xref: /petsc/src/dm/impls/plex/plexcreate.c (revision 030f984af8d8bb4c203755d35bded3c05b3d83ce)
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] = {-2,  0,  0, -3,  0, -2}; /* ??? */
857           PetscInt cone[6];
858 
859           /* no boundary twisting in 3D */
860           cone[0] = faceB; cone[1] = faceT; cone[2] = faceF; cone[3] = faceK; cone[4] = faceR; cone[5] = faceL;
861           ierr    = DMPlexSetCone(dm, cell, cone);CHKERRQ(ierr);
862           ierr    = DMPlexSetConeOrientation(dm, cell, ornt);CHKERRQ(ierr);
863           if (bdX != DM_BOUNDARY_NONE && fx == numXEdges-1 && cutLabel) {ierr = DMLabelSetValue(cutLabel, cell, 2);CHKERRQ(ierr);}
864           if (bdY != DM_BOUNDARY_NONE && fy == numYEdges-1 && cutLabel) {ierr = DMLabelSetValue(cutLabel, cell, 2);CHKERRQ(ierr);}
865           if (bdZ != DM_BOUNDARY_NONE && fz == numZEdges-1 && cutLabel) {ierr = DMLabelSetValue(cutLabel, cell, 2);CHKERRQ(ierr);}
866         }
867       }
868     }
869     /* Build x faces */
870     for (fz = 0; fz < numZEdges; ++fz) {
871       for (fy = 0; fy < numYEdges; ++fy) {
872         for (fx = 0; fx < numXVertices; ++fx) {
873           PetscInt face    = firstXFace + (fz*numYEdges+fy)     *numXVertices+fx;
874           PetscInt edgeL   = firstZEdge + (fy                   *numXVertices+fx)*numZEdges + fz;
875           PetscInt edgeR   = firstZEdge + (((fy+1)%numYVertices)*numXVertices+fx)*numZEdges + fz;
876           PetscInt edgeB   = firstYEdge + (fz                   *numXVertices+fx)*numYEdges + fy;
877           PetscInt edgeT   = firstYEdge + (((fz+1)%numZVertices)*numXVertices+fx)*numYEdges + fy;
878           PetscInt ornt[4] = {0, 0, -1, -1};
879           PetscInt cone[4];
880 
881           if (dim == 3) {
882             /* markers */
883             if (bdX != DM_BOUNDARY_PERIODIC) {
884               if (fx == numXVertices-1) {
885                 ierr = DMSetLabelValue(dm, "Face Sets", face, faceMarkerRight);CHKERRQ(ierr);
886                 ierr = DMSetLabelValue(dm, "marker", face, markerRight);CHKERRQ(ierr);
887               }
888               else if (fx == 0) {
889                 ierr = DMSetLabelValue(dm, "Face Sets", face, faceMarkerLeft);CHKERRQ(ierr);
890                 ierr = DMSetLabelValue(dm, "marker", face, markerLeft);CHKERRQ(ierr);
891               }
892             }
893           }
894           cone[0] = edgeB; cone[1] = edgeR; cone[2] = edgeT; cone[3] = edgeL;
895           ierr    = DMPlexSetCone(dm, face, cone);CHKERRQ(ierr);
896           ierr    = DMPlexSetConeOrientation(dm, face, ornt);CHKERRQ(ierr);
897         }
898       }
899     }
900     /* Build y faces */
901     for (fz = 0; fz < numZEdges; ++fz) {
902       for (fx = 0; fx < numXEdges; ++fx) {
903         for (fy = 0; fy < numYVertices; ++fy) {
904           PetscInt face    = firstYFace + (fz*numXEdges+fx)*numYVertices + fy;
905           PetscInt edgeL   = firstZEdge + (fy*numXVertices+  fx)*numZEdges + fz;
906           PetscInt edgeR   = firstZEdge + (fy*numXVertices+((fx+1)%numXVertices))*numZEdges + fz;
907           PetscInt edgeB   = firstXEdge + (fz                   *numYVertices+fy)*numXEdges + fx;
908           PetscInt edgeT   = firstXEdge + (((fz+1)%numZVertices)*numYVertices+fy)*numXEdges + fx;
909           PetscInt ornt[4] = {0, 0, -1, -1};
910           PetscInt cone[4];
911 
912           if (dim == 3) {
913             /* markers */
914             if (bdY != DM_BOUNDARY_PERIODIC) {
915               if (fy == numYVertices-1) {
916                 ierr = DMSetLabelValue(dm, "Face Sets", face, faceMarkerBack);CHKERRQ(ierr);
917                 ierr = DMSetLabelValue(dm, "marker", face, markerBack);CHKERRQ(ierr);
918               }
919               else if (fy == 0) {
920                 ierr = DMSetLabelValue(dm, "Face Sets", face, faceMarkerFront);CHKERRQ(ierr);
921                 ierr = DMSetLabelValue(dm, "marker", face, markerFront);CHKERRQ(ierr);
922               }
923             }
924           }
925           cone[0] = edgeB; cone[1] = edgeR; cone[2] = edgeT; cone[3] = edgeL;
926           ierr    = DMPlexSetCone(dm, face, cone);CHKERRQ(ierr);
927           ierr    = DMPlexSetConeOrientation(dm, face, ornt);CHKERRQ(ierr);
928         }
929       }
930     }
931     /* Build z faces */
932     for (fy = 0; fy < numYEdges; ++fy) {
933       for (fx = 0; fx < numXEdges; ++fx) {
934         for (fz = 0; fz < numZVertices; fz++) {
935           PetscInt face    = firstZFace + (fy*numXEdges+fx)*numZVertices + fz;
936           PetscInt edgeL   = firstYEdge + (fz*numXVertices+  fx)*numYEdges + fy;
937           PetscInt edgeR   = firstYEdge + (fz*numXVertices+((fx+1)%numXVertices))*numYEdges + fy;
938           PetscInt edgeB   = firstXEdge + (fz*numYVertices+  fy)*numXEdges + fx;
939           PetscInt edgeT   = firstXEdge + (fz*numYVertices+((fy+1)%numYVertices))*numXEdges + fx;
940           PetscInt ornt[4] = {0, 0, -1, -1};
941           PetscInt cone[4];
942 
943           if (dim == 2) {
944             if (bdX == DM_BOUNDARY_TWIST && fx == numXEdges-1) {edgeR += numYEdges-1-2*fy; ornt[1] = -1;}
945             if (bdY == DM_BOUNDARY_TWIST && fy == numYEdges-1) {edgeT += numXEdges-1-2*fx; ornt[2] =  0;}
946             if (bdX != DM_BOUNDARY_NONE && fx == numXEdges-1 && cutLabel) {ierr = DMLabelSetValue(cutLabel, face, 2);CHKERRQ(ierr);}
947             if (bdY != DM_BOUNDARY_NONE && fy == numYEdges-1 && cutLabel) {ierr = DMLabelSetValue(cutLabel, face, 2);CHKERRQ(ierr);}
948           } else {
949             /* markers */
950             if (bdZ != DM_BOUNDARY_PERIODIC) {
951               if (fz == numZVertices-1) {
952                 ierr = DMSetLabelValue(dm, "Face Sets", face, faceMarkerTop);CHKERRQ(ierr);
953                 ierr = DMSetLabelValue(dm, "marker", face, markerTop);CHKERRQ(ierr);
954               }
955               else if (fz == 0) {
956                 ierr = DMSetLabelValue(dm, "Face Sets", face, faceMarkerBottom);CHKERRQ(ierr);
957                 ierr = DMSetLabelValue(dm, "marker", face, markerBottom);CHKERRQ(ierr);
958               }
959             }
960           }
961           cone[0] = edgeB; cone[1] = edgeR; cone[2] = edgeT; cone[3] = edgeL;
962           ierr    = DMPlexSetCone(dm, face, cone);CHKERRQ(ierr);
963           ierr    = DMPlexSetConeOrientation(dm, face, ornt);CHKERRQ(ierr);
964         }
965       }
966     }
967     /* Build Z edges*/
968     for (vy = 0; vy < numYVertices; vy++) {
969       for (vx = 0; vx < numXVertices; vx++) {
970         for (ez = 0; ez < numZEdges; ez++) {
971           const PetscInt edge    = firstZEdge  + (vy*numXVertices+vx)*numZEdges + ez;
972           const PetscInt vertexB = firstVertex + (ez                   *numYVertices+vy)*numXVertices + vx;
973           const PetscInt vertexT = firstVertex + (((ez+1)%numZVertices)*numYVertices+vy)*numXVertices + vx;
974           PetscInt       cone[2];
975 
976           if (dim == 3) {
977             if (bdX != DM_BOUNDARY_PERIODIC) {
978               if (vx == numXVertices-1) {
979                 ierr = DMSetLabelValue(dm, "marker", edge, markerRight);CHKERRQ(ierr);
980               }
981               else if (vx == 0) {
982                 ierr = DMSetLabelValue(dm, "marker", edge, markerLeft);CHKERRQ(ierr);
983               }
984             }
985             if (bdY != DM_BOUNDARY_PERIODIC) {
986               if (vy == numYVertices-1) {
987                 ierr = DMSetLabelValue(dm, "marker", edge, markerBack);CHKERRQ(ierr);
988               }
989               else if (vy == 0) {
990                 ierr = DMSetLabelValue(dm, "marker", edge, markerFront);CHKERRQ(ierr);
991               }
992             }
993           }
994           cone[0] = vertexB; cone[1] = vertexT;
995           ierr = DMPlexSetCone(dm, edge, cone);CHKERRQ(ierr);
996         }
997       }
998     }
999     /* Build Y edges*/
1000     for (vz = 0; vz < numZVertices; vz++) {
1001       for (vx = 0; vx < numXVertices; vx++) {
1002         for (ey = 0; ey < numYEdges; ey++) {
1003           const PetscInt nextv   = (dim == 2 && bdY == DM_BOUNDARY_TWIST && ey == numYEdges-1) ? (numXVertices-vx-1) : (vz*numYVertices+((ey+1)%numYVertices))*numXVertices + vx;
1004           const PetscInt edge    = firstYEdge  + (vz*numXVertices+vx)*numYEdges + ey;
1005           const PetscInt vertexF = firstVertex + (vz*numYVertices+ey)*numXVertices + vx;
1006           const PetscInt vertexK = firstVertex + nextv;
1007           PetscInt       cone[2];
1008 
1009           cone[0] = vertexF; cone[1] = vertexK;
1010           ierr = DMPlexSetCone(dm, edge, cone);CHKERRQ(ierr);
1011           if (dim == 2) {
1012             if ((bdX != DM_BOUNDARY_PERIODIC) && (bdX != DM_BOUNDARY_TWIST)) {
1013               if (vx == numXVertices-1) {
1014                 ierr = DMSetLabelValue(dm, "Face Sets", edge, faceMarkerRight);CHKERRQ(ierr);
1015                 ierr = DMSetLabelValue(dm, "marker", edge,    markerRight);CHKERRQ(ierr);
1016                 ierr = DMSetLabelValue(dm, "marker", cone[0], markerRight);CHKERRQ(ierr);
1017                 if (ey == numYEdges-1) {
1018                   ierr = DMSetLabelValue(dm, "marker", cone[1], markerRight);CHKERRQ(ierr);
1019                 }
1020               } else if (vx == 0) {
1021                 ierr = DMSetLabelValue(dm, "Face Sets", edge, faceMarkerLeft);CHKERRQ(ierr);
1022                 ierr = DMSetLabelValue(dm, "marker", edge,    markerLeft);CHKERRQ(ierr);
1023                 ierr = DMSetLabelValue(dm, "marker", cone[0], markerLeft);CHKERRQ(ierr);
1024                 if (ey == numYEdges-1) {
1025                   ierr = DMSetLabelValue(dm, "marker", cone[1], markerLeft);CHKERRQ(ierr);
1026                 }
1027               }
1028             } else {
1029               if (vx == 0 && cutLabel) {
1030                 ierr = DMLabelSetValue(cutLabel, edge,    1);CHKERRQ(ierr);
1031                 ierr = DMLabelSetValue(cutLabel, cone[0], 1);CHKERRQ(ierr);
1032                 if (ey == numYEdges-1) {
1033                   ierr = DMLabelSetValue(cutLabel, cone[1], 1);CHKERRQ(ierr);
1034                 }
1035               }
1036             }
1037           } else {
1038             if (bdX != DM_BOUNDARY_PERIODIC) {
1039               if (vx == numXVertices-1) {
1040                 ierr = DMSetLabelValue(dm, "marker", edge, markerRight);CHKERRQ(ierr);
1041               } else if (vx == 0) {
1042                 ierr = DMSetLabelValue(dm, "marker", edge, markerLeft);CHKERRQ(ierr);
1043               }
1044             }
1045             if (bdZ != DM_BOUNDARY_PERIODIC) {
1046               if (vz == numZVertices-1) {
1047                 ierr = DMSetLabelValue(dm, "marker", edge, markerTop);CHKERRQ(ierr);
1048               } else if (vz == 0) {
1049                 ierr = DMSetLabelValue(dm, "marker", edge, markerBottom);CHKERRQ(ierr);
1050               }
1051             }
1052           }
1053         }
1054       }
1055     }
1056     /* Build X edges*/
1057     for (vz = 0; vz < numZVertices; vz++) {
1058       for (vy = 0; vy < numYVertices; vy++) {
1059         for (ex = 0; ex < numXEdges; ex++) {
1060           const PetscInt nextv   = (dim == 2 && bdX == DM_BOUNDARY_TWIST && ex == numXEdges-1) ? (numYVertices-vy-1)*numXVertices : (vz*numYVertices+vy)*numXVertices + (ex+1)%numXVertices;
1061           const PetscInt edge    = firstXEdge  + (vz*numYVertices+vy)*numXEdges + ex;
1062           const PetscInt vertexL = firstVertex + (vz*numYVertices+vy)*numXVertices + ex;
1063           const PetscInt vertexR = firstVertex + nextv;
1064           PetscInt       cone[2];
1065 
1066           cone[0] = vertexL; cone[1] = vertexR;
1067           ierr = DMPlexSetCone(dm, edge, cone);CHKERRQ(ierr);
1068           if (dim == 2) {
1069             if ((bdY != DM_BOUNDARY_PERIODIC) && (bdY != DM_BOUNDARY_TWIST)) {
1070               if (vy == numYVertices-1) {
1071                 ierr = DMSetLabelValue(dm, "Face Sets", edge, faceMarkerTop);CHKERRQ(ierr);
1072                 ierr = DMSetLabelValue(dm, "marker", edge,    markerTop);CHKERRQ(ierr);
1073                 ierr = DMSetLabelValue(dm, "marker", cone[0], markerTop);CHKERRQ(ierr);
1074                 if (ex == numXEdges-1) {
1075                   ierr = DMSetLabelValue(dm, "marker", cone[1], markerTop);CHKERRQ(ierr);
1076                 }
1077               } else if (vy == 0) {
1078                 ierr = DMSetLabelValue(dm, "Face Sets", edge, faceMarkerBottom);CHKERRQ(ierr);
1079                 ierr = DMSetLabelValue(dm, "marker", edge,    markerBottom);CHKERRQ(ierr);
1080                 ierr = DMSetLabelValue(dm, "marker", cone[0], markerBottom);CHKERRQ(ierr);
1081                 if (ex == numXEdges-1) {
1082                   ierr = DMSetLabelValue(dm, "marker", cone[1], markerBottom);CHKERRQ(ierr);
1083                 }
1084               }
1085             } else {
1086               if (vy == 0 && cutLabel) {
1087                 ierr = DMLabelSetValue(cutLabel, edge,    1);CHKERRQ(ierr);
1088                 ierr = DMLabelSetValue(cutLabel, cone[0], 1);CHKERRQ(ierr);
1089                 if (ex == numXEdges-1) {
1090                   ierr = DMLabelSetValue(cutLabel, cone[1], 1);CHKERRQ(ierr);
1091                 }
1092               }
1093             }
1094           } else {
1095             if (bdY != DM_BOUNDARY_PERIODIC) {
1096               if (vy == numYVertices-1) {
1097                 ierr = DMSetLabelValue(dm, "marker", edge, markerBack);CHKERRQ(ierr);
1098               }
1099               else if (vy == 0) {
