xref: /petsc/src/dm/impls/plex/plexcreate.c (revision 04679c46d5c988d0c11828c1a1f65f37dca414a7)
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 
1008   Note: Here is the numbering returned for 2 faces in each direction for tensor cells:
1009 $ 10---17---11---18----12
1010 $  |         |         |
1011 $  |         |         |
1012 $ 20    2   22    3    24
1013 $  |         |         |
1014 $  |         |         |
1015 $  7---15----8---16----9
1016 $  |         |         |
1017 $  |         |         |
1018 $ 19    0   21    1   23
1019 $  |         |         |
1020 $  |         |         |
1021 $  4---13----5---14----6
1022 
1023 and for simplicial cells
1024 
1025 $ 14----8---15----9----16
1026 $  |\     5  |\      7 |
1027 $  | \       | \       |
1028 $ 13   2    14    3    15
1029 $  | 4   \   | 6   \   |
1030 $  |       \ |       \ |
1031 $ 11----6---12----7----13
1032 $  |\        |\        |
1033 $  | \    1  | \     3 |
1034 $ 10   0    11    1    12
1035 $  | 0   \   | 2   \   |
1036 $  |       \ |       \ |
1037 $  8----4----9----5----10
1038 
1039   Level: beginner
1040 
1041 .seealso: DMPlexCreateFromFile(), DMPlexCreateHexCylinderMesh(), DMSetType(), DMCreate()
1042 @*/
1043 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)
1044 {
1045   PetscInt       fac[3] = {0, 0, 0};
1046   PetscReal      low[3] = {0, 0, 0};
1047   PetscReal      upp[3] = {1, 1, 1};
1048   DMBoundaryType bdt[3] = {DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE};
1049   PetscInt       i, n;
1050   PetscBool      flg;
1051   PetscErrorCode ierr;
1052 
1053   PetscFunctionBegin;
1054   n    = 3;
1055   ierr = PetscOptionsGetIntArray(NULL, NULL, "-dm_plex_box_faces", fac, &n, &flg);CHKERRQ(ierr);
1056   for (i = 0; i < dim; ++i) fac[i] = faces ? faces[i] : (flg && i < n ? fac[i] : (dim == 1 ? 1 : 4-dim));
1057   if (lower) for (i = 0; i < dim; ++i) low[i] = lower[i];
1058   if (upper) for (i = 0; i < dim; ++i) upp[i] = upper[i];
1059   if (periodicity) for (i = 0; i < dim; ++i) bdt[i] = periodicity[i];
1060   /* Allow bounds to be specified from the command line */
1061   n    = 3;
1062   ierr = PetscOptionsGetRealArray(NULL, NULL, "-dm_plex_box_lower", low, &n, &flg);CHKERRQ(ierr);
1063   if (flg && (n != dim)) SETERRQ2(comm, PETSC_ERR_ARG_SIZ, "Lower box point had %D values, should have been %D", n, dim);
1064   n    = 3;
1065   ierr = PetscOptionsGetRealArray(NULL, NULL, "-dm_plex_box_upper", upp, &n, &flg);CHKERRQ(ierr);
1066   if (flg && (n != dim)) SETERRQ2(comm, PETSC_ERR_ARG_SIZ, "Upper box point had %D values, should have been %D", n, dim);
1067 
1068   if (dim == 1)      {ierr = DMPlexCreateLineMesh_Internal(comm, fac[0], low[0], upp[0], bdt[0], dm);CHKERRQ(ierr);}
1069   else if (simplex)  {ierr = DMPlexCreateBoxMesh_Simplex_Internal(comm, dim, fac, low, upp, bdt, interpolate, dm);CHKERRQ(ierr);}
1070   else               {ierr = DMPlexCreateBoxMesh_Tensor_Internal(comm, dim, fac, low, upp, bdt, interpolate, dm);CHKERRQ(ierr);}
1071   PetscFunctionReturn(0);
1072 }
1073 
1074 /*@
1075   DMPlexCreateWedgeBoxMesh - Creates a 3-D mesh tesselating the (x,y) plane and extruding in the third direction using wedge cells.
1076 
1077   Collective
1078 
1079   Input Parameters:
1080 + comm        - The communicator for the DM object
1081 . faces       - Number of faces per dimension, or NULL for (1, 1, 1)
1082 . lower       - The lower left corner, or NULL for (0, 0, 0)
1083 . upper       - The upper right corner, or NULL for (1, 1, 1)
1084 . periodicity - The boundary type for the X,Y,Z direction, or NULL for DM_BOUNDARY_NONE
1085 . ordExt      - If PETSC_TRUE, orders the extruded cells in the height first. Otherwise, orders the cell on the layers first
1086 - interpolate - Flag to create intermediate mesh pieces (edges, faces)
1087 
1088   Output Parameter:
1089 . dm  - The DM object
1090 
1091   Level: beginner
1092 
1093 .seealso: DMPlexCreateHexCylinderMesh(), DMPlexCreateWedgeCylinderMesh(), DMPlexExtrude(), DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
1094 @*/
1095 PetscErrorCode DMPlexCreateWedgeBoxMesh(MPI_Comm comm, const PetscInt faces[], const PetscReal lower[], const PetscReal upper[], const DMBoundaryType periodicity[], PetscBool ordExt, PetscBool interpolate, DM *dm)
1096 {
1097   DM             bdm, botdm;
1098   PetscInt       i;
1099   PetscInt       fac[3] = {0, 0, 0};
1100   PetscReal      low[3] = {0, 0, 0};
1101   PetscReal      upp[3] = {1, 1, 1};
1102   DMBoundaryType bdt[3] = {DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE};
1103   PetscErrorCode ierr;
1104 
1105   PetscFunctionBegin;
1106   for (i = 0; i < 3; ++i) fac[i] = faces ? (faces[i] > 0 ? faces[i] : 1) : 1;
1107   if (lower) for (i = 0; i < 3; ++i) low[i] = lower[i];
1108   if (upper) for (i = 0; i < 3; ++i) upp[i] = upper[i];
1109   if (periodicity) for (i = 0; i < 3; ++i) bdt[i] = periodicity[i];
1110   for (i = 0; i < 3; ++i) if (bdt[i] != DM_BOUNDARY_NONE) SETERRQ(comm, PETSC_ERR_SUP, "Periodicity not yet supported");
1111 
1112   ierr = DMCreate(comm, &bdm);CHKERRQ(ierr);
1113   ierr = DMSetType(bdm, DMPLEX);CHKERRQ(ierr);
1114   ierr = DMSetDimension(bdm, 1);CHKERRQ(ierr);
1115   ierr = DMSetCoordinateDim(bdm, 2);CHKERRQ(ierr);
1116   ierr = DMPlexCreateSquareBoundary(bdm, low, upp, fac);CHKERRQ(ierr);
1117   ierr = DMPlexGenerate(bdm, NULL, PETSC_FALSE, &botdm);CHKERRQ(ierr);
1118   ierr = DMDestroy(&bdm);CHKERRQ(ierr);
1119   ierr = DMPlexExtrude(botdm, fac[2], upp[2] - low[2], ordExt, interpolate, dm);CHKERRQ(ierr);
1120   if (low[2] != 0.0) {
1121     Vec         v;
1122     PetscScalar *x;
1123     PetscInt    cDim, n;
1124 
1125     ierr = DMGetCoordinatesLocal(*dm, &v);CHKERRQ(ierr);
1126     ierr = VecGetBlockSize(v, &cDim);CHKERRQ(ierr);
1127     ierr = VecGetLocalSize(v, &n);CHKERRQ(ierr);
1128     ierr = VecGetArray(v, &x);CHKERRQ(ierr);
1129     x   += cDim;
1130     for (i=0; i<n; i+=cDim) x[i] += low[2];
1131     ierr = VecRestoreArray(v,&x);CHKERRQ(ierr);
1132     ierr = DMSetCoordinatesLocal(*dm, v);CHKERRQ(ierr);
1133   }
1134   ierr = DMDestroy(&botdm);CHKERRQ(ierr);
1135   PetscFunctionReturn(0);
1136 }
1137 
1138 /*@
1139   DMPlexExtrude - Creates a (d+1)-D mesh by extruding a d-D mesh in the normal direction using prismatic cells.
1140 
1141   Collective on idm
1142 
1143   Input Parameters:
1144 + idm - The mesh to be extruted
1145 . layers - The number of layers
1146 . height - The height of the extruded layer
1147 . ordExt - If PETSC_TRUE, orders the extruded cells in the height first. Otherwise, orders the cell on the layers first
1148 - interpolate - Flag to create intermediate mesh pieces (edges, faces)
1149 
1150   Output Parameter:
1151 . dm  - The DM object
1152 
1153   Notes: The object created is an hybrid mesh, the vertex ordering in the cone of the cell is that of the prismatic cells
1154 
1155   Level: advanced
1156 
1157 .seealso: DMPlexCreateWedgeCylinderMesh(), DMPlexCreateWedgeBoxMesh(), DMPlexSetHybridBounds(), DMSetType(), DMCreate()
1158 @*/
1159 PetscErrorCode DMPlexExtrude(DM idm, PetscInt layers, PetscReal height, PetscBool ordExt, PetscBool interpolate, DM* dm)
1160 {
1161   PetscScalar       *coordsB;
1162   const PetscScalar *coordsA;
1163   PetscReal         *normals = NULL;
1164   Vec               coordinatesA, coordinatesB;
1165   PetscSection      coordSectionA, coordSectionB;
1166   PetscInt          dim, cDim, cDimB, c, l, v, coordSize, *newCone;
1167   PetscInt          cStart, cEnd, vStart, vEnd, cellV, numCells, numVertices;
1168   PetscErrorCode    ierr;
1169 
1170   PetscFunctionBegin;
1171   PetscValidHeaderSpecific(idm, DM_CLASSID, 1);
1172   PetscValidLogicalCollectiveInt(idm, layers, 2);
1173   PetscValidLogicalCollectiveReal(idm, height, 3);
1174   PetscValidLogicalCollectiveBool(idm, interpolate, 4);
1175   ierr = DMGetDimension(idm, &dim);CHKERRQ(ierr);
1176   if (dim < 1 || dim > 3) SETERRQ1(PetscObjectComm((PetscObject)idm), PETSC_ERR_SUP, "Support for dimension %D not coded", dim);
1177 
1178   ierr = DMPlexGetHeightStratum(idm, 0, &cStart, &cEnd);CHKERRQ(ierr);
1179   ierr = DMPlexGetDepthStratum(idm, 0, &vStart, &vEnd);CHKERRQ(ierr);
1180   numCells = (cEnd - cStart)*layers;
1181   numVertices = (vEnd - vStart)*(layers+1);
1182   ierr = DMCreate(PetscObjectComm((PetscObject)idm), dm);CHKERRQ(ierr);
1183   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
1184   ierr = DMSetDimension(*dm, dim+1);CHKERRQ(ierr);
1185   ierr = DMPlexSetChart(*dm, 0, numCells+numVertices);CHKERRQ(ierr);
1186   for (c = cStart, cellV = 0; c < cEnd; ++c) {
1187     PetscInt *closure = NULL;
1188     PetscInt closureSize, numCorners = 0;
1189 
1190     ierr = DMPlexGetTransitiveClosure(idm, c, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
1191     for (v = 0; v < closureSize*2; v += 2) if ((closure[v] >= vStart) && (closure[v] < vEnd)) numCorners++;
1192     ierr = DMPlexRestoreTransitiveClosure(idm, c, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
1193     for (l = 0; l < layers; ++l) {
1194       ierr = DMPlexSetConeSize(*dm, ordExt ? layers*(c - cStart) + l : l*(cEnd - cStart) + c - cStart, 2*numCorners);CHKERRQ(ierr);
1195     }
1196     cellV = PetscMax(numCorners,cellV);
1197   }
1198   ierr = DMPlexSetHybridBounds(*dm, 0, PETSC_DETERMINE, PETSC_DETERMINE, PETSC_DETERMINE);CHKERRQ(ierr);
1199   ierr = DMSetUp(*dm);CHKERRQ(ierr);
1200 
1201   ierr = DMGetCoordinateDim(idm, &cDim);CHKERRQ(ierr);
1202   if (dim != cDim) {
1203     ierr = PetscCalloc1(cDim*(vEnd - vStart), &normals);CHKERRQ(ierr);
1204   }
1205   ierr = PetscMalloc1(3*cellV,&newCone);CHKERRQ(ierr);
1206   for (c = cStart; c < cEnd; ++c) {
1207     PetscInt *closure = NULL;
1208     PetscInt closureSize, numCorners = 0, l;
1209     PetscReal normal[3] = {0, 0, 0};
1210 
1211     if (normals) {
1212       ierr = DMPlexComputeCellGeometryFVM(idm, c, NULL, NULL, normal);CHKERRQ(ierr);
1213     }
1214     ierr = DMPlexGetTransitiveClosure(idm, c, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
1215     for (v = 0; v < closureSize*2; v += 2) {
1216       if ((closure[v] >= vStart) && (closure[v] < vEnd)) {
1217         PetscInt d;
1218 
1219         newCone[numCorners++] = closure[v] - vStart;
1220         if (normals) { for (d = 0; d < cDim; ++d) normals[cDim*(closure[v]-vStart)+d] += normal[d]; }
1221       }
1222     }
1223     switch (numCorners) {
1224     case 4: /* do nothing */
1225     case 2: /* do nothing */
1226       break;
1227     case 3: /* from counter-clockwise to wedge ordering */
1228       l = newCone[1];
1229       newCone[1] = newCone[2];
1230       newCone[2] = l;
1231       break;
1232     default: SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_SUP, "Unsupported number of corners: %D", numCorners);
1233     }
1234     ierr = DMPlexRestoreTransitiveClosure(idm, c, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
1235     for (l = 0; l < layers; ++l) {
1236       PetscInt i;
1237 
1238       for (i = 0; i < numCorners; ++i) {
1239         newCone[  numCorners + i] = ordExt ? (layers+1)*newCone[i] + l     + numCells :     l*(vEnd - vStart) + newCone[i] + numCells;
1240         newCone[2*numCorners + i] = ordExt ? (layers+1)*newCone[i] + l + 1 + numCells : (l+1)*(vEnd - vStart) + newCone[i] + numCells;
1241       }
1242       ierr = DMPlexSetCone(*dm, ordExt ? layers*(c - cStart) + l : l*(cEnd - cStart) + c - cStart, newCone + numCorners);CHKERRQ(ierr);
1243     }
1244   }
1245   ierr = DMPlexSymmetrize(*dm);CHKERRQ(ierr);
1246   ierr = DMPlexStratify(*dm);CHKERRQ(ierr);
1247   ierr = PetscFree(newCone);CHKERRQ(ierr);
1248 
1249   cDimB = cDim == dim ? cDim+1 : cDim;
1250   ierr = DMGetCoordinateSection(*dm, &coordSectionB);CHKERRQ(ierr);
1251   ierr = PetscSectionSetNumFields(coordSectionB, 1);CHKERRQ(ierr);
1252   ierr = PetscSectionSetFieldComponents(coordSectionB, 0, cDimB);CHKERRQ(ierr);
1253   ierr = PetscSectionSetChart(coordSectionB, numCells, numCells+numVertices);CHKERRQ(ierr);
1254   for (v = numCells; v < numCells+numVertices; ++v) {
1255     ierr = PetscSectionSetDof(coordSectionB, v, cDimB);CHKERRQ(ierr);
1256     ierr = PetscSectionSetFieldDof(coordSectionB, v, 0, cDimB);CHKERRQ(ierr);
1257   }
1258   ierr = PetscSectionSetUp(coordSectionB);CHKERRQ(ierr);
1259   ierr = PetscSectionGetStorageSize(coordSectionB, &coordSize);CHKERRQ(ierr);
1260   ierr = VecCreate(PETSC_COMM_SELF, &coordinatesB);CHKERRQ(ierr);
1261   ierr = PetscObjectSetName((PetscObject) coordinatesB, "coordinates");CHKERRQ(ierr);
1262   ierr = VecSetSizes(coordinatesB, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
1263   ierr = VecSetBlockSize(coordinatesB, cDimB);CHKERRQ(ierr);
1264   ierr = VecSetType(coordinatesB,VECSTANDARD);CHKERRQ(ierr);
1265 
1266   ierr = DMGetCoordinateSection(idm, &coordSectionA);CHKERRQ(ierr);
1267   ierr = DMGetCoordinatesLocal(idm, &coordinatesA);CHKERRQ(ierr);
1268   ierr = VecGetArray(coordinatesB, &coordsB);CHKERRQ(ierr);
1269   ierr = VecGetArrayRead(coordinatesA, &coordsA);CHKERRQ(ierr);
1270   for (v = vStart; v < vEnd; ++v) {
1271     const PetscScalar *cptr;
1272     PetscReal         ones2[2] = { 0., 1.}, ones3[3] = { 0., 0., 1.};
1273     PetscReal         *normal, norm, h = height/layers;
1274     PetscInt          offA, d, cDimA = cDim;
1275 
1276     normal = normals ? normals + cDimB*(v - vStart) : (cDim > 1 ? ones3 : ones2);
1277     if (normals) {
1278       for (d = 0, norm = 0.0; d < cDimB; ++d) norm += normal[d]*normal[d];
1279       for (d = 0; d < cDimB; ++d) normal[d] *= 1./PetscSqrtReal(norm);
1280     }
1281 
1282     ierr = PetscSectionGetOffset(coordSectionA, v, &offA);CHKERRQ(ierr);
1283     cptr = coordsA + offA;
1284     for (l = 0; l < layers+1; ++l) {
1285       PetscInt offB, d, newV;
1286 
1287       newV = ordExt ? (layers+1)*(v -vStart) + l + numCells : (vEnd -vStart)*l + (v -vStart) + numCells;
1288       ierr = PetscSectionGetOffset(coordSectionB, newV, &offB);CHKERRQ(ierr);
1289       for (d = 0; d < cDimA; ++d) { coordsB[offB+d]  = cptr[d]; }
1290       for (d = 0; d < cDimB; ++d) { coordsB[offB+d] += l ? normal[d]*h : 0.0; }
1291       cptr    = coordsB + offB;
1292       cDimA   = cDimB;
1293     }
1294   }
1295   ierr = VecRestoreArrayRead(coordinatesA, &coordsA);CHKERRQ(ierr);
1296   ierr = VecRestoreArray(coordinatesB, &coordsB);CHKERRQ(ierr);
1297   ierr = DMSetCoordinatesLocal(*dm, coordinatesB);CHKERRQ(ierr);
1298   ierr = VecDestroy(&coordinatesB);CHKERRQ(ierr);
1299   ierr = PetscFree(normals);CHKERRQ(ierr);
1300   if (interpolate) {
1301     DM idm;
1302 
1303     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
1304     ierr = DMPlexCopyCoordinates(*dm, idm);CHKERRQ(ierr);
1305     ierr = DMDestroy(dm);CHKERRQ(ierr);
1306     *dm  = idm;
1307   }
1308   PetscFunctionReturn(0);
1309 }
1310 
1311 /*@C
1312   DMPlexSetOptionsPrefix - Sets the prefix used for searching for all DM options in the database.
1313 
1314   Logically Collective on dm
1315 
1316   Input Parameters:
1317 + dm - the DM context
1318 - prefix - the prefix to prepend to all option names
1319 
1320   Notes:
1321   A hyphen (-) must NOT be given at the beginning of the prefix name.
1322   The first character of all runtime options is AUTOMATICALLY the hyphen.
1323 
1324   Level: advanced
1325 
1326 .seealso: SNESSetFromOptions()
1327 @*/
1328 PetscErrorCode DMPlexSetOptionsPrefix(DM dm, const char prefix[])
1329 {
1330   DM_Plex       *mesh = (DM_Plex *) dm->data;
1331   PetscErrorCode ierr;
1332 
1333   PetscFunctionBegin;
1334   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1335   ierr = PetscObjectSetOptionsPrefix((PetscObject) dm, prefix);CHKERRQ(ierr);
1336   ierr = PetscObjectSetOptionsPrefix((PetscObject) mesh->partitioner, prefix);CHKERRQ(ierr);
1337   PetscFunctionReturn(0);
1338 }
1339 
1340 /*@
1341   DMPlexCreateHexCylinderMesh - Creates a mesh on the tensor product of the unit interval with the circle (cylinder) using hexahedra.
