xref: /petsc/src/dm/impls/plex/plexcreate.c (revision 0039db0d0110a86bca704eecba868b79cf9a436a)
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 = DMPlexCopyCoordinates(*dm, udm);CHKERRQ(ierr);
954     ierr = DMDestroy(dm);CHKERRQ(ierr);
955     *dm  = udm;
956   }
957   PetscFunctionReturn(0);
958 }
959 
960 /*@C
961   DMPlexCreateBoxMesh - Creates a mesh on the tensor product of unit intervals (box) using simplices or tensor cells (hexahedra).
962 
963   Collective on MPI_Comm
964 
965   Input Parameters:
966 + comm        - The communicator for the DM object
967 . dim         - The spatial dimension
968 . simplex     - PETSC_TRUE for simplices, PETSC_FALSE for tensor cells
969 . faces       - Number of faces per dimension, or NULL for (1,) in 1D and (2, 2) in 2D and (1, 1, 1) in 3D
970 . lower       - The lower left corner, or NULL for (0, 0, 0)
971 . upper       - The upper right corner, or NULL for (1, 1, 1)
972 . periodicity - The boundary type for the X,Y,Z direction, or NULL for DM_BOUNDARY_NONE
973 - interpolate - Flag to create intermediate mesh pieces (edges, faces)
974 
975   Output Parameter:
976 . dm  - The DM object
977 
978   Note: Here is the numbering returned for 2 faces in each direction for tensor cells:
979 $ 10---17---11---18----12
980 $  |         |         |
981 $  |         |         |
982 $ 20    2   22    3    24
983 $  |         |         |
984 $  |         |         |
985 $  7---15----8---16----9
986 $  |         |         |
987 $  |         |         |
988 $ 19    0   21    1   23
989 $  |         |         |
990 $  |         |         |
991 $  4---13----5---14----6
992 
993 and for simplicial cells
994 
995 $ 14----8---15----9----16
996 $  |\     5  |\      7 |
997 $  | \       | \       |
998 $ 13   2    14    3    15
999 $  | 4   \   | 6   \   |
1000 $  |       \ |       \ |
1001 $ 11----6---12----7----13
1002 $  |\        |\        |
1003 $  | \    1  | \     3 |
1004 $ 10   0    11    1    12
1005 $  | 0   \   | 2   \   |
1006 $  |       \ |       \ |
1007 $  8----4----9----5----10
1008 
1009   Level: beginner
1010 
1011 .keywords: DM, create
1012 .seealso: DMPlexCreateFromFile(), DMPlexCreateHexCylinderMesh(), DMSetType(), DMCreate()
1013 @*/
1014 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)
1015 {
1016   PetscInt       i;
1017   PetscInt       fac[3] = {0, 0, 0};
1018   PetscReal      low[3] = {0, 0, 0};
1019   PetscReal      upp[3] = {1, 1, 1};
1020   DMBoundaryType bdt[3] = {DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE};
1021   PetscErrorCode ierr;
1022 
1023   PetscFunctionBegin;
1024   for (i = 0; i < dim; ++i) fac[i] = faces ? faces[i] : (dim == 1 ? 1 : 4-dim);
1025   if (lower) for (i = 0; i < dim; ++i) low[i] = lower[i];
1026   if (upper) for (i = 0; i < dim; ++i) upp[i] = upper[i];
1027   if (periodicity) for (i = 0; i < dim; ++i) bdt[i] = periodicity[i];
1028 
1029   if (dim == 1)      {ierr = DMPlexCreateLineMesh_Internal(comm, fac[0], low[0], upp[0], bdt[0], dm);CHKERRQ(ierr);}
1030   else if (simplex)  {ierr = DMPlexCreateBoxMesh_Simplex_Internal(comm, dim, fac, low, upp, bdt, interpolate, dm);CHKERRQ(ierr);}
1031   else               {ierr = DMPlexCreateBoxMesh_Tensor_Internal(comm, dim, fac, low, upp, bdt, interpolate, dm);CHKERRQ(ierr);}
1032   PetscFunctionReturn(0);
1033 }
1034 
1035 /*@C
1036   DMPlexSetOptionsPrefix - Sets the prefix used for searching for all DM options in the database.
1037 
1038   Logically Collective on DM
1039 
1040   Input Parameters:
1041 + dm - the DM context
1042 - prefix - the prefix to prepend to all option names
1043 
1044   Notes:
1045   A hyphen (-) must NOT be given at the beginning of the prefix name.
1046   The first character of all runtime options is AUTOMATICALLY the hyphen.
1047 
1048   Level: advanced
1049 
1050 .seealso: SNESSetFromOptions()
1051 @*/
1052 PetscErrorCode DMPlexSetOptionsPrefix(DM dm, const char prefix[])
1053 {
1054   DM_Plex       *mesh = (DM_Plex *) dm->data;
1055   PetscErrorCode ierr;
1056 
1057   PetscFunctionBegin;
1058   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1059   ierr = PetscObjectSetOptionsPrefix((PetscObject) dm, prefix);CHKERRQ(ierr);
1060   ierr = PetscObjectSetOptionsPrefix((PetscObject) mesh->partitioner, prefix);CHKERRQ(ierr);
1061   PetscFunctionReturn(0);
1062 }
1063 
1064 /*@
1065   DMPlexCreateHexCylinderMesh - Creates a mesh on the tensor product of the unit interval with the circle (cylinder) using hexahedra.