1100                 ierr = DMSetLabelValue(dm, "marker", edge, markerFront);CHKERRQ(ierr);
1101               }
1102             }
1103             if (bdZ != DM_BOUNDARY_PERIODIC) {
1104               if (vz == numZVertices-1) {
1105                 ierr = DMSetLabelValue(dm, "marker", edge, markerTop);CHKERRQ(ierr);
1106               }
1107               else if (vz == 0) {
1108                 ierr = DMSetLabelValue(dm, "marker", edge, markerBottom);CHKERRQ(ierr);
1109               }
1110             }
1111           }
1112         }
1113       }
1114     }
1115     ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
1116     ierr = DMPlexStratify(dm);CHKERRQ(ierr);
1117     /* Build coordinates */
1118     ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
1119     ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
1120     ierr = PetscSectionSetFieldComponents(coordSection, 0, dim);CHKERRQ(ierr);
1121     ierr = PetscSectionSetChart(coordSection, firstVertex, firstVertex+numVertices);CHKERRQ(ierr);
1122     for (v = firstVertex; v < firstVertex+numVertices; ++v) {
1123       ierr = PetscSectionSetDof(coordSection, v, dim);CHKERRQ(ierr);
1124       ierr = PetscSectionSetFieldDof(coordSection, v, 0, dim);CHKERRQ(ierr);
1125     }
1126     ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
1127     ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
1128     ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
1129     ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
1130     ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
1131     ierr = VecSetBlockSize(coordinates, dim);CHKERRQ(ierr);
1132     ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
1133     ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
1134     for (vz = 0; vz < numZVertices; ++vz) {
1135       for (vy = 0; vy < numYVertices; ++vy) {
1136         for (vx = 0; vx < numXVertices; ++vx) {
1137           coords[((vz*numYVertices+vy)*numXVertices+vx)*dim+0] = lower[0] + ((upper[0] - lower[0])/numXEdges)*vx;
1138           coords[((vz*numYVertices+vy)*numXVertices+vx)*dim+1] = lower[1] + ((upper[1] - lower[1])/numYEdges)*vy;
1139           if (dim == 3) {
1140             coords[((vz*numYVertices+vy)*numXVertices+vx)*dim+2] = lower[2] + ((upper[2] - lower[2])/numZEdges)*vz;
1141           }
1142         }
1143       }
1144     }
1145     ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
1146     ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
1147     ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
1148   }
1149   PetscFunctionReturn(0);
1150 }
1151 
1152 static PetscErrorCode DMPlexCreateBoxMesh_Tensor_Internal(DM dm, PetscInt dim, const PetscInt faces[], const PetscReal lower[], const PetscReal upper[], const DMBoundaryType periodicity[])
1153 {
1154   DMBoundaryType bdt[3] = {DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE};
1155   PetscInt       fac[3] = {0, 0, 0}, d;
1156   PetscErrorCode ierr;
1157 
1158   PetscFunctionBegin;
1159   PetscValidPointer(dm, 1);
1160   PetscValidLogicalCollectiveInt(dm, dim, 2);
1161   ierr = DMSetDimension(dm, dim);CHKERRQ(ierr);
1162   for (d = 0; d < dim; ++d) {fac[d] = faces[d]; bdt[d] = periodicity[d];}
1163   ierr = DMPlexCreateCubeMesh_Internal(dm, lower, upper, fac, bdt[0], bdt[1], bdt[2]);CHKERRQ(ierr);
1164   if (periodicity[0] == DM_BOUNDARY_PERIODIC || periodicity[0] == DM_BOUNDARY_TWIST ||
1165       periodicity[1] == DM_BOUNDARY_PERIODIC || periodicity[1] == DM_BOUNDARY_TWIST ||
1166       (dim > 2 && (periodicity[2] == DM_BOUNDARY_PERIODIC || periodicity[2] == DM_BOUNDARY_TWIST))) {
1167     PetscReal L[3];
1168     PetscReal maxCell[3];
1169 
1170     for (d = 0; d < dim; ++d) {
1171       L[d]       = upper[d] - lower[d];
1172       maxCell[d] = 1.1 * (L[d] / PetscMax(1, faces[d]));
1173     }
1174     ierr = DMSetPeriodicity(dm, PETSC_TRUE, maxCell, L, periodicity);CHKERRQ(ierr);
1175   }
1176   ierr = DMPlexSetRefinementUniform(dm, PETSC_TRUE);CHKERRQ(ierr);
1177   PetscFunctionReturn(0);
1178 }
1179 
1180 static PetscErrorCode DMPlexCreateBoxMesh_Internal(DM dm, PetscInt dim, PetscBool simplex, const PetscInt faces[], const PetscReal lower[], const PetscReal upper[], const DMBoundaryType periodicity[], PetscBool interpolate)
1181 {
1182   PetscErrorCode ierr;
1183 
1184   PetscFunctionBegin;
1185   if (dim == 1)      {ierr = DMPlexCreateLineMesh_Internal(dm, faces[0], lower[0], upper[0], periodicity[0]);CHKERRQ(ierr);}
1186   else if (simplex)  {ierr = DMPlexCreateBoxMesh_Simplex_Internal(dm, dim, faces, lower, upper, periodicity, interpolate);CHKERRQ(ierr);}
1187   else               {ierr = DMPlexCreateBoxMesh_Tensor_Internal(dm, dim, faces, lower, upper, periodicity);CHKERRQ(ierr);}
1188   if (!interpolate && dim > 1 && !simplex) {
1189     DM udm;
1190 
1191     ierr = DMPlexUninterpolate(dm, &udm);CHKERRQ(ierr);
1192     ierr = DMPlexCopyCoordinates(dm, udm);CHKERRQ(ierr);
1193     ierr = DMPlexReplace_Static(dm, &udm);CHKERRQ(ierr);
1194   }
1195   PetscFunctionReturn(0);
1196 }
1197 
1198 /*@C
1199   DMPlexCreateBoxMesh - Creates a mesh on the tensor product of unit intervals (box) using simplices or tensor cells (hexahedra).
1200 
1201   Collective
1202 
1203   Input Parameters:
1204 + comm        - The communicator for the DM object
1205 . dim         - The spatial dimension
1206 . simplex     - PETSC_TRUE for simplices, PETSC_FALSE for tensor cells
1207 . faces       - Number of faces per dimension, or NULL for (1,) in 1D and (2, 2) in 2D and (1, 1, 1) in 3D
1208 . lower       - The lower left corner, or NULL for (0, 0, 0)
1209 . upper       - The upper right corner, or NULL for (1, 1, 1)
1210 . periodicity - The boundary type for the X,Y,Z direction, or NULL for DM_BOUNDARY_NONE
1211 - interpolate - Flag to create intermediate mesh pieces (edges, faces)
1212 
1213   Output Parameter:
1214 . dm  - The DM object
1215 
1216   Note: If you want to customize this mesh using options, you just need to
1217 $  DMCreate(comm, &dm);
1218 $  DMSetType(dm, DMPLEX);
1219 $  DMSetFromOptions(dm);
1220 and use the options on the DMSetFromOptions() page.
1221 
1222   Here is the numbering returned for 2 faces in each direction for tensor cells:
1223 $ 10---17---11---18----12
1224 $  |         |         |
1225 $  |         |         |
1226 $ 20    2   22    3    24
1227 $  |         |         |
1228 $  |         |         |
1229 $  7---15----8---16----9
1230 $  |         |         |
1231 $  |         |         |
1232 $ 19    0   21    1   23
1233 $  |         |         |
1234 $  |         |         |
1235 $  4---13----5---14----6
1236 
1237 and for simplicial cells
1238 
1239 $ 14----8---15----9----16
1240 $  |\     5  |\      7 |
1241 $  | \       | \       |
1242 $ 13   2    14    3    15
1243 $  | 4   \   | 6   \   |
1244 $  |       \ |       \ |
1245 $ 11----6---12----7----13
1246 $  |\        |\        |
1247 $  | \    1  | \     3 |
1248 $ 10   0    11    1    12
1249 $  | 0   \   | 2   \   |
1250 $  |       \ |       \ |
1251 $  8----4----9----5----10
1252 
1253   Level: beginner
1254 
1255 .seealso: DMSetFromOptions(), DMPlexCreateFromFile(), DMPlexCreateHexCylinderMesh(), DMSetType(), DMCreate()
1256 @*/
1257 PetscErrorCode DMPlexCreateBoxMesh(MPI_Comm comm, PetscInt dim, PetscBool simplex, const PetscInt faces[], const PetscReal lower[], const PetscReal upper[], const DMBoundaryType periodicity[], PetscBool interpolate, DM *dm)
1258 {
1259   PetscInt       fac[3] = {1, 1, 1};
1260   PetscReal      low[3] = {0, 0, 0};
1261   PetscReal      upp[3] = {1, 1, 1};
1262   DMBoundaryType bdt[3] = {DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE};
1263   PetscErrorCode ierr;
1264 
1265   PetscFunctionBegin;
1266   ierr = DMCreate(comm,dm);CHKERRQ(ierr);
1267   ierr = DMSetType(*dm,DMPLEX);CHKERRQ(ierr);
1268   ierr = DMPlexCreateBoxMesh_Internal(*dm, dim, simplex, faces ? faces : fac, lower ? lower : low, upper ? upper : upp, periodicity ? periodicity : bdt, interpolate);CHKERRQ(ierr);
1269   PetscFunctionReturn(0);
1270 }
1271 
1272 static PetscErrorCode DMPlexCreateWedgeBoxMesh_Internal(DM dm, const PetscInt faces[], const PetscReal lower[], const PetscReal upper[], const DMBoundaryType periodicity[], 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] = -1; 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] = -1; 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] = -1; ornt[1] = -1; ornt[2] = 0; ornt[3] = -1;
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] = -1; ornt[1] = -1; ornt[2] = -1; 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] = -1; ornt[1] = -1; ornt[2] = -1; ornt[3] = -1;
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_POINT_PRISM_TENSOR:
2505     {
2506       PetscInt    numPoints[2]        = {2, 1};
2507       PetscInt    coneSize[3]         = {2, 0, 0};
2508       PetscInt    cones[2]            = {1, 2};
2509       PetscInt    coneOrientations[2] = {0, 0};
2510       PetscScalar vertexCoords[2]     = {-1.0,  1.0};
2511 
2512       ierr = DMSetDimension(rdm, 1);CHKERRQ(ierr);
2513       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2514     }
2515     break;
2516     case DM_POLYTOPE_TRIANGLE:
2517     {
2518       PetscInt    numPoints[2]        = {3, 1};
2519       PetscInt    coneSize[4]         = {3, 0, 0, 0};
2520       PetscInt    cones[3]            = {1, 2, 3};
2521       PetscInt    coneOrientations[3] = {0, 0, 0};
2522       PetscScalar vertexCoords[6]     = {-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_QUADRILATERAL:
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_SEG_PRISM_TENSOR:
2541     {
2542       PetscInt    numPoints[2]        = {4, 1};
2543       PetscInt    coneSize[5]         = {4, 0, 0, 0, 0};
2544       PetscInt    cones[4]            = {1, 2, 3, 4};
2545       PetscInt    coneOrientations[4] = {0, 0, 0, 0};
2546       PetscScalar vertexCoords[8]     = {-1.0, -1.0,  1.0, -1.0,  -1.0, 1.0,  1.0, 1.0};
2547 
2548       ierr = DMSetDimension(rdm, 2);CHKERRQ(ierr);
2549       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2550     }
2551     break;
2552     case DM_POLYTOPE_TETRAHEDRON:
2553     {
2554       PetscInt    numPoints[2]        = {4, 1};
2555       PetscInt    coneSize[5]         = {4, 0, 0, 0, 0};
2556       PetscInt    cones[4]            = {1, 2, 3, 4};
2557       PetscInt    coneOrientations[4] = {0, 0, 0, 0};
2558       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};
2559 
2560       ierr = DMSetDimension(rdm, 3);CHKERRQ(ierr);
2561       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2562     }
2563     break;
2564     case DM_POLYTOPE_HEXAHEDRON:
2565     {
2566       PetscInt    numPoints[2]        = {8, 1};
2567       PetscInt    coneSize[9]         = {8, 0, 0, 0, 0, 0, 0, 0, 0};
2568       PetscInt    cones[8]            = {1, 2, 3, 4, 5, 6, 7, 8};
2569       PetscInt    coneOrientations[8] = {0, 0, 0, 0, 0, 0, 0, 0};
2570       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,
2571                                          -1.0, -1.0,  1.0,   1.0, -1.0,  1.0,  1.0, 1.0,  1.0,  -1.0,  1.0,  1.0};
2572 
2573       ierr = DMSetDimension(rdm, 3);CHKERRQ(ierr);
2574       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2575     }
2576     break;
2577     case DM_POLYTOPE_TRI_PRISM:
2578     {
2579       PetscInt    numPoints[2]        = {6, 1};
2580       PetscInt    coneSize[7]         = {6, 0, 0, 0, 0, 0, 0};
2581       PetscInt    cones[6]            = {1, 2, 3, 4, 5, 6};
2582       PetscInt    coneOrientations[6] = {0, 0, 0, 0, 0, 0};
2583       PetscScalar vertexCoords[18]    = {-1.0, -1.0, -1.0, -1.0,  1.0, -1.0,   1.0, -1.0, -1.0,
2584                                          -1.0, -1.0,  1.0,  1.0, -1.0,  1.0,  -1.0,  1.0,  1.0};
2585 
2586       ierr = DMSetDimension(rdm, 3);CHKERRQ(ierr);
2587       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2588     }
2589     break;
2590     case DM_POLYTOPE_TRI_PRISM_TENSOR:
2591     {
2592       PetscInt    numPoints[2]        = {6, 1};
2593       PetscInt    coneSize[7]         = {6, 0, 0, 0, 0, 0, 0};
2594       PetscInt    cones[6]            = {1, 2, 3, 4, 5, 6};
2595       PetscInt    coneOrientations[6] = {0, 0, 0, 0, 0, 0};
2596       PetscScalar vertexCoords[18]    = {-1.0, -1.0, -1.0,  1.0, -1.0, -1.0,  -1.0, 1.0, -1.0,
2597                                          -1.0, -1.0,  1.0,  1.0, -1.0,  1.0,  -1.0, 1.0,  1.0};
2598 
2599       ierr = DMSetDimension(rdm, 3);CHKERRQ(ierr);
2600       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2601     }
2602     break;
2603     case DM_POLYTOPE_QUAD_PRISM_TENSOR:
2604     {
2605       PetscInt    numPoints[2]        = {8, 1};
2606       PetscInt    coneSize[9]         = {8, 0, 0, 0, 0, 0, 0, 0, 0};
2607       PetscInt    cones[8]            = {1, 2, 3, 4, 5, 6, 7, 8};
2608       PetscInt    coneOrientations[8] = {0, 0, 0, 0, 0, 0, 0, 0};
2609       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,
2610                                          -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 
2612       ierr = DMSetDimension(rdm, 3);CHKERRQ(ierr);
2613       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2614     }
2615     break;
2616     case DM_POLYTOPE_PYRAMID:
2617     {
2618       PetscInt    numPoints[2]        = {5, 1};
2619       PetscInt    coneSize[6]         = {5, 0, 0, 0, 0, 0};
2620       PetscInt    cones[5]            = {1, 2, 3, 4, 5};
2621       PetscInt    coneOrientations[8] = {0, 0, 0, 0, 0, 0, 0, 0};
2622       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,
2623                                           0.0,  0.0,  1.0};
2624 
2625       ierr = DMSetDimension(rdm, 3);CHKERRQ(ierr);
