xref: /petsc/src/dm/impls/plex/plexcreate.c (revision 2f613bf53f46f9356e00a2ca2bd69453be72fc31)
1 #define PETSCDM_DLL
2 #include <petsc/private/dmpleximpl.h>    /*I   "petscdmplex.h"   I*/
3 #include <petsc/private/hashseti.h>          /*I   "petscdmplex.h"   I*/
4 #include <petscsf.h>
5 
6 PetscLogEvent DMPLEX_CreateFromFile, DMPLEX_BuildFromCellList, DMPLEX_BuildCoordinatesFromCellList;
7 
8 /* External function declarations here */
9 static PetscErrorCode DMInitialize_Plex(DM dm);
10 
11 /* Replace dm with the contents of ndm, and then destroy ndm
12    - Share the DM_Plex structure
13    - Share the coordinates
14    - Share the SF
15 */
16 static PetscErrorCode DMPlexReplace_Static(DM dm, DM *ndm)
17 {
18   PetscSF               sf;
19   DM                    dmNew = *ndm, coordDM, coarseDM;
20   Vec                   coords;
21   PetscBool             isper;
22   const PetscReal      *maxCell, *L;
23   const DMBoundaryType *bd;
24   PetscInt              dim, cdim;
25   PetscErrorCode        ierr;
26 
27   PetscFunctionBegin;
28   if (dm == dmNew) {
29     ierr = DMDestroy(ndm);CHKERRQ(ierr);
30     PetscFunctionReturn(0);
31   }
32   dm->setupcalled = dmNew->setupcalled;
33   ierr = DMGetDimension(dmNew, &dim);CHKERRQ(ierr);
34   ierr = DMSetDimension(dm, dim);CHKERRQ(ierr);
35   ierr = DMGetCoordinateDim(dmNew, &cdim);CHKERRQ(ierr);
36   ierr = DMSetCoordinateDim(dm, cdim);CHKERRQ(ierr);
37   ierr = DMGetPointSF(dmNew, &sf);CHKERRQ(ierr);
38   ierr = DMSetPointSF(dm, sf);CHKERRQ(ierr);
39   ierr = DMGetCoordinateDM(dmNew, &coordDM);CHKERRQ(ierr);
40   ierr = DMGetCoordinatesLocal(dmNew, &coords);CHKERRQ(ierr);
41   ierr = DMSetCoordinateDM(dm, coordDM);CHKERRQ(ierr);
42   ierr = DMSetCoordinatesLocal(dm, coords);CHKERRQ(ierr);
43   /* Do not want to create the coordinate field if it does not already exist, so do not call DMGetCoordinateField() */
44   ierr = DMFieldDestroy(&dm->coordinateField);CHKERRQ(ierr);
45   dm->coordinateField = dmNew->coordinateField;
46   ((DM_Plex *) dmNew->data)->coordFunc = ((DM_Plex *) dm->data)->coordFunc;
47   ierr = DMGetPeriodicity(dmNew, &isper, &maxCell, &L, &bd);CHKERRQ(ierr);
48   ierr = DMSetPeriodicity(dm, isper, maxCell, L, bd);CHKERRQ(ierr);
49   ierr = DMDestroy_Plex(dm);CHKERRQ(ierr);
50   ierr = DMInitialize_Plex(dm);CHKERRQ(ierr);
51   dm->data = dmNew->data;
52   ((DM_Plex *) dmNew->data)->refct++;
53   ierr = DMDestroyLabelLinkList_Internal(dm);CHKERRQ(ierr);
54   ierr = DMCopyLabels(dmNew, dm, PETSC_OWN_POINTER, PETSC_TRUE, DM_COPY_LABELS_FAIL);CHKERRQ(ierr);
55   ierr = DMGetCoarseDM(dmNew,&coarseDM);CHKERRQ(ierr);
56   ierr = DMSetCoarseDM(dm,coarseDM);CHKERRQ(ierr);
57   ierr = DMDestroy(ndm);CHKERRQ(ierr);
58   PetscFunctionReturn(0);
59 }
60 
61 /* Swap dm with the contents of dmNew
62    - Swap the DM_Plex structure
63    - Swap the coordinates
64    - Swap the point PetscSF
65 */
66 static PetscErrorCode DMPlexSwap_Static(DM dmA, DM dmB)
67 {
68   DM              coordDMA, coordDMB;
69   Vec             coordsA,  coordsB;
70   PetscSF         sfA,      sfB;
71   DMField         fieldTmp;
72   void            *tmp;
73   DMLabelLink     listTmp;
74   DMLabel         depthTmp;
75   PetscInt        tmpI;
76   PetscErrorCode  ierr;
77 
78   PetscFunctionBegin;
79   if (dmA == dmB) PetscFunctionReturn(0);
80   ierr = DMGetPointSF(dmA, &sfA);CHKERRQ(ierr);
81   ierr = DMGetPointSF(dmB, &sfB);CHKERRQ(ierr);
82   ierr = PetscObjectReference((PetscObject) sfA);CHKERRQ(ierr);
83   ierr = DMSetPointSF(dmA, sfB);CHKERRQ(ierr);
84   ierr = DMSetPointSF(dmB, sfA);CHKERRQ(ierr);
85   ierr = PetscObjectDereference((PetscObject) sfA);CHKERRQ(ierr);
86 
87   ierr = DMGetCoordinateDM(dmA, &coordDMA);CHKERRQ(ierr);
88   ierr = DMGetCoordinateDM(dmB, &coordDMB);CHKERRQ(ierr);
89   ierr = PetscObjectReference((PetscObject) coordDMA);CHKERRQ(ierr);
90   ierr = DMSetCoordinateDM(dmA, coordDMB);CHKERRQ(ierr);
91   ierr = DMSetCoordinateDM(dmB, coordDMA);CHKERRQ(ierr);
92   ierr = PetscObjectDereference((PetscObject) coordDMA);CHKERRQ(ierr);
93 
94   ierr = DMGetCoordinatesLocal(dmA, &coordsA);CHKERRQ(ierr);
95   ierr = DMGetCoordinatesLocal(dmB, &coordsB);CHKERRQ(ierr);
96   ierr = PetscObjectReference((PetscObject) coordsA);CHKERRQ(ierr);
97   ierr = DMSetCoordinatesLocal(dmA, coordsB);CHKERRQ(ierr);
98   ierr = DMSetCoordinatesLocal(dmB, coordsA);CHKERRQ(ierr);
99   ierr = PetscObjectDereference((PetscObject) coordsA);CHKERRQ(ierr);
100 
101   fieldTmp             = dmA->coordinateField;
102   dmA->coordinateField = dmB->coordinateField;
103   dmB->coordinateField = fieldTmp;
104   tmp       = dmA->data;
105   dmA->data = dmB->data;
106   dmB->data = tmp;
107   listTmp   = dmA->labels;
108   dmA->labels = dmB->labels;
109   dmB->labels = listTmp;
110   depthTmp  = dmA->depthLabel;
111   dmA->depthLabel = dmB->depthLabel;
112   dmB->depthLabel = depthTmp;
113   depthTmp  = dmA->celltypeLabel;
114   dmA->celltypeLabel = dmB->celltypeLabel;
115   dmB->celltypeLabel = depthTmp;
116   tmpI         = dmA->levelup;
117   dmA->levelup = dmB->levelup;
118   dmB->levelup = tmpI;
119   PetscFunctionReturn(0);
120 }
121 
122 static PetscErrorCode DMPlexInterpolateInPlace_Internal(DM dm)
123 {
124   DM             idm;
125   PetscErrorCode ierr;
126 
127   PetscFunctionBegin;
128   ierr = DMPlexInterpolate(dm, &idm);CHKERRQ(ierr);
129   ierr = DMPlexCopyCoordinates(dm, idm);CHKERRQ(ierr);
130   ierr = DMPlexReplace_Static(dm, &idm);CHKERRQ(ierr);
131   PetscFunctionReturn(0);
132 }
133 
134 /*@C
135   DMPlexCreateCoordinateSpace - Creates a finite element space for the coordinates
136 
137   Collective
138 
139   Input Parameters:
140 + DM        - The DM
141 . degree    - The degree of the finite element
142 - coordFunc - An optional function to map new points from refinement to the surface
143 
144   Level: advanced
145 
146 .seealso: PetscFECreateLagrange(), DMGetCoordinateDM()
147 @*/
148 PetscErrorCode DMPlexCreateCoordinateSpace(DM dm, PetscInt degree, PetscPointFunc coordFunc)
149 {
150   DM_Plex       *mesh = (DM_Plex *) dm->data;
151   DM             cdm;
152   PetscDS        cds;
153   PetscFE        fe;
154   PetscClassId   id;
155   PetscErrorCode ierr;
156 
157   PetscFunctionBegin;
158   ierr = DMGetCoordinateDM(dm, &cdm);CHKERRQ(ierr);
159   ierr = DMGetDS(cdm, &cds);CHKERRQ(ierr);
160   ierr = PetscDSGetDiscretization(cds, 0, (PetscObject *) &fe);CHKERRQ(ierr);
161   ierr = PetscObjectGetClassId((PetscObject) fe, &id);CHKERRQ(ierr);
162   if (id != PETSCFE_CLASSID) {
163     PetscBool simplex;
164     PetscInt  dim, dE, qorder;
165 
166     ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
167     ierr = DMGetCoordinateDim(dm, &dE);CHKERRQ(ierr);
168     ierr = DMPlexIsSimplex(dm, &simplex);CHKERRQ(ierr);
169     qorder = degree;
170     ierr = PetscObjectOptionsBegin((PetscObject) cdm);CHKERRQ(ierr);
171     ierr = PetscOptionsBoundedInt("-coord_dm_default_quadrature_order", "Quadrature order is one less than quadrature points per edge", "DMPlexCreateCoordinateSpace", qorder, &qorder, NULL, 0);CHKERRQ(ierr);
172     ierr = PetscOptionsEnd();CHKERRQ(ierr);
173     ierr = PetscFECreateLagrange(PETSC_COMM_SELF, dim, dE, simplex, degree, qorder, &fe);CHKERRQ(ierr);
174     ierr = DMSetField(cdm, 0, NULL, (PetscObject) fe);CHKERRQ(ierr);
175     ierr = DMCreateDS(cdm);CHKERRQ(ierr);
176     ierr = DMProjectCoordinates(dm, fe);CHKERRQ(ierr);
177     ierr = PetscFEDestroy(&fe);CHKERRQ(ierr);
178   }
179   mesh->coordFunc = coordFunc;
180   PetscFunctionReturn(0);
181 }
182 
183 /*@
184   DMPlexCreateDoublet - Creates a mesh of two cells of the specified type, optionally with later refinement.
185 
186   Collective
187 
188   Input Parameters:
189 + comm - The communicator for the DM object
190 . dim - The spatial dimension
191 . simplex - Flag for simplicial cells, otherwise they are tensor product cells
192 . interpolate - Flag to create intermediate mesh pieces (edges, faces)
193 - refinementLimit - A nonzero number indicates the largest admissible volume for a refined cell
194 
195   Output Parameter:
196 . dm - The DM object
197 
198   Level: beginner
199 
200 .seealso: DMSetType(), DMCreate()
201 @*/
202 PetscErrorCode DMPlexCreateDoublet(MPI_Comm comm, PetscInt dim, PetscBool simplex, PetscBool interpolate, PetscReal refinementLimit, DM *newdm)
203 {
204   DM             dm;
205   PetscMPIInt    rank;
206   PetscErrorCode ierr;
207 
208   PetscFunctionBegin;
209   ierr = DMCreate(comm, &dm);CHKERRQ(ierr);
210   ierr = DMSetType(dm, DMPLEX);CHKERRQ(ierr);
211   ierr = DMSetDimension(dm, dim);CHKERRQ(ierr);
212   ierr = MPI_Comm_rank(comm, &rank);CHKERRMPI(ierr);
213   switch (dim) {
214   case 2:
215     if (simplex) {ierr = PetscObjectSetName((PetscObject) dm, "triangular");CHKERRQ(ierr);}
216     else         {ierr = PetscObjectSetName((PetscObject) dm, "quadrilateral");CHKERRQ(ierr);}
217     break;
218   case 3:
219     if (simplex) {ierr = PetscObjectSetName((PetscObject) dm, "tetrahedral");CHKERRQ(ierr);}
220     else         {ierr = PetscObjectSetName((PetscObject) dm, "hexahedral");CHKERRQ(ierr);}
221     break;
222   default:
223     SETERRQ1(comm, PETSC_ERR_ARG_OUTOFRANGE, "Cannot make meshes for dimension %D", dim);
224   }
225   if (rank) {
226     PetscInt numPoints[2] = {0, 0};
227     ierr = DMPlexCreateFromDAG(dm, 1, numPoints, NULL, NULL, NULL, NULL);CHKERRQ(ierr);
228   } else {
229     switch (dim) {
230     case 2:
231       if (simplex) {
232         PetscInt    numPoints[2]        = {4, 2};
233         PetscInt    coneSize[6]         = {3, 3, 0, 0, 0, 0};
234         PetscInt    cones[6]            = {2, 3, 4,  5, 4, 3};
235         PetscInt    coneOrientations[6] = {0, 0, 0,  0, 0, 0};
236         PetscScalar vertexCoords[8]     = {-0.5, 0.5, 0.0, 0.0, 0.0, 1.0, 0.5, 0.5};
237 
238         ierr = DMPlexCreateFromDAG(dm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
239       } else {
240         PetscInt    numPoints[2]        = {6, 2};
241         PetscInt    coneSize[8]         = {4, 4, 0, 0, 0, 0, 0, 0};
242         PetscInt    cones[8]            = {2, 3, 4, 5,  3, 6, 7, 4};
243         PetscInt    coneOrientations[8] = {0, 0, 0, 0,  0, 0, 0, 0};
244         PetscScalar vertexCoords[12]    = {-1.0, -0.5,  0.0, -0.5,  0.0, 0.5,  -1.0, 0.5,  1.0, -0.5,  1.0, 0.5};
245 
246         ierr = DMPlexCreateFromDAG(dm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
247       }
248       break;
249     case 3:
250       if (simplex) {
251         PetscInt    numPoints[2]        = {5, 2};
252         PetscInt    coneSize[7]         = {4, 4, 0, 0, 0, 0, 0};
253         PetscInt    cones[8]            = {4, 3, 5, 2,  5, 3, 4, 6};
254         PetscInt    coneOrientations[8] = {0, 0, 0, 0,  0, 0, 0, 0};
255         PetscScalar vertexCoords[15]    = {-1.0, 0.0, 0.0,  0.0, -1.0, 0.0,  0.0, 0.0, 1.0,  0.0, 1.0, 0.0,  1.0, 0.0, 0.0};
256 
257         ierr = DMPlexCreateFromDAG(dm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
258       } else {
259         PetscInt    numPoints[2]         = {12, 2};
260         PetscInt    coneSize[14]         = {8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0};
261         PetscInt    cones[16]            = {2, 3, 4, 5, 6, 7, 8, 9,  5, 4, 10, 11, 7, 12, 13, 8};
262         PetscInt    coneOrientations[16] = {0, 0, 0, 0, 0, 0, 0, 0,  0, 0,  0,  0, 0,  0,  0, 0};
263         PetscScalar vertexCoords[36]     = {-1.0, -0.5, -0.5,  -1.0,  0.5, -0.5,  0.0,  0.5, -0.5,   0.0, -0.5, -0.5,
264                                             -1.0, -0.5,  0.5,   0.0, -0.5,  0.5,  0.0,  0.5,  0.5,  -1.0,  0.5,  0.5,
265                                              1.0,  0.5, -0.5,   1.0, -0.5, -0.5,  1.0, -0.5,  0.5,   1.0,  0.5,  0.5};
266 
267         ierr = DMPlexCreateFromDAG(dm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
268       }
269       break;
270     default:
271       SETERRQ1(comm, PETSC_ERR_ARG_OUTOFRANGE, "Cannot make meshes for dimension %D", dim);
272     }
273   }
274   *newdm = dm;
275   if (refinementLimit > 0.0) {
276     DM rdm;
277     const char *name;
278 
279     ierr = DMPlexSetRefinementUniform(*newdm, PETSC_FALSE);CHKERRQ(ierr);
280     ierr = DMPlexSetRefinementLimit(*newdm, refinementLimit);CHKERRQ(ierr);
281     ierr = DMRefine(*newdm, comm, &rdm);CHKERRQ(ierr);
282     ierr = PetscObjectGetName((PetscObject) *newdm, &name);CHKERRQ(ierr);
283     ierr = PetscObjectSetName((PetscObject)    rdm,  name);CHKERRQ(ierr);
284     ierr = DMDestroy(newdm);CHKERRQ(ierr);
285     *newdm = rdm;
286   }
287   if (interpolate) {
288     DM idm;
289 
290     ierr = DMPlexInterpolate(*newdm, &idm);CHKERRQ(ierr);
291     ierr = DMDestroy(newdm);CHKERRQ(ierr);
292     *newdm = idm;
293   }
294   PetscFunctionReturn(0);
295 }
296 
297 static PetscErrorCode DMPlexCreateBoxSurfaceMesh_Tensor_1D_Internal(DM dm, const PetscReal lower[], const PetscReal upper[], const PetscInt edges[])
298 {
299   const PetscInt numVertices    = 2;
300   PetscInt       markerRight    = 1;
301   PetscInt       markerLeft     = 1;
302   PetscBool      markerSeparate = PETSC_FALSE;
303   Vec            coordinates;
304   PetscSection   coordSection;
305   PetscScalar   *coords;
306   PetscInt       coordSize;
307   PetscMPIInt    rank;
308   PetscInt       cdim = 1, v;
309   PetscErrorCode ierr;
310 
311   PetscFunctionBegin;
312   ierr = PetscOptionsGetBool(((PetscObject) dm)->options,((PetscObject) dm)->prefix, "-dm_plex_separate_marker", &markerSeparate, NULL);CHKERRQ(ierr);
313   if (markerSeparate) {
314     markerRight  = 2;
315     markerLeft   = 1;
316   }
317   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);CHKERRMPI(ierr);
318   if (!rank) {
319     ierr = DMPlexSetChart(dm, 0, numVertices);CHKERRQ(ierr);
320     ierr = DMSetUp(dm);CHKERRQ(ierr); /* Allocate space for cones */
321     ierr = DMSetLabelValue(dm, "marker", 0, markerLeft);CHKERRQ(ierr);
322     ierr = DMSetLabelValue(dm, "marker", 1, markerRight);CHKERRQ(ierr);
323   }
324   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
325   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
326   /* Build coordinates */
327   ierr = DMSetCoordinateDim(dm, cdim);CHKERRQ(ierr);
328   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
329   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
330   ierr = PetscSectionSetChart(coordSection, 0, numVertices);CHKERRQ(ierr);
331   ierr = PetscSectionSetFieldComponents(coordSection, 0, cdim);CHKERRQ(ierr);
332   for (v = 0; v < numVertices; ++v) {
333     ierr = PetscSectionSetDof(coordSection, v, cdim);CHKERRQ(ierr);
334     ierr = PetscSectionSetFieldDof(coordSection, v, 0, cdim);CHKERRQ(ierr);
335   }
336   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
337   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
338   ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
339   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
340   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
341   ierr = VecSetBlockSize(coordinates, cdim);CHKERRQ(ierr);
342   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
343   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
344   coords[0] = lower[0];
345   coords[1] = upper[0];
346   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
347   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
348   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
349   PetscFunctionReturn(0);
350 }
351 
352 static PetscErrorCode DMPlexCreateBoxSurfaceMesh_Tensor_2D_Internal(DM dm, const PetscReal lower[], const PetscReal upper[], const PetscInt edges[])
353 {
354   const PetscInt numVertices    = (edges[0]+1)*(edges[1]+1);
355   const PetscInt numEdges       = edges[0]*(edges[1]+1) + (edges[0]+1)*edges[1];
356   PetscInt       markerTop      = 1;
357   PetscInt       markerBottom   = 1;
358   PetscInt       markerRight    = 1;
359   PetscInt       markerLeft     = 1;
360   PetscBool      markerSeparate = PETSC_FALSE;
361   Vec            coordinates;
362   PetscSection   coordSection;
363   PetscScalar    *coords;
364   PetscInt       coordSize;
365   PetscMPIInt    rank;
366   PetscInt       v, vx, vy;
367   PetscErrorCode ierr;
368 
369   PetscFunctionBegin;
370   ierr = PetscOptionsGetBool(((PetscObject) dm)->options,((PetscObject) dm)->prefix, "-dm_plex_separate_marker", &markerSeparate, NULL);CHKERRQ(ierr);
371   if (markerSeparate) {
372     markerTop    = 3;
373     markerBottom = 1;
374     markerRight  = 2;
375     markerLeft   = 4;
376   }
377   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);CHKERRMPI(ierr);
378   if (rank == 0) {
379     PetscInt e, ex, ey;
380 
381     ierr = DMPlexSetChart(dm, 0, numEdges+numVertices);CHKERRQ(ierr);
382     for (e = 0; e < numEdges; ++e) {
383       ierr = DMPlexSetConeSize(dm, e, 2);CHKERRQ(ierr);
384     }
385     ierr = DMSetUp(dm);CHKERRQ(ierr); /* Allocate space for cones */
386     for (vx = 0; vx <= edges[0]; vx++) {
387       for (ey = 0; ey < edges[1]; ey++) {
388         PetscInt edge   = vx*edges[1] + ey + edges[0]*(edges[1]+1);
389         PetscInt vertex = ey*(edges[0]+1) + vx + numEdges;
390         PetscInt cone[2];
391 
392         cone[0] = vertex; cone[1] = vertex+edges[0]+1;
393         ierr    = DMPlexSetCone(dm, edge, cone);CHKERRQ(ierr);
394         if (vx == edges[0]) {
395           ierr = DMSetLabelValue(dm, "marker", edge,    markerRight);CHKERRQ(ierr);
396           ierr = DMSetLabelValue(dm, "marker", cone[0], markerRight);CHKERRQ(ierr);
397           if (ey == edges[1]-1) {
398             ierr = DMSetLabelValue(dm, "marker", cone[1], markerRight);CHKERRQ(ierr);
399             ierr = DMSetLabelValue(dm, "Face Sets", cone[1], markerRight);CHKERRQ(ierr);
400           }
401         } else if (vx == 0) {
402           ierr = DMSetLabelValue(dm, "marker", edge,    markerLeft);CHKERRQ(ierr);
403           ierr = DMSetLabelValue(dm, "marker", cone[0], markerLeft);CHKERRQ(ierr);
404           if (ey == edges[1]-1) {
405             ierr = DMSetLabelValue(dm, "marker", cone[1], markerLeft);CHKERRQ(ierr);
406             ierr = DMSetLabelValue(dm, "Face Sets", cone[1], markerLeft);CHKERRQ(ierr);
407           }
408         }
409       }
410     }
411     for (vy = 0; vy <= edges[1]; vy++) {
412       for (ex = 0; ex < edges[0]; ex++) {
413         PetscInt edge   = vy*edges[0]     + ex;
414         PetscInt vertex = vy*(edges[0]+1) + ex + numEdges;
415         PetscInt cone[2];
416 
417         cone[0] = vertex; cone[1] = vertex+1;
418         ierr    = DMPlexSetCone(dm, edge, cone);CHKERRQ(ierr);
419         if (vy == edges[1]) {
420           ierr = DMSetLabelValue(dm, "marker", edge,    markerTop);CHKERRQ(ierr);
421           ierr = DMSetLabelValue(dm, "marker", cone[0], markerTop);CHKERRQ(ierr);
422           if (ex == edges[0]-1) {
423             ierr = DMSetLabelValue(dm, "marker", cone[1], markerTop);CHKERRQ(ierr);
424             ierr = DMSetLabelValue(dm, "Face Sets", cone[1], markerTop);CHKERRQ(ierr);
425           }
426         } else if (vy == 0) {
427           ierr = DMSetLabelValue(dm, "marker", edge,    markerBottom);CHKERRQ(ierr);
428           ierr = DMSetLabelValue(dm, "marker", cone[0], markerBottom);CHKERRQ(ierr);
429           if (ex == edges[0]-1) {
430             ierr = DMSetLabelValue(dm, "marker", cone[1], markerBottom);CHKERRQ(ierr);
431             ierr = DMSetLabelValue(dm, "Face Sets", cone[1], markerBottom);CHKERRQ(ierr);
432           }
433         }
434       }
435     }
436   }
437   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
438   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
439   /* Build coordinates */
440   ierr = DMSetCoordinateDim(dm, 2);CHKERRQ(ierr);
441   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
442   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
443   ierr = PetscSectionSetChart(coordSection, numEdges, numEdges + numVertices);CHKERRQ(ierr);
444   ierr = PetscSectionSetFieldComponents(coordSection, 0, 2);CHKERRQ(ierr);
445   for (v = numEdges; v < numEdges+numVertices; ++v) {
446     ierr = PetscSectionSetDof(coordSection, v, 2);CHKERRQ(ierr);
447     ierr = PetscSectionSetFieldDof(coordSection, v, 0, 2);CHKERRQ(ierr);
448   }
449   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
450   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
451   ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
452   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
453   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
454   ierr = VecSetBlockSize(coordinates, 2);CHKERRQ(ierr);
455   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
456   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
457   for (vy = 0; vy <= edges[1]; ++vy) {
458     for (vx = 0; vx <= edges[0]; ++vx) {
459       coords[(vy*(edges[0]+1)+vx)*2+0] = lower[0] + ((upper[0] - lower[0])/edges[0])*vx;
460       coords[(vy*(edges[0]+1)+vx)*2+1] = lower[1] + ((upper[1] - lower[1])/edges[1])*vy;
461     }
462   }
463   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
464   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
465   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
466   PetscFunctionReturn(0);
467 }
468 
469 static PetscErrorCode DMPlexCreateBoxSurfaceMesh_Tensor_3D_Internal(DM dm, const PetscReal lower[], const PetscReal upper[], const PetscInt faces[])
470 {
471   PetscInt       vertices[3], numVertices;
472   PetscInt       numFaces    = 2*faces[0]*faces[1] + 2*faces[1]*faces[2] + 2*faces[0]*faces[2];
473   Vec            coordinates;
474   PetscSection   coordSection;
475   PetscScalar    *coords;
476   PetscInt       coordSize;
477   PetscMPIInt    rank;
478   PetscInt       v, vx, vy, vz;
479   PetscInt       voffset, iface=0, cone[4];
480   PetscErrorCode ierr;
481 
482   PetscFunctionBegin;
483   if ((faces[0] < 1) || (faces[1] < 1) || (faces[2] < 1)) SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Must have at least 1 face per side");
484   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);CHKERRMPI(ierr);
485   vertices[0] = faces[0]+1; vertices[1] = faces[1]+1; vertices[2] = faces[2]+1;
486   numVertices = vertices[0]*vertices[1]*vertices[2];
487   if (rank == 0) {
488     PetscInt f;
489 
490     ierr = DMPlexSetChart(dm, 0, numFaces+numVertices);CHKERRQ(ierr);
491     for (f = 0; f < numFaces; ++f) {
492       ierr = DMPlexSetConeSize(dm, f, 4);CHKERRQ(ierr);
493     }
494     ierr = DMSetUp(dm);CHKERRQ(ierr); /* Allocate space for cones */
495 
496     /* Side 0 (Top) */
497     for (vy = 0; vy < faces[1]; vy++) {
498       for (vx = 0; vx < faces[0]; vx++) {
499         voffset = numFaces + vertices[0]*vertices[1]*(vertices[2]-1) + vy*vertices[0] + vx;
500         cone[0] = voffset; cone[1] = voffset+1; cone[2] = voffset+vertices[0]+1; cone[3] = voffset+vertices[0];
501         ierr    = DMPlexSetCone(dm, iface, cone);CHKERRQ(ierr);
502         ierr    = DMSetLabelValue(dm, "marker", iface, 1);CHKERRQ(ierr);
503         ierr    = DMSetLabelValue(dm, "marker", voffset+0, 1);CHKERRQ(ierr);
504         ierr    = DMSetLabelValue(dm, "marker", voffset+1, 1);CHKERRQ(ierr);
505         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[0]+0, 1);CHKERRQ(ierr);
506         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[0]+1, 1);CHKERRQ(ierr);
507         iface++;
508       }
509     }
510 
511     /* Side 1 (Bottom) */
512     for (vy = 0; vy < faces[1]; vy++) {
513       for (vx = 0; vx < faces[0]; vx++) {
514         voffset = numFaces + vy*(faces[0]+1) + vx;
515         cone[0] = voffset+1; cone[1] = voffset; cone[2] = voffset+vertices[0]; cone[3] = voffset+vertices[0]+1;
516         ierr    = DMPlexSetCone(dm, iface, cone);CHKERRQ(ierr);
517         ierr    = DMSetLabelValue(dm, "marker", iface, 1);CHKERRQ(ierr);
518         ierr    = DMSetLabelValue(dm, "marker", voffset+0, 1);CHKERRQ(ierr);
519         ierr    = DMSetLabelValue(dm, "marker", voffset+1, 1);CHKERRQ(ierr);
520         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[0]+0, 1);CHKERRQ(ierr);
521         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[0]+1, 1);CHKERRQ(ierr);
522         iface++;
523       }
524     }
525 
526     /* Side 2 (Front) */
527     for (vz = 0; vz < faces[2]; vz++) {
528       for (vx = 0; vx < faces[0]; vx++) {
529         voffset = numFaces + vz*vertices[0]*vertices[1] + vx;
530         cone[0] = voffset; cone[1] = voffset+1; cone[2] = voffset+vertices[0]*vertices[1]+1; cone[3] = voffset+vertices[0]*vertices[1];
531         ierr    = DMPlexSetCone(dm, iface, cone);CHKERRQ(ierr);
532         ierr    = DMSetLabelValue(dm, "marker", iface, 1);CHKERRQ(ierr);
533         ierr    = DMSetLabelValue(dm, "marker", voffset+0, 1);CHKERRQ(ierr);
534         ierr    = DMSetLabelValue(dm, "marker", voffset+1, 1);CHKERRQ(ierr);
535         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[0]*vertices[1]+0, 1);CHKERRQ(ierr);
536         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[0]*vertices[1]+1, 1);CHKERRQ(ierr);
537         iface++;
538       }
539     }
540 
541     /* Side 3 (Back) */
542     for (vz = 0; vz < faces[2]; vz++) {
543       for (vx = 0; vx < faces[0]; vx++) {
544         voffset = numFaces + vz*vertices[0]*vertices[1] + vertices[0]*(vertices[1]-1) + vx;
545         cone[0] = voffset+vertices[0]*vertices[1]; cone[1] = voffset+vertices[0]*vertices[1]+1;
546         cone[2] = voffset+1; cone[3] = voffset;
547         ierr    = DMPlexSetCone(dm, iface, cone);CHKERRQ(ierr);
548         ierr    = DMSetLabelValue(dm, "marker", iface, 1);CHKERRQ(ierr);
549         ierr    = DMSetLabelValue(dm, "marker", voffset+0, 1);CHKERRQ(ierr);
550         ierr    = DMSetLabelValue(dm, "marker", voffset+1, 1);CHKERRQ(ierr);
551         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[0]*vertices[1]+0, 1);CHKERRQ(ierr);
552         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[0]*vertices[1]+1, 1);CHKERRQ(ierr);
553         iface++;
554       }
555     }
556 
557     /* Side 4 (Left) */
558     for (vz = 0; vz < faces[2]; vz++) {
559       for (vy = 0; vy < faces[1]; vy++) {
560         voffset = numFaces + vz*vertices[0]*vertices[1] + vy*vertices[0];
561         cone[0] = voffset; cone[1] = voffset+vertices[0]*vertices[1];
562         cone[2] = voffset+vertices[0]*vertices[1]+vertices[0]; cone[3] = voffset+vertices[0];
563         ierr    = DMPlexSetCone(dm, iface, cone);CHKERRQ(ierr);
564         ierr    = DMSetLabelValue(dm, "marker", iface, 1);CHKERRQ(ierr);
565         ierr    = DMSetLabelValue(dm, "marker", voffset+0, 1);CHKERRQ(ierr);
566         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[0]+0, 1);CHKERRQ(ierr);
567         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[1]+0, 1);CHKERRQ(ierr);
568         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[0]*vertices[1]+vertices[0], 1);CHKERRQ(ierr);
569         iface++;
570       }
571     }
572 
573     /* Side 5 (Right) */
574     for (vz = 0; vz < faces[2]; vz++) {
575       for (vy = 0; vy < faces[1]; vy++) {
576         voffset = numFaces + vz*vertices[0]*vertices[1] + vy*vertices[0] + faces[0];
577         cone[0] = voffset+vertices[0]*vertices[1]; cone[1] = voffset;
578         cone[2] = voffset+vertices[0]; cone[3] = voffset+vertices[0]*vertices[1]+vertices[0];
579         ierr    = DMPlexSetCone(dm, iface, cone);CHKERRQ(ierr);
580         ierr    = DMSetLabelValue(dm, "marker", iface, 1);CHKERRQ(ierr);
581         ierr    = DMSetLabelValue(dm, "marker", voffset+0, 1);CHKERRQ(ierr);
582         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[0]+0, 1);CHKERRQ(ierr);
583         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[0]*vertices[1]+0, 1);CHKERRQ(ierr);
584         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[0]*vertices[1]+vertices[0], 1);CHKERRQ(ierr);
585         iface++;
586       }
587     }
588   }
589   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
590   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
591   /* Build coordinates */
592   ierr = DMSetCoordinateDim(dm, 3);CHKERRQ(ierr);
593   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
594   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
595   ierr = PetscSectionSetChart(coordSection, numFaces, numFaces + numVertices);CHKERRQ(ierr);
596   ierr = PetscSectionSetFieldComponents(coordSection, 0, 3);CHKERRQ(ierr);
597   for (v = numFaces; v < numFaces+numVertices; ++v) {
598     ierr = PetscSectionSetDof(coordSection, v, 3);CHKERRQ(ierr);
599     ierr = PetscSectionSetFieldDof(coordSection, v, 0, 3);CHKERRQ(ierr);
600   }
601   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
602   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
603   ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
604   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
605   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
606   ierr = VecSetBlockSize(coordinates, 3);CHKERRQ(ierr);
607   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
608   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
609   for (vz = 0; vz <= faces[2]; ++vz) {
610     for (vy = 0; vy <= faces[1]; ++vy) {
611       for (vx = 0; vx <= faces[0]; ++vx) {
612         coords[((vz*(faces[1]+1)+vy)*(faces[0]+1)+vx)*3+0] = lower[0] + ((upper[0] - lower[0])/faces[0])*vx;
613         coords[((vz*(faces[1]+1)+vy)*(faces[0]+1)+vx)*3+1] = lower[1] + ((upper[1] - lower[1])/faces[1])*vy;
614         coords[((vz*(faces[1]+1)+vy)*(faces[0]+1)+vx)*3+2] = lower[2] + ((upper[2] - lower[2])/faces[2])*vz;
615       }
616     }
617   }
618   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
619   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
620   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
621   PetscFunctionReturn(0);
622 }
623 
624 static PetscErrorCode DMPlexCreateBoxSurfaceMesh_Internal(DM dm, PetscInt dim, const PetscInt faces[], const PetscReal lower[], const PetscReal upper[], PetscBool interpolate)
625 {
626   PetscErrorCode ierr;
627 
628   PetscFunctionBegin;
629   PetscValidLogicalCollectiveInt(dm, dim, 2);
630   ierr = DMSetDimension(dm, dim-1);CHKERRQ(ierr);
631   ierr = DMSetCoordinateDim(dm, dim);CHKERRQ(ierr);
632   switch (dim) {
633     case 1: ierr = DMPlexCreateBoxSurfaceMesh_Tensor_1D_Internal(dm, lower, upper, faces);CHKERRQ(ierr);break;
634     case 2: ierr = DMPlexCreateBoxSurfaceMesh_Tensor_2D_Internal(dm, lower, upper, faces);CHKERRQ(ierr);break;
635     case 3: ierr = DMPlexCreateBoxSurfaceMesh_Tensor_3D_Internal(dm, lower, upper, faces);CHKERRQ(ierr);break;
636     default: SETERRQ1(PetscObjectComm((PetscObject) dm), PETSC_ERR_SUP, "Dimension not supported: %D", dim);
637   }
638   if (interpolate) {ierr = DMPlexInterpolateInPlace_Internal(dm);CHKERRQ(ierr);}
639   PetscFunctionReturn(0);
640 }
641 
642 /*@C
643   DMPlexCreateBoxSurfaceMesh - Creates a mesh on the surface of the tensor product of unit intervals (box) using tensor cells (hexahedra).
