xref: /petsc/src/dm/impls/plex/plexcreate.c (revision b4db17ed4967172e430e8d3533aad9efd6fc38f9)
1 #define PETSCDM_DLL
2 #include <petsc/private/dmpleximpl.h>    /*I   "petscdmplex.h"   I*/
3 #include <petscdmda.h>
4 #include <petscsf.h>
5 
6 /*@
7   DMPlexCreateDoublet - Creates a mesh of two cells of the specified type, optionally with later refinement.
8 
9   Collective on MPI_Comm
10 
11   Input Parameters:
12 + comm - The communicator for the DM object
13 . dim - The spatial dimension
14 . simplex - Flag for simplicial cells, otherwise they are tensor product cells
15 . interpolate - Flag to create intermediate mesh pieces (edges, faces)
16 . refinementUniform - Flag for uniform parallel refinement
17 - refinementLimit - A nonzero number indicates the largest admissible volume for a refined cell
18 
19   Output Parameter:
20 . dm - The DM object
21 
22   Level: beginner
23 
24 .keywords: DM, create
25 .seealso: DMSetType(), DMCreate()
26 @*/
27 PetscErrorCode DMPlexCreateDoublet(MPI_Comm comm, PetscInt dim, PetscBool simplex, PetscBool interpolate, PetscBool refinementUniform, PetscReal refinementLimit, DM *newdm)
28 {
29   DM             dm;
30   PetscInt       p;
31   PetscMPIInt    rank;
32   PetscErrorCode ierr;
33 
34   PetscFunctionBegin;
35   ierr = DMCreate(comm, &dm);CHKERRQ(ierr);
36   ierr = DMSetType(dm, DMPLEX);CHKERRQ(ierr);
37   ierr = DMSetDimension(dm, dim);CHKERRQ(ierr);
38   ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
39   switch (dim) {
40   case 2:
41     if (simplex) {ierr = PetscObjectSetName((PetscObject) dm, "triangular");CHKERRQ(ierr);}
42     else         {ierr = PetscObjectSetName((PetscObject) dm, "quadrilateral");CHKERRQ(ierr);}
43     break;
44   case 3:
45     if (simplex) {ierr = PetscObjectSetName((PetscObject) dm, "tetrahedral");CHKERRQ(ierr);}
46     else         {ierr = PetscObjectSetName((PetscObject) dm, "hexahedral");CHKERRQ(ierr);}
47     break;
48   default:
49     SETERRQ1(comm, PETSC_ERR_ARG_OUTOFRANGE, "Cannot make meshes for dimension %d", dim);
50   }
51   if (rank) {
52     PetscInt numPoints[2] = {0, 0};
53     ierr = DMPlexCreateFromDAG(dm, 1, numPoints, NULL, NULL, NULL, NULL);CHKERRQ(ierr);
54   } else {
55     switch (dim) {
56     case 2:
57       if (simplex) {
58         PetscInt    numPoints[2]        = {4, 2};
59         PetscInt    coneSize[6]         = {3, 3, 0, 0, 0, 0};
60         PetscInt    cones[6]            = {2, 3, 4,  5, 4, 3};
61         PetscInt    coneOrientations[6] = {0, 0, 0,  0, 0, 0};
62         PetscScalar vertexCoords[8]     = {-0.5, 0.5, 0.0, 0.0, 0.0, 1.0, 0.5, 0.5};
63         PetscInt    markerPoints[8]     = {2, 1, 3, 1, 4, 1, 5, 1};
64 
65         ierr = DMPlexCreateFromDAG(dm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
66         for (p = 0; p < 4; ++p) {ierr = DMSetLabelValue(dm, "marker", markerPoints[p*2], markerPoints[p*2+1]);CHKERRQ(ierr);}
67       } else {
68         PetscInt    numPoints[2]        = {6, 2};
69         PetscInt    coneSize[8]         = {4, 4, 0, 0, 0, 0, 0, 0};
70         PetscInt    cones[8]            = {2, 3, 4, 5,  3, 6, 7, 4};
71         PetscInt    coneOrientations[8] = {0, 0, 0, 0,  0, 0, 0, 0};
72         PetscScalar vertexCoords[12]    = {-1.0, -0.5,  0.0, -0.5,  0.0, 0.5,  -1.0, 0.5,  1.0, -0.5,  1.0, 0.5};
73 
74         ierr = DMPlexCreateFromDAG(dm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
75       }
76       break;
77     case 3:
78       if (simplex) {
79         PetscInt    numPoints[2]        = {5, 2};
80         PetscInt    coneSize[7]         = {4, 4, 0, 0, 0, 0, 0};
81         PetscInt    cones[8]            = {4, 3, 5, 2,  5, 3, 4, 6};
82         PetscInt    coneOrientations[8] = {0, 0, 0, 0,  0, 0, 0, 0};
83         PetscScalar vertexCoords[15]    = {-1.0, 0.0, 0.0,  0.0, -1.0, 0.0,  0.0, 0.0, 1.0,  0.0, 1.0, 0.0,  1.0, 0.0, 0.0};
84         PetscInt    markerPoints[10]    = {2, 1, 3, 1, 4, 1, 5, 1, 6, 1};
85 
86         ierr = DMPlexCreateFromDAG(dm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
87         for (p = 0; p < 5; ++p) {ierr = DMSetLabelValue(dm, "marker", markerPoints[p*2], markerPoints[p*2+1]);CHKERRQ(ierr);}
88       } else {
89         PetscInt    numPoints[2]         = {12, 2};
90         PetscInt    coneSize[14]         = {8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0};
91         PetscInt    cones[16]            = {2, 3, 4, 5, 6, 7, 8, 9,  5, 4, 10, 11, 7, 12, 13, 8};
92         PetscInt    coneOrientations[16] = {0, 0, 0, 0, 0, 0, 0, 0,  0, 0,  0,  0, 0,  0,  0, 0};
93         PetscScalar vertexCoords[36]     = {-1.0, -0.5, -0.5,  -1.0,  0.5, -0.5,  0.0,  0.5, -0.5,   0.0, -0.5, -0.5,
94                                             -1.0, -0.5,  0.5,   0.0, -0.5,  0.5,  0.0,  0.5,  0.5,  -1.0,  0.5,  0.5,
95                                              1.0,  0.5, -0.5,   1.0, -0.5, -0.5,  1.0, -0.5,  0.5,   1.0,  0.5,  0.5};
96 
97         ierr = DMPlexCreateFromDAG(dm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
98       }
99       break;
100     default:
101       SETERRQ1(comm, PETSC_ERR_ARG_OUTOFRANGE, "Cannot make meshes for dimension %d", dim);
102     }
103   }
104   *newdm = dm;
105   if (refinementLimit > 0.0) {
106     DM rdm;
107     const char *name;
108 
109     ierr = DMPlexSetRefinementUniform(*newdm, PETSC_FALSE);CHKERRQ(ierr);
110     ierr = DMPlexSetRefinementLimit(*newdm, refinementLimit);CHKERRQ(ierr);
111     ierr = DMRefine(*newdm, comm, &rdm);CHKERRQ(ierr);
112     ierr = PetscObjectGetName((PetscObject) *newdm, &name);CHKERRQ(ierr);
113     ierr = PetscObjectSetName((PetscObject)    rdm,  name);CHKERRQ(ierr);
114     ierr = DMDestroy(newdm);CHKERRQ(ierr);
115     *newdm = rdm;
116   }
117   if (interpolate) {
118     DM idm;
119 
120     ierr = DMPlexInterpolate(*newdm, &idm);CHKERRQ(ierr);
121     ierr = DMDestroy(newdm);CHKERRQ(ierr);
122     *newdm = idm;
123   }
124   {
125     DM refinedMesh     = NULL;
126     DM distributedMesh = NULL;
127 
128     /* Distribute mesh over processes */
129     ierr = DMPlexDistribute(*newdm, 0, NULL, &distributedMesh);CHKERRQ(ierr);
130     if (distributedMesh) {
131       ierr = DMDestroy(newdm);CHKERRQ(ierr);
132       *newdm = distributedMesh;
133     }
134     if (refinementUniform) {
135       ierr = DMPlexSetRefinementUniform(*newdm, refinementUniform);CHKERRQ(ierr);
136       ierr = DMRefine(*newdm, comm, &refinedMesh);CHKERRQ(ierr);
137       if (refinedMesh) {
138         ierr = DMDestroy(newdm);CHKERRQ(ierr);
139         *newdm = refinedMesh;
140       }
141     }
142   }
143   PetscFunctionReturn(0);
144 }
145 
146 /*@
147   DMPlexCreateSquareBoundary - Creates a 1D mesh the is the boundary of a square lattice.
148 
149   Collective on MPI_Comm
150 
151   Input Parameters:
152 + comm  - The communicator for the DM object
153 . lower - The lower left corner coordinates
154 . upper - The upper right corner coordinates
155 - edges - The number of cells in each direction
156 
157   Output Parameter:
158 . dm  - The DM object
159 
160   Note: Here is the numbering returned for 2 cells in each direction:
161 $ 18--5-17--4--16
162 $  |     |     |
163 $  6    10     3
164 $  |     |     |
165 $ 19-11-20--9--15
166 $  |     |     |
167 $  7     8     2
168 $  |     |     |
169 $ 12--0-13--1--14
170 
171   Level: beginner
172 
173 .keywords: DM, create
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 on MPI_Comm
297 
298   Input Parameters:
299 + comm  - The communicator for the DM object
300 . lower - The lower left front corner coordinates
301 . upper - The upper right back corner coordinates
302 - edges - The number of cells in each direction
303 
304   Output Parameter:
305 . dm  - The DM object
306 
307   Level: beginner
308 
309 .keywords: DM, create
310 .seealso: DMPlexCreateBoxMesh(), DMPlexCreateSquareBoundary(), DMSetType(), DMCreate()
311 @*/
312 PetscErrorCode DMPlexCreateCubeBoundary(DM dm, const PetscReal lower[], const PetscReal upper[], const PetscInt faces[])
313 {
314   PetscInt       vertices[3], numVertices;
315   PetscInt       numFaces    = 2*faces[0]*faces[1] + 2*faces[1]*faces[2] + 2*faces[0]*faces[2];
316   Vec            coordinates;
317   PetscSection   coordSection;
318   PetscScalar    *coords;
319   PetscInt       coordSize;
320   PetscMPIInt    rank;
321   PetscInt       v, vx, vy, vz;
322   PetscInt       voffset, iface=0, cone[4];
323   PetscErrorCode ierr;
324 
325   PetscFunctionBegin;
326   if ((faces[0] < 1) || (faces[1] < 1) || (faces[2] < 1)) SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Must have at least 1 face per side");
327   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);CHKERRQ(ierr);
328   vertices[0] = faces[0]+1; vertices[1] = faces[1]+1; vertices[2] = faces[2]+1;
329   numVertices = vertices[0]*vertices[1]*vertices[2];
330   if (!rank) {
331     PetscInt f;
332 
333     ierr = DMPlexSetChart(dm, 0, numFaces+numVertices);CHKERRQ(ierr);
334     for (f = 0; f < numFaces; ++f) {
335       ierr = DMPlexSetConeSize(dm, f, 4);CHKERRQ(ierr);
336     }
337     ierr = DMSetUp(dm);CHKERRQ(ierr); /* Allocate space for cones */
338     for (v = 0; v < numFaces+numVertices; ++v) {
339       ierr = DMSetLabelValue(dm, "marker", v, 1);CHKERRQ(ierr);
340     }
341 
342     /* Side 0 (Top) */
343     for (vy = 0; vy < faces[1]; vy++) {
344       for (vx = 0; vx < faces[0]; vx++) {
345         voffset = numFaces + vertices[0]*vertices[1]*(vertices[2]-1) + vy*vertices[0] + vx;
346         cone[0] = voffset; cone[1] = voffset+1; cone[2] = voffset+vertices[0]+1; cone[3] = voffset+vertices[0];
347         ierr    = DMPlexSetCone(dm, iface, cone);CHKERRQ(ierr);
348         iface++;
349       }
350     }
351 
352     /* Side 1 (Bottom) */
353     for (vy = 0; vy < faces[1]; vy++) {
354       for (vx = 0; vx < faces[0]; vx++) {
355         voffset = numFaces + vy*(faces[0]+1) + vx;
356         cone[0] = voffset+1; cone[1] = voffset; cone[2] = voffset+vertices[0]; cone[3] = voffset+vertices[0]+1;
357         ierr    = DMPlexSetCone(dm, iface, cone);CHKERRQ(ierr);
358         iface++;
359       }
360     }
361 
362     /* Side 2 (Front) */
363     for (vz = 0; vz < faces[2]; vz++) {
364       for (vx = 0; vx < faces[0]; vx++) {
365         voffset = numFaces + vz*vertices[0]*vertices[1] + vx;
366         cone[0] = voffset; cone[1] = voffset+1; cone[2] = voffset+vertices[0]*vertices[1]+1; cone[3] = voffset+vertices[0]*vertices[1];
367         ierr    = DMPlexSetCone(dm, iface, cone);CHKERRQ(ierr);
368         iface++;
369       }
370     }
371 
372     /* Side 3 (Back) */
373     for (vz = 0; vz < faces[2]; vz++) {
374       for (vx = 0; vx < faces[0]; vx++) {
375         voffset = numFaces + vz*vertices[0]*vertices[1] + vertices[0]*(vertices[1]-1) + vx;
376         cone[0] = voffset+vertices[0]*vertices[1]; cone[1] = voffset+vertices[0]*vertices[1]+1;
377         cone[2] = voffset+1; cone[3] = voffset;
378         ierr    = DMPlexSetCone(dm, iface, cone);CHKERRQ(ierr);
379         iface++;
380       }
381     }
382 
383     /* Side 4 (Left) */
384     for (vz = 0; vz < faces[2]; vz++) {
385       for (vy = 0; vy < faces[1]; vy++) {
386         voffset = numFaces + vz*vertices[0]*vertices[1] + vy*vertices[0];
387         cone[0] = voffset; cone[1] = voffset+vertices[0]*vertices[1];
388         cone[2] = voffset+vertices[0]*vertices[1]+vertices[0]; cone[3] = voffset+vertices[0];
389         ierr    = DMPlexSetCone(dm, iface, cone);CHKERRQ(ierr);
390         iface++;
391       }
392     }
393 
394     /* Side 5 (Right) */
395     for (vz = 0; vz < faces[2]; vz++) {
396       for (vy = 0; vy < faces[1]; vy++) {
397         voffset = numFaces + vz*vertices[0]*vertices[1] + vy*vertices[0] + faces[0];
398         cone[0] = voffset+vertices[0]*vertices[1]; cone[1] = voffset;
399         cone[2] = voffset+vertices[0]; cone[3] = voffset+vertices[0]*vertices[1]+vertices[0];
400         ierr    = DMPlexSetCone(dm, iface, cone);CHKERRQ(ierr);
401         iface++;
402       }
403     }
404   }
405   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
406   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
407   /* Build coordinates */
408   ierr = DMSetCoordinateDim(dm, 3);CHKERRQ(ierr);
409   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
410   ierr = PetscSectionSetChart(coordSection, numFaces, numFaces + numVertices);CHKERRQ(ierr);
411   for (v = numFaces; v < numFaces+numVertices; ++v) {
412     ierr = PetscSectionSetDof(coordSection, v, 3);CHKERRQ(ierr);
413   }
414   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
415   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
416   ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
417   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
418   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
419   ierr = VecSetBlockSize(coordinates, 3);CHKERRQ(ierr);
420   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
421   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
422   for (vz = 0; vz <= faces[2]; ++vz) {
423     for (vy = 0; vy <= faces[1]; ++vy) {
424       for (vx = 0; vx <= faces[0]; ++vx) {
425         coords[((vz*(faces[1]+1)+vy)*(faces[0]+1)+vx)*3+0] = lower[0] + ((upper[0] - lower[0])/faces[0])*vx;
426         coords[((vz*(faces[1]+1)+vy)*(faces[0]+1)+vx)*3+1] = lower[1] + ((upper[1] - lower[1])/faces[1])*vy;
427         coords[((vz*(faces[1]+1)+vy)*(faces[0]+1)+vx)*3+2] = lower[2] + ((upper[2] - lower[2])/faces[2])*vz;
428       }
429     }
430   }
431   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
432   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
433   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
434   PetscFunctionReturn(0);
435 }
436 
437 static PetscErrorCode DMPlexCreateLineMesh_Internal(MPI_Comm comm,PetscInt segments,PetscReal lower,PetscReal upper,DMBoundaryType bd,DM *dm)
438 {
439   PetscInt       i,fStart,fEnd,numCells = 0,numVerts = 0;
440   PetscInt       numPoints[2],*coneSize,*cones,*coneOrientations;
441   PetscScalar    *vertexCoords;
442   PetscReal      L,maxCell;
443   PetscBool      markerSeparate = PETSC_FALSE;
444   PetscInt       markerLeft  = 1, faceMarkerLeft  = 1;
445   PetscInt       markerRight = 1, faceMarkerRight = 2;
446   PetscBool      wrap = (bd == DM_BOUNDARY_PERIODIC || bd == DM_BOUNDARY_TWIST) ? PETSC_TRUE : PETSC_FALSE;
447   PetscMPIInt    rank;
448   PetscErrorCode ierr;
449 
450   PetscFunctionBegin;
451   PetscValidPointer(dm,4);
452 
453   ierr = DMCreate(comm,dm);CHKERRQ(ierr);
454   ierr = DMSetType(*dm,DMPLEX);CHKERRQ(ierr);
455   ierr = DMSetDimension(*dm,1);CHKERRQ(ierr);
456   ierr = DMCreateLabel(*dm,"marker");CHKERRQ(ierr);
457   ierr = DMCreateLabel(*dm,"Face Sets");CHKERRQ(ierr);
458 
459   ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
460   if (!rank) numCells = segments;
461   if (!rank) numVerts = segments + (wrap ? 0 : 1);
462 
463   numPoints[0] = numVerts ; numPoints[1] = numCells;
464   ierr = PetscMalloc4(numCells+numVerts,&coneSize,numCells*2,&cones,numCells+numVerts,&coneOrientations,numVerts,&vertexCoords);CHKERRQ(ierr);
465   ierr = PetscMemzero(coneOrientations,(numCells+numVerts)*sizeof(PetscInt));CHKERRQ(ierr);
466   for (i = 0; i < numCells; ++i) { coneSize[i] = 2; }
