xref: /petsc/src/dm/impls/plex/plexcreate.c (revision b7f6ffafa12eb2d9bbc843a6262863d3adbb8bbb)
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);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) {
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) {
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) numCells = segments;
698   if (!rank) 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) {
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 ? edges[0] : 0;
801     const PetscInt numYEdges    = !rank ? edges[1] : 0;
802     const PetscInt numZEdges    = !rank ? edges[2] : 0;
803     const PetscInt numXVertices = !rank ? (bdX == DM_BOUNDARY_PERIODIC || bdX == DM_BOUNDARY_TWIST ? edges[0] : edges[0]+1) : 0;
804     const PetscInt numYVertices = !rank ? (bdY == DM_BOUNDARY_PERIODIC || bdY == DM_BOUNDARY_TWIST ? edges[1] : edges[1]+1) : 0;
805     const PetscInt numZVertices = !rank ? (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] = {-4,  0,  0, -1,  0, -4}; /* ??? */
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, -2, -2};
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, -2, -2};
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, -2, -2};
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] = -2;}
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[], PetscBool orderHeight, PetscBool interpolate)
1273 {
1274   DM             bdm, vol;
1275   PetscReal      normal[3] = {0., 0., 1.};
1276   PetscInt       i;
1277   PetscErrorCode ierr;
1278 
1279   PetscFunctionBegin;
1280   for (i = 0; i < 3; ++i) if (periodicity[i] != DM_BOUNDARY_NONE) SETERRQ(PetscObjectComm((PetscObject) dm), PETSC_ERR_SUP, "Periodicity not yet supported");
1281   ierr = DMCreate(PetscObjectComm((PetscObject) dm), &bdm);CHKERRQ(ierr);
1282   ierr = DMSetType(bdm, DMPLEX);CHKERRQ(ierr);
1283   ierr = DMSetDimension(bdm, 2);CHKERRQ(ierr);
1284   ierr = DMPlexCreateBoxMesh_Simplex_Internal(bdm, 2, faces, lower, upper, periodicity, interpolate);CHKERRQ(ierr);
1285   ierr = DMPlexExtrude(bdm, faces[2], upper[2] - lower[2], orderHeight, normal, interpolate, &vol);CHKERRQ(ierr);
1286   ierr = DMDestroy(&bdm);CHKERRQ(ierr);
1287   ierr = DMPlexReplace_Static(dm, &vol);CHKERRQ(ierr);
1288   if (lower[2] != 0.0) {
1289     Vec          v;
1290     PetscScalar *x;
1291     PetscInt     cDim, n;
1292 
1293     ierr = DMGetCoordinatesLocal(dm, &v);CHKERRQ(ierr);
1294     ierr = VecGetBlockSize(v, &cDim);CHKERRQ(ierr);
1295     ierr = VecGetLocalSize(v, &n);CHKERRQ(ierr);
1296     ierr = VecGetArray(v, &x);CHKERRQ(ierr);
1297     x   += cDim;
1298     for (i = 0; i < n; i += cDim) x[i] += lower[2];
1299     ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
1300     ierr = DMSetCoordinatesLocal(dm, v);CHKERRQ(ierr);
1301   }
1302   PetscFunctionReturn(0);
1303 }
1304 
1305 /*@
1306   DMPlexCreateWedgeBoxMesh - Creates a 3-D mesh tesselating the (x,y) plane and extruding in the third direction using wedge cells.
1307 
1308   Collective
1309 
1310   Input Parameters:
1311 + comm        - The communicator for the DM object
1312 . faces       - Number of faces per dimension, or NULL for (1, 1, 1)
1313 . lower       - The lower left corner, or NULL for (0, 0, 0)
1314 . upper       - The upper right corner, or NULL for (1, 1, 1)
1315 . periodicity - The boundary type for the X,Y,Z direction, or NULL for DM_BOUNDARY_NONE
1316 . orderHeight - If PETSC_TRUE, orders the extruded cells in the height first. Otherwise, orders the cell on the layers first
1317 - interpolate - Flag to create intermediate mesh pieces (edges, faces)
1318 
1319   Output Parameter:
1320 . dm  - The DM object
1321 
1322   Level: beginner
1323 
1324 .seealso: DMPlexCreateHexCylinderMesh(), DMPlexCreateWedgeCylinderMesh(), DMPlexExtrude(), DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
1325 @*/
1326 PetscErrorCode DMPlexCreateWedgeBoxMesh(MPI_Comm comm, const PetscInt faces[], const PetscReal lower[], const PetscReal upper[], const DMBoundaryType periodicity[], PetscBool orderHeight, PetscBool interpolate, DM *dm)
1327 {
1328   PetscInt       fac[3] = {1, 1, 1};
1329   PetscReal      low[3] = {0, 0, 0};
1330   PetscReal      upp[3] = {1, 1, 1};
1331   DMBoundaryType bdt[3] = {DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE};
1332   PetscErrorCode ierr;
1333 
1334   PetscFunctionBegin;
1335   ierr = DMCreate(comm,dm);CHKERRQ(ierr);
1336   ierr = DMSetType(*dm,DMPLEX);CHKERRQ(ierr);
1337   ierr = DMPlexCreateWedgeBoxMesh_Internal(*dm, faces ? faces : fac, lower ? lower : low, upper ? upper : upp, periodicity ? periodicity : bdt, orderHeight, interpolate);CHKERRQ(ierr);
1338   PetscFunctionReturn(0);
1339 }
1340 
1341 /*@C
1342   DMPlexExtrude - Creates a (d+1)-D mesh by extruding a d-D mesh in the normal direction using prismatic cells.
1343 
1344   Collective on idm
1345 
1346   Input Parameters:
1347 + idm         - The mesh to be extruded
1348 . layers      - The number of layers, or PETSC_DETERMINE to use the default
1349 . height      - The total height of the extrusion, or PETSC_DETERMINE to use the default
1350 . orderHeight - If PETSC_TRUE, orders the extruded cells in the height first. Otherwise, orders the cell on the layers first
1351 . extNormal   - The normal direction in which the mesh should be extruded, or NULL to extrude using the surface normal
1352 - interpolate - Flag to create intermediate mesh pieces (edges, faces)
1353 
1354   Output Parameter:
1355 . dm  - The DM object
1356 
1357   Notes:
1358   The mesh created has prismatic cells, and the vertex ordering in the cone of the cell is that of the tensor prismatic cells. Not currently supported in Fortran.
1359 
1360   Options Database Keys:
1361 +   -dm_plex_extrude_layers <k> - Sets the number of layers k
1362 .   -dm_plex_extrude_height <h> - Sets the total height of the extrusion
1363 .   -dm_plex_extrude_heights <h0,h1,...> - Sets the height of each layer
1364 .   -dm_plex_extrude_order_height - If true, order cells by height first
1365 -   -dm_plex_extrude_normal <n0,...,nd> - Sets the normal vector along which to extrude
1366 
1367   Level: advanced
1368 
1369 .seealso: DMPlexCreateWedgeCylinderMesh(), DMPlexCreateWedgeBoxMesh(), DMSetType(), DMCreate()
1370 @*/
1371 PetscErrorCode DMPlexExtrude(DM idm, PetscInt layers, PetscReal height, PetscBool orderHeight, const PetscReal extNormal[], PetscBool interpolate, DM* dm)
1372 {
1373   PetscScalar       *coordsB;
1374   const PetscScalar *coordsA;
1375   PetscReal         *normals = NULL, *heights = NULL;
1376   PetscReal         clNormal[3];
1377   Vec               coordinatesA, coordinatesB;
1378   PetscSection      coordSectionA, coordSectionB;
1379   PetscInt          dim, cDim, cDimB, c, l, v, coordSize, *newCone, nl;
1380   PetscInt          cStart, cEnd, vStart, vEnd, cellV, numCells, numVertices;
1381   const char       *prefix;
1382   PetscBool         haveCLNormal, flg;
1383   PetscErrorCode    ierr;
1384 
1385   PetscFunctionBegin;
1386   PetscValidHeaderSpecific(idm, DM_CLASSID, 1);
1387   PetscValidLogicalCollectiveInt(idm, layers, 2);
1388   PetscValidLogicalCollectiveReal(idm, height, 3);
1389   PetscValidLogicalCollectiveBool(idm, interpolate, 6);
1390   ierr = DMGetDimension(idm, &dim);CHKERRQ(ierr);
1391   ierr = DMGetCoordinateDim(idm, &cDim);CHKERRQ(ierr);
1392   cDimB = cDim == dim ? cDim+1 : cDim;
1393   if (dim < 1 || dim > 3) SETERRQ1(PetscObjectComm((PetscObject)idm), PETSC_ERR_SUP, "Support for dimension %D not coded", dim);
1394 
1395   ierr = PetscObjectGetOptionsPrefix((PetscObject) idm, &prefix);CHKERRQ(ierr);
1396   if (layers < 0) layers = 1;
1397   ierr = PetscOptionsGetInt(NULL, prefix, "-dm_plex_extrude_layers", &layers, NULL);CHKERRQ(ierr);
1398   if (layers <= 0) SETERRQ1(PetscObjectComm((PetscObject) idm), PETSC_ERR_ARG_OUTOFRANGE, "Number of layers %D must be positive", layers);
1399   if (height < 0.) height = 1.;
1400   ierr = PetscOptionsGetReal(NULL, prefix, "-dm_plex_extrude_height", &height, NULL);CHKERRQ(ierr);
1401   if (height <= 0.) SETERRQ1(PetscObjectComm((PetscObject) idm), PETSC_ERR_ARG_OUTOFRANGE, "Height of layers %g must be positive", (double) height);
1402   ierr = PetscMalloc1(layers, &heights);CHKERRQ(ierr);
1403   nl   = layers;
1404   ierr = PetscOptionsGetRealArray(NULL, prefix, "-dm_plex_extrude_heights", heights, &nl, &flg);CHKERRQ(ierr);
1405   if (flg) {
1406     if (!nl) SETERRQ(PetscObjectComm((PetscObject) idm), PETSC_ERR_ARG_OUTOFRANGE, "Must give at least one height for -dm_plex_extrude_heights");
1407     for (l = nl; l < layers; ++l) heights[l] = heights[l-1];
1408     for (l = 0; l < layers; ++l) if (heights[l] <= 0.) SETERRQ2(PetscObjectComm((PetscObject) idm), PETSC_ERR_ARG_OUTOFRANGE, "Height %g of layers %D must be positive", (double) heights[l], l);
1409   } else {
1410     for (l = 0; l < layers; ++l) heights[l] = height/layers;
1411   }
1412   ierr = PetscOptionsGetBool(NULL, prefix, "-dm_plex_extrude_order_height", &orderHeight, NULL);CHKERRQ(ierr);
1413   c = 3;
1414   ierr = PetscOptionsGetRealArray(NULL, prefix, "-dm_plex_extrude_normal", clNormal, &c, &haveCLNormal);CHKERRQ(ierr);
1415   if (haveCLNormal && c != cDimB) SETERRQ2(PetscObjectComm((PetscObject)idm), PETSC_ERR_ARG_SIZ, "Input normal has size %D != %D extruded coordinate dimension", c, cDimB);
1416 
1417   ierr = DMPlexGetHeightStratum(idm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1418   ierr = DMPlexGetDepthStratum(idm, 0, &vStart, &vEnd);CHKERRQ(ierr);
1419   numCells = (cEnd - cStart)*layers;
1420   numVertices = (vEnd - vStart)*(layers+1);
1421   ierr = DMCreate(PetscObjectComm((PetscObject)idm), dm);CHKERRQ(ierr);
1422   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
1423   ierr = DMSetDimension(*dm, dim+1);CHKERRQ(ierr);
1424   ierr = DMPlexSetChart(*dm, 0, numCells+numVertices);CHKERRQ(ierr);
1425   /* Must create the celltype label here so that we do not automatically try to compute the types */
1426   ierr = DMCreateLabel(*dm, "celltype");CHKERRQ(ierr);
1427   for (c = cStart, cellV = 0; c < cEnd; ++c) {
1428     DMPolytopeType ct, nct;
1429     PetscInt      *closure = NULL;
1430     PetscInt       closureSize, numCorners = 0;
1431 
1432     ierr = DMPlexGetCellType(idm, c, &ct);CHKERRQ(ierr);
1433     switch (ct) {
1434       case DM_POLYTOPE_SEGMENT:       nct = DM_POLYTOPE_SEG_PRISM_TENSOR;break;
1435       case DM_POLYTOPE_TRIANGLE:      nct = DM_POLYTOPE_TRI_PRISM_TENSOR;break;
1436       case DM_POLYTOPE_QUADRILATERAL: nct = DM_POLYTOPE_QUAD_PRISM_TENSOR;break;
1437       default: nct = DM_POLYTOPE_UNKNOWN;
1438     }
1439     ierr = DMPlexGetTransitiveClosure(idm, c, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
1440     for (v = 0; v < closureSize*2; v += 2) if ((closure[v] >= vStart) && (closure[v] < vEnd)) numCorners++;
1441     ierr = DMPlexRestoreTransitiveClosure(idm, c, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
1442     for (l = 0; l < layers; ++l) {
1443       const PetscInt cell = orderHeight ? layers*(c - cStart) + l : l*(cEnd - cStart) + c - cStart;
1444 
1445       ierr = DMPlexSetConeSize(*dm, cell, 2*numCorners);CHKERRQ(ierr);
1446       ierr = DMPlexSetCellType(*dm, cell, nct);CHKERRQ(ierr);
1447     }
1448     cellV = PetscMax(numCorners,cellV);
1449   }
1450   ierr = DMSetUp(*dm);CHKERRQ(ierr);
1451 
1452   if (dim != cDim && !(extNormal || haveCLNormal)) {ierr = PetscCalloc1(cDim*(vEnd - vStart), &normals);CHKERRQ(ierr);}
1453   ierr = PetscMalloc1(3*cellV,&newCone);CHKERRQ(ierr);
1454   for (c = cStart; c < cEnd; ++c) {
1455     PetscInt *closure = NULL;
1456     PetscInt closureSize, numCorners = 0, l;
1457     PetscReal normal[3] = {0, 0, 0};
1458 
1459     if (normals) {ierr = DMPlexComputeCellGeometryFVM(idm, c, NULL, NULL, normal);CHKERRQ(ierr);}
1460     ierr = DMPlexGetTransitiveClosure(idm, c, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
1461     for (v = 0; v < closureSize*2; v += 2) {
1462       if ((closure[v] >= vStart) && (closure[v] < vEnd)) {
1463         PetscInt d;
1464 
1465         newCone[numCorners++] = closure[v] - vStart;
1466         if (normals) {for (d = 0; d < cDim; ++d) normals[cDim*(closure[v]-vStart)+d] += normal[d];}
1467       }
1468     }
1469     ierr = DMPlexRestoreTransitiveClosure(idm, c, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
1470     for (l = 0; l < layers; ++l) {
1471       PetscInt i;
1472 
1473       for (i = 0; i < numCorners; ++i) {
1474         newCone[  numCorners + i] = orderHeight ? (layers+1)*newCone[i] + l     + numCells :     l*(vEnd - vStart) + newCone[i] + numCells;
1475         newCone[2*numCorners + i] = orderHeight ? (layers+1)*newCone[i] + l + 1 + numCells : (l+1)*(vEnd - vStart) + newCone[i] + numCells;
1476       }
1477       ierr = DMPlexSetCone(*dm, orderHeight ? layers*(c - cStart) + l : l*(cEnd - cStart) + c - cStart, newCone + numCorners);CHKERRQ(ierr);
1478     }
1479   }
1480   ierr = DMPlexSymmetrize(*dm);CHKERRQ(ierr);
1481   ierr = DMPlexStratify(*dm);CHKERRQ(ierr);
1482   ierr = PetscFree(newCone);CHKERRQ(ierr);
1483 
1484   ierr = DMGetCoordinateSection(*dm, &coordSectionB);CHKERRQ(ierr);
1485   ierr = PetscSectionSetNumFields(coordSectionB, 1);CHKERRQ(ierr);
1486   ierr = PetscSectionSetFieldComponents(coordSectionB, 0, cDimB);CHKERRQ(ierr);
1487   ierr = PetscSectionSetChart(coordSectionB, numCells, numCells+numVertices);CHKERRQ(ierr);
1488   for (v = numCells; v < numCells+numVertices; ++v) {
1489     ierr = PetscSectionSetDof(coordSectionB, v, cDimB);CHKERRQ(ierr);
1490     ierr = PetscSectionSetFieldDof(coordSectionB, v, 0, cDimB);CHKERRQ(ierr);
1491     ierr = DMPlexSetCellType(*dm, v, DM_POLYTOPE_POINT);CHKERRQ(ierr);
1492   }
1493   ierr = PetscSectionSetUp(coordSectionB);CHKERRQ(ierr);
1494   ierr = PetscSectionGetStorageSize(coordSectionB, &coordSize);CHKERRQ(ierr);
1495   ierr = VecCreate(PETSC_COMM_SELF, &coordinatesB);CHKERRQ(ierr);
1496   ierr = PetscObjectSetName((PetscObject) coordinatesB, "coordinates");CHKERRQ(ierr);
1497   ierr = VecSetSizes(coordinatesB, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
1498   ierr = VecSetBlockSize(coordinatesB, cDimB);CHKERRQ(ierr);
1499   ierr = VecSetType(coordinatesB,VECSTANDARD);CHKERRQ(ierr);
1500 
1501   ierr = DMGetCoordinateSection(idm, &coordSectionA);CHKERRQ(ierr);
1502   ierr = DMGetCoordinatesLocal(idm, &coordinatesA);CHKERRQ(ierr);
1503   ierr = VecGetArray(coordinatesB, &coordsB);CHKERRQ(ierr);
1504   ierr = VecGetArrayRead(coordinatesA, &coordsA);CHKERRQ(ierr);
1505   for (v = vStart; v < vEnd; ++v) {
1506     const PetscScalar *cptr;
1507     PetscReal         ones2[2] = { 0., 1.}, ones3[3] = { 0., 0., 1.};
1508     PetscReal         normal[3];
1509     PetscReal         norm;
1510     PetscInt          offA, d, cDimA = cDim;
1511 
1512     if (normals)           {for (d = 0; d < cDimB; ++d) normal[d] = normals[cDimB*(v - vStart)+d];}
1513     else if (haveCLNormal) {for (d = 0; d < cDimB; ++d) normal[d] = clNormal[d];}
1514     else if (extNormal)    {for (d = 0; d < cDimB; ++d) normal[d] = extNormal[d];}
1515     else if (cDimB == 2)   {for (d = 0; d < cDimB; ++d) normal[d] = ones2[d];}
1516     else if (cDimB == 3)   {for (d = 0; d < cDimB; ++d) normal[d] = ones3[d];}
1517     else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Unable to determine normal for extrusion");
1518     for (d = 0, norm = 0.0; d < cDimB; ++d) norm += normal[d]*normal[d];
1519     for (d = 0; d < cDimB; ++d) normal[d] *= 1./PetscSqrtReal(norm);
1520 
1521     ierr = PetscSectionGetOffset(coordSectionA, v, &offA);CHKERRQ(ierr);
1522     cptr = coordsA + offA;
1523     for (l = 0; l <= layers; ++l) {
1524       PetscInt offB, d, newV;
1525 
1526       newV = orderHeight ? (layers+1)*(v -vStart) + l + numCells : (vEnd -vStart)*l + (v -vStart) + numCells;
1527       ierr = PetscSectionGetOffset(coordSectionB, newV, &offB);CHKERRQ(ierr);
1528       for (d = 0; d < cDimA; ++d) { coordsB[offB+d]  = cptr[d]; }
1529       for (d = 0; d < cDimB; ++d) { coordsB[offB+d] += l ? normal[d]*heights[l-1] : 0.0; }
1530       cptr    = coordsB + offB;
1531       cDimA   = cDimB;
1532     }
1533   }
1534   ierr = VecRestoreArrayRead(coordinatesA, &coordsA);CHKERRQ(ierr);
1535   ierr = VecRestoreArray(coordinatesB, &coordsB);CHKERRQ(ierr);
1536   ierr = DMSetCoordinatesLocal(*dm, coordinatesB);CHKERRQ(ierr);
1537   ierr = VecDestroy(&coordinatesB);CHKERRQ(ierr);
1538   ierr = PetscFree(normals);CHKERRQ(ierr);
1539   ierr = PetscFree(heights);CHKERRQ(ierr);
1540   if (interpolate) {
1541     DM idm;
1542 
1543     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
1544     ierr = DMPlexCopyCoordinates(*dm, idm);CHKERRQ(ierr);
1545     ierr = DMDestroy(dm);CHKERRQ(ierr);
1546     *dm  = idm;
1547   }
1548   PetscFunctionReturn(0);
1549 }
1550 
1551 /*@C
1552   DMPlexSetOptionsPrefix - Sets the prefix used for searching for all DM options in the database.
1553 
1554   Logically Collective on dm
1555 
1556   Input Parameters:
1557 + dm - the DM context
1558 - prefix - the prefix to prepend to all option names
1559 
1560   Notes:
1561   A hyphen (-) must NOT be given at the beginning of the prefix name.
1562   The first character of all runtime options is AUTOMATICALLY the hyphen.
1563 
1564   Level: advanced
1565 
1566 .seealso: SNESSetFromOptions()
1567 @*/
1568 PetscErrorCode DMPlexSetOptionsPrefix(DM dm, const char prefix[])
1569 {
1570   DM_Plex       *mesh = (DM_Plex *) dm->data;
1571   PetscErrorCode ierr;
1572 
1573   PetscFunctionBegin;
1574   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1575   ierr = PetscObjectSetOptionsPrefix((PetscObject) dm, prefix);CHKERRQ(ierr);
1576   ierr = PetscObjectSetOptionsPrefix((PetscObject) mesh->partitioner, prefix);CHKERRQ(ierr);
1577   PetscFunctionReturn(0);
1578 }
1579 
1580 /* Remap geometry to cylinder
1581    TODO: This only works for a single refinement, then it is broken
1582 
1583      Interior square: Linear interpolation is correct
1584      The other cells all have vertices on rays from the origin. We want to uniformly expand the spacing
1585      such that the last vertex is on the unit circle. So the closest and farthest vertices are at distance
1586 
1587        phi     = arctan(y/x)
1588        d_close = sqrt(1/8 + 1/4 sin^2(phi))
1589        d_far   = sqrt(1/2 + sin^2(phi))
1590 
1591      so we remap them using
1592 
1593        x_new = x_close + (x - x_close) (1 - d_close) / (d_far - d_close)
1594        y_new = y_close + (y - y_close) (1 - d_close) / (d_far - d_close)