1066 
1067   Collective on MPI_Comm
1068 
1069   Input Parameters:
1070 + comm      - The communicator for the DM object
1071 . numRefine - The number of regular refinements to the basic 5 cell structure
1072 - periodicZ - The boundary type for the Z direction
1073 
1074   Output Parameter:
1075 . dm  - The DM object
1076 
1077   Note: Here is the output numbering looking from the bottom of the cylinder:
1078 $       17-----14
1079 $        |     |
1080 $        |  2  |
1081 $        |     |
1082 $ 17-----8-----7-----14
1083 $  |     |     |     |
1084 $  |  3  |  0  |  1  |
1085 $  |     |     |     |
1086 $ 19-----5-----6-----13
1087 $        |     |
1088 $        |  4  |
1089 $        |     |
1090 $       19-----13
1091 $
1092 $ and up through the top
1093 $
1094 $       18-----16
1095 $        |     |
1096 $        |  2  |
1097 $        |     |
1098 $ 18----10----11-----16
1099 $  |     |     |     |
1100 $  |  3  |  0  |  1  |
1101 $  |     |     |     |
1102 $ 20-----9----12-----15
1103 $        |     |
1104 $        |  4  |
1105 $        |     |
1106 $       20-----15
1107 
1108   Level: beginner
1109 
1110 .keywords: DM, create
1111 .seealso: DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
1112 @*/
1113 PetscErrorCode DMPlexCreateHexCylinderMesh(MPI_Comm comm, PetscInt numRefine, DMBoundaryType periodicZ, DM *dm)
1114 {
1115   const PetscInt dim = 3;
1116   PetscInt       numCells, numVertices, r;
1117   PetscErrorCode ierr;
1118 
1119   PetscFunctionBegin;
1120   PetscValidPointer(dm, 4);
1121   if (numRefine < 0) SETERRQ1(comm, PETSC_ERR_ARG_OUTOFRANGE, "Number of refinements %D cannot be negative", numRefine);
1122   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
1123   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
1124   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
1125   /* Create topology */
1126   {
1127     PetscInt cone[8], c;
1128 
1129     numCells    = 5;
1130     numVertices = 16;
1131     if (periodicZ == DM_BOUNDARY_PERIODIC) {
1132       numCells   *= 3;
1133       numVertices = 24;
1134     }
1135     ierr = DMPlexSetChart(*dm, 0, numCells+numVertices);CHKERRQ(ierr);
1136     for (c = 0; c < numCells; c++) {ierr = DMPlexSetConeSize(*dm, c, 8);CHKERRQ(ierr);}
1137     ierr = DMSetUp(*dm);CHKERRQ(ierr);
1138     if (periodicZ == DM_BOUNDARY_PERIODIC) {
1139       cone[0] = 15; cone[1] = 18; cone[2] = 17; cone[3] = 16;
1140       cone[4] = 31; cone[5] = 32; cone[6] = 33; cone[7] = 34;
1141       ierr = DMPlexSetCone(*dm, 0, cone);CHKERRQ(ierr);
1142       cone[0] = 16; cone[1] = 17; cone[2] = 24; cone[3] = 23;
1143       cone[4] = 32; cone[5] = 36; cone[6] = 37; cone[7] = 33; /* 22 25 26 21 */
1144       ierr = DMPlexSetCone(*dm, 1, cone);CHKERRQ(ierr);
1145       cone[0] = 18; cone[1] = 27; cone[2] = 24; cone[3] = 17;
1146       cone[4] = 34; cone[5] = 33; cone[6] = 37; cone[7] = 38;
1147       ierr = DMPlexSetCone(*dm, 2, cone);CHKERRQ(ierr);
1148       cone[0] = 29; cone[1] = 27; cone[2] = 18; cone[3] = 15;
1149       cone[4] = 35; cone[5] = 31; cone[6] = 34; cone[7] = 38;
1150       ierr = DMPlexSetCone(*dm, 3, cone);CHKERRQ(ierr);
1151       cone[0] = 29; cone[1] = 15; cone[2] = 16; cone[3] = 23;
1152       cone[4] = 35; cone[5] = 36; cone[6] = 32; cone[7] = 31;
1153       ierr = DMPlexSetCone(*dm, 4, cone);CHKERRQ(ierr);
1154 
1155       cone[0] = 31; cone[1] = 34; cone[2] = 33; cone[3] = 32;
1156       cone[4] = 19; cone[5] = 22; cone[6] = 21; cone[7] = 20;
1157       ierr = DMPlexSetCone(*dm, 5, cone);CHKERRQ(ierr);
