xref: /petsc/src/dm/impls/plex/plexcreate.c (revision 967582eba84cc53dc1fbf6b54d6aa49b7d83bae6)
1 #define PETSCDM_DLL
2 #include <petsc/private/dmpleximpl.h>    /*I   "petscdmplex.h"   I*/
3 #include <petsc/private/hashseti.h>          /*I   "petscdmplex.h"   I*/
4 #include <petscsf.h>
5 
6 PetscLogEvent DMPLEX_CreateFromFile, DMPLEX_CreateFromCellList, DMPLEX_CreateFromCellList_Coordinates;
7 
8 /*@
9   DMPlexCreateDoublet - Creates a mesh of two cells of the specified type, optionally with later refinement.
10 
11   Collective
12 
13   Input Parameters:
14 + comm - The communicator for the DM object
15 . dim - The spatial dimension
16 . simplex - Flag for simplicial cells, otherwise they are tensor product cells
17 . interpolate - Flag to create intermediate mesh pieces (edges, faces)
18 . refinementUniform - Flag for uniform parallel refinement
19 - refinementLimit - A nonzero number indicates the largest admissible volume for a refined cell
20 
21   Output Parameter:
22 . dm - The DM object
23 
24   Level: beginner
25 
26 .seealso: DMSetType(), DMCreate()
27 @*/
28 PetscErrorCode DMPlexCreateDoublet(MPI_Comm comm, PetscInt dim, PetscBool simplex, PetscBool interpolate, PetscBool refinementUniform, PetscReal refinementLimit, DM *newdm)
29 {
30   DM             dm;
31   PetscInt       p;
32   PetscMPIInt    rank;
33   PetscErrorCode ierr;
34 
35   PetscFunctionBegin;
36   ierr = DMCreate(comm, &dm);CHKERRQ(ierr);
37   ierr = DMSetType(dm, DMPLEX);CHKERRQ(ierr);
38   ierr = DMSetDimension(dm, dim);CHKERRQ(ierr);
39   ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
40   switch (dim) {
41   case 2:
42     if (simplex) {ierr = PetscObjectSetName((PetscObject) dm, "triangular");CHKERRQ(ierr);}
43     else         {ierr = PetscObjectSetName((PetscObject) dm, "quadrilateral");CHKERRQ(ierr);}
44     break;
45   case 3:
46     if (simplex) {ierr = PetscObjectSetName((PetscObject) dm, "tetrahedral");CHKERRQ(ierr);}
47     else         {ierr = PetscObjectSetName((PetscObject) dm, "hexahedral");CHKERRQ(ierr);}
48     break;
49   default:
50     SETERRQ1(comm, PETSC_ERR_ARG_OUTOFRANGE, "Cannot make meshes for dimension %d", dim);
51   }
52   if (rank) {
53     PetscInt numPoints[2] = {0, 0};
54     ierr = DMPlexCreateFromDAG(dm, 1, numPoints, NULL, NULL, NULL, NULL);CHKERRQ(ierr);
55   } else {
56     switch (dim) {
57     case 2:
58       if (simplex) {
59         PetscInt    numPoints[2]        = {4, 2};
60         PetscInt    coneSize[6]         = {3, 3, 0, 0, 0, 0};
61         PetscInt    cones[6]            = {2, 3, 4,  5, 4, 3};
62         PetscInt    coneOrientations[6] = {0, 0, 0,  0, 0, 0};
63         PetscScalar vertexCoords[8]     = {-0.5, 0.5, 0.0, 0.0, 0.0, 1.0, 0.5, 0.5};
64         PetscInt    markerPoints[8]     = {2, 1, 3, 1, 4, 1, 5, 1};
65 
66         ierr = DMPlexCreateFromDAG(dm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
67         for (p = 0; p < 4; ++p) {ierr = DMSetLabelValue(dm, "marker", markerPoints[p*2], markerPoints[p*2+1]);CHKERRQ(ierr);}
68       } else {
69         PetscInt    numPoints[2]        = {6, 2};
70         PetscInt    coneSize[8]         = {4, 4, 0, 0, 0, 0, 0, 0};
71         PetscInt    cones[8]            = {2, 3, 4, 5,  3, 6, 7, 4};
72         PetscInt    coneOrientations[8] = {0, 0, 0, 0,  0, 0, 0, 0};
73         PetscScalar vertexCoords[12]    = {-1.0, -0.5,  0.0, -0.5,  0.0, 0.5,  -1.0, 0.5,  1.0, -0.5,  1.0, 0.5};
74 
75         ierr = DMPlexCreateFromDAG(dm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
76       }
77       break;
78     case 3:
79       if (simplex) {
80         PetscInt    numPoints[2]        = {5, 2};
81         PetscInt    coneSize[7]         = {4, 4, 0, 0, 0, 0, 0};
82         PetscInt    cones[8]            = {4, 3, 5, 2,  5, 3, 4, 6};
83         PetscInt    coneOrientations[8] = {0, 0, 0, 0,  0, 0, 0, 0};
84         PetscScalar vertexCoords[15]    = {-1.0, 0.0, 0.0,  0.0, -1.0, 0.0,  0.0, 0.0, 1.0,  0.0, 1.0, 0.0,  1.0, 0.0, 0.0};
85         PetscInt    markerPoints[10]    = {2, 1, 3, 1, 4, 1, 5, 1, 6, 1};
86 
87         ierr = DMPlexCreateFromDAG(dm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
88         for (p = 0; p < 5; ++p) {ierr = DMSetLabelValue(dm, "marker", markerPoints[p*2], markerPoints[p*2+1]);CHKERRQ(ierr);}
89       } else {
90         PetscInt    numPoints[2]         = {12, 2};
91         PetscInt    coneSize[14]         = {8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0};
92         PetscInt    cones[16]            = {2, 3, 4, 5, 6, 7, 8, 9,  5, 4, 10, 11, 7, 12, 13, 8};
93         PetscInt    coneOrientations[16] = {0, 0, 0, 0, 0, 0, 0, 0,  0, 0,  0,  0, 0,  0,  0, 0};
94         PetscScalar vertexCoords[36]     = {-1.0, -0.5, -0.5,  -1.0,  0.5, -0.5,  0.0,  0.5, -0.5,   0.0, -0.5, -0.5,
95                                             -1.0, -0.5,  0.5,   0.0, -0.5,  0.5,  0.0,  0.5,  0.5,  -1.0,  0.5,  0.5,
96                                              1.0,  0.5, -0.5,   1.0, -0.5, -0.5,  1.0, -0.5,  0.5,   1.0,  0.5,  0.5};
97 
98         ierr = DMPlexCreateFromDAG(dm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
99       }
100       break;
101     default:
102       SETERRQ1(comm, PETSC_ERR_ARG_OUTOFRANGE, "Cannot make meshes for dimension %d", dim);
103     }
104   }
105   *newdm = dm;
106   if (refinementLimit > 0.0) {
107     DM rdm;
108     const char *name;
109 
110     ierr = DMPlexSetRefinementUniform(*newdm, PETSC_FALSE);CHKERRQ(ierr);
111     ierr = DMPlexSetRefinementLimit(*newdm, refinementLimit);CHKERRQ(ierr);
112     ierr = DMRefine(*newdm, comm, &rdm);CHKERRQ(ierr);
113     ierr = PetscObjectGetName((PetscObject) *newdm, &name);CHKERRQ(ierr);
114     ierr = PetscObjectSetName((PetscObject)    rdm,  name);CHKERRQ(ierr);
115     ierr = DMDestroy(newdm);CHKERRQ(ierr);
116     *newdm = rdm;
117   }
118   if (interpolate) {
119     DM idm;
120 
121     ierr = DMPlexInterpolate(*newdm, &idm);CHKERRQ(ierr);
122     ierr = DMDestroy(newdm);CHKERRQ(ierr);
123     *newdm = idm;
124   }
125   {
126     DM refinedMesh     = NULL;
127     DM distributedMesh = NULL;
128 
129     /* Distribute mesh over processes */
130     ierr = DMPlexDistribute(*newdm, 0, NULL, &distributedMesh);CHKERRQ(ierr);
131     if (distributedMesh) {
132       ierr = DMDestroy(newdm);CHKERRQ(ierr);
133       *newdm = distributedMesh;
134     }
135     if (refinementUniform) {
136       ierr = DMPlexSetRefinementUniform(*newdm, refinementUniform);CHKERRQ(ierr);
137       ierr = DMRefine(*newdm, comm, &refinedMesh);CHKERRQ(ierr);
138       if (refinedMesh) {
139         ierr = DMDestroy(newdm);CHKERRQ(ierr);
140         *newdm = refinedMesh;
141       }
142     }
143   }
144   PetscFunctionReturn(0);
145 }
146 
147 /*@
148   DMPlexCreateSquareBoundary - Creates a 1D mesh the is the boundary of a square lattice.
149 
150   Collective
151 
152   Input Parameters:
153 + comm  - The communicator for the DM object
154 . lower - The lower left corner coordinates
155 . upper - The upper right corner coordinates
156 - edges - The number of cells in each direction
157 
158   Output Parameter:
159 . dm  - The DM object
160 
161   Note: Here is the numbering returned for 2 cells in each direction:
162 $ 18--5-17--4--16
163 $  |     |     |
164 $  6    10     3
165 $  |     |     |
166 $ 19-11-20--9--15
167 $  |     |     |
168 $  7     8     2
169 $  |     |     |
170 $ 12--0-13--1--14
171 
172   Level: beginner
173 
174 .seealso: DMPlexCreateBoxMesh(), DMPlexCreateCubeBoundary(), DMSetType(), DMCreate()
175 @*/
176 PetscErrorCode DMPlexCreateSquareBoundary(DM dm, const PetscReal lower[], const PetscReal upper[], const PetscInt edges[])
177 {
178   const PetscInt numVertices    = (edges[0]+1)*(edges[1]+1);
179   const PetscInt numEdges       = edges[0]*(edges[1]+1) + (edges[0]+1)*edges[1];
180   PetscInt       markerTop      = 1;
181   PetscInt       markerBottom   = 1;
182   PetscInt       markerRight    = 1;
183   PetscInt       markerLeft     = 1;
184   PetscBool      markerSeparate = PETSC_FALSE;
185   Vec            coordinates;
186   PetscSection   coordSection;
187   PetscScalar    *coords;
188   PetscInt       coordSize;
189   PetscMPIInt    rank;
190   PetscInt       v, vx, vy;
191   PetscErrorCode ierr;
192 
193   PetscFunctionBegin;
194   ierr = PetscOptionsGetBool(((PetscObject) dm)->options,((PetscObject) dm)->prefix, "-dm_plex_separate_marker", &markerSeparate, NULL);CHKERRQ(ierr);
195   if (markerSeparate) {
196     markerTop    = 3;
197     markerBottom = 1;
198     markerRight  = 2;
199     markerLeft   = 4;
200   }
201   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);CHKERRQ(ierr);
202   if (!rank) {
203     PetscInt e, ex, ey;
204 
205     ierr = DMPlexSetChart(dm, 0, numEdges+numVertices);CHKERRQ(ierr);
206     for (e = 0; e < numEdges; ++e) {
207       ierr = DMPlexSetConeSize(dm, e, 2);CHKERRQ(ierr);
208     }
209     ierr = DMSetUp(dm);CHKERRQ(ierr); /* Allocate space for cones */
210     for (vx = 0; vx <= edges[0]; vx++) {
211       for (ey = 0; ey < edges[1]; ey++) {
212         PetscInt edge   = vx*edges[1] + ey + edges[0]*(edges[1]+1);
213         PetscInt vertex = ey*(edges[0]+1) + vx + numEdges;
214         PetscInt cone[2];
215 
216         cone[0] = vertex; cone[1] = vertex+edges[0]+1;
217         ierr    = DMPlexSetCone(dm, edge, cone);CHKERRQ(ierr);
218         if (vx == edges[0]) {
219           ierr = DMSetLabelValue(dm, "marker", edge,    markerRight);CHKERRQ(ierr);
220           ierr = DMSetLabelValue(dm, "marker", cone[0], markerRight);CHKERRQ(ierr);
221           if (ey == edges[1]-1) {
222             ierr = DMSetLabelValue(dm, "marker", cone[1], markerRight);CHKERRQ(ierr);
223             ierr = DMSetLabelValue(dm, "Face Sets", cone[1], markerRight);CHKERRQ(ierr);
224           }
225         } else if (vx == 0) {
226           ierr = DMSetLabelValue(dm, "marker", edge,    markerLeft);CHKERRQ(ierr);
227           ierr = DMSetLabelValue(dm, "marker", cone[0], markerLeft);CHKERRQ(ierr);
228           if (ey == edges[1]-1) {
229             ierr = DMSetLabelValue(dm, "marker", cone[1], markerLeft);CHKERRQ(ierr);
230             ierr = DMSetLabelValue(dm, "Face Sets", cone[1], markerLeft);CHKERRQ(ierr);
231           }
232         }
233       }
234     }
235     for (vy = 0; vy <= edges[1]; vy++) {
236       for (ex = 0; ex < edges[0]; ex++) {
237         PetscInt edge   = vy*edges[0]     + ex;
238         PetscInt vertex = vy*(edges[0]+1) + ex + numEdges;
239         PetscInt cone[2];
240 
241         cone[0] = vertex; cone[1] = vertex+1;
242         ierr    = DMPlexSetCone(dm, edge, cone);CHKERRQ(ierr);
243         if (vy == edges[1]) {
244           ierr = DMSetLabelValue(dm, "marker", edge,    markerTop);CHKERRQ(ierr);
245           ierr = DMSetLabelValue(dm, "marker", cone[0], markerTop);CHKERRQ(ierr);
246           if (ex == edges[0]-1) {
247             ierr = DMSetLabelValue(dm, "marker", cone[1], markerTop);CHKERRQ(ierr);
248             ierr = DMSetLabelValue(dm, "Face Sets", cone[1], markerTop);CHKERRQ(ierr);
249           }
250         } else if (vy == 0) {
251           ierr = DMSetLabelValue(dm, "marker", edge,    markerBottom);CHKERRQ(ierr);
252           ierr = DMSetLabelValue(dm, "marker", cone[0], markerBottom);CHKERRQ(ierr);
253           if (ex == edges[0]-1) {
254             ierr = DMSetLabelValue(dm, "marker", cone[1], markerBottom);CHKERRQ(ierr);
255             ierr = DMSetLabelValue(dm, "Face Sets", cone[1], markerBottom);CHKERRQ(ierr);
256           }
257         }
258       }
259     }
260   }
261   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
262   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
263   /* Build coordinates */
264   ierr = DMSetCoordinateDim(dm, 2);CHKERRQ(ierr);
265   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
266   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
267   ierr = PetscSectionSetChart(coordSection, numEdges, numEdges + numVertices);CHKERRQ(ierr);
268   ierr = PetscSectionSetFieldComponents(coordSection, 0, 2);CHKERRQ(ierr);
269   for (v = numEdges; v < numEdges+numVertices; ++v) {
270     ierr = PetscSectionSetDof(coordSection, v, 2);CHKERRQ(ierr);
271     ierr = PetscSectionSetFieldDof(coordSection, v, 0, 2);CHKERRQ(ierr);
272   }
273   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
274   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
275   ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
276   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
277   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
278   ierr = VecSetBlockSize(coordinates, 2);CHKERRQ(ierr);
279   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
280   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
281   for (vy = 0; vy <= edges[1]; ++vy) {
282     for (vx = 0; vx <= edges[0]; ++vx) {
283       coords[(vy*(edges[0]+1)+vx)*2+0] = lower[0] + ((upper[0] - lower[0])/edges[0])*vx;
284       coords[(vy*(edges[0]+1)+vx)*2+1] = lower[1] + ((upper[1] - lower[1])/edges[1])*vy;
285     }
286   }
287   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
288   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
289   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
290   PetscFunctionReturn(0);
291 }
292 
293 /*@
294   DMPlexCreateCubeBoundary - Creates a 2D mesh that is the boundary of a cubic lattice.
295 
296   Collective
297 
298   Input Parameters:
299 + comm  - The communicator for the DM object
300 . lower - The lower left front corner coordinates
301 . upper - The upper right back corner coordinates
302 - faces - The number of faces in each direction (the same as the number of cells)
303 
304   Output Parameter:
305 . dm  - The DM object
306 
307   Level: beginner
308 
309 .seealso: DMPlexCreateBoxMesh(), DMPlexCreateSquareBoundary(), DMSetType(), DMCreate()
310 @*/
311 PetscErrorCode DMPlexCreateCubeBoundary(DM dm, const PetscReal lower[], const PetscReal upper[], const PetscInt faces[])
312 {
313   PetscInt       vertices[3], numVertices;
314   PetscInt       numFaces    = 2*faces[0]*faces[1] + 2*faces[1]*faces[2] + 2*faces[0]*faces[2];
315   Vec            coordinates;
316   PetscSection   coordSection;
317   PetscScalar    *coords;
318   PetscInt       coordSize;
319   PetscMPIInt    rank;
320   PetscInt       v, vx, vy, vz;
321   PetscInt       voffset, iface=0, cone[4];
322   PetscErrorCode ierr;
323 
324   PetscFunctionBegin;
325   if ((faces[0] < 1) || (faces[1] < 1) || (faces[2] < 1)) SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Must have at least 1 face per side");
326   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);CHKERRQ(ierr);
327   vertices[0] = faces[0]+1; vertices[1] = faces[1]+1; vertices[2] = faces[2]+1;
328   numVertices = vertices[0]*vertices[1]*vertices[2];
329   if (!rank) {
330     PetscInt f;
331 
332     ierr = DMPlexSetChart(dm, 0, numFaces+numVertices);CHKERRQ(ierr);
333     for (f = 0; f < numFaces; ++f) {
334       ierr = DMPlexSetConeSize(dm, f, 4);CHKERRQ(ierr);
335     }
336     ierr = DMSetUp(dm);CHKERRQ(ierr); /* Allocate space for cones */
337 
338     /* Side 0 (Top) */
339     for (vy = 0; vy < faces[1]; vy++) {
340       for (vx = 0; vx < faces[0]; vx++) {
341         voffset = numFaces + vertices[0]*vertices[1]*(vertices[2]-1) + vy*vertices[0] + vx;
342         cone[0] = voffset; cone[1] = voffset+1; cone[2] = voffset+vertices[0]+1; cone[3] = voffset+vertices[0];
343         ierr    = DMPlexSetCone(dm, iface, cone);CHKERRQ(ierr);
344         ierr    = DMSetLabelValue(dm, "marker", iface, 1);CHKERRQ(ierr);
345         ierr    = DMSetLabelValue(dm, "marker", voffset+0, 1);CHKERRQ(ierr);
346         ierr    = DMSetLabelValue(dm, "marker", voffset+1, 1);CHKERRQ(ierr);
347         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[0]+0, 1);CHKERRQ(ierr);
348         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[0]+1, 1);CHKERRQ(ierr);
349         iface++;
350       }
351     }
352 
353     /* Side 1 (Bottom) */
354     for (vy = 0; vy < faces[1]; vy++) {
355       for (vx = 0; vx < faces[0]; vx++) {
356         voffset = numFaces + vy*(faces[0]+1) + vx;
357         cone[0] = voffset+1; cone[1] = voffset; cone[2] = voffset+vertices[0]; cone[3] = voffset+vertices[0]+1;
358         ierr    = DMPlexSetCone(dm, iface, cone);CHKERRQ(ierr);
359         ierr    = DMSetLabelValue(dm, "marker", iface, 1);CHKERRQ(ierr);
360         ierr    = DMSetLabelValue(dm, "marker", voffset+0, 1);CHKERRQ(ierr);
361         ierr    = DMSetLabelValue(dm, "marker", voffset+1, 1);CHKERRQ(ierr);
362         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[0]+0, 1);CHKERRQ(ierr);
363         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[0]+1, 1);CHKERRQ(ierr);
364         iface++;
365       }
366     }
367 
368     /* Side 2 (Front) */
369     for (vz = 0; vz < faces[2]; vz++) {
370       for (vx = 0; vx < faces[0]; vx++) {
371         voffset = numFaces + vz*vertices[0]*vertices[1] + vx;
372         cone[0] = voffset; cone[1] = voffset+1; cone[2] = voffset+vertices[0]*vertices[1]+1; cone[3] = voffset+vertices[0]*vertices[1];
373         ierr    = DMPlexSetCone(dm, iface, cone);CHKERRQ(ierr);
374         ierr    = DMSetLabelValue(dm, "marker", iface, 1);CHKERRQ(ierr);
375         ierr    = DMSetLabelValue(dm, "marker", voffset+0, 1);CHKERRQ(ierr);
376         ierr    = DMSetLabelValue(dm, "marker", voffset+1, 1);CHKERRQ(ierr);
377         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[0]*vertices[1]+0, 1);CHKERRQ(ierr);
378         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[0]*vertices[1]+1, 1);CHKERRQ(ierr);
379         iface++;
380       }
381     }
382 
383     /* Side 3 (Back) */
384     for (vz = 0; vz < faces[2]; vz++) {
385       for (vx = 0; vx < faces[0]; vx++) {
386         voffset = numFaces + vz*vertices[0]*vertices[1] + vertices[0]*(vertices[1]-1) + vx;
387         cone[0] = voffset+vertices[0]*vertices[1]; cone[1] = voffset+vertices[0]*vertices[1]+1;
388         cone[2] = voffset+1; cone[3] = voffset;
389         ierr    = DMPlexSetCone(dm, iface, cone);CHKERRQ(ierr);
390         ierr    = DMSetLabelValue(dm, "marker", iface, 1);CHKERRQ(ierr);
391         ierr    = DMSetLabelValue(dm, "marker", voffset+0, 1);CHKERRQ(ierr);
392         ierr    = DMSetLabelValue(dm, "marker", voffset+1, 1);CHKERRQ(ierr);
393         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[0]*vertices[1]+0, 1);CHKERRQ(ierr);
394         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[0]*vertices[1]+1, 1);CHKERRQ(ierr);
395         iface++;
396       }
397     }
398 
399     /* Side 4 (Left) */
400     for (vz = 0; vz < faces[2]; vz++) {
401       for (vy = 0; vy < faces[1]; vy++) {
402         voffset = numFaces + vz*vertices[0]*vertices[1] + vy*vertices[0];
403         cone[0] = voffset; cone[1] = voffset+vertices[0]*vertices[1];
404         cone[2] = voffset+vertices[0]*vertices[1]+vertices[0]; cone[3] = voffset+vertices[0];
405         ierr    = DMPlexSetCone(dm, iface, cone);CHKERRQ(ierr);
406         ierr    = DMSetLabelValue(dm, "marker", iface, 1);CHKERRQ(ierr);
407         ierr    = DMSetLabelValue(dm, "marker", voffset+0, 1);CHKERRQ(ierr);
408         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[0]+0, 1);CHKERRQ(ierr);
409         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[1]+0, 1);CHKERRQ(ierr);
410         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[0]*vertices[1]+vertices[0], 1);CHKERRQ(ierr);
411         iface++;
412       }
413     }
414 
415     /* Side 5 (Right) */
416     for (vz = 0; vz < faces[2]; vz++) {
417       for (vy = 0; vy < faces[1]; vy++) {
418         voffset = numFaces + vz*vertices[0]*vertices[1] + vy*vertices[0] + faces[0];
419         cone[0] = voffset+vertices[0]*vertices[1]; cone[1] = voffset;
420         cone[2] = voffset+vertices[0]; cone[3] = voffset+vertices[0]*vertices[1]+vertices[0];
421         ierr    = DMPlexSetCone(dm, iface, cone);CHKERRQ(ierr);
422         ierr    = DMSetLabelValue(dm, "marker", iface, 1);CHKERRQ(ierr);
423         ierr    = DMSetLabelValue(dm, "marker", voffset+0, 1);CHKERRQ(ierr);
424         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[0]+0, 1);CHKERRQ(ierr);
425         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[0]*vertices[1]+0, 1);CHKERRQ(ierr);
426         ierr    = DMSetLabelValue(dm, "marker", voffset+vertices[0]*vertices[1]+vertices[0], 1);CHKERRQ(ierr);
427         iface++;
428       }
429     }
430   }
431   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
432   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
433   /* Build coordinates */
434   ierr = DMSetCoordinateDim(dm, 3);CHKERRQ(ierr);
435   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
436   ierr = PetscSectionSetChart(coordSection, numFaces, numFaces + numVertices);CHKERRQ(ierr);
437   for (v = numFaces; v < numFaces+numVertices; ++v) {
438     ierr = PetscSectionSetDof(coordSection, v, 3);CHKERRQ(ierr);
439   }
440   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
441   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
442   ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
443   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
444   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
445   ierr = VecSetBlockSize(coordinates, 3);CHKERRQ(ierr);
446   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
447   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
448   for (vz = 0; vz <= faces[2]; ++vz) {
449     for (vy = 0; vy <= faces[1]; ++vy) {
450       for (vx = 0; vx <= faces[0]; ++vx) {
451         coords[((vz*(faces[1]+1)+vy)*(faces[0]+1)+vx)*3+0] = lower[0] + ((upper[0] - lower[0])/faces[0])*vx;
452         coords[((vz*(faces[1]+1)+vy)*(faces[0]+1)+vx)*3+1] = lower[1] + ((upper[1] - lower[1])/faces[1])*vy;
453         coords[((vz*(faces[1]+1)+vy)*(faces[0]+1)+vx)*3+2] = lower[2] + ((upper[2] - lower[2])/faces[2])*vz;
454       }
455     }
456   }
457   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
458   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
459   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
460   PetscFunctionReturn(0);
461 }
462 
463 static PetscErrorCode DMPlexCreateLineMesh_Internal(MPI_Comm comm,PetscInt segments,PetscReal lower,PetscReal upper,DMBoundaryType bd,DM *dm)
464 {
465   PetscInt       i,fStart,fEnd,numCells = 0,numVerts = 0;
466   PetscInt       numPoints[2],*coneSize,*cones,*coneOrientations;
467   PetscScalar    *vertexCoords;
468   PetscReal      L,maxCell;
469   PetscBool      markerSeparate = PETSC_FALSE;
470   PetscInt       markerLeft  = 1, faceMarkerLeft  = 1;
471   PetscInt       markerRight = 1, faceMarkerRight = 2;
472   PetscBool      wrap = (bd == DM_BOUNDARY_PERIODIC || bd == DM_BOUNDARY_TWIST) ? PETSC_TRUE : PETSC_FALSE;
473   PetscMPIInt    rank;
474   PetscErrorCode ierr;
475 
476   PetscFunctionBegin;
477   PetscValidPointer(dm,4);
478 
479   ierr = DMCreate(comm,dm);CHKERRQ(ierr);
480   ierr = DMSetType(*dm,DMPLEX);CHKERRQ(ierr);
481   ierr = DMSetDimension(*dm,1);CHKERRQ(ierr);
482   ierr = DMCreateLabel(*dm,"marker");CHKERRQ(ierr);
483   ierr = DMCreateLabel(*dm,"Face Sets");CHKERRQ(ierr);
484 
485   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
486   if (!rank) numCells = segments;
487   if (!rank) numVerts = segments + (wrap ? 0 : 1);
488 
489   numPoints[0] = numVerts ; numPoints[1] = numCells;
490   ierr = PetscMalloc4(numCells+numVerts,&coneSize,numCells*2,&cones,numCells+numVerts,&coneOrientations,numVerts,&vertexCoords);CHKERRQ(ierr);
491   ierr = PetscArrayzero(coneOrientations,numCells+numVerts);CHKERRQ(ierr);
492   for (i = 0; i < numCells; ++i) { coneSize[i] = 2; }
493   for (i = 0; i < numVerts; ++i) { coneSize[numCells+i] = 0; }
494   for (i = 0; i < numCells; ++i) { cones[2*i] = numCells + i%numVerts; cones[2*i+1] = numCells + (i+1)%numVerts; }
495   for (i = 0; i < numVerts; ++i) { vertexCoords[i] = lower + (upper-lower)*((PetscReal)i/(PetscReal)numCells); }
496   ierr = DMPlexCreateFromDAG(*dm,1,numPoints,coneSize,cones,coneOrientations,vertexCoords);CHKERRQ(ierr);
497   ierr = PetscFree4(coneSize,cones,coneOrientations,vertexCoords);CHKERRQ(ierr);
498 
499   ierr = PetscOptionsGetBool(((PetscObject)*dm)->options,((PetscObject)*dm)->prefix,"-dm_plex_separate_marker",&markerSeparate,NULL);CHKERRQ(ierr);
500   if (markerSeparate) { markerLeft = faceMarkerLeft; markerRight = faceMarkerRight;}
501   if (!wrap && !rank) {
502     ierr = DMPlexGetHeightStratum(*dm,1,&fStart,&fEnd);CHKERRQ(ierr);
503     ierr = DMSetLabelValue(*dm,"marker",fStart,markerLeft);CHKERRQ(ierr);
504     ierr = DMSetLabelValue(*dm,"marker",fEnd-1,markerRight);CHKERRQ(ierr);
505     ierr = DMSetLabelValue(*dm,"Face Sets",fStart,faceMarkerLeft);CHKERRQ(ierr);
506     ierr = DMSetLabelValue(*dm,"Face Sets",fEnd-1,faceMarkerRight);CHKERRQ(ierr);
507   }
508   if (wrap) {
509     L       = upper - lower;
510     maxCell = (PetscReal)1.1*(L/(PetscReal)PetscMax(1,segments));
511     ierr = DMSetPeriodicity(*dm,PETSC_TRUE,&maxCell,&L,&bd);CHKERRQ(ierr);
512   }
513   PetscFunctionReturn(0);
514 }
515 
516 static PetscErrorCode DMPlexCreateBoxMesh_Simplex_Internal(MPI_Comm comm, PetscInt dim, const PetscInt faces[], const PetscReal lower[], const PetscReal upper[], const DMBoundaryType periodicity[], PetscBool interpolate, DM *dm)
