xref: /petsc/src/dm/impls/plex/plexcreate.c (revision 0e278f6a9e2caa6032d3ea3eff6e05375b0538ce)
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_CreateFromCellList, DMPLEX_CreateFromCellList_Coordinates;
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 . ordExt      - 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 ordExt, 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], ordExt, 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 /*@
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 extruted
1149 . layers - The number of layers
1150 . height - The height of the extruded layer
1151 . ordExt - If PETSC_TRUE, orders the extruded cells in the height first. Otherwise, orders the cell on the layers first
1152 - interpolate - Flag to create intermediate mesh pieces (edges, faces)
1153 
1154   Output Parameter:
1155 . dm  - The DM object
1156 
1157   Notes: The mesh created has prismatic cells, and the vertex ordering in the cone of the cell is that of the tensor prismatic cells.
1158 
1159   Level: advanced
1160 
1161 .seealso: DMPlexCreateWedgeCylinderMesh(), DMPlexCreateWedgeBoxMesh(), DMSetType(), DMCreate()
1162 @*/
1163 PetscErrorCode DMPlexExtrude(DM idm, PetscInt layers, PetscReal height, PetscBool ordExt, PetscBool interpolate, DM* dm)
1164 {
1165   PetscScalar       *coordsB;
1166   const PetscScalar *coordsA;
1167   PetscReal         *normals = NULL;
1168   Vec               coordinatesA, coordinatesB;
1169   PetscSection      coordSectionA, coordSectionB;
1170   PetscInt          dim, cDim, cDimB, c, l, v, coordSize, *newCone;
1171   PetscInt          cStart, cEnd, vStart, vEnd, cellV, numCells, numVertices;
1172   PetscErrorCode    ierr;
1173 
1174   PetscFunctionBegin;
1175   PetscValidHeaderSpecific(idm, DM_CLASSID, 1);
1176   PetscValidLogicalCollectiveInt(idm, layers, 2);
1177   PetscValidLogicalCollectiveReal(idm, height, 3);
1178   PetscValidLogicalCollectiveBool(idm, interpolate, 4);
1179   ierr = DMGetDimension(idm, &dim);CHKERRQ(ierr);
1180   if (dim < 1 || dim > 3) SETERRQ1(PetscObjectComm((PetscObject)idm), PETSC_ERR_SUP, "Support for dimension %D not coded", dim);
1181 
1182   ierr = DMPlexGetHeightStratum(idm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1183   ierr = DMPlexGetDepthStratum(idm, 0, &vStart, &vEnd);CHKERRQ(ierr);
1184   numCells = (cEnd - cStart)*layers;
1185   numVertices = (vEnd - vStart)*(layers+1);
1186   ierr = DMCreate(PetscObjectComm((PetscObject)idm), dm);CHKERRQ(ierr);
1187   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
1188   ierr = DMSetDimension(*dm, dim+1);CHKERRQ(ierr);
1189   ierr = DMPlexSetChart(*dm, 0, numCells+numVertices);CHKERRQ(ierr);
1190   /* Must create the celltype label here so that we do not automatically try to compute the types */
1191   ierr = DMCreateLabel(*dm, "celltype");CHKERRQ(ierr);
1192   for (c = cStart, cellV = 0; c < cEnd; ++c) {
1193     DMPolytopeType ct, nct;
1194     PetscInt      *closure = NULL;
1195     PetscInt       closureSize, numCorners = 0;
1196 
1197     ierr = DMPlexGetCellType(idm, c, &ct);CHKERRQ(ierr);
1198     switch (ct) {
1199       case DM_POLYTOPE_SEGMENT:       nct = DM_POLYTOPE_SEG_PRISM_TENSOR;break;
1200       case DM_POLYTOPE_TRIANGLE:      nct = DM_POLYTOPE_TRI_PRISM_TENSOR;break;
1201       case DM_POLYTOPE_QUADRILATERAL: nct = DM_POLYTOPE_QUAD_PRISM_TENSOR;break;
1202       default: nct = DM_POLYTOPE_UNKNOWN;
1203     }
1204     ierr = DMPlexGetTransitiveClosure(idm, c, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
1205     for (v = 0; v < closureSize*2; v += 2) if ((closure[v] >= vStart) && (closure[v] < vEnd)) numCorners++;
1206     ierr = DMPlexRestoreTransitiveClosure(idm, c, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
1207     for (l = 0; l < layers; ++l) {
1208       const PetscInt cell = ordExt ? layers*(c - cStart) + l : l*(cEnd - cStart) + c - cStart;
1209 
1210       ierr = DMPlexSetConeSize(*dm, cell, 2*numCorners);CHKERRQ(ierr);
1211       ierr = DMPlexSetCellType(*dm, cell, nct);CHKERRQ(ierr);
1212     }
1213     cellV = PetscMax(numCorners,cellV);
1214   }
1215   ierr = DMSetUp(*dm);CHKERRQ(ierr);
1216 
1217   ierr = DMGetCoordinateDim(idm, &cDim);CHKERRQ(ierr);
1218   if (dim != cDim) {
1219     ierr = PetscCalloc1(cDim*(vEnd - vStart), &normals);CHKERRQ(ierr);
1220   }
1221   ierr = PetscMalloc1(3*cellV,&newCone);CHKERRQ(ierr);
1222   for (c = cStart; c < cEnd; ++c) {
1223     PetscInt *closure = NULL;
1224     PetscInt closureSize, numCorners = 0, l;
1225     PetscReal normal[3] = {0, 0, 0};
1226 
1227     if (normals) {
1228       ierr = DMPlexComputeCellGeometryFVM(idm, c, NULL, NULL, normal);CHKERRQ(ierr);
1229     }
1230     ierr = DMPlexGetTransitiveClosure(idm, c, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
1231     for (v = 0; v < closureSize*2; v += 2) {
1232       if ((closure[v] >= vStart) && (closure[v] < vEnd)) {
1233         PetscInt d;
1234 
1235         newCone[numCorners++] = closure[v] - vStart;
1236         if (normals) { for (d = 0; d < cDim; ++d) normals[cDim*(closure[v]-vStart)+d] += normal[d]; }
1237       }
1238     }
1239     ierr = DMPlexRestoreTransitiveClosure(idm, c, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
1240     for (l = 0; l < layers; ++l) {
1241       PetscInt i;
1242 
1243       for (i = 0; i < numCorners; ++i) {
1244         newCone[  numCorners + i] = ordExt ? (layers+1)*newCone[i] + l     + numCells :     l*(vEnd - vStart) + newCone[i] + numCells;
1245         newCone[2*numCorners + i] = ordExt ? (layers+1)*newCone[i] + l + 1 + numCells : (l+1)*(vEnd - vStart) + newCone[i] + numCells;
1246       }
1247       ierr = DMPlexSetCone(*dm, ordExt ? layers*(c - cStart) + l : l*(cEnd - cStart) + c - cStart, newCone + numCorners);CHKERRQ(ierr);
1248     }
1249   }
1250   ierr = DMPlexSymmetrize(*dm);CHKERRQ(ierr);
1251   ierr = DMPlexStratify(*dm);CHKERRQ(ierr);
1252   ierr = PetscFree(newCone);CHKERRQ(ierr);
1253 
1254   cDimB = cDim == dim ? cDim+1 : cDim;
1255   ierr = DMGetCoordinateSection(*dm, &coordSectionB);CHKERRQ(ierr);
1256   ierr = PetscSectionSetNumFields(coordSectionB, 1);CHKERRQ(ierr);
1257   ierr = PetscSectionSetFieldComponents(coordSectionB, 0, cDimB);CHKERRQ(ierr);
1258   ierr = PetscSectionSetChart(coordSectionB, numCells, numCells+numVertices);CHKERRQ(ierr);
1259   for (v = numCells; v < numCells+numVertices; ++v) {
1260     ierr = PetscSectionSetDof(coordSectionB, v, cDimB);CHKERRQ(ierr);
1261     ierr = PetscSectionSetFieldDof(coordSectionB, v, 0, cDimB);CHKERRQ(ierr);
1262     ierr = DMPlexSetCellType(*dm, v, DM_POLYTOPE_POINT);CHKERRQ(ierr);
1263   }
1264   ierr = PetscSectionSetUp(coordSectionB);CHKERRQ(ierr);
1265   ierr = PetscSectionGetStorageSize(coordSectionB, &coordSize);CHKERRQ(ierr);
1266   ierr = VecCreate(PETSC_COMM_SELF, &coordinatesB);CHKERRQ(ierr);
1267   ierr = PetscObjectSetName((PetscObject) coordinatesB, "coordinates");CHKERRQ(ierr);
1268   ierr = VecSetSizes(coordinatesB, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
1269   ierr = VecSetBlockSize(coordinatesB, cDimB);CHKERRQ(ierr);
1270   ierr = VecSetType(coordinatesB,VECSTANDARD);CHKERRQ(ierr);
1271 
1272   ierr = DMGetCoordinateSection(idm, &coordSectionA);CHKERRQ(ierr);
1273   ierr = DMGetCoordinatesLocal(idm, &coordinatesA);CHKERRQ(ierr);
1274   ierr = VecGetArray(coordinatesB, &coordsB);CHKERRQ(ierr);
1275   ierr = VecGetArrayRead(coordinatesA, &coordsA);CHKERRQ(ierr);
1276   for (v = vStart; v < vEnd; ++v) {
1277     const PetscScalar *cptr;
1278     PetscReal         ones2[2] = { 0., 1.}, ones3[3] = { 0., 0., 1.};
1279     PetscReal         *normal, norm, h = height/layers;
1280     PetscInt          offA, d, cDimA = cDim;
1281 
1282     normal = normals ? normals + cDimB*(v - vStart) : (cDim > 1 ? ones3 : ones2);
1283     if (normals) {
1284       for (d = 0, norm = 0.0; d < cDimB; ++d) norm += normal[d]*normal[d];
1285       for (d = 0; d < cDimB; ++d) normal[d] *= 1./PetscSqrtReal(norm);
1286     }
1287 
1288     ierr = PetscSectionGetOffset(coordSectionA, v, &offA);CHKERRQ(ierr);
1289     cptr = coordsA + offA;
1290     for (l = 0; l < layers+1; ++l) {
1291       PetscInt offB, d, newV;
1292 
1293       newV = ordExt ? (layers+1)*(v -vStart) + l + numCells : (vEnd -vStart)*l + (v -vStart) + numCells;
1294       ierr = PetscSectionGetOffset(coordSectionB, newV, &offB);CHKERRQ(ierr);
1295       for (d = 0; d < cDimA; ++d) { coordsB[offB+d]  = cptr[d]; }
1296       for (d = 0; d < cDimB; ++d) { coordsB[offB+d] += l ? normal[d]*h : 0.0; }
1297       cptr    = coordsB + offB;
1298       cDimA   = cDimB;
1299     }
1300   }
1301   ierr = VecRestoreArrayRead(coordinatesA, &coordsA);CHKERRQ(ierr);
1302   ierr = VecRestoreArray(coordinatesB, &coordsB);CHKERRQ(ierr);
1303   ierr = DMSetCoordinatesLocal(*dm, coordinatesB);CHKERRQ(ierr);
1304   ierr = VecDestroy(&coordinatesB);CHKERRQ(ierr);
1305   ierr = PetscFree(normals);CHKERRQ(ierr);
1306   if (interpolate) {
1307     DM idm;
1308 
1309     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
1310     ierr = DMPlexCopyCoordinates(*dm, idm);CHKERRQ(ierr);
1311     ierr = DMDestroy(dm);CHKERRQ(ierr);
1312     *dm  = idm;
1313   }
1314   PetscFunctionReturn(0);
1315 }
1316 
1317 /*@C
1318   DMPlexSetOptionsPrefix - Sets the prefix used for searching for all DM options in the database.
1319 
1320   Logically Collective on dm
1321 
1322   Input Parameters:
1323 + dm - the DM context
1324 - prefix - the prefix to prepend to all option names
1325 
1326   Notes:
1327   A hyphen (-) must NOT be given at the beginning of the prefix name.
1328   The first character of all runtime options is AUTOMATICALLY the hyphen.
1329 
1330   Level: advanced
1331 
1332 .seealso: SNESSetFromOptions()
1333 @*/
1334 PetscErrorCode DMPlexSetOptionsPrefix(DM dm, const char prefix[])
1335 {
1336   DM_Plex       *mesh = (DM_Plex *) dm->data;
1337   PetscErrorCode ierr;
1338 
1339   PetscFunctionBegin;
1340   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1341   ierr = PetscObjectSetOptionsPrefix((PetscObject) dm, prefix);CHKERRQ(ierr);
1342   ierr = PetscObjectSetOptionsPrefix((PetscObject) mesh->partitioner, prefix);CHKERRQ(ierr);
1343   PetscFunctionReturn(0);
1344 }
1345 
1346 /*@
1347   DMPlexCreateHexCylinderMesh - Creates a mesh on the tensor product of the unit interval with the circle (cylinder) using hexahedra.
1348 
1349   Collective
1350 
1351   Input Parameters:
1352 + comm      - The communicator for the DM object
1353 . numRefine - The number of regular refinements to the basic 5 cell structure
1354 - periodicZ - The boundary type for the Z direction
1355 
1356   Output Parameter:
1357 . dm  - The DM object
1358 
1359   Note: Here is the output numbering looking from the bottom of the cylinder:
1360 $       17-----14
1361 $        |     |
1362 $        |  2  |
1363 $        |     |
1364 $ 17-----8-----7-----14
1365 $  |     |     |     |
1366 $  |  3  |  0  |  1  |
1367 $  |     |     |     |
1368 $ 19-----5-----6-----13
1369 $        |     |
1370 $        |  4  |
1371 $        |     |
1372 $       19-----13
1373 $
1374 $ and up through the top
1375 $
1376 $       18-----16
1377 $        |     |
1378 $        |  2  |
1379 $        |     |
1380 $ 18----10----11-----16
1381 $  |     |     |     |
1382 $  |  3  |  0  |  1  |
1383 $  |     |     |     |
1384 $ 20-----9----12-----15
1385 $        |     |
1386 $        |  4  |
1387 $        |     |
1388 $       20-----15
1389 
1390   Level: beginner
1391 
1392 .seealso: DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
1393 @*/
1394 PetscErrorCode DMPlexCreateHexCylinderMesh(MPI_Comm comm, PetscInt numRefine, DMBoundaryType periodicZ, DM *dm)
1395 {
1396   const PetscInt dim = 3;
1397   PetscInt       numCells, numVertices, r;
1398   PetscMPIInt    rank;
1399   PetscErrorCode ierr;
1400 
1401   PetscFunctionBegin;
1402   PetscValidPointer(dm, 4);
1403   ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
1404   if (numRefine < 0) SETERRQ1(comm, PETSC_ERR_ARG_OUTOFRANGE, "Number of refinements %D cannot be negative", numRefine);
1405   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
1406   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
1407   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
1408   /* Create topology */
1409   {
1410     PetscInt cone[8], c;
1411 
1412     numCells    = !rank ?  5 : 0;
1413     numVertices = !rank ? 16 : 0;
1414     if (periodicZ == DM_BOUNDARY_PERIODIC) {
1415       numCells   *= 3;
1416       numVertices = !rank ? 24 : 0;
1417     }
1418     ierr = DMPlexSetChart(*dm, 0, numCells+numVertices);CHKERRQ(ierr);
1419     for (c = 0; c < numCells; c++) {ierr = DMPlexSetConeSize(*dm, c, 8);CHKERRQ(ierr);}
1420     ierr = DMSetUp(*dm);CHKERRQ(ierr);
1421     if (!rank) {
1422       if (periodicZ == DM_BOUNDARY_PERIODIC) {
1423         cone[0] = 15; cone[1] = 18; cone[2] = 17; cone[3] = 16;
1424         cone[4] = 31; cone[5] = 32; cone[6] = 33; cone[7] = 34;
1425         ierr = DMPlexSetCone(*dm, 0, cone);CHKERRQ(ierr);
1426         cone[0] = 16; cone[1] = 17; cone[2] = 24; cone[3] = 23;
1427         cone[4] = 32; cone[5] = 36; cone[6] = 37; cone[7] = 33; /* 22 25 26 21 */
1428         ierr = DMPlexSetCone(*dm, 1, cone);CHKERRQ(ierr);
1429         cone[0] = 18; cone[1] = 27; cone[2] = 24; cone[3] = 17;
1430         cone[4] = 34; cone[5] = 33; cone[6] = 37; cone[7] = 38;
1431         ierr = DMPlexSetCone(*dm, 2, cone);CHKERRQ(ierr);
1432         cone[0] = 29; cone[1] = 27; cone[2] = 18; cone[3] = 15;
1433         cone[4] = 35; cone[5] = 31; cone[6] = 34; cone[7] = 38;
1434         ierr = DMPlexSetCone(*dm, 3, cone);CHKERRQ(ierr);
1435         cone[0] = 29; cone[1] = 15; cone[2] = 16; cone[3] = 23;
1436         cone[4] = 35; cone[5] = 36; cone[6] = 32; cone[7] = 31;
1437         ierr = DMPlexSetCone(*dm, 4, cone);CHKERRQ(ierr);
1438 
1439         cone[0] = 31; cone[1] = 34; cone[2] = 33; cone[3] = 32;
1440         cone[4] = 19; cone[5] = 22; cone[6] = 21; cone[7] = 20;
1441         ierr = DMPlexSetCone(*dm, 5, cone);CHKERRQ(ierr);
1442         cone[0] = 32; cone[1] = 33; cone[2] = 37; cone[3] = 36;
1443         cone[4] = 22; cone[5] = 25; cone[6] = 26; cone[7] = 21;
1444         ierr = DMPlexSetCone(*dm, 6, cone);CHKERRQ(ierr);
1445         cone[0] = 34; cone[1] = 38; cone[2] = 37; cone[3] = 33;
1446         cone[4] = 20; cone[5] = 21; cone[6] = 26; cone[7] = 28;
1447         ierr = DMPlexSetCone(*dm, 7, cone);CHKERRQ(ierr);
1448         cone[0] = 35; cone[1] = 38; cone[2] = 34; cone[3] = 31;
1449         cone[4] = 30; cone[5] = 19; cone[6] = 20; cone[7] = 28;
1450         ierr = DMPlexSetCone(*dm, 8, cone);CHKERRQ(ierr);
1451         cone[0] = 35; cone[1] = 31; cone[2] = 32; cone[3] = 36;
1452         cone[4] = 30; cone[5] = 25; cone[6] = 22; cone[7] = 19;
1453         ierr = DMPlexSetCone(*dm, 9, cone);CHKERRQ(ierr);
1454 
1455         cone[0] = 19; cone[1] = 20; cone[2] = 21; cone[3] = 22;
1456         cone[4] = 15; cone[5] = 16; cone[6] = 17; cone[7] = 18;
1457         ierr = DMPlexSetCone(*dm, 10, cone);CHKERRQ(ierr);
1458         cone[0] = 22; cone[1] = 21; cone[2] = 26; cone[3] = 25;
1459         cone[4] = 16; cone[5] = 23; cone[6] = 24; cone[7] = 17;
