xref: /petsc/src/dm/impls/plex/plexcreate.c (revision 5ef7c680e6885e8965d12e6106072fcdaa8b548d)
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 /*@
9   DMPlexCreateDoublet - Creates a mesh of two cells of the specified type, optionally with later refinement.
10 
11   Collective
12 
13   Input Parameters:
14 + comm - The communicator for the DM object
15 . dim - The spatial dimension
16 . simplex - Flag for simplicial cells, otherwise they are tensor product cells
17 . interpolate - Flag to create intermediate mesh pieces (edges, faces)
18 . refinementUniform - Flag for uniform parallel refinement
19 - refinementLimit - A nonzero number indicates the largest admissible volume for a refined cell
20 
21   Output Parameter:
22 . dm - The DM object
23 
24   Level: beginner
25 
26 .seealso: DMSetType(), DMCreate()
27 @*/
28 PetscErrorCode DMPlexCreateDoublet(MPI_Comm comm, PetscInt dim, PetscBool simplex, PetscBool interpolate, PetscBool refinementUniform, PetscReal refinementLimit, DM *newdm)
29 {
30   DM             dm;
31   PetscInt       p;
32   PetscMPIInt    rank;
33   PetscErrorCode ierr;
34 
35   PetscFunctionBegin;
36   ierr = DMCreate(comm, &dm);CHKERRQ(ierr);
37   ierr = DMSetType(dm, DMPLEX);CHKERRQ(ierr);
38   ierr = DMSetDimension(dm, dim);CHKERRQ(ierr);
39   ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
40   switch (dim) {
41   case 2:
42     if (simplex) {ierr = PetscObjectSetName((PetscObject) dm, "triangular");CHKERRQ(ierr);}
43     else         {ierr = PetscObjectSetName((PetscObject) dm, "quadrilateral");CHKERRQ(ierr);}
44     break;
45   case 3:
46     if (simplex) {ierr = PetscObjectSetName((PetscObject) dm, "tetrahedral");CHKERRQ(ierr);}
47     else         {ierr = PetscObjectSetName((PetscObject) dm, "hexahedral");CHKERRQ(ierr);}
48     break;
49   default:
50     SETERRQ1(comm, PETSC_ERR_ARG_OUTOFRANGE, "Cannot make meshes for dimension %d", dim);
51   }
52   if (rank) {
53     PetscInt numPoints[2] = {0, 0};
54     ierr = DMPlexCreateFromDAG(dm, 1, numPoints, NULL, NULL, NULL, NULL);CHKERRQ(ierr);
55   } else {
56     switch (dim) {
57     case 2:
58       if (simplex) {
59         PetscInt    numPoints[2]        = {4, 2};
60         PetscInt    coneSize[6]         = {3, 3, 0, 0, 0, 0};
61         PetscInt    cones[6]            = {2, 3, 4,  5, 4, 3};
62         PetscInt    coneOrientations[6] = {0, 0, 0,  0, 0, 0};
63         PetscScalar vertexCoords[8]     = {-0.5, 0.5, 0.0, 0.0, 0.0, 1.0, 0.5, 0.5};
64         PetscInt    markerPoints[8]     = {2, 1, 3, 1, 4, 1, 5, 1};
65 
66         ierr = DMPlexCreateFromDAG(dm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
67         for (p = 0; p < 4; ++p) {ierr = DMSetLabelValue(dm, "marker", markerPoints[p*2], markerPoints[p*2+1]);CHKERRQ(ierr);}
68       } else {
69         PetscInt    numPoints[2]        = {6, 2};
70         PetscInt    coneSize[8]         = {4, 4, 0, 0, 0, 0, 0, 0};
71         PetscInt    cones[8]            = {2, 3, 4, 5,  3, 6, 7, 4};
72         PetscInt    coneOrientations[8] = {0, 0, 0, 0,  0, 0, 0, 0};
73         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};
74 
75         ierr = DMPlexCreateFromDAG(dm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
76       }
77       break;
78     case 3:
79       if (simplex) {
80         PetscInt    numPoints[2]        = {5, 2};
81         PetscInt    coneSize[7]         = {4, 4, 0, 0, 0, 0, 0};
82         PetscInt    cones[8]            = {4, 3, 5, 2,  5, 3, 4, 6};
83         PetscInt    coneOrientations[8] = {0, 0, 0, 0,  0, 0, 0, 0};
84         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};
85         PetscInt    markerPoints[10]    = {2, 1, 3, 1, 4, 1, 5, 1, 6, 1};
86 
87         ierr = DMPlexCreateFromDAG(dm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
88         for (p = 0; p < 5; ++p) {ierr = DMSetLabelValue(dm, "marker", markerPoints[p*2], markerPoints[p*2+1]);CHKERRQ(ierr);}
89       } else {
90         PetscInt    numPoints[2]         = {12, 2};
91         PetscInt    coneSize[14]         = {8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0};
92         PetscInt    cones[16]            = {2, 3, 4, 5, 6, 7, 8, 9,  5, 4, 10, 11, 7, 12, 13, 8};
93         PetscInt    coneOrientations[16] = {0, 0, 0, 0, 0, 0, 0, 0,  0, 0,  0,  0, 0,  0,  0, 0};
94         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,
95                                             -1.0, -0.5,  0.5,   0.0, -0.5,  0.5,  0.0,  0.5,  0.5,  -1.0,  0.5,  0.5,
96                                              1.0,  0.5, -0.5,   1.0, -0.5, -0.5,  1.0, -0.5,  0.5,   1.0,  0.5,  0.5};
97 
98         ierr = DMPlexCreateFromDAG(dm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
99       }
100       break;
101     default:
102       SETERRQ1(comm, PETSC_ERR_ARG_OUTOFRANGE, "Cannot make meshes for dimension %d", dim);
103     }
104   }
105   *newdm = dm;
106   if (refinementLimit > 0.0) {
107     DM rdm;
108     const char *name;
109 
110     ierr = DMPlexSetRefinementUniform(*newdm, PETSC_FALSE);CHKERRQ(ierr);
111     ierr = DMPlexSetRefinementLimit(*newdm, refinementLimit);CHKERRQ(ierr);
112     ierr = DMRefine(*newdm, comm, &rdm);CHKERRQ(ierr);
113     ierr = PetscObjectGetName((PetscObject) *newdm, &name);CHKERRQ(ierr);
114     ierr = PetscObjectSetName((PetscObject)    rdm,  name);CHKERRQ(ierr);
115     ierr = DMDestroy(newdm);CHKERRQ(ierr);
116     *newdm = rdm;
117   }
118   if (interpolate) {
119     DM idm;
120 
121     ierr = DMPlexInterpolate(*newdm, &idm);CHKERRQ(ierr);
122     ierr = DMDestroy(newdm);CHKERRQ(ierr);
123     *newdm = idm;
124   }
125   {
126     DM refinedMesh     = NULL;
127     DM distributedMesh = NULL;
128 
129     /* Distribute mesh over processes */
130     ierr = DMPlexDistribute(*newdm, 0, NULL, &distributedMesh);CHKERRQ(ierr);
131     if (distributedMesh) {
132       ierr = DMDestroy(newdm);CHKERRQ(ierr);
133       *newdm = distributedMesh;
134     }
135     if (refinementUniform) {
136       ierr = DMPlexSetRefinementUniform(*newdm, refinementUniform);CHKERRQ(ierr);
137       ierr = DMRefine(*newdm, comm, &refinedMesh);CHKERRQ(ierr);
138       if (refinedMesh) {
139         ierr = DMDestroy(newdm);CHKERRQ(ierr);
140         *newdm = refinedMesh;
141       }
142     }
143   }
144   PetscFunctionReturn(0);
145 }
146 
147 /*@
148   DMPlexCreateSquareBoundary - Creates a 1D mesh the is the boundary of a square lattice.
149 
150   Collective
151 
152   Input Parameters:
153 + comm  - The communicator for the DM object
154 . lower - The lower left corner coordinates
155 . upper - The upper right corner coordinates
156 - edges - The number of cells in each direction
157 
158   Output Parameter:
159 . dm  - The DM object
160 
161   Note: Here is the numbering returned for 2 cells in each direction:
162 $ 18--5-17--4--16
163 $  |     |     |
164 $  6    10     3
165 $  |     |     |
166 $ 19-11-20--9--15
167 $  |     |     |
168 $  7     8     2
169 $  |     |     |
170 $ 12--0-13--1--14
171 
172   Level: beginner
173 
174 .seealso: DMPlexCreateBoxMesh(), DMPlexCreateCubeBoundary(), DMSetType(), DMCreate()
175 @*/
176 PetscErrorCode DMPlexCreateSquareBoundary(DM dm, const PetscReal lower[], const PetscReal upper[], const PetscInt edges[])
177 {
178   const PetscInt numVertices    = (edges[0]+1)*(edges[1]+1);
179   const PetscInt numEdges       = edges[0]*(edges[1]+1) + (edges[0]+1)*edges[1];
180   PetscInt       markerTop      = 1;
181   PetscInt       markerBottom   = 1;
182   PetscInt       markerRight    = 1;
183   PetscInt       markerLeft     = 1;
184   PetscBool      markerSeparate = PETSC_FALSE;
185   Vec            coordinates;
186   PetscSection   coordSection;
187   PetscScalar    *coords;
188   PetscInt       coordSize;
189   PetscMPIInt    rank;
190   PetscInt       v, vx, vy;
191   PetscErrorCode ierr;
192 
193   PetscFunctionBegin;
194   ierr = PetscOptionsGetBool(((PetscObject) dm)->options,((PetscObject) dm)->prefix, "-dm_plex_separate_marker", &markerSeparate, NULL);CHKERRQ(ierr);
195   if (markerSeparate) {
196     markerTop    = 3;
197     markerBottom = 1;
198     markerRight  = 2;
199     markerLeft   = 4;
200   }
201   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);CHKERRQ(ierr);
202   if (!rank) {
203     PetscInt e, ex, ey;
204 
205     ierr = DMPlexSetChart(dm, 0, numEdges+numVertices);CHKERRQ(ierr);
206     for (e = 0; e < numEdges; ++e) {
207       ierr = DMPlexSetConeSize(dm, e, 2);CHKERRQ(ierr);
208     }
209     ierr = DMSetUp(dm);CHKERRQ(ierr); /* Allocate space for cones */
210     for (vx = 0; vx <= edges[0]; vx++) {
211       for (ey = 0; ey < edges[1]; ey++) {
212         PetscInt edge   = vx*edges[1] + ey + edges[0]*(edges[1]+1);
213         PetscInt vertex = ey*(edges[0]+1) + vx + numEdges;
214         PetscInt cone[2];
215 
216         cone[0] = vertex; cone[1] = vertex+edges[0]+1;
217         ierr    = DMPlexSetCone(dm, edge, cone);CHKERRQ(ierr);
218         if (vx == edges[0]) {
219           ierr = DMSetLabelValue(dm, "marker", edge,    markerRight);CHKERRQ(ierr);
220           ierr = DMSetLabelValue(dm, "marker", cone[0], markerRight);CHKERRQ(ierr);
221           if (ey == edges[1]-1) {
222             ierr = DMSetLabelValue(dm, "marker", cone[1], markerRight);CHKERRQ(ierr);
223             ierr = DMSetLabelValue(dm, "Face Sets", cone[1], markerRight);CHKERRQ(ierr);
224           }
225         } else if (vx == 0) {
226           ierr = DMSetLabelValue(dm, "marker", edge,    markerLeft);CHKERRQ(ierr);
227           ierr = DMSetLabelValue(dm, "marker", cone[0], markerLeft);CHKERRQ(ierr);
228           if (ey == edges[1]-1) {
229             ierr = DMSetLabelValue(dm, "marker", cone[1], markerLeft);CHKERRQ(ierr);
230             ierr = DMSetLabelValue(dm, "Face Sets", cone[1], markerLeft);CHKERRQ(ierr);
231           }
232         }
233       }
234     }
235     for (vy = 0; vy <= edges[1]; vy++) {
236       for (ex = 0; ex < edges[0]; ex++) {
237         PetscInt edge   = vy*edges[0]     + ex;
238         PetscInt vertex = vy*(edges[0]+1) + ex + numEdges;
239         PetscInt cone[2];
240 
241         cone[0] = vertex; cone[1] = vertex+1;
242         ierr    = DMPlexSetCone(dm, edge, cone);CHKERRQ(ierr);
243         if (vy == edges[1]) {
244           ierr = DMSetLabelValue(dm, "marker", edge,    markerTop);CHKERRQ(ierr);
245           ierr = DMSetLabelValue(dm, "marker", cone[0], markerTop);CHKERRQ(ierr);
246           if (ex == edges[0]-1) {
247             ierr = DMSetLabelValue(dm, "marker", cone[1], markerTop);CHKERRQ(ierr);
248             ierr = DMSetLabelValue(dm, "Face Sets", cone[1], markerTop);CHKERRQ(ierr);
249           }
250         } else if (vy == 0) {
251           ierr = DMSetLabelValue(dm, "marker", edge,    markerBottom);CHKERRQ(ierr);
252           ierr = DMSetLabelValue(dm, "marker", cone[0], markerBottom);CHKERRQ(ierr);
253           if (ex == edges[0]-1) {
254             ierr = DMSetLabelValue(dm, "marker", cone[1], markerBottom);CHKERRQ(ierr);
255             ierr = DMSetLabelValue(dm, "Face Sets", cone[1], markerBottom);CHKERRQ(ierr);
256           }
257         }
258       }
259     }
260   }
261   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
262   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
263   /* Build coordinates */
264   ierr = DMSetCoordinateDim(dm, 2);CHKERRQ(ierr);
265   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
266   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
267   ierr = PetscSectionSetChart(coordSection, numEdges, numEdges + numVertices);CHKERRQ(ierr);
268   ierr = PetscSectionSetFieldComponents(coordSection, 0, 2);CHKERRQ(ierr);
269   for (v = numEdges; v < numEdges+numVertices; ++v) {
270     ierr = PetscSectionSetDof(coordSection, v, 2);CHKERRQ(ierr);
271     ierr = PetscSectionSetFieldDof(coordSection, v, 0, 2);CHKERRQ(ierr);
272   }
273   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
274   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
275   ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
276   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
277   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
278   ierr = VecSetBlockSize(coordinates, 2);CHKERRQ(ierr);
279   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
280   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
281   for (vy = 0; vy <= edges[1]; ++vy) {
282     for (vx = 0; vx <= edges[0]; ++vx) {
283       coords[(vy*(edges[0]+1)+vx)*2+0] = lower[0] + ((upper[0] - lower[0])/edges[0])*vx;
284       coords[(vy*(edges[0]+1)+vx)*2+1] = lower[1] + ((upper[1] - lower[1])/edges[1])*vy;
285     }
286   }
287   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
288   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
289   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
290   PetscFunctionReturn(0);
291 }
292 
293 /*@
294   DMPlexCreateCubeBoundary - Creates a 2D mesh that is the boundary of a cubic lattice.
295 
296   Collective
297 
298   Input Parameters:
299 + comm  - The communicator for the DM object
300 . lower - The lower left front corner coordinates
301 . upper - The upper right back corner coordinates
302 - faces - The number of faces in each direction (the same as the number of cells)
303 
304   Output Parameter:
305 . dm  - The DM object
306 
307   Level: beginner
308 
309 .seealso: DMPlexCreateBoxMesh(), DMPlexCreateSquareBoundary(), DMSetType(), DMCreate()
310 @*/
311 PetscErrorCode DMPlexCreateCubeBoundary(DM dm, const PetscReal lower[], const PetscReal upper[], const PetscInt faces[])
312 {
313   PetscInt       vertices[3], numVertices;
314   PetscInt       numFaces    = 2*faces[0]*faces[1] + 2*faces[1]*faces[2] + 2*faces[0]*faces[2];
315   Vec            coordinates;
316   PetscSection   coordSection;
317   PetscScalar    *coords;
318   PetscInt       coordSize;
319   PetscMPIInt    rank;
320   PetscInt       v, vx, vy, vz;
321   PetscInt       voffset, iface=0, cone[4];
322   PetscErrorCode ierr;
323 
324   PetscFunctionBegin;
325   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");
326   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);CHKERRQ(ierr);
327   vertices[0] = faces[0]+1; vertices[1] = faces[1]+1; vertices[2] = faces[2]+1;
328   numVertices = vertices[0]*vertices[1]*vertices[2];
329   if (!rank) {
330     PetscInt f;
331 
332     ierr = DMPlexSetChart(dm, 0, numFaces+numVertices);CHKERRQ(ierr);
333     for (f = 0; f < numFaces; ++f) {
334       ierr = DMPlexSetConeSize(dm, f, 4);CHKERRQ(ierr);
335     }
336     ierr = DMSetUp(dm);CHKERRQ(ierr); /* Allocate space for cones */
337 
338     /* Side 0 (Top) */
339     for (vy = 0; vy < faces[1]; vy++) {
340       for (vx = 0; vx < faces[0]; vx++) {
341         voffset = numFaces + vertices[0]*vertices[1]*(vertices[2]-1) + vy*vertices[0] + vx;
342         cone[0] = voffset; cone[1] = voffset+1; cone[2] = voffset+vertices[0]+1; cone[3] = voffset+vertices[0];
343         ierr    = DMPlexSetCone(dm, iface, cone);CHKERRQ(ierr);
344         ierr    = DMSetLabelValue(dm, "marker", iface, 1);CHKERRQ(ierr);
345         ierr    = DMSetLabelValue(dm, "marker", voffset+0, 1);CHKERRQ(ierr);
346         ierr    = DMSetLabelValue(dm, "marker", voffset+1, 1);CHKERRQ(ierr);
347         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[0]+0, 1);CHKERRQ(ierr);
348         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[0]+1, 1);CHKERRQ(ierr);
349         iface++;
350       }
351     }
352 
353     /* Side 1 (Bottom) */
354     for (vy = 0; vy < faces[1]; vy++) {
355       for (vx = 0; vx < faces[0]; vx++) {
356         voffset = numFaces + vy*(faces[0]+1) + vx;
357         cone[0] = voffset+1; cone[1] = voffset; cone[2] = voffset+vertices[0]; cone[3] = voffset+vertices[0]+1;
358         ierr    = DMPlexSetCone(dm, iface, cone);CHKERRQ(ierr);
359         ierr    = DMSetLabelValue(dm, "marker", iface, 1);CHKERRQ(ierr);
360         ierr    = DMSetLabelValue(dm, "marker", voffset+0, 1);CHKERRQ(ierr);
361         ierr    = DMSetLabelValue(dm, "marker", voffset+1, 1);CHKERRQ(ierr);
362         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[0]+0, 1);CHKERRQ(ierr);
363         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[0]+1, 1);CHKERRQ(ierr);
364         iface++;
365       }
366     }
367 
368     /* Side 2 (Front) */
369     for (vz = 0; vz < faces[2]; vz++) {
370       for (vx = 0; vx < faces[0]; vx++) {
371         voffset = numFaces + vz*vertices[0]*vertices[1] + vx;
372         cone[0] = voffset; cone[1] = voffset+1; cone[2] = voffset+vertices[0]*vertices[1]+1; cone[3] = voffset+vertices[0]*vertices[1];
373         ierr    = DMPlexSetCone(dm, iface, cone);CHKERRQ(ierr);
374         ierr    = DMSetLabelValue(dm, "marker", iface, 1);CHKERRQ(ierr);
375         ierr    = DMSetLabelValue(dm, "marker", voffset+0, 1);CHKERRQ(ierr);
376         ierr    = DMSetLabelValue(dm, "marker", voffset+1, 1);CHKERRQ(ierr);
377         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[0]*vertices[1]+0, 1);CHKERRQ(ierr);
378         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[0]*vertices[1]+1, 1);CHKERRQ(ierr);
379         iface++;
380       }
381     }
382 
383     /* Side 3 (Back) */
384     for (vz = 0; vz < faces[2]; vz++) {
385       for (vx = 0; vx < faces[0]; vx++) {
386         voffset = numFaces + vz*vertices[0]*vertices[1] + vertices[0]*(vertices[1]-1) + vx;
387         cone[0] = voffset+vertices[0]*vertices[1]; cone[1] = voffset+vertices[0]*vertices[1]+1;
388         cone[2] = voffset+1; cone[3] = voffset;
389         ierr    = DMPlexSetCone(dm, iface, cone);CHKERRQ(ierr);
390         ierr    = DMSetLabelValue(dm, "marker", iface, 1);CHKERRQ(ierr);
391         ierr    = DMSetLabelValue(dm, "marker", voffset+0, 1);CHKERRQ(ierr);
392         ierr    = DMSetLabelValue(dm, "marker", voffset+1, 1);CHKERRQ(ierr);
393         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[0]*vertices[1]+0, 1);CHKERRQ(ierr);
394         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[0]*vertices[1]+1, 1);CHKERRQ(ierr);
395         iface++;
396       }
397     }
398 
399     /* Side 4 (Left) */
400     for (vz = 0; vz < faces[2]; vz++) {
401       for (vy = 0; vy < faces[1]; vy++) {
402         voffset = numFaces + vz*vertices[0]*vertices[1] + vy*vertices[0];
403         cone[0] = voffset; cone[1] = voffset+vertices[0]*vertices[1];
404         cone[2] = voffset+vertices[0]*vertices[1]+vertices[0]; cone[3] = voffset+vertices[0];
405         ierr    = DMPlexSetCone(dm, iface, cone);CHKERRQ(ierr);
406         ierr    = DMSetLabelValue(dm, "marker", iface, 1);CHKERRQ(ierr);
407         ierr    = DMSetLabelValue(dm, "marker", voffset+0, 1);CHKERRQ(ierr);
408         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[0]+0, 1);CHKERRQ(ierr);
409         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[1]+0, 1);CHKERRQ(ierr);
410         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[0]*vertices[1]+vertices[0], 1);CHKERRQ(ierr);
411         iface++;
412       }
413     }
414 
415     /* Side 5 (Right) */
416     for (vz = 0; vz < faces[2]; vz++) {
417       for (vy = 0; vy < faces[1]; vy++) {
418         voffset = numFaces + vz*vertices[0]*vertices[1] + vy*vertices[0] + faces[0];
419         cone[0] = voffset+vertices[0]*vertices[1]; cone[1] = voffset;
420         cone[2] = voffset+vertices[0]; cone[3] = voffset+vertices[0]*vertices[1]+vertices[0];
421         ierr    = DMPlexSetCone(dm, iface, cone);CHKERRQ(ierr);
422         ierr    = DMSetLabelValue(dm, "marker", iface, 1);CHKERRQ(ierr);
423         ierr    = DMSetLabelValue(dm, "marker", voffset+0, 1);CHKERRQ(ierr);
424         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[0]+0, 1);CHKERRQ(ierr);
425         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[0]*vertices[1]+0, 1);CHKERRQ(ierr);
426         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[0]*vertices[1]+vertices[0], 1);CHKERRQ(ierr);
427         iface++;
428       }
429     }
430   }
431   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
432   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
433   /* Build coordinates */
434   ierr = DMSetCoordinateDim(dm, 3);CHKERRQ(ierr);
435   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
436   ierr = PetscSectionSetChart(coordSection, numFaces, numFaces + numVertices);CHKERRQ(ierr);
437   for (v = numFaces; v < numFaces+numVertices; ++v) {
438     ierr = PetscSectionSetDof(coordSection, v, 3);CHKERRQ(ierr);
439   }
440   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
441   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
442   ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
443   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
444   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
445   ierr = VecSetBlockSize(coordinates, 3);CHKERRQ(ierr);
446   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
447   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
448   for (vz = 0; vz <= faces[2]; ++vz) {
449     for (vy = 0; vy <= faces[1]; ++vy) {
450       for (vx = 0; vx <= faces[0]; ++vx) {
451         coords[((vz*(faces[1]+1)+vy)*(faces[0]+1)+vx)*3+0] = lower[0] + ((upper[0] - lower[0])/faces[0])*vx;
452         coords[((vz*(faces[1]+1)+vy)*(faces[0]+1)+vx)*3+1] = lower[1] + ((upper[1] - lower[1])/faces[1])*vy;
453         coords[((vz*(faces[1]+1)+vy)*(faces[0]+1)+vx)*3+2] = lower[2] + ((upper[2] - lower[2])/faces[2])*vz;
454       }
455     }
456   }
457   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
458   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
459   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
460   PetscFunctionReturn(0);
461 }
462 
463 static PetscErrorCode DMPlexCreateLineMesh_Internal(MPI_Comm comm,PetscInt segments,PetscReal lower,PetscReal upper,DMBoundaryType bd,DM *dm)
464 {
465   PetscInt       i,fStart,fEnd,numCells = 0,numVerts = 0;
466   PetscInt       numPoints[2],*coneSize,*cones,*coneOrientations;
467   PetscScalar    *vertexCoords;
468   PetscReal      L,maxCell;
469   PetscBool      markerSeparate = PETSC_FALSE;
470   PetscInt       markerLeft  = 1, faceMarkerLeft  = 1;
471   PetscInt       markerRight = 1, faceMarkerRight = 2;
472   PetscBool      wrap = (bd == DM_BOUNDARY_PERIODIC || bd == DM_BOUNDARY_TWIST) ? PETSC_TRUE : PETSC_FALSE;
473   PetscMPIInt    rank;
474   PetscErrorCode ierr;
475 
476   PetscFunctionBegin;
477   PetscValidPointer(dm,4);
478 
479   ierr = DMCreate(comm,dm);CHKERRQ(ierr);
480   ierr = DMSetType(*dm,DMPLEX);CHKERRQ(ierr);
481   ierr = DMSetDimension(*dm,1);CHKERRQ(ierr);
482   ierr = DMCreateLabel(*dm,"marker");CHKERRQ(ierr);
483   ierr = DMCreateLabel(*dm,"Face Sets");CHKERRQ(ierr);
484 
485   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
486   if (!rank) numCells = segments;
487   if (!rank) numVerts = segments + (wrap ? 0 : 1);
488 
489   numPoints[0] = numVerts ; numPoints[1] = numCells;
490   ierr = PetscMalloc4(numCells+numVerts,&coneSize,numCells*2,&cones,numCells+numVerts,&coneOrientations,numVerts,&vertexCoords);CHKERRQ(ierr);
491   ierr = PetscArrayzero(coneOrientations,numCells+numVerts);CHKERRQ(ierr);
492   for (i = 0; i < numCells; ++i) { coneSize[i] = 2; }
493   for (i = 0; i < numVerts; ++i) { coneSize[numCells+i] = 0; }
494   for (i = 0; i < numCells; ++i) { cones[2*i] = numCells + i%numVerts; cones[2*i+1] = numCells + (i+1)%numVerts; }
495   for (i = 0; i < numVerts; ++i) { vertexCoords[i] = lower + (upper-lower)*((PetscReal)i/(PetscReal)numCells); }
496   ierr = DMPlexCreateFromDAG(*dm,1,numPoints,coneSize,cones,coneOrientations,vertexCoords);CHKERRQ(ierr);
497   ierr = PetscFree4(coneSize,cones,coneOrientations,vertexCoords);CHKERRQ(ierr);
498 
499   ierr = PetscOptionsGetBool(((PetscObject)*dm)->options,((PetscObject)*dm)->prefix,"-dm_plex_separate_marker",&markerSeparate,NULL);CHKERRQ(ierr);
500   if (markerSeparate) { markerLeft = faceMarkerLeft; markerRight = faceMarkerRight;}
501   if (!wrap && !rank) {
502     ierr = DMPlexGetHeightStratum(*dm,1,&fStart,&fEnd);CHKERRQ(ierr);
503     ierr = DMSetLabelValue(*dm,"marker",fStart,markerLeft);CHKERRQ(ierr);
504     ierr = DMSetLabelValue(*dm,"marker",fEnd-1,markerRight);CHKERRQ(ierr);
505     ierr = DMSetLabelValue(*dm,"Face Sets",fStart,faceMarkerLeft);CHKERRQ(ierr);
506     ierr = DMSetLabelValue(*dm,"Face Sets",fEnd-1,faceMarkerRight);CHKERRQ(ierr);
507   }
508   if (wrap) {
509     L       = upper - lower;
510     maxCell = (PetscReal)1.1*(L/(PetscReal)PetscMax(1,segments));
511     ierr = DMSetPeriodicity(*dm,PETSC_TRUE,&maxCell,&L,&bd);CHKERRQ(ierr);
512   }
513   PetscFunctionReturn(0);
514 }
515 
516 static PetscErrorCode DMPlexCreateBoxMesh_Simplex_Internal(MPI_Comm comm, PetscInt dim, const PetscInt faces[], const PetscReal lower[], const PetscReal upper[], const DMBoundaryType periodicity[], PetscBool interpolate, DM *dm)
517 {
518   DM             boundary;
519   PetscInt       i;
520   PetscErrorCode ierr;
521 
522   PetscFunctionBegin;
523   PetscValidPointer(dm, 4);