517 {
518   DM             boundary;
519   PetscInt       i;
520   PetscErrorCode ierr;
521 
522   PetscFunctionBegin;
523   PetscValidPointer(dm, 4);
524   for (i = 0; i < dim; ++i) if (periodicity[i] != DM_BOUNDARY_NONE) SETERRQ(comm, PETSC_ERR_SUP, "Periodicity is not supported for simplex meshes");
525   ierr = DMCreate(comm, &boundary);CHKERRQ(ierr);
526   PetscValidLogicalCollectiveInt(boundary,dim,2);
527   ierr = DMSetType(boundary, DMPLEX);CHKERRQ(ierr);
528   ierr = DMSetDimension(boundary, dim-1);CHKERRQ(ierr);
529   ierr = DMSetCoordinateDim(boundary, dim);CHKERRQ(ierr);
530   switch (dim) {
531   case 2: ierr = DMPlexCreateSquareBoundary(boundary, lower, upper, faces);CHKERRQ(ierr);break;
532   case 3: ierr = DMPlexCreateCubeBoundary(boundary, lower, upper, faces);CHKERRQ(ierr);break;
533   default: SETERRQ1(comm, PETSC_ERR_SUP, "Dimension not supported: %d", dim);
534   }
535   ierr = DMPlexGenerate(boundary, NULL, interpolate, dm);CHKERRQ(ierr);
536   ierr = DMDestroy(&boundary);CHKERRQ(ierr);
537   PetscFunctionReturn(0);
538 }
539 
540 static PetscErrorCode DMPlexCreateCubeMesh_Internal(DM dm, const PetscReal lower[], const PetscReal upper[], const PetscInt edges[], DMBoundaryType bdX, DMBoundaryType bdY, DMBoundaryType bdZ)
541 {
542   DMLabel        cutLabel = NULL;
543   PetscInt       markerTop      = 1, faceMarkerTop      = 1;
544   PetscInt       markerBottom   = 1, faceMarkerBottom   = 1;
545   PetscInt       markerFront    = 1, faceMarkerFront    = 1;
546   PetscInt       markerBack     = 1, faceMarkerBack     = 1;
547   PetscInt       markerRight    = 1, faceMarkerRight    = 1;
548   PetscInt       markerLeft     = 1, faceMarkerLeft     = 1;
549   PetscInt       dim;
550   PetscBool      markerSeparate = PETSC_FALSE, cutMarker = PETSC_FALSE;
551   PetscMPIInt    rank;
552   PetscErrorCode ierr;
553 
554   PetscFunctionBegin;
555   ierr = DMGetDimension(dm,&dim);CHKERRQ(ierr);
556   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);CHKERRQ(ierr);
557   ierr = DMCreateLabel(dm,"marker");CHKERRQ(ierr);
558   ierr = DMCreateLabel(dm,"Face Sets");CHKERRQ(ierr);
559   ierr = PetscOptionsGetBool(((PetscObject) dm)->options,((PetscObject) dm)->prefix, "-dm_plex_periodic_cut", &cutMarker, NULL);CHKERRQ(ierr);
560   if (bdX == DM_BOUNDARY_PERIODIC || bdX == DM_BOUNDARY_TWIST ||
561       bdY == DM_BOUNDARY_PERIODIC || bdY == DM_BOUNDARY_TWIST ||
562       bdZ == DM_BOUNDARY_PERIODIC || bdZ == DM_BOUNDARY_TWIST) {
563 
564     if (cutMarker) {ierr = DMCreateLabel(dm, "periodic_cut");CHKERRQ(ierr); ierr = DMGetLabel(dm, "periodic_cut", &cutLabel);CHKERRQ(ierr);}
565   }
566   switch (dim) {
567   case 2:
568     faceMarkerTop    = 3;
569     faceMarkerBottom = 1;
570     faceMarkerRight  = 2;
571     faceMarkerLeft   = 4;
572     break;
573   case 3:
574     faceMarkerBottom = 1;
575     faceMarkerTop    = 2;
576     faceMarkerFront  = 3;
577     faceMarkerBack   = 4;
578     faceMarkerRight  = 5;
579     faceMarkerLeft   = 6;
580     break;
581   default:
582     SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Dimension %d not supported",dim);
583     break;
584   }
585   ierr = PetscOptionsGetBool(((PetscObject) dm)->options,((PetscObject) dm)->prefix, "-dm_plex_separate_marker", &markerSeparate, NULL);CHKERRQ(ierr);
586   if (markerSeparate) {
587     markerBottom = faceMarkerBottom;
588     markerTop    = faceMarkerTop;
589     markerFront  = faceMarkerFront;
590     markerBack   = faceMarkerBack;
591     markerRight  = faceMarkerRight;
592     markerLeft   = faceMarkerLeft;
593   }
594   {
595     const PetscInt numXEdges    = !rank ? edges[0] : 0;
596     const PetscInt numYEdges    = !rank ? edges[1] : 0;
597     const PetscInt numZEdges    = !rank ? edges[2] : 0;
598     const PetscInt numXVertices = !rank ? (bdX == DM_BOUNDARY_PERIODIC || bdX == DM_BOUNDARY_TWIST ? edges[0] : edges[0]+1) : 0;
599     const PetscInt numYVertices = !rank ? (bdY == DM_BOUNDARY_PERIODIC || bdY == DM_BOUNDARY_TWIST ? edges[1] : edges[1]+1) : 0;
600     const PetscInt numZVertices = !rank ? (bdZ == DM_BOUNDARY_PERIODIC || bdZ == DM_BOUNDARY_TWIST ? edges[2] : edges[2]+1) : 0;
601     const PetscInt numCells     = numXEdges*numYEdges*numZEdges;
602     const PetscInt numXFaces    = numYEdges*numZEdges;
603     const PetscInt numYFaces    = numXEdges*numZEdges;
604     const PetscInt numZFaces    = numXEdges*numYEdges;
605     const PetscInt numTotXFaces = numXVertices*numXFaces;
606     const PetscInt numTotYFaces = numYVertices*numYFaces;
607     const PetscInt numTotZFaces = numZVertices*numZFaces;
608     const PetscInt numFaces     = numTotXFaces + numTotYFaces + numTotZFaces;
609     const PetscInt numTotXEdges = numXEdges*numYVertices*numZVertices;
610     const PetscInt numTotYEdges = numYEdges*numXVertices*numZVertices;
611     const PetscInt numTotZEdges = numZEdges*numXVertices*numYVertices;
612     const PetscInt numVertices  = numXVertices*numYVertices*numZVertices;
613     const PetscInt numEdges     = numTotXEdges + numTotYEdges + numTotZEdges;
614     const PetscInt firstVertex  = (dim == 2) ? numFaces : numCells;
615     const PetscInt firstXFace   = (dim == 2) ? 0 : numCells + numVertices;
616     const PetscInt firstYFace   = firstXFace + numTotXFaces;
617     const PetscInt firstZFace   = firstYFace + numTotYFaces;
618     const PetscInt firstXEdge   = numCells + numFaces + numVertices;
619     const PetscInt firstYEdge   = firstXEdge + numTotXEdges;
620     const PetscInt firstZEdge   = firstYEdge + numTotYEdges;
621     Vec            coordinates;
622     PetscSection   coordSection;
623     PetscScalar   *coords;
624     PetscInt       coordSize;
625     PetscInt       v, vx, vy, vz;
626     PetscInt       c, f, fx, fy, fz, e, ex, ey, ez;
627 
628     ierr = DMPlexSetChart(dm, 0, numCells+numFaces+numEdges+numVertices);CHKERRQ(ierr);
629     for (c = 0; c < numCells; c++) {
630       ierr = DMPlexSetConeSize(dm, c, 6);CHKERRQ(ierr);
631     }
632     for (f = firstXFace; f < firstXFace+numFaces; ++f) {
633       ierr = DMPlexSetConeSize(dm, f, 4);CHKERRQ(ierr);
634     }
635     for (e = firstXEdge; e < firstXEdge+numEdges; ++e) {
636       ierr = DMPlexSetConeSize(dm, e, 2);CHKERRQ(ierr);
637     }
638     ierr = DMSetUp(dm);CHKERRQ(ierr); /* Allocate space for cones */
639     /* Build cells */
640     for (fz = 0; fz < numZEdges; ++fz) {
641       for (fy = 0; fy < numYEdges; ++fy) {
642         for (fx = 0; fx < numXEdges; ++fx) {
643           PetscInt cell    = (fz*numYEdges + fy)*numXEdges + fx;
644           PetscInt faceB   = firstZFace + (fy*numXEdges+fx)*numZVertices +   fz;
645           PetscInt faceT   = firstZFace + (fy*numXEdges+fx)*numZVertices + ((fz+1)%numZVertices);
646           PetscInt faceF   = firstYFace + (fz*numXEdges+fx)*numYVertices +   fy;
647           PetscInt faceK   = firstYFace + (fz*numXEdges+fx)*numYVertices + ((fy+1)%numYVertices);
648           PetscInt faceL   = firstXFace + (fz*numYEdges+fy)*numXVertices +   fx;
649           PetscInt faceR   = firstXFace + (fz*numYEdges+fy)*numXVertices + ((fx+1)%numXVertices);
650                             /* B,  T,  F,  K,  R,  L */
651           PetscInt ornt[6] = {-4,  0,  0, -1,  0, -4}; /* ??? */
652           PetscInt cone[6];
653 
654           /* no boundary twisting in 3D */
655           cone[0] = faceB; cone[1] = faceT; cone[2] = faceF; cone[3] = faceK; cone[4] = faceR; cone[5] = faceL;
656           ierr    = DMPlexSetCone(dm, cell, cone);CHKERRQ(ierr);
657           ierr    = DMPlexSetConeOrientation(dm, cell, ornt);CHKERRQ(ierr);
658           if (bdX != DM_BOUNDARY_NONE && fx == numXEdges-1 && cutLabel) {ierr = DMLabelSetValue(cutLabel, cell, 2);CHKERRQ(ierr);}
659           if (bdY != DM_BOUNDARY_NONE && fy == numYEdges-1 && cutLabel) {ierr = DMLabelSetValue(cutLabel, cell, 2);CHKERRQ(ierr);}
660           if (bdZ != DM_BOUNDARY_NONE && fz == numZEdges-1 && cutLabel) {ierr = DMLabelSetValue(cutLabel, cell, 2);CHKERRQ(ierr);}
661         }
662       }
663     }
664     /* Build x faces */
665     for (fz = 0; fz < numZEdges; ++fz) {
666       for (fy = 0; fy < numYEdges; ++fy) {
667         for (fx = 0; fx < numXVertices; ++fx) {
668           PetscInt face    = firstXFace + (fz*numYEdges+fy)*numXVertices + fx;
669           PetscInt edgeL   = firstZEdge + (  fy*                 numXVertices+fx)*numZEdges + fz;
670           PetscInt edgeR   = firstZEdge + (((fy+1)%numYVertices)*numXVertices+fx)*numZEdges + fz;
671           PetscInt edgeB   = firstYEdge + (  fz*                 numXVertices+fx)*numYEdges + fy;
672           PetscInt edgeT   = firstYEdge + (((fz+1)%numZVertices)*numXVertices+fx)*numYEdges + fy;
673           PetscInt ornt[4] = {0, 0, -2, -2};
674           PetscInt cone[4];
675 
676           if (dim == 3) {
677             /* markers */
678             if (bdX != DM_BOUNDARY_PERIODIC) {
679               if (fx == numXVertices-1) {
680                 ierr = DMSetLabelValue(dm, "Face Sets", face, faceMarkerRight);CHKERRQ(ierr);
681                 ierr = DMSetLabelValue(dm, "marker", face, markerRight);CHKERRQ(ierr);
682               }
683               else if (fx == 0) {
684                 ierr = DMSetLabelValue(dm, "Face Sets", face, faceMarkerLeft);CHKERRQ(ierr);
685                 ierr = DMSetLabelValue(dm, "marker", face, markerLeft);CHKERRQ(ierr);
686               }
687             }
688           }
689           cone[0] = edgeB; cone[1] = edgeR; cone[2] = edgeT; cone[3] = edgeL;
690           ierr    = DMPlexSetCone(dm, face, cone);CHKERRQ(ierr);
691           ierr    = DMPlexSetConeOrientation(dm, face, ornt);CHKERRQ(ierr);
692         }
693       }
694     }
695     /* Build y faces */
696     for (fz = 0; fz < numZEdges; ++fz) {
697       for (fx = 0; fx < numXEdges; ++fx) {
698         for (fy = 0; fy < numYVertices; ++fy) {
699           PetscInt face    = firstYFace + (fz*numXEdges+fx)*numYVertices + fy;
700           PetscInt edgeL   = firstZEdge + (fy*numXVertices+  fx                 )*numZEdges + fz;
701           PetscInt edgeR   = firstZEdge + (fy*numXVertices+((fx+1)%numXVertices))*numZEdges + fz;
702           PetscInt edgeB   = firstXEdge + (  fz                 *numYVertices+fy)*numXEdges + fx;
703           PetscInt edgeT   = firstXEdge + (((fz+1)%numZVertices)*numYVertices+fy)*numXEdges + fx;
704           PetscInt ornt[4] = {0, 0, -2, -2};
705           PetscInt cone[4];
706 
707           if (dim == 3) {
708             /* markers */
709             if (bdY != DM_BOUNDARY_PERIODIC) {
710               if (fy == numYVertices-1) {
711                 ierr = DMSetLabelValue(dm, "Face Sets", face, faceMarkerBack);CHKERRQ(ierr);
712                 ierr = DMSetLabelValue(dm, "marker", face, markerBack);CHKERRQ(ierr);
713               }
714               else if (fy == 0) {
715                 ierr = DMSetLabelValue(dm, "Face Sets", face, faceMarkerFront);CHKERRQ(ierr);
716                 ierr = DMSetLabelValue(dm, "marker", face, markerFront);CHKERRQ(ierr);
717               }
718             }
719           }
720           cone[0] = edgeB; cone[1] = edgeR; cone[2] = edgeT; cone[3] = edgeL;
721           ierr    = DMPlexSetCone(dm, face, cone);CHKERRQ(ierr);
722           ierr    = DMPlexSetConeOrientation(dm, face, ornt);CHKERRQ(ierr);
723         }
724       }
725     }
726     /* Build z faces */
727     for (fy = 0; fy < numYEdges; ++fy) {
728       for (fx = 0; fx < numXEdges; ++fx) {
729         for (fz = 0; fz < numZVertices; fz++) {
730           PetscInt face    = firstZFace + (fy*numXEdges+fx)*numZVertices + fz;
731           PetscInt edgeL   = firstYEdge + (fz*numXVertices+  fx                 )*numYEdges + fy;
732           PetscInt edgeR   = firstYEdge + (fz*numXVertices+((fx+1)%numXVertices))*numYEdges + fy;
733           PetscInt edgeB   = firstXEdge + (fz*numYVertices+  fy                 )*numXEdges + fx;
734           PetscInt edgeT   = firstXEdge + (fz*numYVertices+((fy+1)%numYVertices))*numXEdges + fx;
735           PetscInt ornt[4] = {0, 0, -2, -2};
736           PetscInt cone[4];
737 
738           if (dim == 2) {
739             if (bdX == DM_BOUNDARY_TWIST && fx == numXEdges-1) {edgeR += numYEdges-1-2*fy; ornt[1] = -2;}
740             if (bdY == DM_BOUNDARY_TWIST && fy == numYEdges-1) {edgeT += numXEdges-1-2*fx; ornt[2] =  0;}
741             if (bdX != DM_BOUNDARY_NONE && fx == numXEdges-1 && cutLabel) {ierr = DMLabelSetValue(cutLabel, face, 2);CHKERRQ(ierr);}
742             if (bdY != DM_BOUNDARY_NONE && fy == numYEdges-1 && cutLabel) {ierr = DMLabelSetValue(cutLabel, face, 2);CHKERRQ(ierr);}
743           } else {
744             /* markers */
745             if (bdZ != DM_BOUNDARY_PERIODIC) {
746               if (fz == numZVertices-1) {
747                 ierr = DMSetLabelValue(dm, "Face Sets", face, faceMarkerTop);CHKERRQ(ierr);
748                 ierr = DMSetLabelValue(dm, "marker", face, markerTop);CHKERRQ(ierr);
749               }
750               else if (fz == 0) {
751                 ierr = DMSetLabelValue(dm, "Face Sets", face, faceMarkerBottom);CHKERRQ(ierr);
752                 ierr = DMSetLabelValue(dm, "marker", face, markerBottom);CHKERRQ(ierr);
753               }
754             }
755           }
756           cone[0] = edgeB; cone[1] = edgeR; cone[2] = edgeT; cone[3] = edgeL;
757           ierr    = DMPlexSetCone(dm, face, cone);CHKERRQ(ierr);
758           ierr    = DMPlexSetConeOrientation(dm, face, ornt);CHKERRQ(ierr);
759         }
760       }
761     }
762     /* Build Z edges*/
763     for (vy = 0; vy < numYVertices; vy++) {
764       for (vx = 0; vx < numXVertices; vx++) {
765         for (ez = 0; ez < numZEdges; ez++) {
766           const PetscInt edge    = firstZEdge  + (vy*numXVertices+vx)*numZEdges + ez;
767           const PetscInt vertexB = firstVertex + (  ez                 *numYVertices+vy)*numXVertices + vx;
768           const PetscInt vertexT = firstVertex + (((ez+1)%numZVertices)*numYVertices+vy)*numXVertices + vx;
769           PetscInt       cone[2];
770 
771           if (dim == 3) {
772             if (bdX != DM_BOUNDARY_PERIODIC) {
773               if (vx == numXVertices-1) {
774                 ierr = DMSetLabelValue(dm, "marker", edge, markerRight);CHKERRQ(ierr);
775               }
776               else if (vx == 0) {
777                 ierr = DMSetLabelValue(dm, "marker", edge, markerLeft);CHKERRQ(ierr);
778               }
779             }
780             if (bdY != DM_BOUNDARY_PERIODIC) {
781               if (vy == numYVertices-1) {
782                 ierr = DMSetLabelValue(dm, "marker", edge, markerBack);CHKERRQ(ierr);
783               }
784               else if (vy == 0) {
785                 ierr = DMSetLabelValue(dm, "marker", edge, markerFront);CHKERRQ(ierr);
786               }
787             }
788           }
789           cone[0] = vertexB; cone[1] = vertexT;
790           ierr = DMPlexSetCone(dm, edge, cone);CHKERRQ(ierr);
791         }
792       }
793     }
794     /* Build Y edges*/
795     for (vz = 0; vz < numZVertices; vz++) {
796       for (vx = 0; vx < numXVertices; vx++) {
797         for (ey = 0; ey < numYEdges; ey++) {
798           const PetscInt nextv   = (dim == 2 && bdY == DM_BOUNDARY_TWIST && ey == numYEdges-1) ? (numXVertices-vx-1) : (vz*numYVertices+((ey+1)%numYVertices))*numXVertices + vx;
799           const PetscInt edge    = firstYEdge  + (vz*numXVertices+vx)*numYEdges + ey;
800           const PetscInt vertexF = firstVertex + (vz*numYVertices+ey)*numXVertices + vx;
801           const PetscInt vertexK = firstVertex + nextv;
802           PetscInt       cone[2];
803 
804           cone[0] = vertexF; cone[1] = vertexK;
805           ierr = DMPlexSetCone(dm, edge, cone);CHKERRQ(ierr);
806           if (dim == 2) {
807             if ((bdX != DM_BOUNDARY_PERIODIC) && (bdX != DM_BOUNDARY_TWIST)) {
808               if (vx == numXVertices-1) {
809                 ierr = DMSetLabelValue(dm, "Face Sets", edge, faceMarkerRight);CHKERRQ(ierr);
810                 ierr = DMSetLabelValue(dm, "marker", edge,    markerRight);CHKERRQ(ierr);
811                 ierr = DMSetLabelValue(dm, "marker", cone[0], markerRight);CHKERRQ(ierr);
812                 if (ey == numYEdges-1) {
813                   ierr = DMSetLabelValue(dm, "marker", cone[1], markerRight);CHKERRQ(ierr);
814                 }
815               } else if (vx == 0) {
816                 ierr = DMSetLabelValue(dm, "Face Sets", edge, faceMarkerLeft);CHKERRQ(ierr);
817                 ierr = DMSetLabelValue(dm, "marker", edge,    markerLeft);CHKERRQ(ierr);
818                 ierr = DMSetLabelValue(dm, "marker", cone[0], markerLeft);CHKERRQ(ierr);
819                 if (ey == numYEdges-1) {
820                   ierr = DMSetLabelValue(dm, "marker", cone[1], markerLeft);CHKERRQ(ierr);
821                 }
822               }
823             } else {
824               if (vx == 0 && cutLabel) {
825                 ierr = DMLabelSetValue(cutLabel, edge,    1);CHKERRQ(ierr);
826                 ierr = DMLabelSetValue(cutLabel, cone[0], 1);CHKERRQ(ierr);
827                 if (ey == numYEdges-1) {
828                   ierr = DMLabelSetValue(cutLabel, cone[1], 1);CHKERRQ(ierr);
829                 }
830               }
831             }
832           } else {
833             if (bdX != DM_BOUNDARY_PERIODIC) {
834               if (vx == numXVertices-1) {
835                 ierr = DMSetLabelValue(dm, "marker", edge, markerRight);CHKERRQ(ierr);
836               } else if (vx == 0) {
837                 ierr = DMSetLabelValue(dm, "marker", edge, markerLeft);CHKERRQ(ierr);
838               }
839             }
840             if (bdZ != DM_BOUNDARY_PERIODIC) {
841               if (vz == numZVertices-1) {
842                 ierr = DMSetLabelValue(dm, "marker", edge, markerTop);CHKERRQ(ierr);
843               } else if (vz == 0) {
844                 ierr = DMSetLabelValue(dm, "marker", edge, markerBottom);CHKERRQ(ierr);
845               }
846             }
847           }
848         }
849       }
850     }
851     /* Build X edges*/
852     for (vz = 0; vz < numZVertices; vz++) {
853       for (vy = 0; vy < numYVertices; vy++) {
854         for (ex = 0; ex < numXEdges; ex++) {
855           const PetscInt nextv   = (dim == 2 && bdX == DM_BOUNDARY_TWIST && ex == numXEdges-1) ? (numYVertices-vy-1)*numXVertices : (vz*numYVertices+vy)*numXVertices + (ex+1)%numXVertices;
856           const PetscInt edge    = firstXEdge  + (vz*numYVertices+vy)*numXEdges + ex;
857           const PetscInt vertexL = firstVertex + (vz*numYVertices+vy)*numXVertices + ex;
858           const PetscInt vertexR = firstVertex + nextv;
859           PetscInt       cone[2];
860 
861           cone[0] = vertexL; cone[1] = vertexR;
862           ierr = DMPlexSetCone(dm, edge, cone);CHKERRQ(ierr);
863           if (dim == 2) {
864             if ((bdY != DM_BOUNDARY_PERIODIC) && (bdY != DM_BOUNDARY_TWIST)) {
865               if (vy == numYVertices-1) {
866                 ierr = DMSetLabelValue(dm, "Face Sets", edge, faceMarkerTop);CHKERRQ(ierr);
867                 ierr = DMSetLabelValue(dm, "marker", edge,    markerTop);CHKERRQ(ierr);
868                 ierr = DMSetLabelValue(dm, "marker", cone[0], markerTop);CHKERRQ(ierr);
869                 if (ex == numXEdges-1) {
870                   ierr = DMSetLabelValue(dm, "marker", cone[1], markerTop);CHKERRQ(ierr);
871                 }
872               } else if (vy == 0) {
873                 ierr = DMSetLabelValue(dm, "Face Sets", edge, faceMarkerBottom);CHKERRQ(ierr);
874                 ierr = DMSetLabelValue(dm, "marker", edge,    markerBottom);CHKERRQ(ierr);
875                 ierr = DMSetLabelValue(dm, "marker", cone[0], markerBottom);CHKERRQ(ierr);
876                 if (ex == numXEdges-1) {
877                   ierr = DMSetLabelValue(dm, "marker", cone[1], markerBottom);CHKERRQ(ierr);
878                 }
879               }
880             } else {
881               if (vy == 0 && cutLabel) {
882                 ierr = DMLabelSetValue(cutLabel, edge,    1);CHKERRQ(ierr);
883                 ierr = DMLabelSetValue(cutLabel, cone[0], 1);CHKERRQ(ierr);
884                 if (ex == numXEdges-1) {
885                   ierr = DMLabelSetValue(cutLabel, cone[1], 1);CHKERRQ(ierr);
886                 }
887               }
888             }
889           } else {
890             if (bdY != DM_BOUNDARY_PERIODIC) {
891               if (vy == numYVertices-1) {
892                 ierr = DMSetLabelValue(dm, "marker", edge, markerBack);CHKERRQ(ierr);
893               }
894               else if (vy == 0) {
895                 ierr = DMSetLabelValue(dm, "marker", edge, markerFront);CHKERRQ(ierr);
896               }
897             }
898             if (bdZ != DM_BOUNDARY_PERIODIC) {
899               if (vz == numZVertices-1) {
900                 ierr = DMSetLabelValue(dm, "marker", edge, markerTop);CHKERRQ(ierr);
901               }
902               else if (vz == 0) {
903                 ierr = DMSetLabelValue(dm, "marker", edge, markerBottom);CHKERRQ(ierr);
904               }
905             }
906           }
907         }
908       }
909     }
910     ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
911     ierr = DMPlexStratify(dm);CHKERRQ(ierr);
912     /* Build coordinates */
913     ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
914     ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
915     ierr = PetscSectionSetFieldComponents(coordSection, 0, dim);CHKERRQ(ierr);
916     ierr = PetscSectionSetChart(coordSection, firstVertex, firstVertex+numVertices);CHKERRQ(ierr);
917     for (v = firstVertex; v < firstVertex+numVertices; ++v) {
918       ierr = PetscSectionSetDof(coordSection, v, dim);CHKERRQ(ierr);
919       ierr = PetscSectionSetFieldDof(coordSection, v, 0, dim);CHKERRQ(ierr);
920     }
921     ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
922     ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
923     ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
924     ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
925     ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
926     ierr = VecSetBlockSize(coordinates, dim);CHKERRQ(ierr);
927     ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
928     ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
929     for (vz = 0; vz < numZVertices; ++vz) {
930       for (vy = 0; vy < numYVertices; ++vy) {
931         for (vx = 0; vx < numXVertices; ++vx) {
932           coords[((vz*numYVertices+vy)*numXVertices+vx)*dim+0] = lower[0] + ((upper[0] - lower[0])/numXEdges)*vx;
933           coords[((vz*numYVertices+vy)*numXVertices+vx)*dim+1] = lower[1] + ((upper[1] - lower[1])/numYEdges)*vy;
934           if (dim == 3) {
935             coords[((vz*numYVertices+vy)*numXVertices+vx)*dim+2] = lower[2] + ((upper[2] - lower[2])/numZEdges)*vz;
936           }
937         }
938       }
939     }
940     ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
941     ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
942     ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
943   }
944   PetscFunctionReturn(0);
945 }
946 
947 static PetscErrorCode DMPlexCreateBoxMesh_Tensor_Internal(MPI_Comm comm, PetscInt dim, const PetscInt faces[], const PetscReal lower[], const PetscReal upper[], const DMBoundaryType periodicity[], PetscBool interpolate, DM *dm)
948 {
949   PetscInt       i;
950   PetscErrorCode ierr;
951 
952   PetscFunctionBegin;
953   PetscValidPointer(dm, 7);
954   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
955   PetscValidLogicalCollectiveInt(*dm,dim,2);
956   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
957   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
958   switch (dim) {
959   case 2: {ierr = DMPlexCreateCubeMesh_Internal(*dm, lower, upper, faces, periodicity[0], periodicity[1], DM_BOUNDARY_NONE);CHKERRQ(ierr);break;}
960   case 3: {ierr = DMPlexCreateCubeMesh_Internal(*dm, lower, upper, faces, periodicity[0], periodicity[1], periodicity[2]);CHKERRQ(ierr);break;}
961   default: SETERRQ1(comm, PETSC_ERR_SUP, "Dimension not supported: %d", dim);
962   }
963   if (periodicity[0] == DM_BOUNDARY_PERIODIC || periodicity[0] == DM_BOUNDARY_TWIST ||
964       periodicity[1] == DM_BOUNDARY_PERIODIC || periodicity[1] == DM_BOUNDARY_TWIST ||
965       (dim > 2 && (periodicity[2] == DM_BOUNDARY_PERIODIC || periodicity[2] == DM_BOUNDARY_TWIST))) {
966     PetscReal L[3];
967     PetscReal maxCell[3];
968 
969     for (i = 0; i < dim; i++) {
970       L[i]       = upper[i] - lower[i];
971       maxCell[i] = 1.1 * (L[i] / PetscMax(1,faces[i]));
972     }
973     ierr = DMSetPeriodicity(*dm,PETSC_TRUE,maxCell,L,periodicity);CHKERRQ(ierr);
974   }
975   if (!interpolate) {
976     DM udm;
977 
978     ierr = DMPlexUninterpolate(*dm, &udm);CHKERRQ(ierr);
979     ierr = DMPlexCopyCoordinates(*dm, udm);CHKERRQ(ierr);
980     ierr = DMDestroy(dm);CHKERRQ(ierr);
981     *dm  = udm;
982   }
983   PetscFunctionReturn(0);
984 }
985 
986 /*@C
987   DMPlexCreateBoxMesh - Creates a mesh on the tensor product of unit intervals (box) using simplices or tensor cells (hexahedra).