644 
645   Collective
646 
647   Input Parameters:
648 + comm        - The communicator for the DM object
649 . dim         - The spatial dimension of the box, so the resulting mesh is has dimension dim-1
650 . faces       - Number of faces per dimension, or NULL for (1,) in 1D and (2, 2) in 2D and (1, 1, 1) in 3D
651 . lower       - The lower left corner, or NULL for (0, 0, 0)
652 . upper       - The upper right corner, or NULL for (1, 1, 1)
653 - interpolate - Flag to create intermediate mesh pieces (edges, faces)
654 
655   Output Parameter:
656 . dm  - The DM object
657 
658   Level: beginner
659 
660 .seealso: DMSetFromOptions(), DMPlexCreateBoxMesh(), DMPlexCreateFromFile(), DMSetType(), DMCreate()
661 @*/
662 PetscErrorCode DMPlexCreateBoxSurfaceMesh(MPI_Comm comm, PetscInt dim, const PetscInt faces[], const PetscReal lower[], const PetscReal upper[], PetscBool interpolate, DM *dm)
663 {
664   PetscInt       fac[3] = {1, 1, 1};
665   PetscReal      low[3] = {0, 0, 0};
666   PetscReal      upp[3] = {1, 1, 1};
667   PetscErrorCode ierr;
668 
669   PetscFunctionBegin;
670   ierr = DMCreate(comm,dm);CHKERRQ(ierr);
671   ierr = DMSetType(*dm,DMPLEX);CHKERRQ(ierr);
672   ierr = DMPlexCreateBoxSurfaceMesh_Internal(*dm, dim, faces ? faces : fac, lower ? lower : low, upper ? upper : upp, interpolate);CHKERRQ(ierr);
673   PetscFunctionReturn(0);
674 }
675 
676 static PetscErrorCode DMPlexCreateLineMesh_Internal(DM dm,PetscInt segments,PetscReal lower,PetscReal upper,DMBoundaryType bd)
677 {
678   PetscInt       i,fStart,fEnd,numCells = 0,numVerts = 0;
679   PetscInt       numPoints[2],*coneSize,*cones,*coneOrientations;
680   PetscScalar    *vertexCoords;
681   PetscReal      L,maxCell;
682   PetscBool      markerSeparate = PETSC_FALSE;
683   PetscInt       markerLeft  = 1, faceMarkerLeft  = 1;
684   PetscInt       markerRight = 1, faceMarkerRight = 2;
685   PetscBool      wrap = (bd == DM_BOUNDARY_PERIODIC || bd == DM_BOUNDARY_TWIST) ? PETSC_TRUE : PETSC_FALSE;
686   PetscMPIInt    rank;
687   PetscErrorCode ierr;
688 
689   PetscFunctionBegin;
690   PetscValidPointer(dm,1);
691 
692   ierr = DMSetDimension(dm,1);CHKERRQ(ierr);
693   ierr = DMCreateLabel(dm,"marker");CHKERRQ(ierr);
694   ierr = DMCreateLabel(dm,"Face Sets");CHKERRQ(ierr);
695 
696   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject) dm),&rank);CHKERRMPI(ierr);
697   if (rank == 0) numCells = segments;
698   if (rank == 0) numVerts = segments + (wrap ? 0 : 1);
699 
700   numPoints[0] = numVerts ; numPoints[1] = numCells;
701   ierr = PetscMalloc4(numCells+numVerts,&coneSize,numCells*2,&cones,numCells+numVerts,&coneOrientations,numVerts,&vertexCoords);CHKERRQ(ierr);
702   ierr = PetscArrayzero(coneOrientations,numCells+numVerts);CHKERRQ(ierr);
703   for (i = 0; i < numCells; ++i) { coneSize[i] = 2; }
704   for (i = 0; i < numVerts; ++i) { coneSize[numCells+i] = 0; }
705   for (i = 0; i < numCells; ++i) { cones[2*i] = numCells + i%numVerts; cones[2*i+1] = numCells + (i+1)%numVerts; }
706   for (i = 0; i < numVerts; ++i) { vertexCoords[i] = lower + (upper-lower)*((PetscReal)i/(PetscReal)numCells); }
707   ierr = DMPlexCreateFromDAG(dm,1,numPoints,coneSize,cones,coneOrientations,vertexCoords);CHKERRQ(ierr);
708   ierr = PetscFree4(coneSize,cones,coneOrientations,vertexCoords);CHKERRQ(ierr);
709 
710   ierr = PetscOptionsGetBool(((PetscObject)dm)->options,((PetscObject)dm)->prefix,"-dm_plex_separate_marker",&markerSeparate,NULL);CHKERRQ(ierr);
711   if (markerSeparate) { markerLeft = faceMarkerLeft; markerRight = faceMarkerRight;}
712   if (!wrap && rank == 0) {
713     ierr = DMPlexGetHeightStratum(dm,1,&fStart,&fEnd);CHKERRQ(ierr);
714     ierr = DMSetLabelValue(dm,"marker",fStart,markerLeft);CHKERRQ(ierr);
715     ierr = DMSetLabelValue(dm,"marker",fEnd-1,markerRight);CHKERRQ(ierr);
716     ierr = DMSetLabelValue(dm,"Face Sets",fStart,faceMarkerLeft);CHKERRQ(ierr);
717     ierr = DMSetLabelValue(dm,"Face Sets",fEnd-1,faceMarkerRight);CHKERRQ(ierr);
718   }
719   if (wrap) {
720     L       = upper - lower;
721     maxCell = (PetscReal)1.1*(L/(PetscReal)PetscMax(1,segments));
722     ierr = DMSetPeriodicity(dm,PETSC_TRUE,&maxCell,&L,&bd);CHKERRQ(ierr);
723   }
724   ierr = DMPlexSetRefinementUniform(dm, PETSC_TRUE);CHKERRQ(ierr);
725   PetscFunctionReturn(0);
726 }
727 
728 static PetscErrorCode DMPlexCreateBoxMesh_Simplex_Internal(DM dm, PetscInt dim, const PetscInt faces[], const PetscReal lower[], const PetscReal upper[], const DMBoundaryType periodicity[], PetscBool interpolate)
729 {
730   DM             boundary, vol;
731   PetscInt       i;
732   PetscErrorCode ierr;
733 
734   PetscFunctionBegin;
735   PetscValidPointer(dm, 1);
736   for (i = 0; i < dim; ++i) if (periodicity[i] != DM_BOUNDARY_NONE) SETERRQ(PetscObjectComm((PetscObject) dm), PETSC_ERR_SUP, "Periodicity is not supported for simplex meshes");
737   ierr = DMCreate(PetscObjectComm((PetscObject) dm), &boundary);CHKERRQ(ierr);
738   ierr = DMSetType(boundary, DMPLEX);CHKERRQ(ierr);
739   ierr = DMPlexCreateBoxSurfaceMesh_Internal(boundary, dim, faces, lower, upper, PETSC_FALSE);CHKERRQ(ierr);
740   ierr = DMPlexGenerate(boundary, NULL, interpolate, &vol);CHKERRQ(ierr);
741   ierr = DMPlexReplace_Static(dm, &vol);CHKERRQ(ierr);
742   ierr = DMDestroy(&boundary);CHKERRQ(ierr);
743   PetscFunctionReturn(0);
744 }
745 
746 static PetscErrorCode DMPlexCreateCubeMesh_Internal(DM dm, const PetscReal lower[], const PetscReal upper[], const PetscInt edges[], DMBoundaryType bdX, DMBoundaryType bdY, DMBoundaryType bdZ)
747 {
748   DMLabel        cutLabel = NULL;
749   PetscInt       markerTop      = 1, faceMarkerTop      = 1;
750   PetscInt       markerBottom   = 1, faceMarkerBottom   = 1;
751   PetscInt       markerFront    = 1, faceMarkerFront    = 1;
752   PetscInt       markerBack     = 1, faceMarkerBack     = 1;
753   PetscInt       markerRight    = 1, faceMarkerRight    = 1;
754   PetscInt       markerLeft     = 1, faceMarkerLeft     = 1;
755   PetscInt       dim;
756   PetscBool      markerSeparate = PETSC_FALSE, cutMarker = PETSC_FALSE;
757   PetscMPIInt    rank;
758   PetscErrorCode ierr;
759 
760   PetscFunctionBegin;
761   ierr = DMGetDimension(dm,&dim);CHKERRQ(ierr);
762   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);CHKERRMPI(ierr);
763   ierr = DMCreateLabel(dm,"marker");CHKERRQ(ierr);
764   ierr = DMCreateLabel(dm,"Face Sets");CHKERRQ(ierr);
765   ierr = PetscOptionsGetBool(((PetscObject) dm)->options,((PetscObject) dm)->prefix, "-dm_plex_periodic_cut", &cutMarker, NULL);CHKERRQ(ierr);
766   if (bdX == DM_BOUNDARY_PERIODIC || bdX == DM_BOUNDARY_TWIST ||
767       bdY == DM_BOUNDARY_PERIODIC || bdY == DM_BOUNDARY_TWIST ||
768       bdZ == DM_BOUNDARY_PERIODIC || bdZ == DM_BOUNDARY_TWIST) {
769 
770     if (cutMarker) {ierr = DMCreateLabel(dm, "periodic_cut");CHKERRQ(ierr); ierr = DMGetLabel(dm, "periodic_cut", &cutLabel);CHKERRQ(ierr);}
771   }
772   switch (dim) {
773   case 2:
774     faceMarkerTop    = 3;
775     faceMarkerBottom = 1;
776     faceMarkerRight  = 2;
777     faceMarkerLeft   = 4;
778     break;
779   case 3:
780     faceMarkerBottom = 1;
781     faceMarkerTop    = 2;
782     faceMarkerFront  = 3;
783     faceMarkerBack   = 4;
784     faceMarkerRight  = 5;
785     faceMarkerLeft   = 6;
786     break;
787   default:
788     SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Dimension %D not supported",dim);
789   }
790   ierr = PetscOptionsGetBool(((PetscObject) dm)->options,((PetscObject) dm)->prefix, "-dm_plex_separate_marker", &markerSeparate, NULL);CHKERRQ(ierr);
791   if (markerSeparate) {
792     markerBottom = faceMarkerBottom;
793     markerTop    = faceMarkerTop;
794     markerFront  = faceMarkerFront;
795     markerBack   = faceMarkerBack;
796     markerRight  = faceMarkerRight;
797     markerLeft   = faceMarkerLeft;
798   }
799   {
800     const PetscInt numXEdges    = rank == 0 ? edges[0] : 0;
801     const PetscInt numYEdges    = rank == 0 ? edges[1] : 0;
802     const PetscInt numZEdges    = rank == 0 ? edges[2] : 0;
803     const PetscInt numXVertices = rank == 0 ? (bdX == DM_BOUNDARY_PERIODIC || bdX == DM_BOUNDARY_TWIST ? edges[0] : edges[0]+1) : 0;
804     const PetscInt numYVertices = rank == 0 ? (bdY == DM_BOUNDARY_PERIODIC || bdY == DM_BOUNDARY_TWIST ? edges[1] : edges[1]+1) : 0;
805     const PetscInt numZVertices = rank == 0 ? (bdZ == DM_BOUNDARY_PERIODIC || bdZ == DM_BOUNDARY_TWIST ? edges[2] : edges[2]+1) : 0;
806     const PetscInt numCells     = numXEdges*numYEdges*numZEdges;
807     const PetscInt numXFaces    = numYEdges*numZEdges;
808     const PetscInt numYFaces    = numXEdges*numZEdges;
809     const PetscInt numZFaces    = numXEdges*numYEdges;
810     const PetscInt numTotXFaces = numXVertices*numXFaces;
811     const PetscInt numTotYFaces = numYVertices*numYFaces;
812     const PetscInt numTotZFaces = numZVertices*numZFaces;
813     const PetscInt numFaces     = numTotXFaces + numTotYFaces + numTotZFaces;
814     const PetscInt numTotXEdges = numXEdges*numYVertices*numZVertices;
815     const PetscInt numTotYEdges = numYEdges*numXVertices*numZVertices;
816     const PetscInt numTotZEdges = numZEdges*numXVertices*numYVertices;
817     const PetscInt numVertices  = numXVertices*numYVertices*numZVertices;
818     const PetscInt numEdges     = numTotXEdges + numTotYEdges + numTotZEdges;
819     const PetscInt firstVertex  = (dim == 2) ? numFaces : numCells;
820     const PetscInt firstXFace   = (dim == 2) ? 0 : numCells + numVertices;
821     const PetscInt firstYFace   = firstXFace + numTotXFaces;
822     const PetscInt firstZFace   = firstYFace + numTotYFaces;
823     const PetscInt firstXEdge   = numCells + numFaces + numVertices;
824     const PetscInt firstYEdge   = firstXEdge + numTotXEdges;
825     const PetscInt firstZEdge   = firstYEdge + numTotYEdges;
826     Vec            coordinates;
827     PetscSection   coordSection;
828     PetscScalar   *coords;
829     PetscInt       coordSize;
830     PetscInt       v, vx, vy, vz;
831     PetscInt       c, f, fx, fy, fz, e, ex, ey, ez;
832 
833     ierr = DMPlexSetChart(dm, 0, numCells+numFaces+numEdges+numVertices);CHKERRQ(ierr);
834     for (c = 0; c < numCells; c++) {
835       ierr = DMPlexSetConeSize(dm, c, 6);CHKERRQ(ierr);
836     }
837     for (f = firstXFace; f < firstXFace+numFaces; ++f) {
838       ierr = DMPlexSetConeSize(dm, f, 4);CHKERRQ(ierr);
839     }
840     for (e = firstXEdge; e < firstXEdge+numEdges; ++e) {
841       ierr = DMPlexSetConeSize(dm, e, 2);CHKERRQ(ierr);
842     }
843     ierr = DMSetUp(dm);CHKERRQ(ierr); /* Allocate space for cones */
844     /* Build cells */
845     for (fz = 0; fz < numZEdges; ++fz) {
846       for (fy = 0; fy < numYEdges; ++fy) {
847         for (fx = 0; fx < numXEdges; ++fx) {
848           PetscInt cell    = (fz*numYEdges + fy)*numXEdges + fx;
849           PetscInt faceB   = firstZFace + (fy*numXEdges+fx)*numZVertices +   fz;
850           PetscInt faceT   = firstZFace + (fy*numXEdges+fx)*numZVertices + ((fz+1)%numZVertices);
851           PetscInt faceF   = firstYFace + (fz*numXEdges+fx)*numYVertices +   fy;
852           PetscInt faceK   = firstYFace + (fz*numXEdges+fx)*numYVertices + ((fy+1)%numYVertices);
853           PetscInt faceL   = firstXFace + (fz*numYEdges+fy)*numXVertices +   fx;
854           PetscInt faceR   = firstXFace + (fz*numYEdges+fy)*numXVertices + ((fx+1)%numXVertices);
855                             /* B,  T,  F,  K,  R,  L */
856           PetscInt ornt[6] = {-2,  0,  0, -3,  0, -2}; /* ??? */
857           PetscInt cone[6];
858 
859           /* no boundary twisting in 3D */
860           cone[0] = faceB; cone[1] = faceT; cone[2] = faceF; cone[3] = faceK; cone[4] = faceR; cone[5] = faceL;
861           ierr    = DMPlexSetCone(dm, cell, cone);CHKERRQ(ierr);
862           ierr    = DMPlexSetConeOrientation(dm, cell, ornt);CHKERRQ(ierr);
863           if (bdX != DM_BOUNDARY_NONE && fx == numXEdges-1 && cutLabel) {ierr = DMLabelSetValue(cutLabel, cell, 2);CHKERRQ(ierr);}
864           if (bdY != DM_BOUNDARY_NONE && fy == numYEdges-1 && cutLabel) {ierr = DMLabelSetValue(cutLabel, cell, 2);CHKERRQ(ierr);}
865           if (bdZ != DM_BOUNDARY_NONE && fz == numZEdges-1 && cutLabel) {ierr = DMLabelSetValue(cutLabel, cell, 2);CHKERRQ(ierr);}
866         }
867       }
868     }
869     /* Build x faces */
870     for (fz = 0; fz < numZEdges; ++fz) {
871       for (fy = 0; fy < numYEdges; ++fy) {
872         for (fx = 0; fx < numXVertices; ++fx) {
873           PetscInt face    = firstXFace + (fz*numYEdges+fy)     *numXVertices+fx;
874           PetscInt edgeL   = firstZEdge + (fy                   *numXVertices+fx)*numZEdges + fz;
875           PetscInt edgeR   = firstZEdge + (((fy+1)%numYVertices)*numXVertices+fx)*numZEdges + fz;
876           PetscInt edgeB   = firstYEdge + (fz                   *numXVertices+fx)*numYEdges + fy;
877           PetscInt edgeT   = firstYEdge + (((fz+1)%numZVertices)*numXVertices+fx)*numYEdges + fy;
878           PetscInt ornt[4] = {0, 0, -1, -1};
879           PetscInt cone[4];
880 
881           if (dim == 3) {
882             /* markers */
883             if (bdX != DM_BOUNDARY_PERIODIC) {
884               if (fx == numXVertices-1) {
885                 ierr = DMSetLabelValue(dm, "Face Sets", face, faceMarkerRight);CHKERRQ(ierr);
886                 ierr = DMSetLabelValue(dm, "marker", face, markerRight);CHKERRQ(ierr);
887               }
888               else if (fx == 0) {
889                 ierr = DMSetLabelValue(dm, "Face Sets", face, faceMarkerLeft);CHKERRQ(ierr);
890                 ierr = DMSetLabelValue(dm, "marker", face, markerLeft);CHKERRQ(ierr);
891               }
892             }
893           }
894           cone[0] = edgeB; cone[1] = edgeR; cone[2] = edgeT; cone[3] = edgeL;
895           ierr    = DMPlexSetCone(dm, face, cone);CHKERRQ(ierr);
896           ierr    = DMPlexSetConeOrientation(dm, face, ornt);CHKERRQ(ierr);
897         }
898       }
899     }
900     /* Build y faces */
901     for (fz = 0; fz < numZEdges; ++fz) {
902       for (fx = 0; fx < numXEdges; ++fx) {
903         for (fy = 0; fy < numYVertices; ++fy) {
904           PetscInt face    = firstYFace + (fz*numXEdges+fx)*numYVertices + fy;
905           PetscInt edgeL   = firstZEdge + (fy*numXVertices+  fx)*numZEdges + fz;
906           PetscInt edgeR   = firstZEdge + (fy*numXVertices+((fx+1)%numXVertices))*numZEdges + fz;
907           PetscInt edgeB   = firstXEdge + (fz                   *numYVertices+fy)*numXEdges + fx;
908           PetscInt edgeT   = firstXEdge + (((fz+1)%numZVertices)*numYVertices+fy)*numXEdges + fx;
909           PetscInt ornt[4] = {0, 0, -1, -1};
910           PetscInt cone[4];
911 
912           if (dim == 3) {
913             /* markers */
914             if (bdY != DM_BOUNDARY_PERIODIC) {
915               if (fy == numYVertices-1) {
916                 ierr = DMSetLabelValue(dm, "Face Sets", face, faceMarkerBack);CHKERRQ(ierr);
917                 ierr = DMSetLabelValue(dm, "marker", face, markerBack);CHKERRQ(ierr);
918               }
919               else if (fy == 0) {
920                 ierr = DMSetLabelValue(dm, "Face Sets", face, faceMarkerFront);CHKERRQ(ierr);
921                 ierr = DMSetLabelValue(dm, "marker", face, markerFront);CHKERRQ(ierr);
922               }
923             }
924           }
925           cone[0] = edgeB; cone[1] = edgeR; cone[2] = edgeT; cone[3] = edgeL;
926           ierr    = DMPlexSetCone(dm, face, cone);CHKERRQ(ierr);
927           ierr    = DMPlexSetConeOrientation(dm, face, ornt);CHKERRQ(ierr);
928         }
929       }
930     }
931     /* Build z faces */
932     for (fy = 0; fy < numYEdges; ++fy) {
933       for (fx = 0; fx < numXEdges; ++fx) {
934         for (fz = 0; fz < numZVertices; fz++) {
935           PetscInt face    = firstZFace + (fy*numXEdges+fx)*numZVertices + fz;
936           PetscInt edgeL   = firstYEdge + (fz*numXVertices+  fx)*numYEdges + fy;
937           PetscInt edgeR   = firstYEdge + (fz*numXVertices+((fx+1)%numXVertices))*numYEdges + fy;
938           PetscInt edgeB   = firstXEdge + (fz*numYVertices+  fy)*numXEdges + fx;
939           PetscInt edgeT   = firstXEdge + (fz*numYVertices+((fy+1)%numYVertices))*numXEdges + fx;
940           PetscInt ornt[4] = {0, 0, -1, -1};
941           PetscInt cone[4];
942 
943           if (dim == 2) {
944             if (bdX == DM_BOUNDARY_TWIST && fx == numXEdges-1) {edgeR += numYEdges-1-2*fy; ornt[1] = -1;}
945             if (bdY == DM_BOUNDARY_TWIST && fy == numYEdges-1) {edgeT += numXEdges-1-2*fx; ornt[2] =  0;}
946             if (bdX != DM_BOUNDARY_NONE && fx == numXEdges-1 && cutLabel) {ierr = DMLabelSetValue(cutLabel, face, 2);CHKERRQ(ierr);}
947             if (bdY != DM_BOUNDARY_NONE && fy == numYEdges-1 && cutLabel) {ierr = DMLabelSetValue(cutLabel, face, 2);CHKERRQ(ierr);}
948           } else {
949             /* markers */
950             if (bdZ != DM_BOUNDARY_PERIODIC) {
951               if (fz == numZVertices-1) {
952                 ierr = DMSetLabelValue(dm, "Face Sets", face, faceMarkerTop);CHKERRQ(ierr);
953                 ierr = DMSetLabelValue(dm, "marker", face, markerTop);CHKERRQ(ierr);
954               }
955               else if (fz == 0) {
956                 ierr = DMSetLabelValue(dm, "Face Sets", face, faceMarkerBottom);CHKERRQ(ierr);
957                 ierr = DMSetLabelValue(dm, "marker", face, markerBottom);CHKERRQ(ierr);
958               }
959             }
960           }
961           cone[0] = edgeB; cone[1] = edgeR; cone[2] = edgeT; cone[3] = edgeL;
962           ierr    = DMPlexSetCone(dm, face, cone);CHKERRQ(ierr);
963           ierr    = DMPlexSetConeOrientation(dm, face, ornt);CHKERRQ(ierr);
964         }
965       }
966     }
967     /* Build Z edges*/
968     for (vy = 0; vy < numYVertices; vy++) {
969       for (vx = 0; vx < numXVertices; vx++) {
970         for (ez = 0; ez < numZEdges; ez++) {
971           const PetscInt edge    = firstZEdge  + (vy*numXVertices+vx)*numZEdges + ez;
972           const PetscInt vertexB = firstVertex + (ez                   *numYVertices+vy)*numXVertices + vx;
973           const PetscInt vertexT = firstVertex + (((ez+1)%numZVertices)*numYVertices+vy)*numXVertices + vx;
974           PetscInt       cone[2];
975 
976           if (dim == 3) {
977             if (bdX != DM_BOUNDARY_PERIODIC) {
978               if (vx == numXVertices-1) {
979                 ierr = DMSetLabelValue(dm, "marker", edge, markerRight);CHKERRQ(ierr);
980               }
981               else if (vx == 0) {
982                 ierr = DMSetLabelValue(dm, "marker", edge, markerLeft);CHKERRQ(ierr);
983               }
984             }
985             if (bdY != DM_BOUNDARY_PERIODIC) {
986               if (vy == numYVertices-1) {
987                 ierr = DMSetLabelValue(dm, "marker", edge, markerBack);CHKERRQ(ierr);
988               }
989               else if (vy == 0) {
990                 ierr = DMSetLabelValue(dm, "marker", edge, markerFront);CHKERRQ(ierr);
991               }
992             }
993           }
994           cone[0] = vertexB; cone[1] = vertexT;
995           ierr = DMPlexSetCone(dm, edge, cone);CHKERRQ(ierr);
996         }
997       }
998     }
999     /* Build Y edges*/
1000     for (vz = 0; vz < numZVertices; vz++) {
1001       for (vx = 0; vx < numXVertices; vx++) {
1002         for (ey = 0; ey < numYEdges; ey++) {
1003           const PetscInt nextv   = (dim == 2 && bdY == DM_BOUNDARY_TWIST && ey == numYEdges-1) ? (numXVertices-vx-1) : (vz*numYVertices+((ey+1)%numYVertices))*numXVertices + vx;
1004           const PetscInt edge    = firstYEdge  + (vz*numXVertices+vx)*numYEdges + ey;
1005           const PetscInt vertexF = firstVertex + (vz*numYVertices+ey)*numXVertices + vx;
1006           const PetscInt vertexK = firstVertex + nextv;
1007           PetscInt       cone[2];
1008 
1009           cone[0] = vertexF; cone[1] = vertexK;
1010           ierr = DMPlexSetCone(dm, edge, cone);CHKERRQ(ierr);
1011           if (dim == 2) {
1012             if ((bdX != DM_BOUNDARY_PERIODIC) && (bdX != DM_BOUNDARY_TWIST)) {
1013               if (vx == numXVertices-1) {
1014                 ierr = DMSetLabelValue(dm, "Face Sets", edge, faceMarkerRight);CHKERRQ(ierr);
1015                 ierr = DMSetLabelValue(dm, "marker", edge,    markerRight);CHKERRQ(ierr);
1016                 ierr = DMSetLabelValue(dm, "marker", cone[0], markerRight);CHKERRQ(ierr);
1017                 if (ey == numYEdges-1) {
1018                   ierr = DMSetLabelValue(dm, "marker", cone[1], markerRight);CHKERRQ(ierr);
1019                 }
1020               } else if (vx == 0) {
1021                 ierr = DMSetLabelValue(dm, "Face Sets", edge, faceMarkerLeft);CHKERRQ(ierr);
1022                 ierr = DMSetLabelValue(dm, "marker", edge,    markerLeft);CHKERRQ(ierr);
1023                 ierr = DMSetLabelValue(dm, "marker", cone[0], markerLeft);CHKERRQ(ierr);
1024                 if (ey == numYEdges-1) {
1025                   ierr = DMSetLabelValue(dm, "marker", cone[1], markerLeft);CHKERRQ(ierr);
1026                 }
1027               }
1028             } else {
1029               if (vx == 0 && cutLabel) {
1030                 ierr = DMLabelSetValue(cutLabel, edge,    1);CHKERRQ(ierr);
1031                 ierr = DMLabelSetValue(cutLabel, cone[0], 1);CHKERRQ(ierr);
1032                 if (ey == numYEdges-1) {
1033                   ierr = DMLabelSetValue(cutLabel, cone[1], 1);CHKERRQ(ierr);
1034                 }
1035               }
1036             }
1037           } else {
1038             if (bdX != DM_BOUNDARY_PERIODIC) {
1039               if (vx == numXVertices-1) {
1040                 ierr = DMSetLabelValue(dm, "marker", edge, markerRight);CHKERRQ(ierr);
1041               } else if (vx == 0) {
1042                 ierr = DMSetLabelValue(dm, "marker", edge, markerLeft);CHKERRQ(ierr);
1043               }
1044             }
1045             if (bdZ != DM_BOUNDARY_PERIODIC) {
1046               if (vz == numZVertices-1) {
1047                 ierr = DMSetLabelValue(dm, "marker", edge, markerTop);CHKERRQ(ierr);
1048               } else if (vz == 0) {
1049                 ierr = DMSetLabelValue(dm, "marker", edge, markerBottom);CHKERRQ(ierr);
1050               }
1051             }
1052           }
1053         }
1054       }
1055     }
1056     /* Build X edges*/
1057     for (vz = 0; vz < numZVertices; vz++) {
1058       for (vy = 0; vy < numYVertices; vy++) {
1059         for (ex = 0; ex < numXEdges; ex++) {
1060           const PetscInt nextv   = (dim == 2 && bdX == DM_BOUNDARY_TWIST && ex == numXEdges-1) ? (numYVertices-vy-1)*numXVertices : (vz*numYVertices+vy)*numXVertices + (ex+1)%numXVertices;
1061           const PetscInt edge    = firstXEdge  + (vz*numYVertices+vy)*numXEdges + ex;
1062           const PetscInt vertexL = firstVertex + (vz*numYVertices+vy)*numXVertices + ex;
1063           const PetscInt vertexR = firstVertex + nextv;
1064           PetscInt       cone[2];
1065 
1066           cone[0] = vertexL; cone[1] = vertexR;
1067           ierr = DMPlexSetCone(dm, edge, cone);CHKERRQ(ierr);
1068           if (dim == 2) {
1069             if ((bdY != DM_BOUNDARY_PERIODIC) && (bdY != DM_BOUNDARY_TWIST)) {
1070               if (vy == numYVertices-1) {
1071                 ierr = DMSetLabelValue(dm, "Face Sets", edge, faceMarkerTop);CHKERRQ(ierr);
1072                 ierr = DMSetLabelValue(dm, "marker", edge,    markerTop);CHKERRQ(ierr);
1073                 ierr = DMSetLabelValue(dm, "marker", cone[0], markerTop);CHKERRQ(ierr);
1074                 if (ex == numXEdges-1) {
1075                   ierr = DMSetLabelValue(dm, "marker", cone[1], markerTop);CHKERRQ(ierr);
1076                 }
1077               } else if (vy == 0) {
1078                 ierr = DMSetLabelValue(dm, "Face Sets", edge, faceMarkerBottom);CHKERRQ(ierr);
1079                 ierr = DMSetLabelValue(dm, "marker", edge,    markerBottom);CHKERRQ(ierr);
1080                 ierr = DMSetLabelValue(dm, "marker", cone[0], markerBottom);CHKERRQ(ierr);
1081                 if (ex == numXEdges-1) {
1082                   ierr = DMSetLabelValue(dm, "marker", cone[1], markerBottom);CHKERRQ(ierr);
1083                 }
1084               }
1085             } else {
1086               if (vy == 0 && cutLabel) {
1087                 ierr = DMLabelSetValue(cutLabel, edge,    1);CHKERRQ(ierr);
1088                 ierr = DMLabelSetValue(cutLabel, cone[0], 1);CHKERRQ(ierr);
1089                 if (ex == numXEdges-1) {
1090                   ierr = DMLabelSetValue(cutLabel, cone[1], 1);CHKERRQ(ierr);
1091                 }
1092               }
1093             }
1094           } else {
1095             if (bdY != DM_BOUNDARY_PERIODIC) {
1096               if (vy == numYVertices-1) {
1097                 ierr = DMSetLabelValue(dm, "marker", edge, markerBack);CHKERRQ(ierr);
1098               }
1099               else if (vy == 0) {
1100                 ierr = DMSetLabelValue(dm, "marker", edge, markerFront);CHKERRQ(ierr);
1101               }
1102             }
1103             if (bdZ != DM_BOUNDARY_PERIODIC) {
