOptionsIntArray("-dm_plex_box_faces", "Number of faces along each dimension", "", faces, &n, &flg);CHKERRQ(ierr);
2556         n    = 3;
2557         ierr = PetscOptionsRealArray("-dm_plex_box_lower", "Lower left corner of box", "", lower, &n, &flg);CHKERRQ(ierr);
2558         if (flg && (n != dim)) SETERRQ2(comm, PETSC_ERR_ARG_SIZ, "Lower box point had %D values, should have been %D", n, dim);
2559         n    = 3;
2560         ierr = PetscOptionsRealArray("-dm_plex_box_upper", "Upper right corner of box", "", upper, &n, &flg);CHKERRQ(ierr);
2561         if (flg && (n != dim)) SETERRQ2(comm, PETSC_ERR_ARG_SIZ, "Upper box point had %D values, should have been %D", n, dim);
2562         n    = 3;
2563         ierr = PetscOptionsEnumArray("-dm_plex_box_bd", "Boundary type for each dimension", "", DMBoundaryTypes, (PetscEnum *) bdt, &n, &flg);CHKERRQ(ierr);
2564         if (flg && (n != dim)) SETERRQ2(comm, PETSC_ERR_ARG_SIZ, "Box boundary types had %D values, should have been %D", n, dim);
2565         switch (cell) {
2566           case DM_POLYTOPE_TRI_PRISM_TENSOR:
2567             ierr = DMPlexCreateWedgeBoxMesh_Internal(dm, faces, lower, upper, bdt);CHKERRQ(ierr);
2568             if (!interpolate) {
2569               DM udm;
2570 
2571               ierr = DMPlexUninterpolate(dm, &udm);CHKERRQ(ierr);
2572               ierr = DMPlexReplace_Static(dm, &udm);CHKERRQ(ierr);
2573             }
2574             break;
2575           default:
2576             ierr = DMPlexCreateBoxMesh_Internal(dm, dim, simplex, faces, lower, upper, bdt, interpolate);CHKERRQ(ierr);
2577             break;
2578         }
2579       }
2580       break;
2581       case DM_SHAPE_BOX_SURFACE:
2582       {
2583         PetscInt  faces[3] = {0, 0, 0};
2584         PetscReal lower[3] = {0, 0, 0};
2585         PetscReal upper[3] = {1, 1, 1};
2586         PetscInt  i, n;
2587 
2588         n    = dim+1;
2589         for (i = 0; i < dim+1; ++i) faces[i] = (dim+1 == 1 ? 1 : 4-(dim+1));
2590         ierr = PetscOptionsIntArray("-dm_plex_box_faces", "Number of faces along each dimension", "", faces, &n, &flg);CHKERRQ(ierr);
2591         n    = 3;
2592         ierr = PetscOptionsRealArray("-dm_plex_box_lower", "Lower left corner of box", "", lower, &n, &flg);CHKERRQ(ierr);
2593         if (flg && (n != dim+1)) SETERRQ2(comm, PETSC_ERR_ARG_SIZ, "Lower box point had %D values, should have been %D", n, dim+1);
2594         n    = 3;
2595         ierr = PetscOptionsRealArray("-dm_plex_box_upper", "Upper right corner of box", "", upper, &n, &flg);CHKERRQ(ierr);
2596         if (flg && (n != dim+1)) SETERRQ2(comm, PETSC_ERR_ARG_SIZ, "Upper box point had %D values, should have been %D", n, dim+1);
2597         ierr = DMPlexCreateBoxSurfaceMesh_Internal(dm, dim+1, faces, lower, upper, interpolate);CHKERRQ(ierr);
2598       }
2599       break;
2600       case DM_SHAPE_SPHERE:
2601       {
2602         PetscReal R = 1.0;
2603 
2604         ierr = PetscOptionsReal("-dm_plex_sphere_radius", "Radius of the sphere", "", R,  &R, &flg);CHKERRQ(ierr);
2605         ierr = DMPlexCreateSphereMesh_Internal(dm, dim, simplex, R);CHKERRQ(ierr);
2606       }
2607       break;
2608       case DM_SHAPE_BALL:
2609       {
2610         PetscReal R = 1.0;
2611 
2612         ierr = PetscOptionsReal("-dm_plex_ball_radius", "Radius of the ball", "", R,  &R, &flg);CHKERRQ(ierr);
2613         ierr = DMPlexCreateBallMesh_Internal(dm, dim, R);CHKERRQ(ierr);
2614       }
2615       break;
2616       case DM_SHAPE_CYLINDER:
2617       {
2618         DMBoundaryType bdt = DM_BOUNDARY_NONE;
2619         PetscInt       Nw  = 6;
2620 
2621         ierr = PetscOptionsEnum("-dm_plex_cylinder_bd", "Boundary type in the z direction", "", DMBoundaryTypes, (PetscEnum) bdt, (PetscEnum *) &bdt, NULL);CHKERRQ(ierr);
2622         ierr = PetscOptionsInt("-dm_plex_cylinder_num_wedges", "Number of wedges around the cylinder", "", Nw, &Nw, NULL);CHKERRQ(ierr);
2623         switch (cell) {
2624           case DM_POLYTOPE_TRI_PRISM_TENSOR:
2625             ierr = DMPlexCreateWedgeCylinderMesh_Internal(dm, Nw, interpolate);CHKERRQ(ierr);
2626             break;
2627           default:
2628             ierr = DMPlexCreateHexCylinderMesh_Internal(dm, bdt);CHKERRQ(ierr);
2629             break;
2630         }
2631       }
2632       break;
2633       default: SETERRQ1(comm, PETSC_ERR_SUP, "Domain shape %s is unsupported", DMPlexShapes[shape]);
2634     }
2635   }
2636   ierr = DMPlexSetRefinementUniform(dm, PETSC_TRUE);CHKERRQ(ierr);
2637   PetscFunctionReturn(0);
2638 }
2639 
2640 PetscErrorCode DMSetFromOptions_NonRefinement_Plex(PetscOptionItems *PetscOptionsObject, DM dm)
2641 {
2642   DM_Plex       *mesh = (DM_Plex*) dm->data;
2643   PetscBool      flg;
2644   char           bdLabel[PETSC_MAX_PATH_LEN];
2645   PetscErrorCode ierr;
2646 
2647   PetscFunctionBegin;
2648   /* Handle viewing */
2649   ierr = PetscOptionsBool("-dm_plex_print_set_values", "Output all set values info", "DMPlexMatSetClosure", PETSC_FALSE, &mesh->printSetValues, NULL);CHKERRQ(ierr);
2650   ierr = PetscOptionsBoundedInt("-dm_plex_print_fem", "Debug output level all fem computations", "DMPlexSNESComputeResidualFEM", 0, &mesh->printFEM, NULL,0);CHKERRQ(ierr);
2651   ierr = PetscOptionsReal("-dm_plex_print_tol", "Tolerance for FEM output", "DMPlexSNESComputeResidualFEM", mesh->printTol, &mesh->printTol, NULL);CHKERRQ(ierr);
2652   ierr = PetscOptionsBoundedInt("-dm_plex_print_l2", "Debug output level all L2 diff computations", "DMComputeL2Diff", 0, &mesh->printL2, NULL,0);CHKERRQ(ierr);
2653   ierr = DMMonitorSetFromOptions(dm, "-dm_plex_monitor_throughput", "Monitor the simulation throughput", "DMPlexMonitorThroughput", DMPlexMonitorThroughput, NULL, &flg);CHKERRQ(ierr);
2654   if (flg) {ierr = PetscLogDefaultBegin();CHKERRQ(ierr);}
2655   /* Labeling */
2656   ierr = PetscOptionsString("-dm_plex_boundary_label", "Label to mark the mesh boundary", "", bdLabel, bdLabel, sizeof(bdLabel), &flg);CHKERRQ(ierr);
2657   if (flg) {ierr = DMPlexCreateBoundaryLabel_Private(dm, bdLabel);CHKERRQ(ierr);}
2658   /* Point Location */
2659   ierr = PetscOptionsBool("-dm_plex_hash_location", "Use grid hashing for point location", "DMInterpolate", PETSC_FALSE, &mesh->useHashLocation, NULL);CHKERRQ(ierr);
2660   /* Partitioning and distribution */
2661   ierr = PetscOptionsBool("-dm_plex_partition_balance", "Attempt to evenly divide points on partition boundary between processes", "DMPlexSetPartitionBalance", PETSC_FALSE, &mesh->partitionBalance, NULL);CHKERRQ(ierr);
2662   /* Generation and remeshing */
2663   ierr = PetscOptionsBool("-dm_plex_remesh_bd", "Allow changes to the boundary on remeshing", "DMAdapt", PETSC_FALSE, &mesh->remeshBd, NULL);CHKERRQ(ierr);
2664   /* Projection behavior */
2665   ierr = PetscOptionsBoundedInt("-dm_plex_max_projection_height", "Maxmimum mesh point height used to project locally", "DMPlexSetMaxProjectionHeight", 0, &mesh->maxProjectionHeight, NULL,0);CHKERRQ(ierr);
2666   ierr = PetscOptionsBool("-dm_plex_regular_refinement", "Use special nested projection algorithm for regular refinement", "DMPlexSetRegularRefinement", mesh->regularRefinement, &mesh->regularRefinement, NULL);CHKERRQ(ierr);
2667   /* Checking structure */
2668   {
2669     PetscBool   flg = PETSC_FALSE, flg2 = PETSC_FALSE, all = PETSC_FALSE;
2670 
2671     ierr = PetscOptionsBool("-dm_plex_check_all", "Perform all checks", NULL, PETSC_FALSE, &all, &flg2);CHKERRQ(ierr);
2672     ierr = PetscOptionsBool("-dm_plex_check_symmetry", "Check that the adjacency information in the mesh is symmetric", "DMPlexCheckSymmetry", PETSC_FALSE, &flg, &flg2);CHKERRQ(ierr);
2673     if (all || (flg && flg2)) {ierr = DMPlexCheckSymmetry(dm);CHKERRQ(ierr);}
2674     ierr = 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);CHKERRQ(ierr);
2675     if (all || (flg && flg2)) {ierr = DMPlexCheckSkeleton(dm, 0);CHKERRQ(ierr);}
2676     ierr = 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);CHKERRQ(ierr);
2677     if (all || (flg && flg2)) {ierr = DMPlexCheckFaces(dm, 0);CHKERRQ(ierr);}
2678     ierr = PetscOptionsBool("-dm_plex_check_geometry", "Check that cells have positive volume", "DMPlexCheckGeometry", PETSC_FALSE, &flg, &flg2);CHKERRQ(ierr);
2679     if (all || (flg && flg2)) {ierr = DMPlexCheckGeometry(dm);CHKERRQ(ierr);}
2680     ierr = PetscOptionsBool("-dm_plex_check_pointsf", "Check some necessary conditions for PointSF", "DMPlexCheckPointSF", PETSC_FALSE, &flg, &flg2);CHKERRQ(ierr);
2681     if (all || (flg && flg2)) {ierr = DMPlexCheckPointSF(dm);CHKERRQ(ierr);}
2682     ierr = PetscOptionsBool("-dm_plex_check_interface_cones", "Check points on inter-partition interfaces have conforming order of cone points", "DMPlexCheckInterfaceCones", PETSC_FALSE, &flg, &flg2);CHKERRQ(ierr);
2683     if (all || (flg && flg2)) {ierr = DMPlexCheckInterfaceCones(dm);CHKERRQ(ierr);}
2684     ierr = PetscOptionsBool("-dm_plex_check_cell_shape", "Check cell shape", "DMPlexCheckCellShape", PETSC_FALSE, &flg, &flg2);CHKERRQ(ierr);
2685     if (flg && flg2) {ierr = DMPlexCheckCellShape(dm, PETSC_TRUE, PETSC_DETERMINE);CHKERRQ(ierr);}
2686   }
2687   {
2688     PetscReal scale = 1.0;
2689 
2690     ierr = PetscOptionsReal("-dm_plex_scale", "Scale factor for mesh coordinates", "DMPlexScale", scale, &scale, &flg);CHKERRQ(ierr);
2691     if (flg) {
2692       Vec coordinates, coordinatesLocal;
2693 
2694       ierr = DMGetCoordinates(dm, &coordinates);CHKERRQ(ierr);
2695       ierr = DMGetCoordinatesLocal(dm, &coordinatesLocal);CHKERRQ(ierr);
2696       ierr = VecScale(coordinates, scale);CHKERRQ(ierr);
2697       ierr = VecScale(coordinatesLocal, scale);CHKERRQ(ierr);
2698     }
2699   }
2700   ierr = PetscPartitionerSetFromOptions(mesh->partitioner);CHKERRQ(ierr);
2701   PetscFunctionReturn(0);
2702 }
2703 
2704 static PetscErrorCode DMSetFromOptions_Plex(PetscOptionItems *PetscOptionsObject,DM dm)
2705 {
2706   PetscFunctionList ordlist;
2707   char              oname[256];
2708   PetscReal         volume = -1.0;
2709   PetscInt          prerefine = 0, refine = 0, r, coarsen = 0, overlap = 0, extLayers = 0, dim;
