xref: /petsc/src/dm/impls/plex/plexcreate.c (revision 390e1bf27627d887df99a9f4d0d0ad68037f55ec)
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 static PetscErrorCode DMPlexCreateCubeMesh_Internal(DM dm, const PetscReal lower[], const PetscReal upper[], const PetscInt edges[], DMBoundaryType bdX, DMBoundaryType bdY, DMBoundaryType bdZ)
437 {
438   PetscInt       markerTop      = 1, faceMarkerTop      = 1;
439   PetscInt       markerBottom   = 1, faceMarkerBottom   = 1;
440   PetscInt       markerFront    = 1, faceMarkerFront    = 1;
441   PetscInt       markerBack     = 1, faceMarkerBack     = 1;
442   PetscInt       markerRight    = 1, faceMarkerRight    = 1;
443   PetscInt       markerLeft     = 1, faceMarkerLeft     = 1;
444   PetscInt       dim;
445   PetscBool      markerSeparate = PETSC_FALSE;
446   PetscMPIInt    rank;
447   PetscErrorCode ierr;
448 
449   PetscFunctionBegin;
450   ierr = DMGetDimension(dm,&dim);CHKERRQ(ierr);
451   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);CHKERRQ(ierr);
452   ierr = DMCreateLabel(dm,"marker");CHKERRQ(ierr);
453   ierr = DMCreateLabel(dm,"Face Sets");CHKERRQ(ierr);
454   switch (dim) {
455   case 2:
456     faceMarkerTop    = 3;
457     faceMarkerBottom = 1;
458     faceMarkerRight  = 2;
459     faceMarkerLeft   = 4;
460     break;
461   case 3:
462     faceMarkerBottom = 1;
463     faceMarkerTop    = 2;
464     faceMarkerFront  = 3;
465     faceMarkerBack   = 4;
466     faceMarkerRight  = 5;
467     faceMarkerLeft   = 6;
468     break;
469   default:
470     SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Dimension %d not supported",dim);
471     break;
472   }
473   ierr = PetscOptionsGetBool(((PetscObject) dm)->options,((PetscObject) dm)->prefix, "-dm_plex_separate_marker", &markerSeparate, NULL);CHKERRQ(ierr);
474   if (markerSeparate) {
475     markerBottom = faceMarkerBottom;
476     markerTop    = faceMarkerTop;
477     markerFront  = faceMarkerFront;
478     markerBack   = faceMarkerBack;
479     markerRight  = faceMarkerRight;
480     markerLeft   = faceMarkerLeft;
481   }
482   {
483     const PetscInt numXEdges    = !rank ? edges[0] : 0;
484     const PetscInt numYEdges    = !rank ? edges[1] : 0;
485     const PetscInt numZEdges    = !rank ? edges[2] : 0;
486     const PetscInt numXVertices = !rank ? (bdX == DM_BOUNDARY_PERIODIC || bdX == DM_BOUNDARY_TWIST ? edges[0] : edges[0]+1) : 0;
487     const PetscInt numYVertices = !rank ? (bdY == DM_BOUNDARY_PERIODIC || bdY == DM_BOUNDARY_TWIST ? edges[1] : edges[1]+1) : 0;
488     const PetscInt numZVertices = !rank ? (bdZ == DM_BOUNDARY_PERIODIC || bdZ == DM_BOUNDARY_TWIST ? edges[2] : edges[2]+1) : 0;
489     const PetscInt numCells     = numXEdges*numYEdges*numZEdges;
490     const PetscInt numXFaces    = numYEdges*numZEdges;
491     const PetscInt numYFaces    = numXEdges*numZEdges;
492     const PetscInt numZFaces    = numXEdges*numYEdges;
493     const PetscInt numTotXFaces = numXVertices*numXFaces;
494     const PetscInt numTotYFaces = numYVertices*numYFaces;
495     const PetscInt numTotZFaces = numZVertices*numZFaces;
496     const PetscInt numFaces     = numTotXFaces + numTotYFaces + numTotZFaces;
497     const PetscInt numTotXEdges = numXEdges*numYVertices*numZVertices;
498     const PetscInt numTotYEdges = numYEdges*numXVertices*numZVertices;
499     const PetscInt numTotZEdges = numZEdges*numXVertices*numYVertices;
500     const PetscInt numVertices  = numXVertices*numYVertices*numZVertices;
501     const PetscInt numEdges     = numTotXEdges + numTotYEdges + numTotZEdges;
502     const PetscInt firstVertex  = (dim == 2) ? numFaces : numCells;
503     const PetscInt firstXFace   = (dim == 2) ? 0 : numCells + numVertices;
504     const PetscInt firstYFace   = firstXFace + numTotXFaces;
505     const PetscInt firstZFace   = firstYFace + numTotYFaces;
506     const PetscInt firstXEdge   = numCells + numFaces + numVertices;
507     const PetscInt firstYEdge   = firstXEdge + numTotXEdges;
508     const PetscInt firstZEdge   = firstYEdge + numTotYEdges;
509     Vec            coordinates;
510     PetscSection   coordSection;
511     PetscScalar   *coords;
512     PetscInt       coordSize;
513     PetscInt       v, vx, vy, vz;
514     PetscInt       c, f, fx, fy, fz, e, ex, ey, ez;
515 
516     ierr = DMPlexSetChart(dm, 0, numCells+numFaces+numEdges+numVertices);CHKERRQ(ierr);
517     for (c = 0; c < numCells; c++) {
518       ierr = DMPlexSetConeSize(dm, c, 6);CHKERRQ(ierr);
519     }
520     for (f = firstXFace; f < firstXFace+numFaces; ++f) {
521       ierr = DMPlexSetConeSize(dm, f, 4);CHKERRQ(ierr);
522     }
523     for (e = firstXEdge; e < firstXEdge+numEdges; ++e) {
524       ierr = DMPlexSetConeSize(dm, e, 2);CHKERRQ(ierr);
525     }
526     ierr = DMSetUp(dm);CHKERRQ(ierr); /* Allocate space for cones */
527     /* Build cells */
528     for (fz = 0; fz < numZEdges; ++fz) {
529       for (fy = 0; fy < numYEdges; ++fy) {
530         for (fx = 0; fx < numXEdges; ++fx) {
531           PetscInt cell    = (fz*numYEdges + fy)*numXEdges + fx;
532           PetscInt faceB   = firstZFace + (fy*numXEdges+fx)*numZVertices +   fz;
533           PetscInt faceT   = firstZFace + (fy*numXEdges+fx)*numZVertices + ((fz+1)%numZVertices);
534           PetscInt faceF   = firstYFace + (fz*numXEdges+fx)*numYVertices +   fy;
535           PetscInt faceK   = firstYFace + (fz*numXEdges+fx)*numYVertices + ((fy+1)%numYVertices);
536           PetscInt faceL   = firstXFace + (fz*numYEdges+fy)*numXVertices +   fx;
537           PetscInt faceR   = firstXFace + (fz*numYEdges+fy)*numXVertices + ((fx+1)%numXVertices);
538                             /* B,  T,  F,  K,  R,  L */
539           PetscInt ornt[6] = {-4,  0,  0, -1,  0, -4}; /* ??? */
540           PetscInt cone[6];
541 
542           /* no boundary twisting in 3D */
543           cone[0] = faceB; cone[1] = faceT; cone[2] = faceF; cone[3] = faceK; cone[4] = faceR; cone[5] = faceL;
544           ierr    = DMPlexSetCone(dm, cell, cone);CHKERRQ(ierr);
545           ierr    = DMPlexSetConeOrientation(dm, cell, ornt);CHKERRQ(ierr);
546         }
547       }
548     }
549     /* Build x faces */
550     for (fz = 0; fz < numZEdges; ++fz) {
551       for (fy = 0; fy < numYEdges; ++fy) {
552         for (fx = 0; fx < numXVertices; ++fx) {
553           PetscInt face    = firstXFace + (fz*numYEdges+fy)*numXVertices + fx;
554           PetscInt edgeL   = firstZEdge + (  fy*                 numXVertices+fx)*numZEdges + fz;
555           PetscInt edgeR   = firstZEdge + (((fy+1)%numYVertices)*numXVertices+fx)*numZEdges + fz;
556           PetscInt edgeB   = firstYEdge + (  fz*                 numXVertices+fx)*numYEdges + fy;
557           PetscInt edgeT   = firstYEdge + (((fz+1)%numZVertices)*numXVertices+fx)*numYEdges + fy;
558           PetscInt ornt[4] = {0, 0, -2, -2};
559           PetscInt cone[4];
560 
561           if (dim == 3) {
562             /* markers */
563             if (bdX != DM_BOUNDARY_PERIODIC) {
564               if (fx == numXVertices-1) {
565                 ierr = DMSetLabelValue(dm, "Face Sets", face, faceMarkerRight);CHKERRQ(ierr);
566                 ierr = DMSetLabelValue(dm, "marker", face, markerRight);CHKERRQ(ierr);
567               }
568               else if (fx == 0) {
569                 ierr = DMSetLabelValue(dm, "Face Sets", face, faceMarkerLeft);CHKERRQ(ierr);
570                 ierr = DMSetLabelValue(dm, "marker", face, markerLeft);CHKERRQ(ierr);
571               }
572             }
573           }
574           cone[0] = edgeB; cone[1] = edgeR; cone[2] = edgeT; cone[3] = edgeL;
575           ierr    = DMPlexSetCone(dm, face, cone);CHKERRQ(ierr);
576           ierr    = DMPlexSetConeOrientation(dm, face, ornt);CHKERRQ(ierr);
577         }
578       }
579     }
580     /* Build y faces */
581     for (fz = 0; fz < numZEdges; ++fz) {
582       for (fx = 0; fx < numXEdges; ++fx) {
583         for (fy = 0; fy < numYVertices; ++fy) {
584           PetscInt face    = firstYFace + (fz*numXEdges+fx)*numYVertices + fy;
585           PetscInt edgeL   = firstZEdge + (fy*numXVertices+  fx                 )*numZEdges + fz;
586           PetscInt edgeR   = firstZEdge + (fy*numXVertices+((fx+1)%numXVertices))*numZEdges + fz;
587           PetscInt edgeB   = firstXEdge + (  fz                 *numYVertices+fy)*numXEdges + fx;
588           PetscInt edgeT   = firstXEdge + (((fz+1)%numZVertices)*numYVertices+fy)*numXEdges + fx;
589           PetscInt ornt[4] = {0, 0, -2, -2};
590           PetscInt cone[4];
591 
592           if (dim == 3) {
593             /* markers */
594             if (bdY != DM_BOUNDARY_PERIODIC) {
595               if (fy == numYVertices-1) {
596                 ierr = DMSetLabelValue(dm, "Face Sets", face, faceMarkerBack);CHKERRQ(ierr);
597                 ierr = DMSetLabelValue(dm, "marker", face, markerBack);CHKERRQ(ierr);
598               }
599               else if (fy == 0) {
600                 ierr = DMSetLabelValue(dm, "Face Sets", face, faceMarkerFront);CHKERRQ(ierr);
601                 ierr = DMSetLabelValue(dm, "marker", face, markerFront);CHKERRQ(ierr);
602               }
603             }
604           }
605           cone[0] = edgeB; cone[1] = edgeR; cone[2] = edgeT; cone[3] = edgeL;
606           ierr    = DMPlexSetCone(dm, face, cone);CHKERRQ(ierr);
607           ierr    = DMPlexSetConeOrientation(dm, face, ornt);CHKERRQ(ierr);
608         }
609       }
610     }
611     /* Build z faces */
612     for (fy = 0; fy < numYEdges; ++fy) {
613       for (fx = 0; fx < numXEdges; ++fx) {
614         for (fz = 0; fz < numZVertices; fz++) {
615           PetscInt face    = firstZFace + (fy*numXEdges+fx)*numZVertices + fz;
616           PetscInt edgeL   = firstYEdge + (fz*numXVertices+  fx                 )*numYEdges + fy;
617           PetscInt edgeR   = firstYEdge + (fz*numXVertices+((fx+1)%numXVertices))*numYEdges + fy;
618           PetscInt edgeB   = firstXEdge + (fz*numYVertices+  fy                 )*numXEdges + fx;
