xref: /petsc/src/dm/impls/plex/plexcreate.c (revision 116ded153d7144465fec82aa740a47e27d228431)
1 #define PETSCDM_DLL
2 #include <petsc/private/dmpleximpl.h>    /*I   "petscdmplex.h"   I*/
3 #include <petscdmda.h>
4 #include <petscsf.h>
5 
6 /*@
7   DMPlexCreateDoublet - Creates a mesh of two cells of the specified type, optionally with later refinement.
8 
9   Collective on MPI_Comm
10 
11   Input Parameters:
12 + comm - The communicator for the DM object
13 . dim - The spatial dimension
14 . simplex - Flag for simplicial cells, otherwise they are tensor product cells
15 . interpolate - Flag to create intermediate mesh pieces (edges, faces)
16 . refinementUniform - Flag for uniform parallel refinement
17 - refinementLimit - A nonzero number indicates the largest admissible volume for a refined cell
18 
19   Output Parameter:
20 . dm  - The DM object
21 
22   Level: beginner
23 
24 .keywords: DM, create
25 .seealso: DMSetType(), DMCreate()
26 @*/
27 PetscErrorCode DMPlexCreateDoublet(MPI_Comm comm, PetscInt dim, PetscBool simplex, PetscBool interpolate, PetscBool refinementUniform, PetscReal refinementLimit, DM *newdm)
28 {
29   DM             dm;
30   PetscInt       p;
31   PetscMPIInt    rank;
32   PetscErrorCode ierr;
33 
34   PetscFunctionBegin;
35   ierr = DMCreate(comm, &dm);CHKERRQ(ierr);
36   ierr = DMSetType(dm, DMPLEX);CHKERRQ(ierr);
37   ierr = DMSetDimension(dm, dim);CHKERRQ(ierr);
38   ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
39   switch (dim) {
40   case 2:
41     if (simplex) {ierr = PetscObjectSetName((PetscObject) dm, "triangular");CHKERRQ(ierr);}
42     else         {ierr = PetscObjectSetName((PetscObject) dm, "quadrilateral");CHKERRQ(ierr);}
43     break;
44   case 3:
45     if (simplex) {ierr = PetscObjectSetName((PetscObject) dm, "tetrahedral");CHKERRQ(ierr);}
46     else         {ierr = PetscObjectSetName((PetscObject) dm, "hexahedral");CHKERRQ(ierr);}
47     break;
48   default:
49     SETERRQ1(comm, PETSC_ERR_ARG_OUTOFRANGE, "Cannot make meshes for dimension %d", dim);
50   }
51   if (rank) {
52     PetscInt numPoints[2] = {0, 0};
53     ierr = DMPlexCreateFromDAG(dm, 1, numPoints, NULL, NULL, NULL, NULL);CHKERRQ(ierr);
54   } else {
55     switch (dim) {
56     case 2:
57       if (simplex) {
58         PetscInt    numPoints[2]        = {4, 2};
59         PetscInt    coneSize[6]         = {3, 3, 0, 0, 0, 0};
60         PetscInt    cones[6]            = {2, 3, 4,  5, 4, 3};
61         PetscInt    coneOrientations[6] = {0, 0, 0,  0, 0, 0};
62         PetscScalar vertexCoords[8]     = {-0.5, 0.5, 0.0, 0.0, 0.0, 1.0, 0.5, 0.5};
63         PetscInt    markerPoints[8]     = {2, 1, 3, 1, 4, 1, 5, 1};
64 
65         ierr = DMPlexCreateFromDAG(dm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
66         for (p = 0; p < 4; ++p) {ierr = DMSetLabelValue(dm, "marker", markerPoints[p*2], markerPoints[p*2+1]);CHKERRQ(ierr);}
67       } else {
68         PetscInt    numPoints[2]        = {6, 2};
69         PetscInt    coneSize[8]         = {4, 4, 0, 0, 0, 0, 0, 0};
70         PetscInt    cones[8]            = {2, 3, 4, 5,  3, 6, 7, 4};
71         PetscInt    coneOrientations[8] = {0, 0, 0, 0,  0, 0, 0, 0};
72         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};
73 
74         ierr = DMPlexCreateFromDAG(dm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
75       }
76       break;
77     case 3:
78       if (simplex) {
79         PetscInt    numPoints[2]        = {5, 2};
80         PetscInt    coneSize[7]         = {4, 4, 0, 0, 0, 0, 0};
81         PetscInt    cones[8]            = {4, 3, 5, 2,  5, 3, 4, 6};
82         PetscInt    coneOrientations[8] = {0, 0, 0, 0,  0, 0, 0, 0};
83         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};
84         PetscInt    markerPoints[10]    = {2, 1, 3, 1, 4, 1, 5, 1, 6, 1};
85 
86         ierr = DMPlexCreateFromDAG(dm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
87         for (p = 0; p < 5; ++p) {ierr = DMSetLabelValue(dm, "marker", markerPoints[p*2], markerPoints[p*2+1]);CHKERRQ(ierr);}
88       } else {
89         PetscInt    numPoints[2]         = {12, 2};
90         PetscInt    coneSize[14]         = {8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0};
91         PetscInt    cones[16]            = {2, 3, 4, 5, 6, 7, 8, 9,  5, 4, 10, 11, 7, 12, 13, 8};
92         PetscInt    coneOrientations[16] = {0, 0, 0, 0, 0, 0, 0, 0,  0, 0,  0,  0, 0,  0,  0, 0};
93         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,
94                                             -1.0, -0.5,  0.5,   0.0, -0.5,  0.5,  0.0,  0.5,  0.5,  -1.0,  0.5,  0.5,
95                                              1.0,  0.5, -0.5,   1.0, -0.5, -0.5,  1.0, -0.5,  0.5,   1.0,  0.5,  0.5};
96 
97         ierr = DMPlexCreateFromDAG(dm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
98       }
99       break;
100     default:
101       SETERRQ1(comm, PETSC_ERR_ARG_OUTOFRANGE, "Cannot make meshes for dimension %d", dim);
102     }
103   }
104   *newdm = dm;
105   if (refinementLimit > 0.0) {
106     DM rdm;
107     const char *name;
108 
109     ierr = DMPlexSetRefinementUniform(*newdm, PETSC_FALSE);CHKERRQ(ierr);
110     ierr = DMPlexSetRefinementLimit(*newdm, refinementLimit);CHKERRQ(ierr);
111     ierr = DMRefine(*newdm, comm, &rdm);CHKERRQ(ierr);
112     ierr = PetscObjectGetName((PetscObject) *newdm, &name);CHKERRQ(ierr);
113     ierr = PetscObjectSetName((PetscObject)    rdm,  name);CHKERRQ(ierr);
114     ierr = DMDestroy(newdm);CHKERRQ(ierr);
115     *newdm = rdm;
116   }
117   if (interpolate) {
118     DM idm = NULL;
119     const char *name;
120 
121     ierr = DMPlexInterpolate(*newdm, &idm);CHKERRQ(ierr);
122     ierr = PetscObjectGetName((PetscObject) *newdm, &name);CHKERRQ(ierr);
123     ierr = PetscObjectSetName((PetscObject)    idm,  name);CHKERRQ(ierr);
124     ierr = DMPlexCopyCoordinates(*newdm, idm);CHKERRQ(ierr);
125     ierr = DMCopyLabels(*newdm, idm);CHKERRQ(ierr);
126     ierr = DMDestroy(newdm);CHKERRQ(ierr);
127     *newdm = idm;
128   }
129   {
130     DM refinedMesh     = NULL;
131     DM distributedMesh = NULL;
132 
133     /* Distribute mesh over processes */
134     ierr = DMPlexDistribute(*newdm, 0, NULL, &distributedMesh);CHKERRQ(ierr);
135     if (distributedMesh) {
136       ierr = DMDestroy(newdm);CHKERRQ(ierr);
137       *newdm = distributedMesh;
138     }
139     if (refinementUniform) {
140       ierr = DMPlexSetRefinementUniform(*newdm, refinementUniform);CHKERRQ(ierr);
141       ierr = DMRefine(*newdm, comm, &refinedMesh);CHKERRQ(ierr);
142       if (refinedMesh) {
143         ierr = DMDestroy(newdm);CHKERRQ(ierr);
144         *newdm = refinedMesh;
145       }
146     }
147   }
148   PetscFunctionReturn(0);
149 }
150 
151 /*@
152   DMPlexCreateSquareBoundary - Creates a 1D mesh the is the boundary of a square lattice.
153 
154   Collective on MPI_Comm
155 
156   Input Parameters:
157 + comm  - The communicator for the DM object
158 . lower - The lower left corner coordinates
159 . upper - The upper right corner coordinates
160 - edges - The number of cells in each direction
161 
162   Output Parameter:
163 . dm  - The DM object
164 
165   Note: Here is the numbering returned for 2 cells in each direction:
166 $ 18--5-17--4--16
167 $  |     |     |
168 $  6    10     3
169 $  |     |     |
170 $ 19-11-20--9--15
171 $  |     |     |
172 $  7     8     2
173 $  |     |     |
174 $ 12--0-13--1--14
175 
176   Level: beginner
177 
178 .keywords: DM, create
179 .seealso: DMPlexCreateBoxMesh(), DMPlexCreateCubeBoundary(), DMSetType(), DMCreate()
180 @*/
181 PetscErrorCode DMPlexCreateSquareBoundary(DM dm, const PetscReal lower[], const PetscReal upper[], const PetscInt edges[])
182 {
183   const PetscInt numVertices    = (edges[0]+1)*(edges[1]+1);
184   const PetscInt numEdges       = edges[0]*(edges[1]+1) + (edges[0]+1)*edges[1];
185   PetscInt       markerTop      = 1;
186   PetscInt       markerBottom   = 1;
187   PetscInt       markerRight    = 1;
188   PetscInt       markerLeft     = 1;
189   PetscBool      markerSeparate = PETSC_FALSE;
190   Vec            coordinates;
191   PetscSection   coordSection;
192   PetscScalar    *coords;
193   PetscInt       coordSize;
194   PetscMPIInt    rank;
195   PetscInt       v, vx, vy;
196   PetscErrorCode ierr;
197 
198   PetscFunctionBegin;
199   ierr = PetscOptionsGetBool(((PetscObject) dm)->options,((PetscObject) dm)->prefix, "-dm_plex_separate_marker", &markerSeparate, NULL);CHKERRQ(ierr);
200   if (markerSeparate) {
201     markerTop    = 3;
202     markerBottom = 1;
203     markerRight  = 2;
204     markerLeft   = 4;
205   }
206   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);CHKERRQ(ierr);
207   if (!rank) {
208     PetscInt e, ex, ey;
209 
210     ierr = DMPlexSetChart(dm, 0, numEdges+numVertices);CHKERRQ(ierr);
211     for (e = 0; e < numEdges; ++e) {
212       ierr = DMPlexSetConeSize(dm, e, 2);CHKERRQ(ierr);
213     }
214     ierr = DMSetUp(dm);CHKERRQ(ierr); /* Allocate space for cones */
215     for (vx = 0; vx <= edges[0]; vx++) {
216       for (ey = 0; ey < edges[1]; ey++) {
217         PetscInt edge   = vx*edges[1] + ey + edges[0]*(edges[1]+1);
218         PetscInt vertex = ey*(edges[0]+1) + vx + numEdges;
219         PetscInt cone[2];
220 
221         cone[0] = vertex; cone[1] = vertex+edges[0]+1;
222         ierr    = DMPlexSetCone(dm, edge, cone);CHKERRQ(ierr);
223         if (vx == edges[0]) {
224           ierr = DMSetLabelValue(dm, "marker", edge,    markerRight);CHKERRQ(ierr);
225           ierr = DMSetLabelValue(dm, "marker", cone[0], markerRight);CHKERRQ(ierr);
226           if (ey == edges[1]-1) {
227             ierr = DMSetLabelValue(dm, "marker", cone[1], markerRight);CHKERRQ(ierr);
228           }
229         } else if (vx == 0) {
230           ierr = DMSetLabelValue(dm, "marker", edge,    markerLeft);CHKERRQ(ierr);
231           ierr = DMSetLabelValue(dm, "marker", cone[0], markerLeft);CHKERRQ(ierr);
232           if (ey == edges[1]-1) {
233             ierr = DMSetLabelValue(dm, "marker", cone[1], markerLeft);CHKERRQ(ierr);
234           }
235         }
236       }
237     }
238     for (vy = 0; vy <= edges[1]; vy++) {
239       for (ex = 0; ex < edges[0]; ex++) {
240         PetscInt edge   = vy*edges[0]     + ex;
241         PetscInt vertex = vy*(edges[0]+1) + ex + numEdges;
242         PetscInt cone[2];
243 
244         cone[0] = vertex; cone[1] = vertex+1;
245         ierr    = DMPlexSetCone(dm, edge, cone);CHKERRQ(ierr);
246         if (vy == edges[1]) {
247           ierr = DMSetLabelValue(dm, "marker", edge,    markerTop);CHKERRQ(ierr);
248           ierr = DMSetLabelValue(dm, "marker", cone[0], markerTop);CHKERRQ(ierr);
249           if (ex == edges[0]-1) {
250             ierr = DMSetLabelValue(dm, "marker", cone[1], markerTop);CHKERRQ(ierr);
251           }
252         } else if (vy == 0) {
253           ierr = DMSetLabelValue(dm, "marker", edge,    markerBottom);CHKERRQ(ierr);
254           ierr = DMSetLabelValue(dm, "marker", cone[0], markerBottom);CHKERRQ(ierr);
255           if (ex == edges[0]-1) {
256             ierr = DMSetLabelValue(dm, "marker", cone[1], markerBottom);CHKERRQ(ierr);
257           }
258         }
259       }
260     }
261   }
262   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
263   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
264   /* Build coordinates */
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 the is the boundary of a cubic lattice.
295 
296   Collective on MPI_Comm
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 - edges - The number of cells in each direction
303 
304   Output Parameter:
305 . dm  - The DM object
306 
307   Level: beginner
308 
309 .keywords: DM, create
310 .seealso: DMPlexCreateBoxMesh(), DMPlexCreateSquareBoundary(), DMSetType(), DMCreate()
311 @*/
312 PetscErrorCode DMPlexCreateCubeBoundary(DM dm, const PetscReal lower[], const PetscReal upper[], const PetscInt faces[])
313 {
314   PetscInt       vertices[3], numVertices;
315   PetscInt       numFaces    = 2*faces[0]*faces[1] + 2*faces[1]*faces[2] + 2*faces[0]*faces[2];
316   Vec            coordinates;
317   PetscSection   coordSection;
318   PetscScalar    *coords;
319   PetscInt       coordSize;
320   PetscMPIInt    rank;
321   PetscInt       v, vx, vy, vz;
322   PetscInt       voffset, iface=0, cone[4];
323   PetscErrorCode ierr;
324 
325   PetscFunctionBegin;
326   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");
327   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);CHKERRQ(ierr);
328   vertices[0] = faces[0]+1; vertices[1] = faces[1]+1; vertices[2] = faces[2]+1;
329   numVertices = vertices[0]*vertices[1]*vertices[2];
330   if (!rank) {
331     PetscInt f;
332 
333     ierr = DMPlexSetChart(dm, 0, numFaces+numVertices);CHKERRQ(ierr);
334     for (f = 0; f < numFaces; ++f) {
335       ierr = DMPlexSetConeSize(dm, f, 4);CHKERRQ(ierr);
336     }
337     ierr = DMSetUp(dm);CHKERRQ(ierr); /* Allocate space for cones */
338     for (v = 0; v < numFaces+numVertices; ++v) {
339       ierr = DMSetLabelValue(dm, "marker", v, 1);CHKERRQ(ierr);
340     }
341 
342     /* Side 0 (Top) */
343     for (vy = 0; vy < faces[1]; vy++) {
344       for (vx = 0; vx < faces[0]; vx++) {
345         voffset = numFaces + vertices[0]*vertices[1]*(vertices[2]-1) + vy*vertices[0] + vx;
346         cone[0] = voffset; cone[1] = voffset+1; cone[2] = voffset+vertices[0]+1; cone[3] = voffset+vertices[0];
347         ierr    = DMPlexSetCone(dm, iface, cone);CHKERRQ(ierr);
348         iface++;
349       }
350     }
351 
352     /* Side 1 (Bottom) */
353     for (vy = 0; vy < faces[1]; vy++) {
354       for (vx = 0; vx < faces[0]; vx++) {
355         voffset = numFaces + vy*(faces[0]+1) + vx;
356         cone[0] = voffset+1; cone[1] = voffset; cone[2] = voffset+vertices[0]; cone[3] = voffset+vertices[0]+1;
357         ierr    = DMPlexSetCone(dm, iface, cone);CHKERRQ(ierr);
358         iface++;
359       }
360     }
361 
362     /* Side 2 (Front) */
363     for (vz = 0; vz < faces[2]; vz++) {
364       for (vx = 0; vx < faces[0]; vx++) {
365         voffset = numFaces + vz*vertices[0]*vertices[1] + vx;
366         cone[0] = voffset; cone[1] = voffset+1; cone[2] = voffset+vertices[0]*vertices[1]+1; cone[3] = voffset+vertices[0]*vertices[1];
367         ierr    = DMPlexSetCone(dm, iface, cone);CHKERRQ(ierr);
368         iface++;
369       }
370     }
371 
372     /* Side 3 (Back) */
373     for (vz = 0; vz < faces[2]; vz++) {
374       for (vx = 0; vx < faces[0]; vx++) {
375         voffset = numFaces + vz*vertices[0]*vertices[1] + vertices[0]*(vertices[1]-1) + vx;
376         cone[0] = voffset+vertices[0]*vertices[1]; cone[1] = voffset+vertices[0]*vertices[1]+1;
377         cone[2] = voffset+1; cone[3] = voffset;
378         ierr    = DMPlexSetCone(dm, iface, cone);CHKERRQ(ierr);
379         iface++;
380       }
381     }
382 
383     /* Side 4 (Left) */
384     for (vz = 0; vz < faces[2]; vz++) {
385       for (vy = 0; vy < faces[1]; vy++) {
386         voffset = numFaces + vz*vertices[0]*vertices[1] + vy*vertices[0];
387         cone[0] = voffset; cone[1] = voffset+vertices[0]*vertices[1];
388         cone[2] = voffset+vertices[0]*vertices[1]+vertices[0]; cone[3] = voffset+vertices[0];
389         ierr    = DMPlexSetCone(dm, iface, cone);CHKERRQ(ierr);
390         iface++;
391       }
392     }
393 
394     /* Side 5 (Right) */
395     for (vz = 0; vz < faces[2]; vz++) {
396       for (vy = 0; vy < faces[1]; vy++) {
397         voffset = numFaces + vz*vertices[0]*vertices[1] + vy*vertices[0] + vx;
398         cone[0] = voffset+vertices[0]*vertices[1]; cone[1] = voffset;
399         cone[2] = voffset+vertices[0]; cone[3] = voffset+vertices[0]*vertices[1]+vertices[0];
400         ierr    = DMPlexSetCone(dm, iface, cone);CHKERRQ(ierr);
401         iface++;
402       }
403     }
404   }
405   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
406   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
407   /* Build coordinates */
408   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
409   ierr = PetscSectionSetChart(coordSection, numFaces, numFaces + numVertices);CHKERRQ(ierr);
410   for (v = numFaces; v < numFaces+numVertices; ++v) {
411     ierr = PetscSectionSetDof(coordSection, v, 3);CHKERRQ(ierr);
412   }
413   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
414   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
415   ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
416   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
417   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
418   ierr = VecSetBlockSize(coordinates, 3);CHKERRQ(ierr);
419   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
420   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
421   for (vz = 0; vz <= faces[2]; ++vz) {
422     for (vy = 0; vy <= faces[1]; ++vy) {
423       for (vx = 0; vx <= faces[0]; ++vx) {
424         coords[((vz*(faces[1]+1)+vy)*(faces[0]+1)+vx)*3+0] = lower[0] + ((upper[0] - lower[0])/faces[0])*vx;
425         coords[((vz*(faces[1]+1)+vy)*(faces[0]+1)+vx)*3+1] = lower[1] + ((upper[1] - lower[1])/faces[1])*vy;
426         coords[((vz*(faces[1]+1)+vy)*(faces[0]+1)+vx)*3+2] = lower[2] + ((upper[2] - lower[2])/faces[2])*vz;