988 
989   Collective
990 
991   Input Parameters:
992 + comm        - The communicator for the DM object
993 . dim         - The spatial dimension
994 . simplex     - PETSC_TRUE for simplices, PETSC_FALSE for tensor cells
995 . faces       - Number of faces per dimension, or NULL for (1,) in 1D and (2, 2) in 2D and (1, 1, 1) in 3D
996 . lower       - The lower left corner, or NULL for (0, 0, 0)
997 . upper       - The upper right corner, or NULL for (1, 1, 1)
998 . periodicity - The boundary type for the X,Y,Z direction, or NULL for DM_BOUNDARY_NONE
999 - interpolate - Flag to create intermediate mesh pieces (edges, faces)
1000 
1001   Output Parameter:
1002 . dm  - The DM object
1003 
1004   Options Database Keys:
1005 + -dm_plex_box_lower <x,y,z> - Specify lower-left-bottom coordinates for the box
1006 . -dm_plex_box_upper <x,y,z> - Specify upper-right-top coordinates for the box
1007 - -dm_plex_box_faces <m,n,p> - Number of faces in each linear direction
1008 
1009   Notes:
1010   The options database keys above take lists of length d in d dimensions.
1011 
1012   Here is the numbering returned for 2 faces in each direction for tensor cells:
1013 $ 10---17---11---18----12
1014 $  |         |         |
1015 $  |         |         |
1016 $ 20    2   22    3    24
1017 $  |         |         |
1018 $  |         |         |
1019 $  7---15----8---16----9
1020 $  |         |         |
1021 $  |         |         |
1022 $ 19    0   21    1   23
1023 $  |         |         |
1024 $  |         |         |
1025 $  4---13----5---14----6
1026 
1027 and for simplicial cells
1028 
1029 $ 14----8---15----9----16
1030 $  |\     5  |\      7 |
1031 $  | \       | \       |
1032 $ 13   2    14    3    15
1033 $  | 4   \   | 6   \   |
1034 $  |       \ |       \ |
1035 $ 11----6---12----7----13
1036 $  |\        |\        |
1037 $  | \    1  | \     3 |
1038 $ 10   0    11    1    12
1039 $  | 0   \   | 2   \   |
1040 $  |       \ |       \ |
1041 $  8----4----9----5----10
1042 
1043   Level: beginner
1044 
1045 .seealso: DMPlexCreateFromFile(), DMPlexCreateHexCylinderMesh(), DMSetType(), DMCreate()
1046 @*/
1047 PetscErrorCode DMPlexCreateBoxMesh(MPI_Comm comm, PetscInt dim, PetscBool simplex, const PetscInt faces[], const PetscReal lower[], const PetscReal upper[], const DMBoundaryType periodicity[], PetscBool interpolate, DM *dm)
1048 {
1049   PetscInt       fac[3] = {0, 0, 0};
1050   PetscReal      low[3] = {0, 0, 0};
1051   PetscReal      upp[3] = {1, 1, 1};
1052   DMBoundaryType bdt[3] = {DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE};
1053   PetscInt       i, n;
1054   PetscBool      flg;
1055   PetscErrorCode ierr;
1056 
1057   PetscFunctionBegin;
1058   n    = 3;
1059   ierr = PetscOptionsGetIntArray(NULL, NULL, "-dm_plex_box_faces", fac, &n, &flg);CHKERRQ(ierr);
1060   for (i = 0; i < dim; ++i) fac[i] = faces ? faces[i] : (flg && i < n ? fac[i] : (dim == 1 ? 1 : 4-dim));
1061   if (lower) for (i = 0; i < dim; ++i) low[i] = lower[i];
1062   if (upper) for (i = 0; i < dim; ++i) upp[i] = upper[i];
1063   if (periodicity) for (i = 0; i < dim; ++i) bdt[i] = periodicity[i];
1064   /* Allow bounds to be specified from the command line */
1065   n    = 3;
1066   ierr = PetscOptionsGetRealArray(NULL, NULL, "-dm_plex_box_lower", low, &n, &flg);CHKERRQ(ierr);
1067   if (flg && (n != dim)) SETERRQ2(comm, PETSC_ERR_ARG_SIZ, "Lower box point had %D values, should have been %D", n, dim);
1068   n    = 3;
1069   ierr = PetscOptionsGetRealArray(NULL, NULL, "-dm_plex_box_upper", upp, &n, &flg);CHKERRQ(ierr);
1070   if (flg && (n != dim)) SETERRQ2(comm, PETSC_ERR_ARG_SIZ, "Upper box point had %D values, should have been %D", n, dim);
1071 
1072   if (dim == 1)      {ierr = DMPlexCreateLineMesh_Internal(comm, fac[0], low[0], upp[0], bdt[0], dm);CHKERRQ(ierr);}
1073   else if (simplex)  {ierr = DMPlexCreateBoxMesh_Simplex_Internal(comm, dim, fac, low, upp, bdt, interpolate, dm);CHKERRQ(ierr);}
1074   else               {ierr = DMPlexCreateBoxMesh_Tensor_Internal(comm, dim, fac, low, upp, bdt, interpolate, dm);CHKERRQ(ierr);}
1075   PetscFunctionReturn(0);
1076 }
1077 
1078 /*@
1079   DMPlexCreateWedgeBoxMesh - Creates a 3-D mesh tesselating the (x,y) plane and extruding in the third direction using wedge cells.
1080 
1081   Collective
1082 
1083   Input Parameters:
1084 + comm        - The communicator for the DM object
1085 . faces       - Number of faces per dimension, or NULL for (1, 1, 1)
1086 . lower       - The lower left corner, or NULL for (0, 0, 0)
1087 . upper       - The upper right corner, or NULL for (1, 1, 1)
1088 . periodicity - The boundary type for the X,Y,Z direction, or NULL for DM_BOUNDARY_NONE
1089 . ordExt      - If PETSC_TRUE, orders the extruded cells in the height first. Otherwise, orders the cell on the layers first
1090 - interpolate - Flag to create intermediate mesh pieces (edges, faces)
1091 
1092   Output Parameter:
1093 . dm  - The DM object
1094 
1095   Level: beginner
1096 
1097 .seealso: DMPlexCreateHexCylinderMesh(), DMPlexCreateWedgeCylinderMesh(), DMPlexExtrude(), DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
1098 @*/
1099 PetscErrorCode DMPlexCreateWedgeBoxMesh(MPI_Comm comm, const PetscInt faces[], const PetscReal lower[], const PetscReal upper[], const DMBoundaryType periodicity[], PetscBool ordExt, PetscBool interpolate, DM *dm)
1100 {
1101   DM             bdm, botdm;
1102   PetscInt       i;
1103   PetscInt       fac[3] = {0, 0, 0};
1104   PetscReal      low[3] = {0, 0, 0};
1105   PetscReal      upp[3] = {1, 1, 1};
1106   DMBoundaryType bdt[3] = {DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE};
1107   PetscErrorCode ierr;
1108 
1109   PetscFunctionBegin;
1110   for (i = 0; i < 3; ++i) fac[i] = faces ? (faces[i] > 0 ? faces[i] : 1) : 1;
1111   if (lower) for (i = 0; i < 3; ++i) low[i] = lower[i];
1112   if (upper) for (i = 0; i < 3; ++i) upp[i] = upper[i];
1113   if (periodicity) for (i = 0; i < 3; ++i) bdt[i] = periodicity[i];
1114   for (i = 0; i < 3; ++i) if (bdt[i] != DM_BOUNDARY_NONE) SETERRQ(comm, PETSC_ERR_SUP, "Periodicity not yet supported");
1115 
1116   ierr = DMCreate(comm, &bdm);CHKERRQ(ierr);
1117   ierr = DMSetType(bdm, DMPLEX);CHKERRQ(ierr);
1118   ierr = DMSetDimension(bdm, 1);CHKERRQ(ierr);
1119   ierr = DMSetCoordinateDim(bdm, 2);CHKERRQ(ierr);
1120   ierr = DMPlexCreateSquareBoundary(bdm, low, upp, fac);CHKERRQ(ierr);
1121   ierr = DMPlexGenerate(bdm, NULL, PETSC_FALSE, &botdm);CHKERRQ(ierr);
1122   ierr = DMDestroy(&bdm);CHKERRQ(ierr);
1123   ierr = DMPlexExtrude(botdm, fac[2], upp[2] - low[2], ordExt, interpolate, dm);CHKERRQ(ierr);
1124   if (low[2] != 0.0) {
1125     Vec         v;
1126     PetscScalar *x;
1127     PetscInt    cDim, n;
1128 
1129     ierr = DMGetCoordinatesLocal(*dm, &v);CHKERRQ(ierr);
1130     ierr = VecGetBlockSize(v, &cDim);CHKERRQ(ierr);
1131     ierr = VecGetLocalSize(v, &n);CHKERRQ(ierr);
1132     ierr = VecGetArray(v, &x);CHKERRQ(ierr);
1133     x   += cDim;
1134     for (i=0; i<n; i+=cDim) x[i] += low[2];
1135     ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
1136     ierr = DMSetCoordinatesLocal(*dm, v);CHKERRQ(ierr);
1137   }
1138   ierr = DMDestroy(&botdm);CHKERRQ(ierr);
1139   PetscFunctionReturn(0);
1140 }
1141 
1142 /*@
1143   DMPlexExtrude - Creates a (d+1)-D mesh by extruding a d-D mesh in the normal direction using prismatic cells.
1144 
1145   Collective on idm
1146 
1147   Input Parameters:
1148 + idm - The mesh to be extruted
1149 . layers - The number of layers
1150 . height - The height of the extruded layer
1151 . ordExt - If PETSC_TRUE, orders the extruded cells in the height first. Otherwise, orders the cell on the layers first
1152 - interpolate - Flag to create intermediate mesh pieces (edges, faces)
1153 
1154   Output Parameter:
1155 . dm  - The DM object
1156 
1157   Notes: The mesh created has prismatic cells, and the vertex ordering in the cone of the cell is that of the tensor prismatic cells.
1158 
1159   Level: advanced
1160 
1161 .seealso: DMPlexCreateWedgeCylinderMesh(), DMPlexCreateWedgeBoxMesh(), DMSetType(), DMCreate()
1162 @*/
1163 PetscErrorCode DMPlexExtrude(DM idm, PetscInt layers, PetscReal height, PetscBool ordExt, PetscBool interpolate, DM* dm)
1164 {
1165   PetscScalar       *coordsB;
1166   const PetscScalar *coordsA;
1167   PetscReal         *normals = NULL;
1168   Vec               coordinatesA, coordinatesB;
1169   PetscSection      coordSectionA, coordSectionB;
1170   PetscInt          dim, cDim, cDimB, c, l, v, coordSize, *newCone;
1171   PetscInt          cStart, cEnd, vStart, vEnd, cellV, numCells, numVertices;
1172   PetscErrorCode    ierr;
1173 
1174   PetscFunctionBegin;
1175   PetscValidHeaderSpecific(idm, DM_CLASSID, 1);
1176   PetscValidLogicalCollectiveInt(idm, layers, 2);
1177   PetscValidLogicalCollectiveReal(idm, height, 3);
1178   PetscValidLogicalCollectiveBool(idm, interpolate, 4);
1179   ierr = DMGetDimension(idm, &dim);CHKERRQ(ierr);
1180   if (dim < 1 || dim > 3) SETERRQ1(PetscObjectComm((PetscObject)idm), PETSC_ERR_SUP, "Support for dimension %D not coded", dim);
1181 
1182   ierr = DMPlexGetHeightStratum(idm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1183   ierr = DMPlexGetDepthStratum(idm, 0, &vStart, &vEnd);CHKERRQ(ierr);
1184   numCells = (cEnd - cStart)*layers;
1185   numVertices = (vEnd - vStart)*(layers+1);
1186   ierr = DMCreate(PetscObjectComm((PetscObject)idm), dm);CHKERRQ(ierr);
1187   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
1188   ierr = DMSetDimension(*dm, dim+1);CHKERRQ(ierr);
1189   ierr = DMPlexSetChart(*dm, 0, numCells+numVertices);CHKERRQ(ierr);
1190   /* Must create the celltype label here so that we do not automatically try to compute the types */
1191   ierr = DMCreateLabel(*dm, "celltype");CHKERRQ(ierr);
1192   for (c = cStart, cellV = 0; c < cEnd; ++c) {
1193     DMPolytopeType ct, nct;
1194     PetscInt      *closure = NULL;
1195     PetscInt       closureSize, numCorners = 0;
1196 
1197     ierr = DMPlexGetCellType(idm, c, &ct);CHKERRQ(ierr);
1198     switch (ct) {
1199       case DM_POLYTOPE_SEGMENT:       nct = DM_POLYTOPE_SEG_PRISM_TENSOR;break;
1200       case DM_POLYTOPE_TRIANGLE:      nct = DM_POLYTOPE_TRI_PRISM_TENSOR;break;
1201       case DM_POLYTOPE_QUADRILATERAL: nct = DM_POLYTOPE_QUAD_PRISM_TENSOR;break;
1202       default: nct = DM_POLYTOPE_UNKNOWN;
1203     }
1204     ierr = DMPlexGetTransitiveClosure(idm, c, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
1205     for (v = 0; v < closureSize*2; v += 2) if ((closure[v] >= vStart) && (closure[v] < vEnd)) numCorners++;
1206     ierr = DMPlexRestoreTransitiveClosure(idm, c, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
1207     for (l = 0; l < layers; ++l) {
1208       const PetscInt cell = ordExt ? layers*(c - cStart) + l : l*(cEnd - cStart) + c - cStart;
1209 
1210       ierr = DMPlexSetConeSize(*dm, cell, 2*numCorners);CHKERRQ(ierr);
1211       ierr = DMPlexSetCellType(*dm, cell, nct);CHKERRQ(ierr);
1212     }
1213     cellV = PetscMax(numCorners,cellV);
1214   }
1215   ierr = DMSetUp(*dm);CHKERRQ(ierr);
1216 
1217   ierr = DMGetCoordinateDim(idm, &cDim);CHKERRQ(ierr);
1218   if (dim != cDim) {
1219     ierr = PetscCalloc1(cDim*(vEnd - vStart), &normals);CHKERRQ(ierr);
1220   }
1221   ierr = PetscMalloc1(3*cellV,&newCone);CHKERRQ(ierr);
1222   for (c = cStart; c < cEnd; ++c) {
1223     PetscInt *closure = NULL;
1224     PetscInt closureSize, numCorners = 0, l;
1225     PetscReal normal[3] = {0, 0, 0};
1226 
1227     if (normals) {
1228       ierr = DMPlexComputeCellGeometryFVM(idm, c, NULL, NULL, normal);CHKERRQ(ierr);
1229     }
1230     ierr = DMPlexGetTransitiveClosure(idm, c, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
1231     for (v = 0; v < closureSize*2; v += 2) {
1232       if ((closure[v] >= vStart) && (closure[v] < vEnd)) {
1233         PetscInt d;
1234 
1235         newCone[numCorners++] = closure[v] - vStart;
1236         if (normals) { for (d = 0; d < cDim; ++d) normals[cDim*(closure[v]-vStart)+d] += normal[d]; }
1237       }
1238     }
1239     ierr = DMPlexRestoreTransitiveClosure(idm, c, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
1240     for (l = 0; l < layers; ++l) {
1241       PetscInt i;
1242 
1243       for (i = 0; i < numCorners; ++i) {
1244         newCone[  numCorners + i] = ordExt ? (layers+1)*newCone[i] + l     + numCells :     l*(vEnd - vStart) + newCone[i] + numCells;
1245         newCone[2*numCorners + i] = ordExt ? (layers+1)*newCone[i] + l + 1 + numCells : (l+1)*(vEnd - vStart) + newCone[i] + numCells;
1246       }
1247       ierr = DMPlexSetCone(*dm, ordExt ? layers*(c - cStart) + l : l*(cEnd - cStart) + c - cStart, newCone + numCorners);CHKERRQ(ierr);
1248     }
1249   }
1250   ierr = DMPlexSymmetrize(*dm);CHKERRQ(ierr);
1251   ierr = DMPlexStratify(*dm);CHKERRQ(ierr);
1252   ierr = PetscFree(newCone);CHKERRQ(ierr);
1253 
1254   cDimB = cDim == dim ? cDim+1 : cDim;
1255   ierr = DMGetCoordinateSection(*dm, &coordSectionB);CHKERRQ(ierr);
1256   ierr = PetscSectionSetNumFields(coordSectionB, 1);CHKERRQ(ierr);
1257   ierr = PetscSectionSetFieldComponents(coordSectionB, 0, cDimB);CHKERRQ(ierr);
1258   ierr = PetscSectionSetChart(coordSectionB, numCells, numCells+numVertices);CHKERRQ(ierr);
1259   for (v = numCells; v < numCells+numVertices; ++v) {
1260     ierr = PetscSectionSetDof(coordSectionB, v, cDimB);CHKERRQ(ierr);
1261     ierr = PetscSectionSetFieldDof(coordSectionB, v, 0, cDimB);CHKERRQ(ierr);
1262     ierr = DMPlexSetCellType(*dm, v, DM_POLYTOPE_POINT);CHKERRQ(ierr);
1263   }
1264   ierr = PetscSectionSetUp(coordSectionB);CHKERRQ(ierr);
1265   ierr = PetscSectionGetStorageSize(coordSectionB, &coordSize);CHKERRQ(ierr);
1266   ierr = VecCreate(PETSC_COMM_SELF, &coordinatesB);CHKERRQ(ierr);
1267   ierr = PetscObjectSetName((PetscObject) coordinatesB, "coordinates");CHKERRQ(ierr);
1268   ierr = VecSetSizes(coordinatesB, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
1269   ierr = VecSetBlockSize(coordinatesB, cDimB);CHKERRQ(ierr);
1270   ierr = VecSetType(coordinatesB,VECSTANDARD);CHKERRQ(ierr);
1271 
1272   ierr = DMGetCoordinateSection(idm, &coordSectionA);CHKERRQ(ierr);
1273   ierr = DMGetCoordinatesLocal(idm, &coordinatesA);CHKERRQ(ierr);
1274   ierr = VecGetArray(coordinatesB, &coordsB);CHKERRQ(ierr);
1275   ierr = VecGetArrayRead(coordinatesA, &coordsA);CHKERRQ(ierr);
1276   for (v = vStart; v < vEnd; ++v) {
1277     const PetscScalar *cptr;
1278     PetscReal         ones2[2] = { 0., 1.}, ones3[3] = { 0., 0., 1.};
1279     PetscReal         *normal, norm, h = height/layers;
1280     PetscInt          offA, d, cDimA = cDim;
1281 
1282     normal = normals ? normals + cDimB*(v - vStart) : (cDim > 1 ? ones3 : ones2);
1283     if (normals) {
1284       for (d = 0, norm = 0.0; d < cDimB; ++d) norm += normal[d]*normal[d];
1285       for (d = 0; d < cDimB; ++d) normal[d] *= 1./PetscSqrtReal(norm);
1286     }
1287 
1288     ierr = PetscSectionGetOffset(coordSectionA, v, &offA);CHKERRQ(ierr);
1289     cptr = coordsA + offA;
1290     for (l = 0; l < layers+1; ++l) {
1291       PetscInt offB, d, newV;
1292 
1293       newV = ordExt ? (layers+1)*(v -vStart) + l + numCells : (vEnd -vStart)*l + (v -vStart) + numCells;
1294       ierr = PetscSectionGetOffset(coordSectionB, newV, &offB);CHKERRQ(ierr);
1295       for (d = 0; d < cDimA; ++d) { coordsB[offB+d]  = cptr[d]; }
1296       for (d = 0; d < cDimB; ++d) { coordsB[offB+d] += l ? normal[d]*h : 0.0; }
1297       cptr    = coordsB + offB;
1298       cDimA   = cDimB;
1299     }
1300   }
1301   ierr = VecRestoreArrayRead(coordinatesA, &coordsA);CHKERRQ(ierr);
1302   ierr = VecRestoreArray(coordinatesB, &coordsB);CHKERRQ(ierr);
1303   ierr = DMSetCoordinatesLocal(*dm, coordinatesB);CHKERRQ(ierr);
1304   ierr = VecDestroy(&coordinatesB);CHKERRQ(ierr);
1305   ierr = PetscFree(normals);CHKERRQ(ierr);
1306   if (interpolate) {
1307     DM idm;
1308 
1309     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
1310     ierr = DMPlexCopyCoordinates(*dm, idm);CHKERRQ(ierr);
1311     ierr = DMDestroy(dm);CHKERRQ(ierr);
1312     *dm  = idm;
1313   }
1314   PetscFunctionReturn(0);
1315 }
1316 
1317 /*@C
1318   DMPlexSetOptionsPrefix - Sets the prefix used for searching for all DM options in the database.
1319 
1320   Logically Collective on dm
1321 
1322   Input Parameters:
1323 + dm - the DM context
1324 - prefix - the prefix to prepend to all option names
1325 
1326   Notes:
1327   A hyphen (-) must NOT be given at the beginning of the prefix name.
1328   The first character of all runtime options is AUTOMATICALLY the hyphen.
1329 
1330   Level: advanced
1331 
1332 .seealso: SNESSetFromOptions()
1333 @*/
1334 PetscErrorCode DMPlexSetOptionsPrefix(DM dm, const char prefix[])
1335 {
1336   DM_Plex       *mesh = (DM_Plex *) dm->data;
1337   PetscErrorCode ierr;
1338 
1339   PetscFunctionBegin;
1340   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1341   ierr = PetscObjectSetOptionsPrefix((PetscObject) dm, prefix);CHKERRQ(ierr);
1342   ierr = PetscObjectSetOptionsPrefix((PetscObject) mesh->partitioner, prefix);CHKERRQ(ierr);
1343   PetscFunctionReturn(0);
1344 }
1345 
1346 /*@
1347   DMPlexCreateHexCylinderMesh - Creates a mesh on the tensor product of the unit interval with the circle (cylinder) using hexahedra.