1460         ierr = DMPlexSetCone(*dm, 11, cone);CHKERRQ(ierr);
1461         cone[0] = 20; cone[1] = 28; cone[2] = 26; cone[3] = 21;
1462         cone[4] = 18; cone[5] = 17; cone[6] = 24; cone[7] = 27;
1463         ierr = DMPlexSetCone(*dm, 12, cone);CHKERRQ(ierr);
1464         cone[0] = 30; cone[1] = 28; cone[2] = 20; cone[3] = 19;
1465         cone[4] = 29; cone[5] = 15; cone[6] = 18; cone[7] = 27;
1466         ierr = DMPlexSetCone(*dm, 13, cone);CHKERRQ(ierr);
1467         cone[0] = 30; cone[1] = 19; cone[2] = 22; cone[3] = 25;
1468         cone[4] = 29; cone[5] = 23; cone[6] = 16; cone[7] = 15;
1469         ierr = DMPlexSetCone(*dm, 14, cone);CHKERRQ(ierr);
1470       } else {
1471         cone[0] =  5; cone[1] =  8; cone[2] =  7; cone[3] =  6;
1472         cone[4] =  9; cone[5] = 12; cone[6] = 11; cone[7] = 10;
1473         ierr = DMPlexSetCone(*dm, 0, cone);CHKERRQ(ierr);
1474         cone[0] =  6; cone[1] =  7; cone[2] = 14; cone[3] = 13;
1475         cone[4] = 12; cone[5] = 15; cone[6] = 16; cone[7] = 11;
1476         ierr = DMPlexSetCone(*dm, 1, cone);CHKERRQ(ierr);
1477         cone[0] =  8; cone[1] = 17; cone[2] = 14; cone[3] =  7;
1478         cone[4] = 10; cone[5] = 11; cone[6] = 16; cone[7] = 18;
1479         ierr = DMPlexSetCone(*dm, 2, cone);CHKERRQ(ierr);
1480         cone[0] = 19; cone[1] = 17; cone[2] =  8; cone[3] =  5;
1481         cone[4] = 20; cone[5] =  9; cone[6] = 10; cone[7] = 18;
1482         ierr = DMPlexSetCone(*dm, 3, cone);CHKERRQ(ierr);
1483         cone[0] = 19; cone[1] =  5; cone[2] =  6; cone[3] = 13;
1484         cone[4] = 20; cone[5] = 15; cone[6] = 12; cone[7] =  9;
1485         ierr = DMPlexSetCone(*dm, 4, cone);CHKERRQ(ierr);
1486       }
1487     }
1488     ierr = DMPlexSymmetrize(*dm);CHKERRQ(ierr);
1489     ierr = DMPlexStratify(*dm);CHKERRQ(ierr);
1490   }
1491   /* Interpolate */
1492   {
1493     DM idm;
1494 
1495     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
1496     ierr = DMDestroy(dm);CHKERRQ(ierr);
1497     *dm  = idm;
1498   }
1499   /* Create cube geometry */
1500   {
1501     Vec             coordinates;
1502     PetscSection    coordSection;
1503     PetscScalar    *coords;
1504     PetscInt        coordSize, v;
1505     const PetscReal dis = 1.0/PetscSqrtReal(2.0);
1506     const PetscReal ds2 = dis/2.0;
1507 
1508     /* Build coordinates */
1509     ierr = DMGetCoordinateSection(*dm, &coordSection);CHKERRQ(ierr);
1510     ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
1511     ierr = PetscSectionSetFieldComponents(coordSection, 0, dim);CHKERRQ(ierr);
1512     ierr = PetscSectionSetChart(coordSection, numCells, numCells+numVertices);CHKERRQ(ierr);
1513     for (v = numCells; v < numCells+numVertices; ++v) {
1514       ierr = PetscSectionSetDof(coordSection, v, dim);CHKERRQ(ierr);
1515       ierr = PetscSectionSetFieldDof(coordSection, v, 0, dim);CHKERRQ(ierr);
1516     }
1517     ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
1518     ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
1519     ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
1520     ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
1521     ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
1522     ierr = VecSetBlockSize(coordinates, dim);CHKERRQ(ierr);
1523     ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
1524     ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
1525     if (!rank) {
1526       coords[0*dim+0] = -ds2; coords[0*dim+1] = -ds2; coords[0*dim+2] = 0.0;
1527       coords[1*dim+0] =  ds2; coords[1*dim+1] = -ds2; coords[1*dim+2] = 0.0;
1528       coords[2*dim+0] =  ds2; coords[2*dim+1] =  ds2; coords[2*dim+2] = 0.0;
1529       coords[3*dim+0] = -ds2; coords[3*dim+1] =  ds2; coords[3*dim+2] = 0.0;
1530       coords[4*dim+0] = -ds2; coords[4*dim+1] = -ds2; coords[4*dim+2] = 1.0;
1531       coords[5*dim+0] = -ds2; coords[5*dim+1] =  ds2; coords[5*dim+2] = 1.0;
1532       coords[6*dim+0] =  ds2; coords[6*dim+1] =  ds2; coords[6*dim+2] = 1.0;
1533       coords[7*dim+0] =  ds2; coords[7*dim+1] = -ds2; coords[7*dim+2] = 1.0;
1534       coords[ 8*dim+0] =  dis; coords[ 8*dim+1] = -dis; coords[ 8*dim+2] = 0.0;
1535       coords[ 9*dim+0] =  dis; coords[ 9*dim+1] =  dis; coords[ 9*dim+2] = 0.0;
1536       coords[10*dim+0] =  dis; coords[10*dim+1] = -dis; coords[10*dim+2] = 1.0;
1537       coords[11*dim+0] =  dis; coords[11*dim+1] =  dis; coords[11*dim+2] = 1.0;
1538       coords[12*dim+0] = -dis; coords[12*dim+1] =  dis; coords[12*dim+2] = 0.0;
1539       coords[13*dim+0] = -dis; coords[13*dim+1] =  dis; coords[13*dim+2] = 1.0;
1540       coords[14*dim+0] = -dis; coords[14*dim+1] = -dis; coords[14*dim+2] = 0.0;
1541       coords[15*dim+0] = -dis; coords[15*dim+1] = -dis; coords[15*dim+2] = 1.0;
1542       if (periodicZ == DM_BOUNDARY_PERIODIC) {
1543         /* 15 31 19 */ coords[16*dim+0] = -ds2; coords[16*dim+1] = -ds2; coords[16*dim+2] = 0.5;
1544         /* 16 32 22 */ coords[17*dim+0] =  ds2; coords[17*dim+1] = -ds2; coords[17*dim+2] = 0.5;
1545         /* 17 33 21 */ coords[18*dim+0] =  ds2; coords[18*dim+1] =  ds2; coords[18*dim+2] = 0.5;
1546         /* 18 34 20 */ coords[19*dim+0] = -ds2; coords[19*dim+1] =  ds2; coords[19*dim+2] = 0.5;
1547         /* 29 35 30 */ coords[20*dim+0] = -dis; coords[20*dim+1] = -dis; coords[20*dim+2] = 0.5;
1548         /* 23 36 25 */ coords[21*dim+0] =  dis; coords[21*dim+1] = -dis; coords[21*dim+2] = 0.5;
1549         /* 24 37 26 */ coords[22*dim+0] =  dis; coords[22*dim+1] =  dis; coords[22*dim+2] = 0.5;
1550         /* 27 38 28 */ coords[23*dim+0] = -dis; coords[23*dim+1] =  dis; coords[23*dim+2] = 0.5;
1551       }
1552     }
1553     ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
1554     ierr = DMSetCoordinatesLocal(*dm, coordinates);CHKERRQ(ierr);
1555     ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
1556   }
1557   /* Create periodicity */
1558   if (periodicZ == DM_BOUNDARY_PERIODIC || periodicZ == DM_BOUNDARY_TWIST) {
1559     PetscReal      L[3];
1560     PetscReal      maxCell[3];
1561     DMBoundaryType bdType[3];
1562     PetscReal      lower[3] = {0.0, 0.0, 0.0};
1563     PetscReal      upper[3] = {1.0, 1.0, 1.5};
1564     PetscInt       i, numZCells = 3;
1565 
1566     bdType[0] = DM_BOUNDARY_NONE;
1567     bdType[1] = DM_BOUNDARY_NONE;
1568     bdType[2] = periodicZ;
1569     for (i = 0; i < dim; i++) {
1570       L[i]       = upper[i] - lower[i];
1571       maxCell[i] = 1.1 * (L[i] / numZCells);
1572     }
1573     ierr = DMSetPeriodicity(*dm, PETSC_TRUE, maxCell, L, bdType);CHKERRQ(ierr);
1574   }
1575   /* Refine topology */
1576   for (r = 0; r < numRefine; ++r) {
1577     DM rdm = NULL;
1578 
1579     ierr = DMRefine(*dm, comm, &rdm);CHKERRQ(ierr);
1580     ierr = DMDestroy(dm);CHKERRQ(ierr);
1581     *dm  = rdm;
1582   }
1583   /* Remap geometry to cylinder
1584        Interior square: Linear interpolation is correct
1585        The other cells all have vertices on rays from the origin. We want to uniformly expand the spacing
1586        such that the last vertex is on the unit circle. So the closest and farthest vertices are at distance
1587 
1588          phi     = arctan(y/x)
1589          d_close = sqrt(1/8 + 1/4 sin^2(phi))
1590          d_far   = sqrt(1/2 + sin^2(phi))
1591 
1592        so we remap them using
1593 
1594          x_new = x_close + (x - x_close) (1 - d_close) / (d_far - d_close)
1595          y_new = y_close + (y - y_close) (1 - d_close) / (d_far - d_close)
1596 
1597        If pi/4 < phi < 3pi/4 or -3pi/4 < phi < -pi/4, then we switch x and y.
1598   */
1599   {
1600     Vec           coordinates;
1601     PetscSection  coordSection;
1602     PetscScalar  *coords;
1603     PetscInt      vStart, vEnd, v;
1604     const PetscReal dis = 1.0/PetscSqrtReal(2.0);
1605     const PetscReal ds2 = 0.5*dis;
1606 
1607     ierr = DMPlexGetDepthStratum(*dm, 0, &vStart, &vEnd);CHKERRQ(ierr);
1608     ierr = DMGetCoordinateSection(*dm, &coordSection);CHKERRQ(ierr);
1609     ierr = DMGetCoordinatesLocal(*dm, &coordinates);CHKERRQ(ierr);
1610     ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
1611     for (v = vStart; v < vEnd; ++v) {
1612       PetscReal phi, sinp, cosp, dc, df, x, y, xc, yc;
1613       PetscInt  off;
1614 
1615       ierr = PetscSectionGetOffset(coordSection, v, &off);CHKERRQ(ierr);
1616       if ((PetscAbsScalar(coords[off+0]) <= ds2) && (PetscAbsScalar(coords[off+1]) <= ds2)) continue;
1617       x    = PetscRealPart(coords[off]);
1618       y    = PetscRealPart(coords[off+1]);
1619       phi  = PetscAtan2Real(y, x);
1620       sinp = PetscSinReal(phi);
1621       cosp = PetscCosReal(phi);
1622       if ((PetscAbsReal(phi) > PETSC_PI/4.0) && (PetscAbsReal(phi) < 3.0*PETSC_PI/4.0)) {
1623         dc = PetscAbsReal(ds2/sinp);
1624         df = PetscAbsReal(dis/sinp);
1625         xc = ds2*x/PetscAbsReal(y);
1626         yc = ds2*PetscSignReal(y);
1627       } else {
1628         dc = PetscAbsReal(ds2/cosp);
1629         df = PetscAbsReal(dis/cosp);
1630         xc = ds2*PetscSignReal(x);
1631         yc = ds2*y/PetscAbsReal(x);
1632       }
1633       coords[off+0] = xc + (coords[off+0] - xc)*(1.0 - dc)/(df - dc);
1634       coords[off+1] = yc + (coords[off+1] - yc)*(1.0 - dc)/(df - dc);
1635     }
1636     ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
1637     if (periodicZ == DM_BOUNDARY_PERIODIC || periodicZ == DM_BOUNDARY_TWIST) {
1638       ierr = DMLocalizeCoordinates(*dm);CHKERRQ(ierr);
1639     }
1640   }
1641   PetscFunctionReturn(0);
1642 }
1643 
1644 /*@
1645   DMPlexCreateWedgeCylinderMesh - Creates a mesh on the tensor product of the unit interval with the circle (cylinder) using wedges.
1646 
1647   Collective
1648 
1649   Input Parameters:
1650 + comm - The communicator for the DM object
1651 . n    - The number of wedges around the origin
1652 - interpolate - Create edges and faces
1653 
1654   Output Parameter:
1655 . dm  - The DM object
1656 
1657   Level: beginner
1658 
1659 .seealso: DMPlexCreateHexCylinderMesh(), DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
1660 @*/
1661 PetscErrorCode DMPlexCreateWedgeCylinderMesh(MPI_Comm comm, PetscInt n, PetscBool interpolate, DM *dm)
1662 {
1663   const PetscInt dim = 3;
1664   PetscInt       numCells, numVertices, v;
1665   PetscMPIInt    rank;
1666   PetscErrorCode ierr;
1667 
1668   PetscFunctionBegin;
1669   PetscValidPointer(dm, 3);
1670   ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
1671   if (n < 0) SETERRQ1(comm, PETSC_ERR_ARG_OUTOFRANGE, "Number of wedges %D cannot be negative", n);
1672   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
1673   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
1674   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
1675   /* Must create the celltype label here so that we do not automatically try to compute the types */
1676   ierr = DMCreateLabel(*dm, "celltype");CHKERRQ(ierr);
1677   /* Create topology */
1678   {
1679     PetscInt cone[6], c;
1680 
1681     numCells    = !rank ?        n : 0;
1682     numVertices = !rank ?  2*(n+1) : 0;
1683     ierr = DMPlexSetChart(*dm, 0, numCells+numVertices);CHKERRQ(ierr);
1684     for (c = 0; c < numCells; c++) {ierr = DMPlexSetConeSize(*dm, c, 6);CHKERRQ(ierr);}
1685     ierr = DMSetUp(*dm);CHKERRQ(ierr);
1686     for (c = 0; c < numCells; c++) {
1687       cone[0] =  c+n*1; cone[1] = (c+1)%n+n*1; cone[2] = 0+3*n;
1688       cone[3] =  c+n*2; cone[4] = (c+1)%n+n*2; cone[5] = 1+3*n;
1689       ierr = DMPlexSetCone(*dm, c, cone);CHKERRQ(ierr);
1690       ierr = DMPlexSetCellType(*dm, c, DM_POLYTOPE_TRI_PRISM_TENSOR);CHKERRQ(ierr);
1691     }
1692     ierr = DMPlexSymmetrize(*dm);CHKERRQ(ierr);
1693     ierr = DMPlexStratify(*dm);CHKERRQ(ierr);
1694   }
1695   for (v = numCells; v < numCells+numVertices; ++v) {
1696     ierr = DMPlexSetCellType(*dm, v, DM_POLYTOPE_POINT);CHKERRQ(ierr);
1697   }
1698   /* Interpolate */
1699   if (interpolate) {
1700     DM idm;
1701 
1702     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
1703     ierr = DMDestroy(dm);CHKERRQ(ierr);
1704     *dm  = idm;
1705   }
1706   /* Create cylinder geometry */
1707   {
1708     Vec          coordinates;
1709     PetscSection coordSection;
1710     PetscScalar *coords;
1711     PetscInt     coordSize, c;
1712 
1713     /* Build coordinates */
1714     ierr = DMGetCoordinateSection(*dm, &coordSection);CHKERRQ(ierr);
1715     ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
1716     ierr = PetscSectionSetFieldComponents(coordSection, 0, dim);CHKERRQ(ierr);
1717     ierr = PetscSectionSetChart(coordSection, numCells, numCells+numVertices);CHKERRQ(ierr);
1718     for (v = numCells; v < numCells+numVertices; ++v) {
1719       ierr = PetscSectionSetDof(coordSection, v, dim);CHKERRQ(ierr);
1720       ierr = PetscSectionSetFieldDof(coordSection, v, 0, dim);CHKERRQ(ierr);
1721     }
1722     ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
1723     ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
1724     ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
1725     ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
1726     ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
1727     ierr = VecSetBlockSize(coordinates, dim);CHKERRQ(ierr);
1728     ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
1729     ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
1730     for (c = 0; c < numCells; c++) {
1731       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;
1732       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;
1733     }
1734     if (!rank) {
1735       coords[(2*n+0)*dim+0] = 0.0; coords[(2*n+0)*dim+1] = 0.0; coords[(2*n+0)*dim+2] = 1.0;
1736       coords[(2*n+1)*dim+0] = 0.0; coords[(2*n+1)*dim+1] = 0.0; coords[(2*n+1)*dim+2] = 0.0;
1737     }
1738     ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
1739     ierr = DMSetCoordinatesLocal(*dm, coordinates);CHKERRQ(ierr);
1740     ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
1741   }
1742   PetscFunctionReturn(0);
1743 }
1744 
1745 PETSC_STATIC_INLINE PetscReal DiffNormReal(PetscInt dim, const PetscReal x[], const PetscReal y[])
1746 {
1747   PetscReal prod = 0.0;
1748   PetscInt  i;
1749   for (i = 0; i < dim; ++i) prod += PetscSqr(x[i] - y[i]);
1750   return PetscSqrtReal(prod);
1751 }
1752 PETSC_STATIC_INLINE PetscReal DotReal(PetscInt dim, const PetscReal x[], const PetscReal y[])
1753 {
1754   PetscReal prod = 0.0;
1755   PetscInt  i;
1756   for (i = 0; i < dim; ++i) prod += x[i]*y[i];
1757   return prod;
1758 }
1759 
1760 /* The first constant is the sphere radius */
1761 static void snapToSphere(PetscInt dim, PetscInt Nf, PetscInt NfAux,
1762                          const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
1763                          const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
1764                          PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
1765 {
1766   PetscReal r = PetscRealPart(constants[0]);
1767   PetscReal norm2 = 0.0, fac;
1768   PetscInt  n = uOff[1] - uOff[0], d;
1769 
1770   for (d = 0; d < n; ++d) norm2 += PetscSqr(PetscRealPart(u[d]));
1771   fac = r/PetscSqrtReal(norm2);
1772   for (d = 0; d < n; ++d) f0[d] = u[d]*fac;