427       }
428     }
429   }
430   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
431   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
432   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
433   PetscFunctionReturn(0);
434 }
435 
436 /*@
437   DMPlexCreateBoxMesh - Creates a mesh on the tensor product of unit intervals (box) using simplices.
438 
439   Collective on MPI_Comm
440 
441   Input Parameters:
442 + comm - The communicator for the DM object
443 . dim - The spatial dimension
444 . numFaces - Number of faces per dimension
445 - interpolate - Flag to create intermediate mesh pieces (edges, faces)
446 
447   Output Parameter:
448 . dm  - The DM object
449 
450   Level: beginner
451 
452 .keywords: DM, create
453 .seealso: DMPlexCreateHexBoxMesh(), DMSetType(), DMCreate()
454 @*/
455 PetscErrorCode DMPlexCreateBoxMesh(MPI_Comm comm, PetscInt dim, PetscInt numFaces, PetscBool interpolate, DM *dm)
456 {
457   DM             boundary;
458   PetscErrorCode ierr;
459 
460   PetscFunctionBegin;
461   PetscValidPointer(dm, 4);
462   ierr = DMCreate(comm, &boundary);CHKERRQ(ierr);
463   PetscValidLogicalCollectiveInt(boundary,dim,2);
464   ierr = DMSetType(boundary, DMPLEX);CHKERRQ(ierr);
465   ierr = DMSetDimension(boundary, dim-1);CHKERRQ(ierr);
466   ierr = DMSetCoordinateDim(boundary, dim);CHKERRQ(ierr);
467   switch (dim) {
468   case 2:
469   {
470     PetscReal lower[2] = {0.0, 0.0};
471     PetscReal upper[2] = {1.0, 1.0};
472     PetscInt  edges[2];
473 
474     edges[0] = numFaces; edges[1] = numFaces;
475     ierr = DMPlexCreateSquareBoundary(boundary, lower, upper, edges);CHKERRQ(ierr);
476     break;
477   }
478   case 3:
479   {
480     PetscReal lower[3] = {0.0, 0.0, 0.0};
481     PetscReal upper[3] = {1.0, 1.0, 1.0};
482     PetscInt  faces[3];
483 
484     faces[0] = numFaces; faces[1] = numFaces; faces[2] = numFaces;
485     ierr = DMPlexCreateCubeBoundary(boundary, lower, upper, faces);CHKERRQ(ierr);
486     break;
487   }
488   default:
489     SETERRQ1(comm, PETSC_ERR_SUP, "Dimension not supported: %d", dim);
490   }
491   ierr = DMPlexGenerate(boundary, NULL, interpolate, dm);CHKERRQ(ierr);
492   ierr = DMDestroy(&boundary);CHKERRQ(ierr);
493   PetscFunctionReturn(0);
494 }
495 
496 static PetscErrorCode DMPlexCreateCubeMesh_Internal(DM dm, const PetscReal lower[], const PetscReal upper[], const PetscInt edges[], DMBoundaryType bdX, DMBoundaryType bdY, DMBoundaryType bdZ)
497 {
498   DMLabel        cutLabel = NULL;
499   PetscInt       markerTop      = 1, faceMarkerTop      = 1;
500   PetscInt       markerBottom   = 1, faceMarkerBottom   = 1;
501   PetscInt       markerFront    = 1, faceMarkerFront    = 1;
502   PetscInt       markerBack     = 1, faceMarkerBack     = 1;
503   PetscInt       markerRight    = 1, faceMarkerRight    = 1;
504   PetscInt       markerLeft     = 1, faceMarkerLeft     = 1;
505   PetscInt       dim;
506   PetscBool      markerSeparate = PETSC_FALSE, cutMarker = PETSC_FALSE;
507   PetscMPIInt    rank;
508   PetscErrorCode ierr;
509 
510   PetscFunctionBegin;
511   ierr = DMGetDimension(dm,&dim);CHKERRQ(ierr);
512   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);CHKERRQ(ierr);
513   ierr = DMCreateLabel(dm,"marker");CHKERRQ(ierr);
514   ierr = DMCreateLabel(dm,"Face Sets");CHKERRQ(ierr);
515   if (bdX == DM_BOUNDARY_PERIODIC || bdX == DM_BOUNDARY_TWIST ||
516       bdY == DM_BOUNDARY_PERIODIC || bdY == DM_BOUNDARY_TWIST ||
517       bdZ == DM_BOUNDARY_PERIODIC || bdZ == DM_BOUNDARY_TWIST) {
518     ierr = PetscOptionsGetBool(((PetscObject) dm)->options,((PetscObject) dm)->prefix, "-dm_plex_periodic_cut", &cutMarker, NULL);CHKERRQ(ierr);
519     if (cutMarker) {ierr = DMCreateLabel(dm, "periodic_cut");CHKERRQ(ierr); ierr = DMGetLabel(dm, "periodic_cut", &cutLabel);CHKERRQ(ierr);}
520   }
521   switch (dim) {
522   case 2:
523     faceMarkerTop    = 3;
524     faceMarkerBottom = 1;
525     faceMarkerRight  = 2;
526     faceMarkerLeft   = 4;
527     break;
528   case 3:
529     faceMarkerBottom = 1;
530     faceMarkerTop    = 2;
531     faceMarkerFront  = 3;
532     faceMarkerBack   = 4;
533     faceMarkerRight  = 5;
534     faceMarkerLeft   = 6;
535     break;
536   default:
537     SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Dimension %d not supported",dim);
538     break;
539   }
540   ierr = PetscOptionsGetBool(((PetscObject) dm)->options,((PetscObject) dm)->prefix, "-dm_plex_separate_marker", &markerSeparate, NULL);CHKERRQ(ierr);
541   if (markerSeparate) {
542     markerBottom = faceMarkerBottom;
543     markerTop    = faceMarkerTop;
544     markerFront  = faceMarkerFront;
545     markerBack   = faceMarkerBack;
546     markerRight  = faceMarkerRight;
547     markerLeft   = faceMarkerLeft;
548   }
549   {
550     const PetscInt numXEdges    = !rank ? edges[0] : 0;
551     const PetscInt numYEdges    = !rank ? edges[1] : 0;
552     const PetscInt numZEdges    = !rank ? edges[2] : 0;
553     const PetscInt numXVertices = !rank ? (bdX == DM_BOUNDARY_PERIODIC || bdX == DM_BOUNDARY_TWIST ? edges[0] : edges[0]+1) : 0;
554     const PetscInt numYVertices = !rank ? (bdY == DM_BOUNDARY_PERIODIC || bdY == DM_BOUNDARY_TWIST ? edges[1] : edges[1]+1) : 0;
555     const PetscInt numZVertices = !rank ? (bdZ == DM_BOUNDARY_PERIODIC || bdZ == DM_BOUNDARY_TWIST ? edges[2] : edges[2]+1) : 0;
556     const PetscInt numCells     = numXEdges*numYEdges*numZEdges;
557     const PetscInt numXFaces    = numYEdges*numZEdges;
558     const PetscInt numYFaces    = numXEdges*numZEdges;
559     const PetscInt numZFaces    = numXEdges*numYEdges;
560     const PetscInt numTotXFaces = numXVertices*numXFaces;
561     const PetscInt numTotYFaces = numYVertices*numYFaces;
562     const PetscInt numTotZFaces = numZVertices*numZFaces;
563     const PetscInt numFaces     = numTotXFaces + numTotYFaces + numTotZFaces;
564     const PetscInt numTotXEdges = numXEdges*numYVertices*numZVertices;
565     const PetscInt numTotYEdges = numYEdges*numXVertices*numZVertices;
566     const PetscInt numTotZEdges = numZEdges*numXVertices*numYVertices;
567     const PetscInt numVertices  = numXVertices*numYVertices*numZVertices;
568     const PetscInt numEdges     = numTotXEdges + numTotYEdges + numTotZEdges;
569     const PetscInt firstVertex  = (dim == 2) ? numFaces : numCells;
570     const PetscInt firstXFace   = (dim == 2) ? 0 : numCells + numVertices;
571     const PetscInt firstYFace   = firstXFace + numTotXFaces;
572     const PetscInt firstZFace   = firstYFace + numTotYFaces;
573     const PetscInt firstXEdge   = numCells + numFaces + numVertices;
574     const PetscInt firstYEdge   = firstXEdge + numTotXEdges;
575     const PetscInt firstZEdge   = firstYEdge + numTotYEdges;
576     Vec            coordinates;
577     PetscSection   coordSection;
578     PetscScalar   *coords;
579     PetscInt       coordSize;
580     PetscInt       v, vx, vy, vz;
581     PetscInt       c, f, fx, fy, fz, e, ex, ey, ez;
582 
583     ierr = DMPlexSetChart(dm, 0, numCells+numFaces+numEdges+numVertices);CHKERRQ(ierr);
584     for (c = 0; c < numCells; c++) {
585       ierr = DMPlexSetConeSize(dm, c, 6);CHKERRQ(ierr);
586     }
587     for (f = firstXFace; f < firstXFace+numFaces; ++f) {
588       ierr = DMPlexSetConeSize(dm, f, 4);CHKERRQ(ierr);
589     }
590     for (e = firstXEdge; e < firstXEdge+numEdges; ++e) {
591       ierr = DMPlexSetConeSize(dm, e, 2);CHKERRQ(ierr);
592     }
593     ierr = DMSetUp(dm);CHKERRQ(ierr); /* Allocate space for cones */
594     /* Build cells */
595     for (fz = 0; fz < numZEdges; ++fz) {
596       for (fy = 0; fy < numYEdges; ++fy) {
597         for (fx = 0; fx < numXEdges; ++fx) {
598           PetscInt cell    = (fz*numYEdges + fy)*numXEdges + fx;
599           PetscInt faceB   = firstZFace + (fy*numXEdges+fx)*numZVertices +   fz;
600           PetscInt faceT   = firstZFace + (fy*numXEdges+fx)*numZVertices + ((fz+1)%numZVertices);
601           PetscInt faceF   = firstYFace + (fz*numXEdges+fx)*numYVertices +   fy;
602           PetscInt faceK   = firstYFace + (fz*numXEdges+fx)*numYVertices + ((fy+1)%numYVertices);
603           PetscInt faceL   = firstXFace + (fz*numYEdges+fy)*numXVertices +   fx;
604           PetscInt faceR   = firstXFace + (fz*numYEdges+fy)*numXVertices + ((fx+1)%numXVertices);
605                             /* B,  T,  F,  K,  R,  L */
606           PetscInt ornt[6] = {-4,  0,  0, -1,  0, -4}; /* ??? */
607           PetscInt cone[6];
608 
609           /* no boundary twisting in 3D */
610           cone[0] = faceB; cone[1] = faceT; cone[2] = faceF; cone[3] = faceK; cone[4] = faceR; cone[5] = faceL;
611           ierr    = DMPlexSetCone(dm, cell, cone);CHKERRQ(ierr);
612           ierr    = DMPlexSetConeOrientation(dm, cell, ornt);CHKERRQ(ierr);
613           if (bdX != DM_BOUNDARY_NONE && fx == numXEdges-1 && cutLabel) {ierr = DMLabelSetValue(cutLabel, cell, 2);CHKERRQ(ierr);}
614           if (bdY != DM_BOUNDARY_NONE && fy == numYEdges-1 && cutLabel) {ierr = DMLabelSetValue(cutLabel, cell, 2);CHKERRQ(ierr);}
615           if (bdZ != DM_BOUNDARY_NONE && fz == numZEdges-1 && cutLabel) {ierr = DMLabelSetValue(cutLabel, cell, 2);CHKERRQ(ierr);}
616         }
617       }
618     }
619     /* Build x faces */
620     for (fz = 0; fz < numZEdges; ++fz) {
621       for (fy = 0; fy < numYEdges; ++fy) {
622         for (fx = 0; fx < numXVertices; ++fx) {
623           PetscInt face    = firstXFace + (fz*numYEdges+fy)*numXVertices + fx;
624           PetscInt edgeL   = firstZEdge + (  fy*                 numXVertices+fx)*numZEdges + fz;
625           PetscInt edgeR   = firstZEdge + (((fy+1)%numYVertices)*numXVertices+fx)*numZEdges + fz;
626           PetscInt edgeB   = firstYEdge + (  fz*                 numXVertices+fx)*numYEdges + fy;
627           PetscInt edgeT   = firstYEdge + (((fz+1)%numZVertices)*numXVertices+fx)*numYEdges + fy;
628           PetscInt ornt[4] = {0, 0, -2, -2};
629           PetscInt cone[4];
630 
631           if (dim == 3) {
632             /* markers */
633             if (bdX != DM_BOUNDARY_PERIODIC) {
634               if (fx == numXVertices-1) {
635                 ierr = DMSetLabelValue(dm, "Face Sets", face, faceMarkerRight);CHKERRQ(ierr);
636                 ierr = DMSetLabelValue(dm, "marker", face, markerRight);CHKERRQ(ierr);
637               }
638               else if (fx == 0) {
639                 ierr = DMSetLabelValue(dm, "Face Sets", face, faceMarkerLeft);CHKERRQ(ierr);
640                 ierr = DMSetLabelValue(dm, "marker", face, markerLeft);CHKERRQ(ierr);
641               }
642             }
643           }
644           cone[0] = edgeB; cone[1] = edgeR; cone[2] = edgeT; cone[3] = edgeL;
645           ierr    = DMPlexSetCone(dm, face, cone);CHKERRQ(ierr);
646           ierr    = DMPlexSetConeOrientation(dm, face, ornt);CHKERRQ(ierr);
647         }
648       }
649     }
650     /* Build y faces */
651     for (fz = 0; fz < numZEdges; ++fz) {
652       for (fx = 0; fx < numXEdges; ++fx) {
653         for (fy = 0; fy < numYVertices; ++fy) {
654           PetscInt face    = firstYFace + (fz*numXEdges+fx)*numYVertices + fy;
655           PetscInt edgeL   = firstZEdge + (fy*numXVertices+  fx                 )*numZEdges + fz;
656           PetscInt edgeR   = firstZEdge + (fy*numXVertices+((fx+1)%numXVertices))*numZEdges + fz;
657           PetscInt edgeB   = firstXEdge + (  fz                 *numYVertices+fy)*numXEdges + fx;
658           PetscInt edgeT   = firstXEdge + (((fz+1)%numZVertices)*numYVertices+fy)*numXEdges + fx;
659           PetscInt ornt[4] = {0, 0, -2, -2};
660           PetscInt cone[4];
661 
662           if (dim == 3) {
663             /* markers */
664             if (bdY != DM_BOUNDARY_PERIODIC) {
665               if (fy == numYVertices-1) {
666                 ierr = DMSetLabelValue(dm, "Face Sets", face, faceMarkerBack);CHKERRQ(ierr);
667                 ierr = DMSetLabelValue(dm, "marker", face, markerBack);CHKERRQ(ierr);
668               }
669               else if (fy == 0) {
670                 ierr = DMSetLabelValue(dm, "Face Sets", face, faceMarkerFront);CHKERRQ(ierr);
671                 ierr = DMSetLabelValue(dm, "marker", face, markerFront);CHKERRQ(ierr);
672               }
673             }
674           }
675           cone[0] = edgeB; cone[1] = edgeR; cone[2] = edgeT; cone[3] = edgeL;
676           ierr    = DMPlexSetCone(dm, face, cone);CHKERRQ(ierr);
677           ierr    = DMPlexSetConeOrientation(dm, face, ornt);CHKERRQ(ierr);
678         }
679       }
680     }
681     /* Build z faces */
682     for (fy = 0; fy < numYEdges; ++fy) {
683       for (fx = 0; fx < numXEdges; ++fx) {
684         for (fz = 0; fz < numZVertices; fz++) {
685           PetscInt face    = firstZFace + (fy*numXEdges+fx)*numZVertices + fz;
686           PetscInt edgeL   = firstYEdge + (fz*numXVertices+  fx                 )*numYEdges + fy;
687           PetscInt edgeR   = firstYEdge + (fz*numXVertices+((fx+1)%numXVertices))*numYEdges + fy;
688           PetscInt edgeB   = firstXEdge + (fz*numYVertices+  fy                 )*numXEdges + fx;
689           PetscInt edgeT   = firstXEdge + (fz*numYVertices+((fy+1)%numYVertices))*numXEdges + fx;
690           PetscInt ornt[4] = {0, 0, -2, -2};
691           PetscInt cone[4];
692 
693           if (dim == 2) {
694             if (bdX == DM_BOUNDARY_TWIST && fx == numXEdges-1) {edgeR += numYEdges-1-2*fy; ornt[1] = -2;}
695             if (bdY == DM_BOUNDARY_TWIST && fy == numYEdges-1) {edgeT += numXEdges-1-2*fx; ornt[2] =  0;}
696             if (bdX != DM_BOUNDARY_NONE && fx == numXEdges-1 && cutLabel) {ierr = DMLabelSetValue(cutLabel, face, 2);CHKERRQ(ierr);}
697             if (bdY != DM_BOUNDARY_NONE && fy == numYEdges-1 && cutLabel) {ierr = DMLabelSetValue(cutLabel, face, 2);CHKERRQ(ierr);}
698           } else {
699             /* markers */
700             if (bdZ != DM_BOUNDARY_PERIODIC) {
701               if (fz == numZVertices-1) {
702                 ierr = DMSetLabelValue(dm, "Face Sets", face, faceMarkerTop);CHKERRQ(ierr);
703                 ierr = DMSetLabelValue(dm, "marker", face, markerTop);CHKERRQ(ierr);
704               }
705               else if (fz == 0) {
706                 ierr = DMSetLabelValue(dm, "Face Sets", face, faceMarkerBottom);CHKERRQ(ierr);
707                 ierr = DMSetLabelValue(dm, "marker", face, markerBottom);CHKERRQ(ierr);
708               }
709             }
710           }
711           cone[0] = edgeB; cone[1] = edgeR; cone[2] = edgeT; cone[3] = edgeL;