524   for (i = 0; i < dim; ++i) if (periodicity[i] != DM_BOUNDARY_NONE) SETERRQ(comm, PETSC_ERR_SUP, "Periodicity is not supported for simplex meshes");
525   ierr = DMCreate(comm, &boundary);CHKERRQ(ierr);
526   PetscValidLogicalCollectiveInt(boundary,dim,2);
527   ierr = DMSetType(boundary, DMPLEX);CHKERRQ(ierr);
528   ierr = DMSetDimension(boundary, dim-1);CHKERRQ(ierr);
529   ierr = DMSetCoordinateDim(boundary, dim);CHKERRQ(ierr);
530   switch (dim) {
531   case 2: ierr = DMPlexCreateSquareBoundary(boundary, lower, upper, faces);CHKERRQ(ierr);break;
532   case 3: ierr = DMPlexCreateCubeBoundary(boundary, lower, upper, faces);CHKERRQ(ierr);break;
533   default: SETERRQ1(comm, PETSC_ERR_SUP, "Dimension not supported: %d", dim);
534   }
535   ierr = DMPlexGenerate(boundary, NULL, interpolate, dm);CHKERRQ(ierr);
536   ierr = DMDestroy(&boundary);CHKERRQ(ierr);
537   PetscFunctionReturn(0);
538 }
539 
540 static PetscErrorCode DMPlexCreateCubeMesh_Internal(DM dm, const PetscReal lower[], const PetscReal upper[], const PetscInt edges[], DMBoundaryType bdX, DMBoundaryType bdY, DMBoundaryType bdZ)
541 {
542   DMLabel        cutLabel = NULL;
543   PetscInt       markerTop      = 1, faceMarkerTop      = 1;
544   PetscInt       markerBottom   = 1, faceMarkerBottom   = 1;
545   PetscInt       markerFront    = 1, faceMarkerFront    = 1;
546   PetscInt       markerBack     = 1, faceMarkerBack     = 1;
547   PetscInt       markerRight    = 1, faceMarkerRight    = 1;
548   PetscInt       markerLeft     = 1, faceMarkerLeft     = 1;
549   PetscInt       dim;
550   PetscBool      markerSeparate = PETSC_FALSE, cutMarker = PETSC_FALSE;
551   PetscMPIInt    rank;
552   PetscErrorCode ierr;
553 
554   PetscFunctionBegin;
555   ierr = DMGetDimension(dm,&dim);CHKERRQ(ierr);
556   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);CHKERRQ(ierr);
557   ierr = DMCreateLabel(dm,"marker");CHKERRQ(ierr);
558   ierr = DMCreateLabel(dm,"Face Sets");CHKERRQ(ierr);
559   ierr = PetscOptionsGetBool(((PetscObject) dm)->options,((PetscObject) dm)->prefix, "-dm_plex_periodic_cut", &cutMarker, NULL);CHKERRQ(ierr);
560   if (bdX == DM_BOUNDARY_PERIODIC || bdX == DM_BOUNDARY_TWIST ||
561       bdY == DM_BOUNDARY_PERIODIC || bdY == DM_BOUNDARY_TWIST ||
562       bdZ == DM_BOUNDARY_PERIODIC || bdZ == DM_BOUNDARY_TWIST) {
563 
564     if (cutMarker) {ierr = DMCreateLabel(dm, "periodic_cut");CHKERRQ(ierr); ierr = DMGetLabel(dm, "periodic_cut", &cutLabel);CHKERRQ(ierr);}
565   }
566   switch (dim) {
567   case 2:
568     faceMarkerTop    = 3;
569     faceMarkerBottom = 1;
570     faceMarkerRight  = 2;
571     faceMarkerLeft   = 4;
572     break;
573   case 3:
574     faceMarkerBottom = 1;
575     faceMarkerTop    = 2;
576     faceMarkerFront  = 3;
577     faceMarkerBack   = 4;
578     faceMarkerRight  = 5;
579     faceMarkerLeft   = 6;
580     break;
581   default:
582     SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Dimension %d not supported",dim);
583     break;
584   }
585   ierr = PetscOptionsGetBool(((PetscObject) dm)->options,((PetscObject) dm)->prefix, "-dm_plex_separate_marker", &markerSeparate, NULL);CHKERRQ(ierr);
586   if (markerSeparate) {
587     markerBottom = faceMarkerBottom;
588     markerTop    = faceMarkerTop;
589     markerFront  = faceMarkerFront;
590     markerBack   = faceMarkerBack;
591     markerRight  = faceMarkerRight;
592     markerLeft   = faceMarkerLeft;
593   }
594   {
595     const PetscInt numXEdges    = !rank ? edges[0] : 0;
596     const PetscInt numYEdges    = !rank ? edges[1] : 0;
597     const PetscInt numZEdges    = !rank ? edges[2] : 0;
598     const PetscInt numXVertices = !rank ? (bdX == DM_BOUNDARY_PERIODIC || bdX == DM_BOUNDARY_TWIST ? edges[0] : edges[0]+1) : 0;
599     const PetscInt numYVertices = !rank ? (bdY == DM_BOUNDARY_PERIODIC || bdY == DM_BOUNDARY_TWIST ? edges[1] : edges[1]+1) : 0;
600     const PetscInt numZVertices = !rank ? (bdZ == DM_BOUNDARY_PERIODIC || bdZ == DM_BOUNDARY_TWIST ? edges[2] : edges[2]+1) : 0;
601     const PetscInt numCells     = numXEdges*numYEdges*numZEdges;
602     const PetscInt numXFaces    = numYEdges*numZEdges;
603     const PetscInt numYFaces    = numXEdges*numZEdges;
604     const PetscInt numZFaces    = numXEdges*numYEdges;
605     const PetscInt numTotXFaces = numXVertices*numXFaces;
606     const PetscInt numTotYFaces = numYVertices*numYFaces;
607     const PetscInt numTotZFaces = numZVertices*numZFaces;
608     const PetscInt numFaces     = numTotXFaces + numTotYFaces + numTotZFaces;
609     const PetscInt numTotXEdges = numXEdges*numYVertices*numZVertices;
610     const PetscInt numTotYEdges = numYEdges*numXVertices*numZVertices;
611     const PetscInt numTotZEdges = numZEdges*numXVertices*numYVertices;
612     const PetscInt numVertices  = numXVertices*numYVertices*numZVertices;
613     const PetscInt numEdges     = numTotXEdges + numTotYEdges + numTotZEdges;
614     const PetscInt firstVertex  = (dim == 2) ? numFaces : numCells;
615     const PetscInt firstXFace   = (dim == 2) ? 0 : numCells + numVertices;
616     const PetscInt firstYFace   = firstXFace + numTotXFaces;
617     const PetscInt firstZFace   = firstYFace + numTotYFaces;
618     const PetscInt firstXEdge   = numCells + numFaces + numVertices;
619     const PetscInt firstYEdge   = firstXEdge + numTotXEdges;
620     const PetscInt firstZEdge   = firstYEdge + numTotYEdges;
621     Vec            coordinates;
622     PetscSection   coordSection;
623     PetscScalar   *coords;
624     PetscInt       coordSize;
625     PetscInt       v, vx, vy, vz;
626     PetscInt       c, f, fx, fy, fz, e, ex, ey, ez;
627 
628     ierr = DMPlexSetChart(dm, 0, numCells+numFaces+numEdges+numVertices);CHKERRQ(ierr);
629     for (c = 0; c < numCells; c++) {
630       ierr = DMPlexSetConeSize(dm, c, 6);CHKERRQ(ierr);
631     }
632     for (f = firstXFace; f < firstXFace+numFaces; ++f) {
633       ierr = DMPlexSetConeSize(dm, f, 4);CHKERRQ(ierr);
634     }
635     for (e = firstXEdge; e < firstXEdge+numEdges; ++e) {
636       ierr = DMPlexSetConeSize(dm, e, 2);CHKERRQ(ierr);
637     }
638     ierr = DMSetUp(dm);CHKERRQ(ierr); /* Allocate space for cones */
639     /* Build cells */
640     for (fz = 0; fz < numZEdges; ++fz) {
641       for (fy = 0; fy < numYEdges; ++fy) {
642         for (fx = 0; fx < numXEdges; ++fx) {
643           PetscInt cell    = (fz*numYEdges + fy)*numXEdges + fx;
644           PetscInt faceB   = firstZFace + (fy*numXEdges+fx)*numZVertices +   fz;
645           PetscInt faceT   = firstZFace + (fy*numXEdges+fx)*numZVertices + ((fz+1)%numZVertices);
646           PetscInt faceF   = firstYFace + (fz*numXEdges+fx)*numYVertices +   fy;
647           PetscInt faceK   = firstYFace + (fz*numXEdges+fx)*numYVertices + ((fy+1)%numYVertices);
648           PetscInt faceL   = firstXFace + (fz*numYEdges+fy)*numXVertices +   fx;
649           PetscInt faceR   = firstXFace + (fz*numYEdges+fy)*numXVertices + ((fx+1)%numXVertices);
650                             /* B,  T,  F,  K,  R,  L */
651           PetscInt ornt[6] = {-4,  0,  0, -1,  0, -4}; /* ??? */
652           PetscInt cone[6];
653 
654           /* no boundary twisting in 3D */
655           cone[0] = faceB; cone[1] = faceT; cone[2] = faceF; cone[3] = faceK; cone[4] = faceR; cone[5] = faceL;
656           ierr    = DMPlexSetCone(dm, cell, cone);CHKERRQ(ierr);
657           ierr    = DMPlexSetConeOrientation(dm, cell, ornt);CHKERRQ(ierr);
658           if (bdX != DM_BOUNDARY_NONE && fx == numXEdges-1 && cutLabel) {ierr = DMLabelSetValue(cutLabel, cell, 2);CHKERRQ(ierr);}
659           if (bdY != DM_BOUNDARY_NONE && fy == numYEdges-1 && cutLabel) {ierr = DMLabelSetValue(cutLabel, cell, 2);CHKERRQ(ierr);}
660           if (bdZ != DM_BOUNDARY_NONE && fz == numZEdges-1 && cutLabel) {ierr = DMLabelSetValue(cutLabel, cell, 2);CHKERRQ(ierr);}
661         }
662       }
663     }
664     /* Build x faces */
665     for (fz = 0; fz < numZEdges; ++fz) {
666       for (fy = 0; fy < numYEdges; ++fy) {
667         for (fx = 0; fx < numXVertices; ++fx) {
668           PetscInt face    = firstXFace + (fz*numYEdges+fy)*numXVertices + fx;
669           PetscInt edgeL   = firstZEdge + (  fy*                 numXVertices+fx)*numZEdges + fz;
670           PetscInt edgeR   = firstZEdge + (((fy+1)%numYVertices)*numXVertices+fx)*numZEdges + fz;
671           PetscInt edgeB   = firstYEdge + (  fz*                 numXVertices+fx)*numYEdges + fy;
672           PetscInt edgeT   = firstYEdge + (((fz+1)%numZVertices)*numXVertices+fx)*numYEdges + fy;
673           PetscInt ornt[4] = {0, 0, -2, -2};
674           PetscInt cone[4];
675 
676           if (dim == 3) {
677             /* markers */
678             if (bdX != DM_BOUNDARY_PERIODIC) {
679               if (fx == numXVertices-1) {
680                 ierr = DMSetLabelValue(dm, "Face Sets", face, faceMarkerRight);CHKERRQ(ierr);
681                 ierr = DMSetLabelValue(dm, "marker", face, markerRight);CHKERRQ(ierr);
682               }
683               else if (fx == 0) {
684                 ierr = DMSetLabelValue(dm, "Face Sets", face, faceMarkerLeft);CHKERRQ(ierr);
685                 ierr = DMSetLabelValue(dm, "marker", face, markerLeft);CHKERRQ(ierr);
686               }
687             }
688           }
689           cone[0] = edgeB; cone[1] = edgeR; cone[2] = edgeT; cone[3] = edgeL;
690           ierr    = DMPlexSetCone(dm, face, cone);CHKERRQ(ierr);
691           ierr    = DMPlexSetConeOrientation(dm, face, ornt);CHKERRQ(ierr);
692         }
693       }
694     }
695     /* Build y faces */
696     for (fz = 0; fz < numZEdges; ++fz) {
697       for (fx = 0; fx < numXEdges; ++fx) {
698         for (fy = 0; fy < numYVertices; ++fy) {
699           PetscInt face    = firstYFace + (fz*numXEdges+fx)*numYVertices + fy;
700           PetscInt edgeL   = firstZEdge + (fy*numXVertices+  fx                 )*numZEdges + fz;
701           PetscInt edgeR   = firstZEdge + (fy*numXVertices+((fx+1)%numXVertices))*numZEdges + fz;
702           PetscInt edgeB   = firstXEdge + (  fz                 *numYVertices+fy)*numXEdges + fx;
703           PetscInt edgeT   = firstXEdge + (((fz+1)%numZVertices)*numYVertices+fy)*numXEdges + fx;
704           PetscInt ornt[4] = {0, 0, -2, -2};
705           PetscInt cone[4];
706 
707           if (dim == 3) {
708             /* markers */
709             if (bdY != DM_BOUNDARY_PERIODIC) {
710               if (fy == numYVertices-1) {
711                 ierr = DMSetLabelValue(dm, "Face Sets", face, faceMarkerBack);CHKERRQ(ierr);
712                 ierr = DMSetLabelValue(dm, "marker", face, markerBack);CHKERRQ(ierr);
713               }
714               else if (fy == 0) {
715                 ierr = DMSetLabelValue(dm, "Face Sets", face, faceMarkerFront);CHKERRQ(ierr);
716                 ierr = DMSetLabelValue(dm, "marker", face, markerFront);CHKERRQ(ierr);
717               }
718             }
719           }
720           cone[0] = edgeB; cone[1] = edgeR; cone[2] = edgeT; cone[3] = edgeL;
721           ierr    = DMPlexSetCone(dm, face, cone);CHKERRQ(ierr);
722           ierr    = DMPlexSetConeOrientation(dm, face, ornt);CHKERRQ(ierr);
723         }
724       }
725     }
726     /* Build z faces */
727     for (fy = 0; fy < numYEdges; ++fy) {
728       for (fx = 0; fx < numXEdges; ++fx) {
729         for (fz = 0; fz < numZVertices; fz++) {
730           PetscInt face    = firstZFace + (fy*numXEdges+fx)*numZVertices + fz;
731           PetscInt edgeL   = firstYEdge + (fz*numXVertices+  fx                 )*numYEdges + fy;
732           PetscInt edgeR   = firstYEdge + (fz*numXVertices+((fx+1)%numXVertices))*numYEdges + fy;
733           PetscInt edgeB   = firstXEdge + (fz*numYVertices+  fy                 )*numXEdges + fx;
734           PetscInt edgeT   = firstXEdge + (fz*numYVertices+((fy+1)%numYVertices))*numXEdges + fx;
735           PetscInt ornt[4] = {0, 0, -2, -2};
736           PetscInt cone[4];
737 
738           if (dim == 2) {
739             if (bdX == DM_BOUNDARY_TWIST && fx == numXEdges-1) {edgeR += numYEdges-1-2*fy; ornt[1] = -2;}
740             if (bdY == DM_BOUNDARY_TWIST && fy == numYEdges-1) {edgeT += numXEdges-1-2*fx; ornt[2] =  0;}
741             if (bdX != DM_BOUNDARY_NONE && fx == numXEdges-1 && cutLabel) {ierr = DMLabelSetValue(cutLabel, face, 2);CHKERRQ(ierr);}
742             if (bdY != DM_BOUNDARY_NONE && fy == numYEdges-1 && cutLabel) {ierr = DMLabelSetValue(cutLabel, face, 2);CHKERRQ(ierr);}
743           } else {
744             /* markers */
745             if (bdZ != DM_BOUNDARY_PERIODIC) {
746               if (fz == numZVertices-1) {
747                 ierr = DMSetLabelValue(dm, "Face Sets", face, faceMarkerTop);CHKERRQ(ierr);
748                 ierr = DMSetLabelValue(dm, "marker", face, markerTop);CHKERRQ(ierr);
749               }
750               else if (fz == 0) {
751                 ierr = DMSetLabelValue(dm, "Face Sets", face, faceMarkerBottom);CHKERRQ(ierr);
752                 ierr = DMSetLabelValue(dm, "marker", face, markerBottom);CHKERRQ(ierr);
753               }
754             }
755           }
756           cone[0] = edgeB; cone[1] = edgeR; cone[2] = edgeT; cone[3] = edgeL;
757           ierr    = DMPlexSetCone(dm, face, cone);CHKERRQ(ierr);
758           ierr    = DMPlexSetConeOrientation(dm, face, ornt);CHKERRQ(ierr);
759         }
760       }
761     }
762     /* Build Z edges*/
763     for (vy = 0; vy < numYVertices; vy++) {
764       for (vx = 0; vx < numXVertices; vx++) {
765         for (ez = 0; ez < numZEdges; ez++) {
766           const PetscInt edge    = firstZEdge  + (vy*numXVertices+vx)*numZEdges + ez;
767           const PetscInt vertexB = firstVertex + (  ez                 *numYVertices+vy)*numXVertices + vx;
768           const PetscInt vertexT = firstVertex + (((ez+1)%numZVertices)*numYVertices+vy)*numXVertices + vx;
769           PetscInt       cone[2];
770 
771           if (dim == 3) {
772             if (bdX != DM_BOUNDARY_PERIODIC) {
773               if (vx == numXVertices-1) {
774                 ierr = DMSetLabelValue(dm, "marker", edge, markerRight);CHKERRQ(ierr);
775               }
776               else if (vx == 0) {
777                 ierr = DMSetLabelValue(dm, "marker", edge, markerLeft);CHKERRQ(ierr);
778               }
779             }
780             if (bdY != DM_BOUNDARY_PERIODIC) {
781               if (vy == numYVertices-1) {
782                 ierr = DMSetLabelValue(dm, "marker", edge, markerBack);CHKERRQ(ierr);
783               }
784               else if (vy == 0) {
785                 ierr = DMSetLabelValue(dm, "marker", edge, markerFront);CHKERRQ(ierr);
786               }
787             }
788           }
789           cone[0] = vertexB; cone[1] = vertexT;
790           ierr = DMPlexSetCone(dm, edge, cone);CHKERRQ(ierr);
791         }
792       }
793     }
794     /* Build Y edges*/
795     for (vz = 0; vz < numZVertices; vz++) {
796       for (vx = 0; vx < numXVertices; vx++) {
797         for (ey = 0; ey < numYEdges; ey++) {
798           const PetscInt nextv   = (dim == 2 && bdY == DM_BOUNDARY_TWIST && ey == numYEdges-1) ? (numXVertices-vx-1) : (vz*numYVertices+((ey+1)%numYVertices))*numXVertices + vx;
799           const PetscInt edge    = firstYEdge  + (vz*numXVertices+vx)*numYEdges + ey;
800           const PetscInt vertexF = firstVertex + (vz*numYVertices+ey)*numXVertices + vx;
801           const PetscInt vertexK = firstVertex + nextv;
802           PetscInt       cone[2];
803 
804           cone[0] = vertexF; cone[1] = vertexK;
805           ierr = DMPlexSetCone(dm, edge, cone);CHKERRQ(ierr);
806           if (dim == 2) {
807             if ((bdX != DM_BOUNDARY_PERIODIC) && (bdX != DM_BOUNDARY_TWIST)) {
808               if (vx == numXVertices-1) {
809                 ierr = DMSetLabelValue(dm, "Face Sets", edge, faceMarkerRight);CHKERRQ(ierr);
810                 ierr = DMSetLabelValue(dm, "marker", edge,    markerRight);CHKERRQ(ierr);
811                 ierr = DMSetLabelValue(dm, "marker", cone[0], markerRight);CHKERRQ(ierr);
812                 if (ey == numYEdges-1) {
813                   ierr = DMSetLabelValue(dm, "marker", cone[1], markerRight);CHKERRQ(ierr);
814                 }
815               } else if (vx == 0) {
816                 ierr = DMSetLabelValue(dm, "Face Sets", edge, faceMarkerLeft);CHKERRQ(ierr);
817                 ierr = DMSetLabelValue(dm, "marker", edge,    markerLeft);CHKERRQ(ierr);
818                 ierr = DMSetLabelValue(dm, "marker", cone[0], markerLeft);CHKERRQ(ierr);
819                 if (ey == numYEdges-1) {
820                   ierr = DMSetLabelValue(dm, "marker", cone[1], markerLeft);CHKERRQ(ierr);
821                 }
822               }
823             } else {
824               if (vx == 0 && cutLabel) {
825                 ierr = DMLabelSetValue(cutLabel, edge,    1);CHKERRQ(ierr);
826                 ierr = DMLabelSetValue(cutLabel, cone[0], 1);CHKERRQ(ierr);
827                 if (ey == numYEdges-1) {
828                   ierr = DMLabelSetValue(cutLabel, cone[1], 1);CHKERRQ(ierr);
829                 }
830               }
831             }
832           } else {
833             if (bdX != DM_BOUNDARY_PERIODIC) {
834               if (vx == numXVertices-1) {
835                 ierr = DMSetLabelValue(dm, "marker", edge, markerRight);CHKERRQ(ierr);
836               } else if (vx == 0) {
837                 ierr = DMSetLabelValue(dm, "marker", edge, markerLeft);CHKERRQ(ierr);
838               }
839             }
840             if (bdZ != DM_BOUNDARY_PERIODIC) {
841               if (vz == numZVertices-1) {
842                 ierr = DMSetLabelValue(dm, "marker", edge, markerTop);CHKERRQ(ierr);
843               } else if (vz == 0) {
844                 ierr = DMSetLabelValue(dm, "marker", edge, markerBottom);CHKERRQ(ierr);
845               }
846             }
847           }
848         }
849       }
850     }
851     /* Build X edges*/
852     for (vz = 0; vz < numZVertices; vz++) {
853       for (vy = 0; vy < numYVertices; vy++) {
854         for (ex = 0; ex < numXEdges; ex++) {
855           const PetscInt nextv   = (dim == 2 && bdX == DM_BOUNDARY_TWIST && ex == numXEdges-1) ? (numYVertices-vy-1)*numXVertices : (vz*numYVertices+vy)*numXVertices + (ex+1)%numXVertices;
856           const PetscInt edge    = firstXEdge  + (vz*numYVertices+vy)*numXEdges + ex;
857           const PetscInt vertexL = firstVertex + (vz*numYVertices+vy)*numXVertices + ex;
858           const PetscInt vertexR = firstVertex + nextv;
859           PetscInt       cone[2];
860 
861           cone[0] = vertexL; cone[1] = vertexR;
862           ierr = DMPlexSetCone(dm, edge, cone);CHKERRQ(ierr);
863           if (dim == 2) {
864             if ((bdY != DM_BOUNDARY_PERIODIC) && (bdY != DM_BOUNDARY_TWIST)) {
865               if (vy == numYVertices-1) {
866                 ierr = DMSetLabelValue(dm, "Face Sets", edge, faceMarkerTop);CHKERRQ(ierr);
867                 ierr = DMSetLabelValue(dm, "marker", edge,    markerTop);CHKERRQ(ierr);
868                 ierr = DMSetLabelValue(dm, "marker", cone[0], markerTop);CHKERRQ(ierr);
869                 if (ex == numXEdges-1) {
870                   ierr = DMSetLabelValue(dm, "marker", cone[1], markerTop);CHKERRQ(ierr);
871                 }
872               } else if (vy == 0) {
873                 ierr = DMSetLabelValue(dm, "Face Sets", edge, faceMarkerBottom);CHKERRQ(ierr);
874                 ierr = DMSetLabelValue(dm, "marker", edge,    markerBottom);CHKERRQ(ierr);
875                 ierr = DMSetLabelValue(dm, "marker", cone[0], markerBottom);CHKERRQ(ierr);
876                 if (ex == numXEdges-1) {
877                   ierr = DMSetLabelValue(dm, "marker", cone[1], markerBottom);CHKERRQ(ierr);
878                 }
879               }
880             } else {
881               if (vy == 0 && cutLabel) {
882                 ierr = DMLabelSetValue(cutLabel, edge,    1);CHKERRQ(ierr);
883                 ierr = DMLabelSetValue(cutLabel, cone[0], 1);CHKERRQ(ierr);
884                 if (ex == numXEdges-1) {
885                   ierr = DMLabelSetValue(cutLabel, cone[1], 1);CHKERRQ(ierr);
886                 }
887               }
888             }
889           } else {
890             if (bdY != DM_BOUNDARY_PERIODIC) {
891               if (vy == numYVertices-1) {
892                 ierr = DMSetLabelValue(dm, "marker", edge, markerBack);CHKERRQ(ierr);
893               }
894               else if (vy == 0) {
895                 ierr = DMSetLabelValue(dm, "marker", edge, markerFront);CHKERRQ(ierr);
896               }
897             }
898             if (bdZ != DM_BOUNDARY_PERIODIC) {
899               if (vz == numZVertices-1) {
900                 ierr = DMSetLabelValue(dm, "marker", edge, markerTop);CHKERRQ(ierr);
901               }
902               else if (vz == 0) {
903                 ierr = DMSetLabelValue(dm, "marker", edge, markerBottom);CHKERRQ(ierr);
904               }
905             }
906           }
907         }
908       }
909     }
910     ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
911     ierr = DMPlexStratify(dm);CHKERRQ(ierr);
912     /* Build coordinates */
913     ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
914     ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
915     ierr = PetscSectionSetFieldComponents(coordSection, 0, dim);CHKERRQ(ierr);
916     ierr = PetscSectionSetChart(coordSection, firstVertex, firstVertex+numVertices);CHKERRQ(ierr);
917     for (v = firstVertex; v < firstVertex+numVertices; ++v) {
918       ierr = PetscSectionSetDof(coordSection, v, dim);CHKERRQ(ierr);
919       ierr = PetscSectionSetFieldDof(coordSection, v, 0, dim);CHKERRQ(ierr);
920     }
921     ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
922     ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
923     ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
924     ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
925     ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
926     ierr = VecSetBlockSize(coordinates, dim);CHKERRQ(ierr);
927     ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
928     ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
929     for (vz = 0; vz < numZVertices; ++vz) {
930       for (vy = 0; vy < numYVertices; ++vy) {
931         for (vx = 0; vx < numXVertices; ++vx) {
932           coords[((vz*numYVertices+vy)*numXVertices+vx)*dim+0] = lower[0] + ((upper[0] - lower[0])/numXEdges)*vx;
933           coords[((vz*numYVertices+vy)*numXVertices+vx)*dim+1] = lower[1] + ((upper[1] - lower[1])/numYEdges)*vy;
934           if (dim == 3) {
935             coords[((vz*numYVertices+vy)*numXVertices+vx)*dim+2] = lower[2] + ((upper[2] - lower[2])/numZEdges)*vz;
936           }
937         }
938       }
939     }
940     ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
941     ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
942     ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
943   }
944   PetscFunctionReturn(0);
945 }
946 
947 static PetscErrorCode DMPlexCreateBoxMesh_Tensor_Internal(MPI_Comm comm, PetscInt dim, const PetscInt faces[], const PetscReal lower[], const PetscReal upper[], const DMBoundaryType periodicity[], PetscBool interpolate, DM *dm)
948 {
949   PetscInt       i;
950   PetscErrorCode ierr;
951 
952   PetscFunctionBegin;
953   PetscValidPointer(dm, 7);
954   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
955   PetscValidLogicalCollectiveInt(*dm,dim,2);
956   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
957   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
958   switch (dim) {
959   case 2: {ierr = DMPlexCreateCubeMesh_Internal(*dm, lower, upper, faces, periodicity[0], periodicity[1], DM_BOUNDARY_NONE);CHKERRQ(ierr);break;}
960   case 3: {ierr = DMPlexCreateCubeMesh_Internal(*dm, lower, upper, faces, periodicity[0], periodicity[1], periodicity[2]);CHKERRQ(ierr);break;}
961   default: SETERRQ1(comm, PETSC_ERR_SUP, "Dimension not supported: %d", dim);
962   }
963   if (periodicity[0] == DM_BOUNDARY_PERIODIC || periodicity[0] == DM_BOUNDARY_TWIST ||
964       periodicity[1] == DM_BOUNDARY_PERIODIC || periodicity[1] == DM_BOUNDARY_TWIST ||
965       (dim > 2 && (periodicity[2] == DM_BOUNDARY_PERIODIC || periodicity[2] == DM_BOUNDARY_TWIST))) {
966     PetscReal L[3];
967     PetscReal maxCell[3];
968 
969     for (i = 0; i < dim; i++) {
970       L[i]       = upper[i] - lower[i];
971       maxCell[i] = 1.1 * (L[i] / PetscMax(1,faces[i]));
972     }
973     ierr = DMSetPeriodicity(*dm,PETSC_TRUE,maxCell,L,periodicity);CHKERRQ(ierr);
974   }
975   if (!interpolate) {
976     DM udm;
977 
978     ierr = DMPlexUninterpolate(*dm, &udm);CHKERRQ(ierr);
979     ierr = DMPlexCopyCoordinates(*dm, udm);CHKERRQ(ierr);
980     ierr = DMDestroy(dm);CHKERRQ(ierr);
981     *dm  = udm;
982   }
983   PetscFunctionReturn(0);
984 }
985 
986 /*@C
987   DMPlexCreateBoxMesh - Creates a mesh on the tensor product of unit intervals (box) using simplices or tensor cells (hexahedra).