2710   PetscBool         uniformOrig, created = PETSC_FALSE, uniform = PETSC_TRUE, distribute = PETSC_FALSE, interpolate = PETSC_TRUE, coordSpace = PETSC_TRUE, remap = PETSC_TRUE, ghostCells = PETSC_FALSE, isHierarchy, ignoreModel = PETSC_FALSE, flg;
2711   PetscErrorCode ierr;
2712 
2713   PetscFunctionBegin;
2714   PetscValidHeaderSpecific(dm, DM_CLASSID, 2);
2715   ierr = PetscOptionsHead(PetscOptionsObject,"DMPlex Options");CHKERRQ(ierr);
2716   /* Handle automatic creation */
2717   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
2718   if (dim < 0) {ierr = DMPlexCreateFromOptions_Internal(PetscOptionsObject, &coordSpace, dm);CHKERRQ(ierr);created = PETSC_TRUE;}
2719   /* Handle interpolation before distribution */
2720   ierr = PetscOptionsBool("-dm_plex_interpolate_pre", "Flag to interpolate mesh before distribution", "", interpolate, &interpolate, &flg);CHKERRQ(ierr);
2721   if (flg) {
2722     DMPlexInterpolatedFlag interpolated;
2723 
2724     ierr = DMPlexIsInterpolated(dm, &interpolated);CHKERRQ(ierr);
2725     if (interpolated == DMPLEX_INTERPOLATED_FULL && !interpolate) {
2726       DM udm;
2727 
2728       ierr = DMPlexUninterpolate(dm, &udm);CHKERRQ(ierr);
2729       ierr = DMPlexReplace_Static(dm, &udm);CHKERRQ(ierr);
2730     } else if (interpolated != DMPLEX_INTERPOLATED_FULL && interpolate) {
2731       DM idm;
2732 
2733       ierr = DMPlexInterpolate(dm, &idm);CHKERRQ(ierr);
2734       ierr = DMPlexReplace_Static(dm, &idm);CHKERRQ(ierr);
2735     }
2736   }
2737   /* Handle DMPlex refinement before distribution */
2738   ierr = PetscOptionsBool("-dm_refine_ignore_model", "Flag to ignore the geometry model when refining", "DMCreate", ignoreModel, &ignoreModel, &flg);CHKERRQ(ierr);
2739   if (flg) {((DM_Plex *) dm->data)->ignoreModel = ignoreModel;}
2740   ierr = DMPlexGetRefinementUniform(dm, &uniformOrig);CHKERRQ(ierr);
2741   ierr = PetscOptionsBoundedInt("-dm_refine_pre", "The number of refinements before distribution", "DMCreate", prerefine, &prerefine, NULL,0);CHKERRQ(ierr);
2742   ierr = PetscOptionsBool("-dm_refine_remap_pre", "Flag to control coordinate remapping", "DMCreate", remap, &remap, NULL);CHKERRQ(ierr);
2743   ierr = PetscOptionsBool("-dm_refine_uniform_pre", "Flag for uniform refinement before distribution", "DMCreate", uniform, &uniform, &flg);CHKERRQ(ierr);
2744   if (flg) {ierr = DMPlexSetRefinementUniform(dm, uniform);CHKERRQ(ierr);}
2745   ierr = PetscOptionsReal("-dm_refine_volume_limit_pre", "The maximum cell volume after refinement before distribution", "DMCreate", volume, &volume, &flg);CHKERRQ(ierr);
2746   if (flg) {
2747     ierr = DMPlexSetRefinementUniform(dm, PETSC_FALSE);CHKERRQ(ierr);
2748     ierr = DMPlexSetRefinementLimit(dm, volume);CHKERRQ(ierr);
2749     prerefine = PetscMax(prerefine, 1);
2750   }
2751   for (r = 0; r < prerefine; ++r) {
2752     DM             rdm;
2753     PetscPointFunc coordFunc = ((DM_Plex*) dm->data)->coordFunc;
2754 
2755     ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2756     ierr = DMRefine(dm, PetscObjectComm((PetscObject) dm), &rdm);CHKERRQ(ierr);
2757     ierr = DMPlexReplace_Static(dm, &rdm);CHKERRQ(ierr);
2758     ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2759     if (coordFunc && remap) {
2760       ierr = DMPlexRemapGeometry(dm, 0.0, coordFunc);CHKERRQ(ierr);
2761       ((DM_Plex*) dm->data)->coordFunc = coordFunc;
2762     }
2763   }
2764   ierr = DMPlexSetRefinementUniform(dm, uniformOrig);CHKERRQ(ierr);
2765   /* Handle DMPlex extrusion before distribution */
2766   ierr = PetscOptionsBoundedInt("-dm_extrude", "The number of layers to extrude", "", extLayers, &extLayers, NULL, 0);CHKERRQ(ierr);
2767   if (extLayers) {
2768     DM edm;
2769 
2770     ierr = DMExtrude(dm, extLayers, &edm);CHKERRQ(ierr);
2771     ierr = DMPlexReplace_Static(dm, &edm);CHKERRQ(ierr);
2772     ((DM_Plex *) dm->data)->coordFunc = NULL;
2773     ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2774     extLayers = 0;
2775   }
2776   /* Handle DMPlex reordering before distribution */
2777   ierr = MatGetOrderingList(&ordlist);CHKERRQ(ierr);
2778   ierr = PetscOptionsFList("-dm_plex_reorder", "Set mesh reordering type", "DMPlexGetOrdering", ordlist, MATORDERINGNATURAL, oname, sizeof(oname), &flg);CHKERRQ(ierr);
2779   if (flg) {
2780     DM pdm;
2781     IS perm;
2782 
2783     ierr = DMPlexGetOrdering(dm, oname, NULL, &perm);CHKERRQ(ierr);
2784     ierr = DMPlexPermute(dm, perm, &pdm);CHKERRQ(ierr);
2785     ierr = ISDestroy(&perm);CHKERRQ(ierr);
2786     ierr = DMPlexReplace_Static(dm, &pdm);CHKERRQ(ierr);
2787     ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2788   }
2789   /* TODO Old-style extrusion which can be removed */
2790   ierr = PetscOptionsBool("-dm_plex_interpolate", "Flag to create edges and faces automatically", "", interpolate, &interpolate, NULL);CHKERRQ(ierr);
2791   /* Handle DMPlex distribution */
2792   ierr = PetscOptionsBool("-dm_distribute", "Flag to redistribute a mesh among processes", "DMCreate", distribute, &distribute, NULL);CHKERRQ(ierr);
2793   ierr = PetscOptionsBoundedInt("-dm_distribute_overlap", "The size of the overlap halo", "DMCreate", overlap, &overlap, NULL, 0);CHKERRQ(ierr);
2794   if (distribute) {
2795     DM               pdm = NULL;
2796     PetscPartitioner part;
2797 
2798     ierr = DMPlexGetPartitioner(dm, &part);CHKERRQ(ierr);
2799     ierr = PetscPartitionerSetFromOptions(part);CHKERRQ(ierr);
2800     ierr = DMPlexDistribute(dm, overlap, NULL, &pdm);CHKERRQ(ierr);
2801     if (pdm) {
2802       ierr = DMPlexReplace_Static(dm, &pdm);CHKERRQ(ierr);
2803     }
2804   }
2805   /* Create coordinate space */
2806   if (created) {
2807     DM_Plex  *mesh = (DM_Plex *) dm->data;
2808     PetscInt  degree = 1;
2809     PetscBool periodic, flg;
2810 
2811     ierr = PetscOptionsBool("-dm_coord_space", "Use an FEM space for coordinates", "", coordSpace, &coordSpace, &flg);CHKERRQ(ierr);
2812     ierr = PetscOptionsInt("-dm_coord_petscspace_degree", "FEM degree for coordinate space", "", degree, &degree, NULL);CHKERRQ(ierr);
2813     if (coordSpace) {ierr = DMPlexCreateCoordinateSpace(dm, degree, mesh->coordFunc);CHKERRQ(ierr);}
2814     if (flg && !coordSpace) {
2815       DM           cdm;
2816       PetscDS      cds;
2817       PetscObject  obj;
2818       PetscClassId id;
2819 
2820       ierr = DMGetCoordinateDM(dm, &cdm);CHKERRQ(ierr);
2821       ierr = DMGetDS(cdm, &cds);CHKERRQ(ierr);
2822       ierr = PetscDSGetDiscretization(cds, 0, &obj);CHKERRQ(ierr);
2823       ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
2824       if (id == PETSCFE_CLASSID) {
2825         PetscContainer dummy;
2826 
2827         ierr = PetscContainerCreate(PETSC_COMM_SELF, &dummy);CHKERRQ(ierr);
2828         ierr = PetscObjectSetName((PetscObject) dummy, "coordinates");CHKERRQ(ierr);
2829         ierr = DMSetField(cdm, 0, NULL, (PetscObject) dummy);CHKERRQ(ierr);
2830         ierr = PetscContainerDestroy(&dummy);CHKERRQ(ierr);
2831         ierr = DMClearDS(cdm);CHKERRQ(ierr);
2832       }
2833       mesh->coordFunc = NULL;
2834     }
2835     ierr = DMLocalizeCoordinates(dm);CHKERRQ(ierr);
2836     ierr = DMGetPeriodicity(dm, &periodic, NULL, NULL, NULL);CHKERRQ(ierr);
2837     if (periodic) {ierr = DMSetPeriodicity(dm, PETSC_TRUE, NULL, NULL, NULL);CHKERRQ(ierr);}
2838   }
2839   /* Handle DMPlex refinement */
2840   remap = PETSC_TRUE;
2841   ierr = PetscOptionsBoundedInt("-dm_refine", "The number of uniform refinements", "DMCreate", refine, &refine, NULL,0);CHKERRQ(ierr);
2842   ierr = PetscOptionsBool("-dm_refine_remap", "Flag to control coordinate remapping", "DMCreate", remap, &remap, NULL);CHKERRQ(ierr);
2843   ierr = PetscOptionsBoundedInt("-dm_refine_hierarchy", "The number of uniform refinements", "DMCreate", refine, &refine, &isHierarchy,0);CHKERRQ(ierr);
2844   if (refine) {ierr = DMPlexSetRefinementUniform(dm, PETSC_TRUE);CHKERRQ(ierr);}
2845   if (refine && isHierarchy) {
2846     DM *dms, coarseDM;
2847 
2848     ierr = DMGetCoarseDM(dm, &coarseDM);CHKERRQ(ierr);
2849     ierr = PetscObjectReference((PetscObject)coarseDM);CHKERRQ(ierr);
2850     ierr = PetscMalloc1(refine,&dms);CHKERRQ(ierr);
2851     ierr = DMRefineHierarchy(dm, refine, dms);CHKERRQ(ierr);
2852     /* Total hack since we do not pass in a pointer */
2853     ierr = DMPlexSwap_Static(dm, dms[refine-1]);CHKERRQ(ierr);
2854     if (refine == 1) {
2855       ierr = DMSetCoarseDM(dm, dms[0]);CHKERRQ(ierr);
2856       ierr = DMPlexSetRegularRefinement(dm, PETSC_TRUE);CHKERRQ(ierr);
2857     } else {
2858       ierr = DMSetCoarseDM(dm, dms[refine-2]);CHKERRQ(ierr);
2859       ierr = DMPlexSetRegularRefinement(dm, PETSC_TRUE);CHKERRQ(ierr);
2860       ierr = DMSetCoarseDM(dms[0], dms[refine-1]);CHKERRQ(ierr);
2861       ierr = DMPlexSetRegularRefinement(dms[0], PETSC_TRUE);CHKERRQ(ierr);
2862     }
2863     ierr = DMSetCoarseDM(dms[refine-1], coarseDM);CHKERRQ(ierr);
2864     ierr = PetscObjectDereference((PetscObject)coarseDM);CHKERRQ(ierr);
2865     /* Free DMs */
2866     for (r = 0; r < refine; ++r) {
2867       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dms[r]);CHKERRQ(ierr);
2868       ierr = DMDestroy(&dms[r]);CHKERRQ(ierr);
2869     }
2870     ierr = PetscFree(dms);CHKERRQ(ierr);
2871   } else {
2872     for (r = 0; r < refine; ++r) {
2873       DM             rdm;
2874       PetscPointFunc coordFunc = ((DM_Plex*) dm->data)->coordFunc;
2875 
2876       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2877       ierr = DMRefine(dm, PetscObjectComm((PetscObject) dm), &rdm);CHKERRQ(ierr);
2878       /* Total hack since we do not pass in a pointer */
2879       ierr = DMPlexReplace_Static(dm, &rdm);CHKERRQ(ierr);
2880       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2881       if (coordFunc && remap) {
2882         ierr = DMPlexRemapGeometry(dm, 0.0, coordFunc);CHKERRQ(ierr);
2883         ((DM_Plex*) dm->data)->coordFunc = coordFunc;
2884       }
2885     }
2886   }
2887   /* Handle DMPlex coarsening */
2888   ierr = PetscOptionsBoundedInt("-dm_coarsen", "Coarsen the mesh", "DMCreate", coarsen, &coarsen, NULL,0);CHKERRQ(ierr);