712           ierr    = DMPlexSetCone(dm, face, cone);CHKERRQ(ierr);
713           ierr    = DMPlexSetConeOrientation(dm, face, ornt);CHKERRQ(ierr);
714         }
715       }
716     }
717     /* Build Z edges*/
718     for (vy = 0; vy < numYVertices; vy++) {
719       for (vx = 0; vx < numXVertices; vx++) {
720         for (ez = 0; ez < numZEdges; ez++) {
721           const PetscInt edge    = firstZEdge  + (vy*numXVertices+vx)*numZEdges + ez;
722           const PetscInt vertexB = firstVertex + (  ez                 *numYVertices+vy)*numXVertices + vx;
723           const PetscInt vertexT = firstVertex + (((ez+1)%numZVertices)*numYVertices+vy)*numXVertices + vx;
724           PetscInt       cone[2];
725 
726           if (dim == 3) {
727             if (bdX != DM_BOUNDARY_PERIODIC) {
728               if (vx == numXVertices-1) {
729                 ierr = DMSetLabelValue(dm, "marker", edge, markerRight);CHKERRQ(ierr);
730               }
731               else if (vx == 0) {
732                 ierr = DMSetLabelValue(dm, "marker", edge, markerLeft);CHKERRQ(ierr);
733               }
734             }
735             if (bdY != DM_BOUNDARY_PERIODIC) {
736               if (vy == numYVertices-1) {
737                 ierr = DMSetLabelValue(dm, "marker", edge, markerBack);CHKERRQ(ierr);
738               }
739               else if (vy == 0) {
740                 ierr = DMSetLabelValue(dm, "marker", edge, markerFront);CHKERRQ(ierr);
741               }
742             }
743           }
744           cone[0] = vertexB; cone[1] = vertexT;
745           ierr = DMPlexSetCone(dm, edge, cone);CHKERRQ(ierr);
746         }
747       }
748     }
749     /* Build Y edges*/
750     for (vz = 0; vz < numZVertices; vz++) {
751       for (vx = 0; vx < numXVertices; vx++) {
752         for (ey = 0; ey < numYEdges; ey++) {
753           const PetscInt nextv   = (dim == 2 && bdY == DM_BOUNDARY_TWIST && ey == numYEdges-1) ? (numXVertices-vx-1) : (vz*numYVertices+((ey+1)%numYVertices))*numXVertices + vx;
754           const PetscInt edge    = firstYEdge  + (vz*numXVertices+vx)*numYEdges + ey;
755           const PetscInt vertexF = firstVertex + (vz*numYVertices+ey)*numXVertices + vx;
756           const PetscInt vertexK = firstVertex + nextv;
757           PetscInt       cone[2];
758 
759           cone[0] = vertexF; cone[1] = vertexK;
760           ierr = DMPlexSetCone(dm, edge, cone);CHKERRQ(ierr);
761           if (dim == 2) {
762             if ((bdX != DM_BOUNDARY_PERIODIC) && (bdX != DM_BOUNDARY_TWIST)) {
763               if (vx == numXVertices-1) {
764                 ierr = DMSetLabelValue(dm, "Face Sets", edge, faceMarkerRight);CHKERRQ(ierr);
765                 ierr = DMSetLabelValue(dm, "marker", edge,    markerRight);CHKERRQ(ierr);
766                 ierr = DMSetLabelValue(dm, "marker", cone[0], markerRight);CHKERRQ(ierr);
767                 if (ey == numYEdges-1) {
768                   ierr = DMSetLabelValue(dm, "marker", cone[1], markerRight);CHKERRQ(ierr);
769                 }
770               } else if (vx == 0) {
771                 ierr = DMSetLabelValue(dm, "Face Sets", edge, faceMarkerLeft);CHKERRQ(ierr);
772                 ierr = DMSetLabelValue(dm, "marker", edge,    markerLeft);CHKERRQ(ierr);
773                 ierr = DMSetLabelValue(dm, "marker", cone[0], markerLeft);CHKERRQ(ierr);
774                 if (ey == numYEdges-1) {
775                   ierr = DMSetLabelValue(dm, "marker", cone[1], markerLeft);CHKERRQ(ierr);
776                 }
777               }
778             } else {
779               if (vx == 0 && cutMarker) {
780                 ierr = DMLabelSetValue(cutLabel, edge,    1);CHKERRQ(ierr);
781                 ierr = DMLabelSetValue(cutLabel, cone[0], 1);CHKERRQ(ierr);
782                 if (ey == numYEdges-1) {
783                   ierr = DMLabelSetValue(cutLabel, cone[1], 1);CHKERRQ(ierr);
784                 }
785               }
786             }
787           } else {
788             if (bdX != DM_BOUNDARY_PERIODIC) {
789               if (vx == numXVertices-1) {
790                 ierr = DMSetLabelValue(dm, "marker", edge, markerRight);CHKERRQ(ierr);
791               } else if (vx == 0) {
792                 ierr = DMSetLabelValue(dm, "marker", edge, markerLeft);CHKERRQ(ierr);
793               }
794             }
795             if (bdZ != DM_BOUNDARY_PERIODIC) {
796               if (vz == numZVertices-1) {
797                 ierr = DMSetLabelValue(dm, "marker", edge, markerTop);CHKERRQ(ierr);
798               } else if (vz == 0) {
799                 ierr = DMSetLabelValue(dm, "marker", edge, markerBottom);CHKERRQ(ierr);
800               }
801             }
802           }
803         }
804       }
805     }
806     /* Build X edges*/
807     for (vz = 0; vz < numZVertices; vz++) {
808       for (vy = 0; vy < numYVertices; vy++) {
809         for (ex = 0; ex < numXEdges; ex++) {
810           const PetscInt nextv   = (dim == 2 && bdX == DM_BOUNDARY_TWIST && ex == numXEdges-1) ? (numYVertices-vy-1)*numXVertices : (vz*numYVertices+vy)*numXVertices + (ex+1)%numXVertices;
811           const PetscInt edge    = firstXEdge  + (vz*numYVertices+vy)*numXEdges + ex;
812           const PetscInt vertexL = firstVertex + (vz*numYVertices+vy)*numXVertices + ex;
813           const PetscInt vertexR = firstVertex + nextv;
814           PetscInt       cone[2];
815 
816           cone[0] = vertexL; cone[1] = vertexR;
817           ierr = DMPlexSetCone(dm, edge, cone);CHKERRQ(ierr);
818           if (dim == 2) {
819             if ((bdY != DM_BOUNDARY_PERIODIC) && (bdY != DM_BOUNDARY_TWIST)) {
820               if (vy == numYVertices-1) {
821                 ierr = DMSetLabelValue(dm, "Face Sets", edge, faceMarkerTop);CHKERRQ(ierr);
822                 ierr = DMSetLabelValue(dm, "marker", edge,    markerTop);CHKERRQ(ierr);
823                 ierr = DMSetLabelValue(dm, "marker", cone[0], markerTop);CHKERRQ(ierr);
824                 if (ex == numXEdges-1) {
825                   ierr = DMSetLabelValue(dm, "marker", cone[1], markerTop);CHKERRQ(ierr);
826                 }
827               } else if (vy == 0) {
828                 ierr = DMSetLabelValue(dm, "Face Sets", edge, faceMarkerBottom);CHKERRQ(ierr);
829                 ierr = DMSetLabelValue(dm, "marker", edge,    markerBottom);CHKERRQ(ierr);
830                 ierr = DMSetLabelValue(dm, "marker", cone[0], markerBottom);CHKERRQ(ierr);
831                 if (ex == numXEdges-1) {
832                   ierr = DMSetLabelValue(dm, "marker", cone[1], markerBottom);CHKERRQ(ierr);
833                 }
834               }
835             } else {
836               if (vy == 0 && cutMarker) {
837                 ierr = DMLabelSetValue(cutLabel, edge,    1);CHKERRQ(ierr);
838                 ierr = DMLabelSetValue(cutLabel, cone[0], 1);CHKERRQ(ierr);
839                 if (ex == numXEdges-1) {
840                   ierr = DMLabelSetValue(cutLabel, cone[1], 1);CHKERRQ(ierr);
841                 }
842               }
843             }
844           } else {
845             if (bdY != DM_BOUNDARY_PERIODIC) {
846               if (vy == numYVertices-1) {
847                 ierr = DMSetLabelValue(dm, "marker", edge, markerBack);CHKERRQ(ierr);
848               }
849               else if (vy == 0) {
850                 ierr = DMSetLabelValue(dm, "marker", edge, markerFront);CHKERRQ(ierr);
851               }
852             }
853             if (bdZ != DM_BOUNDARY_PERIODIC) {
854               if (vz == numZVertices-1) {
855                 ierr = DMSetLabelValue(dm, "marker", edge, markerTop);CHKERRQ(ierr);
856               }
857               else if (vz == 0) {
858                 ierr = DMSetLabelValue(dm, "marker", edge, markerBottom);CHKERRQ(ierr);
859               }
860             }
861           }
862         }
863       }
864     }
865     ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
866     ierr = DMPlexStratify(dm);CHKERRQ(ierr);
867     /* Build coordinates */
868     ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
869     ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
870     ierr = PetscSectionSetFieldComponents(coordSection, 0, dim);CHKERRQ(ierr);
871     ierr = PetscSectionSetChart(coordSection, firstVertex, firstVertex+numVertices);CHKERRQ(ierr);
872     for (v = firstVertex; v < firstVertex+numVertices; ++v) {
873       ierr = PetscSectionSetDof(coordSection, v, dim);CHKERRQ(ierr);
874       ierr = PetscSectionSetFieldDof(coordSection, v, 0, dim);CHKERRQ(ierr);
875     }
876     ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
877     ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
878     ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
879     ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
880     ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
881     ierr = VecSetBlockSize(coordinates, dim);CHKERRQ(ierr);
882     ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
883     ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
884     for (vz = 0; vz < numZVertices; ++vz) {
885       for (vy = 0; vy < numYVertices; ++vy) {
886         for (vx = 0; vx < numXVertices; ++vx) {
887           coords[((vz*numYVertices+vy)*numXVertices+vx)*dim+0] = lower[0] + ((upper[0] - lower[0])/numXEdges)*vx;
888           coords[((vz*numYVertices+vy)*numXVertices+vx)*dim+1] = lower[1] + ((upper[1] - lower[1])/numYEdges)*vy;
889           if (dim == 3) {
890             coords[((vz*numYVertices+vy)*numXVertices+vx)*dim+2] = lower[2] + ((upper[2] - lower[2])/numZEdges)*vz;
891           }
892         }
893       }
894     }
895     ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
896     ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
897     ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
898   }
899   PetscFunctionReturn(0);
900 }
901 
902 /*@
903   DMPlexCreateHexBoxMesh - Creates a mesh on the tensor product of unit intervals (box) using hexahedra.
904 
905   Collective on MPI_Comm
906 
907   Input Parameters:
908 + comm  - The communicator for the DM object
909 . dim   - The spatial dimension
910 . periodicX - The boundary type for the X direction
911 . periodicY - The boundary type for the Y direction
912 . periodicZ - The boundary type for the Z direction
913 - cells - The number of cells in each direction
914 
915   Output Parameter:
916 . dm  - The DM object
917 
918   Note: Here is the numbering returned for 2 cells in each direction:
919 $ 22--8-23--9--24
920 $  |     |     |
921 $ 13  2 14  3  15
922 $  |     |     |
923 $ 19--6-20--7--21
924 $  |     |     |
925 $ 10  0 11  1 12
926 $  |     |     |
927 $ 16--4-17--5--18
928 
929   Level: beginner
930 
931 .keywords: DM, create
932 .seealso: DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
933 @*/
934 PetscErrorCode DMPlexCreateHexBoxMesh(MPI_Comm comm, PetscInt dim, const PetscInt cells[], DMBoundaryType periodicX, DMBoundaryType periodicY, DMBoundaryType periodicZ, DM *dm)
935 {
936   PetscInt       i;
937   PetscErrorCode ierr;
938 
939   PetscFunctionBegin;
940   PetscValidPointer(dm, 7);
941   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
942   PetscValidLogicalCollectiveInt(*dm,dim,2);
943   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
944   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
945   switch (dim) {
946   case 2:
947   {
948     PetscReal lower[3] = {0.0, 0.0, 0.0};
949     PetscReal upper[3] = {1.0, 1.0, 0.0};
950     PetscInt  edges[3];
951 
952     edges[0] = cells[0];
953     edges[1] = cells[1];
954     edges[2] = 0;
955 
956     ierr = DMPlexCreateCubeMesh_Internal(*dm, lower, upper, edges, periodicX, periodicY, DM_BOUNDARY_NONE);CHKERRQ(ierr);
957     if (periodicX == DM_BOUNDARY_PERIODIC || periodicX == DM_BOUNDARY_TWIST ||
958         periodicY == DM_BOUNDARY_PERIODIC || periodicY == DM_BOUNDARY_TWIST) {
959       PetscReal      L[2];
960       PetscReal      maxCell[2];
961       DMBoundaryType bdType[2];
962 
963       bdType[0] = periodicX;
964       bdType[1] = periodicY;
965       for (i = 0; i < dim; i++) {
966         L[i]       = upper[i] - lower[i];
967         maxCell[i] = 1.1 * (L[i] / PetscMax(1,cells[i]));
968       }
969 
970       ierr = DMSetPeriodicity(*dm,maxCell,L,bdType);CHKERRQ(ierr);
971     }
972     break;
973   }
974   case 3:
975   {
976     PetscReal lower[3] = {0.0, 0.0, 0.0};
977     PetscReal upper[3] = {1.0, 1.0, 1.0};
978 
979     ierr = DMPlexCreateCubeMesh_Internal(*dm, lower, upper, cells, periodicX, periodicY, periodicZ);CHKERRQ(ierr);
980     if (periodicX == DM_BOUNDARY_PERIODIC || periodicX == DM_BOUNDARY_TWIST ||
981         periodicY == DM_BOUNDARY_PERIODIC || periodicY == DM_BOUNDARY_TWIST ||
982         periodicZ == DM_BOUNDARY_PERIODIC || periodicZ == DM_BOUNDARY_TWIST) {
983       PetscReal      L[3];
984       PetscReal      maxCell[3];
985       DMBoundaryType bdType[3];
986 
987       bdType[0] = periodicX;
988       bdType[1] = periodicY;
989       bdType[2] = periodicZ;
990       for (i = 0; i < dim; i++) {
991         L[i]       = upper[i] - lower[i];
992         maxCell[i] = 1.1 * (L[i] / cells[i]);
993       }
994 
995       ierr = DMSetPeriodicity(*dm,maxCell,L,bdType);CHKERRQ(ierr);
996     }
997     break;
998   }
999   default:
1000     SETERRQ1(comm, PETSC_ERR_SUP, "Dimension not supported: %d", dim);
1001   }
1002   PetscFunctionReturn(0);
1003 }
1004 
1005 /*@C
1006   DMPlexSetOptionsPrefix - Sets the prefix used for searching for all DM options in the database.
1007 
1008   Logically Collective on DM
1009 
1010   Input Parameters:
1011 + dm - the DM context
1012 - prefix - the prefix to prepend to all option names
1013 
1014   Notes:
1015   A hyphen (-) must NOT be given at the beginning of the prefix name.
1016   The first character of all runtime options is AUTOMATICALLY the hyphen.
1017 
1018   Level: advanced
1019 
1020 .seealso: SNESSetFromOptions()
1021 @*/
1022 PetscErrorCode DMPlexSetOptionsPrefix(DM dm, const char prefix[])
1023 {
1024   DM_Plex       *mesh = (DM_Plex *) dm->data;
1025   PetscErrorCode ierr;
1026 
1027   PetscFunctionBegin;
1028   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1029   ierr = PetscObjectSetOptionsPrefix((PetscObject) dm, prefix);CHKERRQ(ierr);
1030   ierr = PetscObjectSetOptionsPrefix((PetscObject) mesh->partitioner, prefix);CHKERRQ(ierr);
1031   PetscFunctionReturn(0);
1032 }
1033 
1034 /*@
1035   DMPlexCreateHexCylinderMesh - Creates a mesh on the tensor product of the unit interval with the circle (cylinder) using hexahedra.