988 
989   Collective
990 
991   Input Parameters:
992 + comm        - The communicator for the DM object
993 . dim         - The spatial dimension
994 . simplex     - PETSC_TRUE for simplices, PETSC_FALSE for tensor cells
995 . faces       - Number of faces per dimension, or NULL for (1,) in 1D and (2, 2) in 2D and (1, 1, 1) in 3D
996 . lower       - The lower left corner, or NULL for (0, 0, 0)
997 . upper       - The upper right corner, or NULL for (1, 1, 1)
998 . periodicity - The boundary type for the X,Y,Z direction, or NULL for DM_BOUNDARY_NONE
999 - interpolate - Flag to create intermediate mesh pieces (edges, faces)
1000 
1001   Output Parameter:
1002 . dm  - The DM object
1003 
1004   Options Database Keys:
1005 + -dm_plex_box_lower <x,y,z> - Specify lower-left-bottom coordinates for the box
1006 . -dm_plex_box_upper <x,y,z> - Specify upper-right-top coordinates for the box
1007 - -dm_plex_box_faces <m,n,p> - Number of faces in each linear direction
1008 
1009   Notes:
1010   The options database keys above take lists of length d in d dimensions.
1011 
1012   Here is the numbering returned for 2 faces in each direction for tensor cells:
1013 $ 10---17---11---18----12
1014 $  |         |         |
1015 $  |         |         |
1016 $ 20    2   22    3    24
1017 $  |         |         |
1018 $  |         |         |
1019 $  7---15----8---16----9
1020 $  |         |         |
1021 $  |         |         |
1022 $ 19    0   21    1   23
1023 $  |         |         |
1024 $  |         |         |
1025 $  4---13----5---14----6
1026 
1027 and for simplicial cells
1028 
1029 $ 14----8---15----9----16
1030 $  |\     5  |\      7 |
1031 $  | \       | \       |
1032 $ 13   2    14    3    15
1033 $  | 4   \   | 6   \   |
1034 $  |       \ |       \ |
1035 $ 11----6---12----7----13
1036 $  |\        |\        |
1037 $  | \    1  | \     3 |
1038 $ 10   0    11    1    12
1039 $  | 0   \   | 2   \   |
1040 $  |       \ |       \ |
1041 $  8----4----9----5----10
1042 
1043   Level: beginner
1044 
1045 .seealso: DMPlexCreateFromFile(), DMPlexCreateHexCylinderMesh(), DMSetType(), DMCreate()
1046 @*/
1047 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)
1048 {
1049   PetscInt       fac[3] = {0, 0, 0};
1050   PetscReal      low[3] = {0, 0, 0};
1051   PetscReal      upp[3] = {1, 1, 1};
1052   DMBoundaryType bdt[3] = {DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE};
1053   PetscInt       i, n;
1054   PetscBool      flg;
1055   PetscErrorCode ierr;
1056 
1057   PetscFunctionBegin;
1058   n    = 3;
1059   ierr = PetscOptionsGetIntArray(NULL, NULL, "-dm_plex_box_faces", fac, &n, &flg);CHKERRQ(ierr);
1060   for (i = 0; i < dim; ++i) fac[i] = faces ? faces[i] : (flg && i < n ? fac[i] : (dim == 1 ? 1 : 4-dim));
1061   if (lower) for (i = 0; i < dim; ++i) low[i] = lower[i];
1062   if (upper) for (i = 0; i < dim; ++i) upp[i] = upper[i];
1063   if (periodicity) for (i = 0; i < dim; ++i) bdt[i] = periodicity[i];
1064   /* Allow bounds to be specified from the command line */
1065   n    = 3;
1066   ierr = PetscOptionsGetRealArray(NULL, NULL, "-dm_plex_box_lower", low, &n, &flg);CHKERRQ(ierr);
1067   if (flg && (n != dim)) SETERRQ2(comm, PETSC_ERR_ARG_SIZ, "Lower box point had %D values, should have been %D", n, dim);
1068   n    = 3;
1069   ierr = PetscOptionsGetRealArray(NULL, NULL, "-dm_plex_box_upper", upp, &n, &flg);CHKERRQ(ierr);
1070   if (flg && (n != dim)) SETERRQ2(comm, PETSC_ERR_ARG_SIZ, "Upper box point had %D values, should have been %D", n, dim);
1071 
1072   if (dim == 1)      {ierr = DMPlexCreateLineMesh_Internal(comm, fac[0], low[0], upp[0], bdt[0], dm);CHKERRQ(ierr);}
1073   else if (simplex)  {ierr = DMPlexCreateBoxMesh_Simplex_Internal(comm, dim, fac, low, upp, bdt, interpolate, dm);CHKERRQ(ierr);}
1074   else               {ierr = DMPlexCreateBoxMesh_Tensor_Internal(comm, dim, fac, low, upp, bdt, interpolate, dm);CHKERRQ(ierr);}
1075   PetscFunctionReturn(0);
1076 }
1077 
1078 /*@
1079   DMPlexCreateWedgeBoxMesh - Creates a 3-D mesh tesselating the (x,y) plane and extruding in the third direction using wedge cells.
1080 
1081   Collective
1082 
1083   Input Parameters:
1084 + comm        - The communicator for the DM object
1085 . faces       - Number of faces per dimension, or NULL for (1, 1, 1)
1086 . lower       - The lower left corner, or NULL for (0, 0, 0)
1087 . upper       - The upper right corner, or NULL for (1, 1, 1)
1088 . periodicity - The boundary type for the X,Y,Z direction, or NULL for DM_BOUNDARY_NONE
1089 . orderHeight - If PETSC_TRUE, orders the extruded cells in the height first. Otherwise, orders the cell on the layers first
1090 - interpolate - Flag to create intermediate mesh pieces (edges, faces)
1091 
1092   Output Parameter:
1093 . dm  - The DM object
1094 
1095   Level: beginner
1096 
1097 .seealso: DMPlexCreateHexCylinderMesh(), DMPlexCreateWedgeCylinderMesh(), DMPlexExtrude(), DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
1098 @*/
1099 PetscErrorCode DMPlexCreateWedgeBoxMesh(MPI_Comm comm, const PetscInt faces[], const PetscReal lower[], const PetscReal upper[], const DMBoundaryType periodicity[], PetscBool orderHeight, PetscBool interpolate, DM *dm)
1100 {
1101   DM             bdm, botdm;
1102   PetscInt       i;
1103   PetscInt       fac[3] = {0, 0, 0};
1104   PetscReal      low[3] = {0, 0, 0};
1105   PetscReal      upp[3] = {1, 1, 1};
1106   DMBoundaryType bdt[3] = {DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE};
1107   PetscErrorCode ierr;
1108 
1109   PetscFunctionBegin;
1110   for (i = 0; i < 3; ++i) fac[i] = faces ? (faces[i] > 0 ? faces[i] : 1) : 1;
1111   if (lower) for (i = 0; i < 3; ++i) low[i] = lower[i];
1112   if (upper) for (i = 0; i < 3; ++i) upp[i] = upper[i];
1113   if (periodicity) for (i = 0; i < 3; ++i) bdt[i] = periodicity[i];
1114   for (i = 0; i < 3; ++i) if (bdt[i] != DM_BOUNDARY_NONE) SETERRQ(comm, PETSC_ERR_SUP, "Periodicity not yet supported");
1115 
1116   ierr = DMCreate(comm, &bdm);CHKERRQ(ierr);
1117   ierr = DMSetType(bdm, DMPLEX);CHKERRQ(ierr);
1118   ierr = DMSetDimension(bdm, 1);CHKERRQ(ierr);
1119   ierr = DMSetCoordinateDim(bdm, 2);CHKERRQ(ierr);
1120   ierr = DMPlexCreateSquareBoundary(bdm, low, upp, fac);CHKERRQ(ierr);
1121   ierr = DMPlexGenerate(bdm, NULL, PETSC_FALSE, &botdm);CHKERRQ(ierr);
1122   ierr = DMDestroy(&bdm);CHKERRQ(ierr);
1123   ierr = DMPlexExtrude(botdm, fac[2], upp[2] - low[2], orderHeight, NULL, interpolate, dm);CHKERRQ(ierr);
1124   if (low[2] != 0.0) {
1125     Vec         v;
1126     PetscScalar *x;
1127     PetscInt    cDim, n;
1128 
1129     ierr = DMGetCoordinatesLocal(*dm, &v);CHKERRQ(ierr);
1130     ierr = VecGetBlockSize(v, &cDim);CHKERRQ(ierr);
1131     ierr = VecGetLocalSize(v, &n);CHKERRQ(ierr);
1132     ierr = VecGetArray(v, &x);CHKERRQ(ierr);
1133     x   += cDim;
1134     for (i=0; i<n; i+=cDim) x[i] += low[2];
1135     ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
1136     ierr = DMSetCoordinatesLocal(*dm, v);CHKERRQ(ierr);
1137   }
1138   ierr = DMDestroy(&botdm);CHKERRQ(ierr);
1139   PetscFunctionReturn(0);
1140 }
1141 
1142 /*@C
1143   DMPlexExtrude - Creates a (d+1)-D mesh by extruding a d-D mesh in the normal direction using prismatic cells.
1144 
1145   Collective on idm
1146 
1147   Input Parameters:
1148 + idm         - The mesh to be extruded
1149 . layers      - The number of layers, or PETSC_DETERMINE to use the default
1150 . height      - The height of the extruded layer, or PETSC_DETERMINE to use the default
1151 . orderHeight - If PETSC_TRUE, orders the extruded cells in the height first. Otherwise, orders the cell on the layers first
1152 . extNormal   - The normal direction in which the mesh should be extruded, or NULL to extrude using the surface normal
1153 - interpolate - Flag to create intermediate mesh pieces (edges, faces)
1154 
1155   Output Parameter:
1156 . dm  - The DM object
1157 
1158   Notes:
1159   The mesh created has prismatic cells, and the vertex ordering in the cone of the cell is that of the tensor prismatic cells. Not currently supported in Fortran.
1160 
1161   Options Database Keys:
1162 -dm_plex_extrude_layers <k> - Sets the nubmer of layers k
1163 -dm_plex_extrude_height <h> - Sets the height h of each layer
1164 -dm_plex_extrude_order_height - If true, order cells by height first
1165 -dm_plex_extrude_normal <n0,...,nd> - Sets the normal vector along which to extrude
1166 
1167   Level: advanced
1168 
1169 .seealso: DMPlexCreateWedgeCylinderMesh(), DMPlexCreateWedgeBoxMesh(), DMSetType(), DMCreate()
1170 @*/
1171 PetscErrorCode DMPlexExtrude(DM idm, PetscInt layers, PetscReal height, PetscBool orderHeight, const PetscReal extNormal[], PetscBool interpolate, DM* dm)
1172 {
1173   PetscScalar       *coordsB;
1174   const PetscScalar *coordsA;
1175   PetscReal         *normals = NULL;
1176   PetscReal         clNormal[3];
1177   Vec               coordinatesA, coordinatesB;
1178   PetscSection      coordSectionA, coordSectionB;
1179   PetscInt          dim, cDim, cDimB, c, l, v, coordSize, *newCone;
1180   PetscInt          cStart, cEnd, vStart, vEnd, cellV, numCells, numVertices;
1181   const char       *prefix;
1182   PetscBool         haveCLNormal;
1183   PetscErrorCode    ierr;
1184 
1185   PetscFunctionBegin;
1186   PetscValidHeaderSpecific(idm, DM_CLASSID, 1);
1187   PetscValidLogicalCollectiveInt(idm, layers, 2);
1188   PetscValidLogicalCollectiveReal(idm, height, 3);
1189   PetscValidLogicalCollectiveBool(idm, interpolate, 4);
1190   ierr = DMGetDimension(idm, &dim);CHKERRQ(ierr);
1191   ierr = DMGetCoordinateDim(idm, &cDim);CHKERRQ(ierr);
1192   cDimB = cDim == dim ? cDim+1 : cDim;
1193   if (dim < 1 || dim > 3) SETERRQ1(PetscObjectComm((PetscObject)idm), PETSC_ERR_SUP, "Support for dimension %D not coded", dim);
1194 
1195   ierr = PetscObjectGetOptionsPrefix((PetscObject) idm, &prefix);CHKERRQ(ierr);
1196   if (layers < 0) layers = 1;
1197   ierr = PetscOptionsGetInt(NULL, prefix, "-dm_plex_extrude_layers", &layers, NULL);CHKERRQ(ierr);
1198   if (layers <= 0) SETERRQ1(PetscObjectComm((PetscObject) idm), PETSC_ERR_ARG_OUTOFRANGE, "Number of layers %D must be positive", layers);
1199   if (height < 0.) height = 1.;
1200   ierr = PetscOptionsGetReal(NULL, prefix, "-dm_plex_extrude_height", &height, NULL);CHKERRQ(ierr);
1201   if (height <= 0.) SETERRQ1(PetscObjectComm((PetscObject) idm), PETSC_ERR_ARG_OUTOFRANGE, "Height of layers %g must be positive", (double) height);
1202   ierr = PetscOptionsGetBool(NULL, prefix, "-dm_plex_extrude_order_height", &orderHeight, NULL);CHKERRQ(ierr);
1203   c = 3;
1204   ierr = PetscOptionsGetRealArray(NULL, prefix, "-dm_plex_extrude_normal", clNormal, &c, &haveCLNormal);CHKERRQ(ierr);
1205   if (haveCLNormal && c != cDimB) SETERRQ2(PetscObjectComm((PetscObject)idm), PETSC_ERR_ARG_SIZ, "Input normal has size %D != %D extruded coordinate dimension", c, cDimB);
1206 
1207   ierr = DMPlexGetHeightStratum(idm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1208   ierr = DMPlexGetDepthStratum(idm, 0, &vStart, &vEnd);CHKERRQ(ierr);
1209   numCells = (cEnd - cStart)*layers;
1210   numVertices = (vEnd - vStart)*(layers+1);
1211   ierr = DMCreate(PetscObjectComm((PetscObject)idm), dm);CHKERRQ(ierr);
1212   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
1213   ierr = DMSetDimension(*dm, dim+1);CHKERRQ(ierr);
1214   ierr = DMPlexSetChart(*dm, 0, numCells+numVertices);CHKERRQ(ierr);
1215   /* Must create the celltype label here so that we do not automatically try to compute the types */
1216   ierr = DMCreateLabel(*dm, "celltype");CHKERRQ(ierr);
1217   for (c = cStart, cellV = 0; c < cEnd; ++c) {
1218     DMPolytopeType ct, nct;
1219     PetscInt      *closure = NULL;
1220     PetscInt       closureSize, numCorners = 0;
1221 
1222     ierr = DMPlexGetCellType(idm, c, &ct);CHKERRQ(ierr);
1223     switch (ct) {
1224       case DM_POLYTOPE_SEGMENT:       nct = DM_POLYTOPE_SEG_PRISM_TENSOR;break;
1225       case DM_POLYTOPE_TRIANGLE:      nct = DM_POLYTOPE_TRI_PRISM_TENSOR;break;
1226       case DM_POLYTOPE_QUADRILATERAL: nct = DM_POLYTOPE_QUAD_PRISM_TENSOR;break;
1227       default: nct = DM_POLYTOPE_UNKNOWN;
1228     }
1229     ierr = DMPlexGetTransitiveClosure(idm, c, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
1230     for (v = 0; v < closureSize*2; v += 2) if ((closure[v] >= vStart) && (closure[v] < vEnd)) numCorners++;
1231     ierr = DMPlexRestoreTransitiveClosure(idm, c, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
1232     for (l = 0; l < layers; ++l) {
1233       const PetscInt cell = orderHeight ? layers*(c - cStart) + l : l*(cEnd - cStart) + c - cStart;
1234 
1235       ierr = DMPlexSetConeSize(*dm, cell, 2*numCorners);CHKERRQ(ierr);
1236       ierr = DMPlexSetCellType(*dm, cell, nct);CHKERRQ(ierr);
1237     }
1238     cellV = PetscMax(numCorners,cellV);
1239   }
1240   ierr = DMSetUp(*dm);CHKERRQ(ierr);
1241 
1242   if (dim != cDim && !(extNormal || haveCLNormal)) {ierr = PetscCalloc1(cDim*(vEnd - vStart), &normals);CHKERRQ(ierr);}
1243   ierr = PetscMalloc1(3*cellV,&newCone);CHKERRQ(ierr);
1244   for (c = cStart; c < cEnd; ++c) {
1245     PetscInt *closure = NULL;
1246     PetscInt closureSize, numCorners = 0, l;
1247     PetscReal normal[3] = {0, 0, 0};
1248 
1249     if (normals) {ierr = DMPlexComputeCellGeometryFVM(idm, c, NULL, NULL, normal);CHKERRQ(ierr);}
1250     ierr = DMPlexGetTransitiveClosure(idm, c, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
1251     for (v = 0; v < closureSize*2; v += 2) {
1252       if ((closure[v] >= vStart) && (closure[v] < vEnd)) {
1253         PetscInt d;
1254 
1255         newCone[numCorners++] = closure[v] - vStart;
1256         if (normals) {for (d = 0; d < cDim; ++d) normals[cDim*(closure[v]-vStart)+d] += normal[d];}
1257       }
1258     }
1259     ierr = DMPlexRestoreTransitiveClosure(idm, c, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
1260     for (l = 0; l < layers; ++l) {
1261       PetscInt i;
1262 
1263       for (i = 0; i < numCorners; ++i) {
1264         newCone[  numCorners + i] = orderHeight ? (layers+1)*newCone[i] + l     + numCells :     l*(vEnd - vStart) + newCone[i] + numCells;
1265         newCone[2*numCorners + i] = orderHeight ? (layers+1)*newCone[i] + l + 1 + numCells : (l+1)*(vEnd - vStart) + newCone[i] + numCells;
1266       }
1267       ierr = DMPlexSetCone(*dm, orderHeight ? layers*(c - cStart) + l : l*(cEnd - cStart) + c - cStart, newCone + numCorners);CHKERRQ(ierr);
1268     }
1269   }
1270   ierr = DMPlexSymmetrize(*dm);CHKERRQ(ierr);
1271   ierr = DMPlexStratify(*dm);CHKERRQ(ierr);
1272   ierr = PetscFree(newCone);CHKERRQ(ierr);
1273 
1274   ierr = DMGetCoordinateSection(*dm, &coordSectionB);CHKERRQ(ierr);
1275   ierr = PetscSectionSetNumFields(coordSectionB, 1);CHKERRQ(ierr);
1276   ierr = PetscSectionSetFieldComponents(coordSectionB, 0, cDimB);CHKERRQ(ierr);
1277   ierr = PetscSectionSetChart(coordSectionB, numCells, numCells+numVertices);CHKERRQ(ierr);
1278   for (v = numCells; v < numCells+numVertices; ++v) {
1279     ierr = PetscSectionSetDof(coordSectionB, v, cDimB);CHKERRQ(ierr);
1280     ierr = PetscSectionSetFieldDof(coordSectionB, v, 0, cDimB);CHKERRQ(ierr);
1281     ierr = DMPlexSetCellType(*dm, v, DM_POLYTOPE_POINT);CHKERRQ(ierr);
1282   }
1283   ierr = PetscSectionSetUp(coordSectionB);CHKERRQ(ierr);
1284   ierr = PetscSectionGetStorageSize(coordSectionB, &coordSize);CHKERRQ(ierr);
1285   ierr = VecCreate(PETSC_COMM_SELF, &coordinatesB);CHKERRQ(ierr);
1286   ierr = PetscObjectSetName((PetscObject) coordinatesB, "coordinates");CHKERRQ(ierr);
1287   ierr = VecSetSizes(coordinatesB, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
1288   ierr = VecSetBlockSize(coordinatesB, cDimB);CHKERRQ(ierr);
1289   ierr = VecSetType(coordinatesB,VECSTANDARD);CHKERRQ(ierr);
1290 
1291   ierr = DMGetCoordinateSection(idm, &coordSectionA);CHKERRQ(ierr);
1292   ierr = DMGetCoordinatesLocal(idm, &coordinatesA);CHKERRQ(ierr);
1293   ierr = VecGetArray(coordinatesB, &coordsB);CHKERRQ(ierr);
1294   ierr = VecGetArrayRead(coordinatesA, &coordsA);CHKERRQ(ierr);
1295   for (v = vStart; v < vEnd; ++v) {
1296     const PetscScalar *cptr;
1297     PetscReal         ones2[2] = { 0., 1.}, ones3[3] = { 0., 0., 1.};
1298     PetscReal         normal[3];
1299     PetscReal         norm, h = height/layers;
1300     PetscInt          offA, d, cDimA = cDim;
1301 
1302     if (normals)           {for (d = 0; d < cDimB; ++d) normal[d] = normals[cDimB*(v - vStart)+d];}
1303     else if (haveCLNormal) {for (d = 0; d < cDimB; ++d) normal[d] = clNormal[d];}
1304     else if (extNormal)    {for (d = 0; d < cDimB; ++d) normal[d] = extNormal[d];}
1305     else if (cDimB == 2)   {for (d = 0; d < cDimB; ++d) normal[d] = ones2[d];}
1306     else if (cDimB == 3)   {for (d = 0; d < cDimB; ++d) normal[d] = ones3[d];}
1307     else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Unable to determine normal for extrusion");
1308     for (d = 0, norm = 0.0; d < cDimB; ++d) norm += normal[d]*normal[d];
1309     for (d = 0; d < cDimB; ++d) normal[d] *= 1./PetscSqrtReal(norm);
1310 
1311     ierr = PetscSectionGetOffset(coordSectionA, v, &offA);CHKERRQ(ierr);
1312     cptr = coordsA + offA;
1313     for (l = 0; l < layers+1; ++l) {
1314       PetscInt offB, d, newV;
1315 
1316       newV = orderHeight ? (layers+1)*(v -vStart) + l + numCells : (vEnd -vStart)*l + (v -vStart) + numCells;
1317       ierr = PetscSectionGetOffset(coordSectionB, newV, &offB);CHKERRQ(ierr);
1318       for (d = 0; d < cDimA; ++d) { coordsB[offB+d]  = cptr[d]; }
1319       for (d = 0; d < cDimB; ++d) { coordsB[offB+d] += l ? normal[d]*h : 0.0; }
1320       cptr    = coordsB + offB;
1321       cDimA   = cDimB;
1322     }
1323   }
1324   ierr = VecRestoreArrayRead(coordinatesA, &coordsA);CHKERRQ(ierr);
1325   ierr = VecRestoreArray(coordinatesB, &coordsB);CHKERRQ(ierr);
1326   ierr = DMSetCoordinatesLocal(*dm, coordinatesB);CHKERRQ(ierr);
1327   ierr = VecDestroy(&coordinatesB);CHKERRQ(ierr);
1328   ierr = PetscFree(normals);CHKERRQ(ierr);
1329   if (interpolate) {
1330     DM idm;
1331 
1332     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
1333     ierr = DMPlexCopyCoordinates(*dm, idm);CHKERRQ(ierr);
1334     ierr = DMDestroy(dm);CHKERRQ(ierr);
1335     *dm  = idm;
1336   }
1337   PetscFunctionReturn(0);
1338 }
1339 
1340 /*@C
1341   DMPlexSetOptionsPrefix - Sets the prefix used for searching for all DM options in the database.
1342 
1343   Logically Collective on dm
1344 
1345   Input Parameters:
1346 + dm - the DM context
1347 - prefix - the prefix to prepend to all option names
1348 
1349   Notes:
1350   A hyphen (-) must NOT be given at the beginning of the prefix name.
1351   The first character of all runtime options is AUTOMATICALLY the hyphen.
1352 
1353   Level: advanced
1354 
1355 .seealso: SNESSetFromOptions()
1356 @*/
1357 PetscErrorCode DMPlexSetOptionsPrefix(DM dm, const char prefix[])
1358 {
1359   DM_Plex       *mesh = (DM_Plex *) dm->data;
1360   PetscErrorCode ierr;
1361 
1362   PetscFunctionBegin;
1363   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1364   ierr = PetscObjectSetOptionsPrefix((PetscObject) dm, prefix);CHKERRQ(ierr);
1365   ierr = PetscObjectSetOptionsPrefix((PetscObject) mesh->partitioner, prefix);CHKERRQ(ierr);
1366   PetscFunctionReturn(0);
1367 }
1368 
1369 /*@
1370   DMPlexCreateHexCylinderMesh - Creates a mesh on the tensor product of the unit interval with the circle (cylinder) using hexahedra.