1342 
1343   Collective
1344 
1345   Input Parameters:
1346 + comm      - The communicator for the DM object
1347 . numRefine - The number of regular refinements to the basic 5 cell structure
1348 - periodicZ - The boundary type for the Z direction
1349 
1350   Output Parameter:
1351 . dm  - The DM object
1352 
1353   Note: Here is the output numbering looking from the bottom of the cylinder:
1354 $       17-----14
1355 $        |     |
1356 $        |  2  |
1357 $        |     |
1358 $ 17-----8-----7-----14
1359 $  |     |     |     |
1360 $  |  3  |  0  |  1  |
1361 $  |     |     |     |
1362 $ 19-----5-----6-----13
1363 $        |     |
1364 $        |  4  |
1365 $        |     |
1366 $       19-----13
1367 $
1368 $ and up through the top
1369 $
1370 $       18-----16
1371 $        |     |
1372 $        |  2  |
1373 $        |     |
1374 $ 18----10----11-----16
1375 $  |     |     |     |
1376 $  |  3  |  0  |  1  |
1377 $  |     |     |     |
1378 $ 20-----9----12-----15
1379 $        |     |
1380 $        |  4  |
1381 $        |     |
1382 $       20-----15
1383 
1384   Level: beginner
1385 
1386 .seealso: DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
1387 @*/
1388 PetscErrorCode DMPlexCreateHexCylinderMesh(MPI_Comm comm, PetscInt numRefine, DMBoundaryType periodicZ, DM *dm)
1389 {
1390   const PetscInt dim = 3;
1391   PetscInt       numCells, numVertices, r;
1392   PetscMPIInt    rank;
1393   PetscErrorCode ierr;
1394 
1395   PetscFunctionBegin;
1396   PetscValidPointer(dm, 4);
1397   ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
1398   if (numRefine < 0) SETERRQ1(comm, PETSC_ERR_ARG_OUTOFRANGE, "Number of refinements %D cannot be negative", numRefine);
1399   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
1400   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
1401   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
1402   /* Create topology */
1403   {
1404     PetscInt cone[8], c;
1405 
1406     numCells    = !rank ?  5 : 0;
1407     numVertices = !rank ? 16 : 0;
1408     if (periodicZ == DM_BOUNDARY_PERIODIC) {
1409       numCells   *= 3;
1410       numVertices = !rank ? 24 : 0;
1411     }
1412     ierr = DMPlexSetChart(*dm, 0, numCells+numVertices);CHKERRQ(ierr);
1413     for (c = 0; c < numCells; c++) {ierr = DMPlexSetConeSize(*dm, c, 8);CHKERRQ(ierr);}
1414     ierr = DMSetUp(*dm);CHKERRQ(ierr);
1415     if (!rank) {
1416       if (periodicZ == DM_BOUNDARY_PERIODIC) {
1417         cone[0] = 15; cone[1] = 18; cone[2] = 17; cone[3] = 16;
1418         cone[4] = 31; cone[5] = 32; cone[6] = 33; cone[7] = 34;
1419         ierr = DMPlexSetCone(*dm, 0, cone);CHKERRQ(ierr);
1420         cone[0] = 16; cone[1] = 17; cone[2] = 24; cone[3] = 23;
1421         cone[4] = 32; cone[5] = 36; cone[6] = 37; cone[7] = 33; /* 22 25 26 21 */
1422         ierr = DMPlexSetCone(*dm, 1, cone);CHKERRQ(ierr);
1423         cone[0] = 18; cone[1] = 27; cone[2] = 24; cone[3] = 17;
1424         cone[4] = 34; cone[5] = 33; cone[6] = 37; cone[7] = 38;
1425         ierr = DMPlexSetCone(*dm, 2, cone);CHKERRQ(ierr);
1426         cone[0] = 29; cone[1] = 27; cone[2] = 18; cone[3] = 15;
1427         cone[4] = 35; cone[5] = 31; cone[6] = 34; cone[7] = 38;
1428         ierr = DMPlexSetCone(*dm, 3, cone);CHKERRQ(ierr);
1429         cone[0] = 29; cone[1] = 15; cone[2] = 16; cone[3] = 23;
1430         cone[4] = 35; cone[5] = 36; cone[6] = 32; cone[7] = 31;
1431         ierr = DMPlexSetCone(*dm, 4, cone);CHKERRQ(ierr);
1432 
1433         cone[0] = 31; cone[1] = 34; cone[2] = 33; cone[3] = 32;
1434         cone[4] = 19; cone[5] = 22; cone[6] = 21; cone[7] = 20;
1435         ierr = DMPlexSetCone(*dm, 5, cone);CHKERRQ(ierr);
1436         cone[0] = 32; cone[1] = 33; cone[2] = 37; cone[3] = 36;
1437         cone[4] = 22; cone[5] = 25; cone[6] = 26; cone[7] = 21;
1438         ierr = DMPlexSetCone(*dm, 6, cone);CHKERRQ(ierr);
1439         cone[0] = 34; cone[1] = 38; cone[2] = 37; cone[3] = 33;
1440         cone[4] = 20; cone[5] = 21; cone[6] = 26; cone[7] = 28;
1441         ierr = DMPlexSetCone(*dm, 7, cone);CHKERRQ(ierr);
1442         cone[0] = 35; cone[1] = 38; cone[2] = 34; cone[3] = 31;
1443         cone[4] = 30; cone[5] = 19; cone[6] = 20; cone[7] = 28;
1444         ierr = DMPlexSetCone(*dm, 8, cone);CHKERRQ(ierr);
1445         cone[0] = 35; cone[1] = 31; cone[2] = 32; cone[3] = 36;
1446         cone[4] = 30; cone[5] = 25; cone[6] = 22; cone[7] = 19;
1447         ierr = DMPlexSetCone(*dm, 9, cone);CHKERRQ(ierr);
1448 
1449         cone[0] = 19; cone[1] = 20; cone[2] = 21; cone[3] = 22;
1450         cone[4] = 15; cone[5] = 16; cone[6] = 17; cone[7] = 18;
1451         ierr = DMPlexSetCone(*dm, 10, cone);CHKERRQ(ierr);
1452         cone[0] = 22; cone[1] = 21; cone[2] = 26; cone[3] = 25;
1453         cone[4] = 16; cone[5] = 23; cone[6] = 24; cone[7] = 17;
1454         ierr = DMPlexSetCone(*dm, 11, cone);CHKERRQ(ierr);
1455         cone[0] = 20; cone[1] = 28; cone[2] = 26; cone[3] = 21;
1456         cone[4] = 18; cone[5] = 17; cone[6] = 24; cone[7] = 27;
1457         ierr = DMPlexSetCone(*dm, 12, cone);CHKERRQ(ierr);
1458         cone[0] = 30; cone[1] = 28; cone[2] = 20; cone[3] = 19;
1459         cone[4] = 29; cone[5] = 15; cone[6] = 18; cone[7] = 27;
1460         ierr = DMPlexSetCone(*dm, 13, cone);CHKERRQ(ierr);
1461         cone[0] = 30; cone[1] = 19; cone[2] = 22; cone[3] = 25;
1462         cone[4] = 29; cone[5] = 23; cone[6] = 16; cone[7] = 15;
1463         ierr = DMPlexSetCone(*dm, 14, cone);CHKERRQ(ierr);
1464       } else {
1465         cone[0] =  5; cone[1] =  8; cone[2] =  7; cone[3] =  6;
1466         cone[4] =  9; cone[5] = 12; cone[6] = 11; cone[7] = 10;
1467         ierr = DMPlexSetCone(*dm, 0, cone);CHKERRQ(ierr);
1468         cone[0] =  6; cone[1] =  7; cone[2] = 14; cone[3] = 13;
1469         cone[4] = 12; cone[5] = 15; cone[6] = 16; cone[7] = 11;
1470         ierr = DMPlexSetCone(*dm, 1, cone);CHKERRQ(ierr);
1471         cone[0] =  8; cone[1] = 17; cone[2] = 14; cone[3] =  7;
1472         cone[4] = 10; cone[5] = 11; cone[6] = 16; cone[7] = 18;
1473         ierr = DMPlexSetCone(*dm, 2, cone);CHKERRQ(ierr);
1474         cone[0] = 19; cone[1] = 17; cone[2] =  8; cone[3] =  5;
1475         cone[4] = 20; cone[5] =  9; cone[6] = 10; cone[7] = 18;
1476         ierr = DMPlexSetCone(*dm, 3, cone);CHKERRQ(ierr);
1477         cone[0] = 19; cone[1] =  5; cone[2] =  6; cone[3] = 13;
1478         cone[4] = 20; cone[5] = 15; cone[6] = 12; cone[7] =  9;
1479         ierr = DMPlexSetCone(*dm, 4, cone);CHKERRQ(ierr);
1480       }
1481     }
1482     ierr = DMPlexSymmetrize(*dm);CHKERRQ(ierr);
1483     ierr = DMPlexStratify(*dm);CHKERRQ(ierr);
1484   }
1485   /* Interpolate */
1486   {
1487     DM idm;
1488 
1489     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
1490     ierr = DMDestroy(dm);CHKERRQ(ierr);
1491     *dm  = idm;
1492   }
1493   /* Create cube geometry */
1494   {
1495     Vec             coordinates;
1496     PetscSection    coordSection;
1497     PetscScalar    *coords;
1498     PetscInt        coordSize, v;
1499     const PetscReal dis = 1.0/PetscSqrtReal(2.0);
1500     const PetscReal ds2 = dis/2.0;
1501 
1502     /* Build coordinates */
1503     ierr = DMGetCoordinateSection(*dm, &coordSection);CHKERRQ(ierr);
1504     ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
1505     ierr = PetscSectionSetFieldComponents(coordSection, 0, dim);CHKERRQ(ierr);
1506     ierr = PetscSectionSetChart(coordSection, numCells, numCells+numVertices);CHKERRQ(ierr);
1507     for (v = numCells; v < numCells+numVertices; ++v) {
1508       ierr = PetscSectionSetDof(coordSection, v, dim);CHKERRQ(ierr);
1509       ierr = PetscSectionSetFieldDof(coordSection, v, 0, dim);CHKERRQ(ierr);
1510     }
1511     ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
1512     ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
1513     ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
1514     ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
1515     ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
1516     ierr = VecSetBlockSize(coordinates, dim);CHKERRQ(ierr);
1517     ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
1518     ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
1519     if (!rank) {
1520       coords[0*dim+0] = -ds2; coords[0*dim+1] = -ds2; coords[0*dim+2] = 0.0;
1521       coords[1*dim+0] =  ds2; coords[1*dim+1] = -ds2; coords[1*dim+2] = 0.0;
1522       coords[2*dim+0] =  ds2; coords[2*dim+1] =  ds2; coords[2*dim+2] = 0.0;
1523       coords[3*dim+0] = -ds2; coords[3*dim+1] =  ds2; coords[3*dim+2] = 0.0;
1524       coords[4*dim+0] = -ds2; coords[4*dim+1] = -ds2; coords[4*dim+2] = 1.0;
1525       coords[5*dim+0] = -ds2; coords[5*dim+1] =  ds2; coords[5*dim+2] = 1.0;
1526       coords[6*dim+0] =  ds2; coords[6*dim+1] =  ds2; coords[6*dim+2] = 1.0;
1527       coords[7*dim+0] =  ds2; coords[7*dim+1] = -ds2; coords[7*dim+2] = 1.0;
1528       coords[ 8*dim+0] =  dis; coords[ 8*dim+1] = -dis; coords[ 8*dim+2] = 0.0;
1529       coords[ 9*dim+0] =  dis; coords[ 9*dim+1] =  dis; coords[ 9*dim+2] = 0.0;
1530       coords[10*dim+0] =  dis; coords[10*dim+1] = -dis; coords[10*dim+2] = 1.0;
1531       coords[11*dim+0] =  dis; coords[11*dim+1] =  dis; coords[11*dim+2] = 1.0;
1532       coords[12*dim+0] = -dis; coords[12*dim+1] =  dis; coords[12*dim+2] = 0.0;
1533       coords[13*dim+0] = -dis; coords[13*dim+1] =  dis; coords[13*dim+2] = 1.0;
1534       coords[14*dim+0] = -dis; coords[14*dim+1] = -dis; coords[14*dim+2] = 0.0;
1535       coords[15*dim+0] = -dis; coords[15*dim+1] = -dis; coords[15*dim+2] = 1.0;
1536       if (periodicZ == DM_BOUNDARY_PERIODIC) {
1537         /* 15 31 19 */ coords[16*dim+0] = -ds2; coords[16*dim+1] = -ds2; coords[16*dim+2] = 0.5;
1538         /* 16 32 22 */ coords[17*dim+0] =  ds2; coords[17*dim+1] = -ds2; coords[17*dim+2] = 0.5;
1539         /* 17 33 21 */ coords[18*dim+0] =  ds2; coords[18*dim+1] =  ds2; coords[18*dim+2] = 0.5;
1540         /* 18 34 20 */ coords[19*dim+0] = -ds2; coords[19*dim+1] =  ds2; coords[19*dim+2] = 0.5;
1541         /* 29 35 30 */ coords[20*dim+0] = -dis; coords[20*dim+1] = -dis; coords[20*dim+2] = 0.5;
1542         /* 23 36 25 */ coords[21*dim+0] =  dis; coords[21*dim+1] = -dis; coords[21*dim+2] = 0.5;
1543         /* 24 37 26 */ coords[22*dim+0] =  dis; coords[22*dim+1] =  dis; coords[22*dim+2] = 0.5;
1544         /* 27 38 28 */ coords[23*dim+0] = -dis; coords[23*dim+1] =  dis; coords[23*dim+2] = 0.5;
1545       }
1546     }
1547     ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
1548     ierr = DMSetCoordinatesLocal(*dm, coordinates);CHKERRQ(ierr);
1549     ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
1550   }
1551   /* Create periodicity */
1552   if (periodicZ == DM_BOUNDARY_PERIODIC || periodicZ == DM_BOUNDARY_TWIST) {
1553     PetscReal      L[3];
1554     PetscReal      maxCell[3];
1555     DMBoundaryType bdType[3];
1556     PetscReal      lower[3] = {0.0, 0.0, 0.0};
1557     PetscReal      upper[3] = {1.0, 1.0, 1.5};
1558     PetscInt       i, numZCells = 3;
1559 
1560     bdType[0] = DM_BOUNDARY_NONE;
1561     bdType[1] = DM_BOUNDARY_NONE;
1562     bdType[2] = periodicZ;
1563     for (i = 0; i < dim; i++) {
1564       L[i]       = upper[i] - lower[i];
1565       maxCell[i] = 1.1 * (L[i] / numZCells);
1566     }
1567     ierr = DMSetPeriodicity(*dm, PETSC_TRUE, maxCell, L, bdType);CHKERRQ(ierr);
1568   }
1569   /* Refine topology */
1570   for (r = 0; r < numRefine; ++r) {
1571     DM rdm = NULL;
1572 
1573     ierr = DMRefine(*dm, comm, &rdm);CHKERRQ(ierr);
1574     ierr = DMDestroy(dm);CHKERRQ(ierr);
1575     *dm  = rdm;
1576   }
1577   /* Remap geometry to cylinder
1578        Interior square: Linear interpolation is correct
1579        The other cells all have vertices on rays from the origin. We want to uniformly expand the spacing
1580        such that the last vertex is on the unit circle. So the closest and farthest vertices are at distance
1581 
1582          phi     = arctan(y/x)
1583          d_close = sqrt(1/8 + 1/4 sin^2(phi))
1584          d_far   = sqrt(1/2 + sin^2(phi))
1585 
1586        so we remap them using
1587 
1588          x_new = x_close + (x - x_close) (1 - d_close) / (d_far - d_close)
1589          y_new = y_close + (y - y_close) (1 - d_close) / (d_far - d_close)