1158       cone[0] = 32; cone[1] = 33; cone[2] = 37; cone[3] = 36;
1159       cone[4] = 22; cone[5] = 25; cone[6] = 26; cone[7] = 21;
1160       ierr = DMPlexSetCone(*dm, 6, cone);CHKERRQ(ierr);
1161       cone[0] = 34; cone[1] = 38; cone[2] = 37; cone[3] = 33;
1162       cone[4] = 20; cone[5] = 21; cone[6] = 26; cone[7] = 28;
1163       ierr = DMPlexSetCone(*dm, 7, cone);CHKERRQ(ierr);
1164       cone[0] = 35; cone[1] = 38; cone[2] = 34; cone[3] = 31;
1165       cone[4] = 30; cone[5] = 19; cone[6] = 20; cone[7] = 28;
1166       ierr = DMPlexSetCone(*dm, 8, cone);CHKERRQ(ierr);
1167       cone[0] = 35; cone[1] = 31; cone[2] = 32; cone[3] = 36;
1168       cone[4] = 30; cone[5] = 25; cone[6] = 22; cone[7] = 19;
1169       ierr = DMPlexSetCone(*dm, 9, cone);CHKERRQ(ierr);
1170 
1171       cone[0] = 19; cone[1] = 20; cone[2] = 21; cone[3] = 22;
1172       cone[4] = 15; cone[5] = 16; cone[6] = 17; cone[7] = 18;
1173       ierr = DMPlexSetCone(*dm, 10, cone);CHKERRQ(ierr);
1174       cone[0] = 22; cone[1] = 21; cone[2] = 26; cone[3] = 25;
1175       cone[4] = 16; cone[5] = 23; cone[6] = 24; cone[7] = 17;
1176       ierr = DMPlexSetCone(*dm, 11, cone);CHKERRQ(ierr);
1177       cone[0] = 20; cone[1] = 28; cone[2] = 26; cone[3] = 21;
1178       cone[4] = 18; cone[5] = 17; cone[6] = 24; cone[7] = 27;
1179       ierr = DMPlexSetCone(*dm, 12, cone);CHKERRQ(ierr);
1180       cone[0] = 30; cone[1] = 28; cone[2] = 20; cone[3] = 19;
1181       cone[4] = 29; cone[5] = 15; cone[6] = 18; cone[7] = 27;
1182       ierr = DMPlexSetCone(*dm, 13, cone);CHKERRQ(ierr);
1183       cone[0] = 30; cone[1] = 19; cone[2] = 22; cone[3] = 25;
1184       cone[4] = 29; cone[5] = 23; cone[6] = 16; cone[7] = 15;
1185       ierr = DMPlexSetCone(*dm, 14, cone);CHKERRQ(ierr);
1186     } else {
1187       cone[0] =  5; cone[1] =  8; cone[2] =  7; cone[3] =  6;
1188       cone[4] =  9; cone[5] = 12; cone[6] = 11; cone[7] = 10;
1189       ierr = DMPlexSetCone(*dm, 0, cone);CHKERRQ(ierr);
1190       cone[0] =  6; cone[1] =  7; cone[2] = 14; cone[3] = 13;
1191       cone[4] = 12; cone[5] = 15; cone[6] = 16; cone[7] = 11;
1192       ierr = DMPlexSetCone(*dm, 1, cone);CHKERRQ(ierr);
1193       cone[0] =  8; cone[1] = 17; cone[2] = 14; cone[3] =  7;
1194       cone[4] = 10; cone[5] = 11; cone[6] = 16; cone[7] = 18;
1195       ierr = DMPlexSetCone(*dm, 2, cone);CHKERRQ(ierr);
1196       cone[0] = 19; cone[1] = 17; cone[2] =  8; cone[3] =  5;
1197       cone[4] = 20; cone[5] =  9; cone[6] = 10; cone[7] = 18;
1198       ierr = DMPlexSetCone(*dm, 3, cone);CHKERRQ(ierr);
1199       cone[0] = 19; cone[1] =  5; cone[2] =  6; cone[3] = 13;
1200       cone[4] = 20; cone[5] = 15; cone[6] = 12; cone[7] =  9;
1201       ierr = DMPlexSetCone(*dm, 4, cone);CHKERRQ(ierr);
1202     }
1203     ierr = DMPlexSymmetrize(*dm);CHKERRQ(ierr);
1204     ierr = DMPlexStratify(*dm);CHKERRQ(ierr);
1205   }
1206   /* Interpolate */
1207   {
1208     DM idm;
1209 
1210     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
1211     ierr = DMDestroy(dm);CHKERRQ(ierr);
1212     *dm  = idm;
1213   }
1214   /* Create cube geometry */
1215   {
1216     Vec             coordinates;
1217     PetscSection    coordSection;
1218     PetscScalar    *coords;
1219     PetscInt        coordSize, v;
1220     const PetscReal dis = 1.0/PetscSqrtReal(2.0);
1221     const PetscReal ds2 = dis/2.0;
1222 
1223     /* Build coordinates */
1224     ierr = DMGetCoordinateSection(*dm, &coordSection);CHKERRQ(ierr);
1225     ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