1371 
1372   Collective
1373 
1374   Input Parameters:
1375 + comm      - The communicator for the DM object
1376 . numRefine - The number of regular refinements to the basic 5 cell structure
1377 - periodicZ - The boundary type for the Z direction
1378 
1379   Output Parameter:
1380 . dm  - The DM object
1381 
1382   Note: Here is the output numbering looking from the bottom of the cylinder:
1383 $       17-----14
1384 $        |     |
1385 $        |  2  |
1386 $        |     |
1387 $ 17-----8-----7-----14
1388 $  |     |     |     |
1389 $  |  3  |  0  |  1  |
1390 $  |     |     |     |
1391 $ 19-----5-----6-----13
1392 $        |     |
1393 $        |  4  |
1394 $        |     |
1395 $       19-----13
1396 $
1397 $ and up through the top
1398 $
1399 $       18-----16
1400 $        |     |
1401 $        |  2  |
1402 $        |     |
1403 $ 18----10----11-----16
1404 $  |     |     |     |
1405 $  |  3  |  0  |  1  |
1406 $  |     |     |     |
1407 $ 20-----9----12-----15
1408 $        |     |
1409 $        |  4  |
1410 $        |     |
1411 $       20-----15
1412 
1413   Level: beginner
1414 
1415 .seealso: DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
1416 @*/
1417 PetscErrorCode DMPlexCreateHexCylinderMesh(MPI_Comm comm, PetscInt numRefine, DMBoundaryType periodicZ, DM *dm)
1418 {
1419   const PetscInt dim = 3;
1420   PetscInt       numCells, numVertices, r;
1421   PetscMPIInt    rank;
1422   PetscErrorCode ierr;
1423 
1424   PetscFunctionBegin;
1425   PetscValidPointer(dm, 4);
1426   ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
1427   if (numRefine < 0) SETERRQ1(comm, PETSC_ERR_ARG_OUTOFRANGE, "Number of refinements %D cannot be negative", numRefine);
1428   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
1429   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
1430   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
1431   /* Create topology */
1432   {
1433     PetscInt cone[8], c;
1434 
1435     numCells    = !rank ?  5 : 0;
1436     numVertices = !rank ? 16 : 0;
1437     if (periodicZ == DM_BOUNDARY_PERIODIC) {
1438       numCells   *= 3;
1439       numVertices = !rank ? 24 : 0;
1440     }
1441     ierr = DMPlexSetChart(*dm, 0, numCells+numVertices);CHKERRQ(ierr);
1442     for (c = 0; c < numCells; c++) {ierr = DMPlexSetConeSize(*dm, c, 8);CHKERRQ(ierr);}
1443     ierr = DMSetUp(*dm);CHKERRQ(ierr);
1444     if (!rank) {
1445       if (periodicZ == DM_BOUNDARY_PERIODIC) {
1446         cone[0] = 15; cone[1] = 18; cone[2] = 17; cone[3] = 16;
1447         cone[4] = 31; cone[5] = 32; cone[6] = 33; cone[7] = 34;
1448         ierr = DMPlexSetCone(*dm, 0, cone);CHKERRQ(ierr);
1449         cone[0] = 16; cone[1] = 17; cone[2] = 24; cone[3] = 23;
1450         cone[4] = 32; cone[5] = 36; cone[6] = 37; cone[7] = 33; /* 22 25 26 21 */
1451         ierr = DMPlexSetCone(*dm, 1, cone);CHKERRQ(ierr);
1452         cone[0] = 18; cone[1] = 27; cone[2] = 24; cone[3] = 17;
1453         cone[4] = 34; cone[5] = 33; cone[6] = 37; cone[7] = 38;
1454         ierr = DMPlexSetCone(*dm, 2, cone);CHKERRQ(ierr);
1455         cone[0] = 29; cone[1] = 27; cone[2] = 18; cone[3] = 15;
1456         cone[4] = 35; cone[5] = 31; cone[6] = 34; cone[7] = 38;
1457         ierr = DMPlexSetCone(*dm, 3, cone);CHKERRQ(ierr);
1458         cone[0] = 29; cone[1] = 15; cone[2] = 16; cone[3] = 23;
1459         cone[4] = 35; cone[5] = 36; cone[6] = 32; cone[7] = 31;
1460         ierr = DMPlexSetCone(*dm, 4, cone);CHKERRQ(ierr);
1461 
1462         cone[0] = 31; cone[1] = 34; cone[2] = 33; cone[3] = 32;
1463         cone[4] = 19; cone[5] = 22; cone[6] = 21; cone[7] = 20;
1464         ierr = DMPlexSetCone(*dm, 5, cone);CHKERRQ(ierr);
1465         cone[0] = 32; cone[1] = 33; cone[2] = 37; cone[3] = 36;
1466         cone[4] = 22; cone[5] = 25; cone[6] = 26; cone[7] = 21;
1467         ierr = DMPlexSetCone(*dm, 6, cone);CHKERRQ(ierr);
1468         cone[0] = 34; cone[1] = 38; cone[2] = 37; cone[3] = 33;
1469         cone[4] = 20; cone[5] = 21; cone[6] = 26; cone[7] = 28;
1470         ierr = DMPlexSetCone(*dm, 7, cone);CHKERRQ(ierr);
1471         cone[0] = 35; cone[1] = 38; cone[2] = 34; cone[3] = 31;
1472         cone[4] = 30; cone[5] = 19; cone[6] = 20; cone[7] = 28;
1473         ierr = DMPlexSetCone(*dm, 8, cone);CHKERRQ(ierr);
1474         cone[0] = 35; cone[1] = 31; cone[2] = 32; cone[3] = 36;
1475         cone[4] = 30; cone[5] = 25; cone[6] = 22; cone[7] = 19;
1476         ierr = DMPlexSetCone(*dm, 9, cone);CHKERRQ(ierr);
1477 
1478         cone[0] = 19; cone[1] = 20; cone[2] = 21; cone[3] = 22;
1479         cone[4] = 15; cone[5] = 16; cone[6] = 17; cone[7] = 18;
1480         ierr = DMPlexSetCone(*dm, 10, cone);CHKERRQ(ierr);
1481         cone[0] = 22; cone[1] = 21; cone[2] = 26; cone[3] = 25;
1482         cone[4] = 16; cone[5] = 23; cone[6] = 24; cone[7] = 17;
1483         ierr = DMPlexSetCone(*dm, 11, cone);CHKERRQ(ierr);
1484         cone[0] = 20; cone[1] = 28; cone[2] = 26; cone[3] = 21;
1485         cone[4] = 18; cone[5] = 17; cone[6] = 24; cone[7] = 27;
1486         ierr = DMPlexSetCone(*dm, 12, cone);CHKERRQ(ierr);
1487         cone[0] = 30; cone[1] = 28; cone[2] = 20; cone[3] = 19;
1488         cone[4] = 29; cone[5] = 15; cone[6] = 18; cone[7] = 27;
1489         ierr = DMPlexSetCone(*dm, 13, cone);CHKERRQ(ierr);
1490         cone[0] = 30; cone[1] = 19; cone[2] = 22; cone[3] = 25;
1491         cone[4] = 29; cone[5] = 23; cone[6] = 16; cone[7] = 15;
1492         ierr = DMPlexSetCone(*dm, 14, cone);CHKERRQ(ierr);
1493       } else {
1494         cone[0] =  5; cone[1] =  8; cone[2] =  7; cone[3] =  6;
1495         cone[4] =  9; cone[5] = 12; cone[6] = 11; cone[7] = 10;
1496         ierr = DMPlexSetCone(*dm, 0, cone);CHKERRQ(ierr);
1497         cone[0] =  6; cone[1] =  7; cone[2] = 14; cone[3] = 13;
1498         cone[4] = 12; cone[5] = 15; cone[6] = 16; cone[7] = 11;
1499         ierr = DMPlexSetCone(*dm, 1, cone);CHKERRQ(ierr);
1500         cone[0] =  8; cone[1] = 17; cone[2] = 14; cone[3] =  7;
1501         cone[4] = 10; cone[5] = 11; cone[6] = 16; cone[7] = 18;
1502         ierr = DMPlexSetCone(*dm, 2, cone);CHKERRQ(ierr);
1503         cone[0] = 19; cone[1] = 17; cone[2] =  8; cone[3] =  5;
1504         cone[4] = 20; cone[5] =  9; cone[6] = 10; cone[7] = 18;
1505         ierr = DMPlexSetCone(*dm, 3, cone);CHKERRQ(ierr);
1506         cone[0] = 19; cone[1] =  5; cone[2] =  6; cone[3] = 13;
1507         cone[4] = 20; cone[5] = 15; cone[6] = 12; cone[7] =  9;
1508         ierr = DMPlexSetCone(*dm, 4, cone);CHKERRQ(ierr);
1509       }
1510     }
1511     ierr = DMPlexSymmetrize(*dm);CHKERRQ(ierr);
1512     ierr = DMPlexStratify(*dm);CHKERRQ(ierr);
1513   }
1514   /* Interpolate */
1515   {
1516     DM idm;
1517 
1518     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
1519     ierr = DMDestroy(dm);CHKERRQ(ierr);
1520     *dm  = idm;
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) {
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   /* Refine topology */
1599   for (r = 0; r < numRefine; ++r) {
1600     DM rdm = NULL;
1601 
1602     ierr = DMRefine(*dm, comm, &rdm);CHKERRQ(ierr);
1603     ierr = DMDestroy(dm);CHKERRQ(ierr);
1604     *dm  = rdm;
1605   }
1606   /* Remap geometry to cylinder
1607        Interior square: Linear interpolation is correct
1608        The other cells all have vertices on rays from the origin. We want to uniformly expand the spacing
1609        such that the last vertex is on the unit circle. So the closest and farthest vertices are at distance
1610 
1611          phi     = arctan(y/x)
1612          d_close = sqrt(1/8 + 1/4 sin^2(phi))
1613          d_far   = sqrt(1/2 + sin^2(phi))
1614 
1615        so we remap them using
1616 
1617          x_new = x_close + (x - x_close) (1 - d_close) / (d_far - d_close)
1618          y_new = y_close + (y - y_close) (1 - d_close) / (d_far - d_close)
1619 
1620        If pi/4 < phi < 3pi/4 or -3pi/4 < phi < -pi/4, then we switch x and y.
1621   */
1622   {
1623     Vec           coordinates;
1624     PetscSection  coordSection;
1625     PetscScalar  *coords;
1626     PetscInt      vStart, vEnd, v;
1627     const PetscReal dis = 1.0/PetscSqrtReal(2.0);
1628     const PetscReal ds2 = 0.5*dis;
1629 
1630     ierr = DMPlexGetDepthStratum(*dm, 0, &vStart, &vEnd);CHKERRQ(ierr);
1631     ierr = DMGetCoordinateSection(*dm, &coordSection);CHKERRQ(ierr);
1632     ierr = DMGetCoordinatesLocal(*dm, &coordinates);CHKERRQ(ierr);
1633     ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
1634     for (v = vStart; v < vEnd; ++v) {
1635       PetscReal phi, sinp, cosp, dc, df, x, y, xc, yc;
1636       PetscInt  off;
1637 
1638       ierr = PetscSectionGetOffset(coordSection, v, &off);CHKERRQ(ierr);
1639       if ((PetscAbsScalar(coords[off+0]) <= ds2) && (PetscAbsScalar(coords[off+1]) <= ds2)) continue;
1640       x    = PetscRealPart(coords[off]);
1641       y    = PetscRealPart(coords[off+1]);
1642       phi  = PetscAtan2Real(y, x);
1643       sinp = PetscSinReal(phi);
1644       cosp = PetscCosReal(phi);
1645       if ((PetscAbsReal(phi) > PETSC_PI/4.0) && (PetscAbsReal(phi) < 3.0*PETSC_PI/4.0)) {
1646         dc = PetscAbsReal(ds2/sinp);
1647         df = PetscAbsReal(dis/sinp);
1648         xc = ds2*x/PetscAbsReal(y);
1649         yc = ds2*PetscSignReal(y);
1650       } else {
1651         dc = PetscAbsReal(ds2/cosp);
1652         df = PetscAbsReal(dis/cosp);
1653         xc = ds2*PetscSignReal(x);
1654         yc = ds2*y/PetscAbsReal(x);
1655       }
1656       coords[off+0] = xc + (coords[off+0] - xc)*(1.0 - dc)/(df - dc);
1657       coords[off+1] = yc + (coords[off+1] - yc)*(1.0 - dc)/(df - dc);
1658     }
1659     ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
1660     if (periodicZ == DM_BOUNDARY_PERIODIC || periodicZ == DM_BOUNDARY_TWIST) {
1661       ierr = DMLocalizeCoordinates(*dm);CHKERRQ(ierr);
1662     }
1663   }
1664   PetscFunctionReturn(0);
1665 }
1666 
1667 /*@
1668   DMPlexCreateWedgeCylinderMesh - Creates a mesh on the tensor product of the unit interval with the circle (cylinder) using wedges.
1669 
1670   Collective
1671 
1672   Input Parameters:
1673 + comm - The communicator for the DM object
1674 . n    - The number of wedges around the origin
1675 - interpolate - Create edges and faces
1676 
1677   Output Parameter:
1678 . dm  - The DM object
1679 
1680   Level: beginner
1681 
1682 .seealso: DMPlexCreateHexCylinderMesh(), DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
1683 @*/
1684 PetscErrorCode DMPlexCreateWedgeCylinderMesh(MPI_Comm comm, PetscInt n, PetscBool interpolate, DM *dm)
1685 {
1686   const PetscInt dim = 3;
1687   PetscInt       numCells, numVertices, v;
1688   PetscMPIInt    rank;
1689   PetscErrorCode ierr;
1690 
1691   PetscFunctionBegin;
1692   PetscValidPointer(dm, 3);
1693   ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
1694   if (n < 0) SETERRQ1(comm, PETSC_ERR_ARG_OUTOFRANGE, "Number of wedges %D cannot be negative", n);
1695   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
1696   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
1697   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
1698   /* Must create the celltype label here so that we do not automatically try to compute the types */
1699   ierr = DMCreateLabel(*dm, "celltype");CHKERRQ(ierr);
1700   /* Create topology */
1701   {
1702     PetscInt cone[6], c;
1703 
1704     numCells    = !rank ?        n : 0;
1705     numVertices = !rank ?  2*(n+1) : 0;
1706     ierr = DMPlexSetChart(*dm, 0, numCells+numVertices);CHKERRQ(ierr);
1707     for (c = 0; c < numCells; c++) {ierr = DMPlexSetConeSize(*dm, c, 6);CHKERRQ(ierr);}
1708     ierr = DMSetUp(*dm);CHKERRQ(ierr);
1709     for (c = 0; c < numCells; c++) {
1710       cone[0] =  c+n*1; cone[1] = (c+1)%n+n*1; cone[2] = 0+3*n;
1711       cone[3] =  c+n*2; cone[4] = (c+1)%n+n*2; cone[5] = 1+3*n;
1712       ierr = DMPlexSetCone(*dm, c, cone);CHKERRQ(ierr);
1713       ierr = DMPlexSetCellType(*dm, c, DM_POLYTOPE_TRI_PRISM_TENSOR);CHKERRQ(ierr);
1714     }
1715     ierr = DMPlexSymmetrize(*dm);CHKERRQ(ierr);
1716     ierr = DMPlexStratify(*dm);CHKERRQ(ierr);
1717   }
1718   for (v = numCells; v < numCells+numVertices; ++v) {
1719     ierr = DMPlexSetCellType(*dm, v, DM_POLYTOPE_POINT);CHKERRQ(ierr);
1720   }
1721   /* Interpolate */
1722   if (interpolate) {
1723     DM idm;
1724 
1725     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
1726     ierr = DMDestroy(dm);CHKERRQ(ierr);
1727     *dm  = idm;
1728   }
1729   /* Create cylinder geometry */
1730   {
1731     Vec          coordinates;
1732     PetscSection coordSection;
1733     PetscScalar *coords;
1734     PetscInt     coordSize, c;
1735 
1736     /* Build coordinates */
1737     ierr = DMGetCoordinateSection(*dm, &coordSection);CHKERRQ(ierr);
1738     ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
1739     ierr = PetscSectionSetFieldComponents(coordSection, 0, dim);CHKERRQ(ierr);
1740     ierr = PetscSectionSetChart(coordSection, numCells, numCells+numVertices);CHKERRQ(ierr);
1741     for (v = numCells; v < numCells+numVertices; ++v) {
1742       ierr = PetscSectionSetDof(coordSection, v, dim);CHKERRQ(ierr);
1743       ierr = PetscSectionSetFieldDof(coordSection, v, 0, dim);CHKERRQ(ierr);
1744     }
1745     ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
1746     ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
1747     ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
1748     ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
1749     ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
1750     ierr = VecSetBlockSize(coordinates, dim);CHKERRQ(ierr);
1751     ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
1752     ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
1753     for (c = 0; c < numCells; c++) {
1754       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;
1755       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;
1756     }
1757     if (!rank) {
1758       coords[(2*n+0)*dim+0] = 0.0; coords[(2*n+0)*dim+1] = 0.0; coords[(2*n+0)*dim+2] = 1.0;
1759       coords[(2*n+1)*dim+0] = 0.0; coords[(2*n+1)*dim+1] = 0.0; coords[(2*n+1)*dim+2] = 0.0;
1760     }
1761     ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
1762     ierr = DMSetCoordinatesLocal(*dm, coordinates);CHKERRQ(ierr);
1763     ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
1764   }
1765   PetscFunctionReturn(0);
1766 }
1767 
1768 PETSC_STATIC_INLINE PetscReal DiffNormReal(PetscInt dim, const PetscReal x[], const PetscReal y[])
1769 {
1770   PetscReal prod = 0.0;
1771   PetscInt  i;
1772   for (i = 0; i < dim; ++i) prod += PetscSqr(x[i] - y[i]);
1773   return PetscSqrtReal(prod);
1774 }
1775 PETSC_STATIC_INLINE PetscReal DotReal(PetscInt dim, const PetscReal x[], const PetscReal y[])
1776 {
1777   PetscReal prod = 0.0;
1778   PetscInt  i;
1779   for (i = 0; i < dim; ++i) prod += x[i]*y[i];
1780   return prod;
1781 }
1782 
1783 /* The first constant is the sphere radius */
1784 static void snapToSphere(PetscInt dim, PetscInt Nf, PetscInt NfAux,
1785                          const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
1786                          const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
1787                          PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
1788 {
1789   PetscReal r = PetscRealPart(constants[0]);
1790   PetscReal norm2 = 0.0, fac;
1791   PetscInt  n = uOff[1] - uOff[0], d;
1792 
1793   for (d = 0; d < n; ++d) norm2 += PetscSqr(PetscRealPart(u[d]));
1794   fac = r/PetscSqrtReal(norm2);
1795   for (d = 0; d < n; ++d) f0[d] = u[d]*fac;
1796 }
1797 
1798 /*@
1799   DMPlexCreateSphereMesh - Creates a mesh on the d-dimensional sphere, S^d.
1800 
1801   Collective
1802 
1803   Input Parameters:
1804 + comm    - The communicator for the DM object
1805 . dim     - The dimension
1806 . simplex - Use simplices, or tensor product cells
1807 - R       - The radius
1808 
1809   Output Parameter:
1810 . dm  - The DM object
1811 
1812   Level: beginner
1813 
1814 .seealso: DMPlexCreateBallMesh(), DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
1815 @*/
1816 PetscErrorCode DMPlexCreateSphereMesh(MPI_Comm comm, PetscInt dim, PetscBool simplex, PetscReal R, DM *dm)
1817 {
1818   const PetscInt  embedDim = dim+1;
1819   PetscSection    coordSection;
1820   Vec             coordinates;
1821   PetscScalar    *coords;
1822   PetscReal      *coordsIn;
1823   PetscInt        numCells, numEdges, numVerts, firstVertex, v, firstEdge, coordSize, d, c, e;
1824   PetscMPIInt     rank;
1825   PetscErrorCode  ierr;
1826 
1827   PetscFunctionBegin;
1828   PetscValidPointer(dm, 4);
1829   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
1830   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
1831   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
1832   ierr = DMSetCoordinateDim(*dm, dim+1);CHKERRQ(ierr);
1833   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject) *dm), &rank);CHKERRQ(ierr);
1834   switch (dim) {
1835   case 2:
1836     if (simplex) {
1837       DM              idm;
1838       const PetscReal radius    = PetscSqrtReal(1 + PETSC_PHI*PETSC_PHI)/(1.0 + PETSC_PHI);
1839       const PetscReal edgeLen   = 2.0/(1.0 + PETSC_PHI) * (R/radius);
1840       const PetscInt  degree    = 5;
1841       PetscReal       vertex[3] = {0.0, 1.0/(1.0 + PETSC_PHI), PETSC_PHI/(1.0 + PETSC_PHI)};
1842       PetscInt        s[3]      = {1, 1, 1};
1843       PetscInt        cone[3];
1844       PetscInt       *graph, p, i, j, k;
1845 
1846       vertex[0] *= R/radius; vertex[1] *= R/radius; vertex[2] *= R/radius;
1847       numCells    = !rank ? 20 : 0;
1848       numVerts    = !rank ? 12 : 0;
1849       firstVertex = numCells;
1850       /* Use icosahedron, which for a R-sphere has coordinates which are all cyclic permutations of
1851 
1852            (0, \pm 1/\phi+1, \pm \phi/\phi+1)
1853 
1854          where \phi^2 - \phi - 1 = 0, meaning \phi is the golden ratio \frac{1 + \sqrt{5}}{2}. The edge
1855          length is then given by 2/(1+\phi) = 2 * 0.38197 = 0.76393.