467   for (i = 0; i < numVerts; ++i) { coneSize[numCells+i] = 0; }
468   for (i = 0; i < numCells; ++i) { cones[2*i] = numCells + i%numVerts; cones[2*i+1] = numCells + (i+1)%numVerts; }
469   for (i = 0; i < numVerts; ++i) { vertexCoords[i] = lower + (upper-lower)*((PetscReal)i/(PetscReal)numCells); }
470   ierr = DMPlexCreateFromDAG(*dm,1,numPoints,coneSize,cones,coneOrientations,vertexCoords);CHKERRQ(ierr);
471   ierr = PetscFree4(coneSize,cones,coneOrientations,vertexCoords);CHKERRQ(ierr);
472 
473   ierr = PetscOptionsGetBool(((PetscObject)*dm)->options,((PetscObject)*dm)->prefix,"-dm_plex_separate_marker",&markerSeparate,NULL);CHKERRQ(ierr);
474   if (markerSeparate) { markerLeft = faceMarkerLeft; markerRight = faceMarkerRight;}
475   if (!wrap && !rank) {
476     ierr = DMPlexGetHeightStratum(*dm,1,&fStart,&fEnd);CHKERRQ(ierr);
477     ierr = DMSetLabelValue(*dm,"marker",fStart,markerLeft);CHKERRQ(ierr);
478     ierr = DMSetLabelValue(*dm,"marker",fEnd-1,markerRight);CHKERRQ(ierr);
479     ierr = DMSetLabelValue(*dm,"Face Sets",fStart,faceMarkerLeft);CHKERRQ(ierr);
480     ierr = DMSetLabelValue(*dm,"Face Sets",fEnd-1,faceMarkerRight);CHKERRQ(ierr);
481   }
482   if (wrap) {
483     L       = upper - lower;
484     maxCell = (PetscReal)1.1*(L/(PetscReal)PetscMax(1,segments));
485     ierr = DMSetPeriodicity(*dm,PETSC_TRUE,&maxCell,&L,&bd);CHKERRQ(ierr);
486   }
487   PetscFunctionReturn(0);
488 }
489 
490 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)
491 {
492   DM             boundary;
493   PetscInt       i;
494   PetscErrorCode ierr;
495 
496   PetscFunctionBegin;
497   PetscValidPointer(dm, 4);
498   for (i = 0; i < dim; ++i) if (periodicity[i] != DM_BOUNDARY_NONE) SETERRQ(comm, PETSC_ERR_SUP, "Periodicity is not supported for simplex meshes");
499   ierr = DMCreate(comm, &boundary);CHKERRQ(ierr);
500   PetscValidLogicalCollectiveInt(boundary,dim,2);
501   ierr = DMSetType(boundary, DMPLEX);CHKERRQ(ierr);
502   ierr = DMSetDimension(boundary, dim-1);CHKERRQ(ierr);
503   ierr = DMSetCoordinateDim(boundary, dim);CHKERRQ(ierr);
504   switch (dim) {
505   case 2: ierr = DMPlexCreateSquareBoundary(boundary, lower, upper, faces);CHKERRQ(ierr);break;
506   case 3: ierr = DMPlexCreateCubeBoundary(boundary, lower, upper, faces);CHKERRQ(ierr);break;
507   default: SETERRQ1(comm, PETSC_ERR_SUP, "Dimension not supported: %d", dim);
508   }
509   ierr = DMPlexGenerate(boundary, NULL, interpolate, dm);CHKERRQ(ierr);
510   ierr = DMDestroy(&boundary);CHKERRQ(ierr);
511   PetscFunctionReturn(0);
512 }
513 
514 static PetscErrorCode DMPlexCreateCubeMesh_Internal(DM dm, const PetscReal lower[], const PetscReal upper[], const PetscInt edges[], DMBoundaryType bdX, DMBoundaryType bdY, DMBoundaryType bdZ)
515 {
516   DMLabel        cutLabel = NULL;
517   PetscInt       markerTop      = 1, faceMarkerTop      = 1;
518   PetscInt       markerBottom   = 1, faceMarkerBottom   = 1;
519   PetscInt       markerFront    = 1, faceMarkerFront    = 1;
520   PetscInt       markerBack     = 1, faceMarkerBack     = 1;
521   PetscInt       markerRight    = 1, faceMarkerRight    = 1;
522   PetscInt       markerLeft     = 1, faceMarkerLeft     = 1;
523   PetscInt       dim;
524   PetscBool      markerSeparate = PETSC_FALSE, cutMarker = PETSC_FALSE;
525   PetscMPIInt    rank;
526   PetscErrorCode ierr;
527 
528   PetscFunctionBegin;
529   ierr = DMGetDimension(dm,&dim);CHKERRQ(ierr);
530   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);CHKERRQ(ierr);
531   ierr = DMCreateLabel(dm,"marker");CHKERRQ(ierr);
532   ierr = DMCreateLabel(dm,"Face Sets");CHKERRQ(ierr);
533   ierr = PetscOptionsGetBool(((PetscObject) dm)->options,((PetscObject) dm)->prefix, "-dm_plex_periodic_cut", &cutMarker, NULL);CHKERRQ(ierr);
534   if (bdX == DM_BOUNDARY_PERIODIC || bdX == DM_BOUNDARY_TWIST ||
535       bdY == DM_BOUNDARY_PERIODIC || bdY == DM_BOUNDARY_TWIST ||
536       bdZ == DM_BOUNDARY_PERIODIC || bdZ == DM_BOUNDARY_TWIST) {
537 
538     if (cutMarker) {ierr = DMCreateLabel(dm, "periodic_cut");CHKERRQ(ierr); ierr = DMGetLabel(dm, "periodic_cut", &cutLabel);CHKERRQ(ierr);}
539   }
540   switch (dim) {
541   case 2:
542     faceMarkerTop    = 3;
543     faceMarkerBottom = 1;
544     faceMarkerRight  = 2;
545     faceMarkerLeft   = 4;
546     break;
547   case 3:
548     faceMarkerBottom = 1;
549     faceMarkerTop    = 2;
550     faceMarkerFront  = 3;
551     faceMarkerBack   = 4;
552     faceMarkerRight  = 5;
553     faceMarkerLeft   = 6;
554     break;
555   default:
556     SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Dimension %d not supported",dim);
557     break;
558   }
559   ierr = PetscOptionsGetBool(((PetscObject) dm)->options,((PetscObject) dm)->prefix, "-dm_plex_separate_marker", &markerSeparate, NULL);CHKERRQ(ierr);
560   if (markerSeparate) {
561     markerBottom = faceMarkerBottom;
562     markerTop    = faceMarkerTop;
563     markerFront  = faceMarkerFront;
564     markerBack   = faceMarkerBack;
565     markerRight  = faceMarkerRight;
566     markerLeft   = faceMarkerLeft;
567   }
568   {
569     const PetscInt numXEdges    = !rank ? edges[0] : 0;
570     const PetscInt numYEdges    = !rank ? edges[1] : 0;
571     const PetscInt numZEdges    = !rank ? edges[2] : 0;
572     const PetscInt numXVertices = !rank ? (bdX == DM_BOUNDARY_PERIODIC || bdX == DM_BOUNDARY_TWIST ? edges[0] : edges[0]+1) : 0;
573     const PetscInt numYVertices = !rank ? (bdY == DM_BOUNDARY_PERIODIC || bdY == DM_BOUNDARY_TWIST ? edges[1] : edges[1]+1) : 0;
574     const PetscInt numZVertices = !rank ? (bdZ == DM_BOUNDARY_PERIODIC || bdZ == DM_BOUNDARY_TWIST ? edges[2] : edges[2]+1) : 0;
575     const PetscInt numCells     = numXEdges*numYEdges*numZEdges;
576     const PetscInt numXFaces    = numYEdges*numZEdges;
577     const PetscInt numYFaces    = numXEdges*numZEdges;
578     const PetscInt numZFaces    = numXEdges*numYEdges;
579     const PetscInt numTotXFaces = numXVertices*numXFaces;
580     const PetscInt numTotYFaces = numYVertices*numYFaces;
581     const PetscInt numTotZFaces = numZVertices*numZFaces;
582     const PetscInt numFaces     = numTotXFaces + numTotYFaces + numTotZFaces;
583     const PetscInt numTotXEdges = numXEdges*numYVertices*numZVertices;
584     const PetscInt numTotYEdges = numYEdges*numXVertices*numZVertices;
585     const PetscInt numTotZEdges = numZEdges*numXVertices*numYVertices;
586     const PetscInt numVertices  = numXVertices*numYVertices*numZVertices;
587     const PetscInt numEdges     = numTotXEdges + numTotYEdges + numTotZEdges;
588     const PetscInt firstVertex  = (dim == 2) ? numFaces : numCells;
589     const PetscInt firstXFace   = (dim == 2) ? 0 : numCells + numVertices;
590     const PetscInt firstYFace   = firstXFace + numTotXFaces;
591     const PetscInt firstZFace   = firstYFace + numTotYFaces;
592     const PetscInt firstXEdge   = numCells + numFaces + numVertices;
593     const PetscInt firstYEdge   = firstXEdge + numTotXEdges;
594     const PetscInt firstZEdge   = firstYEdge + numTotYEdges;
595     Vec            coordinates;
596     PetscSection   coordSection;
597     PetscScalar   *coords;
598     PetscInt       coordSize;
599     PetscInt       v, vx, vy, vz;
600     PetscInt       c, f, fx, fy, fz, e, ex, ey, ez;
601 
602     ierr = DMPlexSetChart(dm, 0, numCells+numFaces+numEdges+numVertices);CHKERRQ(ierr);
603     for (c = 0; c < numCells; c++) {
604       ierr = DMPlexSetConeSize(dm, c, 6);CHKERRQ(ierr);
605     }
606     for (f = firstXFace; f < firstXFace+numFaces; ++f) {
607       ierr = DMPlexSetConeSize(dm, f, 4);CHKERRQ(ierr);
608     }
609     for (e = firstXEdge; e < firstXEdge+numEdges; ++e) {
610       ierr = DMPlexSetConeSize(dm, e, 2);CHKERRQ(ierr);
611     }
612     ierr = DMSetUp(dm);CHKERRQ(ierr); /* Allocate space for cones */
613     /* Build cells */
614     for (fz = 0; fz < numZEdges; ++fz) {
615       for (fy = 0; fy < numYEdges; ++fy) {
616         for (fx = 0; fx < numXEdges; ++fx) {
617           PetscInt cell    = (fz*numYEdges + fy)*numXEdges + fx;
618           PetscInt faceB   = firstZFace + (fy*numXEdges+fx)*numZVertices +   fz;
619           PetscInt faceT   = firstZFace + (fy*numXEdges+fx)*numZVertices + ((fz+1)%numZVertices);
620           PetscInt faceF   = firstYFace + (fz*numXEdges+fx)*numYVertices +   fy;
621           PetscInt faceK   = firstYFace + (fz*numXEdges+fx)*numYVertices + ((fy+1)%numYVertices);
622           PetscInt faceL   = firstXFace + (fz*numYEdges+fy)*numXVertices +   fx;
623           PetscInt faceR   = firstXFace + (fz*numYEdges+fy)*numXVertices + ((fx+1)%numXVertices);
624                             /* B,  T,  F,  K,  R,  L */
625           PetscInt ornt[6] = {-4,  0,  0, -1,  0, -4}; /* ??? */
626           PetscInt cone[6];
627 
628           /* no boundary twisting in 3D */
629           cone[0] = faceB; cone[1] = faceT; cone[2] = faceF; cone[3] = faceK; cone[4] = faceR; cone[5] = faceL;
630           ierr    = DMPlexSetCone(dm, cell, cone);CHKERRQ(ierr);
631           ierr    = DMPlexSetConeOrientation(dm, cell, ornt);CHKERRQ(ierr);
632           if (bdX != DM_BOUNDARY_NONE && fx == numXEdges-1 && cutLabel) {ierr = DMLabelSetValue(cutLabel, cell, 2);CHKERRQ(ierr);}
633           if (bdY != DM_BOUNDARY_NONE && fy == numYEdges-1 && cutLabel) {ierr = DMLabelSetValue(cutLabel, cell, 2);CHKERRQ(ierr);}
634           if (bdZ != DM_BOUNDARY_NONE && fz == numZEdges-1 && cutLabel) {ierr = DMLabelSetValue(cutLabel, cell, 2);CHKERRQ(ierr);}
635         }
636       }
637     }
638     /* Build x faces */
639     for (fz = 0; fz < numZEdges; ++fz) {
640       for (fy = 0; fy < numYEdges; ++fy) {
641         for (fx = 0; fx < numXVertices; ++fx) {
642           PetscInt face    = firstXFace + (fz*numYEdges+fy)*numXVertices + fx;
643           PetscInt edgeL   = firstZEdge + (  fy*                 numXVertices+fx)*numZEdges + fz;
644           PetscInt edgeR   = firstZEdge + (((fy+1)%numYVertices)*numXVertices+fx)*numZEdges + fz;
645           PetscInt edgeB   = firstYEdge + (  fz*                 numXVertices+fx)*numYEdges + fy;
646           PetscInt edgeT   = firstYEdge + (((fz+1)%numZVertices)*numXVertices+fx)*numYEdges + fy;
647           PetscInt ornt[4] = {0, 0, -2, -2};
648           PetscInt cone[4];
649 
650           if (dim == 3) {
651             /* markers */
652             if (bdX != DM_BOUNDARY_PERIODIC) {
653               if (fx == numXVertices-1) {
654                 ierr = DMSetLabelValue(dm, "Face Sets", face, faceMarkerRight);CHKERRQ(ierr);
655                 ierr = DMSetLabelValue(dm, "marker", face, markerRight);CHKERRQ(ierr);
656               }
657               else if (fx == 0) {
658                 ierr = DMSetLabelValue(dm, "Face Sets", face, faceMarkerLeft);CHKERRQ(ierr);
659                 ierr = DMSetLabelValue(dm, "marker", face, markerLeft);CHKERRQ(ierr);
660               }
661             }
662           }
663           cone[0] = edgeB; cone[1] = edgeR; cone[2] = edgeT; cone[3] = edgeL;
664           ierr    = DMPlexSetCone(dm, face, cone);CHKERRQ(ierr);
665           ierr    = DMPlexSetConeOrientation(dm, face, ornt);CHKERRQ(ierr);
666         }
667       }
668     }
669     /* Build y faces */
670     for (fz = 0; fz < numZEdges; ++fz) {
671       for (fx = 0; fx < numXEdges; ++fx) {
672         for (fy = 0; fy < numYVertices; ++fy) {
673           PetscInt face    = firstYFace + (fz*numXEdges+fx)*numYVertices + fy;
674           PetscInt edgeL   = firstZEdge + (fy*numXVertices+  fx                 )*numZEdges + fz;
675           PetscInt edgeR   = firstZEdge + (fy*numXVertices+((fx+1)%numXVertices))*numZEdges + fz;
676           PetscInt edgeB   = firstXEdge + (  fz                 *numYVertices+fy)*numXEdges + fx;
677           PetscInt edgeT   = firstXEdge + (((fz+1)%numZVertices)*numYVertices+fy)*numXEdges + fx;
678           PetscInt ornt[4] = {0, 0, -2, -2};
679           PetscInt cone[4];
680 
681           if (dim == 3) {
682             /* markers */
683             if (bdY != DM_BOUNDARY_PERIODIC) {
684               if (fy == numYVertices-1) {
685                 ierr = DMSetLabelValue(dm, "Face Sets", face, faceMarkerBack);CHKERRQ(ierr);
686                 ierr = DMSetLabelValue(dm, "marker", face, markerBack);CHKERRQ(ierr);
687               }
688               else if (fy == 0) {
689                 ierr = DMSetLabelValue(dm, "Face Sets", face, faceMarkerFront);CHKERRQ(ierr);
690                 ierr = DMSetLabelValue(dm, "marker", face, markerFront);CHKERRQ(ierr);
691               }
692             }
693           }
694           cone[0] = edgeB; cone[1] = edgeR; cone[2] = edgeT; cone[3] = edgeL;
695           ierr    = DMPlexSetCone(dm, face, cone);CHKERRQ(ierr);
696           ierr    = DMPlexSetConeOrientation(dm, face, ornt);CHKERRQ(ierr);
697         }
698       }
699     }
700     /* Build z faces */
701     for (fy = 0; fy < numYEdges; ++fy) {
702       for (fx = 0; fx < numXEdges; ++fx) {
703         for (fz = 0; fz < numZVertices; fz++) {
704           PetscInt face    = firstZFace + (fy*numXEdges+fx)*numZVertices + fz;
705           PetscInt edgeL   = firstYEdge + (fz*numXVertices+  fx                 )*numYEdges + fy;
706           PetscInt edgeR   = firstYEdge + (fz*numXVertices+((fx+1)%numXVertices))*numYEdges + fy;
707           PetscInt edgeB   = firstXEdge + (fz*numYVertices+  fy                 )*numXEdges + fx;
708           PetscInt edgeT   = firstXEdge + (fz*numYVertices+((fy+1)%numYVertices))*numXEdges + fx;
709           PetscInt ornt[4] = {0, 0, -2, -2};
710           PetscInt cone[4];
711 
712           if (dim == 2) {
713             if (bdX == DM_BOUNDARY_TWIST && fx == numXEdges-1) {edgeR += numYEdges-1-2*fy; ornt[1] = -2;}
714             if (bdY == DM_BOUNDARY_TWIST && fy == numYEdges-1) {edgeT += numXEdges-1-2*fx; ornt[2] =  0;}
715             if (bdX != DM_BOUNDARY_NONE && fx == numXEdges-1 && cutLabel) {ierr = DMLabelSetValue(cutLabel, face, 2);CHKERRQ(ierr);}
716             if (bdY != DM_BOUNDARY_NONE && fy == numYEdges-1 && cutLabel) {ierr = DMLabelSetValue(cutLabel, face, 2);CHKERRQ(ierr);}
717           } else {
718             /* markers */
719             if (bdZ != DM_BOUNDARY_PERIODIC) {
720               if (fz == numZVertices-1) {
721                 ierr = DMSetLabelValue(dm, "Face Sets", face, faceMarkerTop);CHKERRQ(ierr);
722                 ierr = DMSetLabelValue(dm, "marker", face, markerTop);CHKERRQ(ierr);
723               }
724               else if (fz == 0) {
725                 ierr = DMSetLabelValue(dm, "Face Sets", face, faceMarkerBottom);CHKERRQ(ierr);
726                 ierr = DMSetLabelValue(dm, "marker", face, markerBottom);CHKERRQ(ierr);
727               }
728             }
729           }
730           cone[0] = edgeB; cone[1] = edgeR; cone[2] = edgeT; cone[3] = edgeL;
731           ierr    = DMPlexSetCone(dm, face, cone);CHKERRQ(ierr);
732           ierr    = DMPlexSetConeOrientation(dm, face, ornt);CHKERRQ(ierr);
733         }
734       }
735     }
736     /* Build Z edges*/
737     for (vy = 0; vy < numYVertices; vy++) {
738       for (vx = 0; vx < numXVertices; vx++) {
739         for (ez = 0; ez < numZEdges; ez++) {