2626       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2627     }
2628     break;
2629     default: SETERRQ1(PetscObjectComm((PetscObject) rdm), PETSC_ERR_ARG_WRONG, "Cannot create reference cell for cell type %s", DMPolytopeTypes[ct]);
2630   }
2631   {
2632     PetscInt Nv, v;
2633 
2634     /* Must create the celltype label here so that we do not automatically try to compute the types */
2635     ierr = DMCreateLabel(rdm, "celltype");CHKERRQ(ierr);
2636     ierr = DMPlexSetCellType(rdm, 0, ct);CHKERRQ(ierr);
2637     ierr = DMPlexGetChart(rdm, NULL, &Nv);CHKERRQ(ierr);
2638     for (v = 1; v < Nv; ++v) {ierr = DMPlexSetCellType(rdm, v, DM_POLYTOPE_POINT);CHKERRQ(ierr);}
2639   }
2640   ierr = DMPlexInterpolateInPlace_Internal(rdm);CHKERRQ(ierr);
2641   ierr = PetscObjectSetName((PetscObject) rdm, DMPolytopeTypes[ct]);CHKERRQ(ierr);
2642   PetscFunctionReturn(0);
2643 }
2644 
2645 /*@
2646   DMPlexCreateReferenceCell - Create a DMPLEX with the appropriate FEM reference cell
2647 
2648   Collective
2649 
2650   Input Parameters:
2651 + comm - The communicator
2652 - ct   - The cell type of the reference cell
2653 
2654   Output Parameter:
2655 . refdm - The reference cell
2656 
2657   Level: intermediate
2658 
2659 .seealso: DMPlexCreateReferenceCell(), DMPlexCreateBoxMesh()
2660 @*/
2661 PetscErrorCode DMPlexCreateReferenceCell(MPI_Comm comm, DMPolytopeType ct, DM *refdm)
2662 {
2663   PetscErrorCode ierr;
2664 
2665   PetscFunctionBegin;
2666   ierr = DMCreate(comm, refdm);CHKERRQ(ierr);
2667   ierr = DMSetType(*refdm, DMPLEX);CHKERRQ(ierr);
2668   ierr = DMPlexCreateReferenceCell_Internal(*refdm, ct);CHKERRQ(ierr);
2669   PetscFunctionReturn(0);
2670 }
2671 
2672 static PetscErrorCode DMPlexCreateBoundaryLabel_Private(DM dm, const char name[])
2673 {
2674   DM             plex;
2675   DMLabel        label;
2676   PetscBool      hasLabel;
2677   PetscErrorCode ierr;
2678 
2679   PetscFunctionBeginUser;
2680   ierr = DMHasLabel(dm, name, &hasLabel);CHKERRQ(ierr);
2681   if (hasLabel) PetscFunctionReturn(0);
2682   ierr = DMCreateLabel(dm, name);CHKERRQ(ierr);
2683   ierr = DMGetLabel(dm, name, &label);CHKERRQ(ierr);
2684   ierr = DMConvert(dm, DMPLEX, &plex);CHKERRQ(ierr);
2685   ierr = DMPlexMarkBoundaryFaces(plex, 1, label);CHKERRQ(ierr);
2686   ierr = DMDestroy(&plex);CHKERRQ(ierr);
2687   PetscFunctionReturn(0);
2688 }
2689 
2690 const char * const DMPlexShapes[] = {"box", "box_surface", "ball", "sphere", "cylinder", "unknown", "DMPlexShape", "DM_SHAPE_", NULL};
2691 
2692 static PetscErrorCode DMPlexCreateFromOptions_Internal(PetscOptionItems *PetscOptionsObject, PetscBool *useCoordSpace, DM dm)
2693 {
2694   DMPlexShape    shape = DM_SHAPE_BOX;
2695   DMPolytopeType cell  = DM_POLYTOPE_TRIANGLE;
2696   PetscInt       dim   = 2;
2697   PetscBool      simplex = PETSC_TRUE, interpolate = PETSC_TRUE, adjCone = PETSC_FALSE, adjClosure = PETSC_TRUE, refDomain = PETSC_FALSE;
2698   PetscBool      flg, flg2, fflg, bdfflg;
2699   MPI_Comm       comm;
2700   char           filename[PETSC_MAX_PATH_LEN], bdFilename[PETSC_MAX_PATH_LEN];
2701   PetscErrorCode ierr;
2702 
2703   PetscFunctionBegin;
2704   ierr = PetscObjectGetComm((PetscObject) dm, &comm);CHKERRQ(ierr);
2705   /* TODO Turn this into a registration interface */
2706   ierr = PetscOptionsString("-dm_plex_filename", "File containing a mesh", "DMPlexCreateFromFile", filename, filename, sizeof(filename), &fflg);CHKERRQ(ierr);
2707   ierr = PetscOptionsString("-dm_plex_boundary_filename", "File containing a mesh boundary", "DMPlexCreateFromFile", bdFilename, bdFilename, sizeof(bdFilename), &bdfflg);CHKERRQ(ierr);
2708   ierr = PetscOptionsEnum("-dm_plex_cell", "Cell shape", "", DMPolytopeTypes, (PetscEnum) cell, (PetscEnum *) &cell, NULL);CHKERRQ(ierr);
2709   ierr = PetscOptionsBool("-dm_plex_reference_cell_domain", "Use a reference cell domain", "", refDomain, &refDomain, NULL);CHKERRQ(ierr);
2710   ierr = PetscOptionsEnum("-dm_plex_shape", "Shape for built-in mesh", "", DMPlexShapes, (PetscEnum) shape, (PetscEnum *) &shape, &flg);CHKERRQ(ierr);
2711   ierr = PetscOptionsBoundedInt("-dm_plex_dim", "Topological dimension of the mesh", "DMGetDimension", dim, &dim, &flg, 0);CHKERRQ(ierr);
2712   if ((dim < 0) || (dim > 3)) SETERRQ1(comm, PETSC_ERR_ARG_OUTOFRANGE, "Dimension %D should be in [1, 3]", dim);
2713   ierr = PetscOptionsBool("-dm_plex_simplex", "Mesh cell shape", "", simplex,  &simplex, &flg);CHKERRQ(ierr);
2714   ierr = PetscOptionsBool("-dm_plex_interpolate", "Flag to create edges and faces automatically", "", interpolate, &interpolate, &flg);CHKERRQ(ierr);
2715   ierr = PetscOptionsBool("-dm_plex_adj_cone", "Set adjacency direction", "DMSetBasicAdjacency", adjCone,  &adjCone, &flg);CHKERRQ(ierr);
2716   ierr = PetscOptionsBool("-dm_plex_adj_closure", "Set adjacency size", "DMSetBasicAdjacency", adjClosure,  &adjClosure, &flg2);CHKERRQ(ierr);
2717   if (flg || flg2) {ierr = DMSetBasicAdjacency(dm, adjCone, adjClosure);CHKERRQ(ierr);}
2718 
2719   switch (cell) {
2720     case DM_POLYTOPE_POINT:
2721     case DM_POLYTOPE_SEGMENT:
2722     case DM_POLYTOPE_POINT_PRISM_TENSOR:
2723     case DM_POLYTOPE_TRIANGLE:
2724     case DM_POLYTOPE_QUADRILATERAL:
2725     case DM_POLYTOPE_TETRAHEDRON:
2726     case DM_POLYTOPE_HEXAHEDRON:
2727       *useCoordSpace = PETSC_TRUE;break;
2728     default: *useCoordSpace = PETSC_FALSE;break;
2729   }
2730 
2731   if (fflg) {
2732     DM dmnew;
2733 
2734     ierr = DMPlexCreateFromFile(PetscObjectComm((PetscObject) dm), filename, interpolate, &dmnew);CHKERRQ(ierr);
2735     ierr = DMPlexReplace_Static(dm, &dmnew);CHKERRQ(ierr);
2736   } else if (refDomain) {
2737     ierr = DMPlexCreateReferenceCell_Internal(dm, cell);CHKERRQ(ierr);
2738   } else if (bdfflg) {
2739     DM bdm, dmnew;
2740 
2741     ierr = DMPlexCreateFromFile(PetscObjectComm((PetscObject) dm), bdFilename, interpolate, &bdm);CHKERRQ(ierr);
2742     ierr = PetscObjectSetOptionsPrefix((PetscObject) bdm, "bd_");CHKERRQ(ierr);
2743     ierr = DMSetFromOptions(bdm);CHKERRQ(ierr);
2744     ierr = DMPlexGenerate(bdm, NULL, interpolate, &dmnew);CHKERRQ(ierr);
2745     ierr = DMDestroy(&bdm);CHKERRQ(ierr);
2746     ierr = DMPlexReplace_Static(dm, &dmnew);CHKERRQ(ierr);
2747   } else {
2748     ierr = PetscObjectSetName((PetscObject) dm, DMPlexShapes[shape]);CHKERRQ(ierr);
2749     switch (shape) {
2750       case DM_SHAPE_BOX:
2751       {
2752         PetscInt       faces[3] = {0, 0, 0};
2753         PetscReal      lower[3] = {0, 0, 0};
2754         PetscReal      upper[3] = {1, 1, 1};
2755         DMBoundaryType bdt[3]   = {DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE};
2756         PetscInt       i, n;
2757 
2758         n    = dim;
2759         for (i = 0; i < dim; ++i) faces[i] = (dim == 1 ? 1 : 4-dim);
2760         ierr = PetscOptionsIntArray("-dm_plex_box_faces", "Number of faces along each dimension", "", faces, &n, &flg);CHKERRQ(ierr);
2761         n    = 3;
2762         ierr = PetscOptionsRealArray("-dm_plex_box_lower", "Lower left corner of box", "", lower, &n, &flg);CHKERRQ(ierr);
2763         if (flg && (n != dim)) SETERRQ2(comm, PETSC_ERR_ARG_SIZ, "Lower box point had %D values, should have been %D", n, dim);
2764         n    = 3;
2765         ierr = PetscOptionsRealArray("-dm_plex_box_upper", "Upper right corner of box", "", upper, &n, &flg);CHKERRQ(ierr);
2766         if (flg && (n != dim)) SETERRQ2(comm, PETSC_ERR_ARG_SIZ, "Upper box point had %D values, should have been %D", n, dim);
2767         n    = 3;
2768         ierr = PetscOptionsEnumArray("-dm_plex_box_bd", "Boundary type for each dimension", "", DMBoundaryTypes, (PetscEnum *) bdt, &n, &flg);CHKERRQ(ierr);
2769         if (flg && (n != dim)) SETERRQ2(comm, PETSC_ERR_ARG_SIZ, "Box boundary types had %D values, should have been %D", n, dim);
2770         switch (cell) {
2771           case DM_POLYTOPE_TRI_PRISM_TENSOR:
2772             ierr = DMPlexCreateWedgeBoxMesh_Internal(dm, faces, lower, upper, bdt, PETSC_FALSE, interpolate);CHKERRQ(ierr);
2773             break;
2774           default:
2775             ierr = DMPlexCreateBoxMesh_Internal(dm, dim, simplex, faces, lower, upper, bdt, interpolate);CHKERRQ(ierr);
2776             break;
2777         }
2778       }
2779       break;
2780       case DM_SHAPE_BOX_SURFACE:
2781       {
2782         PetscInt  faces[3] = {0, 0, 0};
2783         PetscReal lower[3] = {0, 0, 0};
2784         PetscReal upper[3] = {1, 1, 1};
2785         PetscInt  i, n;
2786 
2787         n    = dim+1;
2788         for (i = 0; i < dim+1; ++i) faces[i] = (dim+1 == 1 ? 1 : 4-(dim+1));
2789         ierr = PetscOptionsIntArray("-dm_plex_box_faces", "Number of faces along each dimension", "", faces, &n, &flg);CHKERRQ(ierr);
2790         n    = 3;
2791         ierr = PetscOptionsRealArray("-dm_plex_box_lower", "Lower left corner of box", "", lower, &n, &flg);CHKERRQ(ierr);
2792         if (flg && (n != dim+1)) SETERRQ2(comm, PETSC_ERR_ARG_SIZ, "Lower box point had %D values, should have been %D", n, dim+1);
2793         n    = 3;
2794         ierr = PetscOptionsRealArray("-dm_plex_box_upper", "Upper right corner of box", "", upper, &n, &flg);CHKERRQ(ierr);
2795         if (flg && (n != dim+1)) SETERRQ2(comm, PETSC_ERR_ARG_SIZ, "Upper box point had %D values, should have been %D", n, dim+1);
2796         ierr = DMPlexCreateBoxSurfaceMesh_Internal(dm, dim+1, faces, lower, upper, interpolate);CHKERRQ(ierr);
2797       }
2798       break;
2799       case DM_SHAPE_SPHERE:
2800       {
2801         PetscReal R = 1.0;
2802 
2803         ierr = PetscOptionsReal("-dm_plex_sphere_radius", "Radius of the sphere", "", R,  &R, &flg);CHKERRQ(ierr);
2804         ierr = DMPlexCreateSphereMesh_Internal(dm, dim, simplex, R);CHKERRQ(ierr);
2805       }
2806       break;
2807       case DM_SHAPE_BALL:
2808       {
2809         PetscReal R = 1.0;
2810 
2811         ierr = PetscOptionsReal("-dm_plex_ball_radius", "Radius of the ball", "", R,  &R, &flg);CHKERRQ(ierr);
2812         ierr = DMPlexCreateBallMesh_Internal(dm, dim, R);CHKERRQ(ierr);
2813       }
2814       break;
2815       case DM_SHAPE_CYLINDER:
2816       {
2817         DMBoundaryType bdt = DM_BOUNDARY_NONE;
2818         PetscInt       Nw  = 6;
2819 
2820         ierr = PetscOptionsEnum("-dm_plex_cylinder_bd", "Boundary type in the z direction", "", DMBoundaryTypes, (PetscEnum) bdt, (PetscEnum *) &bdt, NULL);CHKERRQ(ierr);
2821         ierr = PetscOptionsInt("-dm_plex_cylinder_num_wedges", "Number of wedges around the cylinder", "", Nw, &Nw, NULL);CHKERRQ(ierr);
2822         switch (cell) {
2823           case DM_POLYTOPE_TRI_PRISM_TENSOR:
2824             ierr = DMPlexCreateWedgeCylinderMesh_Internal(dm, Nw, interpolate);CHKERRQ(ierr);
2825             break;
2826           default:
2827             ierr = DMPlexCreateHexCylinderMesh_Internal(dm, bdt);CHKERRQ(ierr);
2828             break;
2829         }
2830       }
2831       break;
2832       default: SETERRQ1(comm, PETSC_ERR_SUP, "Domain shape %s is unsupported", DMPlexShapes[shape]);
2833     }
2834   }
2835   ierr = DMPlexSetRefinementUniform(dm, PETSC_TRUE);CHKERRQ(ierr);
2836   PetscFunctionReturn(0);
2837 }
2838 
2839 PetscErrorCode DMSetFromOptions_NonRefinement_Plex(PetscOptionItems *PetscOptionsObject, DM dm)
2840 {
2841   DM_Plex       *mesh = (DM_Plex*) dm->data;
2842   PetscBool      flg;
2843   char           bdLabel[PETSC_MAX_PATH_LEN];
2844   PetscErrorCode ierr;
2845 
2846   PetscFunctionBegin;
2847   /* Handle viewing */
2848   ierr = PetscOptionsBool("-dm_plex_print_set_values", "Output all set values info", "DMPlexMatSetClosure", PETSC_FALSE, &mesh->printSetValues, NULL);CHKERRQ(ierr);
2849   ierr = PetscOptionsBoundedInt("-dm_plex_print_fem", "Debug output level all fem computations", "DMPlexSNESComputeResidualFEM", 0, &mesh->printFEM, NULL,0);CHKERRQ(ierr);
2850   ierr = PetscOptionsReal("-dm_plex_print_tol", "Tolerance for FEM output", "DMPlexSNESComputeResidualFEM", mesh->printTol, &mesh->printTol, NULL);CHKERRQ(ierr);
2851   ierr = PetscOptionsBoundedInt("-dm_plex_print_l2", "Debug output level all L2 diff computations", "DMComputeL2Diff", 0, &mesh->printL2, NULL,0);CHKERRQ(ierr);
2852   ierr = DMMonitorSetFromOptions(dm, "-dm_plex_monitor_throughput", "Monitor the simulation throughput", "DMPlexMonitorThroughput", DMPlexMonitorThroughput, NULL, &flg);CHKERRQ(ierr);
2853   if (flg) {ierr = PetscLogDefaultBegin();CHKERRQ(ierr);}
2854   /* Labeling */
2855   ierr = PetscOptionsString("-dm_plex_boundary_label", "Label to mark the mesh boundary", "", bdLabel, bdLabel, sizeof(bdLabel), &flg);CHKERRQ(ierr);
2856   if (flg) {ierr = DMPlexCreateBoundaryLabel_Private(dm, bdLabel);CHKERRQ(ierr);}
2857   /* Point Location */
2858   ierr = PetscOptionsBool("-dm_plex_hash_location", "Use grid hashing for point location", "DMInterpolate", PETSC_FALSE, &mesh->useHashLocation, NULL);CHKERRQ(ierr);
2859   /* Partitioning and distribution */
2860   ierr = PetscOptionsBool("-dm_plex_partition_balance", "Attempt to evenly divide points on partition boundary between processes", "DMPlexSetPartitionBalance", PETSC_FALSE, &mesh->partitionBalance, NULL);CHKERRQ(ierr);
2861   /* Generation and remeshing */
2862   ierr = PetscOptionsBool("-dm_plex_remesh_bd", "Allow changes to the boundary on remeshing", "DMAdapt", PETSC_FALSE, &mesh->remeshBd, NULL);CHKERRQ(ierr);
2863   /* Projection behavior */
2864   ierr = PetscOptionsBoundedInt("-dm_plex_max_projection_height", "Maxmimum mesh point height used to project locally", "DMPlexSetMaxProjectionHeight", 0, &mesh->maxProjectionHeight, NULL,0);CHKERRQ(ierr);
