xref: /petsc/src/dm/impls/plex/plexcreate.c (revision 909dfd52d29915732d44f9443658cd10cc8ebe94) !
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   PetscFunctionReturn(0);
2630 }
2631 
2632 /*@
2633   DMPlexCreateReferenceCell - Create a DMPLEX with the appropriate FEM reference cell
2634 
2635   Collective
2636 
2637   Input Parameters:
2638 + comm - The communicator
2639 - ct   - The cell type of the reference cell
2640 
2641   Output Parameter:
2642 . refdm - The reference cell
2643 
2644   Level: intermediate
2645 
2646 .seealso: DMPlexCreateReferenceCell(), DMPlexCreateBoxMesh()
2647 @*/
2648 PetscErrorCode DMPlexCreateReferenceCell(MPI_Comm comm, DMPolytopeType ct, DM *refdm)
2649 {
2650   PetscErrorCode ierr;
2651 
2652   PetscFunctionBegin;
2653   ierr = DMCreate(comm, refdm);CHKERRQ(ierr);
2654   ierr = DMSetType(*refdm, DMPLEX);CHKERRQ(ierr);
2655   ierr = DMPlexCreateReferenceCell_Internal(*refdm, ct);CHKERRQ(ierr);
2656   PetscFunctionReturn(0);
2657 }
2658 
2659 static PetscErrorCode DMPlexCreateBoundaryLabel_Private(DM dm, const char name[])
2660 {
2661   DM             plex;
2662   DMLabel        label;
2663   PetscBool      hasLabel;
2664   PetscErrorCode ierr;
2665 
2666   PetscFunctionBeginUser;
2667   ierr = DMHasLabel(dm, name, &hasLabel);CHKERRQ(ierr);
2668   if (hasLabel) PetscFunctionReturn(0);
2669   ierr = DMCreateLabel(dm, name);CHKERRQ(ierr);
2670   ierr = DMGetLabel(dm, name, &label);CHKERRQ(ierr);
2671   ierr = DMConvert(dm, DMPLEX, &plex);CHKERRQ(ierr);
2672   ierr = DMPlexMarkBoundaryFaces(plex, 1, label);CHKERRQ(ierr);
2673   ierr = DMDestroy(&plex);CHKERRQ(ierr);
2674   PetscFunctionReturn(0);
2675 }
2676 
2677 const char * const DMPlexShapes[] = {"box", "box_surface", "ball", "sphere", "cylinder", "unknown", "DMPlexShape", "DM_SHAPE_", NULL};
2678 
2679 static PetscErrorCode DMPlexCreateFromOptions_Internal(PetscOptionItems *PetscOptionsObject, PetscBool *useCoordSpace, DM dm)
2680 {
2681   DMPlexShape    shape = DM_SHAPE_BOX;
2682   DMPolytopeType cell  = DM_POLYTOPE_TRIANGLE;
2683   PetscInt       dim   = 2;
2684   PetscBool      simplex = PETSC_TRUE, interpolate = PETSC_TRUE, adjCone = PETSC_FALSE, adjClosure = PETSC_TRUE, refDomain = PETSC_FALSE;
2685   PetscBool      flg, flg2, fflg, bdfflg;
2686   MPI_Comm       comm;
2687   char           filename[PETSC_MAX_PATH_LEN], bdFilename[PETSC_MAX_PATH_LEN];
2688   PetscErrorCode ierr;
2689 
2690   PetscFunctionBegin;
2691   ierr = PetscObjectGetComm((PetscObject) dm, &comm);CHKERRQ(ierr);
2692   /* TODO Turn this into a registration interface */
2693   ierr = PetscOptionsString("-dm_plex_filename", "File containing a mesh", "DMPlexCreateFromFile", filename, filename, sizeof(filename), &fflg);CHKERRQ(ierr);
2694   ierr = PetscOptionsString("-dm_plex_boundary_filename", "File containing a mesh boundary", "DMPlexCreateFromFile", bdFilename, bdFilename, sizeof(bdFilename), &bdfflg);CHKERRQ(ierr);
2695   ierr = PetscOptionsEnum("-dm_plex_cell", "Cell shape", "", DMPolytopeTypes, (PetscEnum) cell, (PetscEnum *) &cell, NULL);CHKERRQ(ierr);
2696   ierr = PetscOptionsBool("-dm_plex_reference_cell_domain", "Use a reference cell domain", "", refDomain, &refDomain, NULL);CHKERRQ(ierr);
2697   ierr = PetscOptionsEnum("-dm_plex_shape", "Shape for built-in mesh", "", DMPlexShapes, (PetscEnum) shape, (PetscEnum *) &shape, &flg);CHKERRQ(ierr);
2698   ierr = PetscOptionsBoundedInt("-dm_plex_dim", "Topological dimension of the mesh", "DMGetDimension", dim, &dim, &flg, 0);CHKERRQ(ierr);
2699   if ((dim < 0) || (dim > 3)) SETERRQ1(comm, PETSC_ERR_ARG_OUTOFRANGE, "Dimension %D should be in [1, 3]", dim);
2700   ierr = PetscOptionsBool("-dm_plex_simplex", "Mesh cell shape", "", simplex,  &simplex, &flg);CHKERRQ(ierr);
2701   ierr = PetscOptionsBool("-dm_plex_interpolate", "Flag to create edges and faces automatically", "", interpolate, &interpolate, &flg);CHKERRQ(ierr);
2702   ierr = PetscOptionsBool("-dm_plex_adj_cone", "Set adjacency direction", "DMSetBasicAdjacency", adjCone,  &adjCone, &flg);CHKERRQ(ierr);
2703   ierr = PetscOptionsBool("-dm_plex_adj_closure", "Set adjacency size", "DMSetBasicAdjacency", adjClosure,  &adjClosure, &flg2);CHKERRQ(ierr);
2704   if (flg || flg2) {ierr = DMSetBasicAdjacency(dm, adjCone, adjClosure);CHKERRQ(ierr);}
2705 
2706   switch (cell) {
2707     case DM_POLYTOPE_POINT:
2708     case DM_POLYTOPE_SEGMENT:
2709     case DM_POLYTOPE_POINT_PRISM_TENSOR:
2710     case DM_POLYTOPE_TRIANGLE:
2711     case DM_POLYTOPE_QUADRILATERAL:
2712     case DM_POLYTOPE_TETRAHEDRON:
2713     case DM_POLYTOPE_HEXAHEDRON:
2714       *useCoordSpace = PETSC_TRUE;break;
2715     default: *useCoordSpace = PETSC_FALSE;break;
2716   }
2717 
2718   if (fflg) {
2719     DM dmnew;
2720 
2721     ierr = DMPlexCreateFromFile(PetscObjectComm((PetscObject) dm), filename, interpolate, &dmnew);CHKERRQ(ierr);
2722     ierr = DMPlexReplace_Static(dm, &dmnew);CHKERRQ(ierr);
2723   } else if (refDomain) {
2724     ierr = DMPlexCreateReferenceCell_Internal(dm, cell);CHKERRQ(ierr);
2725   } else if (bdfflg) {
2726     DM bdm, dmnew;
2727 
2728     ierr = DMPlexCreateFromFile(PetscObjectComm((PetscObject) dm), bdFilename, interpolate, &bdm);CHKERRQ(ierr);
2729     ierr = PetscObjectSetOptionsPrefix((PetscObject) bdm, "bd_");CHKERRQ(ierr);
2730     ierr = DMSetFromOptions(bdm);CHKERRQ(ierr);
2731     ierr = DMPlexGenerate(bdm, NULL, interpolate, &dmnew);CHKERRQ(ierr);
2732     ierr = DMDestroy(&bdm);CHKERRQ(ierr);
2733     ierr = DMPlexReplace_Static(dm, &dmnew);CHKERRQ(ierr);
2734   } else {
2735     ierr = PetscObjectSetName((PetscObject) dm, DMPlexShapes[shape]);CHKERRQ(ierr);
2736     switch (shape) {
2737       case DM_SHAPE_BOX:
2738       {
2739         PetscInt       faces[3] = {0, 0, 0};
2740         PetscReal      lower[3] = {0, 0, 0};
2741         PetscReal      upper[3] = {1, 1, 1};
2742         DMBoundaryType bdt[3]   = {DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE};
2743         PetscInt       i, n;
2744 
2745         n    = dim;
2746         for (i = 0; i < dim; ++i) faces[i] = (dim == 1 ? 1 : 4-dim);
2747         ierr = PetscOptionsIntArray("-dm_plex_box_faces", "Number of faces along each dimension", "", faces, &n, &flg);CHKERRQ(ierr);
2748         n    = 3;
2749         ierr = PetscOptionsRealArray("-dm_plex_box_lower", "Lower left corner of box", "", lower, &n, &flg);CHKERRQ(ierr);
2750         if (flg && (n != dim)) SETERRQ2(comm, PETSC_ERR_ARG_SIZ, "Lower box point had %D values, should have been %D", n, dim);
2751         n    = 3;
2752         ierr = PetscOptionsRealArray("-dm_plex_box_upper", "Upper right corner of box", "", upper, &n, &flg);CHKERRQ(ierr);
2753         if (flg && (n != dim)) SETERRQ2(comm, PETSC_ERR_ARG_SIZ, "Upper box point had %D values, should have been %D", n, dim);
2754         n    = 3;
2755         ierr = PetscOptionsEnumArray("-dm_plex_box_bd", "Boundary type for each dimension", "", DMBoundaryTypes, (PetscEnum *) bdt, &n, &flg);CHKERRQ(ierr);
2756         if (flg && (n != dim)) SETERRQ2(comm, PETSC_ERR_ARG_SIZ, "Box boundary types had %D values, should have been %D", n, dim);
2757         switch (cell) {
2758           case DM_POLYTOPE_TRI_PRISM_TENSOR:
2759             ierr = DMPlexCreateWedgeBoxMesh_Internal(dm, faces, lower, upper, bdt, PETSC_FALSE, interpolate);CHKERRQ(ierr);
2760             break;
2761           default:
2762             ierr = DMPlexCreateBoxMesh_Internal(dm, dim, simplex, faces, lower, upper, bdt, interpolate);CHKERRQ(ierr);
2763             break;
2764         }
2765       }
2766       break;
2767       case DM_SHAPE_BOX_SURFACE:
2768       {
2769         PetscInt  faces[3] = {0, 0, 0};
2770         PetscReal lower[3] = {0, 0, 0};
2771         PetscReal upper[3] = {1, 1, 1};
2772         PetscInt  i, n;
2773 
2774         n    = dim+1;
2775         for (i = 0; i < dim+1; ++i) faces[i] = (dim+1 == 1 ? 1 : 4-(dim+1));
2776         ierr = PetscOptionsIntArray("-dm_plex_box_faces", "Number of faces along each dimension", "", faces, &n, &flg);CHKERRQ(ierr);
2777         n    = 3;
2778         ierr = PetscOptionsRealArray("-dm_plex_box_lower", "Lower left corner of box", "", lower, &n, &flg);CHKERRQ(ierr);
2779         if (flg && (n != dim+1)) SETERRQ2(comm, PETSC_ERR_ARG_SIZ, "Lower box point had %D values, should have been %D", n, dim+1);
2780         n    = 3;
2781         ierr = PetscOptionsRealArray("-dm_plex_box_upper", "Upper right corner of box", "", upper, &n, &flg);CHKERRQ(ierr);
2782         if (flg && (n != dim+1)) SETERRQ2(comm, PETSC_ERR_ARG_SIZ, "Upper box point had %D values, should have been %D", n, dim+1);
2783         ierr = DMPlexCreateBoxSurfaceMesh_Internal(dm, dim+1, faces, lower, upper, interpolate);CHKERRQ(ierr);
2784       }
2785       break;
2786       case DM_SHAPE_SPHERE:
2787       {
2788         PetscReal R = 1.0;
2789 
2790         ierr = PetscOptionsReal("-dm_plex_sphere_radius", "Radius of the sphere", "", R,  &R, &flg);CHKERRQ(ierr);
2791         ierr = DMPlexCreateSphereMesh_Internal(dm, dim, simplex, R);CHKERRQ(ierr);
2792       }
2793       break;
2794       case DM_SHAPE_BALL:
2795       {
2796         PetscReal R = 1.0;
2797 
2798         ierr = PetscOptionsReal("-dm_plex_ball_radius", "Radius of the ball", "", R,  &R, &flg);CHKERRQ(ierr);
2799         ierr = DMPlexCreateBallMesh_Internal(dm, dim, R);CHKERRQ(ierr);
2800       }
2801       break;
2802       case DM_SHAPE_CYLINDER:
2803       {
2804         DMBoundaryType bdt = DM_BOUNDARY_NONE;
2805         PetscInt       Nw  = 6;
2806 
2807         ierr = PetscOptionsEnum("-dm_plex_cylinder_bd", "Boundary type in the z direction", "", DMBoundaryTypes, (PetscEnum) bdt, (PetscEnum *) &bdt, NULL);CHKERRQ(ierr);
2808         ierr = PetscOptionsInt("-dm_plex_cylinder_num_wedges", "Number of wedges around the cylinder", "", Nw, &Nw, NULL);CHKERRQ(ierr);