1104               if (vz == numZVertices-1) {
1105                 ierr = DMSetLabelValue(dm, "marker", edge, markerTop);CHKERRQ(ierr);
1106               }
1107               else if (vz == 0) {
1108                 ierr = DMSetLabelValue(dm, "marker", edge, markerBottom);CHKERRQ(ierr);
1109               }
1110             }
1111           }
1112         }
1113       }
1114     }
1115     ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
1116     ierr = DMPlexStratify(dm);CHKERRQ(ierr);
1117     /* Build coordinates */
1118     ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
1119     ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
1120     ierr = PetscSectionSetFieldComponents(coordSection, 0, dim);CHKERRQ(ierr);
1121     ierr = PetscSectionSetChart(coordSection, firstVertex, firstVertex+numVertices);CHKERRQ(ierr);
1122     for (v = firstVertex; v < firstVertex+numVertices; ++v) {
1123       ierr = PetscSectionSetDof(coordSection, v, dim);CHKERRQ(ierr);
1124       ierr = PetscSectionSetFieldDof(coordSection, v, 0, dim);CHKERRQ(ierr);
1125     }
1126     ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
1127     ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
1128     ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
1129     ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
1130     ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
1131     ierr = VecSetBlockSize(coordinates, dim);CHKERRQ(ierr);
1132     ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
1133     ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
1134     for (vz = 0; vz < numZVertices; ++vz) {
1135       for (vy = 0; vy < numYVertices; ++vy) {
1136         for (vx = 0; vx < numXVertices; ++vx) {
1137           coords[((vz*numYVertices+vy)*numXVertices+vx)*dim+0] = lower[0] + ((upper[0] - lower[0])/numXEdges)*vx;
1138           coords[((vz*numYVertices+vy)*numXVertices+vx)*dim+1] = lower[1] + ((upper[1] - lower[1])/numYEdges)*vy;
1139           if (dim == 3) {
1140             coords[((vz*numYVertices+vy)*numXVertices+vx)*dim+2] = lower[2] + ((upper[2] - lower[2])/numZEdges)*vz;
1141           }
1142         }
1143       }
1144     }
1145     ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
1146     ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
1147     ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
1148   }
1149   PetscFunctionReturn(0);
1150 }
1151 
1152 static PetscErrorCode DMPlexCreateBoxMesh_Tensor_Internal(DM dm, PetscInt dim, const PetscInt faces[], const PetscReal lower[], const PetscReal upper[], const DMBoundaryType periodicity[])
1153 {
1154   DMBoundaryType bdt[3] = {DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE};
1155   PetscInt       fac[3] = {0, 0, 0}, d;
1156   PetscErrorCode ierr;
1157 
1158   PetscFunctionBegin;
1159   PetscValidPointer(dm, 1);
1160   PetscValidLogicalCollectiveInt(dm, dim, 2);
1161   ierr = DMSetDimension(dm, dim);CHKERRQ(ierr);
1162   for (d = 0; d < dim; ++d) {fac[d] = faces[d]; bdt[d] = periodicity[d];}
1163   ierr = DMPlexCreateCubeMesh_Internal(dm, lower, upper, fac, bdt[0], bdt[1], bdt[2]);CHKERRQ(ierr);
1164   if (periodicity[0] == DM_BOUNDARY_PERIODIC || periodicity[0] == DM_BOUNDARY_TWIST ||
1165       periodicity[1] == DM_BOUNDARY_PERIODIC || periodicity[1] == DM_BOUNDARY_TWIST ||
1166       (dim > 2 && (periodicity[2] == DM_BOUNDARY_PERIODIC || periodicity[2] == DM_BOUNDARY_TWIST))) {
1167     PetscReal L[3];
1168     PetscReal maxCell[3];
1169 
1170     for (d = 0; d < dim; ++d) {
1171       L[d]       = upper[d] - lower[d];
1172       maxCell[d] = 1.1 * (L[d] / PetscMax(1, faces[d]));
1173     }
1174     ierr = DMSetPeriodicity(dm, PETSC_TRUE, maxCell, L, periodicity);CHKERRQ(ierr);
1175   }
1176   ierr = DMPlexSetRefinementUniform(dm, PETSC_TRUE);CHKERRQ(ierr);
1177   PetscFunctionReturn(0);
1178 }
1179 
1180 static PetscErrorCode DMPlexCreateBoxMesh_Internal(DM dm, PetscInt dim, PetscBool simplex, const PetscInt faces[], const PetscReal lower[], const PetscReal upper[], const DMBoundaryType periodicity[], PetscBool interpolate)
1181 {
1182   PetscErrorCode ierr;
1183 
1184   PetscFunctionBegin;
1185   if (dim == 1)      {ierr = DMPlexCreateLineMesh_Internal(dm, faces[0], lower[0], upper[0], periodicity[0]);CHKERRQ(ierr);}
1186   else if (simplex)  {ierr = DMPlexCreateBoxMesh_Simplex_Internal(dm, dim, faces, lower, upper, periodicity, interpolate);CHKERRQ(ierr);}
1187   else               {ierr = DMPlexCreateBoxMesh_Tensor_Internal(dm, dim, faces, lower, upper, periodicity);CHKERRQ(ierr);}
1188   if (!interpolate && dim > 1 && !simplex) {
1189     DM udm;
1190 
1191     ierr = DMPlexUninterpolate(dm, &udm);CHKERRQ(ierr);
1192     ierr = DMPlexCopyCoordinates(dm, udm);CHKERRQ(ierr);
1193     ierr = DMPlexReplace_Static(dm, &udm);CHKERRQ(ierr);
1194   }
1195   PetscFunctionReturn(0);
1196 }
1197 
1198 /*@C
1199   DMPlexCreateBoxMesh - Creates a mesh on the tensor product of unit intervals (box) using simplices or tensor cells (hexahedra).
1200 
1201   Collective
1202 
1203   Input Parameters:
1204 + comm        - The communicator for the DM object
1205 . dim         - The spatial dimension
1206 . simplex     - PETSC_TRUE for simplices, PETSC_FALSE for tensor cells
1207 . faces       - Number of faces per dimension, or NULL for (1,) in 1D and (2, 2) in 2D and (1, 1, 1) in 3D
1208 . lower       - The lower left corner, or NULL for (0, 0, 0)
1209 . upper       - The upper right corner, or NULL for (1, 1, 1)
1210 . periodicity - The boundary type for the X,Y,Z direction, or NULL for DM_BOUNDARY_NONE
1211 - interpolate - Flag to create intermediate mesh pieces (edges, faces)
1212 
1213   Output Parameter:
1214 . dm  - The DM object
1215 
1216   Note: If you want to customize this mesh using options, you just need to
1217 $  DMCreate(comm, &dm);
1218 $  DMSetType(dm, DMPLEX);
1219 $  DMSetFromOptions(dm);
1220 and use the options on the DMSetFromOptions() page.
1221 
1222   Here is the numbering returned for 2 faces in each direction for tensor cells:
1223 $ 10---17---11---18----12
1224 $  |         |         |
1225 $  |         |         |
1226 $ 20    2   22    3    24
1227 $  |         |         |
1228 $  |         |         |
1229 $  7---15----8---16----9
1230 $  |         |         |
1231 $  |         |         |
1232 $ 19    0   21    1   23
1233 $  |         |         |
1234 $  |         |         |
1235 $  4---13----5---14----6
1236 
1237 and for simplicial cells
1238 
1239 $ 14----8---15----9----16
1240 $  |\     5  |\      7 |
1241 $  | \       | \       |
1242 $ 13   2    14    3    15
1243 $  | 4   \   | 6   \   |
1244 $  |       \ |       \ |
1245 $ 11----6---12----7----13
1246 $  |\        |\        |
1247 $  | \    1  | \     3 |
1248 $ 10   0    11    1    12
1249 $  | 0   \   | 2   \   |
1250 $  |       \ |       \ |
1251 $  8----4----9----5----10
1252 
1253   Level: beginner
1254 
1255 .seealso: DMSetFromOptions(), DMPlexCreateFromFile(), DMPlexCreateHexCylinderMesh(), DMSetType(), DMCreate()
1256 @*/
1257 PetscErrorCode DMPlexCreateBoxMesh(MPI_Comm comm, PetscInt dim, PetscBool simplex, const PetscInt faces[], const PetscReal lower[], const PetscReal upper[], const DMBoundaryType periodicity[], PetscBool interpolate, DM *dm)
1258 {
1259   PetscInt       fac[3] = {1, 1, 1};
1260   PetscReal      low[3] = {0, 0, 0};
1261   PetscReal      upp[3] = {1, 1, 1};
1262   DMBoundaryType bdt[3] = {DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE};
1263   PetscErrorCode ierr;
1264 
1265   PetscFunctionBegin;
1266   ierr = DMCreate(comm,dm);CHKERRQ(ierr);
1267   ierr = DMSetType(*dm,DMPLEX);CHKERRQ(ierr);
1268   ierr = DMPlexCreateBoxMesh_Internal(*dm, dim, simplex, faces ? faces : fac, lower ? lower : low, upper ? upper : upp, periodicity ? periodicity : bdt, interpolate);CHKERRQ(ierr);
1269   PetscFunctionReturn(0);
1270 }
1271 
1272 static PetscErrorCode DMPlexCreateWedgeBoxMesh_Internal(DM dm, const PetscInt faces[], const PetscReal lower[], const PetscReal upper[], const DMBoundaryType periodicity[])
1273 {
1274   DM             bdm, vol;
1275   PetscInt       i;
1276   PetscErrorCode ierr;
1277 
1278   PetscFunctionBegin;
1279   for (i = 0; i < 3; ++i) if (periodicity[i] != DM_BOUNDARY_NONE) SETERRQ(PetscObjectComm((PetscObject) dm), PETSC_ERR_SUP, "Periodicity not yet supported");
1280   ierr = DMCreate(PetscObjectComm((PetscObject) dm), &bdm);CHKERRQ(ierr);
1281   ierr = DMSetType(bdm, DMPLEX);CHKERRQ(ierr);
1282   ierr = DMSetDimension(bdm, 2);CHKERRQ(ierr);
1283   ierr = DMPlexCreateBoxMesh_Simplex_Internal(bdm, 2, faces, lower, upper, periodicity, PETSC_TRUE);CHKERRQ(ierr);
1284   ierr = DMPlexExtrude(bdm, faces[2], upper[2] - lower[2], PETSC_TRUE, PETSC_FALSE, NULL, NULL, &vol);CHKERRQ(ierr);
1285   ierr = DMDestroy(&bdm);CHKERRQ(ierr);
1286   ierr = DMPlexReplace_Static(dm, &vol);CHKERRQ(ierr);
1287   if (lower[2] != 0.0) {
1288     Vec          v;
1289     PetscScalar *x;
1290     PetscInt     cDim, n;
1291 
1292     ierr = DMGetCoordinatesLocal(dm, &v);CHKERRQ(ierr);
1293     ierr = VecGetBlockSize(v, &cDim);CHKERRQ(ierr);
1294     ierr = VecGetLocalSize(v, &n);CHKERRQ(ierr);
1295     ierr = VecGetArray(v, &x);CHKERRQ(ierr);
1296     x   += cDim;
1297     for (i = 0; i < n; i += cDim) x[i] += lower[2];
1298     ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
1299     ierr = DMSetCoordinatesLocal(dm, v);CHKERRQ(ierr);
1300   }
1301   PetscFunctionReturn(0);
1302 }
1303 
1304 /*@
1305   DMPlexCreateWedgeBoxMesh - Creates a 3-D mesh tesselating the (x,y) plane and extruding in the third direction using wedge cells.
1306 
1307   Collective
1308 
1309   Input Parameters:
1310 + comm        - The communicator for the DM object
1311 . faces       - Number of faces per dimension, or NULL for (1, 1, 1)
1312 . lower       - The lower left corner, or NULL for (0, 0, 0)
1313 . upper       - The upper right corner, or NULL for (1, 1, 1)
1314 . periodicity - The boundary type for the X,Y,Z direction, or NULL for DM_BOUNDARY_NONE
1315 . orderHeight - If PETSC_TRUE, orders the extruded cells in the height first. Otherwise, orders the cell on the layers first
1316 - interpolate - Flag to create intermediate mesh pieces (edges, faces)
1317 
1318   Output Parameter:
1319 . dm  - The DM object
1320 
1321   Level: beginner
1322 
1323 .seealso: DMPlexCreateHexCylinderMesh(), DMPlexCreateWedgeCylinderMesh(), DMExtrude(), DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
1324 @*/
1325 PetscErrorCode DMPlexCreateWedgeBoxMesh(MPI_Comm comm, const PetscInt faces[], const PetscReal lower[], const PetscReal upper[], const DMBoundaryType periodicity[], PetscBool orderHeight, PetscBool interpolate, DM *dm)
1326 {
1327   PetscInt       fac[3] = {1, 1, 1};
1328   PetscReal      low[3] = {0, 0, 0};
1329   PetscReal      upp[3] = {1, 1, 1};
1330   DMBoundaryType bdt[3] = {DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE};
1331   PetscErrorCode ierr;
1332 
1333   PetscFunctionBegin;
1334   ierr = DMCreate(comm,dm);CHKERRQ(ierr);
1335   ierr = DMSetType(*dm,DMPLEX);CHKERRQ(ierr);
1336   ierr = DMPlexCreateWedgeBoxMesh_Internal(*dm, faces ? faces : fac, lower ? lower : low, upper ? upper : upp, periodicity ? periodicity : bdt);CHKERRQ(ierr);
1337   if (!interpolate) {
1338     DM udm;
1339 
1340     ierr = DMPlexUninterpolate(*dm, &udm);CHKERRQ(ierr);
1341     ierr = DMPlexReplace_Static(*dm, &udm);CHKERRQ(ierr);
1342   }
1343   PetscFunctionReturn(0);
1344 }
1345 
1346 /*@C
1347   DMPlexSetOptionsPrefix - Sets the prefix used for searching for all DM options in the database.
1348 
1349   Logically Collective on dm
1350 
1351   Input Parameters:
1352 + dm - the DM context
1353 - prefix - the prefix to prepend to all option names
1354 
1355   Notes:
1356   A hyphen (-) must NOT be given at the beginning of the prefix name.
1357   The first character of all runtime options is AUTOMATICALLY the hyphen.
1358 
1359   Level: advanced
1360 
1361 .seealso: SNESSetFromOptions()
1362 @*/
1363 PetscErrorCode DMPlexSetOptionsPrefix(DM dm, const char prefix[])
1364 {
1365   DM_Plex       *mesh = (DM_Plex *) dm->data;
1366   PetscErrorCode ierr;
1367 
1368   PetscFunctionBegin;
1369   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1370   ierr = PetscObjectSetOptionsPrefix((PetscObject) dm, prefix);CHKERRQ(ierr);
1371   ierr = PetscObjectSetOptionsPrefix((PetscObject) mesh->partitioner, prefix);CHKERRQ(ierr);
1372   PetscFunctionReturn(0);
1373 }
1374 
1375 /* Remap geometry to cylinder
1376    TODO: This only works for a single refinement, then it is broken
1377 
1378      Interior square: Linear interpolation is correct
1379      The other cells all have vertices on rays from the origin. We want to uniformly expand the spacing
1380      such that the last vertex is on the unit circle. So the closest and farthest vertices are at distance
1381 
1382        phi     = arctan(y/x)
1383        d_close = sqrt(1/8 + 1/4 sin^2(phi))
1384        d_far   = sqrt(1/2 + sin^2(phi))
1385 
1386      so we remap them using
1387 
1388        x_new = x_close + (x - x_close) (1 - d_close) / (d_far - d_close)
1389        y_new = y_close + (y - y_close) (1 - d_close) / (d_far - d_close)
1390 
1391      If pi/4 < phi < 3pi/4 or -3pi/4 < phi < -pi/4, then we switch x and y.
1392 */
1393 static void snapToCylinder(PetscInt dim, PetscInt Nf, PetscInt NfAux,
1394                            const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
1395                            const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
1396                            PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
1397 {
1398   const PetscReal dis = 1.0/PetscSqrtReal(2.0);
1399   const PetscReal ds2 = 0.5*dis;
1400 
1401   if ((PetscAbsScalar(u[0]) <= ds2) && (PetscAbsScalar(u[1]) <= ds2)) {
1402     f0[0] = u[0];
1403     f0[1] = u[1];
1404   } else {
1405     PetscReal phi, sinp, cosp, dc, df, x, y, xc, yc;
1406 
1407     x    = PetscRealPart(u[0]);
1408     y    = PetscRealPart(u[1]);
1409     phi  = PetscAtan2Real(y, x);
1410     sinp = PetscSinReal(phi);
1411     cosp = PetscCosReal(phi);
1412     if ((PetscAbsReal(phi) > PETSC_PI/4.0) && (PetscAbsReal(phi) < 3.0*PETSC_PI/4.0)) {
1413       dc = PetscAbsReal(ds2/sinp);
1414       df = PetscAbsReal(dis/sinp);
1415       xc = ds2*x/PetscAbsReal(y);
1416       yc = ds2*PetscSignReal(y);
1417     } else {
1418       dc = PetscAbsReal(ds2/cosp);
1419       df = PetscAbsReal(dis/cosp);
1420       xc = ds2*PetscSignReal(x);
1421       yc = ds2*y/PetscAbsReal(x);
1422     }
1423     f0[0] = xc + (u[0] - xc)*(1.0 - dc)/(df - dc);
1424     f0[1] = yc + (u[1] - yc)*(1.0 - dc)/(df - dc);
1425   }
1426   f0[2] = u[2];
1427 }
1428 
1429 static PetscErrorCode DMPlexCreateHexCylinderMesh_Internal(DM dm, DMBoundaryType periodicZ)
1430 {
1431   const PetscInt dim = 3;
1432   PetscInt       numCells, numVertices;
1433   PetscMPIInt    rank;
1434   PetscErrorCode ierr;
1435 
1436   PetscFunctionBegin;
1437   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject) dm), &rank);CHKERRMPI(ierr);
1438   ierr = DMSetDimension(dm, dim);CHKERRQ(ierr);
1439   /* Create topology */
1440   {
1441     PetscInt cone[8], c;
1442 
1443     numCells    = rank == 0 ?  5 : 0;
1444     numVertices = rank == 0 ? 16 : 0;
1445     if (periodicZ == DM_BOUNDARY_PERIODIC) {
1446       numCells   *= 3;
1447       numVertices = rank == 0 ? 24 : 0;
1448     }
1449     ierr = DMPlexSetChart(dm, 0, numCells+numVertices);CHKERRQ(ierr);
1450     for (c = 0; c < numCells; c++) {ierr = DMPlexSetConeSize(dm, c, 8);CHKERRQ(ierr);}
1451     ierr = DMSetUp(dm);CHKERRQ(ierr);
1452     if (rank == 0) {
1453       if (periodicZ == DM_BOUNDARY_PERIODIC) {
1454         cone[0] = 15; cone[1] = 18; cone[2] = 17; cone[3] = 16;
1455         cone[4] = 31; cone[5] = 32; cone[6] = 33; cone[7] = 34;
1456         ierr = DMPlexSetCone(dm, 0, cone);CHKERRQ(ierr);
1457         cone[0] = 16; cone[1] = 17; cone[2] = 24; cone[3] = 23;
1458         cone[4] = 32; cone[5] = 36; cone[6] = 37; cone[7] = 33; /* 22 25 26 21 */
1459         ierr = DMPlexSetCone(dm, 1, cone);CHKERRQ(ierr);
1460         cone[0] = 18; cone[1] = 27; cone[2] = 24; cone[3] = 17;
1461         cone[4] = 34; cone[5] = 33; cone[6] = 37; cone[7] = 38;
1462         ierr = DMPlexSetCone(dm, 2, cone);CHKERRQ(ierr);
1463         cone[0] = 29; cone[1] = 27; cone[2] = 18; cone[3] = 15;
1464         cone[4] = 35; cone[5] = 31; cone[6] = 34; cone[7] = 38;
1465         ierr = DMPlexSetCone(dm, 3, cone);CHKERRQ(ierr);
1466         cone[0] = 29; cone[1] = 15; cone[2] = 16; cone[3] = 23;
1467         cone[4] = 35; cone[5] = 36; cone[6] = 32; cone[7] = 31;
1468         ierr = DMPlexSetCone(dm, 4, cone);CHKERRQ(ierr);
1469 
1470         cone[0] = 31; cone[1] = 34; cone[2] = 33; cone[3] = 32;
1471         cone[4] = 19; cone[5] = 22; cone[6] = 21; cone[7] = 20;
1472         ierr = DMPlexSetCone(dm, 5, cone);CHKERRQ(ierr);
1473         cone[0] = 32; cone[1] = 33; cone[2] = 37; cone[3] = 36;
1474         cone[4] = 22; cone[5] = 25; cone[6] = 26; cone[7] = 21;
1475         ierr = DMPlexSetCone(dm, 6, cone);CHKERRQ(ierr);
1476         cone[0] = 34; cone[1] = 38; cone[2] = 37; cone[3] = 33;
1477         cone[4] = 20; cone[5] = 21; cone[6] = 26; cone[7] = 28;
1478         ierr = DMPlexSetCone(dm, 7, cone);CHKERRQ(ierr);
1479         cone[0] = 35; cone[1] = 38; cone[2] = 34; cone[3] = 31;
1480         cone[4] = 30; cone[5] = 19; cone[6] = 20; cone[7] = 28;
1481         ierr = DMPlexSetCone(dm, 8, cone);CHKERRQ(ierr);
1482         cone[0] = 35; cone[1] = 31; cone[2] = 32; cone[3] = 36;
1483         cone[4] = 30; cone[5] = 25; cone[6] = 22; cone[7] = 19;
1484         ierr = DMPlexSetCone(dm, 9, cone);CHKERRQ(ierr);
1485 
1486         cone[0] = 19; cone[1] = 20; cone[2] = 21; cone[3] = 22;
1487         cone[4] = 15; cone[5] = 16; cone[6] = 17; cone[7] = 18;
1488         ierr = DMPlexSetCone(dm, 10, cone);CHKERRQ(ierr);
1489         cone[0] = 22; cone[1] = 21; cone[2] = 26; cone[3] = 25;
1490         cone[4] = 16; cone[5] = 23; cone[6] = 24; cone[7] = 17;
1491         ierr = DMPlexSetCone(dm, 11, cone);CHKERRQ(ierr);
1492         cone[0] = 20; cone[1] = 28; cone[2] = 26; cone[3] = 21;
1493         cone[4] = 18; cone[5] = 17; cone[6] = 24; cone[7] = 27;
1494         ierr = DMPlexSetCone(dm, 12, cone);CHKERRQ(ierr);
1495         cone[0] = 30; cone[1] = 28; cone[2] = 20; cone[3] = 19;
1496         cone[4] = 29; cone[5] = 15; cone[6] = 18; cone[7] = 27;
1497         ierr = DMPlexSetCone(dm, 13, cone);CHKERRQ(ierr);
1498         cone[0] = 30; cone[1] = 19; cone[2] = 22; cone[3] = 25;
1499         cone[4] = 29; cone[5] = 23; cone[6] = 16; cone[7] = 15;
1500         ierr = DMPlexSetCone(dm, 14, cone);CHKERRQ(ierr);
1501       } else {
1502         cone[0] =  5; cone[1] =  8; cone[2] =  7; cone[3] =  6;
1503         cone[4] =  9; cone[5] = 12; cone[6] = 11; cone[7] = 10;
1504         ierr = DMPlexSetCone(dm, 0, cone);CHKERRQ(ierr);
1505         cone[0] =  6; cone[1] =  7; cone[2] = 14; cone[3] = 13;
1506         cone[4] = 12; cone[5] = 15; cone[6] = 16; cone[7] = 11;
1507         ierr = DMPlexSetCone(dm, 1, cone);CHKERRQ(ierr);
1508         cone[0] =  8; cone[1] = 17; cone[2] = 14; cone[3] =  7;
1509         cone[4] = 10; cone[5] = 11; cone[6] = 16; cone[7] = 18;
1510         ierr = DMPlexSetCone(dm, 2, cone);CHKERRQ(ierr);
1511         cone[0] = 19; cone[1] = 17; cone[2] =  8; cone[3] =  5;
1512         cone[4] = 20; cone[5] =  9; cone[6] = 10; cone[7] = 18;
1513         ierr = DMPlexSetCone(dm, 3, cone);CHKERRQ(ierr);
1514         cone[0] = 19; cone[1] =  5; cone[2] =  6; cone[3] = 13;
1515         cone[4] = 20; cone[5] = 15; cone[6] = 12; cone[7] =  9;
1516         ierr = DMPlexSetCone(dm, 4, cone);CHKERRQ(ierr);
1517       }
1518     }
1519     ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
1520     ierr = DMPlexStratify(dm);CHKERRQ(ierr);
1521   }
1522   /* Create cube geometry */
1523   {
1524     Vec             coordinates;
1525     PetscSection    coordSection;
1526     PetscScalar    *coords;
1527     PetscInt        coordSize, v;
1528     const PetscReal dis = 1.0/PetscSqrtReal(2.0);
1529     const PetscReal ds2 = dis/2.0;
1530 
1531     /* Build coordinates */
1532     ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
1533     ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
1534     ierr = PetscSectionSetFieldComponents(coordSection, 0, dim);CHKERRQ(ierr);
1535     ierr = PetscSectionSetChart(coordSection, numCells, numCells+numVertices);CHKERRQ(ierr);
1536     for (v = numCells; v < numCells+numVertices; ++v) {
1537       ierr = PetscSectionSetDof(coordSection, v, dim);CHKERRQ(ierr);
1538       ierr = PetscSectionSetFieldDof(coordSection, v, 0, dim);CHKERRQ(ierr);
1539     }
1540     ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
1541     ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
1542     ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
1543     ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
1544     ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
1545     ierr = VecSetBlockSize(coordinates, dim);CHKERRQ(ierr);
1546     ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
1547     ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
1548     if (rank == 0) {
1549       coords[0*dim+0] = -ds2; coords[0*dim+1] = -ds2; coords[0*dim+2] = 0.0;
1550       coords[1*dim+0] =  ds2; coords[1*dim+1] = -ds2; coords[1*dim+2] = 0.0;
1551       coords[2*dim+0] =  ds2; coords[2*dim+1] =  ds2; coords[2*dim+2] = 0.0;
1552       coords[3*dim+0] = -ds2; coords[3*dim+1] =  ds2; coords[3*dim+2] = 0.0;
1553       coords[4*dim+0] = -ds2; coords[4*dim+1] = -ds2; coords[4*dim+2] = 1.0;
1554       coords[5*dim+0] = -ds2; coords[5*dim+1] =  ds2; coords[5*dim+2] = 1.0;
1555       coords[6*dim+0] =  ds2; coords[6*dim+1] =  ds2; coords[6*dim+2] = 1.0;
1556       coords[7*dim+0] =  ds2; coords[7*dim+1] = -ds2; coords[7*dim+2] = 1.0;
1557       coords[ 8*dim+0] =  dis; coords[ 8*dim+1] = -dis; coords[ 8*dim+2] = 0.0;
1558       coords[ 9*dim+0] =  dis; coords[ 9*dim+1] =  dis; coords[ 9*dim+2] = 0.0;
1559       coords[10*dim+0] =  dis; coords[10*dim+1] = -dis; coords[10*dim+2] = 1.0;
1560       coords[11*dim+0] =  dis; coords[11*dim+1] =  dis; coords[11*dim+2] = 1.0;
1561       coords[12*dim+0] = -dis; coords[12*dim+1] =  dis; coords[12*dim+2] = 0.0;
1562       coords[13*dim+0] = -dis; coords[13*dim+1] =  dis; coords[13*dim+2] = 1.0;
1563       coords[14*dim+0] = -dis; coords[14*dim+1] = -dis; coords[14*dim+2] = 0.0;
1564       coords[15*dim+0] = -dis; coords[15*dim+1] = -dis; coords[15*dim+2] = 1.0;
1565       if (periodicZ == DM_BOUNDARY_PERIODIC) {
1566         /* 15 31 19 */ coords[16*dim+0] = -ds2; coords[16*dim+1] = -ds2; coords[16*dim+2] = 0.5;
1567         /* 16 32 22 */ coords[17*dim+0] =  ds2; coords[17*dim+1] = -ds2; coords[17*dim+2] = 0.5;
1568         /* 17 33 21 */ coords[18*dim+0] =  ds2; coords[18*dim+1] =  ds2; coords[18*dim+2] = 0.5;
1569         /* 18 34 20 */ coords[19*dim+0] = -ds2; coords[19*dim+1] =  ds2; coords[19*dim+2] = 0.5;
1570         /* 29 35 30 */ coords[20*dim+0] = -dis; coords[20*dim+1] = -dis; coords[20*dim+2] = 0.5;
1571         /* 23 36 25 */ coords[21*dim+0] =  dis; coords[21*dim+1] = -dis; coords[21*dim+2] = 0.5;
1572         /* 24 37 26 */ coords[22*dim+0] =  dis; coords[22*dim+1] =  dis; coords[22*dim+2] = 0.5;
1573         /* 27 38 28 */ coords[23*dim+0] = -dis; coords[23*dim+1] =  dis; coords[23*dim+2] = 0.5;
1574       }
1575     }
1576     ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
1577     ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
1578     ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
1579   }
1580   /* Create periodicity */
1581   if (periodicZ == DM_BOUNDARY_PERIODIC || periodicZ == DM_BOUNDARY_TWIST) {
1582     PetscReal      L[3];
1583     PetscReal      maxCell[3];
1584     DMBoundaryType bdType[3];
1585     PetscReal      lower[3] = {0.0, 0.0, 0.0};
1586     PetscReal      upper[3] = {1.0, 1.0, 1.5};
1587     PetscInt       i, numZCells = 3;
1588 
1589     bdType[0] = DM_BOUNDARY_NONE;
1590     bdType[1] = DM_BOUNDARY_NONE;
1591     bdType[2] = periodicZ;
1592     for (i = 0; i < dim; i++) {
1593       L[i]       = upper[i] - lower[i];
1594       maxCell[i] = 1.1 * (L[i] / numZCells);
1595     }
1596     ierr = DMSetPeriodicity(dm, PETSC_TRUE, maxCell, L, bdType);CHKERRQ(ierr);
1597   }
1598   {
1599     DM          cdm;
1600     PetscDS     cds;
1601     PetscScalar c[2] = {1.0, 1.0};
1602 
1603     ierr = DMPlexCreateCoordinateSpace(dm, 1, snapToCylinder);CHKERRQ(ierr);
1604     ierr = DMGetCoordinateDM(dm, &cdm);CHKERRQ(ierr);
1605     ierr = DMGetDS(cdm, &cds);CHKERRQ(ierr);
1606     ierr = PetscDSSetConstants(cds, 2, c);CHKERRQ(ierr);
1607   }
1608   /* Wait for coordinate creation before doing in-place modification */
1609   ierr = DMPlexInterpolateInPlace_Internal(dm);CHKERRQ(ierr);
1610   PetscFunctionReturn(0);
1611 }
1612 
1613 /*@
1614   DMPlexCreateHexCylinderMesh - Creates a mesh on the tensor product of the unit interval with the circle (cylinder) using hexahedra.