1773 }
1774 
1775 /*@
1776   DMPlexCreateSphereMesh - Creates a mesh on the d-dimensional sphere, S^d.
1777 
1778   Collective
1779 
1780   Input Parameters:
1781 + comm    - The communicator for the DM object
1782 . dim     - The dimension
1783 . simplex - Use simplices, or tensor product cells
1784 - R       - The radius
1785 
1786   Output Parameter:
1787 . dm  - The DM object
1788 
1789   Level: beginner
1790 
1791 .seealso: DMPlexCreateBallMesh(), DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
1792 @*/
1793 PetscErrorCode DMPlexCreateSphereMesh(MPI_Comm comm, PetscInt dim, PetscBool simplex, PetscReal R, DM *dm)
1794 {
1795   const PetscInt  embedDim = dim+1;
1796   PetscSection    coordSection;
1797   Vec             coordinates;
1798   PetscScalar    *coords;
1799   PetscReal      *coordsIn;
1800   PetscInt        numCells, numEdges, numVerts, firstVertex, v, firstEdge, coordSize, d, c, e;
1801   PetscMPIInt     rank;
1802   PetscErrorCode  ierr;
1803 
1804   PetscFunctionBegin;
1805   PetscValidPointer(dm, 4);
1806   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
1807   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
1808   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
1809   ierr = DMSetCoordinateDim(*dm, dim+1);CHKERRQ(ierr);
1810   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject) *dm), &rank);CHKERRQ(ierr);
1811   switch (dim) {
1812   case 2:
1813     if (simplex) {
1814       DM              idm;
1815       const PetscReal radius    = PetscSqrtReal(1 + PETSC_PHI*PETSC_PHI)/(1.0 + PETSC_PHI);
1816       const PetscReal edgeLen   = 2.0/(1.0 + PETSC_PHI) * (R/radius);
1817       const PetscInt  degree    = 5;
1818       PetscReal       vertex[3] = {0.0, 1.0/(1.0 + PETSC_PHI), PETSC_PHI/(1.0 + PETSC_PHI)};
1819       PetscInt        s[3]      = {1, 1, 1};
1820       PetscInt        cone[3];
1821       PetscInt       *graph, p, i, j, k;
1822 
1823       vertex[0] *= R/radius; vertex[1] *= R/radius; vertex[2] *= R/radius;
1824       numCells    = !rank ? 20 : 0;
1825       numVerts    = !rank ? 12 : 0;
1826       firstVertex = numCells;
1827       /* Use icosahedron, which for a R-sphere has coordinates which are all cyclic permutations of
1828 
1829            (0, \pm 1/\phi+1, \pm \phi/\phi+1)
1830 
1831          where \phi^2 - \phi - 1 = 0, meaning \phi is the golden ratio \frac{1 + \sqrt{5}}{2}. The edge
1832          length is then given by 2/(1+\phi) = 2 * 0.38197 = 0.76393.
1833       */
1834       /* Construct vertices */
1835       ierr = PetscCalloc1(numVerts * embedDim, &coordsIn);CHKERRQ(ierr);
1836       if (!rank) {
1837         for (p = 0, i = 0; p < embedDim; ++p) {
1838           for (s[1] = -1; s[1] < 2; s[1] += 2) {
1839             for (s[2] = -1; s[2] < 2; s[2] += 2) {
1840               for (d = 0; d < embedDim; ++d) coordsIn[i*embedDim+d] = s[(d+p)%embedDim]*vertex[(d+p)%embedDim];
1841               ++i;
1842             }
1843           }
1844         }
1845       }
1846       /* Construct graph */
1847       ierr = PetscCalloc1(numVerts * numVerts, &graph);CHKERRQ(ierr);
1848       for (i = 0; i < numVerts; ++i) {
1849         for (j = 0, k = 0; j < numVerts; ++j) {
1850           if (PetscAbsReal(DiffNormReal(embedDim, &coordsIn[i*embedDim], &coordsIn[j*embedDim]) - edgeLen) < PETSC_SMALL) {graph[i*numVerts+j] = 1; ++k;}
1851         }
1852         if (k != degree) SETERRQ3(comm, PETSC_ERR_PLIB, "Invalid icosahedron, vertex %D degree %D != %D", i, k, degree);
1853       }
1854       /* Build Topology */
1855       ierr = DMPlexSetChart(*dm, 0, numCells+numVerts);CHKERRQ(ierr);
1856       for (c = 0; c < numCells; c++) {
1857         ierr = DMPlexSetConeSize(*dm, c, embedDim);CHKERRQ(ierr);
1858       }
1859       ierr = DMSetUp(*dm);CHKERRQ(ierr); /* Allocate space for cones */
1860       /* Cells */
1861       for (i = 0, c = 0; i < numVerts; ++i) {
1862         for (j = 0; j < i; ++j) {
1863           for (k = 0; k < j; ++k) {
1864             if (graph[i*numVerts+j] && graph[j*numVerts+k] && graph[k*numVerts+i]) {
1865               cone[0] = firstVertex+i; cone[1] = firstVertex+j; cone[2] = firstVertex+k;
1866               /* Check orientation */
1867               {
1868                 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}}};
1869                 PetscReal normal[3];
1870                 PetscInt  e, f;
1871 
1872                 for (d = 0; d < embedDim; ++d) {
1873                   normal[d] = 0.0;
1874                   for (e = 0; e < embedDim; ++e) {
1875                     for (f = 0; f < embedDim; ++f) {
1876                       normal[d] += epsilon[d][e][f]*(coordsIn[j*embedDim+e] - coordsIn[i*embedDim+e])*(coordsIn[k*embedDim+f] - coordsIn[i*embedDim+f]);
1877                     }
1878                   }
1879                 }
1880                 if (DotReal(embedDim, normal, &coordsIn[i*embedDim]) < 0) {PetscInt tmp = cone[1]; cone[1] = cone[2]; cone[2] = tmp;}
1881               }
1882               ierr = DMPlexSetCone(*dm, c++, cone);CHKERRQ(ierr);
1883             }
1884           }
1885         }
1886       }
1887       ierr = DMPlexSymmetrize(*dm);CHKERRQ(ierr);
1888       ierr = DMPlexStratify(*dm);CHKERRQ(ierr);
1889       ierr = PetscFree(graph);CHKERRQ(ierr);
1890       /* Interpolate mesh */
1891       ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
1892       ierr = DMDestroy(dm);CHKERRQ(ierr);
1893       *dm  = idm;
1894     } else {
1895       /*
1896         12-21--13
1897          |     |
1898         25  4  24
1899          |     |
1900   12-25--9-16--8-24--13
1901    |     |     |     |
1902   23  5 17  0 15  3  22
1903    |     |     |     |
1904   10-20--6-14--7-19--11
1905          |     |
1906         20  1  19
1907          |     |
1908         10-18--11
1909          |     |
1910         23  2  22
1911          |     |
1912         12-21--13
1913        */
1914       PetscInt cone[4], ornt[4];
1915 
1916       numCells    = !rank ?  6 : 0;
1917       numEdges    = !rank ? 12 : 0;
1918       numVerts    = !rank ?  8 : 0;
1919       firstVertex = numCells;
1920       firstEdge   = numCells + numVerts;
1921       /* Build Topology */
1922       ierr = DMPlexSetChart(*dm, 0, numCells+numEdges+numVerts);CHKERRQ(ierr);
1923       for (c = 0; c < numCells; c++) {
1924         ierr = DMPlexSetConeSize(*dm, c, 4);CHKERRQ(ierr);
1925       }
1926       for (e = firstEdge; e < firstEdge+numEdges; ++e) {
1927         ierr = DMPlexSetConeSize(*dm, e, 2);CHKERRQ(ierr);
1928       }
1929       ierr = DMSetUp(*dm);CHKERRQ(ierr); /* Allocate space for cones */
1930       if (!rank) {
1931         /* Cell 0 */
1932         cone[0] = 14; cone[1] = 15; cone[2] = 16; cone[3] = 17;
1933         ierr = DMPlexSetCone(*dm, 0, cone);CHKERRQ(ierr);
1934         ornt[0] = 0; ornt[1] = 0; ornt[2] = 0; ornt[3] = 0;
1935         ierr = DMPlexSetConeOrientation(*dm, 0, ornt);CHKERRQ(ierr);
1936         /* Cell 1 */
1937         cone[0] = 18; cone[1] = 19; cone[2] = 14; cone[3] = 20;
1938         ierr = DMPlexSetCone(*dm, 1, cone);CHKERRQ(ierr);
1939         ornt[0] = 0; ornt[1] = 0; ornt[2] = -2; ornt[3] = 0;
1940         ierr = DMPlexSetConeOrientation(*dm, 1, ornt);CHKERRQ(ierr);
1941         /* Cell 2 */
1942         cone[0] = 21; cone[1] = 22; cone[2] = 18; cone[3] = 23;
1943         ierr = DMPlexSetCone(*dm, 2, cone);CHKERRQ(ierr);
1944         ornt[0] = 0; ornt[1] = 0; ornt[2] = -2; ornt[3] = 0;
1945         ierr = DMPlexSetConeOrientation(*dm, 2, ornt);CHKERRQ(ierr);
1946         /* Cell 3 */
1947         cone[0] = 19; cone[1] = 22; cone[2] = 24; cone[3] = 15;
1948         ierr = DMPlexSetCone(*dm, 3, cone);CHKERRQ(ierr);
1949         ornt[0] = -2; ornt[1] = -2; ornt[2] = 0; ornt[3] = -2;
1950         ierr = DMPlexSetConeOrientation(*dm, 3, ornt);CHKERRQ(ierr);
1951         /* Cell 4 */
1952         cone[0] = 16; cone[1] = 24; cone[2] = 21; cone[3] = 25;
1953         ierr = DMPlexSetCone(*dm, 4, cone);CHKERRQ(ierr);
1954         ornt[0] = -2; ornt[1] = -2; ornt[2] = -2; ornt[3] = 0;
1955         ierr = DMPlexSetConeOrientation(*dm, 4, ornt);CHKERRQ(ierr);
1956         /* Cell 5 */
1957         cone[0] = 20; cone[1] = 17; cone[2] = 25; cone[3] = 23;
1958         ierr = DMPlexSetCone(*dm, 5, cone);CHKERRQ(ierr);
1959         ornt[0] = -2; ornt[1] = -2; ornt[2] = -2; ornt[3] = -2;
1960         ierr = DMPlexSetConeOrientation(*dm, 5, ornt);CHKERRQ(ierr);
1961         /* Edges */
1962         cone[0] =  6; cone[1] =  7;
1963         ierr = DMPlexSetCone(*dm, 14, cone);CHKERRQ(ierr);
1964         cone[0] =  7; cone[1] =  8;
1965         ierr = DMPlexSetCone(*dm, 15, cone);CHKERRQ(ierr);
1966         cone[0] =  8; cone[1] =  9;
1967         ierr = DMPlexSetCone(*dm, 16, cone);CHKERRQ(ierr);
1968         cone[0] =  9; cone[1] =  6;
1969         ierr = DMPlexSetCone(*dm, 17, cone);CHKERRQ(ierr);
1970         cone[0] = 10; cone[1] = 11;
1971         ierr = DMPlexSetCone(*dm, 18, cone);CHKERRQ(ierr);
1972         cone[0] = 11; cone[1] =  7;
1973         ierr = DMPlexSetCone(*dm, 19, cone);CHKERRQ(ierr);
1974         cone[0] =  6; cone[1] = 10;
1975         ierr = DMPlexSetCone(*dm, 20, cone);CHKERRQ(ierr);
1976         cone[0] = 12; cone[1] = 13;
1977         ierr = DMPlexSetCone(*dm, 21, cone);CHKERRQ(ierr);
1978         cone[0] = 13; cone[1] = 11;
1979         ierr = DMPlexSetCone(*dm, 22, cone);CHKERRQ(ierr);
1980         cone[0] = 10; cone[1] = 12;
1981         ierr = DMPlexSetCone(*dm, 23, cone);CHKERRQ(ierr);
1982         cone[0] = 13; cone[1] =  8;
1983         ierr = DMPlexSetCone(*dm, 24, cone);CHKERRQ(ierr);
1984         cone[0] = 12; cone[1] =  9;
1985         ierr = DMPlexSetCone(*dm, 25, cone);CHKERRQ(ierr);
1986       }
1987       ierr = DMPlexSymmetrize(*dm);CHKERRQ(ierr);
1988       ierr = DMPlexStratify(*dm);CHKERRQ(ierr);
1989       /* Build coordinates */
1990       ierr = PetscCalloc1(numVerts * embedDim, &coordsIn);CHKERRQ(ierr);
1991       if (!rank) {
1992         coordsIn[0*embedDim+0] = -R; coordsIn[0*embedDim+1] =  R; coordsIn[0*embedDim+2] = -R;
1993         coordsIn[1*embedDim+0] =  R; coordsIn[1*embedDim+1] =  R; coordsIn[1*embedDim+2] = -R;
1994         coordsIn[2*embedDim+0] =  R; coordsIn[2*embedDim+1] = -R; coordsIn[2*embedDim+2] = -R;
1995         coordsIn[3*embedDim+0] = -R; coordsIn[3*embedDim+1] = -R; coordsIn[3*embedDim+2] = -R;
1996         coordsIn[4*embedDim+0] = -R; coordsIn[4*embedDim+1] =  R; coordsIn[4*embedDim+2] =  R;
1997         coordsIn[5*embedDim+0] =  R; coordsIn[5*embedDim+1] =  R; coordsIn[5*embedDim+2] =  R;
1998         coordsIn[6*embedDim+0] = -R; coordsIn[6*embedDim+1] = -R; coordsIn[6*embedDim+2] =  R;
1999         coordsIn[7*embedDim+0] =  R; coordsIn[7*embedDim+1] = -R; coordsIn[7*embedDim+2] =  R;
2000       }
2001     }
2002     break;
2003   case 3:
2004     if (simplex) {
2005       DM              idm;
2006       const PetscReal edgeLen         = 1.0/PETSC_PHI;
2007       PetscReal       vertexA[4]      = {0.5, 0.5, 0.5, 0.5};
2008       PetscReal       vertexB[4]      = {1.0, 0.0, 0.0, 0.0};
2009       PetscReal       vertexC[4]      = {0.5, 0.5*PETSC_PHI, 0.5/PETSC_PHI, 0.0};
2010       const PetscInt  degree          = 12;
2011       PetscInt        s[4]            = {1, 1, 1};
2012       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},
2013                                          {2, 0, 1, 3}, {2, 1, 3, 0}, {2, 3, 0, 1}, {3, 0, 2, 1}, {3, 1, 0, 2}, {3, 2, 1, 0}};
2014       PetscInt        cone[4];
2015       PetscInt       *graph, p, i, j, k, l;
2016 
2017       vertexA[0] *= R; vertexA[1] *= R; vertexA[2] *= R; vertexA[3] *= R;
2018       vertexB[0] *= R; vertexB[1] *= R; vertexB[2] *= R; vertexB[3] *= R;
2019       vertexC[0] *= R; vertexC[1] *= R; vertexC[2] *= R; vertexC[3] *= R;
2020       numCells    = !rank ? 600 : 0;
2021       numVerts    = !rank ? 120 : 0;
2022       firstVertex = numCells;
2023       /* Use the 600-cell, which for a unit sphere has coordinates which are
2024 
2025            1/2 (\pm 1, \pm 1,    \pm 1, \pm 1)                          16
2026                (\pm 1,    0,       0,      0)  all cyclic permutations   8
2027            1/2 (\pm 1, \pm phi, \pm 1/phi, 0)  all even permutations    96
2028 
2029          where \phi^2 - \phi - 1 = 0, meaning \phi is the golden ratio \frac{1 + \sqrt{5}}{2}. The edge
2030          length is then given by 1/\phi = 0.61803.