1595 
1596      If pi/4 < phi < 3pi/4 or -3pi/4 < phi < -pi/4, then we switch x and y.
1597 */
1598 static void snapToCylinder(PetscInt dim, PetscInt Nf, PetscInt NfAux,
1599                            const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
1600                            const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
1601                            PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
1602 {
1603   const PetscReal dis = 1.0/PetscSqrtReal(2.0);
1604   const PetscReal ds2 = 0.5*dis;
1605 
1606   if ((PetscAbsScalar(u[0]) <= ds2) && (PetscAbsScalar(u[1]) <= ds2)) {
1607     f0[0] = u[0];
1608     f0[1] = u[1];
1609   } else {
1610     PetscReal phi, sinp, cosp, dc, df, x, y, xc, yc;
1611 
1612     x    = PetscRealPart(u[0]);
1613     y    = PetscRealPart(u[1]);
1614     phi  = PetscAtan2Real(y, x);
1615     sinp = PetscSinReal(phi);
1616     cosp = PetscCosReal(phi);
1617     if ((PetscAbsReal(phi) > PETSC_PI/4.0) && (PetscAbsReal(phi) < 3.0*PETSC_PI/4.0)) {
1618       dc = PetscAbsReal(ds2/sinp);
1619       df = PetscAbsReal(dis/sinp);
1620       xc = ds2*x/PetscAbsReal(y);
1621       yc = ds2*PetscSignReal(y);
1622     } else {
1623       dc = PetscAbsReal(ds2/cosp);
1624       df = PetscAbsReal(dis/cosp);
1625       xc = ds2*PetscSignReal(x);
1626       yc = ds2*y/PetscAbsReal(x);
1627     }
1628     f0[0] = xc + (u[0] - xc)*(1.0 - dc)/(df - dc);
1629     f0[1] = yc + (u[1] - yc)*(1.0 - dc)/(df - dc);
1630   }
1631   f0[2] = u[2];
1632 }
1633 
1634 static PetscErrorCode DMPlexCreateHexCylinderMesh_Internal(DM dm, DMBoundaryType periodicZ)
1635 {
1636   const PetscInt dim = 3;
1637   PetscInt       numCells, numVertices;
1638   PetscMPIInt    rank;
1639   PetscErrorCode ierr;
1640 
1641   PetscFunctionBegin;
1642   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject) dm), &rank);CHKERRMPI(ierr);
1643   ierr = DMSetDimension(dm, dim);CHKERRQ(ierr);
1644   /* Create topology */
1645   {
1646     PetscInt cone[8], c;
1647 
1648     numCells    = !rank ?  5 : 0;
1649     numVertices = !rank ? 16 : 0;
1650     if (periodicZ == DM_BOUNDARY_PERIODIC) {
1651       numCells   *= 3;
1652       numVertices = !rank ? 24 : 0;
1653     }
1654     ierr = DMPlexSetChart(dm, 0, numCells+numVertices);CHKERRQ(ierr);
1655     for (c = 0; c < numCells; c++) {ierr = DMPlexSetConeSize(dm, c, 8);CHKERRQ(ierr);}
1656     ierr = DMSetUp(dm);CHKERRQ(ierr);
1657     if (!rank) {
1658       if (periodicZ == DM_BOUNDARY_PERIODIC) {
1659         cone[0] = 15; cone[1] = 18; cone[2] = 17; cone[3] = 16;
1660         cone[4] = 31; cone[5] = 32; cone[6] = 33; cone[7] = 34;
1661         ierr = DMPlexSetCone(dm, 0, cone);CHKERRQ(ierr);
1662         cone[0] = 16; cone[1] = 17; cone[2] = 24; cone[3] = 23;
1663         cone[4] = 32; cone[5] = 36; cone[6] = 37; cone[7] = 33; /* 22 25 26 21 */
1664         ierr = DMPlexSetCone(dm, 1, cone);CHKERRQ(ierr);
1665         cone[0] = 18; cone[1] = 27; cone[2] = 24; cone[3] = 17;
1666         cone[4] = 34; cone[5] = 33; cone[6] = 37; cone[7] = 38;
1667         ierr = DMPlexSetCone(dm, 2, cone);CHKERRQ(ierr);
1668         cone[0] = 29; cone[1] = 27; cone[2] = 18; cone[3] = 15;
1669         cone[4] = 35; cone[5] = 31; cone[6] = 34; cone[7] = 38;
1670         ierr = DMPlexSetCone(dm, 3, cone);CHKERRQ(ierr);
1671         cone[0] = 29; cone[1] = 15; cone[2] = 16; cone[3] = 23;
1672         cone[4] = 35; cone[5] = 36; cone[6] = 32; cone[7] = 31;
1673         ierr = DMPlexSetCone(dm, 4, cone);CHKERRQ(ierr);
1674 
1675         cone[0] = 31; cone[1] = 34; cone[2] = 33; cone[3] = 32;
1676         cone[4] = 19; cone[5] = 22; cone[6] = 21; cone[7] = 20;
1677         ierr = DMPlexSetCone(dm, 5, cone);CHKERRQ(ierr);
1678         cone[0] = 32; cone[1] = 33; cone[2] = 37; cone[3] = 36;
1679         cone[4] = 22; cone[5] = 25; cone[6] = 26; cone[7] = 21;
1680         ierr = DMPlexSetCone(dm, 6, cone);CHKERRQ(ierr);
1681         cone[0] = 34; cone[1] = 38; cone[2] = 37; cone[3] = 33;
1682         cone[4] = 20; cone[5] = 21; cone[6] = 26; cone[7] = 28;
1683         ierr = DMPlexSetCone(dm, 7, cone);CHKERRQ(ierr);
1684         cone[0] = 35; cone[1] = 38; cone[2] = 34; cone[3] = 31;
1685         cone[4] = 30; cone[5] = 19; cone[6] = 20; cone[7] = 28;
1686         ierr = DMPlexSetCone(dm, 8, cone);CHKERRQ(ierr);
1687         cone[0] = 35; cone[1] = 31; cone[2] = 32; cone[3] = 36;
1688         cone[4] = 30; cone[5] = 25; cone[6] = 22; cone[7] = 19;
1689         ierr = DMPlexSetCone(dm, 9, cone);CHKERRQ(ierr);
1690 
1691         cone[0] = 19; cone[1] = 20; cone[2] = 21; cone[3] = 22;
1692         cone[4] = 15; cone[5] = 16; cone[6] = 17; cone[7] = 18;
1693         ierr = DMPlexSetCone(dm, 10, cone);CHKERRQ(ierr);
1694         cone[0] = 22; cone[1] = 21; cone[2] = 26; cone[3] = 25;
1695         cone[4] = 16; cone[5] = 23; cone[6] = 24; cone[7] = 17;
1696         ierr = DMPlexSetCone(dm, 11, cone);CHKERRQ(ierr);
1697         cone[0] = 20; cone[1] = 28; cone[2] = 26; cone[3] = 21;
1698         cone[4] = 18; cone[5] = 17; cone[6] = 24; cone[7] = 27;
1699         ierr = DMPlexSetCone(dm, 12, cone);CHKERRQ(ierr);
1700         cone[0] = 30; cone[1] = 28; cone[2] = 20; cone[3] = 19;
1701         cone[4] = 29; cone[5] = 15; cone[6] = 18; cone[7] = 27;
1702         ierr = DMPlexSetCone(dm, 13, cone);CHKERRQ(ierr);
1703         cone[0] = 30; cone[1] = 19; cone[2] = 22; cone[3] = 25;
1704         cone[4] = 29; cone[5] = 23; cone[6] = 16; cone[7] = 15;
1705         ierr = DMPlexSetCone(dm, 14, cone);CHKERRQ(ierr);
1706       } else {
1707         cone[0] =  5; cone[1] =  8; cone[2] =  7; cone[3] =  6;
1708         cone[4] =  9; cone[5] = 12; cone[6] = 11; cone[7] = 10;
1709         ierr = DMPlexSetCone(dm, 0, cone);CHKERRQ(ierr);
1710         cone[0] =  6; cone[1] =  7; cone[2] = 14; cone[3] = 13;
1711         cone[4] = 12; cone[5] = 15; cone[6] = 16; cone[7] = 11;
1712         ierr = DMPlexSetCone(dm, 1, cone);CHKERRQ(ierr);
1713         cone[0] =  8; cone[1] = 17; cone[2] = 14; cone[3] =  7;
1714         cone[4] = 10; cone[5] = 11; cone[6] = 16; cone[7] = 18;
1715         ierr = DMPlexSetCone(dm, 2, cone);CHKERRQ(ierr);
1716         cone[0] = 19; cone[1] = 17; cone[2] =  8; cone[3] =  5;
1717         cone[4] = 20; cone[5] =  9; cone[6] = 10; cone[7] = 18;
1718         ierr = DMPlexSetCone(dm, 3, cone);CHKERRQ(ierr);
1719         cone[0] = 19; cone[1] =  5; cone[2] =  6; cone[3] = 13;
1720         cone[4] = 20; cone[5] = 15; cone[6] = 12; cone[7] =  9;
1721         ierr = DMPlexSetCone(dm, 4, cone);CHKERRQ(ierr);
1722       }
1723     }
1724     ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
1725     ierr = DMPlexStratify(dm);CHKERRQ(ierr);
1726   }
1727   /* Create cube geometry */
1728   {
1729     Vec             coordinates;
1730     PetscSection    coordSection;
1731     PetscScalar    *coords;
1732     PetscInt        coordSize, v;
1733     const PetscReal dis = 1.0/PetscSqrtReal(2.0);
1734     const PetscReal ds2 = dis/2.0;
1735 
1736     /* Build coordinates */
1737     ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
1738     ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
1739     ierr = PetscSectionSetFieldComponents(coordSection, 0, dim);CHKERRQ(ierr);
1740     ierr = PetscSectionSetChart(coordSection, numCells, numCells+numVertices);CHKERRQ(ierr);
1741     for (v = numCells; v < numCells+numVertices; ++v) {
1742       ierr = PetscSectionSetDof(coordSection, v, dim);CHKERRQ(ierr);
1743       ierr = PetscSectionSetFieldDof(coordSection, v, 0, dim);CHKERRQ(ierr);
1744     }
1745     ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
1746     ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
1747     ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
1748     ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
1749     ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
1750     ierr = VecSetBlockSize(coordinates, dim);CHKERRQ(ierr);
1751     ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
1752     ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
1753     if (!rank) {
1754       coords[0*dim+0] = -ds2; coords[0*dim+1] = -ds2; coords[0*dim+2] = 0.0;
1755       coords[1*dim+0] =  ds2; coords[1*dim+1] = -ds2; coords[1*dim+2] = 0.0;
1756       coords[2*dim+0] =  ds2; coords[2*dim+1] =  ds2; coords[2*dim+2] = 0.0;
1757       coords[3*dim+0] = -ds2; coords[3*dim+1] =  ds2; coords[3*dim+2] = 0.0;
1758       coords[4*dim+0] = -ds2; coords[4*dim+1] = -ds2; coords[4*dim+2] = 1.0;
1759       coords[5*dim+0] = -ds2; coords[5*dim+1] =  ds2; coords[5*dim+2] = 1.0;
1760       coords[6*dim+0] =  ds2; coords[6*dim+1] =  ds2; coords[6*dim+2] = 1.0;
1761       coords[7*dim+0] =  ds2; coords[7*dim+1] = -ds2; coords[7*dim+2] = 1.0;
1762       coords[ 8*dim+0] =  dis; coords[ 8*dim+1] = -dis; coords[ 8*dim+2] = 0.0;
1763       coords[ 9*dim+0] =  dis; coords[ 9*dim+1] =  dis; coords[ 9*dim+2] = 0.0;
1764       coords[10*dim+0] =  dis; coords[10*dim+1] = -dis; coords[10*dim+2] = 1.0;
1765       coords[11*dim+0] =  dis; coords[11*dim+1] =  dis; coords[11*dim+2] = 1.0;
1766       coords[12*dim+0] = -dis; coords[12*dim+1] =  dis; coords[12*dim+2] = 0.0;
1767       coords[13*dim+0] = -dis; coords[13*dim+1] =  dis; coords[13*dim+2] = 1.0;
1768       coords[14*dim+0] = -dis; coords[14*dim+1] = -dis; coords[14*dim+2] = 0.0;
1769       coords[15*dim+0] = -dis; coords[15*dim+1] = -dis; coords[15*dim+2] = 1.0;
1770       if (periodicZ == DM_BOUNDARY_PERIODIC) {
1771         /* 15 31 19 */ coords[16*dim+0] = -ds2; coords[16*dim+1] = -ds2; coords[16*dim+2] = 0.5;
1772         /* 16 32 22 */ coords[17*dim+0] =  ds2; coords[17*dim+1] = -ds2; coords[17*dim+2] = 0.5;
1773         /* 17 33 21 */ coords[18*dim+0] =  ds2; coords[18*dim+1] =  ds2; coords[18*dim+2] = 0.5;
1774         /* 18 34 20 */ coords[19*dim+0] = -ds2; coords[19*dim+1] =  ds2; coords[19*dim+2] = 0.5;
1775         /* 29 35 30 */ coords[20*dim+0] = -dis; coords[20*dim+1] = -dis; coords[20*dim+2] = 0.5;
1776         /* 23 36 25 */ coords[21*dim+0] =  dis; coords[21*dim+1] = -dis; coords[21*dim+2] = 0.5;
1777         /* 24 37 26 */ coords[22*dim+0] =  dis; coords[22*dim+1] =  dis; coords[22*dim+2] = 0.5;
1778         /* 27 38 28 */ coords[23*dim+0] = -dis; coords[23*dim+1] =  dis; coords[23*dim+2] = 0.5;
1779       }
1780     }
1781     ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
1782     ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
1783     ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
1784   }
1785   /* Create periodicity */
1786   if (periodicZ == DM_BOUNDARY_PERIODIC || periodicZ == DM_BOUNDARY_TWIST) {
1787     PetscReal      L[3];
1788     PetscReal      maxCell[3];
1789     DMBoundaryType bdType[3];
1790     PetscReal      lower[3] = {0.0, 0.0, 0.0};
1791     PetscReal      upper[3] = {1.0, 1.0, 1.5};
1792     PetscInt       i, numZCells = 3;
1793 
1794     bdType[0] = DM_BOUNDARY_NONE;
1795     bdType[1] = DM_BOUNDARY_NONE;
1796     bdType[2] = periodicZ;
1797     for (i = 0; i < dim; i++) {
1798       L[i]       = upper[i] - lower[i];
1799       maxCell[i] = 1.1 * (L[i] / numZCells);
1800     }
1801     ierr = DMSetPeriodicity(dm, PETSC_TRUE, maxCell, L, bdType);CHKERRQ(ierr);
1802   }
1803   {
1804     DM          cdm;
1805     PetscDS     cds;
1806     PetscScalar c[2] = {1.0, 1.0};
1807 
1808     ierr = DMPlexCreateCoordinateSpace(dm, 1, snapToCylinder);CHKERRQ(ierr);
1809     ierr = DMGetCoordinateDM(dm, &cdm);CHKERRQ(ierr);
1810     ierr = DMGetDS(cdm, &cds);CHKERRQ(ierr);
1811     ierr = PetscDSSetConstants(cds, 2, c);CHKERRQ(ierr);
1812   }
1813   /* Wait for coordinate creation before doing in-place modification */
1814   ierr = DMPlexInterpolateInPlace_Internal(dm);CHKERRQ(ierr);
1815   PetscFunctionReturn(0);
1816 }
1817 
1818 /*@
1819   DMPlexCreateHexCylinderMesh - Creates a mesh on the tensor product of the unit interval with the circle (cylinder) using hexahedra.
1820 
1821   Collective
1822 
1823   Input Parameters:
1824 + comm      - The communicator for the DM object
1825 - periodicZ - The boundary type for the Z direction
1826 
1827   Output Parameter:
1828 . dm  - The DM object
1829 
1830   Note:
1831   Here is the output numbering looking from the bottom of the cylinder:
1832 $       17-----14
1833 $        |     |
1834 $        |  2  |
1835 $        |     |
1836 $ 17-----8-----7-----14
1837 $  |     |     |     |
1838 $  |  3  |  0  |  1  |
1839 $  |     |     |     |
1840 $ 19-----5-----6-----13
1841 $        |     |
1842 $        |  4  |
1843 $        |     |
1844 $       19-----13
1845 $
1846 $ and up through the top
1847 $
1848 $       18-----16
1849 $        |     |
1850 $        |  2  |
1851 $        |     |
1852 $ 18----10----11-----16
1853 $  |     |     |     |
1854 $  |  3  |  0  |  1  |
1855 $  |     |     |     |
1856 $ 20-----9----12-----15
1857 $        |     |
1858 $        |  4  |
1859 $        |     |
1860 $       20-----15
1861 
1862   Level: beginner
1863 
1864 .seealso: DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
1865 @*/
1866 PetscErrorCode DMPlexCreateHexCylinderMesh(MPI_Comm comm, DMBoundaryType periodicZ, DM *dm)
1867 {
1868   PetscErrorCode ierr;
1869 
1870   PetscFunctionBegin;
1871   PetscValidPointer(dm, 3);
1872   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
1873   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
1874   ierr = DMPlexCreateHexCylinderMesh_Internal(*dm, periodicZ);CHKERRQ(ierr);
1875   PetscFunctionReturn(0);
1876 }
1877 
1878 static PetscErrorCode DMPlexCreateWedgeCylinderMesh_Internal(DM dm, PetscInt n, PetscBool interpolate)
1879 {
1880   const PetscInt dim = 3;
1881   PetscInt       numCells, numVertices, v;
1882   PetscMPIInt    rank;
1883   PetscErrorCode ierr;
1884 
1885   PetscFunctionBegin;
1886   if (n < 0) SETERRQ1(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_OUTOFRANGE, "Number of wedges %D cannot be negative", n);
1887   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject) dm), &rank);CHKERRMPI(ierr);
1888   ierr = DMSetDimension(dm, dim);CHKERRQ(ierr);
1889   /* Must create the celltype label here so that we do not automatically try to compute the types */
1890   ierr = DMCreateLabel(dm, "celltype");CHKERRQ(ierr);
1891   /* Create topology */
1892   {
1893     PetscInt cone[6], c;
1894 
1895     numCells    = !rank ?        n : 0;
1896     numVertices = !rank ?  2*(n+1) : 0;
1897     ierr = DMPlexSetChart(dm, 0, numCells+numVertices);CHKERRQ(ierr);
1898     for (c = 0; c < numCells; c++) {ierr = DMPlexSetConeSize(dm, c, 6);CHKERRQ(ierr);}
1899     ierr = DMSetUp(dm);CHKERRQ(ierr);
1900     for (c = 0; c < numCells; c++) {
1901       cone[0] =  c+n*1; cone[1] = (c+1)%n+n*1; cone[2] = 0+3*n;
1902       cone[3] =  c+n*2; cone[4] = (c+1)%n+n*2; cone[5] = 1+3*n;
1903       ierr = DMPlexSetCone(dm, c, cone);CHKERRQ(ierr);
1904       ierr = DMPlexSetCellType(dm, c, DM_POLYTOPE_TRI_PRISM_TENSOR);CHKERRQ(ierr);
1905     }
1906     ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
1907     ierr = DMPlexStratify(dm);CHKERRQ(ierr);
1908   }
1909   for (v = numCells; v < numCells+numVertices; ++v) {
1910     ierr = DMPlexSetCellType(dm, v, DM_POLYTOPE_POINT);CHKERRQ(ierr);
1911   }
1912   /* Create cylinder geometry */
1913   {
1914     Vec          coordinates;
1915     PetscSection coordSection;
1916     PetscScalar *coords;
1917     PetscInt     coordSize, c;
1918 
1919     /* Build coordinates */
1920     ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
1921     ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
1922     ierr = PetscSectionSetFieldComponents(coordSection, 0, dim);CHKERRQ(ierr);
1923     ierr = PetscSectionSetChart(coordSection, numCells, numCells+numVertices);CHKERRQ(ierr);
1924     for (v = numCells; v < numCells+numVertices; ++v) {
1925       ierr = PetscSectionSetDof(coordSection, v, dim);CHKERRQ(ierr);
1926       ierr = PetscSectionSetFieldDof(coordSection, v, 0, dim);CHKERRQ(ierr);
1927     }
1928     ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
1929     ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
1930     ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
1931     ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
1932     ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
1933     ierr = VecSetBlockSize(coordinates, dim);CHKERRQ(ierr);
1934     ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
1935     ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
1936     for (c = 0; c < numCells; c++) {
1937       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;
1938       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;
1939     }
1940     if (!rank) {
1941       coords[(2*n+0)*dim+0] = 0.0; coords[(2*n+0)*dim+1] = 0.0; coords[(2*n+0)*dim+2] = 1.0;
1942       coords[(2*n+1)*dim+0] = 0.0; coords[(2*n+1)*dim+1] = 0.0; coords[(2*n+1)*dim+2] = 0.0;
1943     }
1944     ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
1945     ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
1946     ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
1947   }
1948   /* Interpolate */
1949   if (interpolate) {ierr = DMPlexInterpolateInPlace_Internal(dm);CHKERRQ(ierr);}
1950   PetscFunctionReturn(0);
1951 }
1952 
1953 /*@
1954   DMPlexCreateWedgeCylinderMesh - Creates a mesh on the tensor product of the unit interval with the circle (cylinder) using wedges.