2865   ierr = PetscOptionsBool("-dm_plex_regular_refinement", "Use special nested projection algorithm for regular refinement", "DMPlexSetRegularRefinement", mesh->regularRefinement, &mesh->regularRefinement, NULL);CHKERRQ(ierr);
2866   /* Checking structure */
2867   {
2868     PetscBool   flg = PETSC_FALSE, flg2 = PETSC_FALSE, all = PETSC_FALSE;
2869 
2870     ierr = PetscOptionsBool("-dm_plex_check_all", "Perform all checks", NULL, PETSC_FALSE, &all, &flg2);CHKERRQ(ierr);
2871     ierr = PetscOptionsBool("-dm_plex_check_symmetry", "Check that the adjacency information in the mesh is symmetric", "DMPlexCheckSymmetry", PETSC_FALSE, &flg, &flg2);CHKERRQ(ierr);
2872     if (all || (flg && flg2)) {ierr = DMPlexCheckSymmetry(dm);CHKERRQ(ierr);}
2873     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);
2874     if (all || (flg && flg2)) {ierr = DMPlexCheckSkeleton(dm, 0);CHKERRQ(ierr);}
2875     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);
2876     if (all || (flg && flg2)) {ierr = DMPlexCheckFaces(dm, 0);CHKERRQ(ierr);}
2877     ierr = PetscOptionsBool("-dm_plex_check_geometry", "Check that cells have positive volume", "DMPlexCheckGeometry", PETSC_FALSE, &flg, &flg2);CHKERRQ(ierr);
2878     if (all || (flg && flg2)) {ierr = DMPlexCheckGeometry(dm);CHKERRQ(ierr);}
2879     ierr = PetscOptionsBool("-dm_plex_check_pointsf", "Check some necessary conditions for PointSF", "DMPlexCheckPointSF", PETSC_FALSE, &flg, &flg2);CHKERRQ(ierr);
2880     if (all || (flg && flg2)) {ierr = DMPlexCheckPointSF(dm);CHKERRQ(ierr);}
2881     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);
2882     if (all || (flg && flg2)) {ierr = DMPlexCheckInterfaceCones(dm);CHKERRQ(ierr);}
2883     ierr = PetscOptionsBool("-dm_plex_check_cell_shape", "Check cell shape", "DMPlexCheckCellShape", PETSC_FALSE, &flg, &flg2);CHKERRQ(ierr);
2884     if (flg && flg2) {ierr = DMPlexCheckCellShape(dm, PETSC_TRUE, PETSC_DETERMINE);CHKERRQ(ierr);}
2885   }
2886   {
2887     PetscReal scale = 1.0;
2888 
2889     ierr = PetscOptionsReal("-dm_plex_scale", "Scale factor for mesh coordinates", "DMPlexScale", scale, &scale, &flg);CHKERRQ(ierr);
2890     if (flg) {
2891       Vec coordinates, coordinatesLocal;
2892 
2893       ierr = DMGetCoordinates(dm, &coordinates);CHKERRQ(ierr);
2894       ierr = DMGetCoordinatesLocal(dm, &coordinatesLocal);CHKERRQ(ierr);
2895       ierr = VecScale(coordinates, scale);CHKERRQ(ierr);
2896       ierr = VecScale(coordinatesLocal, scale);CHKERRQ(ierr);
2897     }
2898   }
2899   ierr = PetscPartitionerSetFromOptions(mesh->partitioner);CHKERRQ(ierr);
2900   PetscFunctionReturn(0);
2901 }
2902 
2903 static PetscErrorCode DMSetFromOptions_Plex(PetscOptionItems *PetscOptionsObject,DM dm)
2904 {
2905   PetscReal      volume = -1.0, extThickness = 1.0;
2906   PetscInt       prerefine = 0, refine = 0, r, coarsen = 0, overlap = 0, extLayers = 0, dim;
2907   PetscBool      uniformOrig, created = PETSC_FALSE, uniform = PETSC_TRUE, distribute = PETSC_FALSE, interpolate = PETSC_TRUE, extColOrder = PETSC_TRUE, coordSpace = PETSC_TRUE, remap = PETSC_TRUE, ghostCells = PETSC_FALSE, isHierarchy, ignoreModel = PETSC_FALSE, flg;
2908   PetscErrorCode ierr;
2909 
2910   PetscFunctionBegin;
2911   PetscValidHeaderSpecific(dm, DM_CLASSID, 2);
2912   ierr = PetscOptionsHead(PetscOptionsObject,"DMPlex Options");CHKERRQ(ierr);
2913   /* Handle automatic creation */
2914   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
2915   if (dim < 0) {ierr = DMPlexCreateFromOptions_Internal(PetscOptionsObject, &coordSpace, dm);CHKERRQ(ierr);created = PETSC_TRUE;}
2916   /* Handle interpolation before distribution */
2917   ierr = PetscOptionsBool("-dm_plex_interpolate_pre", "Flag to interpolate mesh before distribution", "", interpolate, &interpolate, &flg);CHKERRQ(ierr);
2918   if (flg) {
2919     DMPlexInterpolatedFlag interpolated;
2920 
2921     ierr = DMPlexIsInterpolated(dm, &interpolated);CHKERRQ(ierr);
2922     if (interpolated == DMPLEX_INTERPOLATED_FULL && !interpolate) {
2923       DM udm;
2924 
2925       ierr = DMPlexUninterpolate(dm, &udm);CHKERRQ(ierr);
2926       ierr = DMPlexReplace_Static(dm, &udm);CHKERRQ(ierr);
2927     } else if (interpolated != DMPLEX_INTERPOLATED_FULL && interpolate) {
2928       DM idm;
2929 
2930       ierr = DMPlexInterpolate(dm, &idm);CHKERRQ(ierr);
2931       ierr = DMPlexReplace_Static(dm, &idm);CHKERRQ(ierr);
2932     }
2933   }
2934   /* Handle DMPlex refinement before distribution */
2935   ierr = PetscOptionsBool("-dm_refine_ignore_model", "Flag to ignore the geometry model when refining", "DMCreate", ignoreModel, &ignoreModel, &flg);CHKERRQ(ierr);
2936   if (flg) {((DM_Plex *) dm->data)->ignoreModel = ignoreModel;}
2937   ierr = DMPlexGetRefinementUniform(dm, &uniformOrig);CHKERRQ(ierr);
2938   ierr = PetscOptionsBoundedInt("-dm_refine_pre", "The number of refinements before distribution", "DMCreate", prerefine, &prerefine, NULL,0);CHKERRQ(ierr);
2939   ierr = PetscOptionsBool("-dm_refine_remap_pre", "Flag to control coordinate remapping", "DMCreate", remap, &remap, NULL);CHKERRQ(ierr);
2940   ierr = PetscOptionsBool("-dm_refine_uniform_pre", "Flag for uniform refinement before distribution", "DMCreate", uniform, &uniform, &flg);CHKERRQ(ierr);
2941   if (flg) {ierr = DMPlexSetRefinementUniform(dm, uniform);CHKERRQ(ierr);}
2942   ierr = PetscOptionsReal("-dm_refine_volume_limit_pre", "The maximum cell volume after refinement before distribution", "DMCreate", volume, &volume, &flg);CHKERRQ(ierr);
2943   if (flg) {
2944     ierr = DMPlexSetRefinementUniform(dm, PETSC_FALSE);CHKERRQ(ierr);
2945     ierr = DMPlexSetRefinementLimit(dm, volume);CHKERRQ(ierr);
2946     prerefine = PetscMax(prerefine, 1);
2947   }
2948   for (r = 0; r < prerefine; ++r) {
2949     DM             rdm;
2950     PetscPointFunc coordFunc = ((DM_Plex*) dm->data)->coordFunc;
2951 
2952     ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2953     ierr = DMRefine(dm, PetscObjectComm((PetscObject) dm), &rdm);CHKERRQ(ierr);
2954     ierr = DMPlexReplace_Static(dm, &rdm);CHKERRQ(ierr);
2955     ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2956     if (coordFunc && remap) {
2957       ierr = DMPlexRemapGeometry(dm, 0.0, coordFunc);CHKERRQ(ierr);
2958       ((DM_Plex*) dm->data)->coordFunc = coordFunc;
2959     }
2960   }
2961   ierr = DMPlexSetRefinementUniform(dm, uniformOrig);CHKERRQ(ierr);
2962   /* Handle DMPlex extrusion before distribution */
2963   ierr = PetscOptionsBool("-dm_plex_interpolate", "Flag to create edges and faces automatically", "", interpolate, &interpolate, NULL);CHKERRQ(ierr);
2964   ierr = PetscOptionsBoundedInt("-dm_extrude_layers", "The number of layers to extrude", "", extLayers, &extLayers, NULL, 0);CHKERRQ(ierr);
2965   ierr = PetscOptionsReal("-dm_extrude_thickness", "The thickness of the layer to be extruded", "", extThickness, &extThickness, NULL);CHKERRQ(ierr);
2966   ierr = PetscOptionsBool("-dm_extrude_column_first", "Order the cells in a vertical column first", "", extColOrder, &extColOrder, NULL);CHKERRQ(ierr);
2967   if (extLayers) {
2968     DM edm;
2969 
2970     ierr = DMPlexExtrude(dm, extLayers, extThickness, extColOrder, NULL, interpolate, &edm);CHKERRQ(ierr);
2971     ierr = DMPlexReplace_Static(dm, &edm);CHKERRQ(ierr);
2972   }
2973   /* Handle DMPlex distribution */
2974   ierr = PetscOptionsBool("-dm_distribute", "Flag to redistribute a mesh among processes", "DMCreate", distribute, &distribute, NULL);CHKERRQ(ierr);
2975   ierr = PetscOptionsBoundedInt("-dm_distribute_overlap", "The size of the overlap halo", "DMCreate", overlap, &overlap, NULL, 0);CHKERRQ(ierr);
2976   if (distribute) {
2977     DM               pdm = NULL;
2978     PetscPartitioner part;
2979 
2980     ierr = DMPlexGetPartitioner(dm, &part);CHKERRQ(ierr);
2981     ierr = PetscPartitionerSetFromOptions(part);CHKERRQ(ierr);
2982     ierr = DMPlexDistribute(dm, overlap, NULL, &pdm);CHKERRQ(ierr);
2983     if (pdm) {
2984       ierr = DMPlexReplace_Static(dm, &pdm);CHKERRQ(ierr);
2985     }
2986   }
2987   /* Create coordinate space */
2988   if (created) {
2989     DM_Plex  *mesh = (DM_Plex *) dm->data;
2990     PetscInt  degree = 1;
2991     PetscBool periodic, flg;
2992 
2993     ierr = PetscOptionsBool("-dm_coord_space", "Use an FEM space for coordinates", "", coordSpace, &coordSpace, &flg);CHKERRQ(ierr);
2994     ierr = PetscOptionsInt("-dm_coord_petscspace_degree", "FEM degree for coordinate space", "", degree, &degree, NULL);CHKERRQ(ierr);
2995     if (coordSpace) {ierr = DMPlexCreateCoordinateSpace(dm, degree, mesh->coordFunc);CHKERRQ(ierr);}
2996     if (flg && !coordSpace) {
2997       DM           cdm;
2998       PetscDS      cds;
2999       PetscObject  obj;
3000       PetscClassId id;
3001 
3002       ierr = DMGetCoordinateDM(dm, &cdm);CHKERRQ(ierr);
3003       ierr = DMGetDS(cdm, &cds);CHKERRQ(ierr);
3004       ierr = PetscDSGetDiscretization(cds, 0, &obj);CHKERRQ(ierr);
3005       ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
3006       if (id == PETSCFE_CLASSID) {
3007         PetscContainer dummy;
3008 
3009         ierr = PetscContainerCreate(PETSC_COMM_SELF, &dummy);CHKERRQ(ierr);
3010         ierr = PetscObjectSetName((PetscObject) dummy, "coordinates");CHKERRQ(ierr);
3011         ierr = DMSetField(cdm, 0, NULL, (PetscObject) dummy);CHKERRQ(ierr);
3012         ierr = PetscContainerDestroy(&dummy);CHKERRQ(ierr);
3013         ierr = DMClearDS(cdm);CHKERRQ(ierr);
3014       }
3015       mesh->coordFunc = NULL;
3016     }
3017     ierr = DMLocalizeCoordinates(dm);CHKERRQ(ierr);
3018     ierr = DMGetPeriodicity(dm, &periodic, NULL, NULL, NULL);CHKERRQ(ierr);
3019     if (periodic) {ierr = DMSetPeriodicity(dm, PETSC_TRUE, NULL, NULL, NULL);CHKERRQ(ierr);}
3020   }
3021   /* Handle DMPlex refinement */
3022   remap = PETSC_TRUE;
3023   ierr = PetscOptionsBoundedInt("-dm_refine", "The number of uniform refinements", "DMCreate", refine, &refine, NULL,0);CHKERRQ(ierr);
3024   ierr = PetscOptionsBool("-dm_refine_remap", "Flag to control coordinate remapping", "DMCreate", remap, &remap, NULL);CHKERRQ(ierr);
3025   ierr = PetscOptionsBoundedInt("-dm_refine_hierarchy", "The number of uniform refinements", "DMCreate", refine, &refine, &isHierarchy,0);CHKERRQ(ierr);
3026   if (refine) {ierr = DMPlexSetRefinementUniform(dm, PETSC_TRUE);CHKERRQ(ierr);}
3027   if (refine && isHierarchy) {
3028     DM *dms, coarseDM;
3029 
3030     ierr = DMGetCoarseDM(dm, &coarseDM);CHKERRQ(ierr);
3031     ierr = PetscObjectReference((PetscObject)coarseDM);CHKERRQ(ierr);
3032     ierr = PetscMalloc1(refine,&dms);CHKERRQ(ierr);
3033     ierr = DMRefineHierarchy(dm, refine, dms);CHKERRQ(ierr);
3034     /* Total hack since we do not pass in a pointer */
3035     ierr = DMPlexSwap_Static(dm, dms[refine-1]);CHKERRQ(ierr);
3036     if (refine == 1) {
3037       ierr = DMSetCoarseDM(dm, dms[0]);CHKERRQ(ierr);
3038       ierr = DMPlexSetRegularRefinement(dm, PETSC_TRUE);CHKERRQ(ierr);
3039     } else {
3040       ierr = DMSetCoarseDM(dm, dms[refine-2]);CHKERRQ(ierr);
3041       ierr = DMPlexSetRegularRefinement(dm, PETSC_TRUE);CHKERRQ(ierr);
3042       ierr = DMSetCoarseDM(dms[0], dms[refine-1]);CHKERRQ(ierr);
3043       ierr = DMPlexSetRegularRefinement(dms[0], PETSC_TRUE);CHKERRQ(ierr);
3044     }
3045     ierr = DMSetCoarseDM(dms[refine-1], coarseDM);CHKERRQ(ierr);
3046     ierr = PetscObjectDereference((PetscObject)coarseDM);CHKERRQ(ierr);
3047     /* Free DMs */
3048     for (r = 0; r < refine; ++r) {
3049       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dms[r]);CHKERRQ(ierr);
3050       ierr = DMDestroy(&dms[r]);CHKERRQ(ierr);
3051     }
3052     ierr = PetscFree(dms);CHKERRQ(ierr);
3053   } else {
3054     for (r = 0; r < refine; ++r) {
3055       DM             rdm;
3056       PetscPointFunc coordFunc = ((DM_Plex*) dm->data)->coordFunc;
3057 
3058       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
3059       ierr = DMRefine(dm, PetscObjectComm((PetscObject) dm), &rdm);CHKERRQ(ierr);
3060       /* Total hack since we do not pass in a pointer */
3061       ierr = DMPlexReplace_Static(dm, &rdm);CHKERRQ(ierr);
3062       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
3063       if (coordFunc && remap) {
3064         ierr = DMPlexRemapGeometry(dm, 0.0, coordFunc);CHKERRQ(ierr);
3065         ((DM_Plex*) dm->data)->coordFunc = coordFunc;
3066       }
3067     }
3068   }
3069   /* Handle DMPlex coarsening */
3070   ierr = PetscOptionsBoundedInt("-dm_coarsen", "Coarsen the mesh", "DMCreate", coarsen, &coarsen, NULL,0);CHKERRQ(ierr);
3071   ierr = PetscOptionsBoundedInt("-dm_coarsen_hierarchy", "The number of coarsenings", "DMCreate", coarsen, &coarsen, &isHierarchy,0);CHKERRQ(ierr);
3072   if (coarsen && isHierarchy) {
3073     DM *dms;
3074 
3075     ierr = PetscMalloc1(coarsen, &dms);CHKERRQ(ierr);
3076     ierr = DMCoarsenHierarchy(dm, coarsen, dms);CHKERRQ(ierr);
3077     /* Free DMs */
3078     for (r = 0; r < coarsen; ++r) {
3079       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dms[r]);CHKERRQ(ierr);
3080       ierr = DMDestroy(&dms[r]);CHKERRQ(ierr);
3081     }
3082     ierr = PetscFree(dms);CHKERRQ(ierr);
3083   } else {
3084     for (r = 0; r < coarsen; ++r) {
3085       DM             cdm;
3086       PetscPointFunc coordFunc = ((DM_Plex*) dm->data)->coordFunc;
3087 
3088       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
3089       ierr = DMCoarsen(dm, PetscObjectComm((PetscObject) dm), &cdm);CHKERRQ(ierr);
3090       /* Total hack since we do not pass in a pointer */
3091       ierr = DMPlexReplace_Static(dm, &cdm);CHKERRQ(ierr);
3092       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
3093       if (coordFunc) {
3094         ierr = DMPlexRemapGeometry(dm, 0.0, coordFunc);CHKERRQ(ierr);