2031 
2032          http://buzzard.pugetsound.edu/sage-practice/ch03s03.html
2033          http://mathworld.wolfram.com/600-Cell.html
2034       */
2035       /* Construct vertices */
2036       ierr = PetscCalloc1(numVerts * embedDim, &coordsIn);CHKERRQ(ierr);
2037       i    = 0;
2038       if (!rank) {
2039         for (s[0] = -1; s[0] < 2; s[0] += 2) {
2040           for (s[1] = -1; s[1] < 2; s[1] += 2) {
2041             for (s[2] = -1; s[2] < 2; s[2] += 2) {
2042               for (s[3] = -1; s[3] < 2; s[3] += 2) {
2043                 for (d = 0; d < embedDim; ++d) coordsIn[i*embedDim+d] = s[d]*vertexA[d];
2044                 ++i;
2045               }
2046             }
2047           }
2048         }
2049         for (p = 0; p < embedDim; ++p) {
2050           s[1] = s[2] = s[3] = 1;
2051           for (s[0] = -1; s[0] < 2; s[0] += 2) {
2052             for (d = 0; d < embedDim; ++d) coordsIn[i*embedDim+d] = s[(d+p)%embedDim]*vertexB[(d+p)%embedDim];
2053             ++i;
2054           }
2055         }
2056         for (p = 0; p < 12; ++p) {
2057           s[3] = 1;
2058           for (s[0] = -1; s[0] < 2; s[0] += 2) {
2059             for (s[1] = -1; s[1] < 2; s[1] += 2) {
2060               for (s[2] = -1; s[2] < 2; s[2] += 2) {
2061                 for (d = 0; d < embedDim; ++d) coordsIn[i*embedDim+d] = s[evenPerm[p][d]]*vertexC[evenPerm[p][d]];
2062                 ++i;
2063               }
2064             }
2065           }
2066         }
2067       }
2068       if (i != numVerts) SETERRQ2(comm, PETSC_ERR_PLIB, "Invalid 600-cell, vertices %D != %D", i, numVerts);
2069       /* Construct graph */
2070       ierr = PetscCalloc1(numVerts * numVerts, &graph);CHKERRQ(ierr);
2071       for (i = 0; i < numVerts; ++i) {
2072         for (j = 0, k = 0; j < numVerts; ++j) {
2073           if (PetscAbsReal(DiffNormReal(embedDim, &coordsIn[i*embedDim], &coordsIn[j*embedDim]) - edgeLen) < PETSC_SMALL) {graph[i*numVerts+j] = 1; ++k;}
2074         }
2075         if (k != degree) SETERRQ3(comm, PETSC_ERR_PLIB, "Invalid 600-cell, vertex %D degree %D != %D", i, k, degree);
2076       }
2077       /* Build Topology */
2078       ierr = DMPlexSetChart(*dm, 0, numCells+numVerts);CHKERRQ(ierr);
2079       for (c = 0; c < numCells; c++) {
2080         ierr = DMPlexSetConeSize(*dm, c, embedDim);CHKERRQ(ierr);
2081       }
2082       ierr = DMSetUp(*dm);CHKERRQ(ierr); /* Allocate space for cones */
2083       /* Cells */
2084       if (!rank) {
2085         for (i = 0, c = 0; i < numVerts; ++i) {
2086           for (j = 0; j < i; ++j) {
2087             for (k = 0; k < j; ++k) {
2088               for (l = 0; l < k; ++l) {
2089                 if (graph[i*numVerts+j] && graph[j*numVerts+k] && graph[k*numVerts+i] &&
2090                     graph[l*numVerts+i] && graph[l*numVerts+j] && graph[l*numVerts+k]) {
2091                   cone[0] = firstVertex+i; cone[1] = firstVertex+j; cone[2] = firstVertex+k; cone[3] = firstVertex+l;
2092                   /* Check orientation: https://ef.gy/linear-algebra:normal-vectors-in-higher-dimensional-spaces */
2093                   {
2094                     const PetscInt epsilon[4][4][4][4] = {{{{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}},
2095                                                            {{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  1}, { 0,  0, -1, 0}},
2096                                                            {{0,  0,  0,  0}, { 0, 0,  0, -1}, { 0,  0, 0,  0}, { 0,  1,  0, 0}},
2097                                                            {{0,  0,  0,  0}, { 0, 0,  1,  0}, { 0, -1, 0,  0}, { 0,  0,  0, 0}}},
2098 
2099                                                           {{{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0, -1}, { 0,  0,  1, 0}},
2100                                                            {{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}},
2101                                                            {{0,  0,  0,  1}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, {-1,  0,  0, 0}},
2102                                                            {{0,  0, -1,  0}, { 0, 0,  0,  0}, { 1,  0, 0,  0}, { 0,  0,  0, 0}}},
2103 
2104                                                           {{{0,  0,  0,  0}, { 0, 0,  0,  1}, { 0,  0, 0,  0}, { 0, -1,  0, 0}},
2105                                                            {{0,  0,  0, -1}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 1,  0,  0, 0}},
2106                                                            {{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}},
2107                                                            {{0,  1,  0,  0}, {-1, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}}},
2108 
2109                                                           {{{0,  0,  0,  0}, { 0, 0, -1,  0}, { 0,  1, 0,  0}, { 0,  0,  0, 0}},
2110                                                            {{0,  0,  1,  0}, { 0, 0,  0,  0}, {-1,  0, 0,  0}, { 0,  0,  0, 0}},
2111                                                            {{0, -1,  0,  0}, { 1, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}},
2112                                                            {{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}}}};
2113                     PetscReal normal[4];
2114                     PetscInt  e, f, g;
2115 
2116                     for (d = 0; d < embedDim; ++d) {
2117                       normal[d] = 0.0;
2118                       for (e = 0; e < embedDim; ++e) {
2119                         for (f = 0; f < embedDim; ++f) {
2120                           for (g = 0; g < embedDim; ++g) {
2121                             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]);
2122                           }
2123                         }
2124                       }
2125                     }
2126                     if (DotReal(embedDim, normal, &coordsIn[i*embedDim]) < 0) {PetscInt tmp = cone[1]; cone[1] = cone[2]; cone[2] = tmp;}
2127                   }
2128                   ierr = DMPlexSetCone(*dm, c++, cone);CHKERRQ(ierr);
2129                 }
2130               }
2131             }
2132           }
2133         }
2134       }
2135       ierr = DMPlexSymmetrize(*dm);CHKERRQ(ierr);
2136       ierr = DMPlexStratify(*dm);CHKERRQ(ierr);
2137       ierr = PetscFree(graph);CHKERRQ(ierr);
2138       /* Interpolate mesh */
2139       ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
2140       ierr = DMDestroy(dm);CHKERRQ(ierr);
2141       *dm  = idm;
2142       break;
2143     }
2144   default: SETERRQ1(comm, PETSC_ERR_SUP, "Unsupported dimension for sphere: %D", dim);
2145   }
2146   /* Create coordinates */
2147   ierr = DMGetCoordinateSection(*dm, &coordSection);CHKERRQ(ierr);
2148   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
2149   ierr = PetscSectionSetFieldComponents(coordSection, 0, embedDim);CHKERRQ(ierr);
2150   ierr = PetscSectionSetChart(coordSection, firstVertex, firstVertex+numVerts);CHKERRQ(ierr);
2151   for (v = firstVertex; v < firstVertex+numVerts; ++v) {
2152     ierr = PetscSectionSetDof(coordSection, v, embedDim);CHKERRQ(ierr);
2153     ierr = PetscSectionSetFieldDof(coordSection, v, 0, embedDim);CHKERRQ(ierr);
2154   }
2155   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
2156   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
2157   ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
2158   ierr = VecSetBlockSize(coordinates, embedDim);CHKERRQ(ierr);
2159   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
2160   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
2161   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
2162   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
2163   for (v = 0; v < numVerts; ++v) for (d = 0; d < embedDim; ++d) {coords[v*embedDim+d] = coordsIn[v*embedDim+d];}
2164   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
2165   ierr = DMSetCoordinatesLocal(*dm, coordinates);CHKERRQ(ierr);
2166   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
2167   ierr = PetscFree(coordsIn);CHKERRQ(ierr);
2168   /* Create coordinate function space */
2169   {
2170     DM          cdm;
2171     PetscDS     cds;
2172     PetscFE     fe;
2173     PetscScalar radius = R;
2174     PetscInt    dT, dE;
2175 
2176     ierr = DMGetCoordinateDM(*dm, &cdm);CHKERRQ(ierr);
2177     ierr = DMGetDimension(*dm, &dT);CHKERRQ(ierr);
2178     ierr = DMGetCoordinateDim(*dm, &dE);CHKERRQ(ierr);
2179     ierr = PetscFECreateLagrange(PETSC_COMM_SELF, dT, dE, PETSC_TRUE, 1, -1, &fe);CHKERRQ(ierr);
2180     ierr = DMSetField(cdm, 0, NULL, (PetscObject) fe);CHKERRQ(ierr);
2181     ierr = PetscFEDestroy(&fe);CHKERRQ(ierr);
2182     ierr = DMCreateDS(cdm);CHKERRQ(ierr);
2183 
2184     ierr = DMGetDS(cdm, &cds);CHKERRQ(ierr);
2185     ierr = PetscDSSetConstants(cds, 1, &radius);CHKERRQ(ierr);
2186   }
2187   ((DM_Plex *) (*dm)->data)->coordFunc = snapToSphere;
2188   PetscFunctionReturn(0);
2189 }
2190 
2191 /*@
2192   DMPlexCreateBallMesh - Creates a simplex mesh on the d-dimensional ball, B^d.
2193 
2194   Collective
2195 
2196   Input Parameters:
2197 + comm  - The communicator for the DM object
2198 . dim   - The dimension
2199 - R     - The radius
2200 
2201   Output Parameter:
2202 . dm  - The DM object
2203 
2204   Options Database Keys:
2205 - bd_dm_refine - This will refine the surface mesh preserving the sphere geometry
2206 
2207   Level: beginner
2208 
2209 .seealso: DMPlexCreateSphereMesh(), DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
2210 @*/
2211 PetscErrorCode DMPlexCreateBallMesh(MPI_Comm comm, PetscInt dim, PetscReal R, DM *dm)
2212 {
2213   DM             sdm;
2214   PetscErrorCode ierr;
2215 
2216   PetscFunctionBegin;
2217   ierr = DMPlexCreateSphereMesh(comm, dim-1, PETSC_TRUE, R, &sdm);CHKERRQ(ierr);
2218   ierr = PetscObjectSetOptionsPrefix((PetscObject) sdm, "bd_");CHKERRQ(ierr);
2219   ierr = DMSetFromOptions(sdm);CHKERRQ(ierr);
2220   ierr = DMPlexGenerate(sdm, NULL, PETSC_TRUE, dm);CHKERRQ(ierr);
2221   ierr = DMDestroy(&sdm);CHKERRQ(ierr);
2222   PetscFunctionReturn(0);
2223 }
2224 
2225 /* External function declarations here */
2226 extern PetscErrorCode DMCreateInterpolation_Plex(DM dmCoarse, DM dmFine, Mat *interpolation, Vec *scaling);
2227 extern PetscErrorCode DMCreateInjection_Plex(DM dmCoarse, DM dmFine, Mat *mat);
2228 extern PetscErrorCode DMCreateMassMatrix_Plex(DM dmCoarse, DM dmFine, Mat *mat);
2229 extern PetscErrorCode DMCreateLocalSection_Plex(DM dm);
2230 extern PetscErrorCode DMCreateDefaultConstraints_Plex(DM dm);
2231 extern PetscErrorCode DMCreateMatrix_Plex(DM dm,  Mat *J);
2232 extern PetscErrorCode DMCreateCoordinateDM_Plex(DM dm, DM *cdm);
2233 extern PetscErrorCode DMCreateCoordinateField_Plex(DM dm, DMField *field);
2234 PETSC_INTERN PetscErrorCode DMClone_Plex(DM dm, DM *newdm);
2235 extern PetscErrorCode DMSetUp_Plex(DM dm);
2236 extern PetscErrorCode DMDestroy_Plex(DM dm);
2237 extern PetscErrorCode DMView_Plex(DM dm, PetscViewer viewer);
2238 extern PetscErrorCode DMLoad_Plex(DM dm, PetscViewer viewer);
2239 extern PetscErrorCode DMCreateSubDM_Plex(DM dm, PetscInt numFields, const PetscInt fields[], IS *is, DM *subdm);
2240 extern PetscErrorCode DMCreateSuperDM_Plex(DM dms[], PetscInt len, IS **is, DM *superdm);
2241 static PetscErrorCode DMInitialize_Plex(DM dm);
2242 
2243 /* Replace dm with the contents of dmNew
2244    - Share the DM_Plex structure
2245    - Share the coordinates
2246    - Share the SF
2247 */
2248 static PetscErrorCode DMPlexReplace_Static(DM dm, DM dmNew)
2249 {
2250   PetscSF               sf;
2251   DM                    coordDM, coarseDM;
2252   DMField               coordField;
2253   Vec                   coords;
2254   PetscBool             isper;
2255   const PetscReal      *maxCell, *L;
2256   const DMBoundaryType *bd;
2257   PetscErrorCode        ierr;
2258 
2259   PetscFunctionBegin;
2260   ierr = DMGetPointSF(dmNew, &sf);CHKERRQ(ierr);
2261   ierr = DMSetPointSF(dm, sf);CHKERRQ(ierr);
2262   ierr = DMGetCoordinateDM(dmNew, &coordDM);CHKERRQ(ierr);
2263   ierr = DMGetCoordinatesLocal(dmNew, &coords);CHKERRQ(ierr);
2264   ierr = DMGetCoordinateField(dmNew, &coordField);CHKERRQ(ierr);
2265   ierr = DMSetCoordinateDM(dm, coordDM);CHKERRQ(ierr);
2266   ierr = DMSetCoordinatesLocal(dm, coords);CHKERRQ(ierr);
2267   ierr = DMSetCoordinateField(dm, coordField);CHKERRQ(ierr);
2268   ierr = DMGetPeriodicity(dm, &isper, &maxCell, &L, &bd);CHKERRQ(ierr);
2269   ierr = DMSetPeriodicity(dmNew, isper, maxCell, L, bd);CHKERRQ(ierr);
2270   ierr = DMDestroy_Plex(dm);CHKERRQ(ierr);
2271   ierr = DMInitialize_Plex(dm);CHKERRQ(ierr);
2272   dm->data = dmNew->data;
2273   ((DM_Plex *) dmNew->data)->refct++;
2274   ierr = DMDestroyLabelLinkList_Internal(dm);CHKERRQ(ierr);
2275   ierr = DMCopyLabels(dmNew, dm, PETSC_OWN_POINTER, PETSC_TRUE);CHKERRQ(ierr);
2276   ierr = DMGetCoarseDM(dmNew,&coarseDM);CHKERRQ(ierr);
2277   ierr = DMSetCoarseDM(dm,coarseDM);CHKERRQ(ierr);
2278   PetscFunctionReturn(0);
2279 }
2280 
2281 /* Swap dm with the contents of dmNew
2282    - Swap the DM_Plex structure
2283    - Swap the coordinates
2284    - Swap the point PetscSF
2285 */
2286 static PetscErrorCode DMPlexSwap_Static(DM dmA, DM dmB)
2287 {
2288   DM              coordDMA, coordDMB;
2289   Vec             coordsA,  coordsB;
2290   PetscSF         sfA,      sfB;
2291   void            *tmp;
2292   DMLabelLink     listTmp;
2293   DMLabel         depthTmp;
2294   PetscInt        tmpI;
2295   PetscErrorCode  ierr;
2296 
2297   PetscFunctionBegin;
2298   ierr = DMGetPointSF(dmA, &sfA);CHKERRQ(ierr);
2299   ierr = DMGetPointSF(dmB, &sfB);CHKERRQ(ierr);
2300   ierr = PetscObjectReference((PetscObject) sfA);CHKERRQ(ierr);
2301   ierr = DMSetPointSF(dmA, sfB);CHKERRQ(ierr);
2302   ierr = DMSetPointSF(dmB, sfA);CHKERRQ(ierr);
2303   ierr = PetscObjectDereference((PetscObject) sfA);CHKERRQ(ierr);
2304 
2305   ierr = DMGetCoordinateDM(dmA, &coordDMA);CHKERRQ(ierr);
2306   ierr = DMGetCoordinateDM(dmB, &coordDMB);CHKERRQ(ierr);
2307   ierr = PetscObjectReference((PetscObject) coordDMA);CHKERRQ(ierr);
2308   ierr = DMSetCoordinateDM(dmA, coordDMB);CHKERRQ(ierr);
2309   ierr = DMSetCoordinateDM(dmB, coordDMA);CHKERRQ(ierr);
2310   ierr = PetscObjectDereference((PetscObject) coordDMA);CHKERRQ(ierr);
2311 
2312   ierr = DMGetCoordinatesLocal(dmA, &coordsA);CHKERRQ(ierr);
2313   ierr = DMGetCoordinatesLocal(dmB, &coordsB);CHKERRQ(ierr);
2314   ierr = PetscObjectReference((PetscObject) coordsA);CHKERRQ(ierr);
2315   ierr = DMSetCoordinatesLocal(dmA, coordsB);CHKERRQ(ierr);
2316   ierr = DMSetCoordinatesLocal(dmB, coordsA);CHKERRQ(ierr);
2317   ierr = PetscObjectDereference((PetscObject) coordsA);CHKERRQ(ierr);
2318 
2319   tmp       = dmA->data;
2320   dmA->data = dmB->data;
2321   dmB->data = tmp;
2322   listTmp   = dmA->labels;
2323   dmA->labels = dmB->labels;
2324   dmB->labels = listTmp;
2325   depthTmp  = dmA->depthLabel;
2326   dmA->depthLabel = dmB->depthLabel;
2327   dmB->depthLabel = depthTmp;
2328   depthTmp  = dmA->celltypeLabel;
2329   dmA->celltypeLabel = dmB->celltypeLabel;
2330   dmB->celltypeLabel = depthTmp;
2331   tmpI         = dmA->levelup;
2332   dmA->levelup = dmB->levelup;
2333   dmB->levelup = tmpI;
2334   PetscFunctionReturn(0);
2335 }
2336 
2337 PetscErrorCode DMSetFromOptions_NonRefinement_Plex(PetscOptionItems *PetscOptionsObject,DM dm)
2338 {
2339   DM_Plex       *mesh = (DM_Plex*) dm->data;
2340   PetscBool      flg;
2341   PetscErrorCode ierr;
2342 
2343   PetscFunctionBegin;
2344   /* Handle viewing */
2345   ierr = PetscOptionsBool("-dm_plex_print_set_values", "Output all set values info", "DMPlexMatSetClosure", PETSC_FALSE, &mesh->printSetValues, NULL);CHKERRQ(ierr);
2346   ierr = PetscOptionsBoundedInt("-dm_plex_print_fem", "Debug output level all fem computations", "DMPlexSNESComputeResidualFEM", 0, &mesh->printFEM, NULL,0);CHKERRQ(ierr);