1590 
1591        If pi/4 < phi < 3pi/4 or -3pi/4 < phi < -pi/4, then we switch x and y.
1592   */
1593   {
1594     Vec           coordinates;
1595     PetscSection  coordSection;
1596     PetscScalar  *coords;
1597     PetscInt      vStart, vEnd, v;
1598     const PetscReal dis = 1.0/PetscSqrtReal(2.0);
1599     const PetscReal ds2 = 0.5*dis;
1600 
1601     ierr = DMPlexGetDepthStratum(*dm, 0, &vStart, &vEnd);CHKERRQ(ierr);
1602     ierr = DMGetCoordinateSection(*dm, &coordSection);CHKERRQ(ierr);
1603     ierr = DMGetCoordinatesLocal(*dm, &coordinates);CHKERRQ(ierr);
1604     ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
1605     for (v = vStart; v < vEnd; ++v) {
1606       PetscReal phi, sinp, cosp, dc, df, x, y, xc, yc;
1607       PetscInt  off;
1608 
1609       ierr = PetscSectionGetOffset(coordSection, v, &off);CHKERRQ(ierr);
1610       if ((PetscAbsScalar(coords[off+0]) <= ds2) && (PetscAbsScalar(coords[off+1]) <= ds2)) continue;
1611       x    = PetscRealPart(coords[off]);
1612       y    = PetscRealPart(coords[off+1]);
1613       phi  = PetscAtan2Real(y, x);
1614       sinp = PetscSinReal(phi);
1615       cosp = PetscCosReal(phi);
1616       if ((PetscAbsReal(phi) > PETSC_PI/4.0) && (PetscAbsReal(phi) < 3.0*PETSC_PI/4.0)) {
1617         dc = PetscAbsReal(ds2/sinp);
1618         df = PetscAbsReal(dis/sinp);
1619         xc = ds2*x/PetscAbsReal(y);
1620         yc = ds2*PetscSignReal(y);
1621       } else {
1622         dc = PetscAbsReal(ds2/cosp);
1623         df = PetscAbsReal(dis/cosp);
1624         xc = ds2*PetscSignReal(x);
1625         yc = ds2*y/PetscAbsReal(x);
1626       }
1627       coords[off+0] = xc + (coords[off+0] - xc)*(1.0 - dc)/(df - dc);
1628       coords[off+1] = yc + (coords[off+1] - yc)*(1.0 - dc)/(df - dc);
1629     }
1630     ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
1631     if (periodicZ == DM_BOUNDARY_PERIODIC || periodicZ == DM_BOUNDARY_TWIST) {
1632       ierr = DMLocalizeCoordinates(*dm);CHKERRQ(ierr);
1633     }
1634   }
1635   PetscFunctionReturn(0);
1636 }
1637 
1638 /*@
1639   DMPlexCreateWedgeCylinderMesh - Creates a mesh on the tensor product of the unit interval with the circle (cylinder) using wedges.
1640 
1641   Collective
1642 
1643   Input Parameters:
1644 + comm - The communicator for the DM object
1645 . n    - The number of wedges around the origin
1646 - interpolate - Create edges and faces
1647 
1648   Output Parameter:
1649 . dm  - The DM object
1650 
1651   Level: beginner
1652 
1653 .seealso: DMPlexCreateHexCylinderMesh(), DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
1654 @*/
1655 PetscErrorCode DMPlexCreateWedgeCylinderMesh(MPI_Comm comm, PetscInt n, PetscBool interpolate, DM *dm)
1656 {
1657   const PetscInt dim = 3;
1658   PetscInt       numCells, numVertices;
1659   PetscMPIInt    rank;
1660   PetscErrorCode ierr;
1661 
1662   PetscFunctionBegin;
1663   PetscValidPointer(dm, 3);
1664   ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
1665   if (n < 0) SETERRQ1(comm, PETSC_ERR_ARG_OUTOFRANGE, "Number of wedges %D cannot be negative", n);
1666   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
1667   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
1668   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
1669   /* Create topology */
1670   {
1671     PetscInt cone[6], c;
1672 
1673     numCells    = !rank ?        n : 0;
1674     numVertices = !rank ?  2*(n+1) : 0;
1675     ierr = DMPlexSetChart(*dm, 0, numCells+numVertices);CHKERRQ(ierr);
1676     ierr = DMPlexSetHybridBounds(*dm, 0, PETSC_DETERMINE, PETSC_DETERMINE, PETSC_DETERMINE);CHKERRQ(ierr);
1677     for (c = 0; c < numCells; c++) {ierr = DMPlexSetConeSize(*dm, c, 6);CHKERRQ(ierr);}
1678     ierr = DMSetUp(*dm);CHKERRQ(ierr);
1679     for (c = 0; c < numCells; c++) {
1680       cone[0] =  c+n*1; cone[1] = (c+1)%n+n*1; cone[2] = 0+3*n;
1681       cone[3] =  c+n*2; cone[4] = (c+1)%n+n*2; cone[5] = 1+3*n;
1682       ierr = DMPlexSetCone(*dm, c, cone);CHKERRQ(ierr);
1683     }
1684     ierr = DMPlexSymmetrize(*dm);CHKERRQ(ierr);
1685     ierr = DMPlexStratify(*dm);CHKERRQ(ierr);
1686   }
1687   /* Interpolate */
1688   if (interpolate) {
1689     DM idm;
1690 
1691     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
1692     ierr = DMDestroy(dm);CHKERRQ(ierr);
1693     *dm  = idm;
1694   }
1695   /* Create cylinder geometry */
1696   {
1697     Vec          coordinates;
1698     PetscSection coordSection;
1699     PetscScalar *coords;
1700     PetscInt     coordSize, v, c;
1701 
1702     /* Build coordinates */
1703     ierr = DMGetCoordinateSection(*dm, &coordSection);CHKERRQ(ierr);
1704     ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
1705     ierr = PetscSectionSetFieldComponents(coordSection, 0, dim);CHKERRQ(ierr);
1706     ierr = PetscSectionSetChart(coordSection, numCells, numCells+numVertices);CHKERRQ(ierr);
1707     for (v = numCells; v < numCells+numVertices; ++v) {
1708       ierr = PetscSectionSetDof(coordSection, v, dim);CHKERRQ(ierr);
1709       ierr = PetscSectionSetFieldDof(coordSection, v, 0, dim);CHKERRQ(ierr);
1710     }
1711     ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
1712     ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
1713     ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
1714     ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
1715     ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
1716     ierr = VecSetBlockSize(coordinates, dim);CHKERRQ(ierr);
1717     ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
1718     ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
1719     for (c = 0; c < numCells; c++) {
1720       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;
1721       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;
1722     }
1723     if (!rank) {
1724       coords[(2*n+0)*dim+0] = 0.0; coords[(2*n+0)*dim+1] = 0.0; coords[(2*n+0)*dim+2] = 1.0;
1725       coords[(2*n+1)*dim+0] = 0.0; coords[(2*n+1)*dim+1] = 0.0; coords[(2*n+1)*dim+2] = 0.0;
1726     }
1727     ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
1728     ierr = DMSetCoordinatesLocal(*dm, coordinates);CHKERRQ(ierr);
1729     ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
1730   }
1731   PetscFunctionReturn(0);
1732 }
1733 
1734 PETSC_STATIC_INLINE PetscReal DiffNormReal(PetscInt dim, const PetscReal x[], const PetscReal y[])
1735 {
1736   PetscReal prod = 0.0;
1737   PetscInt  i;
1738   for (i = 0; i < dim; ++i) prod += PetscSqr(x[i] - y[i]);
1739   return PetscSqrtReal(prod);
1740 }
1741 PETSC_STATIC_INLINE PetscReal DotReal(PetscInt dim, const PetscReal x[], const PetscReal y[])
1742 {
1743   PetscReal prod = 0.0;
1744   PetscInt  i;
1745   for (i = 0; i < dim; ++i) prod += x[i]*y[i];
1746   return prod;
1747 }
1748 
1749 /*@
1750   DMPlexCreateSphereMesh - Creates a mesh on the d-dimensional sphere, S^d.
1751 
1752   Collective
1753 
1754   Input Parameters:
1755 + comm  - The communicator for the DM object
1756 . dim   - The dimension
1757 - simplex - Use simplices, or tensor product cells
1758 
1759   Output Parameter:
1760 . dm  - The DM object
1761 
1762   Level: beginner
1763 
1764 .seealso: DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
1765 @*/
1766 PetscErrorCode DMPlexCreateSphereMesh(MPI_Comm comm, PetscInt dim, PetscBool simplex, DM *dm)
1767 {
1768   const PetscInt  embedDim = dim+1;
1769   PetscSection    coordSection;
1770   Vec             coordinates;
1771   PetscScalar    *coords;
1772   PetscReal      *coordsIn;
1773   PetscInt        numCells, numEdges, numVerts, firstVertex, v, firstEdge, coordSize, d, c, e;
1774   PetscMPIInt     rank;
1775   PetscErrorCode  ierr;
1776 
1777   PetscFunctionBegin;
1778   PetscValidPointer(dm, 4);
1779   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
1780   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
1781   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
1782   ierr = DMSetCoordinateDim(*dm, dim+1);CHKERRQ(ierr);
1783   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject) *dm), &rank);CHKERRQ(ierr);
1784   switch (dim) {
1785   case 2:
1786     if (simplex) {
1787       DM              idm;
1788       const PetscReal edgeLen     = 2.0/(1.0 + PETSC_PHI);
1789       const PetscReal vertex[3]   = {0.0, 1.0/(1.0 + PETSC_PHI), PETSC_PHI/(1.0 + PETSC_PHI)};
1790       const PetscInt  degree      = 5;
1791       PetscInt        s[3]        = {1, 1, 1};
1792       PetscInt        cone[3];
1793       PetscInt       *graph, p, i, j, k;
1794 
1795       numCells    = !rank ? 20 : 0;
1796       numVerts    = !rank ? 12 : 0;
1797       firstVertex = numCells;
1798       /* Use icosahedron, which for a unit sphere has coordinates which are all cyclic permutations of
1799 
1800            (0, \pm 1/\phi+1, \pm \phi/\phi+1)
1801 
1802          where \phi^2 - \phi - 1 = 0, meaning \phi is the golden ratio \frac{1 + \sqrt{5}}{2}. The edge
1803          length is then given by 2/\phi = 2 * 0.61803 = 1.23606.
1804       */
1805       /* Construct vertices */
1806       ierr = PetscCalloc1(numVerts * embedDim, &coordsIn);CHKERRQ(ierr);
1807       if (!rank) {
1808         for (p = 0, i = 0; p < embedDim; ++p) {
1809           for (s[1] = -1; s[1] < 2; s[1] += 2) {
1810             for (s[2] = -1; s[2] < 2; s[2] += 2) {
1811               for (d = 0; d < embedDim; ++d) coordsIn[i*embedDim+d] = s[(d+p)%embedDim]*vertex[(d+p)%embedDim];
1812               ++i;
1813             }
1814           }
1815         }
1816       }
1817       /* Construct graph */
1818       ierr = PetscCalloc1(numVerts * numVerts, &graph);CHKERRQ(ierr);
1819       for (i = 0; i < numVerts; ++i) {
1820         for (j = 0, k = 0; j < numVerts; ++j) {
1821           if (PetscAbsReal(DiffNormReal(embedDim, &coordsIn[i*embedDim], &coordsIn[j*embedDim]) - edgeLen) < PETSC_SMALL) {graph[i*numVerts+j] = 1; ++k;}
1822         }
1823         if (k != degree) SETERRQ3(comm, PETSC_ERR_PLIB, "Invalid icosahedron, vertex %D degree %D != %D", i, k, degree);
1824       }
1825       /* Build Topology */
1826       ierr = DMPlexSetChart(*dm, 0, numCells+numVerts);CHKERRQ(ierr);
1827       for (c = 0; c < numCells; c++) {
1828         ierr = DMPlexSetConeSize(*dm, c, embedDim);CHKERRQ(ierr);
1829       }
1830       ierr = DMSetUp(*dm);CHKERRQ(ierr); /* Allocate space for cones */
1831       /* Cells */
1832       for (i = 0, c = 0; i < numVerts; ++i) {
1833         for (j = 0; j < i; ++j) {
1834           for (k = 0; k < j; ++k) {
1835             if (graph[i*numVerts+j] && graph[j*numVerts+k] && graph[k*numVerts+i]) {
1836               cone[0] = firstVertex+i; cone[1] = firstVertex+j; cone[2] = firstVertex+k;
1837               /* Check orientation */
1838               {
1839                 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}}};
1840                 PetscReal normal[3];
1841                 PetscInt  e, f;
1842 
1843                 for (d = 0; d < embedDim; ++d) {
1844                   normal[d] = 0.0;
1845                   for (e = 0; e < embedDim; ++e) {
1846                     for (f = 0; f < embedDim; ++f) {
1847                       normal[d] += epsilon[d][e][f]*(coordsIn[j*embedDim+e] - coordsIn[i*embedDim+e])*(coordsIn[k*embedDim+f] - coordsIn[i*embedDim+f]);
1848                     }
1849                   }
1850                 }
1851                 if (DotReal(embedDim, normal, &coordsIn[i*embedDim]) < 0) {PetscInt tmp = cone[1]; cone[1] = cone[2]; cone[2] = tmp;}
1852               }
1853               ierr = DMPlexSetCone(*dm, c++, cone);CHKERRQ(ierr);
1854             }
1855           }
1856         }
1857       }
1858       ierr = DMPlexSymmetrize(*dm);CHKERRQ(ierr);
1859       ierr = DMPlexStratify(*dm);CHKERRQ(ierr);
1860       ierr = PetscFree(graph);CHKERRQ(ierr);
1861       /* Interpolate mesh */
1862       ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
1863       ierr = DMDestroy(dm);CHKERRQ(ierr);
1864       *dm  = idm;
1865     } else {
1866       /*
1867         12-21--13
1868          |     |
1869         25  4  24
1870          |     |
1871   12-25--9-16--8-24--13
1872    |     |     |     |
1873   23  5 17  0 15  3  22
1874    |     |     |     |
1875   10-20--6-14--7-19--11
1876          |     |
1877         20  1  19
1878          |     |
1879         10-18--11
1880          |     |
1881         23  2  22
1882          |     |
1883         12-21--13
1884        */
1885       const PetscReal dist = 1.0/PetscSqrtReal(3.0);
1886       PetscInt        cone[4], ornt[4];
1887 
1888       numCells    = !rank ?  6 : 0;
1889       numEdges    = !rank ? 12 : 0;
1890       numVerts    = !rank ?  8 : 0;
1891       firstVertex = numCells;
1892       firstEdge   = numCells + numVerts;
1893       /* Build Topology */
1894       ierr = DMPlexSetChart(*dm, 0, numCells+numEdges+numVerts);CHKERRQ(ierr);
1895       for (c = 0; c < numCells; c++) {
1896         ierr = DMPlexSetConeSize(*dm, c, 4);CHKERRQ(ierr);
1897       }
1898       for (e = firstEdge; e < firstEdge+numEdges; ++e) {
1899         ierr = DMPlexSetConeSize(*dm, e, 2);CHKERRQ(ierr);
1900       }
1901       ierr = DMSetUp(*dm);CHKERRQ(ierr); /* Allocate space for cones */
1902       if (!rank) {
1903         /* Cell 0 */
1904         cone[0] = 14; cone[1] = 15; cone[2] = 16; cone[3] = 17;
1905         ierr = DMPlexSetCone(*dm, 0, cone);CHKERRQ(ierr);
1906         ornt[0] = 0; ornt[1] = 0; ornt[2] = 0; ornt[3] = 0;
1907         ierr = DMPlexSetConeOrientation(*dm, 0, ornt);CHKERRQ(ierr);
1908         /* Cell 1 */
1909         cone[0] = 18; cone[1] = 19; cone[2] = 14; cone[3] = 20;
1910         ierr = DMPlexSetCone(*dm, 1, cone);CHKERRQ(ierr);
1911         ornt[0] = 0; ornt[1] = 0; ornt[2] = -2; ornt[3] = 0;
1912         ierr = DMPlexSetConeOrientation(*dm, 1, ornt);CHKERRQ(ierr);
1913         /* Cell 2 */
1914         cone[0] = 21; cone[1] = 22; cone[2] = 18; cone[3] = 23;
1915         ierr = DMPlexSetCone(*dm, 2, cone);CHKERRQ(ierr);
1916         ornt[0] = 0; ornt[1] = 0; ornt[2] = -2; ornt[3] = 0;
1917         ierr = DMPlexSetConeOrientation(*dm, 2, ornt);CHKERRQ(ierr);
1918         /* Cell 3 */
1919         cone[0] = 19; cone[1] = 22; cone[2] = 24; cone[3] = 15;
1920         ierr = DMPlexSetCone(*dm, 3, cone);CHKERRQ(ierr);
1921         ornt[0] = -2; ornt[1] = -2; ornt[2] = 0; ornt[3] = -2;
1922         ierr = DMPlexSetConeOrientation(*dm, 3, ornt);CHKERRQ(ierr);
1923         /* Cell 4 */
1924         cone[0] = 16; cone[1] = 24; cone[2] = 21; cone[3] = 25;
1925         ierr = DMPlexSetCone(*dm, 4, cone);CHKERRQ(ierr);
1926         ornt[0] = -2; ornt[1] = -2; ornt[2] = -2; ornt[3] = 0;
1927         ierr = DMPlexSetConeOrientation(*dm, 4, ornt);CHKERRQ(ierr);
1928         /* Cell 5 */
1929         cone[0] = 20; cone[1] = 17; cone[2] = 25; cone[3] = 23;
1930         ierr = DMPlexSetCone(*dm, 5, cone);CHKERRQ(ierr);
1931         ornt[0] = -2; ornt[1] = -2; ornt[2] = -2; ornt[3] = -2;
1932         ierr = DMPlexSetConeOrientation(*dm, 5, ornt);CHKERRQ(ierr);
1933         /* Edges */
1934         cone[0] =  6; cone[1] =  7;
1935         ierr = DMPlexSetCone(*dm, 14, cone);CHKERRQ(ierr);
1936         cone[0] =  7; cone[1] =  8;
1937         ierr = DMPlexSetCone(*dm, 15, cone);CHKERRQ(ierr);
1938         cone[0] =  8; cone[1] =  9;
1939         ierr = DMPlexSetCone(*dm, 16, cone);CHKERRQ(ierr);
1940         cone[0] =  9; cone[1] =  6;
1941         ierr = DMPlexSetCone(*dm, 17, cone);CHKERRQ(ierr);
1942         cone[0] = 10; cone[1] = 11;