2809         switch (cell) {
2810           case DM_POLYTOPE_TRI_PRISM_TENSOR:
2811             ierr = DMPlexCreateWedgeCylinderMesh_Internal(dm, Nw, interpolate);CHKERRQ(ierr);
2812             break;
2813           default:
2814             ierr = DMPlexCreateHexCylinderMesh_Internal(dm, bdt);CHKERRQ(ierr);
2815             break;
2816         }
2817       }
2818       break;
2819       default: SETERRQ1(comm, PETSC_ERR_SUP, "Domain shape %s is unsupported", DMPlexShapes[shape]);
2820     }
2821   }
2822   ierr = DMPlexSetRefinementUniform(dm, PETSC_TRUE);CHKERRQ(ierr);
2823   PetscFunctionReturn(0);
2824 }
2825 
2826 PetscErrorCode DMSetFromOptions_NonRefinement_Plex(PetscOptionItems *PetscOptionsObject, DM dm)
2827 {
2828   DM_Plex       *mesh = (DM_Plex*) dm->data;
2829   PetscBool      flg;
2830   char           bdLabel[PETSC_MAX_PATH_LEN];
2831   PetscErrorCode ierr;
2832 
2833   PetscFunctionBegin;
2834   /* Handle viewing */
2835   ierr = PetscOptionsBool("-dm_plex_print_set_values", "Output all set values info", "DMPlexMatSetClosure", PETSC_FALSE, &mesh->printSetValues, NULL);CHKERRQ(ierr);
2836   ierr = PetscOptionsBoundedInt("-dm_plex_print_fem", "Debug output level all fem computations", "DMPlexSNESComputeResidualFEM", 0, &mesh->printFEM, NULL,0);CHKERRQ(ierr);
2837   ierr = PetscOptionsReal("-dm_plex_print_tol", "Tolerance for FEM output", "DMPlexSNESComputeResidualFEM", mesh->printTol, &mesh->printTol, NULL);CHKERRQ(ierr);
2838   ierr = PetscOptionsBoundedInt("-dm_plex_print_l2", "Debug output level all L2 diff computations", "DMComputeL2Diff", 0, &mesh->printL2, NULL,0);CHKERRQ(ierr);
2839   ierr = DMMonitorSetFromOptions(dm, "-dm_plex_monitor_throughput", "Monitor the simulation throughput", "DMPlexMonitorThroughput", DMPlexMonitorThroughput, NULL, &flg);CHKERRQ(ierr);
2840   if (flg) {ierr = PetscLogDefaultBegin();CHKERRQ(ierr);}
2841   /* Labeling */
2842   ierr = PetscOptionsString("-dm_plex_boundary_label", "Label to mark the mesh boundary", "", bdLabel, bdLabel, sizeof(bdLabel), &flg);CHKERRQ(ierr);
2843   if (flg) {ierr = DMPlexCreateBoundaryLabel_Private(dm, bdLabel);CHKERRQ(ierr);}
2844   /* Point Location */
2845   ierr = PetscOptionsBool("-dm_plex_hash_location", "Use grid hashing for point location", "DMInterpolate", PETSC_FALSE, &mesh->useHashLocation, NULL);CHKERRQ(ierr);
2846   /* Partitioning and distribution */
2847   ierr = PetscOptionsBool("-dm_plex_partition_balance", "Attempt to evenly divide points on partition boundary between processes", "DMPlexSetPartitionBalance", PETSC_FALSE, &mesh->partitionBalance, NULL);CHKERRQ(ierr);
2848   /* Generation and remeshing */
2849   ierr = PetscOptionsBool("-dm_plex_remesh_bd", "Allow changes to the boundary on remeshing", "DMAdapt", PETSC_FALSE, &mesh->remeshBd, NULL);CHKERRQ(ierr);
2850   /* Projection behavior */
2851   ierr = PetscOptionsBoundedInt("-dm_plex_max_projection_height", "Maxmimum mesh point height used to project locally", "DMPlexSetMaxProjectionHeight", 0, &mesh->maxProjectionHeight, NULL,0);CHKERRQ(ierr);
2852   ierr = PetscOptionsBool("-dm_plex_regular_refinement", "Use special nested projection algorithm for regular refinement", "DMPlexSetRegularRefinement", mesh->regularRefinement, &mesh->regularRefinement, NULL);CHKERRQ(ierr);
2853   ierr = PetscOptionsEnum("-dm_plex_cell_refiner", "Strategy for cell refinment", "", DMPlexCellRefinerTypes, (PetscEnum) mesh->cellRefiner, (PetscEnum *) &mesh->cellRefiner, NULL);CHKERRQ(ierr);
2854   /* Checking structure */
2855   {
2856     PetscBool   flg = PETSC_FALSE, flg2 = PETSC_FALSE, all = PETSC_FALSE;
2857 
2858     ierr = PetscOptionsBool("-dm_plex_check_all", "Perform all checks", NULL, PETSC_FALSE, &all, &flg2);CHKERRQ(ierr);
2859     ierr = PetscOptionsBool("-dm_plex_check_symmetry", "Check that the adjacency information in the mesh is symmetric", "DMPlexCheckSymmetry", PETSC_FALSE, &flg, &flg2);CHKERRQ(ierr);
2860     if (all || (flg && flg2)) {ierr = DMPlexCheckSymmetry(dm);CHKERRQ(ierr);}
2861     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);
2862     if (all || (flg && flg2)) {ierr = DMPlexCheckSkeleton(dm, 0);CHKERRQ(ierr);}
2863     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);
2864     if (all || (flg && flg2)) {ierr = DMPlexCheckFaces(dm, 0);CHKERRQ(ierr);}
2865     ierr = PetscOptionsBool("-dm_plex_check_geometry", "Check that cells have positive volume", "DMPlexCheckGeometry", PETSC_FALSE, &flg, &flg2);CHKERRQ(ierr);
2866     if (all || (flg && flg2)) {ierr = DMPlexCheckGeometry(dm);CHKERRQ(ierr);}
2867     ierr = PetscOptionsBool("-dm_plex_check_pointsf", "Check some necessary conditions for PointSF", "DMPlexCheckPointSF", PETSC_FALSE, &flg, &flg2);CHKERRQ(ierr);
2868     if (all || (flg && flg2)) {ierr = DMPlexCheckPointSF(dm);CHKERRQ(ierr);}
2869     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);
2870     if (all || (flg && flg2)) {ierr = DMPlexCheckInterfaceCones(dm);CHKERRQ(ierr);}
2871     ierr = PetscOptionsBool("-dm_plex_check_cell_shape", "Check cell shape", "DMPlexCheckCellShape", PETSC_FALSE, &flg, &flg2);CHKERRQ(ierr);
2872     if (flg && flg2) {ierr = DMPlexCheckCellShape(dm, PETSC_TRUE, PETSC_DETERMINE);CHKERRQ(ierr);}
2873   }
2874   {
2875     PetscReal scale = 1.0;
2876 
2877     ierr = PetscOptionsReal("-dm_plex_scale", "Scale factor for mesh coordinates", "DMPlexScale", scale, &scale, &flg);CHKERRQ(ierr);
2878     if (flg) {
2879       Vec coordinates, coordinatesLocal;
2880 
2881       ierr = DMGetCoordinates(dm, &coordinates);CHKERRQ(ierr);
2882       ierr = DMGetCoordinatesLocal(dm, &coordinatesLocal);CHKERRQ(ierr);
2883       ierr = VecScale(coordinates, scale);CHKERRQ(ierr);
2884       ierr = VecScale(coordinatesLocal, scale);CHKERRQ(ierr);
2885     }
2886   }
2887   ierr = PetscPartitionerSetFromOptions(mesh->partitioner);CHKERRQ(ierr);
2888   PetscFunctionReturn(0);
2889 }
2890 
2891 static PetscErrorCode DMSetFromOptions_Plex(PetscOptionItems *PetscOptionsObject,DM dm)
2892 {
2893   PetscReal      volume = -1.0, extThickness = 1.0;
2894   PetscInt       prerefine = 0, refine = 0, r, coarsen = 0, overlap = 0, extLayers = 0, dim;
2895   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, flg;
2896   PetscErrorCode ierr;
2897 
2898   PetscFunctionBegin;
2899   PetscValidHeaderSpecific(dm, DM_CLASSID, 2);
2900   ierr = PetscOptionsHead(PetscOptionsObject,"DMPlex Options");CHKERRQ(ierr);
2901   /* Handle automatic creation */
2902   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
2903   if (dim < 0) {ierr = DMPlexCreateFromOptions_Internal(PetscOptionsObject, &coordSpace, dm);CHKERRQ(ierr);created = PETSC_TRUE;}
2904   /* Handle DMPlex refinement before distribution */
2905   ierr = DMPlexGetRefinementUniform(dm, &uniformOrig);CHKERRQ(ierr);
2906   ierr = PetscOptionsBoundedInt("-dm_refine_pre", "The number of refinements before distribution", "DMCreate", prerefine, &prerefine, NULL,0);CHKERRQ(ierr);
2907   ierr = PetscOptionsBool("-dm_refine_remap_pre", "Flag to control coordinate remapping", "DMCreate", remap, &remap, NULL);CHKERRQ(ierr);
2908   ierr = PetscOptionsBool("-dm_refine_uniform_pre", "Flag for uniform refinement before distribution", "DMCreate", uniform, &uniform, &flg);CHKERRQ(ierr);
2909   if (flg) {ierr = DMPlexSetRefinementUniform(dm, uniform);CHKERRQ(ierr);}
2910   ierr = PetscOptionsReal("-dm_refine_volume_limit_pre", "The maximum cell volume after refinement before distribution", "DMCreate", volume, &volume, &flg);CHKERRQ(ierr);
2911   if (flg) {
2912     ierr = DMPlexSetRefinementUniform(dm, PETSC_FALSE);CHKERRQ(ierr);
2913     ierr = DMPlexSetRefinementLimit(dm, volume);CHKERRQ(ierr);
2914     prerefine = PetscMax(prerefine, 1);
2915   }
2916   for (r = 0; r < prerefine; ++r) {
2917     DM             rdm;
2918     PetscPointFunc coordFunc = ((DM_Plex*) dm->data)->coordFunc;
2919 
2920     ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2921     ierr = DMRefine(dm, PetscObjectComm((PetscObject) dm), &rdm);CHKERRQ(ierr);
2922     ierr = DMPlexReplace_Static(dm, &rdm);CHKERRQ(ierr);
2923     ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2924     if (coordFunc && remap) {
2925       ierr = DMPlexRemapGeometry(dm, 0.0, coordFunc);CHKERRQ(ierr);
2926       ((DM_Plex*) dm->data)->coordFunc = coordFunc;
2927     }
2928   }
2929   ierr = DMPlexSetRefinementUniform(dm, uniformOrig);CHKERRQ(ierr);
2930   /* Handle DMPlex extrusion before distribution */
2931   ierr = PetscOptionsBool("-dm_plex_interpolate", "Flag to create edges and faces automatically", "", interpolate, &interpolate, NULL);CHKERRQ(ierr);
2932   ierr = PetscOptionsBoundedInt("-dm_extrude_layers", "The number of layers to extrude", "", extLayers, &extLayers, NULL, 0);CHKERRQ(ierr);
2933   ierr = PetscOptionsReal("-dm_extrude_thickness", "The thickness of the layer to be extruded", "", extThickness, &extThickness, NULL);CHKERRQ(ierr);
2934   ierr = PetscOptionsBool("-dm_extrude_column_first", "Order the cells in a vertical column first", "", extColOrder, &extColOrder, NULL);CHKERRQ(ierr);
2935   if (extLayers) {
2936     DM edm;
2937 
2938     ierr = DMPlexExtrude(dm, extLayers, extThickness, extColOrder, NULL, interpolate, &edm);CHKERRQ(ierr);
2939     ierr = DMPlexReplace_Static(dm, &edm);CHKERRQ(ierr);
2940   }
2941   /* Handle DMPlex distribution */
2942   ierr = PetscOptionsBool("-dm_distribute", "Flag to redistribute a mesh among processes", "DMCreate", distribute, &distribute, NULL);CHKERRQ(ierr);
2943   ierr = PetscOptionsBoundedInt("-dm_distribute_overlap", "The size of the overlap halo", "DMCreate", overlap, &overlap, NULL, 0);CHKERRQ(ierr);
2944   if (distribute) {
2945     DM               pdm = NULL;
2946     PetscPartitioner part;
2947 
2948     ierr = DMPlexGetPartitioner(dm, &part);CHKERRQ(ierr);