1615 
1616   Collective
1617 
1618   Input Parameters:
1619 + comm      - The communicator for the DM object
1620 - periodicZ - The boundary type for the Z direction
1621 
1622   Output Parameter:
1623 . dm  - The DM object
1624 
1625   Note:
1626   Here is the output numbering looking from the bottom of the cylinder:
1627 $       17-----14
1628 $        |     |
1629 $        |  2  |
1630 $        |     |
1631 $ 17-----8-----7-----14
1632 $  |     |     |     |
1633 $  |  3  |  0  |  1  |
1634 $  |     |     |     |
1635 $ 19-----5-----6-----13
1636 $        |     |
1637 $        |  4  |
1638 $        |     |
1639 $       19-----13
1640 $
1641 $ and up through the top
1642 $
1643 $       18-----16
1644 $        |     |
1645 $        |  2  |
1646 $        |     |
1647 $ 18----10----11-----16
1648 $  |     |     |     |
1649 $  |  3  |  0  |  1  |
1650 $  |     |     |     |
1651 $ 20-----9----12-----15
1652 $        |     |
1653 $        |  4  |
1654 $        |     |
1655 $       20-----15
1656 
1657   Level: beginner
1658 
1659 .seealso: DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
1660 @*/
1661 PetscErrorCode DMPlexCreateHexCylinderMesh(MPI_Comm comm, DMBoundaryType periodicZ, DM *dm)
1662 {
1663   PetscErrorCode ierr;
1664 
1665   PetscFunctionBegin;
1666   PetscValidPointer(dm, 3);
1667   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
1668   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
1669   ierr = DMPlexCreateHexCylinderMesh_Internal(*dm, periodicZ);CHKERRQ(ierr);
1670   PetscFunctionReturn(0);
1671 }
1672 
1673 static PetscErrorCode DMPlexCreateWedgeCylinderMesh_Internal(DM dm, PetscInt n, PetscBool interpolate)
1674 {
1675   const PetscInt dim = 3;
1676   PetscInt       numCells, numVertices, v;
1677   PetscMPIInt    rank;
1678   PetscErrorCode ierr;
1679 
1680   PetscFunctionBegin;
1681   if (n < 0) SETERRQ1(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_OUTOFRANGE, "Number of wedges %D cannot be negative", n);
1682   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject) dm), &rank);CHKERRMPI(ierr);
1683   ierr = DMSetDimension(dm, dim);CHKERRQ(ierr);
1684   /* Must create the celltype label here so that we do not automatically try to compute the types */
1685   ierr = DMCreateLabel(dm, "celltype");CHKERRQ(ierr);
1686   /* Create topology */
1687   {
1688     PetscInt cone[6], c;
1689 
1690     numCells    = rank == 0 ?        n : 0;
1691     numVertices = rank == 0 ?  2*(n+1) : 0;
1692     ierr = DMPlexSetChart(dm, 0, numCells+numVertices);CHKERRQ(ierr);
1693     for (c = 0; c < numCells; c++) {ierr = DMPlexSetConeSize(dm, c, 6);CHKERRQ(ierr);}
1694     ierr = DMSetUp(dm);CHKERRQ(ierr);
1695     for (c = 0; c < numCells; c++) {
1696       cone[0] =  c+n*1; cone[1] = (c+1)%n+n*1; cone[2] = 0+3*n;
1697       cone[3] =  c+n*2; cone[4] = (c+1)%n+n*2; cone[5] = 1+3*n;
1698       ierr = DMPlexSetCone(dm, c, cone);CHKERRQ(ierr);
1699       ierr = DMPlexSetCellType(dm, c, DM_POLYTOPE_TRI_PRISM_TENSOR);CHKERRQ(ierr);
1700     }
1701     ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
1702     ierr = DMPlexStratify(dm);CHKERRQ(ierr);
1703   }
1704   for (v = numCells; v < numCells+numVertices; ++v) {
1705     ierr = DMPlexSetCellType(dm, v, DM_POLYTOPE_POINT);CHKERRQ(ierr);
1706   }
1707   /* Create cylinder geometry */
1708   {
1709     Vec          coordinates;
1710     PetscSection coordSection;
1711     PetscScalar *coords;
1712     PetscInt     coordSize, c;
1713 
1714     /* Build coordinates */
1715     ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
1716     ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
1717     ierr = PetscSectionSetFieldComponents(coordSection, 0, dim);CHKERRQ(ierr);
1718     ierr = PetscSectionSetChart(coordSection, numCells, numCells+numVertices);CHKERRQ(ierr);
1719     for (v = numCells; v < numCells+numVertices; ++v) {
1720       ierr = PetscSectionSetDof(coordSection, v, dim);CHKERRQ(ierr);
1721       ierr = PetscSectionSetFieldDof(coordSection, v, 0, dim);CHKERRQ(ierr);
1722     }
1723     ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
1724     ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
1725     ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
1726     ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
1727     ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
1728     ierr = VecSetBlockSize(coordinates, dim);CHKERRQ(ierr);
1729     ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
1730     ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
1731     for (c = 0; c < numCells; c++) {
1732       coords[(c+0*n)*dim+0] = PetscCosReal(2.0*c*PETSC_PI/n); coords[(c+0*n)*dim+1] = PetscSinReal(2.0*c*PETSC_PI/n); coords[(c+0*n)*dim+2] = 1.0;
1733       coords[(c+1*n)*dim+0] = PetscCosReal(2.0*c*PETSC_PI/n); coords[(c+1*n)*dim+1] = PetscSinReal(2.0*c*PETSC_PI/n); coords[(c+1*n)*dim+2] = 0.0;
1734     }
1735     if (rank == 0) {
1736       coords[(2*n+0)*dim+0] = 0.0; coords[(2*n+0)*dim+1] = 0.0; coords[(2*n+0)*dim+2] = 1.0;
1737       coords[(2*n+1)*dim+0] = 0.0; coords[(2*n+1)*dim+1] = 0.0; coords[(2*n+1)*dim+2] = 0.0;
1738     }
1739     ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
1740     ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
1741     ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
1742   }
1743   /* Interpolate */
1744   if (interpolate) {ierr = DMPlexInterpolateInPlace_Internal(dm);CHKERRQ(ierr);}
1745   PetscFunctionReturn(0);
1746 }
1747 
1748 /*@
1749   DMPlexCreateWedgeCylinderMesh - Creates a mesh on the tensor product of the unit interval with the circle (cylinder) using wedges.
1750 
1751   Collective
1752 
1753   Input Parameters:
1754 + comm - The communicator for the DM object
1755 . n    - The number of wedges around the origin
1756 - interpolate - Create edges and faces
1757 
1758   Output Parameter:
1759 . dm  - The DM object
1760 
1761   Level: beginner
1762 
1763 .seealso: DMPlexCreateHexCylinderMesh(), DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
1764 @*/
1765 PetscErrorCode DMPlexCreateWedgeCylinderMesh(MPI_Comm comm, PetscInt n, PetscBool interpolate, DM *dm)
1766 {
1767   PetscErrorCode ierr;
1768 
1769   PetscFunctionBegin;
1770   PetscValidPointer(dm, 4);
1771   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
1772   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
1773   ierr = DMPlexCreateWedgeCylinderMesh_Internal(*dm, n, interpolate);CHKERRQ(ierr);
1774   PetscFunctionReturn(0);
1775 }
1776 
1777 PETSC_STATIC_INLINE PetscReal DiffNormReal(PetscInt dim, const PetscReal x[], const PetscReal y[])
1778 {
1779   PetscReal prod = 0.0;
1780   PetscInt  i;
1781   for (i = 0; i < dim; ++i) prod += PetscSqr(x[i] - y[i]);
1782   return PetscSqrtReal(prod);
1783 }
1784 PETSC_STATIC_INLINE PetscReal DotReal(PetscInt dim, const PetscReal x[], const PetscReal y[])
1785 {
1786   PetscReal prod = 0.0;
1787   PetscInt  i;
1788   for (i = 0; i < dim; ++i) prod += x[i]*y[i];
1789   return prod;
1790 }
1791 
1792 /* The first constant is the sphere radius */
1793 static void snapToSphere(PetscInt dim, PetscInt Nf, PetscInt NfAux,
1794                          const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
1795                          const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
1796                          PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
1797 {
1798   PetscReal r = PetscRealPart(constants[0]);
1799   PetscReal norm2 = 0.0, fac;
1800   PetscInt  n = uOff[1] - uOff[0], d;
1801 
1802   for (d = 0; d < n; ++d) norm2 += PetscSqr(PetscRealPart(u[d]));
1803   fac = r/PetscSqrtReal(norm2);
1804   for (d = 0; d < n; ++d) f0[d] = u[d]*fac;
1805 }
1806 
1807 static PetscErrorCode DMPlexCreateSphereMesh_Internal(DM dm, PetscInt dim, PetscBool simplex, PetscReal R)
1808 {
1809   const PetscInt  embedDim = dim+1;
1810   PetscSection    coordSection;
1811   Vec             coordinates;
1812   PetscScalar    *coords;
1813   PetscReal      *coordsIn;
1814   PetscInt        numCells, numEdges, numVerts, firstVertex, v, firstEdge, coordSize, d, c, e;
1815   PetscMPIInt     rank;
1816   PetscErrorCode  ierr;
1817 
1818   PetscFunctionBegin;
1819   PetscValidLogicalCollectiveBool(dm, simplex, 3);
1820   ierr = DMSetDimension(dm, dim);CHKERRQ(ierr);
1821   ierr = DMSetCoordinateDim(dm, dim+1);CHKERRQ(ierr);
1822   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject) dm), &rank);CHKERRMPI(ierr);
1823   switch (dim) {
1824   case 2:
1825     if (simplex) {
1826       const PetscReal radius    = PetscSqrtReal(1 + PETSC_PHI*PETSC_PHI)/(1.0 + PETSC_PHI);
1827       const PetscReal edgeLen   = 2.0/(1.0 + PETSC_PHI) * (R/radius);
1828       const PetscInt  degree    = 5;
1829       PetscReal       vertex[3] = {0.0, 1.0/(1.0 + PETSC_PHI), PETSC_PHI/(1.0 + PETSC_PHI)};
1830       PetscInt        s[3]      = {1, 1, 1};
1831       PetscInt        cone[3];
1832       PetscInt       *graph, p, i, j, k;
1833 
1834       vertex[0] *= R/radius; vertex[1] *= R/radius; vertex[2] *= R/radius;
1835       numCells    = rank == 0 ? 20 : 0;
1836       numVerts    = rank == 0 ? 12 : 0;
1837       firstVertex = numCells;
1838       /* Use icosahedron, which for a R-sphere has coordinates which are all cyclic permutations of
1839 
1840            (0, \pm 1/\phi+1, \pm \phi/\phi+1)
1841 
1842          where \phi^2 - \phi - 1 = 0, meaning \phi is the golden ratio \frac{1 + \sqrt{5}}{2}. The edge
1843          length is then given by 2/(1+\phi) = 2 * 0.38197 = 0.76393.
1844       */
1845       /* Construct vertices */
1846       ierr = PetscCalloc1(numVerts * embedDim, &coordsIn);CHKERRQ(ierr);
1847       if (rank == 0) {
1848         for (p = 0, i = 0; p < embedDim; ++p) {
1849           for (s[1] = -1; s[1] < 2; s[1] += 2) {
1850             for (s[2] = -1; s[2] < 2; s[2] += 2) {
1851               for (d = 0; d < embedDim; ++d) coordsIn[i*embedDim+d] = s[(d+p)%embedDim]*vertex[(d+p)%embedDim];
1852               ++i;
1853             }
1854           }
1855         }
1856       }
1857       /* Construct graph */
1858       ierr = PetscCalloc1(numVerts * numVerts, &graph);CHKERRQ(ierr);
1859       for (i = 0; i < numVerts; ++i) {
1860         for (j = 0, k = 0; j < numVerts; ++j) {
1861           if (PetscAbsReal(DiffNormReal(embedDim, &coordsIn[i*embedDim], &coordsIn[j*embedDim]) - edgeLen) < PETSC_SMALL) {graph[i*numVerts+j] = 1; ++k;}
1862         }
1863         if (k != degree) SETERRQ3(PetscObjectComm((PetscObject) dm), PETSC_ERR_PLIB, "Invalid icosahedron, vertex %D degree %D != %D", i, k, degree);
1864       }
1865       /* Build Topology */
1866       ierr = DMPlexSetChart(dm, 0, numCells+numVerts);CHKERRQ(ierr);
1867       for (c = 0; c < numCells; c++) {
1868         ierr = DMPlexSetConeSize(dm, c, embedDim);CHKERRQ(ierr);
1869       }
1870       ierr = DMSetUp(dm);CHKERRQ(ierr); /* Allocate space for cones */
1871       /* Cells */
1872       for (i = 0, c = 0; i < numVerts; ++i) {
1873         for (j = 0; j < i; ++j) {
1874           for (k = 0; k < j; ++k) {
1875             if (graph[i*numVerts+j] && graph[j*numVerts+k] && graph[k*numVerts+i]) {
1876               cone[0] = firstVertex+i; cone[1] = firstVertex+j; cone[2] = firstVertex+k;
1877               /* Check orientation */
1878               {
1879                 const PetscInt epsilon[3][3][3] = {{{0, 0, 0}, {0, 0, 1}, {0, -1, 0}}, {{0, 0, -1}, {0, 0, 0}, {1, 0, 0}}, {{0, 1, 0}, {-1, 0, 0}, {0, 0, 0}}};
1880                 PetscReal normal[3];
1881                 PetscInt  e, f;
1882 
1883                 for (d = 0; d < embedDim; ++d) {
1884                   normal[d] = 0.0;
1885                   for (e = 0; e < embedDim; ++e) {
1886                     for (f = 0; f < embedDim; ++f) {
1887                       normal[d] += epsilon[d][e][f]*(coordsIn[j*embedDim+e] - coordsIn[i*embedDim+e])*(coordsIn[k*embedDim+f] - coordsIn[i*embedDim+f]);
1888                     }
1889                   }
1890                 }
1891                 if (DotReal(embedDim, normal, &coordsIn[i*embedDim]) < 0) {PetscInt tmp = cone[1]; cone[1] = cone[2]; cone[2] = tmp;}
1892               }
1893               ierr = DMPlexSetCone(dm, c++, cone);CHKERRQ(ierr);
1894             }
1895           }
1896         }
1897       }
1898       ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
1899       ierr = DMPlexStratify(dm);CHKERRQ(ierr);
1900       ierr = PetscFree(graph);CHKERRQ(ierr);
1901     } else {
1902       /*
1903         12-21--13
1904          |     |
1905         25  4  24
1906          |     |
1907   12-25--9-16--8-24--13
1908    |     |     |     |
1909   23  5 17  0 15  3  22
1910    |     |     |     |
1911   10-20--6-14--7-19--11
1912          |     |
1913         20  1  19
1914          |     |
1915         10-18--11
1916          |     |
1917         23  2  22
1918          |     |
1919         12-21--13
1920        */
1921       PetscInt cone[4], ornt[4];
1922 
1923       numCells    = rank == 0 ?  6 : 0;
1924       numEdges    = rank == 0 ? 12 : 0;
1925       numVerts    = rank == 0 ?  8 : 0;
1926       firstVertex = numCells;
1927       firstEdge   = numCells + numVerts;
1928       /* Build Topology */
1929       ierr = DMPlexSetChart(dm, 0, numCells+numEdges+numVerts);CHKERRQ(ierr);
1930       for (c = 0; c < numCells; c++) {
1931         ierr = DMPlexSetConeSize(dm, c, 4);CHKERRQ(ierr);
1932       }
1933       for (e = firstEdge; e < firstEdge+numEdges; ++e) {
1934         ierr = DMPlexSetConeSize(dm, e, 2);CHKERRQ(ierr);
1935       }
1936       ierr = DMSetUp(dm);CHKERRQ(ierr); /* Allocate space for cones */
1937       if (rank == 0) {
1938         /* Cell 0 */
1939         cone[0] = 14; cone[1] = 15; cone[2] = 16; cone[3] = 17;
1940         ierr = DMPlexSetCone(dm, 0, cone);CHKERRQ(ierr);
1941         ornt[0] = 0; ornt[1] = 0; ornt[2] = 0; ornt[3] = 0;
1942         ierr = DMPlexSetConeOrientation(dm, 0, ornt);CHKERRQ(ierr);
1943         /* Cell 1 */
1944         cone[0] = 18; cone[1] = 19; cone[2] = 14; cone[3] = 20;
1945         ierr = DMPlexSetCone(dm, 1, cone);CHKERRQ(ierr);
1946         ornt[0] = 0; ornt[1] = 0; ornt[2] = -1; ornt[3] = 0;
1947         ierr = DMPlexSetConeOrientation(dm, 1, ornt);CHKERRQ(ierr);
1948         /* Cell 2 */
1949         cone[0] = 21; cone[1] = 22; cone[2] = 18; cone[3] = 23;
1950         ierr = DMPlexSetCone(dm, 2, cone);CHKERRQ(ierr);
1951         ornt[0] = 0; ornt[1] = 0; ornt[2] = -1; ornt[3] = 0;
1952         ierr = DMPlexSetConeOrientation(dm, 2, ornt);CHKERRQ(ierr);
1953         /* Cell 3 */
1954         cone[0] = 19; cone[1] = 22; cone[2] = 24; cone[3] = 15;
1955         ierr = DMPlexSetCone(dm, 3, cone);CHKERRQ(ierr);
1956         ornt[0] = -1; ornt[1] = -1; ornt[2] = 0; ornt[3] = -1;
1957         ierr = DMPlexSetConeOrientation(dm, 3, ornt);CHKERRQ(ierr);
1958         /* Cell 4 */
1959         cone[0] = 16; cone[1] = 24; cone[2] = 21; cone[3] = 25;
1960         ierr = DMPlexSetCone(dm, 4, cone);CHKERRQ(ierr);
1961         ornt[0] = -1; ornt[1] = -1; ornt[2] = -1; ornt[3] = 0;
1962         ierr = DMPlexSetConeOrientation(dm, 4, ornt);CHKERRQ(ierr);
1963         /* Cell 5 */
1964         cone[0] = 20; cone[1] = 17; cone[2] = 25; cone[3] = 23;
1965         ierr = DMPlexSetCone(dm, 5, cone);CHKERRQ(ierr);
1966         ornt[0] = -1; ornt[1] = -1; ornt[2] = -1; ornt[3] = -1;
1967         ierr = DMPlexSetConeOrientation(dm, 5, ornt);CHKERRQ(ierr);
1968         /* Edges */
1969         cone[0] =  6; cone[1] =  7;
1970         ierr = DMPlexSetCone(dm, 14, cone);CHKERRQ(ierr);
1971         cone[0] =  7; cone[1] =  8;
1972         ierr = DMPlexSetCone(dm, 15, cone);CHKERRQ(ierr);
1973         cone[0] =  8; cone[1] =  9;
1974         ierr = DMPlexSetCone(dm, 16, cone);CHKERRQ(ierr);
1975         cone[0] =  9; cone[1] =  6;
1976         ierr = DMPlexSetCone(dm, 17, cone);CHKERRQ(ierr);
1977         cone[0] = 10; cone[1] = 11;
1978         ierr = DMPlexSetCone(dm, 18, cone);CHKERRQ(ierr);
1979         cone[0] = 11; cone[1] =  7;
1980         ierr = DMPlexSetCone(dm, 19, cone);CHKERRQ(ierr);
1981         cone[0] =  6; cone[1] = 10;
1982         ierr = DMPlexSetCone(dm, 20, cone);CHKERRQ(ierr);
1983         cone[0] = 12; cone[1] = 13;
1984         ierr = DMPlexSetCone(dm, 21, cone);CHKERRQ(ierr);
1985         cone[0] = 13; cone[1] = 11;
1986         ierr = DMPlexSetCone(dm, 22, cone);CHKERRQ(ierr);
1987         cone[0] = 10; cone[1] = 12;
1988         ierr = DMPlexSetCone(dm, 23, cone);CHKERRQ(ierr);
1989         cone[0] = 13; cone[1] =  8;
1990         ierr = DMPlexSetCone(dm, 24, cone);CHKERRQ(ierr);
1991         cone[0] = 12; cone[1] =  9;
1992         ierr = DMPlexSetCone(dm, 25, cone);CHKERRQ(ierr);
1993       }
1994       ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
1995       ierr = DMPlexStratify(dm);CHKERRQ(ierr);
1996       /* Build coordinates */
1997       ierr = PetscCalloc1(numVerts * embedDim, &coordsIn);CHKERRQ(ierr);
1998       if (rank == 0) {
1999         coordsIn[0*embedDim+0] = -R; coordsIn[0*embedDim+1] =  R; coordsIn[0*embedDim+2] = -R;
2000         coordsIn[1*embedDim+0] =  R; coordsIn[1*embedDim+1] =  R; coordsIn[1*embedDim+2] = -R;
2001         coordsIn[2*embedDim+0] =  R; coordsIn[2*embedDim+1] = -R; coordsIn[2*embedDim+2] = -R;
2002         coordsIn[3*embedDim+0] = -R; coordsIn[3*embedDim+1] = -R; coordsIn[3*embedDim+2] = -R;
2003         coordsIn[4*embedDim+0] = -R; coordsIn[4*embedDim+1] =  R; coordsIn[4*embedDim+2] =  R;
2004         coordsIn[5*embedDim+0] =  R; coordsIn[5*embedDim+1] =  R; coordsIn[5*embedDim+2] =  R;
2005         coordsIn[6*embedDim+0] = -R; coordsIn[6*embedDim+1] = -R; coordsIn[6*embedDim+2] =  R;
2006         coordsIn[7*embedDim+0] =  R; coordsIn[7*embedDim+1] = -R; coordsIn[7*embedDim+2] =  R;
2007       }
2008     }
2009     break;
2010   case 3:
2011     if (simplex) {
2012       const PetscReal edgeLen         = 1.0/PETSC_PHI;
2013       PetscReal       vertexA[4]      = {0.5, 0.5, 0.5, 0.5};
2014       PetscReal       vertexB[4]      = {1.0, 0.0, 0.0, 0.0};
2015       PetscReal       vertexC[4]      = {0.5, 0.5*PETSC_PHI, 0.5/PETSC_PHI, 0.0};
2016       const PetscInt  degree          = 12;
2017       PetscInt        s[4]            = {1, 1, 1};
2018       PetscInt        evenPerm[12][4] = {{0, 1, 2, 3}, {0, 2, 3, 1}, {0, 3, 1, 2}, {1, 0, 3, 2}, {1, 2, 0, 3}, {1, 3, 2, 0},
2019                                          {2, 0, 1, 3}, {2, 1, 3, 0}, {2, 3, 0, 1}, {3, 0, 2, 1}, {3, 1, 0, 2}, {3, 2, 1, 0}};
2020       PetscInt        cone[4];
2021       PetscInt       *graph, p, i, j, k, l;
2022 
2023       vertexA[0] *= R; vertexA[1] *= R; vertexA[2] *= R; vertexA[3] *= R;
2024       vertexB[0] *= R; vertexB[1] *= R; vertexB[2] *= R; vertexB[3] *= R;
2025       vertexC[0] *= R; vertexC[1] *= R; vertexC[2] *= R; vertexC[3] *= R;
2026       numCells    = rank == 0 ? 600 : 0;
2027       numVerts    = rank == 0 ? 120 : 0;
2028       firstVertex = numCells;
2029       /* Use the 600-cell, which for a unit sphere has coordinates which are
2030 
2031            1/2 (\pm 1, \pm 1,    \pm 1, \pm 1)                          16
2032                (\pm 1,    0,       0,      0)  all cyclic permutations   8
2033            1/2 (\pm 1, \pm phi, \pm 1/phi, 0)  all even permutations    96
2034 
2035          where \phi^2 - \phi - 1 = 0, meaning \phi is the golden ratio \frac{1 + \sqrt{5}}{2}. The edge
2036          length is then given by 1/\phi = 0.61803.