1955 
1956   Collective
1957 
1958   Input Parameters:
1959 + comm - The communicator for the DM object
1960 . n    - The number of wedges around the origin
1961 - interpolate - Create edges and faces
1962 
1963   Output Parameter:
1964 . dm  - The DM object
1965 
1966   Level: beginner
1967 
1968 .seealso: DMPlexCreateHexCylinderMesh(), DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
1969 @*/
1970 PetscErrorCode DMPlexCreateWedgeCylinderMesh(MPI_Comm comm, PetscInt n, PetscBool interpolate, DM *dm)
1971 {
1972   PetscErrorCode ierr;
1973 
1974   PetscFunctionBegin;
1975   PetscValidPointer(dm, 4);
1976   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
1977   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
1978   ierr = DMPlexCreateWedgeCylinderMesh_Internal(*dm, n, interpolate);CHKERRQ(ierr);
1979   PetscFunctionReturn(0);
1980 }
1981 
1982 PETSC_STATIC_INLINE PetscReal DiffNormReal(PetscInt dim, const PetscReal x[], const PetscReal y[])
1983 {
1984   PetscReal prod = 0.0;
1985   PetscInt  i;
1986   for (i = 0; i < dim; ++i) prod += PetscSqr(x[i] - y[i]);
1987   return PetscSqrtReal(prod);
1988 }
1989 PETSC_STATIC_INLINE PetscReal DotReal(PetscInt dim, const PetscReal x[], const PetscReal y[])
1990 {
1991   PetscReal prod = 0.0;
1992   PetscInt  i;
1993   for (i = 0; i < dim; ++i) prod += x[i]*y[i];
1994   return prod;
1995 }
1996 
1997 /* The first constant is the sphere radius */
1998 static void snapToSphere(PetscInt dim, PetscInt Nf, PetscInt NfAux,
1999                          const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
2000                          const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
2001                          PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
2002 {
2003   PetscReal r = PetscRealPart(constants[0]);
2004   PetscReal norm2 = 0.0, fac;
2005   PetscInt  n = uOff[1] - uOff[0], d;
2006 
2007   for (d = 0; d < n; ++d) norm2 += PetscSqr(PetscRealPart(u[d]));
2008   fac = r/PetscSqrtReal(norm2);
2009   for (d = 0; d < n; ++d) f0[d] = u[d]*fac;
2010 }
2011 
2012 static PetscErrorCode DMPlexCreateSphereMesh_Internal(DM dm, PetscInt dim, PetscBool simplex, PetscReal R)
2013 {
2014   const PetscInt  embedDim = dim+1;
2015   PetscSection    coordSection;
2016   Vec             coordinates;
2017   PetscScalar    *coords;
2018   PetscReal      *coordsIn;
2019   PetscInt        numCells, numEdges, numVerts, firstVertex, v, firstEdge, coordSize, d, c, e;
2020   PetscMPIInt     rank;
2021   PetscErrorCode  ierr;
2022 
2023   PetscFunctionBegin;
2024   PetscValidLogicalCollectiveBool(dm, simplex, 3);
2025   ierr = DMSetDimension(dm, dim);CHKERRQ(ierr);
2026   ierr = DMSetCoordinateDim(dm, dim+1);CHKERRQ(ierr);
2027   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject) dm), &rank);CHKERRMPI(ierr);
2028   switch (dim) {
2029   case 2:
2030     if (simplex) {
2031       const PetscReal radius    = PetscSqrtReal(1 + PETSC_PHI*PETSC_PHI)/(1.0 + PETSC_PHI);
2032       const PetscReal edgeLen   = 2.0/(1.0 + PETSC_PHI) * (R/radius);
2033       const PetscInt  degree    = 5;
2034       PetscReal       vertex[3] = {0.0, 1.0/(1.0 + PETSC_PHI), PETSC_PHI/(1.0 + PETSC_PHI)};
2035       PetscInt        s[3]      = {1, 1, 1};
2036       PetscInt        cone[3];
2037       PetscInt       *graph, p, i, j, k;
2038 
2039       vertex[0] *= R/radius; vertex[1] *= R/radius; vertex[2] *= R/radius;
2040       numCells    = !rank ? 20 : 0;
2041       numVerts    = !rank ? 12 : 0;
2042       firstVertex = numCells;
2043       /* Use icosahedron, which for a R-sphere has coordinates which are all cyclic permutations of
2044 
2045            (0, \pm 1/\phi+1, \pm \phi/\phi+1)
2046 
2047          where \phi^2 - \phi - 1 = 0, meaning \phi is the golden ratio \frac{1 + \sqrt{5}}{2}. The edge
2048          length is then given by 2/(1+\phi) = 2 * 0.38197 = 0.76393.
2049       */
2050       /* Construct vertices */
2051       ierr = PetscCalloc1(numVerts * embedDim, &coordsIn);CHKERRQ(ierr);
2052       if (!rank) {
2053         for (p = 0, i = 0; p < embedDim; ++p) {
2054           for (s[1] = -1; s[1] < 2; s[1] += 2) {
2055             for (s[2] = -1; s[2] < 2; s[2] += 2) {
2056               for (d = 0; d < embedDim; ++d) coordsIn[i*embedDim+d] = s[(d+p)%embedDim]*vertex[(d+p)%embedDim];
2057               ++i;
2058             }
2059           }
2060         }
2061       }
2062       /* Construct graph */
2063       ierr = PetscCalloc1(numVerts * numVerts, &graph);CHKERRQ(ierr);
2064       for (i = 0; i < numVerts; ++i) {
2065         for (j = 0, k = 0; j < numVerts; ++j) {
2066           if (PetscAbsReal(DiffNormReal(embedDim, &coordsIn[i*embedDim], &coordsIn[j*embedDim]) - edgeLen) < PETSC_SMALL) {graph[i*numVerts+j] = 1; ++k;}
2067         }
2068         if (k != degree) SETERRQ3(PetscObjectComm((PetscObject) dm), PETSC_ERR_PLIB, "Invalid icosahedron, vertex %D degree %D != %D", i, k, degree);
2069       }
2070       /* Build Topology */
2071       ierr = DMPlexSetChart(dm, 0, numCells+numVerts);CHKERRQ(ierr);
2072       for (c = 0; c < numCells; c++) {
2073         ierr = DMPlexSetConeSize(dm, c, embedDim);CHKERRQ(ierr);
2074       }
2075       ierr = DMSetUp(dm);CHKERRQ(ierr); /* Allocate space for cones */
2076       /* Cells */
2077       for (i = 0, c = 0; i < numVerts; ++i) {
2078         for (j = 0; j < i; ++j) {
2079           for (k = 0; k < j; ++k) {
2080             if (graph[i*numVerts+j] && graph[j*numVerts+k] && graph[k*numVerts+i]) {
2081               cone[0] = firstVertex+i; cone[1] = firstVertex+j; cone[2] = firstVertex+k;
2082               /* Check orientation */
2083               {
2084                 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}}};
2085                 PetscReal normal[3];
2086                 PetscInt  e, f;
2087 
2088                 for (d = 0; d < embedDim; ++d) {
2089                   normal[d] = 0.0;
2090                   for (e = 0; e < embedDim; ++e) {
2091                     for (f = 0; f < embedDim; ++f) {
2092                       normal[d] += epsilon[d][e][f]*(coordsIn[j*embedDim+e] - coordsIn[i*embedDim+e])*(coordsIn[k*embedDim+f] - coordsIn[i*embedDim+f]);
2093                     }
2094                   }
2095                 }
2096                 if (DotReal(embedDim, normal, &coordsIn[i*embedDim]) < 0) {PetscInt tmp = cone[1]; cone[1] = cone[2]; cone[2] = tmp;}
2097               }
2098               ierr = DMPlexSetCone(dm, c++, cone);CHKERRQ(ierr);
2099             }
2100           }
2101         }
2102       }
2103       ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
2104       ierr = DMPlexStratify(dm);CHKERRQ(ierr);
2105       ierr = PetscFree(graph);CHKERRQ(ierr);
2106     } else {
2107       /*
2108         12-21--13
2109          |     |
2110         25  4  24
2111          |     |
2112   12-25--9-16--8-24--13
2113    |     |     |     |
2114   23  5 17  0 15  3  22
2115    |     |     |     |
2116   10-20--6-14--7-19--11
2117          |     |
2118         20  1  19
2119          |     |
2120         10-18--11
2121          |     |
2122         23  2  22
2123          |     |
2124         12-21--13
2125        */
2126       PetscInt cone[4], ornt[4];
2127 
2128       numCells    = !rank ?  6 : 0;
2129       numEdges    = !rank ? 12 : 0;
2130       numVerts    = !rank ?  8 : 0;
2131       firstVertex = numCells;
2132       firstEdge   = numCells + numVerts;
2133       /* Build Topology */
2134       ierr = DMPlexSetChart(dm, 0, numCells+numEdges+numVerts);CHKERRQ(ierr);
2135       for (c = 0; c < numCells; c++) {
2136         ierr = DMPlexSetConeSize(dm, c, 4);CHKERRQ(ierr);
2137       }
2138       for (e = firstEdge; e < firstEdge+numEdges; ++e) {
2139         ierr = DMPlexSetConeSize(dm, e, 2);CHKERRQ(ierr);
2140       }
2141       ierr = DMSetUp(dm);CHKERRQ(ierr); /* Allocate space for cones */
2142       if (!rank) {
2143         /* Cell 0 */
2144         cone[0] = 14; cone[1] = 15; cone[2] = 16; cone[3] = 17;
2145         ierr = DMPlexSetCone(dm, 0, cone);CHKERRQ(ierr);
2146         ornt[0] = 0; ornt[1] = 0; ornt[2] = 0; ornt[3] = 0;
2147         ierr = DMPlexSetConeOrientation(dm, 0, ornt);CHKERRQ(ierr);
2148         /* Cell 1 */
2149         cone[0] = 18; cone[1] = 19; cone[2] = 14; cone[3] = 20;
2150         ierr = DMPlexSetCone(dm, 1, cone);CHKERRQ(ierr);
2151         ornt[0] = 0; ornt[1] = 0; ornt[2] = -2; ornt[3] = 0;
2152         ierr = DMPlexSetConeOrientation(dm, 1, ornt);CHKERRQ(ierr);
2153         /* Cell 2 */
2154         cone[0] = 21; cone[1] = 22; cone[2] = 18; cone[3] = 23;
2155         ierr = DMPlexSetCone(dm, 2, cone);CHKERRQ(ierr);
2156         ornt[0] = 0; ornt[1] = 0; ornt[2] = -2; ornt[3] = 0;
2157         ierr = DMPlexSetConeOrientation(dm, 2, ornt);CHKERRQ(ierr);
2158         /* Cell 3 */
2159         cone[0] = 19; cone[1] = 22; cone[2] = 24; cone[3] = 15;
2160         ierr = DMPlexSetCone(dm, 3, cone);CHKERRQ(ierr);
2161         ornt[0] = -2; ornt[1] = -2; ornt[2] = 0; ornt[3] = -2;
2162         ierr = DMPlexSetConeOrientation(dm, 3, ornt);CHKERRQ(ierr);
2163         /* Cell 4 */
2164         cone[0] = 16; cone[1] = 24; cone[2] = 21; cone[3] = 25;
2165         ierr = DMPlexSetCone(dm, 4, cone);CHKERRQ(ierr);
2166         ornt[0] = -2; ornt[1] = -2; ornt[2] = -2; ornt[3] = 0;
2167         ierr = DMPlexSetConeOrientation(dm, 4, ornt);CHKERRQ(ierr);
2168         /* Cell 5 */
2169         cone[0] = 20; cone[1] = 17; cone[2] = 25; cone[3] = 23;
2170         ierr = DMPlexSetCone(dm, 5, cone);CHKERRQ(ierr);
2171         ornt[0] = -2; ornt[1] = -2; ornt[2] = -2; ornt[3] = -2;
2172         ierr = DMPlexSetConeOrientation(dm, 5, ornt);CHKERRQ(ierr);
2173         /* Edges */
2174         cone[0] =  6; cone[1] =  7;
2175         ierr = DMPlexSetCone(dm, 14, cone);CHKERRQ(ierr);
2176         cone[0] =  7; cone[1] =  8;
2177         ierr = DMPlexSetCone(dm, 15, cone);CHKERRQ(ierr);
2178         cone[0] =  8; cone[1] =  9;
2179         ierr = DMPlexSetCone(dm, 16, cone);CHKERRQ(ierr);
2180         cone[0] =  9; cone[1] =  6;
2181         ierr = DMPlexSetCone(dm, 17, cone);CHKERRQ(ierr);
2182         cone[0] = 10; cone[1] = 11;
2183         ierr = DMPlexSetCone(dm, 18, cone);CHKERRQ(ierr);
2184         cone[0] = 11; cone[1] =  7;
2185         ierr = DMPlexSetCone(dm, 19, cone);CHKERRQ(ierr);
2186         cone[0] =  6; cone[1] = 10;
2187         ierr = DMPlexSetCone(dm, 20, cone);CHKERRQ(ierr);
2188         cone[0] = 12; cone[1] = 13;
2189         ierr = DMPlexSetCone(dm, 21, cone);CHKERRQ(ierr);
2190         cone[0] = 13; cone[1] = 11;
2191         ierr = DMPlexSetCone(dm, 22, cone);CHKERRQ(ierr);
2192         cone[0] = 10; cone[1] = 12;
2193         ierr = DMPlexSetCone(dm, 23, cone);CHKERRQ(ierr);
2194         cone[0] = 13; cone[1] =  8;
2195         ierr = DMPlexSetCone(dm, 24, cone);CHKERRQ(ierr);
2196         cone[0] = 12; cone[1] =  9;
2197         ierr = DMPlexSetCone(dm, 25, cone);CHKERRQ(ierr);
2198       }
2199       ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
2200       ierr = DMPlexStratify(dm);CHKERRQ(ierr);
2201       /* Build coordinates */
2202       ierr = PetscCalloc1(numVerts * embedDim, &coordsIn);CHKERRQ(ierr);
2203       if (!rank) {
2204         coordsIn[0*embedDim+0] = -R; coordsIn[0*embedDim+1] =  R; coordsIn[0*embedDim+2] = -R;
2205         coordsIn[1*embedDim+0] =  R; coordsIn[1*embedDim+1] =  R; coordsIn[1*embedDim+2] = -R;
2206         coordsIn[2*embedDim+0] =  R; coordsIn[2*embedDim+1] = -R; coordsIn[2*embedDim+2] = -R;
2207         coordsIn[3*embedDim+0] = -R; coordsIn[3*embedDim+1] = -R; coordsIn[3*embedDim+2] = -R;
2208         coordsIn[4*embedDim+0] = -R; coordsIn[4*embedDim+1] =  R; coordsIn[4*embedDim+2] =  R;
2209         coordsIn[5*embedDim+0] =  R; coordsIn[5*embedDim+1] =  R; coordsIn[5*embedDim+2] =  R;
2210         coordsIn[6*embedDim+0] = -R; coordsIn[6*embedDim+1] = -R; coordsIn[6*embedDim+2] =  R;
2211         coordsIn[7*embedDim+0] =  R; coordsIn[7*embedDim+1] = -R; coordsIn[7*embedDim+2] =  R;
2212       }
2213     }
2214     break;
2215   case 3:
2216     if (simplex) {
2217       const PetscReal edgeLen         = 1.0/PETSC_PHI;
2218       PetscReal       vertexA[4]      = {0.5, 0.5, 0.5, 0.5};
2219       PetscReal       vertexB[4]      = {1.0, 0.0, 0.0, 0.0};
2220       PetscReal       vertexC[4]      = {0.5, 0.5*PETSC_PHI, 0.5/PETSC_PHI, 0.0};
2221       const PetscInt  degree          = 12;
2222       PetscInt        s[4]            = {1, 1, 1};
2223       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},
2224                                          {2, 0, 1, 3}, {2, 1, 3, 0}, {2, 3, 0, 1}, {3, 0, 2, 1}, {3, 1, 0, 2}, {3, 2, 1, 0}};
2225       PetscInt        cone[4];
2226       PetscInt       *graph, p, i, j, k, l;
2227 
2228       vertexA[0] *= R; vertexA[1] *= R; vertexA[2] *= R; vertexA[3] *= R;
2229       vertexB[0] *= R; vertexB[1] *= R; vertexB[2] *= R; vertexB[3] *= R;
2230       vertexC[0] *= R; vertexC[1] *= R; vertexC[2] *= R; vertexC[3] *= R;
2231       numCells    = !rank ? 600 : 0;
2232       numVerts    = !rank ? 120 : 0;
2233       firstVertex = numCells;
2234       /* Use the 600-cell, which for a unit sphere has coordinates which are
2235 
2236            1/2 (\pm 1, \pm 1,    \pm 1, \pm 1)                          16
2237                (\pm 1,    0,       0,      0)  all cyclic permutations   8
2238            1/2 (\pm 1, \pm phi, \pm 1/phi, 0)  all even permutations    96
2239 
2240          where \phi^2 - \phi - 1 = 0, meaning \phi is the golden ratio \frac{1 + \sqrt{5}}{2}. The edge
2241          length is then given by 1/\phi = 0.61803.
2242 
2243          http://buzzard.pugetsound.edu/sage-practice/ch03s03.html
2244          http://mathworld.wolfram.com/600-Cell.html
2245       */
2246       /* Construct vertices */
2247       ierr = PetscCalloc1(numVerts * embedDim, &coordsIn);CHKERRQ(ierr);
2248       i    = 0;
2249       if (!rank) {
2250         for (s[0] = -1; s[0] < 2; s[0] += 2) {
2251           for (s[1] = -1; s[1] < 2; s[1] += 2) {
2252             for (s[2] = -1; s[2] < 2; s[2] += 2) {
2253               for (s[3] = -1; s[3] < 2; s[3] += 2) {
2254                 for (d = 0; d < embedDim; ++d) coordsIn[i*embedDim+d] = s[d]*vertexA[d];
2255                 ++i;
2256               }
2257             }
2258           }
2259         }
2260         for (p = 0; p < embedDim; ++p) {
2261           s[1] = s[2] = s[3] = 1;
2262           for (s[0] = -1; s[0] < 2; s[0] += 2) {
2263             for (d = 0; d < embedDim; ++d) coordsIn[i*embedDim+d] = s[(d+p)%embedDim]*vertexB[(d+p)%embedDim];
2264             ++i;
2265           }
2266         }
2267         for (p = 0; p < 12; ++p) {
2268           s[3] = 1;
2269           for (s[0] = -1; s[0] < 2; s[0] += 2) {
2270             for (s[1] = -1; s[1] < 2; s[1] += 2) {
2271               for (s[2] = -1; s[2] < 2; s[2] += 2) {
2272                 for (d = 0; d < embedDim; ++d) coordsIn[i*embedDim+d] = s[evenPerm[p][d]]*vertexC[evenPerm[p][d]];
2273                 ++i;
2274               }
2275             }
2276           }
2277         }
2278       }
2279       if (i != numVerts) SETERRQ2(PetscObjectComm((PetscObject) dm), PETSC_ERR_PLIB, "Invalid 600-cell, vertices %D != %D", i, numVerts);
2280       /* Construct graph */
2281       ierr = PetscCalloc1(numVerts * numVerts, &graph);CHKERRQ(ierr);
2282       for (i = 0; i < numVerts; ++i) {
2283         for (j = 0, k = 0; j < numVerts; ++j) {
2284           if (PetscAbsReal(DiffNormReal(embedDim, &coordsIn[i*embedDim], &coordsIn[j*embedDim]) - edgeLen) < PETSC_SMALL) {graph[i*numVerts+j] = 1; ++k;}
2285         }
2286         if (k != degree) SETERRQ3(PetscObjectComm((PetscObject) dm), PETSC_ERR_PLIB, "Invalid 600-cell, vertex %D degree %D != %D", i, k, degree);
2287       }
2288       /* Build Topology */
2289       ierr = DMPlexSetChart(dm, 0, numCells+numVerts);CHKERRQ(ierr);
2290       for (c = 0; c < numCells; c++) {
2291         ierr = DMPlexSetConeSize(dm, c, embedDim);CHKERRQ(ierr);
2292       }
2293       ierr = DMSetUp(dm);CHKERRQ(ierr); /* Allocate space for cones */
2294       /* Cells */
2295       if (!rank) {
2296         for (i = 0, c = 0; i < numVerts; ++i) {
2297           for (j = 0; j < i; ++j) {
2298             for (k = 0; k < j; ++k) {
2299               for (l = 0; l < k; ++l) {
2300                 if (graph[i*numVerts+j] && graph[j*numVerts+k] && graph[k*numVerts+i] &&
2301                     graph[l*numVerts+i] && graph[l*numVerts+j] && graph[l*numVerts+k]) {
2302                   cone[0] = firstVertex+i; cone[1] = firstVertex+j; cone[2] = firstVertex+k; cone[3] = firstVertex+l;
2303                   /* Check orientation: https://ef.gy/linear-algebra:normal-vectors-in-higher-dimensional-spaces */
2304                   {
2305                     const PetscInt epsilon[4][4][4][4] = {{{{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}},
2306                                                            {{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  1}, { 0,  0, -1, 0}},
2307                                                            {{0,  0,  0,  0}, { 0, 0,  0, -1}, { 0,  0, 0,  0}, { 0,  1,  0, 0}},
2308                                                            {{0,  0,  0,  0}, { 0, 0,  1,  0}, { 0, -1, 0,  0}, { 0,  0,  0, 0}}},
2309 
2310                                                           {{{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0, -1}, { 0,  0,  1, 0}},
2311                                                            {{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}},
2312                                                            {{0,  0,  0,  1}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, {-1,  0,  0, 0}},
2313                                                            {{0,  0, -1,  0}, { 0, 0,  0,  0}, { 1,  0, 0,  0}, { 0,  0,  0, 0}}},
2314 
2315                                                           {{{0,  0,  0,  0}, { 0, 0,  0,  1}, { 0,  0, 0,  0}, { 0, -1,  0, 0}},
2316                                                            {{0,  0,  0, -1}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 1,  0,  0, 0}},
2317                                                            {{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}},
2318                                                            {{0,  1,  0,  0}, {-1, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}}},
2319 
2320                                                           {{{0,  0,  0,  0}, { 0, 0, -1,  0}, { 0,  1, 0,  0}, { 0,  0,  0, 0}},
2321                                                            {{0,  0,  1,  0}, { 0, 0,  0,  0}, {-1,  0, 0,  0}, { 0,  0,  0, 0}},
2322                                                            {{0, -1,  0,  0}, { 1, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}},
2323                                                            {{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}}}};
2324                     PetscReal normal[4];
2325                     PetscInt  e, f, g;
2326 
2327                     for (d = 0; d < embedDim; ++d) {
2328                       normal[d] = 0.0;
2329                       for (e = 0; e < embedDim; ++e) {
2330                         for (f = 0; f < embedDim; ++f) {
2331                           for (g = 0; g < embedDim; ++g) {
2332                             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]);
2333                           }
2334                         }
2335                       }
2336                     }
2337                     if (DotReal(embedDim, normal, &coordsIn[i*embedDim]) < 0) {PetscInt tmp = cone[1]; cone[1] = cone[2]; cone[2] = tmp;}
2338                   }
2339                   ierr = DMPlexSetCone(dm, c++, cone);CHKERRQ(ierr);
2340                 }
2341               }
2342             }
2343           }
2344         }
2345       }
2346       ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
2347       ierr = DMPlexStratify(dm);CHKERRQ(ierr);
2348       ierr = PetscFree(graph);CHKERRQ(ierr);
2349       break;
2350     }
2351   default: SETERRQ1(PetscObjectComm((PetscObject) dm), PETSC_ERR_SUP, "Unsupported dimension for sphere: %D", dim);
2352   }
2353   /* Create coordinates */
2354   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
2355   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
2356   ierr = PetscSectionSetFieldComponents(coordSection, 0, embedDim);CHKERRQ(ierr);
2357   ierr = PetscSectionSetChart(coordSection, firstVertex, firstVertex+numVerts);CHKERRQ(ierr);
2358   for (v = firstVertex; v < firstVertex+numVerts; ++v) {
2359     ierr = PetscSectionSetDof(coordSection, v, embedDim);CHKERRQ(ierr);
2360     ierr = PetscSectionSetFieldDof(coordSection, v, 0, embedDim);CHKERRQ(ierr);
2361   }
2362   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
2363   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
2364   ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
2365   ierr = VecSetBlockSize(coordinates, embedDim);CHKERRQ(ierr);
2366   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
2367   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
2368   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
2369   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
2370   for (v = 0; v < numVerts; ++v) for (d = 0; d < embedDim; ++d) {coords[v*embedDim+d] = coordsIn[v*embedDim+d];}
2371   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
2372   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
2373   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
2374   ierr = PetscFree(coordsIn);CHKERRQ(ierr);
2375   {
2376     DM          cdm;
2377     PetscDS     cds;
2378     PetscScalar c = R;
2379 
2380     ierr = DMPlexCreateCoordinateSpace(dm, 1, snapToSphere);CHKERRQ(ierr);
2381     ierr = DMGetCoordinateDM(dm, &cdm);CHKERRQ(ierr);
2382     ierr = DMGetDS(cdm, &cds);CHKERRQ(ierr);
2383     ierr = PetscDSSetConstants(cds, 1, &c);CHKERRQ(ierr);
2384   }
2385   /* Wait for coordinate creation before doing in-place modification */
2386   if (simplex) {ierr = DMPlexInterpolateInPlace_Internal(dm);CHKERRQ(ierr);}