740           const PetscInt edge    = firstZEdge  + (vy*numXVertices+vx)*numZEdges + ez;
741           const PetscInt vertexB = firstVertex + (  ez                 *numYVertices+vy)*numXVertices + vx;
742           const PetscInt vertexT = firstVertex + (((ez+1)%numZVertices)*numYVertices+vy)*numXVertices + vx;
743           PetscInt       cone[2];
744 
745           if (dim == 3) {
746             if (bdX != DM_BOUNDARY_PERIODIC) {
747               if (vx == numXVertices-1) {
748                 ierr = DMSetLabelValue(dm, "marker", edge, markerRight);CHKERRQ(ierr);
749               }
750               else if (vx == 0) {
751                 ierr = DMSetLabelValue(dm, "marker", edge, markerLeft);CHKERRQ(ierr);
752               }
753             }
754             if (bdY != DM_BOUNDARY_PERIODIC) {
755               if (vy == numYVertices-1) {
756                 ierr = DMSetLabelValue(dm, "marker", edge, markerBack);CHKERRQ(ierr);
757               }
758               else if (vy == 0) {
759                 ierr = DMSetLabelValue(dm, "marker", edge, markerFront);CHKERRQ(ierr);
760               }
761             }
762           }
763           cone[0] = vertexB; cone[1] = vertexT;
764           ierr = DMPlexSetCone(dm, edge, cone);CHKERRQ(ierr);
765         }
766       }
767     }
768     /* Build Y edges*/
769     for (vz = 0; vz < numZVertices; vz++) {
770       for (vx = 0; vx < numXVertices; vx++) {
771         for (ey = 0; ey < numYEdges; ey++) {
772           const PetscInt nextv   = (dim == 2 && bdY == DM_BOUNDARY_TWIST && ey == numYEdges-1) ? (numXVertices-vx-1) : (vz*numYVertices+((ey+1)%numYVertices))*numXVertices + vx;
773           const PetscInt edge    = firstYEdge  + (vz*numXVertices+vx)*numYEdges + ey;
774           const PetscInt vertexF = firstVertex + (vz*numYVertices+ey)*numXVertices + vx;
775           const PetscInt vertexK = firstVertex + nextv;
776           PetscInt       cone[2];
777 
778           cone[0] = vertexF; cone[1] = vertexK;
779           ierr = DMPlexSetCone(dm, edge, cone);CHKERRQ(ierr);
780           if (dim == 2) {
781             if ((bdX != DM_BOUNDARY_PERIODIC) && (bdX != DM_BOUNDARY_TWIST)) {
782               if (vx == numXVertices-1) {
783                 ierr = DMSetLabelValue(dm, "Face Sets", edge, faceMarkerRight);CHKERRQ(ierr);
784                 ierr = DMSetLabelValue(dm, "marker", edge,    markerRight);CHKERRQ(ierr);
785                 ierr = DMSetLabelValue(dm, "marker", cone[0], markerRight);CHKERRQ(ierr);
786                 if (ey == numYEdges-1) {
787                   ierr = DMSetLabelValue(dm, "marker", cone[1], markerRight);CHKERRQ(ierr);
788                 }
789               } else if (vx == 0) {
790                 ierr = DMSetLabelValue(dm, "Face Sets", edge, faceMarkerLeft);CHKERRQ(ierr);
791                 ierr = DMSetLabelValue(dm, "marker", edge,    markerLeft);CHKERRQ(ierr);
792                 ierr = DMSetLabelValue(dm, "marker", cone[0], markerLeft);CHKERRQ(ierr);
793                 if (ey == numYEdges-1) {
794                   ierr = DMSetLabelValue(dm, "marker", cone[1], markerLeft);CHKERRQ(ierr);
795                 }
796               }
797             } else {
798               if (vx == 0 && cutLabel) {
799                 ierr = DMLabelSetValue(cutLabel, edge,    1);CHKERRQ(ierr);
800                 ierr = DMLabelSetValue(cutLabel, cone[0], 1);CHKERRQ(ierr);
801                 if (ey == numYEdges-1) {
802                   ierr = DMLabelSetValue(cutLabel, cone[1], 1);CHKERRQ(ierr);
803                 }
804               }
805             }
806           } else {
807             if (bdX != DM_BOUNDARY_PERIODIC) {
808               if (vx == numXVertices-1) {
809                 ierr = DMSetLabelValue(dm, "marker", edge, markerRight);CHKERRQ(ierr);
810               } else if (vx == 0) {
811                 ierr = DMSetLabelValue(dm, "marker", edge, markerLeft);CHKERRQ(ierr);
812               }
813             }
814             if (bdZ != DM_BOUNDARY_PERIODIC) {
815               if (vz == numZVertices-1) {
816                 ierr = DMSetLabelValue(dm, "marker", edge, markerTop);CHKERRQ(ierr);
817               } else if (vz == 0) {
818                 ierr = DMSetLabelValue(dm, "marker", edge, markerBottom);CHKERRQ(ierr);
819               }
820             }
821           }
822         }
823       }
824     }
825     /* Build X edges*/
826     for (vz = 0; vz < numZVertices; vz++) {
827       for (vy = 0; vy < numYVertices; vy++) {
828         for (ex = 0; ex < numXEdges; ex++) {
829           const PetscInt nextv   = (dim == 2 && bdX == DM_BOUNDARY_TWIST && ex == numXEdges-1) ? (numYVertices-vy-1)*numXVertices : (vz*numYVertices+vy)*numXVertices + (ex+1)%numXVertices;
830           const PetscInt edge    = firstXEdge  + (vz*numYVertices+vy)*numXEdges + ex;
831           const PetscInt vertexL = firstVertex + (vz*numYVertices+vy)*numXVertices + ex;
832           const PetscInt vertexR = firstVertex + nextv;
833           PetscInt       cone[2];
834 
835           cone[0] = vertexL; cone[1] = vertexR;
836           ierr = DMPlexSetCone(dm, edge, cone);CHKERRQ(ierr);
837           if (dim == 2) {
838             if ((bdY != DM_BOUNDARY_PERIODIC) && (bdY != DM_BOUNDARY_TWIST)) {
839               if (vy == numYVertices-1) {
840                 ierr = DMSetLabelValue(dm, "Face Sets", edge, faceMarkerTop);CHKERRQ(ierr);
841                 ierr = DMSetLabelValue(dm, "marker", edge,    markerTop);CHKERRQ(ierr);
842                 ierr = DMSetLabelValue(dm, "marker", cone[0], markerTop);CHKERRQ(ierr);
843                 if (ex == numXEdges-1) {
844                   ierr = DMSetLabelValue(dm, "marker", cone[1], markerTop);CHKERRQ(ierr);
845                 }
846               } else if (vy == 0) {
847                 ierr = DMSetLabelValue(dm, "Face Sets", edge, faceMarkerBottom);CHKERRQ(ierr);
848                 ierr = DMSetLabelValue(dm, "marker", edge,    markerBottom);CHKERRQ(ierr);
849                 ierr = DMSetLabelValue(dm, "marker", cone[0], markerBottom);CHKERRQ(ierr);
850                 if (ex == numXEdges-1) {
851                   ierr = DMSetLabelValue(dm, "marker", cone[1], markerBottom);CHKERRQ(ierr);
852                 }
853               }
854             } else {
855               if (vy == 0 && cutLabel) {
856                 ierr = DMLabelSetValue(cutLabel, edge,    1);CHKERRQ(ierr);
857                 ierr = DMLabelSetValue(cutLabel, cone[0], 1);CHKERRQ(ierr);
858                 if (ex == numXEdges-1) {
859                   ierr = DMLabelSetValue(cutLabel, cone[1], 1);CHKERRQ(ierr);
860                 }
861               }
862             }
863           } else {
864             if (bdY != DM_BOUNDARY_PERIODIC) {
865               if (vy == numYVertices-1) {
866                 ierr = DMSetLabelValue(dm, "marker", edge, markerBack);CHKERRQ(ierr);
867               }
868               else if (vy == 0) {
869                 ierr = DMSetLabelValue(dm, "marker", edge, markerFront);CHKERRQ(ierr);
870               }
871             }
872             if (bdZ != DM_BOUNDARY_PERIODIC) {
873               if (vz == numZVertices-1) {
874                 ierr = DMSetLabelValue(dm, "marker", edge, markerTop);CHKERRQ(ierr);
875               }
876               else if (vz == 0) {
877                 ierr = DMSetLabelValue(dm, "marker", edge, markerBottom);CHKERRQ(ierr);
878               }
879             }
880           }
881         }
882       }
883     }
884     ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
885     ierr = DMPlexStratify(dm);CHKERRQ(ierr);
886     /* Build coordinates */
887     ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
888     ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
889     ierr = PetscSectionSetFieldComponents(coordSection, 0, dim);CHKERRQ(ierr);
890     ierr = PetscSectionSetChart(coordSection, firstVertex, firstVertex+numVertices);CHKERRQ(ierr);
891     for (v = firstVertex; v < firstVertex+numVertices; ++v) {
892       ierr = PetscSectionSetDof(coordSection, v, dim);CHKERRQ(ierr);
893       ierr = PetscSectionSetFieldDof(coordSection, v, 0, dim);CHKERRQ(ierr);
894     }
895     ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
896     ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
897     ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
898     ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
899     ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
900     ierr = VecSetBlockSize(coordinates, dim);CHKERRQ(ierr);
901     ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
902     ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
903     for (vz = 0; vz < numZVertices; ++vz) {
904       for (vy = 0; vy < numYVertices; ++vy) {
905         for (vx = 0; vx < numXVertices; ++vx) {
906           coords[((vz*numYVertices+vy)*numXVertices+vx)*dim+0] = lower[0] + ((upper[0] - lower[0])/numXEdges)*vx;
907           coords[((vz*numYVertices+vy)*numXVertices+vx)*dim+1] = lower[1] + ((upper[1] - lower[1])/numYEdges)*vy;
908           if (dim == 3) {
909             coords[((vz*numYVertices+vy)*numXVertices+vx)*dim+2] = lower[2] + ((upper[2] - lower[2])/numZEdges)*vz;
910           }
911         }
912       }
913     }
914     ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
915     ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
916     ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
917   }
918   PetscFunctionReturn(0);
919 }
920 
921 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)
922 {
923   PetscInt       i;
924   PetscErrorCode ierr;
925 
926   PetscFunctionBegin;
927   PetscValidPointer(dm, 7);
928   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
929   PetscValidLogicalCollectiveInt(*dm,dim,2);
930   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
931   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
932   switch (dim) {
933   case 2: {ierr = DMPlexCreateCubeMesh_Internal(*dm, lower, upper, faces, periodicity[0], periodicity[1], DM_BOUNDARY_NONE);CHKERRQ(ierr);break;}
934   case 3: {ierr = DMPlexCreateCubeMesh_Internal(*dm, lower, upper, faces, periodicity[0], periodicity[1], periodicity[2]);CHKERRQ(ierr);break;}
935   default: SETERRQ1(comm, PETSC_ERR_SUP, "Dimension not supported: %d", dim);
936   }
937   if (periodicity[0] == DM_BOUNDARY_PERIODIC || periodicity[0] == DM_BOUNDARY_TWIST ||
938       periodicity[1] == DM_BOUNDARY_PERIODIC || periodicity[1] == DM_BOUNDARY_TWIST ||
939       (dim > 2 && (periodicity[2] == DM_BOUNDARY_PERIODIC || periodicity[2] == DM_BOUNDARY_TWIST))) {
940     PetscReal L[3];
941     PetscReal maxCell[3];
942 
943     for (i = 0; i < dim; i++) {
944       L[i]       = upper[i] - lower[i];
945       maxCell[i] = 1.1 * (L[i] / PetscMax(1,faces[i]));
946     }
947     ierr = DMSetPeriodicity(*dm,PETSC_TRUE,maxCell,L,periodicity);CHKERRQ(ierr);
948   }
949   if (!interpolate) {
950     DM udm;
951 
952     ierr = DMPlexUninterpolate(*dm, &udm);CHKERRQ(ierr);
953     ierr = DMDestroy(dm);CHKERRQ(ierr);
954     *dm  = udm;
955   }
956   PetscFunctionReturn(0);
957 }
958 
959 /*@C
960   DMPlexCreateBoxMesh - Creates a mesh on the tensor product of unit intervals (box) using simplices or tensor cells (hexahedra).
961 
962   Collective on MPI_Comm
963 
964   Input Parameters:
965 + comm        - The communicator for the DM object
966 . dim         - The spatial dimension
967 . simplex     - PETSC_TRUE for simplices, PETSC_FALSE for tensor cells
968 . faces       - Number of faces per dimension, or NULL for (1,) in 1D and (2, 2) in 2D and (1, 1, 1) in 3D
969 . lower       - The lower left corner, or NULL for (0, 0, 0)
970 . upper       - The upper right corner, or NULL for (1, 1, 1)
971 . periodicity - The boundary type for the X,Y,Z direction, or NULL for DM_BOUNDARY_NONE
972 - interpolate - Flag to create intermediate mesh pieces (edges, faces)
973 
974   Output Parameter:
975 . dm  - The DM object
976 
977   Note: Here is the numbering returned for 2 faces in each direction for tensor cells:
978 $ 10---17---11---18----12
979 $  |         |         |
980 $  |         |         |
981 $ 20    2   22    3    24
982 $  |         |         |
983 $  |         |         |
984 $  7---15----8---16----9
985 $  |         |         |
986 $  |         |         |
987 $ 19    0   21    1   23
988 $  |         |         |
989 $  |         |         |
990 $  4---13----5---14----6
991 
992 and for simplicial cells
993 
994 $ 14----8---15----9----16
995 $  |\     5  |\      7 |
996 $  | \       | \       |
997 $ 13   2    14    3    15
998 $  | 4   \   | 6   \   |
999 $  |       \ |       \ |
1000 $ 11----6---12----7----13
1001 $  |\        |\        |
1002 $  | \    1  | \     3 |
1003 $ 10   0    11    1    12
1004 $  | 0   \   | 2   \   |
1005 $  |       \ |       \ |
1006 $  8----4----9----5----10
1007 
1008   Level: beginner
1009 
1010 .keywords: DM, create
1011 .seealso: DMPlexCreateFromFile(), DMPlexCreateHexCylinderMesh(), DMSetType(), DMCreate()
1012 @*/
1013 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)
1014 {
1015   PetscInt       i;
1016   PetscInt       fac[3] = {0, 0, 0};
1017   PetscReal      low[3] = {0, 0, 0};
1018   PetscReal      upp[3] = {1, 1, 1};
1019   DMBoundaryType bdt[3] = {DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE};
1020   PetscErrorCode ierr;
1021 
1022   PetscFunctionBegin;
1023   for (i = 0; i < dim; ++i) fac[i] = faces ? faces[i] : (dim == 1 ? 1 : 4-dim);
1024   if (lower) for (i = 0; i < dim; ++i) low[i] = lower[i];
1025   if (upper) for (i = 0; i < dim; ++i) upp[i] = upper[i];
1026   if (periodicity) for (i = 0; i < dim; ++i) bdt[i] = periodicity[i];
1027 
1028   if (dim == 1)      {ierr = DMPlexCreateLineMesh_Internal(comm, fac[0], low[0], upp[0], bdt[0], dm);CHKERRQ(ierr);}
1029   else if (simplex)  {ierr = DMPlexCreateBoxMesh_Simplex_Internal(comm, dim, fac, low, upp, bdt, interpolate, dm);CHKERRQ(ierr);}
1030   else               {ierr = DMPlexCreateBoxMesh_Tensor_Internal(comm, dim, fac, low, upp, bdt, interpolate, dm);CHKERRQ(ierr);}
1031   PetscFunctionReturn(0);
1032 }
1033 
1034 /*@C
1035   DMPlexSetOptionsPrefix - Sets the prefix used for searching for all DM options in the database.
1036 
1037   Logically Collective on DM
1038 
1039   Input Parameters:
1040 + dm - the DM context
1041 - prefix - the prefix to prepend to all option names
1042 
1043   Notes:
1044   A hyphen (-) must NOT be given at the beginning of the prefix name.
1045   The first character of all runtime options is AUTOMATICALLY the hyphen.
1046 
1047   Level: advanced
1048 
1049 .seealso: SNESSetFromOptions()
1050 @*/
1051 PetscErrorCode DMPlexSetOptionsPrefix(DM dm, const char prefix[])
1052 {
1053   DM_Plex       *mesh = (DM_Plex *) dm->data;
1054   PetscErrorCode ierr;
1055 
1056   PetscFunctionBegin;
1057   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1058   ierr = PetscObjectSetOptionsPrefix((PetscObject) dm, prefix);CHKERRQ(ierr);
1059   ierr = PetscObjectSetOptionsPrefix((PetscObject) mesh->partitioner, prefix);CHKERRQ(ierr);
1060   PetscFunctionReturn(0);
1061 }
1062 
1063 /*@
1064   DMPlexCreateHexCylinderMesh - Creates a mesh on the tensor product of the unit interval with the circle (cylinder) using hexahedra.