2889   ierr = PetscOptionsBoundedInt("-dm_coarsen_hierarchy", "The number of coarsenings", "DMCreate", coarsen, &coarsen, &isHierarchy,0);CHKERRQ(ierr);
2890   if (coarsen && isHierarchy) {
2891     DM *dms;
2892 
2893     ierr = PetscMalloc1(coarsen, &dms);CHKERRQ(ierr);
2894     ierr = DMCoarsenHierarchy(dm, coarsen, dms);CHKERRQ(ierr);
2895     /* Free DMs */
2896     for (r = 0; r < coarsen; ++r) {
2897       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dms[r]);CHKERRQ(ierr);
2898       ierr = DMDestroy(&dms[r]);CHKERRQ(ierr);
2899     }
2900     ierr = PetscFree(dms);CHKERRQ(ierr);
2901   } else {
2902     for (r = 0; r < coarsen; ++r) {
2903       DM             cdm;
2904       PetscPointFunc coordFunc = ((DM_Plex*) dm->data)->coordFunc;
2905 
2906       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2907       ierr = DMCoarsen(dm, PetscObjectComm((PetscObject) dm), &cdm);CHKERRQ(ierr);
2908       /* Total hack since we do not pass in a pointer */
2909       ierr = DMPlexReplace_Static(dm, &cdm);CHKERRQ(ierr);
2910       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2911       if (coordFunc) {
2912         ierr = DMPlexRemapGeometry(dm, 0.0, coordFunc);CHKERRQ(ierr);
2913         ((DM_Plex*) dm->data)->coordFunc = coordFunc;
2914       }
2915     }
2916   }
2917   /* Handle ghost cells */
2918   ierr = PetscOptionsBool("-dm_plex_create_fv_ghost_cells", "Flag to create finite volume ghost cells on the boundary", "DMCreate", ghostCells, &ghostCells, NULL);CHKERRQ(ierr);
2919   if (ghostCells) {
2920     DM   gdm;
2921     char lname[PETSC_MAX_PATH_LEN];
2922 
2923     lname[0] = '\0';
2924     ierr = PetscOptionsString("-dm_plex_fv_ghost_cells_label", "Label name for ghost cells boundary", "DMCreate", lname, lname, sizeof(lname), &flg);CHKERRQ(ierr);
2925     ierr = DMPlexConstructGhostCells(dm, flg ? lname : NULL, NULL, &gdm);CHKERRQ(ierr);
2926     ierr = DMPlexReplace_Static(dm, &gdm);CHKERRQ(ierr);
2927   }
2928   /* Handle */
2929   ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2930   ierr = PetscOptionsTail();CHKERRQ(ierr);
2931   PetscFunctionReturn(0);
2932 }
2933 
2934 static PetscErrorCode DMCreateGlobalVector_Plex(DM dm,Vec *vec)
2935 {
2936   PetscErrorCode ierr;
2937 
2938   PetscFunctionBegin;
2939   ierr = DMCreateGlobalVector_Section_Private(dm,vec);CHKERRQ(ierr);
2940   /* ierr = VecSetOperation(*vec, VECOP_DUPLICATE, (void(*)(void)) VecDuplicate_MPI_DM);CHKERRQ(ierr); */
2941   ierr = VecSetOperation(*vec, VECOP_VIEW, (void (*)(void)) VecView_Plex);CHKERRQ(ierr);
2942   ierr = VecSetOperation(*vec, VECOP_VIEWNATIVE, (void (*)(void)) VecView_Plex_Native);CHKERRQ(ierr);
2943   ierr = VecSetOperation(*vec, VECOP_LOAD, (void (*)(void)) VecLoad_Plex);CHKERRQ(ierr);
2944   ierr = VecSetOperation(*vec, VECOP_LOADNATIVE, (void (*)(void)) VecLoad_Plex_Native);CHKERRQ(ierr);
2945   PetscFunctionReturn(0);
2946 }
2947 
2948 static PetscErrorCode DMCreateLocalVector_Plex(DM dm,Vec *vec)
2949 {
2950   PetscErrorCode ierr;
2951 
2952   PetscFunctionBegin;
2953   ierr = DMCreateLocalVector_Section_Private(dm,vec);CHKERRQ(ierr);
2954   ierr = VecSetOperation(*vec, VECOP_VIEW, (void (*)(void)) VecView_Plex_Local);CHKERRQ(ierr);
2955   ierr = VecSetOperation(*vec, VECOP_LOAD, (void (*)(void)) VecLoad_Plex_Local);CHKERRQ(ierr);
2956   PetscFunctionReturn(0);
2957 }
2958 
2959 static PetscErrorCode DMGetDimPoints_Plex(DM dm, PetscInt dim, PetscInt *pStart, PetscInt *pEnd)
2960 {
2961   PetscInt       depth, d;
2962   PetscErrorCode ierr;
2963 
2964   PetscFunctionBegin;
2965   ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
2966   if (depth == 1) {
2967     ierr = DMGetDimension(dm, &d);CHKERRQ(ierr);
2968     if (dim == 0)      {ierr = DMPlexGetDepthStratum(dm, dim, pStart, pEnd);CHKERRQ(ierr);}
2969     else if (dim == d) {ierr = DMPlexGetDepthStratum(dm, 1, pStart, pEnd);CHKERRQ(ierr);}
2970     else               {*pStart = 0; *pEnd = 0;}
2971   } else {
2972     ierr = DMPlexGetDepthStratum(dm, dim, pStart, pEnd);CHKERRQ(ierr);
2973   }
2974   PetscFunctionReturn(0);
2975 }
2976 
2977 static PetscErrorCode DMGetNeighbors_Plex(DM dm, PetscInt *nranks, const PetscMPIInt *ranks[])
2978 {
2979   PetscSF           sf;
2980   PetscInt          niranks, njranks, n;
2981   const PetscMPIInt *iranks, *jranks;
2982   DM_Plex           *data = (DM_Plex*) dm->data;
2983   PetscErrorCode    ierr;
2984 
2985   PetscFunctionBegin;
2986   ierr = DMGetPointSF(dm, &sf);CHKERRQ(ierr);
2987   if (!data->neighbors) {
2988     ierr = PetscSFSetUp(sf);CHKERRQ(ierr);
2989     ierr = PetscSFGetRootRanks(sf, &njranks, &jranks, NULL, NULL, NULL);CHKERRQ(ierr);
2990     ierr = PetscSFGetLeafRanks(sf, &niranks, &iranks, NULL, NULL);CHKERRQ(ierr);
2991     ierr = PetscMalloc1(njranks + niranks + 1, &data->neighbors);CHKERRQ(ierr);
2992     ierr = PetscArraycpy(data->neighbors + 1, jranks, njranks);CHKERRQ(ierr);
2993     ierr = PetscArraycpy(data->neighbors + njranks + 1, iranks, niranks);CHKERRQ(ierr);
2994     n = njranks + niranks;
2995     ierr = PetscSortRemoveDupsMPIInt(&n, data->neighbors + 1);CHKERRQ(ierr);
2996     /* The following cast should never fail: can't have more neighbors than PETSC_MPI_INT_MAX */
2997     ierr = PetscMPIIntCast(n, data->neighbors);CHKERRQ(ierr);
2998   }
2999   if (nranks) *nranks = data->neighbors[0];
3000   if (ranks) {
3001     if (data->neighbors[0]) *ranks = data->neighbors + 1;
3002     else                    *ranks = NULL;
3003   }
3004   PetscFunctionReturn(0);
3005 }
3006 
3007 PETSC_INTERN PetscErrorCode DMInterpolateSolution_Plex(DM, DM, Mat, Vec, Vec);
3008 
3009 static PetscErrorCode DMInitialize_Plex(DM dm)
3010 {
3011   PetscErrorCode ierr;
3012 
3013   PetscFunctionBegin;
3014   dm->ops->view                            = DMView_Plex;
3015   dm->ops->load                            = DMLoad_Plex;
3016   dm->ops->setfromoptions                  = DMSetFromOptions_Plex;
3017   dm->ops->clone                           = DMClone_Plex;
3018   dm->ops->setup                           = DMSetUp_Plex;
3019   dm->ops->createlocalsection              = DMCreateLocalSection_Plex;
3020   dm->ops->createdefaultconstraints        = DMCreateDefaultConstraints_Plex;
3021   dm->ops->createglobalvector              = DMCreateGlobalVector_Plex;
3022   dm->ops->createlocalvector               = DMCreateLocalVector_Plex;
3023   dm->ops->getlocaltoglobalmapping         = NULL;
3024   dm->ops->createfieldis                   = NULL;
3025   dm->ops->createcoordinatedm              = DMCreateCoordinateDM_Plex;
3026   dm->ops->createcoordinatefield           = DMCreateCoordinateField_Plex;
3027   dm->ops->getcoloring                     = NULL;
3028   dm->ops->creatematrix                    = DMCreateMatrix_Plex;
3029   dm->ops->createinterpolation             = DMCreateInterpolation_Plex;
3030   dm->ops->createmassmatrix                = DMCreateMassMatrix_Plex;
3031   dm->ops->createinjection                 = DMCreateInjection_Plex;
3032   dm->ops->refine                          = DMRefine_Plex;
3033   dm->ops->coarsen                         = DMCoarsen_Plex;
3034   dm->ops->refinehierarchy                 = DMRefineHierarchy_Plex;
3035   dm->ops->coarsenhierarchy                = DMCoarsenHierarchy_Plex;
3036   dm->ops->adaptlabel                      = DMAdaptLabel_Plex;
3037   dm->ops->adaptmetric                     = DMAdaptMetric_Plex;
3038   dm->ops->extrude                         = DMExtrude_Plex;
3039   dm->ops->globaltolocalbegin              = NULL;
3040   dm->ops->globaltolocalend                = NULL;
3041   dm->ops->localtoglobalbegin              = NULL;
3042   dm->ops->localtoglobalend                = NULL;
3043   dm->ops->destroy                         = DMDestroy_Plex;
3044   dm->ops->createsubdm                     = DMCreateSubDM_Plex;
3045   dm->ops->createsuperdm                   = DMCreateSuperDM_Plex;
3046   dm->ops->getdimpoints                    = DMGetDimPoints_Plex;
3047   dm->ops->locatepoints                    = DMLocatePoints_Plex;
3048   dm->ops->projectfunctionlocal            = DMProjectFunctionLocal_Plex;
3049   dm->ops->projectfunctionlabellocal       = DMProjectFunctionLabelLocal_Plex;
3050   dm->ops->projectfieldlocal               = DMProjectFieldLocal_Plex;
3051   dm->ops->projectfieldlabellocal          = DMProjectFieldLabelLocal_Plex;
3052   dm->ops->projectbdfieldlabellocal        = DMProjectBdFieldLabelLocal_Plex;
3053   dm->ops->computel2diff                   = DMComputeL2Diff_Plex;
3054   dm->ops->computel2gradientdiff           = DMComputeL2GradientDiff_Plex;
3055   dm->ops->computel2fielddiff              = DMComputeL2FieldDiff_Plex;
3056   dm->ops->getneighbors                    = DMGetNeighbors_Plex;
3057   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMPlexInsertBoundaryValues_C",DMPlexInsertBoundaryValues_Plex);CHKERRQ(ierr);
3058   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMPlexInsertTimeDerviativeBoundaryValues_C",DMPlexInsertTimeDerivativeBoundaryValues_Plex);CHKERRQ(ierr);
3059   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMSetUpGLVisViewer_C",DMSetUpGLVisViewer_Plex);CHKERRQ(ierr);
3060   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMCreateNeumannOverlap_C",DMCreateNeumannOverlap_Plex);CHKERRQ(ierr);
3061   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMPlexGetOverlap_C",DMPlexGetOverlap_Plex);CHKERRQ(ierr);
3062   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMInterpolateSolution_C",DMInterpolateSolution_Plex);CHKERRQ(ierr);
3063   PetscFunctionReturn(0);
3064 }
3065 
3066 PETSC_INTERN PetscErrorCode DMClone_Plex(DM dm, DM *newdm)
3067 {
3068   DM_Plex        *mesh = (DM_Plex *) dm->data;
3069   PetscErrorCode ierr;
3070 
3071   PetscFunctionBegin;
3072   mesh->refct++;
3073   (*newdm)->data = mesh;
3074   ierr = PetscObjectChangeTypeName((PetscObject) *newdm, DMPLEX);CHKERRQ(ierr);
3075   ierr = DMInitialize_Plex(*newdm);CHKERRQ(ierr);
3076   PetscFunctionReturn(0);
3077 }
3078 
3079 /*MC
3080   DMPLEX = "plex" - A DM object that encapsulates an unstructured mesh, or CW Complex, which can be expressed using a Hasse Diagram.