2387   PetscFunctionReturn(0);
2388 }
2389 
2390 /*@
2391   DMPlexCreateSphereMesh - Creates a mesh on the d-dimensional sphere, S^d.
2392 
2393   Collective
2394 
2395   Input Parameters:
2396 + comm    - The communicator for the DM object
2397 . dim     - The dimension
2398 . simplex - Use simplices, or tensor product cells
2399 - R       - The radius
2400 
2401   Output Parameter:
2402 . dm  - The DM object
2403 
2404   Level: beginner
2405 
2406 .seealso: DMPlexCreateBallMesh(), DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
2407 @*/
2408 PetscErrorCode DMPlexCreateSphereMesh(MPI_Comm comm, PetscInt dim, PetscBool simplex, PetscReal R, DM *dm)
2409 {
2410   PetscErrorCode ierr;
2411 
2412   PetscFunctionBegin;
2413   PetscValidPointer(dm, 5);
2414   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
2415   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
2416   ierr = DMPlexCreateSphereMesh_Internal(*dm, dim, simplex, R);CHKERRQ(ierr);
2417   PetscFunctionReturn(0);
2418 }
2419 
2420 static PetscErrorCode DMPlexCreateBallMesh_Internal(DM dm, PetscInt dim, PetscReal R)
2421 {
2422   DM             sdm, vol;
2423   DMLabel        bdlabel;
2424   PetscErrorCode ierr;
2425 
2426   PetscFunctionBegin;
2427   ierr = DMCreate(PetscObjectComm((PetscObject) dm), &sdm);CHKERRQ(ierr);
2428   ierr = DMSetType(sdm, DMPLEX);CHKERRQ(ierr);
2429   ierr = PetscObjectSetOptionsPrefix((PetscObject) sdm, "bd_");CHKERRQ(ierr);
2430   ierr = DMPlexCreateSphereMesh_Internal(sdm, dim-1, PETSC_TRUE, R);CHKERRQ(ierr);
2431   ierr = DMSetFromOptions(sdm);CHKERRQ(ierr);
2432   ierr = DMViewFromOptions(sdm, NULL, "-dm_view");CHKERRQ(ierr);
2433   ierr = DMPlexGenerate(sdm, NULL, PETSC_TRUE, &vol);CHKERRQ(ierr);
2434   ierr = DMDestroy(&sdm);CHKERRQ(ierr);
2435   ierr = DMPlexReplace_Static(dm, &vol);CHKERRQ(ierr);
2436   ierr = DMCreateLabel(dm, "marker");CHKERRQ(ierr);
2437   ierr = DMGetLabel(dm, "marker", &bdlabel);CHKERRQ(ierr);
2438   ierr = DMPlexMarkBoundaryFaces(dm, PETSC_DETERMINE, bdlabel);CHKERRQ(ierr);
2439   ierr = DMPlexLabelComplete(dm, bdlabel);CHKERRQ(ierr);
2440   PetscFunctionReturn(0);
2441 }
2442 
2443 /*@
2444   DMPlexCreateBallMesh - Creates a simplex mesh on the d-dimensional ball, B^d.
2445 
2446   Collective
2447 
2448   Input Parameters:
2449 + comm  - The communicator for the DM object
2450 . dim   - The dimension
2451 - R     - The radius
2452 
2453   Output Parameter:
2454 . dm  - The DM object
2455 
2456   Options Database Keys:
2457 - bd_dm_refine - This will refine the surface mesh preserving the sphere geometry
2458 
2459   Level: beginner
2460 
2461 .seealso: DMPlexCreateSphereMesh(), DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
2462 @*/
2463 PetscErrorCode DMPlexCreateBallMesh(MPI_Comm comm, PetscInt dim, PetscReal R, DM *dm)
2464 {
2465   PetscErrorCode ierr;
2466 
2467   PetscFunctionBegin;
2468   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
2469   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
2470   ierr = DMPlexCreateBallMesh_Internal(*dm, dim, R);CHKERRQ(ierr);
2471   PetscFunctionReturn(0);
2472 }
2473 
2474 static PetscErrorCode DMPlexCreateReferenceCell_Internal(DM rdm, DMPolytopeType ct)
2475 {
2476   PetscErrorCode ierr;
2477 
2478   PetscFunctionBegin;
2479   switch (ct) {
2480     case DM_POLYTOPE_POINT:
2481     {
2482       PetscInt    numPoints[1]        = {1};
2483       PetscInt    coneSize[1]         = {0};
2484       PetscInt    cones[1]            = {0};
2485       PetscInt    coneOrientations[1] = {0};
2486       PetscScalar vertexCoords[1]     = {0.0};
2487 
2488       ierr = DMSetDimension(rdm, 0);CHKERRQ(ierr);
2489       ierr = DMPlexCreateFromDAG(rdm, 0, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2490     }
2491     break;
2492     case DM_POLYTOPE_SEGMENT:
2493     {
2494       PetscInt    numPoints[2]        = {2, 1};
2495       PetscInt    coneSize[3]         = {2, 0, 0};
2496       PetscInt    cones[2]            = {1, 2};
2497       PetscInt    coneOrientations[2] = {0, 0};
2498       PetscScalar vertexCoords[2]     = {-1.0,  1.0};
2499 
2500       ierr = DMSetDimension(rdm, 1);CHKERRQ(ierr);
2501       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2502     }
2503     break;
2504     case DM_POLYTOPE_TRIANGLE:
2505     {
2506       PetscInt    numPoints[2]        = {3, 1};
2507       PetscInt    coneSize[4]         = {3, 0, 0, 0};
2508       PetscInt    cones[3]            = {1, 2, 3};
2509       PetscInt    coneOrientations[3] = {0, 0, 0};
2510       PetscScalar vertexCoords[6]     = {-1.0, -1.0,  1.0, -1.0,  -1.0, 1.0};
2511 
2512       ierr = DMSetDimension(rdm, 2);CHKERRQ(ierr);
2513       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2514     }
2515     break;
2516     case DM_POLYTOPE_QUADRILATERAL:
2517     {
2518       PetscInt    numPoints[2]        = {4, 1};
2519       PetscInt    coneSize[5]         = {4, 0, 0, 0, 0};
2520       PetscInt    cones[4]            = {1, 2, 3, 4};
2521       PetscInt    coneOrientations[4] = {0, 0, 0, 0};
2522       PetscScalar vertexCoords[8]     = {-1.0, -1.0,  1.0, -1.0,  1.0, 1.0,  -1.0, 1.0};
2523 
2524       ierr = DMSetDimension(rdm, 2);CHKERRQ(ierr);
2525       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2526     }
2527     break;
2528     case DM_POLYTOPE_SEG_PRISM_TENSOR:
2529     {
2530       PetscInt    numPoints[2]        = {4, 1};
2531       PetscInt    coneSize[5]         = {4, 0, 0, 0, 0};
2532       PetscInt    cones[4]            = {1, 2, 3, 4};
2533       PetscInt    coneOrientations[4] = {0, 0, 0, 0};
2534       PetscScalar vertexCoords[8]     = {-1.0, -1.0,  1.0, -1.0,  -1.0, 1.0,  1.0, 1.0};
2535 
2536       ierr = DMSetDimension(rdm, 2);CHKERRQ(ierr);
2537       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2538     }
2539     break;
2540     case DM_POLYTOPE_TETRAHEDRON:
2541     {
2542       PetscInt    numPoints[2]        = {4, 1};
2543       PetscInt    coneSize[5]         = {4, 0, 0, 0, 0};
2544       PetscInt    cones[4]            = {1, 3, 2, 4};
2545       PetscInt    coneOrientations[4] = {0, 0, 0, 0};
2546       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};
2547 
2548       ierr = DMSetDimension(rdm, 3);CHKERRQ(ierr);
2549       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2550     }
2551     break;
2552     case DM_POLYTOPE_HEXAHEDRON:
2553     {
2554       PetscInt    numPoints[2]        = {8, 1};
2555       PetscInt    coneSize[9]         = {8, 0, 0, 0, 0, 0, 0, 0, 0};
2556       PetscInt    cones[8]            = {1, 4, 3, 2, 5, 6, 7, 8};
2557       PetscInt    coneOrientations[8] = {0, 0, 0, 0, 0, 0, 0, 0};
2558       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,
2559                                          -1.0, -1.0,  1.0,  1.0, -1.0,  1.0,  1.0, 1.0,  1.0,  -1.0, 1.0,  1.0};
2560 
2561       ierr = DMSetDimension(rdm, 3);CHKERRQ(ierr);
2562       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2563     }
2564     break;
2565     case DM_POLYTOPE_TRI_PRISM:
2566     {
2567       PetscInt    numPoints[2]        = {6, 1};
2568       PetscInt    coneSize[7]         = {6, 0, 0, 0, 0, 0, 0};
2569       PetscInt    cones[6]            = {1, 3, 2, 4, 5, 6};
2570       PetscInt    coneOrientations[6] = {0, 0, 0, 0, 0, 0};
2571       PetscScalar vertexCoords[18]    = {-1.0, -1.0, -1.0,  1.0, -1.0, -1.0,  -1.0, 1.0, -1.0,
2572                                          -1.0, -1.0,  1.0,  1.0, -1.0,  1.0,  -1.0, 1.0,  1.0};
2573 
2574       ierr = DMSetDimension(rdm, 3);CHKERRQ(ierr);
2575       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2576     }
2577     break;
2578     case DM_POLYTOPE_TRI_PRISM_TENSOR:
2579     {
2580       PetscInt    numPoints[2]        = {6, 1};
2581       PetscInt    coneSize[7]         = {6, 0, 0, 0, 0, 0, 0};
2582       PetscInt    cones[6]            = {1, 2, 3, 4, 5, 6};
2583       PetscInt    coneOrientations[6] = {0, 0, 0, 0, 0, 0};
2584       PetscScalar vertexCoords[18]    = {-1.0, -1.0, -1.0,  1.0, -1.0, -1.0,  -1.0, 1.0, -1.0,
2585                                          -1.0, -1.0,  1.0,  1.0, -1.0,  1.0,  -1.0, 1.0,  1.0};
2586 
2587       ierr = DMSetDimension(rdm, 3);CHKERRQ(ierr);
2588       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2589     }
2590     break;
2591     case DM_POLYTOPE_QUAD_PRISM_TENSOR:
2592     {
2593       PetscInt    numPoints[2]        = {8, 1};
2594       PetscInt    coneSize[9]         = {8, 0, 0, 0, 0, 0, 0, 0, 0};
2595       PetscInt    cones[8]            = {1, 2, 3, 4, 5, 6, 7, 8};
2596       PetscInt    coneOrientations[8] = {0, 0, 0, 0, 0, 0, 0, 0};
2597       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,
2598                                          -1.0, -1.0,  1.0,  1.0, -1.0,  1.0,  1.0, 1.0,  1.0,  -1.0, 1.0,  1.0};
2599 
2600       ierr = DMSetDimension(rdm, 3);CHKERRQ(ierr);
2601       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2602     }
2603     break;
2604     case DM_POLYTOPE_PYRAMID:
2605     {
2606       PetscInt    numPoints[2]        = {5, 1};
2607       PetscInt    coneSize[6]         = {5, 0, 0, 0, 0, 0};
2608       PetscInt    cones[5]            = {1, 4, 3, 2, 5};
2609       PetscInt    coneOrientations[8] = {0, 0, 0, 0, 0, 0, 0, 0};
2610       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,
2611                                           0.0,  0.0,  1.0};
2612 
2613       ierr = DMSetDimension(rdm, 3);CHKERRQ(ierr);
2614       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2615     }
2616     break;
2617     default: SETERRQ1(PetscObjectComm((PetscObject) rdm), PETSC_ERR_ARG_WRONG, "Cannot create reference cell for cell type %s", DMPolytopeTypes[ct]);
2618   }
2619   {
2620     PetscInt Nv, v;
2621 
2622     /* Must create the celltype label here so that we do not automatically try to compute the types */
2623     ierr = DMCreateLabel(rdm, "celltype");CHKERRQ(ierr);
2624     ierr = DMPlexSetCellType(rdm, 0, ct);CHKERRQ(ierr);
2625     ierr = DMPlexGetChart(rdm, NULL, &Nv);CHKERRQ(ierr);
2626     for (v = 1; v < Nv; ++v) {ierr = DMPlexSetCellType(rdm, v, DM_POLYTOPE_POINT);CHKERRQ(ierr);}
2627   }
2628   ierr = DMPlexInterpolateInPlace_Internal(rdm);CHKERRQ(ierr);
2629   ierr = PetscObjectSetName((PetscObject) rdm, DMPolytopeTypes[ct]);CHKERRQ(ierr);
2630   PetscFunctionReturn(0);
2631 }
2632 
2633 /*@
2634   DMPlexCreateReferenceCell - Create a DMPLEX with the appropriate FEM reference cell
2635 
2636   Collective
2637 
2638   Input Parameters:
2639 + comm - The communicator
2640 - ct   - The cell type of the reference cell
2641 
2642   Output Parameter:
2643 . refdm - The reference cell
2644 
2645   Level: intermediate
2646 
2647 .seealso: DMPlexCreateReferenceCell(), DMPlexCreateBoxMesh()
2648 @*/
2649 PetscErrorCode DMPlexCreateReferenceCell(MPI_Comm comm, DMPolytopeType ct, DM *refdm)
2650 {
2651   PetscErrorCode ierr;
2652 
2653   PetscFunctionBegin;
2654   ierr = DMCreate(comm, refdm);CHKERRQ(ierr);
2655   ierr = DMSetType(*refdm, DMPLEX);CHKERRQ(ierr);
2656   ierr = DMPlexCreateReferenceCell_Internal(*refdm, ct);CHKERRQ(ierr);
2657   PetscFunctionReturn(0);
2658 }
2659 
2660 static PetscErrorCode DMPlexCreateBoundaryLabel_Private(DM dm, const char name[])
2661 {
2662   DM             plex;
2663   DMLabel        label;
2664   PetscBool      hasLabel;
2665   PetscErrorCode ierr;
2666 
2667   PetscFunctionBeginUser;
2668   ierr = DMHasLabel(dm, name, &hasLabel);CHKERRQ(ierr);
2669   if (hasLabel) PetscFunctionReturn(0);
2670   ierr = DMCreateLabel(dm, name);CHKERRQ(ierr);
2671   ierr = DMGetLabel(dm, name, &label);CHKERRQ(ierr);
2672   ierr = DMConvert(dm, DMPLEX, &plex);CHKERRQ(ierr);
2673   ierr = DMPlexMarkBoundaryFaces(plex, 1, label);CHKERRQ(ierr);
2674   ierr = DMDestroy(&plex);CHKERRQ(ierr);
2675   PetscFunctionReturn(0);
2676 }
2677 
2678 const char * const DMPlexShapes[] = {"box", "box_surface", "ball", "sphere", "cylinder", "unknown", "DMPlexShape", "DM_SHAPE_", NULL};
2679 
2680 static PetscErrorCode DMPlexCreateFromOptions_Internal(PetscOptionItems *PetscOptionsObject, PetscBool *useCoordSpace, DM dm)
2681 {
2682   DMPlexShape    shape = DM_SHAPE_BOX;
2683   DMPolytopeType cell  = DM_POLYTOPE_TRIANGLE;
2684   PetscInt       dim   = 2;
2685   PetscBool      simplex = PETSC_TRUE, interpolate = PETSC_TRUE, adjCone = PETSC_FALSE, adjClosure = PETSC_TRUE, refDomain = PETSC_FALSE;
2686   PetscBool      flg, flg2, fflg, bdfflg;
2687   MPI_Comm       comm;
2688   char           filename[PETSC_MAX_PATH_LEN], bdFilename[PETSC_MAX_PATH_LEN];
2689   PetscErrorCode ierr;
2690 
2691   PetscFunctionBegin;
2692   ierr = PetscObjectGetComm((PetscObject) dm, &comm);CHKERRQ(ierr);
2693   /* TODO Turn this into a registration interface */
2694   ierr = PetscOptionsString("-dm_plex_filename", "File containing a mesh", "DMPlexCreateFromFile", filename, filename, sizeof(filename), &fflg);CHKERRQ(ierr);
2695   ierr = PetscOptionsString("-dm_plex_boundary_filename", "File containing a mesh boundary", "DMPlexCreateFromFile", bdFilename, bdFilename, sizeof(bdFilename), &bdfflg);CHKERRQ(ierr);
2696   ierr = PetscOptionsEnum("-dm_plex_cell", "Cell shape", "", DMPolytopeTypes, (PetscEnum) cell, (PetscEnum *) &cell, NULL);CHKERRQ(ierr);
2697   ierr = PetscOptionsBool("-dm_plex_reference_cell_domain", "Use a reference cell domain", "", refDomain, &refDomain, NULL);CHKERRQ(ierr);
2698   ierr = PetscOptionsEnum("-dm_plex_shape", "Shape for built-in mesh", "", DMPlexShapes, (PetscEnum) shape, (PetscEnum *) &shape, &flg);CHKERRQ(ierr);
2699   ierr = PetscOptionsBoundedInt("-dm_plex_dim", "Topological dimension of the mesh", "DMGetDimension", dim, &dim, &flg, 0);CHKERRQ(ierr);
2700   if ((dim < 0) || (dim > 3)) SETERRQ1(comm, PETSC_ERR_ARG_OUTOFRANGE, "Dimension %D should be in [1, 3]", dim);
2701   ierr = PetscOptionsBool("-dm_plex_simplex", "Mesh cell shape", "", simplex,  &simplex, &flg);CHKERRQ(ierr);
2702   ierr = PetscOptionsBool("-dm_plex_interpolate", "Flag to create edges and faces automatically", "", interpolate, &interpolate, &flg);CHKERRQ(ierr);
2703   ierr = PetscOptionsBool("-dm_plex_adj_cone", "Set adjacency direction", "DMSetBasicAdjacency", adjCone,  &adjCone, &flg);CHKERRQ(ierr);
2704   ierr = PetscOptionsBool("-dm_plex_adj_closure", "Set adjacency size", "DMSetBasicAdjacency", adjClosure,  &adjClosure, &flg2);CHKERRQ(ierr);
2705   if (flg || flg2) {ierr = DMSetBasicAdjacency(dm, adjCone, adjClosure);CHKERRQ(ierr);}
2706 
2707   switch (cell) {
2708     case DM_POLYTOPE_POINT:
2709     case DM_POLYTOPE_SEGMENT:
2710     case DM_POLYTOPE_POINT_PRISM_TENSOR:
2711     case DM_POLYTOPE_TRIANGLE:
2712     case DM_POLYTOPE_QUADRILATERAL:
2713     case DM_POLYTOPE_TETRAHEDRON:
2714     case DM_POLYTOPE_HEXAHEDRON:
2715       *useCoordSpace = PETSC_TRUE;break;
2716     default: *useCoordSpace = PETSC_FALSE;break;
2717   }
2718 
2719   if (fflg) {
2720     DM dmnew;
2721 
2722     ierr = DMPlexCreateFromFile(PetscObjectComm((PetscObject) dm), filename, interpolate, &dmnew);CHKERRQ(ierr);
2723     ierr = DMPlexReplace_Static(dm, &dmnew);CHKERRQ(ierr);
2724   } else if (refDomain) {
2725     ierr = DMPlexCreateReferenceCell_Internal(dm, cell);CHKERRQ(ierr);
2726   } else if (bdfflg) {
2727     DM bdm, dmnew;
2728 
2729     ierr = DMPlexCreateFromFile(PetscObjectComm((PetscObject) dm), bdFilename, interpolate, &bdm);CHKERRQ(ierr);
2730     ierr = PetscObjectSetOptionsPrefix((PetscObject) bdm, "bd_");CHKERRQ(ierr);
2731     ierr = DMSetFromOptions(bdm);CHKERRQ(ierr);
2732     ierr = DMPlexGenerate(bdm, NULL, interpolate, &dmnew);CHKERRQ(ierr);
2733     ierr = DMDestroy(&bdm);CHKERRQ(ierr);
2734     ierr = DMPlexReplace_Static(dm, &dmnew);CHKERRQ(ierr);
2735   } else {
2736     ierr = PetscObjectSetName((PetscObject) dm, DMPlexShapes[shape]);CHKERRQ(ierr);
2737     switch (shape) {
2738       case DM_SHAPE_BOX:
2739       {
2740         PetscInt       faces[3] = {0, 0, 0};
2741         PetscReal      lower[3] = {0, 0, 0};
2742         PetscReal      upper[3] = {1, 1, 1};
2743         DMBoundaryType bdt[3]   = {DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE};
2744         PetscInt       i, n;
2745 
2746         n    = dim;
2747         for (i = 0; i < dim; ++i) faces[i] = (dim == 1 ? 1 : 4-dim);
2748         ierr = PetscOptionsIntArray("-dm_plex_box_faces", "Number of faces along each dimension", "", faces, &n, &flg);CHKERRQ(ierr);
2749         n    = 3;
2750         ierr = PetscOptionsRealArray("-dm_plex_box_lower", "Lower left corner of box", "", lower, &n, &flg);CHKERRQ(ierr);
2751         if (flg && (n != dim)) SETERRQ2(comm, PETSC_ERR_ARG_SIZ, "Lower box point had %D values, should have been %D", n, dim);
2752         n    = 3;
2753         ierr = PetscOptionsRealArray("-dm_plex_box_upper", "Upper right corner of box", "", upper, &n, &flg);CHKERRQ(ierr);
2754         if (flg && (n != dim)) SETERRQ2(comm, PETSC_ERR_ARG_SIZ, "Upper box point had %D values, should have been %D", n, dim);
2755         n    = 3;
2756         ierr = PetscOptionsEnumArray("-dm_plex_box_bd", "Boundary type for each dimension", "", DMBoundaryTypes, (PetscEnum *) bdt, &n, &flg);CHKERRQ(ierr);
2757         if (flg && (n != dim)) SETERRQ2(comm, PETSC_ERR_ARG_SIZ, "Box boundary types had %D values, should have been %D", n, dim);
2758         switch (cell) {
2759           case DM_POLYTOPE_TRI_PRISM_TENSOR:
2760             ierr = DMPlexCreateWedgeBoxMesh_Internal(dm, faces, lower, upper, bdt, PETSC_FALSE, interpolate);CHKERRQ(ierr);
2761             break;
2762           default:
2763             ierr = DMPlexCreateBoxMesh_Internal(dm, dim, simplex, faces, lower, upper, bdt, interpolate);CHKERRQ(ierr);
2764             break;
2765         }
2766       }
2767       break;
2768       case DM_SHAPE_BOX_SURFACE:
2769       {
2770         PetscInt  faces[3] = {0, 0, 0};
2771         PetscReal lower[3] = {0, 0, 0};
2772         PetscReal upper[3] = {1, 1, 1};
2773         PetscInt  i, n;
2774 
2775         n    = dim+1;
2776         for (i = 0; i < dim+1; ++i) faces[i] = (dim+1 == 1 ? 1 : 4-(dim+1));
2777         ierr = PetscOptionsIntArray("-dm_plex_box_faces", "Number of faces along each dimension", "", faces, &n, &flg);CHKERRQ(ierr);
2778         n    = 3;
2779         ierr = PetscOptionsRealArray("-dm_plex_box_lower", "Lower left corner of box", "", lower, &n, &flg);CHKERRQ(ierr);
2780         if (flg && (n != dim+1)) SETERRQ2(comm, PETSC_ERR_ARG_SIZ, "Lower box point had %D values, should have been %D", n, dim+1);
2781         n    = 3;
2782         ierr = PetscOptionsRealArray("-dm_plex_box_upper", "Upper right corner of box", "", upper, &n, &flg);CHKERRQ(ierr);
2783         if (flg && (n != dim+1)) SETERRQ2(comm, PETSC_ERR_ARG_SIZ, "Upper box point had %D values, should have been %D", n, dim+1);
2784         ierr = DMPlexCreateBoxSurfaceMesh_Internal(dm, dim+1, faces, lower, upper, interpolate);CHKERRQ(ierr);
2785       }
2786       break;
2787       case DM_SHAPE_SPHERE:
2788       {
2789         PetscReal R = 1.0;
2790 
2791         ierr = PetscOptionsReal("-dm_plex_sphere_radius", "Radius of the sphere", "", R,  &R, &flg);CHKERRQ(ierr);
2792         ierr = DMPlexCreateSphereMesh_Internal(dm, dim, simplex, R);CHKERRQ(ierr);
2793       }
2794       break;
2795       case DM_SHAPE_BALL:
2796       {
2797         PetscReal R = 1.0;
2798 
2799         ierr = PetscOptionsReal("-dm_plex_ball_radius", "Radius of the ball", "", R,  &R, &flg);CHKERRQ(ierr);
2800         ierr = DMPlexCreateBallMesh_Internal(dm, dim, R);CHKERRQ(ierr);
2801       }
2802       break;
2803       case DM_SHAPE_CYLINDER:
2804       {
2805         DMBoundaryType bdt = DM_BOUNDARY_NONE;
2806         PetscInt       Nw  = 6;
2807 
2808         ierr = PetscOptionsEnum("-dm_plex_cylinder_bd", "Boundary type in the z direction", "", DMBoundaryTypes, (PetscEnum) bdt, (PetscEnum *) &bdt, NULL);CHKERRQ(ierr);
2809         ierr = PetscOptionsInt("-dm_plex_cylinder_num_wedges", "Number of wedges around the cylinder", "", Nw, &Nw, NULL);CHKERRQ(ierr);
2810         switch (cell) {
2811           case DM_POLYTOPE_TRI_PRISM_TENSOR:
2812             ierr = DMPlexCreateWedgeCylinderMesh_Internal(dm, Nw, interpolate);CHKERRQ(ierr);
2813             break;
2814           default:
2815             ierr = DMPlexCreateHexCylinderMesh_Internal(dm, bdt);CHKERRQ(ierr);
2816             break;
2817         }
2818       }
2819       break;
2820       default: SETERRQ1(comm, PETSC_ERR_SUP, "Domain shape %s is unsupported", DMPlexShapes[shape]);
2821     }
2822   }
2823   ierr = DMPlexSetRefinementUniform(dm, PETSC_TRUE);CHKERRQ(ierr);
2824   PetscFunctionReturn(0);
2825 }
2826 
2827 PetscErrorCode DMSetFromOptions_NonRefinement_Plex(PetscOptionItems *PetscOptionsObject, DM dm)
2828 {
2829   DM_Plex       *mesh = (DM_Plex*) dm->data;
2830   PetscBool      flg;
2831   char           bdLabel[PETSC_MAX_PATH_LEN];
2832   PetscErrorCode ierr;
2833 
2834   PetscFunctionBegin;
2835   /* Handle viewing */
2836   ierr = PetscOptionsBool("-dm_plex_print_set_values", "Output all set values info", "DMPlexMatSetClosure", PETSC_FALSE, &mesh->printSetValues, NULL);CHKERRQ(ierr);
2837   ierr = PetscOptionsBoundedInt("-dm_plex_print_fem", "Debug output level all fem computations", "DMPlexSNESComputeResidualFEM", 0, &mesh->printFEM, NULL,0);CHKERRQ(ierr);
2838   ierr = PetscOptionsReal("-dm_plex_print_tol", "Tolerance for FEM output", "DMPlexSNESComputeResidualFEM", mesh->printTol, &mesh->printTol, NULL);CHKERRQ(ierr);
2839   ierr = PetscOptionsBoundedInt("-dm_plex_print_l2", "Debug output level all L2 diff computations", "DMComputeL2Diff", 0, &mesh->printL2, NULL,0);CHKERRQ(ierr);
2840   ierr = DMMonitorSetFromOptions(dm, "-dm_plex_monitor_throughput", "Monitor the simulation throughput", "DMPlexMonitorThroughput", DMPlexMonitorThroughput, NULL, &flg);CHKERRQ(ierr);
2841   if (flg) {ierr = PetscLogDefaultBegin();CHKERRQ(ierr);}
2842   /* Labeling */
2843   ierr = PetscOptionsString("-dm_plex_boundary_label", "Label to mark the mesh boundary", "", bdLabel, bdLabel, sizeof(bdLabel), &flg);CHKERRQ(ierr);
2844   if (flg) {ierr = DMPlexCreateBoundaryLabel_Private(dm, bdLabel);CHKERRQ(ierr);}
2845   /* Point Location */
2846   ierr = PetscOptionsBool("-dm_plex_hash_location", "Use grid hashing for point location", "DMInterpolate", PETSC_FALSE, &mesh->useHashLocation, NULL);CHKERRQ(ierr);
2847   /* Partitioning and distribution */
2848   ierr = PetscOptionsBool("-dm_plex_partition_balance", "Attempt to evenly divide points on partition boundary between processes", "DMPlexSetPartitionBalance", PETSC_FALSE, &mesh->partitionBalance, NULL);CHKERRQ(ierr);
2849   /* Generation and remeshing */
2850   ierr = PetscOptionsBool("-dm_plex_remesh_bd", "Allow changes to the boundary on remeshing", "DMAdapt", PETSC_FALSE, &mesh->remeshBd, NULL);CHKERRQ(ierr);
2851   /* Projection behavior */
2852   ierr = PetscOptionsBoundedInt("-dm_plex_max_projection_height", "Maxmimum mesh point height used to project locally", "DMPlexSetMaxProjectionHeight", 0, &mesh->maxProjectionHeight, NULL,0);CHKERRQ(ierr);
2853   ierr = PetscOptionsBool("-dm_plex_regular_refinement", "Use special nested projection algorithm for regular refinement", "DMPlexSetRegularRefinement", mesh->regularRefinement, &mesh->regularRefinement, NULL);CHKERRQ(ierr);
2854   ierr = PetscOptionsEnum("-dm_plex_cell_refiner", "Strategy for cell refinment", "", DMPlexCellRefinerTypes, (PetscEnum) mesh->cellRefiner, (PetscEnum *) &mesh->cellRefiner, NULL);CHKERRQ(ierr);
2855   /* Checking structure */
2856   {
2857     PetscBool   flg = PETSC_FALSE, flg2 = PETSC_FALSE, all = PETSC_FALSE;
2858 
2859     ierr = PetscOptionsBool("-dm_plex_check_all", "Perform all checks", NULL, PETSC_FALSE, &all, &flg2);CHKERRQ(ierr);
2860     ierr = PetscOptionsBool("-dm_plex_check_symmetry", "Check that the adjacency information in the mesh is symmetric", "DMPlexCheckSymmetry", PETSC_FALSE, &flg, &flg2);CHKERRQ(ierr);
2861     if (all || (flg && flg2)) {ierr = DMPlexCheckSymmetry(dm);CHKERRQ(ierr);}
2862     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);
2863     if (all || (flg && flg2)) {ierr = DMPlexCheckSkeleton(dm, 0);CHKERRQ(ierr);}
2864     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);
2865     if (all || (flg && flg2)) {ierr = DMPlexCheckFaces(dm, 0);CHKERRQ(ierr);}
2866     ierr = PetscOptionsBool("-dm_plex_check_geometry", "Check that cells have positive volume", "DMPlexCheckGeometry", PETSC_FALSE, &flg, &flg2);CHKERRQ(ierr);
2867     if (all || (flg && flg2)) {ierr = DMPlexCheckGeometry(dm);CHKERRQ(ierr);}
2868     ierr = PetscOptionsBool("-dm_plex_check_pointsf", "Check some necessary conditions for PointSF", "DMPlexCheckPointSF", PETSC_FALSE, &flg, &flg2);CHKERRQ(ierr);
2869     if (all || (flg && flg2)) {ierr = DMPlexCheckPointSF(dm);CHKERRQ(ierr);}
2870     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);
2871     if (all || (flg && flg2)) {ierr = DMPlexCheckInterfaceCones(dm);CHKERRQ(ierr);}
2872     ierr = PetscOptionsBool("-dm_plex_check_cell_shape", "Check cell shape", "DMPlexCheckCellShape", PETSC_FALSE, &flg, &flg2);CHKERRQ(ierr);
2873     if (flg && flg2) {ierr = DMPlexCheckCellShape(dm, PETSC_TRUE, PETSC_DETERMINE);CHKERRQ(ierr);}
2874   }
2875   {
2876     PetscReal scale = 1.0;
2877 
2878     ierr = PetscOptionsReal("-dm_plex_scale", "Scale factor for mesh coordinates", "DMPlexScale", scale, &scale, &flg);CHKERRQ(ierr);
2879     if (flg) {
2880       Vec coordinates, coordinatesLocal;
2881 
2882       ierr = DMGetCoordinates(dm, &coordinates);CHKERRQ(ierr);
2883       ierr = DMGetCoordinatesLocal(dm, &coordinatesLocal);CHKERRQ(ierr);
2884       ierr = VecScale(coordinates, scale);CHKERRQ(ierr);
2885       ierr = VecScale(coordinatesLocal, scale);CHKERRQ(ierr);
2886     }
2887   }
2888   ierr = PetscPartitionerSetFromOptions(mesh->partitioner);CHKERRQ(ierr);
2889   PetscFunctionReturn(0);
2890 }
2891 
2892 static PetscErrorCode DMSetFromOptions_Plex(PetscOptionItems *PetscOptionsObject,DM dm)
2893 {
2894   PetscReal      volume = -1.0, extThickness = 1.0;
2895   PetscInt       prerefine = 0, refine = 0, r, coarsen = 0, overlap = 0, extLayers = 0, dim;
2896   PetscBool      uniformOrig, created = PETSC_FALSE, uniform = PETSC_TRUE, distribute = PETSC_FALSE, interpolate = PETSC_TRUE, extColOrder = PETSC_TRUE, coordSpace = PETSC_TRUE, remap = PETSC_TRUE, ghostCells = PETSC_FALSE, isHierarchy, ignoreModel = PETSC_FALSE, flg;
2897   PetscErrorCode ierr;
2898 
2899   PetscFunctionBegin;
2900   PetscValidHeaderSpecific(dm, DM_CLASSID, 2);
2901   ierr = PetscOptionsHead(PetscOptionsObject,"DMPlex Options");CHKERRQ(ierr);
2902   /* Handle automatic creation */
2903   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
2904   if (dim < 0) {ierr = DMPlexCreateFromOptions_Internal(PetscOptionsObject, &coordSpace, dm);CHKERRQ(ierr);created = PETSC_TRUE;}
2905   /* Handle DMPlex refinement before distribution */
2906   ierr = PetscOptionsBool("-dm_refine_ignore_model", "Flag to ignore the geometry model when refining", "DMCreate", ignoreModel, &ignoreModel, &flg);CHKERRQ(ierr);
2907   if (flg) {((DM_Plex *) dm->data)->ignoreModel = ignoreModel;}
2908   ierr = DMPlexGetRefinementUniform(dm, &uniformOrig);CHKERRQ(ierr);
2909   ierr = PetscOptionsBoundedInt("-dm_refine_pre", "The number of refinements before distribution", "DMCreate", prerefine, &prerefine, NULL,0);CHKERRQ(ierr);
2910   ierr = PetscOptionsBool("-dm_refine_remap_pre", "Flag to control coordinate remapping", "DMCreate", remap, &remap, NULL);CHKERRQ(ierr);
2911   ierr = PetscOptionsBool("-dm_refine_uniform_pre", "Flag for uniform refinement before distribution", "DMCreate", uniform, &uniform, &flg);CHKERRQ(ierr);
2912   if (flg) {ierr = DMPlexSetRefinementUniform(dm, uniform);CHKERRQ(ierr);}
2913   ierr = PetscOptionsReal("-dm_refine_volume_limit_pre", "The maximum cell volume after refinement before distribution", "DMCreate", volume, &volume, &flg);CHKERRQ(ierr);
2914   if (flg) {
2915     ierr = DMPlexSetRefinementUniform(dm, PETSC_FALSE);CHKERRQ(ierr);
2916     ierr = DMPlexSetRefinementLimit(dm, volume);CHKERRQ(ierr);
2917     prerefine = PetscMax(prerefine, 1);
2918   }
2919   for (r = 0; r < prerefine; ++r) {
2920     DM             rdm;
2921     PetscPointFunc coordFunc = ((DM_Plex*) dm->data)->coordFunc;
2922 
2923     ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2924     ierr = DMRefine(dm, PetscObjectComm((PetscObject) dm), &rdm);CHKERRQ(ierr);
2925     ierr = DMPlexReplace_Static(dm, &rdm);CHKERRQ(ierr);
2926     ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2927     if (coordFunc && remap) {
2928       ierr = DMPlexRemapGeometry(dm, 0.0, coordFunc);CHKERRQ(ierr);
2929       ((DM_Plex*) dm->data)->coordFunc = coordFunc;
2930     }
2931   }
2932   ierr = DMPlexSetRefinementUniform(dm, uniformOrig);CHKERRQ(ierr);
2933   /* Handle DMPlex extrusion before distribution */
2934   ierr = PetscOptionsBool("-dm_plex_interpolate", "Flag to create edges and faces automatically", "", interpolate, &interpolate, NULL);CHKERRQ(ierr);
2935   ierr = PetscOptionsBoundedInt("-dm_extrude_layers", "The number of layers to extrude", "", extLayers, &extLayers, NULL, 0);CHKERRQ(ierr);
2936   ierr = PetscOptionsReal("-dm_extrude_thickness", "The thickness of the layer to be extruded", "", extThickness, &extThickness, NULL);CHKERRQ(ierr);
2937   ierr = PetscOptionsBool("-dm_extrude_column_first", "Order the cells in a vertical column first", "", extColOrder, &extColOrder, NULL);CHKERRQ(ierr);
2938   if (extLayers) {
2939     DM edm;
2940 
2941     ierr = DMPlexExtrude(dm, extLayers, extThickness, extColOrder, NULL, interpolate, &edm);CHKERRQ(ierr);
2942     ierr = DMPlexReplace_Static(dm, &edm);CHKERRQ(ierr);
2943   }
2944   /* Handle DMPlex distribution */
2945   ierr = PetscOptionsBool("-dm_distribute", "Flag to redistribute a mesh among processes", "DMCreate", distribute, &distribute, NULL);CHKERRQ(ierr);
2946   ierr = PetscOptionsBoundedInt("-dm_distribute_overlap", "The size of the overlap halo", "DMCreate", overlap, &overlap, NULL, 0);CHKERRQ(ierr);
2947   if (distribute) {
2948     DM               pdm = NULL;
2949     PetscPartitioner part;
2950 
2951     ierr = DMPlexGetPartitioner(dm, &part);CHKERRQ(ierr);
2952     ierr = PetscPartitionerSetFromOptions(part);CHKERRQ(ierr);
2953     ierr = DMPlexDistribute(dm, overlap, NULL, &pdm);CHKERRQ(ierr);
2954     if (pdm) {
2955       ierr = DMPlexReplace_Static(dm, &pdm);CHKERRQ(ierr);
2956     }
2957   }
2958   /* Create coordinate space */
2959   if (created) {
2960     DM_Plex  *mesh = (DM_Plex *) dm->data;
2961     PetscInt  degree = 1;
2962     PetscBool periodic, flg;
2963 
2964     ierr = PetscOptionsBool("-dm_coord_space", "Use an FEM space for coordinates", "", coordSpace, &coordSpace, &flg);CHKERRQ(ierr);
2965     ierr = PetscOptionsInt("-dm_coord_petscspace_degree", "FEM degree for coordinate space", "", degree, &degree, NULL);CHKERRQ(ierr);
2966     if (coordSpace) {ierr = DMPlexCreateCoordinateSpace(dm, degree, mesh->coordFunc);CHKERRQ(ierr);}
2967     if (flg && !coordSpace) {
2968       DM           cdm;
2969       PetscDS      cds;
2970       PetscObject  obj;
2971       PetscClassId id;
2972 
2973       ierr = DMGetCoordinateDM(dm, &cdm);CHKERRQ(ierr);
2974       ierr = DMGetDS(cdm, &cds);CHKERRQ(ierr);
2975       ierr = PetscDSGetDiscretization(cds, 0, &obj);CHKERRQ(ierr);
2976       ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
2977       if (id == PETSCFE_CLASSID) {
2978         PetscContainer dummy;
2979 
2980         ierr = PetscContainerCreate(PETSC_COMM_SELF, &dummy);CHKERRQ(ierr);
2981         ierr = PetscObjectSetName((PetscObject) dummy, "coordinates");CHKERRQ(ierr);
2982         ierr = DMSetField(cdm, 0, NULL, (PetscObject) dummy);CHKERRQ(ierr);
2983         ierr = PetscContainerDestroy(&dummy);CHKERRQ(ierr);
2984         ierr = DMClearDS(cdm);CHKERRQ(ierr);
2985       }
2986       mesh->coordFunc = NULL;
2987     }
2988     ierr = DMLocalizeCoordinates(dm);CHKERRQ(ierr);
2989     ierr = DMGetPeriodicity(dm, &periodic, NULL, NULL, NULL);CHKERRQ(ierr);
2990     if (periodic) {ierr = DMSetPeriodicity(dm, PETSC_TRUE, NULL, NULL, NULL);CHKERRQ(ierr);}
2991   }
2992   /* Handle DMPlex refinement */
2993   remap = PETSC_TRUE;
2994   ierr = PetscOptionsBoundedInt("-dm_refine", "The number of uniform refinements", "DMCreate", refine, &refine, NULL,0);CHKERRQ(ierr);
2995   ierr = PetscOptionsBool("-dm_refine_remap", "Flag to control coordinate remapping", "DMCreate", remap, &remap, NULL);CHKERRQ(ierr);
2996   ierr = PetscOptionsBoundedInt("-dm_refine_hierarchy", "The number of uniform refinements", "DMCreate", refine, &refine, &isHierarchy,0);CHKERRQ(ierr);
2997   if (refine) {ierr = DMPlexSetRefinementUniform(dm, PETSC_TRUE);CHKERRQ(ierr);}
2998   if (refine && isHierarchy) {
2999     DM *dms, coarseDM;
3000 
3001     ierr = DMGetCoarseDM(dm, &coarseDM);CHKERRQ(ierr);
3002     ierr = PetscObjectReference((PetscObject)coarseDM);CHKERRQ(ierr);
3003     ierr = PetscMalloc1(refine,&dms);CHKERRQ(ierr);
3004     ierr = DMRefineHierarchy(dm, refine, dms);CHKERRQ(ierr);
3005     /* Total hack since we do not pass in a pointer */
3006     ierr = DMPlexSwap_Static(dm, dms[refine-1]);CHKERRQ(ierr);
3007     if (refine == 1) {
3008       ierr = DMSetCoarseDM(dm, dms[0]);CHKERRQ(ierr);
3009       ierr = DMPlexSetRegularRefinement(dm, PETSC_TRUE);CHKERRQ(ierr);
3010     } else {
3011       ierr = DMSetCoarseDM(dm, dms[refine-2]);CHKERRQ(ierr);
3012       ierr = DMPlexSetRegularRefinement(dm, PETSC_TRUE);CHKERRQ(ierr);
3013       ierr = DMSetCoarseDM(dms[0], dms[refine-1]);CHKERRQ(ierr);
3014       ierr = DMPlexSetRegularRefinement(dms[0], PETSC_TRUE);CHKERRQ(ierr);
3015     }
3016     ierr = DMSetCoarseDM(dms[refine-1], coarseDM);CHKERRQ(ierr);
3017     ierr = PetscObjectDereference((PetscObject)coarseDM);CHKERRQ(ierr);
3018     /* Free DMs */
3019     for (r = 0; r < refine; ++r) {
3020       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dms[r]);CHKERRQ(ierr);
3021       ierr = DMDestroy(&dms[r]);CHKERRQ(ierr);
3022     }
3023     ierr = PetscFree(dms);CHKERRQ(ierr);
3024   } else {
3025     for (r = 0; r < refine; ++r) {
3026       DM             rdm;
3027       PetscPointFunc coordFunc = ((DM_Plex*) dm->data)->coordFunc;
3028 
3029       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
3030       ierr = DMRefine(dm, PetscObjectComm((PetscObject) dm), &rdm);CHKERRQ(ierr);
3031       /* Total hack since we do not pass in a pointer */
3032       ierr = DMPlexReplace_Static(dm, &rdm);CHKERRQ(ierr);
3033       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
3034       if (coordFunc && remap) {