1065 
1066   Collective on MPI_Comm
1067 
1068   Input Parameters:
1069 + comm      - The communicator for the DM object
1070 . numRefine - The number of regular refinements to the basic 5 cell structure
1071 - periodicZ - The boundary type for the Z direction
1072 
1073   Output Parameter:
1074 . dm  - The DM object
1075 
1076   Note: Here is the output numbering looking from the bottom of the cylinder:
1077 $       17-----14
1078 $        |     |
1079 $        |  2  |
1080 $        |     |
1081 $ 17-----8-----7-----14
1082 $  |     |     |     |
1083 $  |  3  |  0  |  1  |
1084 $  |     |     |     |
1085 $ 19-----5-----6-----13
1086 $        |     |
1087 $        |  4  |
1088 $        |     |
1089 $       19-----13
1090 $
1091 $ and up through the top
1092 $
1093 $       18-----16
1094 $        |     |
1095 $        |  2  |
1096 $        |     |
1097 $ 18----10----11-----16
1098 $  |     |     |     |
1099 $  |  3  |  0  |  1  |
1100 $  |     |     |     |
1101 $ 20-----9----12-----15
1102 $        |     |
1103 $        |  4  |
1104 $        |     |
1105 $       20-----15
1106 
1107   Level: beginner
1108 
1109 .keywords: DM, create
1110 .seealso: DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
1111 @*/
1112 PetscErrorCode DMPlexCreateHexCylinderMesh(MPI_Comm comm, PetscInt numRefine, DMBoundaryType periodicZ, DM *dm)
1113 {
1114   const PetscInt dim = 3;
1115   PetscInt       numCells, numVertices, r;
1116   PetscErrorCode ierr;
1117 
1118   PetscFunctionBegin;
1119   PetscValidPointer(dm, 4);
1120   if (numRefine < 0) SETERRQ1(comm, PETSC_ERR_ARG_OUTOFRANGE, "Number of refinements %D cannot be negative", numRefine);
1121   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
1122   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
1123   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
1124   /* Create topology */
1125   {
1126     PetscInt cone[8], c;
1127 
1128     numCells    = 5;
1129     numVertices = 16;
1130     if (periodicZ == DM_BOUNDARY_PERIODIC) {
1131       numCells   *= 3;
1132       numVertices = 24;
1133     }
1134     ierr = DMPlexSetChart(*dm, 0, numCells+numVertices);CHKERRQ(ierr);
1135     for (c = 0; c < numCells; c++) {ierr = DMPlexSetConeSize(*dm, c, 8);CHKERRQ(ierr);}
1136     ierr = DMSetUp(*dm);CHKERRQ(ierr);
1137     if (periodicZ == DM_BOUNDARY_PERIODIC) {
1138       cone[0] = 15; cone[1] = 18; cone[2] = 17; cone[3] = 16;
1139       cone[4] = 31; cone[5] = 32; cone[6] = 33; cone[7] = 34;
1140       ierr = DMPlexSetCone(*dm, 0, cone);CHKERRQ(ierr);
1141       cone[0] = 16; cone[1] = 17; cone[2] = 24; cone[3] = 23;
1142       cone[4] = 32; cone[5] = 36; cone[6] = 37; cone[7] = 33; /* 22 25 26 21 */
1143       ierr = DMPlexSetCone(*dm, 1, cone);CHKERRQ(ierr);
1144       cone[0] = 18; cone[1] = 27; cone[2] = 24; cone[3] = 17;
1145       cone[4] = 34; cone[5] = 33; cone[6] = 37; cone[7] = 38;
1146       ierr = DMPlexSetCone(*dm, 2, cone);CHKERRQ(ierr);
1147       cone[0] = 29; cone[1] = 27; cone[2] = 18; cone[3] = 15;
1148       cone[4] = 35; cone[5] = 31; cone[6] = 34; cone[7] = 38;
1149       ierr = DMPlexSetCone(*dm, 3, cone);CHKERRQ(ierr);
1150       cone[0] = 29; cone[1] = 15; cone[2] = 16; cone[3] = 23;
1151       cone[4] = 35; cone[5] = 36; cone[6] = 32; cone[7] = 31;
1152       ierr = DMPlexSetCone(*dm, 4, cone);CHKERRQ(ierr);
1153 
1154       cone[0] = 31; cone[1] = 34; cone[2] = 33; cone[3] = 32;
1155       cone[4] = 19; cone[5] = 22; cone[6] = 21; cone[7] = 20;
1156       ierr = DMPlexSetCone(*dm, 5, cone);CHKERRQ(ierr);
1157       cone[0] = 32; cone[1] = 33; cone[2] = 37; cone[3] = 36;
1158       cone[4] = 22; cone[5] = 25; cone[6] = 26; cone[7] = 21;
1159       ierr = DMPlexSetCone(*dm, 6, cone);CHKERRQ(ierr);
1160       cone[0] = 34; cone[1] = 38; cone[2] = 37; cone[3] = 33;
1161       cone[4] = 20; cone[5] = 21; cone[6] = 26; cone[7] = 28;
1162       ierr = DMPlexSetCone(*dm, 7, cone);CHKERRQ(ierr);
1163       cone[0] = 35; cone[1] = 38; cone[2] = 34; cone[3] = 31;
1164       cone[4] = 30; cone[5] = 19; cone[6] = 20; cone[7] = 28;
1165       ierr = DMPlexSetCone(*dm, 8, cone);CHKERRQ(ierr);
1166       cone[0] = 35; cone[1] = 31; cone[2] = 32; cone[3] = 36;
1167       cone[4] = 30; cone[5] = 25; cone[6] = 22; cone[7] = 19;
1168       ierr = DMPlexSetCone(*dm, 9, cone);CHKERRQ(ierr);
1169 
1170       cone[0] = 19; cone[1] = 20; cone[2] = 21; cone[3] = 22;
1171       cone[4] = 15; cone[5] = 16; cone[6] = 17; cone[7] = 18;
1172       ierr = DMPlexSetCone(*dm, 10, cone);CHKERRQ(ierr);
1173       cone[0] = 22; cone[1] = 21; cone[2] = 26; cone[3] = 25;
1174       cone[4] = 16; cone[5] = 23; cone[6] = 24; cone[7] = 17;
1175       ierr = DMPlexSetCone(*dm, 11, cone);CHKERRQ(ierr);
1176       cone[0] = 20; cone[1] = 28; cone[2] = 26; cone[3] = 21;
1177       cone[4] = 18; cone[5] = 17; cone[6] = 24; cone[7] = 27;
1178       ierr = DMPlexSetCone(*dm, 12, cone);CHKERRQ(ierr);
1179       cone[0] = 30; cone[1] = 28; cone[2] = 20; cone[3] = 19;
1180       cone[4] = 29; cone[5] = 15; cone[6] = 18; cone[7] = 27;
1181       ierr = DMPlexSetCone(*dm, 13, cone);CHKERRQ(ierr);
1182       cone[0] = 30; cone[1] = 19; cone[2] = 22; cone[3] = 25;
1183       cone[4] = 29; cone[5] = 23; cone[6] = 16; cone[7] = 15;
1184       ierr = DMPlexSetCone(*dm, 14, cone);CHKERRQ(ierr);
1185     } else {
1186       cone[0] =  5; cone[1] =  8; cone[2] =  7; cone[3] =  6;
1187       cone[4] =  9; cone[5] = 12; cone[6] = 11; cone[7] = 10;
1188       ierr = DMPlexSetCone(*dm, 0, cone);CHKERRQ(ierr);
1189       cone[0] =  6; cone[1] =  7; cone[2] = 14; cone[3] = 13;
1190       cone[4] = 12; cone[5] = 15; cone[6] = 16; cone[7] = 11;
1191       ierr = DMPlexSetCone(*dm, 1, cone);CHKERRQ(ierr);
1192       cone[0] =  8; cone[1] = 17; cone[2] = 14; cone[3] =  7;
1193       cone[4] = 10; cone[5] = 11; cone[6] = 16; cone[7] = 18;
1194       ierr = DMPlexSetCone(*dm, 2, cone);CHKERRQ(ierr);
1195       cone[0] = 19; cone[1] = 17; cone[2] =  8; cone[3] =  5;
1196       cone[4] = 20; cone[5] =  9; cone[6] = 10; cone[7] = 18;
1197       ierr = DMPlexSetCone(*dm, 3, cone);CHKERRQ(ierr);
1198       cone[0] = 19; cone[1] =  5; cone[2] =  6; cone[3] = 13;
1199       cone[4] = 20; cone[5] = 15; cone[6] = 12; cone[7] =  9;
1200       ierr = DMPlexSetCone(*dm, 4, cone);CHKERRQ(ierr);
1201     }
1202     ierr = DMPlexSymmetrize(*dm);CHKERRQ(ierr);
1203     ierr = DMPlexStratify(*dm);CHKERRQ(ierr);
1204   }
1205   /* Interpolate */
1206   {
1207     DM idm;
1208 
1209     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
1210     ierr = DMDestroy(dm);CHKERRQ(ierr);
1211     *dm  = idm;
1212   }
1213   /* Create cube geometry */
1214   {
1215     Vec             coordinates;
1216     PetscSection    coordSection;
1217     PetscScalar    *coords;
1218     PetscInt        coordSize, v;
1219     const PetscReal dis = 1.0/PetscSqrtReal(2.0);
1220     const PetscReal ds2 = dis/2.0;
1221 
1222     /* Build coordinates */
1223     ierr = DMGetCoordinateSection(*dm, &coordSection);CHKERRQ(ierr);
1224     ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
1225     ierr = PetscSectionSetFieldComponents(coordSection, 0, dim);CHKERRQ(ierr);
1226     ierr = PetscSectionSetChart(coordSection, numCells, numCells+numVertices);CHKERRQ(ierr);
1227     for (v = numCells; v < numCells+numVertices; ++v) {
1228       ierr = PetscSectionSetDof(coordSection, v, dim);CHKERRQ(ierr);
1229       ierr = PetscSectionSetFieldDof(coordSection, v, 0, dim);CHKERRQ(ierr);
1230     }
1231     ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
1232     ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
1233     ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
1234     ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
1235     ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
1236     ierr = VecSetBlockSize(coordinates, dim);CHKERRQ(ierr);
1237     ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
1238     ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
1239     coords[0*dim+0] = -ds2; coords[0*dim+1] = -ds2; coords[0*dim+2] = 0.0;
1240     coords[1*dim+0] =  ds2; coords[1*dim+1] = -ds2; coords[1*dim+2] = 0.0;
1241     coords[2*dim+0] =  ds2; coords[2*dim+1] =  ds2; coords[2*dim+2] = 0.0;
1242     coords[3*dim+0] = -ds2; coords[3*dim+1] =  ds2; coords[3*dim+2] = 0.0;
1243     coords[4*dim+0] = -ds2; coords[4*dim+1] = -ds2; coords[4*dim+2] = 1.0;
1244     coords[5*dim+0] = -ds2; coords[5*dim+1] =  ds2; coords[5*dim+2] = 1.0;
1245     coords[6*dim+0] =  ds2; coords[6*dim+1] =  ds2; coords[6*dim+2] = 1.0;
1246     coords[7*dim+0] =  ds2; coords[7*dim+1] = -ds2; coords[7*dim+2] = 1.0;
1247     coords[ 8*dim+0] =  dis; coords[ 8*dim+1] = -dis; coords[ 8*dim+2] = 0.0;
1248     coords[ 9*dim+0] =  dis; coords[ 9*dim+1] =  dis; coords[ 9*dim+2] = 0.0;
1249     coords[10*dim+0] =  dis; coords[10*dim+1] = -dis; coords[10*dim+2] = 1.0;
1250     coords[11*dim+0] =  dis; coords[11*dim+1] =  dis; coords[11*dim+2] = 1.0;
1251     coords[12*dim+0] = -dis; coords[12*dim+1] =  dis; coords[12*dim+2] = 0.0;
1252     coords[13*dim+0] = -dis; coords[13*dim+1] =  dis; coords[13*dim+2] = 1.0;
1253     coords[14*dim+0] = -dis; coords[14*dim+1] = -dis; coords[14*dim+2] = 0.0;
1254     coords[15*dim+0] = -dis; coords[15*dim+1] = -dis; coords[15*dim+2] = 1.0;
1255     if (periodicZ == DM_BOUNDARY_PERIODIC) {
1256       /* 15 31 19 */ coords[16*dim+0] = -ds2; coords[16*dim+1] = -ds2; coords[16*dim+2] = 0.5;
1257       /* 16 32 22 */ coords[17*dim+0] =  ds2; coords[17*dim+1] = -ds2; coords[17*dim+2] = 0.5;
1258       /* 17 33 21 */ coords[18*dim+0] =  ds2; coords[18*dim+1] =  ds2; coords[18*dim+2] = 0.5;
1259       /* 18 34 20 */ coords[19*dim+0] = -ds2; coords[19*dim+1] =  ds2; coords[19*dim+2] = 0.5;
1260       /* 29 35 30 */ coords[20*dim+0] = -dis; coords[20*dim+1] = -dis; coords[20*dim+2] = 0.5;
1261       /* 23 36 25 */ coords[21*dim+0] =  dis; coords[21*dim+1] = -dis; coords[21*dim+2] = 0.5;
1262       /* 24 37 26 */ coords[22*dim+0] =  dis; coords[22*dim+1] =  dis; coords[22*dim+2] = 0.5;
1263       /* 27 38 28 */ coords[23*dim+0] = -dis; coords[23*dim+1] =  dis; coords[23*dim+2] = 0.5;
1264     }
1265     ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
1266     ierr = DMSetCoordinatesLocal(*dm, coordinates);CHKERRQ(ierr);
1267     ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
1268   }
1269   /* Create periodicity */
1270   if (periodicZ == DM_BOUNDARY_PERIODIC || periodicZ == DM_BOUNDARY_TWIST) {
1271     PetscReal      L[3];
1272     PetscReal      maxCell[3];
1273     DMBoundaryType bdType[3];
1274     PetscReal      lower[3] = {0.0, 0.0, 0.0};
1275     PetscReal      upper[3] = {1.0, 1.0, 1.5};
1276     PetscInt       i, numZCells = 3;
1277 
1278     bdType[0] = DM_BOUNDARY_NONE;
1279     bdType[1] = DM_BOUNDARY_NONE;
1280     bdType[2] = periodicZ;
1281     for (i = 0; i < dim; i++) {
1282       L[i]       = upper[i] - lower[i];
1283       maxCell[i] = 1.1 * (L[i] / numZCells);
1284     }
1285     ierr = DMSetPeriodicity(*dm, PETSC_TRUE, maxCell, L, bdType);CHKERRQ(ierr);
1286   }
1287   /* Refine topology */
1288   for (r = 0; r < numRefine; ++r) {
1289     DM rdm = NULL;
1290 
1291     ierr = DMRefine(*dm, comm, &rdm);CHKERRQ(ierr);
1292     ierr = DMDestroy(dm);CHKERRQ(ierr);
1293     *dm  = rdm;
1294   }
1295   /* Remap geometry to cylinder
1296        Interior square: Linear interpolation is correct
1297        The other cells all have vertices on rays from the origin. We want to uniformly expand the spacing
1298        such that the last vertex is on the unit circle. So the closest and farthest vertices are at distance
1299 
1300          phi     = arctan(y/x)
1301          d_close = sqrt(1/8 + 1/4 sin^2(phi))
1302          d_far   = sqrt(1/2 + sin^2(phi))
1303 
1304        so we remap them using
1305 
1306          x_new = x_close + (x - x_close) (1 - d_close) / (d_far - d_close)
1307          y_new = y_close + (y - y_close) (1 - d_close) / (d_far - d_close)
1308 
1309        If pi/4 < phi < 3pi/4 or -3pi/4 < phi < -pi/4, then we switch x and y.
1310   */
1311   {
1312     Vec           coordinates;
1313     PetscSection  coordSection;
1314     PetscScalar  *coords;
1315     PetscInt      vStart, vEnd, v;
1316     const PetscReal dis = 1.0/PetscSqrtReal(2.0);
1317     const PetscReal ds2 = 0.5*dis;
1318 
1319     ierr = DMPlexGetDepthStratum(*dm, 0, &vStart, &vEnd);CHKERRQ(ierr);
1320     ierr = DMGetCoordinateSection(*dm, &coordSection);CHKERRQ(ierr);
1321     ierr = DMGetCoordinatesLocal(*dm, &coordinates);CHKERRQ(ierr);
1322     ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
1323     for (v = vStart; v < vEnd; ++v) {
1324       PetscReal phi, sinp, cosp, dc, df, x, y, xc, yc;
1325       PetscInt  off;
1326 
1327       ierr = PetscSectionGetOffset(coordSection, v, &off);CHKERRQ(ierr);
1328       if ((PetscAbsScalar(coords[off+0]) <= ds2) && (PetscAbsScalar(coords[off+1]) <= ds2)) continue;
1329       x    = PetscRealPart(coords[off]);
1330       y    = PetscRealPart(coords[off+1]);
1331       phi  = PetscAtan2Real(y, x);
1332       sinp = PetscSinReal(phi);
1333       cosp = PetscCosReal(phi);
1334       if ((PetscAbsReal(phi) > PETSC_PI/4.0) && (PetscAbsReal(phi) < 3.0*PETSC_PI/4.0)) {
1335         dc = PetscAbsReal(ds2/sinp);
1336         df = PetscAbsReal(dis/sinp);
1337         xc = ds2*x/PetscAbsReal(y);
1338         yc = ds2*PetscSignReal(y);
1339       } else {
1340         dc = PetscAbsReal(ds2/cosp);
1341         df = PetscAbsReal(dis/cosp);
1342         xc = ds2*PetscSignReal(x);
1343         yc = ds2*y/PetscAbsReal(x);
1344       }
1345       coords[off+0] = xc + (coords[off+0] - xc)*(1.0 - dc)/(df - dc);
1346       coords[off+1] = yc + (coords[off+1] - yc)*(1.0 - dc)/(df - dc);
1347     }
1348     ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
1349     if (periodicZ == DM_BOUNDARY_PERIODIC || periodicZ == DM_BOUNDARY_TWIST) {
1350       ierr = DMLocalizeCoordinates(*dm);CHKERRQ(ierr);
1351     }
1352   }
1353   PetscFunctionReturn(0);
1354 }
1355 
1356 /*@
1357   DMPlexCreateWedgeCylinderMesh - Creates a mesh on the tensor product of the unit interval with the circle (cylinder) using wedges.
1358 
1359   Collective on MPI_Comm
1360 
1361   Input Parameters:
1362 + comm - The communicator for the DM object
1363 . n    - The number of wedges around the origin
1364 - interpolate - Create edges and faces
1365 
1366   Output Parameter:
1367 . dm  - The DM object
1368 
1369   Level: beginner
1370 
1371 .keywords: DM, create
1372 .seealso: DMPlexCreateHexCylinderMesh(), DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
1373 @*/
1374 PetscErrorCode DMPlexCreateWedgeCylinderMesh(MPI_Comm comm, PetscInt n, PetscBool interpolate, DM *dm)
1375 {
1376   const PetscInt dim = 3;
1377   PetscInt       numCells, numVertices;
1378   PetscErrorCode ierr;
1379 
1380   PetscFunctionBegin;
1381   PetscValidPointer(dm, 3);
1382   if (n < 0) SETERRQ1(comm, PETSC_ERR_ARG_OUTOFRANGE, "Number of wedges %D cannot be negative", n);
1383   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
1384   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
1385   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
1386   /* Create topology */
1387   {
1388     PetscInt cone[6], c;
1389 
1390     numCells    = n;
1391     numVertices = 2*(n+1);
1392     ierr = DMPlexSetChart(*dm, 0, numCells+numVertices);CHKERRQ(ierr);
1393     for (c = 0; c < numCells; c++) {ierr = DMPlexSetConeSize(*dm, c, 6);CHKERRQ(ierr);}
1394     ierr = DMSetUp(*dm);CHKERRQ(ierr);
1395     for (c = 0; c < numCells; c++) {
1396       cone[0] =  c+n*1; cone[1] = (c+1)%n+n*1; cone[2] = 0+3*n;
1397       cone[3] =  c+n*2; cone[4] = (c+1)%n+n*2; cone[5] = 1+3*n;
1398       ierr = DMPlexSetCone(*dm, c, cone);CHKERRQ(ierr);
1399     }
1400     ierr = DMPlexSymmetrize(*dm);CHKERRQ(ierr);
1401     ierr = DMPlexStratify(*dm);CHKERRQ(ierr);
1402   }
1403   /* Interpolate */
1404   if (interpolate) {
1405     DM idm;
1406 
1407     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
1408     ierr = DMDestroy(dm);CHKERRQ(ierr);
1409     *dm  = idm;
1410   }
1411   /* Create cylinder geometry */
1412   {
1413     Vec          coordinates;
1414     PetscSection coordSection;
1415     PetscScalar *coords;
1416     PetscInt     coordSize, v, c;
1417 
1418     /* Build coordinates */
1419     ierr = DMGetCoordinateSection(*dm, &coordSection);CHKERRQ(ierr);
1420     ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
1421     ierr = PetscSectionSetFieldComponents(coordSection, 0, dim);CHKERRQ(ierr);
1422     ierr = PetscSectionSetChart(coordSection, numCells, numCells+numVertices);CHKERRQ(ierr);
1423     for (v = numCells; v < numCells+numVertices; ++v) {
1424       ierr = PetscSectionSetDof(coordSection, v, dim);CHKERRQ(ierr);
1425       ierr = PetscSectionSetFieldDof(coordSection, v, 0, dim);CHKERRQ(ierr);
1426     }
1427     ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
1428     ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
1429     ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
1430     ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
1431     ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
1432     ierr = VecSetBlockSize(coordinates, dim);CHKERRQ(ierr);
1433     ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
1434     ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
1435     for (c = 0; c < numCells; c++) {
1436       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;
1437       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;
1438     }
1439     coords[(2*n+0)*dim+0] = 0.0; coords[(2*n+0)*dim+1] = 0.0; coords[(2*n+0)*dim+2] = 1.0;
1440     coords[(2*n+1)*dim+0] = 0.0; coords[(2*n+1)*dim+1] = 0.0; coords[(2*n+1)*dim+2] = 0.0;
1441     ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
1442     ierr = DMSetCoordinatesLocal(*dm, coordinates);CHKERRQ(ierr);
1443     ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
1444   }
1445   PetscFunctionReturn(0);
1446 }
1447 
1448 PETSC_STATIC_INLINE PetscReal DiffNormReal(PetscInt dim, const PetscReal x[], const PetscReal y[])
1449 {
1450   PetscReal prod = 0.0;
1451   PetscInt  i;
1452   for (i = 0; i < dim; ++i) prod += PetscSqr(x[i] - y[i]);
1453   return PetscSqrtReal(prod);
1454 }
1455 PETSC_STATIC_INLINE PetscReal DotReal(PetscInt dim, const PetscReal x[], const PetscReal y[])
1456 {
1457   PetscReal prod = 0.0;
1458   PetscInt  i;
1459   for (i = 0; i < dim; ++i) prod += x[i]*y[i];
1460   return prod;
1461 }
1462 
1463 /*@
1464   DMPlexCreateSphereMesh - Creates a mesh on the d-dimensional sphere, S^d.
1465 
1466   Collective on MPI_Comm
1467 
1468   Input Parameters:
1469 . comm  - The communicator for the DM object
1470 . dim   - The dimension
1471 - simplex - Use simplices, or tensor product cells
1472 
1473   Output Parameter:
1474 . dm  - The DM object
1475 
1476   Level: beginner
1477 
1478 .keywords: DM, create
1479 .seealso: DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
1480 @*/
1481 PetscErrorCode DMPlexCreateSphereMesh(MPI_Comm comm, PetscInt dim, PetscBool simplex, DM *dm)
1482 {
1483   const PetscInt  embedDim = dim+1;
1484   PetscSection    coordSection;
1485   Vec             coordinates;
1486   PetscScalar    *coords;
1487   PetscReal      *coordsIn;
1488   PetscInt        numCells, numEdges, numVerts, firstVertex, v, firstEdge, coordSize, d, c, e;
1489   PetscMPIInt     rank;
1490   PetscErrorCode  ierr;
1491 
1492   PetscFunctionBegin;
1493   PetscValidPointer(dm, 4);
1494   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
1495   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
1496   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
1497   ierr = DMSetCoordinateDim(*dm, dim+1);CHKERRQ(ierr);
1498   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject) *dm), &rank);CHKERRQ(ierr);
1499   switch (dim) {
1500   case 2:
1501     if (simplex) {
1502       DM              idm;
1503       const PetscReal edgeLen     = 2.0/(1.0 + PETSC_PHI);
1504       const PetscReal vertex[3]   = {0.0, 1.0/(1.0 + PETSC_PHI), PETSC_PHI/(1.0 + PETSC_PHI)};
1505       const PetscInt  degree      = 5;
1506       PetscInt        s[3]        = {1, 1, 1};
1507       PetscInt        cone[3];
1508       PetscInt       *graph, p, i, j, k;
1509 
1510       numCells    = !rank ? 20 : 0;
1511       numVerts    = !rank ? 12 : 0;
1512       firstVertex = numCells;
1513       /* Use icosahedron, which for a unit sphere has coordinates which are all cyclic permutations of
1514 
1515            (0, \pm 1/\phi+1, \pm \phi/\phi+1)
1516 
1517          where \phi^2 - \phi - 1 = 0, meaning \phi is the golden ratio \frac{1 + \sqrt{5}}{2}. The edge
1518          length is then given by 2/\phi = 2 * 2.73606 = 5.47214.