1856       */
1857       /* Construct vertices */
1858       ierr = PetscCalloc1(numVerts * embedDim, &coordsIn);CHKERRQ(ierr);
1859       if (!rank) {
1860         for (p = 0, i = 0; p < embedDim; ++p) {
1861           for (s[1] = -1; s[1] < 2; s[1] += 2) {
1862             for (s[2] = -1; s[2] < 2; s[2] += 2) {
1863               for (d = 0; d < embedDim; ++d) coordsIn[i*embedDim+d] = s[(d+p)%embedDim]*vertex[(d+p)%embedDim];
1864               ++i;
1865             }
1866           }
1867         }
1868       }
1869       /* Construct graph */
1870       ierr = PetscCalloc1(numVerts * numVerts, &graph);CHKERRQ(ierr);
1871       for (i = 0; i < numVerts; ++i) {
1872         for (j = 0, k = 0; j < numVerts; ++j) {
1873           if (PetscAbsReal(DiffNormReal(embedDim, &coordsIn[i*embedDim], &coordsIn[j*embedDim]) - edgeLen) < PETSC_SMALL) {graph[i*numVerts+j] = 1; ++k;}
1874         }
1875         if (k != degree) SETERRQ3(comm, PETSC_ERR_PLIB, "Invalid icosahedron, vertex %D degree %D != %D", i, k, degree);
1876       }
1877       /* Build Topology */
1878       ierr = DMPlexSetChart(*dm, 0, numCells+numVerts);CHKERRQ(ierr);
1879       for (c = 0; c < numCells; c++) {
1880         ierr = DMPlexSetConeSize(*dm, c, embedDim);CHKERRQ(ierr);
1881       }
1882       ierr = DMSetUp(*dm);CHKERRQ(ierr); /* Allocate space for cones */
1883       /* Cells */
1884       for (i = 0, c = 0; i < numVerts; ++i) {
1885         for (j = 0; j < i; ++j) {
1886           for (k = 0; k < j; ++k) {
1887             if (graph[i*numVerts+j] && graph[j*numVerts+k] && graph[k*numVerts+i]) {
1888               cone[0] = firstVertex+i; cone[1] = firstVertex+j; cone[2] = firstVertex+k;
1889               /* Check orientation */
1890               {
1891                 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}}};
1892                 PetscReal normal[3];
1893                 PetscInt  e, f;
1894 
1895                 for (d = 0; d < embedDim; ++d) {
1896                   normal[d] = 0.0;
1897                   for (e = 0; e < embedDim; ++e) {
1898                     for (f = 0; f < embedDim; ++f) {
1899                       normal[d] += epsilon[d][e][f]*(coordsIn[j*embedDim+e] - coordsIn[i*embedDim+e])*(coordsIn[k*embedDim+f] - coordsIn[i*embedDim+f]);
1900                     }
1901                   }
1902                 }
1903                 if (DotReal(embedDim, normal, &coordsIn[i*embedDim]) < 0) {PetscInt tmp = cone[1]; cone[1] = cone[2]; cone[2] = tmp;}
1904               }
1905               ierr = DMPlexSetCone(*dm, c++, cone);CHKERRQ(ierr);
1906             }
1907           }
1908         }
1909       }
1910       ierr = DMPlexSymmetrize(*dm);CHKERRQ(ierr);
1911       ierr = DMPlexStratify(*dm);CHKERRQ(ierr);
1912       ierr = PetscFree(graph);CHKERRQ(ierr);
1913       /* Interpolate mesh */
1914       ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
1915       ierr = DMDestroy(dm);CHKERRQ(ierr);
1916       *dm  = idm;
1917     } else {
1918       /*
1919         12-21--13
1920          |     |
1921         25  4  24
1922          |     |
1923   12-25--9-16--8-24--13
1924    |     |     |     |
1925   23  5 17  0 15  3  22
1926    |     |     |     |
1927   10-20--6-14--7-19--11
1928          |     |
1929         20  1  19
1930          |     |
1931         10-18--11
1932          |     |
1933         23  2  22
1934          |     |
1935         12-21--13
1936        */
1937       PetscInt cone[4], ornt[4];
1938 
1939       numCells    = !rank ?  6 : 0;
1940       numEdges    = !rank ? 12 : 0;
1941       numVerts    = !rank ?  8 : 0;
1942       firstVertex = numCells;
1943       firstEdge   = numCells + numVerts;
1944       /* Build Topology */
1945       ierr = DMPlexSetChart(*dm, 0, numCells+numEdges+numVerts);CHKERRQ(ierr);
1946       for (c = 0; c < numCells; c++) {
1947         ierr = DMPlexSetConeSize(*dm, c, 4);CHKERRQ(ierr);
1948       }
1949       for (e = firstEdge; e < firstEdge+numEdges; ++e) {
1950         ierr = DMPlexSetConeSize(*dm, e, 2);CHKERRQ(ierr);
1951       }
1952       ierr = DMSetUp(*dm);CHKERRQ(ierr); /* Allocate space for cones */
1953       if (!rank) {
1954         /* Cell 0 */
1955         cone[0] = 14; cone[1] = 15; cone[2] = 16; cone[3] = 17;
1956         ierr = DMPlexSetCone(*dm, 0, cone);CHKERRQ(ierr);
1957         ornt[0] = 0; ornt[1] = 0; ornt[2] = 0; ornt[3] = 0;
1958         ierr = DMPlexSetConeOrientation(*dm, 0, ornt);CHKERRQ(ierr);
1959         /* Cell 1 */
1960         cone[0] = 18; cone[1] = 19; cone[2] = 14; cone[3] = 20;
1961         ierr = DMPlexSetCone(*dm, 1, cone);CHKERRQ(ierr);
1962         ornt[0] = 0; ornt[1] = 0; ornt[2] = -2; ornt[3] = 0;
1963         ierr = DMPlexSetConeOrientation(*dm, 1, ornt);CHKERRQ(ierr);
1964         /* Cell 2 */
1965         cone[0] = 21; cone[1] = 22; cone[2] = 18; cone[3] = 23;
1966         ierr = DMPlexSetCone(*dm, 2, cone);CHKERRQ(ierr);
1967         ornt[0] = 0; ornt[1] = 0; ornt[2] = -2; ornt[3] = 0;
1968         ierr = DMPlexSetConeOrientation(*dm, 2, ornt);CHKERRQ(ierr);
1969         /* Cell 3 */
1970         cone[0] = 19; cone[1] = 22; cone[2] = 24; cone[3] = 15;
1971         ierr = DMPlexSetCone(*dm, 3, cone);CHKERRQ(ierr);
1972         ornt[0] = -2; ornt[1] = -2; ornt[2] = 0; ornt[3] = -2;
1973         ierr = DMPlexSetConeOrientation(*dm, 3, ornt);CHKERRQ(ierr);
1974         /* Cell 4 */
1975         cone[0] = 16; cone[1] = 24; cone[2] = 21; cone[3] = 25;
1976         ierr = DMPlexSetCone(*dm, 4, cone);CHKERRQ(ierr);
1977         ornt[0] = -2; ornt[1] = -2; ornt[2] = -2; ornt[3] = 0;
1978         ierr = DMPlexSetConeOrientation(*dm, 4, ornt);CHKERRQ(ierr);
1979         /* Cell 5 */
1980         cone[0] = 20; cone[1] = 17; cone[2] = 25; cone[3] = 23;
1981         ierr = DMPlexSetCone(*dm, 5, cone);CHKERRQ(ierr);
1982         ornt[0] = -2; ornt[1] = -2; ornt[2] = -2; ornt[3] = -2;
1983         ierr = DMPlexSetConeOrientation(*dm, 5, ornt);CHKERRQ(ierr);
1984         /* Edges */
1985         cone[0] =  6; cone[1] =  7;
1986         ierr = DMPlexSetCone(*dm, 14, cone);CHKERRQ(ierr);
1987         cone[0] =  7; cone[1] =  8;
1988         ierr = DMPlexSetCone(*dm, 15, cone);CHKERRQ(ierr);
1989         cone[0] =  8; cone[1] =  9;
1990         ierr = DMPlexSetCone(*dm, 16, cone);CHKERRQ(ierr);
1991         cone[0] =  9; cone[1] =  6;
1992         ierr = DMPlexSetCone(*dm, 17, cone);CHKERRQ(ierr);
1993         cone[0] = 10; cone[1] = 11;
1994         ierr = DMPlexSetCone(*dm, 18, cone);CHKERRQ(ierr);
1995         cone[0] = 11; cone[1] =  7;
1996         ierr = DMPlexSetCone(*dm, 19, cone);CHKERRQ(ierr);
1997         cone[0] =  6; cone[1] = 10;
1998         ierr = DMPlexSetCone(*dm, 20, cone);CHKERRQ(ierr);
1999         cone[0] = 12; cone[1] = 13;
2000         ierr = DMPlexSetCone(*dm, 21, cone);CHKERRQ(ierr);
2001         cone[0] = 13; cone[1] = 11;
2002         ierr = DMPlexSetCone(*dm, 22, cone);CHKERRQ(ierr);
2003         cone[0] = 10; cone[1] = 12;
2004         ierr = DMPlexSetCone(*dm, 23, cone);CHKERRQ(ierr);
2005         cone[0] = 13; cone[1] =  8;
2006         ierr = DMPlexSetCone(*dm, 24, cone);CHKERRQ(ierr);
2007         cone[0] = 12; cone[1] =  9;
2008         ierr = DMPlexSetCone(*dm, 25, cone);CHKERRQ(ierr);
2009       }
2010       ierr = DMPlexSymmetrize(*dm);CHKERRQ(ierr);
2011       ierr = DMPlexStratify(*dm);CHKERRQ(ierr);
2012       /* Build coordinates */
2013       ierr = PetscCalloc1(numVerts * embedDim, &coordsIn);CHKERRQ(ierr);
2014       if (!rank) {
2015         coordsIn[0*embedDim+0] = -R; coordsIn[0*embedDim+1] =  R; coordsIn[0*embedDim+2] = -R;
2016         coordsIn[1*embedDim+0] =  R; coordsIn[1*embedDim+1] =  R; coordsIn[1*embedDim+2] = -R;
2017         coordsIn[2*embedDim+0] =  R; coordsIn[2*embedDim+1] = -R; coordsIn[2*embedDim+2] = -R;
2018         coordsIn[3*embedDim+0] = -R; coordsIn[3*embedDim+1] = -R; coordsIn[3*embedDim+2] = -R;
2019         coordsIn[4*embedDim+0] = -R; coordsIn[4*embedDim+1] =  R; coordsIn[4*embedDim+2] =  R;
2020         coordsIn[5*embedDim+0] =  R; coordsIn[5*embedDim+1] =  R; coordsIn[5*embedDim+2] =  R;
2021         coordsIn[6*embedDim+0] = -R; coordsIn[6*embedDim+1] = -R; coordsIn[6*embedDim+2] =  R;
2022         coordsIn[7*embedDim+0] =  R; coordsIn[7*embedDim+1] = -R; coordsIn[7*embedDim+2] =  R;
2023       }
2024     }
2025     break;
2026   case 3:
2027     if (simplex) {
2028       DM              idm;
2029       const PetscReal edgeLen         = 1.0/PETSC_PHI;
2030       PetscReal       vertexA[4]      = {0.5, 0.5, 0.5, 0.5};
2031       PetscReal       vertexB[4]      = {1.0, 0.0, 0.0, 0.0};
2032       PetscReal       vertexC[4]      = {0.5, 0.5*PETSC_PHI, 0.5/PETSC_PHI, 0.0};
2033       const PetscInt  degree          = 12;
2034       PetscInt        s[4]            = {1, 1, 1};
2035       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},
2036                                          {2, 0, 1, 3}, {2, 1, 3, 0}, {2, 3, 0, 1}, {3, 0, 2, 1}, {3, 1, 0, 2}, {3, 2, 1, 0}};
2037       PetscInt        cone[4];
2038       PetscInt       *graph, p, i, j, k, l;
2039 
2040       vertexA[0] *= R; vertexA[1] *= R; vertexA[2] *= R; vertexA[3] *= R;
2041       vertexB[0] *= R; vertexB[1] *= R; vertexB[2] *= R; vertexB[3] *= R;
2042       vertexC[0] *= R; vertexC[1] *= R; vertexC[2] *= R; vertexC[3] *= R;
2043       numCells    = !rank ? 600 : 0;
2044       numVerts    = !rank ? 120 : 0;
2045       firstVertex = numCells;
2046       /* Use the 600-cell, which for a unit sphere has coordinates which are
2047 
2048            1/2 (\pm 1, \pm 1,    \pm 1, \pm 1)                          16
2049                (\pm 1,    0,       0,      0)  all cyclic permutations   8
2050            1/2 (\pm 1, \pm phi, \pm 1/phi, 0)  all even permutations    96
2051 
2052          where \phi^2 - \phi - 1 = 0, meaning \phi is the golden ratio \frac{1 + \sqrt{5}}{2}. The edge
2053          length is then given by 1/\phi = 0.61803.
2054 
2055          http://buzzard.pugetsound.edu/sage-practice/ch03s03.html
2056          http://mathworld.wolfram.com/600-Cell.html
2057       */
2058       /* Construct vertices */
2059       ierr = PetscCalloc1(numVerts * embedDim, &coordsIn);CHKERRQ(ierr);
2060       i    = 0;
2061       if (!rank) {
2062         for (s[0] = -1; s[0] < 2; s[0] += 2) {
2063           for (s[1] = -1; s[1] < 2; s[1] += 2) {
2064             for (s[2] = -1; s[2] < 2; s[2] += 2) {
2065               for (s[3] = -1; s[3] < 2; s[3] += 2) {
2066                 for (d = 0; d < embedDim; ++d) coordsIn[i*embedDim+d] = s[d]*vertexA[d];
2067                 ++i;
2068               }
2069             }
2070           }
2071         }
2072         for (p = 0; p < embedDim; ++p) {
2073           s[1] = s[2] = s[3] = 1;
2074           for (s[0] = -1; s[0] < 2; s[0] += 2) {
2075             for (d = 0; d < embedDim; ++d) coordsIn[i*embedDim+d] = s[(d+p)%embedDim]*vertexB[(d+p)%embedDim];
2076             ++i;
2077           }
2078         }
2079         for (p = 0; p < 12; ++p) {
2080           s[3] = 1;
2081           for (s[0] = -1; s[0] < 2; s[0] += 2) {
2082             for (s[1] = -1; s[1] < 2; s[1] += 2) {
2083               for (s[2] = -1; s[2] < 2; s[2] += 2) {
2084                 for (d = 0; d < embedDim; ++d) coordsIn[i*embedDim+d] = s[evenPerm[p][d]]*vertexC[evenPerm[p][d]];
2085                 ++i;
2086               }
2087             }
2088           }
2089         }
2090       }
2091       if (i != numVerts) SETERRQ2(comm, PETSC_ERR_PLIB, "Invalid 600-cell, vertices %D != %D", i, numVerts);
2092       /* Construct graph */
2093       ierr = PetscCalloc1(numVerts * numVerts, &graph);CHKERRQ(ierr);
2094       for (i = 0; i < numVerts; ++i) {
2095         for (j = 0, k = 0; j < numVerts; ++j) {
2096           if (PetscAbsReal(DiffNormReal(embedDim, &coordsIn[i*embedDim], &coordsIn[j*embedDim]) - edgeLen) < PETSC_SMALL) {graph[i*numVerts+j] = 1; ++k;}
2097         }
2098         if (k != degree) SETERRQ3(comm, PETSC_ERR_PLIB, "Invalid 600-cell, vertex %D degree %D != %D", i, k, degree);
2099       }
2100       /* Build Topology */
2101       ierr = DMPlexSetChart(*dm, 0, numCells+numVerts);CHKERRQ(ierr);
2102       for (c = 0; c < numCells; c++) {
2103         ierr = DMPlexSetConeSize(*dm, c, embedDim);CHKERRQ(ierr);
2104       }
2105       ierr = DMSetUp(*dm);CHKERRQ(ierr); /* Allocate space for cones */
2106       /* Cells */
2107       if (!rank) {
2108         for (i = 0, c = 0; i < numVerts; ++i) {
2109           for (j = 0; j < i; ++j) {
2110             for (k = 0; k < j; ++k) {
2111               for (l = 0; l < k; ++l) {
2112                 if (graph[i*numVerts+j] && graph[j*numVerts+k] && graph[k*numVerts+i] &&
2113                     graph[l*numVerts+i] && graph[l*numVerts+j] && graph[l*numVerts+k]) {
2114                   cone[0] = firstVertex+i; cone[1] = firstVertex+j; cone[2] = firstVertex+k; cone[3] = firstVertex+l;
2115                   /* Check orientation: https://ef.gy/linear-algebra:normal-vectors-in-higher-dimensional-spaces */
2116                   {
2117                     const PetscInt epsilon[4][4][4][4] = {{{{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}},
2118                                                            {{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  1}, { 0,  0, -1, 0}},
2119                                                            {{0,  0,  0,  0}, { 0, 0,  0, -1}, { 0,  0, 0,  0}, { 0,  1,  0, 0}},
2120                                                            {{0,  0,  0,  0}, { 0, 0,  1,  0}, { 0, -1, 0,  0}, { 0,  0,  0, 0}}},
2121 
2122                                                           {{{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0, -1}, { 0,  0,  1, 0}},
2123                                                            {{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}},
2124                                                            {{0,  0,  0,  1}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, {-1,  0,  0, 0}},
2125                                                            {{0,  0, -1,  0}, { 0, 0,  0,  0}, { 1,  0, 0,  0}, { 0,  0,  0, 0}}},
2126 
2127                                                           {{{0,  0,  0,  0}, { 0, 0,  0,  1}, { 0,  0, 0,  0}, { 0, -1,  0, 0}},
2128                                                            {{0,  0,  0, -1}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 1,  0,  0, 0}},
2129                                                            {{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}},
2130                                                            {{0,  1,  0,  0}, {-1, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}}},
2131 
2132                                                           {{{0,  0,  0,  0}, { 0, 0, -1,  0}, { 0,  1, 0,  0}, { 0,  0,  0, 0}},
2133                                                            {{0,  0,  1,  0}, { 0, 0,  0,  0}, {-1,  0, 0,  0}, { 0,  0,  0, 0}},
2134                                                            {{0, -1,  0,  0}, { 1, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}},
2135                                                            {{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}}}};
2136                     PetscReal normal[4];
2137                     PetscInt  e, f, g;
2138 
2139                     for (d = 0; d < embedDim; ++d) {
2140                       normal[d] = 0.0;
2141                       for (e = 0; e < embedDim; ++e) {
2142                         for (f = 0; f < embedDim; ++f) {
2143                           for (g = 0; g < embedDim; ++g) {
2144                             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]);
2145                           }
2146                         }
2147                       }
2148                     }
2149                     if (DotReal(embedDim, normal, &coordsIn[i*embedDim]) < 0) {PetscInt tmp = cone[1]; cone[1] = cone[2]; cone[2] = tmp;}
2150                   }
2151                   ierr = DMPlexSetCone(*dm, c++, cone);CHKERRQ(ierr);
2152                 }
2153               }
2154             }
2155           }
2156         }
2157       }
2158       ierr = DMPlexSymmetrize(*dm);CHKERRQ(ierr);
2159       ierr = DMPlexStratify(*dm);CHKERRQ(ierr);
2160       ierr = PetscFree(graph);CHKERRQ(ierr);
2161       /* Interpolate mesh */
2162       ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
2163       ierr = DMDestroy(dm);CHKERRQ(ierr);
2164       *dm  = idm;
2165       break;
2166     }
2167   default: SETERRQ1(comm, PETSC_ERR_SUP, "Unsupported dimension for sphere: %D", dim);
2168   }
2169   /* Create coordinates */
2170   ierr = DMGetCoordinateSection(*dm, &coordSection);CHKERRQ(ierr);
2171   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
2172   ierr = PetscSectionSetFieldComponents(coordSection, 0, embedDim);CHKERRQ(ierr);
2173   ierr = PetscSectionSetChart(coordSection, firstVertex, firstVertex+numVerts);CHKERRQ(ierr);
2174   for (v = firstVertex; v < firstVertex+numVerts; ++v) {
2175     ierr = PetscSectionSetDof(coordSection, v, embedDim);CHKERRQ(ierr);
2176     ierr = PetscSectionSetFieldDof(coordSection, v, 0, embedDim);CHKERRQ(ierr);
2177   }
2178   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
2179   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
2180   ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
2181   ierr = VecSetBlockSize(coordinates, embedDim);CHKERRQ(ierr);
2182   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
2183   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
2184   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
2185   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
2186   for (v = 0; v < numVerts; ++v) for (d = 0; d < embedDim; ++d) {coords[v*embedDim+d] = coordsIn[v*embedDim+d];}
2187   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
2188   ierr = DMSetCoordinatesLocal(*dm, coordinates);CHKERRQ(ierr);
2189   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
2190   ierr = PetscFree(coordsIn);CHKERRQ(ierr);
2191   /* Create coordinate function space */
2192   {
2193     DM          cdm;
2194     PetscDS     cds;
2195     PetscFE     fe;
2196     PetscScalar radius = R;
2197     PetscInt    dT, dE;
2198 
2199     ierr = DMGetCoordinateDM(*dm, &cdm);CHKERRQ(ierr);
2200     ierr = DMGetDimension(*dm, &dT);CHKERRQ(ierr);
2201     ierr = DMGetCoordinateDim(*dm, &dE);CHKERRQ(ierr);
2202     ierr = PetscFECreateLagrange(PETSC_COMM_SELF, dT, dE, PETSC_TRUE, 1, -1, &fe);CHKERRQ(ierr);
2203     ierr = DMSetField(cdm, 0, NULL, (PetscObject) fe);CHKERRQ(ierr);
2204     ierr = PetscFEDestroy(&fe);CHKERRQ(ierr);
2205     ierr = DMCreateDS(cdm);CHKERRQ(ierr);
2206 
2207     ierr = DMGetDS(cdm, &cds);CHKERRQ(ierr);
2208     ierr = PetscDSSetConstants(cds, 1, &radius);CHKERRQ(ierr);
2209   }
2210   ((DM_Plex *) (*dm)->data)->coordFunc = snapToSphere;
2211   PetscFunctionReturn(0);
2212 }
2213 
2214 /*@
2215   DMPlexCreateBallMesh - Creates a simplex mesh on the d-dimensional ball, B^d.
2216 
2217   Collective
2218 
2219   Input Parameters:
2220 + comm  - The communicator for the DM object
2221 . dim   - The dimension
2222 - R     - The radius
2223 
2224   Output Parameter:
2225 . dm  - The DM object
2226 
2227   Options Database Keys:
2228 - bd_dm_refine - This will refine the surface mesh preserving the sphere geometry
2229 
2230   Level: beginner
2231 
2232 .seealso: DMPlexCreateSphereMesh(), DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
2233 @*/
2234 PetscErrorCode DMPlexCreateBallMesh(MPI_Comm comm, PetscInt dim, PetscReal R, DM *dm)
2235 {
2236   DM             sdm;
2237   PetscErrorCode ierr;
2238 
2239   PetscFunctionBegin;
2240   ierr = DMPlexCreateSphereMesh(comm, dim-1, PETSC_TRUE, R, &sdm);CHKERRQ(ierr);
2241   ierr = PetscObjectSetOptionsPrefix((PetscObject) sdm, "bd_");CHKERRQ(ierr);
2242   ierr = DMSetFromOptions(sdm);CHKERRQ(ierr);
2243   ierr = DMPlexGenerate(sdm, NULL, PETSC_TRUE, dm);CHKERRQ(ierr);
2244   ierr = DMDestroy(&sdm);CHKERRQ(ierr);
2245   PetscFunctionReturn(0);
2246 }
2247 
2248 /* External function declarations here */
2249 extern PetscErrorCode DMCreateInterpolation_Plex(DM dmCoarse, DM dmFine, Mat *interpolation, Vec *scaling);
2250 extern PetscErrorCode DMCreateInjection_Plex(DM dmCoarse, DM dmFine, Mat *mat);
2251 extern PetscErrorCode DMCreateMassMatrix_Plex(DM dmCoarse, DM dmFine, Mat *mat);
2252 extern PetscErrorCode DMCreateLocalSection_Plex(DM dm);
2253 extern PetscErrorCode DMCreateDefaultConstraints_Plex(DM dm);
2254 extern PetscErrorCode DMCreateMatrix_Plex(DM dm,  Mat *J);
2255 extern PetscErrorCode DMCreateCoordinateDM_Plex(DM dm, DM *cdm);
2256 extern PetscErrorCode DMCreateCoordinateField_Plex(DM dm, DMField *field);
2257 PETSC_INTERN PetscErrorCode DMClone_Plex(DM dm, DM *newdm);
2258 extern PetscErrorCode DMSetUp_Plex(DM dm);
2259 extern PetscErrorCode DMDestroy_Plex(DM dm);
2260 extern PetscErrorCode DMView_Plex(DM dm, PetscViewer viewer);
2261 extern PetscErrorCode DMLoad_Plex(DM dm, PetscViewer viewer);
2262 extern PetscErrorCode DMCreateSubDM_Plex(DM dm, PetscInt numFields, const PetscInt fields[], IS *is, DM *subdm);
2263 extern PetscErrorCode DMCreateSuperDM_Plex(DM dms[], PetscInt len, IS **is, DM *superdm);
2264 static PetscErrorCode DMInitialize_Plex(DM dm);
2265 
2266 /* Replace dm with the contents of dmNew
2267    - Share the DM_Plex structure
2268    - Share the coordinates
2269    - Share the SF
2270 */
2271 static PetscErrorCode DMPlexReplace_Static(DM dm, DM dmNew)
2272 {
2273   PetscSF               sf;
2274   DM                    coordDM, coarseDM;
2275   DMField               coordField;
2276   Vec                   coords;
2277   PetscBool             isper;
2278   const PetscReal      *maxCell, *L;
2279   const DMBoundaryType *bd;
2280   PetscErrorCode        ierr;
2281 
2282   PetscFunctionBegin;
2283   ierr = DMGetPointSF(dmNew, &sf);CHKERRQ(ierr);
2284   ierr = DMSetPointSF(dm, sf);CHKERRQ(ierr);
2285   ierr = DMGetCoordinateDM(dmNew, &coordDM);CHKERRQ(ierr);
2286   ierr = DMGetCoordinatesLocal(dmNew, &coords);CHKERRQ(ierr);
2287   ierr = DMGetCoordinateField(dmNew, &coordField);CHKERRQ(ierr);
2288   ierr = DMSetCoordinateDM(dm, coordDM);CHKERRQ(ierr);
2289   ierr = DMSetCoordinatesLocal(dm, coords);CHKERRQ(ierr);
2290   ierr = DMSetCoordinateField(dm, coordField);CHKERRQ(ierr);
2291   ierr = DMGetPeriodicity(dm, &isper, &maxCell, &L, &bd);CHKERRQ(ierr);
2292   ierr = DMSetPeriodicity(dmNew, isper, maxCell, L, bd);CHKERRQ(ierr);
2293   ierr = DMDestroy_Plex(dm);CHKERRQ(ierr);
2294   ierr = DMInitialize_Plex(dm);CHKERRQ(ierr);
2295   dm->data = dmNew->data;
2296   ((DM_Plex *) dmNew->data)->refct++;
2297   ierr = DMDestroyLabelLinkList_Internal(dm);CHKERRQ(ierr);
2298   ierr = DMCopyLabels(dmNew, dm, PETSC_OWN_POINTER, PETSC_TRUE);CHKERRQ(ierr);
2299   ierr = DMGetCoarseDM(dmNew,&coarseDM);CHKERRQ(ierr);
2300   ierr = DMSetCoarseDM(dm,coarseDM);CHKERRQ(ierr);
2301   PetscFunctionReturn(0);
2302 }
2303 
2304 /* Swap dm with the contents of dmNew
2305    - Swap the DM_Plex structure
2306    - Swap the coordinates
2307    - Swap the point PetscSF
2308 */
2309 static PetscErrorCode DMPlexSwap_Static(DM dmA, DM dmB)
2310 {
2311   DM              coordDMA, coordDMB;
2312   Vec             coordsA,  coordsB;
2313   PetscSF         sfA,      sfB;
2314   void            *tmp;
2315   DMLabelLink     listTmp;
2316   DMLabel         depthTmp;
2317   PetscInt        tmpI;
2318   PetscErrorCode  ierr;
2319 
2320   PetscFunctionBegin;
2321   ierr = DMGetPointSF(dmA, &sfA);CHKERRQ(ierr);
2322   ierr = DMGetPointSF(dmB, &sfB);CHKERRQ(ierr);
2323   ierr = PetscObjectReference((PetscObject) sfA);CHKERRQ(ierr);
2324   ierr = DMSetPointSF(dmA, sfB);CHKERRQ(ierr);
2325   ierr = DMSetPointSF(dmB, sfA);CHKERRQ(ierr);
2326   ierr = PetscObjectDereference((PetscObject) sfA);CHKERRQ(ierr);
2327 
2328   ierr = DMGetCoordinateDM(dmA, &coordDMA);CHKERRQ(ierr);
2329   ierr = DMGetCoordinateDM(dmB, &coordDMB);CHKERRQ(ierr);