3035         ierr = DMPlexRemapGeometry(dm, 0.0, coordFunc);CHKERRQ(ierr);
3036         ((DM_Plex*) dm->data)->coordFunc = coordFunc;
3037       }
3038     }
3039   }
3040   /* Handle DMPlex coarsening */
3041   ierr = PetscOptionsBoundedInt("-dm_coarsen", "Coarsen the mesh", "DMCreate", coarsen, &coarsen, NULL,0);CHKERRQ(ierr);
3042   ierr = PetscOptionsBoundedInt("-dm_coarsen_hierarchy", "The number of coarsenings", "DMCreate", coarsen, &coarsen, &isHierarchy,0);CHKERRQ(ierr);
3043   if (coarsen && isHierarchy) {
3044     DM *dms;
3045 
3046     ierr = PetscMalloc1(coarsen, &dms);CHKERRQ(ierr);
3047     ierr = DMCoarsenHierarchy(dm, coarsen, dms);CHKERRQ(ierr);
3048     /* Free DMs */
3049     for (r = 0; r < coarsen; ++r) {
3050       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dms[r]);CHKERRQ(ierr);
3051       ierr = DMDestroy(&dms[r]);CHKERRQ(ierr);
3052     }
3053     ierr = PetscFree(dms);CHKERRQ(ierr);
3054   } else {
3055     for (r = 0; r < coarsen; ++r) {
3056       DM             cdm;
3057       PetscPointFunc coordFunc = ((DM_Plex*) dm->data)->coordFunc;
3058 
3059       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
3060       ierr = DMCoarsen(dm, PetscObjectComm((PetscObject) dm), &cdm);CHKERRQ(ierr);
3061       /* Total hack since we do not pass in a pointer */
3062       ierr = DMPlexReplace_Static(dm, &cdm);CHKERRQ(ierr);
3063       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
3064       if (coordFunc) {
3065         ierr = DMPlexRemapGeometry(dm, 0.0, coordFunc);CHKERRQ(ierr);
3066         ((DM_Plex*) dm->data)->coordFunc = coordFunc;
3067       }
3068     }
3069   }
3070   /* Handle ghost cells */
3071   ierr = PetscOptionsBool("-dm_plex_create_fv_ghost_cells", "Flag to create finite volume ghost cells on the boundary", "DMCreate", ghostCells, &ghostCells, NULL);CHKERRQ(ierr);
3072   if (ghostCells) {
3073     DM   gdm;
3074     char lname[PETSC_MAX_PATH_LEN];
3075 
3076     lname[0] = '\0';
3077     ierr = PetscOptionsString("-dm_plex_fv_ghost_cells_label", "Label name for ghost cells boundary", "DMCreate", lname, lname, sizeof(lname), &flg);CHKERRQ(ierr);
3078     ierr = DMPlexConstructGhostCells(dm, flg ? lname : NULL, NULL, &gdm);CHKERRQ(ierr);
3079     ierr = DMPlexReplace_Static(dm, &gdm);CHKERRQ(ierr);
3080   }
3081   /* Handle */
3082   ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
3083   ierr = PetscOptionsTail();CHKERRQ(ierr);
3084   PetscFunctionReturn(0);
3085 }
3086 
3087 static PetscErrorCode DMCreateGlobalVector_Plex(DM dm,Vec *vec)
3088 {
3089   PetscErrorCode ierr;
3090 
3091   PetscFunctionBegin;
3092   ierr = DMCreateGlobalVector_Section_Private(dm,vec);CHKERRQ(ierr);
3093   /* ierr = VecSetOperation(*vec, VECOP_DUPLICATE, (void(*)(void)) VecDuplicate_MPI_DM);CHKERRQ(ierr); */
3094   ierr = VecSetOperation(*vec, VECOP_VIEW, (void (*)(void)) VecView_Plex);CHKERRQ(ierr);
3095   ierr = VecSetOperation(*vec, VECOP_VIEWNATIVE, (void (*)(void)) VecView_Plex_Native);CHKERRQ(ierr);
3096   ierr = VecSetOperation(*vec, VECOP_LOAD, (void (*)(void)) VecLoad_Plex);CHKERRQ(ierr);
3097   ierr = VecSetOperation(*vec, VECOP_LOADNATIVE, (void (*)(void)) VecLoad_Plex_Native);CHKERRQ(ierr);
3098   PetscFunctionReturn(0);
3099 }
3100 
3101 static PetscErrorCode DMCreateLocalVector_Plex(DM dm,Vec *vec)
3102 {
3103   PetscErrorCode ierr;
3104 
3105   PetscFunctionBegin;
3106   ierr = DMCreateLocalVector_Section_Private(dm,vec);CHKERRQ(ierr);
3107   ierr = VecSetOperation(*vec, VECOP_VIEW, (void (*)(void)) VecView_Plex_Local);CHKERRQ(ierr);
3108   ierr = VecSetOperation(*vec, VECOP_LOAD, (void (*)(void)) VecLoad_Plex_Local);CHKERRQ(ierr);
3109   PetscFunctionReturn(0);
3110 }
3111 
3112 static PetscErrorCode DMGetDimPoints_Plex(DM dm, PetscInt dim, PetscInt *pStart, PetscInt *pEnd)
3113 {
3114   PetscInt       depth, d;
3115   PetscErrorCode ierr;
3116 
3117   PetscFunctionBegin;
3118   ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
3119   if (depth == 1) {
3120     ierr = DMGetDimension(dm, &d);CHKERRQ(ierr);
3121     if (dim == 0)      {ierr = DMPlexGetDepthStratum(dm, dim, pStart, pEnd);CHKERRQ(ierr);}
3122     else if (dim == d) {ierr = DMPlexGetDepthStratum(dm, 1, pStart, pEnd);CHKERRQ(ierr);}
3123     else               {*pStart = 0; *pEnd = 0;}
3124   } else {
3125     ierr = DMPlexGetDepthStratum(dm, dim, pStart, pEnd);CHKERRQ(ierr);
3126   }
3127   PetscFunctionReturn(0);
3128 }
3129 
3130 static PetscErrorCode DMGetNeighbors_Plex(DM dm, PetscInt *nranks, const PetscMPIInt *ranks[])
3131 {
3132   PetscSF           sf;
3133   PetscInt          niranks, njranks, n;
3134   const PetscMPIInt *iranks, *jranks;
3135   DM_Plex           *data = (DM_Plex*) dm->data;
3136   PetscErrorCode    ierr;
3137 
3138   PetscFunctionBegin;
3139   ierr = DMGetPointSF(dm, &sf);CHKERRQ(ierr);
3140   if (!data->neighbors) {
3141     ierr = PetscSFSetUp(sf);CHKERRQ(ierr);
3142     ierr = PetscSFGetRootRanks(sf, &njranks, &jranks, NULL, NULL, NULL);CHKERRQ(ierr);
3143     ierr = PetscSFGetLeafRanks(sf, &niranks, &iranks, NULL, NULL);CHKERRQ(ierr);
3144     ierr = PetscMalloc1(njranks + niranks + 1, &data->neighbors);CHKERRQ(ierr);
3145     ierr = PetscArraycpy(data->neighbors + 1, jranks, njranks);CHKERRQ(ierr);
3146     ierr = PetscArraycpy(data->neighbors + njranks + 1, iranks, niranks);CHKERRQ(ierr);
3147     n = njranks + niranks;
3148     ierr = PetscSortRemoveDupsMPIInt(&n, data->neighbors + 1);CHKERRQ(ierr);
3149     /* The following cast should never fail: can't have more neighbors than PETSC_MPI_INT_MAX */
3150     ierr = PetscMPIIntCast(n, data->neighbors);CHKERRQ(ierr);
3151   }
3152   if (nranks) *nranks = data->neighbors[0];
3153   if (ranks) {
3154     if (data->neighbors[0]) *ranks = data->neighbors + 1;
3155     else                    *ranks = NULL;
3156   }
3157   PetscFunctionReturn(0);
3158 }
3159 
3160 PETSC_INTERN PetscErrorCode DMInterpolateSolution_Plex(DM, DM, Mat, Vec, Vec);
3161 
3162 static PetscErrorCode DMInitialize_Plex(DM dm)
3163 {
3164   PetscErrorCode ierr;
3165 
3166   PetscFunctionBegin;
3167   dm->ops->view                            = DMView_Plex;
3168   dm->ops->load                            = DMLoad_Plex;
3169   dm->ops->setfromoptions                  = DMSetFromOptions_Plex;
3170   dm->ops->clone                           = DMClone_Plex;
3171   dm->ops->setup                           = DMSetUp_Plex;
3172   dm->ops->createlocalsection              = DMCreateLocalSection_Plex;
3173   dm->ops->createdefaultconstraints        = DMCreateDefaultConstraints_Plex;
3174   dm->ops->createglobalvector              = DMCreateGlobalVector_Plex;
3175   dm->ops->createlocalvector               = DMCreateLocalVector_Plex;
3176   dm->ops->getlocaltoglobalmapping         = NULL;
3177   dm->ops->createfieldis                   = NULL;
3178   dm->ops->createcoordinatedm              = DMCreateCoordinateDM_Plex;
3179   dm->ops->createcoordinatefield           = DMCreateCoordinateField_Plex;
3180   dm->ops->getcoloring                     = NULL;
3181   dm->ops->creatematrix                    = DMCreateMatrix_Plex;
3182   dm->ops->createinterpolation             = DMCreateInterpolation_Plex;
3183   dm->ops->createmassmatrix                = DMCreateMassMatrix_Plex;
3184   dm->ops->createinjection                 = DMCreateInjection_Plex;
3185   dm->ops->refine                          = DMRefine_Plex;
3186   dm->ops->coarsen                         = DMCoarsen_Plex;
3187   dm->ops->refinehierarchy                 = DMRefineHierarchy_Plex;
3188   dm->ops->coarsenhierarchy                = DMCoarsenHierarchy_Plex;
3189   dm->ops->adaptlabel                      = DMAdaptLabel_Plex;
3190   dm->ops->adaptmetric                     = DMAdaptMetric_Plex;
3191   dm->ops->globaltolocalbegin              = NULL;
3192   dm->ops->globaltolocalend                = NULL;
3193   dm->ops->localtoglobalbegin              = NULL;
3194   dm->ops->localtoglobalend                = NULL;
3195   dm->ops->destroy                         = DMDestroy_Plex;
3196   dm->ops->createsubdm                     = DMCreateSubDM_Plex;
3197   dm->ops->createsuperdm                   = DMCreateSuperDM_Plex;
3198   dm->ops->getdimpoints                    = DMGetDimPoints_Plex;
3199   dm->ops->locatepoints                    = DMLocatePoints_Plex;
3200   dm->ops->projectfunctionlocal            = DMProjectFunctionLocal_Plex;
3201   dm->ops->projectfunctionlabellocal       = DMProjectFunctionLabelLocal_Plex;
3202   dm->ops->projectfieldlocal               = DMProjectFieldLocal_Plex;
3203   dm->ops->projectfieldlabellocal          = DMProjectFieldLabelLocal_Plex;
3204   dm->ops->projectbdfieldlabellocal        = DMProjectBdFieldLabelLocal_Plex;
3205   dm->ops->computel2diff                   = DMComputeL2Diff_Plex;
3206   dm->ops->computel2gradientdiff           = DMComputeL2GradientDiff_Plex;
3207   dm->ops->computel2fielddiff              = DMComputeL2FieldDiff_Plex;
3208   dm->ops->getneighbors                    = DMGetNeighbors_Plex;
3209   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMPlexInsertBoundaryValues_C",DMPlexInsertBoundaryValues_Plex);CHKERRQ(ierr);
3210   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMPlexInsertTimeDerviativeBoundaryValues_C",DMPlexInsertTimeDerivativeBoundaryValues_Plex);CHKERRQ(ierr);
3211   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMSetUpGLVisViewer_C",DMSetUpGLVisViewer_Plex);CHKERRQ(ierr);
3212   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMCreateNeumannOverlap_C",DMCreateNeumannOverlap_Plex);CHKERRQ(ierr);
3213   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMPlexGetOverlap_C",DMPlexGetOverlap_Plex);CHKERRQ(ierr);
3214   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMInterpolateSolution_C",DMInterpolateSolution_Plex);CHKERRQ(ierr);
3215   PetscFunctionReturn(0);
3216 }
3217 
3218 PETSC_INTERN PetscErrorCode DMClone_Plex(DM dm, DM *newdm)
3219 {
3220   DM_Plex        *mesh = (DM_Plex *) dm->data;
3221   PetscErrorCode ierr;
3222 
3223   PetscFunctionBegin;
3224   mesh->refct++;
3225   (*newdm)->data = mesh;
3226   ierr = PetscObjectChangeTypeName((PetscObject) *newdm, DMPLEX);CHKERRQ(ierr);
3227   ierr = DMInitialize_Plex(*newdm);CHKERRQ(ierr);
3228   PetscFunctionReturn(0);
3229 }
3230 
3231 /*MC
3232   DMPLEX = "plex" - A DM object that encapsulates an unstructured mesh, or CW Complex, which can be expressed using a Hasse Diagram.
3233                     In the local representation, Vecs contain all unknowns in the interior and shared boundary. This is
3234                     specified by a PetscSection object. Ownership in the global representation is determined by
3235                     ownership of the underlying DMPlex points. This is specified by another PetscSection object.
3236 
3237   Options Database Keys:
3238 + -dm_refine_pre                     - Refine mesh before distribution
3239 + -dm_refine_uniform_pre             - Choose uniform or generator-based refinement
3240 + -dm_refine_volume_limit_pre        - Cell volume limit after pre-refinement using generator
3241 . -dm_distribute                     - Distribute mesh across processes
3242 . -dm_distribute_overlap             - Number of cells to overlap for distribution
3243 . -dm_refine                         - Refine mesh after distribution
3244 . -dm_plex_hash_location             - Use grid hashing for point location
3245 . -dm_plex_partition_balance         - Attempt to evenly divide points on partition boundary between processes
3246 . -dm_plex_remesh_bd                 - Allow changes to the boundary on remeshing
3247 . -dm_plex_max_projection_height     - Maxmimum mesh point height used to project locally
3248 . -dm_plex_regular_refinement        - Use special nested projection algorithm for regular refinement
3249 . -dm_plex_check_all                 - Perform all shecks below
3250 . -dm_plex_check_symmetry            - Check that the adjacency information in the mesh is symmetric
3251 . -dm_plex_check_skeleton <celltype> - Check that each cell has the correct number of vertices
3252 . -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
3253 . -dm_plex_check_geometry            - Check that cells have positive volume
3254 . -dm_view :mesh.tex:ascii_latex     - View the mesh in LaTeX/TikZ
3255 . -dm_plex_view_scale <num>          - Scale the TikZ
3256 - -dm_plex_print_fem <num>           - View FEM assembly information, such as element vectors and matrices
3257 
3258   Level: intermediate
3259 
3260 .seealso: DMType, DMPlexCreate(), DMCreate(), DMSetType()
3261 M*/
3262 
3263 PETSC_EXTERN PetscErrorCode DMCreate_Plex(DM dm)
3264 {
3265   DM_Plex       *mesh;
3266   PetscInt       unit;
3267   PetscErrorCode ierr;
3268 
3269   PetscFunctionBegin;
3270   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
3271   ierr     = PetscNewLog(dm,&mesh);CHKERRQ(ierr);
3272   dm->data = mesh;
3273 
3274   mesh->refct             = 1;
3275   ierr                    = PetscSectionCreate(PetscObjectComm((PetscObject)dm), &mesh->coneSection);CHKERRQ(ierr);
3276   mesh->maxConeSize       = 0;
3277   mesh->cones             = NULL;
3278   mesh->coneOrientations  = NULL;
3279   ierr                    = PetscSectionCreate(PetscObjectComm((PetscObject)dm), &mesh->supportSection);CHKERRQ(ierr);
3280   mesh->maxSupportSize    = 0;
3281   mesh->supports          = NULL;
3282   mesh->refinementUniform = PETSC_TRUE;
3283   mesh->refinementLimit   = -1.0;
3284   mesh->interpolated      = DMPLEX_INTERPOLATED_INVALID;
3285   mesh->interpolatedCollective = DMPLEX_INTERPOLATED_INVALID;
3286 
3287   mesh->facesTmp = NULL;
3288 
3289   mesh->tetgenOpts   = NULL;
3290   mesh->triangleOpts = NULL;
3291   ierr = PetscPartitionerCreate(PetscObjectComm((PetscObject)dm), &mesh->partitioner);CHKERRQ(ierr);
3292   mesh->remeshBd     = PETSC_FALSE;
3293 
3294   mesh->subpointMap = NULL;
3295 
3296   for (unit = 0; unit < NUM_PETSC_UNITS; ++unit) mesh->scale[unit] = 1.0;
3297 
3298   mesh->regularRefinement   = PETSC_FALSE;
3299   mesh->depthState          = -1;
3300   mesh->celltypeState       = -1;
3301   mesh->globalVertexNumbers = NULL;
3302   mesh->globalCellNumbers   = NULL;
3303   mesh->anchorSection       = NULL;
3304   mesh->anchorIS            = NULL;
3305   mesh->createanchors       = NULL;
3306   mesh->computeanchormatrix = NULL;
3307   mesh->parentSection       = NULL;
3308   mesh->parents             = NULL;
3309   mesh->childIDs            = NULL;
3310   mesh->childSection        = NULL;
3311   mesh->children            = NULL;
3312   mesh->referenceTree       = NULL;
3313   mesh->getchildsymmetry    = NULL;
3314   mesh->vtkCellHeight       = 0;
3315   mesh->useAnchors          = PETSC_FALSE;
3316 
3317   mesh->maxProjectionHeight = 0;
3318 
3319   mesh->neighbors           = NULL;
3320 
3321   mesh->printSetValues = PETSC_FALSE;
3322   mesh->printFEM       = 0;
3323   mesh->printTol       = 1.0e-10;
3324 
3325   ierr = DMInitialize_Plex(dm);CHKERRQ(ierr);
3326   PetscFunctionReturn(0);
3327 }
3328 
3329 /*@
3330   DMPlexCreate - Creates a DMPlex object, which encapsulates an unstructured mesh, or CW complex, which can be expressed using a Hasse Diagram.
3331 
3332   Collective
3333 
3334   Input Parameter:
3335 . comm - The communicator for the DMPlex object
3336 
3337   Output Parameter:
3338 . mesh  - The DMPlex object
3339 
3340   Level: beginner
3341 
3342 @*/
3343 PetscErrorCode DMPlexCreate(MPI_Comm comm, DM *mesh)
3344 {
3345   PetscErrorCode ierr;
3346 
3347   PetscFunctionBegin;
3348   PetscValidPointer(mesh,2);
3349   ierr = DMCreate(comm, mesh);CHKERRQ(ierr);
3350   ierr = DMSetType(*mesh, DMPLEX);CHKERRQ(ierr);
3351   PetscFunctionReturn(0);
3352 }
3353 
3354 /*@C
3355   DMPlexBuildFromCellListParallel - Build distributed DMPLEX topology from a list of vertices for each cell (common mesh generator output)
3356 
3357   Input Parameters:
3358 + dm - The DM
3359 . numCells - The number of cells owned by this process
3360 . numVertices - The number of vertices owned by this process, or PETSC_DECIDE
3361 . NVertices - The global number of vertices, or PETSC_DECIDE
3362 . numCorners - The number of vertices for each cell
3363 - cells - An array of numCells*numCorners numbers, the global vertex numbers for each cell
3364 
3365   Output Parameter:
3366 . vertexSF - (Optional) SF describing complete vertex ownership
3367 
3368   Notes:
3369   Two triangles sharing a face
3370 $
3371 $        2
3372 $      / | \
3373 $     /  |  \
3374 $    /   |   \
3375 $   0  0 | 1  3
3376 $    \   |   /
3377 $     \  |  /
3378 $      \ | /
3379 $        1
3380 would have input
3381 $  numCells = 2, numVertices = 4
3382 $  cells = [0 1 2  1 3 2]
3383 $
3384 which would result in the DMPlex
3385 $
3386 $        4
3387 $      / | \
3388 $     /  |  \
3389 $    /   |   \
3390 $   2  0 | 1  5
3391 $    \   |   /
3392 $     \  |  /
3393 $      \ | /
3394 $        3
3395 
3396   Vertices are implicitly numbered consecutively 0,...,NVertices.
3397   Each rank owns a chunk of numVertices consecutive vertices.
3398   If numVertices is PETSC_DECIDE, PETSc will distribute them as evenly as possible using PetscLayout.
3399   If both NVertices and numVertices are PETSC_DECIDE, NVertices is computed by PETSc as the maximum vertex index in cells + 1.