1943         ierr = DMPlexSetCone(*dm, 18, cone);CHKERRQ(ierr);
1944         cone[0] = 11; cone[1] =  7;
1945         ierr = DMPlexSetCone(*dm, 19, cone);CHKERRQ(ierr);
1946         cone[0] =  6; cone[1] = 10;
1947         ierr = DMPlexSetCone(*dm, 20, cone);CHKERRQ(ierr);
1948         cone[0] = 12; cone[1] = 13;
1949         ierr = DMPlexSetCone(*dm, 21, cone);CHKERRQ(ierr);
1950         cone[0] = 13; cone[1] = 11;
1951         ierr = DMPlexSetCone(*dm, 22, cone);CHKERRQ(ierr);
1952         cone[0] = 10; cone[1] = 12;
1953         ierr = DMPlexSetCone(*dm, 23, cone);CHKERRQ(ierr);
1954         cone[0] = 13; cone[1] =  8;
1955         ierr = DMPlexSetCone(*dm, 24, cone);CHKERRQ(ierr);
1956         cone[0] = 12; cone[1] =  9;
1957         ierr = DMPlexSetCone(*dm, 25, cone);CHKERRQ(ierr);
1958       }
1959       ierr = DMPlexSymmetrize(*dm);CHKERRQ(ierr);
1960       ierr = DMPlexStratify(*dm);CHKERRQ(ierr);
1961       /* Build coordinates */
1962       ierr = PetscCalloc1(numVerts * embedDim, &coordsIn);CHKERRQ(ierr);
1963       if (!rank) {
1964         coordsIn[0*embedDim+0] = -dist; coordsIn[0*embedDim+1] =  dist; coordsIn[0*embedDim+2] = -dist;
1965         coordsIn[1*embedDim+0] =  dist; coordsIn[1*embedDim+1] =  dist; coordsIn[1*embedDim+2] = -dist;
1966         coordsIn[2*embedDim+0] =  dist; coordsIn[2*embedDim+1] = -dist; coordsIn[2*embedDim+2] = -dist;
1967         coordsIn[3*embedDim+0] = -dist; coordsIn[3*embedDim+1] = -dist; coordsIn[3*embedDim+2] = -dist;
1968         coordsIn[4*embedDim+0] = -dist; coordsIn[4*embedDim+1] =  dist; coordsIn[4*embedDim+2] =  dist;
1969         coordsIn[5*embedDim+0] =  dist; coordsIn[5*embedDim+1] =  dist; coordsIn[5*embedDim+2] =  dist;
1970         coordsIn[6*embedDim+0] = -dist; coordsIn[6*embedDim+1] = -dist; coordsIn[6*embedDim+2] =  dist;
1971         coordsIn[7*embedDim+0] =  dist; coordsIn[7*embedDim+1] = -dist; coordsIn[7*embedDim+2] =  dist;
1972       }
1973     }
1974     break;
1975   case 3:
1976     if (simplex) {
1977       DM              idm;
1978       const PetscReal edgeLen         = 1.0/PETSC_PHI;
1979       const PetscReal vertexA[4]      = {0.5, 0.5, 0.5, 0.5};
1980       const PetscReal vertexB[4]      = {1.0, 0.0, 0.0, 0.0};
1981       const PetscReal vertexC[4]      = {0.5, 0.5*PETSC_PHI, 0.5/PETSC_PHI, 0.0};
1982       const PetscInt  degree          = 12;
1983       PetscInt        s[4]            = {1, 1, 1};
1984       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},
1985                                          {2, 0, 1, 3}, {2, 1, 3, 0}, {2, 3, 0, 1}, {3, 0, 2, 1}, {3, 1, 0, 2}, {3, 2, 1, 0}};
1986       PetscInt        cone[4];
1987       PetscInt       *graph, p, i, j, k, l;
1988 
1989       numCells    = !rank ? 600 : 0;
1990       numVerts    = !rank ? 120 : 0;
1991       firstVertex = numCells;
1992       /* Use the 600-cell, which for a unit sphere has coordinates which are
1993 
1994            1/2 (\pm 1, \pm 1,    \pm 1, \pm 1)                          16
1995                (\pm 1,    0,       0,      0)  all cyclic permutations   8
1996            1/2 (\pm 1, \pm phi, \pm 1/phi, 0)  all even permutations    96
1997 
1998          where \phi^2 - \phi - 1 = 0, meaning \phi is the golden ratio \frac{1 + \sqrt{5}}{2}. The edge
1999          length is then given by 1/\phi = 0.61803.
2000 
2001          http://buzzard.pugetsound.edu/sage-practice/ch03s03.html
2002          http://mathworld.wolfram.com/600-Cell.html
2003       */
2004       /* Construct vertices */
2005       ierr = PetscCalloc1(numVerts * embedDim, &coordsIn);CHKERRQ(ierr);
2006       i    = 0;
2007       if (!rank) {
2008         for (s[0] = -1; s[0] < 2; s[0] += 2) {
2009           for (s[1] = -1; s[1] < 2; s[1] += 2) {
2010             for (s[2] = -1; s[2] < 2; s[2] += 2) {
2011               for (s[3] = -1; s[3] < 2; s[3] += 2) {
2012                 for (d = 0; d < embedDim; ++d) coordsIn[i*embedDim+d] = s[d]*vertexA[d];
2013                 ++i;
2014               }
2015             }
2016           }
2017         }
2018         for (p = 0; p < embedDim; ++p) {
2019           s[1] = s[2] = s[3] = 1;
2020           for (s[0] = -1; s[0] < 2; s[0] += 2) {
2021             for (d = 0; d < embedDim; ++d) coordsIn[i*embedDim+d] = s[(d+p)%embedDim]*vertexB[(d+p)%embedDim];
2022             ++i;
2023           }
2024         }
2025         for (p = 0; p < 12; ++p) {
2026           s[3] = 1;
2027           for (s[0] = -1; s[0] < 2; s[0] += 2) {
2028             for (s[1] = -1; s[1] < 2; s[1] += 2) {
2029               for (s[2] = -1; s[2] < 2; s[2] += 2) {
2030                 for (d = 0; d < embedDim; ++d) coordsIn[i*embedDim+d] = s[evenPerm[p][d]]*vertexC[evenPerm[p][d]];
2031                 ++i;
2032               }
2033             }
2034           }
2035         }
2036       }
2037       if (i != numVerts) SETERRQ2(comm, PETSC_ERR_PLIB, "Invalid 600-cell, vertices %D != %D", i, numVerts);
2038       /* Construct graph */
2039       ierr = PetscCalloc1(numVerts * numVerts, &graph);CHKERRQ(ierr);
2040       for (i = 0; i < numVerts; ++i) {
2041         for (j = 0, k = 0; j < numVerts; ++j) {
2042           if (PetscAbsReal(DiffNormReal(embedDim, &coordsIn[i*embedDim], &coordsIn[j*embedDim]) - edgeLen) < PETSC_SMALL) {graph[i*numVerts+j] = 1; ++k;}
2043         }
2044         if (k != degree) SETERRQ3(comm, PETSC_ERR_PLIB, "Invalid 600-cell, vertex %D degree %D != %D", i, k, degree);
2045       }
2046       /* Build Topology */
2047       ierr = DMPlexSetChart(*dm, 0, numCells+numVerts);CHKERRQ(ierr);
2048       for (c = 0; c < numCells; c++) {
2049         ierr = DMPlexSetConeSize(*dm, c, embedDim);CHKERRQ(ierr);
2050       }
2051       ierr = DMSetUp(*dm);CHKERRQ(ierr); /* Allocate space for cones */
2052       /* Cells */
2053       if (!rank) {
2054         for (i = 0, c = 0; i < numVerts; ++i) {
2055           for (j = 0; j < i; ++j) {
2056             for (k = 0; k < j; ++k) {
2057               for (l = 0; l < k; ++l) {
2058                 if (graph[i*numVerts+j] && graph[j*numVerts+k] && graph[k*numVerts+i] &&
2059                     graph[l*numVerts+i] && graph[l*numVerts+j] && graph[l*numVerts+k]) {
2060                   cone[0] = firstVertex+i; cone[1] = firstVertex+j; cone[2] = firstVertex+k; cone[3] = firstVertex+l;
2061                   /* Check orientation: https://ef.gy/linear-algebra:normal-vectors-in-higher-dimensional-spaces */
2062                   {
2063                     const PetscInt epsilon[4][4][4][4] = {{{{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}},
2064                                                            {{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  1}, { 0,  0, -1, 0}},
2065                                                            {{0,  0,  0,  0}, { 0, 0,  0, -1}, { 0,  0, 0,  0}, { 0,  1,  0, 0}},
2066                                                            {{0,  0,  0,  0}, { 0, 0,  1,  0}, { 0, -1, 0,  0}, { 0,  0,  0, 0}}},
2067 
2068                                                           {{{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0, -1}, { 0,  0,  1, 0}},
2069                                                            {{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}},
2070                                                            {{0,  0,  0,  1}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, {-1,  0,  0, 0}},
2071                                                            {{0,  0, -1,  0}, { 0, 0,  0,  0}, { 1,  0, 0,  0}, { 0,  0,  0, 0}}},
2072 
2073                                                           {{{0,  0,  0,  0}, { 0, 0,  0,  1}, { 0,  0, 0,  0}, { 0, -1,  0, 0}},
2074                                                            {{0,  0,  0, -1}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 1,  0,  0, 0}},
2075                                                            {{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}},
2076                                                            {{0,  1,  0,  0}, {-1, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}}},
2077 
2078                                                           {{{0,  0,  0,  0}, { 0, 0, -1,  0}, { 0,  1, 0,  0}, { 0,  0,  0, 0}},
2079                                                            {{0,  0,  1,  0}, { 0, 0,  0,  0}, {-1,  0, 0,  0}, { 0,  0,  0, 0}},
2080                                                            {{0, -1,  0,  0}, { 1, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}},
2081                                                            {{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}}}};
2082                     PetscReal normal[4];
2083                     PetscInt  e, f, g;
2084 
2085                     for (d = 0; d < embedDim; ++d) {
2086                       normal[d] = 0.0;
2087                       for (e = 0; e < embedDim; ++e) {
2088                         for (f = 0; f < embedDim; ++f) {
2089                           for (g = 0; g < embedDim; ++g) {
2090                             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]);
2091                           }
2092                         }
2093                       }
2094                     }
2095                     if (DotReal(embedDim, normal, &coordsIn[i*embedDim]) < 0) {PetscInt tmp = cone[1]; cone[1] = cone[2]; cone[2] = tmp;}
2096                   }
2097                   ierr = DMPlexSetCone(*dm, c++, cone);CHKERRQ(ierr);
2098                 }
2099               }
2100             }
2101           }
2102         }
2103       }
2104       ierr = DMPlexSymmetrize(*dm);CHKERRQ(ierr);
2105       ierr = DMPlexStratify(*dm);CHKERRQ(ierr);
2106       ierr = PetscFree(graph);CHKERRQ(ierr);
2107       /* Interpolate mesh */
2108       ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
2109       ierr = DMDestroy(dm);CHKERRQ(ierr);
2110       *dm  = idm;
2111       break;
2112     }
2113   default: SETERRQ1(comm, PETSC_ERR_SUP, "Unsupported dimension for sphere: %D", dim);
2114   }
2115   /* Create coordinates */
2116   ierr = DMGetCoordinateSection(*dm, &coordSection);CHKERRQ(ierr);
2117   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
2118   ierr = PetscSectionSetFieldComponents(coordSection, 0, embedDim);CHKERRQ(ierr);
2119   ierr = PetscSectionSetChart(coordSection, firstVertex, firstVertex+numVerts);CHKERRQ(ierr);
2120   for (v = firstVertex; v < firstVertex+numVerts; ++v) {
2121     ierr = PetscSectionSetDof(coordSection, v, embedDim);CHKERRQ(ierr);
2122     ierr = PetscSectionSetFieldDof(coordSection, v, 0, embedDim);CHKERRQ(ierr);
2123   }
2124   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
2125   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
2126   ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
2127   ierr = VecSetBlockSize(coordinates, embedDim);CHKERRQ(ierr);
2128   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
2129   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
2130   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
2131   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
2132   for (v = 0; v < numVerts; ++v) for (d = 0; d < embedDim; ++d) {coords[v*embedDim+d] = coordsIn[v*embedDim+d];}
2133   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
2134   ierr = DMSetCoordinatesLocal(*dm, coordinates);CHKERRQ(ierr);
2135   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
2136   ierr = PetscFree(coordsIn);CHKERRQ(ierr);
2137   PetscFunctionReturn(0);
2138 }
2139 
2140 /* External function declarations here */
2141 extern PetscErrorCode DMCreateInterpolation_Plex(DM dmCoarse, DM dmFine, Mat *interpolation, Vec *scaling);
2142 extern PetscErrorCode DMCreateInjection_Plex(DM dmCoarse, DM dmFine, Mat *mat);
2143 extern PetscErrorCode DMCreateMassMatrix_Plex(DM dmCoarse, DM dmFine, Mat *mat);
2144 extern PetscErrorCode DMCreateLocalSection_Plex(DM dm);
2145 extern PetscErrorCode DMCreateDefaultConstraints_Plex(DM dm);
2146 extern PetscErrorCode DMCreateMatrix_Plex(DM dm,  Mat *J);
2147 extern PetscErrorCode DMCreateCoordinateDM_Plex(DM dm, DM *cdm);
2148 extern PetscErrorCode DMCreateCoordinateField_Plex(DM dm, DMField *field);
2149 PETSC_INTERN PetscErrorCode DMClone_Plex(DM dm, DM *newdm);
2150 extern PetscErrorCode DMSetUp_Plex(DM dm);
2151 extern PetscErrorCode DMDestroy_Plex(DM dm);
2152 extern PetscErrorCode DMView_Plex(DM dm, PetscViewer viewer);
2153 extern PetscErrorCode DMLoad_Plex(DM dm, PetscViewer viewer);
2154 extern PetscErrorCode DMCreateSubDM_Plex(DM dm, PetscInt numFields, const PetscInt fields[], IS *is, DM *subdm);
2155 extern PetscErrorCode DMCreateSuperDM_Plex(DM dms[], PetscInt len, IS **is, DM *superdm);
2156 static PetscErrorCode DMInitialize_Plex(DM dm);
2157 
2158 /* Replace dm with the contents of dmNew
2159    - Share the DM_Plex structure
2160    - Share the coordinates
2161    - Share the SF
2162 */
2163 static PetscErrorCode DMPlexReplace_Static(DM dm, DM dmNew)
2164 {
2165   PetscSF               sf;
2166   DM                    coordDM, coarseDM;
2167   Vec                   coords;
2168   PetscBool             isper;
2169   const PetscReal      *maxCell, *L;
2170   const DMBoundaryType *bd;
2171   PetscErrorCode        ierr;
2172 
2173   PetscFunctionBegin;
2174   ierr = DMGetPointSF(dmNew, &sf);CHKERRQ(ierr);
2175   ierr = DMSetPointSF(dm, sf);CHKERRQ(ierr);
2176   ierr = DMGetCoordinateDM(dmNew, &coordDM);CHKERRQ(ierr);
2177   ierr = DMGetCoordinatesLocal(dmNew, &coords);CHKERRQ(ierr);
2178   ierr = DMSetCoordinateDM(dm, coordDM);CHKERRQ(ierr);
2179   ierr = DMSetCoordinatesLocal(dm, coords);CHKERRQ(ierr);
2180   ierr = DMGetPeriodicity(dm, &isper, &maxCell, &L, &bd);CHKERRQ(ierr);
2181   ierr = DMSetPeriodicity(dmNew, isper, maxCell, L, bd);CHKERRQ(ierr);
2182   ierr = DMDestroy_Plex(dm);CHKERRQ(ierr);
2183   ierr = DMInitialize_Plex(dm);CHKERRQ(ierr);
2184   dm->data = dmNew->data;
2185   ((DM_Plex *) dmNew->data)->refct++;
2186   ierr = DMDestroyLabelLinkList_Internal(dm);CHKERRQ(ierr);
2187   ierr = DMCopyLabels(dmNew, dm, PETSC_OWN_POINTER, PETSC_TRUE);CHKERRQ(ierr);
2188   ierr = DMGetCoarseDM(dmNew,&coarseDM);CHKERRQ(ierr);
2189   ierr = DMSetCoarseDM(dm,coarseDM);CHKERRQ(ierr);
2190   PetscFunctionReturn(0);
2191 }
2192 
2193 /* Swap dm with the contents of dmNew
2194    - Swap the DM_Plex structure
2195    - Swap the coordinates
2196    - Swap the point PetscSF
2197 */
2198 static PetscErrorCode DMPlexSwap_Static(DM dmA, DM dmB)
2199 {
2200   DM              coordDMA, coordDMB;
2201   Vec             coordsA,  coordsB;
2202   PetscSF         sfA,      sfB;
2203   void            *tmp;
2204   DMLabelLink     listTmp;
2205   DMLabel         depthTmp;
2206   PetscInt        tmpI;
2207   PetscErrorCode  ierr;
2208 
2209   PetscFunctionBegin;
2210   ierr = DMGetPointSF(dmA, &sfA);CHKERRQ(ierr);
2211   ierr = DMGetPointSF(dmB, &sfB);CHKERRQ(ierr);
2212   ierr = PetscObjectReference((PetscObject) sfA);CHKERRQ(ierr);
2213   ierr = DMSetPointSF(dmA, sfB);CHKERRQ(ierr);
2214   ierr = DMSetPointSF(dmB, sfA);CHKERRQ(ierr);
2215   ierr = PetscObjectDereference((PetscObject) sfA);CHKERRQ(ierr);
2216 
2217   ierr = DMGetCoordinateDM(dmA, &coordDMA);CHKERRQ(ierr);
2218   ierr = DMGetCoordinateDM(dmB, &coordDMB);CHKERRQ(ierr);
2219   ierr = PetscObjectReference((PetscObject) coordDMA);CHKERRQ(ierr);
2220   ierr = DMSetCoordinateDM(dmA, coordDMB);CHKERRQ(ierr);
2221   ierr = DMSetCoordinateDM(dmB, coordDMA);CHKERRQ(ierr);
2222   ierr = PetscObjectDereference((PetscObject) coordDMA);CHKERRQ(ierr);