2347   ierr = PetscOptionsReal("-dm_plex_print_tol", "Tolerance for FEM output", "DMPlexSNESComputeResidualFEM", mesh->printTol, &mesh->printTol, NULL);CHKERRQ(ierr);
2348   ierr = PetscOptionsBoundedInt("-dm_plex_print_l2", "Debug output level all L2 diff computations", "DMComputeL2Diff", 0, &mesh->printL2, NULL,0);CHKERRQ(ierr);
2349   ierr = DMMonitorSetFromOptions(dm, "-dm_plex_monitor_throughput", "Monitor the simulation throughput", "DMPlexMonitorThroughput", DMPlexMonitorThroughput, NULL, &flg);CHKERRQ(ierr);
2350   if (flg) {ierr = PetscLogDefaultBegin();CHKERRQ(ierr);}
2351   /* Point Location */
2352   ierr = PetscOptionsBool("-dm_plex_hash_location", "Use grid hashing for point location", "DMInterpolate", PETSC_FALSE, &mesh->useHashLocation, NULL);CHKERRQ(ierr);
2353   /* Partitioning and distribution */
2354   ierr = PetscOptionsBool("-dm_plex_partition_balance", "Attempt to evenly divide points on partition boundary between processes", "DMPlexSetPartitionBalance", PETSC_FALSE, &mesh->partitionBalance, NULL);CHKERRQ(ierr);
2355   /* Generation and remeshing */
2356   ierr = PetscOptionsBool("-dm_plex_remesh_bd", "Allow changes to the boundary on remeshing", "DMAdapt", PETSC_FALSE, &mesh->remeshBd, NULL);CHKERRQ(ierr);
2357   /* Projection behavior */
2358   ierr = PetscOptionsBoundedInt("-dm_plex_max_projection_height", "Maxmimum mesh point height used to project locally", "DMPlexSetMaxProjectionHeight", 0, &mesh->maxProjectionHeight, NULL,0);CHKERRQ(ierr);
2359   ierr = PetscOptionsBool("-dm_plex_regular_refinement", "Use special nested projection algorithm for regular refinement", "DMPlexSetRegularRefinement", mesh->regularRefinement, &mesh->regularRefinement, NULL);CHKERRQ(ierr);
2360   ierr = PetscOptionsEnum("-dm_plex_cell_refiner", "Strategy for cell refinment", "ex40.c", DMPlexCellRefinerTypes, (PetscEnum) mesh->cellRefiner, (PetscEnum *) &mesh->cellRefiner, NULL);CHKERRQ(ierr);
2361   /* Checking structure */
2362   {
2363     PetscBool   flg = PETSC_FALSE, flg2 = PETSC_FALSE, all = PETSC_FALSE;
2364 
2365     ierr = PetscOptionsBool("-dm_plex_check_all", "Perform all checks", NULL, PETSC_FALSE, &all, &flg2);CHKERRQ(ierr);
2366     ierr = PetscOptionsBool("-dm_plex_check_symmetry", "Check that the adjacency information in the mesh is symmetric", "DMPlexCheckSymmetry", PETSC_FALSE, &flg, &flg2);CHKERRQ(ierr);
2367     if (all || (flg && flg2)) {ierr = DMPlexCheckSymmetry(dm);CHKERRQ(ierr);}
2368     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);
2369     if (all || (flg && flg2)) {ierr = DMPlexCheckSkeleton(dm, 0);CHKERRQ(ierr);}
2370     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);
2371     if (all || (flg && flg2)) {ierr = DMPlexCheckFaces(dm, 0);CHKERRQ(ierr);}
2372     ierr = PetscOptionsBool("-dm_plex_check_geometry", "Check that cells have positive volume", "DMPlexCheckGeometry", PETSC_FALSE, &flg, &flg2);CHKERRQ(ierr);
2373     if (all || (flg && flg2)) {ierr = DMPlexCheckGeometry(dm);CHKERRQ(ierr);}
2374     ierr = PetscOptionsBool("-dm_plex_check_pointsf", "Check some necessary conditions for PointSF", "DMPlexCheckPointSF", PETSC_FALSE, &flg, &flg2);CHKERRQ(ierr);
2375     if (all || (flg && flg2)) {ierr = DMPlexCheckPointSF(dm);CHKERRQ(ierr);}
2376     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);
2377     if (all || (flg && flg2)) {ierr = DMPlexCheckInterfaceCones(dm);CHKERRQ(ierr);}
2378     ierr = PetscOptionsBool("-dm_plex_check_cell_shape", "Check cell shape", "DMPlexCheckCellShape", PETSC_FALSE, &flg, &flg2);CHKERRQ(ierr);
2379     if (flg && flg2) {ierr = DMPlexCheckCellShape(dm, PETSC_TRUE, PETSC_DETERMINE);CHKERRQ(ierr);}
2380   }
2381 
2382   ierr = PetscPartitionerSetFromOptions(mesh->partitioner);CHKERRQ(ierr);
2383   PetscFunctionReturn(0);
2384 }
2385 
2386 static PetscErrorCode DMSetFromOptions_Plex(PetscOptionItems *PetscOptionsObject,DM dm)
2387 {
2388   PetscInt       refine = 0, coarsen = 0, r;
2389   PetscBool      isHierarchy;
2390   PetscErrorCode ierr;
2391 
2392   PetscFunctionBegin;
2393   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
2394   ierr = PetscOptionsHead(PetscOptionsObject,"DMPlex Options");CHKERRQ(ierr);
2395   /* Handle DMPlex refinement */
2396   ierr = PetscOptionsBoundedInt("-dm_refine", "The number of uniform refinements", "DMCreate", refine, &refine, NULL,0);CHKERRQ(ierr);
2397   ierr = PetscOptionsBoundedInt("-dm_refine_hierarchy", "The number of uniform refinements", "DMCreate", refine, &refine, &isHierarchy,0);CHKERRQ(ierr);
2398   if (refine) {ierr = DMPlexSetRefinementUniform(dm, PETSC_TRUE);CHKERRQ(ierr);}
2399   if (refine && isHierarchy) {
2400     DM *dms, coarseDM;
2401 
2402     ierr = DMGetCoarseDM(dm, &coarseDM);CHKERRQ(ierr);
2403     ierr = PetscObjectReference((PetscObject)coarseDM);CHKERRQ(ierr);
2404     ierr = PetscMalloc1(refine,&dms);CHKERRQ(ierr);
2405     ierr = DMRefineHierarchy(dm, refine, dms);CHKERRQ(ierr);
2406     /* Total hack since we do not pass in a pointer */
2407     ierr = DMPlexSwap_Static(dm, dms[refine-1]);CHKERRQ(ierr);
2408     if (refine == 1) {
2409       ierr = DMSetCoarseDM(dm, dms[0]);CHKERRQ(ierr);
2410       ierr = DMPlexSetRegularRefinement(dm, PETSC_TRUE);CHKERRQ(ierr);
2411     } else {
2412       ierr = DMSetCoarseDM(dm, dms[refine-2]);CHKERRQ(ierr);
2413       ierr = DMPlexSetRegularRefinement(dm, PETSC_TRUE);CHKERRQ(ierr);
2414       ierr = DMSetCoarseDM(dms[0], dms[refine-1]);CHKERRQ(ierr);
2415       ierr = DMPlexSetRegularRefinement(dms[0], PETSC_TRUE);CHKERRQ(ierr);
2416     }
2417     ierr = DMSetCoarseDM(dms[refine-1], coarseDM);CHKERRQ(ierr);
2418     ierr = PetscObjectDereference((PetscObject)coarseDM);CHKERRQ(ierr);
2419     /* Free DMs */
2420     for (r = 0; r < refine; ++r) {
2421       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dms[r]);CHKERRQ(ierr);
2422       ierr = DMDestroy(&dms[r]);CHKERRQ(ierr);
2423     }
2424     ierr = PetscFree(dms);CHKERRQ(ierr);
2425   } else {
2426     for (r = 0; r < refine; ++r) {
2427       DM refinedMesh;
2428       PetscPointFunc coordFunc = ((DM_Plex*) dm->data)->coordFunc;
2429 
2430       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2431       ierr = DMRefine(dm, PetscObjectComm((PetscObject) dm), &refinedMesh);CHKERRQ(ierr);
2432       /* Total hack since we do not pass in a pointer */
2433       ierr = DMPlexReplace_Static(dm, refinedMesh);CHKERRQ(ierr);
2434       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2435       if (coordFunc) {
2436         ierr = DMPlexRemapGeometry(dm, 0.0, coordFunc);CHKERRQ(ierr);
2437         ((DM_Plex*) dm->data)->coordFunc = coordFunc;
2438       }
2439       ierr = DMDestroy(&refinedMesh);CHKERRQ(ierr);
2440     }
2441   }
2442   /* Handle DMPlex coarsening */
2443   ierr = PetscOptionsBoundedInt("-dm_coarsen", "Coarsen the mesh", "DMCreate", coarsen, &coarsen, NULL,0);CHKERRQ(ierr);
2444   ierr = PetscOptionsBoundedInt("-dm_coarsen_hierarchy", "The number of coarsenings", "DMCreate", coarsen, &coarsen, &isHierarchy,0);CHKERRQ(ierr);
2445   if (coarsen && isHierarchy) {
2446     DM *dms;
2447 
2448     ierr = PetscMalloc1(coarsen, &dms);CHKERRQ(ierr);
2449     ierr = DMCoarsenHierarchy(dm, coarsen, dms);CHKERRQ(ierr);
2450     /* Free DMs */
2451     for (r = 0; r < coarsen; ++r) {
2452       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dms[r]);CHKERRQ(ierr);
2453       ierr = DMDestroy(&dms[r]);CHKERRQ(ierr);
2454     }
2455     ierr = PetscFree(dms);CHKERRQ(ierr);
2456   } else {
2457     for (r = 0; r < coarsen; ++r) {
2458       DM coarseMesh;
2459 
2460       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2461       ierr = DMCoarsen(dm, PetscObjectComm((PetscObject) dm), &coarseMesh);CHKERRQ(ierr);
2462       /* Total hack since we do not pass in a pointer */
2463       ierr = DMPlexReplace_Static(dm, coarseMesh);CHKERRQ(ierr);
2464       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2465       ierr = DMDestroy(&coarseMesh);CHKERRQ(ierr);
2466     }
2467   }
2468   /* Handle */
2469   ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2470   ierr = PetscOptionsTail();CHKERRQ(ierr);
2471   PetscFunctionReturn(0);
2472 }
2473 
2474 static PetscErrorCode DMCreateGlobalVector_Plex(DM dm,Vec *vec)
2475 {
2476   PetscErrorCode ierr;
2477 
2478   PetscFunctionBegin;
2479   ierr = DMCreateGlobalVector_Section_Private(dm,vec);CHKERRQ(ierr);
2480   /* ierr = VecSetOperation(*vec, VECOP_DUPLICATE, (void(*)(void)) VecDuplicate_MPI_DM);CHKERRQ(ierr); */
2481   ierr = VecSetOperation(*vec, VECOP_VIEW, (void (*)(void)) VecView_Plex);CHKERRQ(ierr);
2482   ierr = VecSetOperation(*vec, VECOP_VIEWNATIVE, (void (*)(void)) VecView_Plex_Native);CHKERRQ(ierr);
2483   ierr = VecSetOperation(*vec, VECOP_LOAD, (void (*)(void)) VecLoad_Plex);CHKERRQ(ierr);
2484   ierr = VecSetOperation(*vec, VECOP_LOADNATIVE, (void (*)(void)) VecLoad_Plex_Native);CHKERRQ(ierr);
2485   PetscFunctionReturn(0);
2486 }
2487 
2488 static PetscErrorCode DMCreateLocalVector_Plex(DM dm,Vec *vec)
2489 {
2490   PetscErrorCode ierr;
2491 
2492   PetscFunctionBegin;
2493   ierr = DMCreateLocalVector_Section_Private(dm,vec);CHKERRQ(ierr);
2494   ierr = VecSetOperation(*vec, VECOP_VIEW, (void (*)(void)) VecView_Plex_Local);CHKERRQ(ierr);
2495   ierr = VecSetOperation(*vec, VECOP_LOAD, (void (*)(void)) VecLoad_Plex_Local);CHKERRQ(ierr);
2496   PetscFunctionReturn(0);
2497 }
2498 
2499 static PetscErrorCode DMGetDimPoints_Plex(DM dm, PetscInt dim, PetscInt *pStart, PetscInt *pEnd)
2500 {
2501   PetscInt       depth, d;
2502   PetscErrorCode ierr;
2503 
2504   PetscFunctionBegin;
2505   ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
2506   if (depth == 1) {
2507     ierr = DMGetDimension(dm, &d);CHKERRQ(ierr);
2508     if (dim == 0)      {ierr = DMPlexGetDepthStratum(dm, dim, pStart, pEnd);CHKERRQ(ierr);}
2509     else if (dim == d) {ierr = DMPlexGetDepthStratum(dm, 1, pStart, pEnd);CHKERRQ(ierr);}
2510     else               {*pStart = 0; *pEnd = 0;}
2511   } else {
2512     ierr = DMPlexGetDepthStratum(dm, dim, pStart, pEnd);CHKERRQ(ierr);
2513   }
2514   PetscFunctionReturn(0);
2515 }
2516 
2517 static PetscErrorCode DMGetNeighbors_Plex(DM dm, PetscInt *nranks, const PetscMPIInt *ranks[])
2518 {
2519   PetscSF           sf;
2520   PetscInt          niranks, njranks, n;
2521   const PetscMPIInt *iranks, *jranks;
2522   DM_Plex           *data = (DM_Plex*) dm->data;
2523   PetscErrorCode    ierr;
2524 
2525   PetscFunctionBegin;
2526   ierr = DMGetPointSF(dm, &sf);CHKERRQ(ierr);
2527   if (!data->neighbors) {
2528     ierr = PetscSFGetRootRanks(sf, &njranks, &jranks, NULL, NULL, NULL);CHKERRQ(ierr);
2529     ierr = PetscSFGetLeafRanks(sf, &niranks, &iranks, NULL, NULL);CHKERRQ(ierr);
2530     ierr = PetscMalloc1(njranks + niranks + 1, &data->neighbors);CHKERRQ(ierr);
2531     ierr = PetscArraycpy(data->neighbors + 1, jranks, njranks);CHKERRQ(ierr);
2532     ierr = PetscArraycpy(data->neighbors + njranks + 1, iranks, niranks);CHKERRQ(ierr);
2533     n = njranks + niranks;
2534     ierr = PetscSortRemoveDupsMPIInt(&n, data->neighbors + 1);CHKERRQ(ierr);
2535     /* The following cast should never fail: can't have more neighbors than PETSC_MPI_INT_MAX */
2536     ierr = PetscMPIIntCast(n, data->neighbors);CHKERRQ(ierr);
2537   }
2538   if (nranks) *nranks = data->neighbors[0];
2539   if (ranks) {
2540     if (data->neighbors[0]) *ranks = data->neighbors + 1;
2541     else                    *ranks = NULL;
2542   }
2543   PetscFunctionReturn(0);
2544 }
2545 
2546 static PetscErrorCode DMInitialize_Plex(DM dm)
2547 {
2548   PetscErrorCode ierr;
2549 
2550   PetscFunctionBegin;
2551   dm->ops->view                            = DMView_Plex;
2552   dm->ops->load                            = DMLoad_Plex;
2553   dm->ops->setfromoptions                  = DMSetFromOptions_Plex;
2554   dm->ops->clone                           = DMClone_Plex;
2555   dm->ops->setup                           = DMSetUp_Plex;
2556   dm->ops->createlocalsection              = DMCreateLocalSection_Plex;
2557   dm->ops->createdefaultconstraints        = DMCreateDefaultConstraints_Plex;
2558   dm->ops->createglobalvector              = DMCreateGlobalVector_Plex;
2559   dm->ops->createlocalvector               = DMCreateLocalVector_Plex;
2560   dm->ops->getlocaltoglobalmapping         = NULL;
2561   dm->ops->createfieldis                   = NULL;
2562   dm->ops->createcoordinatedm              = DMCreateCoordinateDM_Plex;
2563   dm->ops->createcoordinatefield           = DMCreateCoordinateField_Plex;
2564   dm->ops->getcoloring                     = NULL;
2565   dm->ops->creatematrix                    = DMCreateMatrix_Plex;
2566   dm->ops->createinterpolation             = DMCreateInterpolation_Plex;
2567   dm->ops->createmassmatrix                = DMCreateMassMatrix_Plex;
2568   dm->ops->createinjection                 = DMCreateInjection_Plex;
2569   dm->ops->refine                          = DMRefine_Plex;
2570   dm->ops->coarsen                         = DMCoarsen_Plex;
2571   dm->ops->refinehierarchy                 = DMRefineHierarchy_Plex;
2572   dm->ops->coarsenhierarchy                = DMCoarsenHierarchy_Plex;
2573   dm->ops->adaptlabel                      = DMAdaptLabel_Plex;
2574   dm->ops->adaptmetric                     = DMAdaptMetric_Plex;
2575   dm->ops->globaltolocalbegin              = NULL;
2576   dm->ops->globaltolocalend                = NULL;
2577   dm->ops->localtoglobalbegin              = NULL;
2578   dm->ops->localtoglobalend                = NULL;
2579   dm->ops->destroy                         = DMDestroy_Plex;
2580   dm->ops->createsubdm                     = DMCreateSubDM_Plex;
2581   dm->ops->createsuperdm                   = DMCreateSuperDM_Plex;
2582   dm->ops->getdimpoints                    = DMGetDimPoints_Plex;
2583   dm->ops->locatepoints                    = DMLocatePoints_Plex;
2584   dm->ops->projectfunctionlocal            = DMProjectFunctionLocal_Plex;
2585   dm->ops->projectfunctionlabellocal       = DMProjectFunctionLabelLocal_Plex;
2586   dm->ops->projectfieldlocal               = DMProjectFieldLocal_Plex;
2587   dm->ops->projectfieldlabellocal          = DMProjectFieldLabelLocal_Plex;
2588   dm->ops->projectbdfieldlabellocal        = DMProjectBdFieldLabelLocal_Plex;
2589   dm->ops->computel2diff                   = DMComputeL2Diff_Plex;
2590   dm->ops->computel2gradientdiff           = DMComputeL2GradientDiff_Plex;
2591   dm->ops->computel2fielddiff              = DMComputeL2FieldDiff_Plex;
2592   dm->ops->getneighbors                    = DMGetNeighbors_Plex;
2593   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMPlexInsertBoundaryValues_C",DMPlexInsertBoundaryValues_Plex);CHKERRQ(ierr);
2594   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMSetUpGLVisViewer_C",DMSetUpGLVisViewer_Plex);CHKERRQ(ierr);
2595   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMCreateNeumannOverlap_C",DMCreateNeumannOverlap_Plex);CHKERRQ(ierr);
2596   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMPlexGetOverlap_C",DMPlexGetOverlap_Plex);CHKERRQ(ierr);
2597   PetscFunctionReturn(0);
2598 }
2599 
2600 PETSC_INTERN PetscErrorCode DMClone_Plex(DM dm, DM *newdm)
2601 {
2602   DM_Plex        *mesh = (DM_Plex *) dm->data;
2603   PetscErrorCode ierr;
2604 
2605   PetscFunctionBegin;
2606   mesh->refct++;
2607   (*newdm)->data = mesh;
2608   ierr = PetscObjectChangeTypeName((PetscObject) *newdm, DMPLEX);CHKERRQ(ierr);
2609   ierr = DMInitialize_Plex(*newdm);CHKERRQ(ierr);
2610   PetscFunctionReturn(0);
2611 }
2612 
2613 /*MC
2614   DMPLEX = "plex" - A DM object that encapsulates an unstructured mesh, or CW Complex, which can be expressed using a Hasse Diagram.
2615                     In the local representation, Vecs contain all unknowns in the interior and shared boundary. This is
2616                     specified by a PetscSection object. Ownership in the global representation is determined by
2617                     ownership of the underlying DMPlex points. This is specified by another PetscSection object.