2330   ierr = PetscObjectReference((PetscObject) coordDMA);CHKERRQ(ierr);
2331   ierr = DMSetCoordinateDM(dmA, coordDMB);CHKERRQ(ierr);
2332   ierr = DMSetCoordinateDM(dmB, coordDMA);CHKERRQ(ierr);
2333   ierr = PetscObjectDereference((PetscObject) coordDMA);CHKERRQ(ierr);
2334 
2335   ierr = DMGetCoordinatesLocal(dmA, &coordsA);CHKERRQ(ierr);
2336   ierr = DMGetCoordinatesLocal(dmB, &coordsB);CHKERRQ(ierr);
2337   ierr = PetscObjectReference((PetscObject) coordsA);CHKERRQ(ierr);
2338   ierr = DMSetCoordinatesLocal(dmA, coordsB);CHKERRQ(ierr);
2339   ierr = DMSetCoordinatesLocal(dmB, coordsA);CHKERRQ(ierr);
2340   ierr = PetscObjectDereference((PetscObject) coordsA);CHKERRQ(ierr);
2341 
2342   tmp       = dmA->data;
2343   dmA->data = dmB->data;
2344   dmB->data = tmp;
2345   listTmp   = dmA->labels;
2346   dmA->labels = dmB->labels;
2347   dmB->labels = listTmp;
2348   depthTmp  = dmA->depthLabel;
2349   dmA->depthLabel = dmB->depthLabel;
2350   dmB->depthLabel = depthTmp;
2351   depthTmp  = dmA->celltypeLabel;
2352   dmA->celltypeLabel = dmB->celltypeLabel;
2353   dmB->celltypeLabel = depthTmp;
2354   tmpI         = dmA->levelup;
2355   dmA->levelup = dmB->levelup;
2356   dmB->levelup = tmpI;
2357   PetscFunctionReturn(0);
2358 }
2359 
2360 PetscErrorCode DMSetFromOptions_NonRefinement_Plex(PetscOptionItems *PetscOptionsObject,DM dm)
2361 {
2362   DM_Plex       *mesh = (DM_Plex*) dm->data;
2363   PetscBool      flg;
2364   PetscErrorCode ierr;
2365 
2366   PetscFunctionBegin;
2367   /* Handle viewing */
2368   ierr = PetscOptionsBool("-dm_plex_print_set_values", "Output all set values info", "DMPlexMatSetClosure", PETSC_FALSE, &mesh->printSetValues, NULL);CHKERRQ(ierr);
2369   ierr = PetscOptionsBoundedInt("-dm_plex_print_fem", "Debug output level all fem computations", "DMPlexSNESComputeResidualFEM", 0, &mesh->printFEM, NULL,0);CHKERRQ(ierr);
2370   ierr = PetscOptionsReal("-dm_plex_print_tol", "Tolerance for FEM output", "DMPlexSNESComputeResidualFEM", mesh->printTol, &mesh->printTol, NULL);CHKERRQ(ierr);
2371   ierr = PetscOptionsBoundedInt("-dm_plex_print_l2", "Debug output level all L2 diff computations", "DMComputeL2Diff", 0, &mesh->printL2, NULL,0);CHKERRQ(ierr);
2372   ierr = DMMonitorSetFromOptions(dm, "-dm_plex_monitor_throughput", "Monitor the simulation throughput", "DMPlexMonitorThroughput", DMPlexMonitorThroughput, NULL, &flg);CHKERRQ(ierr);
2373   if (flg) {ierr = PetscLogDefaultBegin();CHKERRQ(ierr);}
2374   /* Point Location */
2375   ierr = PetscOptionsBool("-dm_plex_hash_location", "Use grid hashing for point location", "DMInterpolate", PETSC_FALSE, &mesh->useHashLocation, NULL);CHKERRQ(ierr);
2376   /* Partitioning and distribution */
2377   ierr = PetscOptionsBool("-dm_plex_partition_balance", "Attempt to evenly divide points on partition boundary between processes", "DMPlexSetPartitionBalance", PETSC_FALSE, &mesh->partitionBalance, NULL);CHKERRQ(ierr);
2378   /* Generation and remeshing */
2379   ierr = PetscOptionsBool("-dm_plex_remesh_bd", "Allow changes to the boundary on remeshing", "DMAdapt", PETSC_FALSE, &mesh->remeshBd, NULL);CHKERRQ(ierr);
2380   /* Projection behavior */
2381   ierr = PetscOptionsBoundedInt("-dm_plex_max_projection_height", "Maxmimum mesh point height used to project locally", "DMPlexSetMaxProjectionHeight", 0, &mesh->maxProjectionHeight, NULL,0);CHKERRQ(ierr);
2382   ierr = PetscOptionsBool("-dm_plex_regular_refinement", "Use special nested projection algorithm for regular refinement", "DMPlexSetRegularRefinement", mesh->regularRefinement, &mesh->regularRefinement, NULL);CHKERRQ(ierr);
2383   ierr = PetscOptionsEnum("-dm_plex_cell_refiner", "Strategy for cell refinment", "ex40.c", DMPlexCellRefinerTypes, (PetscEnum) mesh->cellRefiner, (PetscEnum *) &mesh->cellRefiner, NULL);CHKERRQ(ierr);
2384   /* Checking structure */
2385   {
2386     PetscBool   flg = PETSC_FALSE, flg2 = PETSC_FALSE, all = PETSC_FALSE;
2387 
2388     ierr = PetscOptionsBool("-dm_plex_check_all", "Perform all checks", NULL, PETSC_FALSE, &all, &flg2);CHKERRQ(ierr);
2389     ierr = PetscOptionsBool("-dm_plex_check_symmetry", "Check that the adjacency information in the mesh is symmetric", "DMPlexCheckSymmetry", PETSC_FALSE, &flg, &flg2);CHKERRQ(ierr);
2390     if (all || (flg && flg2)) {ierr = DMPlexCheckSymmetry(dm);CHKERRQ(ierr);}
2391     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);
2392     if (all || (flg && flg2)) {ierr = DMPlexCheckSkeleton(dm, 0);CHKERRQ(ierr);}
2393     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);
2394     if (all || (flg && flg2)) {ierr = DMPlexCheckFaces(dm, 0);CHKERRQ(ierr);}
2395     ierr = PetscOptionsBool("-dm_plex_check_geometry", "Check that cells have positive volume", "DMPlexCheckGeometry", PETSC_FALSE, &flg, &flg2);CHKERRQ(ierr);
2396     if (all || (flg && flg2)) {ierr = DMPlexCheckGeometry(dm);CHKERRQ(ierr);}
2397     ierr = PetscOptionsBool("-dm_plex_check_pointsf", "Check some necessary conditions for PointSF", "DMPlexCheckPointSF", PETSC_FALSE, &flg, &flg2);CHKERRQ(ierr);
2398     if (all || (flg && flg2)) {ierr = DMPlexCheckPointSF(dm);CHKERRQ(ierr);}
2399     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);
2400     if (all || (flg && flg2)) {ierr = DMPlexCheckInterfaceCones(dm);CHKERRQ(ierr);}
2401     ierr = PetscOptionsBool("-dm_plex_check_cell_shape", "Check cell shape", "DMPlexCheckCellShape", PETSC_FALSE, &flg, &flg2);CHKERRQ(ierr);
2402     if (flg && flg2) {ierr = DMPlexCheckCellShape(dm, PETSC_TRUE, PETSC_DETERMINE);CHKERRQ(ierr);}
2403   }
2404 
2405   ierr = PetscPartitionerSetFromOptions(mesh->partitioner);CHKERRQ(ierr);
2406   PetscFunctionReturn(0);
2407 }
2408 
2409 static PetscErrorCode DMSetFromOptions_Plex(PetscOptionItems *PetscOptionsObject,DM dm)
2410 {
2411   PetscInt       refine = 0, coarsen = 0, r;
2412   PetscBool      isHierarchy;
2413   PetscErrorCode ierr;
2414 
2415   PetscFunctionBegin;
2416   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
2417   ierr = PetscOptionsHead(PetscOptionsObject,"DMPlex Options");CHKERRQ(ierr);
2418   /* Handle DMPlex refinement */
2419   ierr = PetscOptionsBoundedInt("-dm_refine", "The number of uniform refinements", "DMCreate", refine, &refine, NULL,0);CHKERRQ(ierr);
2420   ierr = PetscOptionsBoundedInt("-dm_refine_hierarchy", "The number of uniform refinements", "DMCreate", refine, &refine, &isHierarchy,0);CHKERRQ(ierr);
2421   if (refine) {ierr = DMPlexSetRefinementUniform(dm, PETSC_TRUE);CHKERRQ(ierr);}
2422   if (refine && isHierarchy) {
2423     DM *dms, coarseDM;
2424 
2425     ierr = DMGetCoarseDM(dm, &coarseDM);CHKERRQ(ierr);
2426     ierr = PetscObjectReference((PetscObject)coarseDM);CHKERRQ(ierr);
2427     ierr = PetscMalloc1(refine,&dms);CHKERRQ(ierr);
2428     ierr = DMRefineHierarchy(dm, refine, dms);CHKERRQ(ierr);
2429     /* Total hack since we do not pass in a pointer */
2430     ierr = DMPlexSwap_Static(dm, dms[refine-1]);CHKERRQ(ierr);
2431     if (refine == 1) {
2432       ierr = DMSetCoarseDM(dm, dms[0]);CHKERRQ(ierr);
2433       ierr = DMPlexSetRegularRefinement(dm, PETSC_TRUE);CHKERRQ(ierr);
2434     } else {
2435       ierr = DMSetCoarseDM(dm, dms[refine-2]);CHKERRQ(ierr);
2436       ierr = DMPlexSetRegularRefinement(dm, PETSC_TRUE);CHKERRQ(ierr);
2437       ierr = DMSetCoarseDM(dms[0], dms[refine-1]);CHKERRQ(ierr);
2438       ierr = DMPlexSetRegularRefinement(dms[0], PETSC_TRUE);CHKERRQ(ierr);
2439     }
2440     ierr = DMSetCoarseDM(dms[refine-1], coarseDM);CHKERRQ(ierr);
2441     ierr = PetscObjectDereference((PetscObject)coarseDM);CHKERRQ(ierr);
2442     /* Free DMs */
2443     for (r = 0; r < refine; ++r) {
2444       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dms[r]);CHKERRQ(ierr);
2445       ierr = DMDestroy(&dms[r]);CHKERRQ(ierr);
2446     }
2447     ierr = PetscFree(dms);CHKERRQ(ierr);
2448   } else {
2449     for (r = 0; r < refine; ++r) {
2450       DM refinedMesh;
2451       PetscPointFunc coordFunc = ((DM_Plex*) dm->data)->coordFunc;
2452 
2453       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2454       ierr = DMRefine(dm, PetscObjectComm((PetscObject) dm), &refinedMesh);CHKERRQ(ierr);
2455       /* Total hack since we do not pass in a pointer */
2456       ierr = DMPlexReplace_Static(dm, refinedMesh);CHKERRQ(ierr);
2457       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2458       if (coordFunc) {
2459         ierr = DMPlexRemapGeometry(dm, 0.0, coordFunc);CHKERRQ(ierr);
2460         ((DM_Plex*) dm->data)->coordFunc = coordFunc;
2461       }
2462       ierr = DMDestroy(&refinedMesh);CHKERRQ(ierr);
2463     }
2464   }
2465   /* Handle DMPlex coarsening */
2466   ierr = PetscOptionsBoundedInt("-dm_coarsen", "Coarsen the mesh", "DMCreate", coarsen, &coarsen, NULL,0);CHKERRQ(ierr);
2467   ierr = PetscOptionsBoundedInt("-dm_coarsen_hierarchy", "The number of coarsenings", "DMCreate", coarsen, &coarsen, &isHierarchy,0);CHKERRQ(ierr);
2468   if (coarsen && isHierarchy) {
2469     DM *dms;
2470 
2471     ierr = PetscMalloc1(coarsen, &dms);CHKERRQ(ierr);
2472     ierr = DMCoarsenHierarchy(dm, coarsen, dms);CHKERRQ(ierr);
2473     /* Free DMs */
2474     for (r = 0; r < coarsen; ++r) {
2475       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dms[r]);CHKERRQ(ierr);
2476       ierr = DMDestroy(&dms[r]);CHKERRQ(ierr);
2477     }
2478     ierr = PetscFree(dms);CHKERRQ(ierr);
2479   } else {
2480     for (r = 0; r < coarsen; ++r) {
2481       DM coarseMesh;
2482 
2483       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2484       ierr = DMCoarsen(dm, PetscObjectComm((PetscObject) dm), &coarseMesh);CHKERRQ(ierr);
2485       /* Total hack since we do not pass in a pointer */
2486       ierr = DMPlexReplace_Static(dm, coarseMesh);CHKERRQ(ierr);
2487       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2488       ierr = DMDestroy(&coarseMesh);CHKERRQ(ierr);
2489     }
2490   }
2491   /* Handle */
2492   ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2493   ierr = PetscOptionsTail();CHKERRQ(ierr);
2494   PetscFunctionReturn(0);
2495 }
2496 
2497 static PetscErrorCode DMCreateGlobalVector_Plex(DM dm,Vec *vec)
2498 {
2499   PetscErrorCode ierr;
2500 
2501   PetscFunctionBegin;
2502   ierr = DMCreateGlobalVector_Section_Private(dm,vec);CHKERRQ(ierr);
2503   /* ierr = VecSetOperation(*vec, VECOP_DUPLICATE, (void(*)(void)) VecDuplicate_MPI_DM);CHKERRQ(ierr); */
2504   ierr = VecSetOperation(*vec, VECOP_VIEW, (void (*)(void)) VecView_Plex);CHKERRQ(ierr);
2505   ierr = VecSetOperation(*vec, VECOP_VIEWNATIVE, (void (*)(void)) VecView_Plex_Native);CHKERRQ(ierr);
2506   ierr = VecSetOperation(*vec, VECOP_LOAD, (void (*)(void)) VecLoad_Plex);CHKERRQ(ierr);
2507   ierr = VecSetOperation(*vec, VECOP_LOADNATIVE, (void (*)(void)) VecLoad_Plex_Native);CHKERRQ(ierr);
2508   PetscFunctionReturn(0);
2509 }
2510 
2511 static PetscErrorCode DMCreateLocalVector_Plex(DM dm,Vec *vec)
2512 {
2513   PetscErrorCode ierr;
2514 
2515   PetscFunctionBegin;
2516   ierr = DMCreateLocalVector_Section_Private(dm,vec);CHKERRQ(ierr);
2517   ierr = VecSetOperation(*vec, VECOP_VIEW, (void (*)(void)) VecView_Plex_Local);CHKERRQ(ierr);
2518   ierr = VecSetOperation(*vec, VECOP_LOAD, (void (*)(void)) VecLoad_Plex_Local);CHKERRQ(ierr);
2519   PetscFunctionReturn(0);
2520 }
2521 
2522 static PetscErrorCode DMGetDimPoints_Plex(DM dm, PetscInt dim, PetscInt *pStart, PetscInt *pEnd)
2523 {
2524   PetscInt       depth, d;
2525   PetscErrorCode ierr;
2526 
2527   PetscFunctionBegin;
2528   ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
2529   if (depth == 1) {
2530     ierr = DMGetDimension(dm, &d);CHKERRQ(ierr);
2531     if (dim == 0)      {ierr = DMPlexGetDepthStratum(dm, dim, pStart, pEnd);CHKERRQ(ierr);}
2532     else if (dim == d) {ierr = DMPlexGetDepthStratum(dm, 1, pStart, pEnd);CHKERRQ(ierr);}
2533     else               {*pStart = 0; *pEnd = 0;}
2534   } else {
2535     ierr = DMPlexGetDepthStratum(dm, dim, pStart, pEnd);CHKERRQ(ierr);
2536   }
2537   PetscFunctionReturn(0);
2538 }
2539 
2540 static PetscErrorCode DMGetNeighbors_Plex(DM dm, PetscInt *nranks, const PetscMPIInt *ranks[])
2541 {
2542   PetscSF           sf;
2543   PetscInt          niranks, njranks, n;
2544   const PetscMPIInt *iranks, *jranks;
2545   DM_Plex           *data = (DM_Plex*) dm->data;
2546   PetscErrorCode    ierr;
2547 
2548   PetscFunctionBegin;
2549   ierr = DMGetPointSF(dm, &sf);CHKERRQ(ierr);
2550   if (!data->neighbors) {
2551     ierr = PetscSFGetRootRanks(sf, &njranks, &jranks, NULL, NULL, NULL);CHKERRQ(ierr);
2552     ierr = PetscSFGetLeafRanks(sf, &niranks, &iranks, NULL, NULL);CHKERRQ(ierr);
2553     ierr = PetscMalloc1(njranks + niranks + 1, &data->neighbors);CHKERRQ(ierr);
2554     ierr = PetscArraycpy(data->neighbors + 1, jranks, njranks);CHKERRQ(ierr);
2555     ierr = PetscArraycpy(data->neighbors + njranks + 1, iranks, niranks);CHKERRQ(ierr);
2556     n = njranks + niranks;
2557     ierr = PetscSortRemoveDupsMPIInt(&n, data->neighbors + 1);CHKERRQ(ierr);
2558     /* The following cast should never fail: can't have more neighbors than PETSC_MPI_INT_MAX */
2559     ierr = PetscMPIIntCast(n, data->neighbors);CHKERRQ(ierr);
2560   }
2561   if (nranks) *nranks = data->neighbors[0];
2562   if (ranks) {
2563     if (data->neighbors[0]) *ranks = data->neighbors + 1;
2564     else                    *ranks = NULL;
2565   }
2566   PetscFunctionReturn(0);
2567 }
2568 
2569 static PetscErrorCode DMInitialize_Plex(DM dm)
2570 {
2571   PetscErrorCode ierr;
2572 
2573   PetscFunctionBegin;
2574   dm->ops->view                            = DMView_Plex;
2575   dm->ops->load                            = DMLoad_Plex;
2576   dm->ops->setfromoptions                  = DMSetFromOptions_Plex;
2577   dm->ops->clone                           = DMClone_Plex;
2578   dm->ops->setup                           = DMSetUp_Plex;
2579   dm->ops->createlocalsection              = DMCreateLocalSection_Plex;
2580   dm->ops->createdefaultconstraints        = DMCreateDefaultConstraints_Plex;
2581   dm->ops->createglobalvector              = DMCreateGlobalVector_Plex;
2582   dm->ops->createlocalvector               = DMCreateLocalVector_Plex;
2583   dm->ops->getlocaltoglobalmapping         = NULL;
2584   dm->ops->createfieldis                   = NULL;
2585   dm->ops->createcoordinatedm              = DMCreateCoordinateDM_Plex;
2586   dm->ops->createcoordinatefield           = DMCreateCoordinateField_Plex;
2587   dm->ops->getcoloring                     = NULL;
2588   dm->ops->creatematrix                    = DMCreateMatrix_Plex;
2589   dm->ops->createinterpolation             = DMCreateInterpolation_Plex;
2590   dm->ops->createmassmatrix                = DMCreateMassMatrix_Plex;
2591   dm->ops->createinjection                 = DMCreateInjection_Plex;
2592   dm->ops->refine                          = DMRefine_Plex;
2593   dm->ops->coarsen                         = DMCoarsen_Plex;
2594   dm->ops->refinehierarchy                 = DMRefineHierarchy_Plex;
2595   dm->ops->coarsenhierarchy                = DMCoarsenHierarchy_Plex;
2596   dm->ops->adaptlabel                      = DMAdaptLabel_Plex;
2597   dm->ops->adaptmetric                     = DMAdaptMetric_Plex;
2598   dm->ops->globaltolocalbegin              = NULL;
2599   dm->ops->globaltolocalend                = NULL;
2600   dm->ops->localtoglobalbegin              = NULL;
2601   dm->ops->localtoglobalend                = NULL;
2602   dm->ops->destroy                         = DMDestroy_Plex;
2603   dm->ops->createsubdm                     = DMCreateSubDM_Plex;
2604   dm->ops->createsuperdm                   = DMCreateSuperDM_Plex;
2605   dm->ops->getdimpoints                    = DMGetDimPoints_Plex;
2606   dm->ops->locatepoints                    = DMLocatePoints_Plex;
2607   dm->ops->projectfunctionlocal            = DMProjectFunctionLocal_Plex;
2608   dm->ops->projectfunctionlabellocal       = DMProjectFunctionLabelLocal_Plex;
2609   dm->ops->projectfieldlocal               = DMProjectFieldLocal_Plex;
2610   dm->ops->projectfieldlabellocal          = DMProjectFieldLabelLocal_Plex;
2611   dm->ops->projectbdfieldlabellocal        = DMProjectBdFieldLabelLocal_Plex;
2612   dm->ops->computel2diff                   = DMComputeL2Diff_Plex;
2613   dm->ops->computel2gradientdiff           = DMComputeL2GradientDiff_Plex;
2614   dm->ops->computel2fielddiff              = DMComputeL2FieldDiff_Plex;
2615   dm->ops->getneighbors                    = DMGetNeighbors_Plex;
2616   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMPlexInsertBoundaryValues_C",DMPlexInsertBoundaryValues_Plex);CHKERRQ(ierr);
2617   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMSetUpGLVisViewer_C",DMSetUpGLVisViewer_Plex);CHKERRQ(ierr);
2618   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMCreateNeumannOverlap_C",DMCreateNeumannOverlap_Plex);CHKERRQ(ierr);
2619   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMPlexGetOverlap_C",DMPlexGetOverlap_Plex);CHKERRQ(ierr);
2620   PetscFunctionReturn(0);
2621 }
2622 
2623 PETSC_INTERN PetscErrorCode DMClone_Plex(DM dm, DM *newdm)
2624 {
2625   DM_Plex        *mesh = (DM_Plex *) dm->data;
2626   PetscErrorCode ierr;
2627 
2628   PetscFunctionBegin;
2629   mesh->refct++;
2630   (*newdm)->data = mesh;
2631   ierr = PetscObjectChangeTypeName((PetscObject) *newdm, DMPLEX);CHKERRQ(ierr);
2632   ierr = DMInitialize_Plex(*newdm);CHKERRQ(ierr);
2633   PetscFunctionReturn(0);
2634 }
2635 
2636 /*MC
2637   DMPLEX = "plex" - A DM object that encapsulates an unstructured mesh, or CW Complex, which can be expressed using a Hasse Diagram.
2638                     In the local representation, Vecs contain all unknowns in the interior and shared boundary. This is
2639                     specified by a PetscSection object. Ownership in the global representation is determined by
2640                     ownership of the underlying DMPlex points. This is specified by another PetscSection object.
2641 
2642   Options Database Keys:
2643 + -dm_plex_hash_location             - Use grid hashing for point location
2644 . -dm_plex_partition_balance         - Attempt to evenly divide points on partition boundary between processes
2645 . -dm_plex_remesh_bd                 - Allow changes to the boundary on remeshing
2646 . -dm_plex_max_projection_height     - Maxmimum mesh point height used to project locally
2647 . -dm_plex_regular_refinement        - Use special nested projection algorithm for regular refinement
2648 . -dm_plex_check_symmetry            - Check that the adjacency information in the mesh is symmetric
2649 . -dm_plex_check_skeleton <celltype> - Check that each cell has the correct number of vertices
2650 . -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
2651 . -dm_plex_check_geometry            - Check that cells have positive volume
2652 . -dm_view :mesh.tex:ascii_latex     - View the mesh in LaTeX/TikZ
2653 . -dm_plex_view_scale <num>          - Scale the TikZ
2654 - -dm_plex_print_fem <num>           - View FEM assembly information, such as element vectors and matrices
2655 
2656 
2657   Level: intermediate
2658 
2659 .seealso: DMType, DMPlexCreate(), DMCreate(), DMSetType()
2660 M*/
2661 
2662 PETSC_EXTERN PetscErrorCode DMCreate_Plex(DM dm)
2663 {
2664   DM_Plex       *mesh;
2665   PetscInt       unit;
2666   PetscErrorCode ierr;
2667 
2668   PetscFunctionBegin;
2669   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
2670   ierr     = PetscNewLog(dm,&mesh);CHKERRQ(ierr);
2671   dm->dim  = 0;
2672   dm->data = mesh;
2673 
2674   mesh->refct             = 1;
2675   ierr                    = PetscSectionCreate(PetscObjectComm((PetscObject)dm), &mesh->coneSection);CHKERRQ(ierr);
2676   mesh->maxConeSize       = 0;
2677   mesh->cones             = NULL;
2678   mesh->coneOrientations  = NULL;
2679   ierr                    = PetscSectionCreate(PetscObjectComm((PetscObject)dm), &mesh->supportSection);CHKERRQ(ierr);
2680   mesh->maxSupportSize    = 0;
2681   mesh->supports          = NULL;
2682   mesh->refinementUniform = PETSC_TRUE;
2683   mesh->refinementLimit   = -1.0;
2684   mesh->interpolated      = DMPLEX_INTERPOLATED_INVALID;
2685   mesh->interpolatedCollective = DMPLEX_INTERPOLATED_INVALID;
2686 
2687   mesh->facesTmp = NULL;
2688 
2689   mesh->tetgenOpts   = NULL;
2690   mesh->triangleOpts = NULL;
2691   ierr = PetscPartitionerCreate(PetscObjectComm((PetscObject)dm), &mesh->partitioner);CHKERRQ(ierr);
2692   mesh->remeshBd     = PETSC_FALSE;
2693 
2694   mesh->subpointMap = NULL;
2695 
2696   for (unit = 0; unit < NUM_PETSC_UNITS; ++unit) mesh->scale[unit] = 1.0;
2697 
2698   mesh->regularRefinement   = PETSC_FALSE;
2699   mesh->depthState          = -1;
2700   mesh->celltypeState       = -1;
2701   mesh->globalVertexNumbers = NULL;
2702   mesh->globalCellNumbers   = NULL;
2703   mesh->anchorSection       = NULL;
2704   mesh->anchorIS            = NULL;
2705   mesh->createanchors       = NULL;
2706   mesh->computeanchormatrix = NULL;
2707   mesh->parentSection       = NULL;
2708   mesh->parents             = NULL;
2709   mesh->childIDs            = NULL;
2710   mesh->childSection        = NULL;
2711   mesh->children            = NULL;
2712   mesh->referenceTree       = NULL;
2713   mesh->getchildsymmetry    = NULL;
2714   mesh->vtkCellHeight       = 0;
2715   mesh->useAnchors          = PETSC_FALSE;
2716 
2717   mesh->maxProjectionHeight = 0;
2718 
2719   mesh->neighbors           = NULL;
2720 
2721   mesh->printSetValues = PETSC_FALSE;
2722   mesh->printFEM       = 0;
2723   mesh->printTol       = 1.0e-10;
2724 
2725   ierr = DMInitialize_Plex(dm);CHKERRQ(ierr);
2726   PetscFunctionReturn(0);
2727 }
2728 
2729 /*@
2730   DMPlexCreate - Creates a DMPlex object, which encapsulates an unstructured mesh, or CW complex, which can be expressed using a Hasse Diagram.
2731 
2732   Collective
2733 
2734   Input Parameter:
2735 . comm - The communicator for the DMPlex object
2736 
2737   Output Parameter:
2738 . mesh  - The DMPlex object
2739 
2740   Level: beginner
2741 
2742 @*/
2743 PetscErrorCode DMPlexCreate(MPI_Comm comm, DM *mesh)
2744 {
2745   PetscErrorCode ierr;
2746 
2747   PetscFunctionBegin;
2748   PetscValidPointer(mesh,2);
2749   ierr = DMCreate(comm, mesh);CHKERRQ(ierr);
2750   ierr = DMSetType(*mesh, DMPLEX);CHKERRQ(ierr);
2751   PetscFunctionReturn(0);
2752 }
2753 
2754 static PetscErrorCode DMPlexInvertCell_Internal(PetscInt dim, PetscInt numCorners, PetscInt cone[])
2755 {
2756   PetscErrorCode ierr;
2757 
2758   PetscFunctionBegin;
2759   if (dim != 3) PetscFunctionReturn(0);
2760   switch (numCorners) {
2761   case 4: ierr = DMPlexInvertCell(DM_POLYTOPE_TETRAHEDRON,cone);CHKERRQ(ierr); break;
2762   case 6: ierr = DMPlexInvertCell(DM_POLYTOPE_TRI_PRISM,cone);CHKERRQ(ierr); break;
2763   case 8: ierr = DMPlexInvertCell(DM_POLYTOPE_HEXAHEDRON,cone);CHKERRQ(ierr); break;
2764   default: break;
2765   }
2766   PetscFunctionReturn(0);
2767 }
2768 
2769 // TODO: invertCells should be removed or added also to DMPlexCreateFromCellListParallelPetsc() and DMPlexCreateFromCellListPetsc()
2770 /*@C
2771   DMPlexBuildFromCellListParallel - Build distributed DMPLEX topology from a list of vertices for each cell (common mesh generator output)
2772 
2773   Input Parameters:
2774 + dm - The DM
2775 . numCells - The number of cells owned by this process
2776 . numVertices - The number of vertices owned by this process
2777 . numCorners - The number of vertices for each cell
2778 . cells - An array of numCells*numCorners numbers, the global vertex numbers for each cell
2779 - invertCells - Flag indicating that cells should be inverted (e.g. XDMF format)
2780 
2781   Output Parameter:
2782 . vertexSF - (Optional) SF describing complete vertex ownership
2783 
2784   Notes:
2785   Two triangles sharing a face
2786 $
2787 $        2
2788 $      / | \
2789 $     /  |  \
2790 $    /   |   \
2791 $   0  0 | 1  3
2792 $    \   |   /
2793 $     \  |  /
2794 $      \ | /
2795 $        1
2796 would have input
2797 $  numCells = 2, numVertices = 4
2798 $  cells = [0 1 2  1 3 2]