2223 
2224   ierr = DMGetCoordinatesLocal(dmA, &coordsA);CHKERRQ(ierr);
2225   ierr = DMGetCoordinatesLocal(dmB, &coordsB);CHKERRQ(ierr);
2226   ierr = PetscObjectReference((PetscObject) coordsA);CHKERRQ(ierr);
2227   ierr = DMSetCoordinatesLocal(dmA, coordsB);CHKERRQ(ierr);
2228   ierr = DMSetCoordinatesLocal(dmB, coordsA);CHKERRQ(ierr);
2229   ierr = PetscObjectDereference((PetscObject) coordsA);CHKERRQ(ierr);
2230 
2231   tmp       = dmA->data;
2232   dmA->data = dmB->data;
2233   dmB->data = tmp;
2234   listTmp   = dmA->labels;
2235   dmA->labels = dmB->labels;
2236   dmB->labels = listTmp;
2237   depthTmp  = dmA->depthLabel;
2238   dmA->depthLabel = dmB->depthLabel;
2239   dmB->depthLabel = depthTmp;
2240   depthTmp  = dmA->celltypeLabel;
2241   dmA->celltypeLabel = dmB->celltypeLabel;
2242   dmB->celltypeLabel = depthTmp;
2243   tmpI         = dmA->levelup;
2244   dmA->levelup = dmB->levelup;
2245   dmB->levelup = tmpI;
2246   PetscFunctionReturn(0);
2247 }
2248 
2249 PetscErrorCode DMSetFromOptions_NonRefinement_Plex(PetscOptionItems *PetscOptionsObject,DM dm)
2250 {
2251   DM_Plex       *mesh = (DM_Plex*) dm->data;
2252   PetscBool      flg;
2253   PetscErrorCode ierr;
2254 
2255   PetscFunctionBegin;
2256   /* Handle viewing */
2257   ierr = PetscOptionsBool("-dm_plex_print_set_values", "Output all set values info", "DMPlexMatSetClosure", PETSC_FALSE, &mesh->printSetValues, NULL);CHKERRQ(ierr);
2258   ierr = PetscOptionsBoundedInt("-dm_plex_print_fem", "Debug output level all fem computations", "DMPlexSNESComputeResidualFEM", 0, &mesh->printFEM, NULL,0);CHKERRQ(ierr);
2259   ierr = PetscOptionsReal("-dm_plex_print_tol", "Tolerance for FEM output", "DMPlexSNESComputeResidualFEM", mesh->printTol, &mesh->printTol, NULL);CHKERRQ(ierr);
2260   ierr = PetscOptionsBoundedInt("-dm_plex_print_l2", "Debug output level all L2 diff computations", "DMComputeL2Diff", 0, &mesh->printL2, NULL,0);CHKERRQ(ierr);
2261   ierr = DMMonitorSetFromOptions(dm, "-dm_plex_monitor_throughput", "Monitor the simulation throughput", "DMPlexMonitorThroughput", DMPlexMonitorThroughput, NULL, &flg);CHKERRQ(ierr);
2262   if (flg) {ierr = PetscLogDefaultBegin();CHKERRQ(ierr);}
2263   /* Point Location */
2264   ierr = PetscOptionsBool("-dm_plex_hash_location", "Use grid hashing for point location", "DMInterpolate", PETSC_FALSE, &mesh->useHashLocation, NULL);CHKERRQ(ierr);
2265   /* Partitioning and distribution */
2266   ierr = PetscOptionsBool("-dm_plex_partition_balance", "Attempt to evenly divide points on partition boundary between processes", "DMPlexSetPartitionBalance", PETSC_FALSE, &mesh->partitionBalance, NULL);CHKERRQ(ierr);
2267   /* Generation and remeshing */
2268   ierr = PetscOptionsBool("-dm_plex_remesh_bd", "Allow changes to the boundary on remeshing", "DMAdapt", PETSC_FALSE, &mesh->remeshBd, NULL);CHKERRQ(ierr);
2269   /* Projection behavior */
2270   ierr = PetscOptionsBoundedInt("-dm_plex_max_projection_height", "Maxmimum mesh point height used to project locally", "DMPlexSetMaxProjectionHeight", 0, &mesh->maxProjectionHeight, NULL,0);CHKERRQ(ierr);
2271   ierr = PetscOptionsBool("-dm_plex_regular_refinement", "Use special nested projection algorithm for regular refinement", "DMPlexSetRegularRefinement", mesh->regularRefinement, &mesh->regularRefinement, NULL);CHKERRQ(ierr);
2272   /* Checking structure */
2273   {
2274     PetscBool   flg = PETSC_FALSE, flg2 = PETSC_FALSE, all = PETSC_FALSE;
2275 
2276     ierr = PetscOptionsBool("-dm_plex_check_all", "Perform all checks", NULL, PETSC_FALSE, &all, &flg2);CHKERRQ(ierr);
2277     ierr = PetscOptionsBool("-dm_plex_check_symmetry", "Check that the adjacency information in the mesh is symmetric", "DMPlexCheckSymmetry", PETSC_FALSE, &flg, &flg2);CHKERRQ(ierr);
2278     if (all || (flg && flg2)) {ierr = DMPlexCheckSymmetry(dm);CHKERRQ(ierr);}
2279     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);
2280     if (all || (flg && flg2)) {ierr = DMPlexCheckSkeleton(dm, 0);CHKERRQ(ierr);}
2281     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);
2282     if (all || (flg && flg2)) {ierr = DMPlexCheckFaces(dm, 0);CHKERRQ(ierr);}
2283     ierr = PetscOptionsBool("-dm_plex_check_geometry", "Check that cells have positive volume", "DMPlexCheckGeometry", PETSC_FALSE, &flg, &flg2);CHKERRQ(ierr);
2284     if (all || (flg && flg2)) {ierr = DMPlexCheckGeometry(dm);CHKERRQ(ierr);}
2285     ierr = PetscOptionsBool("-dm_plex_check_pointsf", "Check some necessary conditions for PointSF", "DMPlexCheckPointSF", PETSC_FALSE, &flg, &flg2);CHKERRQ(ierr);
2286     if (all || (flg && flg2)) {ierr = DMPlexCheckPointSF(dm);CHKERRQ(ierr);}
2287     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);
2288     if (all || (flg && flg2)) {ierr = DMPlexCheckInterfaceCones(dm);CHKERRQ(ierr);}
2289   }
2290 
2291   ierr = PetscPartitionerSetFromOptions(mesh->partitioner);CHKERRQ(ierr);
2292   PetscFunctionReturn(0);
2293 }
2294 
2295 static PetscErrorCode DMSetFromOptions_Plex(PetscOptionItems *PetscOptionsObject,DM dm)
2296 {
2297   PetscInt       refine = 0, coarsen = 0, r;
2298   PetscBool      isHierarchy;
2299   PetscErrorCode ierr;
2300 
2301   PetscFunctionBegin;
2302   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
2303   ierr = PetscOptionsHead(PetscOptionsObject,"DMPlex Options");CHKERRQ(ierr);
2304   /* Handle DMPlex refinement */
2305   ierr = PetscOptionsBoundedInt("-dm_refine", "The number of uniform refinements", "DMCreate", refine, &refine, NULL,0);CHKERRQ(ierr);
2306   ierr = PetscOptionsBoundedInt("-dm_refine_hierarchy", "The number of uniform refinements", "DMCreate", refine, &refine, &isHierarchy,0);CHKERRQ(ierr);
2307   if (refine) {ierr = DMPlexSetRefinementUniform(dm, PETSC_TRUE);CHKERRQ(ierr);}
2308   if (refine && isHierarchy) {
2309     DM *dms, coarseDM;
2310 
2311     ierr = DMGetCoarseDM(dm, &coarseDM);CHKERRQ(ierr);
2312     ierr = PetscObjectReference((PetscObject)coarseDM);CHKERRQ(ierr);
2313     ierr = PetscMalloc1(refine,&dms);CHKERRQ(ierr);
2314     ierr = DMRefineHierarchy(dm, refine, dms);CHKERRQ(ierr);
2315     /* Total hack since we do not pass in a pointer */
2316     ierr = DMPlexSwap_Static(dm, dms[refine-1]);CHKERRQ(ierr);
2317     if (refine == 1) {
2318       ierr = DMSetCoarseDM(dm, dms[0]);CHKERRQ(ierr);
2319       ierr = DMPlexSetRegularRefinement(dm, PETSC_TRUE);CHKERRQ(ierr);
2320     } else {
2321       ierr = DMSetCoarseDM(dm, dms[refine-2]);CHKERRQ(ierr);
2322       ierr = DMPlexSetRegularRefinement(dm, PETSC_TRUE);CHKERRQ(ierr);
2323       ierr = DMSetCoarseDM(dms[0], dms[refine-1]);CHKERRQ(ierr);
2324       ierr = DMPlexSetRegularRefinement(dms[0], PETSC_TRUE);CHKERRQ(ierr);
2325     }
2326     ierr = DMSetCoarseDM(dms[refine-1], coarseDM);CHKERRQ(ierr);
2327     ierr = PetscObjectDereference((PetscObject)coarseDM);CHKERRQ(ierr);
2328     /* Free DMs */
2329     for (r = 0; r < refine; ++r) {
2330       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dms[r]);CHKERRQ(ierr);
2331       ierr = DMDestroy(&dms[r]);CHKERRQ(ierr);
2332     }
2333     ierr = PetscFree(dms);CHKERRQ(ierr);
2334   } else {
2335     for (r = 0; r < refine; ++r) {
2336       DM refinedMesh;
2337 
2338       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2339       ierr = DMRefine(dm, PetscObjectComm((PetscObject) dm), &refinedMesh);CHKERRQ(ierr);
2340       /* Total hack since we do not pass in a pointer */
2341       ierr = DMPlexReplace_Static(dm, refinedMesh);CHKERRQ(ierr);
2342       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2343       ierr = DMDestroy(&refinedMesh);CHKERRQ(ierr);
2344     }
2345   }
2346   /* Handle DMPlex coarsening */
2347   ierr = PetscOptionsBoundedInt("-dm_coarsen", "Coarsen the mesh", "DMCreate", coarsen, &coarsen, NULL,0);CHKERRQ(ierr);
2348   ierr = PetscOptionsBoundedInt("-dm_coarsen_hierarchy", "The number of coarsenings", "DMCreate", coarsen, &coarsen, &isHierarchy,0);CHKERRQ(ierr);
2349   if (coarsen && isHierarchy) {
2350     DM *dms;
2351 
2352     ierr = PetscMalloc1(coarsen, &dms);CHKERRQ(ierr);
2353     ierr = DMCoarsenHierarchy(dm, coarsen, dms);CHKERRQ(ierr);
2354     /* Free DMs */
2355     for (r = 0; r < coarsen; ++r) {
2356       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dms[r]);CHKERRQ(ierr);
2357       ierr = DMDestroy(&dms[r]);CHKERRQ(ierr);
2358     }
2359     ierr = PetscFree(dms);CHKERRQ(ierr);
2360   } else {
2361     for (r = 0; r < coarsen; ++r) {
2362       DM coarseMesh;
2363 
2364       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2365       ierr = DMCoarsen(dm, PetscObjectComm((PetscObject) dm), &coarseMesh);CHKERRQ(ierr);
2366       /* Total hack since we do not pass in a pointer */
2367       ierr = DMPlexReplace_Static(dm, coarseMesh);CHKERRQ(ierr);
2368       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2369       ierr = DMDestroy(&coarseMesh);CHKERRQ(ierr);
2370     }
2371   }
2372   /* Handle */
2373   ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2374   ierr = PetscOptionsTail();CHKERRQ(ierr);
2375   PetscFunctionReturn(0);
2376 }
2377 
2378 static PetscErrorCode DMCreateGlobalVector_Plex(DM dm,Vec *vec)
2379 {
2380   PetscErrorCode ierr;
2381 
2382   PetscFunctionBegin;
2383   ierr = DMCreateGlobalVector_Section_Private(dm,vec);CHKERRQ(ierr);
2384   /* ierr = VecSetOperation(*vec, VECOP_DUPLICATE, (void(*)(void)) VecDuplicate_MPI_DM);CHKERRQ(ierr); */
2385   ierr = VecSetOperation(*vec, VECOP_VIEW, (void (*)(void)) VecView_Plex);CHKERRQ(ierr);
2386   ierr = VecSetOperation(*vec, VECOP_VIEWNATIVE, (void (*)(void)) VecView_Plex_Native);CHKERRQ(ierr);
2387   ierr = VecSetOperation(*vec, VECOP_LOAD, (void (*)(void)) VecLoad_Plex);CHKERRQ(ierr);
2388   ierr = VecSetOperation(*vec, VECOP_LOADNATIVE, (void (*)(void)) VecLoad_Plex_Native);CHKERRQ(ierr);
2389   PetscFunctionReturn(0);
2390 }
2391 
2392 static PetscErrorCode DMCreateLocalVector_Plex(DM dm,Vec *vec)
2393 {
2394   PetscErrorCode ierr;
2395 
2396   PetscFunctionBegin;
2397   ierr = DMCreateLocalVector_Section_Private(dm,vec);CHKERRQ(ierr);
2398   ierr = VecSetOperation(*vec, VECOP_VIEW, (void (*)(void)) VecView_Plex_Local);CHKERRQ(ierr);
2399   ierr = VecSetOperation(*vec, VECOP_LOAD, (void (*)(void)) VecLoad_Plex_Local);CHKERRQ(ierr);
2400   PetscFunctionReturn(0);
2401 }
2402 
2403 static PetscErrorCode DMGetDimPoints_Plex(DM dm, PetscInt dim, PetscInt *pStart, PetscInt *pEnd)
2404 {
2405   PetscInt       depth, d;
2406   PetscErrorCode ierr;
2407 
2408   PetscFunctionBegin;
2409   ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
2410   if (depth == 1) {
2411     ierr = DMGetDimension(dm, &d);CHKERRQ(ierr);
2412     if (dim == 0)      {ierr = DMPlexGetDepthStratum(dm, dim, pStart, pEnd);CHKERRQ(ierr);}
2413     else if (dim == d) {ierr = DMPlexGetDepthStratum(dm, 1, pStart, pEnd);CHKERRQ(ierr);}
2414     else               {*pStart = 0; *pEnd = 0;}
2415   } else {
2416     ierr = DMPlexGetDepthStratum(dm, dim, pStart, pEnd);CHKERRQ(ierr);
2417   }
2418   PetscFunctionReturn(0);
2419 }
2420 
2421 static PetscErrorCode DMGetNeighbors_Plex(DM dm, PetscInt *nranks, const PetscMPIInt *ranks[])
2422 {
2423   PetscSF        sf;
2424   PetscErrorCode ierr;
2425 
2426   PetscFunctionBegin;
2427   ierr = DMGetPointSF(dm, &sf);CHKERRQ(ierr);
2428   ierr = PetscSFGetRootRanks(sf, nranks, ranks, NULL, NULL, NULL);CHKERRQ(ierr);
2429   PetscFunctionReturn(0);
2430 }
2431 
2432 static PetscErrorCode DMInitialize_Plex(DM dm)
2433 {
2434   PetscErrorCode ierr;
2435 
2436   PetscFunctionBegin;
2437   dm->ops->view                            = DMView_Plex;
2438   dm->ops->load                            = DMLoad_Plex;
2439   dm->ops->setfromoptions                  = DMSetFromOptions_Plex;
2440   dm->ops->clone                           = DMClone_Plex;
2441   dm->ops->setup                           = DMSetUp_Plex;
2442   dm->ops->createlocalsection              = DMCreateLocalSection_Plex;
2443   dm->ops->createdefaultconstraints        = DMCreateDefaultConstraints_Plex;
2444   dm->ops->createglobalvector              = DMCreateGlobalVector_Plex;
2445   dm->ops->createlocalvector               = DMCreateLocalVector_Plex;
2446   dm->ops->getlocaltoglobalmapping         = NULL;
2447   dm->ops->createfieldis                   = NULL;
2448   dm->ops->createcoordinatedm              = DMCreateCoordinateDM_Plex;
2449   dm->ops->createcoordinatefield           = DMCreateCoordinateField_Plex;
2450   dm->ops->getcoloring                     = NULL;
2451   dm->ops->creatematrix                    = DMCreateMatrix_Plex;
2452   dm->ops->createinterpolation             = DMCreateInterpolation_Plex;
2453   dm->ops->createmassmatrix                = DMCreateMassMatrix_Plex;
2454   dm->ops->createinjection                 = DMCreateInjection_Plex;
2455   dm->ops->refine                          = DMRefine_Plex;
2456   dm->ops->coarsen                         = DMCoarsen_Plex;
2457   dm->ops->refinehierarchy                 = DMRefineHierarchy_Plex;
2458   dm->ops->coarsenhierarchy                = DMCoarsenHierarchy_Plex;
2459   dm->ops->adaptlabel                      = DMAdaptLabel_Plex;
2460   dm->ops->adaptmetric                     = DMAdaptMetric_Plex;
2461   dm->ops->globaltolocalbegin              = NULL;
2462   dm->ops->globaltolocalend                = NULL;
2463   dm->ops->localtoglobalbegin              = NULL;
2464   dm->ops->localtoglobalend                = NULL;
2465   dm->ops->destroy                         = DMDestroy_Plex;
2466   dm->ops->createsubdm                     = DMCreateSubDM_Plex;
2467   dm->ops->createsuperdm                   = DMCreateSuperDM_Plex;
2468   dm->ops->getdimpoints                    = DMGetDimPoints_Plex;
2469   dm->ops->locatepoints                    = DMLocatePoints_Plex;
2470   dm->ops->projectfunctionlocal            = DMProjectFunctionLocal_Plex;
2471   dm->ops->projectfunctionlabellocal       = DMProjectFunctionLabelLocal_Plex;
2472   dm->ops->projectfieldlocal               = DMProjectFieldLocal_Plex;
2473   dm->ops->projectfieldlabellocal          = DMProjectFieldLabelLocal_Plex;
2474   dm->ops->computel2diff                   = DMComputeL2Diff_Plex;
2475   dm->ops->computel2gradientdiff           = DMComputeL2GradientDiff_Plex;
2476   dm->ops->computel2fielddiff              = DMComputeL2FieldDiff_Plex;
2477   dm->ops->getneighbors                    = DMGetNeighbors_Plex;
2478   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMPlexInsertBoundaryValues_C",DMPlexInsertBoundaryValues_Plex);CHKERRQ(ierr);
2479   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMSetUpGLVisViewer_C",DMSetUpGLVisViewer_Plex);CHKERRQ(ierr);
2480   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMCreateNeumannOverlap_C",DMCreateNeumannOverlap_Plex);CHKERRQ(ierr);
2481   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMPlexGetOverlap_C",DMPlexGetOverlap_Plex);CHKERRQ(ierr);
2482   PetscFunctionReturn(0);
2483 }
2484 
2485 PETSC_INTERN PetscErrorCode DMClone_Plex(DM dm, DM *newdm)
2486 {
2487   DM_Plex        *mesh = (DM_Plex *) dm->data;
2488   PetscErrorCode ierr;
2489 
2490   PetscFunctionBegin;
2491   mesh->refct++;
2492   (*newdm)->data = mesh;
2493   ierr = PetscObjectChangeTypeName((PetscObject) *newdm, DMPLEX);CHKERRQ(ierr);
2494   ierr = DMInitialize_Plex(*newdm);CHKERRQ(ierr);
2495   PetscFunctionReturn(0);
2496 }
2497 
2498 /*MC
2499   DMPLEX = "plex" - A DM object that encapsulates an unstructured mesh, or CW Complex, which can be expressed using a Hasse Diagram.