1036 
1037   Collective on MPI_Comm
1038 
1039   Input Parameters:
1040 + comm      - The communicator for the DM object
1041 . numRefine - The number of regular refinements to the basic 5 cell structure
1042 - periodicZ - The boundary type for the Z direction
1043 
1044   Output Parameter:
1045 . dm  - The DM object
1046 
1047   Note: Here is the output numbering looking from the bottom of the cylinder:
1048 $       17-----14
1049 $        |     |
1050 $        |  2  |
1051 $        |     |
1052 $ 17-----8-----7-----14
1053 $  |     |     |     |
1054 $  |  3  |  0  |  1  |
1055 $  |     |     |     |
1056 $ 19-----5-----6-----13
1057 $        |     |
1058 $        |  4  |
1059 $        |     |
1060 $       19-----13
1061 $
1062 $ and up through the top
1063 $
1064 $       18-----16
1065 $        |     |
1066 $        |  2  |
1067 $        |     |
1068 $ 18----10----11-----16
1069 $  |     |     |     |
1070 $  |  3  |  0  |  1  |
1071 $  |     |     |     |
1072 $ 20-----9----12-----15
1073 $        |     |
1074 $        |  4  |
1075 $        |     |
1076 $       20-----15
1077 
1078   Level: beginner
1079 
1080 .keywords: DM, create
1081 .seealso: DMPlexCreateHexBoxMesh(), DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
1082 @*/
1083 PetscErrorCode DMPlexCreateHexCylinderMesh(MPI_Comm comm, PetscInt numRefine, DMBoundaryType periodicZ, DM *dm)
1084 {
1085   const PetscInt dim = 3;
1086   PetscInt       numCells, numVertices, r;
1087   PetscErrorCode ierr;
1088 
1089   PetscFunctionBegin;
1090   PetscValidPointer(dm, 4);
1091   if (numRefine < 0) SETERRQ1(comm, PETSC_ERR_ARG_OUTOFRANGE, "Number of refinements %D cannot be negative", numRefine);
1092   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
1093   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
1094   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
1095   /* Create topology */
1096   {
1097     PetscInt cone[8], c;
1098 
1099     numCells    = 5;
1100     numVertices = 16;
1101     if (periodicZ == DM_BOUNDARY_PERIODIC) {
1102       numCells   *= 3;
1103       numVertices = 24;
1104     }
1105     ierr = DMPlexSetChart(*dm, 0, numCells+numVertices);CHKERRQ(ierr);
1106     for (c = 0; c < numCells; c++) {ierr = DMPlexSetConeSize(*dm, c, 8);CHKERRQ(ierr);}
1107     ierr = DMSetUp(*dm);CHKERRQ(ierr);
1108     if (periodicZ == DM_BOUNDARY_PERIODIC) {
1109       cone[0] = 15; cone[1] = 18; cone[2] = 17; cone[3] = 16;
1110       cone[4] = 31; cone[5] = 32; cone[6] = 33; cone[7] = 34;
1111       ierr = DMPlexSetCone(*dm, 0, cone);CHKERRQ(ierr);
1112       cone[0] = 16; cone[1] = 17; cone[2] = 24; cone[3] = 23;
1113       cone[4] = 32; cone[5] = 36; cone[6] = 37; cone[7] = 33; /* 22 25 26 21 */
1114       ierr = DMPlexSetCone(*dm, 1, cone);CHKERRQ(ierr);
1115       cone[0] = 18; cone[1] = 27; cone[2] = 24; cone[3] = 17;
1116       cone[4] = 34; cone[5] = 33; cone[6] = 37; cone[7] = 38;
1117       ierr = DMPlexSetCone(*dm, 2, cone);CHKERRQ(ierr);
1118       cone[0] = 29; cone[1] = 27; cone[2] = 18; cone[3] = 15;
1119       cone[4] = 35; cone[5] = 31; cone[6] = 34; cone[7] = 38;
1120       ierr = DMPlexSetCone(*dm, 3, cone);CHKERRQ(ierr);
1121       cone[0] = 29; cone[1] = 15; cone[2] = 16; cone[3] = 23;
1122       cone[4] = 35; cone[5] = 36; cone[6] = 32; cone[7] = 31;
1123       ierr = DMPlexSetCone(*dm, 4, cone);CHKERRQ(ierr);
1124 
1125       cone[0] = 31; cone[1] = 34; cone[2] = 33; cone[3] = 32;
1126       cone[4] = 19; cone[5] = 22; cone[6] = 21; cone[7] = 20;
1127       ierr = DMPlexSetCone(*dm, 5, cone);CHKERRQ(ierr);
1128       cone[0] = 32; cone[1] = 33; cone[2] = 37; cone[3] = 36;
1129       cone[4] = 22; cone[5] = 25; cone[6] = 26; cone[7] = 21;
1130       ierr = DMPlexSetCone(*dm, 6, cone);CHKERRQ(ierr);
1131       cone[0] = 34; cone[1] = 38; cone[2] = 37; cone[3] = 33;
1132       cone[4] = 20; cone[5] = 21; cone[6] = 26; cone[7] = 28;
1133       ierr = DMPlexSetCone(*dm, 7, cone);CHKERRQ(ierr);
1134       cone[0] = 35; cone[1] = 38; cone[2] = 34; cone[3] = 31;
1135       cone[4] = 30; cone[5] = 19; cone[6] = 20; cone[7] = 28;
1136       ierr = DMPlexSetCone(*dm, 8, cone);CHKERRQ(ierr);
1137       cone[0] = 35; cone[1] = 31; cone[2] = 32; cone[3] = 36;
1138       cone[4] = 30; cone[5] = 25; cone[6] = 22; cone[7] = 19;
1139       ierr = DMPlexSetCone(*dm, 9, cone);CHKERRQ(ierr);
1140 
1141       cone[0] = 19; cone[1] = 20; cone[2] = 21; cone[3] = 22;
1142       cone[4] = 15; cone[5] = 16; cone[6] = 17; cone[7] = 18;
1143       ierr = DMPlexSetCone(*dm, 10, cone);CHKERRQ(ierr);
1144       cone[0] = 22; cone[1] = 21; cone[2] = 26; cone[3] = 25;
1145       cone[4] = 16; cone[5] = 23; cone[6] = 24; cone[7] = 17;
1146       ierr = DMPlexSetCone(*dm, 11, cone);CHKERRQ(ierr);
1147       cone[0] = 20; cone[1] = 28; cone[2] = 26; cone[3] = 21;
1148       cone[4] = 18; cone[5] = 17; cone[6] = 24; cone[7] = 27;
1149       ierr = DMPlexSetCone(*dm, 12, cone);CHKERRQ(ierr);
1150       cone[0] = 30; cone[1] = 28; cone[2] = 20; cone[3] = 19;
1151       cone[4] = 29; cone[5] = 15; cone[6] = 18; cone[7] = 27;
1152       ierr = DMPlexSetCone(*dm, 13, cone);CHKERRQ(ierr);
1153       cone[0] = 30; cone[1] = 19; cone[2] = 22; cone[3] = 25;
1154       cone[4] = 29; cone[5] = 23; cone[6] = 16; cone[7] = 15;
1155       ierr = DMPlexSetCone(*dm, 14, cone);CHKERRQ(ierr);
1156     } else {
1157       cone[0] =  5; cone[1] =  8; cone[2] =  7; cone[3] =  6;
1158       cone[4] =  9; cone[5] = 12; cone[6] = 11; cone[7] = 10;
1159       ierr = DMPlexSetCone(*dm, 0, cone);CHKERRQ(ierr);
1160       cone[0] =  6; cone[1] =  7; cone[2] = 14; cone[3] = 13;
1161       cone[4] = 12; cone[5] = 15; cone[6] = 16; cone[7] = 11;
1162       ierr = DMPlexSetCone(*dm, 1, cone);CHKERRQ(ierr);
1163       cone[0] =  8; cone[1] = 17; cone[2] = 14; cone[3] =  7;
1164       cone[4] = 10; cone[5] = 11; cone[6] = 16; cone[7] = 18;
1165       ierr = DMPlexSetCone(*dm, 2, cone);CHKERRQ(ierr);
1166       cone[0] = 19; cone[1] = 17; cone[2] =  8; cone[3] =  5;
1167       cone[4] = 20; cone[5] =  9; cone[6] = 10; cone[7] = 18;
1168       ierr = DMPlexSetCone(*dm, 3, cone);CHKERRQ(ierr);
1169       cone[0] = 19; cone[1] =  5; cone[2] =  6; cone[3] = 13;
1170       cone[4] = 20; cone[5] = 15; cone[6] = 12; cone[7] =  9;
1171       ierr = DMPlexSetCone(*dm, 4, cone);CHKERRQ(ierr);
1172     }
1173     ierr = DMPlexSymmetrize(*dm);CHKERRQ(ierr);
1174     ierr = DMPlexStratify(*dm);CHKERRQ(ierr);
1175   }
1176   /* Interpolate */
1177   {
1178     DM idm = NULL;
1179 
1180     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
1181     ierr = DMDestroy(dm);CHKERRQ(ierr);
1182     *dm  = idm;
1183   }
1184   /* Create cube geometry */
1185   {
1186     Vec             coordinates;
1187     PetscSection    coordSection;
1188     PetscScalar    *coords;
1189     PetscInt        coordSize, v;
1190     const PetscReal dis = 1.0/PetscSqrtReal(2.0);
1191     const PetscReal ds2 = dis/2.0;
1192 
1193     /* Build coordinates */
1194     ierr = DMGetCoordinateSection(*dm, &coordSection);CHKERRQ(ierr);
1195     ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
1196     ierr = PetscSectionSetFieldComponents(coordSection, 0, dim);CHKERRQ(ierr);
1197     ierr = PetscSectionSetChart(coordSection, numCells, numCells+numVertices);CHKERRQ(ierr);
1198     for (v = numCells; v < numCells+numVertices; ++v) {
1199       ierr = PetscSectionSetDof(coordSection, v, dim);CHKERRQ(ierr);
1200       ierr = PetscSectionSetFieldDof(coordSection, v, 0, dim);CHKERRQ(ierr);
1201     }
1202     ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
1203     ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
1204     ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
1205     ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
1206     ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
1207     ierr = VecSetBlockSize(coordinates, dim);CHKERRQ(ierr);
1208     ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
1209     ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
1210     coords[0*dim+0] = -ds2; coords[0*dim+1] = -ds2; coords[0*dim+2] = 0.0;
1211     coords[1*dim+0] =  ds2; coords[1*dim+1] = -ds2; coords[1*dim+2] = 0.0;
1212     coords[2*dim+0] =  ds2; coords[2*dim+1] =  ds2; coords[2*dim+2] = 0.0;
1213     coords[3*dim+0] = -ds2; coords[3*dim+1] =  ds2; coords[3*dim+2] = 0.0;
1214     coords[4*dim+0] = -ds2; coords[4*dim+1] = -ds2; coords[4*dim+2] = 1.0;
1215     coords[5*dim+0] = -ds2; coords[5*dim+1] =  ds2; coords[5*dim+2] = 1.0;
1216     coords[6*dim+0] =  ds2; coords[6*dim+1] =  ds2; coords[6*dim+2] = 1.0;
1217     coords[7*dim+0] =  ds2; coords[7*dim+1] = -ds2; coords[7*dim+2] = 1.0;
1218     coords[ 8*dim+0] =  dis; coords[ 8*dim+1] = -dis; coords[ 8*dim+2] = 0.0;
1219     coords[ 9*dim+0] =  dis; coords[ 9*dim+1] =  dis; coords[ 9*dim+2] = 0.0;
1220     coords[10*dim+0] =  dis; coords[10*dim+1] = -dis; coords[10*dim+2] = 1.0;
1221     coords[11*dim+0] =  dis; coords[11*dim+1] =  dis; coords[11*dim+2] = 1.0;
1222     coords[12*dim+0] = -dis; coords[12*dim+1] =  dis; coords[12*dim+2] = 0.0;
1223     coords[13*dim+0] = -dis; coords[13*dim+1] =  dis; coords[13*dim+2] = 1.0;
1224     coords[14*dim+0] = -dis; coords[14*dim+1] = -dis; coords[14*dim+2] = 0.0;
1225     coords[15*dim+0] = -dis; coords[15*dim+1] = -dis; coords[15*dim+2] = 1.0;
1226     if (periodicZ == DM_BOUNDARY_PERIODIC) {
1227       /* 15 31 19 */ coords[16*dim+0] = -ds2; coords[16*dim+1] = -ds2; coords[16*dim+2] = 0.5;
1228       /* 16 32 22 */ coords[17*dim+0] =  ds2; coords[17*dim+1] = -ds2; coords[17*dim+2] = 0.5;
1229       /* 17 33 21 */ coords[18*dim+0] =  ds2; coords[18*dim+1] =  ds2; coords[18*dim+2] = 0.5;
1230       /* 18 34 20 */ coords[19*dim+0] = -ds2; coords[19*dim+1] =  ds2; coords[19*dim+2] = 0.5;
1231       /* 29 35 30 */ coords[20*dim+0] = -dis; coords[20*dim+1] = -dis; coords[20*dim+2] = 0.5;
1232       /* 23 36 25 */ coords[21*dim+0] =  dis; coords[21*dim+1] = -dis; coords[21*dim+2] = 0.5;
1233       /* 24 37 26 */ coords[22*dim+0] =  dis; coords[22*dim+1] =  dis; coords[22*dim+2] = 0.5;
1234       /* 27 38 28 */ coords[23*dim+0] = -dis; coords[23*dim+1] =  dis; coords[23*dim+2] = 0.5;
1235     }
1236     ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
1237     ierr = DMSetCoordinatesLocal(*dm, coordinates);CHKERRQ(ierr);
1238     ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
1239   }
1240   /* Create periodicity */
1241   if (periodicZ == DM_BOUNDARY_PERIODIC || periodicZ == DM_BOUNDARY_TWIST) {
1242     PetscReal      L[3];
1243     PetscReal      maxCell[3];
1244     DMBoundaryType bdType[3];
1245     PetscReal      lower[3] = {0.0, 0.0, 0.0};
1246     PetscReal      upper[3] = {1.0, 1.0, 1.5};
1247     PetscInt       i, numZCells = 3;
1248 
1249     bdType[0] = DM_BOUNDARY_NONE;
1250     bdType[1] = DM_BOUNDARY_NONE;
1251     bdType[2] = periodicZ;
1252     for (i = 0; i < dim; i++) {
1253       L[i]       = upper[i] - lower[i];
1254       maxCell[i] = 1.1 * (L[i] / numZCells);
1255     }
1256     ierr = DMSetPeriodicity(*dm, maxCell, L, bdType);CHKERRQ(ierr);
1257   }
1258   /* Refine topology */
1259   for (r = 0; r < numRefine; ++r) {
1260     DM rdm = NULL;
1261 
1262     ierr = DMRefine(*dm, comm, &rdm);CHKERRQ(ierr);
1263     ierr = DMDestroy(dm);CHKERRQ(ierr);
1264     *dm  = rdm;
1265   }
1266   /* Remap geometry to cylinder
1267        Interior square: Linear interpolation is correct
1268        The other cells all have vertices on rays from the origin. We want to uniformly expand the spacing
1269        such that the last vertex is on the unit circle. So the closest and farthest vertices are at distance
1270 
1271          phi     = arctan(y/x)
1272          d_close = sqrt(1/8 + 1/4 sin^2(phi))
1273          d_far   = sqrt(1/2 + sin^2(phi))
1274 
1275        so we remap them using
1276 
1277          x_new = x_close + (x - x_close) (1 - d_close) / (d_far - d_close)
1278          y_new = y_close + (y - y_close) (1 - d_close) / (d_far - d_close)
1279 
1280        If pi/4 < phi < 3pi/4 or -3pi/4 < phi < -pi/4, then we switch x and y.
1281   */
1282   {
1283     Vec           coordinates;
1284     PetscSection  coordSection;
1285     PetscScalar  *coords;
1286     PetscInt      vStart, vEnd, v;
1287     const PetscReal dis = 1.0/PetscSqrtReal(2.0);
1288     const PetscReal ds2 = 0.5*dis;
1289 
1290     ierr = DMPlexGetDepthStratum(*dm, 0, &vStart, &vEnd);CHKERRQ(ierr);
1291     ierr = DMGetCoordinateSection(*dm, &coordSection);CHKERRQ(ierr);
1292     ierr = DMGetCoordinatesLocal(*dm, &coordinates);CHKERRQ(ierr);
1293     ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
1294     for (v = vStart; v < vEnd; ++v) {
1295       PetscReal phi, sinp, cosp, dc, df, x, y, xc, yc;
1296       PetscInt  off;
1297 
1298       ierr = PetscSectionGetOffset(coordSection, v, &off);CHKERRQ(ierr);
1299       if ((PetscAbsScalar(coords[off+0]) <= ds2) && (PetscAbsScalar(coords[off+1]) <= ds2)) continue;
1300       x    = PetscRealPart(coords[off]);
1301       y    = PetscRealPart(coords[off+1]);
1302       phi  = PetscAtan2Real(y, x);
1303       sinp = PetscSinReal(phi);
1304       cosp = PetscCosReal(phi);
1305       if ((PetscAbsReal(phi) > PETSC_PI/4.0) && (PetscAbsReal(phi) < 3.0*PETSC_PI/4.0)) {
1306         dc = PetscAbsReal(ds2/sinp);
1307         df = PetscAbsReal(dis/sinp);
1308         xc = ds2*x/PetscAbsScalar(y);
1309         yc = ds2*PetscSignReal(y);
1310       } else {
1311         dc = PetscAbsReal(ds2/cosp);
1312         df = PetscAbsReal(dis/cosp);
1313         xc = ds2*PetscSignReal(x);
1314         yc = ds2*y/PetscAbsScalar(x);
1315       }
1316       coords[off+0] = xc + (coords[off+0] - xc)*(1.0 - dc)/(df - dc);
1317       coords[off+1] = yc + (coords[off+1] - yc)*(1.0 - dc)/(df - dc);
1318     }
1319     ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
1320     if (periodicZ == DM_BOUNDARY_PERIODIC || periodicZ == DM_BOUNDARY_TWIST) {
1321       ierr = DMLocalizeCoordinates(*dm);CHKERRQ(ierr);
1322     }
1323   }
1324   PetscFunctionReturn(0);
1325 }
1326 
1327 PETSC_STATIC_INLINE PetscReal DiffNormReal(PetscInt dim, const PetscReal x[], const PetscReal y[])
1328 {
1329   PetscReal prod = 0.0;
1330   PetscInt  i;
1331   for (i = 0; i < dim; ++i) prod += PetscSqr(x[i] - y[i]);
1332   return PetscSqrtReal(prod);
1333 }
1334 PETSC_STATIC_INLINE PetscReal DotReal(PetscInt dim, const PetscReal x[], const PetscReal y[])
1335 {
1336   PetscReal prod = 0.0;
1337   PetscInt  i;
1338   for (i = 0; i < dim; ++i) prod += x[i]*y[i];
1339   return prod;
1340 }
1341 
1342 #undef __FUNCT__
1343 #define __FUNCT__ "DMPlexCreateSphereMesh"
1344 /*@
1345   DMPlexCreateSphereMesh - Creates a mesh on the d-dimensional sphere, S^d.
1346 
1347   Collective on MPI_Comm
1348 
1349   Input Parameters:
1350 . comm  - The communicator for the DM object
1351 . dim   - The dimension
1352 - simplex - Use simplices, or tensor product cells
1353 
1354   Output Parameter:
1355 . dm  - The DM object
1356 
1357   Level: beginner
1358 
1359 .keywords: DM, create
1360 .seealso: DMPlexCreateBoxMesh(), DMPlexCreateHexBoxMesh(), DMSetType(), DMCreate()
1361 @*/
1362 PetscErrorCode DMPlexCreateSphereMesh(MPI_Comm comm, PetscInt dim, PetscBool simplex, DM *dm)
1363 {
1364   const PetscInt  embedDim = dim+1;
1365   PetscSection    coordSection;
1366   Vec             coordinates;
1367   PetscScalar    *coords;
1368   PetscReal      *coordsIn;
1369   PetscInt        numCells, numEdges, numVerts, firstVertex, v, firstEdge, coordSize, d, c, e;
1370   PetscMPIInt     rank;
1371   PetscErrorCode  ierr;
1372 
1373   PetscFunctionBegin;
1374   PetscValidPointer(dm, 4);
1375   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
1376   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
1377   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
1378   ierr = DMSetCoordinateDim(*dm, dim+1);CHKERRQ(ierr);
1379   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject) *dm), &rank);CHKERRQ(ierr);
1380   switch (dim) {
1381   case 2:
1382     if (simplex) {
1383       DM              idm         = NULL;
1384       const PetscReal edgeLen     = 2.0/(1.0 + PETSC_PHI);
1385       const PetscReal vertex[3]   = {0.0, 1.0/(1.0 + PETSC_PHI), PETSC_PHI/(1.0 + PETSC_PHI)};
1386       const PetscInt  degree      = 5;
1387       PetscInt        s[3]        = {1, 1, 1};
1388       PetscInt        cone[3];
1389       PetscInt       *graph, p, i, j, k;
1390 
1391       numCells    = !rank ? 20 : 0;
1392       numEdges    = !rank ? 30 : 0;
1393       numVerts    = !rank ? 12 : 0;
1394       firstVertex = numCells;
1395       firstEdge   = numCells + numVerts;
1396       /* Use icosahedron, which for a unit sphere has coordinates which are all cyclic permutations of
1397 
1398            (0, \pm 1/\phi+1, \pm \phi/\phi+1)
1399 
1400          where \phi^2 - \phi - 1 = 0, meaning \phi is the golden ratio \frac{1 + \sqrt{5}}{2}. The edge
1401          length is then given by 2/\phi = 2 * 2.73606 = 5.47214.