2799 $
2800 which would result in the DMPlex
2801 $
2802 $        4
2803 $      / | \
2804 $     /  |  \
2805 $    /   |   \
2806 $   2  0 | 1  5
2807 $    \   |   /
2808 $     \  |  /
2809 $      \ | /
2810 $        3
2811 
2812   The cell distribution is arbitrary non-overlapping, independent of the vertex distribution.
2813 
2814   Not currently supported in Fortran.
2815 
2816   Level: advanced
2817 
2818 .seealso: DMPlexBuildFromCellList(), DMPlexCreateFromCellListParallelPetsc(), DMPlexBuildCoordinatesFromCellListParallel()
2819 @*/
2820 PetscErrorCode DMPlexBuildFromCellListParallel(DM dm, PetscInt numCells, PetscInt numVertices, PetscInt numCorners, const PetscInt cells[], PetscBool invertCells, PetscSF *vertexSF)
2821 {
2822   PetscSF         sfPoint, sfVert;
2823   PetscLayout     vLayout;
2824   PetscHSetI      vhash;
2825   PetscSFNode    *remoteVerticesAdj, *vertexLocal, *vertexOwner, *remoteVertex;
2826   const PetscInt *vrange;
2827   PetscInt        numVerticesAdj, off = 0, *verticesAdj, numVerticesGhost = 0, *localVertex, *cone, c, p, v, g, dim;
2828   PetscMPIInt     rank, size;
2829   PetscErrorCode  ierr;
2830 
2831   PetscFunctionBegin;
2832   ierr = PetscLogEventBegin(DMPLEX_BuildFromCellList,dm,0,0,0);CHKERRQ(ierr);
2833   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject) dm), &rank);CHKERRQ(ierr);
2834   ierr = MPI_Comm_size(PetscObjectComm((PetscObject) dm), &size);CHKERRQ(ierr);
2835   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
2836   /* Partition vertices */
2837   ierr = PetscLayoutCreate(PetscObjectComm((PetscObject) dm), &vLayout);CHKERRQ(ierr);
2838   ierr = PetscLayoutSetLocalSize(vLayout, numVertices);CHKERRQ(ierr);
2839   ierr = PetscLayoutSetBlockSize(vLayout, 1);CHKERRQ(ierr);
2840   ierr = PetscLayoutSetUp(vLayout);CHKERRQ(ierr);
2841   ierr = PetscLayoutGetRanges(vLayout, &vrange);CHKERRQ(ierr);
2842   /* Count vertices and map them to procs */
2843   ierr = PetscHSetICreate(&vhash);CHKERRQ(ierr);
2844   for (c = 0; c < numCells; ++c) {
2845     for (p = 0; p < numCorners; ++p) {
2846       ierr = PetscHSetIAdd(vhash, cells[c*numCorners+p]);CHKERRQ(ierr);
2847     }
2848   }
2849   ierr = PetscHSetIGetSize(vhash, &numVerticesAdj);CHKERRQ(ierr);
2850   ierr = PetscMalloc1(numVerticesAdj, &verticesAdj);CHKERRQ(ierr);
2851   ierr = PetscHSetIGetElems(vhash, &off, verticesAdj);CHKERRQ(ierr);
2852   ierr = PetscHSetIDestroy(&vhash);CHKERRQ(ierr);
2853   if (off != numVerticesAdj) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Invalid number of local vertices %D should be %D", off, numVerticesAdj);
2854   ierr = PetscSortInt(numVerticesAdj, verticesAdj);CHKERRQ(ierr);
2855   ierr = PetscMalloc1(numVerticesAdj, &remoteVerticesAdj);CHKERRQ(ierr);
2856   for (v = 0; v < numVerticesAdj; ++v) {
2857     const PetscInt gv = verticesAdj[v];
2858     PetscInt       vrank;
2859 
2860     ierr = PetscFindInt(gv, size+1, vrange, &vrank);CHKERRQ(ierr);
2861     vrank = vrank < 0 ? -(vrank+2) : vrank;
2862     remoteVerticesAdj[v].index = gv - vrange[vrank];
2863     remoteVerticesAdj[v].rank  = vrank;
2864   }
2865   /* Create cones */
2866   ierr = DMPlexSetChart(dm, 0, numCells+numVerticesAdj);CHKERRQ(ierr);
2867   for (c = 0; c < numCells; ++c) {ierr = DMPlexSetConeSize(dm, c, numCorners);CHKERRQ(ierr);}
2868   ierr = DMSetUp(dm);CHKERRQ(ierr);
2869   ierr = DMGetWorkArray(dm, numCorners, MPIU_INT, &cone);CHKERRQ(ierr);
2870   for (c = 0; c < numCells; ++c) {
2871     for (p = 0; p < numCorners; ++p) {
2872       const PetscInt gv = cells[c*numCorners+p];
2873       PetscInt       lv;
2874 
2875       ierr = PetscFindInt(gv, numVerticesAdj, verticesAdj, &lv);CHKERRQ(ierr);
2876       if (lv < 0) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Could not find global vertex %D in local connectivity", gv);
2877       cone[p] = lv+numCells;
2878     }
2879     if (invertCells) {ierr = DMPlexInvertCell_Internal(dim, numCorners, cone);CHKERRQ(ierr);}
2880     ierr = DMPlexSetCone(dm, c, cone);CHKERRQ(ierr);
2881   }
2882   ierr = DMRestoreWorkArray(dm, numCorners, MPIU_INT, &cone);CHKERRQ(ierr);
2883   /* Create SF for vertices */
2884   ierr = PetscSFCreate(PetscObjectComm((PetscObject)dm), &sfVert);CHKERRQ(ierr);
2885   ierr = PetscObjectSetName((PetscObject) sfVert, "Vertex Ownership SF");CHKERRQ(ierr);
2886   ierr = PetscSFSetFromOptions(sfVert);CHKERRQ(ierr);
2887   ierr = PetscSFSetGraph(sfVert, numVertices, numVerticesAdj, NULL, PETSC_OWN_POINTER, remoteVerticesAdj, PETSC_OWN_POINTER);CHKERRQ(ierr);
2888   ierr = PetscFree(verticesAdj);CHKERRQ(ierr);
2889   /* Build pointSF */
2890   ierr = PetscMalloc2(numVerticesAdj, &vertexLocal, numVertices, &vertexOwner);CHKERRQ(ierr);
2891   for (v = 0; v < numVerticesAdj; ++v) {vertexLocal[v].index = v+numCells; vertexLocal[v].rank = rank;}
2892   for (v = 0; v < numVertices;    ++v) {vertexOwner[v].index = -1;         vertexOwner[v].rank = -1;}
2893   ierr = PetscSFReduceBegin(sfVert, MPIU_2INT, vertexLocal, vertexOwner, MPI_MAXLOC);CHKERRQ(ierr);
2894   ierr = PetscSFReduceEnd(sfVert, MPIU_2INT, vertexLocal, vertexOwner, MPI_MAXLOC);CHKERRQ(ierr);
2895   for (v = 0; v < numVertices;    ++v) if (vertexOwner[v].rank < 0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Global vertex %d on rank %d was unclaimed", v + vrange[rank], rank);
2896   ierr = PetscSFBcastBegin(sfVert, MPIU_2INT, vertexOwner, vertexLocal);CHKERRQ(ierr);
2897   ierr = PetscSFBcastEnd(sfVert, MPIU_2INT, vertexOwner, vertexLocal);CHKERRQ(ierr);
2898   for (v = 0; v < numVerticesAdj; ++v) if (vertexLocal[v].rank != rank) ++numVerticesGhost;
2899   ierr = PetscMalloc1(numVerticesGhost, &localVertex);CHKERRQ(ierr);
2900   ierr = PetscMalloc1(numVerticesGhost, &remoteVertex);CHKERRQ(ierr);
2901   for (v = 0, g = 0; v < numVerticesAdj; ++v) {
2902     if (vertexLocal[v].rank != rank) {
2903       localVertex[g]        = v+numCells;
2904       remoteVertex[g].index = vertexLocal[v].index;
2905       remoteVertex[g].rank  = vertexLocal[v].rank;
2906       ++g;
2907     }
2908   }
2909   ierr = PetscFree2(vertexLocal, vertexOwner);CHKERRQ(ierr);
2910   if (g != numVerticesGhost) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid number of vertex ghosts %D should be %D", g, numVerticesGhost);
2911   ierr = DMGetPointSF(dm, &sfPoint);CHKERRQ(ierr);
2912   ierr = PetscObjectSetName((PetscObject) sfPoint, "point SF");CHKERRQ(ierr);
2913   ierr = PetscSFSetGraph(sfPoint, numCells+numVerticesAdj, numVerticesGhost, localVertex, PETSC_OWN_POINTER, remoteVertex, PETSC_OWN_POINTER);CHKERRQ(ierr);
2914   ierr = PetscLayoutDestroy(&vLayout);CHKERRQ(ierr);
2915   /* Fill in the rest of the topology structure */
2916   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
2917   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
2918   ierr = PetscLogEventEnd(DMPLEX_BuildFromCellList,dm,0,0,0);CHKERRQ(ierr);
2919   if (vertexSF) *vertexSF = sfVert;
2920   else {ierr = PetscSFDestroy(&sfVert);CHKERRQ(ierr);}
2921   PetscFunctionReturn(0);
2922 }
2923 
2924 /*@C
2925   DMPlexBuildCoordinatesFromCellListParallel - Build DM coordinates from a list of coordinates for each owned vertex (common mesh generator output)
2926 
2927   Input Parameters:
2928 + dm - The DM
2929 . spaceDim - The spatial dimension used for coordinates
2930 . numCells - The number of cells owned by this process
2931 . sfVert - SF describing complete vertex ownership
2932 - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex
2933 
2934   Level: advanced
2935 
2936   Notes:
2937   Not currently supported in Fortran.
2938 
2939 .seealso: DMPlexBuildCoordinatesFromCellList(), DMPlexCreateFromCellListParallelPetsc(), DMPlexBuildFromCellListParallel()
2940 @*/
2941 PetscErrorCode DMPlexBuildCoordinatesFromCellListParallel(DM dm, PetscInt spaceDim, PetscInt numCells, PetscSF sfVert, const PetscReal vertexCoords[])
2942 {
2943   PetscSection   coordSection;
2944   Vec            coordinates;
2945   PetscScalar   *coords;
2946   PetscInt       numVertices, numVerticesAdj, coordSize, v;
2947   PetscErrorCode ierr;
2948 
2949   PetscFunctionBegin;
2950   ierr = PetscLogEventBegin(DMPLEX_BuildCoordinatesFromCellList,dm,0,0,0);CHKERRQ(ierr);
2951   ierr = DMSetCoordinateDim(dm, spaceDim);CHKERRQ(ierr);
2952   ierr = PetscSFGetGraph(sfVert, &numVertices, &numVerticesAdj, NULL, NULL);CHKERRQ(ierr);
2953   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
2954   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
2955   ierr = PetscSectionSetFieldComponents(coordSection, 0, spaceDim);CHKERRQ(ierr);
2956   ierr = PetscSectionSetChart(coordSection, numCells, numCells + numVerticesAdj);CHKERRQ(ierr);
2957   for (v = numCells; v < numCells+numVerticesAdj; ++v) {
2958     ierr = PetscSectionSetDof(coordSection, v, spaceDim);CHKERRQ(ierr);
2959     ierr = PetscSectionSetFieldDof(coordSection, v, 0, spaceDim);CHKERRQ(ierr);
2960   }
2961   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
2962   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
2963   ierr = VecCreate(PetscObjectComm((PetscObject)dm), &coordinates);CHKERRQ(ierr);
2964   ierr = VecSetBlockSize(coordinates, spaceDim);CHKERRQ(ierr);
2965   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
2966   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
2967   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
2968   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
2969   {
2970     MPI_Datatype coordtype;
2971 
2972     /* Need a temp buffer for coords if we have complex/single */
2973     ierr = MPI_Type_contiguous(spaceDim, MPIU_SCALAR, &coordtype);CHKERRQ(ierr);
2974     ierr = MPI_Type_commit(&coordtype);CHKERRQ(ierr);
2975 #if defined(PETSC_USE_COMPLEX)
2976     {
2977     PetscScalar *svertexCoords;
2978     PetscInt    i;
2979     ierr = PetscMalloc1(numVertices*spaceDim,&svertexCoords);CHKERRQ(ierr);
2980     for (i=0; i<numVertices*spaceDim; i++) svertexCoords[i] = vertexCoords[i];
2981     ierr = PetscSFBcastBegin(sfVert, coordtype, svertexCoords, coords);CHKERRQ(ierr);
2982     ierr = PetscSFBcastEnd(sfVert, coordtype, svertexCoords, coords);CHKERRQ(ierr);
2983     ierr = PetscFree(svertexCoords);CHKERRQ(ierr);
2984     }
2985 #else
2986     ierr = PetscSFBcastBegin(sfVert, coordtype, vertexCoords, coords);CHKERRQ(ierr);
2987     ierr = PetscSFBcastEnd(sfVert, coordtype, vertexCoords, coords);CHKERRQ(ierr);
2988 #endif
2989     ierr = MPI_Type_free(&coordtype);CHKERRQ(ierr);
2990   }
2991   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
2992   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
2993   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
2994   ierr = PetscLogEventEnd(DMPLEX_BuildCoordinatesFromCellList,dm,0,0,0);CHKERRQ(ierr);
2995   PetscFunctionReturn(0);
2996 }
2997 
2998 /*@
2999   DMPlexCreateFromCellListParallelPetsc - Create distributed DMPLEX from a list of vertices for each cell (common mesh generator output)
3000 
3001   Input Parameters:
3002 + comm - The communicator
3003 . dim - The topological dimension of the mesh
3004 . numCells - The number of cells owned by this process
3005 . numVertices - The number of vertices owned by this process
3006 . numCorners - The number of vertices for each cell
3007 . interpolate - Flag indicating that intermediate mesh entities (faces, edges) should be created automatically
3008 . cells - An array of numCells*numCorners numbers, the global vertex numbers for each cell
3009 . spaceDim - The spatial dimension used for coordinates
3010 - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex
3011 
3012   Output Parameter:
3013 + dm - The DM
3014 - vertexSF - (Optional) SF describing complete vertex ownership
3015 
3016   Notes:
3017   This function is just a convenient sequence of DMCreate(), DMSetType(), DMSetDimension(),
3018   DMPlexBuildFromCellListParallel(), DMPlexInterpolate(), DMPlexBuildCoordinatesFromCellListParallel()
3019 
3020   Level: intermediate
3021 
3022 .seealso: DMPlexCreateFromCellListPetsc(), DMPlexBuildFromCellListParallel(), DMPlexBuildCoordinatesFromCellListParallel(), DMPlexCreateFromDAG(), DMPlexCreate()
3023 @*/
3024 PetscErrorCode DMPlexCreateFromCellListParallelPetsc(MPI_Comm comm, PetscInt dim, PetscInt numCells, PetscInt numVertices, PetscInt numCorners, PetscBool interpolate, const PetscInt cells[], PetscInt spaceDim, const PetscReal vertexCoords[], PetscSF *vertexSF, DM *dm)
3025 {
3026   PetscSF        sfVert;
3027   PetscErrorCode ierr;
3028 
3029   PetscFunctionBegin;
3030   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
3031   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
3032   PetscValidLogicalCollectiveInt(*dm, dim, 2);
3033   PetscValidLogicalCollectiveInt(*dm, spaceDim, 8);
3034   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
3035   ierr = DMPlexBuildFromCellListParallel(*dm, numCells, numVertices, numCorners, cells, PETSC_FALSE, &sfVert);CHKERRQ(ierr);
3036   if (interpolate) {
3037     DM idm;
3038 
3039     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
3040     ierr = DMDestroy(dm);CHKERRQ(ierr);
3041     *dm  = idm;
3042   }
3043   ierr = DMPlexBuildCoordinatesFromCellListParallel(*dm, spaceDim, numCells, sfVert, vertexCoords);CHKERRQ(ierr);
3044   if (vertexSF) *vertexSF = sfVert;
3045   else {ierr = PetscSFDestroy(&sfVert);CHKERRQ(ierr);}
3046   PetscFunctionReturn(0);
3047 }
3048 
3049 
3050 /*@
3051   DMPlexCreateFromCellListParallel - Deprecated, use DMPlexCreateFromCellListParallelPetsc()
3052 
3053   Level: deprecated
3054 
3055 .seealso: DMPlexCreateFromCellListParallelPetsc()
3056 @*/
3057 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)
3058 {
3059   PetscErrorCode ierr;
3060   PetscInt       i;
3061   PetscInt       *pintCells;
3062 
3063   PetscFunctionBegin;
3064   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));
3065   if (sizeof(int) == sizeof(PetscInt)) {
3066     pintCells = (PetscInt *) cells;
3067   } else {
3068     ierr = PetscMalloc1(numCells*numCorners, &pintCells);CHKERRQ(ierr);
3069     for (i = 0; i < numCells*numCorners; i++) {
3070       pintCells[i] = (PetscInt) cells[i];
3071     }
3072   }
3073   ierr = DMPlexCreateFromCellListParallelPetsc(comm, dim, numCells, numVertices, numCorners, interpolate, pintCells, spaceDim, vertexCoords, vertexSF, dm);CHKERRQ(ierr);
3074   if (sizeof(int) != sizeof(PetscInt)) {
3075     ierr = PetscFree(pintCells);CHKERRQ(ierr);
3076   }
3077   PetscFunctionReturn(0);
3078 }
3079 
3080 // TODO: invertCells should be removed or added also to DMPlexCreateFromCellListParallelPetsc() and DMPlexCreateFromCellListPetsc()
3081 /*@C
3082   DMPlexBuildFromCellList - Build DMPLEX topology from a list of vertices for each cell (common mesh generator output)
3083 
3084   Input Parameters:
3085 + dm - The DM
3086 . numCells - The number of cells owned by this process
3087 . numVertices - The number of vertices owned by this process
3088 . numCorners - The number of vertices for each cell
3089 . cells - An array of numCells*numCorners numbers, the global vertex numbers for each cell
3090 - invertCells - Flag indicating that cells should be inverted (e.g. XDMF format)
3091 
3092   Level: advanced
3093 
3094   Notes:
3095   Two triangles sharing a face
3096 $
3097 $        2
3098 $      / | \
3099 $     /  |  \
3100 $    /   |   \
3101 $   0  0 | 1  3
3102 $    \   |   /
3103 $     \  |  /
3104 $      \ | /
3105 $        1
3106 would have input
3107 $  numCells = 2, numVertices = 4
3108 $  cells = [0 1 2  1 3 2]
3109 $
3110 which would result in the DMPlex
3111 $
3112 $        4
3113 $      / | \
3114 $     /  |  \
3115 $    /   |   \
3116 $   2  0 | 1  5
3117 $    \   |   /
3118 $     \  |  /
3119 $      \ | /
3120 $        3
3121 
3122   Not currently supported in Fortran.
3123 
3124 .seealso: DMPlexBuildFromCellListParallel(), DMPlexBuildCoordinatesFromCellList(), DMPlexCreateFromCellListPetsc()
3125 @*/
3126 PetscErrorCode DMPlexBuildFromCellList(DM dm, PetscInt numCells, PetscInt numVertices, PetscInt numCorners, const PetscInt cells[], PetscBool invertCells)
3127 {
3128   PetscInt      *cone, c, p, dim;
3129   PetscErrorCode ierr;
3130 
3131   PetscFunctionBegin;
3132   ierr = PetscLogEventBegin(DMPLEX_BuildFromCellList,dm,0,0,0);CHKERRQ(ierr);
3133   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
3134   ierr = DMPlexSetChart(dm, 0, numCells+numVertices);CHKERRQ(ierr);
3135   for (c = 0; c < numCells; ++c) {
3136     ierr = DMPlexSetConeSize(dm, c, numCorners);CHKERRQ(ierr);
3137   }
3138   ierr = DMSetUp(dm);CHKERRQ(ierr);
3139   ierr = DMGetWorkArray(dm, numCorners, MPIU_INT, &cone);CHKERRQ(ierr);
3140   for (c = 0; c < numCells; ++c) {
3141     for (p = 0; p < numCorners; ++p) {
3142       cone[p] = cells[c*numCorners+p]+numCells;
3143     }
3144     if (invertCells) {ierr = DMPlexInvertCell_Internal(dim, numCorners, cone);CHKERRQ(ierr); }
3145     ierr = DMPlexSetCone(dm, c, cone);CHKERRQ(ierr);
3146   }
3147   ierr = DMRestoreWorkArray(dm, numCorners, MPIU_INT, &cone);CHKERRQ(ierr);
3148   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
3149   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
3150   ierr = PetscLogEventEnd(DMPLEX_BuildFromCellList,dm,0,0,0);CHKERRQ(ierr);
3151   PetscFunctionReturn(0);
3152 }
3153 
3154 /*@C
3155   DMPlexBuildCoordinatesFromCellList - Build DM coordinates from a list of coordinates for each owned vertex (common mesh generator output)
3156 
3157   Input Parameters:
3158 + dm - The DM
3159 . spaceDim - The spatial dimension used for coordinates
3160 . numCells - The number of cells owned by this process
3161 . numVertices - The number of vertices owned by this process
3162 - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex
3163 
3164   Level: advanced
3165 
3166   Notes:
3167   Not currently supported in Fortran.
3168 
3169 .seealso: DMPlexBuildCoordinatesFromCellListParallel(), DMPlexCreateFromCellListPetsc(), DMPlexBuildFromCellList()
3170 @*/
3171 PetscErrorCode DMPlexBuildCoordinatesFromCellList(DM dm, PetscInt spaceDim, PetscInt numCells, PetscInt numVertices, const PetscReal vertexCoords[])
3172 {
3173   PetscSection   coordSection;
3174   Vec            coordinates;
3175   DM             cdm;
3176   PetscScalar   *coords;
3177   PetscInt       v, d;
3178   PetscErrorCode ierr;
3179 
3180   PetscFunctionBegin;
3181   ierr = PetscLogEventBegin(DMPLEX_BuildCoordinatesFromCellList,dm,0,0,0);CHKERRQ(ierr);
3182   ierr = DMSetCoordinateDim(dm, spaceDim);CHKERRQ(ierr);
3183   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
3184   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
3185   ierr = PetscSectionSetFieldComponents(coordSection, 0, spaceDim);CHKERRQ(ierr);
3186   ierr = PetscSectionSetChart(coordSection, numCells, numCells + numVertices);CHKERRQ(ierr);
3187   for (v = numCells; v < numCells+numVertices; ++v) {
3188     ierr = PetscSectionSetDof(coordSection, v, spaceDim);CHKERRQ(ierr);
3189     ierr = PetscSectionSetFieldDof(coordSection, v, 0, spaceDim);CHKERRQ(ierr);
3190   }
3191   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
3192 
3193   ierr = DMGetCoordinateDM(dm, &cdm);CHKERRQ(ierr);
3194   ierr = DMCreateLocalVector(cdm, &coordinates);CHKERRQ(ierr);
3195   ierr = VecSetBlockSize(coordinates, spaceDim);CHKERRQ(ierr);
3196   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
3197   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
3198   for (v = 0; v < numVertices; ++v) {
3199     for (d = 0; d < spaceDim; ++d) {
3200       coords[v*spaceDim+d] = vertexCoords[v*spaceDim+d];
3201     }
3202   }
3203   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
3204   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
3205   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
3206   ierr = PetscLogEventEnd(DMPLEX_BuildCoordinatesFromCellList,dm,0,0,0);CHKERRQ(ierr);
3207   PetscFunctionReturn(0);
3208 }
3209 
3210 /*@
3211   DMPlexCreateFromCellListPetsc - Create DMPLEX from a list of vertices for each cell (common mesh generator output)
3212 
3213   Input Parameters:
3214 + comm - The communicator
3215 . dim - The topological dimension of the mesh
3216 . numCells - The number of cells
3217 . numVertices - The number of vertices
3218 . numCorners - The number of vertices for each cell
3219 . interpolate - Flag indicating that intermediate mesh entities (faces, edges) should be created automatically
3220 . cells - An array of numCells*numCorners numbers, the vertices for each cell
3221 . spaceDim - The spatial dimension used for coordinates
3222 - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex
3223 
3224   Output Parameter:
3225 . dm - The DM
3226 
3227   Notes:
3228   This function is just a convenient sequence of DMCreate(), DMSetType(), DMSetDimension(), DMPlexBuildFromCellList(),
3229   DMPlexInterpolate(), DMPlexBuildCoordinatesFromCellList()
3230 
3231   Level: intermediate
3232 
3233 .seealso: DMPlexCreateFromCellListParallelPetsc(), DMPlexBuildFromCellList(), DMPlexBuildCoordinatesFromCellList(), DMPlexCreateFromDAG(), DMPlexCreate()
3234 @*/
3235 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)
3236 {
3237   PetscErrorCode ierr;
3238 
3239   PetscFunctionBegin;
3240   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.");
3241   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
3242   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
3243   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
3244   ierr = DMPlexBuildFromCellList(*dm, numCells, numVertices, numCorners, cells, PETSC_FALSE);CHKERRQ(ierr);
3245   if (interpolate) {
3246     DM idm;
3247 
3248     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
3249     ierr = DMDestroy(dm);CHKERRQ(ierr);
3250     *dm  = idm;
3251   }
3252   ierr = DMPlexBuildCoordinatesFromCellList(*dm, spaceDim, numCells, numVertices, vertexCoords);CHKERRQ(ierr);
3253   PetscFunctionReturn(0);
3254 }
3255 
3256 /*@
3257   DMPlexCreateFromCellList - Deprecated, use DMPlexCreateFromCellListPetsc()
3258 
3259   Level: deprecated
3260 
3261 .seealso: DMPlexCreateFromCellListPetsc()
3262 @*/
3263 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)
3264 {
3265   PetscErrorCode ierr;
3266   PetscInt       i;
3267   PetscInt       *pintCells;
3268   PetscReal      *prealVC;
3269 
3270   PetscFunctionBegin;
3271   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));
3272   if (sizeof(int) == sizeof(PetscInt)) {
3273     pintCells = (PetscInt *) cells;
3274   } else {
3275     ierr = PetscMalloc1(numCells*numCorners, &pintCells);CHKERRQ(ierr);
3276     for (i = 0; i < numCells*numCorners; i++) {
3277       pintCells[i] = (PetscInt) cells[i];
3278     }
3279   }
3280   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));
3281   if (sizeof(double) == sizeof(PetscReal)) {
3282     prealVC = (PetscReal *) vertexCoords;
3283   } else {
3284     ierr = PetscMalloc1(numVertices*spaceDim, &prealVC);CHKERRQ(ierr);
3285     for (i = 0; i < numVertices*spaceDim; i++) {
3286       prealVC[i] = (PetscReal) vertexCoords[i];
3287     }
3288   }
3289   ierr = DMPlexCreateFromCellListPetsc(comm, dim, numCells, numVertices, numCorners, interpolate, pintCells, spaceDim, prealVC, dm);CHKERRQ(ierr);
3290   if (sizeof(int) != sizeof(PetscInt)) {
3291     ierr = PetscFree(pintCells);CHKERRQ(ierr);
3292   }
3293   if (sizeof(double) != sizeof(PetscReal)) {
3294     ierr = PetscFree(prealVC);CHKERRQ(ierr);
3295   }
3296   PetscFunctionReturn(0);
3297 }
3298 
3299 /*@
3300   DMPlexCreateFromDAG - This takes as input the adjacency-list representation of the Directed Acyclic Graph (Hasse Diagram) encoding a mesh, and produces a DM
3301 
3302   Input Parameters:
3303 + dm - The empty DM object, usually from DMCreate() and DMSetDimension()
3304 . depth - The depth of the DAG
3305 . numPoints - Array of size depth + 1 containing the number of points at each depth
3306 . coneSize - The cone size of each point
3307 . cones - The concatenation of the cone points for each point, the cone list must be oriented correctly for each point
3308 . coneOrientations - The orientation of each cone point
3309 - vertexCoords - An array of numPoints[0]*spacedim numbers representing the coordinates of each vertex, with spacedim the value set via DMSetCoordinateDim()
3310 
3311   Output Parameter:
3312 . dm - The DM
3313 
3314   Note: Two triangles sharing a face would have input
3315 $  depth = 1, numPoints = [4 2], coneSize = [3 3 0 0 0 0]
3316 $  cones = [2 3 4  3 5 4], coneOrientations = [0 0 0  0 0 0]
3317 $ vertexCoords = [-1.0 0.0  0.0 -1.0  0.0 1.0  1.0 0.0]
3318 $
3319 which would result in the DMPlex
3320 $
3321 $        4
3322 $      / | \
3323 $     /  |  \
3324 $    /   |   \
3325 $   2  0 | 1  5
3326 $    \   |   /
3327 $     \  |  /
3328 $      \ | /
3329 $        3
3330 $
3331 $ Notice that all points are numbered consecutively, unlike DMPlexCreateFromCellListPetsc()
3332 
3333   Level: advanced
3334 
3335 .seealso: DMPlexCreateFromCellListPetsc(), DMPlexCreate()
3336 @*/
3337 PetscErrorCode DMPlexCreateFromDAG(DM dm, PetscInt depth, const PetscInt numPoints[], const PetscInt coneSize[], const PetscInt cones[], const PetscInt coneOrientations[], const PetscScalar vertexCoords[])
3338 {
3339   Vec            coordinates;
3340   PetscSection   coordSection;
3341   PetscScalar    *coords;
3342   PetscInt       coordSize, firstVertex = -1, pStart = 0, pEnd = 0, p, v, dim, dimEmbed, d, off;
3343   PetscErrorCode ierr;
3344 
3345   PetscFunctionBegin;
3346   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
3347   ierr = DMGetCoordinateDim(dm, &dimEmbed);CHKERRQ(ierr);
3348   if (dimEmbed < dim) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Embedding dimension %d cannot be less than intrinsic dimension %d",dimEmbed,dim);
3349   for (d = 0; d <= depth; ++d) pEnd += numPoints[d];
3350   ierr = DMPlexSetChart(dm, pStart, pEnd);CHKERRQ(ierr);
3351   for (p = pStart; p < pEnd; ++p) {
3352     ierr = DMPlexSetConeSize(dm, p, coneSize[p-pStart]);CHKERRQ(ierr);
3353     if (firstVertex < 0 && !coneSize[p - pStart]) {
3354       firstVertex = p - pStart;
3355     }
3356   }
3357   if (firstVertex < 0 && numPoints[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Expected %d vertices but could not find any", numPoints[0]);
3358   ierr = DMSetUp(dm);CHKERRQ(ierr); /* Allocate space for cones */
3359   for (p = pStart, off = 0; p < pEnd; off += coneSize[p-pStart], ++p) {
3360     ierr = DMPlexSetCone(dm, p, &cones[off]);CHKERRQ(ierr);
3361     ierr = DMPlexSetConeOrientation(dm, p, &coneOrientations[off]);CHKERRQ(ierr);
3362   }
3363   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
3364   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
3365   /* Build coordinates */
3366   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
3367   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
3368   ierr = PetscSectionSetFieldComponents(coordSection, 0, dimEmbed);CHKERRQ(ierr);
3369   ierr = PetscSectionSetChart(coordSection, firstVertex, firstVertex+numPoints[0]);CHKERRQ(ierr);
3370   for (v = firstVertex; v < firstVertex+numPoints[0]; ++v) {
3371     ierr = PetscSectionSetDof(coordSection, v, dimEmbed);CHKERRQ(ierr);
3372     ierr = PetscSectionSetFieldDof(coordSection, v, 0, dimEmbed);CHKERRQ(ierr);
3373   }
3374   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
3375   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
3376   ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
3377   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
3378   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
3379   ierr = VecSetBlockSize(coordinates, dimEmbed);CHKERRQ(ierr);
3380   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
3381   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
3382   for (v = 0; v < numPoints[0]; ++v) {
3383     PetscInt off;
3384 
3385     ierr = PetscSectionGetOffset(coordSection, v+firstVertex, &off);CHKERRQ(ierr);
3386     for (d = 0; d < dimEmbed; ++d) {
3387       coords[off+d] = vertexCoords[v*dimEmbed+d];