619           PetscInt edgeT   = firstXEdge + (fz*numYVertices+((fy+1)%numYVertices))*numXEdges + fx;
620           PetscInt ornt[4] = {0, 0, -2, -2};
621           PetscInt cone[4];
622 
623           if (dim == 2) {
624             if (bdX == DM_BOUNDARY_TWIST && fx == numXEdges-1) {edgeR += numYEdges-1-2*fy; ornt[1] = -2;}
625             if (bdY == DM_BOUNDARY_TWIST && fy == numYEdges-1) {edgeT += numXEdges-1-2*fx; ornt[2] =  0;}
626           }
627           else {
628             /* markers */
629             if (bdZ != DM_BOUNDARY_PERIODIC) {
630               if (fz == numZVertices-1) {
631                 ierr = DMSetLabelValue(dm, "Face Sets", face, faceMarkerTop);CHKERRQ(ierr);
632                 ierr = DMSetLabelValue(dm, "marker", face, markerTop);CHKERRQ(ierr);
633               }
634               else if (fz == 0) {
635                 ierr = DMSetLabelValue(dm, "Face Sets", face, faceMarkerBottom);CHKERRQ(ierr);
636                 ierr = DMSetLabelValue(dm, "marker", face, markerBottom);CHKERRQ(ierr);
637               }
638             }
639           }
640           cone[0] = edgeB; cone[1] = edgeR; cone[2] = edgeT; cone[3] = edgeL;
641           ierr    = DMPlexSetCone(dm, face, cone);CHKERRQ(ierr);
642           ierr    = DMPlexSetConeOrientation(dm, face, ornt);CHKERRQ(ierr);
643         }
644       }
645     }
646     /* Build Z edges*/
647     for (vy = 0; vy < numYVertices; vy++) {
648       for (vx = 0; vx < numXVertices; vx++) {
649         for (ez = 0; ez < numZEdges; ez++) {
650           const PetscInt edge    = firstZEdge  + (vy*numXVertices+vx)*numZEdges + ez;
651           const PetscInt vertexB = firstVertex + (  ez                 *numYVertices+vy)*numXVertices + vx;
652           const PetscInt vertexT = firstVertex + (((ez+1)%numZVertices)*numYVertices+vy)*numXVertices + vx;
653           PetscInt       cone[2];
654 
655           if (dim == 3) {
656             if (bdX != DM_BOUNDARY_PERIODIC) {
657               if (vx == numXVertices-1) {
658                 ierr = DMSetLabelValue(dm, "marker", edge, markerRight);CHKERRQ(ierr);
659               }
660               else if (vx == 0) {
661                 ierr = DMSetLabelValue(dm, "marker", edge, markerLeft);CHKERRQ(ierr);
662               }
663             }
664             if (bdY != DM_BOUNDARY_PERIODIC) {
665               if (vy == numYVertices-1) {
666                 ierr = DMSetLabelValue(dm, "marker", edge, markerBack);CHKERRQ(ierr);
667               }
668               else if (vy == 0) {
669                 ierr = DMSetLabelValue(dm, "marker", edge, markerFront);CHKERRQ(ierr);
670               }
671             }
672           }
673           cone[0] = vertexB; cone[1] = vertexT;
674           ierr = DMPlexSetCone(dm, edge, cone);CHKERRQ(ierr);
675         }
676       }
677     }
678     /* Build Y edges*/
679     for (vz = 0; vz < numZVertices; vz++) {
680       for (vx = 0; vx < numXVertices; vx++) {
681         for (ey = 0; ey < numYEdges; ey++) {
682           const PetscInt nextv   = (dim == 2 && bdY == DM_BOUNDARY_TWIST && ey == numYEdges-1) ? (numXVertices-vx-1) : (vz*numYVertices+((ey+1)%numYVertices))*numXVertices + vx;
683           const PetscInt edge    = firstYEdge  + (vz*numXVertices+vx)*numYEdges + ey;
684           const PetscInt vertexF = firstVertex + (vz*numYVertices+ey)*numXVertices + vx;
685           const PetscInt vertexK = firstVertex + nextv;
686           PetscInt       cone[2];
687 
688           cone[0] = vertexF; cone[1] = vertexK;
689           ierr = DMPlexSetCone(dm, edge, cone);CHKERRQ(ierr);
690           if (dim == 2) {
691             if ((bdX != DM_BOUNDARY_PERIODIC) && (bdX != DM_BOUNDARY_TWIST)) {
692               if (vx == numXVertices-1) {
693                 ierr = DMSetLabelValue(dm, "Face Sets", edge, faceMarkerRight);CHKERRQ(ierr);
694                 ierr = DMSetLabelValue(dm, "marker", edge,    markerRight);CHKERRQ(ierr);
695                 ierr = DMSetLabelValue(dm, "marker", cone[0], markerRight);CHKERRQ(ierr);
696                 if (ey == numYEdges-1) {
697                   ierr = DMSetLabelValue(dm, "marker", cone[1], markerRight);CHKERRQ(ierr);
698                 }
699               }
700               else if (vx == 0) {
701                 ierr = DMSetLabelValue(dm, "Face Sets", edge, faceMarkerLeft);CHKERRQ(ierr);
702                 ierr = DMSetLabelValue(dm, "marker", edge,    markerLeft);CHKERRQ(ierr);
703                 ierr = DMSetLabelValue(dm, "marker", cone[0], markerLeft);CHKERRQ(ierr);
704                 if (ey == numYEdges-1) {
705                   ierr = DMSetLabelValue(dm, "marker", cone[1], markerLeft);CHKERRQ(ierr);
706                 }
707               }
708             }
709           }
710           else {
711             if (bdX != DM_BOUNDARY_PERIODIC) {
712               if (vx == numXVertices-1) {
713                 ierr = DMSetLabelValue(dm, "marker", edge, markerRight);CHKERRQ(ierr);
714               }
715               else if (vx == 0) {
716                 ierr = DMSetLabelValue(dm, "marker", edge, markerLeft);CHKERRQ(ierr);
717               }
718             }
719             if (bdZ != DM_BOUNDARY_PERIODIC) {
720               if (vz == numZVertices-1) {
721                 ierr = DMSetLabelValue(dm, "marker", edge, markerTop);CHKERRQ(ierr);
722               }
723               else if (vz == 0) {
724                 ierr = DMSetLabelValue(dm, "marker", edge, markerBottom);CHKERRQ(ierr);
725               }
726             }
727           }
728         }
729       }
730     }
731     /* Build X edges*/
732     for (vz = 0; vz < numZVertices; vz++) {
733       for (vy = 0; vy < numYVertices; vy++) {
734         for (ex = 0; ex < numXEdges; ex++) {
735           const PetscInt nextv   = (dim == 2 && bdX == DM_BOUNDARY_TWIST && ex == numXEdges-1) ? (numYVertices-vy-1)*numXVertices : (vz*numYVertices+vy)*numXVertices + (ex+1)%numXVertices;
736           const PetscInt edge    = firstXEdge  + (vz*numYVertices+vy)*numXEdges + ex;
737           const PetscInt vertexL = firstVertex + (vz*numYVertices+vy)*numXVertices + ex;
738           const PetscInt vertexR = firstVertex + nextv;
739           PetscInt       cone[2];
740 
741           cone[0] = vertexL; cone[1] = vertexR;
742           ierr = DMPlexSetCone(dm, edge, cone);CHKERRQ(ierr);
743           if (dim == 2) {
744             if ((bdY != DM_BOUNDARY_PERIODIC) && (bdY != DM_BOUNDARY_TWIST)) {
745               if (vy == numYVertices-1) {
746                 ierr = DMSetLabelValue(dm, "Face Sets", edge, faceMarkerTop);CHKERRQ(ierr);
747                 ierr = DMSetLabelValue(dm, "marker", edge,    markerTop);CHKERRQ(ierr);
748                 ierr = DMSetLabelValue(dm, "marker", cone[0], markerTop);CHKERRQ(ierr);
749                 if (ex == numXEdges-1) {
750                   ierr = DMSetLabelValue(dm, "marker", cone[1], markerTop);CHKERRQ(ierr);
751                 }
752               }
753               else if (vy == 0) {
754                 ierr = DMSetLabelValue(dm, "Face Sets", edge, faceMarkerBottom);CHKERRQ(ierr);
755                 ierr = DMSetLabelValue(dm, "marker", edge,    markerBottom);CHKERRQ(ierr);
756                 ierr = DMSetLabelValue(dm, "marker", cone[0], markerBottom);CHKERRQ(ierr);
757                 if (ex == numXEdges-1) {
758                   ierr = DMSetLabelValue(dm, "marker", cone[1], markerBottom);CHKERRQ(ierr);
759                 }
760               }
761             }
762           }
763           else {
764             if (bdY != DM_BOUNDARY_PERIODIC) {
765               if (vy == numYVertices-1) {
766                 ierr = DMSetLabelValue(dm, "marker", edge, markerBack);CHKERRQ(ierr);
767               }
768               else if (vy == 0) {
769                 ierr = DMSetLabelValue(dm, "marker", edge, markerFront);CHKERRQ(ierr);
770               }
771             }
772             if (bdZ != DM_BOUNDARY_PERIODIC) {
773               if (vz == numZVertices-1) {
774                 ierr = DMSetLabelValue(dm, "marker", edge, markerTop);CHKERRQ(ierr);
775               }
776               else if (vz == 0) {
777                 ierr = DMSetLabelValue(dm, "marker", edge, markerBottom);CHKERRQ(ierr);
778               }
779             }
780           }
781         }
782       }
783     }
784     ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
785     ierr = DMPlexStratify(dm);CHKERRQ(ierr);
786     /* Build coordinates */
787     ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
788     ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
789     ierr = PetscSectionSetFieldComponents(coordSection, 0, dim);CHKERRQ(ierr);
790     ierr = PetscSectionSetChart(coordSection, firstVertex, firstVertex+numVertices);CHKERRQ(ierr);
791     for (v = firstVertex; v < firstVertex+numVertices; ++v) {
792       ierr = PetscSectionSetDof(coordSection, v, dim);CHKERRQ(ierr);
793       ierr = PetscSectionSetFieldDof(coordSection, v, 0, dim);CHKERRQ(ierr);
794     }
795     ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
796     ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
797     ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
798     ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
799     ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
800     ierr = VecSetBlockSize(coordinates, dim);CHKERRQ(ierr);
801     ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
802     ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
803     for (vz = 0; vz < numZVertices; ++vz) {
804       for (vy = 0; vy < numYVertices; ++vy) {
805         for (vx = 0; vx < numXVertices; ++vx) {
806           coords[((vz*numYVertices+vy)*numXVertices+vx)*dim+0] = lower[0] + ((upper[0] - lower[0])/numXEdges)*vx;
807           coords[((vz*numYVertices+vy)*numXVertices+vx)*dim+1] = lower[1] + ((upper[1] - lower[1])/numYEdges)*vy;
808           if (dim == 3) {
809             coords[((vz*numYVertices+vy)*numXVertices+vx)*dim+2] = lower[2] + ((upper[2] - lower[2])/numZEdges)*vz;