1519        */
1520       /* Construct vertices */
1521       ierr = PetscCalloc1(numVerts * embedDim, &coordsIn);CHKERRQ(ierr);
1522       for (p = 0, i = 0; p < embedDim; ++p) {
1523         for (s[1] = -1; s[1] < 2; s[1] += 2) {
1524           for (s[2] = -1; s[2] < 2; s[2] += 2) {
1525             for (d = 0; d < embedDim; ++d) coordsIn[i*embedDim+d] = s[(d+p)%embedDim]*vertex[(d+p)%embedDim];
1526             ++i;
1527           }
1528         }
1529       }
1530       /* Construct graph */
1531       ierr = PetscCalloc1(numVerts * numVerts, &graph);CHKERRQ(ierr);
1532       for (i = 0; i < numVerts; ++i) {
1533         for (j = 0, k = 0; j < numVerts; ++j) {
1534           if (PetscAbsReal(DiffNormReal(embedDim, &coordsIn[i*embedDim], &coordsIn[j*embedDim]) - edgeLen) < PETSC_SMALL) {graph[i*numVerts+j] = 1; ++k;}
1535         }
1536         if (k != degree) SETERRQ3(comm, PETSC_ERR_PLIB, "Invalid icosahedron, vertex %D degree %D != %D", i, k, degree);
1537       }
1538       /* Build Topology */
1539       ierr = DMPlexSetChart(*dm, 0, numCells+numVerts);CHKERRQ(ierr);
1540       for (c = 0; c < numCells; c++) {
1541         ierr = DMPlexSetConeSize(*dm, c, embedDim);CHKERRQ(ierr);
1542       }
1543       ierr = DMSetUp(*dm);CHKERRQ(ierr); /* Allocate space for cones */
1544       /* Cells */
1545       for (i = 0, c = 0; i < numVerts; ++i) {
1546         for (j = 0; j < i; ++j) {
1547           for (k = 0; k < j; ++k) {
1548             if (graph[i*numVerts+j] && graph[j*numVerts+k] && graph[k*numVerts+i]) {
1549               cone[0] = firstVertex+i; cone[1] = firstVertex+j; cone[2] = firstVertex+k;
1550               /* Check orientation */
1551               {
1552                 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}}};
1553                 PetscReal normal[3];
1554                 PetscInt  e, f;
1555 
1556                 for (d = 0; d < embedDim; ++d) {
1557                   normal[d] = 0.0;
1558                   for (e = 0; e < embedDim; ++e) {
1559                     for (f = 0; f < embedDim; ++f) {
1560                       normal[d] += epsilon[d][e][f]*(coordsIn[j*embedDim+e] - coordsIn[i*embedDim+e])*(coordsIn[k*embedDim+f] - coordsIn[i*embedDim+f]);
1561                     }
1562                   }
1563                 }
1564                 if (DotReal(embedDim, normal, &coordsIn[i*embedDim]) < 0) {PetscInt tmp = cone[1]; cone[1] = cone[2]; cone[2] = tmp;}
1565               }
1566               ierr = DMPlexSetCone(*dm, c++, cone);CHKERRQ(ierr);
1567             }
1568           }
1569         }
1570       }
1571       ierr = DMPlexSymmetrize(*dm);CHKERRQ(ierr);
1572       ierr = DMPlexStratify(*dm);CHKERRQ(ierr);
1573       ierr = PetscFree(graph);CHKERRQ(ierr);
1574       /* Interpolate mesh */
1575       ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
1576       ierr = DMDestroy(dm);CHKERRQ(ierr);
1577       *dm  = idm;
1578     } else {
1579       /*
1580         12-21--13
1581          |     |
1582         25  4  24
1583          |     |
1584   12-25--9-16--8-24--13
1585    |     |     |     |
1586   23  5 17  0 15  3  22
1587    |     |     |     |
1588   10-20--6-14--7-19--11
1589          |     |
1590         20  1  19
1591          |     |
1592         10-18--11
1593          |     |
1594         23  2  22
1595          |     |
1596         12-21--13
1597        */
1598       const PetscReal dist = 1.0/PetscSqrtReal(3.0);
1599       PetscInt        cone[4], ornt[4];
1600 
1601       numCells    = !rank ?  6 : 0;
1602       numEdges    = !rank ? 12 : 0;
1603       numVerts    = !rank ?  8 : 0;
1604       firstVertex = numCells;
1605       firstEdge   = numCells + numVerts;
1606       /* Build Topology */
1607       ierr = DMPlexSetChart(*dm, 0, numCells+numEdges+numVerts);CHKERRQ(ierr);
1608       for (c = 0; c < numCells; c++) {
1609         ierr = DMPlexSetConeSize(*dm, c, 4);CHKERRQ(ierr);
1610       }
1611       for (e = firstEdge; e < firstEdge+numEdges; ++e) {
1612         ierr = DMPlexSetConeSize(*dm, e, 2);CHKERRQ(ierr);
1613       }
1614       ierr = DMSetUp(*dm);CHKERRQ(ierr); /* Allocate space for cones */
1615       /* Cell 0 */
1616       cone[0] = 14; cone[1] = 15; cone[2] = 16; cone[3] = 17;
1617       ierr = DMPlexSetCone(*dm, 0, cone);CHKERRQ(ierr);
1618       ornt[0] = 0; ornt[1] = 0; ornt[2] = 0; ornt[3] = 0;
1619       ierr = DMPlexSetConeOrientation(*dm, 0, ornt);CHKERRQ(ierr);
1620       /* Cell 1 */
1621       cone[0] = 18; cone[1] = 19; cone[2] = 14; cone[3] = 20;
1622       ierr = DMPlexSetCone(*dm, 1, cone);CHKERRQ(ierr);
1623       ornt[0] = 0; ornt[1] = 0; ornt[2] = -2; ornt[3] = 0;
1624       ierr = DMPlexSetConeOrientation(*dm, 1, ornt);CHKERRQ(ierr);
1625       /* Cell 2 */
1626       cone[0] = 21; cone[1] = 22; cone[2] = 18; cone[3] = 23;
1627       ierr = DMPlexSetCone(*dm, 2, cone);CHKERRQ(ierr);
1628       ornt[0] = 0; ornt[1] = 0; ornt[2] = -2; ornt[3] = 0;
1629       ierr = DMPlexSetConeOrientation(*dm, 2, ornt);CHKERRQ(ierr);
1630       /* Cell 3 */
1631       cone[0] = 19; cone[1] = 22; cone[2] = 24; cone[3] = 15;
1632       ierr = DMPlexSetCone(*dm, 3, cone);CHKERRQ(ierr);
1633       ornt[0] = -2; ornt[1] = -2; ornt[2] = 0; ornt[3] = -2;
1634       ierr = DMPlexSetConeOrientation(*dm, 3, ornt);CHKERRQ(ierr);
1635       /* Cell 4 */
1636       cone[0] = 16; cone[1] = 24; cone[2] = 21; cone[3] = 25;
1637       ierr = DMPlexSetCone(*dm, 4, cone);CHKERRQ(ierr);
1638       ornt[0] = -2; ornt[1] = -2; ornt[2] = -2; ornt[3] = 0;
1639       ierr = DMPlexSetConeOrientation(*dm, 4, ornt);CHKERRQ(ierr);
1640       /* Cell 5 */
1641       cone[0] = 20; cone[1] = 17; cone[2] = 25; cone[3] = 23;
1642       ierr = DMPlexSetCone(*dm, 5, cone);CHKERRQ(ierr);
1643       ornt[0] = -2; ornt[1] = -2; ornt[2] = -2; ornt[3] = -2;
1644       ierr = DMPlexSetConeOrientation(*dm, 5, ornt);CHKERRQ(ierr);
1645       /* Edges */
1646       cone[0] =  6; cone[1] =  7;
1647       ierr = DMPlexSetCone(*dm, 14, cone);CHKERRQ(ierr);
1648       cone[0] =  7; cone[1] =  8;
1649       ierr = DMPlexSetCone(*dm, 15, cone);CHKERRQ(ierr);
1650       cone[0] =  8; cone[1] =  9;
1651       ierr = DMPlexSetCone(*dm, 16, cone);CHKERRQ(ierr);
1652       cone[0] =  9; cone[1] =  6;
1653       ierr = DMPlexSetCone(*dm, 17, cone);CHKERRQ(ierr);
1654       cone[0] = 10; cone[1] = 11;
1655       ierr = DMPlexSetCone(*dm, 18, cone);CHKERRQ(ierr);
1656       cone[0] = 11; cone[1] =  7;
1657       ierr = DMPlexSetCone(*dm, 19, cone);CHKERRQ(ierr);
1658       cone[0] =  6; cone[1] = 10;
1659       ierr = DMPlexSetCone(*dm, 20, cone);CHKERRQ(ierr);
1660       cone[0] = 12; cone[1] = 13;
1661       ierr = DMPlexSetCone(*dm, 21, cone);CHKERRQ(ierr);
1662       cone[0] = 13; cone[1] = 11;
1663       ierr = DMPlexSetCone(*dm, 22, cone);CHKERRQ(ierr);
1664       cone[0] = 10; cone[1] = 12;
1665       ierr = DMPlexSetCone(*dm, 23, cone);CHKERRQ(ierr);
1666       cone[0] = 13; cone[1] =  8;
1667       ierr = DMPlexSetCone(*dm, 24, cone);CHKERRQ(ierr);
1668       cone[0] = 12; cone[1] =  9;
1669       ierr = DMPlexSetCone(*dm, 25, cone);CHKERRQ(ierr);
1670       ierr = DMPlexSymmetrize(*dm);CHKERRQ(ierr);
1671       ierr = DMPlexStratify(*dm);CHKERRQ(ierr);
1672       /* Build coordinates */
1673       ierr = PetscCalloc1(numVerts * embedDim, &coordsIn);CHKERRQ(ierr);
1674       coordsIn[0*embedDim+0] = -dist; coordsIn[0*embedDim+1] =  dist; coordsIn[0*embedDim+2] = -dist;
1675       coordsIn[1*embedDim+0] =  dist; coordsIn[1*embedDim+1] =  dist; coordsIn[1*embedDim+2] = -dist;
1676       coordsIn[2*embedDim+0] =  dist; coordsIn[2*embedDim+1] = -dist; coordsIn[2*embedDim+2] = -dist;
1677       coordsIn[3*embedDim+0] = -dist; coordsIn[3*embedDim+1] = -dist; coordsIn[3*embedDim+2] = -dist;
1678       coordsIn[4*embedDim+0] = -dist; coordsIn[4*embedDim+1] =  dist; coordsIn[4*embedDim+2] =  dist;
1679       coordsIn[5*embedDim+0] =  dist; coordsIn[5*embedDim+1] =  dist; coordsIn[5*embedDim+2] =  dist;
1680       coordsIn[6*embedDim+0] = -dist; coordsIn[6*embedDim+1] = -dist; coordsIn[6*embedDim+2] =  dist;
1681       coordsIn[7*embedDim+0] =  dist; coordsIn[7*embedDim+1] = -dist; coordsIn[7*embedDim+2] =  dist;
1682     }
1683     break;
1684   case 3:
1685     if (simplex) {
1686       DM              idm;
1687       const PetscReal edgeLen         = 1.0/PETSC_PHI;
1688       const PetscReal vertexA[4]      = {0.5, 0.5, 0.5, 0.5};
1689       const PetscReal vertexB[4]      = {1.0, 0.0, 0.0, 0.0};
1690       const PetscReal vertexC[4]      = {0.5, 0.5*PETSC_PHI, 0.5/PETSC_PHI, 0.0};
1691       const PetscInt  degree          = 12;
1692       PetscInt        s[4]            = {1, 1, 1};
1693       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},
1694                                          {2, 0, 1, 3}, {2, 1, 3, 0}, {2, 3, 0, 1}, {3, 0, 2, 1}, {3, 1, 0, 2}, {3, 2, 1, 0}};
1695       PetscInt        cone[4];
1696       PetscInt       *graph, p, i, j, k, l;
1697 
1698       numCells    = !rank ? 600 : 0;
1699       numVerts    = !rank ? 120 : 0;
1700       firstVertex = numCells;
1701       /* Use the 600-cell, which for a unit sphere has coordinates which are
1702 
1703            1/2 (\pm 1, \pm 1,    \pm 1, \pm 1)                          16
1704                (\pm 1,    0,       0,      0)  all cyclic permutations   8
1705            1/2 (\pm 1, \pm phi, \pm 1/phi, 0)  all even permutations    96
1706 
1707          where \phi^2 - \phi - 1 = 0, meaning \phi is the golden ratio \frac{1 + \sqrt{5}}{2}. The edge
1708          length is then given by 1/\phi = 2.73606.
1709 
1710          http://buzzard.pugetsound.edu/sage-practice/ch03s03.html
1711          http://mathworld.wolfram.com/600-Cell.html
1712        */
1713       /* Construct vertices */
1714       ierr = PetscCalloc1(numVerts * embedDim, &coordsIn);CHKERRQ(ierr);
1715       i    = 0;
1716       for (s[0] = -1; s[0] < 2; s[0] += 2) {
1717         for (s[1] = -1; s[1] < 2; s[1] += 2) {
1718           for (s[2] = -1; s[2] < 2; s[2] += 2) {
1719             for (s[3] = -1; s[3] < 2; s[3] += 2) {
1720               for (d = 0; d < embedDim; ++d) coordsIn[i*embedDim+d] = s[d]*vertexA[d];
1721               ++i;
1722             }
1723           }
1724         }
1725       }
1726       for (p = 0; p < embedDim; ++p) {
1727         s[1] = s[2] = s[3] = 1;
1728         for (s[0] = -1; s[0] < 2; s[0] += 2) {
1729           for (d = 0; d < embedDim; ++d) coordsIn[i*embedDim+d] = s[(d+p)%embedDim]*vertexB[(d+p)%embedDim];
1730           ++i;
1731         }
1732       }
1733       for (p = 0; p < 12; ++p) {
1734         s[3] = 1;
1735         for (s[0] = -1; s[0] < 2; s[0] += 2) {
1736           for (s[1] = -1; s[1] < 2; s[1] += 2) {
1737             for (s[2] = -1; s[2] < 2; s[2] += 2) {
1738               for (d = 0; d < embedDim; ++d) coordsIn[i*embedDim+d] = s[evenPerm[p][d]]*vertexC[evenPerm[p][d]];
1739               ++i;
1740             }
1741           }
1742         }
1743       }
1744       if (i != numVerts) SETERRQ2(comm, PETSC_ERR_PLIB, "Invalid 600-cell, vertices %D != %D", i, numVerts);
1745       /* Construct graph */
1746       ierr = PetscCalloc1(numVerts * numVerts, &graph);CHKERRQ(ierr);
1747       for (i = 0; i < numVerts; ++i) {
1748         for (j = 0, k = 0; j < numVerts; ++j) {
1749           if (PetscAbsReal(DiffNormReal(embedDim, &coordsIn[i*embedDim], &coordsIn[j*embedDim]) - edgeLen) < PETSC_SMALL) {graph[i*numVerts+j] = 1; ++k;}
1750         }
1751         if (k != degree) SETERRQ3(comm, PETSC_ERR_PLIB, "Invalid 600-cell, vertex %D degree %D != %D", i, k, degree);
1752       }
1753       /* Build Topology */
1754       ierr = DMPlexSetChart(*dm, 0, numCells+numVerts);CHKERRQ(ierr);
1755       for (c = 0; c < numCells; c++) {
1756         ierr = DMPlexSetConeSize(*dm, c, embedDim);CHKERRQ(ierr);
1757       }
1758       ierr = DMSetUp(*dm);CHKERRQ(ierr); /* Allocate space for cones */
1759       /* Cells */
1760       for (i = 0, c = 0; i < numVerts; ++i) {
1761         for (j = 0; j < i; ++j) {
1762           for (k = 0; k < j; ++k) {
1763             for (l = 0; l < k; ++l) {
1764               if (graph[i*numVerts+j] && graph[j*numVerts+k] && graph[k*numVerts+i] &&
1765                   graph[l*numVerts+i] && graph[l*numVerts+j] && graph[l*numVerts+k]) {
1766                 cone[0] = firstVertex+i; cone[1] = firstVertex+j; cone[2] = firstVertex+k; cone[3] = firstVertex+l;
1767                 /* Check orientation: https://ef.gy/linear-algebra:normal-vectors-in-higher-dimensional-spaces */
1768                 {
1769                   const PetscInt epsilon[4][4][4][4] = {{{{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}},
1770                                                          {{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  1}, { 0,  0, -1, 0}},
1771                                                          {{0,  0,  0,  0}, { 0, 0,  0, -1}, { 0,  0, 0,  0}, { 0,  1,  0, 0}},
1772                                                          {{0,  0,  0,  0}, { 0, 0,  1,  0}, { 0, -1, 0,  0}, { 0,  0,  0, 0}}},
1773 
1774                                                         {{{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0, -1}, { 0,  0,  1, 0}},
1775                                                          {{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}},
1776                                                          {{0,  0,  0,  1}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, {-1,  0,  0, 0}},
1777                                                          {{0,  0, -1,  0}, { 0, 0,  0,  0}, { 1,  0, 0,  0}, { 0,  0,  0, 0}}},
1778 
1779                                                         {{{0,  0,  0,  0}, { 0, 0,  0,  1}, { 0,  0, 0,  0}, { 0, -1,  0, 0}},
1780                                                          {{0,  0,  0, -1}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 1,  0,  0, 0}},
1781                                                          {{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}},
1782                                                          {{0,  1,  0,  0}, {-1, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}}},
1783 
1784                                                         {{{0,  0,  0,  0}, { 0, 0, -1,  0}, { 0,  1, 0,  0}, { 0,  0,  0, 0}},
1785                                                          {{0,  0,  1,  0}, { 0, 0,  0,  0}, {-1,  0, 0,  0}, { 0,  0,  0, 0}},
1786                                                          {{0, -1,  0,  0}, { 1, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}},
1787                                                          {{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}}}};
1788                   PetscReal normal[4];
1789                   PetscInt  e, f, g;
1790 
1791                   for (d = 0; d < embedDim; ++d) {
1792                     normal[d] = 0.0;
1793                     for (e = 0; e < embedDim; ++e) {
1794                       for (f = 0; f < embedDim; ++f) {
1795                         for (g = 0; g < embedDim; ++g) {
1796                           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]);
1797                         }
1798                       }
1799                     }
1800                   }
1801                   if (DotReal(embedDim, normal, &coordsIn[i*embedDim]) < 0) {PetscInt tmp = cone[1]; cone[1] = cone[2]; cone[2] = tmp;}
1802                 }
1803                 ierr = DMPlexSetCone(*dm, c++, cone);CHKERRQ(ierr);
1804               }
1805             }
1806           }
1807         }
1808       }
1809       ierr = DMPlexSymmetrize(*dm);CHKERRQ(ierr);
1810       ierr = DMPlexStratify(*dm);CHKERRQ(ierr);
1811       ierr = PetscFree(graph);CHKERRQ(ierr);
1812       /* Interpolate mesh */
1813       ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
1814       ierr = DMDestroy(dm);CHKERRQ(ierr);
1815       *dm  = idm;
1816       break;
1817     }
1818   default: SETERRQ1(comm, PETSC_ERR_SUP, "Unsupported dimension for sphere: %D", dim);
1819   }
1820   /* Create coordinates */
1821   ierr = DMGetCoordinateSection(*dm, &coordSection);CHKERRQ(ierr);
1822   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
1823   ierr = PetscSectionSetFieldComponents(coordSection, 0, embedDim);CHKERRQ(ierr);
1824   ierr = PetscSectionSetChart(coordSection, firstVertex, firstVertex+numVerts);CHKERRQ(ierr);
1825   for (v = firstVertex; v < firstVertex+numVerts; ++v) {
1826     ierr = PetscSectionSetDof(coordSection, v, embedDim);CHKERRQ(ierr);
1827     ierr = PetscSectionSetFieldDof(coordSection, v, 0, embedDim);CHKERRQ(ierr);
1828   }
1829   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
1830   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
1831   ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
1832   ierr = VecSetBlockSize(coordinates, embedDim);CHKERRQ(ierr);
1833   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
1834   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
1835   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
1836   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