1402        */
1403       /* Construct vertices */
1404       ierr = PetscCalloc1(numVerts * embedDim, &coordsIn);CHKERRQ(ierr);
1405       for (p = 0, i = 0; p < embedDim; ++p) {
1406         for (s[1] = -1; s[1] < 2; s[1] += 2) {
1407           for (s[2] = -1; s[2] < 2; s[2] += 2) {
1408             for (d = 0; d < embedDim; ++d) coordsIn[i*embedDim+d] = s[(d+p)%embedDim]*vertex[(d+p)%embedDim];
1409             ++i;
1410           }
1411         }
1412       }
1413       /* Construct graph */
1414       ierr = PetscCalloc1(numVerts * numVerts, &graph);CHKERRQ(ierr);
1415       for (i = 0; i < numVerts; ++i) {
1416         for (j = 0, k = 0; j < numVerts; ++j) {
1417           if (PetscAbsReal(DiffNormReal(embedDim, &coordsIn[i*embedDim], &coordsIn[j*embedDim]) - edgeLen) < PETSC_SMALL) {graph[i*numVerts+j] = 1; ++k;}
1418         }
1419         if (k != degree) SETERRQ3(comm, PETSC_ERR_PLIB, "Invalid icosahedron, vertex %D degree %D != %D", i, k, degree);
1420       }
1421       /* Build Topology */
1422       ierr = DMPlexSetChart(*dm, 0, numCells+numVerts);CHKERRQ(ierr);
1423       for (c = 0; c < numCells; c++) {
1424         ierr = DMPlexSetConeSize(*dm, c, embedDim);CHKERRQ(ierr);
1425       }
1426       ierr = DMSetUp(*dm);CHKERRQ(ierr); /* Allocate space for cones */
1427       /* Cells */
1428       for (i = 0, c = 0; i < numVerts; ++i) {
1429         for (j = 0; j < i; ++j) {
1430           for (k = 0; k < j; ++k) {
1431             if (graph[i*numVerts+j] && graph[j*numVerts+k] && graph[k*numVerts+i]) {
1432               cone[0] = firstVertex+i; cone[1] = firstVertex+j; cone[2] = firstVertex+k;
1433               /* Check orientation */
1434               {
1435                 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}}};
1436                 PetscReal normal[3];
1437                 PetscInt  e, f;
1438 
1439                 for (d = 0; d < embedDim; ++d) {
1440                   normal[d] = 0.0;
1441                   for (e = 0; e < embedDim; ++e) {
1442                     for (f = 0; f < embedDim; ++f) {
1443                       normal[d] += epsilon[d][e][f]*(coordsIn[j*embedDim+e] - coordsIn[i*embedDim+e])*(coordsIn[k*embedDim+f] - coordsIn[i*embedDim+f]);
1444                     }
1445                   }
1446                 }
1447                 if (DotReal(embedDim, normal, &coordsIn[i*embedDim]) < 0) {PetscInt tmp = cone[1]; cone[1] = cone[2]; cone[2] = tmp;}
1448               }
1449               ierr = DMPlexSetCone(*dm, c++, cone);CHKERRQ(ierr);
1450             }
1451           }
1452         }
1453       }
1454       ierr = DMPlexSymmetrize(*dm);CHKERRQ(ierr);
1455       ierr = DMPlexStratify(*dm);CHKERRQ(ierr);
1456       ierr = PetscFree(graph);CHKERRQ(ierr);
1457       /* Interpolate mesh */
1458       ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
1459       ierr = DMDestroy(dm);CHKERRQ(ierr);
1460       *dm  = idm;
1461     } else {
1462       /*
1463         12-21--13
1464          |     |
1465         25  4  24
1466          |     |
1467   12-25--9-16--8-24--13
1468    |     |     |     |
1469   23  5 17  0 15  3  22
1470    |     |     |     |
1471   10-20--6-14--7-19--11
1472          |     |
1473         20  1  19
1474          |     |
1475         10-18--11
1476          |     |
1477         23  2  22
1478          |     |
1479         12-21--13
1480        */
1481       const PetscReal dist = 1.0/PetscSqrtReal(3.0);
1482       PetscInt        cone[4], ornt[4];
1483 
1484       numCells    = !rank ?  6 : 0;
1485       numEdges    = !rank ? 12 : 0;
1486       numVerts    = !rank ?  8 : 0;
1487       firstVertex = numCells;
1488       firstEdge   = numCells + numVerts;
1489       /* Build Topology */
1490       ierr = DMPlexSetChart(*dm, 0, numCells+numEdges+numVerts);CHKERRQ(ierr);
1491       for (c = 0; c < numCells; c++) {
1492         ierr = DMPlexSetConeSize(*dm, c, 4);CHKERRQ(ierr);
1493       }
1494       for (e = firstEdge; e < firstEdge+numEdges; ++e) {
1495         ierr = DMPlexSetConeSize(*dm, e, 2);CHKERRQ(ierr);
1496       }
1497       ierr = DMSetUp(*dm);CHKERRQ(ierr); /* Allocate space for cones */
1498       /* Cell 0 */
1499       cone[0] = 14; cone[1] = 15; cone[2] = 16; cone[3] = 17;
1500       ierr = DMPlexSetCone(*dm, 0, cone);CHKERRQ(ierr);
1501       ornt[0] = 0; ornt[1] = 0; ornt[2] = 0; ornt[3] = 0;
1502       ierr = DMPlexSetConeOrientation(*dm, 0, ornt);CHKERRQ(ierr);
1503       /* Cell 1 */
1504       cone[0] = 18; cone[1] = 19; cone[2] = 14; cone[3] = 20;
1505       ierr = DMPlexSetCone(*dm, 1, cone);CHKERRQ(ierr);
1506       ornt[0] = 0; ornt[1] = 0; ornt[2] = -2; ornt[3] = 0;
1507       ierr = DMPlexSetConeOrientation(*dm, 1, ornt);CHKERRQ(ierr);
1508       /* Cell 2 */
1509       cone[0] = 21; cone[1] = 22; cone[2] = 18; cone[3] = 23;
1510       ierr = DMPlexSetCone(*dm, 2, cone);CHKERRQ(ierr);
1511       ornt[0] = 0; ornt[1] = 0; ornt[2] = -2; ornt[3] = 0;
1512       ierr = DMPlexSetConeOrientation(*dm, 2, ornt);CHKERRQ(ierr);
1513       /* Cell 3 */
1514       cone[0] = 19; cone[1] = 22; cone[2] = 24; cone[3] = 15;
1515       ierr = DMPlexSetCone(*dm, 3, cone);CHKERRQ(ierr);
1516       ornt[0] = -2; ornt[1] = -2; ornt[2] = 0; ornt[3] = -2;
1517       ierr = DMPlexSetConeOrientation(*dm, 3, ornt);CHKERRQ(ierr);
1518       /* Cell 4 */
1519       cone[0] = 16; cone[1] = 24; cone[2] = 21; cone[3] = 25;
1520       ierr = DMPlexSetCone(*dm, 4, cone);CHKERRQ(ierr);
1521       ornt[0] = -2; ornt[1] = -2; ornt[2] = -2; ornt[3] = 0;
1522       ierr = DMPlexSetConeOrientation(*dm, 4, ornt);CHKERRQ(ierr);
1523       /* Cell 5 */
1524       cone[0] = 20; cone[1] = 17; cone[2] = 25; cone[3] = 23;
1525       ierr = DMPlexSetCone(*dm, 5, cone);CHKERRQ(ierr);
1526       ornt[0] = -2; ornt[1] = -2; ornt[2] = -2; ornt[3] = -2;
1527       ierr = DMPlexSetConeOrientation(*dm, 5, ornt);CHKERRQ(ierr);
1528       /* Edges */
1529       cone[0] =  6; cone[1] =  7;
1530       ierr = DMPlexSetCone(*dm, 14, cone);CHKERRQ(ierr);
1531       cone[0] =  7; cone[1] =  8;
1532       ierr = DMPlexSetCone(*dm, 15, cone);CHKERRQ(ierr);
1533       cone[0] =  8; cone[1] =  9;
1534       ierr = DMPlexSetCone(*dm, 16, cone);CHKERRQ(ierr);
1535       cone[0] =  9; cone[1] =  6;
1536       ierr = DMPlexSetCone(*dm, 17, cone);CHKERRQ(ierr);
1537       cone[0] = 10; cone[1] = 11;
1538       ierr = DMPlexSetCone(*dm, 18, cone);CHKERRQ(ierr);
1539       cone[0] = 11; cone[1] =  7;
1540       ierr = DMPlexSetCone(*dm, 19, cone);CHKERRQ(ierr);
1541       cone[0] =  6; cone[1] = 10;
1542       ierr = DMPlexSetCone(*dm, 20, cone);CHKERRQ(ierr);
1543       cone[0] = 12; cone[1] = 13;
1544       ierr = DMPlexSetCone(*dm, 21, cone);CHKERRQ(ierr);
1545       cone[0] = 13; cone[1] = 11;
1546       ierr = DMPlexSetCone(*dm, 22, cone);CHKERRQ(ierr);
1547       cone[0] = 10; cone[1] = 12;
1548       ierr = DMPlexSetCone(*dm, 23, cone);CHKERRQ(ierr);
1549       cone[0] = 13; cone[1] =  8;
1550       ierr = DMPlexSetCone(*dm, 24, cone);CHKERRQ(ierr);
1551       cone[0] = 12; cone[1] =  9;
1552       ierr = DMPlexSetCone(*dm, 25, cone);CHKERRQ(ierr);
1553       ierr = DMPlexSymmetrize(*dm);CHKERRQ(ierr);
1554       ierr = DMPlexStratify(*dm);CHKERRQ(ierr);
1555       /* Build coordinates */
1556       ierr = PetscCalloc1(numVerts * embedDim, &coordsIn);CHKERRQ(ierr);
1557       coordsIn[0*embedDim+0] = -dist; coordsIn[0*embedDim+1] =  dist; coordsIn[0*embedDim+2] = -dist;
1558       coordsIn[1*embedDim+0] =  dist; coordsIn[1*embedDim+1] =  dist; coordsIn[1*embedDim+2] = -dist;
1559       coordsIn[2*embedDim+0] =  dist; coordsIn[2*embedDim+1] = -dist; coordsIn[2*embedDim+2] = -dist;
1560       coordsIn[3*embedDim+0] = -dist; coordsIn[3*embedDim+1] = -dist; coordsIn[3*embedDim+2] = -dist;
1561       coordsIn[4*embedDim+0] = -dist; coordsIn[4*embedDim+1] =  dist; coordsIn[4*embedDim+2] =  dist;
1562       coordsIn[5*embedDim+0] =  dist; coordsIn[5*embedDim+1] =  dist; coordsIn[5*embedDim+2] =  dist;
1563       coordsIn[6*embedDim+0] = -dist; coordsIn[6*embedDim+1] = -dist; coordsIn[6*embedDim+2] =  dist;
1564       coordsIn[7*embedDim+0] =  dist; coordsIn[7*embedDim+1] = -dist; coordsIn[7*embedDim+2] =  dist;
1565     }
1566     break;
1567   case 3:
1568     if (simplex) {
1569       DM              idm             = NULL;
1570       const PetscReal edgeLen         = 1.0/PETSC_PHI;
1571       const PetscReal vertexA[4]      = {0.5, 0.5, 0.5, 0.5};
1572       const PetscReal vertexB[4]      = {1.0, 0.0, 0.0, 0.0};
1573       const PetscReal vertexC[4]      = {0.5, 0.5*PETSC_PHI, 0.5/PETSC_PHI, 0.0};
1574       const PetscInt  degree          = 12;
1575       PetscInt        s[4]            = {1, 1, 1};
1576       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},
1577                                          {2, 0, 1, 3}, {2, 1, 3, 0}, {2, 3, 0, 1}, {3, 0, 2, 1}, {3, 1, 0, 2}, {3, 2, 1, 0}};
1578       PetscInt        cone[4];
1579       PetscInt       *graph, p, i, j, k, l;
1580 
1581       numCells    = !rank ? 600 : 0;
1582       numVerts    = !rank ? 120 : 0;
1583       firstVertex = numCells;
1584       /* Use the 600-cell, which for a unit sphere has coordinates which are
1585 
1586            1/2 (\pm 1, \pm 1,    \pm 1, \pm 1)                          16
1587                (\pm 1,    0,       0,      0)  all cyclic permutations   8
1588            1/2 (\pm 1, \pm phi, \pm 1/phi, 0)  all even permutations    96
1589 
1590          where \phi^2 - \phi - 1 = 0, meaning \phi is the golden ratio \frac{1 + \sqrt{5}}{2}. The edge
1591          length is then given by 1/\phi = 2.73606.
1592 
1593          http://buzzard.pugetsound.edu/sage-practice/ch03s03.html
1594          http://mathworld.wolfram.com/600-Cell.html
1595        */
1596       /* Construct vertices */
1597       ierr = PetscCalloc1(numVerts * embedDim, &coordsIn);CHKERRQ(ierr);
1598       i    = 0;
1599       for (s[0] = -1; s[0] < 2; s[0] += 2) {
1600         for (s[1] = -1; s[1] < 2; s[1] += 2) {
1601           for (s[2] = -1; s[2] < 2; s[2] += 2) {
1602             for (s[3] = -1; s[3] < 2; s[3] += 2) {
1603               for (d = 0; d < embedDim; ++d) coordsIn[i*embedDim+d] = s[d]*vertexA[d];
1604               ++i;
1605             }
1606           }
1607         }
1608       }
1609       for (p = 0; p < embedDim; ++p) {
1610         s[1] = s[2] = s[3] = 1;
1611         for (s[0] = -1; s[0] < 2; s[0] += 2) {
1612           for (d = 0; d < embedDim; ++d) coordsIn[i*embedDim+d] = s[(d+p)%embedDim]*vertexB[(d+p)%embedDim];
1613           ++i;
1614         }
1615       }
1616       for (p = 0; p < 12; ++p) {
1617         s[3] = 1;
1618         for (s[0] = -1; s[0] < 2; s[0] += 2) {
1619           for (s[1] = -1; s[1] < 2; s[1] += 2) {
1620             for (s[2] = -1; s[2] < 2; s[2] += 2) {
1621               for (d = 0; d < embedDim; ++d) coordsIn[i*embedDim+d] = s[evenPerm[p][d]]*vertexC[evenPerm[p][d]];
1622               ++i;
1623             }
1624           }
1625         }
1626       }
1627       if (i != numVerts) SETERRQ2(comm, PETSC_ERR_PLIB, "Invalid 600-cell, vertices %D != %D", i, numVerts);
1628       /* Construct graph */
1629       ierr = PetscCalloc1(numVerts * numVerts, &graph);CHKERRQ(ierr);
1630       for (i = 0; i < numVerts; ++i) {
1631         for (j = 0, k = 0; j < numVerts; ++j) {
1632           if (PetscAbsReal(DiffNormReal(embedDim, &coordsIn[i*embedDim], &coordsIn[j*embedDim]) - edgeLen) < PETSC_SMALL) {graph[i*numVerts+j] = 1; ++k;}
1633         }
1634         if (k != degree) SETERRQ3(comm, PETSC_ERR_PLIB, "Invalid 600-cell, vertex %D degree %D != %D", i, k, degree);
1635       }
1636       /* Build Topology */
1637       ierr = DMPlexSetChart(*dm, 0, numCells+numVerts);CHKERRQ(ierr);
1638       for (c = 0; c < numCells; c++) {
1639         ierr = DMPlexSetConeSize(*dm, c, embedDim);CHKERRQ(ierr);
1640       }
1641       ierr = DMSetUp(*dm);CHKERRQ(ierr); /* Allocate space for cones */
1642       /* Cells */
1643       for (i = 0, c = 0; i < numVerts; ++i) {
1644         for (j = 0; j < i; ++j) {
1645           for (k = 0; k < j; ++k) {
1646             for (l = 0; l < k; ++l) {
1647               if (graph[i*numVerts+j] && graph[j*numVerts+k] && graph[k*numVerts+i] &&
1648                   graph[l*numVerts+i] && graph[l*numVerts+j] && graph[l*numVerts+k]) {
1649                 cone[0] = firstVertex+i; cone[1] = firstVertex+j; cone[2] = firstVertex+k; cone[3] = firstVertex+l;
1650                 /* Check orientation: https://ef.gy/linear-algebra:normal-vectors-in-higher-dimensional-spaces */
1651                 {
1652                   const PetscInt epsilon[4][4][4][4] = {{{{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}},
1653                                                          {{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  1}, { 0,  0, -1, 0}},
1654                                                          {{0,  0,  0,  0}, { 0, 0,  0, -1}, { 0,  0, 0,  0}, { 0,  1,  0, 0}},
1655                                                          {{0,  0,  0,  0}, { 0, 0,  1,  0}, { 0, -1, 0,  0}, { 0,  0,  0, 0}}},
1656 
1657                                                         {{{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0, -1}, { 0,  0,  1, 0}},
1658                                                          {{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}},
1659                                                          {{0,  0,  0,  1}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, {-1,  0,  0, 0}},
1660                                                          {{0,  0, -1,  0}, { 0, 0,  0,  0}, { 1,  0, 0,  0}, { 0,  0,  0, 0}}},
1661 
1662                                                         {{{0,  0,  0,  0}, { 0, 0,  0,  1}, { 0,  0, 0,  0}, { 0, -1,  0, 0}},
1663                                                          {{0,  0,  0, -1}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 1,  0,  0, 0}},
1664                                                          {{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}},
1665                                                          {{0,  1,  0,  0}, {-1, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}}},
1666 
1667                                                         {{{0,  0,  0,  0}, { 0, 0, -1,  0}, { 0,  1, 0,  0}, { 0,  0,  0, 0}},
1668                                                          {{0,  0,  1,  0}, { 0, 0,  0,  0}, {-1,  0, 0,  0}, { 0,  0,  0, 0}},
1669                                                          {{0, -1,  0,  0}, { 1, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}},
1670                                                          {{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}}}};
1671                   PetscReal normal[4];
1672                   PetscInt  e, f, g;
1673 
1674                   for (d = 0; d < embedDim; ++d) {
1675                     normal[d] = 0.0;
1676                     for (e = 0; e < embedDim; ++e) {
1677                       for (f = 0; f < embedDim; ++f) {
1678                         for (g = 0; g < embedDim; ++g) {
1679                           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]);
1680                         }
1681                       }
1682                     }
1683                   }
1684                   if (DotReal(embedDim, normal, &coordsIn[i*embedDim]) < 0) {PetscInt tmp = cone[1]; cone[1] = cone[2]; cone[2] = tmp;}
1685                 }
1686                 ierr = DMPlexSetCone(*dm, c++, cone);CHKERRQ(ierr);
1687               }
1688             }
1689           }
1690         }
1691       }
1692       ierr = DMPlexSymmetrize(*dm);CHKERRQ(ierr);
1693       ierr = DMPlexStratify(*dm);CHKERRQ(ierr);
1694       ierr = PetscFree(graph);CHKERRQ(ierr);
1695       /* Interpolate mesh */
1696       ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
1697       ierr = DMDestroy(dm);CHKERRQ(ierr);
1698       *dm  = idm;
1699       break;
1700     }
1701   default: SETERRQ1(comm, PETSC_ERR_SUP, "Unsupported dimension for sphere: %D", dim);
1702   }
1703   /* Create coordinates */
1704   ierr = DMGetCoordinateSection(*dm, &coordSection);CHKERRQ(ierr);
1705   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
1706   ierr = PetscSectionSetFieldComponents(coordSection, 0, embedDim);CHKERRQ(ierr);
1707   ierr = PetscSectionSetChart(coordSection, firstVertex, firstVertex+numVerts);CHKERRQ(ierr);
1708   for (v = firstVertex; v < firstVertex+numVerts; ++v) {
1709     ierr = PetscSectionSetDof(coordSection, v, embedDim);CHKERRQ(ierr);
1710     ierr = PetscSectionSetFieldDof(coordSection, v, 0, embedDim);CHKERRQ(ierr);
1711   }
1712   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
1713   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
1714   ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