1226     ierr = PetscSectionSetFieldComponents(coordSection, 0, dim);CHKERRQ(ierr);
1227     ierr = PetscSectionSetChart(coordSection, numCells, numCells+numVertices);CHKERRQ(ierr);
1228     for (v = numCells; v < numCells+numVertices; ++v) {
1229       ierr = PetscSectionSetDof(coordSection, v, dim);CHKERRQ(ierr);
1230       ierr = PetscSectionSetFieldDof(coordSection, v, 0, dim);CHKERRQ(ierr);
1231     }
1232     ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
1233     ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
1234     ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
1235     ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
1236     ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
1237     ierr = VecSetBlockSize(coordinates, dim);CHKERRQ(ierr);
1238     ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
1239     ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
1240     coords[0*dim+0] = -ds2; coords[0*dim+1] = -ds2; coords[0*dim+2] = 0.0;
1241     coords[1*dim+0] =  ds2; coords[1*dim+1] = -ds2; coords[1*dim+2] = 0.0;
1242     coords[2*dim+0] =  ds2; coords[2*dim+1] =  ds2; coords[2*dim+2] = 0.0;
1243     coords[3*dim+0] = -ds2; coords[3*dim+1] =  ds2; coords[3*dim+2] = 0.0;
1244     coords[4*dim+0] = -ds2; coords[4*dim+1] = -ds2; coords[4*dim+2] = 1.0;
1245     coords[5*dim+0] = -ds2; coords[5*dim+1] =  ds2; coords[5*dim+2] = 1.0;
1246     coords[6*dim+0] =  ds2; coords[6*dim+1] =  ds2; coords[6*dim+2] = 1.0;
1247     coords[7*dim+0] =  ds2; coords[7*dim+1] = -ds2; coords[7*dim+2] = 1.0;
1248     coords[ 8*dim+0] =  dis; coords[ 8*dim+1] = -dis; coords[ 8*dim+2] = 0.0;
1249     coords[ 9*dim+0] =  dis; coords[ 9*dim+1] =  dis; coords[ 9*dim+2] = 0.0;
1250     coords[10*dim+0] =  dis; coords[10*dim+1] = -dis; coords[10*dim+2] = 1.0;
1251     coords[11*dim+0] =  dis; coords[11*dim+1] =  dis; coords[11*dim+2] = 1.0;
1252     coords[12*dim+0] = -dis; coords[12*dim+1] =  dis; coords[12*dim+2] = 0.0;
1253     coords[13*dim+0] = -dis; coords[13*dim+1] =  dis; coords[13*dim+2] = 1.0;
1254     coords[14*dim+0] = -dis; coords[14*dim+1] = -dis; coords[14*dim+2] = 0.0;
1255     coords[15*dim+0] = -dis; coords[15*dim+1] = -dis; coords[15*dim+2] = 1.0;
1256     if (periodicZ == DM_BOUNDARY_PERIODIC) {
1257       /* 15 31 19 */ coords[16*dim+0] = -ds2; coords[16*dim+1] = -ds2; coords[16*dim+2] = 0.5;
1258       /* 16 32 22 */ coords[17*dim+0] =  ds2; coords[17*dim+1] = -ds2; coords[17*dim+2] = 0.5;
1259       /* 17 33 21 */ coords[18*dim+0] =  ds2; coords[18*dim+1] =  ds2; coords[18*dim+2] = 0.5;
1260       /* 18 34 20 */ coords[19*dim+0] = -ds2; coords[19*dim+1] =  ds2; coords[19*dim+2] = 0.5;
1261       /* 29 35 30 */ coords[20*dim+0] = -dis; coords[20*dim+1] = -dis; coords[20*dim+2] = 0.5;
1262       /* 23 36 25 */ coords[21*dim+0] =  dis; coords[21*dim+1] = -dis; coords[21*dim+2] = 0.5;
1263       /* 24 37 26 */ coords[22*dim+0] =  dis; coords[22*dim+1] =  dis; coords[22*dim+2] = 0.5;
1264       /* 27 38 28 */ coords[23*dim+0] = -dis; coords[23*dim+1] =  dis; coords[23*dim+2] = 0.5;
1265     }
1266     ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
1267     ierr = DMSetCoordinatesLocal(*dm, coordinates);CHKERRQ(ierr);
1268     ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
1269   }
1270   /* Create periodicity */
1271   if (periodicZ == DM_BOUNDARY_PERIODIC || periodicZ == DM_BOUNDARY_TWIST) {
1272     PetscReal      L[3];
1273     PetscReal      maxCell[3];
1274     DMBoundaryType bdType[3];
1275     PetscReal      lower[3] = {0.0, 0.0, 0.0};