2618 
2619   Options Database Keys:
2620 + -dm_plex_hash_location             - Use grid hashing for point location
2621 . -dm_plex_partition_balance         - Attempt to evenly divide points on partition boundary between processes
2622 . -dm_plex_remesh_bd                 - Allow changes to the boundary on remeshing
2623 . -dm_plex_max_projection_height     - Maxmimum mesh point height used to project locally
2624 . -dm_plex_regular_refinement        - Use special nested projection algorithm for regular refinement
2625 . -dm_plex_check_symmetry            - Check that the adjacency information in the mesh is symmetric
2626 . -dm_plex_check_skeleton <celltype> - Check that each cell has the correct number of vertices
2627 . -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
2628 . -dm_plex_check_geometry            - Check that cells have positive volume
2629 . -dm_view :mesh.tex:ascii_latex     - View the mesh in LaTeX/TikZ
2630 . -dm_plex_view_scale <num>          - Scale the TikZ
2631 - -dm_plex_print_fem <num>           - View FEM assembly information, such as element vectors and matrices
2632 
2633 
2634   Level: intermediate
2635 
2636 .seealso: DMType, DMPlexCreate(), DMCreate(), DMSetType()
2637 M*/
2638 
2639 PETSC_EXTERN PetscErrorCode DMCreate_Plex(DM dm)
2640 {
2641   DM_Plex       *mesh;
2642   PetscInt       unit;
2643   PetscErrorCode ierr;
2644 
2645   PetscFunctionBegin;
2646   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
2647   ierr     = PetscNewLog(dm,&mesh);CHKERRQ(ierr);
2648   dm->dim  = 0;
2649   dm->data = mesh;
2650 
2651   mesh->refct             = 1;
2652   ierr                    = PetscSectionCreate(PetscObjectComm((PetscObject)dm), &mesh->coneSection);CHKERRQ(ierr);
2653   mesh->maxConeSize       = 0;
2654   mesh->cones             = NULL;
2655   mesh->coneOrientations  = NULL;
2656   ierr                    = PetscSectionCreate(PetscObjectComm((PetscObject)dm), &mesh->supportSection);CHKERRQ(ierr);
2657   mesh->maxSupportSize    = 0;
2658   mesh->supports          = NULL;
2659   mesh->refinementUniform = PETSC_TRUE;
2660   mesh->refinementLimit   = -1.0;
2661   mesh->interpolated      = DMPLEX_INTERPOLATED_INVALID;
2662   mesh->interpolatedCollective = DMPLEX_INTERPOLATED_INVALID;
2663 
2664   mesh->facesTmp = NULL;
2665 
2666   mesh->tetgenOpts   = NULL;
2667   mesh->triangleOpts = NULL;
2668   ierr = PetscPartitionerCreate(PetscObjectComm((PetscObject)dm), &mesh->partitioner);CHKERRQ(ierr);
2669   mesh->remeshBd     = PETSC_FALSE;
2670 
2671   mesh->subpointMap = NULL;
2672 
2673   for (unit = 0; unit < NUM_PETSC_UNITS; ++unit) mesh->scale[unit] = 1.0;
2674 
2675   mesh->regularRefinement   = PETSC_FALSE;
2676   mesh->depthState          = -1;
2677   mesh->celltypeState       = -1;
2678   mesh->globalVertexNumbers = NULL;
2679   mesh->globalCellNumbers   = NULL;
2680   mesh->anchorSection       = NULL;
2681   mesh->anchorIS            = NULL;
2682   mesh->createanchors       = NULL;
2683   mesh->computeanchormatrix = NULL;
2684   mesh->parentSection       = NULL;
2685   mesh->parents             = NULL;
2686   mesh->childIDs            = NULL;
2687   mesh->childSection        = NULL;
2688   mesh->children            = NULL;
2689   mesh->referenceTree       = NULL;
2690   mesh->getchildsymmetry    = NULL;
2691   mesh->vtkCellHeight       = 0;
2692   mesh->useAnchors          = PETSC_FALSE;
2693 
2694   mesh->maxProjectionHeight = 0;
2695 
2696   mesh->neighbors           = NULL;
2697 
2698   mesh->printSetValues = PETSC_FALSE;
2699   mesh->printFEM       = 0;
2700   mesh->printTol       = 1.0e-10;
2701 
2702   ierr = DMInitialize_Plex(dm);CHKERRQ(ierr);
2703   PetscFunctionReturn(0);
2704 }
2705 
2706 /*@
2707   DMPlexCreate - Creates a DMPlex object, which encapsulates an unstructured mesh, or CW complex, which can be expressed using a Hasse Diagram.
2708 
2709   Collective
2710 
2711   Input Parameter:
2712 . comm - The communicator for the DMPlex object
2713 
2714   Output Parameter:
2715 . mesh  - The DMPlex object
2716 
2717   Level: beginner
2718 
2719 @*/
2720 PetscErrorCode DMPlexCreate(MPI_Comm comm, DM *mesh)
2721 {
2722   PetscErrorCode ierr;
2723 
2724   PetscFunctionBegin;
2725   PetscValidPointer(mesh,2);
2726   ierr = DMCreate(comm, mesh);CHKERRQ(ierr);
2727   ierr = DMSetType(*mesh, DMPLEX);CHKERRQ(ierr);
2728   PetscFunctionReturn(0);
2729 }
2730 
2731 static PetscErrorCode DMPlexInvertCell_Internal(PetscInt dim, PetscInt numCorners, PetscInt cone[])
2732 {
2733   PetscErrorCode ierr;
2734 
2735   PetscFunctionBegin;
2736   if (dim != 3) PetscFunctionReturn(0);
2737   switch (numCorners) {
2738   case 4: ierr = DMPlexInvertCell(DM_POLYTOPE_TETRAHEDRON,cone);CHKERRQ(ierr); break;
2739   case 6: ierr = DMPlexInvertCell(DM_POLYTOPE_TRI_PRISM,cone);CHKERRQ(ierr); break;
2740   case 8: ierr = DMPlexInvertCell(DM_POLYTOPE_HEXAHEDRON,cone);CHKERRQ(ierr); break;
2741   default: break;
2742   }
2743   PetscFunctionReturn(0);
2744 }
2745 
2746 /*
2747   This takes as input the common mesh generator output, a list of the vertices for each cell, but vertex numbers are global and an SF is built for them
2748 */
2749 /* TODO: invertCells and spaceDim arguments could be added also to to DMPlexCreateFromCellListParallel(), DMPlexBuildFromCellList_Internal() and DMPlexCreateFromCellList() */
2750 PetscErrorCode DMPlexBuildFromCellList_Parallel_Internal(DM dm, PetscInt spaceDim, PetscInt numCells, PetscInt numVertices, PetscInt numCorners, const int cells[], PetscBool invertCells, PetscSF *sfVert)
2751 {
2752   PetscSF         sfPoint;
2753   PetscLayout     vLayout;
2754   PetscHSetI      vhash;
2755   PetscSFNode    *remoteVerticesAdj, *vertexLocal, *vertexOwner, *remoteVertex;
2756   const PetscInt *vrange;
2757   PetscInt        numVerticesAdj, off = 0, *verticesAdj, numVerticesGhost = 0, *localVertex, *cone, c, p, v, g;
2758   PetscMPIInt     rank, size;
2759   PetscErrorCode  ierr;
2760 
2761   PetscFunctionBegin;
2762   ierr = PetscLogEventBegin(DMPLEX_CreateFromCellList,dm,0,0,0);CHKERRQ(ierr);
2763   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject) dm), &rank);CHKERRQ(ierr);
2764   ierr = MPI_Comm_size(PetscObjectComm((PetscObject) dm), &size);CHKERRQ(ierr);
2765   /* Partition vertices */
2766   ierr = PetscLayoutCreate(PetscObjectComm((PetscObject) dm), &vLayout);CHKERRQ(ierr);
2767   ierr = PetscLayoutSetLocalSize(vLayout, numVertices);CHKERRQ(ierr);
2768   ierr = PetscLayoutSetBlockSize(vLayout, 1);CHKERRQ(ierr);
2769   ierr = PetscLayoutSetUp(vLayout);CHKERRQ(ierr);
2770   ierr = PetscLayoutGetRanges(vLayout, &vrange);CHKERRQ(ierr);
2771   /* Count vertices and map them to procs */
2772   ierr = PetscHSetICreate(&vhash);CHKERRQ(ierr);
2773   for (c = 0; c < numCells; ++c) {
2774     for (p = 0; p < numCorners; ++p) {
2775       ierr = PetscHSetIAdd(vhash, cells[c*numCorners+p]);CHKERRQ(ierr);
2776     }
2777   }
2778   ierr = PetscHSetIGetSize(vhash, &numVerticesAdj);CHKERRQ(ierr);
2779   ierr = PetscMalloc1(numVerticesAdj, &verticesAdj);CHKERRQ(ierr);
2780   ierr = PetscHSetIGetElems(vhash, &off, verticesAdj);CHKERRQ(ierr);
2781   ierr = PetscHSetIDestroy(&vhash);CHKERRQ(ierr);
2782   if (off != numVerticesAdj) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Invalid number of local vertices %D should be %D", off, numVerticesAdj);
2783   ierr = PetscSortInt(numVerticesAdj, verticesAdj);CHKERRQ(ierr);
2784   ierr = PetscMalloc1(numVerticesAdj, &remoteVerticesAdj);CHKERRQ(ierr);
2785   for (v = 0; v < numVerticesAdj; ++v) {
2786     const PetscInt gv = verticesAdj[v];
2787     PetscInt       vrank;
2788 
2789     ierr = PetscFindInt(gv, size+1, vrange, &vrank);CHKERRQ(ierr);
2790     vrank = vrank < 0 ? -(vrank+2) : vrank;
2791     remoteVerticesAdj[v].index = gv - vrange[vrank];
2792     remoteVerticesAdj[v].rank  = vrank;
2793   }
2794   /* Create cones */
2795   ierr = DMPlexSetChart(dm, 0, numCells+numVerticesAdj);CHKERRQ(ierr);
2796   for (c = 0; c < numCells; ++c) {ierr = DMPlexSetConeSize(dm, c, numCorners);CHKERRQ(ierr);}
2797   ierr = DMSetUp(dm);CHKERRQ(ierr);
2798   ierr = DMGetWorkArray(dm, numCorners, MPIU_INT, &cone);CHKERRQ(ierr);
2799   for (c = 0; c < numCells; ++c) {
2800     for (p = 0; p < numCorners; ++p) {
2801       const PetscInt gv = cells[c*numCorners+p];
2802       PetscInt       lv;
2803 
2804       ierr = PetscFindInt(gv, numVerticesAdj, verticesAdj, &lv);CHKERRQ(ierr);
2805       if (lv < 0) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Could not find global vertex %D in local connectivity", gv);
2806       cone[p] = lv+numCells;
2807     }
2808     if (invertCells) { ierr = DMPlexInvertCell_Internal(spaceDim, numCorners, cone);CHKERRQ(ierr); }
2809     ierr = DMPlexSetCone(dm, c, cone);CHKERRQ(ierr);
2810   }
2811   ierr = DMRestoreWorkArray(dm, numCorners, MPIU_INT, &cone);CHKERRQ(ierr);
2812   /* Create SF for vertices */
2813   ierr = PetscSFCreate(PetscObjectComm((PetscObject)dm), sfVert);CHKERRQ(ierr);
2814   ierr = PetscObjectSetName((PetscObject) *sfVert, "Vertex Ownership SF");CHKERRQ(ierr);
2815   ierr = PetscSFSetFromOptions(*sfVert);CHKERRQ(ierr);
2816   ierr = PetscSFSetGraph(*sfVert, numVertices, numVerticesAdj, NULL, PETSC_OWN_POINTER, remoteVerticesAdj, PETSC_OWN_POINTER);CHKERRQ(ierr);
2817   ierr = PetscFree(verticesAdj);CHKERRQ(ierr);
2818   /* Build pointSF */
2819   ierr = PetscMalloc2(numVerticesAdj, &vertexLocal, numVertices, &vertexOwner);CHKERRQ(ierr);
2820   for (v = 0; v < numVerticesAdj; ++v) {vertexLocal[v].index = v+numCells; vertexLocal[v].rank = rank;}
2821   for (v = 0; v < numVertices;    ++v) {vertexOwner[v].index = -1;         vertexOwner[v].rank = -1;}
2822   ierr = PetscSFReduceBegin(*sfVert, MPIU_2INT, vertexLocal, vertexOwner, MPI_MAXLOC);CHKERRQ(ierr);
2823   ierr = PetscSFReduceEnd(*sfVert, MPIU_2INT, vertexLocal, vertexOwner, MPI_MAXLOC);CHKERRQ(ierr);
2824   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);
2825   ierr = PetscSFBcastBegin(*sfVert, MPIU_2INT, vertexOwner, vertexLocal);CHKERRQ(ierr);
2826   ierr = PetscSFBcastEnd(*sfVert, MPIU_2INT, vertexOwner, vertexLocal);CHKERRQ(ierr);
2827   for (v = 0; v < numVerticesAdj; ++v) if (vertexLocal[v].rank != rank) ++numVerticesGhost;
2828   ierr = PetscMalloc1(numVerticesGhost, &localVertex);CHKERRQ(ierr);
2829   ierr = PetscMalloc1(numVerticesGhost, &remoteVertex);CHKERRQ(ierr);
2830   for (v = 0, g = 0; v < numVerticesAdj; ++v) {
2831     if (vertexLocal[v].rank != rank) {
2832       localVertex[g]        = v+numCells;
2833       remoteVertex[g].index = vertexLocal[v].index;
2834       remoteVertex[g].rank  = vertexLocal[v].rank;
2835       ++g;
2836     }
2837   }
2838   ierr = PetscFree2(vertexLocal, vertexOwner);CHKERRQ(ierr);
2839   if (g != numVerticesGhost) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid number of vertex ghosts %D should be %D", g, numVerticesGhost);
2840   ierr = DMGetPointSF(dm, &sfPoint);CHKERRQ(ierr);
2841   ierr = PetscObjectSetName((PetscObject) sfPoint, "point SF");CHKERRQ(ierr);
2842   ierr = PetscSFSetGraph(sfPoint, numCells+numVerticesAdj, numVerticesGhost, localVertex, PETSC_OWN_POINTER, remoteVertex, PETSC_OWN_POINTER);CHKERRQ(ierr);
2843   ierr = PetscLayoutDestroy(&vLayout);CHKERRQ(ierr);
2844   /* Fill in the rest of the topology structure */
2845   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
2846   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
2847   ierr = PetscLogEventEnd(DMPLEX_CreateFromCellList,dm,0,0,0);CHKERRQ(ierr);
2848   PetscFunctionReturn(0);
2849 }
2850 
2851 /*
2852   This takes as input the coordinates for each owned vertex
2853 */
2854 PetscErrorCode DMPlexBuildCoordinates_Parallel_Internal(DM dm, PetscInt spaceDim, PetscInt numCells, PetscInt numV, PetscSF sfVert, const PetscReal vertexCoords[])
2855 {
2856   PetscSection   coordSection;
2857   Vec            coordinates;
2858   PetscScalar   *coords;
2859   PetscInt       numVertices, numVerticesAdj, coordSize, v;
2860   PetscErrorCode ierr;
2861 
2862   PetscFunctionBegin;
2863   ierr = PetscLogEventBegin(DMPLEX_CreateFromCellList_Coordinates,dm,0,0,0);CHKERRQ(ierr);
2864   ierr = DMSetCoordinateDim(dm, spaceDim);CHKERRQ(ierr);
2865   ierr = PetscSFGetGraph(sfVert, &numVertices, &numVerticesAdj, NULL, NULL);CHKERRQ(ierr);
2866   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
2867   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
2868   ierr = PetscSectionSetFieldComponents(coordSection, 0, spaceDim);CHKERRQ(ierr);
2869   ierr = PetscSectionSetChart(coordSection, numCells, numCells + numVerticesAdj);CHKERRQ(ierr);
2870   for (v = numCells; v < numCells+numVerticesAdj; ++v) {
2871     ierr = PetscSectionSetDof(coordSection, v, spaceDim);CHKERRQ(ierr);
2872     ierr = PetscSectionSetFieldDof(coordSection, v, 0, spaceDim);CHKERRQ(ierr);
2873   }
2874   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
2875   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
2876   ierr = VecCreate(PetscObjectComm((PetscObject)dm), &coordinates);CHKERRQ(ierr);
2877   ierr = VecSetBlockSize(coordinates, spaceDim);CHKERRQ(ierr);
2878   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
2879   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
2880   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
2881   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
2882   {
2883     MPI_Datatype coordtype;
2884 
2885     /* Need a temp buffer for coords if we have complex/single */
2886     ierr = MPI_Type_contiguous(spaceDim, MPIU_SCALAR, &coordtype);CHKERRQ(ierr);
2887     ierr = MPI_Type_commit(&coordtype);CHKERRQ(ierr);
2888 #if defined(PETSC_USE_COMPLEX)
2889     {
2890     PetscScalar *svertexCoords;
2891     PetscInt    i;
2892     ierr = PetscMalloc1(numV*spaceDim,&svertexCoords);CHKERRQ(ierr);
2893     for (i=0; i<numV*spaceDim; i++) svertexCoords[i] = vertexCoords[i];
2894     ierr = PetscSFBcastBegin(sfVert, coordtype, svertexCoords, coords);CHKERRQ(ierr);
2895     ierr = PetscSFBcastEnd(sfVert, coordtype, svertexCoords, coords);CHKERRQ(ierr);
2896     ierr = PetscFree(svertexCoords);CHKERRQ(ierr);
2897     }
2898 #else
2899     ierr = PetscSFBcastBegin(sfVert, coordtype, vertexCoords, coords);CHKERRQ(ierr);
2900     ierr = PetscSFBcastEnd(sfVert, coordtype, vertexCoords, coords);CHKERRQ(ierr);
2901 #endif
2902     ierr = MPI_Type_free(&coordtype);CHKERRQ(ierr);
2903   }
2904   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
2905   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
2906   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
2907   ierr = PetscLogEventEnd(DMPLEX_CreateFromCellList_Coordinates,dm,0,0,0);CHKERRQ(ierr);
2908   PetscFunctionReturn(0);
2909 }
2910 
2911 /*@
2912   DMPlexCreateFromCellListParallel - This takes as input common mesh generator output, a list of the vertices for each cell, and produces a DM
2913 
2914   Input Parameters:
2915 + comm - The communicator
2916 . dim - The topological dimension of the mesh
2917 . numCells - The number of cells owned by this process
2918 . numVertices - The number of vertices owned by this process
2919 . numCorners - The number of vertices for each cell
2920 . interpolate - Flag indicating that intermediate mesh entities (faces, edges) should be created automatically
2921 . cells - An array of numCells*numCorners numbers, the global vertex numbers for each cell
2922 . spaceDim - The spatial dimension used for coordinates
2923 - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex
2924 
2925   Output Parameter:
2926 + dm - The DM
2927 - vertexSF - Optional, SF describing complete vertex ownership
2928 
2929   Note: Two triangles sharing a face
2930 $
2931 $        2
2932 $      / | \
2933 $     /  |  \
2934 $    /   |   \
2935 $   0  0 | 1  3
2936 $    \   |   /
2937 $     \  |  /
2938 $      \ | /
2939 $        1
2940 would have input
2941 $  numCells = 2, numVertices = 4
2942 $  cells = [0 1 2  1 3 2]
2943 $
2944 which would result in the DMPlex
2945 $
2946 $        4
2947 $      / | \
2948 $     /  |  \
2949 $    /   |   \
2950 $   2  0 | 1  5
2951 $    \   |   /
2952 $     \  |  /
2953 $      \ | /
2954 $        3
2955 
2956   Level: beginner
2957 
2958 .seealso: DMPlexCreateFromCellList(), DMPlexCreateFromDAG(), DMPlexCreate()
2959 @*/
2960 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)
2961 {
2962   PetscSF        sfVert;
2963   PetscErrorCode ierr;
2964 
2965   PetscFunctionBegin;
2966   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
2967   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
2968   PetscValidLogicalCollectiveInt(*dm, dim, 2);
2969   PetscValidLogicalCollectiveInt(*dm, spaceDim, 8);
2970   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
2971   ierr = DMPlexBuildFromCellList_Parallel_Internal(*dm, spaceDim, numCells, numVertices, numCorners, cells, PETSC_FALSE, &sfVert);CHKERRQ(ierr);
2972   if (interpolate) {