3081                     In the local representation, Vecs contain all unknowns in the interior and shared boundary. This is
3082                     specified by a PetscSection object. Ownership in the global representation is determined by
3083                     ownership of the underlying DMPlex points. This is specified by another PetscSection object.
3084 
3085   Options Database Keys:
3086 + -dm_refine_pre                     - Refine mesh before distribution
3087 + -dm_refine_uniform_pre             - Choose uniform or generator-based refinement
3088 + -dm_refine_volume_limit_pre        - Cell volume limit after pre-refinement using generator
3089 . -dm_distribute                     - Distribute mesh across processes
3090 . -dm_distribute_overlap             - Number of cells to overlap for distribution
3091 . -dm_refine                         - Refine mesh after distribution
3092 . -dm_plex_hash_location             - Use grid hashing for point location
3093 . -dm_plex_hash_box_faces <n,m,p>    - The number of divisions in each direction of the grid hash
3094 . -dm_plex_partition_balance         - Attempt to evenly divide points on partition boundary between processes
3095 . -dm_plex_remesh_bd                 - Allow changes to the boundary on remeshing
3096 . -dm_plex_max_projection_height     - Maxmimum mesh point height used to project locally
3097 . -dm_plex_regular_refinement        - Use special nested projection algorithm for regular refinement
3098 . -dm_plex_check_all                 - Perform all shecks below
3099 . -dm_plex_check_symmetry            - Check that the adjacency information in the mesh is symmetric
3100 . -dm_plex_check_skeleton <celltype> - Check that each cell has the correct number of vertices
3101 . -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
3102 . -dm_plex_check_geometry            - Check that cells have positive volume
3103 . -dm_view :mesh.tex:ascii_latex     - View the mesh in LaTeX/TikZ
3104 . -dm_plex_view_scale <num>          - Scale the TikZ
3105 - -dm_plex_print_fem <num>           - View FEM assembly information, such as element vectors and matrices
3106 
3107   Level: intermediate
3108 
3109 .seealso: DMType, DMPlexCreate(), DMCreate(), DMSetType()
3110 M*/
3111 
3112 PETSC_EXTERN PetscErrorCode DMCreate_Plex(DM dm)
3113 {
3114   DM_Plex       *mesh;
3115   PetscInt       unit;
3116   PetscErrorCode ierr;
3117 
3118   PetscFunctionBegin;
3119   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
3120   ierr     = PetscNewLog(dm,&mesh);CHKERRQ(ierr);
3121   dm->data = mesh;
3122 
3123   mesh->refct             = 1;
3124   ierr                    = PetscSectionCreate(PetscObjectComm((PetscObject)dm), &mesh->coneSection);CHKERRQ(ierr);
3125   mesh->maxConeSize       = 0;
3126   mesh->cones             = NULL;
3127   mesh->coneOrientations  = NULL;
3128   ierr                    = PetscSectionCreate(PetscObjectComm((PetscObject)dm), &mesh->supportSection);CHKERRQ(ierr);
3129   mesh->maxSupportSize    = 0;
3130   mesh->supports          = NULL;
3131   mesh->refinementUniform = PETSC_TRUE;
3132   mesh->refinementLimit   = -1.0;
3133   mesh->interpolated      = DMPLEX_INTERPOLATED_INVALID;
3134   mesh->interpolatedCollective = DMPLEX_INTERPOLATED_INVALID;
3135 
3136   mesh->facesTmp = NULL;
3137 
3138   mesh->tetgenOpts   = NULL;
3139   mesh->triangleOpts = NULL;
3140   ierr = PetscPartitionerCreate(PetscObjectComm((PetscObject)dm), &mesh->partitioner);CHKERRQ(ierr);
3141   mesh->remeshBd     = PETSC_FALSE;
3142 
3143   mesh->subpointMap = NULL;
3144 
3145   for (unit = 0; unit < NUM_PETSC_UNITS; ++unit) mesh->scale[unit] = 1.0;
3146 
3147   mesh->regularRefinement   = PETSC_FALSE;
3148   mesh->depthState          = -1;
3149   mesh->celltypeState       = -1;
3150   mesh->globalVertexNumbers = NULL;
3151   mesh->globalCellNumbers   = NULL;
3152   mesh->anchorSection       = NULL;
3153   mesh->anchorIS            = NULL;
3154   mesh->createanchors       = NULL;
3155   mesh->computeanchormatrix = NULL;
3156   mesh->parentSection       = NULL;
3157   mesh->parents             = NULL;
3158   mesh->childIDs            = NULL;
3159   mesh->childSection        = NULL;
3160   mesh->children            = NULL;
3161   mesh->referenceTree       = NULL;
3162   mesh->getchildsymmetry    = NULL;
3163   mesh->vtkCellHeight       = 0;
3164   mesh->useAnchors          = PETSC_FALSE;
3165 
3166   mesh->maxProjectionHeight = 0;
3167 
3168   mesh->neighbors           = NULL;
3169 
3170   mesh->printSetValues = PETSC_FALSE;
3171   mesh->printFEM       = 0;
3172   mesh->printTol       = 1.0e-10;
3173 
3174   ierr = DMInitialize_Plex(dm);CHKERRQ(ierr);
3175   PetscFunctionReturn(0);
3176 }
3177 
3178 /*@
3179   DMPlexCreate - Creates a DMPlex object, which encapsulates an unstructured mesh, or CW complex, which can be expressed using a Hasse Diagram.
3180 
3181   Collective
3182 
3183   Input Parameter:
3184 . comm - The communicator for the DMPlex object
3185 
3186   Output Parameter:
3187 . mesh  - The DMPlex object
3188 
3189   Level: beginner
3190 
3191 @*/
3192 PetscErrorCode DMPlexCreate(MPI_Comm comm, DM *mesh)
3193 {
3194   PetscErrorCode ierr;
3195 
3196   PetscFunctionBegin;
3197   PetscValidPointer(mesh,2);
3198   ierr = DMCreate(comm, mesh);CHKERRQ(ierr);
3199   ierr = DMSetType(*mesh, DMPLEX);CHKERRQ(ierr);
3200   PetscFunctionReturn(0);
3201 }
3202 
3203 /*@C
3204   DMPlexBuildFromCellListParallel - Build distributed DMPLEX topology from a list of vertices for each cell (common mesh generator output)
3205 
3206   Input Parameters:
3207 + dm - The DM
3208 . numCells - The number of cells owned by this process
3209 . numVertices - The number of vertices owned by this process, or PETSC_DECIDE
3210 . NVertices - The global number of vertices, or PETSC_DECIDE
3211 . numCorners - The number of vertices for each cell
3212 - cells - An array of numCells*numCorners numbers, the global vertex numbers for each cell
3213 
3214   Output Parameter:
3215 . vertexSF - (Optional) SF describing complete vertex ownership
3216 
3217   Notes:
3218   Two triangles sharing a face
3219 $
3220 $        2
3221 $      / | \
3222 $     /  |  \
3223 $    /   |   \
3224 $   0  0 | 1  3
3225 $    \   |   /
3226 $     \  |  /
3227 $      \ | /
3228 $        1
3229 would have input
3230 $  numCells = 2, numVertices = 4
3231 $  cells = [0 1 2  1 3 2]
3232 $
3233 which would result in the DMPlex
3234 $
3235 $        4
3236 $      / | \
3237 $     /  |  \
3238 $    /   |   \
3239 $   2  0 | 1  5
3240 $    \   |   /
3241 $     \  |  /
3242 $      \ | /
3243 $        3
3244 
3245   Vertices are implicitly numbered consecutively 0,...,NVertices.
3246   Each rank owns a chunk of numVertices consecutive vertices.
3247   If numVertices is PETSC_DECIDE, PETSc will distribute them as evenly as possible using PetscLayout.
3248   If both NVertices and numVertices are PETSC_DECIDE, NVertices is computed by PETSc as the maximum vertex index in cells + 1.