2500                     In the local representation, Vecs contain all unknowns in the interior and shared boundary. This is
2501                     specified by a PetscSection object. Ownership in the global representation is determined by
2502                     ownership of the underlying DMPlex points. This is specified by another PetscSection object.
2503 
2504   Options Database Keys:
2505 + -dm_plex_hash_location             - Use grid hashing for point location
2506 . -dm_plex_partition_balance         - Attempt to evenly divide points on partition boundary between processes
2507 . -dm_plex_remesh_bd                 - Allow changes to the boundary on remeshing
2508 . -dm_plex_max_projection_height     - Maxmimum mesh point height used to project locally
2509 . -dm_plex_regular_refinement        - Use special nested projection algorithm for regular refinement
2510 . -dm_plex_check_symmetry            - Check that the adjacency information in the mesh is symmetric
2511 . -dm_plex_check_skeleton <celltype> - Check that each cell has the correct number of vertices
2512 . -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
2513 . -dm_plex_check_geometry            - Check that cells have positive volume
2514 . -dm_view :mesh.tex:ascii_latex     - View the mesh in LaTeX/TikZ
2515 . -dm_plex_view_scale <num>          - Scale the TikZ
2516 - -dm_plex_print_fem <num>           - View FEM assembly information, such as element vectors and matrices
2517 
2518 
2519   Level: intermediate
2520 
2521 .seealso: DMType, DMPlexCreate(), DMCreate(), DMSetType()
2522 M*/
2523 
2524 PETSC_EXTERN PetscErrorCode DMCreate_Plex(DM dm)
2525 {
2526   DM_Plex        *mesh;
2527   PetscInt       unit, d;
2528   PetscErrorCode ierr;
2529 
2530   PetscFunctionBegin;
2531   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
2532   ierr     = PetscNewLog(dm,&mesh);CHKERRQ(ierr);
2533   dm->dim  = 0;
2534   dm->data = mesh;
2535 
2536   mesh->refct             = 1;
2537   ierr                    = PetscSectionCreate(PetscObjectComm((PetscObject)dm), &mesh->coneSection);CHKERRQ(ierr);
2538   mesh->maxConeSize       = 0;
2539   mesh->cones             = NULL;
2540   mesh->coneOrientations  = NULL;
2541   ierr                    = PetscSectionCreate(PetscObjectComm((PetscObject)dm), &mesh->supportSection);CHKERRQ(ierr);
2542   mesh->maxSupportSize    = 0;
2543   mesh->supports          = NULL;
2544   mesh->refinementUniform = PETSC_TRUE;
2545   mesh->refinementLimit   = -1.0;
2546   mesh->ghostCellStart    = -1;
2547   mesh->interpolated      = DMPLEX_INTERPOLATED_INVALID;
2548   mesh->interpolatedCollective = DMPLEX_INTERPOLATED_INVALID;
2549 
2550   mesh->facesTmp = NULL;
2551 
2552   mesh->tetgenOpts   = NULL;
2553   mesh->triangleOpts = NULL;
2554   ierr = PetscPartitionerCreate(PetscObjectComm((PetscObject)dm), &mesh->partitioner);CHKERRQ(ierr);
2555   mesh->remeshBd     = PETSC_FALSE;
2556 
2557   mesh->subpointMap = NULL;
2558 
2559   for (unit = 0; unit < NUM_PETSC_UNITS; ++unit) mesh->scale[unit] = 1.0;
2560 
2561   mesh->regularRefinement   = PETSC_FALSE;
2562   mesh->depthState          = -1;
2563   mesh->celltypeState       = -1;
2564   mesh->globalVertexNumbers = NULL;
2565   mesh->globalCellNumbers   = NULL;
2566   mesh->anchorSection       = NULL;
2567   mesh->anchorIS            = NULL;
2568   mesh->createanchors       = NULL;
2569   mesh->computeanchormatrix = NULL;
2570   mesh->parentSection       = NULL;
2571   mesh->parents             = NULL;
2572   mesh->childIDs            = NULL;
2573   mesh->childSection        = NULL;
2574   mesh->children            = NULL;
2575   mesh->referenceTree       = NULL;
2576   mesh->getchildsymmetry    = NULL;
2577   for (d = 0; d < 8; ++d) mesh->hybridPointMax[d] = PETSC_DETERMINE;
2578   mesh->vtkCellHeight       = 0;
2579   mesh->useAnchors          = PETSC_FALSE;
2580 
2581   mesh->maxProjectionHeight = 0;
2582 
2583   mesh->printSetValues = PETSC_FALSE;
2584   mesh->printFEM       = 0;
2585   mesh->printTol       = 1.0e-10;
2586 
2587   ierr = DMInitialize_Plex(dm);CHKERRQ(ierr);
2588   PetscFunctionReturn(0);
2589 }
2590 
2591 /*@
2592   DMPlexCreate - Creates a DMPlex object, which encapsulates an unstructured mesh, or CW complex, which can be expressed using a Hasse Diagram.
2593 
2594   Collective
2595 
2596   Input Parameter:
2597 . comm - The communicator for the DMPlex object
2598 
2599   Output Parameter:
2600 . mesh  - The DMPlex object
2601 
2602   Level: beginner
2603 
2604 @*/
2605 PetscErrorCode DMPlexCreate(MPI_Comm comm, DM *mesh)
2606 {
2607   PetscErrorCode ierr;
2608 
2609   PetscFunctionBegin;
2610   PetscValidPointer(mesh,2);
2611   ierr = DMCreate(comm, mesh);CHKERRQ(ierr);
2612   ierr = DMSetType(*mesh, DMPLEX);CHKERRQ(ierr);
2613   PetscFunctionReturn(0);
2614 }
2615 
2616 /*
2617   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
2618 */
2619 /* TODO: invertCells and spaceDim arguments could be added also to to DMPlexCreateFromCellListParallel(), DMPlexBuildFromCellList_Internal() and DMPlexCreateFromCellList() */
2620 PetscErrorCode DMPlexBuildFromCellList_Parallel_Internal(DM dm, PetscInt spaceDim, PetscInt numCells, PetscInt numVertices, PetscInt numCorners, const int cells[], PetscBool invertCells, PetscSF *sfVert)
2621 {
2622   PetscSF         sfPoint;
2623   PetscLayout     vLayout;
2624   PetscHSetI      vhash;
2625   PetscSFNode    *remoteVerticesAdj, *vertexLocal, *vertexOwner, *remoteVertex;
2626   const PetscInt *vrange;
2627   PetscInt        numVerticesAdj, off = 0, *verticesAdj, numVerticesGhost = 0, *localVertex, *cone, c, p, v, g;
2628   PetscMPIInt     rank, size;
2629   PetscErrorCode  ierr;
2630 
2631   PetscFunctionBegin;
2632   ierr = PetscLogEventBegin(DMPLEX_CreateFromCellList,dm,0,0,0);CHKERRQ(ierr);
2633   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject) dm), &rank);CHKERRQ(ierr);
2634   ierr = MPI_Comm_size(PetscObjectComm((PetscObject) dm), &size);CHKERRQ(ierr);
2635   /* Partition vertices */
2636   ierr = PetscLayoutCreate(PetscObjectComm((PetscObject) dm), &vLayout);CHKERRQ(ierr);
2637   ierr = PetscLayoutSetLocalSize(vLayout, numVertices);CHKERRQ(ierr);
2638   ierr = PetscLayoutSetBlockSize(vLayout, 1);CHKERRQ(ierr);
2639   ierr = PetscLayoutSetUp(vLayout);CHKERRQ(ierr);
2640   ierr = PetscLayoutGetRanges(vLayout, &vrange);CHKERRQ(ierr);
2641   /* Count vertices and map them to procs */
2642   ierr = PetscHSetICreate(&vhash);CHKERRQ(ierr);
2643   for (c = 0; c < numCells; ++c) {
2644     for (p = 0; p < numCorners; ++p) {
2645       ierr = PetscHSetIAdd(vhash, cells[c*numCorners+p]);CHKERRQ(ierr);
2646     }
2647   }
2648   ierr = PetscHSetIGetSize(vhash, &numVerticesAdj);CHKERRQ(ierr);
2649   ierr = PetscMalloc1(numVerticesAdj, &verticesAdj);CHKERRQ(ierr);
2650   ierr = PetscHSetIGetElems(vhash, &off, verticesAdj);CHKERRQ(ierr);
2651   ierr = PetscHSetIDestroy(&vhash);CHKERRQ(ierr);
2652   if (off != numVerticesAdj) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Invalid number of local vertices %D should be %D", off, numVerticesAdj);
2653   ierr = PetscSortInt(numVerticesAdj, verticesAdj);CHKERRQ(ierr);
2654   ierr = PetscMalloc1(numVerticesAdj, &remoteVerticesAdj);CHKERRQ(ierr);
2655   for (v = 0; v < numVerticesAdj; ++v) {
2656     const PetscInt gv = verticesAdj[v];
2657     PetscInt       vrank;
2658 
2659     ierr = PetscFindInt(gv, size+1, vrange, &vrank);CHKERRQ(ierr);
2660     vrank = vrank < 0 ? -(vrank+2) : vrank;
2661     remoteVerticesAdj[v].index = gv - vrange[vrank];
2662     remoteVerticesAdj[v].rank  = vrank;
2663   }
2664   /* Create cones */
2665   ierr = DMPlexSetChart(dm, 0, numCells+numVerticesAdj);CHKERRQ(ierr);
2666   for (c = 0; c < numCells; ++c) {ierr = DMPlexSetConeSize(dm, c, numCorners);CHKERRQ(ierr);}
2667   ierr = DMSetUp(dm);CHKERRQ(ierr);
2668   ierr = DMGetWorkArray(dm, numCorners, MPIU_INT, &cone);CHKERRQ(ierr);
2669   for (c = 0; c < numCells; ++c) {
2670     for (p = 0; p < numCorners; ++p) {
2671       const PetscInt gv = cells[c*numCorners+p];
2672       PetscInt       lv;
2673 
2674       ierr = PetscFindInt(gv, numVerticesAdj, verticesAdj, &lv);CHKERRQ(ierr);
2675       if (lv < 0) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Could not find global vertex %D in local connectivity", gv);
2676       cone[p] = lv+numCells;
2677     }
2678     if (invertCells) { ierr = DMPlexInvertCell_Internal(spaceDim, numCorners, cone);CHKERRQ(ierr); }
2679     ierr = DMPlexSetCone(dm, c, cone);CHKERRQ(ierr);
2680   }
2681   ierr = DMRestoreWorkArray(dm, numCorners, MPIU_INT, &cone);CHKERRQ(ierr);
2682   /* Create SF for vertices */
2683   ierr = PetscSFCreate(PetscObjectComm((PetscObject)dm), sfVert);CHKERRQ(ierr);
2684   ierr = PetscObjectSetName((PetscObject) *sfVert, "Vertex Ownership SF");CHKERRQ(ierr);
2685   ierr = PetscSFSetFromOptions(*sfVert);CHKERRQ(ierr);
2686   ierr = PetscSFSetGraph(*sfVert, numVertices, numVerticesAdj, NULL, PETSC_OWN_POINTER, remoteVerticesAdj, PETSC_OWN_POINTER);CHKERRQ(ierr);
2687   ierr = PetscFree(verticesAdj);CHKERRQ(ierr);
2688   /* Build pointSF */
2689   ierr = PetscMalloc2(numVerticesAdj, &vertexLocal, numVertices, &vertexOwner);CHKERRQ(ierr);
2690   for (v = 0; v < numVerticesAdj; ++v) {vertexLocal[v].index = v+numCells; vertexLocal[v].rank = rank;}
2691   for (v = 0; v < numVertices;    ++v) {vertexOwner[v].index = -1;         vertexOwner[v].rank = -1;}
2692   ierr = PetscSFReduceBegin(*sfVert, MPIU_2INT, vertexLocal, vertexOwner, MPI_MAXLOC);CHKERRQ(ierr);
2693   ierr = PetscSFReduceEnd(*sfVert, MPIU_2INT, vertexLocal, vertexOwner, MPI_MAXLOC);CHKERRQ(ierr);
2694   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);
2695   ierr = PetscSFBcastBegin(*sfVert, MPIU_2INT, vertexOwner, vertexLocal);CHKERRQ(ierr);
2696   ierr = PetscSFBcastEnd(*sfVert, MPIU_2INT, vertexOwner, vertexLocal);CHKERRQ(ierr);
2697   for (v = 0; v < numVerticesAdj; ++v) if (vertexLocal[v].rank != rank) ++numVerticesGhost;
2698   ierr = PetscMalloc1(numVerticesGhost, &localVertex);CHKERRQ(ierr);
2699   ierr = PetscMalloc1(numVerticesGhost, &remoteVertex);CHKERRQ(ierr);
2700   for (v = 0, g = 0; v < numVerticesAdj; ++v) {
2701     if (vertexLocal[v].rank != rank) {
2702       localVertex[g]        = v+numCells;
2703       remoteVertex[g].index = vertexLocal[v].index;
2704       remoteVertex[g].rank  = vertexLocal[v].rank;
2705       ++g;
2706     }
2707   }
2708   ierr = PetscFree2(vertexLocal, vertexOwner);CHKERRQ(ierr);
2709   if (g != numVerticesGhost) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid number of vertex ghosts %D should be %D", g, numVerticesGhost);
2710   ierr = DMGetPointSF(dm, &sfPoint);CHKERRQ(ierr);
2711   ierr = PetscObjectSetName((PetscObject) sfPoint, "point SF");CHKERRQ(ierr);
2712   ierr = PetscSFSetGraph(sfPoint, numCells+numVerticesAdj, numVerticesGhost, localVertex, PETSC_OWN_POINTER, remoteVertex, PETSC_OWN_POINTER);CHKERRQ(ierr);
2713   ierr = PetscLayoutDestroy(&vLayout);CHKERRQ(ierr);
2714   /* Fill in the rest of the topology structure */
2715   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
2716   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
2717   ierr = PetscLogEventEnd(DMPLEX_CreateFromCellList,dm,0,0,0);CHKERRQ(ierr);
2718   PetscFunctionReturn(0);
2719 }
2720 
2721 /*
2722   This takes as input the coordinates for each owned vertex
2723 */
2724 PetscErrorCode DMPlexBuildCoordinates_Parallel_Internal(DM dm, PetscInt spaceDim, PetscInt numCells, PetscInt numV, PetscSF sfVert, const PetscReal vertexCoords[])
2725 {
2726   PetscSection   coordSection;
2727   Vec            coordinates;
2728   PetscScalar   *coords;
2729   PetscInt       numVertices, numVerticesAdj, coordSize, v;
2730   PetscErrorCode ierr;
2731 
2732   PetscFunctionBegin;
2733   ierr = PetscLogEventBegin(DMPLEX_CreateFromCellList_Coordinates,dm,0,0,0);CHKERRQ(ierr);
2734   ierr = DMSetCoordinateDim(dm, spaceDim);CHKERRQ(ierr);
2735   ierr = PetscSFGetGraph(sfVert, &numVertices, &numVerticesAdj, NULL, NULL);CHKERRQ(ierr);
2736   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
2737   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
2738   ierr = PetscSectionSetFieldComponents(coordSection, 0, spaceDim);CHKERRQ(ierr);
2739   ierr = PetscSectionSetChart(coordSection, numCells, numCells + numVerticesAdj);CHKERRQ(ierr);
2740   for (v = numCells; v < numCells+numVerticesAdj; ++v) {
2741     ierr = PetscSectionSetDof(coordSection, v, spaceDim);CHKERRQ(ierr);
2742     ierr = PetscSectionSetFieldDof(coordSection, v, 0, spaceDim);CHKERRQ(ierr);
2743   }
2744   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
2745   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
2746   ierr = VecCreate(PetscObjectComm((PetscObject)dm), &coordinates);CHKERRQ(ierr);
2747   ierr = VecSetBlockSize(coordinates, spaceDim);CHKERRQ(ierr);
2748   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
2749   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
2750   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
2751   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
2752   {
2753     MPI_Datatype coordtype;
2754 
2755     /* Need a temp buffer for coords if we have complex/single */
2756     ierr = MPI_Type_contiguous(spaceDim, MPIU_SCALAR, &coordtype);CHKERRQ(ierr);
2757     ierr = MPI_Type_commit(&coordtype);CHKERRQ(ierr);
2758 #if defined(PETSC_USE_COMPLEX)
2759     {
2760     PetscScalar *svertexCoords;
2761     PetscInt    i;
2762     ierr = PetscMalloc1(numV*spaceDim,&svertexCoords);CHKERRQ(ierr);
2763     for (i=0; i<numV*spaceDim; i++) svertexCoords[i] = vertexCoords[i];