3095         ((DM_Plex*) dm->data)->coordFunc = coordFunc;
3096       }
3097     }
3098   }
3099   /* Handle ghost cells */
3100   ierr = PetscOptionsBool("-dm_plex_create_fv_ghost_cells", "Flag to create finite volume ghost cells on the boundary", "DMCreate", ghostCells, &ghostCells, NULL);CHKERRQ(ierr);
3101   if (ghostCells) {
3102     DM   gdm;
3103     char lname[PETSC_MAX_PATH_LEN];
3104 
3105     lname[0] = '\0';
3106     ierr = PetscOptionsString("-dm_plex_fv_ghost_cells_label", "Label name for ghost cells boundary", "DMCreate", lname, lname, sizeof(lname), &flg);CHKERRQ(ierr);
3107     ierr = DMPlexConstructGhostCells(dm, flg ? lname : NULL, NULL, &gdm);CHKERRQ(ierr);
3108     ierr = DMPlexReplace_Static(dm, &gdm);CHKERRQ(ierr);
3109   }
3110   /* Handle */
3111   ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
3112   ierr = PetscOptionsTail();CHKERRQ(ierr);
3113   PetscFunctionReturn(0);
3114 }
3115 
3116 static PetscErrorCode DMCreateGlobalVector_Plex(DM dm,Vec *vec)
3117 {
3118   PetscErrorCode ierr;
3119 
3120   PetscFunctionBegin;
3121   ierr = DMCreateGlobalVector_Section_Private(dm,vec);CHKERRQ(ierr);
3122   /* ierr = VecSetOperation(*vec, VECOP_DUPLICATE, (void(*)(void)) VecDuplicate_MPI_DM);CHKERRQ(ierr); */
3123   ierr = VecSetOperation(*vec, VECOP_VIEW, (void (*)(void)) VecView_Plex);CHKERRQ(ierr);
3124   ierr = VecSetOperation(*vec, VECOP_VIEWNATIVE, (void (*)(void)) VecView_Plex_Native);CHKERRQ(ierr);
3125   ierr = VecSetOperation(*vec, VECOP_LOAD, (void (*)(void)) VecLoad_Plex);CHKERRQ(ierr);
3126   ierr = VecSetOperation(*vec, VECOP_LOADNATIVE, (void (*)(void)) VecLoad_Plex_Native);CHKERRQ(ierr);
3127   PetscFunctionReturn(0);
3128 }
3129 
3130 static PetscErrorCode DMCreateLocalVector_Plex(DM dm,Vec *vec)
3131 {
3132   PetscErrorCode ierr;
3133 
3134   PetscFunctionBegin;
3135   ierr = DMCreateLocalVector_Section_Private(dm,vec);CHKERRQ(ierr);
3136   ierr = VecSetOperation(*vec, VECOP_VIEW, (void (*)(void)) VecView_Plex_Local);CHKERRQ(ierr);
3137   ierr = VecSetOperation(*vec, VECOP_LOAD, (void (*)(void)) VecLoad_Plex_Local);CHKERRQ(ierr);
3138   PetscFunctionReturn(0);
3139 }
3140 
3141 static PetscErrorCode DMGetDimPoints_Plex(DM dm, PetscInt dim, PetscInt *pStart, PetscInt *pEnd)
3142 {
3143   PetscInt       depth, d;
3144   PetscErrorCode ierr;
3145 
3146   PetscFunctionBegin;
3147   ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
3148   if (depth == 1) {
3149     ierr = DMGetDimension(dm, &d);CHKERRQ(ierr);
3150     if (dim == 0)      {ierr = DMPlexGetDepthStratum(dm, dim, pStart, pEnd);CHKERRQ(ierr);}
3151     else if (dim == d) {ierr = DMPlexGetDepthStratum(dm, 1, pStart, pEnd);CHKERRQ(ierr);}
3152     else               {*pStart = 0; *pEnd = 0;}
3153   } else {
3154     ierr = DMPlexGetDepthStratum(dm, dim, pStart, pEnd);CHKERRQ(ierr);
3155   }
3156   PetscFunctionReturn(0);
3157 }
3158 
3159 static PetscErrorCode DMGetNeighbors_Plex(DM dm, PetscInt *nranks, const PetscMPIInt *ranks[])
3160 {
3161   PetscSF           sf;
3162   PetscInt          niranks, njranks, n;
3163   const PetscMPIInt *iranks, *jranks;
3164   DM_Plex           *data = (DM_Plex*) dm->data;
3165   PetscErrorCode    ierr;
3166 
3167   PetscFunctionBegin;
3168   ierr = DMGetPointSF(dm, &sf);CHKERRQ(ierr);
3169   if (!data->neighbors) {
3170     ierr = PetscSFSetUp(sf);CHKERRQ(ierr);
3171     ierr = PetscSFGetRootRanks(sf, &njranks, &jranks, NULL, NULL, NULL);CHKERRQ(ierr);
3172     ierr = PetscSFGetLeafRanks(sf, &niranks, &iranks, NULL, NULL);CHKERRQ(ierr);
3173     ierr = PetscMalloc1(njranks + niranks + 1, &data->neighbors);CHKERRQ(ierr);
3174     ierr = PetscArraycpy(data->neighbors + 1, jranks, njranks);CHKERRQ(ierr);
3175     ierr = PetscArraycpy(data->neighbors + njranks + 1, iranks, niranks);CHKERRQ(ierr);
3176     n = njranks + niranks;
3177     ierr = PetscSortRemoveDupsMPIInt(&n, data->neighbors + 1);CHKERRQ(ierr);
3178     /* The following cast should never fail: can't have more neighbors than PETSC_MPI_INT_MAX */
3179     ierr = PetscMPIIntCast(n, data->neighbors);CHKERRQ(ierr);
3180   }
3181   if (nranks) *nranks = data->neighbors[0];
3182   if (ranks) {
3183     if (data->neighbors[0]) *ranks = data->neighbors + 1;
3184     else                    *ranks = NULL;
3185   }
3186   PetscFunctionReturn(0);
3187 }
3188 
3189 PETSC_INTERN PetscErrorCode DMInterpolateSolution_Plex(DM, DM, Mat, Vec, Vec);
3190 
3191 static PetscErrorCode DMInitialize_Plex(DM dm)
3192 {
3193   PetscErrorCode ierr;
3194 
3195   PetscFunctionBegin;
3196   dm->ops->view                            = DMView_Plex;
3197   dm->ops->load                            = DMLoad_Plex;
3198   dm->ops->setfromoptions                  = DMSetFromOptions_Plex;
3199   dm->ops->clone                           = DMClone_Plex;
3200   dm->ops->setup                           = DMSetUp_Plex;
3201   dm->ops->createlocalsection              = DMCreateLocalSection_Plex;
3202   dm->ops->createdefaultconstraints        = DMCreateDefaultConstraints_Plex;
3203   dm->ops->createglobalvector              = DMCreateGlobalVector_Plex;
3204   dm->ops->createlocalvector               = DMCreateLocalVector_Plex;
3205   dm->ops->getlocaltoglobalmapping         = NULL;
3206   dm->ops->createfieldis                   = NULL;
3207   dm->ops->createcoordinatedm              = DMCreateCoordinateDM_Plex;
3208   dm->ops->createcoordinatefield           = DMCreateCoordinateField_Plex;
3209   dm->ops->getcoloring                     = NULL;
3210   dm->ops->creatematrix                    = DMCreateMatrix_Plex;
3211   dm->ops->createinterpolation             = DMCreateInterpolation_Plex;
3212   dm->ops->createmassmatrix                = DMCreateMassMatrix_Plex;
3213   dm->ops->createinjection                 = DMCreateInjection_Plex;
3214   dm->ops->refine                          = DMRefine_Plex;
3215   dm->ops->coarsen                         = DMCoarsen_Plex;
3216   dm->ops->refinehierarchy                 = DMRefineHierarchy_Plex;
3217   dm->ops->coarsenhierarchy                = DMCoarsenHierarchy_Plex;
3218   dm->ops->adaptlabel                      = DMAdaptLabel_Plex;
3219   dm->ops->adaptmetric                     = DMAdaptMetric_Plex;
3220   dm->ops->globaltolocalbegin              = NULL;
3221   dm->ops->globaltolocalend                = NULL;
3222   dm->ops->localtoglobalbegin              = NULL;
3223   dm->ops->localtoglobalend                = NULL;
3224   dm->ops->destroy                         = DMDestroy_Plex;
3225   dm->ops->createsubdm                     = DMCreateSubDM_Plex;
3226   dm->ops->createsuperdm                   = DMCreateSuperDM_Plex;
3227   dm->ops->getdimpoints                    = DMGetDimPoints_Plex;
3228   dm->ops->locatepoints                    = DMLocatePoints_Plex;
3229   dm->ops->projectfunctionlocal            = DMProjectFunctionLocal_Plex;
3230   dm->ops->projectfunctionlabellocal       = DMProjectFunctionLabelLocal_Plex;
3231   dm->ops->projectfieldlocal               = DMProjectFieldLocal_Plex;
3232   dm->ops->projectfieldlabellocal          = DMProjectFieldLabelLocal_Plex;
3233   dm->ops->projectbdfieldlabellocal        = DMProjectBdFieldLabelLocal_Plex;
3234   dm->ops->computel2diff                   = DMComputeL2Diff_Plex;
3235   dm->ops->computel2gradientdiff           = DMComputeL2GradientDiff_Plex;
3236   dm->ops->computel2fielddiff              = DMComputeL2FieldDiff_Plex;
3237   dm->ops->getneighbors                    = DMGetNeighbors_Plex;
3238   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMPlexInsertBoundaryValues_C",DMPlexInsertBoundaryValues_Plex);CHKERRQ(ierr);
3239   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMPlexInsertTimeDerviativeBoundaryValues_C",DMPlexInsertTimeDerivativeBoundaryValues_Plex);CHKERRQ(ierr);
3240   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMSetUpGLVisViewer_C",DMSetUpGLVisViewer_Plex);CHKERRQ(ierr);
3241   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMCreateNeumannOverlap_C",DMCreateNeumannOverlap_Plex);CHKERRQ(ierr);
3242   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMPlexGetOverlap_C",DMPlexGetOverlap_Plex);CHKERRQ(ierr);
3243   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMInterpolateSolution_C",DMInterpolateSolution_Plex);CHKERRQ(ierr);
3244   PetscFunctionReturn(0);
3245 }
3246 
3247 PETSC_INTERN PetscErrorCode DMClone_Plex(DM dm, DM *newdm)
3248 {
3249   DM_Plex        *mesh = (DM_Plex *) dm->data;
3250   PetscErrorCode ierr;
3251 
3252   PetscFunctionBegin;
3253   mesh->refct++;
3254   (*newdm)->data = mesh;
3255   ierr = PetscObjectChangeTypeName((PetscObject) *newdm, DMPLEX);CHKERRQ(ierr);
3256   ierr = DMInitialize_Plex(*newdm);CHKERRQ(ierr);
3257   PetscFunctionReturn(0);
3258 }
3259 
3260 /*MC
3261   DMPLEX = "plex" - A DM object that encapsulates an unstructured mesh, or CW Complex, which can be expressed using a Hasse Diagram.
3262                     In the local representation, Vecs contain all unknowns in the interior and shared boundary. This is
3263                     specified by a PetscSection object. Ownership in the global representation is determined by
3264                     ownership of the underlying DMPlex points. This is specified by another PetscSection object.
3265 
3266   Options Database Keys:
3267 + -dm_refine_pre                     - Refine mesh before distribution
3268 + -dm_refine_uniform_pre             - Choose uniform or generator-based refinement
3269 + -dm_refine_volume_limit_pre        - Cell volume limit after pre-refinement using generator
3270 . -dm_distribute                     - Distribute mesh across processes
3271 . -dm_distribute_overlap             - Number of cells to overlap for distribution
3272 . -dm_refine                         - Refine mesh after distribution
3273 . -dm_plex_hash_location             - Use grid hashing for point location
3274 . -dm_plex_partition_balance         - Attempt to evenly divide points on partition boundary between processes
3275 . -dm_plex_remesh_bd                 - Allow changes to the boundary on remeshing
3276 . -dm_plex_max_projection_height     - Maxmimum mesh point height used to project locally
3277 . -dm_plex_regular_refinement        - Use special nested projection algorithm for regular refinement
3278 . -dm_plex_check_all                 - Perform all shecks below
3279 . -dm_plex_check_symmetry            - Check that the adjacency information in the mesh is symmetric
3280 . -dm_plex_check_skeleton <celltype> - Check that each cell has the correct number of vertices
3281 . -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
3282 . -dm_plex_check_geometry            - Check that cells have positive volume
3283 . -dm_view :mesh.tex:ascii_latex     - View the mesh in LaTeX/TikZ
3284 . -dm_plex_view_scale <num>          - Scale the TikZ
3285 - -dm_plex_print_fem <num>           - View FEM assembly information, such as element vectors and matrices
3286 
3287   Level: intermediate
3288 
3289 .seealso: DMType, DMPlexCreate(), DMCreate(), DMSetType()
3290 M*/
3291 
3292 PETSC_EXTERN PetscErrorCode DMCreate_Plex(DM dm)
3293 {
3294   DM_Plex       *mesh;
3295   PetscInt       unit;
3296   PetscErrorCode ierr;
3297 
3298   PetscFunctionBegin;
3299   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
3300   ierr     = PetscNewLog(dm,&mesh);CHKERRQ(ierr);
3301   dm->data = mesh;
3302 
3303   mesh->refct             = 1;
3304   ierr                    = PetscSectionCreate(PetscObjectComm((PetscObject)dm), &mesh->coneSection);CHKERRQ(ierr);
3305   mesh->maxConeSize       = 0;
3306   mesh->cones             = NULL;
3307   mesh->coneOrientations  = NULL;
3308   ierr                    = PetscSectionCreate(PetscObjectComm((PetscObject)dm), &mesh->supportSection);CHKERRQ(ierr);
3309   mesh->maxSupportSize    = 0;
3310   mesh->supports          = NULL;
3311   mesh->refinementUniform = PETSC_TRUE;
3312   mesh->refinementLimit   = -1.0;
3313   mesh->interpolated      = DMPLEX_INTERPOLATED_INVALID;
3314   mesh->interpolatedCollective = DMPLEX_INTERPOLATED_INVALID;
3315 
3316   mesh->facesTmp = NULL;
3317 
3318   mesh->tetgenOpts   = NULL;
3319   mesh->triangleOpts = NULL;
3320   ierr = PetscPartitionerCreate(PetscObjectComm((PetscObject)dm), &mesh->partitioner);CHKERRQ(ierr);
3321   mesh->remeshBd     = PETSC_FALSE;
3322 
3323   mesh->subpointMap = NULL;
3324 
3325   for (unit = 0; unit < NUM_PETSC_UNITS; ++unit) mesh->scale[unit] = 1.0;
3326 
3327   mesh->regularRefinement   = PETSC_FALSE;
3328   mesh->depthState          = -1;
3329   mesh->celltypeState       = -1;
3330   mesh->globalVertexNumbers = NULL;
3331   mesh->globalCellNumbers   = NULL;
3332   mesh->anchorSection       = NULL;
3333   mesh->anchorIS            = NULL;
3334   mesh->createanchors       = NULL;
3335   mesh->computeanchormatrix = NULL;
3336   mesh->parentSection       = NULL;
3337   mesh->parents             = NULL;
3338   mesh->childIDs            = NULL;
3339   mesh->childSection        = NULL;
3340   mesh->children            = NULL;
3341   mesh->referenceTree       = NULL;
3342   mesh->getchildsymmetry    = NULL;
3343   mesh->vtkCellHeight       = 0;
3344   mesh->useAnchors          = PETSC_FALSE;
3345 
3346   mesh->maxProjectionHeight = 0;
3347 
3348   mesh->neighbors           = NULL;
3349 
3350   mesh->printSetValues = PETSC_FALSE;
3351   mesh->printFEM       = 0;
3352   mesh->printTol       = 1.0e-10;
3353 
3354   ierr = DMInitialize_Plex(dm);CHKERRQ(ierr);
3355   PetscFunctionReturn(0);
3356 }
3357 
3358 /*@
3359   DMPlexCreate - Creates a DMPlex object, which encapsulates an unstructured mesh, or CW complex, which can be expressed using a Hasse Diagram.