3249   If only NVertices is PETSC_DECIDE, it is computed as the sum of numVertices over all ranks.
3250 
3251   The cell distribution is arbitrary non-overlapping, independent of the vertex distribution.
3252 
3253   Not currently supported in Fortran.
3254 
3255   Level: advanced
3256 
3257 .seealso: DMPlexBuildFromCellList(), DMPlexCreateFromCellListParallelPetsc(), DMPlexBuildCoordinatesFromCellListParallel()
3258 @*/
3259 PetscErrorCode DMPlexBuildFromCellListParallel(DM dm, PetscInt numCells, PetscInt numVertices, PetscInt NVertices, PetscInt numCorners, const PetscInt cells[], PetscSF *vertexSF)
3260 {
3261   PetscSF         sfPoint;
3262   PetscLayout     layout;
3263   PetscInt        numVerticesAdj, *verticesAdj, *cones, c, p, dim;
3264   PetscMPIInt     rank, size;
3265   PetscErrorCode  ierr;
3266 
3267   PetscFunctionBegin;
3268   PetscValidLogicalCollectiveInt(dm,NVertices,4);
3269   ierr = PetscLogEventBegin(DMPLEX_BuildFromCellList,dm,0,0,0);CHKERRQ(ierr);
3270   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject) dm), &rank);CHKERRMPI(ierr);
3271   ierr = MPI_Comm_size(PetscObjectComm((PetscObject) dm), &size);CHKERRMPI(ierr);
3272   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
3273   /* Get/check global number of vertices */
3274   {
3275     PetscInt NVerticesInCells, i;
3276     const PetscInt len = numCells * numCorners;
3277 
3278     /* NVerticesInCells = max(cells) + 1 */
3279     NVerticesInCells = PETSC_MIN_INT;
3280     for (i=0; i<len; i++) if (cells[i] > NVerticesInCells) NVerticesInCells = cells[i];
3281     ++NVerticesInCells;
3282     ierr = MPI_Allreduce(MPI_IN_PLACE, &NVerticesInCells, 1, MPIU_INT, MPI_MAX, PetscObjectComm((PetscObject) dm));CHKERRMPI(ierr);
3283 
3284     if (numVertices == PETSC_DECIDE && NVertices == PETSC_DECIDE) NVertices = NVerticesInCells;
3285     else if (NVertices != PETSC_DECIDE && NVertices < NVerticesInCells) SETERRQ2(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_WRONG, "Specified global number of vertices %D must be greater than or equal to the number of vertices in cells %D",NVertices,NVerticesInCells);
3286   }
3287   /* Count locally unique vertices */
3288   {
3289     PetscHSetI vhash;
3290     PetscInt off = 0;
3291 
3292     ierr = PetscHSetICreate(&vhash);CHKERRQ(ierr);
3293     for (c = 0; c < numCells; ++c) {
3294       for (p = 0; p < numCorners; ++p) {
3295         ierr = PetscHSetIAdd(vhash, cells[c*numCorners+p]);CHKERRQ(ierr);
3296       }
3297     }
3298     ierr = PetscHSetIGetSize(vhash, &numVerticesAdj);CHKERRQ(ierr);
3299     ierr = PetscMalloc1(numVerticesAdj, &verticesAdj);CHKERRQ(ierr);
3300     ierr = PetscHSetIGetElems(vhash, &off, verticesAdj);CHKERRQ(ierr);
3301     ierr = PetscHSetIDestroy(&vhash);CHKERRQ(ierr);
3302     if (off != numVerticesAdj) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Invalid number of local vertices %D should be %D", off, numVerticesAdj);
3303   }
3304   ierr = PetscSortInt(numVerticesAdj, verticesAdj);CHKERRQ(ierr);
3305   /* Create cones */
3306   ierr = DMPlexSetChart(dm, 0, numCells+numVerticesAdj);CHKERRQ(ierr);
3307   for (c = 0; c < numCells; ++c) {ierr = DMPlexSetConeSize(dm, c, numCorners);CHKERRQ(ierr);}
3308   ierr = DMSetUp(dm);CHKERRQ(ierr);
3309   ierr = DMPlexGetCones(dm,&cones);CHKERRQ(ierr);
3310   for (c = 0; c < numCells; ++c) {
3311     for (p = 0; p < numCorners; ++p) {
3312       const PetscInt gv = cells[c*numCorners+p];
3313       PetscInt       lv;
3314 
3315       /* Positions within verticesAdj form 0-based local vertex numbering;
3316          we need to shift it by numCells to get correct DAG points (cells go first) */
3317       ierr = PetscFindInt(gv, numVerticesAdj, verticesAdj, &lv);CHKERRQ(ierr);
3318       if (lv < 0) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Could not find global vertex %D in local connectivity", gv);
3319       cones[c*numCorners+p] = lv+numCells;
3320     }
3321   }
3322   /* Build point sf */
3323   ierr = PetscLayoutCreate(PetscObjectComm((PetscObject)dm), &layout);CHKERRQ(ierr);
3324   ierr = PetscLayoutSetSize(layout, NVertices);CHKERRQ(ierr);
3325   ierr = PetscLayoutSetLocalSize(layout, numVertices);CHKERRQ(ierr);
3326   ierr = PetscLayoutSetBlockSize(layout, 1);CHKERRQ(ierr);
3327   ierr = PetscSFCreateByMatchingIndices(layout, numVerticesAdj, verticesAdj, NULL, numCells, numVerticesAdj, verticesAdj, NULL, numCells, vertexSF, &sfPoint);CHKERRQ(ierr);
3328   ierr = PetscLayoutDestroy(&layout);CHKERRQ(ierr);
3329   ierr = PetscFree(verticesAdj);CHKERRQ(ierr);
3330   ierr = PetscObjectSetName((PetscObject) sfPoint, "point SF");CHKERRQ(ierr);
3331   if (dm->sf) {
3332     const char *prefix;
3333 
3334     ierr = PetscObjectGetOptionsPrefix((PetscObject)dm->sf, &prefix);CHKERRQ(ierr);
3335     ierr = PetscObjectSetOptionsPrefix((PetscObject)sfPoint, prefix);CHKERRQ(ierr);
3336   }
3337   ierr = DMSetPointSF(dm, sfPoint);CHKERRQ(ierr);
3338   ierr = PetscSFDestroy(&sfPoint);CHKERRQ(ierr);
3339   if (vertexSF) {ierr = PetscObjectSetName((PetscObject)(*vertexSF), "Vertex Ownership SF");CHKERRQ(ierr);}
3340   /* Fill in the rest of the topology structure */
3341   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
3342   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
3343   ierr = PetscLogEventEnd(DMPLEX_BuildFromCellList,dm,0,0,0);CHKERRQ(ierr);
3344   PetscFunctionReturn(0);
3345 }
3346 
3347 /*@C
3348   DMPlexBuildCoordinatesFromCellListParallel - Build DM coordinates from a list of coordinates for each owned vertex (common mesh generator output)
3349 
3350   Input Parameters:
3351 + dm - The DM
3352 . spaceDim - The spatial dimension used for coordinates
3353 . sfVert - SF describing complete vertex ownership
3354 - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex
3355 
3356   Level: advanced
3357 
3358   Notes:
3359   Not currently supported in Fortran.
3360 
3361 .seealso: DMPlexBuildCoordinatesFromCellList(), DMPlexCreateFromCellListParallelPetsc(), DMPlexBuildFromCellListParallel()
3362 @*/
3363 PetscErrorCode DMPlexBuildCoordinatesFromCellListParallel(DM dm, PetscInt spaceDim, PetscSF sfVert, const PetscReal vertexCoords[])
3364 {
3365   PetscSection   coordSection;
3366   Vec            coordinates;
3367   PetscScalar   *coords;
3368   PetscInt       numVertices, numVerticesAdj, coordSize, v, vStart, vEnd;
3369   PetscErrorCode ierr;
3370 
3371   PetscFunctionBegin;
3372   ierr = PetscLogEventBegin(DMPLEX_BuildCoordinatesFromCellList,dm,0,0,0);CHKERRQ(ierr);
3373   ierr = DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);CHKERRQ(ierr);
3374   if (vStart < 0 || vEnd < 0) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "DM is not set up properly. DMPlexBuildFromCellList() should be called first.");
3375   ierr = DMSetCoordinateDim(dm, spaceDim);CHKERRQ(ierr);
3376   ierr = PetscSFGetGraph(sfVert, &numVertices, &numVerticesAdj, NULL, NULL);CHKERRQ(ierr);
3377   if (vEnd - vStart != numVerticesAdj) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Supplied sfVert has wrong number of leaves = %D != %D = vEnd - vStart",numVerticesAdj,vEnd - vStart);
3378   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
3379   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
3380   ierr = PetscSectionSetFieldComponents(coordSection, 0, spaceDim);CHKERRQ(ierr);
3381   ierr = PetscSectionSetChart(coordSection, vStart, vEnd);CHKERRQ(ierr);
3382   for (v = vStart; v < vEnd; ++v) {
3383     ierr = PetscSectionSetDof(coordSection, v, spaceDim);CHKERRQ(ierr);
3384     ierr = PetscSectionSetFieldDof(coordSection, v, 0, spaceDim);CHKERRQ(ierr);
3385   }
3386   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
3387   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
3388   ierr = VecCreate(PetscObjectComm((PetscObject)dm), &coordinates);CHKERRQ(ierr);
3389   ierr = VecSetBlockSize(coordinates, spaceDim);CHKERRQ(ierr);
3390   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
3391   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
3392   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
3393   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
3394   {
3395     MPI_Datatype coordtype;
3396 
3397     /* Need a temp buffer for coords if we have complex/single */
3398     ierr = MPI_Type_contiguous(spaceDim, MPIU_SCALAR, &coordtype);CHKERRMPI(ierr);
3399     ierr = MPI_Type_commit(&coordtype);CHKERRMPI(ierr);
3400 #if defined(PETSC_USE_COMPLEX)
3401     {
3402     PetscScalar *svertexCoords;
3403     PetscInt    i;
3404     ierr = PetscMalloc1(numVertices*spaceDim,&svertexCoords);CHKERRQ(ierr);
3405     for (i=0; i<numVertices*spaceDim; i++) svertexCoords[i] = vertexCoords[i];
3406     ierr = PetscSFBcastBegin(sfVert, coordtype, svertexCoords, coords,MPI_REPLACE);CHKERRQ(ierr);
3407     ierr = PetscSFBcastEnd(sfVert, coordtype, svertexCoords, coords,MPI_REPLACE);CHKERRQ(ierr);
3408     ierr = PetscFree(svertexCoords);CHKERRQ(ierr);
3409     }
3410 #else
3411     ierr = PetscSFBcastBegin(sfVert, coordtype, vertexCoords, coords,MPI_REPLACE);CHKERRQ(ierr);
3412     ierr = PetscSFBcastEnd(sfVert, coordtype, vertexCoords, coords,MPI_REPLACE);CHKERRQ(ierr);
3413 #endif
3414     ierr = MPI_Type_free(&coordtype);CHKERRMPI(ierr);
3415   }
3416   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
3417   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
3418   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
3419   ierr = PetscLogEventEnd(DMPLEX_BuildCoordinatesFromCellList,dm,0,0,0);CHKERRQ(ierr);
3420   PetscFunctionReturn(0);
3421 }
3422 
3423 /*@
3424   DMPlexCreateFromCellListParallelPetsc - Create distributed DMPLEX from a list of vertices for each cell (common mesh generator output)
3425 
3426   Input Parameters:
3427 + comm - The communicator
3428 . dim - The topological dimension of the mesh
3429 . numCells - The number of cells owned by this process
3430 . numVertices - The number of vertices owned by this process, or PETSC_DECIDE
3431 . NVertices - The global number of vertices, or PETSC_DECIDE
3432 . numCorners - The number of vertices for each cell
3433 . interpolate - Flag indicating that intermediate mesh entities (faces, edges) should be created automatically
3434 . cells - An array of numCells*numCorners numbers, the global vertex numbers for each cell