1715   ierr = VecSetBlockSize(coordinates, embedDim);CHKERRQ(ierr);
1716   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
1717   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
1718   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
1719   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
1720   for (v = 0; v < numVerts; ++v) for (d = 0; d < embedDim; ++d) {coords[v*embedDim+d] = coordsIn[v*embedDim+d];}
1721   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
1722   ierr = DMSetCoordinatesLocal(*dm, coordinates);CHKERRQ(ierr);
1723   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
1724   ierr = PetscFree(coordsIn);CHKERRQ(ierr);
1725   PetscFunctionReturn(0);
1726 }
1727 
1728 /* External function declarations here */
1729 extern PetscErrorCode DMCreateInterpolation_Plex(DM dmCoarse, DM dmFine, Mat *interpolation, Vec *scaling);
1730 extern PetscErrorCode DMCreateInjection_Plex(DM dmCoarse, DM dmFine, Mat *mat);
1731 extern PetscErrorCode DMCreateDefaultSection_Plex(DM dm);
1732 extern PetscErrorCode DMCreateDefaultConstraints_Plex(DM dm);
1733 extern PetscErrorCode DMCreateMatrix_Plex(DM dm,  Mat *J);
1734 extern PetscErrorCode DMCreateCoordinateDM_Plex(DM dm, DM *cdm);
1735 PETSC_INTERN PetscErrorCode DMClone_Plex(DM dm, DM *newdm);
1736 extern PetscErrorCode DMSetUp_Plex(DM dm);
1737 extern PetscErrorCode DMDestroy_Plex(DM dm);
1738 extern PetscErrorCode DMView_Plex(DM dm, PetscViewer viewer);
1739 extern PetscErrorCode DMLoad_Plex(DM dm, PetscViewer viewer);
1740 extern PetscErrorCode DMCreateSubDM_Plex(DM dm, PetscInt numFields, PetscInt fields[], IS *is, DM *subdm);
1741 
1742 /* Replace dm with the contents of dmNew
1743    - Share the DM_Plex structure
1744    - Share the coordinates
1745    - Share the SF
1746 */
1747 static PetscErrorCode DMPlexReplace_Static(DM dm, DM dmNew)
1748 {
1749   PetscSF          sf;
1750   DM               coordDM, coarseDM;
1751   Vec              coords;
1752   const PetscReal *maxCell, *L;
1753   const DMBoundaryType *bd;
1754   PetscErrorCode   ierr;
1755 
1756   PetscFunctionBegin;
1757   ierr = DMGetPointSF(dmNew, &sf);CHKERRQ(ierr);
1758   ierr = DMSetPointSF(dm, sf);CHKERRQ(ierr);
1759   ierr = DMGetCoordinateDM(dmNew, &coordDM);CHKERRQ(ierr);
1760   ierr = DMGetCoordinatesLocal(dmNew, &coords);CHKERRQ(ierr);
1761   ierr = DMSetCoordinateDM(dm, coordDM);CHKERRQ(ierr);
1762   ierr = DMSetCoordinatesLocal(dm, coords);CHKERRQ(ierr);
1763   ierr = DMGetPeriodicity(dm, &maxCell, &L, &bd);CHKERRQ(ierr);
1764   if (L) {ierr = DMSetPeriodicity(dmNew, maxCell, L, bd);CHKERRQ(ierr);}
1765   ierr = DMDestroy_Plex(dm);CHKERRQ(ierr);
1766   dm->data = dmNew->data;
1767   ((DM_Plex *) dmNew->data)->refct++;
1768   dmNew->labels->refct++;
1769   if (!--(dm->labels->refct)) {
1770     DMLabelLink next = dm->labels->next;
1771 
1772     /* destroy the labels */
1773     while (next) {
1774       DMLabelLink tmp = next->next;
1775 
1776       ierr = DMLabelDestroy(&next->label);CHKERRQ(ierr);
1777       ierr = PetscFree(next);CHKERRQ(ierr);
1778       next = tmp;
1779     }
1780     ierr = PetscFree(dm->labels);CHKERRQ(ierr);
1781   }
1782   dm->labels = dmNew->labels;
1783   dm->depthLabel = dmNew->depthLabel;
1784   ierr = DMGetCoarseDM(dmNew,&coarseDM);CHKERRQ(ierr);
1785   ierr = DMSetCoarseDM(dm,coarseDM);CHKERRQ(ierr);
1786   PetscFunctionReturn(0);
1787 }
1788 
1789 /* Swap dm with the contents of dmNew
1790    - Swap the DM_Plex structure
1791    - Swap the coordinates
1792    - Swap the point PetscSF
1793 */
1794 static PetscErrorCode DMPlexSwap_Static(DM dmA, DM dmB)
1795 {
1796   DM              coordDMA, coordDMB;
1797   Vec             coordsA,  coordsB;
1798   PetscSF         sfA,      sfB;
1799   void            *tmp;
1800   DMLabelLinkList listTmp;
1801   DMLabel         depthTmp;
1802   PetscErrorCode  ierr;
1803 
1804   PetscFunctionBegin;
1805   ierr = DMGetPointSF(dmA, &sfA);CHKERRQ(ierr);
1806   ierr = DMGetPointSF(dmB, &sfB);CHKERRQ(ierr);
1807   ierr = PetscObjectReference((PetscObject) sfA);CHKERRQ(ierr);
1808   ierr = DMSetPointSF(dmA, sfB);CHKERRQ(ierr);
1809   ierr = DMSetPointSF(dmB, sfA);CHKERRQ(ierr);
1810   ierr = PetscObjectDereference((PetscObject) sfA);CHKERRQ(ierr);
1811 
1812   ierr = DMGetCoordinateDM(dmA, &coordDMA);CHKERRQ(ierr);
1813   ierr = DMGetCoordinateDM(dmB, &coordDMB);CHKERRQ(ierr);
1814   ierr = PetscObjectReference((PetscObject) coordDMA);CHKERRQ(ierr);
1815   ierr = DMSetCoordinateDM(dmA, coordDMB);CHKERRQ(ierr);
1816   ierr = DMSetCoordinateDM(dmB, coordDMA);CHKERRQ(ierr);
1817   ierr = PetscObjectDereference((PetscObject) coordDMA);CHKERRQ(ierr);
1818 
1819   ierr = DMGetCoordinatesLocal(dmA, &coordsA);CHKERRQ(ierr);
1820   ierr = DMGetCoordinatesLocal(dmB, &coordsB);CHKERRQ(ierr);
1821   ierr = PetscObjectReference((PetscObject) coordsA);CHKERRQ(ierr);
1822   ierr = DMSetCoordinatesLocal(dmA, coordsB);CHKERRQ(ierr);
1823   ierr = DMSetCoordinatesLocal(dmB, coordsA);CHKERRQ(ierr);
1824   ierr = PetscObjectDereference((PetscObject) coordsA);CHKERRQ(ierr);
1825 
1826   tmp       = dmA->data;
1827   dmA->data = dmB->data;
1828   dmB->data = tmp;
1829   listTmp   = dmA->labels;
1830   dmA->labels = dmB->labels;
1831   dmB->labels = listTmp;
1832   depthTmp  = dmA->depthLabel;
1833   dmA->depthLabel = dmB->depthLabel;
1834   dmB->depthLabel = depthTmp;
1835   PetscFunctionReturn(0);
1836 }
1837 
1838 PetscErrorCode DMSetFromOptions_NonRefinement_Plex(PetscOptionItems *PetscOptionsObject,DM dm)
1839 {
1840   DM_Plex       *mesh = (DM_Plex*) dm->data;
1841   PetscErrorCode ierr;
1842 
1843   PetscFunctionBegin;
1844   /* Handle viewing */
1845   ierr = PetscOptionsBool("-dm_plex_print_set_values", "Output all set values info", "DMView", PETSC_FALSE, &mesh->printSetValues, NULL);CHKERRQ(ierr);
1846   ierr = PetscOptionsInt("-dm_plex_print_fem", "Debug output level all fem computations", "DMView", 0, &mesh->printFEM, NULL);CHKERRQ(ierr);
1847   ierr = PetscOptionsReal("-dm_plex_print_tol", "Tolerance for FEM output", "DMView", mesh->printTol, &mesh->printTol, NULL);CHKERRQ(ierr);
1848   /* Point Location */
1849   ierr = PetscOptionsBool("-dm_plex_hash_location", "Use grid hashing for point location", "DMView", PETSC_FALSE, &mesh->useHashLocation, NULL);CHKERRQ(ierr);
1850   /* Generation and remeshing */
1851   ierr = PetscOptionsBool("-dm_plex_remesh_bd", "Allow changes to the boundary on remeshing", "DMView", PETSC_FALSE, &mesh->remeshBd, NULL);CHKERRQ(ierr);
1852   /* Projection behavior */
1853   ierr = PetscOptionsInt("-dm_plex_max_projection_height", "Maxmimum mesh point height used to project locally", "DMPlexSetMaxProjectionHeight", 0, &mesh->maxProjectionHeight, NULL);CHKERRQ(ierr);
1854   ierr = PetscOptionsBool("-dm_plex_regular_refinement", "Use special nested projection algorithm for regular refinement", "DMPlexSetRegularRefinement", mesh->regularRefinement, &mesh->regularRefinement, NULL);CHKERRQ(ierr);
1855 
1856   ierr = PetscPartitionerSetFromOptions(mesh->partitioner);CHKERRQ(ierr);
1857   PetscFunctionReturn(0);
1858 }
1859 
1860 static PetscErrorCode DMSetFromOptions_Plex(PetscOptionItems *PetscOptionsObject,DM dm)
1861 {
1862   PetscInt       refine = 0, coarsen = 0, r;
1863   PetscBool      isHierarchy;
1864   PetscErrorCode ierr;
1865 
1866   PetscFunctionBegin;
1867   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1868   ierr = PetscOptionsHead(PetscOptionsObject,"DMPlex Options");CHKERRQ(ierr);
1869   /* Handle DMPlex refinement */
1870   ierr = PetscOptionsInt("-dm_refine", "The number of uniform refinements", "DMCreate", refine, &refine, NULL);CHKERRQ(ierr);
1871   ierr = PetscOptionsInt("-dm_refine_hierarchy", "The number of uniform refinements", "DMCreate", refine, &refine, &isHierarchy);CHKERRQ(ierr);
1872   if (refine) {ierr = DMPlexSetRefinementUniform(dm, PETSC_TRUE);CHKERRQ(ierr);}
1873   if (refine && isHierarchy) {
1874     DM *dms, coarseDM;
1875 
1876     ierr = DMGetCoarseDM(dm, &coarseDM);CHKERRQ(ierr);
1877     ierr = PetscObjectReference((PetscObject)coarseDM);CHKERRQ(ierr);
1878     ierr = PetscMalloc1(refine,&dms);CHKERRQ(ierr);
1879     ierr = DMRefineHierarchy(dm, refine, dms);CHKERRQ(ierr);
1880     /* Total hack since we do not pass in a pointer */
1881     ierr = DMPlexSwap_Static(dm, dms[refine-1]);CHKERRQ(ierr);
1882     if (refine == 1) {
1883       ierr = DMSetCoarseDM(dm, dms[0]);CHKERRQ(ierr);
1884       ierr = DMPlexSetRegularRefinement(dm, PETSC_TRUE);CHKERRQ(ierr);
1885     } else {
1886       ierr = DMSetCoarseDM(dm, dms[refine-2]);CHKERRQ(ierr);
1887       ierr = DMPlexSetRegularRefinement(dm, PETSC_TRUE);CHKERRQ(ierr);
1888       ierr = DMSetCoarseDM(dms[0], dms[refine-1]);CHKERRQ(ierr);
1889       ierr = DMPlexSetRegularRefinement(dms[0], PETSC_TRUE);CHKERRQ(ierr);
1890     }
1891     ierr = DMSetCoarseDM(dms[refine-1], coarseDM);CHKERRQ(ierr);
1892     ierr = PetscObjectDereference((PetscObject)coarseDM);CHKERRQ(ierr);
1893     /* Free DMs */
1894     for (r = 0; r < refine; ++r) {
1895       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dms[r]);CHKERRQ(ierr);
1896       ierr = DMDestroy(&dms[r]);CHKERRQ(ierr);
1897     }
1898     ierr = PetscFree(dms);CHKERRQ(ierr);
1899   } else {
1900     for (r = 0; r < refine; ++r) {
1901       DM refinedMesh;
1902 
1903       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
1904       ierr = DMRefine(dm, PetscObjectComm((PetscObject) dm), &refinedMesh);CHKERRQ(ierr);
1905       /* Total hack since we do not pass in a pointer */
1906       ierr = DMPlexReplace_Static(dm, refinedMesh);CHKERRQ(ierr);
1907       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
1908       ierr = DMDestroy(&refinedMesh);CHKERRQ(ierr);
1909     }
1910   }
1911   /* Handle DMPlex coarsening */
1912   ierr = PetscOptionsInt("-dm_coarsen", "Coarsen the mesh", "DMCreate", coarsen, &coarsen, NULL);CHKERRQ(ierr);
1913   ierr = PetscOptionsInt("-dm_coarsen_hierarchy", "The number of coarsenings", "DMCreate", coarsen, &coarsen, &isHierarchy);CHKERRQ(ierr);
1914   if (coarsen && isHierarchy) {
1915     DM *dms;
1916 
1917     ierr = PetscMalloc1(coarsen, &dms);CHKERRQ(ierr);
1918     ierr = DMCoarsenHierarchy(dm, coarsen, dms);CHKERRQ(ierr);
1919     /* Free DMs */
1920     for (r = 0; r < coarsen; ++r) {
1921       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dms[r]);CHKERRQ(ierr);
1922       ierr = DMDestroy(&dms[r]);CHKERRQ(ierr);
1923     }
1924     ierr = PetscFree(dms);CHKERRQ(ierr);
1925   } else {
1926     for (r = 0; r < coarsen; ++r) {
1927       DM coarseMesh;
1928 
1929       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
1930       ierr = DMCoarsen(dm, PetscObjectComm((PetscObject) dm), &coarseMesh);CHKERRQ(ierr);
1931       /* Total hack since we do not pass in a pointer */
1932       ierr = DMPlexReplace_Static(dm, coarseMesh);CHKERRQ(ierr);
1933       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
1934       ierr = DMDestroy(&coarseMesh);CHKERRQ(ierr);
1935     }
1936   }
1937   /* Handle */
1938   ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
1939   ierr = PetscOptionsTail();CHKERRQ(ierr);
1940   PetscFunctionReturn(0);
1941 }
1942 
1943 static PetscErrorCode DMCreateGlobalVector_Plex(DM dm,Vec *vec)
1944 {
1945   PetscErrorCode ierr;
1946 
1947   PetscFunctionBegin;
1948   ierr = DMCreateGlobalVector_Section_Private(dm,vec);CHKERRQ(ierr);
1949   /* ierr = VecSetOperation(*vec, VECOP_DUPLICATE, (void(*)(void)) VecDuplicate_MPI_DM);CHKERRQ(ierr); */
1950   ierr = VecSetOperation(*vec, VECOP_VIEW, (void (*)(void)) VecView_Plex);CHKERRQ(ierr);
1951   ierr = VecSetOperation(*vec, VECOP_VIEWNATIVE, (void (*)(void)) VecView_Plex_Native);CHKERRQ(ierr);
1952   ierr = VecSetOperation(*vec, VECOP_LOAD, (void (*)(void)) VecLoad_Plex);CHKERRQ(ierr);
1953   ierr = VecSetOperation(*vec, VECOP_LOADNATIVE, (void (*)(void)) VecLoad_Plex_Native);CHKERRQ(ierr);
1954   PetscFunctionReturn(0);
1955 }
1956 
1957 static PetscErrorCode DMCreateLocalVector_Plex(DM dm,Vec *vec)
1958 {
1959   PetscErrorCode ierr;
1960 
1961   PetscFunctionBegin;
1962   ierr = DMCreateLocalVector_Section_Private(dm,vec);CHKERRQ(ierr);
1963   ierr = VecSetOperation(*vec, VECOP_VIEW, (void (*)(void)) VecView_Plex_Local);CHKERRQ(ierr);
1964   ierr = VecSetOperation(*vec, VECOP_LOAD, (void (*)(void)) VecLoad_Plex_Local);CHKERRQ(ierr);
1965   PetscFunctionReturn(0);
1966 }
1967 
1968 static PetscErrorCode DMGetDimPoints_Plex(DM dm, PetscInt dim, PetscInt *pStart, PetscInt *pEnd)
1969 {
1970   PetscInt       depth, d;
1971   PetscErrorCode ierr;
1972 
1973   PetscFunctionBegin;
1974   ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
1975   if (depth == 1) {
1976     ierr = DMGetDimension(dm, &d);CHKERRQ(ierr);
1977     if (dim == 0)      {ierr = DMPlexGetDepthStratum(dm, dim, pStart, pEnd);CHKERRQ(ierr);}
1978     else if (dim == d) {ierr = DMPlexGetDepthStratum(dm, 1, pStart, pEnd);CHKERRQ(ierr);}
1979     else               {*pStart = 0; *pEnd = 0;}
1980   } else {
1981     ierr = DMPlexGetDepthStratum(dm, dim, pStart, pEnd);CHKERRQ(ierr);
1982   }
1983   PetscFunctionReturn(0);
1984 }
1985 
1986 static PetscErrorCode DMGetNeighors_Plex(DM dm, PetscInt *nranks, const PetscMPIInt *ranks[])
1987 {
1988   PetscSF        sf;
1989   PetscErrorCode ierr;
1990 
1991   PetscFunctionBegin;
1992   ierr = DMGetPointSF(dm, &sf);CHKERRQ(ierr);
1993   ierr = PetscSFGetRanks(sf, nranks, ranks, NULL, NULL, NULL);CHKERRQ(ierr);
1994   PetscFunctionReturn(0);
1995 }
1996 
1997 static PetscErrorCode DMInitialize_Plex(DM dm)
1998 {
1999   PetscErrorCode ierr;
2000 
2001   PetscFunctionBegin;
2002   dm->ops->view                            = DMView_Plex;
2003   dm->ops->load                            = DMLoad_Plex;
2004   dm->ops->setfromoptions                  = DMSetFromOptions_Plex;
2005   dm->ops->clone                           = DMClone_Plex;
2006   dm->ops->setup                           = DMSetUp_Plex;
2007   dm->ops->createdefaultsection            = DMCreateDefaultSection_Plex;
2008   dm->ops->createdefaultconstraints        = DMCreateDefaultConstraints_Plex;
2009   dm->ops->createglobalvector              = DMCreateGlobalVector_Plex;
2010   dm->ops->createlocalvector               = DMCreateLocalVector_Plex;
2011   dm->ops->getlocaltoglobalmapping         = NULL;
2012   dm->ops->createfieldis                   = NULL;
2013   dm->ops->createcoordinatedm              = DMCreateCoordinateDM_Plex;
2014   dm->ops->getcoloring                     = NULL;
2015   dm->ops->creatematrix                    = DMCreateMatrix_Plex;
2016   dm->ops->createinterpolation             = DMCreateInterpolation_Plex;
2017   dm->ops->getaggregates                   = NULL;
2018   dm->ops->getinjection                    = DMCreateInjection_Plex;
2019   dm->ops->refine                          = DMRefine_Plex;
2020   dm->ops->coarsen                         = DMCoarsen_Plex;
2021   dm->ops->refinehierarchy                 = DMRefineHierarchy_Plex;
2022   dm->ops->coarsenhierarchy                = DMCoarsenHierarchy_Plex;
2023   dm->ops->globaltolocalbegin              = NULL;
2024   dm->ops->globaltolocalend                = NULL;
2025   dm->ops->localtoglobalbegin              = NULL;
2026   dm->ops->localtoglobalend                = NULL;
2027   dm->ops->destroy                         = DMDestroy_Plex;
2028   dm->ops->createsubdm                     = DMCreateSubDM_Plex;
2029   dm->ops->getdimpoints                    = DMGetDimPoints_Plex;
2030   dm->ops->locatepoints                    = DMLocatePoints_Plex;
2031   dm->ops->projectfunctionlocal            = DMProjectFunctionLocal_Plex;
2032   dm->ops->projectfunctionlabellocal       = DMProjectFunctionLabelLocal_Plex;
2033   dm->ops->projectfieldlocal               = DMProjectFieldLocal_Plex;
2034   dm->ops->projectfieldlabellocal          = DMProjectFieldLabelLocal_Plex;
2035   dm->ops->computel2diff                   = DMComputeL2Diff_Plex;
2036   dm->ops->computel2gradientdiff           = DMComputeL2GradientDiff_Plex;
2037   dm->ops->computel2fielddiff              = DMComputeL2FieldDiff_Plex;
2038   dm->ops->getneighbors                    = DMGetNeighors_Plex;
2039   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMAdaptLabel_C",DMAdaptLabel_Plex);CHKERRQ(ierr);
2040   PetscFunctionReturn(0);
2041 }
2042 
2043 PETSC_INTERN PetscErrorCode DMClone_Plex(DM dm, DM *newdm)
2044 {
2045   DM_Plex        *mesh = (DM_Plex *) dm->data;
2046   PetscErrorCode ierr;
2047 
2048   PetscFunctionBegin;
2049   mesh->refct++;
2050   (*newdm)->data = mesh;
2051   ierr = PetscObjectChangeTypeName((PetscObject) *newdm, DMPLEX);CHKERRQ(ierr);
2052   ierr = DMInitialize_Plex(*newdm);CHKERRQ(ierr);
2053   PetscFunctionReturn(0);
2054 }
2055 
2056 /*MC
2057   DMPLEX = "plex" - A DM object that encapsulates an unstructured mesh, or CW Complex, which can be expressed using a Hasse Diagram.