2949     ierr = PetscPartitionerSetFromOptions(part);CHKERRQ(ierr);
2950     ierr = DMPlexDistribute(dm, overlap, NULL, &pdm);CHKERRQ(ierr);
2951     if (pdm) {
2952       ierr = DMPlexReplace_Static(dm, &pdm);CHKERRQ(ierr);
2953     }
2954   }
2955   /* Create coordinate space */
2956   if (created) {
2957     DM_Plex  *mesh = (DM_Plex *) dm->data;
2958     PetscInt  degree = 1;
2959     PetscBool periodic, flg;
2960 
2961     ierr = PetscOptionsBool("-dm_coord_space", "Use an FEM space for coordinates", "", coordSpace, &coordSpace, &flg);CHKERRQ(ierr);
2962     ierr = PetscOptionsInt("-dm_coord_petscspace_degree", "FEM degree for coordinate space", "", degree, &degree, NULL);CHKERRQ(ierr);
2963     if (coordSpace) {ierr = DMPlexCreateCoordinateSpace(dm, degree, mesh->coordFunc);CHKERRQ(ierr);}
2964     if (flg && !coordSpace) {
2965       DM           cdm;
2966       PetscDS      cds;
2967       PetscObject  obj;
2968       PetscClassId id;
2969 
2970       ierr = DMGetCoordinateDM(dm, &cdm);CHKERRQ(ierr);
2971       ierr = DMGetDS(cdm, &cds);CHKERRQ(ierr);
2972       ierr = PetscDSGetDiscretization(cds, 0, &obj);CHKERRQ(ierr);
2973       ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
2974       if (id == PETSCFE_CLASSID) {
2975         PetscContainer dummy;
2976 
2977         ierr = PetscContainerCreate(PETSC_COMM_SELF, &dummy);CHKERRQ(ierr);
2978         ierr = PetscObjectSetName((PetscObject) dummy, "coordinates");CHKERRQ(ierr);
2979         ierr = DMSetField(cdm, 0, NULL, (PetscObject) dummy);CHKERRQ(ierr);
2980         ierr = PetscContainerDestroy(&dummy);CHKERRQ(ierr);
2981         ierr = DMClearDS(cdm);CHKERRQ(ierr);
2982       }
2983       mesh->coordFunc = NULL;
2984     }
2985     ierr = DMLocalizeCoordinates(dm);CHKERRQ(ierr);
2986     ierr = DMGetPeriodicity(dm, &periodic, NULL, NULL, NULL);CHKERRQ(ierr);
2987     if (periodic) {ierr = DMSetPeriodicity(dm, PETSC_TRUE, NULL, NULL, NULL);CHKERRQ(ierr);}
2988   }
2989   /* Handle DMPlex refinement */
2990   remap = PETSC_TRUE;
2991   ierr = PetscOptionsBoundedInt("-dm_refine", "The number of uniform refinements", "DMCreate", refine, &refine, NULL,0);CHKERRQ(ierr);
2992   ierr = PetscOptionsBool("-dm_refine_remap", "Flag to control coordinate remapping", "DMCreate", remap, &remap, NULL);CHKERRQ(ierr);
2993   ierr = PetscOptionsBoundedInt("-dm_refine_hierarchy", "The number of uniform refinements", "DMCreate", refine, &refine, &isHierarchy,0);CHKERRQ(ierr);
2994   if (refine) {ierr = DMPlexSetRefinementUniform(dm, PETSC_TRUE);CHKERRQ(ierr);}
2995   if (refine && isHierarchy) {
2996     DM *dms, coarseDM;
2997 
2998     ierr = DMGetCoarseDM(dm, &coarseDM);CHKERRQ(ierr);
2999     ierr = PetscObjectReference((PetscObject)coarseDM);CHKERRQ(ierr);
3000     ierr = PetscMalloc1(refine,&dms);CHKERRQ(ierr);
3001     ierr = DMRefineHierarchy(dm, refine, dms);CHKERRQ(ierr);
3002     /* Total hack since we do not pass in a pointer */
3003     ierr = DMPlexSwap_Static(dm, dms[refine-1]);CHKERRQ(ierr);
3004     if (refine == 1) {
3005       ierr = DMSetCoarseDM(dm, dms[0]);CHKERRQ(ierr);
3006       ierr = DMPlexSetRegularRefinement(dm, PETSC_TRUE);CHKERRQ(ierr);
3007     } else {
3008       ierr = DMSetCoarseDM(dm, dms[refine-2]);CHKERRQ(ierr);
3009       ierr = DMPlexSetRegularRefinement(dm, PETSC_TRUE);CHKERRQ(ierr);
3010       ierr = DMSetCoarseDM(dms[0], dms[refine-1]);CHKERRQ(ierr);
3011       ierr = DMPlexSetRegularRefinement(dms[0], PETSC_TRUE);CHKERRQ(ierr);
3012     }
3013     ierr = DMSetCoarseDM(dms[refine-1], coarseDM);CHKERRQ(ierr);
3014     ierr = PetscObjectDereference((PetscObject)coarseDM);CHKERRQ(ierr);
3015     /* Free DMs */
3016     for (r = 0; r < refine; ++r) {
3017       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dms[r]);CHKERRQ(ierr);
3018       ierr = DMDestroy(&dms[r]);CHKERRQ(ierr);
3019     }
3020     ierr = PetscFree(dms);CHKERRQ(ierr);
3021   } else {
3022     for (r = 0; r < refine; ++r) {
3023       DM             rdm;
3024       PetscPointFunc coordFunc = ((DM_Plex*) dm->data)->coordFunc;
3025 
3026       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
3027       ierr = DMRefine(dm, PetscObjectComm((PetscObject) dm), &rdm);CHKERRQ(ierr);
3028       /* Total hack since we do not pass in a pointer */
3029       ierr = DMPlexReplace_Static(dm, &rdm);CHKERRQ(ierr);
3030       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
3031       if (coordFunc && remap) {
3032         ierr = DMPlexRemapGeometry(dm, 0.0, coordFunc);CHKERRQ(ierr);
3033         ((DM_Plex*) dm->data)->coordFunc = coordFunc;
3034       }
3035     }
3036   }
3037   /* Handle DMPlex coarsening */
3038   ierr = PetscOptionsBoundedInt("-dm_coarsen", "Coarsen the mesh", "DMCreate", coarsen, &coarsen, NULL,0);CHKERRQ(ierr);
3039   ierr = PetscOptionsBoundedInt("-dm_coarsen_hierarchy", "The number of coarsenings", "DMCreate", coarsen, &coarsen, &isHierarchy,0);CHKERRQ(ierr);
3040   if (coarsen && isHierarchy) {
3041     DM *dms;
3042 
3043     ierr = PetscMalloc1(coarsen, &dms);CHKERRQ(ierr);
3044     ierr = DMCoarsenHierarchy(dm, coarsen, dms);CHKERRQ(ierr);
3045     /* Free DMs */
3046     for (r = 0; r < coarsen; ++r) {
3047       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dms[r]);CHKERRQ(ierr);
3048       ierr = DMDestroy(&dms[r]);CHKERRQ(ierr);
3049     }
3050     ierr = PetscFree(dms);CHKERRQ(ierr);
3051   } else {
3052     for (r = 0; r < coarsen; ++r) {
3053       DM             cdm;
3054       PetscPointFunc coordFunc = ((DM_Plex*) dm->data)->coordFunc;
3055 
3056       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
3057       ierr = DMCoarsen(dm, PetscObjectComm((PetscObject) dm), &cdm);CHKERRQ(ierr);
3058       /* Total hack since we do not pass in a pointer */
3059       ierr = DMPlexReplace_Static(dm, &cdm);CHKERRQ(ierr);
3060       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
3061       if (coordFunc) {
3062         ierr = DMPlexRemapGeometry(dm, 0.0, coordFunc);CHKERRQ(ierr);
3063         ((DM_Plex*) dm->data)->coordFunc = coordFunc;
3064       }
3065     }
3066   }
3067   /* Handle ghost cells */
3068   ierr = PetscOptionsBool("-dm_plex_create_fv_ghost_cells", "Flag to create finite volume ghost cells on the boundary", "DMCreate", ghostCells, &ghostCells, NULL);CHKERRQ(ierr);
3069   if (ghostCells) {
3070     DM   gdm;
3071     char lname[PETSC_MAX_PATH_LEN];
3072 
3073     lname[0] = '\0';
3074     ierr = PetscOptionsString("-dm_plex_fv_ghost_cells_label", "Label name for ghost cells boundary", "DMCreate", lname, lname, sizeof(lname), &flg);CHKERRQ(ierr);
3075     ierr = DMPlexConstructGhostCells(dm, flg ? lname : NULL, NULL, &gdm);CHKERRQ(ierr);
3076     ierr = DMPlexReplace_Static(dm, &gdm);CHKERRQ(ierr);
3077   }
3078   /* Handle */
3079   ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
3080   ierr = PetscOptionsTail();CHKERRQ(ierr);
3081   PetscFunctionReturn(0);
3082 }
3083 
3084 static PetscErrorCode DMCreateGlobalVector_Plex(DM dm,Vec *vec)
3085 {
3086   PetscErrorCode ierr;
3087 
3088   PetscFunctionBegin;
3089   ierr = DMCreateGlobalVector_Section_Private(dm,vec);CHKERRQ(ierr);
3090   /* ierr = VecSetOperation(*vec, VECOP_DUPLICATE, (void(*)(void)) VecDuplicate_MPI_DM);CHKERRQ(ierr); */
3091   ierr = VecSetOperation(*vec, VECOP_VIEW, (void (*)(void)) VecView_Plex);CHKERRQ(ierr);
3092   ierr = VecSetOperation(*vec, VECOP_VIEWNATIVE, (void (*)(void)) VecView_Plex_Native);CHKERRQ(ierr);
3093   ierr = VecSetOperation(*vec, VECOP_LOAD, (void (*)(void)) VecLoad_Plex);CHKERRQ(ierr);
3094   ierr = VecSetOperation(*vec, VECOP_LOADNATIVE, (void (*)(void)) VecLoad_Plex_Native);CHKERRQ(ierr);
3095   PetscFunctionReturn(0);
3096 }
3097 
3098 static PetscErrorCode DMCreateLocalVector_Plex(DM dm,Vec *vec)
3099 {
3100   PetscErrorCode ierr;
3101 
3102   PetscFunctionBegin;
3103   ierr = DMCreateLocalVector_Section_Private(dm,vec);CHKERRQ(ierr);
3104   ierr = VecSetOperation(*vec, VECOP_VIEW, (void (*)(void)) VecView_Plex_Local);CHKERRQ(ierr);
3105   ierr = VecSetOperation(*vec, VECOP_LOAD, (void (*)(void)) VecLoad_Plex_Local);CHKERRQ(ierr);
3106   PetscFunctionReturn(0);
3107 }
3108 
3109 static PetscErrorCode DMGetDimPoints_Plex(DM dm, PetscInt dim, PetscInt *pStart, PetscInt *pEnd)
3110 {
3111   PetscInt       depth, d;
3112   PetscErrorCode ierr;
3113 
3114   PetscFunctionBegin;
3115   ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
3116   if (depth == 1) {
3117     ierr = DMGetDimension(dm, &d);CHKERRQ(ierr);
3118     if (dim == 0)      {ierr = DMPlexGetDepthStratum(dm, dim, pStart, pEnd);CHKERRQ(ierr);}
3119     else if (dim == d) {ierr = DMPlexGetDepthStratum(dm, 1, pStart, pEnd);CHKERRQ(ierr);}
3120     else               {*pStart = 0; *pEnd = 0;}
3121   } else {
3122     ierr = DMPlexGetDepthStratum(dm, dim, pStart, pEnd);CHKERRQ(ierr);
3123   }
3124   PetscFunctionReturn(0);
3125 }
3126 
3127 static PetscErrorCode DMGetNeighbors_Plex(DM dm, PetscInt *nranks, const PetscMPIInt *ranks[])
3128 {
3129   PetscSF           sf;
3130   PetscInt          niranks, njranks, n;
3131   const PetscMPIInt *iranks, *jranks;
3132   DM_Plex           *data = (DM_Plex*) dm->data;
3133   PetscErrorCode    ierr;
3134 
3135   PetscFunctionBegin;
3136   ierr = DMGetPointSF(dm, &sf);CHKERRQ(ierr);
3137   if (!data->neighbors) {
3138     ierr = PetscSFSetUp(sf);CHKERRQ(ierr);
3139     ierr = PetscSFGetRootRanks(sf, &njranks, &jranks, NULL, NULL, NULL);CHKERRQ(ierr);
3140     ierr = PetscSFGetLeafRanks(sf, &niranks, &iranks, NULL, NULL);CHKERRQ(ierr);
3141     ierr = PetscMalloc1(njranks + niranks + 1, &data->neighbors);CHKERRQ(ierr);
3142     ierr = PetscArraycpy(data->neighbors + 1, jranks, njranks);CHKERRQ(ierr);
3143     ierr = PetscArraycpy(data->neighbors + njranks + 1, iranks, niranks);CHKERRQ(ierr);
3144     n = njranks + niranks;