810           }
811         }
812       }
813     }
814     ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
815     ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
816     ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
817   }
818   PetscFunctionReturn(0);
819 }
820 
821 /*@
822   DMPlexCreateSquareMesh - Creates a 2D mesh for a square lattice.
823 
824   Collective on MPI_Comm
825 
826   Input Parameters:
827 + comm  - The communicator for the DM object
828 . lower - The lower left corner coordinates
829 . upper - The upper right corner coordinates
830 . edges - The number of cells in each direction
831 . bdX   - The boundary type for the X direction
832 - bdY   - The boundary type for the Y direction
833 
834   Output Parameter:
835 . dm  - The DM object
836 
837   Note: Here is the numbering returned for 2 cells in each direction:
838 $ 22--8-23--9--24
839 $  |     |     |
840 $ 13  2 14  3  15
841 $  |     |     |
842 $ 19--6-20--7--21
843 $  |     |     |
844 $ 10  0 11  1 12
845 $  |     |     |
846 $ 16--4-17--5--18
847 
848   Level: beginner
849 
850 .keywords: DM, create
851 .seealso: DMPlexCreateBoxMesh(), DMPlexCreateSquareBoundary(), DMPlexCreateCubeBoundary(), DMSetType(), DMCreate()
852 @*/
853 PetscErrorCode DMPlexCreateSquareMesh(DM dm, const PetscReal lower[], const PetscReal upper[], const PetscInt edges[], DMBoundaryType bdX, DMBoundaryType bdY)
854 {
855   PetscReal      lower3[3], upper3[3];
856   PetscInt       edges3[3];
857   PetscErrorCode ierr;
858 
859   PetscFunctionBegin;
860   lower3[0] = lower[0]; lower3[1] = lower[1]; lower3[2] = 0.;
861   upper3[0] = upper[0]; upper3[1] = upper[1]; upper3[2] = 0.;
862   edges3[0] = edges[0]; edges3[1] = edges[1]; edges3[2] = 0;
863   ierr = DMPlexCreateCubeMesh_Internal(dm, lower3, upper3, edges3, bdX, bdY, DM_BOUNDARY_NONE);CHKERRQ(ierr);
864   PetscFunctionReturn(0);
865 }
866 
867 /*@
868   DMPlexCreateBoxMesh - Creates a mesh on the tensor product of unit intervals (box) using simplices.
869 
870   Collective on MPI_Comm
871 
872   Input Parameters:
873 + comm - The communicator for the DM object
874 . dim - The spatial dimension
875 . numFaces - Number of faces per dimension
876 - interpolate - Flag to create intermediate mesh pieces (edges, faces)
877 
878   Output Parameter:
879 . dm  - The DM object
880 
881   Level: beginner
882 
883 .keywords: DM, create
884 .seealso: DMPlexCreateHexBoxMesh(), DMSetType(), DMCreate()
885 @*/
886 PetscErrorCode DMPlexCreateBoxMesh(MPI_Comm comm, PetscInt dim, PetscInt numFaces, PetscBool interpolate, DM *dm)
887 {
888   DM             boundary;
889   PetscErrorCode ierr;
890 
891   PetscFunctionBegin;
892   PetscValidPointer(dm, 4);
893   ierr = DMCreate(comm, &boundary);CHKERRQ(ierr);
894   PetscValidLogicalCollectiveInt(boundary,dim,2);
895   ierr = DMSetType(boundary, DMPLEX);CHKERRQ(ierr);
896   ierr = DMSetDimension(boundary, dim-1);CHKERRQ(ierr);
897   ierr = DMSetCoordinateDim(boundary, dim);CHKERRQ(ierr);
898   switch (dim) {
899   case 2:
900   {
901     PetscReal lower[2] = {0.0, 0.0};
902     PetscReal upper[2] = {1.0, 1.0};
903     PetscInt  edges[2];
904 
905     edges[0] = numFaces; edges[1] = numFaces;
906     ierr = DMPlexCreateSquareBoundary(boundary, lower, upper, edges);CHKERRQ(ierr);
907     break;
908   }
909   case 3:
910   {
911     PetscReal lower[3] = {0.0, 0.0, 0.0};
912     PetscReal upper[3] = {1.0, 1.0, 1.0};
913     PetscInt  faces[3];
914 
915     faces[0] = numFaces; faces[1] = numFaces; faces[2] = numFaces;
916     ierr = DMPlexCreateCubeBoundary(boundary, lower, upper, faces);CHKERRQ(ierr);
917     break;
918   }
919   default:
920     SETERRQ1(comm, PETSC_ERR_SUP, "Dimension not supported: %d", dim);
921   }
922   ierr = DMPlexGenerate(boundary, NULL, interpolate, dm);CHKERRQ(ierr);
923   ierr = DMDestroy(&boundary);CHKERRQ(ierr);
924   PetscFunctionReturn(0);
925 }
926 
927 /*@
928   DMPlexCreateHexBoxMesh - Creates a mesh on the tensor product of unit intervals (box) using hexahedra.
929 
930   Collective on MPI_Comm
931 
932   Input Parameters:
933 + comm  - The communicator for the DM object
934 . dim   - The spatial dimension
935 . periodicX - The boundary type for the X direction
936 . periodicY - The boundary type for the Y direction
937 . periodicZ - The boundary type for the Z direction
938 - cells - The number of cells in each direction
939 
940   Output Parameter:
941 . dm  - The DM object
942 
943   Level: beginner
944 
945 .keywords: DM, create
946 .seealso: DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
947 @*/
948 PetscErrorCode DMPlexCreateHexBoxMesh(MPI_Comm comm, PetscInt dim, const PetscInt cells[], DMBoundaryType periodicX, DMBoundaryType periodicY, DMBoundaryType periodicZ, DM *dm)
949 {
950   PetscInt       i;
951   PetscErrorCode ierr;
952 
953   PetscFunctionBegin;
954   PetscValidPointer(dm, 7);
955   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
956   PetscValidLogicalCollectiveInt(*dm,dim,2);
957   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
958   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
959   switch (dim) {
960   case 2:
961   {
962     PetscReal lower[2] = {0.0, 0.0};
963     PetscReal upper[2] = {1.0, 1.0};
964 
965     ierr = DMPlexCreateSquareMesh(*dm, lower, upper, cells, periodicX, periodicY);CHKERRQ(ierr);
966     if (periodicX == DM_BOUNDARY_PERIODIC || periodicX == DM_BOUNDARY_TWIST ||
967         periodicY == DM_BOUNDARY_PERIODIC || periodicY == DM_BOUNDARY_TWIST) {
968       PetscReal      L[2];
969       PetscReal      maxCell[2];
970       DMBoundaryType bdType[2];
971 
972       bdType[0] = periodicX;
973       bdType[1] = periodicY;
974       for (i = 0; i < dim; i++) {
975         L[i]       = upper[i] - lower[i];
976         maxCell[i] = 1.1 * (L[i] / cells[i]);
977       }
978 
979       ierr = DMSetPeriodicity(*dm,maxCell,L,bdType);CHKERRQ(ierr);
980     }
981     break;
982   }
983   case 3:
984   {
985     PetscReal lower[3] = {0.0, 0.0, 0.0};
986     PetscReal upper[3] = {1.0, 1.0, 1.0};
987 
988     ierr = DMPlexCreateCubeMesh_Internal(*dm, lower, upper, cells, periodicX, periodicY, periodicZ);CHKERRQ(ierr);
989     if (periodicX == DM_BOUNDARY_PERIODIC || periodicX == DM_BOUNDARY_TWIST ||
990         periodicY == DM_BOUNDARY_PERIODIC || periodicY == DM_BOUNDARY_TWIST ||
991         periodicZ == DM_BOUNDARY_PERIODIC || periodicZ == DM_BOUNDARY_TWIST) {
992       PetscReal      L[3];
993       PetscReal      maxCell[3];
994       DMBoundaryType bdType[3];
995 
996       bdType[0] = periodicX;
997       bdType[1] = periodicY;
998       bdType[2] = periodicZ;
999       for (i = 0; i < dim; i++) {
1000         L[i]       = upper[i] - lower[i];
1001         maxCell[i] = 1.1 * (L[i] / cells[i]);
1002       }
1003 
1004       ierr = DMSetPeriodicity(*dm,maxCell,L,bdType);CHKERRQ(ierr);
1005     }
1006     break;
1007   }
1008   default:
1009     SETERRQ1(comm, PETSC_ERR_SUP, "Dimension not supported: %d", dim);
1010   }
1011   PetscFunctionReturn(0);
1012 }
1013 
1014 /* External function declarations here */
1015 extern PetscErrorCode DMCreateInterpolation_Plex(DM dmCoarse, DM dmFine, Mat *interpolation, Vec *scaling);
1016 extern PetscErrorCode DMCreateInjection_Plex(DM dmCoarse, DM dmFine, Mat *mat);
1017 extern PetscErrorCode DMCreateDefaultSection_Plex(DM dm);
1018 extern PetscErrorCode DMCreateDefaultConstraints_Plex(DM dm);
1019 extern PetscErrorCode DMCreateMatrix_Plex(DM dm,  Mat *J);
1020 extern PetscErrorCode DMCreateCoordinateDM_Plex(DM dm, DM *cdm);
1021 extern PetscErrorCode DMRefine_Plex(DM dm, MPI_Comm comm, DM *dmRefined);
1022 extern PetscErrorCode DMCoarsen_Plex(DM dm, MPI_Comm comm, DM *dmCoarsened);
1023 extern PetscErrorCode DMAdaptLabel_Plex(DM dm, DMLabel adaptLabel, DM *dmRefined);
1024 extern PetscErrorCode DMRefineHierarchy_Plex(DM dm, PetscInt nlevels, DM dmRefined[]);
1025 extern PetscErrorCode DMCoarsenHierarchy_Plex(DM dm, PetscInt nlevels, DM dmCoarsened[]);
1026 extern PetscErrorCode DMClone_Plex(DM dm, DM *newdm);
1027 extern PetscErrorCode DMSetUp_Plex(DM dm);
1028 extern PetscErrorCode DMDestroy_Plex(DM dm);
1029 extern PetscErrorCode DMView_Plex(DM dm, PetscViewer viewer);
1030 extern PetscErrorCode DMLoad_Plex(DM dm, PetscViewer viewer);
1031 extern PetscErrorCode DMCreateSubDM_Plex(DM dm, PetscInt numFields, PetscInt fields[], IS *is, DM *subdm);
1032 extern PetscErrorCode DMLocatePoints_Plex(DM dm, Vec v, DMPointLocationType ltype, PetscSF cellSF);
1033 extern PetscErrorCode DMProjectFunctionLocal_Plex(DM,PetscReal,PetscErrorCode(**)(PetscInt,PetscReal,const PetscReal[],PetscInt,PetscScalar *,void *),void **,InsertMode,Vec);