2973     DM idm;
2974 
2975     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
2976     ierr = DMDestroy(dm);CHKERRQ(ierr);
2977     *dm  = idm;
2978   }
2979   ierr = DMPlexBuildCoordinates_Parallel_Internal(*dm, spaceDim, numCells, numVertices, sfVert, vertexCoords);CHKERRQ(ierr);
2980   if (vertexSF) *vertexSF = sfVert;
2981   else {ierr = PetscSFDestroy(&sfVert);CHKERRQ(ierr);}
2982   PetscFunctionReturn(0);
2983 }
2984 
2985 /*
2986   This takes as input the common mesh generator output, a list of the vertices for each cell
2987 */
2988 PetscErrorCode DMPlexBuildFromCellList_Internal(DM dm, PetscInt spaceDim, PetscInt numCells, PetscInt numVertices, PetscInt numCorners, const int cells[], PetscBool invertCells)
2989 {
2990   PetscInt      *cone, c, p;
2991   PetscErrorCode ierr;
2992 
2993   PetscFunctionBegin;
2994   ierr = PetscLogEventBegin(DMPLEX_CreateFromCellList,dm,0,0,0);CHKERRQ(ierr);
2995   ierr = DMPlexSetChart(dm, 0, numCells+numVertices);CHKERRQ(ierr);
2996   for (c = 0; c < numCells; ++c) {
2997     ierr = DMPlexSetConeSize(dm, c, numCorners);CHKERRQ(ierr);
2998   }
2999   ierr = DMSetUp(dm);CHKERRQ(ierr);
3000   ierr = DMGetWorkArray(dm, numCorners, MPIU_INT, &cone);CHKERRQ(ierr);
3001   for (c = 0; c < numCells; ++c) {
3002     for (p = 0; p < numCorners; ++p) {
3003       cone[p] = cells[c*numCorners+p]+numCells;
3004     }
3005     if (invertCells) { ierr = DMPlexInvertCell_Internal(spaceDim, numCorners, cone);CHKERRQ(ierr); }
3006     ierr = DMPlexSetCone(dm, c, cone);CHKERRQ(ierr);
3007   }
3008   ierr = DMRestoreWorkArray(dm, numCorners, MPIU_INT, &cone);CHKERRQ(ierr);
3009   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
3010   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
3011   ierr = PetscLogEventEnd(DMPLEX_CreateFromCellList,dm,0,0,0);CHKERRQ(ierr);
3012   PetscFunctionReturn(0);
3013 }
3014 
3015 /*
3016   This takes as input the coordinates for each vertex
3017 */
3018 PetscErrorCode DMPlexBuildCoordinates_Internal(DM dm, PetscInt spaceDim, PetscInt numCells, PetscInt numVertices, const double vertexCoords[])
3019 {
3020   PetscSection   coordSection;
3021   Vec            coordinates;
3022   DM             cdm;
3023   PetscScalar   *coords;
3024   PetscInt       v, d;
3025   PetscErrorCode ierr;
3026 
3027   PetscFunctionBegin;
3028   ierr = PetscLogEventBegin(DMPLEX_CreateFromCellList_Coordinates,dm,0,0,0);CHKERRQ(ierr);
3029   ierr = DMSetCoordinateDim(dm, spaceDim);CHKERRQ(ierr);
3030   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
3031   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
3032   ierr = PetscSectionSetFieldComponents(coordSection, 0, spaceDim);CHKERRQ(ierr);
3033   ierr = PetscSectionSetChart(coordSection, numCells, numCells + numVertices);CHKERRQ(ierr);
3034   for (v = numCells; v < numCells+numVertices; ++v) {
3035     ierr = PetscSectionSetDof(coordSection, v, spaceDim);CHKERRQ(ierr);
3036     ierr = PetscSectionSetFieldDof(coordSection, v, 0, spaceDim);CHKERRQ(ierr);
3037   }
3038   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
3039 
3040   ierr = DMGetCoordinateDM(dm, &cdm);CHKERRQ(ierr);
3041   ierr = DMCreateLocalVector(cdm, &coordinates);CHKERRQ(ierr);
3042   ierr = VecSetBlockSize(coordinates, spaceDim);CHKERRQ(ierr);
3043   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
3044   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
3045   for (v = 0; v < numVertices; ++v) {
3046     for (d = 0; d < spaceDim; ++d) {
3047       coords[v*spaceDim+d] = vertexCoords[v*spaceDim+d];
3048     }
3049   }
3050   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
3051   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
3052   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
3053   ierr = PetscLogEventEnd(DMPLEX_CreateFromCellList_Coordinates,dm,0,0,0);CHKERRQ(ierr);
3054   PetscFunctionReturn(0);
3055 }
3056 
3057 /*@
3058   DMPlexCreateFromCellList - This takes as input common mesh generator output, a list of the vertices for each cell, and produces a DM
3059 
3060   Input Parameters:
3061 + comm - The communicator
3062 . dim - The topological dimension of the mesh
3063 . numCells - The number of cells
3064 . numVertices - The number of vertices
3065 . numCorners - The number of vertices for each cell
3066 . interpolate - Flag indicating that intermediate mesh entities (faces, edges) should be created automatically
3067 . cells - An array of numCells*numCorners numbers, the vertices for each cell
3068 . spaceDim - The spatial dimension used for coordinates
3069 - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex
3070 
3071   Output Parameter:
3072 . dm - The DM
3073 
3074   Note: Two triangles sharing a face
3075 $
3076 $        2
3077 $      / | \
3078 $     /  |  \
3079 $    /   |   \
3080 $   0  0 | 1  3
3081 $    \   |   /
3082 $     \  |  /
3083 $      \ | /
3084 $        1
3085 would have input
3086 $  numCells = 2, numVertices = 4
3087 $  cells = [0 1 2  1 3 2]
3088 $
3089 which would result in the DMPlex
3090 $
3091 $        4
3092 $      / | \
3093 $     /  |  \
3094 $    /   |   \
3095 $   2  0 | 1  5
3096 $    \   |   /
3097 $     \  |  /
3098 $      \ | /
3099 $        3
3100 
3101   Level: beginner
3102 
3103 .seealso: DMPlexCreateFromDAG(), DMPlexCreate()
3104 @*/
3105 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)
3106 {
3107   PetscErrorCode ierr;
3108 
3109   PetscFunctionBegin;
3110   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.");
3111   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
3112   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
3113   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
3114   ierr = DMPlexBuildFromCellList_Internal(*dm, spaceDim, numCells, numVertices, numCorners, cells, PETSC_FALSE);CHKERRQ(ierr);
3115   if (interpolate) {
3116     DM idm;
3117 
3118     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
3119     ierr = DMDestroy(dm);CHKERRQ(ierr);
3120     *dm  = idm;
3121   }
3122   ierr = DMPlexBuildCoordinates_Internal(*dm, spaceDim, numCells, numVertices, vertexCoords);CHKERRQ(ierr);
3123   PetscFunctionReturn(0);
3124 }
3125 
3126 /*@
3127   DMPlexCreateFromDAG - This takes as input the adjacency-list representation of the Directed Acyclic Graph (Hasse Diagram) encoding a mesh, and produces a DM
3128 
3129   Input Parameters:
3130 + dm - The empty DM object, usually from DMCreate() and DMSetDimension()
3131 . depth - The depth of the DAG
3132 . numPoints - Array of size depth + 1 containing the number of points at each depth
3133 . coneSize - The cone size of each point
3134 . cones - The concatenation of the cone points for each point, the cone list must be oriented correctly for each point
3135 . coneOrientations - The orientation of each cone point
3136 - vertexCoords - An array of numPoints[0]*spacedim numbers representing the coordinates of each vertex, with spacedim the value set via DMSetCoordinateDim()
3137 
3138   Output Parameter:
3139 . dm - The DM
3140 
3141   Note: Two triangles sharing a face would have input
3142 $  depth = 1, numPoints = [4 2], coneSize = [3 3 0 0 0 0]
3143 $  cones = [2 3 4  3 5 4], coneOrientations = [0 0 0  0 0 0]
3144 $ vertexCoords = [-1.0 0.0  0.0 -1.0  0.0 1.0  1.0 0.0]
3145 $
3146 which would result in the DMPlex
3147 $
3148 $        4
3149 $      / | \
3150 $     /  |  \
3151 $    /   |   \
3152 $   2  0 | 1  5
3153 $    \   |   /
3154 $     \  |  /
3155 $      \ | /
3156 $        3
3157 $
3158 $ Notice that all points are numbered consecutively, unlikely DMPlexCreateFromCellList()
3159 
3160   Level: advanced
3161 
3162 .seealso: DMPlexCreateFromCellList(), DMPlexCreate()
3163 @*/
3164 PetscErrorCode DMPlexCreateFromDAG(DM dm, PetscInt depth, const PetscInt numPoints[], const PetscInt coneSize[], const PetscInt cones[], const PetscInt coneOrientations[], const PetscScalar vertexCoords[])
3165 {
3166   Vec            coordinates;
3167   PetscSection   coordSection;
3168   PetscScalar    *coords;
3169   PetscInt       coordSize, firstVertex = -1, pStart = 0, pEnd = 0, p, v, dim, dimEmbed, d, off;
3170   PetscErrorCode ierr;
3171 
3172   PetscFunctionBegin;
3173   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
3174   ierr = DMGetCoordinateDim(dm, &dimEmbed);CHKERRQ(ierr);
3175   if (dimEmbed < dim) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Embedding dimension %d cannot be less than intrinsic dimension %d",dimEmbed,dim);
3176   for (d = 0; d <= depth; ++d) pEnd += numPoints[d];
3177   ierr = DMPlexSetChart(dm, pStart, pEnd);CHKERRQ(ierr);
3178   for (p = pStart; p < pEnd; ++p) {
3179     ierr = DMPlexSetConeSize(dm, p, coneSize[p-pStart]);CHKERRQ(ierr);
3180     if (firstVertex < 0 && !coneSize[p - pStart]) {
3181       firstVertex = p - pStart;
3182     }
3183   }
3184   if (firstVertex < 0 && numPoints[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Expected %d vertices but could not find any", numPoints[0]);
3185   ierr = DMSetUp(dm);CHKERRQ(ierr); /* Allocate space for cones */
3186   for (p = pStart, off = 0; p < pEnd; off += coneSize[p-pStart], ++p) {
3187     ierr = DMPlexSetCone(dm, p, &cones[off]);CHKERRQ(ierr);
3188     ierr = DMPlexSetConeOrientation(dm, p, &coneOrientations[off]);CHKERRQ(ierr);
3189   }
3190   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
3191   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
3192   /* Build coordinates */
3193   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
3194   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
3195   ierr = PetscSectionSetFieldComponents(coordSection, 0, dimEmbed);CHKERRQ(ierr);
3196   ierr = PetscSectionSetChart(coordSection, firstVertex, firstVertex+numPoints[0]);CHKERRQ(ierr);
3197   for (v = firstVertex; v < firstVertex+numPoints[0]; ++v) {
3198     ierr = PetscSectionSetDof(coordSection, v, dimEmbed);CHKERRQ(ierr);
3199     ierr = PetscSectionSetFieldDof(coordSection, v, 0, dimEmbed);CHKERRQ(ierr);
3200   }
3201   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
3202   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
3203   ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
3204   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
3205   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
3206   ierr = VecSetBlockSize(coordinates, dimEmbed);CHKERRQ(ierr);
3207   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
3208   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
3209   for (v = 0; v < numPoints[0]; ++v) {
3210     PetscInt off;
3211 
3212     ierr = PetscSectionGetOffset(coordSection, v+firstVertex, &off);CHKERRQ(ierr);
3213     for (d = 0; d < dimEmbed; ++d) {
3214       coords[off+d] = vertexCoords[v*dimEmbed+d];
3215     }
3216   }
3217   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
3218   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
3219   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
3220   PetscFunctionReturn(0);
3221 }
3222 
3223 /*@C
3224   DMPlexCreateCellVertexFromFile - Create a DMPlex mesh from a simple cell-vertex file.
3225 
3226 + comm        - The MPI communicator
3227 . filename    - Name of the .dat file
3228 - interpolate - Create faces and edges in the mesh
3229 
3230   Output Parameter:
3231 . dm  - The DM object representing the mesh
3232 
3233   Note: The format is the simplest possible:
3234 $ Ne
3235 $ v0 v1 ... vk
3236 $ Nv
3237 $ x y z marker
3238 
3239   Level: beginner
3240 
3241 .seealso: DMPlexCreateFromFile(), DMPlexCreateMedFromFile(), DMPlexCreateGmsh(), DMPlexCreate()
3242 @*/
3243 PetscErrorCode DMPlexCreateCellVertexFromFile(MPI_Comm comm, const char filename[], PetscBool interpolate, DM *dm)
3244 {
3245   DMLabel         marker;
3246   PetscViewer     viewer;
3247   Vec             coordinates;
3248   PetscSection    coordSection;
3249   PetscScalar    *coords;
3250   char            line[PETSC_MAX_PATH_LEN];
3251   PetscInt        dim = 3, cdim = 3, coordSize, v, c, d;
3252   PetscMPIInt     rank;
3253   int             snum, Nv, Nc;
3254   PetscErrorCode  ierr;
3255 
3256   PetscFunctionBegin;
3257   ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
3258   ierr = PetscViewerCreate(comm, &viewer);CHKERRQ(ierr);
3259   ierr = PetscViewerSetType(viewer, PETSCVIEWERASCII);CHKERRQ(ierr);
3260   ierr = PetscViewerFileSetMode(viewer, FILE_MODE_READ);CHKERRQ(ierr);
3261   ierr = PetscViewerFileSetName(viewer, filename);CHKERRQ(ierr);
3262   if (!rank) {
3263     ierr = PetscViewerRead(viewer, line, 2, NULL, PETSC_STRING);CHKERRQ(ierr);
3264     snum = sscanf(line, "%d %d", &Nc, &Nv);
3265     if (snum != 2) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unable to parse cell-vertex file: %s", line);
3266   } else {
3267     Nc = Nv = 0;
3268   }
3269   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
3270   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
3271   ierr = DMPlexSetChart(*dm, 0, Nc+Nv);CHKERRQ(ierr);
3272   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
3273   ierr = DMSetCoordinateDim(*dm, cdim);CHKERRQ(ierr);
3274   /* Read topology */
3275   if (!rank) {
3276     PetscInt cone[8], corners = 8;
3277     int      vbuf[8], v;
3278 
3279     for (c = 0; c < Nc; ++c) {ierr = DMPlexSetConeSize(*dm, c, corners);CHKERRQ(ierr);}
3280     ierr = DMSetUp(*dm);CHKERRQ(ierr);
3281     for (c = 0; c < Nc; ++c) {
3282       ierr = PetscViewerRead(viewer, line, corners, NULL, PETSC_STRING);CHKERRQ(ierr);
3283       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]);
3284       if (snum != corners) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unable to parse cell-vertex file: %s", line);
3285       for (v = 0; v < corners; ++v) cone[v] = vbuf[v] + Nc;
3286       /* Hexahedra are inverted */
3287       {
3288         PetscInt tmp = cone[1];
3289         cone[1] = cone[3];
3290         cone[3] = tmp;
3291       }
3292       ierr = DMPlexSetCone(*dm, c, cone);CHKERRQ(ierr);
3293     }
3294   }
3295   ierr = DMPlexSymmetrize(*dm);CHKERRQ(ierr);
3296   ierr = DMPlexStratify(*dm);CHKERRQ(ierr);
3297   /* Read coordinates */
3298   ierr = DMGetCoordinateSection(*dm, &coordSection);CHKERRQ(ierr);
3299   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
3300   ierr = PetscSectionSetFieldComponents(coordSection, 0, cdim);CHKERRQ(ierr);
3301   ierr = PetscSectionSetChart(coordSection, Nc, Nc + Nv);CHKERRQ(ierr);
3302   for (v = Nc; v < Nc+Nv; ++v) {
3303     ierr = PetscSectionSetDof(coordSection, v, cdim);CHKERRQ(ierr);
3304     ierr = PetscSectionSetFieldDof(coordSection, v, 0, cdim);CHKERRQ(ierr);
3305   }
3306   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
3307   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
3308   ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
3309   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
3310   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
3311   ierr = VecSetBlockSize(coordinates, cdim);CHKERRQ(ierr);
3312   ierr = VecSetType(coordinates, VECSTANDARD);CHKERRQ(ierr);
3313   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
3314   if (!rank) {
3315     double x[3];
3316     int    val;
3317 
3318     ierr = DMCreateLabel(*dm, "marker");CHKERRQ(ierr);
3319     ierr = DMGetLabel(*dm, "marker", &marker);CHKERRQ(ierr);
3320     for (v = 0; v < Nv; ++v) {
3321       ierr = PetscViewerRead(viewer, line, 4, NULL, PETSC_STRING);CHKERRQ(ierr);
3322       snum = sscanf(line, "%lg %lg %lg %d", &x[0], &x[1], &x[2], &val);
3323       if (snum != 4) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unable to parse cell-vertex file: %s", line);
3324       for (d = 0; d < cdim; ++d) coords[v*cdim+d] = x[d];
3325       if (val) {ierr = DMLabelSetValue(marker, v+Nc, val);CHKERRQ(ierr);}
3326     }
3327   }
3328   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
3329   ierr = DMSetCoordinatesLocal(*dm, coordinates);CHKERRQ(ierr);
3330   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
3331   ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
3332   if (interpolate) {
3333     DM      idm;
3334     DMLabel bdlabel;
3335 
3336     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
3337     ierr = DMDestroy(dm);CHKERRQ(ierr);
3338     *dm  = idm;
3339 
3340     ierr = DMGetLabel(*dm, "marker", &bdlabel);CHKERRQ(ierr);
3341     ierr = DMPlexMarkBoundaryFaces(*dm, PETSC_DETERMINE, bdlabel);CHKERRQ(ierr);
3342     ierr = DMPlexLabelComplete(*dm, bdlabel);CHKERRQ(ierr);
3343   }
3344   PetscFunctionReturn(0);
3345 }
3346 
3347 /*@C
3348   DMPlexCreateFromFile - This takes a filename and produces a DM
3349 
3350   Input Parameters:
3351 + comm - The communicator
3352 . filename - A file name
3353 - interpolate - Flag to create intermediate mesh pieces (edges, faces)
3354 
3355   Output Parameter:
3356 . dm - The DM
3357 
3358   Options Database Keys:
3359 . -dm_plex_create_from_hdf5_xdmf - use the PETSC_VIEWER_HDF5_XDMF format for reading HDF5