1348 
1349   Collective
1350 
1351   Input Parameters:
1352 + comm      - The communicator for the DM object
1353 . numRefine - The number of regular refinements to the basic 5 cell structure
1354 - periodicZ - The boundary type for the Z direction
1355 
1356   Output Parameter:
1357 . dm  - The DM object
1358 
1359   Note: Here is the output numbering looking from the bottom of the cylinder:
1360 $       17-----14
1361 $        |     |
1362 $        |  2  |
1363 $        |     |
1364 $ 17-----8-----7-----14
1365 $  |     |     |     |
1366 $  |  3  |  0  |  1  |
1367 $  |     |     |     |
1368 $ 19-----5-----6-----13
1369 $        |     |
1370 $        |  4  |
1371 $        |     |
1372 $       19-----13
1373 $
1374 $ and up through the top
1375 $
1376 $       18-----16
1377 $        |     |
1378 $        |  2  |
1379 $        |     |
1380 $ 18----10----11-----16
1381 $  |     |     |     |
1382 $  |  3  |  0  |  1  |
1383 $  |     |     |     |
1384 $ 20-----9----12-----15
1385 $        |     |
1386 $        |  4  |
1387 $        |     |
1388 $       20-----15
1389 
1390   Level: beginner
1391 
1392 .seealso: DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
1393 @*/
1394 PetscErrorCode DMPlexCreateHexCylinderMesh(MPI_Comm comm, PetscInt numRefine, DMBoundaryType periodicZ, DM *dm)
1395 {
1396   const PetscInt dim = 3;
1397   PetscInt       numCells, numVertices, r;
1398   PetscMPIInt    rank;
1399   PetscErrorCode ierr;
1400 
1401   PetscFunctionBegin;
1402   PetscValidPointer(dm, 4);
1403   ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
1404   if (numRefine < 0) SETERRQ1(comm, PETSC_ERR_ARG_OUTOFRANGE, "Number of refinements %D cannot be negative", numRefine);
1405   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
1406   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
1407   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
1408   /* Create topology */
1409   {
1410     PetscInt cone[8], c;
1411 
1412     numCells    = !rank ?  5 : 0;
1413     numVertices = !rank ? 16 : 0;
1414     if (periodicZ == DM_BOUNDARY_PERIODIC) {
1415       numCells   *= 3;
1416       numVertices = !rank ? 24 : 0;
1417     }
1418     ierr = DMPlexSetChart(*dm, 0, numCells+numVertices);CHKERRQ(ierr);
1419     for (c = 0; c < numCells; c++) {ierr = DMPlexSetConeSize(*dm, c, 8);CHKERRQ(ierr);}
1420     ierr = DMSetUp(*dm);CHKERRQ(ierr);
1421     if (!rank) {
1422       if (periodicZ == DM_BOUNDARY_PERIODIC) {
1423         cone[0] = 15; cone[1] = 18; cone[2] = 17; cone[3] = 16;
1424         cone[4] = 31; cone[5] = 32; cone[6] = 33; cone[7] = 34;
1425         ierr = DMPlexSetCone(*dm, 0, cone);CHKERRQ(ierr);
1426         cone[0] = 16; cone[1] = 17; cone[2] = 24; cone[3] = 23;
1427         cone[4] = 32; cone[5] = 36; cone[6] = 37; cone[7] = 33; /* 22 25 26 21 */
1428         ierr = DMPlexSetCone(*dm, 1, cone);CHKERRQ(ierr);
1429         cone[0] = 18; cone[1] = 27; cone[2] = 24; cone[3] = 17;
1430         cone[4] = 34; cone[5] = 33; cone[6] = 37; cone[7] = 38;
1431         ierr = DMPlexSetCone(*dm, 2, cone);CHKERRQ(ierr);
1432         cone[0] = 29; cone[1] = 27; cone[2] = 18; cone[3] = 15;
1433         cone[4] = 35; cone[5] = 31; cone[6] = 34; cone[7] = 38;
1434         ierr = DMPlexSetCone(*dm, 3, cone);CHKERRQ(ierr);
1435         cone[0] = 29; cone[1] = 15; cone[2] = 16; cone[3] = 23;
1436         cone[4] = 35; cone[5] = 36; cone[6] = 32; cone[7] = 31;
1437         ierr = DMPlexSetCone(*dm, 4, cone);CHKERRQ(ierr);
1438 
1439         cone[0] = 31; cone[1] = 34; cone[2] = 33; cone[3] = 32;
1440         cone[4] = 19; cone[5] = 22; cone[6] = 21; cone[7] = 20;
1441         ierr = DMPlexSetCone(*dm, 5, cone);CHKERRQ(ierr);
1442         cone[0] = 32; cone[1] = 33; cone[2] = 37; cone[3] = 36;
1443         cone[4] = 22; cone[5] = 25; cone[6] = 26; cone[7] = 21;
1444         ierr = DMPlexSetCone(*dm, 6, cone);CHKERRQ(ierr);
1445         cone[0] = 34; cone[1] = 38; cone[2] = 37; cone[3] = 33;
1446         cone[4] = 20; cone[5] = 21; cone[6] = 26; cone[7] = 28;
1447         ierr = DMPlexSetCone(*dm, 7, cone);CHKERRQ(ierr);
1448         cone[0] = 35; cone[1] = 38; cone[2] = 34; cone[3] = 31;
1449         cone[4] = 30; cone[5] = 19; cone[6] = 20; cone[7] = 28;
1450         ierr = DMPlexSetCone(*dm, 8, cone);CHKERRQ(ierr);
1451         cone[0] = 35; cone[1] = 31; cone[2] = 32; cone[3] = 36;
1452         cone[4] = 30; cone[5] = 25; cone[6] = 22; cone[7] = 19;
1453         ierr = DMPlexSetCone(*dm, 9, cone);CHKERRQ(ierr);
1454 
1455         cone[0] = 19; cone[1] = 20; cone[2] = 21; cone[3] = 22;
1456         cone[4] = 15; cone[5] = 16; cone[6] = 17; cone[7] = 18;
1457         ierr = DMPlexSetCone(*dm, 10, cone);CHKERRQ(ierr);
1458         cone[0] = 22; cone[1] = 21; cone[2] = 26; cone[3] = 25;
1459         cone[4] = 16; cone[5] = 23; cone[6] = 24; cone[7] = 17;
1460         ierr = DMPlexSetCone(*dm, 11, cone);CHKERRQ(ierr);
1461         cone[0] = 20; cone[1] = 28; cone[2] = 26; cone[3] = 21;
1462         cone[4] = 18; cone[5] = 17; cone[6] = 24; cone[7] = 27;
1463         ierr = DMPlexSetCone(*dm, 12, cone);CHKERRQ(ierr);
1464         cone[0] = 30; cone[1] = 28; cone[2] = 20; cone[3] = 19;
1465         cone[4] = 29; cone[5] = 15; cone[6] = 18; cone[7] = 27;
1466         ierr = DMPlexSetCone(*dm, 13, cone);CHKERRQ(ierr);
1467         cone[0] = 30; cone[1] = 19; cone[2] = 22; cone[3] = 25;
1468         cone[4] = 29; cone[5] = 23; cone[6] = 16; cone[7] = 15;
1469         ierr = DMPlexSetCone(*dm, 14, cone);CHKERRQ(ierr);
1470       } else {
1471         cone[0] =  5; cone[1] =  8; cone[2] =  7; cone[3] =  6;
1472         cone[4] =  9; cone[5] = 12; cone[6] = 11; cone[7] = 10;
1473         ierr = DMPlexSetCone(*dm, 0, cone);CHKERRQ(ierr);
1474         cone[0] =  6; cone[1] =  7; cone[2] = 14; cone[3] = 13;
1475         cone[4] = 12; cone[5] = 15; cone[6] = 16; cone[7] = 11;
1476         ierr = DMPlexSetCone(*dm, 1, cone);CHKERRQ(ierr);
1477         cone[0] =  8; cone[1] = 17; cone[2] = 14; cone[3] =  7;
1478         cone[4] = 10; cone[5] = 11; cone[6] = 16; cone[7] = 18;
1479         ierr = DMPlexSetCone(*dm, 2, cone);CHKERRQ(ierr);
1480         cone[0] = 19; cone[1] = 17; cone[2] =  8; cone[3] =  5;
1481         cone[4] = 20; cone[5] =  9; cone[6] = 10; cone[7] = 18;
1482         ierr = DMPlexSetCone(*dm, 3, cone);CHKERRQ(ierr);
1483         cone[0] = 19; cone[1] =  5; cone[2] =  6; cone[3] = 13;
1484         cone[4] = 20; cone[5] = 15; cone[6] = 12; cone[7] =  9;
1485         ierr = DMPlexSetCone(*dm, 4, cone);CHKERRQ(ierr);
1486       }
1487     }
1488     ierr = DMPlexSymmetrize(*dm);CHKERRQ(ierr);
1489     ierr = DMPlexStratify(*dm);CHKERRQ(ierr);
1490   }
1491   /* Interpolate */
1492   {
1493     DM idm;
1494 
1495     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
1496     ierr = DMDestroy(dm);CHKERRQ(ierr);
1497     *dm  = idm;
1498   }
1499   /* Create cube geometry */
1500   {
1501     Vec             coordinates;
1502     PetscSection    coordSection;
1503     PetscScalar    *coords;
1504     PetscInt        coordSize, v;
1505     const PetscReal dis = 1.0/PetscSqrtReal(2.0);
1506     const PetscReal ds2 = dis/2.0;
1507 
1508     /* Build coordinates */
1509     ierr = DMGetCoordinateSection(*dm, &coordSection);CHKERRQ(ierr);
1510     ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
1511     ierr = PetscSectionSetFieldComponents(coordSection, 0, dim);CHKERRQ(ierr);
1512     ierr = PetscSectionSetChart(coordSection, numCells, numCells+numVertices);CHKERRQ(ierr);
1513     for (v = numCells; v < numCells+numVertices; ++v) {
1514       ierr = PetscSectionSetDof(coordSection, v, dim);CHKERRQ(ierr);
1515       ierr = PetscSectionSetFieldDof(coordSection, v, 0, dim);CHKERRQ(ierr);
1516     }
1517     ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
1518     ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
1519     ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
1520     ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
1521     ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
1522     ierr = VecSetBlockSize(coordinates, dim);CHKERRQ(ierr);
1523     ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
1524     ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
1525     if (!rank) {
1526       coords[0*dim+0] = -ds2; coords[0*dim+1] = -ds2; coords[0*dim+2] = 0.0;
1527       coords[1*dim+0] =  ds2; coords[1*dim+1] = -ds2; coords[1*dim+2] = 0.0;
1528       coords[2*dim+0] =  ds2; coords[2*dim+1] =  ds2; coords[2*dim+2] = 0.0;
1529       coords[3*dim+0] = -ds2; coords[3*dim+1] =  ds2; coords[3*dim+2] = 0.0;
1530       coords[4*dim+0] = -ds2; coords[4*dim+1] = -ds2; coords[4*dim+2] = 1.0;
1531       coords[5*dim+0] = -ds2; coords[5*dim+1] =  ds2; coords[5*dim+2] = 1.0;
1532       coords[6*dim+0] =  ds2; coords[6*dim+1] =  ds2; coords[6*dim+2] = 1.0;
1533       coords[7*dim+0] =  ds2; coords[7*dim+1] = -ds2; coords[7*dim+2] = 1.0;
1534       coords[ 8*dim+0] =  dis; coords[ 8*dim+1] = -dis; coords[ 8*dim+2] = 0.0;
1535       coords[ 9*dim+0] =  dis; coords[ 9*dim+1] =  dis; coords[ 9*dim+2] = 0.0;
1536       coords[10*dim+0] =  dis; coords[10*dim+1] = -dis; coords[10*dim+2] = 1.0;
1537       coords[11*dim+0] =  dis; coords[11*dim+1] =  dis; coords[11*dim+2] = 1.0;
1538       coords[12*dim+0] = -dis; coords[12*dim+1] =  dis; coords[12*dim+2] = 0.0;
1539       coords[13*dim+0] = -dis; coords[13*dim+1] =  dis; coords[13*dim+2] = 1.0;
1540       coords[14*dim+0] = -dis; coords[14*dim+1] = -dis; coords[14*dim+2] = 0.0;
1541       coords[15*dim+0] = -dis; coords[15*dim+1] = -dis; coords[15*dim+2] = 1.0;
1542       if (periodicZ == DM_BOUNDARY_PERIODIC) {
1543         /* 15 31 19 */ coords[16*dim+0] = -ds2; coords[16*dim+1] = -ds2; coords[16*dim+2] = 0.5;
1544         /* 16 32 22 */ coords[17*dim+0] =  ds2; coords[17*dim+1] = -ds2; coords[17*dim+2] = 0.5;
1545         /* 17 33 21 */ coords[18*dim+0] =  ds2; coords[18*dim+1] =  ds2; coords[18*dim+2] = 0.5;
1546         /* 18 34 20 */ coords[19*dim+0] = -ds2; coords[19*dim+1] =  ds2; coords[19*dim+2] = 0.5;
1547         /* 29 35 30 */ coords[20*dim+0] = -dis; coords[20*dim+1] = -dis; coords[20*dim+2] = 0.5;
1548         /* 23 36 25 */ coords[21*dim+0] =  dis; coords[21*dim+1] = -dis; coords[21*dim+2] = 0.5;
1549         /* 24 37 26 */ coords[22*dim+0] =  dis; coords[22*dim+1] =  dis; coords[22*dim+2] = 0.5;
1550         /* 27 38 28 */ coords[23*dim+0] = -dis; coords[23*dim+1] =  dis; coords[23*dim+2] = 0.5;
1551       }
1552     }
1553     ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
1554     ierr = DMSetCoordinatesLocal(*dm, coordinates);CHKERRQ(ierr);
1555     ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
1556   }
1557   /* Create periodicity */
1558   if (periodicZ == DM_BOUNDARY_PERIODIC || periodicZ == DM_BOUNDARY_TWIST) {
1559     PetscReal      L[3];
1560     PetscReal      maxCell[3];
1561     DMBoundaryType bdType[3];
1562     PetscReal      lower[3] = {0.0, 0.0, 0.0};
1563     PetscReal      upper[3] = {1.0, 1.0, 1.5};
1564     PetscInt       i, numZCells = 3;
1565 
1566     bdType[0] = DM_BOUNDARY_NONE;
1567     bdType[1] = DM_BOUNDARY_NONE;
1568     bdType[2] = periodicZ;
1569     for (i = 0; i < dim; i++) {
1570       L[i]       = upper[i] - lower[i];
1571       maxCell[i] = 1.1 * (L[i] / numZCells);
1572     }
1573     ierr = DMSetPeriodicity(*dm, PETSC_TRUE, maxCell, L, bdType);CHKERRQ(ierr);
1574   }
1575   /* Refine topology */
1576   for (r = 0; r < numRefine; ++r) {
1577     DM rdm = NULL;
1578 
1579     ierr = DMRefine(*dm, comm, &rdm);CHKERRQ(ierr);
1580     ierr = DMDestroy(dm);CHKERRQ(ierr);
1581     *dm  = rdm;
1582   }
1583   /* Remap geometry to cylinder
1584        Interior square: Linear interpolation is correct
1585        The other cells all have vertices on rays from the origin. We want to uniformly expand the spacing
1586        such that the last vertex is on the unit circle. So the closest and farthest vertices are at distance
1587 
1588          phi     = arctan(y/x)
1589          d_close = sqrt(1/8 + 1/4 sin^2(phi))
1590          d_far   = sqrt(1/2 + sin^2(phi))
1591 
1592        so we remap them using
1593 
1594          x_new = x_close + (x - x_close) (1 - d_close) / (d_far - d_close)
1595          y_new = y_close + (y - y_close) (1 - d_close) / (d_far - d_close)
1596 
1597        If pi/4 < phi < 3pi/4 or -3pi/4 < phi < -pi/4, then we switch x and y.
1598   */
1599   {
1600     Vec           coordinates;
1601     PetscSection  coordSection;
1602     PetscScalar  *coords;
1603     PetscInt      vStart, vEnd, v;
1604     const PetscReal dis = 1.0/PetscSqrtReal(2.0);
1605     const PetscReal ds2 = 0.5*dis;
1606 
1607     ierr = DMPlexGetDepthStratum(*dm, 0, &vStart, &vEnd);CHKERRQ(ierr);
1608     ierr = DMGetCoordinateSection(*dm, &coordSection);CHKERRQ(ierr);
1609     ierr = DMGetCoordinatesLocal(*dm, &coordinates);CHKERRQ(ierr);
1610     ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
1611     for (v = vStart; v < vEnd; ++v) {
1612       PetscReal phi, sinp, cosp, dc, df, x, y, xc, yc;
1613       PetscInt  off;
1614 
1615       ierr = PetscSectionGetOffset(coordSection, v, &off);CHKERRQ(ierr);
1616       if ((PetscAbsScalar(coords[off+0]) <= ds2) && (PetscAbsScalar(coords[off+1]) <= ds2)) continue;
1617       x    = PetscRealPart(coords[off]);
1618       y    = PetscRealPart(coords[off+1]);
1619       phi  = PetscAtan2Real(y, x);
1620       sinp = PetscSinReal(phi);
1621       cosp = PetscCosReal(phi);
1622       if ((PetscAbsReal(phi) > PETSC_PI/4.0) && (PetscAbsReal(phi) < 3.0*PETSC_PI/4.0)) {
1623         dc = PetscAbsReal(ds2/sinp);
1624         df = PetscAbsReal(dis/sinp);
1625         xc = ds2*x/PetscAbsReal(y);
1626         yc = ds2*PetscSignReal(y);
1627       } else {
1628         dc = PetscAbsReal(ds2/cosp);
1629         df = PetscAbsReal(dis/cosp);
1630         xc = ds2*PetscSignReal(x);
1631         yc = ds2*y/PetscAbsReal(x);
1632       }
1633       coords[off+0] = xc + (coords[off+0] - xc)*(1.0 - dc)/(df - dc);
1634       coords[off+1] = yc + (coords[off+1] - yc)*(1.0 - dc)/(df - dc);
1635     }
1636     ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
1637     if (periodicZ == DM_BOUNDARY_PERIODIC || periodicZ == DM_BOUNDARY_TWIST) {
1638       ierr = DMLocalizeCoordinates(*dm);CHKERRQ(ierr);
1639     }
1640   }
1641   PetscFunctionReturn(0);
1642 }
1643 
1644 /*@
1645   DMPlexCreateWedgeCylinderMesh - Creates a mesh on the tensor product of the unit interval with the circle (cylinder) using wedges.
1646 
1647   Collective
1648 
1649   Input Parameters:
1650 + comm - The communicator for the DM object
1651 . n    - The number of wedges around the origin
1652 - interpolate - Create edges and faces
1653 
1654   Output Parameter:
1655 . dm  - The DM object
1656 
1657   Level: beginner
1658 
1659 .seealso: DMPlexCreateHexCylinderMesh(), DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
1660 @*/
1661 PetscErrorCode DMPlexCreateWedgeCylinderMesh(MPI_Comm comm, PetscInt n, PetscBool interpolate, DM *dm)
1662 {
1663   const PetscInt dim = 3;
1664   PetscInt       numCells, numVertices, v;
1665   PetscMPIInt    rank;
1666   PetscErrorCode ierr;
1667 
1668   PetscFunctionBegin;
1669   PetscValidPointer(dm, 3);
1670   ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
1671   if (n < 0) SETERRQ1(comm, PETSC_ERR_ARG_OUTOFRANGE, "Number of wedges %D cannot be negative", n);
1672   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
1673   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
1674   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
1675   /* Must create the celltype label here so that we do not automatically try to compute the types */
1676   ierr = DMCreateLabel(*dm, "celltype");CHKERRQ(ierr);
1677   /* Create topology */
1678   {
1679     PetscInt cone[6], c;
1680 
1681     numCells    = !rank ?        n : 0;
1682     numVertices = !rank ?  2*(n+1) : 0;
1683     ierr = DMPlexSetChart(*dm, 0, numCells+numVertices);CHKERRQ(ierr);
1684     for (c = 0; c < numCells; c++) {ierr = DMPlexSetConeSize(*dm, c, 6);CHKERRQ(ierr);}
1685     ierr = DMSetUp(*dm);CHKERRQ(ierr);
1686     for (c = 0; c < numCells; c++) {
1687       cone[0] =  c+n*1; cone[1] = (c+1)%n+n*1; cone[2] = 0+3*n;
1688       cone[3] =  c+n*2; cone[4] = (c+1)%n+n*2; cone[5] = 1+3*n;
1689       ierr = DMPlexSetCone(*dm, c, cone);CHKERRQ(ierr);
1690       ierr = DMPlexSetCellType(*dm, c, DM_POLYTOPE_TRI_PRISM_TENSOR);CHKERRQ(ierr);
1691     }
1692     ierr = DMPlexSymmetrize(*dm);CHKERRQ(ierr);
1693     ierr = DMPlexStratify(*dm);CHKERRQ(ierr);
1694   }
1695   for (v = numCells; v < numCells+numVertices; ++v) {
1696     ierr = DMPlexSetCellType(*dm, v, DM_POLYTOPE_POINT);CHKERRQ(ierr);
1697   }
1698   /* Interpolate */
1699   if (interpolate) {
1700     DM idm;
1701 
1702     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
1703     ierr = DMDestroy(dm);CHKERRQ(ierr);
1704     *dm  = idm;
1705   }
1706   /* Create cylinder geometry */
1707   {
1708     Vec          coordinates;
1709     PetscSection coordSection;
1710     PetscScalar *coords;
1711     PetscInt     coordSize, c;
1712 
1713     /* Build coordinates */
1714     ierr = DMGetCoordinateSection(*dm, &coordSection);CHKERRQ(ierr);
1715     ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
1716     ierr = PetscSectionSetFieldComponents(coordSection, 0, dim);CHKERRQ(ierr);
1717     ierr = PetscSectionSetChart(coordSection, numCells, numCells+numVertices);CHKERRQ(ierr);
1718     for (v = numCells; v < numCells+numVertices; ++v) {
1719       ierr = PetscSectionSetDof(coordSection, v, dim);CHKERRQ(ierr);
1720       ierr = PetscSectionSetFieldDof(coordSection, v, 0, dim);CHKERRQ(ierr);
1721     }
1722     ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
1723     ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
1724     ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
1725     ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
1726     ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
1727     ierr = VecSetBlockSize(coordinates, dim);CHKERRQ(ierr);
1728     ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
1729     ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
1730     for (c = 0; c < numCells; c++) {
1731       coords[(c+0*n)*dim+0] = PetscCosReal(2.0*c*PETSC_PI/n); coords[(c+0*n)*dim+1] = PetscSinReal(2.0*c*PETSC_PI/n); coords[(c+0*n)*dim+2] = 1.0;
1732       coords[(c+1*n)*dim+0] = PetscCosReal(2.0*c*PETSC_PI/n); coords[(c+1*n)*dim+1] = PetscSinReal(2.0*c*PETSC_PI/n); coords[(c+1*n)*dim+2] = 0.0;
1733     }
1734     if (!rank) {
1735       coords[(2*n+0)*dim+0] = 0.0; coords[(2*n+0)*dim+1] = 0.0; coords[(2*n+0)*dim+2] = 1.0;
1736       coords[(2*n+1)*dim+0] = 0.0; coords[(2*n+1)*dim+1] = 0.0; coords[(2*n+1)*dim+2] = 0.0;
1737     }
1738     ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
1739     ierr = DMSetCoordinatesLocal(*dm, coordinates);CHKERRQ(ierr);
1740     ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
1741   }
1742   PetscFunctionReturn(0);
1743 }
1744 
1745 PETSC_STATIC_INLINE PetscReal DiffNormReal(PetscInt dim, const PetscReal x[], const PetscReal y[])
1746 {
1747   PetscReal prod = 0.0;
1748   PetscInt  i;
1749   for (i = 0; i < dim; ++i) prod += PetscSqr(x[i] - y[i]);
1750   return PetscSqrtReal(prod);
1751 }
1752 PETSC_STATIC_INLINE PetscReal DotReal(PetscInt dim, const PetscReal x[], const PetscReal y[])
1753 {
1754   PetscReal prod = 0.0;
1755   PetscInt  i;
1756   for (i = 0; i < dim; ++i) prod += x[i]*y[i];
1757   return prod;
1758 }
1759 
1760 /*@
1761   DMPlexCreateSphereMesh - Creates a mesh on the d-dimensional sphere, S^d.
1762 
1763   Collective
1764 
1765   Input Parameters:
1766 + comm  - The communicator for the DM object
1767 . dim   - The dimension
1768 - simplex - Use simplices, or tensor product cells
1769 
1770   Output Parameter:
1771 . dm  - The DM object
1772 
1773   Level: beginner
1774 
1775 .seealso: DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
1776 @*/
1777 PetscErrorCode DMPlexCreateSphereMesh(MPI_Comm comm, PetscInt dim, PetscBool simplex, DM *dm)
1778 {
1779   const PetscInt  embedDim = dim+1;
1780   PetscSection    coordSection;
1781   Vec             coordinates;
1782   PetscScalar    *coords;
1783   PetscReal      *coordsIn;
1784   PetscInt        numCells, numEdges, numVerts, firstVertex, v, firstEdge, coordSize, d, c, e;
1785   PetscMPIInt     rank;
1786   PetscErrorCode  ierr;
1787 
1788   PetscFunctionBegin;
1789   PetscValidPointer(dm, 4);
1790   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
1791   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
1792   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
1793   ierr = DMSetCoordinateDim(*dm, dim+1);CHKERRQ(ierr);
1794   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject) *dm), &rank);CHKERRQ(ierr);
1795   switch (dim) {
1796   case 2:
1797     if (simplex) {
1798       DM              idm;
1799       const PetscReal edgeLen     = 2.0/(1.0 + PETSC_PHI);
1800       const PetscReal vertex[3]   = {0.0, 1.0/(1.0 + PETSC_PHI), PETSC_PHI/(1.0 + PETSC_PHI)};
1801       const PetscInt  degree      = 5;
1802       PetscInt        s[3]        = {1, 1, 1};
1803       PetscInt        cone[3];
1804       PetscInt       *graph, p, i, j, k;
1805 
1806       numCells    = !rank ? 20 : 0;
1807       numVerts    = !rank ? 12 : 0;
1808       firstVertex = numCells;
1809       /* Use icosahedron, which for a unit sphere has coordinates which are all cyclic permutations of
1810 
1811            (0, \pm 1/\phi+1, \pm \phi/\phi+1)
1812 
1813          where \phi^2 - \phi - 1 = 0, meaning \phi is the golden ratio \frac{1 + \sqrt{5}}{2}. The edge
1814          length is then given by 2/\phi = 2 * 0.61803 = 1.23606.