2058                     In the local representation, Vecs contain all unknowns in the interior and shared boundary. This is
2059                     specified by a PetscSection object. Ownership in the global representation is determined by
2060                     ownership of the underlying DMPlex points. This is specified by another PetscSection object.
2061 
2062   Level: intermediate
2063 
2064 .seealso: DMType, DMPlexCreate(), DMCreate(), DMSetType()
2065 M*/
2066 
2067 PETSC_EXTERN PetscErrorCode DMCreate_Plex(DM dm)
2068 {
2069   DM_Plex        *mesh;
2070   PetscInt       unit, d;
2071   PetscErrorCode ierr;
2072 
2073   PetscFunctionBegin;
2074   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
2075   ierr     = PetscNewLog(dm,&mesh);CHKERRQ(ierr);
2076   dm->dim  = 0;
2077   dm->data = mesh;
2078 
2079   mesh->refct             = 1;
2080   ierr                    = PetscSectionCreate(PetscObjectComm((PetscObject)dm), &mesh->coneSection);CHKERRQ(ierr);
2081   mesh->maxConeSize       = 0;
2082   mesh->cones             = NULL;
2083   mesh->coneOrientations  = NULL;
2084   ierr                    = PetscSectionCreate(PetscObjectComm((PetscObject)dm), &mesh->supportSection);CHKERRQ(ierr);
2085   mesh->maxSupportSize    = 0;
2086   mesh->supports          = NULL;
2087   mesh->refinementUniform = PETSC_TRUE;
2088   mesh->refinementLimit   = -1.0;
2089 
2090   mesh->facesTmp = NULL;
2091 
2092   mesh->tetgenOpts   = NULL;
2093   mesh->triangleOpts = NULL;
2094   ierr = PetscPartitionerCreate(PetscObjectComm((PetscObject)dm), &mesh->partitioner);CHKERRQ(ierr);
2095   mesh->remeshBd     = PETSC_FALSE;
2096 
2097   mesh->subpointMap = NULL;
2098 
2099   for (unit = 0; unit < NUM_PETSC_UNITS; ++unit) mesh->scale[unit] = 1.0;
2100 
2101   mesh->regularRefinement   = PETSC_FALSE;
2102   mesh->depthState          = -1;
2103   mesh->globalVertexNumbers = NULL;
2104   mesh->globalCellNumbers   = NULL;
2105   mesh->anchorSection       = NULL;
2106   mesh->anchorIS            = NULL;
2107   mesh->createanchors       = NULL;
2108   mesh->computeanchormatrix = NULL;
2109   mesh->parentSection       = NULL;
2110   mesh->parents             = NULL;
2111   mesh->childIDs            = NULL;
2112   mesh->childSection        = NULL;
2113   mesh->children            = NULL;
2114   mesh->referenceTree       = NULL;
2115   mesh->getchildsymmetry    = NULL;
2116   for (d = 0; d < 8; ++d) mesh->hybridPointMax[d] = PETSC_DETERMINE;
2117   mesh->vtkCellHeight       = 0;
2118   mesh->useCone             = PETSC_FALSE;
2119   mesh->useClosure          = PETSC_TRUE;
2120   mesh->useAnchors          = PETSC_FALSE;
2121 
2122   mesh->maxProjectionHeight = 0;
2123 
2124   mesh->printSetValues = PETSC_FALSE;
2125   mesh->printFEM       = 0;
2126   mesh->printTol       = 1.0e-10;
2127 
2128   ierr = DMInitialize_Plex(dm);CHKERRQ(ierr);
2129   PetscFunctionReturn(0);
2130 }
2131 
2132 /*@
2133   DMPlexCreate - Creates a DMPlex object, which encapsulates an unstructured mesh, or CW complex, which can be expressed using a Hasse Diagram.
2134 
2135   Collective on MPI_Comm
2136 
2137   Input Parameter:
2138 . comm - The communicator for the DMPlex object
2139 
2140   Output Parameter:
2141 . mesh  - The DMPlex object
2142 
2143   Level: beginner
2144 
2145 .keywords: DMPlex, create
2146 @*/
2147 PetscErrorCode DMPlexCreate(MPI_Comm comm, DM *mesh)
2148 {
2149   PetscErrorCode ierr;
2150 
2151   PetscFunctionBegin;
2152   PetscValidPointer(mesh,2);
2153   ierr = DMCreate(comm, mesh);CHKERRQ(ierr);
2154   ierr = DMSetType(*mesh, DMPLEX);CHKERRQ(ierr);
2155   PetscFunctionReturn(0);
2156 }
2157 
2158 /*
2159   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
2160 */
2161 static PetscErrorCode DMPlexBuildFromCellList_Parallel_Private(DM dm, PetscInt numCells, PetscInt numVertices, PetscInt numCorners, const int cells[], PetscSF *sfVert)
2162 {
2163   PetscSF         sfPoint;
2164   PetscLayout     vLayout;
2165   PetscHashI      vhash;
2166   PetscSFNode    *remoteVerticesAdj, *vertexLocal, *vertexOwner, *remoteVertex;
2167   const PetscInt *vrange;
2168   PetscInt        numVerticesAdj, off, *verticesAdj, numVerticesGhost = 0, *localVertex, *cone, c, p, v, g;
2169   PETSC_UNUSED PetscHashIIter ret, iter;
2170   PetscMPIInt     rank, size;
2171   PetscErrorCode  ierr;
2172 
2173   PetscFunctionBegin;
2174   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject) dm), &rank);CHKERRQ(ierr);
2175   ierr = MPI_Comm_size(PetscObjectComm((PetscObject) dm), &size);CHKERRQ(ierr);
2176   /* Partition vertices */
2177   ierr = PetscLayoutCreate(PetscObjectComm((PetscObject) dm), &vLayout);CHKERRQ(ierr);
2178   ierr = PetscLayoutSetLocalSize(vLayout, numVertices);CHKERRQ(ierr);
2179   ierr = PetscLayoutSetBlockSize(vLayout, 1);CHKERRQ(ierr);
2180   ierr = PetscLayoutSetUp(vLayout);CHKERRQ(ierr);
2181   ierr = PetscLayoutGetRanges(vLayout, &vrange);CHKERRQ(ierr);
2182   /* Count vertices and map them to procs */
2183   PetscHashICreate(vhash);
2184   for (c = 0; c < numCells; ++c) {
2185     for (p = 0; p < numCorners; ++p) {
2186       PetscHashIPut(vhash, cells[c*numCorners+p], ret, iter);
2187     }
2188   }
2189   PetscHashISize(vhash, numVerticesAdj);
2190   ierr = PetscMalloc1(numVerticesAdj, &verticesAdj);CHKERRQ(ierr);
2191   off = 0; ierr = PetscHashIGetKeys(vhash, &off, verticesAdj);CHKERRQ(ierr);
2192   if (off != numVerticesAdj) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Invalid number of local vertices %D should be %D", off, numVerticesAdj);
2193   ierr = PetscSortInt(numVerticesAdj, verticesAdj);CHKERRQ(ierr);
2194   ierr = PetscMalloc1(numVerticesAdj, &remoteVerticesAdj);CHKERRQ(ierr);
2195   for (v = 0; v < numVerticesAdj; ++v) {
2196     const PetscInt gv = verticesAdj[v];
2197     PetscInt       vrank;
2198 
2199     ierr = PetscFindInt(gv, size+1, vrange, &vrank);CHKERRQ(ierr);
2200     vrank = vrank < 0 ? -(vrank+2) : vrank;
2201     remoteVerticesAdj[v].index = gv - vrange[vrank];
2202     remoteVerticesAdj[v].rank  = vrank;
2203   }
2204   /* Create cones */
2205   ierr = DMPlexSetChart(dm, 0, numCells+numVerticesAdj);CHKERRQ(ierr);
2206   for (c = 0; c < numCells; ++c) {ierr = DMPlexSetConeSize(dm, c, numCorners);CHKERRQ(ierr);}
2207   ierr = DMSetUp(dm);CHKERRQ(ierr);
2208   ierr = DMGetWorkArray(dm, numCorners, PETSC_INT, &cone);CHKERRQ(ierr);
2209   for (c = 0; c < numCells; ++c) {
2210     for (p = 0; p < numCorners; ++p) {
2211       const PetscInt gv = cells[c*numCorners+p];
2212       PetscInt       lv;
2213 
2214       ierr = PetscFindInt(gv, numVerticesAdj, verticesAdj, &lv);CHKERRQ(ierr);
2215       if (lv < 0) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Could not find global vertex %D in local connectivity", gv);
2216       cone[p] = lv+numCells;
2217     }
2218     ierr = DMPlexSetCone(dm, c, cone);CHKERRQ(ierr);
2219   }
2220   ierr = DMRestoreWorkArray(dm, numCorners, PETSC_INT, &cone);CHKERRQ(ierr);
2221   /* Create SF for vertices */
2222   ierr = PetscSFCreate(PetscObjectComm((PetscObject)dm), sfVert);CHKERRQ(ierr);
2223   ierr = PetscObjectSetName((PetscObject) *sfVert, "Vertex Ownership SF");CHKERRQ(ierr);
2224   ierr = PetscSFSetFromOptions(*sfVert);CHKERRQ(ierr);
2225   ierr = PetscSFSetGraph(*sfVert, numVertices, numVerticesAdj, NULL, PETSC_OWN_POINTER, remoteVerticesAdj, PETSC_OWN_POINTER);CHKERRQ(ierr);
2226   ierr = PetscFree(verticesAdj);CHKERRQ(ierr);
2227   /* Build pointSF */
2228   ierr = PetscMalloc2(numVerticesAdj, &vertexLocal, numVertices, &vertexOwner);CHKERRQ(ierr);
2229   for (v = 0; v < numVerticesAdj; ++v) {vertexLocal[v].index = v+numCells; vertexLocal[v].rank = rank;}
2230   for (v = 0; v < numVertices;    ++v) {vertexOwner[v].index = -1;         vertexOwner[v].rank = -1;}
2231   ierr = PetscSFReduceBegin(*sfVert, MPIU_2INT, vertexLocal, vertexOwner, MPI_MAXLOC);CHKERRQ(ierr);
2232   ierr = PetscSFReduceEnd(*sfVert, MPIU_2INT, vertexLocal, vertexOwner, MPI_MAXLOC);CHKERRQ(ierr);
2233   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);
2234   ierr = PetscSFBcastBegin(*sfVert, MPIU_2INT, vertexOwner, vertexLocal);CHKERRQ(ierr);
2235   ierr = PetscSFBcastEnd(*sfVert, MPIU_2INT, vertexOwner, vertexLocal);CHKERRQ(ierr);
2236   for (v = 0; v < numVerticesAdj; ++v) if (vertexLocal[v].rank != rank) ++numVerticesGhost;
2237   ierr = PetscMalloc1(numVerticesGhost, &localVertex);CHKERRQ(ierr);
2238   ierr = PetscMalloc1(numVerticesGhost, &remoteVertex);CHKERRQ(ierr);
2239   for (v = 0, g = 0; v < numVerticesAdj; ++v) {
2240     if (vertexLocal[v].rank != rank) {
2241       localVertex[g]        = v+numCells;
2242       remoteVertex[g].index = vertexLocal[v].index;
2243       remoteVertex[g].rank  = vertexLocal[v].rank;
2244       ++g;
2245     }
2246   }
2247   ierr = PetscFree2(vertexLocal, vertexOwner);CHKERRQ(ierr);
2248   if (g != numVerticesGhost) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid number of vertex ghosts %D should be %D", g, numVerticesGhost);
2249   ierr = DMGetPointSF(dm, &sfPoint);CHKERRQ(ierr);
2250   ierr = PetscObjectSetName((PetscObject) sfPoint, "point SF");CHKERRQ(ierr);
2251   ierr = PetscSFSetGraph(sfPoint, numCells+numVerticesAdj, numVerticesGhost, localVertex, PETSC_OWN_POINTER, remoteVertex, PETSC_OWN_POINTER);CHKERRQ(ierr);
2252   ierr = PetscLayoutDestroy(&vLayout);CHKERRQ(ierr);
2253   PetscHashIDestroy(vhash);
2254   /* Fill in the rest of the topology structure */
2255   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
2256   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
2257   PetscFunctionReturn(0);
2258 }
2259 
2260 /*
2261   This takes as input the coordinates for each owned vertex
2262 */
2263 static PetscErrorCode DMPlexBuildCoordinates_Parallel_Private(DM dm, PetscInt spaceDim, PetscInt numCells, PetscInt numV, PetscSF sfVert, const PetscReal vertexCoords[])
2264 {
2265   PetscSection   coordSection;
2266   Vec            coordinates;
2267   PetscScalar   *coords;
2268   PetscInt       numVertices, numVerticesAdj, coordSize, v;
2269   PetscErrorCode ierr;
2270 
2271   PetscFunctionBegin;
2272   ierr = PetscSFGetGraph(sfVert, &numVertices, &numVerticesAdj, NULL, NULL);CHKERRQ(ierr);
2273   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
2274   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
2275   ierr = PetscSectionSetFieldComponents(coordSection, 0, spaceDim);CHKERRQ(ierr);
2276   ierr = PetscSectionSetChart(coordSection, numCells, numCells + numVerticesAdj);CHKERRQ(ierr);
2277   for (v = numCells; v < numCells+numVerticesAdj; ++v) {
2278     ierr = PetscSectionSetDof(coordSection, v, spaceDim);CHKERRQ(ierr);
2279     ierr = PetscSectionSetFieldDof(coordSection, v, 0, spaceDim);CHKERRQ(ierr);
2280   }
2281   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
2282   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
2283   ierr = VecCreate(PetscObjectComm((PetscObject)dm), &coordinates);CHKERRQ(ierr);
2284   ierr = VecSetBlockSize(coordinates, spaceDim);CHKERRQ(ierr);
2285   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
2286   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
2287   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
2288   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
2289   {
2290     MPI_Datatype coordtype;
2291 
2292     /* Need a temp buffer for coords if we have complex/single */
2293     ierr = MPI_Type_contiguous(spaceDim, MPIU_SCALAR, &coordtype);CHKERRQ(ierr);
2294     ierr = MPI_Type_commit(&coordtype);CHKERRQ(ierr);
2295 #if defined(PETSC_USE_COMPLEX)
2296     {
2297     PetscScalar *svertexCoords;
2298     PetscInt    i;
2299     ierr = PetscMalloc1(numV*spaceDim,&svertexCoords);CHKERRQ(ierr);
2300     for (i=0; i<numV*spaceDim; i++) svertexCoords[i] = vertexCoords[i];
2301     ierr = PetscSFBcastBegin(sfVert, coordtype, svertexCoords, coords);CHKERRQ(ierr);
2302     ierr = PetscSFBcastEnd(sfVert, coordtype, svertexCoords, coords);CHKERRQ(ierr);
2303     ierr = PetscFree(svertexCoords);CHKERRQ(ierr);
2304     }
2305 #else
2306     ierr = PetscSFBcastBegin(sfVert, coordtype, vertexCoords, coords);CHKERRQ(ierr);
2307     ierr = PetscSFBcastEnd(sfVert, coordtype, vertexCoords, coords);CHKERRQ(ierr);
2308 #endif
2309     ierr = MPI_Type_free(&coordtype);CHKERRQ(ierr);
2310   }
2311   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
2312   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
2313   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
2314   PetscFunctionReturn(0);
2315 }
2316 
2317 /*@C
2318   DMPlexCreateFromCellListParallel - This takes as input common mesh generator output, a list of the vertices for each cell, and produces a DM
2319 
2320   Input Parameters:
2321 + comm - The communicator
2322 . dim - The topological dimension of the mesh
2323 . numCells - The number of cells owned by this process
2324 . numVertices - The number of vertices owned by this process
2325 . numCorners - The number of vertices for each cell
2326 . interpolate - Flag indicating that intermediate mesh entities (faces, edges) should be created automatically
2327 . cells - An array of numCells*numCorners numbers, the global vertex numbers for each cell
2328 . spaceDim - The spatial dimension used for coordinates
2329 - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex
2330 
2331   Output Parameter:
2332 + dm - The DM
2333 - vertexSF - Optional, SF describing complete vertex ownership
2334 
2335   Note: Two triangles sharing a face
2336 $
2337 $        2
2338 $      / | \
2339 $     /  |  \
2340 $    /   |   \
2341 $   0  0 | 1  3
2342 $    \   |   /
2343 $     \  |  /
2344 $      \ | /
2345 $        1
2346 would have input
2347 $  numCells = 2, numVertices = 4
2348 $  cells = [0 1 2  1 3 2]
2349 $
2350 which would result in the DMPlex
2351 $
2352 $        4
2353 $      / | \
2354 $     /  |  \
2355 $    /   |   \
2356 $   2  0 | 1  5
2357 $    \   |   /
2358 $     \  |  /
2359 $      \ | /
2360 $        3
2361 
2362   Level: beginner
2363 
2364 .seealso: DMPlexCreateFromCellList(), DMPlexCreateFromDAG(), DMPlexCreate()
2365 @*/
2366 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)
2367 {
2368   PetscSF        sfVert;
2369   PetscErrorCode ierr;
2370 
2371   PetscFunctionBegin;
2372   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
2373   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
2374   PetscValidLogicalCollectiveInt(*dm, dim, 2);
2375   PetscValidLogicalCollectiveInt(*dm, spaceDim, 8);
2376   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
2377   ierr = DMPlexBuildFromCellList_Parallel_Private(*dm, numCells, numVertices, numCorners, cells, &sfVert);CHKERRQ(ierr);
2378   if (interpolate) {
2379     DM idm = NULL;
2380 
2381     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
2382     ierr = DMDestroy(dm);CHKERRQ(ierr);
2383     *dm  = idm;
2384   }
2385   ierr = DMPlexBuildCoordinates_Parallel_Private(*dm, spaceDim, numCells, numVertices,sfVert, vertexCoords);CHKERRQ(ierr);
2386   if (vertexSF) *vertexSF = sfVert;
2387   else {ierr = PetscSFDestroy(&sfVert);CHKERRQ(ierr);}
2388   PetscFunctionReturn(0);
2389 }
2390 
2391 /*
2392   This takes as input the common mesh generator output, a list of the vertices for each cell
2393 */
2394 static PetscErrorCode DMPlexBuildFromCellList_Private(DM dm, PetscInt numCells, PetscInt numVertices, PetscInt numCorners, const int cells[])
2395 {
2396   PetscInt      *cone, c, p;
2397   PetscErrorCode ierr;
2398 
2399   PetscFunctionBegin;
2400   ierr = DMPlexSetChart(dm, 0, numCells+numVertices);CHKERRQ(ierr);
2401   for (c = 0; c < numCells; ++c) {
2402     ierr = DMPlexSetConeSize(dm, c, numCorners);CHKERRQ(ierr);
2403   }
2404   ierr = DMSetUp(dm);CHKERRQ(ierr);
2405   ierr = DMGetWorkArray(dm, numCorners, PETSC_INT, &cone);CHKERRQ(ierr);
2406   for (c = 0; c < numCells; ++c) {
2407     for (p = 0; p < numCorners; ++p) {
2408       cone[p] = cells[c*numCorners+p]+numCells;
2409     }
2410     ierr = DMPlexSetCone(dm, c, cone);CHKERRQ(ierr);
2411   }
2412   ierr = DMRestoreWorkArray(dm, numCorners, PETSC_INT, &cone);CHKERRQ(ierr);
2413   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
2414   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
2415   PetscFunctionReturn(0);
2416 }
2417 
2418 /*
2419   This takes as input the coordinates for each vertex
2420 */
2421 static PetscErrorCode DMPlexBuildCoordinates_Private(DM dm, PetscInt spaceDim, PetscInt numCells, PetscInt numVertices, const double vertexCoords[])
2422 {