1034 extern PetscErrorCode DMProjectFunctionLabelLocal_Plex(DM,PetscReal,DMLabel,PetscInt,const PetscInt[],PetscErrorCode(**)(PetscInt,PetscReal,const PetscReal[],PetscInt,PetscScalar *,void *),void **,InsertMode,Vec);
1035 extern PetscErrorCode DMProjectFieldLocal_Plex(DM,PetscReal,Vec,void (**)(PetscInt,PetscInt,PetscInt,const PetscInt[],const PetscInt[],const PetscScalar[],const PetscScalar[],const PetscScalar[],const PetscInt[],const PetscInt[],const PetscScalar[],const PetscScalar[],const PetscScalar[],PetscReal,const PetscReal[],PetscScalar[]),InsertMode,Vec);
1036 extern PetscErrorCode DMProjectFieldLabelLocal_Plex(DM,PetscReal,DMLabel,PetscInt,const PetscInt[],Vec,void (**)(PetscInt,PetscInt,PetscInt,const PetscInt[],const PetscInt[],const PetscScalar[],const PetscScalar[],const PetscScalar[],const PetscInt[],const PetscInt[],const PetscScalar[],const PetscScalar[],const PetscScalar[],PetscReal,const PetscReal[],PetscScalar[]),InsertMode,Vec);
1037 extern PetscErrorCode DMComputeL2Diff_Plex(DM,PetscReal,PetscErrorCode(**)(PetscInt,PetscReal,const PetscReal[],PetscInt,PetscScalar *,void *),void **,Vec,PetscReal *);
1038 extern PetscErrorCode DMComputeL2GradientDiff_Plex(DM,PetscReal,PetscErrorCode(**)(PetscInt,PetscReal,const PetscReal[], const PetscReal[],PetscInt,PetscScalar *,void *),void **,Vec,const PetscReal [],PetscReal *);
1039 extern PetscErrorCode DMComputeL2FieldDiff_Plex(DM,PetscReal,PetscErrorCode(**)(PetscInt,PetscReal,const PetscReal[],PetscInt,PetscScalar *,void *),void **,Vec,PetscReal *);
1040 
1041 /* Replace dm with the contents of dmNew
1042    - Share the DM_Plex structure
1043    - Share the coordinates
1044    - Share the SF
1045 */
1046 static PetscErrorCode DMPlexReplace_Static(DM dm, DM dmNew)
1047 {
1048   PetscSF          sf;
1049   DM               coordDM, coarseDM;
1050   Vec              coords;
1051   const PetscReal *maxCell, *L;
1052   const DMBoundaryType *bd;
1053   PetscErrorCode   ierr;
1054 
1055   PetscFunctionBegin;
1056   ierr = DMGetPointSF(dmNew, &sf);CHKERRQ(ierr);
1057   ierr = DMSetPointSF(dm, sf);CHKERRQ(ierr);
1058   ierr = DMGetCoordinateDM(dmNew, &coordDM);CHKERRQ(ierr);
1059   ierr = DMGetCoordinatesLocal(dmNew, &coords);CHKERRQ(ierr);
1060   ierr = DMSetCoordinateDM(dm, coordDM);CHKERRQ(ierr);
1061   ierr = DMSetCoordinatesLocal(dm, coords);CHKERRQ(ierr);
1062   ierr = DMGetPeriodicity(dm, &maxCell, &L, &bd);CHKERRQ(ierr);
1063   if (L) {ierr = DMSetPeriodicity(dmNew, maxCell, L, bd);CHKERRQ(ierr);}
1064   ierr = DMDestroy_Plex(dm);CHKERRQ(ierr);
1065   dm->data = dmNew->data;
1066   ((DM_Plex *) dmNew->data)->refct++;
1067   dmNew->labels->refct++;
1068   if (!--(dm->labels->refct)) {
1069     DMLabelLink next = dm->labels->next;
1070 
1071     /* destroy the labels */
1072     while (next) {
1073       DMLabelLink tmp = next->next;
1074 
1075       ierr = DMLabelDestroy(&next->label);CHKERRQ(ierr);
1076       ierr = PetscFree(next);CHKERRQ(ierr);
1077       next = tmp;
1078     }
1079     ierr = PetscFree(dm->labels);CHKERRQ(ierr);
1080   }
1081   dm->labels = dmNew->labels;
1082   dm->depthLabel = dmNew->depthLabel;
1083   ierr = DMGetCoarseDM(dmNew,&coarseDM);CHKERRQ(ierr);
1084   ierr = DMSetCoarseDM(dm,coarseDM);CHKERRQ(ierr);
1085   PetscFunctionReturn(0);
1086 }
1087 
1088 /* Swap dm with the contents of dmNew
1089    - Swap the DM_Plex structure
1090    - Swap the coordinates
1091    - Swap the point PetscSF
1092 */
1093 static PetscErrorCode DMPlexSwap_Static(DM dmA, DM dmB)
1094 {
1095   DM              coordDMA, coordDMB;
1096   Vec             coordsA,  coordsB;
1097   PetscSF         sfA,      sfB;
1098   void            *tmp;
1099   DMLabelLinkList listTmp;
1100   DMLabel         depthTmp;
1101   PetscErrorCode  ierr;
1102 
1103   PetscFunctionBegin;
1104   ierr = DMGetPointSF(dmA, &sfA);CHKERRQ(ierr);
1105   ierr = DMGetPointSF(dmB, &sfB);CHKERRQ(ierr);
1106   ierr = PetscObjectReference((PetscObject) sfA);CHKERRQ(ierr);
1107   ierr = DMSetPointSF(dmA, sfB);CHKERRQ(ierr);
1108   ierr = DMSetPointSF(dmB, sfA);CHKERRQ(ierr);
1109   ierr = PetscObjectDereference((PetscObject) sfA);CHKERRQ(ierr);
1110 
1111   ierr = DMGetCoordinateDM(dmA, &coordDMA);CHKERRQ(ierr);
1112   ierr = DMGetCoordinateDM(dmB, &coordDMB);CHKERRQ(ierr);
1113   ierr = PetscObjectReference((PetscObject) coordDMA);CHKERRQ(ierr);
1114   ierr = DMSetCoordinateDM(dmA, coordDMB);CHKERRQ(ierr);
1115   ierr = DMSetCoordinateDM(dmB, coordDMA);CHKERRQ(ierr);
1116   ierr = PetscObjectDereference((PetscObject) coordDMA);CHKERRQ(ierr);
1117 
1118   ierr = DMGetCoordinatesLocal(dmA, &coordsA);CHKERRQ(ierr);
1119   ierr = DMGetCoordinatesLocal(dmB, &coordsB);CHKERRQ(ierr);
1120   ierr = PetscObjectReference((PetscObject) coordsA);CHKERRQ(ierr);
1121   ierr = DMSetCoordinatesLocal(dmA, coordsB);CHKERRQ(ierr);
1122   ierr = DMSetCoordinatesLocal(dmB, coordsA);CHKERRQ(ierr);
1123   ierr = PetscObjectDereference((PetscObject) coordsA);CHKERRQ(ierr);
1124 
1125   tmp       = dmA->data;
1126   dmA->data = dmB->data;
1127   dmB->data = tmp;
1128   listTmp   = dmA->labels;
1129   dmA->labels = dmB->labels;
1130   dmB->labels = listTmp;
1131   depthTmp  = dmA->depthLabel;
1132   dmA->depthLabel = dmB->depthLabel;
1133   dmB->depthLabel = depthTmp;
1134   PetscFunctionReturn(0);
1135 }
1136 
1137 PetscErrorCode  DMSetFromOptions_NonRefinement_Plex(PetscOptionItems *PetscOptionsObject,DM dm)
1138 {
1139   DM_Plex       *mesh = (DM_Plex*) dm->data;
1140   PetscErrorCode ierr;
1141 
1142   PetscFunctionBegin;
1143   /* Handle viewing */
1144   ierr = PetscOptionsBool("-dm_plex_print_set_values", "Output all set values info", "DMView", PETSC_FALSE, &mesh->printSetValues, NULL);CHKERRQ(ierr);
1145   ierr = PetscOptionsInt("-dm_plex_print_fem", "Debug output level all fem computations", "DMView", 0, &mesh->printFEM, NULL);CHKERRQ(ierr);
1146   ierr = PetscOptionsReal("-dm_plex_print_tol", "Tolerance for FEM output", "DMView", mesh->printTol, &mesh->printTol, NULL);CHKERRQ(ierr);
1147   /* Point Location */
1148   ierr = PetscOptionsBool("-dm_plex_hash_location", "Use grid hashing for point location", "DMView", PETSC_FALSE, &mesh->useHashLocation, NULL);CHKERRQ(ierr);
1149   /* Generation and remeshing */
1150   ierr = PetscOptionsBool("-dm_plex_remesh_bd", "Allow changes to the boundary on remeshing", "DMView", PETSC_FALSE, &mesh->remeshBd, NULL);CHKERRQ(ierr);
1151   /* Projection behavior */
1152   ierr = PetscOptionsInt("-dm_plex_max_projection_height", "Maxmimum mesh point height used to project locally", "DMPlexSetMaxProjectionHeight", 0, &mesh->maxProjectionHeight, NULL);CHKERRQ(ierr);
1153   ierr = PetscOptionsBool("-dm_plex_regular_refinement", "Use special nested projection algorithm for regular refinement", "DMPlexSetRegularRefinement", mesh->regularRefinement, &mesh->regularRefinement, NULL);CHKERRQ(ierr);
1154   PetscFunctionReturn(0);
1155 }
1156 
1157 PetscErrorCode  DMSetFromOptions_Plex(PetscOptionItems *PetscOptionsObject,DM dm)
1158 {
1159   PetscInt       refine = 0, coarsen = 0, r;
1160   PetscBool      isHierarchy;
1161   PetscErrorCode ierr;
1162 
1163   PetscFunctionBegin;
1164   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1165   ierr = PetscOptionsHead(PetscOptionsObject,"DMPlex Options");CHKERRQ(ierr);
1166   /* Handle DMPlex refinement */
1167   ierr = PetscOptionsInt("-dm_refine", "The number of uniform refinements", "DMCreate", refine, &refine, NULL);CHKERRQ(ierr);
1168   ierr = PetscOptionsInt("-dm_refine_hierarchy", "The number of uniform refinements", "DMCreate", refine, &refine, &isHierarchy);CHKERRQ(ierr);
1169   if (refine) {ierr = DMPlexSetRefinementUniform(dm, PETSC_TRUE);CHKERRQ(ierr);}
1170   if (refine && isHierarchy) {
1171     DM *dms, coarseDM;
1172 
1173     ierr = DMGetCoarseDM(dm, &coarseDM);CHKERRQ(ierr);
1174     ierr = PetscObjectReference((PetscObject)coarseDM);CHKERRQ(ierr);
1175     ierr = PetscMalloc1(refine,&dms);CHKERRQ(ierr);
1176     ierr = DMRefineHierarchy(dm, refine, dms);CHKERRQ(ierr);
1177     /* Total hack since we do not pass in a pointer */
1178     ierr = DMPlexSwap_Static(dm, dms[refine-1]);CHKERRQ(ierr);
1179     if (refine == 1) {
1180       ierr = DMSetCoarseDM(dm, dms[0]);CHKERRQ(ierr);
1181       ierr = DMPlexSetRegularRefinement(dm, PETSC_TRUE);CHKERRQ(ierr);
1182     } else {
1183       ierr = DMSetCoarseDM(dm, dms[refine-2]);CHKERRQ(ierr);
1184       ierr = DMPlexSetRegularRefinement(dm, PETSC_TRUE);CHKERRQ(ierr);