1815       */
1816       /* Construct vertices */
1817       ierr = PetscCalloc1(numVerts * embedDim, &coordsIn);CHKERRQ(ierr);
1818       if (!rank) {
1819         for (p = 0, i = 0; p < embedDim; ++p) {
1820           for (s[1] = -1; s[1] < 2; s[1] += 2) {
1821             for (s[2] = -1; s[2] < 2; s[2] += 2) {
1822               for (d = 0; d < embedDim; ++d) coordsIn[i*embedDim+d] = s[(d+p)%embedDim]*vertex[(d+p)%embedDim];
1823               ++i;
1824             }
1825           }
1826         }
1827       }
1828       /* Construct graph */
1829       ierr = PetscCalloc1(numVerts * numVerts, &graph);CHKERRQ(ierr);
1830       for (i = 0; i < numVerts; ++i) {
1831         for (j = 0, k = 0; j < numVerts; ++j) {
1832           if (PetscAbsReal(DiffNormReal(embedDim, &coordsIn[i*embedDim], &coordsIn[j*embedDim]) - edgeLen) < PETSC_SMALL) {graph[i*numVerts+j] = 1; ++k;}
1833         }
1834         if (k != degree) SETERRQ3(comm, PETSC_ERR_PLIB, "Invalid icosahedron, vertex %D degree %D != %D", i, k, degree);
1835       }
1836       /* Build Topology */
1837       ierr = DMPlexSetChart(*dm, 0, numCells+numVerts);CHKERRQ(ierr);
1838       for (c = 0; c < numCells; c++) {
1839         ierr = DMPlexSetConeSize(*dm, c, embedDim);CHKERRQ(ierr);
1840       }
1841       ierr = DMSetUp(*dm);CHKERRQ(ierr); /* Allocate space for cones */
1842       /* Cells */
1843       for (i = 0, c = 0; i < numVerts; ++i) {
1844         for (j = 0; j < i; ++j) {
1845           for (k = 0; k < j; ++k) {
1846             if (graph[i*numVerts+j] && graph[j*numVerts+k] && graph[k*numVerts+i]) {
1847               cone[0] = firstVertex+i; cone[1] = firstVertex+j; cone[2] = firstVertex+k;
1848               /* Check orientation */
1849               {
1850                 const PetscInt epsilon[3][3][3] = {{{0, 0, 0}, {0, 0, 1}, {0, -1, 0}}, {{0, 0, -1}, {0, 0, 0}, {1, 0, 0}}, {{0, 1, 0}, {-1, 0, 0}, {0, 0, 0}}};
1851                 PetscReal normal[3];
1852                 PetscInt  e, f;
1853 
1854                 for (d = 0; d < embedDim; ++d) {
1855                   normal[d] = 0.0;
1856                   for (e = 0; e < embedDim; ++e) {
1857                     for (f = 0; f < embedDim; ++f) {
1858                       normal[d] += epsilon[d][e][f]*(coordsIn[j*embedDim+e] - coordsIn[i*embedDim+e])*(coordsIn[k*embedDim+f] - coordsIn[i*embedDim+f]);
1859                     }
1860                   }
1861                 }
1862                 if (DotReal(embedDim, normal, &coordsIn[i*embedDim]) < 0) {PetscInt tmp = cone[1]; cone[1] = cone[2]; cone[2] = tmp;}
1863               }
1864               ierr = DMPlexSetCone(*dm, c++, cone);CHKERRQ(ierr);
1865             }
1866           }
1867         }
1868       }
1869       ierr = DMPlexSymmetrize(*dm);CHKERRQ(ierr);
1870       ierr = DMPlexStratify(*dm);CHKERRQ(ierr);
1871       ierr = PetscFree(graph);CHKERRQ(ierr);
1872       /* Interpolate mesh */
1873       ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
1874       ierr = DMDestroy(dm);CHKERRQ(ierr);
1875       *dm  = idm;
1876     } else {
1877       /*
1878         12-21--13
1879          |     |
1880         25  4  24
1881          |     |
1882   12-25--9-16--8-24--13
1883    |     |     |     |
1884   23  5 17  0 15  3  22
1885    |     |     |     |
1886   10-20--6-14--7-19--11
1887          |     |
1888         20  1  19
1889          |     |
1890         10-18--11
1891          |     |
1892         23  2  22
1893          |     |
1894         12-21--13
1895        */
1896       const PetscReal dist = 1.0/PetscSqrtReal(3.0);
1897       PetscInt        cone[4], ornt[4];
1898 
1899       numCells    = !rank ?  6 : 0;
1900       numEdges    = !rank ? 12 : 0;
1901       numVerts    = !rank ?  8 : 0;
1902       firstVertex = numCells;
1903       firstEdge   = numCells + numVerts;
1904       /* Build Topology */
1905       ierr = DMPlexSetChart(*dm, 0, numCells+numEdges+numVerts);CHKERRQ(ierr);
1906       for (c = 0; c < numCells; c++) {
1907         ierr = DMPlexSetConeSize(*dm, c, 4);CHKERRQ(ierr);
1908       }
1909       for (e = firstEdge; e < firstEdge+numEdges; ++e) {
1910         ierr = DMPlexSetConeSize(*dm, e, 2);CHKERRQ(ierr);
1911       }
1912       ierr = DMSetUp(*dm);CHKERRQ(ierr); /* Allocate space for cones */
1913       if (!rank) {
1914         /* Cell 0 */
1915         cone[0] = 14; cone[1] = 15; cone[2] = 16; cone[3] = 17;
1916         ierr = DMPlexSetCone(*dm, 0, cone);CHKERRQ(ierr);
1917         ornt[0] = 0; ornt[1] = 0; ornt[2] = 0; ornt[3] = 0;
1918         ierr = DMPlexSetConeOrientation(*dm, 0, ornt);CHKERRQ(ierr);
1919         /* Cell 1 */
1920         cone[0] = 18; cone[1] = 19; cone[2] = 14; cone[3] = 20;
1921         ierr = DMPlexSetCone(*dm, 1, cone);CHKERRQ(ierr);
1922         ornt[0] = 0; ornt[1] = 0; ornt[2] = -2; ornt[3] = 0;
1923         ierr = DMPlexSetConeOrientation(*dm, 1, ornt);CHKERRQ(ierr);
1924         /* Cell 2 */
1925         cone[0] = 21; cone[1] = 22; cone[2] = 18; cone[3] = 23;
1926         ierr = DMPlexSetCone(*dm, 2, cone);CHKERRQ(ierr);
1927         ornt[0] = 0; ornt[1] = 0; ornt[2] = -2; ornt[3] = 0;
1928         ierr = DMPlexSetConeOrientation(*dm, 2, ornt);CHKERRQ(ierr);
1929         /* Cell 3 */
1930         cone[0] = 19; cone[1] = 22; cone[2] = 24; cone[3] = 15;
1931         ierr = DMPlexSetCone(*dm, 3, cone);CHKERRQ(ierr);
1932         ornt[0] = -2; ornt[1] = -2; ornt[2] = 0; ornt[3] = -2;
1933         ierr = DMPlexSetConeOrientation(*dm, 3, ornt);CHKERRQ(ierr);
1934         /* Cell 4 */
1935         cone[0] = 16; cone[1] = 24; cone[2] = 21; cone[3] = 25;
1936         ierr = DMPlexSetCone(*dm, 4, cone);CHKERRQ(ierr);
1937         ornt[0] = -2; ornt[1] = -2; ornt[2] = -2; ornt[3] = 0;
1938         ierr = DMPlexSetConeOrientation(*dm, 4, ornt);CHKERRQ(ierr);
1939         /* Cell 5 */
1940         cone[0] = 20; cone[1] = 17; cone[2] = 25; cone[3] = 23;
1941         ierr = DMPlexSetCone(*dm, 5, cone);CHKERRQ(ierr);
1942         ornt[0] = -2; ornt[1] = -2; ornt[2] = -2; ornt[3] = -2;
1943         ierr = DMPlexSetConeOrientation(*dm, 5, ornt);CHKERRQ(ierr);
1944         /* Edges */
1945         cone[0] =  6; cone[1] =  7;
1946         ierr = DMPlexSetCone(*dm, 14, cone);CHKERRQ(ierr);
1947         cone[0] =  7; cone[1] =  8;
1948         ierr = DMPlexSetCone(*dm, 15, cone);CHKERRQ(ierr);
1949         cone[0] =  8; cone[1] =  9;
1950         ierr = DMPlexSetCone(*dm, 16, cone);CHKERRQ(ierr);
1951         cone[0] =  9; cone[1] =  6;
1952         ierr = DMPlexSetCone(*dm, 17, cone);CHKERRQ(ierr);
1953         cone[0] = 10; cone[1] = 11;
1954         ierr = DMPlexSetCone(*dm, 18, cone);CHKERRQ(ierr);
1955         cone[0] = 11; cone[1] =  7;
1956         ierr = DMPlexSetCone(*dm, 19, cone);CHKERRQ(ierr);
1957         cone[0] =  6; cone[1] = 10;
1958         ierr = DMPlexSetCone(*dm, 20, cone);CHKERRQ(ierr);
1959         cone[0] = 12; cone[1] = 13;
1960         ierr = DMPlexSetCone(*dm, 21, cone);CHKERRQ(ierr);
1961         cone[0] = 13; cone[1] = 11;
1962         ierr = DMPlexSetCone(*dm, 22, cone);CHKERRQ(ierr);
1963         cone[0] = 10; cone[1] = 12;
1964         ierr = DMPlexSetCone(*dm, 23, cone);CHKERRQ(ierr);
1965         cone[0] = 13; cone[1] =  8;
1966         ierr = DMPlexSetCone(*dm, 24, cone);CHKERRQ(ierr);
1967         cone[0] = 12; cone[1] =  9;
1968         ierr = DMPlexSetCone(*dm, 25, cone);CHKERRQ(ierr);
1969       }
1970       ierr = DMPlexSymmetrize(*dm);CHKERRQ(ierr);
1971       ierr = DMPlexStratify(*dm);CHKERRQ(ierr);
1972       /* Build coordinates */
1973       ierr = PetscCalloc1(numVerts * embedDim, &coordsIn);CHKERRQ(ierr);
1974       if (!rank) {
1975         coordsIn[0*embedDim+0] = -dist; coordsIn[0*embedDim+1] =  dist; coordsIn[0*embedDim+2] = -dist;
1976         coordsIn[1*embedDim+0] =  dist; coordsIn[1*embedDim+1] =  dist; coordsIn[1*embedDim+2] = -dist;
1977         coordsIn[2*embedDim+0] =  dist; coordsIn[2*embedDim+1] = -dist; coordsIn[2*embedDim+2] = -dist;
1978         coordsIn[3*embedDim+0] = -dist; coordsIn[3*embedDim+1] = -dist; coordsIn[3*embedDim+2] = -dist;
1979         coordsIn[4*embedDim+0] = -dist; coordsIn[4*embedDim+1] =  dist; coordsIn[4*embedDim+2] =  dist;
1980         coordsIn[5*embedDim+0] =  dist; coordsIn[5*embedDim+1] =  dist; coordsIn[5*embedDim+2] =  dist;
1981         coordsIn[6*embedDim+0] = -dist; coordsIn[6*embedDim+1] = -dist; coordsIn[6*embedDim+2] =  dist;
1982         coordsIn[7*embedDim+0] =  dist; coordsIn[7*embedDim+1] = -dist; coordsIn[7*embedDim+2] =  dist;
1983       }
1984     }
1985     break;
1986   case 3:
1987     if (simplex) {
1988       DM              idm;
1989       const PetscReal edgeLen         = 1.0/PETSC_PHI;
1990       const PetscReal vertexA[4]      = {0.5, 0.5, 0.5, 0.5};
1991       const PetscReal vertexB[4]      = {1.0, 0.0, 0.0, 0.0};
1992       const PetscReal vertexC[4]      = {0.5, 0.5*PETSC_PHI, 0.5/PETSC_PHI, 0.0};
1993       const PetscInt  degree          = 12;
1994       PetscInt        s[4]            = {1, 1, 1};
1995       PetscInt        evenPerm[12][4] = {{0, 1, 2, 3}, {0, 2, 3, 1}, {0, 3, 1, 2}, {1, 0, 3, 2}, {1, 2, 0, 3}, {1, 3, 2, 0},
1996                                          {2, 0, 1, 3}, {2, 1, 3, 0}, {2, 3, 0, 1}, {3, 0, 2, 1}, {3, 1, 0, 2}, {3, 2, 1, 0}};
1997       PetscInt        cone[4];
1998       PetscInt       *graph, p, i, j, k, l;
1999 
2000       numCells    = !rank ? 600 : 0;
2001       numVerts    = !rank ? 120 : 0;
2002       firstVertex = numCells;
2003       /* Use the 600-cell, which for a unit sphere has coordinates which are
2004 
2005            1/2 (\pm 1, \pm 1,    \pm 1, \pm 1)                          16
2006                (\pm 1,    0,       0,      0)  all cyclic permutations   8
2007            1/2 (\pm 1, \pm phi, \pm 1/phi, 0)  all even permutations    96
2008 
2009          where \phi^2 - \phi - 1 = 0, meaning \phi is the golden ratio \frac{1 + \sqrt{5}}{2}. The edge
2010          length is then given by 1/\phi = 0.61803.
2011 
2012          http://buzzard.pugetsound.edu/sage-practice/ch03s03.html
2013          http://mathworld.wolfram.com/600-Cell.html
2014       */
2015       /* Construct vertices */
2016       ierr = PetscCalloc1(numVerts * embedDim, &coordsIn);CHKERRQ(ierr);
2017       i    = 0;
2018       if (!rank) {
2019         for (s[0] = -1; s[0] < 2; s[0] += 2) {
2020           for (s[1] = -1; s[1] < 2; s[1] += 2) {
2021             for (s[2] = -1; s[2] < 2; s[2] += 2) {
2022               for (s[3] = -1; s[3] < 2; s[3] += 2) {
2023                 for (d = 0; d < embedDim; ++d) coordsIn[i*embedDim+d] = s[d]*vertexA[d];
2024                 ++i;
2025               }
2026             }
2027           }
2028         }
2029         for (p = 0; p < embedDim; ++p) {
2030           s[1] = s[2] = s[3] = 1;
2031           for (s[0] = -1; s[0] < 2; s[0] += 2) {
2032             for (d = 0; d < embedDim; ++d) coordsIn[i*embedDim+d] = s[(d+p)%embedDim]*vertexB[(d+p)%embedDim];
2033             ++i;
2034           }
2035         }
2036         for (p = 0; p < 12; ++p) {
2037           s[3] = 1;
2038           for (s[0] = -1; s[0] < 2; s[0] += 2) {
2039             for (s[1] = -1; s[1] < 2; s[1] += 2) {
2040               for (s[2] = -1; s[2] < 2; s[2] += 2) {
2041                 for (d = 0; d < embedDim; ++d) coordsIn[i*embedDim+d] = s[evenPerm[p][d]]*vertexC[evenPerm[p][d]];
2042                 ++i;
2043               }
2044             }
2045           }
2046         }
2047       }
2048       if (i != numVerts) SETERRQ2(comm, PETSC_ERR_PLIB, "Invalid 600-cell, vertices %D != %D", i, numVerts);
2049       /* Construct graph */
2050       ierr = PetscCalloc1(numVerts * numVerts, &graph);CHKERRQ(ierr);
2051       for (i = 0; i < numVerts; ++i) {
2052         for (j = 0, k = 0; j < numVerts; ++j) {
2053           if (PetscAbsReal(DiffNormReal(embedDim, &coordsIn[i*embedDim], &coordsIn[j*embedDim]) - edgeLen) < PETSC_SMALL) {graph[i*numVerts+j] = 1; ++k;}
2054         }
2055         if (k != degree) SETERRQ3(comm, PETSC_ERR_PLIB, "Invalid 600-cell, vertex %D degree %D != %D", i, k, degree);
2056       }
2057       /* Build Topology */
2058       ierr = DMPlexSetChart(*dm, 0, numCells+numVerts);CHKERRQ(ierr);
2059       for (c = 0; c < numCells; c++) {
2060         ierr = DMPlexSetConeSize(*dm, c, embedDim);CHKERRQ(ierr);
2061       }
2062       ierr = DMSetUp(*dm);CHKERRQ(ierr); /* Allocate space for cones */
2063       /* Cells */
2064       if (!rank) {
2065         for (i = 0, c = 0; i < numVerts; ++i) {
2066           for (j = 0; j < i; ++j) {
2067             for (k = 0; k < j; ++k) {
2068               for (l = 0; l < k; ++l) {
2069                 if (graph[i*numVerts+j] && graph[j*numVerts+k] && graph[k*numVerts+i] &&
2070                     graph[l*numVerts+i] && graph[l*numVerts+j] && graph[l*numVerts+k]) {
2071                   cone[0] = firstVertex+i; cone[1] = firstVertex+j; cone[2] = firstVertex+k; cone[3] = firstVertex+l;
2072                   /* Check orientation: https://ef.gy/linear-algebra:normal-vectors-in-higher-dimensional-spaces */
2073                   {
2074                     const PetscInt epsilon[4][4][4][4] = {{{{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}},
2075                                                            {{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  1}, { 0,  0, -1, 0}},
2076                                                            {{0,  0,  0,  0}, { 0, 0,  0, -1}, { 0,  0, 0,  0}, { 0,  1,  0, 0}},
2077                                                            {{0,  0,  0,  0}, { 0, 0,  1,  0}, { 0, -1, 0,  0}, { 0,  0,  0, 0}}},
2078 
2079                                                           {{{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0, -1}, { 0,  0,  1, 0}},
2080                                                            {{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}},
2081                                                            {{0,  0,  0,  1}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, {-1,  0,  0, 0}},
2082                                                            {{0,  0, -1,  0}, { 0, 0,  0,  0}, { 1,  0, 0,  0}, { 0,  0,  0, 0}}},
2083 
2084                                                           {{{0,  0,  0,  0}, { 0, 0,  0,  1}, { 0,  0, 0,  0}, { 0, -1,  0, 0}},
2085                                                            {{0,  0,  0, -1}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 1,  0,  0, 0}},
2086                                                            {{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}},
2087                                                            {{0,  1,  0,  0}, {-1, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}}},
2088 
2089                                                           {{{0,  0,  0,  0}, { 0, 0, -1,  0}, { 0,  1, 0,  0}, { 0,  0,  0, 0}},
2090                                                            {{0,  0,  1,  0}, { 0, 0,  0,  0}, {-1,  0, 0,  0}, { 0,  0,  0, 0}},
2091                                                            {{0, -1,  0,  0}, { 1, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}},
2092                                                            {{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}}}};
2093                     PetscReal normal[4];
2094                     PetscInt  e, f, g;
2095 
2096                     for (d = 0; d < embedDim; ++d) {
2097                       normal[d] = 0.0;
2098                       for (e = 0; e < embedDim; ++e) {
2099                         for (f = 0; f < embedDim; ++f) {
2100                           for (g = 0; g < embedDim; ++g) {
2101                             normal[d] += epsilon[d][e][f][g]*(coordsIn[j*embedDim+e] - coordsIn[i*embedDim+e])*(coordsIn[k*embedDim+f] - coordsIn[i*embedDim+f])*(coordsIn[l*embedDim+f] - coordsIn[i*embedDim+f]);
2102                           }
2103                         }
2104                       }
2105                     }
2106                     if (DotReal(embedDim, normal, &coordsIn[i*embedDim]) < 0) {PetscInt tmp = cone[1]; cone[1] = cone[2]; cone[2] = tmp;}
2107                   }
2108                   ierr = DMPlexSetCone(*dm, c++, cone);CHKERRQ(ierr);
2109                 }
2110               }
2111             }
2112           }
2113         }
2114       }
2115       ierr = DMPlexSymmetrize(*dm);CHKERRQ(ierr);
2116       ierr = DMPlexStratify(*dm);CHKERRQ(ierr);
2117       ierr = PetscFree(graph);CHKERRQ(ierr);
2118       /* Interpolate mesh */
2119       ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
2120       ierr = DMDestroy(dm);CHKERRQ(ierr);
2121       *dm  = idm;
2122       break;
2123     }
2124   default: SETERRQ1(comm, PETSC_ERR_SUP, "Unsupported dimension for sphere: %D", dim);
2125   }
2126   /* Create coordinates */
2127   ierr = DMGetCoordinateSection(*dm, &coordSection);CHKERRQ(ierr);
2128   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
2129   ierr = PetscSectionSetFieldComponents(coordSection, 0, embedDim);CHKERRQ(ierr);
2130   ierr = PetscSectionSetChart(coordSection, firstVertex, firstVertex+numVerts);CHKERRQ(ierr);
2131   for (v = firstVertex; v < firstVertex+numVerts; ++v) {
2132     ierr = PetscSectionSetDof(coordSection, v, embedDim);CHKERRQ(ierr);
2133     ierr = PetscSectionSetFieldDof(coordSection, v, 0, embedDim);CHKERRQ(ierr);
2134   }
2135   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
2136   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
2137   ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
2138   ierr = VecSetBlockSize(coordinates, embedDim);CHKERRQ(ierr);
2139   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
2140   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
2141   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
2142   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
2143   for (v = 0; v < numVerts; ++v) for (d = 0; d < embedDim; ++d) {coords[v*embedDim+d] = coordsIn[v*embedDim+d];}
2144   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
2145   ierr = DMSetCoordinatesLocal(*dm, coordinates);CHKERRQ(ierr);
2146   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
2147   ierr = PetscFree(coordsIn);CHKERRQ(ierr);
2148   PetscFunctionReturn(0);
2149 }
2150 
2151 /* External function declarations here */
2152 extern PetscErrorCode DMCreateInterpolation_Plex(DM dmCoarse, DM dmFine, Mat *interpolation, Vec *scaling);
2153 extern PetscErrorCode DMCreateInjection_Plex(DM dmCoarse, DM dmFine, Mat *mat);
2154 extern PetscErrorCode DMCreateMassMatrix_Plex(DM dmCoarse, DM dmFine, Mat *mat);
2155 extern PetscErrorCode DMCreateLocalSection_Plex(DM dm);
2156 extern PetscErrorCode DMCreateDefaultConstraints_Plex(DM dm);
2157 extern PetscErrorCode DMCreateMatrix_Plex(DM dm,  Mat *J);
2158 extern PetscErrorCode DMCreateCoordinateDM_Plex(DM dm, DM *cdm);
2159 extern PetscErrorCode DMCreateCoordinateField_Plex(DM dm, DMField *field);
2160 PETSC_INTERN PetscErrorCode DMClone_Plex(DM dm, DM *newdm);
2161 extern PetscErrorCode DMSetUp_Plex(DM dm);
2162 extern PetscErrorCode DMDestroy_Plex(DM dm);
2163 extern PetscErrorCode DMView_Plex(DM dm, PetscViewer viewer);
2164 extern PetscErrorCode DMLoad_Plex(DM dm, PetscViewer viewer);
2165 extern PetscErrorCode DMCreateSubDM_Plex(DM dm, PetscInt numFields, const PetscInt fields[], IS *is, DM *subdm);
2166 extern PetscErrorCode DMCreateSuperDM_Plex(DM dms[], PetscInt len, IS **is, DM *superdm);
2167 static PetscErrorCode DMInitialize_Plex(DM dm);
2168 
2169 /* Replace dm with the contents of dmNew
2170    - Share the DM_Plex structure
2171    - Share the coordinates
2172    - Share the SF
2173 */
2174 static PetscErrorCode DMPlexReplace_Static(DM dm, DM dmNew)
2175 {
2176   PetscSF               sf;
2177   DM                    coordDM, coarseDM;
2178   Vec                   coords;
2179   PetscBool             isper;
2180   const PetscReal      *maxCell, *L;
2181   const DMBoundaryType *bd;
2182   PetscErrorCode        ierr;
2183 
2184   PetscFunctionBegin;
2185   ierr = DMGetPointSF(dmNew, &sf);CHKERRQ(ierr);
2186   ierr = DMSetPointSF(dm, sf);CHKERRQ(ierr);
2187   ierr = DMGetCoordinateDM(dmNew, &coordDM);CHKERRQ(ierr);
2188   ierr = DMGetCoordinatesLocal(dmNew, &coords);CHKERRQ(ierr);
2189   ierr = DMSetCoordinateDM(dm, coordDM);CHKERRQ(ierr);
2190   ierr = DMSetCoordinatesLocal(dm, coords);CHKERRQ(ierr);
2191   ierr = DMGetPeriodicity(dm, &isper, &maxCell, &L, &bd);CHKERRQ(ierr);
2192   ierr = DMSetPeriodicity(dmNew, isper, maxCell, L, bd);CHKERRQ(ierr);
2193   ierr = DMDestroy_Plex(dm);CHKERRQ(ierr);
2194   ierr = DMInitialize_Plex(dm);CHKERRQ(ierr);
2195   dm->data = dmNew->data;
2196   ((DM_Plex *) dmNew->data)->refct++;
2197   ierr = DMDestroyLabelLinkList_Internal(dm);CHKERRQ(ierr);
2198   ierr = DMCopyLabels(dmNew, dm, PETSC_OWN_POINTER, PETSC_TRUE);CHKERRQ(ierr);
2199   ierr = DMGetCoarseDM(dmNew,&coarseDM);CHKERRQ(ierr);
2200   ierr = DMSetCoarseDM(dm,coarseDM);CHKERRQ(ierr);
2201   PetscFunctionReturn(0);
2202 }
2203 
2204 /* Swap dm with the contents of dmNew
2205    - Swap the DM_Plex structure
2206    - Swap the coordinates
2207    - Swap the point PetscSF
2208 */
2209 static PetscErrorCode DMPlexSwap_Static(DM dmA, DM dmB)
2210 {
2211   DM              coordDMA, coordDMB;
2212   Vec             coordsA,  coordsB;
2213   PetscSF         sfA,      sfB;
2214   void            *tmp;
2215   DMLabelLink     listTmp;
2216   DMLabel         depthTmp;
2217   PetscInt        tmpI;
2218   PetscErrorCode  ierr;
2219 
2220   PetscFunctionBegin;
2221   ierr = DMGetPointSF(dmA, &sfA);CHKERRQ(ierr);
2222   ierr = DMGetPointSF(dmB, &sfB);CHKERRQ(ierr);
2223   ierr = PetscObjectReference((PetscObject) sfA);CHKERRQ(ierr);
2224   ierr = DMSetPointSF(dmA, sfB);CHKERRQ(ierr);
2225   ierr = DMSetPointSF(dmB, sfA);CHKERRQ(ierr);
2226   ierr = PetscObjectDereference((PetscObject) sfA);CHKERRQ(ierr);
2227 
2228   ierr = DMGetCoordinateDM(dmA, &coordDMA);CHKERRQ(ierr);
2229   ierr = DMGetCoordinateDM(dmB, &coordDMB);CHKERRQ(ierr);