3145     ierr = PetscSortRemoveDupsMPIInt(&n, data->neighbors + 1);CHKERRQ(ierr);
3146     /* The following cast should never fail: can't have more neighbors than PETSC_MPI_INT_MAX */
3147     ierr = PetscMPIIntCast(n, data->neighbors);CHKERRQ(ierr);
3148   }
3149   if (nranks) *nranks = data->neighbors[0];
3150   if (ranks) {
3151     if (data->neighbors[0]) *ranks = data->neighbors + 1;
3152     else                    *ranks = NULL;
3153   }
3154   PetscFunctionReturn(0);
3155 }
3156 
3157 PETSC_INTERN PetscErrorCode DMInterpolateSolution_Plex(DM, DM, Mat, Vec, Vec);
3158 
3159 static PetscErrorCode DMInitialize_Plex(DM dm)
3160 {
3161   PetscErrorCode ierr;
3162 
3163   PetscFunctionBegin;
3164   dm->ops->view                            = DMView_Plex;
3165   dm->ops->load                            = DMLoad_Plex;
3166   dm->ops->setfromoptions                  = DMSetFromOptions_Plex;
3167   dm->ops->clone                           = DMClone_Plex;
3168   dm->ops->setup                           = DMSetUp_Plex;
3169   dm->ops->createlocalsection              = DMCreateLocalSection_Plex;
3170   dm->ops->createdefaultconstraints        = DMCreateDefaultConstraints_Plex;
3171   dm->ops->createglobalvector              = DMCreateGlobalVector_Plex;
3172   dm->ops->createlocalvector               = DMCreateLocalVector_Plex;
3173   dm->ops->getlocaltoglobalmapping         = NULL;
3174   dm->ops->createfieldis                   = NULL;
3175   dm->ops->createcoordinatedm              = DMCreateCoordinateDM_Plex;
3176   dm->ops->createcoordinatefield           = DMCreateCoordinateField_Plex;
3177   dm->ops->getcoloring                     = NULL;
3178   dm->ops->creatematrix                    = DMCreateMatrix_Plex;
3179   dm->ops->createinterpolation             = DMCreateInterpolation_Plex;
3180   dm->ops->createmassmatrix                = DMCreateMassMatrix_Plex;
3181   dm->ops->createinjection                 = DMCreateInjection_Plex;
3182   dm->ops->refine                          = DMRefine_Plex;
3183   dm->ops->coarsen                         = DMCoarsen_Plex;
3184   dm->ops->refinehierarchy                 = DMRefineHierarchy_Plex;
3185   dm->ops->coarsenhierarchy                = DMCoarsenHierarchy_Plex;
3186   dm->ops->adaptlabel                      = DMAdaptLabel_Plex;
3187   dm->ops->adaptmetric                     = DMAdaptMetric_Plex;
3188   dm->ops->globaltolocalbegin              = NULL;
3189   dm->ops->globaltolocalend                = NULL;
3190   dm->ops->localtoglobalbegin              = NULL;
3191   dm->ops->localtoglobalend                = NULL;
3192   dm->ops->destroy                         = DMDestroy_Plex;
3193   dm->ops->createsubdm                     = DMCreateSubDM_Plex;
3194   dm->ops->createsuperdm                   = DMCreateSuperDM_Plex;
3195   dm->ops->getdimpoints                    = DMGetDimPoints_Plex;
3196   dm->ops->locatepoints                    = DMLocatePoints_Plex;
3197   dm->ops->projectfunctionlocal            = DMProjectFunctionLocal_Plex;
3198   dm->ops->projectfunctionlabellocal       = DMProjectFunctionLabelLocal_Plex;
3199   dm->ops->projectfieldlocal               = DMProjectFieldLocal_Plex;
3200   dm->ops->projectfieldlabellocal          = DMProjectFieldLabelLocal_Plex;
3201   dm->ops->projectbdfieldlabellocal        = DMProjectBdFieldLabelLocal_Plex;
3202   dm->ops->computel2diff                   = DMComputeL2Diff_Plex;
3203   dm->ops->computel2gradientdiff           = DMComputeL2GradientDiff_Plex;
3204   dm->ops->computel2fielddiff              = DMComputeL2FieldDiff_Plex;
3205   dm->ops->getneighbors                    = DMGetNeighbors_Plex;
3206   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMPlexInsertBoundaryValues_C",DMPlexInsertBoundaryValues_Plex);CHKERRQ(ierr);
3207   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMPlexInsertTimeDerviativeBoundaryValues_C",DMPlexInsertTimeDerivativeBoundaryValues_Plex);CHKERRQ(ierr);
3208   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMSetUpGLVisViewer_C",DMSetUpGLVisViewer_Plex);CHKERRQ(ierr);
3209   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMCreateNeumannOverlap_C",DMCreateNeumannOverlap_Plex);CHKERRQ(ierr);
3210   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMPlexGetOverlap_C",DMPlexGetOverlap_Plex);CHKERRQ(ierr);
3211   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMInterpolateSolution_C",DMInterpolateSolution_Plex);CHKERRQ(ierr);
3212   PetscFunctionReturn(0);
3213 }
3214 
3215 PETSC_INTERN PetscErrorCode DMClone_Plex(DM dm, DM *newdm)
3216 {
3217   DM_Plex        *mesh = (DM_Plex *) dm->data;
3218   PetscErrorCode ierr;
3219 
3220   PetscFunctionBegin;
3221   mesh->refct++;
3222   (*newdm)->data = mesh;
3223   ierr = PetscObjectChangeTypeName((PetscObject) *newdm, DMPLEX);CHKERRQ(ierr);
3224   ierr = DMInitialize_Plex(*newdm);CHKERRQ(ierr);
3225   PetscFunctionReturn(0);
3226 }
3227 
3228 /*MC
3229   DMPLEX = "plex" - A DM object that encapsulates an unstructured mesh, or CW Complex, which can be expressed using a Hasse Diagram.
3230                     In the local representation, Vecs contain all unknowns in the interior and shared boundary. This is
3231                     specified by a PetscSection object. Ownership in the global representation is determined by
3232                     ownership of the underlying DMPlex points. This is specified by another PetscSection object.
3233 
3234   Options Database Keys:
3235 + -dm_refine_pre                     - Refine mesh before distribution
3236 + -dm_refine_uniform_pre             - Choose uniform or generator-based refinement
3237 + -dm_refine_volume_limit_pre        - Cell volume limit after pre-refinement using generator
3238 . -dm_distribute                     - Distribute mesh across processes
3239 . -dm_distribute_overlap             - Number of cells to overlap for distribution
3240 . -dm_refine                         - Refine mesh after distribution
3241 . -dm_plex_hash_location             - Use grid hashing for point location
3242 . -dm_plex_partition_balance         - Attempt to evenly divide points on partition boundary between processes
3243 . -dm_plex_remesh_bd                 - Allow changes to the boundary on remeshing
3244 . -dm_plex_max_projection_height     - Maxmimum mesh point height used to project locally
3245 . -dm_plex_regular_refinement        - Use special nested projection algorithm for regular refinement
3246 . -dm_plex_check_all                 - Perform all shecks below
3247 . -dm_plex_check_symmetry            - Check that the adjacency information in the mesh is symmetric
3248 . -dm_plex_check_skeleton <celltype> - Check that each cell has the correct number of vertices
3249 . -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
3250 . -dm_plex_check_geometry            - Check that cells have positive volume
3251 . -dm_view :mesh.tex:ascii_latex     - View the mesh in LaTeX/TikZ
3252 . -dm_plex_view_scale <num>          - Scale the TikZ
3253 - -dm_plex_print_fem <num>           - View FEM assembly information, such as element vectors and matrices
3254 
3255 
3256   Level: intermediate
3257 
3258 .seealso: DMType, DMPlexCreate(), DMCreate(), DMSetType()
3259 M*/
3260 
3261 PETSC_EXTERN PetscErrorCode DMCreate_Plex(DM dm)
3262 {
3263   DM_Plex       *mesh;
3264   PetscInt       unit;
3265   PetscErrorCode ierr;
3266 
3267   PetscFunctionBegin;
3268   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
3269   ierr     = PetscNewLog(dm,&mesh);CHKERRQ(ierr);
3270   dm->data = mesh;
3271 
3272   mesh->refct             = 1;
3273   ierr                    = PetscSectionCreate(PetscObjectComm((PetscObject)dm), &mesh->coneSection);CHKERRQ(ierr);
3274   mesh->maxConeSize       = 0;
3275   mesh->cones             = NULL;
3276   mesh->coneOrientations  = NULL;
3277   ierr                    = PetscSectionCreate(PetscObjectComm((PetscObject)dm), &mesh->supportSection);CHKERRQ(ierr);
3278   mesh->maxSupportSize    = 0;
3279   mesh->supports          = NULL;
3280   mesh->refinementUniform = PETSC_TRUE;
3281   mesh->refinementLimit   = -1.0;
3282   mesh->interpolated      = DMPLEX_INTERPOLATED_INVALID;
3283   mesh->interpolatedCollective = DMPLEX_INTERPOLATED_INVALID;
3284 
3285   mesh->facesTmp = NULL;
3286 
3287   mesh->tetgenOpts   = NULL;
3288   mesh->triangleOpts = NULL;
3289   ierr = PetscPartitionerCreate(PetscObjectComm((PetscObject)dm), &mesh->partitioner);CHKERRQ(ierr);
3290   mesh->remeshBd     = PETSC_FALSE;
3291 
3292   mesh->subpointMap = NULL;
3293 
3294   for (unit = 0; unit < NUM_PETSC_UNITS; ++unit) mesh->scale[unit] = 1.0;
3295 
3296   mesh->regularRefinement   = PETSC_FALSE;
3297   mesh->depthState          = -1;
3298   mesh->celltypeState       = -1;
3299   mesh->globalVertexNumbers = NULL;
3300   mesh->globalCellNumbers   = NULL;
3301   mesh->anchorSection       = NULL;
3302   mesh->anchorIS            = NULL;
3303   mesh->createanchors       = NULL;
3304   mesh->computeanchormatrix = NULL;
3305   mesh->parentSection       = NULL;
3306   mesh->parents             = NULL;
3307   mesh->childIDs            = NULL;
3308   mesh->childSection        = NULL;
3309   mesh->children            = NULL;
3310   mesh->referenceTree       = NULL;
3311   mesh->getchildsymmetry    = NULL;
3312   mesh->vtkCellHeight       = 0;
3313   mesh->useAnchors          = PETSC_FALSE;
3314 
3315   mesh->maxProjectionHeight = 0;
3316 
3317   mesh->neighbors           = NULL;
3318 
3319   mesh->printSetValues = PETSC_FALSE;
3320   mesh->printFEM       = 0;
3321   mesh->printTol       = 1.0e-10;
3322 
3323   ierr = DMInitialize_Plex(dm);CHKERRQ(ierr);
3324   PetscFunctionReturn(0);
3325 }
3326 
3327 /*@
3328   DMPlexCreate - Creates a DMPlex object, which encapsulates an unstructured mesh, or CW complex, which can be expressed using a Hasse Diagram.