3435 . spaceDim - The spatial dimension used for coordinates
3436 - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex
3437 
3438   Output Parameters:
3439 + dm - The DM
3440 - vertexSF - (Optional) SF describing complete vertex ownership
3441 
3442   Notes:
3443   This function is just a convenient sequence of DMCreate(), DMSetType(), DMSetDimension(),
3444   DMPlexBuildFromCellListParallel(), DMPlexInterpolate(), DMPlexBuildCoordinatesFromCellListParallel()
3445 
3446   See DMPlexBuildFromCellListParallel() for an example and details about the topology-related parameters.
3447   See DMPlexBuildCoordinatesFromCellListParallel() for details about the geometry-related parameters.
3448 
3449   Level: intermediate
3450 
3451 .seealso: DMPlexCreateFromCellListPetsc(), DMPlexBuildFromCellListParallel(), DMPlexBuildCoordinatesFromCellListParallel(), DMPlexCreateFromDAG(), DMPlexCreate()
3452 @*/
3453 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, DM *dm)
3454 {
3455   PetscSF        sfVert;
3456   PetscErrorCode ierr;
3457 
3458   PetscFunctionBegin;
3459   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
3460   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
3461   PetscValidLogicalCollectiveInt(*dm, dim, 2);
3462   PetscValidLogicalCollectiveInt(*dm, spaceDim, 9);
3463   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
3464   ierr = DMPlexBuildFromCellListParallel(*dm, numCells, numVertices, NVertices, numCorners, cells, &sfVert);CHKERRQ(ierr);
3465   if (interpolate) {
3466     DM idm;
3467 
3468     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
3469     ierr = DMDestroy(dm);CHKERRQ(ierr);
3470     *dm  = idm;
3471   }
3472   ierr = DMPlexBuildCoordinatesFromCellListParallel(*dm, spaceDim, sfVert, vertexCoords);CHKERRQ(ierr);
3473   if (vertexSF) *vertexSF = sfVert;
3474   else {ierr = PetscSFDestroy(&sfVert);CHKERRQ(ierr);}
3475   PetscFunctionReturn(0);
3476 }
3477 
3478 /*@
3479   DMPlexCreateFromCellListParallel - Deprecated, use DMPlexCreateFromCellListParallelPetsc()
3480 
3481   Level: deprecated
3482 
3483 .seealso: DMPlexCreateFromCellListParallelPetsc()
3484 @*/
3485 PetscErrorCode DMPlexCreateFromCellListParallel(MPI_Comm comm, PetscInt dim, PetscInt numCells, PetscInt numVertices, PetscInt numCorners, PetscBool interpolate, const int cells[], PetscInt spaceDim, const PetscReal vertexCoords[], PetscSF *vertexSF, DM *dm)
3486 {
3487   PetscErrorCode ierr;
3488   PetscInt       i;
3489   PetscInt       *pintCells;
3490 
3491   PetscFunctionBegin;
3492   if (sizeof(int) > sizeof(PetscInt)) SETERRQ2(comm, PETSC_ERR_ARG_SIZ, "Size of int %zd greater than size of PetscInt %zd. Reconfigure PETSc --with-64-bit-indices=1", sizeof(int), sizeof(PetscInt));
3493   if (sizeof(int) == sizeof(PetscInt)) {
3494     pintCells = (PetscInt *) cells;
3495   } else {
3496     ierr = PetscMalloc1(numCells*numCorners, &pintCells);CHKERRQ(ierr);
3497     for (i = 0; i < numCells*numCorners; i++) {
3498       pintCells[i] = (PetscInt) cells[i];
3499     }
3500   }
3501   ierr = DMPlexCreateFromCellListParallelPetsc(comm, dim, numCells, numVertices, PETSC_DECIDE, numCorners, interpolate, pintCells, spaceDim, vertexCoords, vertexSF, dm);CHKERRQ(ierr);
3502   if (sizeof(int) != sizeof(PetscInt)) {
3503     ierr = PetscFree(pintCells);CHKERRQ(ierr);
3504   }
3505   PetscFunctionReturn(0);
3506 }
3507 
3508 /*@C
3509   DMPlexBuildFromCellList - Build DMPLEX topology from a list of vertices for each cell (common mesh generator output)
3510 
3511   Input Parameters:
3512 + dm - The DM
3513 . numCells - The number of cells owned by this process
3514 . numVertices - The number of vertices owned by this process, or PETSC_DECIDE
3515 . numCorners - The number of vertices for each cell
3516 - cells - An array of numCells*numCorners numbers, the global vertex numbers for each cell
3517 
3518   Level: advanced
3519 
3520   Notes:
3521   Two triangles sharing a face
3522 $
3523 $        2
3524 $      / | \
3525 $     /  |  \
3526 $    /   |   \
3527 $   0  0 | 1  3
3528 $    \   |   /
3529 $     \  |  /
3530 $      \ | /
3531 $        1
3532 would have input
3533 $  numCells = 2, numVertices = 4
3534 $  cells = [0 1 2  1 3 2]
3535 $
3536 which would result in the DMPlex
3537 $
3538 $        4
3539 $      / | \
3540 $     /  |  \
3541 $    /   |   \
3542 $   2  0 | 1  5
3543 $    \   |   /
3544 $     \  |  /
3545 $      \ | /
3546 $        3
3547 
3548   If numVertices is PETSC_DECIDE, it is computed by PETSc as the maximum vertex index in cells + 1.
3549 
3550   Not currently supported in Fortran.
3551 
3552 .seealso: DMPlexBuildFromCellListParallel(), DMPlexBuildCoordinatesFromCellList(), DMPlexCreateFromCellListPetsc()
3553 @*/
3554 PetscErrorCode DMPlexBuildFromCellList(DM dm, PetscInt numCells, PetscInt numVertices, PetscInt numCorners, const PetscInt cells[])
3555 {
3556   PetscInt      *cones, c, p, dim;
3557   PetscErrorCode ierr;
3558 
3559   PetscFunctionBegin;
3560   ierr = PetscLogEventBegin(DMPLEX_BuildFromCellList,dm,0,0,0);CHKERRQ(ierr);
3561   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
3562   /* Get/check global number of vertices */
3563   {
3564     PetscInt NVerticesInCells, i;
3565     const PetscInt len = numCells * numCorners;
3566 
3567     /* NVerticesInCells = max(cells) + 1 */
3568     NVerticesInCells = PETSC_MIN_INT;
3569     for (i=0; i<len; i++) if (cells[i] > NVerticesInCells) NVerticesInCells = cells[i];
3570     ++NVerticesInCells;
3571 
3572     if (numVertices == PETSC_DECIDE) numVertices = NVerticesInCells;
3573     else if (numVertices < NVerticesInCells) SETERRQ2(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_WRONG, "Specified number of vertices %D must be greater than or equal to the number of vertices in cells %D",numVertices,NVerticesInCells);
3574   }
3575   ierr = DMPlexSetChart(dm, 0, numCells+numVertices);CHKERRQ(ierr);
3576   for (c = 0; c < numCells; ++c) {
3577     ierr = DMPlexSetConeSize(dm, c, numCorners);CHKERRQ(ierr);
3578   }
3579   ierr = DMSetUp(dm);CHKERRQ(ierr);
3580   ierr = DMPlexGetCones(dm,&cones);CHKERRQ(ierr);
3581   for (c = 0; c < numCells; ++c) {
3582     for (p = 0; p < numCorners; ++p) {
3583       cones[c*numCorners+p] = cells[c*numCorners+p]+numCells;
3584     }
3585   }
3586   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
3587   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
3588   ierr = PetscLogEventEnd(DMPLEX_BuildFromCellList,dm,0,0,0);CHKERRQ(ierr);
3589   PetscFunctionReturn(0);
3590 }
3591 
3592 /*@C
3593   DMPlexBuildCoordinatesFromCellList - Build DM coordinates from a list of coordinates for each owned vertex (common mesh generator output)
3594 
3595   Input Parameters:
3596 + dm - The DM
3597 . spaceDim - The spatial dimension used for coordinates
3598 - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex
3599 
3600   Level: advanced
3601 
3602   Notes:
3603   Not currently supported in Fortran.
3604 
3605 .seealso: DMPlexBuildCoordinatesFromCellListParallel(), DMPlexCreateFromCellListPetsc(), DMPlexBuildFromCellList()
3606 @*/
3607 PetscErrorCode DMPlexBuildCoordinatesFromCellList(DM dm, PetscInt spaceDim, const PetscReal vertexCoords[])
3608 {
3609   PetscSection   coordSection;
3610   Vec            coordinates;
3611   DM             cdm;
3612   PetscScalar   *coords;
3613   PetscInt       v, vStart, vEnd, d;
3614   PetscErrorCode ierr;
3615 
3616   PetscFunctionBegin;
3617   ierr = PetscLogEventBegin(DMPLEX_BuildCoordinatesFromCellList,dm,0,0,0);CHKERRQ(ierr);
3618   ierr = DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);CHKERRQ(ierr);
3619   if (vStart < 0 || vEnd < 0) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "DM is not set up properly. DMPlexBuildFromCellList() should be called first.");
3620   ierr = DMSetCoordinateDim(dm, spaceDim);CHKERRQ(ierr);
3621   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
3622   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
3623   ierr = PetscSectionSetFieldComponents(coordSection, 0, spaceDim);CHKERRQ(ierr);
3624   ierr = PetscSectionSetChart(coordSection, vStart, vEnd);CHKERRQ(ierr);
3625   for (v = vStart; v < vEnd; ++v) {
3626     ierr = PetscSectionSetDof(coordSection, v, spaceDim);CHKERRQ(ierr);
3627     ierr = PetscSectionSetFieldDof(coordSection, v, 0, spaceDim);CHKERRQ(ierr);
3628   }
3629   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
3630 
3631   ierr = DMGetCoordinateDM(dm, &cdm);CHKERRQ(ierr);
3632   ierr = DMCreateLocalVector(cdm, &coordinates);CHKERRQ(ierr);
3633   ierr = VecSetBlockSize(coordinates, spaceDim);CHKERRQ(ierr);
3634   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
3635   ierr = VecGetArrayWrite(coordinates, &coords);CHKERRQ(ierr);
3636   for (v = 0; v < vEnd-vStart; ++v) {
3637     for (d = 0; d < spaceDim; ++d) {
3638       coords[v*spaceDim+d] = vertexCoords[v*spaceDim+d];
3639     }
3640   }
3641   ierr = VecRestoreArrayWrite(coordinates, &coords);CHKERRQ(ierr);
3642   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
3643   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
3644   ierr = PetscLogEventEnd(DMPLEX_BuildCoordinatesFromCellList,dm,0,0,0);CHKERRQ(ierr);
3645   PetscFunctionReturn(0);
3646 }
3647 
3648 /*@
3649   DMPlexCreateFromCellListPetsc - Create DMPLEX from a list of vertices for each cell (common mesh generator output), but only process 0 takes in the input
3650 
3651   Collective on comm
3652 
3653   Input Parameters:
3654 + comm - The communicator
3655 . dim - The topological dimension of the mesh
3656 . numCells - The number of cells, only on process 0
3657 . numVertices - The number of vertices owned by this process, or PETSC_DECIDE, only on process 0
3658 . numCorners - The number of vertices for each cell, only on process 0
3659 . interpolate - Flag indicating that intermediate mesh entities (faces, edges) should be created automatically
3660 . cells - An array of numCells*numCorners numbers, the vertices for each cell, only on process 0
3661 . spaceDim - The spatial dimension used for coordinates
3662 - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex, only on process 0
3663 
3664   Output Parameter:
3665 . dm - The DM, which only has points on process 0
3666 
3667   Notes:
3668   This function is just a convenient sequence of DMCreate(), DMSetType(), DMSetDimension(), DMPlexBuildFromCellList(),