2230   ierr = PetscObjectReference((PetscObject) coordDMA);CHKERRQ(ierr);
2231   ierr = DMSetCoordinateDM(dmA, coordDMB);CHKERRQ(ierr);
2232   ierr = DMSetCoordinateDM(dmB, coordDMA);CHKERRQ(ierr);
2233   ierr = PetscObjectDereference((PetscObject) coordDMA);CHKERRQ(ierr);
2234 
2235   ierr = DMGetCoordinatesLocal(dmA, &coordsA);CHKERRQ(ierr);
2236   ierr = DMGetCoordinatesLocal(dmB, &coordsB);CHKERRQ(ierr);
2237   ierr = PetscObjectReference((PetscObject) coordsA);CHKERRQ(ierr);
2238   ierr = DMSetCoordinatesLocal(dmA, coordsB);CHKERRQ(ierr);
2239   ierr = DMSetCoordinatesLocal(dmB, coordsA);CHKERRQ(ierr);
2240   ierr = PetscObjectDereference((PetscObject) coordsA);CHKERRQ(ierr);
2241 
2242   tmp       = dmA->data;
2243   dmA->data = dmB->data;
2244   dmB->data = tmp;
2245   listTmp   = dmA->labels;
2246   dmA->labels = dmB->labels;
2247   dmB->labels = listTmp;
2248   depthTmp  = dmA->depthLabel;
2249   dmA->depthLabel = dmB->depthLabel;
2250   dmB->depthLabel = depthTmp;
2251   depthTmp  = dmA->celltypeLabel;
2252   dmA->celltypeLabel = dmB->celltypeLabel;
2253   dmB->celltypeLabel = depthTmp;
2254   tmpI         = dmA->levelup;
2255   dmA->levelup = dmB->levelup;
2256   dmB->levelup = tmpI;
2257   PetscFunctionReturn(0);
2258 }
2259 
2260 PetscErrorCode DMSetFromOptions_NonRefinement_Plex(PetscOptionItems *PetscOptionsObject,DM dm)
2261 {
2262   DM_Plex       *mesh = (DM_Plex*) dm->data;
2263   PetscBool      flg;
2264   PetscErrorCode ierr;
2265 
2266   PetscFunctionBegin;
2267   /* Handle viewing */
2268   ierr = PetscOptionsBool("-dm_plex_print_set_values", "Output all set values info", "DMPlexMatSetClosure", PETSC_FALSE, &mesh->printSetValues, NULL);CHKERRQ(ierr);
2269   ierr = PetscOptionsBoundedInt("-dm_plex_print_fem", "Debug output level all fem computations", "DMPlexSNESComputeResidualFEM", 0, &mesh->printFEM, NULL,0);CHKERRQ(ierr);
2270   ierr = PetscOptionsReal("-dm_plex_print_tol", "Tolerance for FEM output", "DMPlexSNESComputeResidualFEM", mesh->printTol, &mesh->printTol, NULL);CHKERRQ(ierr);
2271   ierr = PetscOptionsBoundedInt("-dm_plex_print_l2", "Debug output level all L2 diff computations", "DMComputeL2Diff", 0, &mesh->printL2, NULL,0);CHKERRQ(ierr);
2272   ierr = DMMonitorSetFromOptions(dm, "-dm_plex_monitor_throughput", "Monitor the simulation throughput", "DMPlexMonitorThroughput", DMPlexMonitorThroughput, NULL, &flg);CHKERRQ(ierr);
2273   if (flg) {ierr = PetscLogDefaultBegin();CHKERRQ(ierr);}
2274   /* Point Location */
2275   ierr = PetscOptionsBool("-dm_plex_hash_location", "Use grid hashing for point location", "DMInterpolate", PETSC_FALSE, &mesh->useHashLocation, NULL);CHKERRQ(ierr);
2276   /* Partitioning and distribution */
2277   ierr = PetscOptionsBool("-dm_plex_partition_balance", "Attempt to evenly divide points on partition boundary between processes", "DMPlexSetPartitionBalance", PETSC_FALSE, &mesh->partitionBalance, NULL);CHKERRQ(ierr);
2278   /* Generation and remeshing */
2279   ierr = PetscOptionsBool("-dm_plex_remesh_bd", "Allow changes to the boundary on remeshing", "DMAdapt", PETSC_FALSE, &mesh->remeshBd, NULL);CHKERRQ(ierr);
2280   /* Projection behavior */
2281   ierr = PetscOptionsBoundedInt("-dm_plex_max_projection_height", "Maxmimum mesh point height used to project locally", "DMPlexSetMaxProjectionHeight", 0, &mesh->maxProjectionHeight, NULL,0);CHKERRQ(ierr);
2282   ierr = PetscOptionsBool("-dm_plex_regular_refinement", "Use special nested projection algorithm for regular refinement", "DMPlexSetRegularRefinement", mesh->regularRefinement, &mesh->regularRefinement, NULL);CHKERRQ(ierr);
2283   ierr = PetscOptionsEnum("-dm_plex_cell_refiner", "Strategy for cell refinment", "ex40.c", DMPlexCellRefinerTypes, (PetscEnum) mesh->cellRefiner, (PetscEnum *) &mesh->cellRefiner, NULL);CHKERRQ(ierr);
2284   /* Checking structure */
2285   {
2286     PetscBool   flg = PETSC_FALSE, flg2 = PETSC_FALSE, all = PETSC_FALSE;
2287 
2288     ierr = PetscOptionsBool("-dm_plex_check_all", "Perform all checks", NULL, PETSC_FALSE, &all, &flg2);CHKERRQ(ierr);
2289     ierr = PetscOptionsBool("-dm_plex_check_symmetry", "Check that the adjacency information in the mesh is symmetric", "DMPlexCheckSymmetry", PETSC_FALSE, &flg, &flg2);CHKERRQ(ierr);
2290     if (all || (flg && flg2)) {ierr = DMPlexCheckSymmetry(dm);CHKERRQ(ierr);}
2291     ierr = PetscOptionsBool("-dm_plex_check_skeleton", "Check that each cell has the correct number of vertices (only for homogeneous simplex or tensor meshes)", "DMPlexCheckSkeleton", PETSC_FALSE, &flg, &flg2);CHKERRQ(ierr);
2292     if (all || (flg && flg2)) {ierr = DMPlexCheckSkeleton(dm, 0);CHKERRQ(ierr);}
2293     ierr = PetscOptionsBool("-dm_plex_check_faces", "Check that the faces of each cell give a vertex order this is consistent with what we expect from the cell type", "DMPlexCheckFaces", PETSC_FALSE, &flg, &flg2);CHKERRQ(ierr);
2294     if (all || (flg && flg2)) {ierr = DMPlexCheckFaces(dm, 0);CHKERRQ(ierr);}
2295     ierr = PetscOptionsBool("-dm_plex_check_geometry", "Check that cells have positive volume", "DMPlexCheckGeometry", PETSC_FALSE, &flg, &flg2);CHKERRQ(ierr);
2296     if (all || (flg && flg2)) {ierr = DMPlexCheckGeometry(dm);CHKERRQ(ierr);}
2297     ierr = PetscOptionsBool("-dm_plex_check_pointsf", "Check some necessary conditions for PointSF", "DMPlexCheckPointSF", PETSC_FALSE, &flg, &flg2);CHKERRQ(ierr);
2298     if (all || (flg && flg2)) {ierr = DMPlexCheckPointSF(dm);CHKERRQ(ierr);}
2299     ierr = PetscOptionsBool("-dm_plex_check_interface_cones", "Check points on inter-partition interfaces have conforming order of cone points", "DMPlexCheckInterfaceCones", PETSC_FALSE, &flg, &flg2);CHKERRQ(ierr);
2300     if (all || (flg && flg2)) {ierr = DMPlexCheckInterfaceCones(dm);CHKERRQ(ierr);}
2301     ierr = PetscOptionsBool("-dm_plex_check_cell_shape", "Check cell shape", "DMPlexCheckCellShape", PETSC_FALSE, &flg, &flg2);CHKERRQ(ierr);
2302     if (flg && flg2) {ierr = DMPlexCheckCellShape(dm, PETSC_TRUE, PETSC_DETERMINE);CHKERRQ(ierr);}
2303   }
2304 
2305   ierr = PetscPartitionerSetFromOptions(mesh->partitioner);CHKERRQ(ierr);
2306   PetscFunctionReturn(0);
2307 }
2308 
2309 static PetscErrorCode DMSetFromOptions_Plex(PetscOptionItems *PetscOptionsObject,DM dm)
2310 {
2311   PetscInt       refine = 0, coarsen = 0, r;
2312   PetscBool      isHierarchy;
2313   PetscErrorCode ierr;
2314 
2315   PetscFunctionBegin;
2316   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
2317   ierr = PetscOptionsHead(PetscOptionsObject,"DMPlex Options");CHKERRQ(ierr);
2318   /* Handle DMPlex refinement */
2319   ierr = PetscOptionsBoundedInt("-dm_refine", "The number of uniform refinements", "DMCreate", refine, &refine, NULL,0);CHKERRQ(ierr);
2320   ierr = PetscOptionsBoundedInt("-dm_refine_hierarchy", "The number of uniform refinements", "DMCreate", refine, &refine, &isHierarchy,0);CHKERRQ(ierr);
2321   if (refine) {ierr = DMPlexSetRefinementUniform(dm, PETSC_TRUE);CHKERRQ(ierr);}
2322   if (refine && isHierarchy) {
2323     DM *dms, coarseDM;
2324 
2325     ierr = DMGetCoarseDM(dm, &coarseDM);CHKERRQ(ierr);
2326     ierr = PetscObjectReference((PetscObject)coarseDM);CHKERRQ(ierr);
2327     ierr = PetscMalloc1(refine,&dms);CHKERRQ(ierr);
2328     ierr = DMRefineHierarchy(dm, refine, dms);CHKERRQ(ierr);
2329     /* Total hack since we do not pass in a pointer */
2330     ierr = DMPlexSwap_Static(dm, dms[refine-1]);CHKERRQ(ierr);
2331     if (refine == 1) {
2332       ierr = DMSetCoarseDM(dm, dms[0]);CHKERRQ(ierr);
2333       ierr = DMPlexSetRegularRefinement(dm, PETSC_TRUE);CHKERRQ(ierr);
2334     } else {
2335       ierr = DMSetCoarseDM(dm, dms[refine-2]);CHKERRQ(ierr);
2336       ierr = DMPlexSetRegularRefinement(dm, PETSC_TRUE);CHKERRQ(ierr);
2337       ierr = DMSetCoarseDM(dms[0], dms[refine-1]);CHKERRQ(ierr);
2338       ierr = DMPlexSetRegularRefinement(dms[0], PETSC_TRUE);CHKERRQ(ierr);
2339     }
2340     ierr = DMSetCoarseDM(dms[refine-1], coarseDM);CHKERRQ(ierr);
2341     ierr = PetscObjectDereference((PetscObject)coarseDM);CHKERRQ(ierr);
2342     /* Free DMs */
2343     for (r = 0; r < refine; ++r) {
2344       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dms[r]);CHKERRQ(ierr);
2345       ierr = DMDestroy(&dms[r]);CHKERRQ(ierr);
2346     }
2347     ierr = PetscFree(dms);CHKERRQ(ierr);
2348   } else {
2349     for (r = 0; r < refine; ++r) {
2350       DM refinedMesh;
2351 
2352       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2353       ierr = DMRefine(dm, PetscObjectComm((PetscObject) dm), &refinedMesh);CHKERRQ(ierr);
2354       /* Total hack since we do not pass in a pointer */
2355       ierr = DMPlexReplace_Static(dm, refinedMesh);CHKERRQ(ierr);
2356       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2357       ierr = DMDestroy(&refinedMesh);CHKERRQ(ierr);
2358     }
2359   }
2360   /* Handle DMPlex coarsening */
2361   ierr = PetscOptionsBoundedInt("-dm_coarsen", "Coarsen the mesh", "DMCreate", coarsen, &coarsen, NULL,0);CHKERRQ(ierr);
2362   ierr = PetscOptionsBoundedInt("-dm_coarsen_hierarchy", "The number of coarsenings", "DMCreate", coarsen, &coarsen, &isHierarchy,0);CHKERRQ(ierr);
2363   if (coarsen && isHierarchy) {
2364     DM *dms;
2365 
2366     ierr = PetscMalloc1(coarsen, &dms);CHKERRQ(ierr);
2367     ierr = DMCoarsenHierarchy(dm, coarsen, dms);CHKERRQ(ierr);
2368     /* Free DMs */
2369     for (r = 0; r < coarsen; ++r) {
2370       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dms[r]);CHKERRQ(ierr);
2371       ierr = DMDestroy(&dms[r]);CHKERRQ(ierr);
2372     }
2373     ierr = PetscFree(dms);CHKERRQ(ierr);
2374   } else {
2375     for (r = 0; r < coarsen; ++r) {
2376       DM coarseMesh;
2377 
2378       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2379       ierr = DMCoarsen(dm, PetscObjectComm((PetscObject) dm), &coarseMesh);CHKERRQ(ierr);
2380       /* Total hack since we do not pass in a pointer */
2381       ierr = DMPlexReplace_Static(dm, coarseMesh);CHKERRQ(ierr);
2382       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2383       ierr = DMDestroy(&coarseMesh);CHKERRQ(ierr);
2384     }
2385   }
2386   /* Handle */
2387   ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2388   ierr = PetscOptionsTail();CHKERRQ(ierr);
2389   PetscFunctionReturn(0);
2390 }
2391 
2392 static PetscErrorCode DMCreateGlobalVector_Plex(DM dm,Vec *vec)
2393 {
2394   PetscErrorCode ierr;
2395 
2396   PetscFunctionBegin;
2397   ierr = DMCreateGlobalVector_Section_Private(dm,vec);CHKERRQ(ierr);
2398   /* ierr = VecSetOperation(*vec, VECOP_DUPLICATE, (void(*)(void)) VecDuplicate_MPI_DM);CHKERRQ(ierr); */
2399   ierr = VecSetOperation(*vec, VECOP_VIEW, (void (*)(void)) VecView_Plex);CHKERRQ(ierr);
2400   ierr = VecSetOperation(*vec, VECOP_VIEWNATIVE, (void (*)(void)) VecView_Plex_Native);CHKERRQ(ierr);
2401   ierr = VecSetOperation(*vec, VECOP_LOAD, (void (*)(void)) VecLoad_Plex);CHKERRQ(ierr);
2402   ierr = VecSetOperation(*vec, VECOP_LOADNATIVE, (void (*)(void)) VecLoad_Plex_Native);CHKERRQ(ierr);
2403   PetscFunctionReturn(0);
2404 }
2405 
2406 static PetscErrorCode DMCreateLocalVector_Plex(DM dm,Vec *vec)
2407 {
2408   PetscErrorCode ierr;
2409 
2410   PetscFunctionBegin;
2411   ierr = DMCreateLocalVector_Section_Private(dm,vec);CHKERRQ(ierr);
2412   ierr = VecSetOperation(*vec, VECOP_VIEW, (void (*)(void)) VecView_Plex_Local);CHKERRQ(ierr);
2413   ierr = VecSetOperation(*vec, VECOP_LOAD, (void (*)(void)) VecLoad_Plex_Local);CHKERRQ(ierr);
2414   PetscFunctionReturn(0);
2415 }
2416 
2417 static PetscErrorCode DMGetDimPoints_Plex(DM dm, PetscInt dim, PetscInt *pStart, PetscInt *pEnd)
2418 {
2419   PetscInt       depth, d;
2420   PetscErrorCode ierr;
2421 
2422   PetscFunctionBegin;
2423   ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
2424   if (depth == 1) {
2425     ierr = DMGetDimension(dm, &d);CHKERRQ(ierr);
2426     if (dim == 0)      {ierr = DMPlexGetDepthStratum(dm, dim, pStart, pEnd);CHKERRQ(ierr);}
2427     else if (dim == d) {ierr = DMPlexGetDepthStratum(dm, 1, pStart, pEnd);CHKERRQ(ierr);}
2428     else               {*pStart = 0; *pEnd = 0;}
2429   } else {
2430     ierr = DMPlexGetDepthStratum(dm, dim, pStart, pEnd);CHKERRQ(ierr);
2431   }
2432   PetscFunctionReturn(0);
2433 }
2434 
2435 static PetscErrorCode DMGetNeighbors_Plex(DM dm, PetscInt *nranks, const PetscMPIInt *ranks[])
2436 {
2437   PetscSF           sf;
2438   PetscInt          niranks, njranks, n;
2439   const PetscMPIInt *iranks, *jranks;
2440   DM_Plex           *data = (DM_Plex*) dm->data;
2441   PetscErrorCode    ierr;
2442 
2443   PetscFunctionBegin;
2444   ierr = DMGetPointSF(dm, &sf);CHKERRQ(ierr);
2445   if (!data->neighbors) {
2446     ierr = PetscSFGetRootRanks(sf, &njranks, &jranks, NULL, NULL, NULL);CHKERRQ(ierr);
2447     ierr = PetscSFGetLeafRanks(sf, &niranks, &iranks, NULL, NULL);CHKERRQ(ierr);
2448     ierr = PetscMalloc1(njranks + niranks + 1, &data->neighbors);CHKERRQ(ierr);
2449     ierr = PetscArraycpy(data->neighbors + 1, jranks, njranks);CHKERRQ(ierr);
2450     ierr = PetscArraycpy(data->neighbors + njranks + 1, iranks, niranks);CHKERRQ(ierr);
2451     n = njranks + niranks;
2452     ierr = PetscSortRemoveDupsMPIInt(&n, data->neighbors + 1);CHKERRQ(ierr);
2453     /* The following cast should never fail: can't have more neighbors than PETSC_MPI_INT_MAX */
2454     ierr = PetscMPIIntCast(n, data->neighbors);CHKERRQ(ierr);
2455   }
2456   if (nranks) *nranks = data->neighbors[0];
2457   if (ranks) {
2458     if (data->neighbors[0]) *ranks = data->neighbors + 1;
2459     else                    *ranks = NULL;
2460   }
2461   PetscFunctionReturn(0);
2462 }
2463 
2464 static PetscErrorCode DMInitialize_Plex(DM dm)
2465 {
2466   PetscErrorCode ierr;
2467 
2468   PetscFunctionBegin;
2469   dm->ops->view                            = DMView_Plex;
2470   dm->ops->load                            = DMLoad_Plex;
2471   dm->ops->setfromoptions                  = DMSetFromOptions_Plex;
2472   dm->ops->clone                           = DMClone_Plex;
2473   dm->ops->setup                           = DMSetUp_Plex;
2474   dm->ops->createlocalsection              = DMCreateLocalSection_Plex;
2475   dm->ops->createdefaultconstraints        = DMCreateDefaultConstraints_Plex;
2476   dm->ops->createglobalvector              = DMCreateGlobalVector_Plex;
2477   dm->ops->createlocalvector               = DMCreateLocalVector_Plex;
2478   dm->ops->getlocaltoglobalmapping         = NULL;
2479   dm->ops->createfieldis                   = NULL;
2480   dm->ops->createcoordinatedm              = DMCreateCoordinateDM_Plex;
2481   dm->ops->createcoordinatefield           = DMCreateCoordinateField_Plex;
2482   dm->ops->getcoloring                     = NULL;
2483   dm->ops->creatematrix                    = DMCreateMatrix_Plex;
2484   dm->ops->createinterpolation             = DMCreateInterpolation_Plex;
2485   dm->ops->createmassmatrix                = DMCreateMassMatrix_Plex;
2486   dm->ops->createinjection                 = DMCreateInjection_Plex;
2487   dm->ops->refine                          = DMRefine_Plex;
2488   dm->ops->coarsen                         = DMCoarsen_Plex;
2489   dm->ops->refinehierarchy                 = DMRefineHierarchy_Plex;
2490   dm->ops->coarsenhierarchy                = DMCoarsenHierarchy_Plex;
2491   dm->ops->adaptlabel                      = DMAdaptLabel_Plex;
2492   dm->ops->adaptmetric                     = DMAdaptMetric_Plex;
2493   dm->ops->globaltolocalbegin              = NULL;
2494   dm->ops->globaltolocalend                = NULL;
2495   dm->ops->localtoglobalbegin              = NULL;
2496   dm->ops->localtoglobalend                = NULL;
2497   dm->ops->destroy                         = DMDestroy_Plex;
2498   dm->ops->createsubdm                     = DMCreateSubDM_Plex;
2499   dm->ops->createsuperdm                   = DMCreateSuperDM_Plex;
2500   dm->ops->getdimpoints                    = DMGetDimPoints_Plex;
2501   dm->ops->locatepoints                    = DMLocatePoints_Plex;
2502   dm->ops->projectfunctionlocal            = DMProjectFunctionLocal_Plex;
2503   dm->ops->projectfunctionlabellocal       = DMProjectFunctionLabelLocal_Plex;
2504   dm->ops->projectfieldlocal               = DMProjectFieldLocal_Plex;
2505   dm->ops->projectfieldlabellocal          = DMProjectFieldLabelLocal_Plex;
2506   dm->ops->computel2diff                   = DMComputeL2Diff_Plex;
2507   dm->ops->computel2gradientdiff           = DMComputeL2GradientDiff_Plex;
2508   dm->ops->computel2fielddiff              = DMComputeL2FieldDiff_Plex;
2509   dm->ops->getneighbors                    = DMGetNeighbors_Plex;
2510   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMPlexInsertBoundaryValues_C",DMPlexInsertBoundaryValues_Plex);CHKERRQ(ierr);
2511   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMSetUpGLVisViewer_C",DMSetUpGLVisViewer_Plex);CHKERRQ(ierr);
2512   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMCreateNeumannOverlap_C",DMCreateNeumannOverlap_Plex);CHKERRQ(ierr);
2513   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMPlexGetOverlap_C",DMPlexGetOverlap_Plex);CHKERRQ(ierr);
2514   PetscFunctionReturn(0);
2515 }
2516 
2517 PETSC_INTERN PetscErrorCode DMClone_Plex(DM dm, DM *newdm)
2518 {
2519   DM_Plex        *mesh = (DM_Plex *) dm->data;
2520   PetscErrorCode ierr;
2521 
2522   PetscFunctionBegin;
2523   mesh->refct++;
2524   (*newdm)->data = mesh;
2525   ierr = PetscObjectChangeTypeName((PetscObject) *newdm, DMPLEX);CHKERRQ(ierr);
2526   ierr = DMInitialize_Plex(*newdm);CHKERRQ(ierr);
2527   PetscFunctionReturn(0);
2528 }
2529 
2530 /*MC
2531   DMPLEX = "plex" - A DM object that encapsulates an unstructured mesh, or CW Complex, which can be expressed using a Hasse Diagram.
2532                     In the local representation, Vecs contain all unknowns in the interior and shared boundary. This is
2533                     specified by a PetscSection object. Ownership in the global representation is determined by
2534                     ownership of the underlying DMPlex points. This is specified by another PetscSection object.
2535 
2536   Options Database Keys:
2537 + -dm_plex_hash_location             - Use grid hashing for point location
2538 . -dm_plex_partition_balance         - Attempt to evenly divide points on partition boundary between processes
2539 . -dm_plex_remesh_bd                 - Allow changes to the boundary on remeshing
2540 . -dm_plex_max_projection_height     - Maxmimum mesh point height used to project locally
2541 . -dm_plex_regular_refinement        - Use special nested projection algorithm for regular refinement
2542 . -dm_plex_check_symmetry            - Check that the adjacency information in the mesh is symmetric
2543 . -dm_plex_check_skeleton <celltype> - Check that each cell has the correct number of vertices
2544 . -dm_plex_check_faces <celltype>    - Check that the faces of each cell give a vertex order this is consistent with what we expect from the cell type
2545 . -dm_plex_check_geometry            - Check that cells have positive volume
2546 . -dm_view :mesh.tex:ascii_latex     - View the mesh in LaTeX/TikZ
2547 . -dm_plex_view_scale <num>          - Scale the TikZ
2548 - -dm_plex_print_fem <num>           - View FEM assembly information, such as element vectors and matrices
2549 
2550 
2551   Level: intermediate
2552 
2553 .seealso: DMType, DMPlexCreate(), DMCreate(), DMSetType()
2554 M*/
2555 
2556 PETSC_EXTERN PetscErrorCode DMCreate_Plex(DM dm)
2557 {
2558   DM_Plex       *mesh;
2559   PetscInt       unit;
2560   PetscErrorCode ierr;
2561 
2562   PetscFunctionBegin;
2563   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
2564   ierr     = PetscNewLog(dm,&mesh);CHKERRQ(ierr);
2565   dm->dim  = 0;
2566   dm->data = mesh;
2567 
2568   mesh->refct             = 1;
2569   ierr                    = PetscSectionCreate(PetscObjectComm((PetscObject)dm), &mesh->coneSection);CHKERRQ(ierr);
2570   mesh->maxConeSize       = 0;
2571   mesh->cones             = NULL;
2572   mesh->coneOrientations  = NULL;
2573   ierr                    = PetscSectionCreate(PetscObjectComm((PetscObject)dm), &mesh->supportSection);CHKERRQ(ierr);
2574   mesh->maxSupportSize    = 0;
2575   mesh->supports          = NULL;
2576   mesh->refinementUniform = PETSC_TRUE;
2577   mesh->refinementLimit   = -1.0;
2578   mesh->interpolated      = DMPLEX_INTERPOLATED_INVALID;
2579   mesh->interpolatedCollective = DMPLEX_INTERPOLATED_INVALID;
2580 
2581   mesh->facesTmp = NULL;
2582 
2583   mesh->tetgenOpts   = NULL;
2584   mesh->triangleOpts = NULL;
2585   ierr = PetscPartitionerCreate(PetscObjectComm((PetscObject)dm), &mesh->partitioner);CHKERRQ(ierr);
2586   mesh->remeshBd     = PETSC_FALSE;
2587 
2588   mesh->subpointMap = NULL;
2589 
2590   for (unit = 0; unit < NUM_PETSC_UNITS; ++unit) mesh->scale[unit] = 1.0;
2591 
2592   mesh->regularRefinement   = PETSC_FALSE;
2593   mesh->depthState          = -1;
2594   mesh->celltypeState       = -1;
2595   mesh->globalVertexNumbers = NULL;
2596   mesh->globalCellNumbers   = NULL;
2597   mesh->anchorSection       = NULL;
2598   mesh->anchorIS            = NULL;
2599   mesh->createanchors       = NULL;
2600   mesh->computeanchormatrix = NULL;
2601   mesh->parentSection       = NULL;
2602   mesh->parents             = NULL;
2603   mesh->childIDs            = NULL;
2604   mesh->childSection        = NULL;
2605   mesh->children            = NULL;
2606   mesh->referenceTree       = NULL;
2607   mesh->getchildsymmetry    = NULL;
2608   mesh->vtkCellHeight       = 0;
2609   mesh->useAnchors          = PETSC_FALSE;
2610 
2611   mesh->maxProjectionHeight = 0;
2612 
2613   mesh->neighbors           = NULL;
2614 
2615   mesh->printSetValues = PETSC_FALSE;
2616   mesh->printFEM       = 0;
2617   mesh->printTol       = 1.0e-10;
2618 
2619   ierr = DMInitialize_Plex(dm);CHKERRQ(ierr);
2620   PetscFunctionReturn(0);
2621 }
2622 
2623 /*@
2624   DMPlexCreate - Creates a DMPlex object, which encapsulates an unstructured mesh, or CW complex, which can be expressed using a Hasse Diagram.