2037 
2038          http://buzzard.pugetsound.edu/sage-practice/ch03s03.html
2039          http://mathworld.wolfram.com/600-Cell.html
2040       */
2041       /* Construct vertices */
2042       ierr = PetscCalloc1(numVerts * embedDim, &coordsIn);CHKERRQ(ierr);
2043       i    = 0;
2044       if (rank == 0) {
2045         for (s[0] = -1; s[0] < 2; s[0] += 2) {
2046           for (s[1] = -1; s[1] < 2; s[1] += 2) {
2047             for (s[2] = -1; s[2] < 2; s[2] += 2) {
2048               for (s[3] = -1; s[3] < 2; s[3] += 2) {
2049                 for (d = 0; d < embedDim; ++d) coordsIn[i*embedDim+d] = s[d]*vertexA[d];
2050                 ++i;
2051               }
2052             }
2053           }
2054         }
2055         for (p = 0; p < embedDim; ++p) {
2056           s[1] = s[2] = s[3] = 1;
2057           for (s[0] = -1; s[0] < 2; s[0] += 2) {
2058             for (d = 0; d < embedDim; ++d) coordsIn[i*embedDim+d] = s[(d+p)%embedDim]*vertexB[(d+p)%embedDim];
2059             ++i;
2060           }
2061         }
2062         for (p = 0; p < 12; ++p) {
2063           s[3] = 1;
2064           for (s[0] = -1; s[0] < 2; s[0] += 2) {
2065             for (s[1] = -1; s[1] < 2; s[1] += 2) {
2066               for (s[2] = -1; s[2] < 2; s[2] += 2) {
2067                 for (d = 0; d < embedDim; ++d) coordsIn[i*embedDim+d] = s[evenPerm[p][d]]*vertexC[evenPerm[p][d]];
2068                 ++i;
2069               }
2070             }
2071           }
2072         }
2073       }
2074       if (i != numVerts) SETERRQ2(PetscObjectComm((PetscObject) dm), PETSC_ERR_PLIB, "Invalid 600-cell, vertices %D != %D", i, numVerts);
2075       /* Construct graph */
2076       ierr = PetscCalloc1(numVerts * numVerts, &graph);CHKERRQ(ierr);
2077       for (i = 0; i < numVerts; ++i) {
2078         for (j = 0, k = 0; j < numVerts; ++j) {
2079           if (PetscAbsReal(DiffNormReal(embedDim, &coordsIn[i*embedDim], &coordsIn[j*embedDim]) - edgeLen) < PETSC_SMALL) {graph[i*numVerts+j] = 1; ++k;}
2080         }
2081         if (k != degree) SETERRQ3(PetscObjectComm((PetscObject) dm), PETSC_ERR_PLIB, "Invalid 600-cell, vertex %D degree %D != %D", i, k, degree);
2082       }
2083       /* Build Topology */
2084       ierr = DMPlexSetChart(dm, 0, numCells+numVerts);CHKERRQ(ierr);
2085       for (c = 0; c < numCells; c++) {
2086         ierr = DMPlexSetConeSize(dm, c, embedDim);CHKERRQ(ierr);
2087       }
2088       ierr = DMSetUp(dm);CHKERRQ(ierr); /* Allocate space for cones */
2089       /* Cells */
2090       if (rank == 0) {
2091         for (i = 0, c = 0; i < numVerts; ++i) {
2092           for (j = 0; j < i; ++j) {
2093             for (k = 0; k < j; ++k) {
2094               for (l = 0; l < k; ++l) {
2095                 if (graph[i*numVerts+j] && graph[j*numVerts+k] && graph[k*numVerts+i] &&
2096                     graph[l*numVerts+i] && graph[l*numVerts+j] && graph[l*numVerts+k]) {
2097                   cone[0] = firstVertex+i; cone[1] = firstVertex+j; cone[2] = firstVertex+k; cone[3] = firstVertex+l;
2098                   /* Check orientation: https://ef.gy/linear-algebra:normal-vectors-in-higher-dimensional-spaces */
2099                   {
2100                     const PetscInt epsilon[4][4][4][4] = {{{{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}},
2101                                                            {{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  1}, { 0,  0, -1, 0}},
2102                                                            {{0,  0,  0,  0}, { 0, 0,  0, -1}, { 0,  0, 0,  0}, { 0,  1,  0, 0}},
2103                                                            {{0,  0,  0,  0}, { 0, 0,  1,  0}, { 0, -1, 0,  0}, { 0,  0,  0, 0}}},
2104 
2105                                                           {{{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0, -1}, { 0,  0,  1, 0}},
2106                                                            {{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}},
2107                                                            {{0,  0,  0,  1}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, {-1,  0,  0, 0}},
2108                                                            {{0,  0, -1,  0}, { 0, 0,  0,  0}, { 1,  0, 0,  0}, { 0,  0,  0, 0}}},
2109 
2110                                                           {{{0,  0,  0,  0}, { 0, 0,  0,  1}, { 0,  0, 0,  0}, { 0, -1,  0, 0}},
2111                                                            {{0,  0,  0, -1}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 1,  0,  0, 0}},
2112                                                            {{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}},
2113                                                            {{0,  1,  0,  0}, {-1, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}}},
2114 
2115                                                           {{{0,  0,  0,  0}, { 0, 0, -1,  0}, { 0,  1, 0,  0}, { 0,  0,  0, 0}},
2116                                                            {{0,  0,  1,  0}, { 0, 0,  0,  0}, {-1,  0, 0,  0}, { 0,  0,  0, 0}},
2117                                                            {{0, -1,  0,  0}, { 1, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}},
2118                                                            {{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}}}};
2119                     PetscReal normal[4];
2120                     PetscInt  e, f, g;
2121 
2122                     for (d = 0; d < embedDim; ++d) {
2123                       normal[d] = 0.0;
2124                       for (e = 0; e < embedDim; ++e) {
2125                         for (f = 0; f < embedDim; ++f) {
2126                           for (g = 0; g < embedDim; ++g) {
2127                             normal[d] += epsilon[d][e][f][g]*(coordsIn[j*embedDim+e] - coordsIn[i*embedDim+e])*(coordsIn[k*embedDim+f] - coordsIn[i*embedDim+f])*(coordsIn[l*embedDim+f] - coordsIn[i*embedDim+f]);
2128                           }
2129                         }
2130                       }
2131                     }
2132                     if (DotReal(embedDim, normal, &coordsIn[i*embedDim]) < 0) {PetscInt tmp = cone[1]; cone[1] = cone[2]; cone[2] = tmp;}
2133                   }
2134                   ierr = DMPlexSetCone(dm, c++, cone);CHKERRQ(ierr);
2135                 }
2136               }
2137             }
2138           }
2139         }
2140       }
2141       ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
2142       ierr = DMPlexStratify(dm);CHKERRQ(ierr);
2143       ierr = PetscFree(graph);CHKERRQ(ierr);
2144       break;
2145     }
2146   default: SETERRQ1(PetscObjectComm((PetscObject) dm), PETSC_ERR_SUP, "Unsupported dimension for sphere: %D", dim);
2147   }
2148   /* Create coordinates */
2149   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
2150   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
2151   ierr = PetscSectionSetFieldComponents(coordSection, 0, embedDim);CHKERRQ(ierr);
2152   ierr = PetscSectionSetChart(coordSection, firstVertex, firstVertex+numVerts);CHKERRQ(ierr);
2153   for (v = firstVertex; v < firstVertex+numVerts; ++v) {
2154     ierr = PetscSectionSetDof(coordSection, v, embedDim);CHKERRQ(ierr);
2155     ierr = PetscSectionSetFieldDof(coordSection, v, 0, embedDim);CHKERRQ(ierr);
2156   }
2157   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
2158   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
2159   ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
2160   ierr = VecSetBlockSize(coordinates, embedDim);CHKERRQ(ierr);
2161   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
2162   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
2163   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
2164   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
2165   for (v = 0; v < numVerts; ++v) for (d = 0; d < embedDim; ++d) {coords[v*embedDim+d] = coordsIn[v*embedDim+d];}
2166   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
2167   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
2168   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
2169   ierr = PetscFree(coordsIn);CHKERRQ(ierr);
2170   {
2171     DM          cdm;
2172     PetscDS     cds;
2173     PetscScalar c = R;
2174 
2175     ierr = DMPlexCreateCoordinateSpace(dm, 1, snapToSphere);CHKERRQ(ierr);
2176     ierr = DMGetCoordinateDM(dm, &cdm);CHKERRQ(ierr);
2177     ierr = DMGetDS(cdm, &cds);CHKERRQ(ierr);
2178     ierr = PetscDSSetConstants(cds, 1, &c);CHKERRQ(ierr);
2179   }
2180   /* Wait for coordinate creation before doing in-place modification */
2181   if (simplex) {ierr = DMPlexInterpolateInPlace_Internal(dm);CHKERRQ(ierr);}
2182   PetscFunctionReturn(0);
2183 }
2184 
2185 /*@
2186   DMPlexCreateSphereMesh - Creates a mesh on the d-dimensional sphere, S^d.
2187 
2188   Collective
2189 
2190   Input Parameters:
2191 + comm    - The communicator for the DM object
2192 . dim     - The dimension
2193 . simplex - Use simplices, or tensor product cells
2194 - R       - The radius
2195 
2196   Output Parameter:
2197 . dm  - The DM object
2198 
2199   Level: beginner
2200 
2201 .seealso: DMPlexCreateBallMesh(), DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
2202 @*/
2203 PetscErrorCode DMPlexCreateSphereMesh(MPI_Comm comm, PetscInt dim, PetscBool simplex, PetscReal R, DM *dm)
2204 {
2205   PetscErrorCode ierr;
2206 
2207   PetscFunctionBegin;
2208   PetscValidPointer(dm, 5);
2209   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
2210   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
2211   ierr = DMPlexCreateSphereMesh_Internal(*dm, dim, simplex, R);CHKERRQ(ierr);
2212   PetscFunctionReturn(0);
2213 }
2214 
2215 static PetscErrorCode DMPlexCreateBallMesh_Internal(DM dm, PetscInt dim, PetscReal R)
2216 {
2217   DM             sdm, vol;
2218   DMLabel        bdlabel;
2219   PetscErrorCode ierr;
2220 
2221   PetscFunctionBegin;
2222   ierr = DMCreate(PetscObjectComm((PetscObject) dm), &sdm);CHKERRQ(ierr);
2223   ierr = DMSetType(sdm, DMPLEX);CHKERRQ(ierr);
2224   ierr = PetscObjectSetOptionsPrefix((PetscObject) sdm, "bd_");CHKERRQ(ierr);
2225   ierr = DMPlexCreateSphereMesh_Internal(sdm, dim-1, PETSC_TRUE, R);CHKERRQ(ierr);
2226   ierr = DMSetFromOptions(sdm);CHKERRQ(ierr);
2227   ierr = DMViewFromOptions(sdm, NULL, "-dm_view");CHKERRQ(ierr);
2228   ierr = DMPlexGenerate(sdm, NULL, PETSC_TRUE, &vol);CHKERRQ(ierr);
2229   ierr = DMDestroy(&sdm);CHKERRQ(ierr);
2230   ierr = DMPlexReplace_Static(dm, &vol);CHKERRQ(ierr);
2231   ierr = DMCreateLabel(dm, "marker");CHKERRQ(ierr);
2232   ierr = DMGetLabel(dm, "marker", &bdlabel);CHKERRQ(ierr);
2233   ierr = DMPlexMarkBoundaryFaces(dm, PETSC_DETERMINE, bdlabel);CHKERRQ(ierr);
2234   ierr = DMPlexLabelComplete(dm, bdlabel);CHKERRQ(ierr);
2235   PetscFunctionReturn(0);
2236 }
2237 
2238 /*@
2239   DMPlexCreateBallMesh - Creates a simplex mesh on the d-dimensional ball, B^d.
2240 
2241   Collective
2242 
2243   Input Parameters:
2244 + comm  - The communicator for the DM object
2245 . dim   - The dimension
2246 - R     - The radius
2247 
2248   Output Parameter:
2249 . dm  - The DM object
2250 
2251   Options Database Keys:
2252 - bd_dm_refine - This will refine the surface mesh preserving the sphere geometry
2253 
2254   Level: beginner
2255 
2256 .seealso: DMPlexCreateSphereMesh(), DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
2257 @*/
2258 PetscErrorCode DMPlexCreateBallMesh(MPI_Comm comm, PetscInt dim, PetscReal R, DM *dm)
2259 {
2260   PetscErrorCode ierr;
2261 
2262   PetscFunctionBegin;
2263   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
2264   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
2265   ierr = DMPlexCreateBallMesh_Internal(*dm, dim, R);CHKERRQ(ierr);
2266   PetscFunctionReturn(0);
2267 }
2268 
2269 static PetscErrorCode DMPlexCreateReferenceCell_Internal(DM rdm, DMPolytopeType ct)
2270 {
2271   PetscErrorCode ierr;
2272 
2273   PetscFunctionBegin;
2274   switch (ct) {
2275     case DM_POLYTOPE_POINT:
2276     {
2277       PetscInt    numPoints[1]        = {1};
2278       PetscInt    coneSize[1]         = {0};
2279       PetscInt    cones[1]            = {0};
2280       PetscInt    coneOrientations[1] = {0};
2281       PetscScalar vertexCoords[1]     = {0.0};
2282 
2283       ierr = DMSetDimension(rdm, 0);CHKERRQ(ierr);
2284       ierr = DMPlexCreateFromDAG(rdm, 0, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2285     }
2286     break;
2287     case DM_POLYTOPE_SEGMENT:
2288     {
2289       PetscInt    numPoints[2]        = {2, 1};
2290       PetscInt    coneSize[3]         = {2, 0, 0};
2291       PetscInt    cones[2]            = {1, 2};
2292       PetscInt    coneOrientations[2] = {0, 0};
2293       PetscScalar vertexCoords[2]     = {-1.0,  1.0};
2294 
2295       ierr = DMSetDimension(rdm, 1);CHKERRQ(ierr);
2296       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2297     }
2298     break;
2299     case DM_POLYTOPE_POINT_PRISM_TENSOR:
2300     {
2301       PetscInt    numPoints[2]        = {2, 1};
2302       PetscInt    coneSize[3]         = {2, 0, 0};
2303       PetscInt    cones[2]            = {1, 2};
2304       PetscInt    coneOrientations[2] = {0, 0};
2305       PetscScalar vertexCoords[2]     = {-1.0,  1.0};
2306 
2307       ierr = DMSetDimension(rdm, 1);CHKERRQ(ierr);
2308       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2309     }
2310     break;
2311     case DM_POLYTOPE_TRIANGLE:
2312     {
2313       PetscInt    numPoints[2]        = {3, 1};
2314       PetscInt    coneSize[4]         = {3, 0, 0, 0};
2315       PetscInt    cones[3]            = {1, 2, 3};
2316       PetscInt    coneOrientations[3] = {0, 0, 0};
2317       PetscScalar vertexCoords[6]     = {-1.0, -1.0,  1.0, -1.0,  -1.0, 1.0};
2318 
2319       ierr = DMSetDimension(rdm, 2);CHKERRQ(ierr);
2320       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2321     }
2322     break;
2323     case DM_POLYTOPE_QUADRILATERAL:
2324     {
2325       PetscInt    numPoints[2]        = {4, 1};
2326       PetscInt    coneSize[5]         = {4, 0, 0, 0, 0};
2327       PetscInt    cones[4]            = {1, 2, 3, 4};
2328       PetscInt    coneOrientations[4] = {0, 0, 0, 0};
2329       PetscScalar vertexCoords[8]     = {-1.0, -1.0,  1.0, -1.0,  1.0, 1.0,  -1.0, 1.0};
2330 
2331       ierr = DMSetDimension(rdm, 2);CHKERRQ(ierr);
2332       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2333     }
2334     break;
2335     case DM_POLYTOPE_SEG_PRISM_TENSOR:
2336     {
2337       PetscInt    numPoints[2]        = {4, 1};
2338       PetscInt    coneSize[5]         = {4, 0, 0, 0, 0};
2339       PetscInt    cones[4]            = {1, 2, 3, 4};
2340       PetscInt    coneOrientations[4] = {0, 0, 0, 0};
2341       PetscScalar vertexCoords[8]     = {-1.0, -1.0,  1.0, -1.0,  -1.0, 1.0,  1.0, 1.0};
2342 
2343       ierr = DMSetDimension(rdm, 2);CHKERRQ(ierr);
2344       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2345     }
2346     break;
2347     case DM_POLYTOPE_TETRAHEDRON:
2348     {
2349       PetscInt    numPoints[2]        = {4, 1};
2350       PetscInt    coneSize[5]         = {4, 0, 0, 0, 0};
2351       PetscInt    cones[4]            = {1, 2, 3, 4};
2352       PetscInt    coneOrientations[4] = {0, 0, 0, 0};
2353       PetscScalar vertexCoords[12]    = {-1.0, -1.0, -1.0,  -1.0, 1.0, -1.0,  1.0, -1.0, -1.0,  -1.0, -1.0, 1.0};
2354 
2355       ierr = DMSetDimension(rdm, 3);CHKERRQ(ierr);
2356       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2357     }
2358     break;
2359     case DM_POLYTOPE_HEXAHEDRON:
2360     {
2361       PetscInt    numPoints[2]        = {8, 1};
2362       PetscInt    coneSize[9]         = {8, 0, 0, 0, 0, 0, 0, 0, 0};
2363       PetscInt    cones[8]            = {1, 2, 3, 4, 5, 6, 7, 8};
2364       PetscInt    coneOrientations[8] = {0, 0, 0, 0, 0, 0, 0, 0};
2365       PetscScalar vertexCoords[24]    = {-1.0, -1.0, -1.0,  -1.0,  1.0, -1.0,  1.0, 1.0, -1.0,   1.0, -1.0, -1.0,
2366                                          -1.0, -1.0,  1.0,   1.0, -1.0,  1.0,  1.0, 1.0,  1.0,  -1.0,  1.0,  1.0};
2367 
2368       ierr = DMSetDimension(rdm, 3);CHKERRQ(ierr);
2369       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2370     }
2371     break;
2372     case DM_POLYTOPE_TRI_PRISM:
2373     {
2374       PetscInt    numPoints[2]        = {6, 1};
2375       PetscInt    coneSize[7]         = {6, 0, 0, 0, 0, 0, 0};
2376       PetscInt    cones[6]            = {1, 2, 3, 4, 5, 6};
2377       PetscInt    coneOrientations[6] = {0, 0, 0, 0, 0, 0};
2378       PetscScalar vertexCoords[18]    = {-1.0, -1.0, -1.0, -1.0,  1.0, -1.0,   1.0, -1.0, -1.0,
2379                                          -1.0, -1.0,  1.0,  1.0, -1.0,  1.0,  -1.0,  1.0,  1.0};
2380 
2381       ierr = DMSetDimension(rdm, 3);CHKERRQ(ierr);
2382       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2383     }
2384     break;
2385     case DM_POLYTOPE_TRI_PRISM_TENSOR:
2386     {
2387       PetscInt    numPoints[2]        = {6, 1};
2388       PetscInt    coneSize[7]         = {6, 0, 0, 0, 0, 0, 0};
2389       PetscInt    cones[6]            = {1, 2, 3, 4, 5, 6};
2390       PetscInt    coneOrientations[6] = {0, 0, 0, 0, 0, 0};
2391       PetscScalar vertexCoords[18]    = {-1.0, -1.0, -1.0,  1.0, -1.0, -1.0,  -1.0, 1.0, -1.0,
2392                                          -1.0, -1.0,  1.0,  1.0, -1.0,  1.0,  -1.0, 1.0,  1.0};
2393 
2394       ierr = DMSetDimension(rdm, 3);CHKERRQ(ierr);
2395       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2396     }
2397     break;
2398     case DM_POLYTOPE_QUAD_PRISM_TENSOR:
2399     {
2400       PetscInt    numPoints[2]        = {8, 1};
2401       PetscInt    coneSize[9]         = {8, 0, 0, 0, 0, 0, 0, 0, 0};
2402       PetscInt    cones[8]            = {1, 2, 3, 4, 5, 6, 7, 8};
2403       PetscInt    coneOrientations[8] = {0, 0, 0, 0, 0, 0, 0, 0};
2404       PetscScalar vertexCoords[24]    = {-1.0, -1.0, -1.0,  1.0, -1.0, -1.0,  1.0, 1.0, -1.0,  -1.0, 1.0, -1.0,
2405                                          -1.0, -1.0,  1.0,  1.0, -1.0,  1.0,  1.0, 1.0,  1.0,  -1.0, 1.0,  1.0};
2406 
2407       ierr = DMSetDimension(rdm, 3);CHKERRQ(ierr);
2408       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2409     }
2410     break;
2411     case DM_POLYTOPE_PYRAMID:
2412     {
2413       PetscInt    numPoints[2]        = {5, 1};
2414       PetscInt    coneSize[6]         = {5, 0, 0, 0, 0, 0};
2415       PetscInt    cones[5]            = {1, 2, 3, 4, 5};
2416       PetscInt    coneOrientations[8] = {0, 0, 0, 0, 0, 0, 0, 0};
2417       PetscScalar vertexCoords[24]    = {-1.0, -1.0, -1.0,  -1.0, 1.0, -1.0,  1.0, 1.0, -1.0,  1.0, -1.0, -1.0,
2418                                           0.0,  0.0,  1.0};
2419 
2420       ierr = DMSetDimension(rdm, 3);CHKERRQ(ierr);
2421       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2422     }
2423     break;
2424     default: SETERRQ1(PetscObjectComm((PetscObject) rdm), PETSC_ERR_ARG_WRONG, "Cannot create reference cell for cell type %s", DMPolytopeTypes[ct]);
2425   }
2426   {
2427     PetscInt Nv, v;
2428 
2429     /* Must create the celltype label here so that we do not automatically try to compute the types */
2430     ierr = DMCreateLabel(rdm, "celltype");CHKERRQ(ierr);
2431     ierr = DMPlexSetCellType(rdm, 0, ct);CHKERRQ(ierr);
2432     ierr = DMPlexGetChart(rdm, NULL, &Nv);CHKERRQ(ierr);
2433     for (v = 1; v < Nv; ++v) {ierr = DMPlexSetCellType(rdm, v, DM_POLYTOPE_POINT);CHKERRQ(ierr);}
2434   }
2435   ierr = DMPlexInterpolateInPlace_Internal(rdm);CHKERRQ(ierr);
2436   ierr = PetscObjectSetName((PetscObject) rdm, DMPolytopeTypes[ct]);CHKERRQ(ierr);
2437   PetscFunctionReturn(0);
2438 }
2439 
2440 /*@
2441   DMPlexCreateReferenceCell - Create a DMPLEX with the appropriate FEM reference cell
2442 
2443   Collective
2444 
2445   Input Parameters:
2446 + comm - The communicator
2447 - ct   - The cell type of the reference cell
2448 
2449   Output Parameter:
2450 . refdm - The reference cell
2451 
2452   Level: intermediate
2453 
2454 .seealso: DMPlexCreateReferenceCell(), DMPlexCreateBoxMesh()
2455 @*/
2456 PetscErrorCode DMPlexCreateReferenceCell(MPI_Comm comm, DMPolytopeType ct, DM *refdm)
2457 {
2458   PetscErrorCode ierr;
2459 
2460   PetscFunctionBegin;
2461   ierr = DMCreate(comm, refdm);CHKERRQ(ierr);
2462   ierr = DMSetType(*refdm, DMPLEX);CHKERRQ(ierr);
2463   ierr = DMPlexCreateReferenceCell_Internal(*refdm, ct);CHKERRQ(ierr);
2464   PetscFunctionReturn(0);
2465 }
2466 
2467 static PetscErrorCode DMPlexCreateBoundaryLabel_Private(DM dm, const char name[])
2468 {
2469   DM             plex;
2470   DMLabel        label;
2471   PetscBool      hasLabel;
2472   PetscErrorCode ierr;
2473 
2474   PetscFunctionBeginUser;
2475   ierr = DMHasLabel(dm, name, &hasLabel);CHKERRQ(ierr);
2476   if (hasLabel) PetscFunctionReturn(0);
2477   ierr = DMCreateLabel(dm, name);CHKERRQ(ierr);
2478   ierr = DMGetLabel(dm, name, &label);CHKERRQ(ierr);
2479   ierr = DMConvert(dm, DMPLEX, &plex);CHKERRQ(ierr);
2480   ierr = DMPlexMarkBoundaryFaces(plex, 1, label);CHKERRQ(ierr);
2481   ierr = DMDestroy(&plex);CHKERRQ(ierr);
2482   PetscFunctionReturn(0);
2483 }
2484 
2485 const char * const DMPlexShapes[] = {"box", "box_surface", "ball", "sphere", "cylinder", "unknown", "DMPlexShape", "DM_SHAPE_", NULL};
2486 
2487 static PetscErrorCode DMPlexCreateFromOptions_Internal(PetscOptionItems *PetscOptionsObject, PetscBool *useCoordSpace, DM dm)
2488 {
2489   DMPlexShape    shape = DM_SHAPE_BOX;
2490   DMPolytopeType cell  = DM_POLYTOPE_TRIANGLE;
2491   PetscInt       dim   = 2;
2492   PetscBool      simplex = PETSC_TRUE, interpolate = PETSC_TRUE, adjCone = PETSC_FALSE, adjClosure = PETSC_TRUE, refDomain = PETSC_FALSE;
2493   PetscBool      flg, flg2, fflg, bdfflg;
2494   MPI_Comm       comm;
2495   char           filename[PETSC_MAX_PATH_LEN], bdFilename[PETSC_MAX_PATH_LEN];
2496   PetscErrorCode ierr;
2497 
2498   PetscFunctionBegin;
2499   ierr = PetscObjectGetComm((PetscObject) dm, &comm);CHKERRQ(ierr);
2500   /* TODO Turn this into a registration interface */
2501   ierr = PetscOptionsString("-dm_plex_filename", "File containing a mesh", "DMPlexCreateFromFile", filename, filename, sizeof(filename), &fflg);CHKERRQ(ierr);
2502   ierr = PetscOptionsString("-dm_plex_boundary_filename", "File containing a mesh boundary", "DMPlexCreateFromFile", bdFilename, bdFilename, sizeof(bdFilename), &bdfflg);CHKERRQ(ierr);
2503   ierr = PetscOptionsEnum("-dm_plex_cell", "Cell shape", "", DMPolytopeTypes, (PetscEnum) cell, (PetscEnum *) &cell, NULL);CHKERRQ(ierr);
2504   ierr = PetscOptionsBool("-dm_plex_reference_cell_domain", "Use a reference cell domain", "", refDomain, &refDomain, NULL);CHKERRQ(ierr);
2505   ierr = PetscOptionsEnum("-dm_plex_shape", "Shape for built-in mesh", "", DMPlexShapes, (PetscEnum) shape, (PetscEnum *) &shape, &flg);CHKERRQ(ierr);
2506   ierr = PetscOptionsBoundedInt("-dm_plex_dim", "Topological dimension of the mesh", "DMGetDimension", dim, &dim, &flg, 0);CHKERRQ(ierr);
2507   if ((dim < 0) || (dim > 3)) SETERRQ1(comm, PETSC_ERR_ARG_OUTOFRANGE, "Dimension %D should be in [1, 3]", dim);
2508   ierr = PetscOptionsBool("-dm_plex_simplex", "Mesh cell shape", "", simplex,  &simplex, &flg);CHKERRQ(ierr);
2509   ierr = PetscOptionsBool("-dm_plex_interpolate", "Flag to create edges and faces automatically", "", interpolate, &interpolate, &flg);CHKERRQ(ierr);
2510   ierr = PetscOptionsBool("-dm_plex_adj_cone", "Set adjacency direction", "DMSetBasicAdjacency", adjCone,  &adjCone, &flg);CHKERRQ(ierr);
2511   ierr = PetscOptionsBool("-dm_plex_adj_closure", "Set adjacency size", "DMSetBasicAdjacency", adjClosure,  &adjClosure, &flg2);CHKERRQ(ierr);
2512   if (flg || flg2) {ierr = DMSetBasicAdjacency(dm, adjCone, adjClosure);CHKERRQ(ierr);}
2513 
2514   switch (cell) {
2515     case DM_POLYTOPE_POINT:
2516     case DM_POLYTOPE_SEGMENT:
2517     case DM_POLYTOPE_POINT_PRISM_TENSOR:
2518     case DM_POLYTOPE_TRIANGLE:
2519     case DM_POLYTOPE_QUADRILATERAL:
2520     case DM_POLYTOPE_TETRAHEDRON:
2521     case DM_POLYTOPE_HEXAHEDRON:
2522       *useCoordSpace = PETSC_TRUE;break;
2523     default: *useCoordSpace = PETSC_FALSE;break;
2524   }
2525 
2526   if (fflg) {
2527     DM dmnew;
2528 
2529     ierr = DMPlexCreateFromFile(PetscObjectComm((PetscObject) dm), filename, interpolate, &dmnew);CHKERRQ(ierr);
2530     ierr = DMPlexReplace_Static(dm, &dmnew);CHKERRQ(ierr);
2531   } else if (refDomain) {
2532     ierr = DMPlexCreateReferenceCell_Internal(dm, cell);CHKERRQ(ierr);
2533   } else if (bdfflg) {
2534     DM bdm, dmnew;
2535 
2536     ierr = DMPlexCreateFromFile(PetscObjectComm((PetscObject) dm), bdFilename, interpolate, &bdm);CHKERRQ(ierr);
2537     ierr = PetscObjectSetOptionsPrefix((PetscObject) bdm, "bd_");CHKERRQ(ierr);
2538     ierr = DMSetFromOptions(bdm);CHKERRQ(ierr);
2539     ierr = DMPlexGenerate(bdm, NULL, interpolate, &dmnew);CHKERRQ(ierr);
2540     ierr = DMDestroy(&bdm);CHKERRQ(ierr);
2541     ierr = DMPlexReplace_Static(dm, &dmnew);CHKERRQ(ierr);
2542   } else {
2543     ierr = PetscObjectSetName((PetscObject) dm, DMPlexShapes[shape]);CHKERRQ(ierr);
2544     switch (shape) {
2545       case DM_SHAPE_BOX:
2546       {
2547         PetscInt       faces[3] = {0, 0, 0};
2548         PetscReal      lower[3] = {0, 0, 0};
2549         PetscReal      upper[3] = {1, 1, 1};
2550         DMBoundaryType bdt[3]   = {DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE};
2551         PetscInt       i, n;
2552 
2553         n    = dim;
2554         for (i = 0; i < dim; ++i) faces[i] = (dim == 1 ? 1 : 4-dim);
2555         ierr = PetscOptionsIntArray("-dm_plex_box_faces", "Number of faces along each dimension", "", faces, &n, &flg);CHKERRQ(ierr);
2556         n    = 3;
2557         ierr = PetscOptionsRealArray("-dm_plex_box_lower", "Lower left corner of box", "", lower, &n, &flg);CHKERRQ(ierr);
2558         if (flg && (n != dim)) SETERRQ2(comm, PETSC_ERR_ARG_SIZ, "Lower box point had %D values, should have been %D", n, dim);
2559         n    = 3;
2560         ierr = PetscOptionsRealArray("-dm_plex_box_upper", "Upper right corner of box", "", upper, &n, &flg);CHKERRQ(ierr);
2561         if (flg && (n != dim)) SETERRQ2(comm, PETSC_ERR_ARG_SIZ, "Upper box point had %D values, should have been %D", n, dim);
2562         n    = 3;
2563         ierr = PetscOptionsEnumArray("-dm_plex_box_bd", "Boundary type for each dimension", "", DMBoundaryTypes, (PetscEnum *) bdt, &n, &flg);CHKERRQ(ierr);
2564         if (flg && (n != dim)) SETERRQ2(comm, PETSC_ERR_ARG_SIZ, "Box boundary types had %D values, should have been %D", n, dim);
2565         switch (cell) {
2566           case DM_POLYTOPE_TRI_PRISM_TENSOR:
2567             ierr = DMPlexCreateWedgeBoxMesh_Internal(dm, faces, lower, upper, bdt);CHKERRQ(ierr);
2568             if (!interpolate) {
2569               DM udm;
2570 
2571               ierr = DMPlexUninterpolate(dm, &udm);CHKERRQ(ierr);
2572               ierr = DMPlexReplace_Static(dm, &udm);CHKERRQ(ierr);
2573             }
2574             break;
2575           default:
2576             ierr = DMPlexCreateBoxMesh_Internal(dm, dim, simplex, faces, lower, upper, bdt, interpolate);CHKERRQ(ierr);
2577             break;
2578         }
2579       }
2580       break;
2581       case DM_SHAPE_BOX_SURFACE:
2582       {
2583         PetscInt  faces[3] = {0, 0, 0};
2584         PetscReal lower[3] = {0, 0, 0};
2585         PetscReal upper[3] = {1, 1, 1};
2586         PetscInt  i, n;
2587 
2588         n    = dim+1;
2589         for (i = 0; i < dim+1; ++i) faces[i] = (dim+1 == 1 ? 1 : 4-(dim+1));
2590         ierr = PetscOptionsIntArray("-dm_plex_box_faces", "Number of faces along each dimension", "", faces, &n, &flg);CHKERRQ(ierr);
2591         n    = 3;