3360 
3361   Use -dm_plex_create_ prefix to pass options to the internal PetscViewer, e.g.
3362 $ -dm_plex_create_viewer_hdf5_collective
3363 
3364   Level: beginner
3365 
3366 .seealso: DMPlexCreateFromDAG(), DMPlexCreateFromCellList(), DMPlexCreate()
3367 @*/
3368 PetscErrorCode DMPlexCreateFromFile(MPI_Comm comm, const char filename[], PetscBool interpolate, DM *dm)
3369 {
3370   const char    *extGmsh    = ".msh";
3371   const char    *extGmsh2   = ".msh2";
3372   const char    *extGmsh4   = ".msh4";
3373   const char    *extCGNS    = ".cgns";
3374   const char    *extExodus  = ".exo";
3375   const char    *extGenesis = ".gen";
3376   const char    *extFluent  = ".cas";
3377   const char    *extHDF5    = ".h5";
3378   const char    *extMed     = ".med";
3379   const char    *extPLY     = ".ply";
3380   const char    *extCV      = ".dat";
3381   size_t         len;
3382   PetscBool      isGmsh, isGmsh2, isGmsh4, isCGNS, isExodus, isGenesis, isFluent, isHDF5, isMed, isPLY, isCV;
3383   PetscMPIInt    rank;
3384   PetscErrorCode ierr;
3385 
3386   PetscFunctionBegin;
3387   PetscValidCharPointer(filename, 2);
3388   PetscValidPointer(dm, 4);
3389   ierr = DMInitializePackage();CHKERRQ(ierr);
3390   ierr = PetscLogEventBegin(DMPLEX_CreateFromFile,0,0,0,0);CHKERRQ(ierr);
3391   ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
3392   ierr = PetscStrlen(filename, &len);CHKERRQ(ierr);
3393   if (!len) SETERRQ(comm, PETSC_ERR_ARG_WRONG, "Filename must be a valid path");
3394   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extGmsh,    4, &isGmsh);CHKERRQ(ierr);
3395   ierr = PetscStrncmp(&filename[PetscMax(0,len-5)], extGmsh2,   5, &isGmsh2);CHKERRQ(ierr);
3396   ierr = PetscStrncmp(&filename[PetscMax(0,len-5)], extGmsh4,   5, &isGmsh4);CHKERRQ(ierr);
3397   ierr = PetscStrncmp(&filename[PetscMax(0,len-5)], extCGNS,    5, &isCGNS);CHKERRQ(ierr);
3398   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extExodus,  4, &isExodus);CHKERRQ(ierr);
3399   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extGenesis, 4, &isGenesis);CHKERRQ(ierr);
3400   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extFluent,  4, &isFluent);CHKERRQ(ierr);
3401   ierr = PetscStrncmp(&filename[PetscMax(0,len-3)], extHDF5,    3, &isHDF5);CHKERRQ(ierr);
3402   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extMed,     4, &isMed);CHKERRQ(ierr);
3403   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extPLY,     4, &isPLY);CHKERRQ(ierr);
3404   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extCV,      4, &isCV);CHKERRQ(ierr);
3405   if (isGmsh || isGmsh2 || isGmsh4) {
3406     ierr = DMPlexCreateGmshFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
3407   } else if (isCGNS) {
3408     ierr = DMPlexCreateCGNSFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
3409   } else if (isExodus || isGenesis) {
3410     ierr = DMPlexCreateExodusFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
3411   } else if (isFluent) {
3412     ierr = DMPlexCreateFluentFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
3413   } else if (isHDF5) {
3414     PetscBool      load_hdf5_xdmf = PETSC_FALSE;
3415     PetscViewer viewer;
3416 
3417     /* PETSC_VIEWER_HDF5_XDMF is used if the filename ends with .xdmf.h5, or if -dm_plex_create_from_hdf5_xdmf option is present */
3418     ierr = PetscStrncmp(&filename[PetscMax(0,len-8)], ".xdmf",  5, &load_hdf5_xdmf);CHKERRQ(ierr);
3419     ierr = PetscOptionsGetBool(NULL, NULL, "-dm_plex_create_from_hdf5_xdmf", &load_hdf5_xdmf, NULL);CHKERRQ(ierr);
3420     ierr = PetscViewerCreate(comm, &viewer);CHKERRQ(ierr);
3421     ierr = PetscViewerSetType(viewer, PETSCVIEWERHDF5);CHKERRQ(ierr);
3422     ierr = PetscViewerSetOptionsPrefix(viewer, "dm_plex_create_");CHKERRQ(ierr);
3423     ierr = PetscViewerSetFromOptions(viewer);CHKERRQ(ierr);
3424     ierr = PetscViewerFileSetMode(viewer, FILE_MODE_READ);CHKERRQ(ierr);
3425     ierr = PetscViewerFileSetName(viewer, filename);CHKERRQ(ierr);
3426     ierr = DMCreate(comm, dm);CHKERRQ(ierr);
3427     ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
3428     if (load_hdf5_xdmf) {ierr = PetscViewerPushFormat(viewer, PETSC_VIEWER_HDF5_XDMF);CHKERRQ(ierr);}
3429     ierr = DMLoad(*dm, viewer);CHKERRQ(ierr);
3430     if (load_hdf5_xdmf) {ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);}
3431     ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
3432 
3433     if (interpolate) {
3434       DM idm;
3435 
3436       ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
3437       ierr = DMDestroy(dm);CHKERRQ(ierr);
3438       *dm  = idm;
3439     }
3440   } else if (isMed) {
3441     ierr = DMPlexCreateMedFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
3442   } else if (isPLY) {
3443     ierr = DMPlexCreatePLYFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
3444   } else if (isCV) {
3445     ierr = DMPlexCreateCellVertexFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
3446   } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cannot load file %s: unrecognized extension", filename);
3447   ierr = PetscLogEventEnd(DMPLEX_CreateFromFile,0,0,0,0);CHKERRQ(ierr);
3448   PetscFunctionReturn(0);
3449 }
3450 
3451 /*@
3452   DMPlexCreateReferenceCellByType - Create a DMPLEX with the appropriate FEM reference cell
3453 
3454   Collective
3455 
3456   Input Parameters:
3457 + comm - The communicator
3458 - ct   - The cell type of the reference cell
3459 
3460   Output Parameter:
3461 . refdm - The reference cell
3462 
3463   Level: intermediate
3464 
3465 .seealso: DMPlexCreateReferenceCell(), DMPlexCreateBoxMesh()
3466 @*/
3467 PetscErrorCode DMPlexCreateReferenceCellByType(MPI_Comm comm, DMPolytopeType ct, DM *refdm)
3468 {
3469   DM             rdm;
3470   Vec            coords;
3471   PetscErrorCode ierr;
3472 
3473   PetscFunctionBegin;
3474   ierr = DMCreate(comm, &rdm);CHKERRQ(ierr);
3475   ierr = DMSetType(rdm, DMPLEX);CHKERRQ(ierr);
3476   switch (ct) {
3477     case DM_POLYTOPE_POINT:
3478     {
3479       PetscInt    numPoints[1]        = {1};
3480       PetscInt    coneSize[1]         = {0};
3481       PetscInt    cones[1]            = {0};
3482       PetscInt    coneOrientations[1] = {0};
3483       PetscScalar vertexCoords[1]     = {0.0};
3484 
3485       ierr = DMSetDimension(rdm, 0);CHKERRQ(ierr);
3486       ierr = DMPlexCreateFromDAG(rdm, 0, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
3487     }
3488     break;
3489     case DM_POLYTOPE_SEGMENT:
3490     {
3491       PetscInt    numPoints[2]        = {2, 1};
3492       PetscInt    coneSize[3]         = {2, 0, 0};
3493       PetscInt    cones[2]            = {1, 2};
3494       PetscInt    coneOrientations[2] = {0, 0};
3495       PetscScalar vertexCoords[2]     = {-1.0,  1.0};
3496 
3497       ierr = DMSetDimension(rdm, 1);CHKERRQ(ierr);
3498       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
3499     }
3500     break;
3501     case DM_POLYTOPE_TRIANGLE:
3502     {
3503       PetscInt    numPoints[2]        = {3, 1};
3504       PetscInt    coneSize[4]         = {3, 0, 0, 0};
3505       PetscInt    cones[3]            = {1, 2, 3};
3506       PetscInt    coneOrientations[3] = {0, 0, 0};
3507       PetscScalar vertexCoords[6]     = {-1.0, -1.0,  1.0, -1.0,  -1.0, 1.0};
3508 
3509       ierr = DMSetDimension(rdm, 2);CHKERRQ(ierr);
3510       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
3511     }
3512     break;
3513     case DM_POLYTOPE_QUADRILATERAL:
3514     {
3515       PetscInt    numPoints[2]        = {4, 1};
3516       PetscInt    coneSize[5]         = {4, 0, 0, 0, 0};
3517       PetscInt    cones[4]            = {1, 2, 3, 4};
3518       PetscInt    coneOrientations[4] = {0, 0, 0, 0};
3519       PetscScalar vertexCoords[8]     = {-1.0, -1.0,  1.0, -1.0,  1.0, 1.0,  -1.0, 1.0};
3520 
3521       ierr = DMSetDimension(rdm, 2);CHKERRQ(ierr);
3522       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
3523     }
3524     break;
3525     case DM_POLYTOPE_SEG_PRISM_TENSOR:
3526     {
3527       PetscInt    numPoints[2]        = {4, 1};
3528       PetscInt    coneSize[5]         = {4, 0, 0, 0, 0};
3529       PetscInt    cones[4]            = {1, 2, 3, 4};
3530       PetscInt    coneOrientations[4] = {0, 0, 0, 0};
3531       PetscScalar vertexCoords[8]     = {-1.0, -1.0,  1.0, -1.0,  -1.0, 1.0,  1.0, 1.0};
3532 
3533       ierr = DMSetDimension(rdm, 2);CHKERRQ(ierr);
3534       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
3535     }
3536     break;
3537     case DM_POLYTOPE_TETRAHEDRON:
3538     {
3539       PetscInt    numPoints[2]        = {4, 1};
3540       PetscInt    coneSize[5]         = {4, 0, 0, 0, 0};
3541       PetscInt    cones[4]            = {1, 3, 2, 4};
3542       PetscInt    coneOrientations[4] = {0, 0, 0, 0};
3543       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};
3544 
3545       ierr = DMSetDimension(rdm, 3);CHKERRQ(ierr);
3546       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
3547     }
3548     break;
3549     case DM_POLYTOPE_HEXAHEDRON:
3550     {
3551       PetscInt    numPoints[2]        = {8, 1};
3552       PetscInt    coneSize[9]         = {8, 0, 0, 0, 0, 0, 0, 0, 0};
3553       PetscInt    cones[8]            = {1, 4, 3, 2, 5, 6, 7, 8};
3554       PetscInt    coneOrientations[8] = {0, 0, 0, 0, 0, 0, 0, 0};
3555       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,
3556                                          -1.0, -1.0,  1.0,  1.0, -1.0,  1.0,  1.0, 1.0,  1.0,  -1.0, 1.0,  1.0};
3557 
3558       ierr = DMSetDimension(rdm, 3);CHKERRQ(ierr);
3559       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
3560     }
3561     break;
3562     case DM_POLYTOPE_TRI_PRISM:
3563     {
3564       PetscInt    numPoints[2]        = {6, 1};
3565       PetscInt    coneSize[7]         = {6, 0, 0, 0, 0, 0, 0};
3566       PetscInt    cones[6]            = {1, 3, 2, 4, 5, 6};
3567       PetscInt    coneOrientations[6] = {0, 0, 0, 0, 0, 0};
3568       PetscScalar vertexCoords[18]    = {-1.0, -1.0, -1.0,  1.0, -1.0, -1.0,  -1.0, 1.0, -1.0,
3569                                          -1.0, -1.0,  1.0,  1.0, -1.0,  1.0,  -1.0, 1.0,  1.0};
3570 
3571       ierr = DMSetDimension(rdm, 3);CHKERRQ(ierr);
3572       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
3573     }
3574     break;
3575     case DM_POLYTOPE_TRI_PRISM_TENSOR:
3576     {
3577       PetscInt    numPoints[2]        = {6, 1};
3578       PetscInt    coneSize[7]         = {6, 0, 0, 0, 0, 0, 0};
3579       PetscInt    cones[6]            = {1, 2, 3, 4, 5, 6};
3580       PetscInt    coneOrientations[6] = {0, 0, 0, 0, 0, 0};
3581       PetscScalar vertexCoords[18]    = {-1.0, -1.0, -1.0,  1.0, -1.0, -1.0,  -1.0, 1.0, -1.0,
3582                                          -1.0, -1.0,  1.0,  1.0, -1.0,  1.0,  -1.0, 1.0,  1.0};
3583 
3584       ierr = DMSetDimension(rdm, 3);CHKERRQ(ierr);
3585       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
3586     }
3587     break;
3588     case DM_POLYTOPE_QUAD_PRISM_TENSOR:
3589     {
3590       PetscInt    numPoints[2]        = {8, 1};
3591       PetscInt    coneSize[9]         = {8, 0, 0, 0, 0, 0, 0, 0, 0};
3592       PetscInt    cones[8]            = {1, 2, 3, 4, 5, 6, 7, 8};
3593       PetscInt    coneOrientations[8] = {0, 0, 0, 0, 0, 0, 0, 0};
3594       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,
3595                                          -1.0, -1.0,  1.0,  1.0, -1.0,  1.0,  1.0, 1.0,  1.0,  -1.0, 1.0,  1.0};
3596 
3597       ierr = DMSetDimension(rdm, 3);CHKERRQ(ierr);
3598       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
3599     }
3600     break;
3601     default: SETERRQ1(comm, PETSC_ERR_ARG_WRONG, "Cannot create reference cell for cell type %s", DMPolytopeTypes[ct]);
3602   }
3603   {
3604     PetscInt Nv, v;
3605 
3606     /* Must create the celltype label here so that we do not automatically try to compute the types */
3607     ierr = DMCreateLabel(rdm, "celltype");CHKERRQ(ierr);
3608     ierr = DMPlexSetCellType(rdm, 0, ct);CHKERRQ(ierr);
3609     ierr = DMPlexGetChart(rdm, NULL, &Nv);CHKERRQ(ierr);
3610     for (v = 1; v < Nv; ++v) {ierr = DMPlexSetCellType(rdm, v, DM_POLYTOPE_POINT);CHKERRQ(ierr);}
3611   }
3612   ierr = DMPlexInterpolate(rdm, refdm);CHKERRQ(ierr);
3613   if (rdm->coordinateDM) {
3614     DM           ncdm;
3615     PetscSection cs;
3616     PetscInt     pEnd = -1;
3617 
3618     ierr = DMGetLocalSection(rdm->coordinateDM, &cs);CHKERRQ(ierr);
3619     if (cs) {ierr = PetscSectionGetChart(cs, NULL, &pEnd);CHKERRQ(ierr);}
3620     if (pEnd >= 0) {
3621       ierr = DMClone(*refdm, &ncdm);CHKERRQ(ierr);
3622       ierr = DMCopyDisc(rdm->coordinateDM, ncdm);CHKERRQ(ierr);
3623       ierr = DMSetLocalSection(ncdm, cs);CHKERRQ(ierr);
3624       ierr = DMSetCoordinateDM(*refdm, ncdm);CHKERRQ(ierr);
3625       ierr = DMDestroy(&ncdm);CHKERRQ(ierr);
3626     }
3627   }
3628   ierr = DMGetCoordinatesLocal(rdm, &coords);CHKERRQ(ierr);
3629   if (coords) {
3630     ierr = DMSetCoordinatesLocal(*refdm, coords);CHKERRQ(ierr);
3631   } else {
3632     ierr = DMGetCoordinates(rdm, &coords);CHKERRQ(ierr);
3633     if (coords) {ierr = DMSetCoordinates(*refdm, coords);CHKERRQ(ierr);}
3634   }
3635   ierr = DMDestroy(&rdm);CHKERRQ(ierr);
3636   PetscFunctionReturn(0);
3637 }
3638 
3639 /*@
3640   DMPlexCreateReferenceCell - Create a DMPLEX with the appropriate FEM reference cell
3641 
3642   Collective
3643 
3644   Input Parameters:
3645 + comm    - The communicator
3646 . dim     - The spatial dimension
3647 - simplex - Flag for simplex, otherwise use a tensor-product cell
3648 
3649   Output Parameter:
3650 . refdm - The reference cell
3651 
3652   Level: intermediate
3653 
3654 .seealso: DMPlexCreateReferenceCellByType(), DMPlexCreateBoxMesh()
3655 @*/
3656 PetscErrorCode DMPlexCreateReferenceCell(MPI_Comm comm, PetscInt dim, PetscBool simplex, DM *refdm)
3657 {
3658   PetscErrorCode ierr;
3659 
3660   PetscFunctionBeginUser;
3661   switch (dim) {
3662   case 0: ierr = DMPlexCreateReferenceCellByType(comm, DM_POLYTOPE_POINT, refdm);CHKERRQ(ierr);break;
3663   case 1: ierr = DMPlexCreateReferenceCellByType(comm, DM_POLYTOPE_SEGMENT, refdm);CHKERRQ(ierr);break;
3664   case 2:
3665     if (simplex) {ierr = DMPlexCreateReferenceCellByType(comm, DM_POLYTOPE_TRIANGLE, refdm);CHKERRQ(ierr);}
3666     else         {ierr = DMPlexCreateReferenceCellByType(comm, DM_POLYTOPE_QUADRILATERAL, refdm);CHKERRQ(ierr);}
3667     break;
3668   case 3:
3669     if (simplex) {ierr = DMPlexCreateReferenceCellByType(comm, DM_POLYTOPE_TETRAHEDRON, refdm);CHKERRQ(ierr);}
3670     else         {ierr = DMPlexCreateReferenceCellByType(comm, DM_POLYTOPE_HEXAHEDRON, refdm);CHKERRQ(ierr);}
3671     break;
3672   default:
3673     SETERRQ1(comm, PETSC_ERR_ARG_WRONG, "Cannot create reference cell for dimension %D", dim);
3674   }
3675   PetscFunctionReturn(0);
3676 }
3677