2764     ierr = PetscSFBcastBegin(sfVert, coordtype, svertexCoords, coords);CHKERRQ(ierr);
2765     ierr = PetscSFBcastEnd(sfVert, coordtype, svertexCoords, coords);CHKERRQ(ierr);
2766     ierr = PetscFree(svertexCoords);CHKERRQ(ierr);
2767     }
2768 #else
2769     ierr = PetscSFBcastBegin(sfVert, coordtype, vertexCoords, coords);CHKERRQ(ierr);
2770     ierr = PetscSFBcastEnd(sfVert, coordtype, vertexCoords, coords);CHKERRQ(ierr);
2771 #endif
2772     ierr = MPI_Type_free(&coordtype);CHKERRQ(ierr);
2773   }
2774   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
2775   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
2776   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
2777   ierr = PetscLogEventEnd(DMPLEX_CreateFromCellList_Coordinates,dm,0,0,0);CHKERRQ(ierr);
2778   PetscFunctionReturn(0);
2779 }
2780 
2781 /*@
2782   DMPlexCreateFromCellListParallel - This takes as input common mesh generator output, a list of the vertices for each cell, and produces a DM
2783 
2784   Input Parameters:
2785 + comm - The communicator
2786 . dim - The topological dimension of the mesh
2787 . numCells - The number of cells owned by this process
2788 . numVertices - The number of vertices owned by this process
2789 . numCorners - The number of vertices for each cell
2790 . interpolate - Flag indicating that intermediate mesh entities (faces, edges) should be created automatically
2791 . cells - An array of numCells*numCorners numbers, the global vertex numbers for each cell
2792 . spaceDim - The spatial dimension used for coordinates
2793 - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex
2794 
2795   Output Parameter:
2796 + dm - The DM
2797 - vertexSF - Optional, SF describing complete vertex ownership
2798 
2799   Note: Two triangles sharing a face
2800 $
2801 $        2
2802 $      / | \
2803 $     /  |  \
2804 $    /   |   \
2805 $   0  0 | 1  3
2806 $    \   |   /
2807 $     \  |  /
2808 $      \ | /
2809 $        1
2810 would have input
2811 $  numCells = 2, numVertices = 4
2812 $  cells = [0 1 2  1 3 2]
2813 $
2814 which would result in the DMPlex
2815 $
2816 $        4
2817 $      / | \
2818 $     /  |  \
2819 $    /   |   \
2820 $   2  0 | 1  5
2821 $    \   |   /
2822 $     \  |  /
2823 $      \ | /
2824 $        3
2825 
2826   Level: beginner
2827 
2828 .seealso: DMPlexCreateFromCellList(), DMPlexCreateFromDAG(), DMPlexCreate()
2829 @*/
2830 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)
2831 {
2832   PetscSF        sfVert;
2833   PetscErrorCode ierr;
2834 
2835   PetscFunctionBegin;
2836   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
2837   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
2838   PetscValidLogicalCollectiveInt(*dm, dim, 2);
2839   PetscValidLogicalCollectiveInt(*dm, spaceDim, 8);
2840   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
2841   ierr = DMPlexBuildFromCellList_Parallel_Internal(*dm, spaceDim, numCells, numVertices, numCorners, cells, PETSC_FALSE, &sfVert);CHKERRQ(ierr);
2842   if (interpolate) {
2843     DM idm;
2844 
2845     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
2846     ierr = DMDestroy(dm);CHKERRQ(ierr);
2847     *dm  = idm;
2848   }
2849   ierr = DMPlexBuildCoordinates_Parallel_Internal(*dm, spaceDim, numCells, numVertices, sfVert, vertexCoords);CHKERRQ(ierr);
2850   if (vertexSF) *vertexSF = sfVert;
2851   else {ierr = PetscSFDestroy(&sfVert);CHKERRQ(ierr);}
2852   PetscFunctionReturn(0);
2853 }
2854 
2855 /*
2856   This takes as input the common mesh generator output, a list of the vertices for each cell
2857 */
2858 PetscErrorCode DMPlexBuildFromCellList_Internal(DM dm, PetscInt spaceDim, PetscInt numCells, PetscInt numVertices, PetscInt numCorners, const int cells[], PetscBool invertCells)
2859 {
2860   PetscInt      *cone, c, p;
2861   PetscErrorCode ierr;
2862 
2863   PetscFunctionBegin;
2864   ierr = PetscLogEventBegin(DMPLEX_CreateFromCellList,dm,0,0,0);CHKERRQ(ierr);
2865   ierr = DMPlexSetChart(dm, 0, numCells+numVertices);CHKERRQ(ierr);
2866   for (c = 0; c < numCells; ++c) {
2867     ierr = DMPlexSetConeSize(dm, c, numCorners);CHKERRQ(ierr);
2868   }
2869   ierr = DMSetUp(dm);CHKERRQ(ierr);
2870   ierr = DMGetWorkArray(dm, numCorners, MPIU_INT, &cone);CHKERRQ(ierr);
2871   for (c = 0; c < numCells; ++c) {
2872     for (p = 0; p < numCorners; ++p) {
2873       cone[p] = cells[c*numCorners+p]+numCells;
2874     }
2875     if (invertCells) { ierr = DMPlexInvertCell_Internal(spaceDim, numCorners, cone);CHKERRQ(ierr); }
2876     ierr = DMPlexSetCone(dm, c, cone);CHKERRQ(ierr);
2877   }
2878   ierr = DMRestoreWorkArray(dm, numCorners, MPIU_INT, &cone);CHKERRQ(ierr);
2879   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
2880   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
2881   ierr = PetscLogEventEnd(DMPLEX_CreateFromCellList,dm,0,0,0);CHKERRQ(ierr);
2882   PetscFunctionReturn(0);
2883 }
2884 
2885 /*
2886   This takes as input the coordinates for each vertex
2887 */
2888 PetscErrorCode DMPlexBuildCoordinates_Internal(DM dm, PetscInt spaceDim, PetscInt numCells, PetscInt numVertices, const double vertexCoords[])
2889 {
2890   PetscSection   coordSection;
2891   Vec            coordinates;
2892   DM             cdm;
2893   PetscScalar   *coords;
2894   PetscInt       v, d;
2895   PetscErrorCode ierr;
2896 
2897   PetscFunctionBegin;
2898   ierr = PetscLogEventBegin(DMPLEX_CreateFromCellList_Coordinates,dm,0,0,0);CHKERRQ(ierr);
2899   ierr = DMSetCoordinateDim(dm, spaceDim);CHKERRQ(ierr);
2900   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
2901   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
2902   ierr = PetscSectionSetFieldComponents(coordSection, 0, spaceDim);CHKERRQ(ierr);
2903   ierr = PetscSectionSetChart(coordSection, numCells, numCells + numVertices);CHKERRQ(ierr);
2904   for (v = numCells; v < numCells+numVertices; ++v) {
2905     ierr = PetscSectionSetDof(coordSection, v, spaceDim);CHKERRQ(ierr);
2906     ierr = PetscSectionSetFieldDof(coordSection, v, 0, spaceDim);CHKERRQ(ierr);
2907   }
2908   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
2909 
2910   ierr = DMGetCoordinateDM(dm, &cdm);CHKERRQ(ierr);
2911   ierr = DMCreateLocalVector(cdm, &coordinates);CHKERRQ(ierr);
2912   ierr = VecSetBlockSize(coordinates, spaceDim);CHKERRQ(ierr);
2913   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
2914   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
2915   for (v = 0; v < numVertices; ++v) {
2916     for (d = 0; d < spaceDim; ++d) {
2917       coords[v*spaceDim+d] = vertexCoords[v*spaceDim+d];
2918     }
2919   }
2920   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
2921   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
2922   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
2923   ierr = PetscLogEventEnd(DMPLEX_CreateFromCellList_Coordinates,dm,0,0,0);CHKERRQ(ierr);
2924   PetscFunctionReturn(0);
2925 }
2926 
2927 /*@
2928   DMPlexCreateFromCellList - This takes as input common mesh generator output, a list of the vertices for each cell, and produces a DM
2929 
2930   Input Parameters:
2931 + comm - The communicator
2932 . dim - The topological dimension of the mesh
2933 . numCells - The number of cells
2934 . numVertices - The number of vertices
2935 . numCorners - The number of vertices for each cell
2936 . interpolate - Flag indicating that intermediate mesh entities (faces, edges) should be created automatically
2937 . cells - An array of numCells*numCorners numbers, the vertices for each cell
2938 . spaceDim - The spatial dimension used for coordinates
2939 - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex
2940 
2941   Output Parameter:
2942 . dm - The DM
2943 
2944   Note: Two triangles sharing a face
2945 $
2946 $        2
2947 $      / | \
2948 $     /  |  \
2949 $    /   |   \
2950 $   0  0 | 1  3
2951 $    \   |   /
2952 $     \  |  /
2953 $      \ | /
2954 $        1
2955 would have input
2956 $  numCells = 2, numVertices = 4
2957 $  cells = [0 1 2  1 3 2]
2958 $
2959 which would result in the DMPlex
2960 $
2961 $        4
2962 $      / | \
2963 $     /  |  \
2964 $    /   |   \
2965 $   2  0 | 1  5
2966 $    \   |   /
2967 $     \  |  /
2968 $      \ | /
2969 $        3
2970 
2971   Level: beginner
2972 
2973 .seealso: DMPlexCreateFromDAG(), DMPlexCreate()
2974 @*/
2975 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)
2976 {
2977   PetscErrorCode ierr;
2978 
2979   PetscFunctionBegin;
2980   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
2981   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
2982   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
2983   ierr = DMPlexBuildFromCellList_Internal(*dm, spaceDim, numCells, numVertices, numCorners, cells, PETSC_FALSE);CHKERRQ(ierr);
2984   if (interpolate) {
2985     DM idm;
2986 
2987     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
2988     ierr = DMDestroy(dm);CHKERRQ(ierr);
2989     *dm  = idm;
2990   }
2991   ierr = DMPlexBuildCoordinates_Internal(*dm, spaceDim, numCells, numVertices, vertexCoords);CHKERRQ(ierr);
2992   PetscFunctionReturn(0);
2993 }
2994 
2995 /*@
2996   DMPlexCreateFromDAG - This takes as input the adjacency-list representation of the Directed Acyclic Graph (Hasse Diagram) encoding a mesh, and produces a DM
2997 
2998   Input Parameters:
2999 + dm - The empty DM object, usually from DMCreate() and DMSetDimension()
3000 . depth - The depth of the DAG
3001 . numPoints - Array of size depth + 1 containing the number of points at each depth
3002 . coneSize - The cone size of each point
3003 . cones - The concatenation of the cone points for each point, the cone list must be oriented correctly for each point
3004 . coneOrientations - The orientation of each cone point
3005 - vertexCoords - An array of numPoints[0]*spacedim numbers representing the coordinates of each vertex, with spacedim the value set via DMSetCoordinateDim()
3006 
3007   Output Parameter:
3008 . dm - The DM
3009 
3010   Note: Two triangles sharing a face would have input
3011 $  depth = 1, numPoints = [4 2], coneSize = [3 3 0 0 0 0]
3012 $  cones = [2 3 4  3 5 4], coneOrientations = [0 0 0  0 0 0]
3013 $ vertexCoords = [-1.0 0.0  0.0 -1.0  0.0 1.0  1.0 0.0]
3014 $
3015 which would result in the DMPlex
3016 $
3017 $        4
3018 $      / | \
3019 $     /  |  \
3020 $    /   |   \
3021 $   2  0 | 1  5
3022 $    \   |   /
3023 $     \  |  /
3024 $      \ | /
3025 $        3
3026 $
3027 $ Notice that all points are numbered consecutively, unlikely DMPlexCreateFromCellList()
3028 
3029   Level: advanced
3030 
3031 .seealso: DMPlexCreateFromCellList(), DMPlexCreate()
3032 @*/
3033 PetscErrorCode DMPlexCreateFromDAG(DM dm, PetscInt depth, const PetscInt numPoints[], const PetscInt coneSize[], const PetscInt cones[], const PetscInt coneOrientations[], const PetscScalar vertexCoords[])
3034 {
3035   Vec            coordinates;
3036   PetscSection   coordSection;
3037   PetscScalar    *coords;
3038   PetscInt       coordSize, firstVertex = -1, pStart = 0, pEnd = 0, p, v, dim, dimEmbed, d, off;
3039   PetscErrorCode ierr;
3040 
3041   PetscFunctionBegin;
3042   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
3043   ierr = DMGetCoordinateDim(dm, &dimEmbed);CHKERRQ(ierr);
3044   if (dimEmbed < dim) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Embedding dimension %d cannot be less than intrinsic dimension %d",dimEmbed,dim);
3045   for (d = 0; d <= depth; ++d) pEnd += numPoints[d];
3046   ierr = DMPlexSetChart(dm, pStart, pEnd);CHKERRQ(ierr);
3047   for (p = pStart; p < pEnd; ++p) {
3048     ierr = DMPlexSetConeSize(dm, p, coneSize[p-pStart]);CHKERRQ(ierr);
3049     if (firstVertex < 0 && !coneSize[p - pStart]) {
3050       firstVertex = p - pStart;
3051     }
3052   }
3053   if (firstVertex < 0 && numPoints[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Expected %d vertices but could not find any", numPoints[0]);
3054   ierr = DMSetUp(dm);CHKERRQ(ierr); /* Allocate space for cones */
3055   for (p = pStart, off = 0; p < pEnd; off += coneSize[p-pStart], ++p) {
3056     ierr = DMPlexSetCone(dm, p, &cones[off]);CHKERRQ(ierr);
3057     ierr = DMPlexSetConeOrientation(dm, p, &coneOrientations[off]);CHKERRQ(ierr);
3058   }
3059   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
3060   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
3061   /* Build coordinates */
3062   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
3063   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
3064   ierr = PetscSectionSetFieldComponents(coordSection, 0, dimEmbed);CHKERRQ(ierr);
3065   ierr = PetscSectionSetChart(coordSection, firstVertex, firstVertex+numPoints[0]);CHKERRQ(ierr);
3066   for (v = firstVertex; v < firstVertex+numPoints[0]; ++v) {
3067     ierr = PetscSectionSetDof(coordSection, v, dimEmbed);CHKERRQ(ierr);
3068     ierr = PetscSectionSetFieldDof(coordSection, v, 0, dimEmbed);CHKERRQ(ierr);
3069   }
3070   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
3071   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
3072   ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
3073   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
3074   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
3075   ierr = VecSetBlockSize(coordinates, dimEmbed);CHKERRQ(ierr);
3076   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
3077   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
3078   for (v = 0; v < numPoints[0]; ++v) {
3079     PetscInt off;
3080 
3081     ierr = PetscSectionGetOffset(coordSection, v+firstVertex, &off);CHKERRQ(ierr);
3082     for (d = 0; d < dimEmbed; ++d) {
3083       coords[off+d] = vertexCoords[v*dimEmbed+d];