2592         ierr = PetscOptionsRealArray("-dm_plex_box_lower", "Lower left corner of box", "", lower, &n, &flg);CHKERRQ(ierr);
2593         if (flg && (n != dim+1)) SETERRQ2(comm, PETSC_ERR_ARG_SIZ, "Lower box point had %D values, should have been %D", n, dim+1);
2594         n    = 3;
2595         ierr = PetscOptionsRealArray("-dm_plex_box_upper", "Upper right corner of box", "", upper, &n, &flg);CHKERRQ(ierr);
2596         if (flg && (n != dim+1)) SETERRQ2(comm, PETSC_ERR_ARG_SIZ, "Upper box point had %D values, should have been %D", n, dim+1);
2597         ierr = DMPlexCreateBoxSurfaceMesh_Internal(dm, dim+1, faces, lower, upper, interpolate);CHKERRQ(ierr);
2598       }
2599       break;
2600       case DM_SHAPE_SPHERE:
2601       {
2602         PetscReal R = 1.0;
2603 
2604         ierr = PetscOptionsReal("-dm_plex_sphere_radius", "Radius of the sphere", "", R,  &R, &flg);CHKERRQ(ierr);
2605         ierr = DMPlexCreateSphereMesh_Internal(dm, dim, simplex, R);CHKERRQ(ierr);
2606       }
2607       break;
2608       case DM_SHAPE_BALL:
2609       {
2610         PetscReal R = 1.0;
2611 
2612         ierr = PetscOptionsReal("-dm_plex_ball_radius", "Radius of the ball", "", R,  &R, &flg);CHKERRQ(ierr);
2613         ierr = DMPlexCreateBallMesh_Internal(dm, dim, R);CHKERRQ(ierr);
2614       }
2615       break;
2616       case DM_SHAPE_CYLINDER:
2617       {
2618         DMBoundaryType bdt = DM_BOUNDARY_NONE;
2619         PetscInt       Nw  = 6;
2620 
2621         ierr = PetscOptionsEnum("-dm_plex_cylinder_bd", "Boundary type in the z direction", "", DMBoundaryTypes, (PetscEnum) bdt, (PetscEnum *) &bdt, NULL);CHKERRQ(ierr);
2622         ierr = PetscOptionsInt("-dm_plex_cylinder_num_wedges", "Number of wedges around the cylinder", "", Nw, &Nw, NULL);CHKERRQ(ierr);
2623         switch (cell) {
2624           case DM_POLYTOPE_TRI_PRISM_TENSOR:
2625             ierr = DMPlexCreateWedgeCylinderMesh_Internal(dm, Nw, interpolate);CHKERRQ(ierr);
2626             break;
2627           default:
2628             ierr = DMPlexCreateHexCylinderMesh_Internal(dm, bdt);CHKERRQ(ierr);
2629             break;
2630         }
2631       }
2632       break;
2633       default: SETERRQ1(comm, PETSC_ERR_SUP, "Domain shape %s is unsupported", DMPlexShapes[shape]);
2634     }
2635   }
2636   ierr = DMPlexSetRefinementUniform(dm, PETSC_TRUE);CHKERRQ(ierr);
2637   PetscFunctionReturn(0);
2638 }
2639 
2640 PetscErrorCode DMSetFromOptions_NonRefinement_Plex(PetscOptionItems *PetscOptionsObject, DM dm)
2641 {
2642   DM_Plex       *mesh = (DM_Plex*) dm->data;
2643   PetscBool      flg;
2644   char           bdLabel[PETSC_MAX_PATH_LEN];
2645   PetscErrorCode ierr;
2646 
2647   PetscFunctionBegin;
2648   /* Handle viewing */
2649   ierr = PetscOptionsBool("-dm_plex_print_set_values", "Output all set values info", "DMPlexMatSetClosure", PETSC_FALSE, &mesh->printSetValues, NULL);CHKERRQ(ierr);
2650   ierr = PetscOptionsBoundedInt("-dm_plex_print_fem", "Debug output level all fem computations", "DMPlexSNESComputeResidualFEM", 0, &mesh->printFEM, NULL,0);CHKERRQ(ierr);
2651   ierr = PetscOptionsReal("-dm_plex_print_tol", "Tolerance for FEM output", "DMPlexSNESComputeResidualFEM", mesh->printTol, &mesh->printTol, NULL);CHKERRQ(ierr);
2652   ierr = PetscOptionsBoundedInt("-dm_plex_print_l2", "Debug output level all L2 diff computations", "DMComputeL2Diff", 0, &mesh->printL2, NULL,0);CHKERRQ(ierr);
2653   ierr = DMMonitorSetFromOptions(dm, "-dm_plex_monitor_throughput", "Monitor the simulation throughput", "DMPlexMonitorThroughput", DMPlexMonitorThroughput, NULL, &flg);CHKERRQ(ierr);
2654   if (flg) {ierr = PetscLogDefaultBegin();CHKERRQ(ierr);}
2655   /* Labeling */
2656   ierr = PetscOptionsString("-dm_plex_boundary_label", "Label to mark the mesh boundary", "", bdLabel, bdLabel, sizeof(bdLabel), &flg);CHKERRQ(ierr);
2657   if (flg) {ierr = DMPlexCreateBoundaryLabel_Private(dm, bdLabel);CHKERRQ(ierr);}
2658   /* Point Location */
2659   ierr = PetscOptionsBool("-dm_plex_hash_location", "Use grid hashing for point location", "DMInterpolate", PETSC_FALSE, &mesh->useHashLocation, NULL);CHKERRQ(ierr);
2660   /* Partitioning and distribution */
2661   ierr = PetscOptionsBool("-dm_plex_partition_balance", "Attempt to evenly divide points on partition boundary between processes", "DMPlexSetPartitionBalance", PETSC_FALSE, &mesh->partitionBalance, NULL);CHKERRQ(ierr);
2662   /* Generation and remeshing */
2663   ierr = PetscOptionsBool("-dm_plex_remesh_bd", "Allow changes to the boundary on remeshing", "DMAdapt", PETSC_FALSE, &mesh->remeshBd, NULL);CHKERRQ(ierr);
2664   /* Projection behavior */
2665   ierr = PetscOptionsBoundedInt("-dm_plex_max_projection_height", "Maxmimum mesh point height used to project locally", "DMPlexSetMaxProjectionHeight", 0, &mesh->maxProjectionHeight, NULL,0);CHKERRQ(ierr);
2666   ierr = PetscOptionsBool("-dm_plex_regular_refinement", "Use special nested projection algorithm for regular refinement", "DMPlexSetRegularRefinement", mesh->regularRefinement, &mesh->regularRefinement, NULL);CHKERRQ(ierr);
2667   /* Checking structure */
2668   {
2669     PetscBool   flg = PETSC_FALSE, flg2 = PETSC_FALSE, all = PETSC_FALSE;
2670 
2671     ierr = PetscOptionsBool("-dm_plex_check_all", "Perform all checks", NULL, PETSC_FALSE, &all, &flg2);CHKERRQ(ierr);
2672     ierr = PetscOptionsBool("-dm_plex_check_symmetry", "Check that the adjacency information in the mesh is symmetric", "DMPlexCheckSymmetry", PETSC_FALSE, &flg, &flg2);CHKERRQ(ierr);
2673     if (all || (flg && flg2)) {ierr = DMPlexCheckSymmetry(dm);CHKERRQ(ierr);}
2674     ierr = PetscOptionsBool("-dm_plex_check_skeleton", "Check that each cell has the correct number of vertices (only for homogeneous simplex or tensor meshes)", "DMPlexCheckSkeleton", PETSC_FALSE, &flg, &flg2);CHKERRQ(ierr);
2675     if (all || (flg && flg2)) {ierr = DMPlexCheckSkeleton(dm, 0);CHKERRQ(ierr);}
2676     ierr = PetscOptionsBool("-dm_plex_check_faces", "Check that the faces of each cell give a vertex order this is consistent with what we expect from the cell type", "DMPlexCheckFaces", PETSC_FALSE, &flg, &flg2);CHKERRQ(ierr);
2677     if (all || (flg && flg2)) {ierr = DMPlexCheckFaces(dm, 0);CHKERRQ(ierr);}
2678     ierr = PetscOptionsBool("-dm_plex_check_geometry", "Check that cells have positive volume", "DMPlexCheckGeometry", PETSC_FALSE, &flg, &flg2);CHKERRQ(ierr);
2679     if (all || (flg && flg2)) {ierr = DMPlexCheckGeometry(dm);CHKERRQ(ierr);}
2680     ierr = PetscOptionsBool("-dm_plex_check_pointsf", "Check some necessary conditions for PointSF", "DMPlexCheckPointSF", PETSC_FALSE, &flg, &flg2);CHKERRQ(ierr);
2681     if (all || (flg && flg2)) {ierr = DMPlexCheckPointSF(dm);CHKERRQ(ierr);}
2682     ierr = PetscOptionsBool("-dm_plex_check_interface_cones", "Check points on inter-partition interfaces have conforming order of cone points", "DMPlexCheckInterfaceCones", PETSC_FALSE, &flg, &flg2);CHKERRQ(ierr);
2683     if (all || (flg && flg2)) {ierr = DMPlexCheckInterfaceCones(dm);CHKERRQ(ierr);}
2684     ierr = PetscOptionsBool("-dm_plex_check_cell_shape", "Check cell shape", "DMPlexCheckCellShape", PETSC_FALSE, &flg, &flg2);CHKERRQ(ierr);
2685     if (flg && flg2) {ierr = DMPlexCheckCellShape(dm, PETSC_TRUE, PETSC_DETERMINE);CHKERRQ(ierr);}
2686   }
2687   {
2688     PetscReal scale = 1.0;
2689 
2690     ierr = PetscOptionsReal("-dm_plex_scale", "Scale factor for mesh coordinates", "DMPlexScale", scale, &scale, &flg);CHKERRQ(ierr);
2691     if (flg) {
2692       Vec coordinates, coordinatesLocal;
2693 
2694       ierr = DMGetCoordinates(dm, &coordinates);CHKERRQ(ierr);
2695       ierr = DMGetCoordinatesLocal(dm, &coordinatesLocal);CHKERRQ(ierr);
2696       ierr = VecScale(coordinates, scale);CHKERRQ(ierr);
2697       ierr = VecScale(coordinatesLocal, scale);CHKERRQ(ierr);
2698     }
2699   }
2700   ierr = PetscPartitionerSetFromOptions(mesh->partitioner);CHKERRQ(ierr);
2701   PetscFunctionReturn(0);
2702 }
2703 
2704 static PetscErrorCode DMSetFromOptions_Plex(PetscOptionItems *PetscOptionsObject,DM dm)
2705 {
2706   PetscReal      volume = -1.0;
2707   PetscInt       prerefine = 0, refine = 0, r, coarsen = 0, overlap = 0, extLayers = 0, dim;
2708   PetscBool      uniformOrig, created = PETSC_FALSE, uniform = PETSC_TRUE, distribute = PETSC_FALSE, interpolate = PETSC_TRUE, coordSpace = PETSC_TRUE, remap = PETSC_TRUE, ghostCells = PETSC_FALSE, isHierarchy, ignoreModel = PETSC_FALSE, flg;
2709   PetscErrorCode ierr;
2710 
2711   PetscFunctionBegin;
2712   PetscValidHeaderSpecific(dm, DM_CLASSID, 2);
2713   ierr = PetscOptionsHead(PetscOptionsObject,"DMPlex Options");CHKERRQ(ierr);
2714   /* Handle automatic creation */
2715   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
2716   if (dim < 0) {ierr = DMPlexCreateFromOptions_Internal(PetscOptionsObject, &coordSpace, dm);CHKERRQ(ierr);created = PETSC_TRUE;}
2717   /* Handle interpolation before distribution */
2718   ierr = PetscOptionsBool("-dm_plex_interpolate_pre", "Flag to interpolate mesh before distribution", "", interpolate, &interpolate, &flg);CHKERRQ(ierr);
2719   if (flg) {
2720     DMPlexInterpolatedFlag interpolated;
2721 
2722     ierr = DMPlexIsInterpolated(dm, &interpolated);CHKERRQ(ierr);
2723     if (interpolated == DMPLEX_INTERPOLATED_FULL && !interpolate) {
2724       DM udm;
2725 
2726       ierr = DMPlexUninterpolate(dm, &udm);CHKERRQ(ierr);
2727       ierr = DMPlexReplace_Static(dm, &udm);CHKERRQ(ierr);
2728     } else if (interpolated != DMPLEX_INTERPOLATED_FULL && interpolate) {
2729       DM idm;
2730 
2731       ierr = DMPlexInterpolate(dm, &idm);CHKERRQ(ierr);
2732       ierr = DMPlexReplace_Static(dm, &idm);CHKERRQ(ierr);
2733     }
2734   }
2735   /* Handle DMPlex refinement before distribution */
2736   ierr = PetscOptionsBool("-dm_refine_ignore_model", "Flag to ignore the geometry model when refining", "DMCreate", ignoreModel, &ignoreModel, &flg);CHKERRQ(ierr);
2737   if (flg) {((DM_Plex *) dm->data)->ignoreModel = ignoreModel;}
2738   ierr = DMPlexGetRefinementUniform(dm, &uniformOrig);CHKERRQ(ierr);
2739   ierr = PetscOptionsBoundedInt("-dm_refine_pre", "The number of refinements before distribution", "DMCreate", prerefine, &prerefine, NULL,0);CHKERRQ(ierr);
2740   ierr = PetscOptionsBool("-dm_refine_remap_pre", "Flag to control coordinate remapping", "DMCreate", remap, &remap, NULL);CHKERRQ(ierr);
2741   ierr = PetscOptionsBool("-dm_refine_uniform_pre", "Flag for uniform refinement before distribution", "DMCreate", uniform, &uniform, &flg);CHKERRQ(ierr);
2742   if (flg) {ierr = DMPlexSetRefinementUniform(dm, uniform);CHKERRQ(ierr);}
2743   ierr = PetscOptionsReal("-dm_refine_volume_limit_pre", "The maximum cell volume after refinement before distribution", "DMCreate", volume, &volume, &flg);CHKERRQ(ierr);
2744   if (flg) {
2745     ierr = DMPlexSetRefinementUniform(dm, PETSC_FALSE);CHKERRQ(ierr);
2746     ierr = DMPlexSetRefinementLimit(dm, volume);CHKERRQ(ierr);
2747     prerefine = PetscMax(prerefine, 1);
2748   }
2749   for (r = 0; r < prerefine; ++r) {
2750     DM             rdm;
2751     PetscPointFunc coordFunc = ((DM_Plex*) dm->data)->coordFunc;
2752 
2753     ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2754     ierr = DMRefine(dm, PetscObjectComm((PetscObject) dm), &rdm);CHKERRQ(ierr);
2755     ierr = DMPlexReplace_Static(dm, &rdm);CHKERRQ(ierr);
2756     ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2757     if (coordFunc && remap) {
2758       ierr = DMPlexRemapGeometry(dm, 0.0, coordFunc);CHKERRQ(ierr);
2759       ((DM_Plex*) dm->data)->coordFunc = coordFunc;
2760     }
2761   }
2762   ierr = DMPlexSetRefinementUniform(dm, uniformOrig);CHKERRQ(ierr);
2763   /* Handle DMPlex extrusion before distribution */
2764   ierr = PetscOptionsBoundedInt("-dm_extrude", "The number of layers to extrude", "", extLayers, &extLayers, NULL, 0);CHKERRQ(ierr);
2765   if (extLayers) {
2766     DM edm;
2767 
2768     ierr = DMExtrude(dm, extLayers, &edm);CHKERRQ(ierr);
2769     ierr = DMPlexReplace_Static(dm, &edm);CHKERRQ(ierr);
2770     ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2771     extLayers = 0;
2772   }
2773   /* TODO Old-style extrusion which can be removed */
2774   ierr = PetscOptionsBool("-dm_plex_interpolate", "Flag to create edges and faces automatically", "", interpolate, &interpolate, NULL);CHKERRQ(ierr);
2775   /* Handle DMPlex distribution */
2776   ierr = PetscOptionsBool("-dm_distribute", "Flag to redistribute a mesh among processes", "DMCreate", distribute, &distribute, NULL);CHKERRQ(ierr);
2777   ierr = PetscOptionsBoundedInt("-dm_distribute_overlap", "The size of the overlap halo", "DMCreate", overlap, &overlap, NULL, 0);CHKERRQ(ierr);
2778   if (distribute) {
2779     DM               pdm = NULL;
2780     PetscPartitioner part;
2781 
2782     ierr = DMPlexGetPartitioner(dm, &part);CHKERRQ(ierr);
2783     ierr = PetscPartitionerSetFromOptions(part);CHKERRQ(ierr);
2784     ierr = DMPlexDistribute(dm, overlap, NULL, &pdm);CHKERRQ(ierr);
2785     if (pdm) {
2786       ierr = DMPlexReplace_Static(dm, &pdm);CHKERRQ(ierr);
2787     }
2788   }
2789   /* Create coordinate space */
2790   if (created) {
2791     DM_Plex  *mesh = (DM_Plex *) dm->data;
2792     PetscInt  degree = 1;
2793     PetscBool periodic, flg;
2794 
2795     ierr = PetscOptionsBool("-dm_coord_space", "Use an FEM space for coordinates", "", coordSpace, &coordSpace, &flg);CHKERRQ(ierr);
2796     ierr = PetscOptionsInt("-dm_coord_petscspace_degree", "FEM degree for coordinate space", "", degree, &degree, NULL);CHKERRQ(ierr);
2797     if (coordSpace) {ierr = DMPlexCreateCoordinateSpace(dm, degree, mesh->coordFunc);CHKERRQ(ierr);}
2798     if (flg && !coordSpace) {
2799       DM           cdm;
2800       PetscDS      cds;
2801       PetscObject  obj;
2802       PetscClassId id;
2803 
2804       ierr = DMGetCoordinateDM(dm, &cdm);CHKERRQ(ierr);
2805       ierr = DMGetDS(cdm, &cds);CHKERRQ(ierr);
2806       ierr = PetscDSGetDiscretization(cds, 0, &obj);CHKERRQ(ierr);
2807       ierr = PetscObjectGetClassId(obj, &id);CHKERRQ(ierr);
2808       if (id == PETSCFE_CLASSID) {
2809         PetscContainer dummy;
2810 
2811         ierr = PetscContainerCreate(PETSC_COMM_SELF, &dummy);CHKERRQ(ierr);
2812         ierr = PetscObjectSetName((PetscObject) dummy, "coordinates");CHKERRQ(ierr);
2813         ierr = DMSetField(cdm, 0, NULL, (PetscObject) dummy);CHKERRQ(ierr);
2814         ierr = PetscContainerDestroy(&dummy);CHKERRQ(ierr);
2815         ierr = DMClearDS(cdm);CHKERRQ(ierr);
2816       }
2817       mesh->coordFunc = NULL;
2818     }
2819     ierr = DMLocalizeCoordinates(dm);CHKERRQ(ierr);
2820     ierr = DMGetPeriodicity(dm, &periodic, NULL, NULL, NULL);CHKERRQ(ierr);
2821     if (periodic) {ierr = DMSetPeriodicity(dm, PETSC_TRUE, NULL, NULL, NULL);CHKERRQ(ierr);}
2822   }
2823   /* Handle DMPlex refinement */
2824   remap = PETSC_TRUE;
2825   ierr = PetscOptionsBoundedInt("-dm_refine", "The number of uniform refinements", "DMCreate", refine, &refine, NULL,0);CHKERRQ(ierr);
2826   ierr = PetscOptionsBool("-dm_refine_remap", "Flag to control coordinate remapping", "DMCreate", remap, &remap, NULL);CHKERRQ(ierr);
2827   ierr = PetscOptionsBoundedInt("-dm_refine_hierarchy", "The number of uniform refinements", "DMCreate", refine, &refine, &isHierarchy,0);CHKERRQ(ierr);
2828   if (refine) {ierr = DMPlexSetRefinementUniform(dm, PETSC_TRUE);CHKERRQ(ierr);}
2829   if (refine && isHierarchy) {
2830     DM *dms, coarseDM;
2831 
2832     ierr = DMGetCoarseDM(dm, &coarseDM);CHKERRQ(ierr);
2833     ierr = PetscObjectReference((PetscObject)coarseDM);CHKERRQ(ierr);
2834     ierr = PetscMalloc1(refine,&dms);CHKERRQ(ierr);
2835     ierr = DMRefineHierarchy(dm, refine, dms);CHKERRQ(ierr);
2836     /* Total hack since we do not pass in a pointer */
2837     ierr = DMPlexSwap_Static(dm, dms[refine-1]);CHKERRQ(ierr);
2838     if (refine == 1) {
2839       ierr = DMSetCoarseDM(dm, dms[0]);CHKERRQ(ierr);
2840       ierr = DMPlexSetRegularRefinement(dm, PETSC_TRUE);CHKERRQ(ierr);
2841     } else {
2842       ierr = DMSetCoarseDM(dm, dms[refine-2]);CHKERRQ(ierr);
2843       ierr = DMPlexSetRegularRefinement(dm, PETSC_TRUE);CHKERRQ(ierr);
2844       ierr = DMSetCoarseDM(dms[0], dms[refine-1]);CHKERRQ(ierr);
2845       ierr = DMPlexSetRegularRefinement(dms[0], PETSC_TRUE);CHKERRQ(ierr);
2846     }
2847     ierr = DMSetCoarseDM(dms[refine-1], coarseDM);CHKERRQ(ierr);
2848     ierr = PetscObjectDereference((PetscObject)coarseDM);CHKERRQ(ierr);
2849     /* Free DMs */
2850     for (r = 0; r < refine; ++r) {
2851       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dms[r]);CHKERRQ(ierr);
2852       ierr = DMDestroy(&dms[r]);CHKERRQ(ierr);
2853     }
2854     ierr = PetscFree(dms);CHKERRQ(ierr);
2855   } else {
2856     for (r = 0; r < refine; ++r) {
2857       DM             rdm;
2858       PetscPointFunc coordFunc = ((DM_Plex*) dm->data)->coordFunc;
2859 
2860       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2861       ierr = DMRefine(dm, PetscObjectComm((PetscObject) dm), &rdm);CHKERRQ(ierr);
2862       /* Total hack since we do not pass in a pointer */
2863       ierr = DMPlexReplace_Static(dm, &rdm);CHKERRQ(ierr);
2864       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2865       if (coordFunc && remap) {
2866         ierr = DMPlexRemapGeometry(dm, 0.0, coordFunc);CHKERRQ(ierr);
2867         ((DM_Plex*) dm->data)->coordFunc = coordFunc;
2868       }
2869     }
2870   }
2871   /* Handle DMPlex coarsening */
2872   ierr = PetscOptionsBoundedInt("-dm_coarsen", "Coarsen the mesh", "DMCreate", coarsen, &coarsen, NULL,0);CHKERRQ(ierr);
2873   ierr = PetscOptionsBoundedInt("-dm_coarsen_hierarchy", "The number of coarsenings", "DMCreate", coarsen, &coarsen, &isHierarchy,0);CHKERRQ(ierr);
2874   if (coarsen && isHierarchy) {
2875     DM *dms;
2876 
2877     ierr = PetscMalloc1(coarsen, &dms);CHKERRQ(ierr);
2878     ierr = DMCoarsenHierarchy(dm, coarsen, dms);CHKERRQ(ierr);
2879     /* Free DMs */
2880     for (r = 0; r < coarsen; ++r) {
2881       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dms[r]);CHKERRQ(ierr);
2882       ierr = DMDestroy(&dms[r]);CHKERRQ(ierr);
2883     }
2884     ierr = PetscFree(dms);CHKERRQ(ierr);
2885   } else {
2886     for (r = 0; r < coarsen; ++r) {
2887       DM             cdm;
2888       PetscPointFunc coordFunc = ((DM_Plex*) dm->data)->coordFunc;
2889 
2890       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2891       ierr = DMCoarsen(dm, PetscObjectComm((PetscObject) dm), &cdm);CHKERRQ(ierr);
2892       /* Total hack since we do not pass in a pointer */
2893       ierr = DMPlexReplace_Static(dm, &cdm);CHKERRQ(ierr);
2894       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2895       if (coordFunc) {
2896         ierr = DMPlexRemapGeometry(dm, 0.0, coordFunc);CHKERRQ(ierr);
2897         ((DM_Plex*) dm->data)->coordFunc = coordFunc;
2898       }
2899     }
2900   }
2901   /* Handle ghost cells */
2902   ierr = PetscOptionsBool("-dm_plex_create_fv_ghost_cells", "Flag to create finite volume ghost cells on the boundary", "DMCreate", ghostCells, &ghostCells, NULL);CHKERRQ(ierr);
2903   if (ghostCells) {
2904     DM   gdm;
2905     char lname[PETSC_MAX_PATH_LEN];
2906 
2907     lname[0] = '\0';
2908     ierr = PetscOptionsString("-dm_plex_fv_ghost_cells_label", "Label name for ghost cells boundary", "DMCreate", lname, lname, sizeof(lname), &flg);CHKERRQ(ierr);
2909     ierr = DMPlexConstructGhostCells(dm, flg ? lname : NULL, NULL, &gdm);CHKERRQ(ierr);
2910     ierr = DMPlexReplace_Static(dm, &gdm);CHKERRQ(ierr);
2911   }
2912   /* Handle */
2913   ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2914   ierr = PetscOptionsTail();CHKERRQ(ierr);
2915   PetscFunctionReturn(0);
2916 }
2917 
2918 static PetscErrorCode DMCreateGlobalVector_Plex(DM dm,Vec *vec)
2919 {
2920   PetscErrorCode ierr;
2921 
2922   PetscFunctionBegin;
2923   ierr = DMCreateGlobalVector_Section_Private(dm,vec);CHKERRQ(ierr);
2924   /* ierr = VecSetOperation(*vec, VECOP_DUPLICATE, (void(*)(void)) VecDuplicate_MPI_DM);CHKERRQ(ierr); */
2925   ierr = VecSetOperation(*vec, VECOP_VIEW, (void (*)(void)) VecView_Plex);CHKERRQ(ierr);
2926   ierr = VecSetOperation(*vec, VECOP_VIEWNATIVE, (void (*)(void)) VecView_Plex_Native);CHKERRQ(ierr);
2927   ierr = VecSetOperation(*vec, VECOP_LOAD, (void (*)(void)) VecLoad_Plex);CHKERRQ(ierr);
2928   ierr = VecSetOperation(*vec, VECOP_LOADNATIVE, (void (*)(void)) VecLoad_Plex_Native);CHKERRQ(ierr);
2929   PetscFunctionReturn(0);
2930 }
2931 
2932 static PetscErrorCode DMCreateLocalVector_Plex(DM dm,Vec *vec)
2933 {
2934   PetscErrorCode ierr;
2935 
2936   PetscFunctionBegin;
2937   ierr = DMCreateLocalVector_Section_Private(dm,vec);CHKERRQ(ierr);
2938   ierr = VecSetOperation(*vec, VECOP_VIEW, (void (*)(void)) VecView_Plex_Local);CHKERRQ(ierr);
2939   ierr = VecSetOperation(*vec, VECOP_LOAD, (void (*)(void)) VecLoad_Plex_Local);CHKERRQ(ierr);
2940   PetscFunctionReturn(0);
2941 }
2942 
2943 static PetscErrorCode DMGetDimPoints_Plex(DM dm, PetscInt dim, PetscInt *pStart, PetscInt *pEnd)
2944 {
2945   PetscInt       depth, d;
2946   PetscErrorCode ierr;
2947 
2948   PetscFunctionBegin;
2949   ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
2950   if (depth == 1) {
2951     ierr = DMGetDimension(dm, &d);CHKERRQ(ierr);
2952     if (dim == 0)      {ierr = DMPlexGetDepthStratum(dm, dim, pStart, pEnd);CHKERRQ(ierr);}
2953     else if (dim == d) {ierr = DMPlexGetDepthStratum(dm, 1, pStart, pEnd);CHKERRQ(ierr);}
2954     else               {*pStart = 0; *pEnd = 0;}
2955   } else {
2956     ierr = DMPlexGetDepthStratum(dm, dim, pStart, pEnd);CHKERRQ(ierr);
2957   }
2958   PetscFunctionReturn(0);
2959 }
2960 
2961 static PetscErrorCode DMGetNeighbors_Plex(DM dm, PetscInt *nranks, const PetscMPIInt *ranks[])
2962 {
2963   PetscSF           sf;
2964   PetscInt          niranks, njranks, n;
2965   const PetscMPIInt *iranks, *jranks;
2966   DM_Plex           *data = (DM_Plex*) dm->data;
2967   PetscErrorCode    ierr;
2968 
2969   PetscFunctionBegin;
2970   ierr = DMGetPointSF(dm, &sf);CHKERRQ(ierr);
2971   if (!data->neighbors) {
2972     ierr = PetscSFSetUp(sf);CHKERRQ(ierr);
2973     ierr = PetscSFGetRootRanks(sf, &njranks, &jranks, NULL, NULL, NULL);CHKERRQ(ierr);
2974     ierr = PetscSFGetLeafRanks(sf, &niranks, &iranks, NULL, NULL);CHKERRQ(ierr);
2975     ierr = PetscMalloc1(njranks + niranks + 1, &data->neighbors);CHKERRQ(ierr);
2976     ierr = PetscArraycpy(data->neighbors + 1, jranks, njranks);CHKERRQ(ierr);
2977     ierr = PetscArraycpy(data->neighbors + njranks + 1, iranks, niranks);CHKERRQ(ierr);
2978     n = njranks + niranks;
2979     ierr = PetscSortRemoveDupsMPIInt(&n, data->neighbors + 1);CHKERRQ(ierr);
2980     /* The following cast should never fail: can't have more neighbors than PETSC_MPI_INT_MAX */
2981     ierr = PetscMPIIntCast(n, data->neighbors);CHKERRQ(ierr);
2982   }
2983   if (nranks) *nranks = data->neighbors[0];
2984   if (ranks) {
2985     if (data->neighbors[0]) *ranks = data->neighbors + 1;
2986     else                    *ranks = NULL;
2987   }
2988   PetscFunctionReturn(0);
2989 }
2990 
2991 PETSC_INTERN PetscErrorCode DMInterpolateSolution_Plex(DM, DM, Mat, Vec, Vec);
2992 
2993 static PetscErrorCode DMInitialize_Plex(DM dm)
2994 {
2995   PetscErrorCode ierr;
2996 
2997   PetscFunctionBegin;
2998   dm->ops->view                            = DMView_Plex;
2999   dm->ops->load                            = DMLoad_Plex;
3000   dm->ops->setfromoptions                  = DMSetFromOptions_Plex;
3001   dm->ops->clone                           = DMClone_Plex;
3002   dm->ops->setup                           = DMSetUp_Plex;
3003   dm->ops->createlocalsection              = DMCreateLocalSection_Plex;
3004   dm->ops->createdefaultconstraints        = DMCreateDefaultConstraints_Plex;
3005   dm->ops->createglobalvector              = DMCreateGlobalVector_Plex;
3006   dm->ops->createlocalvector               = DMCreateLocalVector_Plex;
3007   dm->ops->getlocaltoglobalmapping         = NULL;
3008   dm->ops->createfieldis                   = NULL;
3009   dm->ops->createcoordinatedm              = DMCreateCoordinateDM_Plex;
3010   dm->ops->createcoordinatefield           = DMCreateCoordinateField_Plex;
3011   dm->ops->getcoloring                     = NULL;
3012   dm->ops->creatematrix                    = DMCreateMatrix_Plex;
3013   dm->ops->createinterpolation             = DMCreateInterpolation_Plex;
3014   dm->ops->createmassmatrix                = DMCreateMassMatrix_Plex;
3015   dm->ops->createinjection                 = DMCreateInjection_Plex;
3016   dm->ops->refine                          = DMRefine_Plex;
3017   dm->ops->coarsen                         = DMCoarsen_Plex;
3018   dm->ops->refinehierarchy                 = DMRefineHierarchy_Plex;
3019   dm->ops->coarsenhierarchy                = DMCoarsenHierarchy_Plex;
3020   dm->ops->adaptlabel                      = DMAdaptLabel_Plex;
3021   dm->ops->adaptmetric                     = DMAdaptMetric_Plex;
3022   dm->ops->extrude                         = DMExtrude_Plex;
3023   dm->ops->globaltolocalbegin              = NULL;
3024   dm->ops->globaltolocalend                = NULL;
3025   dm->ops->localtoglobalbegin              = NULL;
3026   dm->ops->localtoglobalend                = NULL;
3027   dm->ops->destroy                         = DMDestroy_Plex;
3028   dm->ops->createsubdm                     = DMCreateSubDM_Plex;
3029   dm->ops->createsuperdm                   = DMCreateSuperDM_Plex;
3030   dm->ops->getdimpoints                    = DMGetDimPoints_Plex;
3031   dm->ops->locatepoints                    = DMLocatePoints_Plex;
3032   dm->ops->projectfunctionlocal            = DMProjectFunctionLocal_Plex;
3033   dm->ops->projectfunctionlabellocal       = DMProjectFunctionLabelLocal_Plex;
3034   dm->ops->projectfieldlocal               = DMProjectFieldLocal_Plex;
3035   dm->ops->projectfieldlabellocal          = DMProjectFieldLabelLocal_Plex;
3036   dm->ops->projectbdfieldlabellocal        = DMProjectBdFieldLabelLocal_Plex;
3037   dm->ops->computel2diff                   = DMComputeL2Diff_Plex;
3038   dm->ops->computel2gradientdiff           = DMComputeL2GradientDiff_Plex;
3039   dm->ops->computel2fielddiff              = DMComputeL2FieldDiff_Plex;
3040   dm->ops->getneighbors                    = DMGetNeighbors_Plex;
3041   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMPlexInsertBoundaryValues_C",DMPlexInsertBoundaryValues_Plex);CHKERRQ(ierr);
3042   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMPlexInsertTimeDerviativeBoundaryValues_C",DMPlexInsertTimeDerivativeBoundaryValues_Plex);CHKERRQ(ierr);
3043   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMSetUpGLVisViewer_C",DMSetUpGLVisViewer_Plex);CHKERRQ(ierr);
3044   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMCreateNeumannOverlap_C",DMCreateNeumannOverlap_Plex);CHKERRQ(ierr);
3045   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMPlexGetOverlap_C",DMPlexGetOverlap_Plex);CHKERRQ(ierr);
3046   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMInterpolateSolution_C",DMInterpolateSolution_Plex);CHKERRQ(ierr);
3047   PetscFunctionReturn(0);
3048 }
3049 
3050 PETSC_INTERN PetscErrorCode DMClone_Plex(DM dm, DM *newdm)
3051 {
3052   DM_Plex        *mesh = (DM_Plex *) dm->data;
3053   PetscErrorCode ierr;
3054 
3055   PetscFunctionBegin;
3056   mesh->refct++;
3057   (*newdm)->data = mesh;
3058   ierr = PetscObjectChangeTypeName((PetscObject) *newdm, DMPLEX);CHKERRQ(ierr);
3059   ierr = DMInitialize_Plex(*newdm);CHKERRQ(ierr);
3060   PetscFunctionReturn(0);
3061 }
3062 
3063 /*MC
3064   DMPLEX = "plex" - A DM object that encapsulates an unstructured mesh, or CW Complex, which can be expressed using a Hasse Diagram.