3669   DMPlexInterpolate(), DMPlexBuildCoordinatesFromCellList()
3670 
3671   See DMPlexBuildFromCellList() for an example and details about the topology-related parameters.
3672   See DMPlexBuildCoordinatesFromCellList() for details about the geometry-related parameters.
3673   See DMPlexCreateFromCellListParallelPetsc() for parallel input
3674 
3675   Level: intermediate
3676 
3677 .seealso: DMPlexCreateFromCellListParallelPetsc(), DMPlexBuildFromCellList(), DMPlexBuildCoordinatesFromCellList(), DMPlexCreateFromDAG(), DMPlexCreate()
3678 @*/
3679 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)
3680 {
3681   PetscMPIInt    rank;
3682   PetscErrorCode ierr;
3683 
3684   PetscFunctionBegin;
3685   if (!dim) SETERRQ(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.");
3686   ierr = MPI_Comm_rank(comm, &rank);CHKERRMPI(ierr);
3687   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
3688   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
3689   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
3690   if (!rank) {ierr = DMPlexBuildFromCellList(*dm, numCells, numVertices, numCorners, cells);CHKERRQ(ierr);}
3691   else       {ierr = DMPlexBuildFromCellList(*dm, 0, 0, 0, NULL);CHKERRQ(ierr);}
3692   if (interpolate) {
3693     DM idm;
3694 
3695     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
3696     ierr = DMDestroy(dm);CHKERRQ(ierr);
3697     *dm  = idm;
3698   }
3699   if (!rank) {ierr = DMPlexBuildCoordinatesFromCellList(*dm, spaceDim, vertexCoords);CHKERRQ(ierr);}
3700   else       {ierr = DMPlexBuildCoordinatesFromCellList(*dm, spaceDim, NULL);CHKERRQ(ierr);}
3701   PetscFunctionReturn(0);
3702 }
3703 
3704 /*@
3705   DMPlexCreateFromCellList - Deprecated, use DMPlexCreateFromCellListPetsc()
3706 
3707   Level: deprecated
3708 
3709 .seealso: DMPlexCreateFromCellListPetsc()
3710 @*/
3711 PetscErrorCode DMPlexCreateFromCellList(MPI_Comm comm, PetscInt dim, PetscInt numCells, PetscInt numVertices, PetscInt numCorners, PetscBool interpolate, const int cells[], PetscInt spaceDim, const double vertexCoords[], DM *dm)
3712 {
3713   PetscErrorCode ierr;
3714   PetscInt       i;
3715   PetscInt       *pintCells;
3716   PetscReal      *prealVC;
3717 
3718   PetscFunctionBegin;
3719   if (sizeof(int) > sizeof(PetscInt)) SETERRQ2(comm, PETSC_ERR_ARG_SIZ, "Size of int %zd greater than size of PetscInt %zd. Reconfigure PETSc --with-64-bit-indices=1", sizeof(int), sizeof(PetscInt));
3720   if (sizeof(int) == sizeof(PetscInt)) {
3721     pintCells = (PetscInt *) cells;
3722   } else {
3723     ierr = PetscMalloc1(numCells*numCorners, &pintCells);CHKERRQ(ierr);
3724     for (i = 0; i < numCells*numCorners; i++) {
3725       pintCells[i] = (PetscInt) cells[i];
3726     }
3727   }
3728   if (sizeof(double) > sizeof(PetscReal)) SETERRQ2(comm, PETSC_ERR_ARG_SIZ, "Size of double %zd greater than size of PetscReal %zd. Reconfigure PETSc --with-precision=<higher precision>.", sizeof(double), sizeof(PetscReal));
3729   if (sizeof(double) == sizeof(PetscReal)) {
3730     prealVC = (PetscReal *) vertexCoords;
3731   } else {
3732     ierr = PetscMalloc1(numVertices*spaceDim, &prealVC);CHKERRQ(ierr);
3733     for (i = 0; i < numVertices*spaceDim; i++) {
3734       prealVC[i] = (PetscReal) vertexCoords[i];
3735     }
3736   }
3737   ierr = DMPlexCreateFromCellListPetsc(comm, dim, numCells, numVertices, numCorners, interpolate, pintCells, spaceDim, prealVC, dm);CHKERRQ(ierr);
3738   if (sizeof(int) != sizeof(PetscInt)) {
3739     ierr = PetscFree(pintCells);CHKERRQ(ierr);
3740   }
3741   if (sizeof(double) != sizeof(PetscReal)) {
3742     ierr = PetscFree(prealVC);CHKERRQ(ierr);
3743   }
3744   PetscFunctionReturn(0);
3745 }
3746 
3747 /*@
3748   DMPlexCreateFromDAG - This takes as input the adjacency-list representation of the Directed Acyclic Graph (Hasse Diagram) encoding a mesh, and produces a DM
3749 
3750   Input Parameters:
3751 + dm - The empty DM object, usually from DMCreate() and DMSetDimension()
3752 . depth - The depth of the DAG
3753 . numPoints - Array of size depth + 1 containing the number of points at each depth
3754 . coneSize - The cone size of each point
3755 . cones - The concatenation of the cone points for each point, the cone list must be oriented correctly for each point
3756 . coneOrientations - The orientation of each cone point
3757 - vertexCoords - An array of numPoints[0]*spacedim numbers representing the coordinates of each vertex, with spacedim the value set via DMSetCoordinateDim()
3758 
3759   Output Parameter:
3760 . dm - The DM
3761 
3762   Note: Two triangles sharing a face would have input
3763 $  depth = 1, numPoints = [4 2], coneSize = [3 3 0 0 0 0]
3764 $  cones = [2 3 4  3 5 4], coneOrientations = [0 0 0  0 0 0]
3765 $ vertexCoords = [-1.0 0.0  0.0 -1.0  0.0 1.0  1.0 0.0]
3766 $
3767 which would result in the DMPlex
3768 $
3769 $        4
3770 $      / | \
3771 $     /  |  \
3772 $    /   |   \
3773 $   2  0 | 1  5
3774 $    \   |   /
3775 $     \  |  /
3776 $      \ | /
3777 $        3
3778 $
3779 $ Notice that all points are numbered consecutively, unlike DMPlexCreateFromCellListPetsc()
3780 
3781   Level: advanced
3782 
3783 .seealso: DMPlexCreateFromCellListPetsc(), DMPlexCreate()
3784 @*/
3785 PetscErrorCode DMPlexCreateFromDAG(DM dm, PetscInt depth, const PetscInt numPoints[], const PetscInt coneSize[], const PetscInt cones[], const PetscInt coneOrientations[], const PetscScalar vertexCoords[])
3786 {
3787   Vec            coordinates;
3788   PetscSection   coordSection;
3789   PetscScalar    *coords;
3790   PetscInt       coordSize, firstVertex = -1, pStart = 0, pEnd = 0, p, v, dim, dimEmbed, d, off;
3791   PetscErrorCode ierr;
3792 
3793   PetscFunctionBegin;
3794   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
3795   ierr = DMGetCoordinateDim(dm, &dimEmbed);CHKERRQ(ierr);
3796   if (dimEmbed < dim) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Embedding dimension %D cannot be less than intrinsic dimension %d",dimEmbed,dim);
3797   for (d = 0; d <= depth; ++d) pEnd += numPoints[d];
3798   ierr = DMPlexSetChart(dm, pStart, pEnd);CHKERRQ(ierr);
3799   for (p = pStart; p < pEnd; ++p) {
3800     ierr = DMPlexSetConeSize(dm, p, coneSize[p-pStart]);CHKERRQ(ierr);
3801     if (firstVertex < 0 && !coneSize[p - pStart]) {
3802       firstVertex = p - pStart;
3803     }
3804   }
3805   if (firstVertex < 0 && numPoints[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Expected %D vertices but could not find any", numPoints[0]);
3806   ierr = DMSetUp(dm);CHKERRQ(ierr); /* Allocate space for cones */
3807   for (p = pStart, off = 0; p < pEnd; off += coneSize[p-pStart], ++p) {
3808     ierr = DMPlexSetCone(dm, p, &cones[off]);CHKERRQ(ierr);
3809     ierr = DMPlexSetConeOrientation(dm, p, &coneOrientations[off]);CHKERRQ(ierr);
3810   }
3811   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
3812   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
3813   /* Build coordinates */
3814   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
3815   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
3816   ierr = PetscSectionSetFieldComponents(coordSection, 0, dimEmbed);CHKERRQ(ierr);
3817   ierr = PetscSectionSetChart(coordSection, firstVertex, firstVertex+numPoints[0]);CHKERRQ(ierr);
3818   for (v = firstVertex; v < firstVertex+numPoints[0]; ++v) {
3819     ierr = PetscSectionSetDof(coordSection, v, dimEmbed);CHKERRQ(ierr);
3820     ierr = PetscSectionSetFieldDof(coordSection, v, 0, dimEmbed);CHKERRQ(ierr);
3821   }
3822   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
3823   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
3824   ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
3825   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
3826   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
3827   ierr = VecSetBlockSize(coordinates, dimEmbed);CHKERRQ(ierr);
3828   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
3829   if (vertexCoords) {
3830     ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
3831     for (v = 0; v < numPoints[0]; ++v) {
3832       PetscInt off;
3833 
3834       ierr = PetscSectionGetOffset(coordSection, v+firstVertex, &off);CHKERRQ(ierr);
3835       for (d = 0; d < dimEmbed; ++d) {
3836         coords[off+d] = vertexCoords[v*dimEmbed+d];
3837       }
3838     }
3839   }
3840   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
3841   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
3842   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
3843   PetscFunctionReturn(0);
3844 }
3845 
3846 /*@C
3847   DMPlexCreateCellVertexFromFile - Create a DMPlex mesh from a simple cell-vertex file.
3848 
3849 + comm        - The MPI communicator
3850 . filename    - Name of the .dat file
3851 - interpolate - Create faces and edges in the mesh
3852 
3853   Output Parameter:
3854 . dm  - The DM object representing the mesh
3855 
3856   Note: The format is the simplest possible:
3857 $ Ne
3858 $ v0 v1 ... vk
3859 $ Nv
3860 $ x y z marker
3861 
3862   Level: beginner
3863 
3864 .seealso: DMPlexCreateFromFile(), DMPlexCreateMedFromFile(), DMPlexCreateGmsh(), DMPlexCreate()
3865 @*/
3866 PetscErrorCode DMPlexCreateCellVertexFromFile(MPI_Comm comm, const char filename[], PetscBool interpolate, DM *dm)
3867 {
3868   DMLabel         marker;
3869   PetscViewer     viewer;
3870   Vec             coordinates;
3871   PetscSection    coordSection;
3872   PetscScalar    *coords;
3873   char            line[PETSC_MAX_PATH_LEN];
3874   PetscInt        dim = 3, cdim = 3, coordSize, v, c, d;
3875   PetscMPIInt     rank;
3876   int             snum, Nv, Nc, Ncn, Nl;
3877   PetscErrorCode  ierr;
3878 
3879   PetscFunctionBegin;
3880   ierr = MPI_Comm_rank(comm, &rank);CHKERRMPI(ierr);
3881   ierr = PetscViewerCreate(comm, &viewer);CHKERRQ(ierr);
3882   ierr = PetscViewerSetType(viewer, PETSCVIEWERASCII);CHKERRQ(ierr);
3883   ierr = PetscViewerFileSetMode(viewer, FILE_MODE_READ);CHKERRQ(ierr);
3884   ierr = PetscViewerFileSetName(viewer, filename);CHKERRQ(ierr);
3885   if (rank == 0) {
3886     ierr = PetscViewerRead(viewer, line, 4, NULL, PETSC_STRING);CHKERRQ(ierr);
3887     snum = sscanf(line, "%d %d %d %d", &Nc, &Nv, &Ncn, &Nl);
3888     if (snum != 4) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unable to parse cell-vertex file: %s", line);
3889   } else {
3890     Nc = Nv = Ncn = Nl = 0;
3891   }
3892   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
3893   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
3894   ierr = DMPlexSetChart(*dm, 0, Nc+Nv);CHKERRQ(ierr);
3895   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
3896   ierr = DMSetCoordinateDim(*dm, cdim);CHKERRQ(ierr);
3897   /* Read topology */
3898   if (rank == 0) {
3899     char     format[PETSC_MAX_PATH_LEN];
3900     PetscInt cone[8];
3901     int      vbuf[8], v;
3902 
3903     for (c = 0; c < Ncn; ++c) {format[c*3+0] = '%'; format[c*3+1] = 'd'; format[c*3+2] = ' ';}
3904     format[Ncn*3-1] = '\0';
3905     for (c = 0; c < Nc; ++c) {ierr = DMPlexSetConeSize(*dm, c, Ncn);CHKERRQ(ierr);}
3906     ierr = DMSetUp(*dm);CHKERRQ(ierr);
3907     for (c = 0; c < Nc; ++c) {
3908       ierr = PetscViewerRead(viewer, line, Ncn, NULL, PETSC_STRING);CHKERRQ(ierr);
3909       switch (Ncn) {