1276     PetscReal      upper[3] = {1.0, 1.0, 1.5};
1277     PetscInt       i, numZCells = 3;
1278 
1279     bdType[0] = DM_BOUNDARY_NONE;
1280     bdType[1] = DM_BOUNDARY_NONE;
1281     bdType[2] = periodicZ;
1282     for (i = 0; i < dim; i++) {
1283       L[i]       = upper[i] - lower[i];
1284       maxCell[i] = 1.1 * (L[i] / numZCells);
1285     }
1286     ierr = DMSetPeriodicity(*dm, PETSC_TRUE, maxCell, L, bdType);CHKERRQ(ierr);
1287   }
1288   /* Refine topology */
1289   for (r = 0; r < numRefine; ++r) {
1290     DM rdm = NULL;
1291 
1292     ierr = DMRefine(*dm, comm, &rdm);CHKERRQ(ierr);
1293     ierr = DMDestroy(dm);CHKERRQ(ierr);
1294     *dm  = rdm;
1295   }
1296   /* Remap geometry to cylinder
1297        Interior square: Linear interpolation is correct
1298        The other cells all have vertices on rays from the origin. We want to uniformly expand the spacing
1299        such that the last vertex is on the unit circle. So the closest and farthest vertices are at distance
1300 
1301          phi     = arctan(y/x)
1302          d_close = sqrt(1/8 + 1/4 sin^2(phi))
1303          d_far   = sqrt(1/2 + sin^2(phi))
1304 
1305        so we remap them using
1306 
1307          x_new = x_close + (x - x_close) (1 - d_close) / (d_far - d_close)
1308          y_new = y_close + (y - y_close) (1 - d_close) / (d_far - d_close)
1309 
1310        If pi/4 < phi < 3pi/4 or -3pi/4 < phi < -pi/4, then we switch x and y.
1311   */
1312   {
1313     Vec           coordinates;
1314     PetscSection  coordSection;
1315     PetscScalar  *coords;
1316     PetscInt      vStart, vEnd, v;
1317     const PetscReal dis = 1.0/PetscSqrtReal(2.0);
1318     const PetscReal ds2 = 0.5*dis;
1319 
1320     ierr = DMPlexGetDepthStratum(*dm, 0, &vStart, &vEnd);CHKERRQ(ierr);
1321     ierr = DMGetCoordinateSection(*dm, &coordSection);CHKERRQ(ierr);
1322     ierr = DMGetCoordinatesLocal(*dm, &coordinates);CHKERRQ(ierr);
1323     ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
1324     for (v = vStart; v < vEnd; ++v) {
1325       PetscReal phi, sinp, cosp, dc, df, x, y, xc, yc;
1326       PetscInt  off;
1327 
1328       ierr = PetscSectionGetOffset(coordSection, v, &off);CHKERRQ(ierr);
1329       if ((PetscAbsScalar(coords[off+0]) <= ds2) && (PetscAbsScalar(coords[off+1]) <= ds2)) continue;
1330       x    = PetscRealPart(coords[off]);
1331       y    = PetscRealPart(coords[off+1]);
1332       phi  = PetscAtan2Real(y, x);
1333       sinp = PetscSinReal(phi);
1334       cosp = PetscCosReal(phi);
1335       if ((PetscAbsReal(phi) > PETSC_PI/4.0) && (PetscAbsReal(phi) < 3.0*PETSC_PI/4.0)) {
1336         dc = PetscAbsReal(ds2/sinp);
1337         df = PetscAbsReal(dis/sinp);
1338         xc = ds2*x/PetscAbsReal(y);
1339         yc = ds2*PetscSignReal(y);
1340       } else {
1341         dc = PetscAbsReal(ds2/cosp);
1342         df = PetscAbsReal(dis/cosp);
1343         xc = ds2*PetscSignReal(x);
1344         yc = ds2*y/PetscAbsReal(x);
1345       }
1346       coords[off+0] = xc + (coords[off+0] - xc)*(1.0 - dc)/(df - dc);
1347       coords[off+1] = yc + (coords[off+1] - yc)*(1.0 - dc)/(df - dc);
1348     }
1349     ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
1350     if (periodicZ == DM_BOUNDARY_PERIODIC || periodicZ == DM_BOUNDARY_TWIST) {
1351       ierr = DMLocalizeCoordinates(*dm);CHKERRQ(ierr);
1352     }
1353   }
1354   PetscFunctionReturn(0);
1355 }
1356 
1357 /*@
1358   DMPlexCreateWedgeCylinderMesh - Creates a mesh on the tensor product of the unit interval with the circle (cylinder) using wedges.