3065                     In the local representation, Vecs contain all unknowns in the interior and shared boundary. This is
3066                     specified by a PetscSection object. Ownership in the global representation is determined by
3067                     ownership of the underlying DMPlex points. This is specified by another PetscSection object.
3068 
3069   Options Database Keys:
3070 + -dm_refine_pre                     - Refine mesh before distribution
3071 + -dm_refine_uniform_pre             - Choose uniform or generator-based refinement
3072 + -dm_refine_volume_limit_pre        - Cell volume limit after pre-refinement using generator
3073 . -dm_distribute                     - Distribute mesh across processes
3074 . -dm_distribute_overlap             - Number of cells to overlap for distribution
3075 . -dm_refine                         - Refine mesh after distribution
3076 . -dm_plex_hash_location             - Use grid hashing for point location
3077 . -dm_plex_hash_box_faces <n,m,p>    - The number of divisions in each direction of the grid hash
3078 . -dm_plex_partition_balance         - Attempt to evenly divide points on partition boundary between processes
3079 . -dm_plex_remesh_bd                 - Allow changes to the boundary on remeshing
3080 . -dm_plex_max_projection_height     - Maxmimum mesh point height used to project locally
3081 . -dm_plex_regular_refinement        - Use special nested projection algorithm for regular refinement
3082 . -dm_plex_check_all                 - Perform all shecks below
3083 . -dm_plex_check_symmetry            - Check that the adjacency information in the mesh is symmetric
3084 . -dm_plex_check_skeleton <celltype> - Check that each cell has the correct number of vertices
3085 . -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
3086 . -dm_plex_check_geometry            - Check that cells have positive volume
3087 . -dm_view :mesh.tex:ascii_latex     - View the mesh in LaTeX/TikZ
3088 . -dm_plex_view_scale <num>          - Scale the TikZ
3089 - -dm_plex_print_fem <num>           - View FEM assembly information, such as element vectors and matrices
3090 
3091   Level: intermediate
3092 
3093 .seealso: DMType, DMPlexCreate(), DMCreate(), DMSetType()
3094 M*/
3095 
3096 PETSC_EXTERN PetscErrorCode DMCreate_Plex(DM dm)
3097 {
3098   DM_Plex       *mesh;
3099   PetscInt       unit;
3100   PetscErrorCode ierr;
3101 
3102   PetscFunctionBegin;
3103   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
3104   ierr     = PetscNewLog(dm,&mesh);CHKERRQ(ierr);
3105   dm->data = mesh;
3106 
3107   mesh->refct             = 1;
3108   ierr                    = PetscSectionCreate(PetscObjectComm((PetscObject)dm), &mesh->coneSection);CHKERRQ(ierr);
3109   mesh->maxConeSize       = 0;
3110   mesh->cones             = NULL;
3111   mesh->coneOrientations  = NULL;
3112   ierr                    = PetscSectionCreate(PetscObjectComm((PetscObject)dm), &mesh->supportSection);CHKERRQ(ierr);
3113   mesh->maxSupportSize    = 0;
3114   mesh->supports          = NULL;
3115   mesh->refinementUniform = PETSC_TRUE;
3116   mesh->refinementLimit   = -1.0;
3117   mesh->interpolated      = DMPLEX_INTERPOLATED_INVALID;
3118   mesh->interpolatedCollective = DMPLEX_INTERPOLATED_INVALID;
3119 
3120   mesh->facesTmp = NULL;
3121 
3122   mesh->tetgenOpts   = NULL;
3123   mesh->triangleOpts = NULL;
3124   ierr = PetscPartitionerCreate(PetscObjectComm((PetscObject)dm), &mesh->partitioner);CHKERRQ(ierr);
3125   mesh->remeshBd     = PETSC_FALSE;
3126 
3127   mesh->subpointMap = NULL;
3128 
3129   for (unit = 0; unit < NUM_PETSC_UNITS; ++unit) mesh->scale[unit] = 1.0;
3130 
3131   mesh->regularRefinement   = PETSC_FALSE;
3132   mesh->depthState          = -1;
3133   mesh->celltypeState       = -1;
3134   mesh->globalVertexNumbers = NULL;
3135   mesh->globalCellNumbers   = NULL;
3136   mesh->anchorSection       = NULL;
3137   mesh->anchorIS            = NULL;
3138   mesh->createanchors       = NULL;
3139   mesh->computeanchormatrix = NULL;
3140   mesh->parentSection       = NULL;
3141   mesh->parents             = NULL;
3142   mesh->childIDs            = NULL;
3143   mesh->childSection        = NULL;
3144   mesh->children            = NULL;
3145   mesh->referenceTree       = NULL;
3146   mesh->getchildsymmetry    = NULL;
3147   mesh->vtkCellHeight       = 0;
3148   mesh->useAnchors          = PETSC_FALSE;
3149 
3150   mesh->maxProjectionHeight = 0;
3151 
3152   mesh->neighbors           = NULL;
3153 
3154   mesh->printSetValues = PETSC_FALSE;
3155   mesh->printFEM       = 0;
3156   mesh->printTol       = 1.0e-10;
3157 
3158   ierr = DMInitialize_Plex(dm);CHKERRQ(ierr);
3159   PetscFunctionReturn(0);
3160 }
3161 
3162 /*@
3163   DMPlexCreate - Creates a DMPlex object, which encapsulates an unstructured mesh, or CW complex, which can be expressed using a Hasse Diagram.
3164 
3165   Collective
3166 
3167   Input Parameter:
3168 . comm - The communicator for the DMPlex object
3169 
3170   Output Parameter:
3171 . mesh  - The DMPlex object
3172 
3173   Level: beginner
3174 
3175 @*/
3176 PetscErrorCode DMPlexCreate(MPI_Comm comm, DM *mesh)
3177 {
3178   PetscErrorCode ierr;
3179 
3180   PetscFunctionBegin;
3181   PetscValidPointer(mesh,2);
3182   ierr = DMCreate(comm, mesh);CHKERRQ(ierr);
3183   ierr = DMSetType(*mesh, DMPLEX);CHKERRQ(ierr);
3184   PetscFunctionReturn(0);
3185 }
3186 
3187 /*@C
3188   DMPlexBuildFromCellListParallel - Build distributed DMPLEX topology from a list of vertices for each cell (common mesh generator output)
3189 
3190   Input Parameters:
3191 + dm - The DM
3192 . numCells - The number of cells owned by this process
3193 . numVertices - The number of vertices owned by this process, or PETSC_DECIDE
3194 . NVertices - The global number of vertices, or PETSC_DECIDE
3195 . numCorners - The number of vertices for each cell
3196 - cells - An array of numCells*numCorners numbers, the global vertex numbers for each cell
3197 
3198   Output Parameter:
3199 . vertexSF - (Optional) SF describing complete vertex ownership
3200 
3201   Notes:
3202   Two triangles sharing a face
3203 $
3204 $        2
3205 $      / | \
3206 $     /  |  \
3207 $    /   |   \
3208 $   0  0 | 1  3
3209 $    \   |   /
3210 $     \  |  /
3211 $      \ | /
3212 $        1
3213 would have input
3214 $  numCells = 2, numVertices = 4
3215 $  cells = [0 1 2  1 3 2]
3216 $
3217 which would result in the DMPlex
3218 $
3219 $        4
3220 $      / | \
3221 $     /  |  \
3222 $    /   |   \
3223 $   2  0 | 1  5
3224 $    \   |   /
3225 $     \  |  /
3226 $      \ | /
3227 $        3
3228 
3229   Vertices are implicitly numbered consecutively 0,...,NVertices.
3230   Each rank owns a chunk of numVertices consecutive vertices.
3231   If numVertices is PETSC_DECIDE, PETSc will distribute them as evenly as possible using PetscLayout.
3232   If both NVertices and numVertices are PETSC_DECIDE, NVertices is computed by PETSc as the maximum vertex index in cells + 1.
3233   If only NVertices is PETSC_DECIDE, it is computed as the sum of numVertices over all ranks.
3234 
3235   The cell distribution is arbitrary non-overlapping, independent of the vertex distribution.
3236 
3237   Not currently supported in Fortran.
3238 
3239   Level: advanced
3240 
3241 .seealso: DMPlexBuildFromCellList(), DMPlexCreateFromCellListParallelPetsc(), DMPlexBuildCoordinatesFromCellListParallel()
3242 @*/
3243 PetscErrorCode DMPlexBuildFromCellListParallel(DM dm, PetscInt numCells, PetscInt numVertices, PetscInt NVertices, PetscInt numCorners, const PetscInt cells[], PetscSF *vertexSF)
3244 {
3245   PetscSF         sfPoint;
3246   PetscLayout     layout;
3247   PetscInt        numVerticesAdj, *verticesAdj, *cones, c, p, dim;
3248   PetscMPIInt     rank, size;
3249   PetscErrorCode  ierr;
3250 
3251   PetscFunctionBegin;
3252   PetscValidLogicalCollectiveInt(dm,NVertices,4);
3253   ierr = PetscLogEventBegin(DMPLEX_BuildFromCellList,dm,0,0,0);CHKERRQ(ierr);
3254   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject) dm), &rank);CHKERRMPI(ierr);
3255   ierr = MPI_Comm_size(PetscObjectComm((PetscObject) dm), &size);CHKERRMPI(ierr);
3256   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
3257   /* Get/check global number of vertices */
3258   {
3259     PetscInt NVerticesInCells, i;
3260     const PetscInt len = numCells * numCorners;
3261 
3262     /* NVerticesInCells = max(cells) + 1 */
3263     NVerticesInCells = PETSC_MIN_INT;
3264     for (i=0; i<len; i++) if (cells[i] > NVerticesInCells) NVerticesInCells = cells[i];
3265     ++NVerticesInCells;
3266     ierr = MPI_Allreduce(MPI_IN_PLACE, &NVerticesInCells, 1, MPIU_INT, MPI_MAX, PetscObjectComm((PetscObject) dm));CHKERRMPI(ierr);
3267 
3268     if (numVertices == PETSC_DECIDE && NVertices == PETSC_DECIDE) NVertices = NVerticesInCells;
3269     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);
3270   }
3271   /* Count locally unique vertices */
3272   {
3273     PetscHSetI vhash;
3274     PetscInt off = 0;
3275 
3276     ierr = PetscHSetICreate(&vhash);CHKERRQ(ierr);
3277     for (c = 0; c < numCells; ++c) {
3278       for (p = 0; p < numCorners; ++p) {
3279         ierr = PetscHSetIAdd(vhash, cells[c*numCorners+p]);CHKERRQ(ierr);
3280       }
3281     }
3282     ierr = PetscHSetIGetSize(vhash, &numVerticesAdj);CHKERRQ(ierr);
3283     ierr = PetscMalloc1(numVerticesAdj, &verticesAdj);CHKERRQ(ierr);
3284     ierr = PetscHSetIGetElems(vhash, &off, verticesAdj);CHKERRQ(ierr);
3285     ierr = PetscHSetIDestroy(&vhash);CHKERRQ(ierr);
3286     if (off != numVerticesAdj) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Invalid number of local vertices %D should be %D", off, numVerticesAdj);
3287   }
3288   ierr = PetscSortInt(numVerticesAdj, verticesAdj);CHKERRQ(ierr);
3289   /* Create cones */
3290   ierr = DMPlexSetChart(dm, 0, numCells+numVerticesAdj);CHKERRQ(ierr);
3291   for (c = 0; c < numCells; ++c) {ierr = DMPlexSetConeSize(dm, c, numCorners);CHKERRQ(ierr);}
3292   ierr = DMSetUp(dm);CHKERRQ(ierr);
3293   ierr = DMPlexGetCones(dm,&cones);CHKERRQ(ierr);
3294   for (c = 0; c < numCells; ++c) {
3295     for (p = 0; p < numCorners; ++p) {
3296       const PetscInt gv = cells[c*numCorners+p];
3297       PetscInt       lv;
3298 
3299       /* Positions within verticesAdj form 0-based local vertex numbering;
3300          we need to shift it by numCells to get correct DAG points (cells go first) */
3301       ierr = PetscFindInt(gv, numVerticesAdj, verticesAdj, &lv);CHKERRQ(ierr);
3302       if (lv < 0) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Could not find global vertex %D in local connectivity", gv);
3303       cones[c*numCorners+p] = lv+numCells;
3304     }
3305   }
3306   /* Build point sf */
3307   ierr = PetscLayoutCreate(PetscObjectComm((PetscObject)dm), &layout);CHKERRQ(ierr);
3308   ierr = PetscLayoutSetSize(layout, NVertices);CHKERRQ(ierr);
3309   ierr = PetscLayoutSetLocalSize(layout, numVertices);CHKERRQ(ierr);
3310   ierr = PetscLayoutSetBlockSize(layout, 1);CHKERRQ(ierr);
3311   ierr = PetscSFCreateByMatchingIndices(layout, numVerticesAdj, verticesAdj, NULL, numCells, numVerticesAdj, verticesAdj, NULL, numCells, vertexSF, &sfPoint);CHKERRQ(ierr);
3312   ierr = PetscLayoutDestroy(&layout);CHKERRQ(ierr);
3313   ierr = PetscFree(verticesAdj);CHKERRQ(ierr);
3314   ierr = PetscObjectSetName((PetscObject) sfPoint, "point SF");CHKERRQ(ierr);
3315   if (dm->sf) {
3316     const char *prefix;
3317 
3318     ierr = PetscObjectGetOptionsPrefix((PetscObject)dm->sf, &prefix);CHKERRQ(ierr);
3319     ierr = PetscObjectSetOptionsPrefix((PetscObject)sfPoint, prefix);CHKERRQ(ierr);
3320   }
3321   ierr = DMSetPointSF(dm, sfPoint);CHKERRQ(ierr);
3322   ierr = PetscSFDestroy(&sfPoint);CHKERRQ(ierr);
3323   if (vertexSF) {ierr = PetscObjectSetName((PetscObject)(*vertexSF), "Vertex Ownership SF");CHKERRQ(ierr);}
3324   /* Fill in the rest of the topology structure */
3325   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
3326   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
3327   ierr = PetscLogEventEnd(DMPLEX_BuildFromCellList,dm,0,0,0);CHKERRQ(ierr);
3328   PetscFunctionReturn(0);
3329 }
3330 
3331 /*@C
3332   DMPlexBuildCoordinatesFromCellListParallel - Build DM coordinates from a list of coordinates for each owned vertex (common mesh generator output)
3333 
3334   Input Parameters:
3335 + dm - The DM
3336 . spaceDim - The spatial dimension used for coordinates
3337 . sfVert - SF describing complete vertex ownership
3338 - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex
3339 
3340   Level: advanced
3341 
3342   Notes:
3343   Not currently supported in Fortran.
3344 
3345 .seealso: DMPlexBuildCoordinatesFromCellList(), DMPlexCreateFromCellListParallelPetsc(), DMPlexBuildFromCellListParallel()
3346 @*/
3347 PetscErrorCode DMPlexBuildCoordinatesFromCellListParallel(DM dm, PetscInt spaceDim, PetscSF sfVert, const PetscReal vertexCoords[])
3348 {
3349   PetscSection   coordSection;
3350   Vec            coordinates;
3351   PetscScalar   *coords;
3352   PetscInt       numVertices, numVerticesAdj, coordSize, v, vStart, vEnd;
3353   PetscErrorCode ierr;
3354 
3355   PetscFunctionBegin;
3356   ierr = PetscLogEventBegin(DMPLEX_BuildCoordinatesFromCellList,dm,0,0,0);CHKERRQ(ierr);
3357   ierr = DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);CHKERRQ(ierr);
3358   if (vStart < 0 || vEnd < 0) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "DM is not set up properly. DMPlexBuildFromCellList() should be called first.");
3359   ierr = DMSetCoordinateDim(dm, spaceDim);CHKERRQ(ierr);
3360   ierr = PetscSFGetGraph(sfVert, &numVertices, &numVerticesAdj, NULL, NULL);CHKERRQ(ierr);
3361   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);
3362   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
3363   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
3364   ierr = PetscSectionSetFieldComponents(coordSection, 0, spaceDim);CHKERRQ(ierr);
3365   ierr = PetscSectionSetChart(coordSection, vStart, vEnd);CHKERRQ(ierr);
3366   for (v = vStart; v < vEnd; ++v) {
3367     ierr = PetscSectionSetDof(coordSection, v, spaceDim);CHKERRQ(ierr);
3368     ierr = PetscSectionSetFieldDof(coordSection, v, 0, spaceDim);CHKERRQ(ierr);
3369   }
3370   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
3371   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
3372   ierr = VecCreate(PetscObjectComm((PetscObject)dm), &coordinates);CHKERRQ(ierr);
3373   ierr = VecSetBlockSize(coordinates, spaceDim);CHKERRQ(ierr);
3374   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
3375   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
3376   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
3377   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
3378   {
3379     MPI_Datatype coordtype;
3380 
3381     /* Need a temp buffer for coords if we have complex/single */
3382     ierr = MPI_Type_contiguous(spaceDim, MPIU_SCALAR, &coordtype);CHKERRMPI(ierr);
3383     ierr = MPI_Type_commit(&coordtype);CHKERRMPI(ierr);
3384 #if defined(PETSC_USE_COMPLEX)
3385     {
3386     PetscScalar *svertexCoords;
3387     PetscInt    i;
3388     ierr = PetscMalloc1(numVertices*spaceDim,&svertexCoords);CHKERRQ(ierr);
3389     for (i=0; i<numVertices*spaceDim; i++) svertexCoords[i] = vertexCoords[i];
3390     ierr = PetscSFBcastBegin(sfVert, coordtype, svertexCoords, coords,MPI_REPLACE);CHKERRQ(ierr);
3391     ierr = PetscSFBcastEnd(sfVert, coordtype, svertexCoords, coords,MPI_REPLACE);CHKERRQ(ierr);
3392     ierr = PetscFree(svertexCoords);CHKERRQ(ierr);
3393     }
3394 #else
3395     ierr = PetscSFBcastBegin(sfVert, coordtype, vertexCoords, coords,MPI_REPLACE);CHKERRQ(ierr);
3396     ierr = PetscSFBcastEnd(sfVert, coordtype, vertexCoords, coords,MPI_REPLACE);CHKERRQ(ierr);
3397 #endif
3398     ierr = MPI_Type_free(&coordtype);CHKERRMPI(ierr);
3399   }
3400   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
3401   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
3402   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
3403   ierr = PetscLogEventEnd(DMPLEX_BuildCoordinatesFromCellList,dm,0,0,0);CHKERRQ(ierr);
3404   PetscFunctionReturn(0);
3405 }
3406 
3407 /*@
3408   DMPlexCreateFromCellListParallelPetsc - Create distributed DMPLEX from a list of vertices for each cell (common mesh generator output)
3409 
3410   Input Parameters:
3411 + comm - The communicator
3412 . dim - The topological dimension of the mesh
3413 . numCells - The number of cells owned by this process
3414 . numVertices - The number of vertices owned by this process, or PETSC_DECIDE
3415 . NVertices - The global number of vertices, or PETSC_DECIDE
3416 . numCorners - The number of vertices for each cell
3417 . interpolate - Flag indicating that intermediate mesh entities (faces, edges) should be created automatically
3418 . cells - An array of numCells*numCorners numbers, the global vertex numbers for each cell
3419 . spaceDim - The spatial dimension used for coordinates
3420 - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex
3421 
3422   Output Parameters:
3423 + dm - The DM
3424 - vertexSF - (Optional) SF describing complete vertex ownership
3425 
3426   Notes:
3427   This function is just a convenient sequence of DMCreate(), DMSetType(), DMSetDimension(),
3428   DMPlexBuildFromCellListParallel(), DMPlexInterpolate(), DMPlexBuildCoordinatesFromCellListParallel()
3429 
3430   See DMPlexBuildFromCellListParallel() for an example and details about the topology-related parameters.
3431   See DMPlexBuildCoordinatesFromCellListParallel() for details about the geometry-related parameters.
3432 
3433   Level: intermediate
3434 
3435 .seealso: DMPlexCreateFromCellListPetsc(), DMPlexBuildFromCellListParallel(), DMPlexBuildCoordinatesFromCellListParallel(), DMPlexCreateFromDAG(), DMPlexCreate()
3436 @*/
3437 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)
3438 {
3439   PetscSF        sfVert;
3440   PetscErrorCode ierr;
3441 
3442   PetscFunctionBegin;
3443   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
3444   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
3445   PetscValidLogicalCollectiveInt(*dm, dim, 2);
3446   PetscValidLogicalCollectiveInt(*dm, spaceDim, 9);
3447   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
3448   ierr = DMPlexBuildFromCellListParallel(*dm, numCells, numVertices, NVertices, numCorners, cells, &sfVert);CHKERRQ(ierr);
3449   if (interpolate) {
3450     DM idm;
3451 
3452     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
3453     ierr = DMDestroy(dm);CHKERRQ(ierr);
3454     *dm  = idm;
3455   }
3456   ierr = DMPlexBuildCoordinatesFromCellListParallel(*dm, spaceDim, sfVert, vertexCoords);CHKERRQ(ierr);
3457   if (vertexSF) *vertexSF = sfVert;
3458   else {ierr = PetscSFDestroy(&sfVert);CHKERRQ(ierr);}
3459   PetscFunctionReturn(0);
3460 }
3461 
3462 /*@
3463   DMPlexCreateFromCellListParallel - Deprecated, use DMPlexCreateFromCellListParallelPetsc()
3464 
3465   Level: deprecated
3466 
3467 .seealso: DMPlexCreateFromCellListParallelPetsc()
3468 @*/
3469 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)
3470 {
3471   PetscErrorCode ierr;
3472   PetscInt       i;
3473   PetscInt       *pintCells;
3474 
3475   PetscFunctionBegin;
3476   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));
3477   if (sizeof(int) == sizeof(PetscInt)) {
3478     pintCells = (PetscInt *) cells;
3479   } else {
3480     ierr = PetscMalloc1(numCells*numCorners, &pintCells);CHKERRQ(ierr);
3481     for (i = 0; i < numCells*numCorners; i++) {
3482       pintCells[i] = (PetscInt) cells[i];
3483     }
3484   }
3485   ierr = DMPlexCreateFromCellListParallelPetsc(comm, dim, numCells, numVertices, PETSC_DECIDE, numCorners, interpolate, pintCells, spaceDim, vertexCoords, vertexSF, dm);CHKERRQ(ierr);
3486   if (sizeof(int) != sizeof(PetscInt)) {
3487     ierr = PetscFree(pintCells);CHKERRQ(ierr);
3488   }
3489   PetscFunctionReturn(0);
3490 }
3491 
3492 /*@C
3493   DMPlexBuildFromCellList - Build DMPLEX topology from a list of vertices for each cell (common mesh generator output)
3494 
3495   Input Parameters:
3496 + dm - The DM
3497 . numCells - The number of cells owned by this process
3498 . numVertices - The number of vertices owned by this process, or PETSC_DECIDE
3499 . numCorners - The number of vertices for each cell
3500 - cells - An array of numCells*numCorners numbers, the global vertex numbers for each cell
3501 
3502   Level: advanced
3503 
3504   Notes:
3505   Two triangles sharing a face
3506 $
3507 $        2
3508 $      / | \
3509 $     /  |  \
3510 $    /   |   \
3511 $   0  0 | 1  3
3512 $    \   |   /
3513 $     \  |  /
3514 $      \ | /
3515 $        1
3516 would have input
3517 $  numCells = 2, numVertices = 4
3518 $  cells = [0 1 2  1 3 2]