3084     }
3085   }
3086   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
3087   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
3088   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
3089   PetscFunctionReturn(0);
3090 }
3091 
3092 /*@C
3093   DMPlexCreateCellVertexFromFile - Create a DMPlex mesh from a simple cell-vertex file.
3094 
3095 + comm        - The MPI communicator
3096 . filename    - Name of the .dat file
3097 - interpolate - Create faces and edges in the mesh
3098 
3099   Output Parameter:
3100 . dm  - The DM object representing the mesh
3101 
3102   Note: The format is the simplest possible:
3103 $ Ne
3104 $ v0 v1 ... vk
3105 $ Nv
3106 $ x y z marker
3107 
3108   Level: beginner
3109 
3110 .seealso: DMPlexCreateFromFile(), DMPlexCreateMedFromFile(), DMPlexCreateGmsh(), DMPlexCreate()
3111 @*/
3112 PetscErrorCode DMPlexCreateCellVertexFromFile(MPI_Comm comm, const char filename[], PetscBool interpolate, DM *dm)
3113 {
3114   DMLabel         marker;
3115   PetscViewer     viewer;
3116   Vec             coordinates;
3117   PetscSection    coordSection;
3118   PetscScalar    *coords;
3119   char            line[PETSC_MAX_PATH_LEN];
3120   PetscInt        dim = 3, cdim = 3, coordSize, v, c, d;
3121   PetscMPIInt     rank;
3122   int             snum, Nv, Nc;
3123   PetscErrorCode  ierr;
3124 
3125   PetscFunctionBegin;
3126   ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
3127   ierr = PetscViewerCreate(comm, &viewer);CHKERRQ(ierr);
3128   ierr = PetscViewerSetType(viewer, PETSCVIEWERASCII);CHKERRQ(ierr);
3129   ierr = PetscViewerFileSetMode(viewer, FILE_MODE_READ);CHKERRQ(ierr);
3130   ierr = PetscViewerFileSetName(viewer, filename);CHKERRQ(ierr);
3131   if (!rank) {
3132     ierr = PetscViewerRead(viewer, line, 2, NULL, PETSC_STRING);CHKERRQ(ierr);
3133     snum = sscanf(line, "%d %d", &Nc, &Nv);
3134     if (snum != 2) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unable to parse cell-vertex file: %s", line);
3135   } else {
3136     Nc = Nv = 0;
3137   }
3138   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
3139   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
3140   ierr = DMPlexSetChart(*dm, 0, Nc+Nv);CHKERRQ(ierr);
3141   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
3142   ierr = DMSetCoordinateDim(*dm, cdim);CHKERRQ(ierr);
3143   /* Read topology */
3144   if (!rank) {
3145     PetscInt cone[8], corners = 8;
3146     int      vbuf[8], v;
3147 
3148     for (c = 0; c < Nc; ++c) {ierr = DMPlexSetConeSize(*dm, c, corners);CHKERRQ(ierr);}
3149     ierr = DMSetUp(*dm);CHKERRQ(ierr);
3150     for (c = 0; c < Nc; ++c) {
3151       ierr = PetscViewerRead(viewer, line, corners, NULL, PETSC_STRING);CHKERRQ(ierr);
3152       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]);
3153       if (snum != corners) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unable to parse cell-vertex file: %s", line);
3154       for (v = 0; v < corners; ++v) cone[v] = vbuf[v] + Nc;
3155       /* Hexahedra are inverted */
3156       {
3157         PetscInt tmp = cone[1];
3158         cone[1] = cone[3];
3159         cone[3] = tmp;
3160       }
3161       ierr = DMPlexSetCone(*dm, c, cone);CHKERRQ(ierr);
3162     }
3163   }
3164   ierr = DMPlexSymmetrize(*dm);CHKERRQ(ierr);
3165   ierr = DMPlexStratify(*dm);CHKERRQ(ierr);
3166   /* Read coordinates */
3167   ierr = DMGetCoordinateSection(*dm, &coordSection);CHKERRQ(ierr);
3168   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
3169   ierr = PetscSectionSetFieldComponents(coordSection, 0, cdim);CHKERRQ(ierr);
3170   ierr = PetscSectionSetChart(coordSection, Nc, Nc + Nv);CHKERRQ(ierr);
3171   for (v = Nc; v < Nc+Nv; ++v) {
3172     ierr = PetscSectionSetDof(coordSection, v, cdim);CHKERRQ(ierr);
3173     ierr = PetscSectionSetFieldDof(coordSection, v, 0, cdim);CHKERRQ(ierr);
3174   }
3175   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
3176   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
3177   ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
3178   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
3179   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
3180   ierr = VecSetBlockSize(coordinates, cdim);CHKERRQ(ierr);
3181   ierr = VecSetType(coordinates, VECSTANDARD);CHKERRQ(ierr);
3182   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
3183   if (!rank) {
3184     double x[3];
3185     int    val;
3186 
3187     ierr = DMCreateLabel(*dm, "marker");CHKERRQ(ierr);
3188     ierr = DMGetLabel(*dm, "marker", &marker);CHKERRQ(ierr);
3189     for (v = 0; v < Nv; ++v) {
3190       ierr = PetscViewerRead(viewer, line, 4, NULL, PETSC_STRING);CHKERRQ(ierr);
3191       snum = sscanf(line, "%lg %lg %lg %d", &x[0], &x[1], &x[2], &val);
3192       if (snum != 4) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unable to parse cell-vertex file: %s", line);
3193       for (d = 0; d < cdim; ++d) coords[v*cdim+d] = x[d];
3194       if (val) {ierr = DMLabelSetValue(marker, v+Nc, val);CHKERRQ(ierr);}
3195     }
3196   }
3197   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
3198   ierr = DMSetCoordinatesLocal(*dm, coordinates);CHKERRQ(ierr);
3199   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
3200   ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
3201   if (interpolate) {
3202     DM      idm;
3203     DMLabel bdlabel;
3204 
3205     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
3206     ierr = DMDestroy(dm);CHKERRQ(ierr);
3207     *dm  = idm;
3208 
3209     ierr = DMGetLabel(*dm, "marker", &bdlabel);CHKERRQ(ierr);
3210     ierr = DMPlexMarkBoundaryFaces(*dm, PETSC_DETERMINE, bdlabel);CHKERRQ(ierr);
3211     ierr = DMPlexLabelComplete(*dm, bdlabel);CHKERRQ(ierr);
3212   }
3213   PetscFunctionReturn(0);
3214 }
3215 
3216 /*@C
3217   DMPlexCreateFromFile - This takes a filename and produces a DM
3218 
3219   Input Parameters:
3220 + comm - The communicator
3221 . filename - A file name
3222 - interpolate - Flag to create intermediate mesh pieces (edges, faces)
3223 
3224   Output Parameter:
3225 . dm - The DM
3226 
3227   Options Database Keys:
3228 . -dm_plex_create_from_hdf5_xdmf - use the PETSC_VIEWER_HDF5_XDMF format for reading HDF5
3229 
3230   Use -dm_plex_create_ prefix to pass options to the internal PetscViewer, e.g.
3231 $ -dm_plex_create_viewer_hdf5_collective
3232 
3233   Level: beginner
3234 
3235 .seealso: DMPlexCreateFromDAG(), DMPlexCreateFromCellList(), DMPlexCreate()
3236 @*/
3237 PetscErrorCode DMPlexCreateFromFile(MPI_Comm comm, const char filename[], PetscBool interpolate, DM *dm)
3238 {
3239   const char    *extGmsh    = ".msh";
3240   const char    *extGmsh2   = ".msh2";
3241   const char    *extGmsh4   = ".msh4";
3242   const char    *extCGNS    = ".cgns";
3243   const char    *extExodus  = ".exo";
3244   const char    *extGenesis = ".gen";
3245   const char    *extFluent  = ".cas";
3246   const char    *extHDF5    = ".h5";
3247   const char    *extMed     = ".med";
3248   const char    *extPLY     = ".ply";
3249   const char    *extCV      = ".dat";
3250   size_t         len;
3251   PetscBool      isGmsh, isGmsh2, isGmsh4, isCGNS, isExodus, isGenesis, isFluent, isHDF5, isMed, isPLY, isCV;
3252   PetscMPIInt    rank;
3253   PetscErrorCode ierr;
3254 
3255   PetscFunctionBegin;
3256   PetscValidCharPointer(filename, 2);
3257   PetscValidPointer(dm, 4);
3258   ierr = DMInitializePackage();CHKERRQ(ierr);
3259   ierr = PetscLogEventBegin(DMPLEX_CreateFromFile,0,0,0,0);CHKERRQ(ierr);
3260   ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
3261   ierr = PetscStrlen(filename, &len);CHKERRQ(ierr);
3262   if (!len) SETERRQ(comm, PETSC_ERR_ARG_WRONG, "Filename must be a valid path");
3263   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extGmsh,    4, &isGmsh);CHKERRQ(ierr);
3264   ierr = PetscStrncmp(&filename[PetscMax(0,len-5)], extGmsh2,   5, &isGmsh2);CHKERRQ(ierr);
3265   ierr = PetscStrncmp(&filename[PetscMax(0,len-5)], extGmsh4,   5, &isGmsh4);CHKERRQ(ierr);
3266   ierr = PetscStrncmp(&filename[PetscMax(0,len-5)], extCGNS,    5, &isCGNS);CHKERRQ(ierr);
3267   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extExodus,  4, &isExodus);CHKERRQ(ierr);
3268   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extGenesis, 4, &isGenesis);CHKERRQ(ierr);
3269   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extFluent,  4, &isFluent);CHKERRQ(ierr);
3270   ierr = PetscStrncmp(&filename[PetscMax(0,len-3)], extHDF5,    3, &isHDF5);CHKERRQ(ierr);
3271   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extMed,     4, &isMed);CHKERRQ(ierr);
3272   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extPLY,     4, &isPLY);CHKERRQ(ierr);
3273   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extCV,      4, &isCV);CHKERRQ(ierr);
3274   if (isGmsh || isGmsh2 || isGmsh4) {
3275     ierr = DMPlexCreateGmshFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
3276   } else if (isCGNS) {
3277     ierr = DMPlexCreateCGNSFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
3278   } else if (isExodus || isGenesis) {
3279     ierr = DMPlexCreateExodusFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
3280   } else if (isFluent) {
3281     ierr = DMPlexCreateFluentFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
3282   } else if (isHDF5) {
3283     PetscBool      load_hdf5_xdmf = PETSC_FALSE;
3284     PetscViewer viewer;
3285 
3286     /* PETSC_VIEWER_HDF5_XDMF is used if the filename ends with .xdmf.h5, or if -dm_plex_create_from_hdf5_xdmf option is present */
3287     ierr = PetscStrncmp(&filename[PetscMax(0,len-8)], ".xdmf",  5, &load_hdf5_xdmf);CHKERRQ(ierr);
3288     ierr = PetscOptionsGetBool(NULL, NULL, "-dm_plex_create_from_hdf5_xdmf", &load_hdf5_xdmf, NULL);CHKERRQ(ierr);
3289     ierr = PetscViewerCreate(comm, &viewer);CHKERRQ(ierr);
3290     ierr = PetscViewerSetType(viewer, PETSCVIEWERHDF5);CHKERRQ(ierr);
3291     ierr = PetscViewerSetOptionsPrefix(viewer, "dm_plex_create_");CHKERRQ(ierr);
3292     ierr = PetscViewerSetFromOptions(viewer);CHKERRQ(ierr);
3293     ierr = PetscViewerFileSetMode(viewer, FILE_MODE_READ);CHKERRQ(ierr);
3294     ierr = PetscViewerFileSetName(viewer, filename);CHKERRQ(ierr);
3295     ierr = DMCreate(comm, dm);CHKERRQ(ierr);
3296     ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
3297     if (load_hdf5_xdmf) {ierr = PetscViewerPushFormat(viewer, PETSC_VIEWER_HDF5_XDMF);CHKERRQ(ierr);}
3298     ierr = DMLoad(*dm, viewer);CHKERRQ(ierr);
3299     if (load_hdf5_xdmf) {ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);}
3300     ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
3301 
3302     if (interpolate) {
3303       DM idm;
3304 
3305       ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
3306       ierr = DMDestroy(dm);CHKERRQ(ierr);
3307       *dm  = idm;
3308     }
3309   } else if (isMed) {
3310     ierr = DMPlexCreateMedFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
3311   } else if (isPLY) {
3312     ierr = DMPlexCreatePLYFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
3313   } else if (isCV) {
3314     ierr = DMPlexCreateCellVertexFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
3315   } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cannot load file %s: unrecognized extension", filename);
3316   ierr = PetscLogEventEnd(DMPLEX_CreateFromFile,0,0,0,0);CHKERRQ(ierr);
3317   PetscFunctionReturn(0);
3318 }
3319 
3320 /*@
3321   DMPlexCreateReferenceCell - Create a DMPLEX with the appropriate FEM reference cell
3322 
3323   Collective
3324 
3325   Input Parameters:
3326 + comm    - The communicator
3327 . dim     - The spatial dimension
3328 - simplex - Flag for simplex, otherwise use a tensor-product cell
3329 
3330   Output Parameter:
3331 . refdm - The reference cell
3332 
3333   Level: intermediate
3334 
3335 .seealso:
3336 @*/
3337 PetscErrorCode DMPlexCreateReferenceCell(MPI_Comm comm, PetscInt dim, PetscBool simplex, DM *refdm)
3338 {
3339   DM             rdm;
3340   Vec            coords;
3341   PetscErrorCode ierr;
3342 
3343   PetscFunctionBeginUser;
3344   ierr = DMCreate(comm, &rdm);CHKERRQ(ierr);
3345   ierr = DMSetType(rdm, DMPLEX);CHKERRQ(ierr);
3346   ierr = DMSetDimension(rdm, dim);CHKERRQ(ierr);
3347   switch (dim) {
3348   case 0:
3349   {
3350     PetscInt    numPoints[1]        = {1};
3351     PetscInt    coneSize[1]         = {0};
3352     PetscInt    cones[1]            = {0};
3353     PetscInt    coneOrientations[1] = {0};
3354     PetscScalar vertexCoords[1]     = {0.0};
3355 
3356     ierr = DMPlexCreateFromDAG(rdm, 0, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
3357   }
3358   break;
3359   case 1:
3360   {
3361     PetscInt    numPoints[2]        = {2, 1};
3362     PetscInt    coneSize[3]         = {2, 0, 0};
3363     PetscInt    cones[2]            = {1, 2};
3364     PetscInt    coneOrientations[2] = {0, 0};
3365     PetscScalar vertexCoords[2]     = {-1.0,  1.0};
3366 
3367     ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
3368   }
3369   break;
3370   case 2:
3371     if (simplex) {
3372       PetscInt    numPoints[2]        = {3, 1};
3373       PetscInt    coneSize[4]         = {3, 0, 0, 0};
3374       PetscInt    cones[3]            = {1, 2, 3};
3375       PetscInt    coneOrientations[3] = {0, 0, 0};
3376       PetscScalar vertexCoords[6]     = {-1.0, -1.0,  1.0, -1.0,  -1.0, 1.0};
3377 
3378       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
3379     } else {
3380       PetscInt    numPoints[2]        = {4, 1};
3381       PetscInt    coneSize[5]         = {4, 0, 0, 0, 0};
3382       PetscInt    cones[4]            = {1, 2, 3, 4};
3383       PetscInt    coneOrientations[4] = {0, 0, 0, 0};
3384       PetscScalar vertexCoords[8]     = {-1.0, -1.0,  1.0, -1.0,  1.0, 1.0,  -1.0, 1.0};
3385 
3386       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
3387     }
3388   break;
3389   case 3:
3390     if (simplex) {
3391       PetscInt    numPoints[2]        = {4, 1};
3392       PetscInt    coneSize[5]         = {4, 0, 0, 0, 0};
3393       PetscInt    cones[4]            = {1, 3, 2, 4};
3394       PetscInt    coneOrientations[4] = {0, 0, 0, 0};
3395       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};
3396 
3397       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
3398     } else {
3399       PetscInt    numPoints[2]        = {8, 1};
3400       PetscInt    coneSize[9]         = {8, 0, 0, 0, 0, 0, 0, 0, 0};
3401       PetscInt    cones[8]            = {1, 4, 3, 2, 5, 6, 7, 8};
3402       PetscInt    coneOrientations[8] = {0, 0, 0, 0, 0, 0, 0, 0};
3403       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,
3404                                          -1.0, -1.0,  1.0,  1.0, -1.0,  1.0,  1.0, 1.0,  1.0,  -1.0, 1.0,  1.0};
3405 
3406       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
3407     }
3408   break;
3409   default:
3410     SETERRQ1(comm, PETSC_ERR_ARG_WRONG, "Cannot create reference cell for dimension %d", dim);
3411   }
3412   ierr = DMPlexInterpolate(rdm, refdm);CHKERRQ(ierr);
3413   if (rdm->coordinateDM) {
3414     DM           ncdm;
3415     PetscSection cs;
3416     PetscInt     pEnd = -1;
3417 
3418     ierr = DMGetLocalSection(rdm->coordinateDM, &cs);CHKERRQ(ierr);
3419     if (cs) {ierr = PetscSectionGetChart(cs, NULL, &pEnd);CHKERRQ(ierr);}
3420     if (pEnd >= 0) {
3421       ierr = DMClone(*refdm, &ncdm);CHKERRQ(ierr);
3422       ierr = DMCopyDisc(rdm->coordinateDM, ncdm);CHKERRQ(ierr);
3423       ierr = DMSetLocalSection(ncdm, cs);CHKERRQ(ierr);
3424       ierr = DMSetCoordinateDM(*refdm, ncdm);CHKERRQ(ierr);
3425       ierr = DMDestroy(&ncdm);CHKERRQ(ierr);
3426     }
3427   }
3428   ierr = DMGetCoordinatesLocal(rdm, &coords);CHKERRQ(ierr);
3429   if (coords) {
3430     ierr = DMSetCoordinatesLocal(*refdm, coords);CHKERRQ(ierr);
3431   } else {
3432     ierr = DMGetCoordinates(rdm, &coords);CHKERRQ(ierr);
3433     if (coords) {ierr = DMSetCoordinates(*refdm, coords);CHKERRQ(ierr);}
3434   }
3435   ierr = DMDestroy(&rdm);CHKERRQ(ierr);
3436   PetscFunctionReturn(0);
3437 }
3438