1359 
1360   Collective on MPI_Comm
1361 
1362   Input Parameters:
1363 + comm - The communicator for the DM object
1364 . n    - The number of wedges around the origin
1365 - interpolate - Create edges and faces
1366 
1367   Output Parameter:
1368 . dm  - The DM object
1369 
1370   Level: beginner
1371 
1372 .keywords: DM, create
1373 .seealso: DMPlexCreateHexCylinderMesh(), DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
1374 @*/
1375 PetscErrorCode DMPlexCreateWedgeCylinderMesh(MPI_Comm comm, PetscInt n, PetscBool interpolate, DM *dm)
1376 {
1377   const PetscInt dim = 3;
1378   PetscInt       numCells, numVertices;
1379   PetscErrorCode ierr;
1380 
1381   PetscFunctionBegin;
1382   PetscValidPointer(dm, 3);
1383   if (n < 0) SETERRQ1(comm, PETSC_ERR_ARG_OUTOFRANGE, "Number of wedges %D cannot be negative", n);
1384   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
1385   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
1386   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
1387   /* Create topology */
1388   {
1389     PetscInt cone[6], c;
1390 
1391     numCells    = n;
1392     numVertices = 2*(n+1);
1393     ierr = DMPlexSetChart(*dm, 0, numCells+numVertices);CHKERRQ(ierr);
1394     for (c = 0; c < numCells; c++) {ierr = DMPlexSetConeSize(*dm, c, 6);CHKERRQ(ierr);}
1395     ierr = DMSetUp(*dm);CHKERRQ(ierr);
1396     for (c = 0; c < numCells; c++) {
1397       cone[0] =  c+n*1; cone[1] = (c+1)%n+n*1; cone[2] = 0+3*n;
1398       cone[3] =  c+n*2; cone[4] = (c+1)%n+n*2; cone[5] = 1+3*n;
1399       ierr = DMPlexSetCone(*dm, c, cone);CHKERRQ(ierr);
1400     }
1401     ierr = DMPlexSymmetrize(*dm);CHKERRQ(ierr);
1402     ierr = DMPlexStratify(*dm);CHKERRQ(ierr);
1403   }
1404   /* Interpolate */
1405   if (interpolate) {
1406     DM idm;
1407 
1408     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
1409     ierr = DMDestroy(dm);CHKERRQ(ierr);
1410     *dm  = idm;
1411   }
1412   /* Create cylinder geometry */
1413   {
1414     Vec          coordinates;
1415     PetscSection coordSection;
1416     PetscScalar *coords;
1417     PetscInt     coordSize, v, c;
1418 
1419     /* Build coordinates */
1420     ierr = DMGetCoordinateSection(*dm, &coordSection);CHKERRQ(ierr);
1421     ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
1422     ierr = PetscSectionSetFieldComponents(coordSection, 0, dim);CHKERRQ(ierr);
1423     ierr = PetscSectionSetChart(coordSection, numCells, numCells+numVertices);CHKERRQ(ierr);
1424     for (v = numCells; v < numCells+numVertices; ++v) {
1425       ierr = PetscSectionSetDof(coordSection, v, dim);CHKERRQ(ierr);
1426       ierr = PetscSectionSetFieldDof(coordSection, v, 0, dim);CHKERRQ(ierr);
1427     }
1428     ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
1429     ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
1430     ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
1431     ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
1432     ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
1433     ierr = VecSetBlockSize(coordinates, dim);CHKERRQ(ierr);
1434     ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
1435     ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
1436     for (c = 0; c < numCells; c++) {
1437       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;
1438       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;
1439     }
1440     coords[(2*n+0)*dim+0] = 0.0; coords[(2*n+0)*dim+1] = 0.0; coords[(2*n+0)*dim+2] = 1.0;
1441     coords[(2*n+1)*dim+0] = 0.0; coords[(2*n+1)*dim+1] = 0.0; coords[(2*n+1)*dim+2] = 0.0;
1442     ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
1443     ierr = DMSetCoordinatesLocal(*dm, coordinates);CHKERRQ(ierr);
1444     ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
1445   }
1446   PetscFunctionReturn(0);
1447 }
1448 
1449 PETSC_STATIC_INLINE PetscReal DiffNormReal(PetscInt dim, const PetscReal x[], const PetscReal y[])
1450 {
1451   PetscReal prod = 0.0;
1452   PetscInt  i;
1453   for (i = 0; i < dim; ++i) prod += PetscSqr(x[i] - y[i]);
1454   return PetscSqrtReal(prod);
1455 }
1456 PETSC_STATIC_INLINE PetscReal DotReal(PetscInt dim, const PetscReal x[], const PetscReal y[])
1457 {
1458   PetscReal prod = 0.0;
1459   PetscInt  i;
1460   for (i = 0; i < dim; ++i) prod += x[i]*y[i];
1461   return prod;