1185       ierr = DMSetCoarseDM(dms[0], dms[refine-1]);CHKERRQ(ierr);
1186       ierr = DMPlexSetRegularRefinement(dms[0], PETSC_TRUE);CHKERRQ(ierr);
1187     }
1188     ierr = DMSetCoarseDM(dms[refine-1], coarseDM);CHKERRQ(ierr);
1189     ierr = PetscObjectDereference((PetscObject)coarseDM);CHKERRQ(ierr);
1190     /* Free DMs */
1191     for (r = 0; r < refine; ++r) {
1192       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dms[r]);CHKERRQ(ierr);
1193       ierr = DMDestroy(&dms[r]);CHKERRQ(ierr);
1194     }
1195     ierr = PetscFree(dms);CHKERRQ(ierr);
1196   } else {
1197     for (r = 0; r < refine; ++r) {
1198       DM refinedMesh;
1199 
1200       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
1201       ierr = DMRefine(dm, PetscObjectComm((PetscObject) dm), &refinedMesh);CHKERRQ(ierr);
1202       /* Total hack since we do not pass in a pointer */
1203       ierr = DMPlexReplace_Static(dm, refinedMesh);CHKERRQ(ierr);
1204       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
1205       ierr = DMDestroy(&refinedMesh);CHKERRQ(ierr);
1206     }
1207   }
1208   /* Handle DMPlex coarsening */
1209   ierr = PetscOptionsInt("-dm_coarsen", "Coarsen the mesh", "DMCreate", coarsen, &coarsen, NULL);CHKERRQ(ierr);
1210   ierr = PetscOptionsInt("-dm_coarsen_hierarchy", "The number of coarsenings", "DMCreate", coarsen, &coarsen, &isHierarchy);CHKERRQ(ierr);
1211   if (coarsen && isHierarchy) {
1212     DM *dms;
1213 
1214     ierr = PetscMalloc1(coarsen, &dms);CHKERRQ(ierr);
1215     ierr = DMCoarsenHierarchy(dm, coarsen, dms);CHKERRQ(ierr);
1216     /* Free DMs */
1217     for (r = 0; r < coarsen; ++r) {
1218       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dms[r]);CHKERRQ(ierr);
1219       ierr = DMDestroy(&dms[r]);CHKERRQ(ierr);
1220     }
1221     ierr = PetscFree(dms);CHKERRQ(ierr);
1222   } else {
1223     for (r = 0; r < coarsen; ++r) {
1224       DM coarseMesh;
1225 
1226       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
1227       ierr = DMCoarsen(dm, PetscObjectComm((PetscObject) dm), &coarseMesh);CHKERRQ(ierr);
1228       /* Total hack since we do not pass in a pointer */
1229       ierr = DMPlexReplace_Static(dm, coarseMesh);CHKERRQ(ierr);
1230       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
1231       ierr = DMDestroy(&coarseMesh);CHKERRQ(ierr);
1232     }
1233   }
1234   /* Handle */
1235   ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
1236   ierr = PetscOptionsTail();CHKERRQ(ierr);
1237   PetscFunctionReturn(0);
1238 }
1239 
1240 static PetscErrorCode DMCreateGlobalVector_Plex(DM dm,Vec *vec)
1241 {
1242   PetscErrorCode ierr;
1243 
1244   PetscFunctionBegin;
1245   ierr = DMCreateGlobalVector_Section_Private(dm,vec);CHKERRQ(ierr);
1246   /* ierr = VecSetOperation(*vec, VECOP_DUPLICATE, (void(*)(void)) VecDuplicate_MPI_DM);CHKERRQ(ierr); */
1247   ierr = VecSetOperation(*vec, VECOP_VIEW, (void (*)(void)) VecView_Plex);CHKERRQ(ierr);
1248   ierr = VecSetOperation(*vec, VECOP_VIEWNATIVE, (void (*)(void)) VecView_Plex_Native);CHKERRQ(ierr);
1249   ierr = VecSetOperation(*vec, VECOP_LOAD, (void (*)(void)) VecLoad_Plex);CHKERRQ(ierr);
1250   ierr = VecSetOperation(*vec, VECOP_LOADNATIVE, (void (*)(void)) VecLoad_Plex_Native);CHKERRQ(ierr);
1251   PetscFunctionReturn(0);
1252 }
1253 
1254 static PetscErrorCode DMCreateLocalVector_Plex(DM dm,Vec *vec)
1255 {
1256   PetscErrorCode ierr;
1257 
1258   PetscFunctionBegin;
1259   ierr = DMCreateLocalVector_Section_Private(dm,vec);CHKERRQ(ierr);
1260   ierr = VecSetOperation(*vec, VECOP_VIEW, (void (*)(void)) VecView_Plex_Local);CHKERRQ(ierr);
1261   ierr = VecSetOperation(*vec, VECOP_LOAD, (void (*)(void)) VecLoad_Plex_Local);CHKERRQ(ierr);
1262   PetscFunctionReturn(0);
1263 }
1264 
1265 static PetscErrorCode DMGetDimPoints_Plex(DM dm, PetscInt dim, PetscInt *pStart, PetscInt *pEnd)
1266 {
1267   PetscInt       depth, d;
1268   PetscErrorCode ierr;
1269 
1270   PetscFunctionBegin;
1271   ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
1272   if (depth == 1) {
1273     ierr = DMGetDimension(dm, &d);CHKERRQ(ierr);
1274     if (dim == 0)      {ierr = DMPlexGetDepthStratum(dm, dim, pStart, pEnd);CHKERRQ(ierr);}
1275     else if (dim == d) {ierr = DMPlexGetDepthStratum(dm, 1, pStart, pEnd);CHKERRQ(ierr);}
1276     else               {*pStart = 0; *pEnd = 0;}
1277   } else {
1278     ierr = DMPlexGetDepthStratum(dm, dim, pStart, pEnd);CHKERRQ(ierr);
1279   }
1280   PetscFunctionReturn(0);
1281 }
1282 
1283 static PetscErrorCode DMGetNeighors_Plex(DM dm, PetscInt *nranks, const PetscMPIInt *ranks[])
1284 {
1285   PetscSF        sf;
1286   PetscErrorCode ierr;
1287 
1288   PetscFunctionBegin;
1289   ierr = DMGetPointSF(dm, &sf);CHKERRQ(ierr);
1290   ierr = PetscSFGetRanks(sf, nranks, ranks, NULL, NULL, NULL);CHKERRQ(ierr);
1291   PetscFunctionReturn(0);
1292 }
1293 
1294 PetscErrorCode DMInitialize_Plex(DM dm)
1295 {
1296   PetscErrorCode ierr;
1297 
1298   PetscFunctionBegin;
1299   dm->ops->view                            = DMView_Plex;
1300   dm->ops->load                            = DMLoad_Plex;
1301   dm->ops->setfromoptions                  = DMSetFromOptions_Plex;
1302   dm->ops->clone                           = DMClone_Plex;
1303   dm->ops->setup                           = DMSetUp_Plex;
1304   dm->ops->createdefaultsection            = DMCreateDefaultSection_Plex;
1305   dm->ops->createdefaultconstraints        = DMCreateDefaultConstraints_Plex;
1306   dm->ops->createglobalvector              = DMCreateGlobalVector_Plex;
1307   dm->ops->createlocalvector               = DMCreateLocalVector_Plex;
1308   dm->ops->getlocaltoglobalmapping         = NULL;
1309   dm->ops->createfieldis                   = NULL;
1310   dm->ops->createcoordinatedm              = DMCreateCoordinateDM_Plex;
1311   dm->ops->getcoloring                     = NULL;
1312   dm->ops->creatematrix                    = DMCreateMatrix_Plex;
1313   dm->ops->createinterpolation             = DMCreateInterpolation_Plex;
1314   dm->ops->getaggregates                   = NULL;
1315   dm->ops->getinjection                    = DMCreateInjection_Plex;
1316   dm->ops->refine                          = DMRefine_Plex;
1317   dm->ops->coarsen                         = DMCoarsen_Plex;
1318   dm->ops->refinehierarchy                 = DMRefineHierarchy_Plex;
1319   dm->ops->coarsenhierarchy                = DMCoarsenHierarchy_Plex;
1320   dm->ops->globaltolocalbegin              = NULL;
1321   dm->ops->globaltolocalend                = NULL;
1322   dm->ops->localtoglobalbegin              = NULL;
1323   dm->ops->localtoglobalend                = NULL;
1324   dm->ops->destroy                         = DMDestroy_Plex;
1325   dm->ops->createsubdm                     = DMCreateSubDM_Plex;
1326   dm->ops->getdimpoints                    = DMGetDimPoints_Plex;
1327   dm->ops->locatepoints                    = DMLocatePoints_Plex;
1328   dm->ops->projectfunctionlocal            = DMProjectFunctionLocal_Plex;
1329   dm->ops->projectfunctionlabellocal       = DMProjectFunctionLabelLocal_Plex;
1330   dm->ops->projectfieldlocal               = DMProjectFieldLocal_Plex;
1331   dm->ops->projectfieldlabellocal          = DMProjectFieldLabelLocal_Plex;
1332   dm->ops->computel2diff                   = DMComputeL2Diff_Plex;
1333   dm->ops->computel2gradientdiff           = DMComputeL2GradientDiff_Plex;
1334   dm->ops->computel2fielddiff              = DMComputeL2FieldDiff_Plex;
1335   dm->ops->getneighbors                    = DMGetNeighors_Plex;
1336   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMAdaptLabel_C",DMAdaptLabel_Plex);CHKERRQ(ierr);
1337   PetscFunctionReturn(0);
1338 }
1339 
1340 PetscErrorCode DMClone_Plex(DM dm, DM *newdm)
1341 {
1342   DM_Plex        *mesh = (DM_Plex *) dm->data;
1343   PetscErrorCode ierr;
1344 
1345   PetscFunctionBegin;
1346   mesh->refct++;
1347   (*newdm)->data = mesh;
1348   ierr = PetscObjectChangeTypeName((PetscObject) *newdm, DMPLEX);CHKERRQ(ierr);
1349   ierr = DMInitialize_Plex(*newdm);CHKERRQ(ierr);
1350   PetscFunctionReturn(0);
1351 }
1352 
1353 /*MC
1354   DMPLEX = "plex" - A DM object that encapsulates an unstructured mesh, or CW Complex, which can be expressed using a Hasse Diagram.
1355                     In the local representation, Vecs contain all unknowns in the interior and shared boundary. This is
1356                     specified by a PetscSection object. Ownership in the global representation is determined by
1357                     ownership of the underlying DMPlex points. This is specified by another PetscSection object.