1837   for (v = 0; v < numVerts; ++v) for (d = 0; d < embedDim; ++d) {coords[v*embedDim+d] = coordsIn[v*embedDim+d];}
1838   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
1839   ierr = DMSetCoordinatesLocal(*dm, coordinates);CHKERRQ(ierr);
1840   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
1841   ierr = PetscFree(coordsIn);CHKERRQ(ierr);
1842   PetscFunctionReturn(0);
1843 }
1844 
1845 /* External function declarations here */
1846 extern PetscErrorCode DMCreateInterpolation_Plex(DM dmCoarse, DM dmFine, Mat *interpolation, Vec *scaling);
1847 extern PetscErrorCode DMCreateInjection_Plex(DM dmCoarse, DM dmFine, Mat *mat);
1848 extern PetscErrorCode DMCreateMassMatrix_Plex(DM dmCoarse, DM dmFine, Mat *mat);
1849 extern PetscErrorCode DMCreateDefaultSection_Plex(DM dm);
1850 extern PetscErrorCode DMCreateDefaultConstraints_Plex(DM dm);
1851 extern PetscErrorCode DMCreateMatrix_Plex(DM dm,  Mat *J);
1852 extern PetscErrorCode DMCreateCoordinateDM_Plex(DM dm, DM *cdm);
1853 PETSC_INTERN PetscErrorCode DMClone_Plex(DM dm, DM *newdm);
1854 extern PetscErrorCode DMSetUp_Plex(DM dm);
1855 extern PetscErrorCode DMDestroy_Plex(DM dm);
1856 extern PetscErrorCode DMView_Plex(DM dm, PetscViewer viewer);
1857 extern PetscErrorCode DMLoad_Plex(DM dm, PetscViewer viewer);
1858 extern PetscErrorCode DMCreateSubDM_Plex(DM dm, PetscInt numFields, const PetscInt fields[], IS *is, DM *subdm);
1859 static PetscErrorCode DMInitialize_Plex(DM dm);
1860 
1861 /* Replace dm with the contents of dmNew
1862    - Share the DM_Plex structure
1863    - Share the coordinates
1864    - Share the SF
1865 */
1866 static PetscErrorCode DMPlexReplace_Static(DM dm, DM dmNew)
1867 {
1868   PetscSF               sf;
1869   DM                    coordDM, coarseDM;
1870   Vec                   coords;
1871   PetscBool             isper;
1872   const PetscReal      *maxCell, *L;
1873   const DMBoundaryType *bd;
1874   PetscErrorCode        ierr;
1875 
1876   PetscFunctionBegin;
1877   ierr = DMGetPointSF(dmNew, &sf);CHKERRQ(ierr);
1878   ierr = DMSetPointSF(dm, sf);CHKERRQ(ierr);
1879   ierr = DMGetCoordinateDM(dmNew, &coordDM);CHKERRQ(ierr);
1880   ierr = DMGetCoordinatesLocal(dmNew, &coords);CHKERRQ(ierr);
1881   ierr = DMSetCoordinateDM(dm, coordDM);CHKERRQ(ierr);
1882   ierr = DMSetCoordinatesLocal(dm, coords);CHKERRQ(ierr);
1883   ierr = DMGetPeriodicity(dm, &isper, &maxCell, &L, &bd);CHKERRQ(ierr);
1884   ierr = DMSetPeriodicity(dmNew, isper, maxCell, L, bd);CHKERRQ(ierr);
1885   ierr = DMDestroy_Plex(dm);CHKERRQ(ierr);
1886   ierr = DMInitialize_Plex(dm);CHKERRQ(ierr);
1887   dm->data = dmNew->data;
1888   ((DM_Plex *) dmNew->data)->refct++;
1889   dmNew->labels->refct++;
1890   if (!--(dm->labels->refct)) {
1891     DMLabelLink next = dm->labels->next;
1892 
1893     /* destroy the labels */
1894     while (next) {
1895       DMLabelLink tmp = next->next;
1896 
1897       ierr = DMLabelDestroy(&next->label);CHKERRQ(ierr);
1898       ierr = PetscFree(next);CHKERRQ(ierr);
1899       next = tmp;
1900     }
1901     ierr = PetscFree(dm->labels);CHKERRQ(ierr);
1902   }
1903   dm->labels = dmNew->labels;
1904   dm->depthLabel = dmNew->depthLabel;
1905   ierr = DMGetCoarseDM(dmNew,&coarseDM);CHKERRQ(ierr);
1906   ierr = DMSetCoarseDM(dm,coarseDM);CHKERRQ(ierr);
1907   PetscFunctionReturn(0);
1908 }
1909 
1910 /* Swap dm with the contents of dmNew
1911    - Swap the DM_Plex structure
1912    - Swap the coordinates
1913    - Swap the point PetscSF
1914 */
1915 static PetscErrorCode DMPlexSwap_Static(DM dmA, DM dmB)
1916 {
1917   DM              coordDMA, coordDMB;
1918   Vec             coordsA,  coordsB;
1919   PetscSF         sfA,      sfB;
1920   void            *tmp;
1921   DMLabelLinkList listTmp;
1922   DMLabel         depthTmp;
1923   PetscErrorCode  ierr;
1924 
1925   PetscFunctionBegin;
1926   ierr = DMGetPointSF(dmA, &sfA);CHKERRQ(ierr);
1927   ierr = DMGetPointSF(dmB, &sfB);CHKERRQ(ierr);
1928   ierr = PetscObjectReference((PetscObject) sfA);CHKERRQ(ierr);
1929   ierr = DMSetPointSF(dmA, sfB);CHKERRQ(ierr);
1930   ierr = DMSetPointSF(dmB, sfA);CHKERRQ(ierr);
1931   ierr = PetscObjectDereference((PetscObject) sfA);CHKERRQ(ierr);
1932 
1933   ierr = DMGetCoordinateDM(dmA, &coordDMA);CHKERRQ(ierr);
1934   ierr = DMGetCoordinateDM(dmB, &coordDMB);CHKERRQ(ierr);
1935   ierr = PetscObjectReference((PetscObject) coordDMA);CHKERRQ(ierr);
1936   ierr = DMSetCoordinateDM(dmA, coordDMB);CHKERRQ(ierr);
1937   ierr = DMSetCoordinateDM(dmB, coordDMA);CHKERRQ(ierr);
1938   ierr = PetscObjectDereference((PetscObject) coordDMA);CHKERRQ(ierr);
1939 
1940   ierr = DMGetCoordinatesLocal(dmA, &coordsA);CHKERRQ(ierr);
1941   ierr = DMGetCoordinatesLocal(dmB, &coordsB);CHKERRQ(ierr);
1942   ierr = PetscObjectReference((PetscObject) coordsA);CHKERRQ(ierr);
1943   ierr = DMSetCoordinatesLocal(dmA, coordsB);CHKERRQ(ierr);
1944   ierr = DMSetCoordinatesLocal(dmB, coordsA);CHKERRQ(ierr);
1945   ierr = PetscObjectDereference((PetscObject) coordsA);CHKERRQ(ierr);
1946 
1947   tmp       = dmA->data;
1948   dmA->data = dmB->data;
1949   dmB->data = tmp;
1950   listTmp   = dmA->labels;
1951   dmA->labels = dmB->labels;
1952   dmB->labels = listTmp;
1953   depthTmp  = dmA->depthLabel;
1954   dmA->depthLabel = dmB->depthLabel;
1955   dmB->depthLabel = depthTmp;
1956   PetscFunctionReturn(0);
1957 }
1958 
1959 PetscErrorCode DMSetFromOptions_NonRefinement_Plex(PetscOptionItems *PetscOptionsObject,DM dm)
1960 {
1961   DM_Plex       *mesh = (DM_Plex*) dm->data;
1962   PetscErrorCode ierr;
1963 
1964   PetscFunctionBegin;
1965   /* Handle viewing */
1966   ierr = PetscOptionsBool("-dm_plex_print_set_values", "Output all set values info", "DMView", PETSC_FALSE, &mesh->printSetValues, NULL);CHKERRQ(ierr);
1967   ierr = PetscOptionsInt("-dm_plex_print_fem", "Debug output level all fem computations", "DMView", 0, &mesh->printFEM, NULL);CHKERRQ(ierr);
1968   ierr = PetscOptionsReal("-dm_plex_print_tol", "Tolerance for FEM output", "DMView", mesh->printTol, &mesh->printTol, NULL);CHKERRQ(ierr);
1969   /* Point Location */
1970   ierr = PetscOptionsBool("-dm_plex_hash_location", "Use grid hashing for point location", "DMView", PETSC_FALSE, &mesh->useHashLocation, NULL);CHKERRQ(ierr);
1971   /* Generation and remeshing */
1972   ierr = PetscOptionsBool("-dm_plex_remesh_bd", "Allow changes to the boundary on remeshing", "DMView", PETSC_FALSE, &mesh->remeshBd, NULL);CHKERRQ(ierr);
1973   /* Projection behavior */
1974   ierr = PetscOptionsInt("-dm_plex_max_projection_height", "Maxmimum mesh point height used to project locally", "DMPlexSetMaxProjectionHeight", 0, &mesh->maxProjectionHeight, NULL);CHKERRQ(ierr);
1975   ierr = PetscOptionsBool("-dm_plex_regular_refinement", "Use special nested projection algorithm for regular refinement", "DMPlexSetRegularRefinement", mesh->regularRefinement, &mesh->regularRefinement, NULL);CHKERRQ(ierr);
1976 
1977   ierr = PetscPartitionerSetFromOptions(mesh->partitioner);CHKERRQ(ierr);
1978   PetscFunctionReturn(0);
1979 }
1980 
1981 static PetscErrorCode DMSetFromOptions_Plex(PetscOptionItems *PetscOptionsObject,DM dm)
1982 {
1983   PetscInt       refine = 0, coarsen = 0, r;
1984   PetscBool      isHierarchy;
1985   PetscErrorCode ierr;
1986 
1987   PetscFunctionBegin;
1988   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1989   ierr = PetscOptionsHead(PetscOptionsObject,"DMPlex Options");CHKERRQ(ierr);
1990   /* Handle DMPlex refinement */
1991   ierr = PetscOptionsInt("-dm_refine", "The number of uniform refinements", "DMCreate", refine, &refine, NULL);CHKERRQ(ierr);
1992   ierr = PetscOptionsInt("-dm_refine_hierarchy", "The number of uniform refinements", "DMCreate", refine, &refine, &isHierarchy);CHKERRQ(ierr);
1993   if (refine) {ierr = DMPlexSetRefinementUniform(dm, PETSC_TRUE);CHKERRQ(ierr);}
1994   if (refine && isHierarchy) {
1995     DM *dms, coarseDM;
1996 
1997     ierr = DMGetCoarseDM(dm, &coarseDM);CHKERRQ(ierr);
1998     ierr = PetscObjectReference((PetscObject)coarseDM);CHKERRQ(ierr);
1999     ierr = PetscMalloc1(refine,&dms);CHKERRQ(ierr);
2000     ierr = DMRefineHierarchy(dm, refine, dms);CHKERRQ(ierr);
2001     /* Total hack since we do not pass in a pointer */
2002     ierr = DMPlexSwap_Static(dm, dms[refine-1]);CHKERRQ(ierr);
2003     if (refine == 1) {
2004       ierr = DMSetCoarseDM(dm, dms[0]);CHKERRQ(ierr);
2005       ierr = DMPlexSetRegularRefinement(dm, PETSC_TRUE);CHKERRQ(ierr);
2006     } else {
2007       ierr = DMSetCoarseDM(dm, dms[refine-2]);CHKERRQ(ierr);
2008       ierr = DMPlexSetRegularRefinement(dm, PETSC_TRUE);CHKERRQ(ierr);
2009       ierr = DMSetCoarseDM(dms[0], dms[refine-1]);CHKERRQ(ierr);
2010       ierr = DMPlexSetRegularRefinement(dms[0], PETSC_TRUE);CHKERRQ(ierr);
2011     }
2012     ierr = DMSetCoarseDM(dms[refine-1], coarseDM);CHKERRQ(ierr);
2013     ierr = PetscObjectDereference((PetscObject)coarseDM);CHKERRQ(ierr);
2014     /* Free DMs */
2015     for (r = 0; r < refine; ++r) {
2016       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dms[r]);CHKERRQ(ierr);
2017       ierr = DMDestroy(&dms[r]);CHKERRQ(ierr);
2018     }
2019     ierr = PetscFree(dms);CHKERRQ(ierr);
2020   } else {
2021     for (r = 0; r < refine; ++r) {
2022       DM refinedMesh;
2023 
2024       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2025       ierr = DMRefine(dm, PetscObjectComm((PetscObject) dm), &refinedMesh);CHKERRQ(ierr);
2026       /* Total hack since we do not pass in a pointer */
2027       ierr = DMPlexReplace_Static(dm, refinedMesh);CHKERRQ(ierr);
2028       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2029       ierr = DMDestroy(&refinedMesh);CHKERRQ(ierr);
2030     }
2031   }
2032   /* Handle DMPlex coarsening */
2033   ierr = PetscOptionsInt("-dm_coarsen", "Coarsen the mesh", "DMCreate", coarsen, &coarsen, NULL);CHKERRQ(ierr);
2034   ierr = PetscOptionsInt("-dm_coarsen_hierarchy", "The number of coarsenings", "DMCreate", coarsen, &coarsen, &isHierarchy);CHKERRQ(ierr);
2035   if (coarsen && isHierarchy) {
2036     DM *dms;
2037 
2038     ierr = PetscMalloc1(coarsen, &dms);CHKERRQ(ierr);
2039     ierr = DMCoarsenHierarchy(dm, coarsen, dms);CHKERRQ(ierr);
2040     /* Free DMs */
2041     for (r = 0; r < coarsen; ++r) {
2042       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dms[r]);CHKERRQ(ierr);
2043       ierr = DMDestroy(&dms[r]);CHKERRQ(ierr);
2044     }
2045     ierr = PetscFree(dms);CHKERRQ(ierr);
2046   } else {
2047     for (r = 0; r < coarsen; ++r) {
2048       DM coarseMesh;
2049 
2050       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2051       ierr = DMCoarsen(dm, PetscObjectComm((PetscObject) dm), &coarseMesh);CHKERRQ(ierr);
2052       /* Total hack since we do not pass in a pointer */
2053       ierr = DMPlexReplace_Static(dm, coarseMesh);CHKERRQ(ierr);
2054       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2055       ierr = DMDestroy(&coarseMesh);CHKERRQ(ierr);
2056     }
2057   }
2058   /* Handle */
2059   ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2060   ierr = PetscOptionsTail();CHKERRQ(ierr);
2061   PetscFunctionReturn(0);
2062 }
2063 
2064 static PetscErrorCode DMCreateGlobalVector_Plex(DM dm,Vec *vec)
2065 {
2066   PetscErrorCode ierr;
2067 
2068   PetscFunctionBegin;
2069   ierr = DMCreateGlobalVector_Section_Private(dm,vec);CHKERRQ(ierr);
2070   /* ierr = VecSetOperation(*vec, VECOP_DUPLICATE, (void(*)(void)) VecDuplicate_MPI_DM);CHKERRQ(ierr); */
2071   ierr = VecSetOperation(*vec, VECOP_VIEW, (void (*)(void)) VecView_Plex);CHKERRQ(ierr);
2072   ierr = VecSetOperation(*vec, VECOP_VIEWNATIVE, (void (*)(void)) VecView_Plex_Native);CHKERRQ(ierr);
2073   ierr = VecSetOperation(*vec, VECOP_LOAD, (void (*)(void)) VecLoad_Plex);CHKERRQ(ierr);
2074   ierr = VecSetOperation(*vec, VECOP_LOADNATIVE, (void (*)(void)) VecLoad_Plex_Native);CHKERRQ(ierr);
2075   PetscFunctionReturn(0);
2076 }
2077 
2078 static PetscErrorCode DMCreateLocalVector_Plex(DM dm,Vec *vec)
2079 {
2080   PetscErrorCode ierr;
2081 
2082   PetscFunctionBegin;
2083   ierr = DMCreateLocalVector_Section_Private(dm,vec);CHKERRQ(ierr);
2084   ierr = VecSetOperation(*vec, VECOP_VIEW, (void (*)(void)) VecView_Plex_Local);CHKERRQ(ierr);
2085   ierr = VecSetOperation(*vec, VECOP_LOAD, (void (*)(void)) VecLoad_Plex_Local);CHKERRQ(ierr);
2086   PetscFunctionReturn(0);
2087 }
2088 
2089 static PetscErrorCode DMGetDimPoints_Plex(DM dm, PetscInt dim, PetscInt *pStart, PetscInt *pEnd)
2090 {
2091   PetscInt       depth, d;
2092   PetscErrorCode ierr;
2093 
2094   PetscFunctionBegin;
2095   ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
2096   if (depth == 1) {
2097     ierr = DMGetDimension(dm, &d);CHKERRQ(ierr);
2098     if (dim == 0)      {ierr = DMPlexGetDepthStratum(dm, dim, pStart, pEnd);CHKERRQ(ierr);}
2099     else if (dim == d) {ierr = DMPlexGetDepthStratum(dm, 1, pStart, pEnd);CHKERRQ(ierr);}
2100     else               {*pStart = 0; *pEnd = 0;}
2101   } else {
2102     ierr = DMPlexGetDepthStratum(dm, dim, pStart, pEnd);CHKERRQ(ierr);
2103   }
2104   PetscFunctionReturn(0);
2105 }
2106 
2107 static PetscErrorCode DMGetNeighors_Plex(DM dm, PetscInt *nranks, const PetscMPIInt *ranks[])
2108 {
2109   PetscSF        sf;
2110   PetscErrorCode ierr;
2111 
2112   PetscFunctionBegin;
2113   ierr = DMGetPointSF(dm, &sf);CHKERRQ(ierr);
2114   ierr = PetscSFGetRanks(sf, nranks, ranks, NULL, NULL, NULL);CHKERRQ(ierr);
2115   PetscFunctionReturn(0);
2116 }
2117 
2118 static PetscErrorCode DMInitialize_Plex(DM dm)
2119 {
2120   PetscErrorCode ierr;
2121 
2122   PetscFunctionBegin;
2123   dm->ops->view                            = DMView_Plex;
2124   dm->ops->load                            = DMLoad_Plex;
2125   dm->ops->setfromoptions                  = DMSetFromOptions_Plex;
2126   dm->ops->clone                           = DMClone_Plex;
2127   dm->ops->setup                           = DMSetUp_Plex;
2128   dm->ops->createdefaultsection            = DMCreateDefaultSection_Plex;
2129   dm->ops->createdefaultconstraints        = DMCreateDefaultConstraints_Plex;
2130   dm->ops->createglobalvector              = DMCreateGlobalVector_Plex;
2131   dm->ops->createlocalvector               = DMCreateLocalVector_Plex;
2132   dm->ops->getlocaltoglobalmapping         = NULL;
2133   dm->ops->createfieldis                   = NULL;
2134   dm->ops->createcoordinatedm              = DMCreateCoordinateDM_Plex;
2135   dm->ops->getcoloring                     = NULL;
2136   dm->ops->creatematrix                    = DMCreateMatrix_Plex;
2137   dm->ops->createinterpolation             = DMCreateInterpolation_Plex;
2138   dm->ops->createmassmatrix                = DMCreateMassMatrix_Plex;
2139   dm->ops->getaggregates                   = NULL;
2140   dm->ops->getinjection                    = DMCreateInjection_Plex;
2141   dm->ops->refine                          = DMRefine_Plex;
2142   dm->ops->coarsen                         = DMCoarsen_Plex;
2143   dm->ops->refinehierarchy                 = DMRefineHierarchy_Plex;
2144   dm->ops->coarsenhierarchy                = DMCoarsenHierarchy_Plex;
2145   dm->ops->adaptlabel                      = DMAdaptLabel_Plex;
2146   dm->ops->adaptmetric                     = DMAdaptMetric_Plex;
2147   dm->ops->globaltolocalbegin              = NULL;
2148   dm->ops->globaltolocalend                = NULL;
2149   dm->ops->localtoglobalbegin              = NULL;
2150   dm->ops->localtoglobalend                = NULL;
2151   dm->ops->destroy                         = DMDestroy_Plex;
2152   dm->ops->createsubdm                     = DMCreateSubDM_Plex;
2153   dm->ops->getdimpoints                    = DMGetDimPoints_Plex;
2154   dm->ops->locatepoints                    = DMLocatePoints_Plex;
2155   dm->ops->projectfunctionlocal            = DMProjectFunctionLocal_Plex;
2156   dm->ops->projectfunctionlabellocal       = DMProjectFunctionLabelLocal_Plex;
2157   dm->ops->projectfieldlocal               = DMProjectFieldLocal_Plex;
2158   dm->ops->projectfieldlabellocal          = DMProjectFieldLabelLocal_Plex;
2159   dm->ops->computel2diff                   = DMComputeL2Diff_Plex;
2160   dm->ops->computel2gradientdiff           = DMComputeL2GradientDiff_Plex;
2161   dm->ops->computel2fielddiff              = DMComputeL2FieldDiff_Plex;
2162   dm->ops->getneighbors                    = DMGetNeighors_Plex;
2163   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMPlexInsertBoundaryValues_C",DMPlexInsertBoundaryValues_Plex);CHKERRQ(ierr);
2164   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMSetUpGLVisViewer_C",DMSetUpGLVisViewer_Plex);CHKERRQ(ierr);
2165   PetscFunctionReturn(0);
2166 }
2167 
2168 PETSC_INTERN PetscErrorCode DMClone_Plex(DM dm, DM *newdm)
2169 {
2170   DM_Plex        *mesh = (DM_Plex *) dm->data;
2171   PetscErrorCode ierr;
2172 
2173   PetscFunctionBegin;
2174   mesh->refct++;
2175   (*newdm)->data = mesh;
2176   ierr = PetscObjectChangeTypeName((PetscObject) *newdm, DMPLEX);CHKERRQ(ierr);
2177   ierr = DMInitialize_Plex(*newdm);CHKERRQ(ierr);
2178   PetscFunctionReturn(0);
2179 }
2180 
2181 /*MC
2182   DMPLEX = "plex" - A DM object that encapsulates an unstructured mesh, or CW Complex, which can be expressed using a Hasse Diagram.