1462 }
1463 
1464 /*@
1465   DMPlexCreateSphereMesh - Creates a mesh on the d-dimensional sphere, S^d.
1466 
1467   Collective on MPI_Comm
1468 
1469   Input Parameters:
1470 . comm  - The communicator for the DM object
1471 . dim   - The dimension
1472 - simplex - Use simplices, or tensor product cells
1473 
1474   Output Parameter:
1475 . dm  - The DM object
1476 
1477   Level: beginner
1478 
1479 .keywords: DM, create
1480 .seealso: DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
1481 @*/
1482 PetscErrorCode DMPlexCreateSphereMesh(MPI_Comm comm, PetscInt dim, PetscBool simplex, DM *dm)
1483 {
1484   const PetscInt  embedDim = dim+1;
1485   PetscSection    coordSection;
1486   Vec             coordinates;
1487   PetscScalar    *coords;
1488   PetscReal      *coordsIn;
1489   PetscInt        numCells, numEdges, numVerts, firstVertex, v, firstEdge, coordSize, d, c, e;
1490   PetscMPIInt     rank;
1491   PetscErrorCode  ierr;
1492 
1493   PetscFunctionBegin;
1494   PetscValidPointer(dm, 4);
1495   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
1496   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
1497   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
1498   ierr = DMSetCoordinateDim(*dm, dim+1);CHKERRQ(ierr);
1499   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject) *dm), &rank);CHKERRQ(ierr);
1500   switch (dim) {
1501   case 2:
1502     if (simplex) {
1503       DM              idm;
1504       const PetscReal edgeLen     = 2.0/(1.0 + PETSC_PHI);
1505       const PetscReal vertex[3]   = {0.0, 1.0/(1.0 + PETSC_PHI), PETSC_PHI/(1.0 + PETSC_PHI)};
1506       const PetscInt  degree      = 5;
1507       PetscInt        s[3]        = {1, 1, 1};
1508       PetscInt        cone[3];
1509       PetscInt       *graph, p, i, j, k;
1510 
1511       numCells    = !rank ? 20 : 0;
1512       numVerts    = !rank ? 12 : 0;
1513       firstVertex = numCells;
1514       /* Use icosahedron, which for a unit sphere has coordinates which are all cyclic permutations of
1515 
1516            (0, \pm 1/\phi+1, \pm \phi/\phi+1)
1517 
1518          where \phi^2 - \phi - 1 = 0, meaning \phi is the golden ratio \frac{1 + \sqrt{5}}{2}. The edge
1519          length is then given by 2/\phi = 2 * 2.73606 = 5.47214.
1520        */
1521       /* Construct vertices */
1522       ierr = PetscCalloc1(numVerts * embedDim, &coordsIn);CHKERRQ(ierr);
1523       for (p = 0, i = 0; p < embedDim; ++p) {
1524         for (s[1] = -1; s[1] < 2; s[1] += 2) {
1525           for (s[2] = -1; s[2] < 2; s[2] += 2) {
1526             for (d = 0; d < embedDim; ++d) coordsIn[i*embedDim+d] = s[(d+p)%embedDim]*vertex[(d+p)%embedDim];
1527             ++i;
1528           }
1529         }
1530       }
1531       /* Construct graph */
1532       ierr = PetscCalloc1(numVerts * numVerts, &graph);CHKERRQ(ierr);
1533       for (i = 0; i < numVerts; ++i) {
1534         for (j = 0, k = 0; j < numVerts; ++j) {
1535           if (PetscAbsReal(DiffNormReal(embedDim, &coordsIn[i*embedDim], &coordsIn[j*embedDim]) - edgeLen) < PETSC_SMALL) {graph[i*numVerts+j] = 1; ++k;}
1536         }
1537         if (k != degree) SETERRQ3(comm, PETSC_ERR_PLIB, "Invalid icosahedron, vertex %D degree %D != %D", i, k, degree);
1538       }
1539       /* Build Topology */
1540       ierr = DMPlexSetChart(*dm, 0, numCells+numVerts);CHKERRQ(ierr);
1541       for (c = 0; c < numCells; c++) {
1542         ierr = DMPlexSetConeSize(*dm, c, embedDim);CHKERRQ(ierr);
1543       }
1544       ierr = DMSetUp(*dm);CHKERRQ(ierr); /* Allocate space for cones */
1545       /* Cells */