2625 
2626   Collective
2627 
2628   Input Parameter:
2629 . comm - The communicator for the DMPlex object
2630 
2631   Output Parameter:
2632 . mesh  - The DMPlex object
2633 
2634   Level: beginner
2635 
2636 @*/
2637 PetscErrorCode DMPlexCreate(MPI_Comm comm, DM *mesh)
2638 {
2639   PetscErrorCode ierr;
2640 
2641   PetscFunctionBegin;
2642   PetscValidPointer(mesh,2);
2643   ierr = DMCreate(comm, mesh);CHKERRQ(ierr);
2644   ierr = DMSetType(*mesh, DMPLEX);CHKERRQ(ierr);
2645   PetscFunctionReturn(0);
2646 }
2647 
2648 static PetscErrorCode DMPlexInvertCell_Internal(PetscInt dim, PetscInt numCorners, PetscInt cone[])
2649 {
2650   PetscErrorCode ierr;
2651 
2652   PetscFunctionBegin;
2653   if (dim != 3) PetscFunctionReturn(0);
2654   switch (numCorners) {
2655   case 4: ierr = DMPlexInvertCell(DM_POLYTOPE_TETRAHEDRON,cone);CHKERRQ(ierr); break;
2656   case 6: ierr = DMPlexInvertCell(DM_POLYTOPE_TRI_PRISM,cone);CHKERRQ(ierr); break;
2657   case 8: ierr = DMPlexInvertCell(DM_POLYTOPE_HEXAHEDRON,cone);CHKERRQ(ierr); break;
2658   default: break;
2659   }
2660   PetscFunctionReturn(0);
2661 }
2662 
2663 /*
2664   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
2665 */
2666 /* TODO: invertCells and spaceDim arguments could be added also to to DMPlexCreateFromCellListParallel(), DMPlexBuildFromCellList_Internal() and DMPlexCreateFromCellList() */
2667 PetscErrorCode DMPlexBuildFromCellList_Parallel_Internal(DM dm, PetscInt spaceDim, PetscInt numCells, PetscInt numVertices, PetscInt numCorners, const int cells[], PetscBool invertCells, PetscSF *sfVert)
2668 {
2669   PetscSF         sfPoint;
2670   PetscLayout     vLayout;
2671   PetscHSetI      vhash;
2672   PetscSFNode    *remoteVerticesAdj, *vertexLocal, *vertexOwner, *remoteVertex;
2673   const PetscInt *vrange;
2674   PetscInt        numVerticesAdj, off = 0, *verticesAdj, numVerticesGhost = 0, *localVertex, *cone, c, p, v, g;
2675   PetscMPIInt     rank, size;
2676   PetscErrorCode  ierr;
2677 
2678   PetscFunctionBegin;
2679   ierr = PetscLogEventBegin(DMPLEX_CreateFromCellList,dm,0,0,0);CHKERRQ(ierr);
2680   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject) dm), &rank);CHKERRQ(ierr);
2681   ierr = MPI_Comm_size(PetscObjectComm((PetscObject) dm), &size);CHKERRQ(ierr);
2682   /* Partition vertices */
2683   ierr = PetscLayoutCreate(PetscObjectComm((PetscObject) dm), &vLayout);CHKERRQ(ierr);
2684   ierr = PetscLayoutSetLocalSize(vLayout, numVertices);CHKERRQ(ierr);
2685   ierr = PetscLayoutSetBlockSize(vLayout, 1);CHKERRQ(ierr);
2686   ierr = PetscLayoutSetUp(vLayout);CHKERRQ(ierr);
2687   ierr = PetscLayoutGetRanges(vLayout, &vrange);CHKERRQ(ierr);
2688   /* Count vertices and map them to procs */
2689   ierr = PetscHSetICreate(&vhash);CHKERRQ(ierr);
2690   for (c = 0; c < numCells; ++c) {
2691     for (p = 0; p < numCorners; ++p) {
2692       ierr = PetscHSetIAdd(vhash, cells[c*numCorners+p]);CHKERRQ(ierr);
2693     }
2694   }
2695   ierr = PetscHSetIGetSize(vhash, &numVerticesAdj);CHKERRQ(ierr);
2696   ierr = PetscMalloc1(numVerticesAdj, &verticesAdj);CHKERRQ(ierr);
2697   ierr = PetscHSetIGetElems(vhash, &off, verticesAdj);CHKERRQ(ierr);
2698   ierr = PetscHSetIDestroy(&vhash);CHKERRQ(ierr);
2699   if (off != numVerticesAdj) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Invalid number of local vertices %D should be %D", off, numVerticesAdj);
2700   ierr = PetscSortInt(numVerticesAdj, verticesAdj);CHKERRQ(ierr);
2701   ierr = PetscMalloc1(numVerticesAdj, &remoteVerticesAdj);CHKERRQ(ierr);
2702   for (v = 0; v < numVerticesAdj; ++v) {
2703     const PetscInt gv = verticesAdj[v];
2704     PetscInt       vrank;
2705 
2706     ierr = PetscFindInt(gv, size+1, vrange, &vrank);CHKERRQ(ierr);
2707     vrank = vrank < 0 ? -(vrank+2) : vrank;
2708     remoteVerticesAdj[v].index = gv - vrange[vrank];
2709     remoteVerticesAdj[v].rank  = vrank;
2710   }
2711   /* Create cones */
2712   ierr = DMPlexSetChart(dm, 0, numCells+numVerticesAdj);CHKERRQ(ierr);
2713   for (c = 0; c < numCells; ++c) {ierr = DMPlexSetConeSize(dm, c, numCorners);CHKERRQ(ierr);}
2714   ierr = DMSetUp(dm);CHKERRQ(ierr);
2715   ierr = DMGetWorkArray(dm, numCorners, MPIU_INT, &cone);CHKERRQ(ierr);
2716   for (c = 0; c < numCells; ++c) {
2717     for (p = 0; p < numCorners; ++p) {
2718       const PetscInt gv = cells[c*numCorners+p];
2719       PetscInt       lv;
2720 
2721       ierr = PetscFindInt(gv, numVerticesAdj, verticesAdj, &lv);CHKERRQ(ierr);
2722       if (lv < 0) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Could not find global vertex %D in local connectivity", gv);
2723       cone[p] = lv+numCells;
2724     }
2725     if (invertCells) { ierr = DMPlexInvertCell_Internal(spaceDim, numCorners, cone);CHKERRQ(ierr); }
2726     ierr = DMPlexSetCone(dm, c, cone);CHKERRQ(ierr);
2727   }
2728   ierr = DMRestoreWorkArray(dm, numCorners, MPIU_INT, &cone);CHKERRQ(ierr);
2729   /* Create SF for vertices */
2730   ierr = PetscSFCreate(PetscObjectComm((PetscObject)dm), sfVert);CHKERRQ(ierr);
2731   ierr = PetscObjectSetName((PetscObject) *sfVert, "Vertex Ownership SF");CHKERRQ(ierr);
2732   ierr = PetscSFSetFromOptions(*sfVert);CHKERRQ(ierr);
2733   ierr = PetscSFSetGraph(*sfVert, numVertices, numVerticesAdj, NULL, PETSC_OWN_POINTER, remoteVerticesAdj, PETSC_OWN_POINTER);CHKERRQ(ierr);
2734   ierr = PetscFree(verticesAdj);CHKERRQ(ierr);
2735   /* Build pointSF */
2736   ierr = PetscMalloc2(numVerticesAdj, &vertexLocal, numVertices, &vertexOwner);CHKERRQ(ierr);
2737   for (v = 0; v < numVerticesAdj; ++v) {vertexLocal[v].index = v+numCells; vertexLocal[v].rank = rank;}
2738   for (v = 0; v < numVertices;    ++v) {vertexOwner[v].index = -1;         vertexOwner[v].rank = -1;}
2739   ierr = PetscSFReduceBegin(*sfVert, MPIU_2INT, vertexLocal, vertexOwner, MPI_MAXLOC);CHKERRQ(ierr);
2740   ierr = PetscSFReduceEnd(*sfVert, MPIU_2INT, vertexLocal, vertexOwner, MPI_MAXLOC);CHKERRQ(ierr);
2741   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);
2742   ierr = PetscSFBcastBegin(*sfVert, MPIU_2INT, vertexOwner, vertexLocal);CHKERRQ(ierr);
2743   ierr = PetscSFBcastEnd(*sfVert, MPIU_2INT, vertexOwner, vertexLocal);CHKERRQ(ierr);
2744   for (v = 0; v < numVerticesAdj; ++v) if (vertexLocal[v].rank != rank) ++numVerticesGhost;
2745   ierr = PetscMalloc1(numVerticesGhost, &localVertex);CHKERRQ(ierr);
2746   ierr = PetscMalloc1(numVerticesGhost, &remoteVertex);CHKERRQ(ierr);
2747   for (v = 0, g = 0; v < numVerticesAdj; ++v) {
2748     if (vertexLocal[v].rank != rank) {
2749       localVertex[g]        = v+numCells;
2750       remoteVertex[g].index = vertexLocal[v].index;
2751       remoteVertex[g].rank  = vertexLocal[v].rank;
2752       ++g;
2753     }
2754   }
2755   ierr = PetscFree2(vertexLocal, vertexOwner);CHKERRQ(ierr);
2756   if (g != numVerticesGhost) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid number of vertex ghosts %D should be %D", g, numVerticesGhost);
2757   ierr = DMGetPointSF(dm, &sfPoint);CHKERRQ(ierr);
2758   ierr = PetscObjectSetName((PetscObject) sfPoint, "point SF");CHKERRQ(ierr);
2759   ierr = PetscSFSetGraph(sfPoint, numCells+numVerticesAdj, numVerticesGhost, localVertex, PETSC_OWN_POINTER, remoteVertex, PETSC_OWN_POINTER);CHKERRQ(ierr);
2760   ierr = PetscLayoutDestroy(&vLayout);CHKERRQ(ierr);
2761   /* Fill in the rest of the topology structure */
2762   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
2763   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
2764   ierr = PetscLogEventEnd(DMPLEX_CreateFromCellList,dm,0,0,0);CHKERRQ(ierr);
2765   PetscFunctionReturn(0);
2766 }
2767 
2768 /*
2769   This takes as input the coordinates for each owned vertex
2770 */
2771 PetscErrorCode DMPlexBuildCoordinates_Parallel_Internal(DM dm, PetscInt spaceDim, PetscInt numCells, PetscInt numV, PetscSF sfVert, const PetscReal vertexCoords[])
2772 {
2773   PetscSection   coordSection;
2774   Vec            coordinates;
2775   PetscScalar   *coords;
2776   PetscInt       numVertices, numVerticesAdj, coordSize, v;
2777   PetscErrorCode ierr;
2778 
2779   PetscFunctionBegin;
2780   ierr = PetscLogEventBegin(DMPLEX_CreateFromCellList_Coordinates,dm,0,0,0);CHKERRQ(ierr);
2781   ierr = DMSetCoordinateDim(dm, spaceDim);CHKERRQ(ierr);
2782   ierr = PetscSFGetGraph(sfVert, &numVertices, &numVerticesAdj, NULL, NULL);CHKERRQ(ierr);
2783   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
2784   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
2785   ierr = PetscSectionSetFieldComponents(coordSection, 0, spaceDim);CHKERRQ(ierr);
2786   ierr = PetscSectionSetChart(coordSection, numCells, numCells + numVerticesAdj);CHKERRQ(ierr);
2787   for (v = numCells; v < numCells+numVerticesAdj; ++v) {
2788     ierr = PetscSectionSetDof(coordSection, v, spaceDim);CHKERRQ(ierr);
2789     ierr = PetscSectionSetFieldDof(coordSection, v, 0, spaceDim);CHKERRQ(ierr);
2790   }
2791   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
2792   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
2793   ierr = VecCreate(PetscObjectComm((PetscObject)dm), &coordinates);CHKERRQ(ierr);
2794   ierr = VecSetBlockSize(coordinates, spaceDim);CHKERRQ(ierr);
2795   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
2796   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
2797   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
2798   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
2799   {
2800     MPI_Datatype coordtype;
2801 
2802     /* Need a temp buffer for coords if we have complex/single */
2803     ierr = MPI_Type_contiguous(spaceDim, MPIU_SCALAR, &coordtype);CHKERRQ(ierr);
2804     ierr = MPI_Type_commit(&coordtype);CHKERRQ(ierr);
2805 #if defined(PETSC_USE_COMPLEX)
2806     {
2807     PetscScalar *svertexCoords;
2808     PetscInt    i;
2809     ierr = PetscMalloc1(numV*spaceDim,&svertexCoords);CHKERRQ(ierr);
2810     for (i=0; i<numV*spaceDim; i++) svertexCoords[i] = vertexCoords[i];
2811     ierr = PetscSFBcastBegin(sfVert, coordtype, svertexCoords, coords);CHKERRQ(ierr);
2812     ierr = PetscSFBcastEnd(sfVert, coordtype, svertexCoords, coords);CHKERRQ(ierr);
2813     ierr = PetscFree(svertexCoords);CHKERRQ(ierr);
2814     }
2815 #else
2816     ierr = PetscSFBcastBegin(sfVert, coordtype, vertexCoords, coords);CHKERRQ(ierr);
2817     ierr = PetscSFBcastEnd(sfVert, coordtype, vertexCoords, coords);CHKERRQ(ierr);
2818 #endif
2819     ierr = MPI_Type_free(&coordtype);CHKERRQ(ierr);
2820   }
2821   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
2822   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
2823   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
2824   ierr = PetscLogEventEnd(DMPLEX_CreateFromCellList_Coordinates,dm,0,0,0);CHKERRQ(ierr);
2825   PetscFunctionReturn(0);
2826 }
2827 
2828 /*@
2829   DMPlexCreateFromCellListParallel - This takes as input common mesh generator output, a list of the vertices for each cell, and produces a DM
2830 
2831   Input Parameters:
2832 + comm - The communicator
2833 . dim - The topological dimension of the mesh
2834 . numCells - The number of cells owned by this process
2835 . numVertices - The number of vertices owned by this process
2836 . numCorners - The number of vertices for each cell
2837 . interpolate - Flag indicating that intermediate mesh entities (faces, edges) should be created automatically
2838 . cells - An array of numCells*numCorners numbers, the global vertex numbers for each cell
2839 . spaceDim - The spatial dimension used for coordinates
2840 - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex
2841 
2842   Output Parameter:
2843 + dm - The DM
2844 - vertexSF - Optional, SF describing complete vertex ownership
2845 
2846   Note: Two triangles sharing a face
2847 $
2848 $        2
2849 $      / | \
2850 $     /  |  \
2851 $    /   |   \
2852 $   0  0 | 1  3
2853 $    \   |   /
2854 $     \  |  /
2855 $      \ | /
2856 $        1
2857 would have input
2858 $  numCells = 2, numVertices = 4
2859 $  cells = [0 1 2  1 3 2]
2860 $
2861 which would result in the DMPlex
2862 $
2863 $        4
2864 $      / | \
2865 $     /  |  \
2866 $    /   |   \
2867 $   2  0 | 1  5
2868 $    \   |   /
2869 $     \  |  /
2870 $      \ | /
2871 $        3
2872 
2873   Level: beginner
2874 
2875 .seealso: DMPlexCreateFromCellList(), DMPlexCreateFromDAG(), DMPlexCreate()
2876 @*/
2877 PetscErrorCode DMPlexCreateFromCellListParallel(MPI_Comm comm, PetscInt dim, PetscInt numCells, PetscInt numVertices, PetscInt numCorners, PetscBool interpolate, const int cells[], PetscInt spaceDim, const PetscReal vertexCoords[], PetscSF *vertexSF, DM *dm)
2878 {
2879   PetscSF        sfVert;
2880   PetscErrorCode ierr;
2881 
2882   PetscFunctionBegin;
2883   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
2884   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
2885   PetscValidLogicalCollectiveInt(*dm, dim, 2);
2886   PetscValidLogicalCollectiveInt(*dm, spaceDim, 8);
2887   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
2888   ierr = DMPlexBuildFromCellList_Parallel_Internal(*dm, spaceDim, numCells, numVertices, numCorners, cells, PETSC_FALSE, &sfVert);CHKERRQ(ierr);
2889   if (interpolate) {
2890     DM idm;
2891 
2892     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
2893     ierr = DMDestroy(dm);CHKERRQ(ierr);
2894     *dm  = idm;
2895   }
2896   ierr = DMPlexBuildCoordinates_Parallel_Internal(*dm, spaceDim, numCells, numVertices, sfVert, vertexCoords);CHKERRQ(ierr);
2897   if (vertexSF) *vertexSF = sfVert;
2898   else {ierr = PetscSFDestroy(&sfVert);CHKERRQ(ierr);}
2899   PetscFunctionReturn(0);
2900 }
2901 
2902 /*
2903   This takes as input the common mesh generator output, a list of the vertices for each cell
2904 */
2905 PetscErrorCode DMPlexBuildFromCellList_Internal(DM dm, PetscInt spaceDim, PetscInt numCells, PetscInt numVertices, PetscInt numCorners, const int cells[], PetscBool invertCells)
2906 {
2907   PetscInt      *cone, c, p;
2908   PetscErrorCode ierr;
2909 
2910   PetscFunctionBegin;
2911   ierr = PetscLogEventBegin(DMPLEX_CreateFromCellList,dm,0,0,0);CHKERRQ(ierr);
2912   ierr = DMPlexSetChart(dm, 0, numCells+numVertices);CHKERRQ(ierr);
2913   for (c = 0; c < numCells; ++c) {
2914     ierr = DMPlexSetConeSize(dm, c, numCorners);CHKERRQ(ierr);
2915   }
2916   ierr = DMSetUp(dm);CHKERRQ(ierr);
2917   ierr = DMGetWorkArray(dm, numCorners, MPIU_INT, &cone);CHKERRQ(ierr);
2918   for (c = 0; c < numCells; ++c) {
2919     for (p = 0; p < numCorners; ++p) {
2920       cone[p] = cells[c*numCorners+p]+numCells;
2921     }
2922     if (invertCells) { ierr = DMPlexInvertCell_Internal(spaceDim, numCorners, cone);CHKERRQ(ierr); }
2923     ierr = DMPlexSetCone(dm, c, cone);CHKERRQ(ierr);
2924   }
2925   ierr = DMRestoreWorkArray(dm, numCorners, MPIU_INT, &cone);CHKERRQ(ierr);
2926   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
2927   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
2928   ierr = PetscLogEventEnd(DMPLEX_CreateFromCellList,dm,0,0,0);CHKERRQ(ierr);
2929   PetscFunctionReturn(0);
2930 }
2931 
2932 /*
2933   This takes as input the coordinates for each vertex
2934 */
2935 PetscErrorCode DMPlexBuildCoordinates_Internal(DM dm, PetscInt spaceDim, PetscInt numCells, PetscInt numVertices, const double vertexCoords[])
2936 {
2937   PetscSection   coordSection;
2938   Vec            coordinates;
2939   DM             cdm;
2940   PetscScalar   *coords;
2941   PetscInt       v, d;
2942   PetscErrorCode ierr;
2943 
2944   PetscFunctionBegin;
2945   ierr = PetscLogEventBegin(DMPLEX_CreateFromCellList_Coordinates,dm,0,0,0);CHKERRQ(ierr);
2946   ierr = DMSetCoordinateDim(dm, spaceDim);CHKERRQ(ierr);
2947   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
2948   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
2949   ierr = PetscSectionSetFieldComponents(coordSection, 0, spaceDim);CHKERRQ(ierr);
2950   ierr = PetscSectionSetChart(coordSection, numCells, numCells + numVertices);CHKERRQ(ierr);
2951   for (v = numCells; v < numCells+numVertices; ++v) {
2952     ierr = PetscSectionSetDof(coordSection, v, spaceDim);CHKERRQ(ierr);
2953     ierr = PetscSectionSetFieldDof(coordSection, v, 0, spaceDim);CHKERRQ(ierr);
2954   }
2955   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
2956 
2957   ierr = DMGetCoordinateDM(dm, &cdm);CHKERRQ(ierr);
2958   ierr = DMCreateLocalVector(cdm, &coordinates);CHKERRQ(ierr);
2959   ierr = VecSetBlockSize(coordinates, spaceDim);CHKERRQ(ierr);
2960   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
2961   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
2962   for (v = 0; v < numVertices; ++v) {
2963     for (d = 0; d < spaceDim; ++d) {
2964       coords[v*spaceDim+d] = vertexCoords[v*spaceDim+d];
2965     }
2966   }
2967   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
2968   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
2969   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
2970   ierr = PetscLogEventEnd(DMPLEX_CreateFromCellList_Coordinates,dm,0,0,0);CHKERRQ(ierr);
2971   PetscFunctionReturn(0);
2972 }
2973 
2974 /*@
2975   DMPlexCreateFromCellList - This takes as input common mesh generator output, a list of the vertices for each cell, and produces a DM
2976 
2977   Input Parameters:
2978 + comm - The communicator
2979 . dim - The topological dimension of the mesh
2980 . numCells - The number of cells
2981 . numVertices - The number of vertices
2982 . numCorners - The number of vertices for each cell
2983 . interpolate - Flag indicating that intermediate mesh entities (faces, edges) should be created automatically
2984 . cells - An array of numCells*numCorners numbers, the vertices for each cell
2985 . spaceDim - The spatial dimension used for coordinates
2986 - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex
2987 
2988   Output Parameter:
2989 . dm - The DM
2990 
2991   Note: Two triangles sharing a face
2992 $
2993 $        2
2994 $      / | \
2995 $     /  |  \
2996 $    /   |   \
2997 $   0  0 | 1  3
2998 $    \   |   /
2999 $     \  |  /
3000 $      \ | /
3001 $        1
3002 would have input
3003 $  numCells = 2, numVertices = 4
3004 $  cells = [0 1 2  1 3 2]
3005 $
3006 which would result in the DMPlex
3007 $
3008 $        4
3009 $      / | \
3010 $     /  |  \
3011 $    /   |   \
3012 $   2  0 | 1  5
3013 $    \   |   /
3014 $     \  |  /
3015 $      \ | /
3016 $        3
3017 
3018   Level: beginner
3019 
3020 .seealso: DMPlexCreateFromDAG(), DMPlexCreate()
3021 @*/
3022 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)
3023 {
3024   PetscErrorCode ierr;
3025 
3026   PetscFunctionBegin;
3027   if (!dim) SETERRQ(comm, PETSC_ERR_ARG_OUTOFRANGE, "This is not appropriate for 0-dimensional meshes. Consider either creating the DM using DMPlexCreateFromDAG(), by hand, or using DMSwarm.");
3028   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
3029   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
3030   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
3031   ierr = DMPlexBuildFromCellList_Internal(*dm, spaceDim, numCells, numVertices, numCorners, cells, PETSC_FALSE);CHKERRQ(ierr);
3032   if (interpolate) {
3033     DM idm;
3034 
3035     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
3036     ierr = DMDestroy(dm);CHKERRQ(ierr);
3037     *dm  = idm;
3038   }
3039   ierr = DMPlexBuildCoordinates_Internal(*dm, spaceDim, numCells, numVertices, vertexCoords);CHKERRQ(ierr);
3040   PetscFunctionReturn(0);
3041 }
3042 
3043 /*@
3044   DMPlexCreateFromDAG - This takes as input the adjacency-list representation of the Directed Acyclic Graph (Hasse Diagram) encoding a mesh, and produces a DM
3045 
3046   Input Parameters:
3047 + dm - The empty DM object, usually from DMCreate() and DMSetDimension()
3048 . depth - The depth of the DAG
3049 . numPoints - Array of size depth + 1 containing the number of points at each depth
3050 . coneSize - The cone size of each point
3051 . cones - The concatenation of the cone points for each point, the cone list must be oriented correctly for each point
3052 . coneOrientations - The orientation of each cone point
3053 - vertexCoords - An array of numPoints[0]*spacedim numbers representing the coordinates of each vertex, with spacedim the value set via DMSetCoordinateDim()
3054 
3055   Output Parameter:
3056 . dm - The DM
3057 
3058   Note: Two triangles sharing a face would have input
3059 $  depth = 1, numPoints = [4 2], coneSize = [3 3 0 0 0 0]
3060 $  cones = [2 3 4  3 5 4], coneOrientations = [0 0 0  0 0 0]
3061 $ vertexCoords = [-1.0 0.0  0.0 -1.0  0.0 1.0  1.0 0.0]
3062 $
3063 which would result in the DMPlex
3064 $
3065 $        4
3066 $      / | \
3067 $     /  |  \
3068 $    /   |   \
3069 $   2  0 | 1  5
3070 $    \   |   /
3071 $     \  |  /
3072 $      \ | /
3073 $        3
3074 $
3075 $ Notice that all points are numbered consecutively, unlikely DMPlexCreateFromCellList()
3076 
3077   Level: advanced
3078 
3079 .seealso: DMPlexCreateFromCellList(), DMPlexCreate()
3080 @*/
3081 PetscErrorCode DMPlexCreateFromDAG(DM dm, PetscInt depth, const PetscInt numPoints[], const PetscInt coneSize[], const PetscInt cones[], const PetscInt coneOrientations[], const PetscScalar vertexCoords[])
3082 {
3083   Vec            coordinates;
3084   PetscSection   coordSection;
3085   PetscScalar    *coords;
3086   PetscInt       coordSize, firstVertex = -1, pStart = 0, pEnd = 0, p, v, dim, dimEmbed, d, off;
3087   PetscErrorCode ierr;
3088 
3089   PetscFunctionBegin;
3090   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
3091   ierr = DMGetCoordinateDim(dm, &dimEmbed);CHKERRQ(ierr);
3092   if (dimEmbed < dim) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Embedding dimension %d cannot be less than intrinsic dimension %d",dimEmbed,dim);
3093   for (d = 0; d <= depth; ++d) pEnd += numPoints[d];
3094   ierr = DMPlexSetChart(dm, pStart, pEnd);CHKERRQ(ierr);
3095   for (p = pStart; p < pEnd; ++p) {
3096     ierr = DMPlexSetConeSize(dm, p, coneSize[p-pStart]);CHKERRQ(ierr);
3097     if (firstVertex < 0 && !coneSize[p - pStart]) {
3098       firstVertex = p - pStart;
3099     }
3100   }
3101   if (firstVertex < 0 && numPoints[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Expected %d vertices but could not find any", numPoints[0]);
3102   ierr = DMSetUp(dm);CHKERRQ(ierr); /* Allocate space for cones */
3103   for (p = pStart, off = 0; p < pEnd; off += coneSize[p-pStart], ++p) {
3104     ierr = DMPlexSetCone(dm, p, &cones[off]);CHKERRQ(ierr);
3105     ierr = DMPlexSetConeOrientation(dm, p, &coneOrientations[off]);CHKERRQ(ierr);
3106   }
3107   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
3108   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
3109   /* Build coordinates */
3110   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
3111   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
3112   ierr = PetscSectionSetFieldComponents(coordSection, 0, dimEmbed);CHKERRQ(ierr);
3113   ierr = PetscSectionSetChart(coordSection, firstVertex, firstVertex+numPoints[0]);CHKERRQ(ierr);
3114   for (v = firstVertex; v < firstVertex+numPoints[0]; ++v) {
3115     ierr = PetscSectionSetDof(coordSection, v, dimEmbed);CHKERRQ(ierr);
3116     ierr = PetscSectionSetFieldDof(coordSection, v, 0, dimEmbed);CHKERRQ(ierr);
3117   }
3118   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
3119   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
3120   ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
3121   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
3122   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
3123   ierr = VecSetBlockSize(coordinates, dimEmbed);CHKERRQ(ierr);
3124   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
3125   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
3126   for (v = 0; v < numPoints[0]; ++v) {
3127     PetscInt off;
3128 
3129     ierr = PetscSectionGetOffset(coordSection, v+firstVertex, &off);CHKERRQ(ierr);
3130     for (d = 0; d < dimEmbed; ++d) {
3131       coords[off+d] = vertexCoords[v*dimEmbed+d];