3519 $
3520 which would result in the DMPlex
3521 $
3522 $        4
3523 $      / | \
3524 $     /  |  \
3525 $    /   |   \
3526 $   2  0 | 1  5
3527 $    \   |   /
3528 $     \  |  /
3529 $      \ | /
3530 $        3
3531 
3532   If numVertices is PETSC_DECIDE, it is computed by PETSc as the maximum vertex index in cells + 1.
3533 
3534   Not currently supported in Fortran.
3535 
3536 .seealso: DMPlexBuildFromCellListParallel(), DMPlexBuildCoordinatesFromCellList(), DMPlexCreateFromCellListPetsc()
3537 @*/
3538 PetscErrorCode DMPlexBuildFromCellList(DM dm, PetscInt numCells, PetscInt numVertices, PetscInt numCorners, const PetscInt cells[])
3539 {
3540   PetscInt      *cones, c, p, dim;
3541   PetscErrorCode ierr;
3542 
3543   PetscFunctionBegin;
3544   ierr = PetscLogEventBegin(DMPLEX_BuildFromCellList,dm,0,0,0);CHKERRQ(ierr);
3545   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
3546   /* Get/check global number of vertices */
3547   {
3548     PetscInt NVerticesInCells, i;
3549     const PetscInt len = numCells * numCorners;
3550 
3551     /* NVerticesInCells = max(cells) + 1 */
3552     NVerticesInCells = PETSC_MIN_INT;
3553     for (i=0; i<len; i++) if (cells[i] > NVerticesInCells) NVerticesInCells = cells[i];
3554     ++NVerticesInCells;
3555 
3556     if (numVertices == PETSC_DECIDE) numVertices = NVerticesInCells;
3557     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);
3558   }
3559   ierr = DMPlexSetChart(dm, 0, numCells+numVertices);CHKERRQ(ierr);
3560   for (c = 0; c < numCells; ++c) {
3561     ierr = DMPlexSetConeSize(dm, c, numCorners);CHKERRQ(ierr);
3562   }
3563   ierr = DMSetUp(dm);CHKERRQ(ierr);
3564   ierr = DMPlexGetCones(dm,&cones);CHKERRQ(ierr);
3565   for (c = 0; c < numCells; ++c) {
3566     for (p = 0; p < numCorners; ++p) {
3567       cones[c*numCorners+p] = cells[c*numCorners+p]+numCells;
3568     }
3569   }
3570   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
3571   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
3572   ierr = PetscLogEventEnd(DMPLEX_BuildFromCellList,dm,0,0,0);CHKERRQ(ierr);
3573   PetscFunctionReturn(0);
3574 }
3575 
3576 /*@C
3577   DMPlexBuildCoordinatesFromCellList - Build DM coordinates from a list of coordinates for each owned vertex (common mesh generator output)
3578 
3579   Input Parameters:
3580 + dm - The DM
3581 . spaceDim - The spatial dimension used for coordinates
3582 - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex
3583 
3584   Level: advanced
3585 
3586   Notes:
3587   Not currently supported in Fortran.
3588 
3589 .seealso: DMPlexBuildCoordinatesFromCellListParallel(), DMPlexCreateFromCellListPetsc(), DMPlexBuildFromCellList()
3590 @*/
3591 PetscErrorCode DMPlexBuildCoordinatesFromCellList(DM dm, PetscInt spaceDim, const PetscReal vertexCoords[])
3592 {
3593   PetscSection   coordSection;
3594   Vec            coordinates;
3595   DM             cdm;
3596   PetscScalar   *coords;
3597   PetscInt       v, vStart, vEnd, d;
3598   PetscErrorCode ierr;
3599 
3600   PetscFunctionBegin;
3601   ierr = PetscLogEventBegin(DMPLEX_BuildCoordinatesFromCellList,dm,0,0,0);CHKERRQ(ierr);
3602   ierr = DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);CHKERRQ(ierr);
3603   if (vStart < 0 || vEnd < 0) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "DM is not set up properly. DMPlexBuildFromCellList() should be called first.");
3604   ierr = DMSetCoordinateDim(dm, spaceDim);CHKERRQ(ierr);
3605   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
3606   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
3607   ierr = PetscSectionSetFieldComponents(coordSection, 0, spaceDim);CHKERRQ(ierr);
3608   ierr = PetscSectionSetChart(coordSection, vStart, vEnd);CHKERRQ(ierr);
3609   for (v = vStart; v < vEnd; ++v) {
3610     ierr = PetscSectionSetDof(coordSection, v, spaceDim);CHKERRQ(ierr);
3611     ierr = PetscSectionSetFieldDof(coordSection, v, 0, spaceDim);CHKERRQ(ierr);
3612   }
3613   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
3614 
3615   ierr = DMGetCoordinateDM(dm, &cdm);CHKERRQ(ierr);
3616   ierr = DMCreateLocalVector(cdm, &coordinates);CHKERRQ(ierr);
3617   ierr = VecSetBlockSize(coordinates, spaceDim);CHKERRQ(ierr);
3618   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
3619   ierr = VecGetArrayWrite(coordinates, &coords);CHKERRQ(ierr);
3620   for (v = 0; v < vEnd-vStart; ++v) {
3621     for (d = 0; d < spaceDim; ++d) {
3622       coords[v*spaceDim+d] = vertexCoords[v*spaceDim+d];
3623     }
3624   }
3625   ierr = VecRestoreArrayWrite(coordinates, &coords);CHKERRQ(ierr);
3626   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
3627   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
3628   ierr = PetscLogEventEnd(DMPLEX_BuildCoordinatesFromCellList,dm,0,0,0);CHKERRQ(ierr);
3629   PetscFunctionReturn(0);
3630 }
3631 
3632 /*@
3633   DMPlexCreateFromCellListPetsc - Create DMPLEX from a list of vertices for each cell (common mesh generator output), but only process 0 takes in the input
3634 
3635   Collective on comm
3636 
3637   Input Parameters:
3638 + comm - The communicator
3639 . dim - The topological dimension of the mesh
3640 . numCells - The number of cells, only on process 0
3641 . numVertices - The number of vertices owned by this process, or PETSC_DECIDE, only on process 0
3642 . numCorners - The number of vertices for each cell, only on process 0
3643 . interpolate - Flag indicating that intermediate mesh entities (faces, edges) should be created automatically
3644 . cells - An array of numCells*numCorners numbers, the vertices for each cell, only on process 0
3645 . spaceDim - The spatial dimension used for coordinates
3646 - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex, only on process 0
3647 
3648   Output Parameter:
3649 . dm - The DM, which only has points on process 0
3650 
3651   Notes:
3652   This function is just a convenient sequence of DMCreate(), DMSetType(), DMSetDimension(), DMPlexBuildFromCellList(),
3653   DMPlexInterpolate(), DMPlexBuildCoordinatesFromCellList()
3654 
3655   See DMPlexBuildFromCellList() for an example and details about the topology-related parameters.
3656   See DMPlexBuildCoordinatesFromCellList() for details about the geometry-related parameters.
3657   See DMPlexCreateFromCellListParallelPetsc() for parallel input
3658 
3659   Level: intermediate
3660 
3661 .seealso: DMPlexCreateFromCellListParallelPetsc(), DMPlexBuildFromCellList(), DMPlexBuildCoordinatesFromCellList(), DMPlexCreateFromDAG(), DMPlexCreate()
3662 @*/
3663 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)
3664 {
3665   PetscMPIInt    rank;
3666   PetscErrorCode ierr;
3667 
3668   PetscFunctionBegin;
3669   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.");
3670   ierr = MPI_Comm_rank(comm, &rank);CHKERRMPI(ierr);
3671   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
3672   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
3673   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
3674   if (!rank) {ierr = DMPlexBuildFromCellList(*dm, numCells, numVertices, numCorners, cells);CHKERRQ(ierr);}
3675   else       {ierr = DMPlexBuildFromCellList(*dm, 0, 0, 0, NULL);CHKERRQ(ierr);}
3676   if (interpolate) {
3677     DM idm;
3678 
3679     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
3680     ierr = DMDestroy(dm);CHKERRQ(ierr);
3681     *dm  = idm;
3682   }
3683   if (!rank) {ierr = DMPlexBuildCoordinatesFromCellList(*dm, spaceDim, vertexCoords);CHKERRQ(ierr);}
3684   else       {ierr = DMPlexBuildCoordinatesFromCellList(*dm, spaceDim, NULL);CHKERRQ(ierr);}
3685   PetscFunctionReturn(0);
3686 }
3687 
3688 /*@
3689   DMPlexCreateFromCellList - Deprecated, use DMPlexCreateFromCellListPetsc()
3690 
3691   Level: deprecated
3692 
3693 .seealso: DMPlexCreateFromCellListPetsc()
3694 @*/
3695 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)
3696 {
3697   PetscErrorCode ierr;
3698   PetscInt       i;
3699   PetscInt       *pintCells;
3700   PetscReal      *prealVC;
3701 
3702   PetscFunctionBegin;
3703   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));
3704   if (sizeof(int) == sizeof(PetscInt)) {
3705     pintCells = (PetscInt *) cells;
3706   } else {
3707     ierr = PetscMalloc1(numCells*numCorners, &pintCells);CHKERRQ(ierr);
3708     for (i = 0; i < numCells*numCorners; i++) {
3709       pintCells[i] = (PetscInt) cells[i];
3710     }
3711   }
3712   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));
3713   if (sizeof(double) == sizeof(PetscReal)) {
3714     prealVC = (PetscReal *) vertexCoords;
3715   } else {
3716     ierr = PetscMalloc1(numVertices*spaceDim, &prealVC);CHKERRQ(ierr);
3717     for (i = 0; i < numVertices*spaceDim; i++) {
3718       prealVC[i] = (PetscReal) vertexCoords[i];
3719     }
3720   }
3721   ierr = DMPlexCreateFromCellListPetsc(comm, dim, numCells, numVertices, numCorners, interpolate, pintCells, spaceDim, prealVC, dm);CHKERRQ(ierr);
3722   if (sizeof(int) != sizeof(PetscInt)) {
3723     ierr = PetscFree(pintCells);CHKERRQ(ierr);
3724   }
3725   if (sizeof(double) != sizeof(PetscReal)) {
3726     ierr = PetscFree(prealVC);CHKERRQ(ierr);
3727   }
3728   PetscFunctionReturn(0);
3729 }
3730 
3731 /*@
3732   DMPlexCreateFromDAG - This takes as input the adjacency-list representation of the Directed Acyclic Graph (Hasse Diagram) encoding a mesh, and produces a DM
3733 
3734   Input Parameters:
3735 + dm - The empty DM object, usually from DMCreate() and DMSetDimension()
3736 . depth - The depth of the DAG
3737 . numPoints - Array of size depth + 1 containing the number of points at each depth
3738 . coneSize - The cone size of each point
3739 . cones - The concatenation of the cone points for each point, the cone list must be oriented correctly for each point
3740 . coneOrientations - The orientation of each cone point
3741 - vertexCoords - An array of numPoints[0]*spacedim numbers representing the coordinates of each vertex, with spacedim the value set via DMSetCoordinateDim()
3742 
3743   Output Parameter:
3744 . dm - The DM
3745 
3746   Note: Two triangles sharing a face would have input
3747 $  depth = 1, numPoints = [4 2], coneSize = [3 3 0 0 0 0]
3748 $  cones = [2 3 4  3 5 4], coneOrientations = [0 0 0  0 0 0]
3749 $ vertexCoords = [-1.0 0.0  0.0 -1.0  0.0 1.0  1.0 0.0]
3750 $
3751 which would result in the DMPlex
3752 $
3753 $        4
3754 $      / | \
3755 $     /  |  \
3756 $    /   |   \
3757 $   2  0 | 1  5
3758 $    \   |   /
3759 $     \  |  /
3760 $      \ | /
3761 $        3
3762 $
3763 $ Notice that all points are numbered consecutively, unlike DMPlexCreateFromCellListPetsc()
3764 
3765   Level: advanced
3766 
3767 .seealso: DMPlexCreateFromCellListPetsc(), DMPlexCreate()
3768 @*/
3769 PetscErrorCode DMPlexCreateFromDAG(DM dm, PetscInt depth, const PetscInt numPoints[], const PetscInt coneSize[], const PetscInt cones[], const PetscInt coneOrientations[], const PetscScalar vertexCoords[])
3770 {
3771   Vec            coordinates;
3772   PetscSection   coordSection;
3773   PetscScalar    *coords;
3774   PetscInt       coordSize, firstVertex = -1, pStart = 0, pEnd = 0, p, v, dim, dimEmbed, d, off;
3775   PetscErrorCode ierr;
3776 
3777   PetscFunctionBegin;
3778   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
3779   ierr = DMGetCoordinateDim(dm, &dimEmbed);CHKERRQ(ierr);
3780   if (dimEmbed < dim) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Embedding dimension %D cannot be less than intrinsic dimension %d",dimEmbed,dim);
3781   for (d = 0; d <= depth; ++d) pEnd += numPoints[d];
3782   ierr = DMPlexSetChart(dm, pStart, pEnd);CHKERRQ(ierr);
3783   for (p = pStart; p < pEnd; ++p) {
3784     ierr = DMPlexSetConeSize(dm, p, coneSize[p-pStart]);CHKERRQ(ierr);
3785     if (firstVertex < 0 && !coneSize[p - pStart]) {
3786       firstVertex = p - pStart;
3787     }
3788   }
3789   if (firstVertex < 0 && numPoints[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Expected %D vertices but could not find any", numPoints[0]);
3790   ierr = DMSetUp(dm);CHKERRQ(ierr); /* Allocate space for cones */
3791   for (p = pStart, off = 0; p < pEnd; off += coneSize[p-pStart], ++p) {
3792     ierr = DMPlexSetCone(dm, p, &cones[off]);CHKERRQ(ierr);
3793     ierr = DMPlexSetConeOrientation(dm, p, &coneOrientations[off]);CHKERRQ(ierr);
3794   }
3795   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
3796   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
3797   /* Build coordinates */
3798   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
3799   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
3800   ierr = PetscSectionSetFieldComponents(coordSection, 0, dimEmbed);CHKERRQ(ierr);
3801   ierr = PetscSectionSetChart(coordSection, firstVertex, firstVertex+numPoints[0]);CHKERRQ(ierr);
3802   for (v = firstVertex; v < firstVertex+numPoints[0]; ++v) {
3803     ierr = PetscSectionSetDof(coordSection, v, dimEmbed);CHKERRQ(ierr);
3804     ierr = PetscSectionSetFieldDof(coordSection, v, 0, dimEmbed);CHKERRQ(ierr);
3805   }
3806   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
3807   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
3808   ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
3809   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
3810   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
3811   ierr = VecSetBlockSize(coordinates, dimEmbed);CHKERRQ(ierr);
3812   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
3813   if (vertexCoords) {
3814     ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
3815     for (v = 0; v < numPoints[0]; ++v) {
3816       PetscInt off;
3817 
3818       ierr = PetscSectionGetOffset(coordSection, v+firstVertex, &off);CHKERRQ(ierr);
3819       for (d = 0; d < dimEmbed; ++d) {
3820         coords[off+d] = vertexCoords[v*dimEmbed+d];
3821       }
3822     }
3823   }
3824   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
3825   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
3826   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
3827   PetscFunctionReturn(0);
3828 }
3829 
3830 /*@C
3831   DMPlexCreateCellVertexFromFile - Create a DMPlex mesh from a simple cell-vertex file.
3832 
3833 + comm        - The MPI communicator
3834 . filename    - Name of the .dat file
3835 - interpolate - Create faces and edges in the mesh
3836 
3837   Output Parameter:
3838 . dm  - The DM object representing the mesh
3839 
3840   Note: The format is the simplest possible:
3841 $ Ne
3842 $ v0 v1 ... vk
3843 $ Nv
3844 $ x y z marker
3845 
3846   Level: beginner
3847 
3848 .seealso: DMPlexCreateFromFile(), DMPlexCreateMedFromFile(), DMPlexCreateGmsh(), DMPlexCreate()
3849 @*/
3850 PetscErrorCode DMPlexCreateCellVertexFromFile(MPI_Comm comm, const char filename[], PetscBool interpolate, DM *dm)
3851 {
3852   DMLabel         marker;
3853   PetscViewer     viewer;
3854   Vec             coordinates;
3855   PetscSection    coordSection;
3856   PetscScalar    *coords;
3857   char            line[PETSC_MAX_PATH_LEN];
3858   PetscInt        dim = 3, cdim = 3, coordSize, v, c, d;
3859   PetscMPIInt     rank;
3860   int             snum, Nv, Nc;
3861   PetscErrorCode  ierr;
3862 
3863   PetscFunctionBegin;
3864   ierr = MPI_Comm_rank(comm, &rank);CHKERRMPI(ierr);
3865   ierr = PetscViewerCreate(comm, &viewer);CHKERRQ(ierr);
3866   ierr = PetscViewerSetType(viewer, PETSCVIEWERASCII);CHKERRQ(ierr);
3867   ierr = PetscViewerFileSetMode(viewer, FILE_MODE_READ);CHKERRQ(ierr);
3868   ierr = PetscViewerFileSetName(viewer, filename);CHKERRQ(ierr);
3869   if (rank == 0) {
3870     ierr = PetscViewerRead(viewer, line, 2, NULL, PETSC_STRING);CHKERRQ(ierr);
3871     snum = sscanf(line, "%d %d", &Nc, &Nv);
3872     if (snum != 2) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unable to parse cell-vertex file: %s", line);
3873   } else {
3874     Nc = Nv = 0;
3875   }
3876   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
3877   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
3878   ierr = DMPlexSetChart(*dm, 0, Nc+Nv);CHKERRQ(ierr);
3879   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
3880   ierr = DMSetCoordinateDim(*dm, cdim);CHKERRQ(ierr);
3881   /* Read topology */
3882   if (rank == 0) {
3883     PetscInt cone[8], corners = 8;
3884     int      vbuf[8], v;
3885 
3886     for (c = 0; c < Nc; ++c) {ierr = DMPlexSetConeSize(*dm, c, corners);CHKERRQ(ierr);}
3887     ierr = DMSetUp(*dm);CHKERRQ(ierr);
3888     for (c = 0; c < Nc; ++c) {
3889       ierr = PetscViewerRead(viewer, line, corners, NULL, PETSC_STRING);CHKERRQ(ierr);
3890       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]);
3891       if (snum != corners) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unable to parse cell-vertex file: %s", line);
3892       for (v = 0; v < corners; ++v) cone[v] = vbuf[v] + Nc;
3893       /* Hexahedra are inverted */
3894       {
3895         PetscInt tmp = cone[1];
3896         cone[1] = cone[3];
3897         cone[3] = tmp;
3898       }
3899       ierr = DMPlexSetCone(*dm, c, cone);CHKERRQ(ierr);
3900     }
3901   }
3902   ierr = DMPlexSymmetrize(*dm);CHKERRQ(ierr);
3903   ierr = DMPlexStratify(*dm);CHKERRQ(ierr);
3904   /* Read coordinates */
3905   ierr = DMGetCoordinateSection(*dm, &coordSection);CHKERRQ(ierr);
3906   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
3907   ierr = PetscSectionSetFieldComponents(coordSection, 0, cdim);CHKERRQ(ierr);
3908   ierr = PetscSectionSetChart(coordSection, Nc, Nc + Nv);CHKERRQ(ierr);
3909   for (v = Nc; v < Nc+Nv; ++v) {
3910     ierr = PetscSectionSetDof(coordSection, v, cdim);CHKERRQ(ierr);
3911     ierr = PetscSectionSetFieldDof(coordSection, v, 0, cdim);CHKERRQ(ierr);
3912   }
3913   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
3914   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
3915   ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
3916   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
3917   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
3918   ierr = VecSetBlockSize(coordinates, cdim);CHKERRQ(ierr);
3919   ierr = VecSetType(coordinates, VECSTANDARD);CHKERRQ(ierr);
3920   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
3921   if (rank == 0) {
3922     double x[3];
3923     int    val;
3924 
3925     ierr = DMCreateLabel(*dm, "marker");CHKERRQ(ierr);
3926     ierr = DMGetLabel(*dm, "marker", &marker);CHKERRQ(ierr);
3927     for (v = 0; v < Nv; ++v) {
3928       ierr = PetscViewerRead(viewer, line, 4, NULL, PETSC_STRING);CHKERRQ(ierr);
3929       snum = sscanf(line, "%lg %lg %lg %d", &x[0], &x[1], &x[2], &val);
3930       if (snum != 4) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unable to parse cell-vertex file: %s", line);
3931       for (d = 0; d < cdim; ++d) coords[v*cdim+d] = x[d];
3932       if (val) {ierr = DMLabelSetValue(marker, v+Nc, val);CHKERRQ(ierr);}
3933     }
3934   }
3935   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
3936   ierr = DMSetCoordinatesLocal(*dm, coordinates);CHKERRQ(ierr);
3937   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
3938   ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
3939   if (interpolate) {
3940     DM      idm;
3941     DMLabel bdlabel;
3942 
3943     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
3944     ierr = DMDestroy(dm);CHKERRQ(ierr);
3945     *dm  = idm;
3946 
3947     ierr = DMGetLabel(*dm, "marker", &bdlabel);CHKERRQ(ierr);
3948     ierr = DMPlexMarkBoundaryFaces(*dm, PETSC_DETERMINE, bdlabel);CHKERRQ(ierr);
3949     ierr = DMPlexLabelComplete(*dm, bdlabel);CHKERRQ(ierr);
3950   }
3951   PetscFunctionReturn(0);
3952 }
3953 
3954 /*@C
3955   DMPlexCreateFromFile - This takes a filename and produces a DM
3956 
3957   Input Parameters:
3958 + comm - The communicator
3959 . filename - A file name
3960 - interpolate - Flag to create intermediate mesh pieces (edges, faces)
3961 
3962   Output Parameter:
3963 . dm - The DM
3964 
3965   Options Database Keys:
3966 . -dm_plex_create_from_hdf5_xdmf - use the PETSC_VIEWER_HDF5_XDMF format for reading HDF5
3967 
3968   Use -dm_plex_create_ prefix to pass options to the internal PetscViewer, e.g.
3969 $ -dm_plex_create_viewer_hdf5_collective
3970 
3971   Level: beginner
3972 
3973 .seealso: DMPlexCreateFromDAG(), DMPlexCreateFromCellListPetsc(), DMPlexCreate()
3974 @*/
3975 PetscErrorCode DMPlexCreateFromFile(MPI_Comm comm, const char filename[], PetscBool interpolate, DM *dm)
3976 {
3977   const char    *extGmsh      = ".msh";
3978   const char    *extGmsh2     = ".msh2";
3979   const char    *extGmsh4     = ".msh4";
3980   const char    *extCGNS      = ".cgns";
3981   const char    *extExodus    = ".exo";
3982   const char    *extGenesis   = ".gen";
3983   const char    *extFluent    = ".cas";
3984   const char    *extHDF5      = ".h5";
3985   const char    *extMed       = ".med";
3986   const char    *extPLY       = ".ply";
3987   const char    *extEGADSLite = ".egadslite";
3988   const char    *extEGADS     = ".egads";
3989   const char    *extIGES      = ".igs";
3990   const char    *extSTEP      = ".stp";
3991   const char    *extCV        = ".dat";
3992   size_t         len;
3993   PetscBool      isGmsh, isGmsh2, isGmsh4, isCGNS, isExodus, isGenesis, isFluent, isHDF5, isMed, isPLY, isEGADSLite, isEGADS, isIGES, isSTEP, isCV;
3994   PetscMPIInt    rank;
3995   PetscErrorCode ierr;
3996 
3997   PetscFunctionBegin;
3998   PetscValidCharPointer(filename, 2);
3999   PetscValidPointer(dm, 4);
4000   ierr = DMInitializePackage();CHKERRQ(ierr);
4001   ierr = PetscLogEventBegin(DMPLEX_CreateFromFile,0,0,0,0);CHKERRQ(ierr);
4002   ierr = MPI_Comm_rank(comm, &rank);CHKERRMPI(ierr);
4003   ierr = PetscStrlen(filename, &len);CHKERRQ(ierr);
4004   if (!len) SETERRQ(comm, PETSC_ERR_ARG_WRONG, "Filename must be a valid path");
4005   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)],  extGmsh,      4, &isGmsh);CHKERRQ(ierr);
4006   ierr = PetscStrncmp(&filename[PetscMax(0,len-5)],  extGmsh2,     5, &isGmsh2);CHKERRQ(ierr);
4007   ierr = PetscStrncmp(&filename[PetscMax(0,len-5)],  extGmsh4,     5, &isGmsh4);CHKERRQ(ierr);
4008   ierr = PetscStrncmp(&filename[PetscMax(0,len-5)],  extCGNS,      5, &isCGNS);CHKERRQ(ierr);
4009   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)],  extExodus,    4, &isExodus);CHKERRQ(ierr);
4010   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)],  extGenesis,   4, &isGenesis);CHKERRQ(ierr);
4011   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)],  extFluent,    4, &isFluent);CHKERRQ(ierr);
4012   ierr = PetscStrncmp(&filename[PetscMax(0,len-3)],  extHDF5,      3, &isHDF5);CHKERRQ(ierr);
4013   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)],  extMed,       4, &isMed);CHKERRQ(ierr);
4014   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)],  extPLY,       4, &isPLY);CHKERRQ(ierr);
4015   ierr = PetscStrncmp(&filename[PetscMax(0,len-10)], extEGADSLite, 10, &isEGADSLite);CHKERRQ(ierr);
4016   ierr = PetscStrncmp(&filename[PetscMax(0,len-6)],  extEGADS,     6, &isEGADS);CHKERRQ(ierr);
4017   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)],  extIGES,      4, &isIGES);CHKERRQ(ierr);
4018   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)],  extSTEP,      4, &isSTEP);CHKERRQ(ierr);
4019   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)],  extCV,        4, &isCV);CHKERRQ(ierr);
4020   if (isGmsh || isGmsh2 || isGmsh4) {
4021     ierr = DMPlexCreateGmshFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
4022   } else if (isCGNS) {
4023     ierr = DMPlexCreateCGNSFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
4024   } else if (isExodus || isGenesis) {
4025     ierr = DMPlexCreateExodusFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
4026   } else if (isFluent) {
4027     ierr = DMPlexCreateFluentFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
4028   } else if (isHDF5) {
4029     PetscBool      load_hdf5_xdmf = PETSC_FALSE;
4030     PetscViewer viewer;
4031 
4032     /* PETSC_VIEWER_HDF5_XDMF is used if the filename ends with .xdmf.h5, or if -dm_plex_create_from_hdf5_xdmf option is present */
4033     ierr = PetscStrncmp(&filename[PetscMax(0,len-8)], ".xdmf",  5, &load_hdf5_xdmf);CHKERRQ(ierr);
4034     ierr = PetscOptionsGetBool(NULL, NULL, "-dm_plex_create_from_hdf5_xdmf", &load_hdf5_xdmf, NULL);CHKERRQ(ierr);
4035     ierr = PetscViewerCreate(comm, &viewer);CHKERRQ(ierr);
4036     ierr = PetscViewerSetType(viewer, PETSCVIEWERHDF5);CHKERRQ(ierr);
4037     ierr = PetscViewerSetOptionsPrefix(viewer, "dm_plex_create_");CHKERRQ(ierr);
4038     ierr = PetscViewerSetFromOptions(viewer);CHKERRQ(ierr);
4039     ierr = PetscViewerFileSetMode(viewer, FILE_MODE_READ);CHKERRQ(ierr);
4040     ierr = PetscViewerFileSetName(viewer, filename);CHKERRQ(ierr);
4041     ierr = DMCreate(comm, dm);CHKERRQ(ierr);
4042     ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
4043     if (load_hdf5_xdmf) {ierr = PetscViewerPushFormat(viewer, PETSC_VIEWER_HDF5_XDMF);CHKERRQ(ierr);}
4044     ierr = DMLoad(*dm, viewer);CHKERRQ(ierr);
4045     if (load_hdf5_xdmf) {ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);}
4046     ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
4047 
4048     if (interpolate) {
4049       DM idm;
4050 
4051       ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
4052       ierr = DMDestroy(dm);CHKERRQ(ierr);
4053       *dm  = idm;
4054     }
4055   } else if (isMed) {
4056     ierr = DMPlexCreateMedFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
4057   } else if (isPLY) {
4058     ierr = DMPlexCreatePLYFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
4059   } else if (isEGADSLite || isEGADS || isIGES || isSTEP) {
4060     if (isEGADSLite) {ierr = DMPlexCreateEGADSLiteFromFile(comm, filename, dm);CHKERRQ(ierr);}
4061     else             {ierr = DMPlexCreateEGADSFromFile(comm, filename, dm);CHKERRQ(ierr);}
4062     if (!interpolate) {
4063       DM udm;
4064 
4065       ierr = DMPlexUninterpolate(*dm, &udm);CHKERRQ(ierr);
4066       ierr = DMDestroy(dm);CHKERRQ(ierr);
4067       *dm  = udm;
4068     }
4069   } else if (isCV) {
4070     ierr = DMPlexCreateCellVertexFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
4071   } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cannot load file %s: unrecognized extension", filename);
4072   ierr = PetscLogEventEnd(DMPLEX_CreateFromFile,0,0,0,0);CHKERRQ(ierr);
4073   PetscFunctionReturn(0);
4074 }
4075