3910         case 2: snum = sscanf(line, format, &vbuf[0], &vbuf[1]);break;
3911         case 3: snum = sscanf(line, format, &vbuf[0], &vbuf[1], &vbuf[2]);break;
3912         case 4: snum = sscanf(line, format, &vbuf[0], &vbuf[1], &vbuf[2], &vbuf[3]);break;
3913         case 6: snum = sscanf(line, format, &vbuf[0], &vbuf[1], &vbuf[2], &vbuf[3], &vbuf[4], &vbuf[5]);break;
3914         case 8: snum = sscanf(line, format, &vbuf[0], &vbuf[1], &vbuf[2], &vbuf[3], &vbuf[4], &vbuf[5], &vbuf[6], &vbuf[7]);break;
3915         default: SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "No cell shape with %D vertices", Ncn);
3916       }
3917       if (snum != Ncn) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unable to parse cell-vertex file: %s", line);
3918       for (v = 0; v < Ncn; ++v) cone[v] = vbuf[v] + Nc;
3919       /* Hexahedra are inverted */
3920       if (Ncn == 8) {
3921         PetscInt tmp = cone[1];
3922         cone[1] = cone[3];
3923         cone[3] = tmp;
3924       }
3925       ierr = DMPlexSetCone(*dm, c, cone);CHKERRQ(ierr);
3926     }
3927   }
3928   ierr = DMPlexSymmetrize(*dm);CHKERRQ(ierr);
3929   ierr = DMPlexStratify(*dm);CHKERRQ(ierr);
3930   /* Read coordinates */
3931   ierr = DMGetCoordinateSection(*dm, &coordSection);CHKERRQ(ierr);
3932   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
3933   ierr = PetscSectionSetFieldComponents(coordSection, 0, cdim);CHKERRQ(ierr);
3934   ierr = PetscSectionSetChart(coordSection, Nc, Nc + Nv);CHKERRQ(ierr);
3935   for (v = Nc; v < Nc+Nv; ++v) {
3936     ierr = PetscSectionSetDof(coordSection, v, cdim);CHKERRQ(ierr);
3937     ierr = PetscSectionSetFieldDof(coordSection, v, 0, cdim);CHKERRQ(ierr);
3938   }
3939   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
3940   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
3941   ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
3942   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
3943   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
3944   ierr = VecSetBlockSize(coordinates, cdim);CHKERRQ(ierr);
3945   ierr = VecSetType(coordinates, VECSTANDARD);CHKERRQ(ierr);
3946   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
3947   if (rank == 0) {
3948     char   format[PETSC_MAX_PATH_LEN];
3949     double x[3];
3950     int    l, val[3];
3951 
3952     if (Nl) {
3953       for (l = 0; l < Nl; ++l) {format[l*3+0] = '%'; format[l*3+1] = 'd'; format[l*3+2] = ' ';}
3954       format[Nl*3-1] = '\0';
3955       ierr = DMCreateLabel(*dm, "marker");CHKERRQ(ierr);
3956       ierr = DMGetLabel(*dm, "marker", &marker);CHKERRQ(ierr);
3957     }
3958     for (v = 0; v < Nv; ++v) {
3959       ierr = PetscViewerRead(viewer, line, 3+Nl, NULL, PETSC_STRING);CHKERRQ(ierr);
3960       snum = sscanf(line, "%lg %lg %lg", &x[0], &x[1], &x[2]);
3961       if (snum != 3) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unable to parse cell-vertex file: %s", line);
3962       switch (Nl) {
3963         case 0: snum = 0;break;
3964         case 1: snum = sscanf(line, format, &val[0]);break;
3965         case 2: snum = sscanf(line, format, &val[0], &val[1]);break;
3966         case 3: snum = sscanf(line, format, &val[0], &val[1], &val[2]);break;
3967         default: SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_SUP, "Request support for %D labels", Nl);
3968       }
3969       if (snum != Nl) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unable to parse cell-vertex file: %s", line);
3970       for (d = 0; d < cdim; ++d) coords[v*cdim+d] = x[d];
3971       for (l = 0; l < Nl; ++l) {ierr = DMLabelSetValue(marker, v+Nc, val[l]);CHKERRQ(ierr);}
3972     }
3973   }
3974   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
3975   ierr = DMSetCoordinatesLocal(*dm, coordinates);CHKERRQ(ierr);
3976   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
3977   ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
3978   if (interpolate) {
3979     DM      idm;
3980     DMLabel bdlabel;
3981 
3982     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
3983     ierr = DMDestroy(dm);CHKERRQ(ierr);
3984     *dm  = idm;
3985 
3986     if (!Nl) {
3987       ierr = DMCreateLabel(*dm, "marker");CHKERRQ(ierr);
3988       ierr = DMGetLabel(*dm, "marker", &bdlabel);CHKERRQ(ierr);
3989       ierr = DMPlexMarkBoundaryFaces(*dm, PETSC_DETERMINE, bdlabel);CHKERRQ(ierr);
3990       ierr = DMPlexLabelComplete(*dm, bdlabel);CHKERRQ(ierr);
3991     }
3992   }
3993   PetscFunctionReturn(0);
3994 }
3995 
3996 /*@C
3997   DMPlexCreateFromFile - This takes a filename and produces a DM
3998 
3999   Input Parameters:
4000 + comm - The communicator
4001 . filename - A file name
4002 - interpolate - Flag to create intermediate mesh pieces (edges, faces)
4003 
4004   Output Parameter:
4005 . dm - The DM
4006 
4007   Options Database Keys:
4008 . -dm_plex_create_from_hdf5_xdmf - use the PETSC_VIEWER_HDF5_XDMF format for reading HDF5
4009 
4010   Use -dm_plex_create_ prefix to pass options to the internal PetscViewer, e.g.
4011 $ -dm_plex_create_viewer_hdf5_collective
4012 
4013   Level: beginner
4014 
4015 .seealso: DMPlexCreateFromDAG(), DMPlexCreateFromCellListPetsc(), DMPlexCreate()
4016 @*/
4017 PetscErrorCode DMPlexCreateFromFile(MPI_Comm comm, const char filename[], PetscBool interpolate, DM *dm)
4018 {
4019   const char    *extGmsh      = ".msh";
4020   const char    *extGmsh2     = ".msh2";
4021   const char    *extGmsh4     = ".msh4";
4022   const char    *extCGNS      = ".cgns";
4023   const char    *extExodus    = ".exo";
4024   const char    *extGenesis   = ".gen";
4025   const char    *extFluent    = ".cas";
4026   const char    *extHDF5      = ".h5";
4027   const char    *extMed       = ".med";
4028   const char    *extPLY       = ".ply";
4029   const char    *extEGADSLite = ".egadslite";
4030   const char    *extEGADS     = ".egads";
4031   const char    *extIGES      = ".igs";
4032   const char    *extSTEP      = ".stp";
4033   const char    *extCV        = ".dat";
4034   size_t         len;
4035   PetscBool      isGmsh, isGmsh2, isGmsh4, isCGNS, isExodus, isGenesis, isFluent, isHDF5, isMed, isPLY, isEGADSLite, isEGADS, isIGES, isSTEP, isCV;
4036   PetscMPIInt    rank;
4037   PetscErrorCode ierr;
4038 
4039   PetscFunctionBegin;
4040   PetscValidCharPointer(filename, 2);
4041   PetscValidPointer(dm, 4);
4042   ierr = DMInitializePackage();CHKERRQ(ierr);
4043   ierr = PetscLogEventBegin(DMPLEX_CreateFromFile,0,0,0,0);CHKERRQ(ierr);
4044   ierr = MPI_Comm_rank(comm, &rank);CHKERRMPI(ierr);
4045   ierr = PetscStrlen(filename, &len);CHKERRQ(ierr);
4046   if (!len) SETERRQ(comm, PETSC_ERR_ARG_WRONG, "Filename must be a valid path");
4047   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)],  extGmsh,      4, &isGmsh);CHKERRQ(ierr);
4048   ierr = PetscStrncmp(&filename[PetscMax(0,len-5)],  extGmsh2,     5, &isGmsh2);CHKERRQ(ierr);
4049   ierr = PetscStrncmp(&filename[PetscMax(0,len-5)],  extGmsh4,     5, &isGmsh4);CHKERRQ(ierr);
4050   ierr = PetscStrncmp(&filename[PetscMax(0,len-5)],  extCGNS,      5, &isCGNS);CHKERRQ(ierr);
4051   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)],  extExodus,    4, &isExodus);CHKERRQ(ierr);
4052   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)],  extGenesis,   4, &isGenesis);CHKERRQ(ierr);
4053   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)],  extFluent,    4, &isFluent);CHKERRQ(ierr);
4054   ierr = PetscStrncmp(&filename[PetscMax(0,len-3)],  extHDF5,      3, &isHDF5);CHKERRQ(ierr);
4055   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)],  extMed,       4, &isMed);CHKERRQ(ierr);
4056   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)],  extPLY,       4, &isPLY);CHKERRQ(ierr);
4057   ierr = PetscStrncmp(&filename[PetscMax(0,len-10)], extEGADSLite, 10, &isEGADSLite);CHKERRQ(ierr);
4058   ierr = PetscStrncmp(&filename[PetscMax(0,len-6)],  extEGADS,     6, &isEGADS);CHKERRQ(ierr);
4059   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)],  extIGES,      4, &isIGES);CHKERRQ(ierr);
4060   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)],  extSTEP,      4, &isSTEP);CHKERRQ(ierr);
4061   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)],  extCV,        4, &isCV);CHKERRQ(ierr);
4062   if (isGmsh || isGmsh2 || isGmsh4) {
4063     ierr = DMPlexCreateGmshFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
4064   } else if (isCGNS) {
4065     ierr = DMPlexCreateCGNSFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
4066   } else if (isExodus || isGenesis) {
4067     ierr = DMPlexCreateExodusFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
4068   } else if (isFluent) {
4069     ierr = DMPlexCreateFluentFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
4070   } else if (isHDF5) {
4071     PetscBool      load_hdf5_xdmf = PETSC_FALSE;
4072     PetscViewer viewer;
4073 
4074     /* PETSC_VIEWER_HDF5_XDMF is used if the filename ends with .xdmf.h5, or if -dm_plex_create_from_hdf5_xdmf option is present */
4075     ierr = PetscStrncmp(&filename[PetscMax(0,len-8)], ".xdmf",  5, &load_hdf5_xdmf);CHKERRQ(ierr);
4076     ierr = PetscOptionsGetBool(NULL, NULL, "-dm_plex_create_from_hdf5_xdmf", &load_hdf5_xdmf, NULL);CHKERRQ(ierr);
4077     ierr = PetscViewerCreate(comm, &viewer);CHKERRQ(ierr);
4078     ierr = PetscViewerSetType(viewer, PETSCVIEWERHDF5);CHKERRQ(ierr);
4079     ierr = PetscViewerSetOptionsPrefix(viewer, "dm_plex_create_");CHKERRQ(ierr);
4080     ierr = PetscViewerSetFromOptions(viewer);CHKERRQ(ierr);
4081     ierr = PetscViewerFileSetMode(viewer, FILE_MODE_READ);CHKERRQ(ierr);
4082     ierr = PetscViewerFileSetName(viewer, filename);CHKERRQ(ierr);
4083     ierr = DMCreate(comm, dm);CHKERRQ(ierr);
4084     ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
4085     if (load_hdf5_xdmf) {ierr = PetscViewerPushFormat(viewer, PETSC_VIEWER_HDF5_XDMF);CHKERRQ(ierr);}
4086     ierr = DMLoad(*dm, viewer);CHKERRQ(ierr);
4087     if (load_hdf5_xdmf) {ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);}
4088     ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
4089 
4090     if (interpolate) {
4091       DM idm;
4092 
4093       ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
4094       ierr = DMDestroy(dm);CHKERRQ(ierr);
4095       *dm  = idm;
4096     }
4097   } else if (isMed) {
4098     ierr = DMPlexCreateMedFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
4099   } else if (isPLY) {
4100     ierr = DMPlexCreatePLYFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
4101   } else if (isEGADSLite || isEGADS || isIGES || isSTEP) {
4102     if (isEGADSLite) {ierr = DMPlexCreateEGADSLiteFromFile(comm, filename, dm);CHKERRQ(ierr);}
4103     else             {ierr = DMPlexCreateEGADSFromFile(comm, filename, dm);CHKERRQ(ierr);}
4104     if (!interpolate) {
4105       DM udm;
4106 
4107       ierr = DMPlexUninterpolate(*dm, &udm);CHKERRQ(ierr);
4108       ierr = DMDestroy(dm);CHKERRQ(ierr);
4109       *dm  = udm;
4110     }
4111   } else if (isCV) {
4112     ierr = DMPlexCreateCellVertexFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
4113   } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cannot load file %s: unrecognized extension", filename);
4114   ierr = PetscLogEventEnd(DMPLEX_CreateFromFile,0,0,0,0);CHKERRQ(ierr);
4115   PetscFunctionReturn(0);
4116 }
4117