3329 
3330   Collective
3331 
3332   Input Parameter:
3333 . comm - The communicator for the DMPlex object
3334 
3335   Output Parameter:
3336 . mesh  - The DMPlex object
3337 
3338   Level: beginner
3339 
3340 @*/
3341 PetscErrorCode DMPlexCreate(MPI_Comm comm, DM *mesh)
3342 {
3343   PetscErrorCode ierr;
3344 
3345   PetscFunctionBegin;
3346   PetscValidPointer(mesh,2);
3347   ierr = DMCreate(comm, mesh);CHKERRQ(ierr);
3348   ierr = DMSetType(*mesh, DMPLEX);CHKERRQ(ierr);
3349   PetscFunctionReturn(0);
3350 }
3351 
3352 /*@C
3353   DMPlexBuildFromCellListParallel - Build distributed DMPLEX topology from a list of vertices for each cell (common mesh generator output)
3354 
3355   Input Parameters:
3356 + dm - The DM
3357 . numCells - The number of cells owned by this process
3358 . numVertices - The number of vertices owned by this process, or PETSC_DECIDE
3359 . NVertices - The global number of vertices, or PETSC_DECIDE
3360 . numCorners - The number of vertices for each cell
3361 - cells - An array of numCells*numCorners numbers, the global vertex numbers for each cell
3362 
3363   Output Parameter:
3364 . vertexSF - (Optional) SF describing complete vertex ownership
3365 
3366   Notes:
3367   Two triangles sharing a face
3368 $
3369 $        2
3370 $      / | \
3371 $     /  |  \
3372 $    /   |   \
3373 $   0  0 | 1  3
3374 $    \   |   /
3375 $     \  |  /
3376 $      \ | /
3377 $        1
3378 would have input
3379 $  numCells = 2, numVertices = 4
3380 $  cells = [0 1 2  1 3 2]
3381 $
3382 which would result in the DMPlex
3383 $
3384 $        4
3385 $      / | \
3386 $     /  |  \
3387 $    /   |   \
3388 $   2  0 | 1  5
3389 $    \   |   /
3390 $     \  |  /
3391 $      \ | /
3392 $        3
3393 
3394   Vertices are implicitly numbered consecutively 0,...,NVertices.
3395   Each rank owns a chunk of numVertices consecutive vertices.
3396   If numVertices is PETSC_DECIDE, PETSc will distribute them as evenly as possible using PetscLayout.
3397   If both NVertices and numVertices are PETSC_DECIDE, NVertices is computed by PETSc as the maximum vertex index in cells + 1.
3398   If only NVertices is PETSC_DECIDE, it is computed as the sum of numVertices over all ranks.
3399 
3400   The cell distribution is arbitrary non-overlapping, independent of the vertex distribution.
3401 
3402   Not currently supported in Fortran.
3403 
3404   Level: advanced
3405 
3406 .seealso: DMPlexBuildFromCellList(), DMPlexCreateFromCellListParallelPetsc(), DMPlexBuildCoordinatesFromCellListParallel()
3407 @*/
3408 PetscErrorCode DMPlexBuildFromCellListParallel(DM dm, PetscInt numCells, PetscInt numVertices, PetscInt NVertices, PetscInt numCorners, const PetscInt cells[], PetscSF *vertexSF)
3409 {
3410   PetscSF         sfPoint;
3411   PetscLayout     layout;
3412   PetscInt        numVerticesAdj, *verticesAdj, *cones, c, p, dim;
3413   PetscMPIInt     rank, size;
3414   PetscErrorCode  ierr;
3415 
3416   PetscFunctionBegin;
3417   PetscValidLogicalCollectiveInt(dm,NVertices,4);
3418   ierr = PetscLogEventBegin(DMPLEX_BuildFromCellList,dm,0,0,0);CHKERRQ(ierr);
3419   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject) dm), &rank);CHKERRMPI(ierr);
3420   ierr = MPI_Comm_size(PetscObjectComm((PetscObject) dm), &size);CHKERRMPI(ierr);
3421   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
3422   /* Get/check global number of vertices */
3423   {
3424     PetscInt NVerticesInCells, i;
3425     const PetscInt len = numCells * numCorners;
3426 
3427     /* NVerticesInCells = max(cells) + 1 */
3428     NVerticesInCells = PETSC_MIN_INT;
3429     for (i=0; i<len; i++) if (cells[i] > NVerticesInCells) NVerticesInCells = cells[i];
3430     ++NVerticesInCells;
3431     ierr = MPI_Allreduce(MPI_IN_PLACE, &NVerticesInCells, 1, MPIU_INT, MPI_MAX, PetscObjectComm((PetscObject) dm));CHKERRMPI(ierr);
3432 
3433     if (numVertices == PETSC_DECIDE && NVertices == PETSC_DECIDE) NVertices = NVerticesInCells;
3434     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);
3435   }
3436   /* Count locally unique vertices */
3437   {
3438     PetscHSetI vhash;
3439     PetscInt off = 0;
3440 
3441     ierr = PetscHSetICreate(&vhash);CHKERRQ(ierr);
3442     for (c = 0; c < numCells; ++c) {
3443       for (p = 0; p < numCorners; ++p) {
3444         ierr = PetscHSetIAdd(vhash, cells[c*numCorners+p]);CHKERRQ(ierr);
3445       }
3446     }
3447     ierr = PetscHSetIGetSize(vhash, &numVerticesAdj);CHKERRQ(ierr);
3448     ierr = PetscMalloc1(numVerticesAdj, &verticesAdj);CHKERRQ(ierr);
3449     ierr = PetscHSetIGetElems(vhash, &off, verticesAdj);CHKERRQ(ierr);
3450     ierr = PetscHSetIDestroy(&vhash);CHKERRQ(ierr);
3451     if (off != numVerticesAdj) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Invalid number of local vertices %D should be %D", off, numVerticesAdj);
3452   }
3453   ierr = PetscSortInt(numVerticesAdj, verticesAdj);CHKERRQ(ierr);
3454   /* Create cones */
3455   ierr = DMPlexSetChart(dm, 0, numCells+numVerticesAdj);CHKERRQ(ierr);
3456   for (c = 0; c < numCells; ++c) {ierr = DMPlexSetConeSize(dm, c, numCorners);CHKERRQ(ierr);}
3457   ierr = DMSetUp(dm);CHKERRQ(ierr);
3458   ierr = DMPlexGetCones(dm,&cones);CHKERRQ(ierr);
3459   for (c = 0; c < numCells; ++c) {
3460     for (p = 0; p < numCorners; ++p) {
3461       const PetscInt gv = cells[c*numCorners+p];
3462       PetscInt       lv;
3463 
3464       /* Positions within verticesAdj form 0-based local vertex numbering;
3465          we need to shift it by numCells to get correct DAG points (cells go first) */
3466       ierr = PetscFindInt(gv, numVerticesAdj, verticesAdj, &lv);CHKERRQ(ierr);
3467       if (lv < 0) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Could not find global vertex %D in local connectivity", gv);
3468       cones[c*numCorners+p] = lv+numCells;
3469     }
3470   }
3471   /* Build point sf */
3472   ierr = PetscLayoutCreate(PetscObjectComm((PetscObject)dm), &layout);CHKERRQ(ierr);
3473   ierr = PetscLayoutSetSize(layout, NVertices);CHKERRQ(ierr);
3474   ierr = PetscLayoutSetLocalSize(layout, numVertices);CHKERRQ(ierr);
3475   ierr = PetscLayoutSetBlockSize(layout, 1);CHKERRQ(ierr);
3476   ierr = PetscSFCreateByMatchingIndices(layout, numVerticesAdj, verticesAdj, NULL, numCells, numVerticesAdj, verticesAdj, NULL, numCells, vertexSF, &sfPoint);CHKERRQ(ierr);
3477   ierr = PetscLayoutDestroy(&layout);CHKERRQ(ierr);
3478   ierr = PetscFree(verticesAdj);CHKERRQ(ierr);
3479   ierr = PetscObjectSetName((PetscObject) sfPoint, "point SF");CHKERRQ(ierr);
3480   if (dm->sf) {
3481     const char *prefix;
3482 
3483     ierr = PetscObjectGetOptionsPrefix((PetscObject)dm->sf, &prefix);CHKERRQ(ierr);
3484     ierr = PetscObjectSetOptionsPrefix((PetscObject)sfPoint, prefix);CHKERRQ(ierr);
3485   }
3486   ierr = DMSetPointSF(dm, sfPoint);CHKERRQ(ierr);
3487   ierr = PetscSFDestroy(&sfPoint);CHKERRQ(ierr);
3488   if (vertexSF) {ierr = PetscObjectSetName((PetscObject)(*vertexSF), "Vertex Ownership SF");CHKERRQ(ierr);}
3489   /* Fill in the rest of the topology structure */
3490   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
3491   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
3492   ierr = PetscLogEventEnd(DMPLEX_BuildFromCellList,dm,0,0,0);CHKERRQ(ierr);
3493   PetscFunctionReturn(0);
3494 }
3495 
3496 /*@C
3497   DMPlexBuildCoordinatesFromCellListParallel - Build DM coordinates from a list of coordinates for each owned vertex (common mesh generator output)