3388     }
3389   }
3390   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
3391   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
3392   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
3393   PetscFunctionReturn(0);
3394 }
3395 
3396 /*@C
3397   DMPlexCreateCellVertexFromFile - Create a DMPlex mesh from a simple cell-vertex file.
3398 
3399 + comm        - The MPI communicator
3400 . filename    - Name of the .dat file
3401 - interpolate - Create faces and edges in the mesh
3402 
3403   Output Parameter:
3404 . dm  - The DM object representing the mesh
3405 
3406   Note: The format is the simplest possible:
3407 $ Ne
3408 $ v0 v1 ... vk
3409 $ Nv
3410 $ x y z marker
3411 
3412   Level: beginner
3413 
3414 .seealso: DMPlexCreateFromFile(), DMPlexCreateMedFromFile(), DMPlexCreateGmsh(), DMPlexCreate()
3415 @*/
3416 PetscErrorCode DMPlexCreateCellVertexFromFile(MPI_Comm comm, const char filename[], PetscBool interpolate, DM *dm)
3417 {
3418   DMLabel         marker;
3419   PetscViewer     viewer;
3420   Vec             coordinates;
3421   PetscSection    coordSection;
3422   PetscScalar    *coords;
3423   char            line[PETSC_MAX_PATH_LEN];
3424   PetscInt        dim = 3, cdim = 3, coordSize, v, c, d;
3425   PetscMPIInt     rank;
3426   int             snum, Nv, Nc;
3427   PetscErrorCode  ierr;
3428 
3429   PetscFunctionBegin;
3430   ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
3431   ierr = PetscViewerCreate(comm, &viewer);CHKERRQ(ierr);
3432   ierr = PetscViewerSetType(viewer, PETSCVIEWERASCII);CHKERRQ(ierr);
3433   ierr = PetscViewerFileSetMode(viewer, FILE_MODE_READ);CHKERRQ(ierr);
3434   ierr = PetscViewerFileSetName(viewer, filename);CHKERRQ(ierr);
3435   if (!rank) {
3436     ierr = PetscViewerRead(viewer, line, 2, NULL, PETSC_STRING);CHKERRQ(ierr);
3437     snum = sscanf(line, "%d %d", &Nc, &Nv);
3438     if (snum != 2) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unable to parse cell-vertex file: %s", line);
3439   } else {
3440     Nc = Nv = 0;
3441   }
3442   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
3443   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
3444   ierr = DMPlexSetChart(*dm, 0, Nc+Nv);CHKERRQ(ierr);
3445   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
3446   ierr = DMSetCoordinateDim(*dm, cdim);CHKERRQ(ierr);
3447   /* Read topology */
3448   if (!rank) {
3449     PetscInt cone[8], corners = 8;
3450     int      vbuf[8], v;
3451 
3452     for (c = 0; c < Nc; ++c) {ierr = DMPlexSetConeSize(*dm, c, corners);CHKERRQ(ierr);}
3453     ierr = DMSetUp(*dm);CHKERRQ(ierr);
3454     for (c = 0; c < Nc; ++c) {
3455       ierr = PetscViewerRead(viewer, line, corners, NULL, PETSC_STRING);CHKERRQ(ierr);
3456       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]);
3457       if (snum != corners) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unable to parse cell-vertex file: %s", line);
3458       for (v = 0; v < corners; ++v) cone[v] = vbuf[v] + Nc;
3459       /* Hexahedra are inverted */
3460       {
3461         PetscInt tmp = cone[1];
3462         cone[1] = cone[3];
3463         cone[3] = tmp;
3464       }
3465       ierr = DMPlexSetCone(*dm, c, cone);CHKERRQ(ierr);
3466     }
3467   }
3468   ierr = DMPlexSymmetrize(*dm);CHKERRQ(ierr);
3469   ierr = DMPlexStratify(*dm);CHKERRQ(ierr);
3470   /* Read coordinates */
3471   ierr = DMGetCoordinateSection(*dm, &coordSection);CHKERRQ(ierr);
3472   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
3473   ierr = PetscSectionSetFieldComponents(coordSection, 0, cdim);CHKERRQ(ierr);
3474   ierr = PetscSectionSetChart(coordSection, Nc, Nc + Nv);CHKERRQ(ierr);
3475   for (v = Nc; v < Nc+Nv; ++v) {
3476     ierr = PetscSectionSetDof(coordSection, v, cdim);CHKERRQ(ierr);
3477     ierr = PetscSectionSetFieldDof(coordSection, v, 0, cdim);CHKERRQ(ierr);
3478   }
3479   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
3480   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
3481   ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
3482   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
3483   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
3484   ierr = VecSetBlockSize(coordinates, cdim);CHKERRQ(ierr);
3485   ierr = VecSetType(coordinates, VECSTANDARD);CHKERRQ(ierr);
3486   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
3487   if (!rank) {
3488     double x[3];
3489     int    val;
3490 
3491     ierr = DMCreateLabel(*dm, "marker");CHKERRQ(ierr);
3492     ierr = DMGetLabel(*dm, "marker", &marker);CHKERRQ(ierr);
3493     for (v = 0; v < Nv; ++v) {
3494       ierr = PetscViewerRead(viewer, line, 4, NULL, PETSC_STRING);CHKERRQ(ierr);
3495       snum = sscanf(line, "%lg %lg %lg %d", &x[0], &x[1], &x[2], &val);
3496       if (snum != 4) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unable to parse cell-vertex file: %s", line);
3497       for (d = 0; d < cdim; ++d) coords[v*cdim+d] = x[d];
3498       if (val) {ierr = DMLabelSetValue(marker, v+Nc, val);CHKERRQ(ierr);}
3499     }
3500   }
3501   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
3502   ierr = DMSetCoordinatesLocal(*dm, coordinates);CHKERRQ(ierr);
3503   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
3504   ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
3505   if (interpolate) {
3506     DM      idm;
3507     DMLabel bdlabel;
3508 
3509     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
3510     ierr = DMDestroy(dm);CHKERRQ(ierr);
3511     *dm  = idm;
3512 
3513     ierr = DMGetLabel(*dm, "marker", &bdlabel);CHKERRQ(ierr);
3514     ierr = DMPlexMarkBoundaryFaces(*dm, PETSC_DETERMINE, bdlabel);CHKERRQ(ierr);
3515     ierr = DMPlexLabelComplete(*dm, bdlabel);CHKERRQ(ierr);
3516   }
3517   PetscFunctionReturn(0);
3518 }
3519 
3520 /*@C
3521   DMPlexCreateFromFile - This takes a filename and produces a DM
3522 
3523   Input Parameters:
3524 + comm - The communicator
3525 . filename - A file name
3526 - interpolate - Flag to create intermediate mesh pieces (edges, faces)
3527 
3528   Output Parameter:
3529 . dm - The DM
3530 
3531   Options Database Keys:
3532 . -dm_plex_create_from_hdf5_xdmf - use the PETSC_VIEWER_HDF5_XDMF format for reading HDF5
3533 
3534   Use -dm_plex_create_ prefix to pass options to the internal PetscViewer, e.g.
3535 $ -dm_plex_create_viewer_hdf5_collective
3536 
3537   Level: beginner
3538 
3539 .seealso: DMPlexCreateFromDAG(), DMPlexCreateFromCellListPetsc(), DMPlexCreate()
3540 @*/
3541 PetscErrorCode DMPlexCreateFromFile(MPI_Comm comm, const char filename[], PetscBool interpolate, DM *dm)
3542 {
3543   const char    *extGmsh    = ".msh";
3544   const char    *extGmsh2   = ".msh2";
3545   const char    *extGmsh4   = ".msh4";
3546   const char    *extCGNS    = ".cgns";
3547   const char    *extExodus  = ".exo";
3548   const char    *extGenesis = ".gen";
3549   const char    *extFluent  = ".cas";
3550   const char    *extHDF5    = ".h5";
3551   const char    *extMed     = ".med";
3552   const char    *extPLY     = ".ply";
3553   const char    *extCV      = ".dat";
3554   size_t         len;
3555   PetscBool      isGmsh, isGmsh2, isGmsh4, isCGNS, isExodus, isGenesis, isFluent, isHDF5, isMed, isPLY, isCV;
3556   PetscMPIInt    rank;
3557   PetscErrorCode ierr;
3558 
3559   PetscFunctionBegin;
3560   PetscValidCharPointer(filename, 2);
3561   PetscValidPointer(dm, 4);
3562   ierr = DMInitializePackage();CHKERRQ(ierr);
3563   ierr = PetscLogEventBegin(DMPLEX_CreateFromFile,0,0,0,0);CHKERRQ(ierr);
3564   ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
3565   ierr = PetscStrlen(filename, &len);CHKERRQ(ierr);
3566   if (!len) SETERRQ(comm, PETSC_ERR_ARG_WRONG, "Filename must be a valid path");
3567   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extGmsh,    4, &isGmsh);CHKERRQ(ierr);
3568   ierr = PetscStrncmp(&filename[PetscMax(0,len-5)], extGmsh2,   5, &isGmsh2);CHKERRQ(ierr);
3569   ierr = PetscStrncmp(&filename[PetscMax(0,len-5)], extGmsh4,   5, &isGmsh4);CHKERRQ(ierr);
3570   ierr = PetscStrncmp(&filename[PetscMax(0,len-5)], extCGNS,    5, &isCGNS);CHKERRQ(ierr);
3571   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extExodus,  4, &isExodus);CHKERRQ(ierr);
3572   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extGenesis, 4, &isGenesis);CHKERRQ(ierr);
3573   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extFluent,  4, &isFluent);CHKERRQ(ierr);
3574   ierr = PetscStrncmp(&filename[PetscMax(0,len-3)], extHDF5,    3, &isHDF5);CHKERRQ(ierr);
3575   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extMed,     4, &isMed);CHKERRQ(ierr);
3576   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extPLY,     4, &isPLY);CHKERRQ(ierr);
3577   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extCV,      4, &isCV);CHKERRQ(ierr);
3578   if (isGmsh || isGmsh2 || isGmsh4) {
3579     ierr = DMPlexCreateGmshFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
3580   } else if (isCGNS) {
3581     ierr = DMPlexCreateCGNSFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
3582   } else if (isExodus || isGenesis) {
3583     ierr = DMPlexCreateExodusFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
3584   } else if (isFluent) {
3585     ierr = DMPlexCreateFluentFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
3586   } else if (isHDF5) {
3587     PetscBool      load_hdf5_xdmf = PETSC_FALSE;
3588     PetscViewer viewer;
3589 
3590     /* PETSC_VIEWER_HDF5_XDMF is used if the filename ends with .xdmf.h5, or if -dm_plex_create_from_hdf5_xdmf option is present */
3591     ierr = PetscStrncmp(&filename[PetscMax(0,len-8)], ".xdmf",  5, &load_hdf5_xdmf);CHKERRQ(ierr);
3592     ierr = PetscOptionsGetBool(NULL, NULL, "-dm_plex_create_from_hdf5_xdmf", &load_hdf5_xdmf, NULL);CHKERRQ(ierr);
3593     ierr = PetscViewerCreate(comm, &viewer);CHKERRQ(ierr);
3594     ierr = PetscViewerSetType(viewer, PETSCVIEWERHDF5);CHKERRQ(ierr);
3595     ierr = PetscViewerSetOptionsPrefix(viewer, "dm_plex_create_");CHKERRQ(ierr);
3596     ierr = PetscViewerSetFromOptions(viewer);CHKERRQ(ierr);
3597     ierr = PetscViewerFileSetMode(viewer, FILE_MODE_READ);CHKERRQ(ierr);
3598     ierr = PetscViewerFileSetName(viewer, filename);CHKERRQ(ierr);
3599     ierr = DMCreate(comm, dm);CHKERRQ(ierr);
3600     ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
3601     if (load_hdf5_xdmf) {ierr = PetscViewerPushFormat(viewer, PETSC_VIEWER_HDF5_XDMF);CHKERRQ(ierr);}
3602     ierr = DMLoad(*dm, viewer);CHKERRQ(ierr);
3603     if (load_hdf5_xdmf) {ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);}
3604     ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
3605 
3606     if (interpolate) {
3607       DM idm;
3608 
3609       ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
3610       ierr = DMDestroy(dm);CHKERRQ(ierr);
3611       *dm  = idm;
3612     }
3613   } else if (isMed) {
3614     ierr = DMPlexCreateMedFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
3615   } else if (isPLY) {
3616     ierr = DMPlexCreatePLYFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
3617   } else if (isCV) {
3618     ierr = DMPlexCreateCellVertexFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
3619   } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cannot load file %s: unrecognized extension", filename);
3620   ierr = PetscLogEventEnd(DMPLEX_CreateFromFile,0,0,0,0);CHKERRQ(ierr);
3621   PetscFunctionReturn(0);
3622 }
3623 
3624 /*@
3625   DMPlexCreateReferenceCellByType - Create a DMPLEX with the appropriate FEM reference cell
3626 
3627   Collective
3628 
3629   Input Parameters:
3630 + comm - The communicator
3631 - ct   - The cell type of the reference cell
3632 
3633   Output Parameter:
3634 . refdm - The reference cell
3635 
3636   Level: intermediate
3637 
3638 .seealso: DMPlexCreateReferenceCell(), DMPlexCreateBoxMesh()
3639 @*/
3640 PetscErrorCode DMPlexCreateReferenceCellByType(MPI_Comm comm, DMPolytopeType ct, DM *refdm)
3641 {
3642   DM             rdm;
3643   Vec            coords;
3644   PetscErrorCode ierr;
3645 
3646   PetscFunctionBegin;
3647   ierr = DMCreate(comm, &rdm);CHKERRQ(ierr);
3648   ierr = DMSetType(rdm, DMPLEX);CHKERRQ(ierr);
3649   switch (ct) {
3650     case DM_POLYTOPE_POINT:
3651     {
3652       PetscInt    numPoints[1]        = {1};
3653       PetscInt    coneSize[1]         = {0};
3654       PetscInt    cones[1]            = {0};
3655       PetscInt    coneOrientations[1] = {0};
3656       PetscScalar vertexCoords[1]     = {0.0};
3657 
3658       ierr = DMSetDimension(rdm, 0);CHKERRQ(ierr);
3659       ierr = DMPlexCreateFromDAG(rdm, 0, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
3660     }
3661     break;
3662     case DM_POLYTOPE_SEGMENT:
3663     {
3664       PetscInt    numPoints[2]        = {2, 1};
3665       PetscInt    coneSize[3]         = {2, 0, 0};
3666       PetscInt    cones[2]            = {1, 2};
3667       PetscInt    coneOrientations[2] = {0, 0};
3668       PetscScalar vertexCoords[2]     = {-1.0,  1.0};
3669 
3670       ierr = DMSetDimension(rdm, 1);CHKERRQ(ierr);
3671       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
3672     }
3673     break;
3674     case DM_POLYTOPE_TRIANGLE:
3675     {
3676       PetscInt    numPoints[2]        = {3, 1};
3677       PetscInt    coneSize[4]         = {3, 0, 0, 0};
3678       PetscInt    cones[3]            = {1, 2, 3};
3679       PetscInt    coneOrientations[3] = {0, 0, 0};
3680       PetscScalar vertexCoords[6]     = {-1.0, -1.0,  1.0, -1.0,  -1.0, 1.0};
3681 
3682       ierr = DMSetDimension(rdm, 2);CHKERRQ(ierr);
3683       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
3684     }
3685     break;
3686     case DM_POLYTOPE_QUADRILATERAL:
3687     {
3688       PetscInt    numPoints[2]        = {4, 1};
3689       PetscInt    coneSize[5]         = {4, 0, 0, 0, 0};
3690       PetscInt    cones[4]            = {1, 2, 3, 4};
3691       PetscInt    coneOrientations[4] = {0, 0, 0, 0};
3692       PetscScalar vertexCoords[8]     = {-1.0, -1.0,  1.0, -1.0,  1.0, 1.0,  -1.0, 1.0};
3693 
3694       ierr = DMSetDimension(rdm, 2);CHKERRQ(ierr);
3695       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
3696     }
3697     break;
3698     case DM_POLYTOPE_SEG_PRISM_TENSOR:
3699     {
3700       PetscInt    numPoints[2]        = {4, 1};
3701       PetscInt    coneSize[5]         = {4, 0, 0, 0, 0};
3702       PetscInt    cones[4]            = {1, 2, 3, 4};
3703       PetscInt    coneOrientations[4] = {0, 0, 0, 0};
3704       PetscScalar vertexCoords[8]     = {-1.0, -1.0,  1.0, -1.0,  -1.0, 1.0,  1.0, 1.0};
3705 
3706       ierr = DMSetDimension(rdm, 2);CHKERRQ(ierr);
3707       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
3708     }
3709     break;
3710     case DM_POLYTOPE_TETRAHEDRON:
3711     {
3712       PetscInt    numPoints[2]        = {4, 1};
3713       PetscInt    coneSize[5]         = {4, 0, 0, 0, 0};
3714       PetscInt    cones[4]            = {1, 3, 2, 4};
3715       PetscInt    coneOrientations[4] = {0, 0, 0, 0};
3716       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};
3717 
3718       ierr = DMSetDimension(rdm, 3);CHKERRQ(ierr);
3719       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
3720     }
3721     break;
3722     case DM_POLYTOPE_HEXAHEDRON:
3723     {
3724       PetscInt    numPoints[2]        = {8, 1};
3725       PetscInt    coneSize[9]         = {8, 0, 0, 0, 0, 0, 0, 0, 0};
3726       PetscInt    cones[8]            = {1, 4, 3, 2, 5, 6, 7, 8};
3727       PetscInt    coneOrientations[8] = {0, 0, 0, 0, 0, 0, 0, 0};
3728       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,
3729                                          -1.0, -1.0,  1.0,  1.0, -1.0,  1.0,  1.0, 1.0,  1.0,  -1.0, 1.0,  1.0};
3730 
3731       ierr = DMSetDimension(rdm, 3);CHKERRQ(ierr);
3732       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
3733     }
3734     break;
3735     case DM_POLYTOPE_TRI_PRISM:
3736     {
3737       PetscInt    numPoints[2]        = {6, 1};
3738       PetscInt    coneSize[7]         = {6, 0, 0, 0, 0, 0, 0};
3739       PetscInt    cones[6]            = {1, 3, 2, 4, 5, 6};
3740       PetscInt    coneOrientations[6] = {0, 0, 0, 0, 0, 0};
3741       PetscScalar vertexCoords[18]    = {-1.0, -1.0, -1.0,  1.0, -1.0, -1.0,  -1.0, 1.0, -1.0,
3742                                          -1.0, -1.0,  1.0,  1.0, -1.0,  1.0,  -1.0, 1.0,  1.0};
3743 
3744       ierr = DMSetDimension(rdm, 3);CHKERRQ(ierr);
3745       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
3746     }
3747     break;
3748     case DM_POLYTOPE_TRI_PRISM_TENSOR:
3749     {
3750       PetscInt    numPoints[2]        = {6, 1};
3751       PetscInt    coneSize[7]         = {6, 0, 0, 0, 0, 0, 0};
3752       PetscInt    cones[6]            = {1, 2, 3, 4, 5, 6};
3753       PetscInt    coneOrientations[6] = {0, 0, 0, 0, 0, 0};
3754       PetscScalar vertexCoords[18]    = {-1.0, -1.0, -1.0,  1.0, -1.0, -1.0,  -1.0, 1.0, -1.0,
3755                                          -1.0, -1.0,  1.0,  1.0, -1.0,  1.0,  -1.0, 1.0,  1.0};
3756 
3757       ierr = DMSetDimension(rdm, 3);CHKERRQ(ierr);
3758       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
3759     }
3760     break;
3761     case DM_POLYTOPE_QUAD_PRISM_TENSOR:
3762     {
3763       PetscInt    numPoints[2]        = {8, 1};
3764       PetscInt    coneSize[9]         = {8, 0, 0, 0, 0, 0, 0, 0, 0};
3765       PetscInt    cones[8]            = {1, 2, 3, 4, 5, 6, 7, 8};
3766       PetscInt    coneOrientations[8] = {0, 0, 0, 0, 0, 0, 0, 0};
3767       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,
3768                                          -1.0, -1.0,  1.0,  1.0, -1.0,  1.0,  1.0, 1.0,  1.0,  -1.0, 1.0,  1.0};
3769 
3770       ierr = DMSetDimension(rdm, 3);CHKERRQ(ierr);
3771       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
3772     }
3773     break;
3774     default: SETERRQ1(comm, PETSC_ERR_ARG_WRONG, "Cannot create reference cell for cell type %s", DMPolytopeTypes[ct]);
3775   }
3776   {
3777     PetscInt Nv, v;
3778 
3779     /* Must create the celltype label here so that we do not automatically try to compute the types */
3780     ierr = DMCreateLabel(rdm, "celltype");CHKERRQ(ierr);
3781     ierr = DMPlexSetCellType(rdm, 0, ct);CHKERRQ(ierr);
3782     ierr = DMPlexGetChart(rdm, NULL, &Nv);CHKERRQ(ierr);
3783     for (v = 1; v < Nv; ++v) {ierr = DMPlexSetCellType(rdm, v, DM_POLYTOPE_POINT);CHKERRQ(ierr);}
3784   }
3785   ierr = DMPlexInterpolate(rdm, refdm);CHKERRQ(ierr);
3786   if (rdm->coordinateDM) {
3787     DM           ncdm;
3788     PetscSection cs;
3789     PetscInt     pEnd = -1;
3790 
3791     ierr = DMGetLocalSection(rdm->coordinateDM, &cs);CHKERRQ(ierr);
3792     if (cs) {ierr = PetscSectionGetChart(cs, NULL, &pEnd);CHKERRQ(ierr);}
3793     if (pEnd >= 0) {
3794       ierr = DMClone(*refdm, &ncdm);CHKERRQ(ierr);
3795       ierr = DMCopyDisc(rdm->coordinateDM, ncdm);CHKERRQ(ierr);
3796       ierr = DMSetLocalSection(ncdm, cs);CHKERRQ(ierr);
3797       ierr = DMSetCoordinateDM(*refdm, ncdm);CHKERRQ(ierr);
3798       ierr = DMDestroy(&ncdm);CHKERRQ(ierr);
3799     }
3800   }
3801   ierr = DMGetCoordinatesLocal(rdm, &coords);CHKERRQ(ierr);
3802   if (coords) {
3803     ierr = DMSetCoordinatesLocal(*refdm, coords);CHKERRQ(ierr);
3804   } else {
3805     ierr = DMGetCoordinates(rdm, &coords);CHKERRQ(ierr);
3806     if (coords) {ierr = DMSetCoordinates(*refdm, coords);CHKERRQ(ierr);}
3807   }
3808   ierr = DMDestroy(&rdm);CHKERRQ(ierr);
3809   PetscFunctionReturn(0);
3810 }
3811 
3812 /*@
3813   DMPlexCreateReferenceCell - Create a DMPLEX with the appropriate FEM reference cell
3814 
3815   Collective
3816 
3817   Input Parameters:
3818 + comm    - The communicator
3819 . dim     - The spatial dimension
3820 - simplex - Flag for simplex, otherwise use a tensor-product cell
3821 
3822   Output Parameter:
3823 . refdm - The reference cell
3824 
3825   Level: intermediate
3826 
3827 .seealso: DMPlexCreateReferenceCellByType(), DMPlexCreateBoxMesh()
3828 @*/
3829 PetscErrorCode DMPlexCreateReferenceCell(MPI_Comm comm, PetscInt dim, PetscBool simplex, DM *refdm)
3830 {
3831   PetscErrorCode ierr;
3832 
3833   PetscFunctionBeginUser;
3834   switch (dim) {
3835   case 0: ierr = DMPlexCreateReferenceCellByType(comm, DM_POLYTOPE_POINT, refdm);CHKERRQ(ierr);break;
3836   case 1: ierr = DMPlexCreateReferenceCellByType(comm, DM_POLYTOPE_SEGMENT, refdm);CHKERRQ(ierr);break;
3837   case 2:
3838     if (simplex) {ierr = DMPlexCreateReferenceCellByType(comm, DM_POLYTOPE_TRIANGLE, refdm);CHKERRQ(ierr);}
3839     else         {ierr = DMPlexCreateReferenceCellByType(comm, DM_POLYTOPE_QUADRILATERAL, refdm);CHKERRQ(ierr);}
3840     break;
3841   case 3:
3842     if (simplex) {ierr = DMPlexCreateReferenceCellByType(comm, DM_POLYTOPE_TETRAHEDRON, refdm);CHKERRQ(ierr);}
3843     else         {ierr = DMPlexCreateReferenceCellByType(comm, DM_POLYTOPE_HEXAHEDRON, refdm);CHKERRQ(ierr);}
3844     break;
3845   default:
3846     SETERRQ1(comm, PETSC_ERR_ARG_WRONG, "Cannot create reference cell for dimension %D", dim);
3847   }
3848   PetscFunctionReturn(0);
3849 }
3850