2183                     In the local representation, Vecs contain all unknowns in the interior and shared boundary. This is
2184                     specified by a PetscSection object. Ownership in the global representation is determined by
2185                     ownership of the underlying DMPlex points. This is specified by another PetscSection object.
2186 
2187   Level: intermediate
2188 
2189 .seealso: DMType, DMPlexCreate(), DMCreate(), DMSetType()
2190 M*/
2191 
2192 PETSC_EXTERN PetscErrorCode DMCreate_Plex(DM dm)
2193 {
2194   DM_Plex        *mesh;
2195   PetscInt       unit, d;
2196   PetscErrorCode ierr;
2197 
2198   PetscFunctionBegin;
2199   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
2200   ierr     = PetscNewLog(dm,&mesh);CHKERRQ(ierr);
2201   dm->dim  = 0;
2202   dm->data = mesh;
2203 
2204   mesh->refct             = 1;
2205   ierr                    = PetscSectionCreate(PetscObjectComm((PetscObject)dm), &mesh->coneSection);CHKERRQ(ierr);
2206   mesh->maxConeSize       = 0;
2207   mesh->cones             = NULL;
2208   mesh->coneOrientations  = NULL;
2209   ierr                    = PetscSectionCreate(PetscObjectComm((PetscObject)dm), &mesh->supportSection);CHKERRQ(ierr);
2210   mesh->maxSupportSize    = 0;
2211   mesh->supports          = NULL;
2212   mesh->refinementUniform = PETSC_TRUE;
2213   mesh->refinementLimit   = -1.0;
2214 
2215   mesh->facesTmp = NULL;
2216 
2217   mesh->tetgenOpts   = NULL;
2218   mesh->triangleOpts = NULL;
2219   ierr = PetscPartitionerCreate(PetscObjectComm((PetscObject)dm), &mesh->partitioner);CHKERRQ(ierr);
2220   mesh->remeshBd     = PETSC_FALSE;
2221 
2222   mesh->subpointMap = NULL;
2223 
2224   for (unit = 0; unit < NUM_PETSC_UNITS; ++unit) mesh->scale[unit] = 1.0;
2225 
2226   mesh->regularRefinement   = PETSC_FALSE;
2227   mesh->depthState          = -1;
2228   mesh->globalVertexNumbers = NULL;
2229   mesh->globalCellNumbers   = NULL;
2230   mesh->anchorSection       = NULL;
2231   mesh->anchorIS            = NULL;
2232   mesh->createanchors       = NULL;
2233   mesh->computeanchormatrix = NULL;
2234   mesh->parentSection       = NULL;
2235   mesh->parents             = NULL;
2236   mesh->childIDs            = NULL;
2237   mesh->childSection        = NULL;
2238   mesh->children            = NULL;
2239   mesh->referenceTree       = NULL;
2240   mesh->getchildsymmetry    = NULL;
2241   for (d = 0; d < 8; ++d) mesh->hybridPointMax[d] = PETSC_DETERMINE;
2242   mesh->vtkCellHeight       = 0;
2243   mesh->useAnchors          = PETSC_FALSE;
2244 
2245   mesh->maxProjectionHeight = 0;
2246 
2247   mesh->printSetValues = PETSC_FALSE;
2248   mesh->printFEM       = 0;
2249   mesh->printTol       = 1.0e-10;
2250 
2251   ierr = DMInitialize_Plex(dm);CHKERRQ(ierr);
2252   PetscFunctionReturn(0);
2253 }
2254 
2255 /*@
2256   DMPlexCreate - Creates a DMPlex object, which encapsulates an unstructured mesh, or CW complex, which can be expressed using a Hasse Diagram.
2257 
2258   Collective on MPI_Comm
2259 
2260   Input Parameter:
2261 . comm - The communicator for the DMPlex object
2262 
2263   Output Parameter:
2264 . mesh  - The DMPlex object
2265 
2266   Level: beginner
2267 
2268 .keywords: DMPlex, create
2269 @*/
2270 PetscErrorCode DMPlexCreate(MPI_Comm comm, DM *mesh)
2271 {
2272   PetscErrorCode ierr;
2273 
2274   PetscFunctionBegin;
2275   PetscValidPointer(mesh,2);
2276   ierr = DMCreate(comm, mesh);CHKERRQ(ierr);
2277   ierr = DMSetType(*mesh, DMPLEX);CHKERRQ(ierr);
2278   PetscFunctionReturn(0);
2279 }
2280 
2281 /*
2282   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
2283 */
2284 static PetscErrorCode DMPlexBuildFromCellList_Parallel_Private(DM dm, PetscInt numCells, PetscInt numVertices, PetscInt numCorners, const int cells[], PetscSF *sfVert)
2285 {
2286   PetscSF         sfPoint;
2287   PetscLayout     vLayout;
2288   PetscHashI      vhash;
2289   PetscSFNode    *remoteVerticesAdj, *vertexLocal, *vertexOwner, *remoteVertex;
2290   const PetscInt *vrange;
2291   PetscInt        numVerticesAdj, off, *verticesAdj, numVerticesGhost = 0, *localVertex, *cone, c, p, v, g;
2292   PETSC_UNUSED PetscHashIIter ret, iter;
2293   PetscMPIInt     rank, size;
2294   PetscErrorCode  ierr;
2295 
2296   PetscFunctionBegin;
2297   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject) dm), &rank);CHKERRQ(ierr);
2298   ierr = MPI_Comm_size(PetscObjectComm((PetscObject) dm), &size);CHKERRQ(ierr);
2299   /* Partition vertices */
2300   ierr = PetscLayoutCreate(PetscObjectComm((PetscObject) dm), &vLayout);CHKERRQ(ierr);
2301   ierr = PetscLayoutSetLocalSize(vLayout, numVertices);CHKERRQ(ierr);
2302   ierr = PetscLayoutSetBlockSize(vLayout, 1);CHKERRQ(ierr);
2303   ierr = PetscLayoutSetUp(vLayout);CHKERRQ(ierr);
2304   ierr = PetscLayoutGetRanges(vLayout, &vrange);CHKERRQ(ierr);
2305   /* Count vertices and map them to procs */
2306   PetscHashICreate(vhash);
2307   for (c = 0; c < numCells; ++c) {
2308     for (p = 0; p < numCorners; ++p) {
2309       PetscHashIPut(vhash, cells[c*numCorners+p], ret, iter);
2310     }
2311   }
2312   PetscHashISize(vhash, numVerticesAdj);
2313   ierr = PetscMalloc1(numVerticesAdj, &verticesAdj);CHKERRQ(ierr);
2314   off = 0; ierr = PetscHashIGetKeys(vhash, &off, verticesAdj);CHKERRQ(ierr);
2315   if (off != numVerticesAdj) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Invalid number of local vertices %D should be %D", off, numVerticesAdj);
2316   ierr = PetscSortInt(numVerticesAdj, verticesAdj);CHKERRQ(ierr);
2317   ierr = PetscMalloc1(numVerticesAdj, &remoteVerticesAdj);CHKERRQ(ierr);
2318   for (v = 0; v < numVerticesAdj; ++v) {
2319     const PetscInt gv = verticesAdj[v];
2320     PetscInt       vrank;
2321 
2322     ierr = PetscFindInt(gv, size+1, vrange, &vrank);CHKERRQ(ierr);
2323     vrank = vrank < 0 ? -(vrank+2) : vrank;
2324     remoteVerticesAdj[v].index = gv - vrange[vrank];
2325     remoteVerticesAdj[v].rank  = vrank;
2326   }
2327   /* Create cones */
2328   ierr = DMPlexSetChart(dm, 0, numCells+numVerticesAdj);CHKERRQ(ierr);
2329   for (c = 0; c < numCells; ++c) {ierr = DMPlexSetConeSize(dm, c, numCorners);CHKERRQ(ierr);}
2330   ierr = DMSetUp(dm);CHKERRQ(ierr);
2331   ierr = DMGetWorkArray(dm, numCorners, MPIU_INT, &cone);CHKERRQ(ierr);
2332   for (c = 0; c < numCells; ++c) {
2333     for (p = 0; p < numCorners; ++p) {
2334       const PetscInt gv = cells[c*numCorners+p];
2335       PetscInt       lv;
2336 
2337       ierr = PetscFindInt(gv, numVerticesAdj, verticesAdj, &lv);CHKERRQ(ierr);
2338       if (lv < 0) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Could not find global vertex %D in local connectivity", gv);
2339       cone[p] = lv+numCells;
2340     }
2341     ierr = DMPlexSetCone(dm, c, cone);CHKERRQ(ierr);
2342   }
2343   ierr = DMRestoreWorkArray(dm, numCorners, MPIU_INT, &cone);CHKERRQ(ierr);
2344   /* Create SF for vertices */
2345   ierr = PetscSFCreate(PetscObjectComm((PetscObject)dm), sfVert);CHKERRQ(ierr);
2346   ierr = PetscObjectSetName((PetscObject) *sfVert, "Vertex Ownership SF");CHKERRQ(ierr);
2347   ierr = PetscSFSetFromOptions(*sfVert);CHKERRQ(ierr);
2348   ierr = PetscSFSetGraph(*sfVert, numVertices, numVerticesAdj, NULL, PETSC_OWN_POINTER, remoteVerticesAdj, PETSC_OWN_POINTER);CHKERRQ(ierr);
2349   ierr = PetscFree(verticesAdj);CHKERRQ(ierr);
2350   /* Build pointSF */
2351   ierr = PetscMalloc2(numVerticesAdj, &vertexLocal, numVertices, &vertexOwner);CHKERRQ(ierr);
2352   for (v = 0; v < numVerticesAdj; ++v) {vertexLocal[v].index = v+numCells; vertexLocal[v].rank = rank;}
2353   for (v = 0; v < numVertices;    ++v) {vertexOwner[v].index = -1;         vertexOwner[v].rank = -1;}
2354   ierr = PetscSFReduceBegin(*sfVert, MPIU_2INT, vertexLocal, vertexOwner, MPI_MAXLOC);CHKERRQ(ierr);
2355   ierr = PetscSFReduceEnd(*sfVert, MPIU_2INT, vertexLocal, vertexOwner, MPI_MAXLOC);CHKERRQ(ierr);
2356   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);
2357   ierr = PetscSFBcastBegin(*sfVert, MPIU_2INT, vertexOwner, vertexLocal);CHKERRQ(ierr);
2358   ierr = PetscSFBcastEnd(*sfVert, MPIU_2INT, vertexOwner, vertexLocal);CHKERRQ(ierr);
2359   for (v = 0; v < numVerticesAdj; ++v) if (vertexLocal[v].rank != rank) ++numVerticesGhost;
2360   ierr = PetscMalloc1(numVerticesGhost, &localVertex);CHKERRQ(ierr);
2361   ierr = PetscMalloc1(numVerticesGhost, &remoteVertex);CHKERRQ(ierr);
2362   for (v = 0, g = 0; v < numVerticesAdj; ++v) {
2363     if (vertexLocal[v].rank != rank) {
2364       localVertex[g]        = v+numCells;
2365       remoteVertex[g].index = vertexLocal[v].index;
2366       remoteVertex[g].rank  = vertexLocal[v].rank;
2367       ++g;
2368     }
2369   }
2370   ierr = PetscFree2(vertexLocal, vertexOwner);CHKERRQ(ierr);
2371   if (g != numVerticesGhost) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid number of vertex ghosts %D should be %D", g, numVerticesGhost);
2372   ierr = DMGetPointSF(dm, &sfPoint);CHKERRQ(ierr);
2373   ierr = PetscObjectSetName((PetscObject) sfPoint, "point SF");CHKERRQ(ierr);
2374   ierr = PetscSFSetGraph(sfPoint, numCells+numVerticesAdj, numVerticesGhost, localVertex, PETSC_OWN_POINTER, remoteVertex, PETSC_OWN_POINTER);CHKERRQ(ierr);
2375   ierr = PetscLayoutDestroy(&vLayout);CHKERRQ(ierr);
2376   PetscHashIDestroy(vhash);
2377   /* Fill in the rest of the topology structure */
2378   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
2379   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
2380   PetscFunctionReturn(0);
2381 }
2382 
2383 /*
2384   This takes as input the coordinates for each owned vertex
2385 */
2386 static PetscErrorCode DMPlexBuildCoordinates_Parallel_Private(DM dm, PetscInt spaceDim, PetscInt numCells, PetscInt numV, PetscSF sfVert, const PetscReal vertexCoords[])
2387 {
2388   PetscSection   coordSection;
2389   Vec            coordinates;
2390   PetscScalar   *coords;
2391   PetscInt       numVertices, numVerticesAdj, coordSize, v;
2392   PetscErrorCode ierr;
2393 
2394   PetscFunctionBegin;
2395   ierr = DMSetCoordinateDim(dm, spaceDim);CHKERRQ(ierr);
2396   ierr = PetscSFGetGraph(sfVert, &numVertices, &numVerticesAdj, NULL, NULL);CHKERRQ(ierr);
2397   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
2398   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
2399   ierr = PetscSectionSetFieldComponents(coordSection, 0, spaceDim);CHKERRQ(ierr);
2400   ierr = PetscSectionSetChart(coordSection, numCells, numCells + numVerticesAdj);CHKERRQ(ierr);
2401   for (v = numCells; v < numCells+numVerticesAdj; ++v) {
2402     ierr = PetscSectionSetDof(coordSection, v, spaceDim);CHKERRQ(ierr);
2403     ierr = PetscSectionSetFieldDof(coordSection, v, 0, spaceDim);CHKERRQ(ierr);
2404   }
2405   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
2406   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
2407   ierr = VecCreate(PetscObjectComm((PetscObject)dm), &coordinates);CHKERRQ(ierr);
2408   ierr = VecSetBlockSize(coordinates, spaceDim);CHKERRQ(ierr);
2409   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
2410   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
2411   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
2412   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
2413   {
2414     MPI_Datatype coordtype;
2415 
2416     /* Need a temp buffer for coords if we have complex/single */
2417     ierr = MPI_Type_contiguous(spaceDim, MPIU_SCALAR, &coordtype);CHKERRQ(ierr);
2418     ierr = MPI_Type_commit(&coordtype);CHKERRQ(ierr);
2419 #if defined(PETSC_USE_COMPLEX)
2420     {
2421     PetscScalar *svertexCoords;
2422     PetscInt    i;
2423     ierr = PetscMalloc1(numV*spaceDim,&svertexCoords);CHKERRQ(ierr);
2424     for (i=0; i<numV*spaceDim; i++) svertexCoords[i] = vertexCoords[i];
2425     ierr = PetscSFBcastBegin(sfVert, coordtype, svertexCoords, coords);CHKERRQ(ierr);
2426     ierr = PetscSFBcastEnd(sfVert, coordtype, svertexCoords, coords);CHKERRQ(ierr);
2427     ierr = PetscFree(svertexCoords);CHKERRQ(ierr);
2428     }
2429 #else
2430     ierr = PetscSFBcastBegin(sfVert, coordtype, vertexCoords, coords);CHKERRQ(ierr);
2431     ierr = PetscSFBcastEnd(sfVert, coordtype, vertexCoords, coords);CHKERRQ(ierr);
2432 #endif
2433     ierr = MPI_Type_free(&coordtype);CHKERRQ(ierr);
2434   }
2435   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
2436   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
2437   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
2438   PetscFunctionReturn(0);
2439 }
2440 
2441 /*@C
2442   DMPlexCreateFromCellListParallel - This takes as input common mesh generator output, a list of the vertices for each cell, and produces a DM
2443 
2444   Input Parameters:
2445 + comm - The communicator
2446 . dim - The topological dimension of the mesh
2447 . numCells - The number of cells owned by this process
2448 . numVertices - The number of vertices owned by this process
2449 . numCorners - The number of vertices for each cell
2450 . interpolate - Flag indicating that intermediate mesh entities (faces, edges) should be created automatically
2451 . cells - An array of numCells*numCorners numbers, the global vertex numbers for each cell
2452 . spaceDim - The spatial dimension used for coordinates
2453 - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex
2454 
2455   Output Parameter:
2456 + dm - The DM
2457 - vertexSF - Optional, SF describing complete vertex ownership
2458 
2459   Note: Two triangles sharing a face
2460 $
2461 $        2
2462 $      / | \
2463 $     /  |  \
2464 $    /   |   \
2465 $   0  0 | 1  3
2466 $    \   |   /
2467 $     \  |  /
2468 $      \ | /
2469 $        1
2470 would have input
2471 $  numCells = 2, numVertices = 4
2472 $  cells = [0 1 2  1 3 2]
2473 $
2474 which would result in the DMPlex
2475 $
2476 $        4
2477 $      / | \
2478 $     /  |  \
2479 $    /   |   \
2480 $   2  0 | 1  5
2481 $    \   |   /
2482 $     \  |  /
2483 $      \ | /
2484 $        3
2485 
2486   Level: beginner
2487 
2488 .seealso: DMPlexCreateFromCellList(), DMPlexCreateFromDAG(), DMPlexCreate()
2489 @*/
2490 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)
2491 {
2492   PetscSF        sfVert;
2493   PetscErrorCode ierr;
2494 
2495   PetscFunctionBegin;
2496   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
2497   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
2498   PetscValidLogicalCollectiveInt(*dm, dim, 2);
2499   PetscValidLogicalCollectiveInt(*dm, spaceDim, 8);
2500   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
2501   ierr = DMPlexBuildFromCellList_Parallel_Private(*dm, numCells, numVertices, numCorners, cells, &sfVert);CHKERRQ(ierr);
2502   if (interpolate) {
2503     DM idm;
2504 
2505     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
2506     ierr = DMDestroy(dm);CHKERRQ(ierr);
2507     *dm  = idm;
2508   }
2509   ierr = DMPlexBuildCoordinates_Parallel_Private(*dm, spaceDim, numCells, numVertices,sfVert, vertexCoords);CHKERRQ(ierr);
2510   if (vertexSF) *vertexSF = sfVert;
2511   else {ierr = PetscSFDestroy(&sfVert);CHKERRQ(ierr);}
2512   PetscFunctionReturn(0);
2513 }
2514 
2515 /*
2516   This takes as input the common mesh generator output, a list of the vertices for each cell
2517 */
2518 static PetscErrorCode DMPlexBuildFromCellList_Private(DM dm, PetscInt numCells, PetscInt numVertices, PetscInt numCorners, const int cells[])
2519 {
2520   PetscInt      *cone, c, p;
2521   PetscErrorCode ierr;
2522 
2523   PetscFunctionBegin;
2524   ierr = DMPlexSetChart(dm, 0, numCells+numVertices);CHKERRQ(ierr);
2525   for (c = 0; c < numCells; ++c) {
2526     ierr = DMPlexSetConeSize(dm, c, numCorners);CHKERRQ(ierr);
2527   }
2528   ierr = DMSetUp(dm);CHKERRQ(ierr);
2529   ierr = DMGetWorkArray(dm, numCorners, MPIU_INT, &cone);CHKERRQ(ierr);
2530   for (c = 0; c < numCells; ++c) {
2531     for (p = 0; p < numCorners; ++p) {
2532       cone[p] = cells[c*numCorners+p]+numCells;
2533     }
2534     ierr = DMPlexSetCone(dm, c, cone);CHKERRQ(ierr);
2535   }
2536   ierr = DMRestoreWorkArray(dm, numCorners, MPIU_INT, &cone);CHKERRQ(ierr);
2537   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
2538   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
2539   PetscFunctionReturn(0);
2540 }
2541 
2542 /*
2543   This takes as input the coordinates for each vertex
2544 */
2545 static PetscErrorCode DMPlexBuildCoordinates_Private(DM dm, PetscInt spaceDim, PetscInt numCells, PetscInt numVertices, const double vertexCoords[])
2546 {
2547   PetscSection   coordSection;
2548   Vec            coordinates;
2549   DM             cdm;
2550   PetscScalar   *coords;
2551   PetscInt       v, d;
2552   PetscErrorCode ierr;
2553 
2554   PetscFunctionBegin;