3400   If only NVertices is PETSC_DECIDE, it is computed as the sum of numVertices over all ranks.
3401 
3402   The cell distribution is arbitrary non-overlapping, independent of the vertex distribution.
3403 
3404   Not currently supported in Fortran.
3405 
3406   Level: advanced
3407 
3408 .seealso: DMPlexBuildFromCellList(), DMPlexCreateFromCellListParallelPetsc(), DMPlexBuildCoordinatesFromCellListParallel()
3409 @*/
3410 PetscErrorCode DMPlexBuildFromCellListParallel(DM dm, PetscInt numCells, PetscInt numVertices, PetscInt NVertices, PetscInt numCorners, const PetscInt cells[], PetscSF *vertexSF)
3411 {
3412   PetscSF         sfPoint;
3413   PetscLayout     layout;
3414   PetscInt        numVerticesAdj, *verticesAdj, *cones, c, p, dim;
3415   PetscMPIInt     rank, size;
3416   PetscErrorCode  ierr;
3417 
3418   PetscFunctionBegin;
3419   PetscValidLogicalCollectiveInt(dm,NVertices,4);
3420   ierr = PetscLogEventBegin(DMPLEX_BuildFromCellList,dm,0,0,0);CHKERRQ(ierr);
3421   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject) dm), &rank);CHKERRMPI(ierr);
3422   ierr = MPI_Comm_size(PetscObjectComm((PetscObject) dm), &size);CHKERRMPI(ierr);
3423   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
3424   /* Get/check global number of vertices */
3425   {
3426     PetscInt NVerticesInCells, i;
3427     const PetscInt len = numCells * numCorners;
3428 
3429     /* NVerticesInCells = max(cells) + 1 */
3430     NVerticesInCells = PETSC_MIN_INT;
3431     for (i=0; i<len; i++) if (cells[i] > NVerticesInCells) NVerticesInCells = cells[i];
3432     ++NVerticesInCells;
3433     ierr = MPI_Allreduce(MPI_IN_PLACE, &NVerticesInCells, 1, MPIU_INT, MPI_MAX, PetscObjectComm((PetscObject) dm));CHKERRMPI(ierr);
3434 
3435     if (numVertices == PETSC_DECIDE && NVertices == PETSC_DECIDE) NVertices = NVerticesInCells;
3436     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);
3437   }
3438   /* Count locally unique vertices */
3439   {
3440     PetscHSetI vhash;
3441     PetscInt off = 0;
3442 
3443     ierr = PetscHSetICreate(&vhash);CHKERRQ(ierr);
3444     for (c = 0; c < numCells; ++c) {
3445       for (p = 0; p < numCorners; ++p) {
3446         ierr = PetscHSetIAdd(vhash, cells[c*numCorners+p]);CHKERRQ(ierr);
3447       }
3448     }
3449     ierr = PetscHSetIGetSize(vhash, &numVerticesAdj);CHKERRQ(ierr);
3450     ierr = PetscMalloc1(numVerticesAdj, &verticesAdj);CHKERRQ(ierr);
3451     ierr = PetscHSetIGetElems(vhash, &off, verticesAdj);CHKERRQ(ierr);
3452     ierr = PetscHSetIDestroy(&vhash);CHKERRQ(ierr);
3453     if (off != numVerticesAdj) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Invalid number of local vertices %D should be %D", off, numVerticesAdj);
3454   }
3455   ierr = PetscSortInt(numVerticesAdj, verticesAdj);CHKERRQ(ierr);
3456   /* Create cones */
3457   ierr = DMPlexSetChart(dm, 0, numCells+numVerticesAdj);CHKERRQ(ierr);
3458   for (c = 0; c < numCells; ++c) {ierr = DMPlexSetConeSize(dm, c, numCorners);CHKERRQ(ierr);}
3459   ierr = DMSetUp(dm);CHKERRQ(ierr);
3460   ierr = DMPlexGetCones(dm,&cones);CHKERRQ(ierr);
3461   for (c = 0; c < numCells; ++c) {
3462     for (p = 0; p < numCorners; ++p) {
3463       const PetscInt gv = cells[c*numCorners+p];
3464       PetscInt       lv;
3465 
3466       /* Positions within verticesAdj form 0-based local vertex numbering;
3467          we need to shift it by numCells to get correct DAG points (cells go first) */
3468       ierr = PetscFindInt(gv, numVerticesAdj, verticesAdj, &lv);CHKERRQ(ierr);
3469       if (lv < 0) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Could not find global vertex %D in local connectivity", gv);
3470       cones[c*numCorners+p] = lv+numCells;
3471     }
3472   }
3473   /* Build point sf */
3474   ierr = PetscLayoutCreate(PetscObjectComm((PetscObject)dm), &layout);CHKERRQ(ierr);
3475   ierr = PetscLayoutSetSize(layout, NVertices);CHKERRQ(ierr);
3476   ierr = PetscLayoutSetLocalSize(layout, numVertices);CHKERRQ(ierr);
3477   ierr = PetscLayoutSetBlockSize(layout, 1);CHKERRQ(ierr);
3478   ierr = PetscSFCreateByMatchingIndices(layout, numVerticesAdj, verticesAdj, NULL, numCells, numVerticesAdj, verticesAdj, NULL, numCells, vertexSF, &sfPoint);CHKERRQ(ierr);
3479   ierr = PetscLayoutDestroy(&layout);CHKERRQ(ierr);
3480   ierr = PetscFree(verticesAdj);CHKERRQ(ierr);
3481   ierr = PetscObjectSetName((PetscObject) sfPoint, "point SF");CHKERRQ(ierr);
3482   if (dm->sf) {
3483     const char *prefix;
3484 
3485     ierr = PetscObjectGetOptionsPrefix((PetscObject)dm->sf, &prefix);CHKERRQ(ierr);
3486     ierr = PetscObjectSetOptionsPrefix((PetscObject)sfPoint, prefix);CHKERRQ(ierr);
3487   }
3488   ierr = DMSetPointSF(dm, sfPoint);CHKERRQ(ierr);
3489   ierr = PetscSFDestroy(&sfPoint);CHKERRQ(ierr);
3490   if (vertexSF) {ierr = PetscObjectSetName((PetscObject)(*vertexSF), "Vertex Ownership SF");CHKERRQ(ierr);}
3491   /* Fill in the rest of the topology structure */
3492   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
3493   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
3494   ierr = PetscLogEventEnd(DMPLEX_BuildFromCellList,dm,0,0,0);CHKERRQ(ierr);
3495   PetscFunctionReturn(0);
3496 }
3497 
3498 /*@C
3499   DMPlexBuildCoordinatesFromCellListParallel - Build DM coordinates from a list of coordinates for each owned vertex (common mesh generator output)
3500 
3501   Input Parameters:
3502 + dm - The DM
3503 . spaceDim - The spatial dimension used for coordinates
3504 . sfVert - SF describing complete vertex ownership
3505 - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex
3506 
3507   Level: advanced
3508 
3509   Notes:
3510   Not currently supported in Fortran.
3511 
3512 .seealso: DMPlexBuildCoordinatesFromCellList(), DMPlexCreateFromCellListParallelPetsc(), DMPlexBuildFromCellListParallel()
3513 @*/
3514 PetscErrorCode DMPlexBuildCoordinatesFromCellListParallel(DM dm, PetscInt spaceDim, PetscSF sfVert, const PetscReal vertexCoords[])
3515 {
3516   PetscSection   coordSection;
3517   Vec            coordinates;
3518   PetscScalar   *coords;
3519   PetscInt       numVertices, numVerticesAdj, coordSize, v, vStart, vEnd;
3520   PetscErrorCode ierr;
3521 
3522   PetscFunctionBegin;
3523   ierr = PetscLogEventBegin(DMPLEX_BuildCoordinatesFromCellList,dm,0,0,0);CHKERRQ(ierr);
3524   ierr = DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);CHKERRQ(ierr);
3525   if (vStart < 0 || vEnd < 0) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "DM is not set up properly. DMPlexBuildFromCellList() should be called first.");
3526   ierr = DMSetCoordinateDim(dm, spaceDim);CHKERRQ(ierr);
3527   ierr = PetscSFGetGraph(sfVert, &numVertices, &numVerticesAdj, NULL, NULL);CHKERRQ(ierr);
3528   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);
3529   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
3530   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
3531   ierr = PetscSectionSetFieldComponents(coordSection, 0, spaceDim);CHKERRQ(ierr);
3532   ierr = PetscSectionSetChart(coordSection, vStart, vEnd);CHKERRQ(ierr);
3533   for (v = vStart; v < vEnd; ++v) {
3534     ierr = PetscSectionSetDof(coordSection, v, spaceDim);CHKERRQ(ierr);
3535     ierr = PetscSectionSetFieldDof(coordSection, v, 0, spaceDim);CHKERRQ(ierr);
3536   }
3537   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
3538   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
3539   ierr = VecCreate(PetscObjectComm((PetscObject)dm), &coordinates);CHKERRQ(ierr);
3540   ierr = VecSetBlockSize(coordinates, spaceDim);CHKERRQ(ierr);
3541   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
3542   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
3543   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
3544   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
3545   {
3546     MPI_Datatype coordtype;
3547 
3548     /* Need a temp buffer for coords if we have complex/single */
3549     ierr = MPI_Type_contiguous(spaceDim, MPIU_SCALAR, &coordtype);CHKERRMPI(ierr);
3550     ierr = MPI_Type_commit(&coordtype);CHKERRMPI(ierr);
3551 #if defined(PETSC_USE_COMPLEX)
3552     {
3553     PetscScalar *svertexCoords;
3554     PetscInt    i;
3555     ierr = PetscMalloc1(numVertices*spaceDim,&svertexCoords);CHKERRQ(ierr);
3556     for (i=0; i<numVertices*spaceDim; i++) svertexCoords[i] = vertexCoords[i];
3557     ierr = PetscSFBcastBegin(sfVert, coordtype, svertexCoords, coords,MPI_REPLACE);CHKERRQ(ierr);
3558     ierr = PetscSFBcastEnd(sfVert, coordtype, svertexCoords, coords,MPI_REPLACE);CHKERRQ(ierr);
3559     ierr = PetscFree(svertexCoords);CHKERRQ(ierr);
3560     }
3561 #else
3562     ierr = PetscSFBcastBegin(sfVert, coordtype, vertexCoords, coords,MPI_REPLACE);CHKERRQ(ierr);
3563     ierr = PetscSFBcastEnd(sfVert, coordtype, vertexCoords, coords,MPI_REPLACE);CHKERRQ(ierr);
3564 #endif
3565     ierr = MPI_Type_free(&coordtype);CHKERRMPI(ierr);
3566   }
3567   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
3568   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
3569   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
3570   ierr = PetscLogEventEnd(DMPLEX_BuildCoordinatesFromCellList,dm,0,0,0);CHKERRQ(ierr);
3571   PetscFunctionReturn(0);
3572 }
3573 
3574 /*@
3575   DMPlexCreateFromCellListParallelPetsc - Create distributed DMPLEX from a list of vertices for each cell (common mesh generator output)
3576 
3577   Input Parameters:
3578 + comm - The communicator
3579 . dim - The topological dimension of the mesh
3580 . numCells - The number of cells owned by this process
3581 . numVertices - The number of vertices owned by this process, or PETSC_DECIDE
3582 . NVertices - The global number of vertices, or PETSC_DECIDE
3583 . numCorners - The number of vertices for each cell
3584 . interpolate - Flag indicating that intermediate mesh entities (faces, edges) should be created automatically
3585 . cells - An array of numCells*numCorners numbers, the global vertex numbers for each cell
3586 . spaceDim - The spatial dimension used for coordinates
3587 - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex
3588 
3589   Output Parameter:
3590 + dm - The DM
3591 - vertexSF - (Optional) SF describing complete vertex ownership
3592 
3593   Notes:
3594   This function is just a convenient sequence of DMCreate(), DMSetType(), DMSetDimension(),
3595   DMPlexBuildFromCellListParallel(), DMPlexInterpolate(), DMPlexBuildCoordinatesFromCellListParallel()
3596 
3597   See DMPlexBuildFromCellListParallel() for an example and details about the topology-related parameters.
3598   See DMPlexBuildCoordinatesFromCellListParallel() for details about the geometry-related parameters.
3599 
3600   Level: intermediate
3601 
3602 .seealso: DMPlexCreateFromCellListPetsc(), DMPlexBuildFromCellListParallel(), DMPlexBuildCoordinatesFromCellListParallel(), DMPlexCreateFromDAG(), DMPlexCreate()
3603 @*/
3604 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)
3605 {
3606   PetscSF        sfVert;
3607   PetscErrorCode ierr;
3608 
3609   PetscFunctionBegin;
3610   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
3611   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
3612   PetscValidLogicalCollectiveInt(*dm, dim, 2);
3613   PetscValidLogicalCollectiveInt(*dm, spaceDim, 9);
3614   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
3615   ierr = DMPlexBuildFromCellListParallel(*dm, numCells, numVertices, NVertices, numCorners, cells, &sfVert);CHKERRQ(ierr);
3616   if (interpolate) {
3617     DM idm;
3618 
3619     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
3620     ierr = DMDestroy(dm);CHKERRQ(ierr);
3621     *dm  = idm;
3622   }
3623   ierr = DMPlexBuildCoordinatesFromCellListParallel(*dm, spaceDim, sfVert, vertexCoords);CHKERRQ(ierr);
3624   if (vertexSF) *vertexSF = sfVert;
3625   else {ierr = PetscSFDestroy(&sfVert);CHKERRQ(ierr);}
3626   PetscFunctionReturn(0);
3627 }
3628 
3629 /*@
3630   DMPlexCreateFromCellListParallel - Deprecated, use DMPlexCreateFromCellListParallelPetsc()
3631 
3632   Level: deprecated
3633 
3634 .seealso: DMPlexCreateFromCellListParallelPetsc()
3635 @*/
3636 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)
3637 {
3638   PetscErrorCode ierr;
3639   PetscInt       i;
3640   PetscInt       *pintCells;
3641 
3642   PetscFunctionBegin;
3643   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));
3644   if (sizeof(int) == sizeof(PetscInt)) {
3645     pintCells = (PetscInt *) cells;
3646   } else {
3647     ierr = PetscMalloc1(numCells*numCorners, &pintCells);CHKERRQ(ierr);
3648     for (i = 0; i < numCells*numCorners; i++) {
3649       pintCells[i] = (PetscInt) cells[i];
3650     }
3651   }
3652   ierr = DMPlexCreateFromCellListParallelPetsc(comm, dim, numCells, numVertices, PETSC_DECIDE, numCorners, interpolate, pintCells, spaceDim, vertexCoords, vertexSF, dm);CHKERRQ(ierr);
3653   if (sizeof(int) != sizeof(PetscInt)) {
3654     ierr = PetscFree(pintCells);CHKERRQ(ierr);
3655   }
3656   PetscFunctionReturn(0);
3657 }
3658 
3659 /*@C
3660   DMPlexBuildFromCellList - Build DMPLEX topology from a list of vertices for each cell (common mesh generator output)
3661 
3662   Input Parameters:
3663 + dm - The DM
3664 . numCells - The number of cells owned by this process
3665 . numVertices - The number of vertices owned by this process, or PETSC_DECIDE
3666 . numCorners - The number of vertices for each cell
3667 - cells - An array of numCells*numCorners numbers, the global vertex numbers for each cell
3668 
3669   Level: advanced
3670 
3671   Notes:
3672   Two triangles sharing a face
3673 $
3674 $        2
3675 $      / | \
3676 $     /  |  \
3677 $    /   |   \
3678 $   0  0 | 1  3
3679 $    \   |   /
3680 $     \  |  /
3681 $      \ | /
3682 $        1
3683 would have input
3684 $  numCells = 2, numVertices = 4
3685 $  cells = [0 1 2  1 3 2]
3686 $
3687 which would result in the DMPlex
3688 $
3689 $        4
3690 $      / | \
3691 $     /  |  \
3692 $    /   |   \
3693 $   2  0 | 1  5
3694 $    \   |   /
3695 $     \  |  /
3696 $      \ | /
3697 $        3
3698 
3699   If numVertices is PETSC_DECIDE, it is computed by PETSc as the maximum vertex index in cells + 1.
3700 
3701   Not currently supported in Fortran.
3702 
3703 .seealso: DMPlexBuildFromCellListParallel(), DMPlexBuildCoordinatesFromCellList(), DMPlexCreateFromCellListPetsc()
3704 @*/
3705 PetscErrorCode DMPlexBuildFromCellList(DM dm, PetscInt numCells, PetscInt numVertices, PetscInt numCorners, const PetscInt cells[])
3706 {
3707   PetscInt      *cones, c, p, dim;
3708   PetscErrorCode ierr;
3709 
3710   PetscFunctionBegin;
3711   ierr = PetscLogEventBegin(DMPLEX_BuildFromCellList,dm,0,0,0);CHKERRQ(ierr);
3712   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
3713   /* Get/check global number of vertices */
3714   {
3715     PetscInt NVerticesInCells, i;
3716     const PetscInt len = numCells * numCorners;
3717 
3718     /* NVerticesInCells = max(cells) + 1 */
3719     NVerticesInCells = PETSC_MIN_INT;
3720     for (i=0; i<len; i++) if (cells[i] > NVerticesInCells) NVerticesInCells = cells[i];
3721     ++NVerticesInCells;
3722 
3723     if (numVertices == PETSC_DECIDE) numVertices = NVerticesInCells;
3724     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);
3725   }
3726   ierr = DMPlexSetChart(dm, 0, numCells+numVertices);CHKERRQ(ierr);
3727   for (c = 0; c < numCells; ++c) {
3728     ierr = DMPlexSetConeSize(dm, c, numCorners);CHKERRQ(ierr);
3729   }
3730   ierr = DMSetUp(dm);CHKERRQ(ierr);
3731   ierr = DMPlexGetCones(dm,&cones);CHKERRQ(ierr);
3732   for (c = 0; c < numCells; ++c) {
3733     for (p = 0; p < numCorners; ++p) {
3734       cones[c*numCorners+p] = cells[c*numCorners+p]+numCells;
3735     }
3736   }
3737   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
3738   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
3739   ierr = PetscLogEventEnd(DMPLEX_BuildFromCellList,dm,0,0,0);CHKERRQ(ierr);
3740   PetscFunctionReturn(0);
3741 }
3742 
3743 /*@C
3744   DMPlexBuildCoordinatesFromCellList - Build DM coordinates from a list of coordinates for each owned vertex (common mesh generator output)
3745 
3746   Input Parameters:
3747 + dm - The DM
3748 . spaceDim - The spatial dimension used for coordinates
3749 - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex
3750 
3751   Level: advanced
3752 
3753   Notes:
3754   Not currently supported in Fortran.
3755 
3756 .seealso: DMPlexBuildCoordinatesFromCellListParallel(), DMPlexCreateFromCellListPetsc(), DMPlexBuildFromCellList()
3757 @*/
3758 PetscErrorCode DMPlexBuildCoordinatesFromCellList(DM dm, PetscInt spaceDim, const PetscReal vertexCoords[])
3759 {
3760   PetscSection   coordSection;
3761   Vec            coordinates;
3762   DM             cdm;
3763   PetscScalar   *coords;
3764   PetscInt       v, vStart, vEnd, d;
3765   PetscErrorCode ierr;
3766 
3767   PetscFunctionBegin;
3768   ierr = PetscLogEventBegin(DMPLEX_BuildCoordinatesFromCellList,dm,0,0,0);CHKERRQ(ierr);
3769   ierr = DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);CHKERRQ(ierr);
3770   if (vStart < 0 || vEnd < 0) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "DM is not set up properly. DMPlexBuildFromCellList() should be called first.");
3771   ierr = DMSetCoordinateDim(dm, spaceDim);CHKERRQ(ierr);
3772   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
3773   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
3774   ierr = PetscSectionSetFieldComponents(coordSection, 0, spaceDim);CHKERRQ(ierr);
3775   ierr = PetscSectionSetChart(coordSection, vStart, vEnd);CHKERRQ(ierr);
3776   for (v = vStart; v < vEnd; ++v) {
3777     ierr = PetscSectionSetDof(coordSection, v, spaceDim);CHKERRQ(ierr);
3778     ierr = PetscSectionSetFieldDof(coordSection, v, 0, spaceDim);CHKERRQ(ierr);
3779   }
3780   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
3781 
3782   ierr = DMGetCoordinateDM(dm, &cdm);CHKERRQ(ierr);
3783   ierr = DMCreateLocalVector(cdm, &coordinates);CHKERRQ(ierr);
3784   ierr = VecSetBlockSize(coordinates, spaceDim);CHKERRQ(ierr);
3785   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
3786   ierr = VecGetArrayWrite(coordinates, &coords);CHKERRQ(ierr);
3787   for (v = 0; v < vEnd-vStart; ++v) {
3788     for (d = 0; d < spaceDim; ++d) {
3789       coords[v*spaceDim+d] = vertexCoords[v*spaceDim+d];
3790     }
3791   }
3792   ierr = VecRestoreArrayWrite(coordinates, &coords);CHKERRQ(ierr);
3793   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
3794   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
3795   ierr = PetscLogEventEnd(DMPLEX_BuildCoordinatesFromCellList,dm,0,0,0);CHKERRQ(ierr);
3796   PetscFunctionReturn(0);
3797 }
3798 
3799 /*@
3800   DMPlexCreateFromCellListPetsc - Create DMPLEX from a list of vertices for each cell (common mesh generator output)
3801 
3802   Input Parameters:
3803 + comm - The communicator
3804 . dim - The topological dimension of the mesh
3805 . numCells - The number of cells
3806 . numVertices - The number of vertices owned by this process, or PETSC_DECIDE
3807 . numCorners - The number of vertices for each cell
3808 . interpolate - Flag indicating that intermediate mesh entities (faces, edges) should be created automatically
3809 . cells - An array of numCells*numCorners numbers, the vertices for each cell
3810 . spaceDim - The spatial dimension used for coordinates
3811 - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex
3812 
3813   Output Parameter:
3814 . dm - The DM
3815 
3816   Notes:
3817   This function is just a convenient sequence of DMCreate(), DMSetType(), DMSetDimension(), DMPlexBuildFromCellList(),