3498 
3499   Input Parameters:
3500 + dm - The DM
3501 . spaceDim - The spatial dimension used for coordinates
3502 . sfVert - SF describing complete vertex ownership
3503 - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex
3504 
3505   Level: advanced
3506 
3507   Notes:
3508   Not currently supported in Fortran.
3509 
3510 .seealso: DMPlexBuildCoordinatesFromCellList(), DMPlexCreateFromCellListParallelPetsc(), DMPlexBuildFromCellListParallel()
3511 @*/
3512 PetscErrorCode DMPlexBuildCoordinatesFromCellListParallel(DM dm, PetscInt spaceDim, PetscSF sfVert, const PetscReal vertexCoords[])
3513 {
3514   PetscSection   coordSection;
3515   Vec            coordinates;
3516   PetscScalar   *coords;
3517   PetscInt       numVertices, numVerticesAdj, coordSize, v, vStart, vEnd;
3518   PetscErrorCode ierr;
3519 
3520   PetscFunctionBegin;
3521   ierr = PetscLogEventBegin(DMPLEX_BuildCoordinatesFromCellList,dm,0,0,0);CHKERRQ(ierr);
3522   ierr = DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);CHKERRQ(ierr);
3523   if (vStart < 0 || vEnd < 0) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "DM is not set up properly. DMPlexBuildFromCellList() should be called first.");
3524   ierr = DMSetCoordinateDim(dm, spaceDim);CHKERRQ(ierr);
3525   ierr = PetscSFGetGraph(sfVert, &numVertices, &numVerticesAdj, NULL, NULL);CHKERRQ(ierr);
3526   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);
3527   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
3528   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
3529   ierr = PetscSectionSetFieldComponents(coordSection, 0, spaceDim);CHKERRQ(ierr);
3530   ierr = PetscSectionSetChart(coordSection, vStart, vEnd);CHKERRQ(ierr);
3531   for (v = vStart; v < vEnd; ++v) {
3532     ierr = PetscSectionSetDof(coordSection, v, spaceDim);CHKERRQ(ierr);
3533     ierr = PetscSectionSetFieldDof(coordSection, v, 0, spaceDim);CHKERRQ(ierr);
3534   }
3535   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
3536   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
3537   ierr = VecCreate(PetscObjectComm((PetscObject)dm), &coordinates);CHKERRQ(ierr);
3538   ierr = VecSetBlockSize(coordinates, spaceDim);CHKERRQ(ierr);
3539   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
3540   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
3541   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
3542   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
3543   {
3544     MPI_Datatype coordtype;
3545 
3546     /* Need a temp buffer for coords if we have complex/single */
3547     ierr = MPI_Type_contiguous(spaceDim, MPIU_SCALAR, &coordtype);CHKERRMPI(ierr);
3548     ierr = MPI_Type_commit(&coordtype);CHKERRMPI(ierr);
3549 #if defined(PETSC_USE_COMPLEX)
3550     {
3551     PetscScalar *svertexCoords;
3552     PetscInt    i;
3553     ierr = PetscMalloc1(numVertices*spaceDim,&svertexCoords);CHKERRQ(ierr);
3554     for (i=0; i<numVertices*spaceDim; i++) svertexCoords[i] = vertexCoords[i];
3555     ierr = PetscSFBcastBegin(sfVert, coordtype, svertexCoords, coords,MPI_REPLACE);CHKERRQ(ierr);
3556     ierr = PetscSFBcastEnd(sfVert, coordtype, svertexCoords, coords,MPI_REPLACE);CHKERRQ(ierr);
3557     ierr = PetscFree(svertexCoords);CHKERRQ(ierr);
3558     }
3559 #else
3560     ierr = PetscSFBcastBegin(sfVert, coordtype, vertexCoords, coords,MPI_REPLACE);CHKERRQ(ierr);
3561     ierr = PetscSFBcastEnd(sfVert, coordtype, vertexCoords, coords,MPI_REPLACE);CHKERRQ(ierr);
3562 #endif
3563     ierr = MPI_Type_free(&coordtype);CHKERRMPI(ierr);
3564   }
3565   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
3566   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
3567   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
3568   ierr = PetscLogEventEnd(DMPLEX_BuildCoordinatesFromCellList,dm,0,0,0);CHKERRQ(ierr);
3569   PetscFunctionReturn(0);
3570 }
3571 
3572 /*@
3573   DMPlexCreateFromCellListParallelPetsc - Create distributed DMPLEX from a list of vertices for each cell (common mesh generator output)
3574 
3575   Input Parameters:
3576 + comm - The communicator
3577 . dim - The topological dimension of the mesh
3578 . numCells - The number of cells owned by this process
3579 . numVertices - The number of vertices owned by this process, or PETSC_DECIDE
3580 . NVertices - The global number of vertices, or PETSC_DECIDE
3581 . numCorners - The number of vertices for each cell
3582 . interpolate - Flag indicating that intermediate mesh entities (faces, edges) should be created automatically
3583 . cells - An array of numCells*numCorners numbers, the global vertex numbers for each cell
3584 . spaceDim - The spatial dimension used for coordinates
3585 - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex
3586 
3587   Output Parameter:
3588 + dm - The DM
3589 - vertexSF - (Optional) SF describing complete vertex ownership
3590 
3591   Notes:
3592   This function is just a convenient sequence of DMCreate(), DMSetType(), DMSetDimension(),
3593   DMPlexBuildFromCellListParallel(), DMPlexInterpolate(), DMPlexBuildCoordinatesFromCellListParallel()
3594 
3595   See DMPlexBuildFromCellListParallel() for an example and details about the topology-related parameters.
3596   See DMPlexBuildCoordinatesFromCellListParallel() for details about the geometry-related parameters.
3597 
3598   Level: intermediate
3599 
3600 .seealso: DMPlexCreateFromCellListPetsc(), DMPlexBuildFromCellListParallel(), DMPlexBuildCoordinatesFromCellListParallel(), DMPlexCreateFromDAG(), DMPlexCreate()
3601 @*/
3602 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)
3603 {
3604   PetscSF        sfVert;
3605   PetscErrorCode ierr;
3606 
3607   PetscFunctionBegin;
3608   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
3609   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
3610   PetscValidLogicalCollectiveInt(*dm, dim, 2);
3611   PetscValidLogicalCollectiveInt(*dm, spaceDim, 9);
3612   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
3613   ierr = DMPlexBuildFromCellListParallel(*dm, numCells, numVertices, NVertices, numCorners, cells, &sfVert);CHKERRQ(ierr);
3614   if (interpolate) {
3615     DM idm;
3616 
3617     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
3618     ierr = DMDestroy(dm);CHKERRQ(ierr);
3619     *dm  = idm;
3620   }
3621   ierr = DMPlexBuildCoordinatesFromCellListParallel(*dm, spaceDim, sfVert, vertexCoords);CHKERRQ(ierr);
3622   if (vertexSF) *vertexSF = sfVert;
3623   else {ierr = PetscSFDestroy(&sfVert);CHKERRQ(ierr);}
3624   PetscFunctionReturn(0);
3625 }
3626 
3627 
3628 /*@
3629   DMPlexCreateFromCellListParallel - Deprecated, use DMPlexCreateFromCellListParallelPetsc()
3630 
3631   Level: deprecated
3632 
3633 .seealso: DMPlexCreateFromCellListParallelPetsc()
3634 @*/
3635 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)
3636 {
3637   PetscErrorCode ierr;
3638   PetscInt       i;
3639   PetscInt       *pintCells;
3640 
3641   PetscFunctionBegin;
3642   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));
3643   if (sizeof(int) == sizeof(PetscInt)) {
3644     pintCells = (PetscInt *) cells;
3645   } else {
3646     ierr = PetscMalloc1(numCells*numCorners, &pintCells);CHKERRQ(ierr);
3647     for (i = 0; i < numCells*numCorners; i++) {
3648       pintCells[i] = (PetscInt) cells[i];
3649     }
3650   }
3651   ierr = DMPlexCreateFromCellListParallelPetsc(comm, dim, numCells, numVertices, PETSC_DECIDE, numCorners, interpolate, pintCells, spaceDim, vertexCoords, vertexSF, dm);CHKERRQ(ierr);
3652   if (sizeof(int) != sizeof(PetscInt)) {
3653     ierr = PetscFree(pintCells);CHKERRQ(ierr);
3654   }
3655   PetscFunctionReturn(0);
3656 }
3657 
3658 /*@C
3659   DMPlexBuildFromCellList - Build DMPLEX topology from a list of vertices for each cell (common mesh generator output)
3660 
3661   Input Parameters:
3662 + dm - The DM
3663 . numCells - The number of cells owned by this process
3664 . numVertices - The number of vertices owned by this process, or PETSC_DECIDE
3665 . numCorners - The number of vertices for each cell
3666 - cells - An array of numCells*numCorners numbers, the global vertex numbers for each cell
3667 
3668   Level: advanced
3669 
3670   Notes:
3671   Two triangles sharing a face
3672 $
3673 $        2
3674 $      / | \
3675 $     /  |  \
3676 $    /   |   \
3677 $   0  0 | 1  3
3678 $    \   |   /
3679 $     \  |  /
3680 $      \ | /
3681 $        1
3682 would have input
3683 $  numCells = 2, numVertices = 4
3684 $  cells = [0 1 2  1 3 2]
3685 $
3686 which would result in the DMPlex
3687 $
3688 $        4
3689 $      / | \
3690 $     /  |  \
3691 $    /   |   \
3692 $   2  0 | 1  5
3693 $    \   |   /
3694 $     \  |  /
3695 $      \ | /
3696 $        3
3697 
3698   If numVertices is PETSC_DECIDE, it is computed by PETSc as the maximum vertex index in cells + 1.
3699 
3700   Not currently supported in Fortran.
3701 
3702 .seealso: DMPlexBuildFromCellListParallel(), DMPlexBuildCoordinatesFromCellList(), DMPlexCreateFromCellListPetsc()
3703 @*/
3704 PetscErrorCode DMPlexBuildFromCellList(DM dm, PetscInt numCells, PetscInt numVertices, PetscInt numCorners, const PetscInt cells[])
3705 {
3706   PetscInt      *cones, c, p, dim;
3707   PetscErrorCode ierr;
3708 
3709   PetscFunctionBegin;
3710   ierr = PetscLogEventBegin(DMPLEX_BuildFromCellList,dm,0,0,0);CHKERRQ(ierr);
3711   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
3712   /* Get/check global number of vertices */
3713   {
3714     PetscInt NVerticesInCells, i;
3715     const PetscInt len = numCells * numCorners;
3716 
3717     /* NVerticesInCells = max(cells) + 1 */
3718     NVerticesInCells = PETSC_MIN_INT;
3719     for (i=0; i<len; i++) if (cells[i] > NVerticesInCells) NVerticesInCells = cells[i];
3720     ++NVerticesInCells;
3721 
3722     if (numVertices == PETSC_DECIDE) numVertices = NVerticesInCells;
3723     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);
3724   }
3725   ierr = DMPlexSetChart(dm, 0, numCells+numVertices);CHKERRQ(ierr);
3726   for (c = 0; c < numCells; ++c) {
3727     ierr = DMPlexSetConeSize(dm, c, numCorners);CHKERRQ(ierr);
3728   }
3729   ierr = DMSetUp(dm);CHKERRQ(ierr);
3730   ierr = DMPlexGetCones(dm,&cones);CHKERRQ(ierr);
3731   for (c = 0; c < numCells; ++c) {
3732     for (p = 0; p < numCorners; ++p) {
3733       cones[c*numCorners+p] = cells[c*numCorners+p]+numCells;
3734     }
3735   }
3736   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
3737   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
3738   ierr = PetscLogEventEnd(DMPLEX_BuildFromCellList,dm,0,0,0);CHKERRQ(ierr);
3739   PetscFunctionReturn(0);
3740 }
3741 
3742 /*@C
3743   DMPlexBuildCoordinatesFromCellList - Build DM coordinates from a list of coordinates for each owned vertex (common mesh generator output)