3132     }
3133   }
3134   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
3135   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
3136   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
3137   PetscFunctionReturn(0);
3138 }
3139 
3140 /*@C
3141   DMPlexCreateCellVertexFromFile - Create a DMPlex mesh from a simple cell-vertex file.
3142 
3143 + comm        - The MPI communicator
3144 . filename    - Name of the .dat file
3145 - interpolate - Create faces and edges in the mesh
3146 
3147   Output Parameter:
3148 . dm  - The DM object representing the mesh
3149 
3150   Note: The format is the simplest possible:
3151 $ Ne
3152 $ v0 v1 ... vk
3153 $ Nv
3154 $ x y z marker
3155 
3156   Level: beginner
3157 
3158 .seealso: DMPlexCreateFromFile(), DMPlexCreateMedFromFile(), DMPlexCreateGmsh(), DMPlexCreate()
3159 @*/
3160 PetscErrorCode DMPlexCreateCellVertexFromFile(MPI_Comm comm, const char filename[], PetscBool interpolate, DM *dm)
3161 {
3162   DMLabel         marker;
3163   PetscViewer     viewer;
3164   Vec             coordinates;
3165   PetscSection    coordSection;
3166   PetscScalar    *coords;
3167   char            line[PETSC_MAX_PATH_LEN];
3168   PetscInt        dim = 3, cdim = 3, coordSize, v, c, d;
3169   PetscMPIInt     rank;
3170   int             snum, Nv, Nc;
3171   PetscErrorCode  ierr;
3172 
3173   PetscFunctionBegin;
3174   ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
3175   ierr = PetscViewerCreate(comm, &viewer);CHKERRQ(ierr);
3176   ierr = PetscViewerSetType(viewer, PETSCVIEWERASCII);CHKERRQ(ierr);
3177   ierr = PetscViewerFileSetMode(viewer, FILE_MODE_READ);CHKERRQ(ierr);
3178   ierr = PetscViewerFileSetName(viewer, filename);CHKERRQ(ierr);
3179   if (!rank) {
3180     ierr = PetscViewerRead(viewer, line, 2, NULL, PETSC_STRING);CHKERRQ(ierr);
3181     snum = sscanf(line, "%d %d", &Nc, &Nv);
3182     if (snum != 2) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unable to parse cell-vertex file: %s", line);
3183   } else {
3184     Nc = Nv = 0;
3185   }
3186   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
3187   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
3188   ierr = DMPlexSetChart(*dm, 0, Nc+Nv);CHKERRQ(ierr);
3189   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
3190   ierr = DMSetCoordinateDim(*dm, cdim);CHKERRQ(ierr);
3191   /* Read topology */
3192   if (!rank) {
3193     PetscInt cone[8], corners = 8;
3194     int      vbuf[8], v;
3195 
3196     for (c = 0; c < Nc; ++c) {ierr = DMPlexSetConeSize(*dm, c, corners);CHKERRQ(ierr);}
3197     ierr = DMSetUp(*dm);CHKERRQ(ierr);
3198     for (c = 0; c < Nc; ++c) {
3199       ierr = PetscViewerRead(viewer, line, corners, NULL, PETSC_STRING);CHKERRQ(ierr);
3200       snum = sscanf(line, "%d %d %d %d %d %d %d %d", &vbuf[0], &vbuf[1], &vbuf[2], &vbuf[3], &vbuf[4], &vbuf[5], &vbuf[6], &vbuf[7]);
3201       if (snum != corners) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unable to parse cell-vertex file: %s", line);
3202       for (v = 0; v < corners; ++v) cone[v] = vbuf[v] + Nc;
3203       /* Hexahedra are inverted */
3204       {
3205         PetscInt tmp = cone[1];
3206         cone[1] = cone[3];
3207         cone[3] = tmp;
3208       }
3209       ierr = DMPlexSetCone(*dm, c, cone);CHKERRQ(ierr);
3210     }
3211   }
3212   ierr = DMPlexSymmetrize(*dm);CHKERRQ(ierr);
3213   ierr = DMPlexStratify(*dm);CHKERRQ(ierr);
3214   /* Read coordinates */
3215   ierr = DMGetCoordinateSection(*dm, &coordSection);CHKERRQ(ierr);
3216   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
3217   ierr = PetscSectionSetFieldComponents(coordSection, 0, cdim);CHKERRQ(ierr);
3218   ierr = PetscSectionSetChart(coordSection, Nc, Nc + Nv);CHKERRQ(ierr);
3219   for (v = Nc; v < Nc+Nv; ++v) {
3220     ierr = PetscSectionSetDof(coordSection, v, cdim);CHKERRQ(ierr);
3221     ierr = PetscSectionSetFieldDof(coordSection, v, 0, cdim);CHKERRQ(ierr);
3222   }
3223   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
3224   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
3225   ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
3226   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
3227   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
3228   ierr = VecSetBlockSize(coordinates, cdim);CHKERRQ(ierr);
3229   ierr = VecSetType(coordinates, VECSTANDARD);CHKERRQ(ierr);
3230   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
3231   if (!rank) {
3232     double x[3];
3233     int    val;
3234 
3235     ierr = DMCreateLabel(*dm, "marker");CHKERRQ(ierr);
3236     ierr = DMGetLabel(*dm, "marker", &marker);CHKERRQ(ierr);
3237     for (v = 0; v < Nv; ++v) {
3238       ierr = PetscViewerRead(viewer, line, 4, NULL, PETSC_STRING);CHKERRQ(ierr);
3239       snum = sscanf(line, "%lg %lg %lg %d", &x[0], &x[1], &x[2], &val);
3240       if (snum != 4) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unable to parse cell-vertex file: %s", line);
3241       for (d = 0; d < cdim; ++d) coords[v*cdim+d] = x[d];
3242       if (val) {ierr = DMLabelSetValue(marker, v+Nc, val);CHKERRQ(ierr);}
3243     }
3244   }
3245   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
3246   ierr = DMSetCoordinatesLocal(*dm, coordinates);CHKERRQ(ierr);
3247   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
3248   ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
3249   if (interpolate) {
3250     DM      idm;
3251     DMLabel bdlabel;
3252 
3253     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
3254     ierr = DMDestroy(dm);CHKERRQ(ierr);
3255     *dm  = idm;
3256 
3257     ierr = DMGetLabel(*dm, "marker", &bdlabel);CHKERRQ(ierr);
3258     ierr = DMPlexMarkBoundaryFaces(*dm, PETSC_DETERMINE, bdlabel);CHKERRQ(ierr);
3259     ierr = DMPlexLabelComplete(*dm, bdlabel);CHKERRQ(ierr);
3260   }
3261   PetscFunctionReturn(0);
3262 }
3263 
3264 /*@C
3265   DMPlexCreateFromFile - This takes a filename and produces a DM
3266 
3267   Input Parameters:
3268 + comm - The communicator
3269 . filename - A file name
3270 - interpolate - Flag to create intermediate mesh pieces (edges, faces)
3271 
3272   Output Parameter:
3273 . dm - The DM
3274 
3275   Options Database Keys:
3276 . -dm_plex_create_from_hdf5_xdmf - use the PETSC_VIEWER_HDF5_XDMF format for reading HDF5
3277 
3278   Use -dm_plex_create_ prefix to pass options to the internal PetscViewer, e.g.
3279 $ -dm_plex_create_viewer_hdf5_collective
3280 
3281   Level: beginner
3282 
3283 .seealso: DMPlexCreateFromDAG(), DMPlexCreateFromCellList(), DMPlexCreate()
3284 @*/
3285 PetscErrorCode DMPlexCreateFromFile(MPI_Comm comm, const char filename[], PetscBool interpolate, DM *dm)
3286 {
3287   const char    *extGmsh    = ".msh";
3288   const char    *extGmsh2   = ".msh2";
3289   const char    *extGmsh4   = ".msh4";
3290   const char    *extCGNS    = ".cgns";
3291   const char    *extExodus  = ".exo";
3292   const char    *extGenesis = ".gen";
3293   const char    *extFluent  = ".cas";
3294   const char    *extHDF5    = ".h5";
3295   const char    *extMed     = ".med";
3296   const char    *extPLY     = ".ply";
3297   const char    *extCV      = ".dat";
3298   size_t         len;
3299   PetscBool      isGmsh, isGmsh2, isGmsh4, isCGNS, isExodus, isGenesis, isFluent, isHDF5, isMed, isPLY, isCV;
3300   PetscMPIInt    rank;
3301   PetscErrorCode ierr;
3302 
3303   PetscFunctionBegin;
3304   PetscValidCharPointer(filename, 2);
3305   PetscValidPointer(dm, 4);
3306   ierr = DMInitializePackage();CHKERRQ(ierr);
3307   ierr = PetscLogEventBegin(DMPLEX_CreateFromFile,0,0,0,0);CHKERRQ(ierr);
3308   ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
3309   ierr = PetscStrlen(filename, &len);CHKERRQ(ierr);
3310   if (!len) SETERRQ(comm, PETSC_ERR_ARG_WRONG, "Filename must be a valid path");
3311   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extGmsh,    4, &isGmsh);CHKERRQ(ierr);
3312   ierr = PetscStrncmp(&filename[PetscMax(0,len-5)], extGmsh2,   5, &isGmsh2);CHKERRQ(ierr);
3313   ierr = PetscStrncmp(&filename[PetscMax(0,len-5)], extGmsh4,   5, &isGmsh4);CHKERRQ(ierr);
3314   ierr = PetscStrncmp(&filename[PetscMax(0,len-5)], extCGNS,    5, &isCGNS);CHKERRQ(ierr);
3315   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extExodus,  4, &isExodus);CHKERRQ(ierr);
3316   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extGenesis, 4, &isGenesis);CHKERRQ(ierr);
3317   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extFluent,  4, &isFluent);CHKERRQ(ierr);
3318   ierr = PetscStrncmp(&filename[PetscMax(0,len-3)], extHDF5,    3, &isHDF5);CHKERRQ(ierr);
3319   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extMed,     4, &isMed);CHKERRQ(ierr);
3320   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extPLY,     4, &isPLY);CHKERRQ(ierr);
3321   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extCV,      4, &isCV);CHKERRQ(ierr);
3322   if (isGmsh || isGmsh2 || isGmsh4) {
3323     ierr = DMPlexCreateGmshFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
3324   } else if (isCGNS) {
3325     ierr = DMPlexCreateCGNSFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
3326   } else if (isExodus || isGenesis) {
3327     ierr = DMPlexCreateExodusFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
3328   } else if (isFluent) {
3329     ierr = DMPlexCreateFluentFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
3330   } else if (isHDF5) {
3331     PetscBool      load_hdf5_xdmf = PETSC_FALSE;
3332     PetscViewer viewer;
3333 
3334     /* PETSC_VIEWER_HDF5_XDMF is used if the filename ends with .xdmf.h5, or if -dm_plex_create_from_hdf5_xdmf option is present */
3335     ierr = PetscStrncmp(&filename[PetscMax(0,len-8)], ".xdmf",  5, &load_hdf5_xdmf);CHKERRQ(ierr);
3336     ierr = PetscOptionsGetBool(NULL, NULL, "-dm_plex_create_from_hdf5_xdmf", &load_hdf5_xdmf, NULL);CHKERRQ(ierr);
3337     ierr = PetscViewerCreate(comm, &viewer);CHKERRQ(ierr);
3338     ierr = PetscViewerSetType(viewer, PETSCVIEWERHDF5);CHKERRQ(ierr);
3339     ierr = PetscViewerSetOptionsPrefix(viewer, "dm_plex_create_");CHKERRQ(ierr);
3340     ierr = PetscViewerSetFromOptions(viewer);CHKERRQ(ierr);
3341     ierr = PetscViewerFileSetMode(viewer, FILE_MODE_READ);CHKERRQ(ierr);
3342     ierr = PetscViewerFileSetName(viewer, filename);CHKERRQ(ierr);
3343     ierr = DMCreate(comm, dm);CHKERRQ(ierr);
3344     ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
3345     if (load_hdf5_xdmf) {ierr = PetscViewerPushFormat(viewer, PETSC_VIEWER_HDF5_XDMF);CHKERRQ(ierr);}
3346     ierr = DMLoad(*dm, viewer);CHKERRQ(ierr);
3347     if (load_hdf5_xdmf) {ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);}
3348     ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
3349 
3350     if (interpolate) {
3351       DM idm;
3352 
3353       ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
3354       ierr = DMDestroy(dm);CHKERRQ(ierr);
3355       *dm  = idm;
3356     }
3357   } else if (isMed) {
3358     ierr = DMPlexCreateMedFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
3359   } else if (isPLY) {
3360     ierr = DMPlexCreatePLYFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
3361   } else if (isCV) {
3362     ierr = DMPlexCreateCellVertexFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
3363   } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cannot load file %s: unrecognized extension", filename);
3364   ierr = PetscLogEventEnd(DMPLEX_CreateFromFile,0,0,0,0);CHKERRQ(ierr);
3365   PetscFunctionReturn(0);
3366 }
3367 
3368 /*@
3369   DMPlexCreateReferenceCellByType - Create a DMPLEX with the appropriate FEM reference cell
3370 
3371   Collective
3372 
3373   Input Parameters:
3374 + comm - The communicator
3375 - ct   - The cell type of the reference cell
3376 
3377   Output Parameter:
3378 . refdm - The reference cell
3379 
3380   Level: intermediate
3381 
3382 .seealso: DMPlexCreateReferenceCell(), DMPlexCreateBoxMesh()
3383 @*/
3384 PetscErrorCode DMPlexCreateReferenceCellByType(MPI_Comm comm, DMPolytopeType ct, DM *refdm)
3385 {
3386   DM             rdm;
3387   Vec            coords;
3388   PetscErrorCode ierr;
3389 
3390   PetscFunctionBegin;
3391   ierr = DMCreate(comm, &rdm);CHKERRQ(ierr);
3392   ierr = DMSetType(rdm, DMPLEX);CHKERRQ(ierr);
3393   switch (ct) {
3394     case DM_POLYTOPE_POINT:
3395     {
3396       PetscInt    numPoints[1]        = {1};
3397       PetscInt    coneSize[1]         = {0};
3398       PetscInt    cones[1]            = {0};
3399       PetscInt    coneOrientations[1] = {0};
3400       PetscScalar vertexCoords[1]     = {0.0};
3401 
3402       ierr = DMSetDimension(rdm, 0);CHKERRQ(ierr);
3403       ierr = DMPlexCreateFromDAG(rdm, 0, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
3404     }
3405     break;
3406     case DM_POLYTOPE_SEGMENT:
3407     {
3408       PetscInt    numPoints[2]        = {2, 1};
3409       PetscInt    coneSize[3]         = {2, 0, 0};
3410       PetscInt    cones[2]            = {1, 2};
3411       PetscInt    coneOrientations[2] = {0, 0};
3412       PetscScalar vertexCoords[2]     = {-1.0,  1.0};
3413 
3414       ierr = DMSetDimension(rdm, 1);CHKERRQ(ierr);
3415       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
3416     }
3417     break;
3418     case DM_POLYTOPE_TRIANGLE:
3419     {
3420       PetscInt    numPoints[2]        = {3, 1};
3421       PetscInt    coneSize[4]         = {3, 0, 0, 0};
3422       PetscInt    cones[3]            = {1, 2, 3};
3423       PetscInt    coneOrientations[3] = {0, 0, 0};
3424       PetscScalar vertexCoords[6]     = {-1.0, -1.0,  1.0, -1.0,  -1.0, 1.0};
3425 
3426       ierr = DMSetDimension(rdm, 2);CHKERRQ(ierr);
3427       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
3428     }
3429     break;
3430     case DM_POLYTOPE_QUADRILATERAL:
3431     {
3432       PetscInt    numPoints[2]        = {4, 1};
3433       PetscInt    coneSize[5]         = {4, 0, 0, 0, 0};
3434       PetscInt    cones[4]            = {1, 2, 3, 4};
3435       PetscInt    coneOrientations[4] = {0, 0, 0, 0};
3436       PetscScalar vertexCoords[8]     = {-1.0, -1.0,  1.0, -1.0,  1.0, 1.0,  -1.0, 1.0};
3437 
3438       ierr = DMSetDimension(rdm, 2);CHKERRQ(ierr);
3439       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
3440     }
3441     break;
3442     case DM_POLYTOPE_SEG_PRISM_TENSOR:
3443     {
3444       PetscInt    numPoints[2]        = {4, 1};
3445       PetscInt    coneSize[5]         = {4, 0, 0, 0, 0};
3446       PetscInt    cones[4]            = {1, 2, 3, 4};
3447       PetscInt    coneOrientations[4] = {0, 0, 0, 0};
3448       PetscScalar vertexCoords[8]     = {-1.0, -1.0,  1.0, -1.0,  -1.0, 1.0,  1.0, 1.0};
3449 
3450       ierr = DMSetDimension(rdm, 2);CHKERRQ(ierr);
3451       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
3452     }
3453     break;
3454     case DM_POLYTOPE_TETRAHEDRON:
3455     {
3456       PetscInt    numPoints[2]        = {4, 1};
3457       PetscInt    coneSize[5]         = {4, 0, 0, 0, 0};
3458       PetscInt    cones[4]            = {1, 3, 2, 4};
3459       PetscInt    coneOrientations[4] = {0, 0, 0, 0};
3460       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};
3461 
3462       ierr = DMSetDimension(rdm, 3);CHKERRQ(ierr);
3463       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
3464     }
3465     break;
3466     case DM_POLYTOPE_HEXAHEDRON:
3467     {
3468       PetscInt    numPoints[2]        = {8, 1};
3469       PetscInt    coneSize[9]         = {8, 0, 0, 0, 0, 0, 0, 0, 0};
3470       PetscInt    cones[8]            = {1, 4, 3, 2, 5, 6, 7, 8};
3471       PetscInt    coneOrientations[8] = {0, 0, 0, 0, 0, 0, 0, 0};
3472       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,
3473                                          -1.0, -1.0,  1.0,  1.0, -1.0,  1.0,  1.0, 1.0,  1.0,  -1.0, 1.0,  1.0};
3474 
3475       ierr = DMSetDimension(rdm, 3);CHKERRQ(ierr);
3476       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
3477     }
3478     break;
3479     case DM_POLYTOPE_TRI_PRISM:
3480     {
3481       PetscInt    numPoints[2]        = {6, 1};
3482       PetscInt    coneSize[7]         = {6, 0, 0, 0, 0, 0, 0};
3483       PetscInt    cones[6]            = {1, 3, 2, 4, 5, 6};
3484       PetscInt    coneOrientations[6] = {0, 0, 0, 0, 0, 0};
3485       PetscScalar vertexCoords[18]    = {-1.0, -1.0, -1.0,  1.0, -1.0, -1.0,  -1.0, 1.0, -1.0,
3486                                          -1.0, -1.0,  1.0,  1.0, -1.0,  1.0,  -1.0, 1.0,  1.0};
3487 
3488       ierr = DMSetDimension(rdm, 3);CHKERRQ(ierr);
3489       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
3490     }
3491     break;
3492     case DM_POLYTOPE_TRI_PRISM_TENSOR:
3493     {
3494       PetscInt    numPoints[2]        = {6, 1};
3495       PetscInt    coneSize[7]         = {6, 0, 0, 0, 0, 0, 0};
3496       PetscInt    cones[6]            = {1, 2, 3, 4, 5, 6};
3497       PetscInt    coneOrientations[6] = {0, 0, 0, 0, 0, 0};
3498       PetscScalar vertexCoords[18]    = {-1.0, -1.0, -1.0,  1.0, -1.0, -1.0,  -1.0, 1.0, -1.0,
3499                                          -1.0, -1.0,  1.0,  1.0, -1.0,  1.0,  -1.0, 1.0,  1.0};
3500 
3501       ierr = DMSetDimension(rdm, 3);CHKERRQ(ierr);
3502       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
3503     }
3504     break;
3505     case DM_POLYTOPE_QUAD_PRISM_TENSOR:
3506     {
3507       PetscInt    numPoints[2]        = {8, 1};
3508       PetscInt    coneSize[9]         = {8, 0, 0, 0, 0, 0, 0, 0, 0};
3509       PetscInt    cones[8]            = {1, 2, 3, 4, 5, 6, 7, 8};
3510       PetscInt    coneOrientations[8] = {0, 0, 0, 0, 0, 0, 0, 0};
3511       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,
3512                                          -1.0, -1.0,  1.0,  1.0, -1.0,  1.0,  1.0, 1.0,  1.0,  -1.0, 1.0,  1.0};
3513 
3514       ierr = DMSetDimension(rdm, 3);CHKERRQ(ierr);
3515       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
3516     }
3517     break;
3518     default: SETERRQ1(comm, PETSC_ERR_ARG_WRONG, "Cannot create reference cell for cell type %s", DMPolytopeTypes[ct]);
3519   }
3520   {
3521     PetscInt Nv, v;
3522 
3523     /* Must create the celltype label here so that we do not automatically try to compute the types */
3524     ierr = DMCreateLabel(rdm, "celltype");CHKERRQ(ierr);
3525     ierr = DMPlexSetCellType(rdm, 0, ct);CHKERRQ(ierr);
3526     ierr = DMPlexGetChart(rdm, NULL, &Nv);CHKERRQ(ierr);
3527     for (v = 1; v < Nv; ++v) {ierr = DMPlexSetCellType(rdm, v, DM_POLYTOPE_POINT);CHKERRQ(ierr);}
3528   }
3529   ierr = DMPlexInterpolate(rdm, refdm);CHKERRQ(ierr);
3530   if (rdm->coordinateDM) {
3531     DM           ncdm;
3532     PetscSection cs;
3533     PetscInt     pEnd = -1;
3534 
3535     ierr = DMGetLocalSection(rdm->coordinateDM, &cs);CHKERRQ(ierr);
3536     if (cs) {ierr = PetscSectionGetChart(cs, NULL, &pEnd);CHKERRQ(ierr);}
3537     if (pEnd >= 0) {
3538       ierr = DMClone(*refdm, &ncdm);CHKERRQ(ierr);
3539       ierr = DMCopyDisc(rdm->coordinateDM, ncdm);CHKERRQ(ierr);
3540       ierr = DMSetLocalSection(ncdm, cs);CHKERRQ(ierr);
3541       ierr = DMSetCoordinateDM(*refdm, ncdm);CHKERRQ(ierr);
3542       ierr = DMDestroy(&ncdm);CHKERRQ(ierr);
3543     }
3544   }
3545   ierr = DMGetCoordinatesLocal(rdm, &coords);CHKERRQ(ierr);
3546   if (coords) {
3547     ierr = DMSetCoordinatesLocal(*refdm, coords);CHKERRQ(ierr);
3548   } else {
3549     ierr = DMGetCoordinates(rdm, &coords);CHKERRQ(ierr);
3550     if (coords) {ierr = DMSetCoordinates(*refdm, coords);CHKERRQ(ierr);}
3551   }
3552   ierr = DMDestroy(&rdm);CHKERRQ(ierr);
3553   PetscFunctionReturn(0);
3554 }
3555 
3556 /*@
3557   DMPlexCreateReferenceCell - Create a DMPLEX with the appropriate FEM reference cell
3558 
3559   Collective
3560 
3561   Input Parameters:
3562 + comm    - The communicator
3563 . dim     - The spatial dimension
3564 - simplex - Flag for simplex, otherwise use a tensor-product cell
3565 
3566   Output Parameter:
3567 . refdm - The reference cell
3568 
3569   Level: intermediate
3570 
3571 .seealso: DMPlexCreateReferenceCellByType(), DMPlexCreateBoxMesh()
3572 @*/
3573 PetscErrorCode DMPlexCreateReferenceCell(MPI_Comm comm, PetscInt dim, PetscBool simplex, DM *refdm)
3574 {
3575   PetscErrorCode ierr;
3576 
3577   PetscFunctionBeginUser;
3578   switch (dim) {
3579   case 0: ierr = DMPlexCreateReferenceCellByType(comm, DM_POLYTOPE_POINT, refdm);CHKERRQ(ierr);break;
3580   case 1: ierr = DMPlexCreateReferenceCellByType(comm, DM_POLYTOPE_SEGMENT, refdm);CHKERRQ(ierr);break;
3581   case 2:
3582     if (simplex) {ierr = DMPlexCreateReferenceCellByType(comm, DM_POLYTOPE_TRIANGLE, refdm);CHKERRQ(ierr);}
3583     else         {ierr = DMPlexCreateReferenceCellByType(comm, DM_POLYTOPE_QUADRILATERAL, refdm);CHKERRQ(ierr);}
3584     break;
3585   case 3:
3586     if (simplex) {ierr = DMPlexCreateReferenceCellByType(comm, DM_POLYTOPE_TETRAHEDRON, refdm);CHKERRQ(ierr);}
3587     else         {ierr = DMPlexCreateReferenceCellByType(comm, DM_POLYTOPE_HEXAHEDRON, refdm);CHKERRQ(ierr);}
3588     break;
3589   default:
3590     SETERRQ1(comm, PETSC_ERR_ARG_WRONG, "Cannot create reference cell for dimension %d", dim);
3591   }
3592   PetscFunctionReturn(0);
3593 }
3594