3818   DMPlexInterpolate(), DMPlexBuildCoordinatesFromCellList()
3819 
3820   See DMPlexBuildFromCellList() for an example and details about the topology-related parameters.
3821   See DMPlexBuildCoordinatesFromCellList() for details about the geometry-related parameters.
3822 
3823   Level: intermediate
3824 
3825 .seealso: DMPlexCreateFromCellListParallelPetsc(), DMPlexBuildFromCellList(), DMPlexBuildCoordinatesFromCellList(), DMPlexCreateFromDAG(), DMPlexCreate()
3826 @*/
3827 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)
3828 {
3829   PetscErrorCode ierr;
3830 
3831   PetscFunctionBegin;
3832   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.");
3833   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
3834   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
3835   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
3836   ierr = DMPlexBuildFromCellList(*dm, numCells, numVertices, numCorners, cells);CHKERRQ(ierr);
3837   if (interpolate) {
3838     DM idm;
3839 
3840     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
3841     ierr = DMDestroy(dm);CHKERRQ(ierr);
3842     *dm  = idm;
3843   }
3844   ierr = DMPlexBuildCoordinatesFromCellList(*dm, spaceDim, vertexCoords);CHKERRQ(ierr);
3845   PetscFunctionReturn(0);
3846 }
3847 
3848 /*@
3849   DMPlexCreateFromCellList - Deprecated, use DMPlexCreateFromCellListPetsc()
3850 
3851   Level: deprecated
3852 
3853 .seealso: DMPlexCreateFromCellListPetsc()
3854 @*/
3855 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)
3856 {
3857   PetscErrorCode ierr;
3858   PetscInt       i;
3859   PetscInt       *pintCells;
3860   PetscReal      *prealVC;
3861 
3862   PetscFunctionBegin;
3863   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));
3864   if (sizeof(int) == sizeof(PetscInt)) {
3865     pintCells = (PetscInt *) cells;
3866   } else {
3867     ierr = PetscMalloc1(numCells*numCorners, &pintCells);CHKERRQ(ierr);
3868     for (i = 0; i < numCells*numCorners; i++) {
3869       pintCells[i] = (PetscInt) cells[i];
3870     }
3871   }
3872   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));
3873   if (sizeof(double) == sizeof(PetscReal)) {
3874     prealVC = (PetscReal *) vertexCoords;
3875   } else {
3876     ierr = PetscMalloc1(numVertices*spaceDim, &prealVC);CHKERRQ(ierr);
3877     for (i = 0; i < numVertices*spaceDim; i++) {
3878       prealVC[i] = (PetscReal) vertexCoords[i];
3879     }
3880   }
3881   ierr = DMPlexCreateFromCellListPetsc(comm, dim, numCells, numVertices, numCorners, interpolate, pintCells, spaceDim, prealVC, dm);CHKERRQ(ierr);
3882   if (sizeof(int) != sizeof(PetscInt)) {
3883     ierr = PetscFree(pintCells);CHKERRQ(ierr);
3884   }
3885   if (sizeof(double) != sizeof(PetscReal)) {
3886     ierr = PetscFree(prealVC);CHKERRQ(ierr);
3887   }
3888   PetscFunctionReturn(0);
3889 }
3890 
3891 /*@
3892   DMPlexCreateFromDAG - This takes as input the adjacency-list representation of the Directed Acyclic Graph (Hasse Diagram) encoding a mesh, and produces a DM
3893 
3894   Input Parameters:
3895 + dm - The empty DM object, usually from DMCreate() and DMSetDimension()
3896 . depth - The depth of the DAG
3897 . numPoints - Array of size depth + 1 containing the number of points at each depth
3898 . coneSize - The cone size of each point
3899 . cones - The concatenation of the cone points for each point, the cone list must be oriented correctly for each point
3900 . coneOrientations - The orientation of each cone point
3901 - vertexCoords - An array of numPoints[0]*spacedim numbers representing the coordinates of each vertex, with spacedim the value set via DMSetCoordinateDim()
3902 
3903   Output Parameter:
3904 . dm - The DM
3905 
3906   Note: Two triangles sharing a face would have input
3907 $  depth = 1, numPoints = [4 2], coneSize = [3 3 0 0 0 0]
3908 $  cones = [2 3 4  3 5 4], coneOrientations = [0 0 0  0 0 0]
3909 $ vertexCoords = [-1.0 0.0  0.0 -1.0  0.0 1.0  1.0 0.0]
3910 $
3911 which would result in the DMPlex
3912 $
3913 $        4
3914 $      / | \
3915 $     /  |  \
3916 $    /   |   \
3917 $   2  0 | 1  5
3918 $    \   |   /
3919 $     \  |  /
3920 $      \ | /
3921 $        3
3922 $
3923 $ Notice that all points are numbered consecutively, unlike DMPlexCreateFromCellListPetsc()
3924 
3925   Level: advanced
3926 
3927 .seealso: DMPlexCreateFromCellListPetsc(), DMPlexCreate()
3928 @*/
3929 PetscErrorCode DMPlexCreateFromDAG(DM dm, PetscInt depth, const PetscInt numPoints[], const PetscInt coneSize[], const PetscInt cones[], const PetscInt coneOrientations[], const PetscScalar vertexCoords[])
3930 {
3931   Vec            coordinates;
3932   PetscSection   coordSection;
3933   PetscScalar    *coords;
3934   PetscInt       coordSize, firstVertex = -1, pStart = 0, pEnd = 0, p, v, dim, dimEmbed, d, off;
3935   PetscErrorCode ierr;
3936 
3937   PetscFunctionBegin;
3938   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
3939   ierr = DMGetCoordinateDim(dm, &dimEmbed);CHKERRQ(ierr);
3940   if (dimEmbed < dim) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Embedding dimension %D cannot be less than intrinsic dimension %d",dimEmbed,dim);
3941   for (d = 0; d <= depth; ++d) pEnd += numPoints[d];
3942   ierr = DMPlexSetChart(dm, pStart, pEnd);CHKERRQ(ierr);
3943   for (p = pStart; p < pEnd; ++p) {
3944     ierr = DMPlexSetConeSize(dm, p, coneSize[p-pStart]);CHKERRQ(ierr);
3945     if (firstVertex < 0 && !coneSize[p - pStart]) {
3946       firstVertex = p - pStart;
3947     }
3948   }
3949   if (firstVertex < 0 && numPoints[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Expected %D vertices but could not find any", numPoints[0]);
3950   ierr = DMSetUp(dm);CHKERRQ(ierr); /* Allocate space for cones */
3951   for (p = pStart, off = 0; p < pEnd; off += coneSize[p-pStart], ++p) {
3952     ierr = DMPlexSetCone(dm, p, &cones[off]);CHKERRQ(ierr);
3953     ierr = DMPlexSetConeOrientation(dm, p, &coneOrientations[off]);CHKERRQ(ierr);
3954   }
3955   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
3956   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
3957   /* Build coordinates */
3958   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
3959   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
3960   ierr = PetscSectionSetFieldComponents(coordSection, 0, dimEmbed);CHKERRQ(ierr);
3961   ierr = PetscSectionSetChart(coordSection, firstVertex, firstVertex+numPoints[0]);CHKERRQ(ierr);
3962   for (v = firstVertex; v < firstVertex+numPoints[0]; ++v) {
3963     ierr = PetscSectionSetDof(coordSection, v, dimEmbed);CHKERRQ(ierr);
3964     ierr = PetscSectionSetFieldDof(coordSection, v, 0, dimEmbed);CHKERRQ(ierr);
3965   }
3966   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
3967   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
3968   ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
3969   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
3970   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
3971   ierr = VecSetBlockSize(coordinates, dimEmbed);CHKERRQ(ierr);
3972   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
3973   if (vertexCoords) {
3974     ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
3975     for (v = 0; v < numPoints[0]; ++v) {
3976       PetscInt off;
3977 
3978       ierr = PetscSectionGetOffset(coordSection, v+firstVertex, &off);CHKERRQ(ierr);
3979       for (d = 0; d < dimEmbed; ++d) {
3980         coords[off+d] = vertexCoords[v*dimEmbed+d];
3981       }
3982     }
3983   }
3984   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
3985   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
3986   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
3987   PetscFunctionReturn(0);
3988 }
3989 
3990 /*@C
3991   DMPlexCreateCellVertexFromFile - Create a DMPlex mesh from a simple cell-vertex file.
3992 
3993 + comm        - The MPI communicator
3994 . filename    - Name of the .dat file
3995 - interpolate - Create faces and edges in the mesh
3996 
3997   Output Parameter:
3998 . dm  - The DM object representing the mesh
3999 
4000   Note: The format is the simplest possible:
4001 $ Ne
4002 $ v0 v1 ... vk
4003 $ Nv
4004 $ x y z marker
4005 
4006   Level: beginner
4007 
4008 .seealso: DMPlexCreateFromFile(), DMPlexCreateMedFromFile(), DMPlexCreateGmsh(), DMPlexCreate()
4009 @*/
4010 PetscErrorCode DMPlexCreateCellVertexFromFile(MPI_Comm comm, const char filename[], PetscBool interpolate, DM *dm)
4011 {
4012   DMLabel         marker;
4013   PetscViewer     viewer;
4014   Vec             coordinates;
4015   PetscSection    coordSection;
4016   PetscScalar    *coords;
4017   char            line[PETSC_MAX_PATH_LEN];
4018   PetscInt        dim = 3, cdim = 3, coordSize, v, c, d;
4019   PetscMPIInt     rank;
4020   int             snum, Nv, Nc;
4021   PetscErrorCode  ierr;
4022 
4023   PetscFunctionBegin;
4024   ierr = MPI_Comm_rank(comm, &rank);CHKERRMPI(ierr);
4025   ierr = PetscViewerCreate(comm, &viewer);CHKERRQ(ierr);
4026   ierr = PetscViewerSetType(viewer, PETSCVIEWERASCII);CHKERRQ(ierr);
4027   ierr = PetscViewerFileSetMode(viewer, FILE_MODE_READ);CHKERRQ(ierr);
4028   ierr = PetscViewerFileSetName(viewer, filename);CHKERRQ(ierr);
4029   if (!rank) {
4030     ierr = PetscViewerRead(viewer, line, 2, NULL, PETSC_STRING);CHKERRQ(ierr);
4031     snum = sscanf(line, "%d %d", &Nc, &Nv);
4032     if (snum != 2) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unable to parse cell-vertex file: %s", line);
4033   } else {
4034     Nc = Nv = 0;
4035   }
4036   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
4037   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
4038   ierr = DMPlexSetChart(*dm, 0, Nc+Nv);CHKERRQ(ierr);
4039   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
4040   ierr = DMSetCoordinateDim(*dm, cdim);CHKERRQ(ierr);
4041   /* Read topology */
4042   if (!rank) {
4043     PetscInt cone[8], corners = 8;
4044     int      vbuf[8], v;
4045 
4046     for (c = 0; c < Nc; ++c) {ierr = DMPlexSetConeSize(*dm, c, corners);CHKERRQ(ierr);}
4047     ierr = DMSetUp(*dm);CHKERRQ(ierr);
4048     for (c = 0; c < Nc; ++c) {
4049       ierr = PetscViewerRead(viewer, line, corners, NULL, PETSC_STRING);CHKERRQ(ierr);
4050       snum = sscanf(line, "%d %d %d %d %d %d %d %d", &vbuf[0], &vbuf[1], &vbuf[2], &vbuf[3], &vbuf[4], &vbuf[5], &vbuf[6], &vbuf[7]);
4051       if (snum != corners) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unable to parse cell-vertex file: %s", line);
4052       for (v = 0; v < corners; ++v) cone[v] = vbuf[v] + Nc;
4053       /* Hexahedra are inverted */
4054       {
4055         PetscInt tmp = cone[1];
4056         cone[1] = cone[3];
4057         cone[3] = tmp;
4058       }
4059       ierr = DMPlexSetCone(*dm, c, cone);CHKERRQ(ierr);
4060     }
4061   }
4062   ierr = DMPlexSymmetrize(*dm);CHKERRQ(ierr);
4063   ierr = DMPlexStratify(*dm);CHKERRQ(ierr);
4064   /* Read coordinates */
4065   ierr = DMGetCoordinateSection(*dm, &coordSection);CHKERRQ(ierr);
4066   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
4067   ierr = PetscSectionSetFieldComponents(coordSection, 0, cdim);CHKERRQ(ierr);
4068   ierr = PetscSectionSetChart(coordSection, Nc, Nc + Nv);CHKERRQ(ierr);
4069   for (v = Nc; v < Nc+Nv; ++v) {
4070     ierr = PetscSectionSetDof(coordSection, v, cdim);CHKERRQ(ierr);
4071     ierr = PetscSectionSetFieldDof(coordSection, v, 0, cdim);CHKERRQ(ierr);
4072   }
4073   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
4074   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
4075   ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
4076   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
4077   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
4078   ierr = VecSetBlockSize(coordinates, cdim);CHKERRQ(ierr);
4079   ierr = VecSetType(coordinates, VECSTANDARD);CHKERRQ(ierr);
4080   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
4081   if (!rank) {
4082     double x[3];
4083     int    val;
4084 
4085     ierr = DMCreateLabel(*dm, "marker");CHKERRQ(ierr);
4086     ierr = DMGetLabel(*dm, "marker", &marker);CHKERRQ(ierr);
4087     for (v = 0; v < Nv; ++v) {
4088       ierr = PetscViewerRead(viewer, line, 4, NULL, PETSC_STRING);CHKERRQ(ierr);
4089       snum = sscanf(line, "%lg %lg %lg %d", &x[0], &x[1], &x[2], &val);
4090       if (snum != 4) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unable to parse cell-vertex file: %s", line);
4091       for (d = 0; d < cdim; ++d) coords[v*cdim+d] = x[d];
4092       if (val) {ierr = DMLabelSetValue(marker, v+Nc, val);CHKERRQ(ierr);}
4093     }
4094   }
4095   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
4096   ierr = DMSetCoordinatesLocal(*dm, coordinates);CHKERRQ(ierr);
4097   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
4098   ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
4099   if (interpolate) {
4100     DM      idm;
4101     DMLabel bdlabel;
4102 
4103     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
4104     ierr = DMDestroy(dm);CHKERRQ(ierr);
4105     *dm  = idm;
4106 
4107     ierr = DMGetLabel(*dm, "marker", &bdlabel);CHKERRQ(ierr);
4108     ierr = DMPlexMarkBoundaryFaces(*dm, PETSC_DETERMINE, bdlabel);CHKERRQ(ierr);
4109     ierr = DMPlexLabelComplete(*dm, bdlabel);CHKERRQ(ierr);
4110   }
4111   PetscFunctionReturn(0);
4112 }
4113 
4114 /*@C
4115   DMPlexCreateFromFile - This takes a filename and produces a DM
4116 
4117   Input Parameters:
4118 + comm - The communicator
4119 . filename - A file name
4120 - interpolate - Flag to create intermediate mesh pieces (edges, faces)
4121 
4122   Output Parameter:
4123 . dm - The DM
4124 
4125   Options Database Keys:
4126 . -dm_plex_create_from_hdf5_xdmf - use the PETSC_VIEWER_HDF5_XDMF format for reading HDF5
4127 
4128   Use -dm_plex_create_ prefix to pass options to the internal PetscViewer, e.g.
4129 $ -dm_plex_create_viewer_hdf5_collective
4130 
4131   Level: beginner
4132 
4133 .seealso: DMPlexCreateFromDAG(), DMPlexCreateFromCellListPetsc(), DMPlexCreate()
4134 @*/
4135 PetscErrorCode DMPlexCreateFromFile(MPI_Comm comm, const char filename[], PetscBool interpolate, DM *dm)
4136 {
4137   const char    *extGmsh      = ".msh";
4138   const char    *extGmsh2     = ".msh2";
4139   const char    *extGmsh4     = ".msh4";
4140   const char    *extCGNS      = ".cgns";
4141   const char    *extExodus    = ".exo";
4142   const char    *extGenesis   = ".gen";
4143   const char    *extFluent    = ".cas";
4144   const char    *extHDF5      = ".h5";
4145   const char    *extMed       = ".med";
4146   const char    *extPLY       = ".ply";
4147   const char    *extEGADSLite = ".egadslite";
4148   const char    *extEGADS     = ".egads";
4149   const char    *extIGES      = ".igs";
4150   const char    *extSTEP      = ".stp";
4151   const char    *extCV        = ".dat";
4152   size_t         len;
4153   PetscBool      isGmsh, isGmsh2, isGmsh4, isCGNS, isExodus, isGenesis, isFluent, isHDF5, isMed, isPLY, isEGADSLite, isEGADS, isIGES, isSTEP, isCV;
4154   PetscMPIInt    rank;
4155   PetscErrorCode ierr;
4156 
4157   PetscFunctionBegin;
4158   PetscValidCharPointer(filename, 2);
4159   PetscValidPointer(dm, 4);
4160   ierr = DMInitializePackage();CHKERRQ(ierr);
4161   ierr = PetscLogEventBegin(DMPLEX_CreateFromFile,0,0,0,0);CHKERRQ(ierr);
4162   ierr = MPI_Comm_rank(comm, &rank);CHKERRMPI(ierr);
4163   ierr = PetscStrlen(filename, &len);CHKERRQ(ierr);
4164   if (!len) SETERRQ(comm, PETSC_ERR_ARG_WRONG, "Filename must be a valid path");
4165   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)],  extGmsh,      4, &isGmsh);CHKERRQ(ierr);
4166   ierr = PetscStrncmp(&filename[PetscMax(0,len-5)],  extGmsh2,     5, &isGmsh2);CHKERRQ(ierr);
4167   ierr = PetscStrncmp(&filename[PetscMax(0,len-5)],  extGmsh4,     5, &isGmsh4);CHKERRQ(ierr);
4168   ierr = PetscStrncmp(&filename[PetscMax(0,len-5)],  extCGNS,      5, &isCGNS);CHKERRQ(ierr);
4169   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)],  extExodus,    4, &isExodus);CHKERRQ(ierr);
4170   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)],  extGenesis,   4, &isGenesis);CHKERRQ(ierr);
4171   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)],  extFluent,    4, &isFluent);CHKERRQ(ierr);
4172   ierr = PetscStrncmp(&filename[PetscMax(0,len-3)],  extHDF5,      3, &isHDF5);CHKERRQ(ierr);
4173   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)],  extMed,       4, &isMed);CHKERRQ(ierr);
4174   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)],  extPLY,       4, &isPLY);CHKERRQ(ierr);
4175   ierr = PetscStrncmp(&filename[PetscMax(0,len-10)], extEGADSLite, 10, &isEGADSLite);CHKERRQ(ierr);
4176   ierr = PetscStrncmp(&filename[PetscMax(0,len-6)],  extEGADS,     6, &isEGADS);CHKERRQ(ierr);
4177   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)],  extIGES,      4, &isIGES);CHKERRQ(ierr);
4178   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)],  extSTEP,      4, &isSTEP);CHKERRQ(ierr);
4179   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)],  extCV,        4, &isCV);CHKERRQ(ierr);
4180   if (isGmsh || isGmsh2 || isGmsh4) {
4181     ierr = DMPlexCreateGmshFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
4182   } else if (isCGNS) {
4183     ierr = DMPlexCreateCGNSFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
4184   } else if (isExodus || isGenesis) {
4185     ierr = DMPlexCreateExodusFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
4186   } else if (isFluent) {
4187     ierr = DMPlexCreateFluentFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
4188   } else if (isHDF5) {
4189     PetscBool      load_hdf5_xdmf = PETSC_FALSE;
4190     PetscViewer viewer;
4191 
4192     /* PETSC_VIEWER_HDF5_XDMF is used if the filename ends with .xdmf.h5, or if -dm_plex_create_from_hdf5_xdmf option is present */
4193     ierr = PetscStrncmp(&filename[PetscMax(0,len-8)], ".xdmf",  5, &load_hdf5_xdmf);CHKERRQ(ierr);
4194     ierr = PetscOptionsGetBool(NULL, NULL, "-dm_plex_create_from_hdf5_xdmf", &load_hdf5_xdmf, NULL);CHKERRQ(ierr);
4195     ierr = PetscViewerCreate(comm, &viewer);CHKERRQ(ierr);
4196     ierr = PetscViewerSetType(viewer, PETSCVIEWERHDF5);CHKERRQ(ierr);
4197     ierr = PetscViewerSetOptionsPrefix(viewer, "dm_plex_create_");CHKERRQ(ierr);
4198     ierr = PetscViewerSetFromOptions(viewer);CHKERRQ(ierr);
4199     ierr = PetscViewerFileSetMode(viewer, FILE_MODE_READ);CHKERRQ(ierr);
4200     ierr = PetscViewerFileSetName(viewer, filename);CHKERRQ(ierr);
4201     ierr = DMCreate(comm, dm);CHKERRQ(ierr);
4202     ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
4203     if (load_hdf5_xdmf) {ierr = PetscViewerPushFormat(viewer, PETSC_VIEWER_HDF5_XDMF);CHKERRQ(ierr);}
4204     ierr = DMLoad(*dm, viewer);CHKERRQ(ierr);
4205     if (load_hdf5_xdmf) {ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);}
4206     ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
4207 
4208     if (interpolate) {
4209       DM idm;
4210 
4211       ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
4212       ierr = DMDestroy(dm);CHKERRQ(ierr);
4213       *dm  = idm;
4214     }
4215   } else if (isMed) {
4216     ierr = DMPlexCreateMedFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
4217   } else if (isPLY) {
4218     ierr = DMPlexCreatePLYFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
4219   } else if (isEGADSLite || isEGADS || isIGES || isSTEP) {
4220     if (isEGADSLite) {ierr = DMPlexCreateEGADSLiteFromFile(comm, filename, dm);CHKERRQ(ierr);}
4221     else             {ierr = DMPlexCreateEGADSFromFile(comm, filename, dm);CHKERRQ(ierr);}
4222     if (!interpolate) {
4223       DM udm;
4224 
4225       ierr = DMPlexUninterpolate(*dm, &udm);CHKERRQ(ierr);
4226       ierr = DMDestroy(dm);CHKERRQ(ierr);
4227       *dm  = udm;
4228     }
4229   } else if (isCV) {
4230     ierr = DMPlexCreateCellVertexFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
4231   } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cannot load file %s: unrecognized extension", filename);
4232   ierr = PetscLogEventEnd(DMPLEX_CreateFromFile,0,0,0,0);CHKERRQ(ierr);
4233   PetscFunctionReturn(0);
4234 }
4235