2555   ierr = DMSetCoordinateDim(dm, spaceDim);CHKERRQ(ierr);
2556   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
2557   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
2558   ierr = PetscSectionSetFieldComponents(coordSection, 0, spaceDim);CHKERRQ(ierr);
2559   ierr = PetscSectionSetChart(coordSection, numCells, numCells + numVertices);CHKERRQ(ierr);
2560   for (v = numCells; v < numCells+numVertices; ++v) {
2561     ierr = PetscSectionSetDof(coordSection, v, spaceDim);CHKERRQ(ierr);
2562     ierr = PetscSectionSetFieldDof(coordSection, v, 0, spaceDim);CHKERRQ(ierr);
2563   }
2564   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
2565 
2566   ierr = DMGetCoordinateDM(dm, &cdm);CHKERRQ(ierr);
2567   ierr = DMCreateLocalVector(cdm, &coordinates);CHKERRQ(ierr);
2568   ierr = VecSetBlockSize(coordinates, spaceDim);CHKERRQ(ierr);
2569   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
2570   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
2571   for (v = 0; v < numVertices; ++v) {
2572     for (d = 0; d < spaceDim; ++d) {
2573       coords[v*spaceDim+d] = vertexCoords[v*spaceDim+d];
2574     }
2575   }
2576   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
2577   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
2578   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
2579   PetscFunctionReturn(0);
2580 }
2581 
2582 /*@C
2583   DMPlexCreateFromCellList - This takes as input common mesh generator output, a list of the vertices for each cell, and produces a DM
2584 
2585   Input Parameters:
2586 + comm - The communicator
2587 . dim - The topological dimension of the mesh
2588 . numCells - The number of cells
2589 . numVertices - The number of vertices
2590 . numCorners - The number of vertices for each cell
2591 . interpolate - Flag indicating that intermediate mesh entities (faces, edges) should be created automatically
2592 . cells - An array of numCells*numCorners numbers, the vertices for each cell
2593 . spaceDim - The spatial dimension used for coordinates
2594 - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex
2595 
2596   Output Parameter:
2597 . dm - The DM
2598 
2599   Note: Two triangles sharing a face
2600 $
2601 $        2
2602 $      / | \
2603 $     /  |  \
2604 $    /   |   \
2605 $   0  0 | 1  3
2606 $    \   |   /
2607 $     \  |  /
2608 $      \ | /
2609 $        1
2610 would have input
2611 $  numCells = 2, numVertices = 4
2612 $  cells = [0 1 2  1 3 2]
2613 $
2614 which would result in the DMPlex
2615 $
2616 $        4
2617 $      / | \
2618 $     /  |  \
2619 $    /   |   \
2620 $   2  0 | 1  5
2621 $    \   |   /
2622 $     \  |  /
2623 $      \ | /
2624 $        3
2625 
2626   Level: beginner
2627 
2628 .seealso: DMPlexCreateFromDAG(), DMPlexCreate()
2629 @*/
2630 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)
2631 {
2632   PetscErrorCode ierr;
2633 
2634   PetscFunctionBegin;
2635   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
2636   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
2637   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
2638   ierr = DMPlexBuildFromCellList_Private(*dm, numCells, numVertices, numCorners, cells);CHKERRQ(ierr);
2639   if (interpolate) {
2640     DM idm;
2641 
2642     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
2643     ierr = DMDestroy(dm);CHKERRQ(ierr);
2644     *dm  = idm;
2645   }
2646   ierr = DMPlexBuildCoordinates_Private(*dm, spaceDim, numCells, numVertices, vertexCoords);CHKERRQ(ierr);
2647   PetscFunctionReturn(0);
2648 }
2649 
2650 /*@
2651   DMPlexCreateFromDAG - This takes as input the adjacency-list representation of the Directed Acyclic Graph (Hasse Diagram) encoding a mesh, and produces a DM
2652 
2653   Input Parameters:
2654 + dm - The empty DM object, usually from DMCreate() and DMSetDimension()
2655 . depth - The depth of the DAG
2656 . numPoints - The number of points at each depth
2657 . coneSize - The cone size of each point
2658 . cones - The concatenation of the cone points for each point, the cone list must be oriented correctly for each point
2659 . coneOrientations - The orientation of each cone point
2660 - vertexCoords - An array of numVertices*dim numbers, the coordinates of each vertex
2661 
2662   Output Parameter:
2663 . dm - The DM
2664 
2665   Note: Two triangles sharing a face would have input
2666 $  depth = 1, numPoints = [4 2], coneSize = [3 3 0 0 0 0]
2667 $  cones = [2 3 4  3 5 4], coneOrientations = [0 0 0  0 0 0]
2668 $ vertexCoords = [-1.0 0.0  0.0 -1.0  0.0 1.0  1.0 0.0]
2669 $
2670 which would result in the DMPlex
2671 $
2672 $        4
2673 $      / | \
2674 $     /  |  \
2675 $    /   |   \
2676 $   2  0 | 1  5
2677 $    \   |   /
2678 $     \  |  /
2679 $      \ | /
2680 $        3
2681 $
2682 $ Notice that all points are numbered consecutively, unlikely DMPlexCreateFromCellList()
2683 
2684   Level: advanced
2685 
2686 .seealso: DMPlexCreateFromCellList(), DMPlexCreate()
2687 @*/
2688 PetscErrorCode DMPlexCreateFromDAG(DM dm, PetscInt depth, const PetscInt numPoints[], const PetscInt coneSize[], const PetscInt cones[], const PetscInt coneOrientations[], const PetscScalar vertexCoords[])
2689 {
2690   Vec            coordinates;
2691   PetscSection   coordSection;
2692   PetscScalar    *coords;
2693   PetscInt       coordSize, firstVertex = -1, pStart = 0, pEnd = 0, p, v, dim, dimEmbed, d, off;
2694   PetscErrorCode ierr;
2695 
2696   PetscFunctionBegin;
2697   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
2698   ierr = DMGetCoordinateDim(dm, &dimEmbed);CHKERRQ(ierr);
2699   if (dimEmbed < dim) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Embedding dimension %d cannot be less than intrinsic dimension %d",dimEmbed,dim);
2700   for (d = 0; d <= depth; ++d) pEnd += numPoints[d];
2701   ierr = DMPlexSetChart(dm, pStart, pEnd);CHKERRQ(ierr);
2702   for (p = pStart; p < pEnd; ++p) {
2703     ierr = DMPlexSetConeSize(dm, p, coneSize[p-pStart]);CHKERRQ(ierr);
2704     if (firstVertex < 0 && !coneSize[p - pStart]) {
2705       firstVertex = p - pStart;
2706     }
2707   }
2708   if (firstVertex < 0 && numPoints[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Expected %d vertices but could not find any", numPoints[0]);
2709   ierr = DMSetUp(dm);CHKERRQ(ierr); /* Allocate space for cones */
2710   for (p = pStart, off = 0; p < pEnd; off += coneSize[p-pStart], ++p) {
2711     ierr = DMPlexSetCone(dm, p, &cones[off]);CHKERRQ(ierr);
2712     ierr = DMPlexSetConeOrientation(dm, p, &coneOrientations[off]);CHKERRQ(ierr);
2713   }
2714   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
2715   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
2716   /* Build coordinates */
2717   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
2718   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
2719   ierr = PetscSectionSetFieldComponents(coordSection, 0, dimEmbed);CHKERRQ(ierr);
2720   ierr = PetscSectionSetChart(coordSection, firstVertex, firstVertex+numPoints[0]);CHKERRQ(ierr);
2721   for (v = firstVertex; v < firstVertex+numPoints[0]; ++v) {
2722     ierr = PetscSectionSetDof(coordSection, v, dimEmbed);CHKERRQ(ierr);
2723     ierr = PetscSectionSetFieldDof(coordSection, v, 0, dimEmbed);CHKERRQ(ierr);
2724   }
2725   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
2726   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
2727   ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
2728   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
2729   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
2730   ierr = VecSetBlockSize(coordinates, dimEmbed);CHKERRQ(ierr);
2731   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
2732   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
2733   for (v = 0; v < numPoints[0]; ++v) {
2734     PetscInt off;
2735 
2736     ierr = PetscSectionGetOffset(coordSection, v+firstVertex, &off);CHKERRQ(ierr);
2737     for (d = 0; d < dimEmbed; ++d) {
2738       coords[off+d] = vertexCoords[v*dimEmbed+d];
2739     }
2740   }
2741   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
2742   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
2743   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
2744   PetscFunctionReturn(0);
2745 }
2746 
2747 /*@C
2748   DMPlexCreateFromFile - This takes a filename and produces a DM
2749 
2750   Input Parameters:
2751 + comm - The communicator
2752 . filename - A file name
2753 - interpolate - Flag to create intermediate mesh pieces (edges, faces)
2754 
2755   Output Parameter:
2756 . dm - The DM
2757 
2758   Level: beginner
2759 
2760 .seealso: DMPlexCreateFromDAG(), DMPlexCreateFromCellList(), DMPlexCreate()
2761 @*/
2762 PetscErrorCode DMPlexCreateFromFile(MPI_Comm comm, const char filename[], PetscBool interpolate, DM *dm)
2763 {
2764   const char    *extGmsh    = ".msh";
2765   const char    *extCGNS    = ".cgns";
2766   const char    *extExodus  = ".exo";
2767   const char    *extGenesis = ".gen";
2768   const char    *extFluent  = ".cas";
2769   const char    *extHDF5    = ".h5";
2770   const char    *extMed     = ".med";
2771   const char    *extPLY     = ".ply";
2772   size_t         len;
2773   PetscBool      isGmsh, isCGNS, isExodus, isGenesis, isFluent, isHDF5, isMed, isPLY;
2774   PetscMPIInt    rank;
2775   PetscErrorCode ierr;
2776 
2777   PetscFunctionBegin;
2778   PetscValidPointer(filename, 2);
2779   PetscValidPointer(dm, 4);
2780   ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
2781   ierr = PetscStrlen(filename, &len);CHKERRQ(ierr);
2782   if (!len) SETERRQ(comm, PETSC_ERR_ARG_WRONG, "Filename must be a valid path");
2783   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extGmsh,    4, &isGmsh);CHKERRQ(ierr);
2784   ierr = PetscStrncmp(&filename[PetscMax(0,len-5)], extCGNS,    5, &isCGNS);CHKERRQ(ierr);
2785   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extExodus,  4, &isExodus);CHKERRQ(ierr);
2786   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extGenesis, 4, &isGenesis);CHKERRQ(ierr);
2787   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extFluent,  4, &isFluent);CHKERRQ(ierr);
2788   ierr = PetscStrncmp(&filename[PetscMax(0,len-3)], extHDF5,    3, &isHDF5);CHKERRQ(ierr);
2789   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extMed,     4, &isMed);CHKERRQ(ierr);
2790   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extPLY,     4, &isPLY);CHKERRQ(ierr);
2791   if (isGmsh) {
2792     ierr = DMPlexCreateGmshFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
2793   } else if (isCGNS) {
2794     ierr = DMPlexCreateCGNSFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
2795   } else if (isExodus || isGenesis) {
2796     ierr = DMPlexCreateExodusFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
2797   } else if (isFluent) {
2798     ierr = DMPlexCreateFluentFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
2799   } else if (isHDF5) {
2800     PetscViewer viewer;
2801 
2802     ierr = PetscViewerCreate(comm, &viewer);CHKERRQ(ierr);
2803     ierr = PetscViewerSetType(viewer, PETSCVIEWERHDF5);CHKERRQ(ierr);
2804     ierr = PetscViewerFileSetMode(viewer, FILE_MODE_READ);CHKERRQ(ierr);
2805     ierr = PetscViewerFileSetName(viewer, filename);CHKERRQ(ierr);
2806     ierr = DMCreate(comm, dm);CHKERRQ(ierr);
2807     ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
2808     ierr = DMLoad(*dm, viewer);CHKERRQ(ierr);
2809     ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
2810 
2811     if (interpolate) {
2812       DM idm;
2813 
2814       ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
2815       ierr = DMDestroy(dm);CHKERRQ(ierr);
2816       *dm  = idm;
2817     }
2818   } else if (isMed) {
2819     ierr = DMPlexCreateMedFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
2820   } else if (isPLY) {
2821     ierr = DMPlexCreatePLYFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
2822   } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cannot load file %s: unrecognized extension", filename);
2823   PetscFunctionReturn(0);
2824 }
2825 
2826 /*@
2827   DMPlexCreateReferenceCell - Create a DMPLEX with the appropriate FEM reference cell
2828 
2829   Collective on comm
2830 
2831   Input Parameters:
2832 + comm    - The communicator
2833 . dim     - The spatial dimension
2834 - simplex - Flag for simplex, otherwise use a tensor-product cell
2835 
2836   Output Parameter:
2837 . refdm - The reference cell
2838 
2839   Level: intermediate
2840 
2841 .keywords: reference cell
2842 .seealso:
2843 @*/
2844 PetscErrorCode DMPlexCreateReferenceCell(MPI_Comm comm, PetscInt dim, PetscBool simplex, DM *refdm)
2845 {
2846   DM             rdm;
2847   Vec            coords;
2848   PetscErrorCode ierr;
2849 
2850   PetscFunctionBeginUser;
2851   ierr = DMCreate(comm, &rdm);CHKERRQ(ierr);
2852   ierr = DMSetType(rdm, DMPLEX);CHKERRQ(ierr);
2853   ierr = DMSetDimension(rdm, dim);CHKERRQ(ierr);
2854   switch (dim) {
2855   case 0:
2856   {
2857     PetscInt    numPoints[1]        = {1};
2858     PetscInt    coneSize[1]         = {0};
2859     PetscInt    cones[1]            = {0};
2860     PetscInt    coneOrientations[1] = {0};
2861     PetscScalar vertexCoords[1]     = {0.0};
2862 
2863     ierr = DMPlexCreateFromDAG(rdm, 0, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2864   }
2865   break;
2866   case 1:
2867   {
2868     PetscInt    numPoints[2]        = {2, 1};
2869     PetscInt    coneSize[3]         = {2, 0, 0};
2870     PetscInt    cones[2]            = {1, 2};
2871     PetscInt    coneOrientations[2] = {0, 0};
2872     PetscScalar vertexCoords[2]     = {-1.0,  1.0};
2873 
2874     ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2875   }
2876   break;
2877   case 2:
2878     if (simplex) {
2879       PetscInt    numPoints[2]        = {3, 1};
2880       PetscInt    coneSize[4]         = {3, 0, 0, 0};
2881       PetscInt    cones[3]            = {1, 2, 3};
2882       PetscInt    coneOrientations[3] = {0, 0, 0};
2883       PetscScalar vertexCoords[6]     = {-1.0, -1.0,  1.0, -1.0,  -1.0, 1.0};
2884 
2885       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2886     } else {
2887       PetscInt    numPoints[2]        = {4, 1};
2888       PetscInt    coneSize[5]         = {4, 0, 0, 0, 0};
2889       PetscInt    cones[4]            = {1, 2, 3, 4};
2890       PetscInt    coneOrientations[4] = {0, 0, 0, 0};
2891       PetscScalar vertexCoords[8]     = {-1.0, -1.0,  1.0, -1.0,  1.0, 1.0,  -1.0, 1.0};
2892 
2893       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2894     }
2895   break;
2896   case 3:
2897     if (simplex) {
2898       PetscInt    numPoints[2]        = {4, 1};
2899       PetscInt    coneSize[5]         = {4, 0, 0, 0, 0};
2900       PetscInt    cones[4]            = {1, 3, 2, 4};
2901       PetscInt    coneOrientations[4] = {0, 0, 0, 0};
2902       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};
2903 
2904       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2905     } else {
2906       PetscInt    numPoints[2]        = {8, 1};
2907       PetscInt    coneSize[9]         = {8, 0, 0, 0, 0, 0, 0, 0, 0};
2908       PetscInt    cones[8]            = {1, 4, 3, 2, 5, 6, 7, 8};
2909       PetscInt    coneOrientations[8] = {0, 0, 0, 0, 0, 0, 0, 0};
2910       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,
2911                                          -1.0, -1.0,  1.0,  1.0, -1.0,  1.0,  1.0, 1.0,  1.0,  -1.0, 1.0,  1.0};
2912 
2913       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2914     }
2915   break;
2916   default:
2917     SETERRQ1(comm, PETSC_ERR_ARG_WRONG, "Cannot create reference cell for dimension %d", dim);
2918   }
2919   ierr = DMPlexInterpolate(rdm, refdm);CHKERRQ(ierr);
2920   if (rdm->coordinateDM) {
2921     DM           ncdm;
2922     PetscSection cs;
2923     PetscInt     pEnd = -1;
2924 
2925     ierr = DMGetDefaultSection(rdm->coordinateDM, &cs);CHKERRQ(ierr);
2926     if (cs) {ierr = PetscSectionGetChart(cs, NULL, &pEnd);CHKERRQ(ierr);}
2927     if (pEnd >= 0) {
2928       ierr = DMClone(rdm->coordinateDM, &ncdm);CHKERRQ(ierr);
2929       ierr = DMSetDefaultSection(ncdm, cs);CHKERRQ(ierr);
2930       ierr = DMSetCoordinateDM(*refdm, ncdm);CHKERRQ(ierr);
2931       ierr = DMDestroy(&ncdm);CHKERRQ(ierr);
2932     }
2933   }
2934   ierr = DMGetCoordinatesLocal(rdm, &coords);CHKERRQ(ierr);
2935   if (coords) {
2936     ierr = DMSetCoordinatesLocal(*refdm, coords);CHKERRQ(ierr);
2937   } else {
2938     ierr = DMGetCoordinates(rdm, &coords);CHKERRQ(ierr);
2939     if (coords) {ierr = DMSetCoordinates(*refdm, coords);CHKERRQ(ierr);}
2940   }
2941   ierr = DMDestroy(&rdm);CHKERRQ(ierr);
2942   PetscFunctionReturn(0);
2943 }
2944