2423   PetscSection   coordSection;
2424   Vec            coordinates;
2425   DM             cdm;
2426   PetscScalar   *coords;
2427   PetscInt       v, d;
2428   PetscErrorCode ierr;
2429 
2430   PetscFunctionBegin;
2431   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
2432   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
2433   ierr = PetscSectionSetFieldComponents(coordSection, 0, spaceDim);CHKERRQ(ierr);
2434   ierr = PetscSectionSetChart(coordSection, numCells, numCells + numVertices);CHKERRQ(ierr);
2435   for (v = numCells; v < numCells+numVertices; ++v) {
2436     ierr = PetscSectionSetDof(coordSection, v, spaceDim);CHKERRQ(ierr);
2437     ierr = PetscSectionSetFieldDof(coordSection, v, 0, spaceDim);CHKERRQ(ierr);
2438   }
2439   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
2440 
2441   ierr = DMGetCoordinateDM(dm, &cdm);CHKERRQ(ierr);
2442   ierr = DMCreateLocalVector(cdm, &coordinates);CHKERRQ(ierr);
2443   ierr = VecSetBlockSize(coordinates, spaceDim);CHKERRQ(ierr);
2444   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
2445   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
2446   for (v = 0; v < numVertices; ++v) {
2447     for (d = 0; d < spaceDim; ++d) {
2448       coords[v*spaceDim+d] = vertexCoords[v*spaceDim+d];
2449     }
2450   }
2451   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
2452   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
2453   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
2454   PetscFunctionReturn(0);
2455 }
2456 
2457 /*@C
2458   DMPlexCreateFromCellList - This takes as input common mesh generator output, a list of the vertices for each cell, and produces a DM
2459 
2460   Input Parameters:
2461 + comm - The communicator
2462 . dim - The topological dimension of the mesh
2463 . numCells - The number of cells
2464 . numVertices - The number of vertices
2465 . numCorners - The number of vertices for each cell
2466 . interpolate - Flag indicating that intermediate mesh entities (faces, edges) should be created automatically
2467 . cells - An array of numCells*numCorners numbers, the vertices for each cell
2468 . spaceDim - The spatial dimension used for coordinates
2469 - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex
2470 
2471   Output Parameter:
2472 . dm - The DM
2473 
2474   Note: Two triangles sharing a face
2475 $
2476 $        2
2477 $      / | \
2478 $     /  |  \
2479 $    /   |   \
2480 $   0  0 | 1  3
2481 $    \   |   /
2482 $     \  |  /
2483 $      \ | /
2484 $        1
2485 would have input
2486 $  numCells = 2, numVertices = 4
2487 $  cells = [0 1 2  1 3 2]
2488 $
2489 which would result in the DMPlex
2490 $
2491 $        4
2492 $      / | \
2493 $     /  |  \
2494 $    /   |   \
2495 $   2  0 | 1  5
2496 $    \   |   /
2497 $     \  |  /
2498 $      \ | /
2499 $        3
2500 
2501   Level: beginner
2502 
2503 .seealso: DMPlexCreateFromDAG(), DMPlexCreate()
2504 @*/
2505 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)
2506 {
2507   PetscErrorCode ierr;
2508 
2509   PetscFunctionBegin;
2510   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
2511   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
2512   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
2513   ierr = DMPlexBuildFromCellList_Private(*dm, numCells, numVertices, numCorners, cells);CHKERRQ(ierr);
2514   if (interpolate) {
2515     DM idm = NULL;
2516 
2517     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
2518     ierr = DMDestroy(dm);CHKERRQ(ierr);
2519     *dm  = idm;
2520   }
2521   ierr = DMPlexBuildCoordinates_Private(*dm, spaceDim, numCells, numVertices, vertexCoords);CHKERRQ(ierr);
2522   PetscFunctionReturn(0);
2523 }
2524 
2525 /*@
2526   DMPlexCreateFromDAG - This takes as input the adjacency-list representation of the Directed Acyclic Graph (Hasse Diagram) encoding a mesh, and produces a DM
2527 
2528   Input Parameters:
2529 + dm - The empty DM object, usually from DMCreate() and DMSetDimension()
2530 . depth - The depth of the DAG
2531 . numPoints - The number of points at each depth
2532 . coneSize - The cone size of each point
2533 . cones - The concatenation of the cone points for each point, the cone list must be oriented correctly for each point
2534 . coneOrientations - The orientation of each cone point
2535 - vertexCoords - An array of numVertices*dim numbers, the coordinates of each vertex
2536 
2537   Output Parameter:
2538 . dm - The DM
2539 
2540   Note: Two triangles sharing a face would have input
2541 $  depth = 1, numPoints = [4 2], coneSize = [3 3 0 0 0 0]
2542 $  cones = [2 3 4  3 5 4], coneOrientations = [0 0 0  0 0 0]
2543 $ vertexCoords = [-1.0 0.0  0.0 -1.0  0.0 1.0  1.0 0.0]
2544 $
2545 which would result in the DMPlex
2546 $
2547 $        4
2548 $      / | \
2549 $     /  |  \
2550 $    /   |   \
2551 $   2  0 | 1  5
2552 $    \   |   /
2553 $     \  |  /
2554 $      \ | /
2555 $        3
2556 $
2557 $ Notice that all points are numbered consecutively, unlikely DMPlexCreateFromCellList()
2558 
2559   Level: advanced
2560 
2561 .seealso: DMPlexCreateFromCellList(), DMPlexCreate()
2562 @*/
2563 PetscErrorCode DMPlexCreateFromDAG(DM dm, PetscInt depth, const PetscInt numPoints[], const PetscInt coneSize[], const PetscInt cones[], const PetscInt coneOrientations[], const PetscScalar vertexCoords[])
2564 {
2565   Vec            coordinates;
2566   PetscSection   coordSection;
2567   PetscScalar    *coords;
2568   PetscInt       coordSize, firstVertex = -1, pStart = 0, pEnd = 0, p, v, dim, dimEmbed, d, off;
2569   PetscErrorCode ierr;
2570 
2571   PetscFunctionBegin;
2572   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
2573   ierr = DMGetCoordinateDim(dm, &dimEmbed);CHKERRQ(ierr);
2574   if (dimEmbed < dim) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Embedding dimension %d cannot be less than intrinsic dimension %d",dimEmbed,dim);
2575   for (d = 0; d <= depth; ++d) pEnd += numPoints[d];
2576   ierr = DMPlexSetChart(dm, pStart, pEnd);CHKERRQ(ierr);
2577   for (p = pStart; p < pEnd; ++p) {
2578     ierr = DMPlexSetConeSize(dm, p, coneSize[p-pStart]);CHKERRQ(ierr);
2579     if (firstVertex < 0 && !coneSize[p - pStart]) {
2580       firstVertex = p - pStart;
2581     }
2582   }
2583   if (firstVertex < 0 && numPoints[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Expected %d vertices but could not find any", numPoints[0]);
2584   ierr = DMSetUp(dm);CHKERRQ(ierr); /* Allocate space for cones */
2585   for (p = pStart, off = 0; p < pEnd; off += coneSize[p-pStart], ++p) {
2586     ierr = DMPlexSetCone(dm, p, &cones[off]);CHKERRQ(ierr);
2587     ierr = DMPlexSetConeOrientation(dm, p, &coneOrientations[off]);CHKERRQ(ierr);
2588   }
2589   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
2590   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
2591   /* Build coordinates */
2592   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
2593   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
2594   ierr = PetscSectionSetFieldComponents(coordSection, 0, dimEmbed);CHKERRQ(ierr);
2595   ierr = PetscSectionSetChart(coordSection, firstVertex, firstVertex+numPoints[0]);CHKERRQ(ierr);
2596   for (v = firstVertex; v < firstVertex+numPoints[0]; ++v) {
2597     ierr = PetscSectionSetDof(coordSection, v, dimEmbed);CHKERRQ(ierr);
2598     ierr = PetscSectionSetFieldDof(coordSection, v, 0, dimEmbed);CHKERRQ(ierr);
2599   }
2600   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
2601   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
2602   ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
2603   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
2604   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
2605   ierr = VecSetBlockSize(coordinates, dimEmbed);CHKERRQ(ierr);
2606   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
2607   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
2608   for (v = 0; v < numPoints[0]; ++v) {
2609     PetscInt off;
2610 
2611     ierr = PetscSectionGetOffset(coordSection, v+firstVertex, &off);CHKERRQ(ierr);
2612     for (d = 0; d < dimEmbed; ++d) {
2613       coords[off+d] = vertexCoords[v*dimEmbed+d];
2614     }
2615   }
2616   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
2617   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
2618   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
2619   PetscFunctionReturn(0);
2620 }
2621 
2622 /*@C
2623   DMPlexCreateFromFile - This takes a filename and produces a DM
2624 
2625   Input Parameters:
2626 + comm - The communicator
2627 . filename - A file name
2628 - interpolate - Flag to create intermediate mesh pieces (edges, faces)
2629 
2630   Output Parameter:
2631 . dm - The DM
2632 
2633   Level: beginner
2634 
2635 .seealso: DMPlexCreateFromDAG(), DMPlexCreateFromCellList(), DMPlexCreate()
2636 @*/
2637 PetscErrorCode DMPlexCreateFromFile(MPI_Comm comm, const char filename[], PetscBool interpolate, DM *dm)
2638 {
2639   const char    *extGmsh   = ".msh";
2640   const char    *extCGNS   = ".cgns";
2641   const char    *extExodus = ".exo";
2642   const char    *extFluent = ".cas";
2643   const char    *extHDF5   = ".h5";
2644   const char    *extMed    = ".med";
2645   const char    *extPLY    = ".ply";
2646   size_t         len;
2647   PetscBool      isGmsh, isCGNS, isExodus, isFluent, isHDF5, isMed, isPLY;
2648   PetscMPIInt    rank;
2649   PetscErrorCode ierr;
2650 
2651   PetscFunctionBegin;
2652   PetscValidPointer(filename, 2);
2653   PetscValidPointer(dm, 4);
2654   ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
2655   ierr = PetscStrlen(filename, &len);CHKERRQ(ierr);
2656   if (!len) SETERRQ(comm, PETSC_ERR_ARG_WRONG, "Filename must be a valid path");
2657   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extGmsh,   4, &isGmsh);CHKERRQ(ierr);
2658   ierr = PetscStrncmp(&filename[PetscMax(0,len-5)], extCGNS,   5, &isCGNS);CHKERRQ(ierr);
2659   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extExodus, 4, &isExodus);CHKERRQ(ierr);
2660   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extFluent, 4, &isFluent);CHKERRQ(ierr);
2661   ierr = PetscStrncmp(&filename[PetscMax(0,len-3)], extHDF5,   3, &isHDF5);CHKERRQ(ierr);
2662   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extMed,    4, &isMed);CHKERRQ(ierr);
2663   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extPLY,    4, &isPLY);CHKERRQ(ierr);
2664   if (isGmsh) {
2665     ierr = DMPlexCreateGmshFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
2666   } else if (isCGNS) {
2667     ierr = DMPlexCreateCGNSFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
2668   } else if (isExodus) {
2669     ierr = DMPlexCreateExodusFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
2670   } else if (isFluent) {
2671     ierr = DMPlexCreateFluentFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
2672   } else if (isHDF5) {
2673     PetscViewer viewer;
2674 
2675     ierr = PetscViewerCreate(comm, &viewer);CHKERRQ(ierr);
2676     ierr = PetscViewerSetType(viewer, PETSCVIEWERHDF5);CHKERRQ(ierr);
2677     ierr = PetscViewerFileSetMode(viewer, FILE_MODE_READ);CHKERRQ(ierr);
2678     ierr = PetscViewerFileSetName(viewer, filename);CHKERRQ(ierr);
2679     ierr = DMCreate(comm, dm);CHKERRQ(ierr);
2680     ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
2681     ierr = DMLoad(*dm, viewer);CHKERRQ(ierr);
2682     ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
2683   } else if (isMed) {
2684     ierr = DMPlexCreateMedFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
2685   } else if (isPLY) {
2686     ierr = DMPlexCreatePLYFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
2687   } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cannot load file %s: unrecognized extension", filename);
2688   PetscFunctionReturn(0);
2689 }
2690 
2691 /*@
2692   DMPlexCreateReferenceCell - Create a DMPLEX with the appropriate FEM reference cell
2693 
2694   Collective on comm
2695 
2696   Input Parameters:
2697 + comm    - The communicator
2698 . dim     - The spatial dimension
2699 - simplex - Flag for simplex, otherwise use a tensor-product cell
2700 
2701   Output Parameter:
2702 . refdm - The reference cell
2703 
2704   Level: intermediate
2705 
2706 .keywords: reference cell
2707 .seealso:
2708 @*/
2709 PetscErrorCode DMPlexCreateReferenceCell(MPI_Comm comm, PetscInt dim, PetscBool simplex, DM *refdm)
2710 {
2711   DM             rdm;
2712   Vec            coords;
2713   PetscErrorCode ierr;
2714 
2715   PetscFunctionBeginUser;
2716   ierr = DMCreate(comm, &rdm);CHKERRQ(ierr);
2717   ierr = DMSetType(rdm, DMPLEX);CHKERRQ(ierr);
2718   ierr = DMSetDimension(rdm, dim);CHKERRQ(ierr);
2719   switch (dim) {
2720   case 0:
2721   {
2722     PetscInt    numPoints[1]        = {1};
2723     PetscInt    coneSize[1]         = {0};
2724     PetscInt    cones[1]            = {0};
2725     PetscInt    coneOrientations[1] = {0};
2726     PetscScalar vertexCoords[1]     = {0.0};
2727 
2728     ierr = DMPlexCreateFromDAG(rdm, 0, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2729   }
2730   break;
2731   case 1:
2732   {
2733     PetscInt    numPoints[2]        = {2, 1};
2734     PetscInt    coneSize[3]         = {2, 0, 0};
2735     PetscInt    cones[2]            = {1, 2};
2736     PetscInt    coneOrientations[2] = {0, 0};
2737     PetscScalar vertexCoords[2]     = {-1.0,  1.0};
2738 
2739     ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2740   }
2741   break;
2742   case 2:
2743     if (simplex) {
2744       PetscInt    numPoints[2]        = {3, 1};
2745       PetscInt    coneSize[4]         = {3, 0, 0, 0};
2746       PetscInt    cones[3]            = {1, 2, 3};
2747       PetscInt    coneOrientations[3] = {0, 0, 0};
2748       PetscScalar vertexCoords[6]     = {-1.0, -1.0,  1.0, -1.0,  -1.0, 1.0};
2749 
2750       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2751     } else {
2752       PetscInt    numPoints[2]        = {4, 1};
2753       PetscInt    coneSize[5]         = {4, 0, 0, 0, 0};
2754       PetscInt    cones[4]            = {1, 2, 3, 4};
2755       PetscInt    coneOrientations[4] = {0, 0, 0, 0};
2756       PetscScalar vertexCoords[8]     = {-1.0, -1.0,  1.0, -1.0,  1.0, 1.0,  -1.0, 1.0};
2757 
2758       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2759     }
2760   break;
2761   case 3:
2762     if (simplex) {
2763       PetscInt    numPoints[2]        = {4, 1};
2764       PetscInt    coneSize[5]         = {4, 0, 0, 0, 0};
2765       PetscInt    cones[4]            = {1, 3, 2, 4};
2766       PetscInt    coneOrientations[4] = {0, 0, 0, 0};
2767       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};
2768 
2769       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2770     } else {
2771       PetscInt    numPoints[2]        = {8, 1};
2772       PetscInt    coneSize[9]         = {8, 0, 0, 0, 0, 0, 0, 0, 0};
2773       PetscInt    cones[8]            = {1, 4, 3, 2, 5, 6, 7, 8};
2774       PetscInt    coneOrientations[8] = {0, 0, 0, 0, 0, 0, 0, 0};
2775       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,
2776                                          -1.0, -1.0,  1.0,  1.0, -1.0,  1.0,  1.0, 1.0,  1.0,  -1.0, 1.0,  1.0};
2777 
2778       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2779     }
2780   break;
2781   default:
2782     SETERRQ1(comm, PETSC_ERR_ARG_WRONG, "Cannot create reference cell for dimension %d", dim);
2783   }
2784   *refdm = NULL;
2785   ierr = DMPlexInterpolate(rdm, refdm);CHKERRQ(ierr);
2786   if (rdm->coordinateDM) {
2787     DM           ncdm;
2788     PetscSection cs;
2789     PetscInt     pEnd = -1;
2790 
2791     ierr = DMGetDefaultSection(rdm->coordinateDM, &cs);CHKERRQ(ierr);
2792     if (cs) {ierr = PetscSectionGetChart(cs, NULL, &pEnd);CHKERRQ(ierr);}
2793     if (pEnd >= 0) {
2794       ierr = DMClone(rdm->coordinateDM, &ncdm);CHKERRQ(ierr);
2795       ierr = DMSetDefaultSection(ncdm, cs);CHKERRQ(ierr);
2796       ierr = DMSetCoordinateDM(*refdm, ncdm);CHKERRQ(ierr);
2797       ierr = DMDestroy(&ncdm);CHKERRQ(ierr);
2798     }
2799   }
2800   ierr = DMGetCoordinatesLocal(rdm, &coords);CHKERRQ(ierr);
2801   if (coords) {
2802     ierr = DMSetCoordinatesLocal(*refdm, coords);CHKERRQ(ierr);
2803   } else {
2804     ierr = DMGetCoordinates(rdm, &coords);CHKERRQ(ierr);
2805     if (coords) {ierr = DMSetCoordinates(*refdm, coords);CHKERRQ(ierr);}
2806   }
2807   ierr = DMDestroy(&rdm);CHKERRQ(ierr);
2808   PetscFunctionReturn(0);
2809 }
2810