3744 
3745   Input Parameters:
3746 + dm - The DM
3747 . spaceDim - The spatial dimension used for coordinates
3748 - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex
3749 
3750   Level: advanced
3751 
3752   Notes:
3753   Not currently supported in Fortran.
3754 
3755 .seealso: DMPlexBuildCoordinatesFromCellListParallel(), DMPlexCreateFromCellListPetsc(), DMPlexBuildFromCellList()
3756 @*/
3757 PetscErrorCode DMPlexBuildCoordinatesFromCellList(DM dm, PetscInt spaceDim, const PetscReal vertexCoords[])
3758 {
3759   PetscSection   coordSection;
3760   Vec            coordinates;
3761   DM             cdm;
3762   PetscScalar   *coords;
3763   PetscInt       v, vStart, vEnd, d;
3764   PetscErrorCode ierr;
3765 
3766   PetscFunctionBegin;
3767   ierr = PetscLogEventBegin(DMPLEX_BuildCoordinatesFromCellList,dm,0,0,0);CHKERRQ(ierr);
3768   ierr = DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);CHKERRQ(ierr);
3769   if (vStart < 0 || vEnd < 0) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "DM is not set up properly. DMPlexBuildFromCellList() should be called first.");
3770   ierr = DMSetCoordinateDim(dm, spaceDim);CHKERRQ(ierr);
3771   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
3772   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
3773   ierr = PetscSectionSetFieldComponents(coordSection, 0, spaceDim);CHKERRQ(ierr);
3774   ierr = PetscSectionSetChart(coordSection, vStart, vEnd);CHKERRQ(ierr);
3775   for (v = vStart; v < vEnd; ++v) {
3776     ierr = PetscSectionSetDof(coordSection, v, spaceDim);CHKERRQ(ierr);
3777     ierr = PetscSectionSetFieldDof(coordSection, v, 0, spaceDim);CHKERRQ(ierr);
3778   }
3779   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
3780 
3781   ierr = DMGetCoordinateDM(dm, &cdm);CHKERRQ(ierr);
3782   ierr = DMCreateLocalVector(cdm, &coordinates);CHKERRQ(ierr);
3783   ierr = VecSetBlockSize(coordinates, spaceDim);CHKERRQ(ierr);
3784   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
3785   ierr = VecGetArrayWrite(coordinates, &coords);CHKERRQ(ierr);
3786   for (v = 0; v < vEnd-vStart; ++v) {
3787     for (d = 0; d < spaceDim; ++d) {
3788       coords[v*spaceDim+d] = vertexCoords[v*spaceDim+d];
3789     }
3790   }
3791   ierr = VecRestoreArrayWrite(coordinates, &coords);CHKERRQ(ierr);
3792   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
3793   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
3794   ierr = PetscLogEventEnd(DMPLEX_BuildCoordinatesFromCellList,dm,0,0,0);CHKERRQ(ierr);
3795   PetscFunctionReturn(0);
3796 }
3797 
3798 /*@
3799   DMPlexCreateFromCellListPetsc - Create DMPLEX from a list of vertices for each cell (common mesh generator output)
3800 
3801   Input Parameters:
3802 + comm - The communicator
3803 . dim - The topological dimension of the mesh
3804 . numCells - The number of cells
3805 . numVertices - The number of vertices owned by this process, or PETSC_DECIDE
3806 . numCorners - The number of vertices for each cell
3807 . interpolate - Flag indicating that intermediate mesh entities (faces, edges) should be created automatically
3808 . cells - An array of numCells*numCorners numbers, the vertices for each cell
3809 . spaceDim - The spatial dimension used for coordinates
3810 - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex
3811 
3812   Output Parameter:
3813 . dm - The DM
3814 
3815   Notes:
3816   This function is just a convenient sequence of DMCreate(), DMSetType(), DMSetDimension(), DMPlexBuildFromCellList(),
3817   DMPlexInterpolate(), DMPlexBuildCoordinatesFromCellList()
3818 
3819   See DMPlexBuildFromCellList() for an example and details about the topology-related parameters.
3820   See DMPlexBuildCoordinatesFromCellList() for details about the geometry-related parameters.
3821 
3822   Level: intermediate
3823 
3824 .seealso: DMPlexCreateFromCellListParallelPetsc(), DMPlexBuildFromCellList(), DMPlexBuildCoordinatesFromCellList(), DMPlexCreateFromDAG(), DMPlexCreate()
3825 @*/
3826 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)
3827 {
3828   PetscErrorCode ierr;
3829 
3830   PetscFunctionBegin;
3831   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.");
3832   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
3833   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
3834   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
3835   ierr = DMPlexBuildFromCellList(*dm, numCells, numVertices, numCorners, cells);CHKERRQ(ierr);
3836   if (interpolate) {
3837     DM idm;
3838 
3839     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
3840     ierr = DMDestroy(dm);CHKERRQ(ierr);
3841     *dm  = idm;
3842   }
3843   ierr = DMPlexBuildCoordinatesFromCellList(*dm, spaceDim, vertexCoords);CHKERRQ(ierr);
3844   PetscFunctionReturn(0);
3845 }
3846 
3847 /*@
3848   DMPlexCreateFromCellList - Deprecated, use DMPlexCreateFromCellListPetsc()
3849 
3850   Level: deprecated
3851 
3852 .seealso: DMPlexCreateFromCellListPetsc()
3853 @*/
3854 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)
3855 {
3856   PetscErrorCode ierr;
3857   PetscInt       i;
3858   PetscInt       *pintCells;
3859   PetscReal      *prealVC;
3860 
3861   PetscFunctionBegin;
3862   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));
3863   if (sizeof(int) == sizeof(PetscInt)) {
3864     pintCells = (PetscInt *) cells;
3865   } else {
3866     ierr = PetscMalloc1(numCells*numCorners, &pintCells);CHKERRQ(ierr);
3867     for (i = 0; i < numCells*numCorners; i++) {
3868       pintCells[i] = (PetscInt) cells[i];
3869     }
3870   }
3871   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));
3872   if (sizeof(double) == sizeof(PetscReal)) {
3873     prealVC = (PetscReal *) vertexCoords;
3874   } else {
3875     ierr = PetscMalloc1(numVertices*spaceDim, &prealVC);CHKERRQ(ierr);
3876     for (i = 0; i < numVertices*spaceDim; i++) {
3877       prealVC[i] = (PetscReal) vertexCoords[i];
3878     }
3879   }
3880   ierr = DMPlexCreateFromCellListPetsc(comm, dim, numCells, numVertices, numCorners, interpolate, pintCells, spaceDim, prealVC, dm);CHKERRQ(ierr);
3881   if (sizeof(int) != sizeof(PetscInt)) {
3882     ierr = PetscFree(pintCells);CHKERRQ(ierr);
3883   }
3884   if (sizeof(double) != sizeof(PetscReal)) {
3885     ierr = PetscFree(prealVC);CHKERRQ(ierr);
3886   }
3887   PetscFunctionReturn(0);
3888 }
3889 
3890 /*@
3891   DMPlexCreateFromDAG - This takes as input the adjacency-list representation of the Directed Acyclic Graph (Hasse Diagram) encoding a mesh, and produces a DM
3892 
3893   Input Parameters:
3894 + dm - The empty DM object, usually from DMCreate() and DMSetDimension()
3895 . depth - The depth of the DAG
3896 . numPoints - Array of size depth + 1 containing the number of points at each depth
3897 . coneSize - The cone size of each point
3898 . cones - The concatenation of the cone points for each point, the cone list must be oriented correctly for each point
3899 . coneOrientations - The orientation of each cone point
3900 - vertexCoords - An array of numPoints[0]*spacedim numbers representing the coordinates of each vertex, with spacedim the value set via DMSetCoordinateDim()
3901 
3902   Output Parameter:
3903 . dm - The DM
3904 
3905   Note: Two triangles sharing a face would have input
3906 $  depth = 1, numPoints = [4 2], coneSize = [3 3 0 0 0 0]
3907 $  cones = [2 3 4  3 5 4], coneOrientations = [0 0 0  0 0 0]
3908 $ vertexCoords = [-1.0 0.0  0.0 -1.0  0.0 1.0  1.0 0.0]
3909 $
3910 which would result in the DMPlex
3911 $
3912 $        4
3913 $      / | \
3914 $     /  |  \
3915 $    /   |   \
3916 $   2  0 | 1  5
3917 $    \   |   /
3918 $     \  |  /
3919 $      \ | /
3920 $        3
3921 $
3922 $ Notice that all points are numbered consecutively, unlike DMPlexCreateFromCellListPetsc()
3923 
3924   Level: advanced
3925 
3926 .seealso: DMPlexCreateFromCellListPetsc(), DMPlexCreate()
3927 @*/
3928 PetscErrorCode DMPlexCreateFromDAG(DM dm, PetscInt depth, const PetscInt numPoints[], const PetscInt coneSize[], const PetscInt cones[], const PetscInt coneOrientations[], const PetscScalar vertexCoords[])
3929 {
3930   Vec            coordinates;
3931   PetscSection   coordSection;
3932   PetscScalar    *coords;
3933   PetscInt       coordSize, firstVertex = -1, pStart = 0, pEnd = 0, p, v, dim, dimEmbed, d, off;
3934   PetscErrorCode ierr;
3935 
3936   PetscFunctionBegin;
3937   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
3938   ierr = DMGetCoordinateDim(dm, &dimEmbed);CHKERRQ(ierr);
3939   if (dimEmbed < dim) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Embedding dimension %D cannot be less than intrinsic dimension %d",dimEmbed,dim);
3940   for (d = 0; d <= depth; ++d) pEnd += numPoints[d];
3941   ierr = DMPlexSetChart(dm, pStart, pEnd);CHKERRQ(ierr);
3942   for (p = pStart; p < pEnd; ++p) {
3943     ierr = DMPlexSetConeSize(dm, p, coneSize[p-pStart]);CHKERRQ(ierr);
3944     if (firstVertex < 0 && !coneSize[p - pStart]) {
3945       firstVertex = p - pStart;
3946     }
3947   }
3948   if (firstVertex < 0 && numPoints[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Expected %D vertices but could not find any", numPoints[0]);
3949   ierr = DMSetUp(dm);CHKERRQ(ierr); /* Allocate space for cones */
3950   for (p = pStart, off = 0; p < pEnd; off += coneSize[p-pStart], ++p) {
3951     ierr = DMPlexSetCone(dm, p, &cones[off]);CHKERRQ(ierr);
3952     ierr = DMPlexSetConeOrientation(dm, p, &coneOrientations[off]);CHKERRQ(ierr);
3953   }
3954   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
3955   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
3956   /* Build coordinates */
3957   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
3958   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
3959   ierr = PetscSectionSetFieldComponents(coordSection, 0, dimEmbed);CHKERRQ(ierr);
3960   ierr = PetscSectionSetChart(coordSection, firstVertex, firstVertex+numPoints[0]);CHKERRQ(ierr);
3961   for (v = firstVertex; v < firstVertex+numPoints[0]; ++v) {
3962     ierr = PetscSectionSetDof(coordSection, v, dimEmbed);CHKERRQ(ierr);
3963     ierr = PetscSectionSetFieldDof(coordSection, v, 0, dimEmbed);CHKERRQ(ierr);
3964   }
3965   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
3966   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
3967   ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
3968   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
3969   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
3970   ierr = VecSetBlockSize(coordinates, dimEmbed);CHKERRQ(ierr);
3971   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
3972   if (vertexCoords) {
3973     ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
3974     for (v = 0; v < numPoints[0]; ++v) {
3975       PetscInt off;
3976 
3977       ierr = PetscSectionGetOffset(coordSection, v+firstVertex, &off);CHKERRQ(ierr);
3978       for (d = 0; d < dimEmbed; ++d) {
3979         coords[off+d] = vertexCoords[v*dimEmbed+d];