1358 
1359   Level: intermediate
1360 
1361 .seealso: DMType, DMPlexCreate(), DMCreate(), DMSetType()
1362 M*/
1363 
1364 PETSC_EXTERN PetscErrorCode DMCreate_Plex(DM dm)
1365 {
1366   DM_Plex        *mesh;
1367   PetscInt       unit, d;
1368   PetscErrorCode ierr;
1369 
1370   PetscFunctionBegin;
1371   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1372   ierr     = PetscNewLog(dm,&mesh);CHKERRQ(ierr);
1373   dm->dim  = 0;
1374   dm->data = mesh;
1375 
1376   mesh->refct             = 1;
1377   ierr                    = PetscSectionCreate(PetscObjectComm((PetscObject)dm), &mesh->coneSection);CHKERRQ(ierr);
1378   mesh->maxConeSize       = 0;
1379   mesh->cones             = NULL;
1380   mesh->coneOrientations  = NULL;
1381   ierr                    = PetscSectionCreate(PetscObjectComm((PetscObject)dm), &mesh->supportSection);CHKERRQ(ierr);
1382   mesh->maxSupportSize    = 0;
1383   mesh->supports          = NULL;
1384   mesh->refinementUniform = PETSC_TRUE;
1385   mesh->refinementLimit   = -1.0;
1386 
1387   mesh->facesTmp = NULL;
1388 
1389   mesh->tetgenOpts   = NULL;
1390   mesh->triangleOpts = NULL;
1391   ierr = PetscPartitionerCreate(PetscObjectComm((PetscObject)dm), &mesh->partitioner);CHKERRQ(ierr);
1392   ierr = PetscPartitionerSetTypeFromOptions_Internal(mesh->partitioner);CHKERRQ(ierr);
1393   mesh->remeshBd     = PETSC_FALSE;
1394 
1395   mesh->subpointMap = NULL;
1396 
1397   for (unit = 0; unit < NUM_PETSC_UNITS; ++unit) mesh->scale[unit] = 1.0;
1398 
1399   mesh->regularRefinement   = PETSC_FALSE;
1400   mesh->depthState          = -1;
1401   mesh->globalVertexNumbers = NULL;
1402   mesh->globalCellNumbers   = NULL;
1403   mesh->anchorSection       = NULL;
1404   mesh->anchorIS            = NULL;
1405   mesh->createanchors       = NULL;
1406   mesh->computeanchormatrix = NULL;
1407   mesh->parentSection       = NULL;
1408   mesh->parents             = NULL;
1409   mesh->childIDs            = NULL;
1410   mesh->childSection        = NULL;
1411   mesh->children            = NULL;
1412   mesh->referenceTree       = NULL;
1413   mesh->getchildsymmetry    = NULL;
1414   for (d = 0; d < 8; ++d) mesh->hybridPointMax[d] = PETSC_DETERMINE;
1415   mesh->vtkCellHeight       = 0;
1416   mesh->useCone             = PETSC_FALSE;
1417   mesh->useClosure          = PETSC_TRUE;
1418   mesh->useAnchors          = PETSC_FALSE;
1419 
1420   mesh->maxProjectionHeight = 0;
1421 
1422   mesh->printSetValues = PETSC_FALSE;
1423   mesh->printFEM       = 0;
1424   mesh->printTol       = 1.0e-10;
1425 
1426   ierr = DMInitialize_Plex(dm);CHKERRQ(ierr);
1427   PetscFunctionReturn(0);
1428 }
1429 
1430 /*@
1431   DMPlexCreate - Creates a DMPlex object, which encapsulates an unstructured mesh, or CW complex, which can be expressed using a Hasse Diagram.
1432 
1433   Collective on MPI_Comm
1434 
1435   Input Parameter:
1436 . comm - The communicator for the DMPlex object
1437 
1438   Output Parameter:
1439 . mesh  - The DMPlex object
1440 
1441   Level: beginner
1442 
1443 .keywords: DMPlex, create
1444 @*/
1445 PetscErrorCode DMPlexCreate(MPI_Comm comm, DM *mesh)
1446 {
1447   PetscErrorCode ierr;
1448 
1449   PetscFunctionBegin;
1450   PetscValidPointer(mesh,2);
1451   ierr = DMCreate(comm, mesh);CHKERRQ(ierr);
1452   ierr = DMSetType(*mesh, DMPLEX);CHKERRQ(ierr);
1453   PetscFunctionReturn(0);
1454 }
1455 
1456 /*
1457   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
1458 */
1459 static PetscErrorCode DMPlexBuildFromCellList_Parallel_Private(DM dm, PetscInt numCells, PetscInt numVertices, PetscInt numCorners, const int cells[], PetscSF *sfVert)
1460 {
1461   PetscSF         sfPoint;
1462   PetscLayout     vLayout;
1463   PetscHashI      vhash;
1464   PetscSFNode    *remoteVerticesAdj, *vertexLocal, *vertexOwner, *remoteVertex;
1465   const PetscInt *vrange;
1466   PetscInt        numVerticesAdj, off, *verticesAdj, numVerticesGhost = 0, *localVertex, *cone, c, p, v, g;
1467   PETSC_UNUSED PetscHashIIter ret, iter;
1468   PetscMPIInt     rank, numProcs;
1469   PetscErrorCode  ierr;
1470 
1471   PetscFunctionBegin;
1472   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject) dm), &rank);CHKERRQ(ierr);
1473   ierr = MPI_Comm_size(PetscObjectComm((PetscObject) dm), &numProcs);CHKERRQ(ierr);
1474   /* Partition vertices */
1475   ierr = PetscLayoutCreate(PetscObjectComm((PetscObject) dm), &vLayout);CHKERRQ(ierr);
1476   ierr = PetscLayoutSetLocalSize(vLayout, numVertices);CHKERRQ(ierr);
1477   ierr = PetscLayoutSetBlockSize(vLayout, 1);CHKERRQ(ierr);
1478   ierr = PetscLayoutSetUp(vLayout);CHKERRQ(ierr);
1479   ierr = PetscLayoutGetRanges(vLayout, &vrange);CHKERRQ(ierr);
1480   /* Count vertices and map them to procs */
1481   PetscHashICreate(vhash);
1482   for (c = 0; c < numCells; ++c) {
1483     for (p = 0; p < numCorners; ++p) {
1484       PetscHashIPut(vhash, cells[c*numCorners+p], ret, iter);
1485     }
1486   }
1487   PetscHashISize(vhash, numVerticesAdj);
1488   ierr = PetscMalloc1(numVerticesAdj, &verticesAdj);CHKERRQ(ierr);
1489   off = 0; ierr = PetscHashIGetKeys(vhash, &off, verticesAdj);CHKERRQ(ierr);
1490   if (off != numVerticesAdj) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Invalid number of local vertices %D should be %D", off, numVerticesAdj);
1491   ierr = PetscMalloc1(numVerticesAdj, &remoteVerticesAdj);CHKERRQ(ierr);
1492   for (v = 0; v < numVerticesAdj; ++v) {
1493     const PetscInt gv = verticesAdj[v];
1494     PetscInt       vrank;
1495 
1496     ierr = PetscFindInt(gv, numProcs+1, vrange, &vrank);CHKERRQ(ierr);
1497     vrank = vrank < 0 ? -(vrank+2) : vrank;
1498     remoteVerticesAdj[v].index = gv - vrange[vrank];
1499     remoteVerticesAdj[v].rank  = vrank;
1500   }
1501   /* Create cones */
1502   ierr = DMPlexSetChart(dm, 0, numCells+numVerticesAdj);CHKERRQ(ierr);
1503   for (c = 0; c < numCells; ++c) {ierr = DMPlexSetConeSize(dm, c, numCorners);CHKERRQ(ierr);}
1504   ierr = DMSetUp(dm);CHKERRQ(ierr);
1505   ierr = DMGetWorkArray(dm, numCorners, PETSC_INT, &cone);CHKERRQ(ierr);
1506   for (c = 0; c < numCells; ++c) {
1507     for (p = 0; p < numCorners; ++p) {
1508       const PetscInt gv = cells[c*numCorners+p];
1509       PetscInt       lv;
1510 
1511       ierr = PetscFindInt(gv, numVerticesAdj, verticesAdj, &lv);CHKERRQ(ierr);
1512       if (lv < 0) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Could not find global vertex %D in local connectivity", gv);
1513       cone[p] = lv+numCells;
1514     }
1515     ierr = DMPlexSetCone(dm, c, cone);CHKERRQ(ierr);
1516   }
1517   ierr = DMRestoreWorkArray(dm, numCorners, PETSC_INT, &cone);CHKERRQ(ierr);
1518   /* Create SF for vertices */
1519   ierr = PetscSFCreate(PetscObjectComm((PetscObject)dm), sfVert);CHKERRQ(ierr);
1520   ierr = PetscObjectSetName((PetscObject) *sfVert, "Vertex Ownership SF");CHKERRQ(ierr);
1521   ierr = PetscSFSetFromOptions(*sfVert);CHKERRQ(ierr);
1522   ierr = PetscSFSetGraph(*sfVert, numVertices, numVerticesAdj, NULL, PETSC_OWN_POINTER, remoteVerticesAdj, PETSC_OWN_POINTER);CHKERRQ(ierr);
1523   ierr = PetscFree(verticesAdj);CHKERRQ(ierr);
1524   /* Build pointSF */
1525   ierr = PetscMalloc2(numVerticesAdj, &vertexLocal, numVertices, &vertexOwner);CHKERRQ(ierr);
1526   for (v = 0; v < numVerticesAdj; ++v) {vertexLocal[v].index = v+numCells; vertexLocal[v].rank = rank;}
1527   for (v = 0; v < numVertices;    ++v) {vertexOwner[v].index = -1;         vertexOwner[v].rank = -1;}
1528   ierr = PetscSFReduceBegin(*sfVert, MPI_2INT, vertexLocal, vertexOwner, MPI_MAXLOC);CHKERRQ(ierr);
1529   ierr = PetscSFReduceEnd(*sfVert, MPI_2INT, vertexLocal, vertexOwner, MPI_MAXLOC);CHKERRQ(ierr);
1530   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);
1531   ierr = PetscSFBcastBegin(*sfVert, MPI_2INT, vertexOwner, vertexLocal);CHKERRQ(ierr);
1532   ierr = PetscSFBcastEnd(*sfVert, MPI_2INT, vertexOwner, vertexLocal);CHKERRQ(ierr);
1533   for (v = 0; v < numVerticesAdj; ++v) if (vertexLocal[v].rank != rank) ++numVerticesGhost;
1534   ierr = PetscMalloc1(numVerticesGhost, &localVertex);CHKERRQ(ierr);
1535   ierr = PetscMalloc1(numVerticesGhost, &remoteVertex);CHKERRQ(ierr);
1536   for (v = 0, g = 0; v < numVerticesAdj; ++v) {
1537     if (vertexLocal[v].rank != rank) {
1538       localVertex[g]        = v+numCells;
1539       remoteVertex[g].index = vertexLocal[v].index;
1540       remoteVertex[g].rank  = vertexLocal[v].rank;
1541       ++g;
1542     }
1543   }
1544   ierr = PetscFree2(vertexLocal, vertexOwner);CHKERRQ(ierr);
1545   if (g != numVerticesGhost) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid number of vertex ghosts %D should be %D", g, numVerticesGhost);
1546   ierr = DMGetPointSF(dm, &sfPoint);CHKERRQ(ierr);
1547   ierr = PetscObjectSetName((PetscObject) sfPoint, "point SF");CHKERRQ(ierr);
1548   ierr = PetscSFSetGraph(sfPoint, numCells+numVerticesAdj, numVerticesGhost, localVertex, PETSC_OWN_POINTER, remoteVertex, PETSC_OWN_POINTER);CHKERRQ(ierr);
1549   ierr = PetscLayoutDestroy(&vLayout);CHKERRQ(ierr);
1550   PetscHashIDestroy(vhash);
1551   /* Fill in the rest of the topology structure */
1552   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
1553   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
1554   PetscFunctionReturn(0);
1555 }
1556 
1557 /*
1558   This takes as input the coordinates for each owned vertex
1559 */
1560 static PetscErrorCode DMPlexBuildCoordinates_Parallel_Private(DM dm, PetscInt spaceDim, PetscInt numCells, PetscSF sfVert, const double vertexCoords[])
1561 {
1562   PetscSection   coordSection;
1563   Vec            coordinates;
1564   PetscScalar   *coords;
1565   PetscInt       numVertices, numVerticesAdj, coordSize, v;
1566   PetscErrorCode ierr;
1567 
1568   PetscFunctionBegin;
1569   ierr = PetscSFGetGraph(sfVert, &numVertices, &numVerticesAdj, NULL, NULL);CHKERRQ(ierr);
1570   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
1571   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
1572   ierr = PetscSectionSetFieldComponents(coordSection, 0, spaceDim);CHKERRQ(ierr);
1573   ierr = PetscSectionSetChart(coordSection, numCells, numCells + numVerticesAdj);CHKERRQ(ierr);
1574   for (v = numCells; v < numCells+numVerticesAdj; ++v) {
1575     ierr = PetscSectionSetDof(coordSection, v, spaceDim);CHKERRQ(ierr);
1576     ierr = PetscSectionSetFieldDof(coordSection, v, 0, spaceDim);CHKERRQ(ierr);
1577   }
1578   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
1579   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
1580   ierr = VecCreate(PetscObjectComm((PetscObject)dm), &coordinates);CHKERRQ(ierr);