3360 
3361   Collective
3362 
3363   Input Parameter:
3364 . comm - The communicator for the DMPlex object
3365 
3366   Output Parameter:
3367 . mesh  - The DMPlex object
3368 
3369   Level: beginner
3370 
3371 @*/
3372 PetscErrorCode DMPlexCreate(MPI_Comm comm, DM *mesh)
3373 {
3374   PetscErrorCode ierr;
3375 
3376   PetscFunctionBegin;
3377   PetscValidPointer(mesh,2);
3378   ierr = DMCreate(comm, mesh);CHKERRQ(ierr);
3379   ierr = DMSetType(*mesh, DMPLEX);CHKERRQ(ierr);
3380   PetscFunctionReturn(0);
3381 }
3382 
3383 /*@C
3384   DMPlexBuildFromCellListParallel - Build distributed DMPLEX topology from a list of vertices for each cell (common mesh generator output)
3385 
3386   Input Parameters:
3387 + dm - The DM
3388 . numCells - The number of cells owned by this process
3389 . numVertices - The number of vertices owned by this process, or PETSC_DECIDE
3390 . NVertices - The global number of vertices, or PETSC_DECIDE
3391 . numCorners - The number of vertices for each cell
3392 - cells - An array of numCells*numCorners numbers, the global vertex numbers for each cell
3393 
3394   Output Parameter:
3395 . vertexSF - (Optional) SF describing complete vertex ownership
3396 
3397   Notes:
3398   Two triangles sharing a face
3399 $
3400 $        2
3401 $      / | \
3402 $     /  |  \
3403 $    /   |   \
3404 $   0  0 | 1  3
3405 $    \   |   /
3406 $     \  |  /
3407 $      \ | /
3408 $        1
3409 would have input
3410 $  numCells = 2, numVertices = 4
3411 $  cells = [0 1 2  1 3 2]
3412 $
3413 which would result in the DMPlex
3414 $
3415 $        4
3416 $      / | \
3417 $     /  |  \
3418 $    /   |   \
3419 $   2  0 | 1  5
3420 $    \   |   /
3421 $     \  |  /
3422 $      \ | /
3423 $        3
3424 
3425   Vertices are implicitly numbered consecutively 0,...,NVertices.
3426   Each rank owns a chunk of numVertices consecutive vertices.
3427   If numVertices is PETSC_DECIDE, PETSc will distribute them as evenly as possible using PetscLayout.
3428   If both NVertices and numVertices are PETSC_DECIDE, NVertices is computed by PETSc as the maximum vertex index in cells + 1.
3429   If only NVertices is PETSC_DECIDE, it is computed as the sum of numVertices over all ranks.
3430 
3431   The cell distribution is arbitrary non-overlapping, independent of the vertex distribution.
3432 
3433   Not currently supported in Fortran.
3434 
3435   Level: advanced
3436 
3437 .seealso: DMPlexBuildFromCellList(), DMPlexCreateFromCellListParallelPetsc(), DMPlexBuildCoordinatesFromCellListParallel()
3438 @*/
3439 PetscErrorCode DMPlexBuildFromCellListParallel(DM dm, PetscInt numCells, PetscInt numVertices, PetscInt NVertices, PetscInt numCorners, const PetscInt cells[], PetscSF *vertexSF)
3440 {
3441   PetscSF         sfPoint;
3442   PetscLayout     layout;
3443   PetscInt        numVerticesAdj, *verticesAdj, *cones, c, p, dim;
3444   PetscMPIInt     rank, size;
3445   PetscErrorCode  ierr;
3446 
3447   PetscFunctionBegin;
3448   PetscValidLogicalCollectiveInt(dm,NVertices,4);
3449   ierr = PetscLogEventBegin(DMPLEX_BuildFromCellList,dm,0,0,0);CHKERRQ(ierr);
3450   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject) dm), &rank);CHKERRMPI(ierr);
3451   ierr = MPI_Comm_size(PetscObjectComm((PetscObject) dm), &size);CHKERRMPI(ierr);
3452   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
3453   /* Get/check global number of vertices */
3454   {
3455     PetscInt NVerticesInCells, i;
3456     const PetscInt len = numCells * numCorners;
3457 
3458     /* NVerticesInCells = max(cells) + 1 */
3459     NVerticesInCells = PETSC_MIN_INT;
3460     for (i=0; i<len; i++) if (cells[i] > NVerticesInCells) NVerticesInCells = cells[i];
3461     ++NVerticesInCells;
3462     ierr = MPI_Allreduce(MPI_IN_PLACE, &NVerticesInCells, 1, MPIU_INT, MPI_MAX, PetscObjectComm((PetscObject) dm));CHKERRMPI(ierr);
3463 
3464     if (numVertices == PETSC_DECIDE && NVertices == PETSC_DECIDE) NVertices = NVerticesInCells;
3465     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);
3466   }
3467   /* Count locally unique vertices */
3468   {
3469     PetscHSetI vhash;
3470     PetscInt off = 0;
3471 
3472     ierr = PetscHSetICreate(&vhash);CHKERRQ(ierr);
3473     for (c = 0; c < numCells; ++c) {
3474       for (p = 0; p < numCorners; ++p) {
3475         ierr = PetscHSetIAdd(vhash, cells[c*numCorners+p]);CHKERRQ(ierr);
3476       }
3477     }
3478     ierr = PetscHSetIGetSize(vhash, &numVerticesAdj);CHKERRQ(ierr);
3479     ierr = PetscMalloc1(numVerticesAdj, &verticesAdj);CHKERRQ(ierr);
3480     ierr = PetscHSetIGetElems(vhash, &off, verticesAdj);CHKERRQ(ierr);
3481     ierr = PetscHSetIDestroy(&vhash);CHKERRQ(ierr);
3482     if (off != numVerticesAdj) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Invalid number of local vertices %D should be %D", off, numVerticesAdj);
3483   }
3484   ierr = PetscSortInt(numVerticesAdj, verticesAdj);CHKERRQ(ierr);
3485   /* Create cones */
3486   ierr = DMPlexSetChart(dm, 0, numCells+numVerticesAdj);CHKERRQ(ierr);
3487   for (c = 0; c < numCells; ++c) {ierr = DMPlexSetConeSize(dm, c, numCorners);CHKERRQ(ierr);}
3488   ierr = DMSetUp(dm);CHKERRQ(ierr);
3489   ierr = DMPlexGetCones(dm,&cones);CHKERRQ(ierr);
3490   for (c = 0; c < numCells; ++c) {
3491     for (p = 0; p < numCorners; ++p) {
3492       const PetscInt gv = cells[c*numCorners+p];
3493       PetscInt       lv;
3494 
3495       /* Positions within verticesAdj form 0-based local vertex numbering;
3496          we need to shift it by numCells to get correct DAG points (cells go first) */
3497       ierr = PetscFindInt(gv, numVerticesAdj, verticesAdj, &lv);CHKERRQ(ierr);
3498       if (lv < 0) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Could not find global vertex %D in local connectivity", gv);
3499       cones[c*numCorners+p] = lv+numCells;
3500     }
3501   }
3502   /* Build point sf */
3503   ierr = PetscLayoutCreate(PetscObjectComm((PetscObject)dm), &layout);CHKERRQ(ierr);
3504   ierr = PetscLayoutSetSize(layout, NVertices);CHKERRQ(ierr);
3505   ierr = PetscLayoutSetLocalSize(layout, numVertices);CHKERRQ(ierr);
3506   ierr = PetscLayoutSetBlockSize(layout, 1);CHKERRQ(ierr);
3507   ierr = PetscSFCreateByMatchingIndices(layout, numVerticesAdj, verticesAdj, NULL, numCells, numVerticesAdj, verticesAdj, NULL, numCells, vertexSF, &sfPoint);CHKERRQ(ierr);
3508   ierr = PetscLayoutDestroy(&layout);CHKERRQ(ierr);
3509   ierr = PetscFree(verticesAdj);CHKERRQ(ierr);
3510   ierr = PetscObjectSetName((PetscObject) sfPoint, "point SF");CHKERRQ(ierr);
3511   if (dm->sf) {
3512     const char *prefix;
3513 
3514     ierr = PetscObjectGetOptionsPrefix((PetscObject)dm->sf, &prefix);CHKERRQ(ierr);
3515     ierr = PetscObjectSetOptionsPrefix((PetscObject)sfPoint, prefix);CHKERRQ(ierr);
3516   }
3517   ierr = DMSetPointSF(dm, sfPoint);CHKERRQ(ierr);
3518   ierr = PetscSFDestroy(&sfPoint);CHKERRQ(ierr);
3519   if (vertexSF) {ierr = PetscObjectSetName((PetscObject)(*vertexSF), "Vertex Ownership SF");CHKERRQ(ierr);}
3520   /* Fill in the rest of the topology structure */
3521   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
3522   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
3523   ierr = PetscLogEventEnd(DMPLEX_BuildFromCellList,dm,0,0,0);CHKERRQ(ierr);
3524   PetscFunctionReturn(0);
3525 }
3526 
3527 /*@C
3528   DMPlexBuildCoordinatesFromCellListParallel - Build DM coordinates from a list of coordinates for each owned vertex (common mesh generator output)
3529 
3530   Input Parameters:
3531 + dm - The DM
3532 . spaceDim - The spatial dimension used for coordinates
3533 . sfVert - SF describing complete vertex ownership
3534 - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex
3535 
3536   Level: advanced
3537 
3538   Notes:
3539   Not currently supported in Fortran.
3540 
3541 .seealso: DMPlexBuildCoordinatesFromCellList(), DMPlexCreateFromCellListParallelPetsc(), DMPlexBuildFromCellListParallel()
3542 @*/
3543 PetscErrorCode DMPlexBuildCoordinatesFromCellListParallel(DM dm, PetscInt spaceDim, PetscSF sfVert, const PetscReal vertexCoords[])
3544 {
3545   PetscSection   coordSection;
3546   Vec            coordinates;
3547   PetscScalar   *coords;
3548   PetscInt       numVertices, numVerticesAdj, coordSize, v, vStart, vEnd;
3549   PetscErrorCode ierr;
3550 
3551   PetscFunctionBegin;
3552   ierr = PetscLogEventBegin(DMPLEX_BuildCoordinatesFromCellList,dm,0,0,0);CHKERRQ(ierr);
3553   ierr = DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);CHKERRQ(ierr);
3554   if (vStart < 0 || vEnd < 0) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "DM is not set up properly. DMPlexBuildFromCellList() should be called first.");
3555   ierr = DMSetCoordinateDim(dm, spaceDim);CHKERRQ(ierr);
3556   ierr = PetscSFGetGraph(sfVert, &numVertices, &numVerticesAdj, NULL, NULL);CHKERRQ(ierr);
3557   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);
3558   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
3559   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
3560   ierr = PetscSectionSetFieldComponents(coordSection, 0, spaceDim);CHKERRQ(ierr);
3561   ierr = PetscSectionSetChart(coordSection, vStart, vEnd);CHKERRQ(ierr);
3562   for (v = vStart; v < vEnd; ++v) {
3563     ierr = PetscSectionSetDof(coordSection, v, spaceDim);CHKERRQ(ierr);
3564     ierr = PetscSectionSetFieldDof(coordSection, v, 0, spaceDim);CHKERRQ(ierr);
3565   }
3566   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
3567   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
3568   ierr = VecCreate(PetscObjectComm((PetscObject)dm), &coordinates);CHKERRQ(ierr);
3569   ierr = VecSetBlockSize(coordinates, spaceDim);CHKERRQ(ierr);
3570   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
3571   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
3572   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
3573   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
3574   {
3575     MPI_Datatype coordtype;
3576 
3577     /* Need a temp buffer for coords if we have complex/single */
3578     ierr = MPI_Type_contiguous(spaceDim, MPIU_SCALAR, &coordtype);CHKERRMPI(ierr);
3579     ierr = MPI_Type_commit(&coordtype);CHKERRMPI(ierr);
3580 #if defined(PETSC_USE_COMPLEX)
3581     {
3582     PetscScalar *svertexCoords;
3583     PetscInt    i;
3584     ierr = PetscMalloc1(numVertices*spaceDim,&svertexCoords);CHKERRQ(ierr);
3585     for (i=0; i<numVertices*spaceDim; i++) svertexCoords[i] = vertexCoords[i];
3586     ierr = PetscSFBcastBegin(sfVert, coordtype, svertexCoords, coords,MPI_REPLACE);CHKERRQ(ierr);
3587     ierr = PetscSFBcastEnd(sfVert, coordtype, svertexCoords, coords,MPI_REPLACE);CHKERRQ(ierr);
3588     ierr = PetscFree(svertexCoords);CHKERRQ(ierr);
3589     }
3590 #else
3591     ierr = PetscSFBcastBegin(sfVert, coordtype, vertexCoords, coords,MPI_REPLACE);CHKERRQ(ierr);
3592     ierr = PetscSFBcastEnd(sfVert, coordtype, vertexCoords, coords,MPI_REPLACE);CHKERRQ(ierr);
3593 #endif
3594     ierr = MPI_Type_free(&coordtype);CHKERRMPI(ierr);
3595   }
3596   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
3597   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
3598   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
3599   ierr = PetscLogEventEnd(DMPLEX_BuildCoordinatesFromCellList,dm,0,0,0);CHKERRQ(ierr);
3600   PetscFunctionReturn(0);
3601 }
3602 
3603 /*@
3604   DMPlexCreateFromCellListParallelPetsc - Create distributed DMPLEX from a list of vertices for each cell (common mesh generator output)
3605 
3606   Input Parameters:
3607 + comm - The communicator
3608 . dim - The topological dimension of the mesh
3609 . numCells - The number of cells owned by this process
3610 . numVertices - The number of vertices owned by this process, or PETSC_DECIDE
3611 . NVertices - The global number of vertices, or PETSC_DECIDE
3612 . numCorners - The number of vertices for each cell
3613 . interpolate - Flag indicating that intermediate mesh entities (faces, edges) should be created automatically
3614 . cells - An array of numCells*numCorners numbers, the global vertex numbers for each cell