3980       }
3981     }
3982   }
3983   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
3984   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
3985   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
3986   PetscFunctionReturn(0);
3987 }
3988 
3989 /*@C
3990   DMPlexCreateCellVertexFromFile - Create a DMPlex mesh from a simple cell-vertex file.
3991 
3992 + comm        - The MPI communicator
3993 . filename    - Name of the .dat file
3994 - interpolate - Create faces and edges in the mesh
3995 
3996   Output Parameter:
3997 . dm  - The DM object representing the mesh
3998 
3999   Note: The format is the simplest possible:
4000 $ Ne
4001 $ v0 v1 ... vk
4002 $ Nv
4003 $ x y z marker
4004 
4005   Level: beginner
4006 
4007 .seealso: DMPlexCreateFromFile(), DMPlexCreateMedFromFile(), DMPlexCreateGmsh(), DMPlexCreate()
4008 @*/
4009 PetscErrorCode DMPlexCreateCellVertexFromFile(MPI_Comm comm, const char filename[], PetscBool interpolate, DM *dm)
4010 {
4011   DMLabel         marker;
4012   PetscViewer     viewer;
4013   Vec             coordinates;
4014   PetscSection    coordSection;
4015   PetscScalar    *coords;
4016   char            line[PETSC_MAX_PATH_LEN];
4017   PetscInt        dim = 3, cdim = 3, coordSize, v, c, d;
4018   PetscMPIInt     rank;
4019   int             snum, Nv, Nc;
4020   PetscErrorCode  ierr;
4021 
4022   PetscFunctionBegin;
4023   ierr = MPI_Comm_rank(comm, &rank);CHKERRMPI(ierr);
4024   ierr = PetscViewerCreate(comm, &viewer);CHKERRQ(ierr);
4025   ierr = PetscViewerSetType(viewer, PETSCVIEWERASCII);CHKERRQ(ierr);
4026   ierr = PetscViewerFileSetMode(viewer, FILE_MODE_READ);CHKERRQ(ierr);
4027   ierr = PetscViewerFileSetName(viewer, filename);CHKERRQ(ierr);
4028   if (!rank) {
4029     ierr = PetscViewerRead(viewer, line, 2, NULL, PETSC_STRING);CHKERRQ(ierr);
4030     snum = sscanf(line, "%d %d", &Nc, &Nv);
4031     if (snum != 2) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unable to parse cell-vertex file: %s", line);
4032   } else {
4033     Nc = Nv = 0;
4034   }
4035   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
4036   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
4037   ierr = DMPlexSetChart(*dm, 0, Nc+Nv);CHKERRQ(ierr);
4038   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
4039   ierr = DMSetCoordinateDim(*dm, cdim);CHKERRQ(ierr);
4040   /* Read topology */
4041   if (!rank) {
4042     PetscInt cone[8], corners = 8;
4043     int      vbuf[8], v;
4044 
4045     for (c = 0; c < Nc; ++c) {ierr = DMPlexSetConeSize(*dm, c, corners);CHKERRQ(ierr);}
4046     ierr = DMSetUp(*dm);CHKERRQ(ierr);
4047     for (c = 0; c < Nc; ++c) {
4048       ierr = PetscViewerRead(viewer, line, corners, NULL, PETSC_STRING);CHKERRQ(ierr);
4049       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]);
4050       if (snum != corners) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unable to parse cell-vertex file: %s", line);
4051       for (v = 0; v < corners; ++v) cone[v] = vbuf[v] + Nc;
4052       /* Hexahedra are inverted */
4053       {
4054         PetscInt tmp = cone[1];
4055         cone[1] = cone[3];
4056         cone[3] = tmp;
4057       }
4058       ierr = DMPlexSetCone(*dm, c, cone);CHKERRQ(ierr);
4059     }
4060   }
4061   ierr = DMPlexSymmetrize(*dm);CHKERRQ(ierr);
4062   ierr = DMPlexStratify(*dm);CHKERRQ(ierr);
4063   /* Read coordinates */
4064   ierr = DMGetCoordinateSection(*dm, &coordSection);CHKERRQ(ierr);
4065   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
4066   ierr = PetscSectionSetFieldComponents(coordSection, 0, cdim);CHKERRQ(ierr);
4067   ierr = PetscSectionSetChart(coordSection, Nc, Nc + Nv);CHKERRQ(ierr);
4068   for (v = Nc; v < Nc+Nv; ++v) {
4069     ierr = PetscSectionSetDof(coordSection, v, cdim);CHKERRQ(ierr);
4070     ierr = PetscSectionSetFieldDof(coordSection, v, 0, cdim);CHKERRQ(ierr);
4071   }
4072   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
4073   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
4074   ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
4075   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
4076   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
4077   ierr = VecSetBlockSize(coordinates, cdim);CHKERRQ(ierr);
4078   ierr = VecSetType(coordinates, VECSTANDARD);CHKERRQ(ierr);
4079   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
4080   if (!rank) {
4081     double x[3];
4082     int    val;
4083 
4084     ierr = DMCreateLabel(*dm, "marker");CHKERRQ(ierr);
4085     ierr = DMGetLabel(*dm, "marker", &marker);CHKERRQ(ierr);
4086     for (v = 0; v < Nv; ++v) {
4087       ierr = PetscViewerRead(viewer, line, 4, NULL, PETSC_STRING);CHKERRQ(ierr);
4088       snum = sscanf(line, "%lg %lg %lg %d", &x[0], &x[1], &x[2], &val);
4089       if (snum != 4) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unable to parse cell-vertex file: %s", line);
4090       for (d = 0; d < cdim; ++d) coords[v*cdim+d] = x[d];
4091       if (val) {ierr = DMLabelSetValue(marker, v+Nc, val);CHKERRQ(ierr);}
4092     }
4093   }
4094   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
4095   ierr = DMSetCoordinatesLocal(*dm, coordinates);CHKERRQ(ierr);
4096   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
4097   ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
4098   if (interpolate) {
4099     DM      idm;
4100     DMLabel bdlabel;
4101 
4102     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
4103     ierr = DMDestroy(dm);CHKERRQ(ierr);
4104     *dm  = idm;
4105 
4106     ierr = DMGetLabel(*dm, "marker", &bdlabel);CHKERRQ(ierr);
4107     ierr = DMPlexMarkBoundaryFaces(*dm, PETSC_DETERMINE, bdlabel);CHKERRQ(ierr);
4108     ierr = DMPlexLabelComplete(*dm, bdlabel);CHKERRQ(ierr);
4109   }
4110   PetscFunctionReturn(0);
4111 }
4112 
4113 /*@C
4114   DMPlexCreateFromFile - This takes a filename and produces a DM
4115 
4116   Input Parameters:
4117 + comm - The communicator
4118 . filename - A file name
4119 - interpolate - Flag to create intermediate mesh pieces (edges, faces)
4120 
4121   Output Parameter:
4122 . dm - The DM
4123 
4124   Options Database Keys:
4125 . -dm_plex_create_from_hdf5_xdmf - use the PETSC_VIEWER_HDF5_XDMF format for reading HDF5
4126 
4127   Use -dm_plex_create_ prefix to pass options to the internal PetscViewer, e.g.
4128 $ -dm_plex_create_viewer_hdf5_collective
4129 
4130   Level: beginner
4131 
4132 .seealso: DMPlexCreateFromDAG(), DMPlexCreateFromCellListPetsc(), DMPlexCreate()
4133 @*/
4134 PetscErrorCode DMPlexCreateFromFile(MPI_Comm comm, const char filename[], PetscBool interpolate, DM *dm)
4135 {
4136   const char    *extGmsh    = ".msh";
4137   const char    *extGmsh2   = ".msh2";
4138   const char    *extGmsh4   = ".msh4";
4139   const char    *extCGNS    = ".cgns";
4140   const char    *extExodus  = ".exo";
4141   const char    *extGenesis = ".gen";
4142   const char    *extFluent  = ".cas";
4143   const char    *extHDF5    = ".h5";
4144   const char    *extMed     = ".med";
4145   const char    *extPLY     = ".ply";
4146   const char    *extEGADS   = ".egadslite";
4147   const char    *extCV      = ".dat";
4148   size_t         len;
4149   PetscBool      isGmsh, isGmsh2, isGmsh4, isCGNS, isExodus, isGenesis, isFluent, isHDF5, isMed, isPLY, isEGADS, isCV;
4150   PetscMPIInt    rank;
4151   PetscErrorCode ierr;
4152 
4153   PetscFunctionBegin;
4154   PetscValidCharPointer(filename, 2);
4155   PetscValidPointer(dm, 4);
4156   ierr = DMInitializePackage();CHKERRQ(ierr);
4157   ierr = PetscLogEventBegin(DMPLEX_CreateFromFile,0,0,0,0);CHKERRQ(ierr);
4158   ierr = MPI_Comm_rank(comm, &rank);CHKERRMPI(ierr);
4159   ierr = PetscStrlen(filename, &len);CHKERRQ(ierr);
4160   if (!len) SETERRQ(comm, PETSC_ERR_ARG_WRONG, "Filename must be a valid path");
4161   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extGmsh,    4, &isGmsh);CHKERRQ(ierr);
4162   ierr = PetscStrncmp(&filename[PetscMax(0,len-5)], extGmsh2,   5, &isGmsh2);CHKERRQ(ierr);
4163   ierr = PetscStrncmp(&filename[PetscMax(0,len-5)], extGmsh4,   5, &isGmsh4);CHKERRQ(ierr);
4164   ierr = PetscStrncmp(&filename[PetscMax(0,len-5)], extCGNS,    5, &isCGNS);CHKERRQ(ierr);
4165   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extExodus,  4, &isExodus);CHKERRQ(ierr);
4166   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extGenesis, 4, &isGenesis);CHKERRQ(ierr);
4167   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extFluent,  4, &isFluent);CHKERRQ(ierr);
4168   ierr = PetscStrncmp(&filename[PetscMax(0,len-3)], extHDF5,    3, &isHDF5);CHKERRQ(ierr);
4169   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extMed,     4, &isMed);CHKERRQ(ierr);
4170   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extPLY,     4, &isPLY);CHKERRQ(ierr);
4171   ierr = PetscStrncmp(&filename[PetscMax(0,len-10)], extEGADS,   9, &isEGADS);CHKERRQ(ierr);
4172   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extCV,      4, &isCV);CHKERRQ(ierr);
4173   if (isGmsh || isGmsh2 || isGmsh4) {
4174     ierr = DMPlexCreateGmshFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
4175   } else if (isCGNS) {
4176     ierr = DMPlexCreateCGNSFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
4177   } else if (isExodus || isGenesis) {
4178     ierr = DMPlexCreateExodusFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
4179   } else if (isFluent) {
4180     ierr = DMPlexCreateFluentFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
4181   } else if (isHDF5) {
4182     PetscBool      load_hdf5_xdmf = PETSC_FALSE;
4183     PetscViewer viewer;
4184 
4185     /* PETSC_VIEWER_HDF5_XDMF is used if the filename ends with .xdmf.h5, or if -dm_plex_create_from_hdf5_xdmf option is present */
4186     ierr = PetscStrncmp(&filename[PetscMax(0,len-8)], ".xdmf",  5, &load_hdf5_xdmf);CHKERRQ(ierr);
4187     ierr = PetscOptionsGetBool(NULL, NULL, "-dm_plex_create_from_hdf5_xdmf", &load_hdf5_xdmf, NULL);CHKERRQ(ierr);
4188     ierr = PetscViewerCreate(comm, &viewer);CHKERRQ(ierr);
4189     ierr = PetscViewerSetType(viewer, PETSCVIEWERHDF5);CHKERRQ(ierr);
4190     ierr = PetscViewerSetOptionsPrefix(viewer, "dm_plex_create_");CHKERRQ(ierr);
4191     ierr = PetscViewerSetFromOptions(viewer);CHKERRQ(ierr);
4192     ierr = PetscViewerFileSetMode(viewer, FILE_MODE_READ);CHKERRQ(ierr);
4193     ierr = PetscViewerFileSetName(viewer, filename);CHKERRQ(ierr);
4194     ierr = DMCreate(comm, dm);CHKERRQ(ierr);
4195     ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
4196     if (load_hdf5_xdmf) {ierr = PetscViewerPushFormat(viewer, PETSC_VIEWER_HDF5_XDMF);CHKERRQ(ierr);}
4197     ierr = DMLoad(*dm, viewer);CHKERRQ(ierr);
4198     if (load_hdf5_xdmf) {ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);}
4199     ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
4200 
4201     if (interpolate) {
4202       DM idm;
4203 
4204       ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
4205       ierr = DMDestroy(dm);CHKERRQ(ierr);
4206       *dm  = idm;
4207     }
4208   } else if (isMed) {
4209     ierr = DMPlexCreateMedFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
4210   } else if (isPLY) {
4211     ierr = DMPlexCreatePLYFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
4212   } else if (isEGADS) {
4213     ierr = DMPlexCreateEGADSFromFile(comm, filename, dm);CHKERRQ(ierr);
4214     if (!interpolate) {
4215       DM udm;
4216 
4217       ierr = DMPlexUninterpolate(*dm, &udm);CHKERRQ(ierr);
4218       ierr = DMDestroy(dm);CHKERRQ(ierr);
4219       *dm  = udm;
4220     }
4221   } else if (isCV) {
4222     ierr = DMPlexCreateCellVertexFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
4223   } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cannot load file %s: unrecognized extension", filename);
4224   ierr = PetscLogEventEnd(DMPLEX_CreateFromFile,0,0,0,0);CHKERRQ(ierr);
4225   PetscFunctionReturn(0);
4226 }
4227