1581   ierr = VecSetBlockSize(coordinates, spaceDim);CHKERRQ(ierr);
1582   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
1583   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
1584   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
1585   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
1586   {
1587     MPI_Datatype coordtype;
1588 
1589     /* Need a temp buffer for coords if we have complex/single */
1590     ierr = MPI_Type_contiguous(spaceDim, MPI_DOUBLE, &coordtype);CHKERRQ(ierr);
1591     ierr = MPI_Type_commit(&coordtype);CHKERRQ(ierr);
1592     ierr = PetscSFBcastBegin(sfVert, coordtype, vertexCoords, coords);CHKERRQ(ierr);
1593     ierr = PetscSFBcastEnd(sfVert, coordtype, vertexCoords, coords);CHKERRQ(ierr);
1594     ierr = MPI_Type_free(&coordtype);CHKERRQ(ierr);
1595   }
1596   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
1597   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
1598   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
1599   PetscFunctionReturn(0);
1600 }
1601 
1602 /*@C
1603   DMPlexCreateFromCellListParallel - This takes as input common mesh generator output, a list of the vertices for each cell, and produces a DM
1604 
1605   Input Parameters:
1606 + comm - The communicator
1607 . dim - The topological dimension of the mesh
1608 . numCells - The number of cells owned by this process
1609 . numVertices - The number of vertices owned by this process
1610 . numCorners - The number of vertices for each cell
1611 . interpolate - Flag indicating that intermediate mesh entities (faces, edges) should be created automatically
1612 . cells - An array of numCells*numCorners numbers, the global vertex numbers for each cell
1613 . spaceDim - The spatial dimension used for coordinates
1614 - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex
1615 
1616   Output Parameter:
1617 . dm - The DM
1618 
1619   Note: Two triangles sharing a face
1620 $
1621 $        2
1622 $      / | \
1623 $     /  |  \
1624 $    /   |   \
1625 $   0  0 | 1  3
1626 $    \   |   /
1627 $     \  |  /
1628 $      \ | /
1629 $        1
1630 would have input
1631 $  numCells = 2, numVertices = 4
1632 $  cells = [0 1 2  1 3 2]
1633 $
1634 which would result in the DMPlex
1635 $
1636 $        4
1637 $      / | \
1638 $     /  |  \
1639 $    /   |   \
1640 $   2  0 | 1  5
1641 $    \   |   /
1642 $     \  |  /
1643 $      \ | /
1644 $        3
1645 
1646   Level: beginner
1647 
1648 .seealso: DMPlexCreateFromCellList(), DMPlexCreateFromDAG(), DMPlexCreate()
1649 @*/
1650 PetscErrorCode DMPlexCreateFromCellListParallel(MPI_Comm comm, PetscInt dim, PetscInt numCells, PetscInt numVertices, PetscInt numCorners, PetscBool interpolate, const int cells[], PetscInt spaceDim, const double vertexCoords[], DM *dm)
1651 {
1652   PetscSF        sfVert;
1653   PetscErrorCode ierr;
1654 
1655   PetscFunctionBegin;
1656   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
1657   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
1658   PetscValidLogicalCollectiveInt(*dm, dim, 2);
1659   PetscValidLogicalCollectiveInt(*dm, spaceDim, 8);
1660   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
1661   ierr = DMPlexBuildFromCellList_Parallel_Private(*dm, numCells, numVertices, numCorners, cells, &sfVert);CHKERRQ(ierr);
1662   if (interpolate) {
1663     DM idm = NULL;
1664 
1665     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
1666     ierr = DMDestroy(dm);CHKERRQ(ierr);
1667     *dm  = idm;
1668   }
1669   ierr = DMPlexBuildCoordinates_Parallel_Private(*dm, spaceDim, numCells, sfVert, vertexCoords);CHKERRQ(ierr);
1670   ierr = PetscSFDestroy(&sfVert);CHKERRQ(ierr);
1671   PetscFunctionReturn(0);
1672 }
1673 
1674 /*
1675   This takes as input the common mesh generator output, a list of the vertices for each cell
1676 */
1677 static PetscErrorCode DMPlexBuildFromCellList_Private(DM dm, PetscInt numCells, PetscInt numVertices, PetscInt numCorners, const int cells[])
1678 {
1679   PetscInt      *cone, c, p;
1680   PetscErrorCode ierr;
1681 
1682   PetscFunctionBegin;
1683   ierr = DMPlexSetChart(dm, 0, numCells+numVertices);CHKERRQ(ierr);
1684   for (c = 0; c < numCells; ++c) {
1685     ierr = DMPlexSetConeSize(dm, c, numCorners);CHKERRQ(ierr);
1686   }
1687   ierr = DMSetUp(dm);CHKERRQ(ierr);
1688   ierr = DMGetWorkArray(dm, numCorners, PETSC_INT, &cone);CHKERRQ(ierr);
1689   for (c = 0; c < numCells; ++c) {
1690     for (p = 0; p < numCorners; ++p) {
1691       cone[p] = cells[c*numCorners+p]+numCells;
1692     }
1693     ierr = DMPlexSetCone(dm, c, cone);CHKERRQ(ierr);
1694   }
1695   ierr = DMRestoreWorkArray(dm, numCorners, PETSC_INT, &cone);CHKERRQ(ierr);
1696   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
1697   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
1698   PetscFunctionReturn(0);
1699 }
1700 
1701 /*
1702   This takes as input the coordinates for each vertex
1703 */
1704 static PetscErrorCode DMPlexBuildCoordinates_Private(DM dm, PetscInt spaceDim, PetscInt numCells, PetscInt numVertices, const double vertexCoords[])
1705 {
1706   PetscSection   coordSection;
1707   Vec            coordinates;
1708   DM             cdm;
1709   PetscScalar   *coords;
1710   PetscInt       v, d;
1711   PetscErrorCode ierr;
1712 
1713   PetscFunctionBegin;
1714   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
1715   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
1716   ierr = PetscSectionSetFieldComponents(coordSection, 0, spaceDim);CHKERRQ(ierr);
1717   ierr = PetscSectionSetChart(coordSection, numCells, numCells + numVertices);CHKERRQ(ierr);
1718   for (v = numCells; v < numCells+numVertices; ++v) {
1719     ierr = PetscSectionSetDof(coordSection, v, spaceDim);CHKERRQ(ierr);
1720     ierr = PetscSectionSetFieldDof(coordSection, v, 0, spaceDim);CHKERRQ(ierr);
1721   }
1722   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
1723 
1724   ierr = DMGetCoordinateDM(dm, &cdm);CHKERRQ(ierr);
1725   ierr = DMCreateLocalVector(cdm, &coordinates);CHKERRQ(ierr);
1726   ierr = VecSetBlockSize(coordinates, spaceDim);CHKERRQ(ierr);
1727   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
1728   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
1729   for (v = 0; v < numVertices; ++v) {
1730     for (d = 0; d < spaceDim; ++d) {
1731       coords[v*spaceDim+d] = vertexCoords[v*spaceDim+d];
1732     }
1733   }
1734   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
1735   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
1736   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
1737   PetscFunctionReturn(0);
1738 }
1739 
1740 /*@C
1741   DMPlexCreateFromCellList - This takes as input common mesh generator output, a list of the vertices for each cell, and produces a DM
1742 
1743   Input Parameters:
1744 + comm - The communicator
1745 . dim - The topological dimension of the mesh
1746 . numCells - The number of cells
1747 . numVertices - The number of vertices
1748 . numCorners - The number of vertices for each cell
1749 . interpolate - Flag indicating that intermediate mesh entities (faces, edges) should be created automatically
1750 . cells - An array of numCells*numCorners numbers, the vertices for each cell
1751 . spaceDim - The spatial dimension used for coordinates
1752 - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex
1753 
1754   Output Parameter:
1755 . dm - The DM
1756 
1757   Note: Two triangles sharing a face
1758 $
1759 $        2
1760 $      / | \
1761 $     /  |  \
1762 $    /   |   \
1763 $   0  0 | 1  3
1764 $    \   |   /
1765 $     \  |  /
1766 $      \ | /
1767 $        1
1768 would have input
1769 $  numCells = 2, numVertices = 4
1770 $  cells = [0 1 2  1 3 2]
1771 $
1772 which would result in the DMPlex
1773 $
1774 $        4
1775 $      / | \
1776 $     /  |  \
1777 $    /   |   \
1778 $   2  0 | 1  5
1779 $    \   |   /
1780 $     \  |  /
1781 $      \ | /
1782 $        3
1783 
1784   Level: beginner
1785 
1786 .seealso: DMPlexCreateFromDAG(), DMPlexCreate()
1787 @*/
1788 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)
1789 {
1790   PetscErrorCode ierr;
1791 
1792   PetscFunctionBegin;
1793   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
1794   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
1795   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
1796   ierr = DMPlexBuildFromCellList_Private(*dm, numCells, numVertices, numCorners, cells);CHKERRQ(ierr);
1797   if (interpolate) {
1798     DM idm = NULL;
1799 
1800     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
1801     ierr = DMDestroy(dm);CHKERRQ(ierr);
1802     *dm  = idm;
1803   }
1804   ierr = DMPlexBuildCoordinates_Private(*dm, spaceDim, numCells, numVertices, vertexCoords);CHKERRQ(ierr);
1805   PetscFunctionReturn(0);
1806 }
1807 
1808 /*@
1809   DMPlexCreateFromDAG - This takes as input the adjacency-list representation of the Directed Acyclic Graph (Hasse Diagram) encoding a mesh, and produces a DM
1810 
1811   Input Parameters:
1812 + dm - The empty DM object, usually from DMCreate() and DMSetDimension()
1813 . depth - The depth of the DAG
1814 . numPoints - The number of points at each depth
1815 . coneSize - The cone size of each point
1816 . cones - The concatenation of the cone points for each point, the cone list must be oriented correctly for each point
1817 . coneOrientations - The orientation of each cone point
1818 - vertexCoords - An array of numVertices*dim numbers, the coordinates of each vertex
1819 
1820   Output Parameter:
1821 . dm - The DM
1822 
1823   Note: Two triangles sharing a face would have input
1824 $  depth = 1, numPoints = [4 2], coneSize = [3 3 0 0 0 0]
1825 $  cones = [2 3 4  3 5 4], coneOrientations = [0 0 0  0 0 0]
1826 $ vertexCoords = [-1.0 0.0  0.0 -1.0  0.0 1.0  1.0 0.0]
1827 $
1828 which would result in the DMPlex
1829 $
1830 $        4
1831 $      / | \
1832 $     /  |  \
1833 $    /   |   \
1834 $   2  0 | 1  5
1835 $    \   |   /
1836 $     \  |  /
1837 $      \ | /
1838 $        3
1839 $
1840 $ Notice that all points are numbered consecutively, unlikely DMPlexCreateFromCellList()
1841 
1842   Level: advanced
1843 
1844 .seealso: DMPlexCreateFromCellList(), DMPlexCreate()
1845 @*/
1846 PetscErrorCode DMPlexCreateFromDAG(DM dm, PetscInt depth, const PetscInt numPoints[], const PetscInt coneSize[], const PetscInt cones[], const PetscInt coneOrientations[], const PetscScalar vertexCoords[])
1847 {
1848   Vec            coordinates;
1849   PetscSection   coordSection;