3615 . spaceDim - The spatial dimension used for coordinates
3616 - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex
3617 
3618   Output Parameter:
3619 + dm - The DM
3620 - vertexSF - (Optional) SF describing complete vertex ownership
3621 
3622   Notes:
3623   This function is just a convenient sequence of DMCreate(), DMSetType(), DMSetDimension(),
3624   DMPlexBuildFromCellListParallel(), DMPlexInterpolate(), DMPlexBuildCoordinatesFromCellListParallel()
3625 
3626   See DMPlexBuildFromCellListParallel() for an example and details about the topology-related parameters.
3627   See DMPlexBuildCoordinatesFromCellListParallel() for details about the geometry-related parameters.
3628 
3629   Level: intermediate
3630 
3631 .seealso: DMPlexCreateFromCellListPetsc(), DMPlexBuildFromCellListParallel(), DMPlexBuildCoordinatesFromCellListParallel(), DMPlexCreateFromDAG(), DMPlexCreate()
3632 @*/
3633 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)
3634 {
3635   PetscSF        sfVert;
3636   PetscErrorCode ierr;
3637 
3638   PetscFunctionBegin;
3639   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
3640   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
3641   PetscValidLogicalCollectiveInt(*dm, dim, 2);
3642   PetscValidLogicalCollectiveInt(*dm, spaceDim, 9);
3643   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
3644   ierr = DMPlexBuildFromCellListParallel(*dm, numCells, numVertices, NVertices, numCorners, cells, &sfVert);CHKERRQ(ierr);
3645   if (interpolate) {
3646     DM idm;
3647 
3648     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
3649     ierr = DMDestroy(dm);CHKERRQ(ierr);
3650     *dm  = idm;
3651   }
3652   ierr = DMPlexBuildCoordinatesFromCellListParallel(*dm, spaceDim, sfVert, vertexCoords);CHKERRQ(ierr);
3653   if (vertexSF) *vertexSF = sfVert;
3654   else {ierr = PetscSFDestroy(&sfVert);CHKERRQ(ierr);}
3655   PetscFunctionReturn(0);
3656 }
3657 
3658 /*@
3659   DMPlexCreateFromCellListParallel - Deprecated, use DMPlexCreateFromCellListParallelPetsc()
3660 
3661   Level: deprecated
3662 
3663 .seealso: DMPlexCreateFromCellListParallelPetsc()
3664 @*/
3665 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)
3666 {
3667   PetscErrorCode ierr;
3668   PetscInt       i;
3669   PetscInt       *pintCells;
3670 
3671   PetscFunctionBegin;
3672   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));
3673   if (sizeof(int) == sizeof(PetscInt)) {
3674     pintCells = (PetscInt *) cells;
3675   } else {
3676     ierr = PetscMalloc1(numCells*numCorners, &pintCells);CHKERRQ(ierr);
3677     for (i = 0; i < numCells*numCorners; i++) {
3678       pintCells[i] = (PetscInt) cells[i];
3679     }
3680   }
3681   ierr = DMPlexCreateFromCellListParallelPetsc(comm, dim, numCells, numVertices, PETSC_DECIDE, numCorners, interpolate, pintCells, spaceDim, vertexCoords, vertexSF, dm);CHKERRQ(ierr);
3682   if (sizeof(int) != sizeof(PetscInt)) {
3683     ierr = PetscFree(pintCells);CHKERRQ(ierr);
3684   }
3685   PetscFunctionReturn(0);
3686 }
3687 
3688 /*@C
3689   DMPlexBuildFromCellList - Build DMPLEX topology from a list of vertices for each cell (common mesh generator output)
3690 
3691   Input Parameters:
3692 + dm - The DM
3693 . numCells - The number of cells owned by this process
3694 . numVertices - The number of vertices owned by this process, or PETSC_DECIDE
3695 . numCorners - The number of vertices for each cell
3696 - cells - An array of numCells*numCorners numbers, the global vertex numbers for each cell
3697 
3698   Level: advanced
3699 
3700   Notes:
3701   Two triangles sharing a face
3702 $
3703 $        2
3704 $      / | \
3705 $     /  |  \
3706 $    /   |   \
3707 $   0  0 | 1  3
3708 $    \   |   /
3709 $     \  |  /
3710 $      \ | /
3711 $        1
3712 would have input
3713 $  numCells = 2, numVertices = 4
3714 $  cells = [0 1 2  1 3 2]
3715 $
3716 which would result in the DMPlex
3717 $
3718 $        4
3719 $      / | \
3720 $     /  |  \
3721 $    /   |   \
3722 $   2  0 | 1  5
3723 $    \   |   /
3724 $     \  |  /
3725 $      \ | /
3726 $        3
3727 
3728   If numVertices is PETSC_DECIDE, it is computed by PETSc as the maximum vertex index in cells + 1.
3729 
3730   Not currently supported in Fortran.
3731 
3732 .seealso: DMPlexBuildFromCellListParallel(), DMPlexBuildCoordinatesFromCellList(), DMPlexCreateFromCellListPetsc()
3733 @*/
3734 PetscErrorCode DMPlexBuildFromCellList(DM dm, PetscInt numCells, PetscInt numVertices, PetscInt numCorners, const PetscInt cells[])
3735 {
3736   PetscInt      *cones, c, p, dim;
3737   PetscErrorCode ierr;
3738 
3739   PetscFunctionBegin;
3740   ierr = PetscLogEventBegin(DMPLEX_BuildFromCellList,dm,0,0,0);CHKERRQ(ierr);
3741   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
3742   /* Get/check global number of vertices */
3743   {
3744     PetscInt NVerticesInCells, i;
3745     const PetscInt len = numCells * numCorners;
3746 
3747     /* NVerticesInCells = max(cells) + 1 */
3748     NVerticesInCells = PETSC_MIN_INT;
3749     for (i=0; i<len; i++) if (cells[i] > NVerticesInCells) NVerticesInCells = cells[i];
3750     ++NVerticesInCells;
3751 
3752     if (numVertices == PETSC_DECIDE) numVertices = NVerticesInCells;
3753     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);
3754   }
3755   ierr = DMPlexSetChart(dm, 0, numCells+numVertices);CHKERRQ(ierr);
3756   for (c = 0; c < numCells; ++c) {
3757     ierr = DMPlexSetConeSize(dm, c, numCorners);CHKERRQ(ierr);
3758   }
3759   ierr = DMSetUp(dm);CHKERRQ(ierr);
3760   ierr = DMPlexGetCones(dm,&cones);CHKERRQ(ierr);
3761   for (c = 0; c < numCells; ++c) {
3762     for (p = 0; p < numCorners; ++p) {
3763       cones[c*numCorners+p] = cells[c*numCorners+p]+numCells;
3764     }
3765   }
3766   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
3767   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
3768   ierr = PetscLogEventEnd(DMPLEX_BuildFromCellList,dm,0,0,0);CHKERRQ(ierr);
3769   PetscFunctionReturn(0);
3770 }
3771 
3772 /*@C
3773   DMPlexBuildCoordinatesFromCellList - Build DM coordinates from a list of coordinates for each owned vertex (common mesh generator output)
3774 
3775   Input Parameters:
3776 + dm - The DM
3777 . spaceDim - The spatial dimension used for coordinates
3778 - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex
3779 
3780   Level: advanced
3781 
3782   Notes:
3783   Not currently supported in Fortran.
3784 
3785 .seealso: DMPlexBuildCoordinatesFromCellListParallel(), DMPlexCreateFromCellListPetsc(), DMPlexBuildFromCellList()
3786 @*/
3787 PetscErrorCode DMPlexBuildCoordinatesFromCellList(DM dm, PetscInt spaceDim, const PetscReal vertexCoords[])
3788 {
3789   PetscSection   coordSection;
3790   Vec            coordinates;
3791   DM             cdm;
3792   PetscScalar   *coords;
3793   PetscInt       v, vStart, vEnd, d;
3794   PetscErrorCode ierr;
3795 
3796   PetscFunctionBegin;
3797   ierr = PetscLogEventBegin(DMPLEX_BuildCoordinatesFromCellList,dm,0,0,0);CHKERRQ(ierr);
3798   ierr = DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);CHKERRQ(ierr);
3799   if (vStart < 0 || vEnd < 0) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "DM is not set up properly. DMPlexBuildFromCellList() should be called first.");
3800   ierr = DMSetCoordinateDim(dm, spaceDim);CHKERRQ(ierr);
3801   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
3802   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
3803   ierr = PetscSectionSetFieldComponents(coordSection, 0, spaceDim);CHKERRQ(ierr);
3804   ierr = PetscSectionSetChart(coordSection, vStart, vEnd);CHKERRQ(ierr);
3805   for (v = vStart; v < vEnd; ++v) {
3806     ierr = PetscSectionSetDof(coordSection, v, spaceDim);CHKERRQ(ierr);
3807     ierr = PetscSectionSetFieldDof(coordSection, v, 0, spaceDim);CHKERRQ(ierr);
3808   }
3809   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
3810 
3811   ierr = DMGetCoordinateDM(dm, &cdm);CHKERRQ(ierr);
3812   ierr = DMCreateLocalVector(cdm, &coordinates);CHKERRQ(ierr);
3813   ierr = VecSetBlockSize(coordinates, spaceDim);CHKERRQ(ierr);
3814   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
3815   ierr = VecGetArrayWrite(coordinates, &coords);CHKERRQ(ierr);
3816   for (v = 0; v < vEnd-vStart; ++v) {
3817     for (d = 0; d < spaceDim; ++d) {
3818       coords[v*spaceDim+d] = vertexCoords[v*spaceDim+d];
3819     }
3820   }
3821   ierr = VecRestoreArrayWrite(coordinates, &coords);CHKERRQ(ierr);
3822   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
3823   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
3824   ierr = PetscLogEventEnd(DMPLEX_BuildCoordinatesFromCellList,dm,0,0,0);CHKERRQ(ierr);
3825   PetscFunctionReturn(0);
3826 }
3827 
3828 /*@
3829   DMPlexCreateFromCellListPetsc - Create DMPLEX from a list of vertices for each cell (common mesh generator output), but only process 0 takes in the input
3830 
3831   Collective on comm
3832 
3833   Input Parameters:
3834 + comm - The communicator
3835 . dim - The topological dimension of the mesh
3836 . numCells - The number of cells, only on process 0
3837 . numVertices - The number of vertices owned by this process, or PETSC_DECIDE, only on process 0
3838 . numCorners - The number of vertices for each cell, only on process 0
3839 . interpolate - Flag indicating that intermediate mesh entities (faces, edges) should be created automatically
3840 . cells - An array of numCells*numCorners numbers, the vertices for each cell, only on process 0
3841 . spaceDim - The spatial dimension used for coordinates
3842 - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex, only on process 0
3843 
3844   Output Parameter:
3845 . dm - The DM, which only has points on process 0
3846 
3847   Notes:
3848   This function is just a convenient sequence of DMCreate(), DMSetType(), DMSetDimension(), DMPlexBuildFromCellList(),
3849   DMPlexInterpolate(), DMPlexBuildCoordinatesFromCellList()
3850 
3851   See DMPlexBuildFromCellList() for an example and details about the topology-related parameters.
3852   See DMPlexBuildCoordinatesFromCellList() for details about the geometry-related parameters.
3853   See DMPlexCreateFromCellListParallelPetsc() for parallel input
3854 
3855   Level: intermediate
3856 
3857 .seealso: DMPlexCreateFromCellListParallelPetsc(), DMPlexBuildFromCellList(), DMPlexBuildCoordinatesFromCellList(), DMPlexCreateFromDAG(), DMPlexCreate()
3858 @*/
3859 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)
3860 {
3861   PetscMPIInt    rank;
3862   PetscErrorCode ierr;
3863 
3864   PetscFunctionBegin;
3865   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.");
3866   ierr = MPI_Comm_rank(comm, &rank);CHKERRMPI(ierr);
3867   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
3868   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
3869   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
3870   if (!rank) {ierr = DMPlexBuildFromCellList(*dm, numCells, numVertices, numCorners, cells);CHKERRQ(ierr);}
3871   else       {ierr = DMPlexBuildFromCellList(*dm, 0, 0, 0, NULL);CHKERRQ(ierr);}
3872   if (interpolate) {
3873     DM idm;
3874 
3875     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
3876     ierr = DMDestroy(dm);CHKERRQ(ierr);
3877     *dm  = idm;
3878   }
3879   if (!rank) {ierr = DMPlexBuildCoordinatesFromCellList(*dm, spaceDim, vertexCoords);CHKERRQ(ierr);}
3880   else       {ierr = DMPlexBuildCoordinatesFromCellList(*dm, spaceDim, NULL);CHKERRQ(ierr);}
3881   PetscFunctionReturn(0);
3882 }
3883 
3884 /*@
3885   DMPlexCreateFromCellList - Deprecated, use DMPlexCreateFromCellListPetsc()
3886 
3887   Level: deprecated
3888 
3889 .seealso: DMPlexCreateFromCellListPetsc()
3890 @*/
3891 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)
3892 {
3893   PetscErrorCode ierr;
3894   PetscInt       i;
3895   PetscInt       *pintCells;
3896   PetscReal      *prealVC;
3897 
3898   PetscFunctionBegin;
3899   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));
3900   if (sizeof(int) == sizeof(PetscInt)) {
3901     pintCells = (PetscInt *) cells;
3902   } else {
3903     ierr = PetscMalloc1(numCells*numCorners, &pintCells);CHKERRQ(ierr);
3904     for (i = 0; i < numCells*numCorners; i++) {
3905       pintCells[i] = (PetscInt) cells[i];
3906     }
3907   }
3908   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));
3909   if (sizeof(double) == sizeof(PetscReal)) {
3910     prealVC = (PetscReal *) vertexCoords;
3911   } else {
3912     ierr = PetscMalloc1(numVertices*spaceDim, &prealVC);CHKERRQ(ierr);
3913     for (i = 0; i < numVertices*spaceDim; i++) {
3914       prealVC[i] = (PetscReal) vertexCoords[i];
3915     }
3916   }
3917   ierr = DMPlexCreateFromCellListPetsc(comm, dim, numCells, numVertices, numCorners, interpolate, pintCells, spaceDim, prealVC, dm);CHKERRQ(ierr);
3918   if (sizeof(int) != sizeof(PetscInt)) {
3919     ierr = PetscFree(pintCells);CHKERRQ(ierr);
3920   }
3921   if (sizeof(double) != sizeof(PetscReal)) {
3922     ierr = PetscFree(prealVC);CHKERRQ(ierr);
3923   }
3924   PetscFunctionReturn(0);
3925 }
3926 
3927 /*@
3928   DMPlexCreateFromDAG - This takes as input the adjacency-list representation of the Directed Acyclic Graph (Hasse Diagram) encoding a mesh, and produces a DM
3929 
3930   Input Parameters:
3931 + dm - The empty DM object, usually from DMCreate() and DMSetDimension()
3932 . depth - The depth of the DAG
3933 . numPoints - Array of size depth + 1 containing the number of points at each depth
3934 . coneSize - The cone size of each point
3935 . cones - The concatenation of the cone points for each point, the cone list must be oriented correctly for each point
3936 . coneOrientations - The orientation of each cone point
3937 - vertexCoords - An array of numPoints[0]*spacedim numbers representing the coordinates of each vertex, with spacedim the value set via DMSetCoordinateDim()
3938 
3939   Output Parameter:
3940 . dm - The DM
3941 
3942   Note: Two triangles sharing a face would have input
3943 $  depth = 1, numPoints = [4 2], coneSize = [3 3 0 0 0 0]
3944 $  cones = [2 3 4  3 5 4], coneOrientations = [0 0 0  0 0 0]
3945 $ vertexCoords = [-1.0 0.0  0.0 -1.0  0.0 1.0  1.0 0.0]
3946 $
3947 which would result in the DMPlex
3948 $
3949 $        4
3950 $      / | \
3951 $     /  |  \
3952 $    /   |   \
3953 $   2  0 | 1  5
3954 $    \   |   /
3955 $     \  |  /
3956 $      \ | /
3957 $        3
3958 $
3959 $ Notice that all points are numbered consecutively, unlike DMPlexCreateFromCellListPetsc()
3960 
3961   Level: advanced
3962 
3963 .seealso: DMPlexCreateFromCellListPetsc(), DMPlexCreate()
3964 @*/
3965 PetscErrorCode DMPlexCreateFromDAG(DM dm, PetscInt depth, const PetscInt numPoints[], const PetscInt coneSize[], const PetscInt cones[], const PetscInt coneOrientations[], const PetscScalar vertexCoords[])
3966 {
3967   Vec            coordinates;
3968   PetscSection   coordSection;
3969   PetscScalar    *coords;
3970   PetscInt       coordSize, firstVertex = -1, pStart = 0, pEnd = 0, p, v, dim, dimEmbed, d, off;
3971   PetscErrorCode ierr;
3972 
3973   PetscFunctionBegin;
3974   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
3975   ierr = DMGetCoordinateDim(dm, &dimEmbed);CHKERRQ(ierr);
3976   if (dimEmbed < dim) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Embedding dimension %D cannot be less than intrinsic dimension %d",dimEmbed,dim);
3977   for (d = 0; d <= depth; ++d) pEnd += numPoints[d];
3978   ierr = DMPlexSetChart(dm, pStart, pEnd);CHKERRQ(ierr);
3979   for (p = pStart; p < pEnd; ++p) {
3980     ierr = DMPlexSetConeSize(dm, p, coneSize[p-pStart]);CHKERRQ(ierr);
3981     if (firstVertex < 0 && !coneSize[p - pStart]) {
3982       firstVertex = p - pStart;
3983     }
3984   }
3985   if (firstVertex < 0 && numPoints[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Expected %D vertices but could not find any", numPoints[0]);
3986   ierr = DMSetUp(dm);CHKERRQ(ierr); /* Allocate space for cones */
3987   for (p = pStart, off = 0; p < pEnd; off += coneSize[p-pStart], ++p) {
3988     ierr = DMPlexSetCone(dm, p, &cones[off]);CHKERRQ(ierr);
3989     ierr = DMPlexSetConeOrientation(dm, p, &coneOrientations[off]);CHKERRQ(ierr);
3990   }
3991   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
3992   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
3993   /* Build coordinates */
3994   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
3995   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
3996   ierr = PetscSectionSetFieldComponents(coordSection, 0, dimEmbed);CHKERRQ(ierr);
3997   ierr = PetscSectionSetChart(coordSection, firstVertex, firstVertex+numPoints[0]);CHKERRQ(ierr);
3998   for (v = firstVertex; v < firstVertex+numPoints[0]; ++v) {
3999     ierr = PetscSectionSetDof(coordSection, v, dimEmbed);CHKERRQ(ierr);
4000     ierr = PetscSectionSetFieldDof(coordSection, v, 0, dimEmbed);CHKERRQ(ierr);
4001   }
4002   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
4003   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
4004   ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
4005   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
4006   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
4007   ierr = VecSetBlockSize(coordinates, dimEmbed);CHKERRQ(ierr);
4008   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
4009   if (vertexCoords) {
4010     ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
4011     for (v = 0; v < numPoints[0]; ++v) {
4012       PetscInt off;
4013 
4014       ierr = PetscSectionGetOffset(coordSection, v+firstVertex, &off);CHKERRQ(ierr);
4015       for (d = 0; d < dimEmbed; ++d) {
4016         coords[off+d] = vertexCoords[v*dimEmbed+d];