1850   PetscScalar    *coords;
1851   PetscInt       coordSize, firstVertex = -1, pStart = 0, pEnd = 0, p, v, dim, dimEmbed, d, off;
1852   PetscErrorCode ierr;
1853 
1854   PetscFunctionBegin;
1855   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1856   ierr = DMGetCoordinateDim(dm, &dimEmbed);CHKERRQ(ierr);
1857   if (dimEmbed < dim) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Embedding dimension %d cannot be less than intrinsic dimension %d",dimEmbed,dim);
1858   for (d = 0; d <= depth; ++d) pEnd += numPoints[d];
1859   ierr = DMPlexSetChart(dm, pStart, pEnd);CHKERRQ(ierr);
1860   for (p = pStart; p < pEnd; ++p) {
1861     ierr = DMPlexSetConeSize(dm, p, coneSize[p-pStart]);CHKERRQ(ierr);
1862     if (firstVertex < 0 && !coneSize[p - pStart]) {
1863       firstVertex = p - pStart;
1864     }
1865   }
1866   if (firstVertex < 0 && numPoints[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Expected %d vertices but could not find any", numPoints[0]);
1867   ierr = DMSetUp(dm);CHKERRQ(ierr); /* Allocate space for cones */
1868   for (p = pStart, off = 0; p < pEnd; off += coneSize[p-pStart], ++p) {
1869     ierr = DMPlexSetCone(dm, p, &cones[off]);CHKERRQ(ierr);
1870     ierr = DMPlexSetConeOrientation(dm, p, &coneOrientations[off]);CHKERRQ(ierr);
1871   }
1872   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
1873   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
1874   /* Build coordinates */
1875   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
1876   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
1877   ierr = PetscSectionSetFieldComponents(coordSection, 0, dimEmbed);CHKERRQ(ierr);
1878   ierr = PetscSectionSetChart(coordSection, firstVertex, firstVertex+numPoints[0]);CHKERRQ(ierr);
1879   for (v = firstVertex; v < firstVertex+numPoints[0]; ++v) {
1880     ierr = PetscSectionSetDof(coordSection, v, dimEmbed);CHKERRQ(ierr);
1881     ierr = PetscSectionSetFieldDof(coordSection, v, 0, dimEmbed);CHKERRQ(ierr);
1882   }
1883   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
1884   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
1885   ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
1886   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
1887   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
1888   ierr = VecSetBlockSize(coordinates, dimEmbed);CHKERRQ(ierr);
1889   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
1890   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
1891   for (v = 0; v < numPoints[0]; ++v) {
1892     PetscInt off;
1893 
1894     ierr = PetscSectionGetOffset(coordSection, v+firstVertex, &off);CHKERRQ(ierr);
1895     for (d = 0; d < dimEmbed; ++d) {
1896       coords[off+d] = vertexCoords[v*dimEmbed+d];
1897     }
1898   }
1899   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
1900   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
1901   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
1902   PetscFunctionReturn(0);
1903 }
1904 
1905 /*@C
1906   DMPlexCreateFromFile - This takes a filename and produces a DM
1907 
1908   Input Parameters:
1909 + comm - The communicator
1910 . filename - A file name
1911 - interpolate - Flag to create intermediate mesh pieces (edges, faces)
1912 
1913   Output Parameter:
1914 . dm - The DM
1915 
1916   Level: beginner
1917 
1918 .seealso: DMPlexCreateFromDAG(), DMPlexCreateFromCellList(), DMPlexCreate()
1919 @*/
1920 PetscErrorCode DMPlexCreateFromFile(MPI_Comm comm, const char filename[], PetscBool interpolate, DM *dm)
1921 {
1922   const char    *extGmsh   = ".msh";
1923   const char    *extCGNS   = ".cgns";
1924   const char    *extExodus = ".exo";
1925   const char    *extFluent = ".cas";
1926   const char    *extHDF5   = ".h5";
1927   size_t         len;
1928   PetscBool      isGmsh, isCGNS, isExodus, isFluent, isHDF5;
1929   PetscMPIInt    rank;
1930   PetscErrorCode ierr;
1931 
1932   PetscFunctionBegin;
1933   PetscValidPointer(filename, 2);
1934   PetscValidPointer(dm, 4);
1935   ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
1936   ierr = PetscStrlen(filename, &len);CHKERRQ(ierr);
1937   if (!len) SETERRQ(comm, PETSC_ERR_ARG_WRONG, "Filename must be a valid path");
1938   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extGmsh,   4, &isGmsh);CHKERRQ(ierr);
1939   ierr = PetscStrncmp(&filename[PetscMax(0,len-5)], extCGNS,   5, &isCGNS);CHKERRQ(ierr);
1940   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extExodus, 4, &isExodus);CHKERRQ(ierr);
1941   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extFluent, 4, &isFluent);CHKERRQ(ierr);
1942   ierr = PetscStrncmp(&filename[PetscMax(0,len-3)], extHDF5,   3, &isHDF5);CHKERRQ(ierr);
1943   if (isGmsh) {
1944     ierr = DMPlexCreateGmshFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
1945   } else if (isCGNS) {
1946     ierr = DMPlexCreateCGNSFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
1947   } else if (isExodus) {
1948     ierr = DMPlexCreateExodusFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
1949   } else if (isFluent) {
1950     ierr = DMPlexCreateFluentFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
1951   } else if (isHDF5) {
1952     PetscViewer viewer;
1953 
1954     ierr = PetscViewerCreate(comm, &viewer);CHKERRQ(ierr);
1955     ierr = PetscViewerSetType(viewer, PETSCVIEWERHDF5);CHKERRQ(ierr);
1956     ierr = PetscViewerFileSetMode(viewer, FILE_MODE_READ);CHKERRQ(ierr);
1957     ierr = PetscViewerFileSetName(viewer, filename);CHKERRQ(ierr);
1958     ierr = DMCreate(comm, dm);CHKERRQ(ierr);
1959     ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
1960     ierr = DMLoad(*dm, viewer);CHKERRQ(ierr);
1961     ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
1962   } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cannot load file %s: unrecognized extension", filename);
1963   PetscFunctionReturn(0);
1964 }
1965 
1966 /*@
1967   DMPlexCreateReferenceCell - Create a DMPLEX with the appropriate FEM reference cell
1968 
1969   Collective on comm
1970 
1971   Input Parameters:
1972 + comm    - The communicator
1973 . dim     - The spatial dimension
1974 - simplex - Flag for simplex, otherwise use a tensor-product cell
1975 
1976   Output Parameter:
1977 . refdm - The reference cell
1978 
1979   Level: intermediate
1980 
1981 .keywords: reference cell
1982 .seealso:
1983 @*/
1984 PetscErrorCode DMPlexCreateReferenceCell(MPI_Comm comm, PetscInt dim, PetscBool simplex, DM *refdm)
1985 {
1986   DM             rdm;
1987   Vec            coords;
1988   PetscErrorCode ierr;
1989 
1990   PetscFunctionBeginUser;
1991   ierr = DMCreate(comm, &rdm);CHKERRQ(ierr);
1992   ierr = DMSetType(rdm, DMPLEX);CHKERRQ(ierr);
1993   ierr = DMSetDimension(rdm, dim);CHKERRQ(ierr);
1994   switch (dim) {
1995   case 0:
1996   {
1997     PetscInt    numPoints[1]        = {1};
1998     PetscInt    coneSize[1]         = {0};
1999     PetscInt    cones[1]            = {0};
2000     PetscInt    coneOrientations[1] = {0};
2001     PetscScalar vertexCoords[1]     = {0.0};
2002 
2003     ierr = DMPlexCreateFromDAG(rdm, 0, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2004   }
2005   break;
2006   case 1:
2007   {
2008     PetscInt    numPoints[2]        = {2, 1};
2009     PetscInt    coneSize[3]         = {2, 0, 0};
2010     PetscInt    cones[2]            = {1, 2};
2011     PetscInt    coneOrientations[2] = {0, 0};
2012     PetscScalar vertexCoords[2]     = {-1.0,  1.0};
2013 
2014     ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2015   }
2016   break;
2017   case 2:
2018     if (simplex) {
2019       PetscInt    numPoints[2]        = {3, 1};
2020       PetscInt    coneSize[4]         = {3, 0, 0, 0};
2021       PetscInt    cones[3]            = {1, 2, 3};
2022       PetscInt    coneOrientations[3] = {0, 0, 0};
2023       PetscScalar vertexCoords[6]     = {-1.0, -1.0,  1.0, -1.0,  -1.0, 1.0};
2024 
2025       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2026     } else {
2027       PetscInt    numPoints[2]        = {4, 1};
2028       PetscInt    coneSize[5]         = {4, 0, 0, 0, 0};
2029       PetscInt    cones[4]            = {1, 2, 3, 4};
2030       PetscInt    coneOrientations[4] = {0, 0, 0, 0};
2031       PetscScalar vertexCoords[8]     = {-1.0, -1.0,  1.0, -1.0,  1.0, 1.0,  -1.0, 1.0};
2032 
2033       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2034     }
2035   break;
2036   case 3:
2037     if (simplex) {
2038       PetscInt    numPoints[2]        = {4, 1};
2039       PetscInt    coneSize[5]         = {4, 0, 0, 0, 0};
2040       PetscInt    cones[4]            = {1, 3, 2, 4};
2041       PetscInt    coneOrientations[4] = {0, 0, 0, 0};
2042       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};
2043 
2044       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2045     } else {
2046       PetscInt    numPoints[2]        = {8, 1};
2047       PetscInt    coneSize[9]         = {8, 0, 0, 0, 0, 0, 0, 0, 0};
2048       PetscInt    cones[8]            = {1, 4, 3, 2, 5, 6, 7, 8};
2049       PetscInt    coneOrientations[8] = {0, 0, 0, 0, 0, 0, 0, 0};
2050       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,
2051                                          -1.0, -1.0,  1.0,  1.0, -1.0,  1.0,  1.0, 1.0,  1.0,  -1.0, 1.0,  1.0};
2052 
2053       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2054     }
2055   break;
2056   default:
2057     SETERRQ1(comm, PETSC_ERR_ARG_WRONG, "Cannot create reference cell for dimension %d", dim);
2058   }
2059   *refdm = NULL;
2060   ierr = DMPlexInterpolate(rdm, refdm);CHKERRQ(ierr);
2061   if (rdm->coordinateDM) {
2062     DM           ncdm;
2063     PetscSection cs;
2064     PetscInt     pEnd = -1;
2065 
2066     ierr = DMGetDefaultSection(rdm->coordinateDM, &cs);CHKERRQ(ierr);
2067     if (cs) {ierr = PetscSectionGetChart(cs, NULL, &pEnd);CHKERRQ(ierr);}
2068     if (pEnd >= 0) {
2069       ierr = DMClone(rdm->coordinateDM, &ncdm);CHKERRQ(ierr);
2070       ierr = DMSetDefaultSection(ncdm, cs);CHKERRQ(ierr);
2071       ierr = DMSetCoordinateDM(*refdm, ncdm);CHKERRQ(ierr);
2072       ierr = DMDestroy(&ncdm);CHKERRQ(ierr);
2073     }
2074   }
2075   ierr = DMGetCoordinatesLocal(rdm, &coords);CHKERRQ(ierr);
2076   if (coords) {
2077     ierr = DMSetCoordinatesLocal(*refdm, coords);CHKERRQ(ierr);
2078   } else {
2079     ierr = DMGetCoordinates(rdm, &coords);CHKERRQ(ierr);
2080     if (coords) {ierr = DMSetCoordinates(*refdm, coords);CHKERRQ(ierr);}
2081   }
2082   ierr = DMDestroy(&rdm);CHKERRQ(ierr);
2083   PetscFunctionReturn(0);
2084 }
2085