4017       }
4018     }
4019   }
4020   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
4021   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
4022   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
4023   PetscFunctionReturn(0);
4024 }
4025 
4026 /*@C
4027   DMPlexCreateCellVertexFromFile - Create a DMPlex mesh from a simple cell-vertex file.
4028 
4029 + comm        - The MPI communicator
4030 . filename    - Name of the .dat file
4031 - interpolate - Create faces and edges in the mesh
4032 
4033   Output Parameter:
4034 . dm  - The DM object representing the mesh
4035 
4036   Note: The format is the simplest possible:
4037 $ Ne
4038 $ v0 v1 ... vk
4039 $ Nv
4040 $ x y z marker
4041 
4042   Level: beginner
4043 
4044 .seealso: DMPlexCreateFromFile(), DMPlexCreateMedFromFile(), DMPlexCreateGmsh(), DMPlexCreate()
4045 @*/
4046 PetscErrorCode DMPlexCreateCellVertexFromFile(MPI_Comm comm, const char filename[], PetscBool interpolate, DM *dm)
4047 {
4048   DMLabel         marker;
4049   PetscViewer     viewer;
4050   Vec             coordinates;
4051   PetscSection    coordSection;
4052   PetscScalar    *coords;
4053   char            line[PETSC_MAX_PATH_LEN];
4054   PetscInt        dim = 3, cdim = 3, coordSize, v, c, d;
4055   PetscMPIInt     rank;
4056   int             snum, Nv, Nc;
4057   PetscErrorCode  ierr;
4058 
4059   PetscFunctionBegin;
4060   ierr = MPI_Comm_rank(comm, &rank);CHKERRMPI(ierr);
4061   ierr = PetscViewerCreate(comm, &viewer);CHKERRQ(ierr);
4062   ierr = PetscViewerSetType(viewer, PETSCVIEWERASCII);CHKERRQ(ierr);
4063   ierr = PetscViewerFileSetMode(viewer, FILE_MODE_READ);CHKERRQ(ierr);
4064   ierr = PetscViewerFileSetName(viewer, filename);CHKERRQ(ierr);
4065   if (!rank) {
4066     ierr = PetscViewerRead(viewer, line, 2, NULL, PETSC_STRING);CHKERRQ(ierr);
4067     snum = sscanf(line, "%d %d", &Nc, &Nv);
4068     if (snum != 2) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unable to parse cell-vertex file: %s", line);
4069   } else {
4070     Nc = Nv = 0;
4071   }
4072   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
4073   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
4074   ierr = DMPlexSetChart(*dm, 0, Nc+Nv);CHKERRQ(ierr);
4075   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
4076   ierr = DMSetCoordinateDim(*dm, cdim);CHKERRQ(ierr);
4077   /* Read topology */
4078   if (!rank) {
4079     PetscInt cone[8], corners = 8;
4080     int      vbuf[8], v;
4081 
4082     for (c = 0; c < Nc; ++c) {ierr = DMPlexSetConeSize(*dm, c, corners);CHKERRQ(ierr);}
4083     ierr = DMSetUp(*dm);CHKERRQ(ierr);
4084     for (c = 0; c < Nc; ++c) {
4085       ierr = PetscViewerRead(viewer, line, corners, NULL, PETSC_STRING);CHKERRQ(ierr);
4086       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]);
4087       if (snum != corners) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unable to parse cell-vertex file: %s", line);
4088       for (v = 0; v < corners; ++v) cone[v] = vbuf[v] + Nc;
4089       /* Hexahedra are inverted */
4090       {
4091         PetscInt tmp = cone[1];
4092         cone[1] = cone[3];
4093         cone[3] = tmp;
4094       }
4095       ierr = DMPlexSetCone(*dm, c, cone);CHKERRQ(ierr);
4096     }
4097   }
4098   ierr = DMPlexSymmetrize(*dm);CHKERRQ(ierr);
4099   ierr = DMPlexStratify(*dm);CHKERRQ(ierr);
4100   /* Read coordinates */
4101   ierr = DMGetCoordinateSection(*dm, &coordSection);CHKERRQ(ierr);
4102   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
4103   ierr = PetscSectionSetFieldComponents(coordSection, 0, cdim);CHKERRQ(ierr);
4104   ierr = PetscSectionSetChart(coordSection, Nc, Nc + Nv);CHKERRQ(ierr);
4105   for (v = Nc; v < Nc+Nv; ++v) {
4106     ierr = PetscSectionSetDof(coordSection, v, cdim);CHKERRQ(ierr);
4107     ierr = PetscSectionSetFieldDof(coordSection, v, 0, cdim);CHKERRQ(ierr);
4108   }
4109   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
4110   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
4111   ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
4112   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
4113   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
4114   ierr = VecSetBlockSize(coordinates, cdim);CHKERRQ(ierr);
4115   ierr = VecSetType(coordinates, VECSTANDARD);CHKERRQ(ierr);
4116   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
4117   if (!rank) {
4118     double x[3];
4119     int    val;
4120 
4121     ierr = DMCreateLabel(*dm, "marker");CHKERRQ(ierr);
4122     ierr = DMGetLabel(*dm, "marker", &marker);CHKERRQ(ierr);
4123     for (v = 0; v < Nv; ++v) {
4124       ierr = PetscViewerRead(viewer, line, 4, NULL, PETSC_STRING);CHKERRQ(ierr);
4125       snum = sscanf(line, "%lg %lg %lg %d", &x[0], &x[1], &x[2], &val);
4126       if (snum != 4) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unable to parse cell-vertex file: %s", line);
4127       for (d = 0; d < cdim; ++d) coords[v*cdim+d] = x[d];
4128       if (val) {ierr = DMLabelSetValue(marker, v+Nc, val);CHKERRQ(ierr);}
4129     }
4130   }
4131   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
4132   ierr = DMSetCoordinatesLocal(*dm, coordinates);CHKERRQ(ierr);
4133   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
4134   ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
4135   if (interpolate) {
4136     DM      idm;
4137     DMLabel bdlabel;
4138 
4139     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
4140     ierr = DMDestroy(dm);CHKERRQ(ierr);
4141     *dm  = idm;
4142 
4143     ierr = DMGetLabel(*dm, "marker", &bdlabel);CHKERRQ(ierr);
4144     ierr = DMPlexMarkBoundaryFaces(*dm, PETSC_DETERMINE, bdlabel);CHKERRQ(ierr);
4145     ierr = DMPlexLabelComplete(*dm, bdlabel);CHKERRQ(ierr);
4146   }
4147   PetscFunctionReturn(0);
4148 }
4149 
4150 /*@C
4151   DMPlexCreateFromFile - This takes a filename and produces a DM
4152 
4153   Input Parameters:
4154 + comm - The communicator
4155 . filename - A file name
4156 - interpolate - Flag to create intermediate mesh pieces (edges, faces)
4157 
4158   Output Parameter:
4159 . dm - The DM
4160 
4161   Options Database Keys:
4162 . -dm_plex_create_from_hdf5_xdmf - use the PETSC_VIEWER_HDF5_XDMF format for reading HDF5
4163 
4164   Use -dm_plex_create_ prefix to pass options to the internal PetscViewer, e.g.
4165 $ -dm_plex_create_viewer_hdf5_collective
4166 
4167   Level: beginner
4168 
4169 .seealso: DMPlexCreateFromDAG(), DMPlexCreateFromCellListPetsc(), DMPlexCreate()
4170 @*/
4171 PetscErrorCode DMPlexCreateFromFile(MPI_Comm comm, const char filename[], PetscBool interpolate, DM *dm)
4172 {
4173   const char    *extGmsh      = ".msh";
4174   const char    *extGmsh2     = ".msh2";
4175   const char    *extGmsh4     = ".msh4";
4176   const char    *extCGNS      = ".cgns";
4177   const char    *extExodus    = ".exo";
4178   const char    *extGenesis   = ".gen";
4179   const char    *extFluent    = ".cas";
4180   const char    *extHDF5      = ".h5";
4181   const char    *extMed       = ".med";
4182   const char    *extPLY       = ".ply";
4183   const char    *extEGADSLite = ".egadslite";
4184   const char    *extEGADS     = ".egads";
4185   const char    *extIGES      = ".igs";
4186   const char    *extSTEP      = ".stp";
4187   const char    *extCV        = ".dat";
4188   size_t         len;
4189   PetscBool      isGmsh, isGmsh2, isGmsh4, isCGNS, isExodus, isGenesis, isFluent, isHDF5, isMed, isPLY, isEGADSLite, isEGADS, isIGES, isSTEP, isCV;
4190   PetscMPIInt    rank;
4191   PetscErrorCode ierr;
4192 
4193   PetscFunctionBegin;
4194   PetscValidCharPointer(filename, 2);
4195   PetscValidPointer(dm, 4);
4196   ierr = DMInitializePackage();CHKERRQ(ierr);
4197   ierr = PetscLogEventBegin(DMPLEX_CreateFromFile,0,0,0,0);CHKERRQ(ierr);
4198   ierr = MPI_Comm_rank(comm, &rank);CHKERRMPI(ierr);
4199   ierr = PetscStrlen(filename, &len);CHKERRQ(ierr);
4200   if (!len) SETERRQ(comm, PETSC_ERR_ARG_WRONG, "Filename must be a valid path");
4201   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)],  extGmsh,      4, &isGmsh);CHKERRQ(ierr);
4202   ierr = PetscStrncmp(&filename[PetscMax(0,len-5)],  extGmsh2,     5, &isGmsh2);CHKERRQ(ierr);
4203   ierr = PetscStrncmp(&filename[PetscMax(0,len-5)],  extGmsh4,     5, &isGmsh4);CHKERRQ(ierr);
4204   ierr = PetscStrncmp(&filename[PetscMax(0,len-5)],  extCGNS,      5, &isCGNS);CHKERRQ(ierr);
4205   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)],  extExodus,    4, &isExodus);CHKERRQ(ierr);
4206   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)],  extGenesis,   4, &isGenesis);CHKERRQ(ierr);
4207   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)],  extFluent,    4, &isFluent);CHKERRQ(ierr);
4208   ierr = PetscStrncmp(&filename[PetscMax(0,len-3)],  extHDF5,      3, &isHDF5);CHKERRQ(ierr);
4209   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)],  extMed,       4, &isMed);CHKERRQ(ierr);
4210   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)],  extPLY,       4, &isPLY);CHKERRQ(ierr);
4211   ierr = PetscStrncmp(&filename[PetscMax(0,len-10)], extEGADSLite, 10, &isEGADSLite);CHKERRQ(ierr);
4212   ierr = PetscStrncmp(&filename[PetscMax(0,len-6)],  extEGADS,     6, &isEGADS);CHKERRQ(ierr);
4213   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)],  extIGES,      4, &isIGES);CHKERRQ(ierr);
4214   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)],  extSTEP,      4, &isSTEP);CHKERRQ(ierr);
4215   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)],  extCV,        4, &isCV);CHKERRQ(ierr);
4216   if (isGmsh || isGmsh2 || isGmsh4) {
4217     ierr = DMPlexCreateGmshFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
4218   } else if (isCGNS) {
4219     ierr = DMPlexCreateCGNSFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
4220   } else if (isExodus || isGenesis) {
4221     ierr = DMPlexCreateExodusFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
4222   } else if (isFluent) {
4223     ierr = DMPlexCreateFluentFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
4224   } else if (isHDF5) {
4225     PetscBool      load_hdf5_xdmf = PETSC_FALSE;
4226     PetscViewer viewer;
4227 
4228     /* PETSC_VIEWER_HDF5_XDMF is used if the filename ends with .xdmf.h5, or if -dm_plex_create_from_hdf5_xdmf option is present */
4229     ierr = PetscStrncmp(&filename[PetscMax(0,len-8)], ".xdmf",  5, &load_hdf5_xdmf);CHKERRQ(ierr);
4230     ierr = PetscOptionsGetBool(NULL, NULL, "-dm_plex_create_from_hdf5_xdmf", &load_hdf5_xdmf, NULL);CHKERRQ(ierr);
4231     ierr = PetscViewerCreate(comm, &viewer);CHKERRQ(ierr);
4232     ierr = PetscViewerSetType(viewer, PETSCVIEWERHDF5);CHKERRQ(ierr);
4233     ierr = PetscViewerSetOptionsPrefix(viewer, "dm_plex_create_");CHKERRQ(ierr);
4234     ierr = PetscViewerSetFromOptions(viewer);CHKERRQ(ierr);
4235     ierr = PetscViewerFileSetMode(viewer, FILE_MODE_READ);CHKERRQ(ierr);
4236     ierr = PetscViewerFileSetName(viewer, filename);CHKERRQ(ierr);
4237     ierr = DMCreate(comm, dm);CHKERRQ(ierr);
4238     ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
4239     if (load_hdf5_xdmf) {ierr = PetscViewerPushFormat(viewer, PETSC_VIEWER_HDF5_XDMF);CHKERRQ(ierr);}
4240     ierr = DMLoad(*dm, viewer);CHKERRQ(ierr);
4241     if (load_hdf5_xdmf) {ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);}
4242     ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
4243 
4244     if (interpolate) {
4245       DM idm;
4246 
4247       ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
4248       ierr = DMDestroy(dm);CHKERRQ(ierr);
4249       *dm  = idm;
4250     }
4251   } else if (isMed) {
4252     ierr = DMPlexCreateMedFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
4253   } else if (isPLY) {
4254     ierr = DMPlexCreatePLYFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
4255   } else if (isEGADSLite || isEGADS || isIGES || isSTEP) {
4256     if (isEGADSLite) {ierr = DMPlexCreateEGADSLiteFromFile(comm, filename, dm);CHKERRQ(ierr);}
4257     else             {ierr = DMPlexCreateEGADSFromFile(comm, filename, dm);CHKERRQ(ierr);}
4258     if (!interpolate) {
4259       DM udm;
4260 
4261       ierr = DMPlexUninterpolate(*dm, &udm);CHKERRQ(ierr);
4262       ierr = DMDestroy(dm);CHKERRQ(ierr);
4263       *dm  = udm;
4264     }
4265   } else if (isCV) {
4266     ierr = DMPlexCreateCellVertexFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
4267   } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cannot load file %s: unrecognized extension", filename);
4268   ierr = PetscLogEventEnd(DMPLEX_CreateFromFile,0,0,0,0);CHKERRQ(ierr);
4269   PetscFunctionReturn(0);
4270 }
4271