1546       for (i = 0, c = 0; i < numVerts; ++i) {
1547         for (j = 0; j < i; ++j) {
1548           for (k = 0; k < j; ++k) {
1549             if (graph[i*numVerts+j] && graph[j*numVerts+k] && graph[k*numVerts+i]) {
1550               cone[0] = firstVertex+i; cone[1] = firstVertex+j; cone[2] = firstVertex+k;
1551               /* Check orientation */
1552               {
1553                 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}}};
1554                 PetscReal normal[3];
1555                 PetscInt  e, f;
1556 
1557                 for (d = 0; d < embedDim; ++d) {
1558                   normal[d] = 0.0;
1559                   for (e = 0; e < embedDim; ++e) {
1560                     for (f = 0; f < embedDim; ++f) {
1561                       normal[d] += epsilon[d][e][f]*(coordsIn[j*embedDim+e] - coordsIn[i*embedDim+e])*(coordsIn[k*embedDim+f] - coordsIn[i*embedDim+f]);
1562                     }
1563                   }
1564                 }
1565                 if (DotReal(embedDim, normal, &coordsIn[i*embedDim]) < 0) {PetscInt tmp = cone[1]; cone[1] = cone[2]; cone[2] = tmp;}
1566               }
1567               ierr = DMPlexSetCone(*dm, c++, cone);CHKERRQ(ierr);
1568             }
1569           }
1570         }
1571       }
1572       ierr = DMPlexSymmetrize(*dm);CHKERRQ(ierr);
1573       ierr = DMPlexStratify(*dm);CHKERRQ(ierr);
1574       ierr = PetscFree(graph);CHKERRQ(ierr);
1575       /* Interpolate mesh */
1576       ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
1577       ierr = DMDestroy(dm);CHKERRQ(ierr);
1578       *dm  = idm;
1579     } else {
1580       /*
1581         12-21--13
1582          |     |
1583         25  4  24
1584          |     |
1585   12-25--9-16--8-24--13
1586    |     |     |     |
1587   23  5 17  0 15  3  22
1588    |     |     |     |
1589   10-20--6-14--7-19--11
1590          |     |
1591         20  1  19
1592          |     |
1593         10-18--11
1594          |     |
1595         23  2  22
1596          |     |
1597         12-21--13
1598        */
1599       const PetscReal dist = 1.0/PetscSqrtReal(3.0);
1600       PetscInt        cone[4], ornt[4];
1601 
1602       numCells    = !rank ?  6 : 0;
1603       numEdges    = !rank ? 12 : 0;
1604       numVerts    = !rank ?  8 : 0;
1605       firstVertex = numCells;
1606       firstEdge   = numCells + numVerts;
1607       /* Build Topology */
1608       ierr = DMPlexSetChart(*dm, 0, numCells+numEdges+numVerts);CHKERRQ(ierr);
1609       for (c = 0; c < numCells; c++) {
1610         ierr = DMPlexSetConeSize(*dm, c, 4);CHKERRQ(ierr);
1611       }
1612       for (e = firstEdge; e < firstEdge+numEdges; ++e) {
1613         ierr = DMPlexSetConeSize(*dm, e, 2);CHKERRQ(ierr);
1614       }
1615       ierr = DMSetUp(*dm);CHKERRQ(ierr); /* Allocate space for cones */
1616       /* Cell 0 */
1617       cone[0] = 14; cone[1] = 15; cone[2] = 16; cone[3] = 17;
1618       ierr = DMPlexSetCone(*dm, 0, cone);CHKERRQ(ierr);
1619       ornt[0] = 0; ornt[1] = 0; ornt[2] = 0; ornt[3] = 0;
1620       ierr = DMPlexSetConeOrientation(*dm, 0, ornt);CHKERRQ(ierr);
1621       /* Cell 1 */
1622       cone[0] = 18; cone[1] = 19; cone[2] = 14; cone[3] = 20;
1623       ierr = DMPlexSetCone(*dm, 1, cone);CHKERRQ(ierr);
1624       ornt[0] = 0; ornt[1] = 0; ornt[2] = -2; ornt[3] = 0;
1625       ierr = DMPlexSetConeOrientation(*dm, 1, ornt);CHKERRQ(ierr);
1626       /* Cell 2 */
1627       cone[0] = 21; cone[1] = 22; cone[2] = 18; cone[3] = 23;
1628       ierr = DMPlexSetCone(*dm, 2, cone);CHKERRQ(ierr);
1629       ornt[0] = 0; ornt[1] = 0; ornt[2] = -2; ornt[3] = 0;
1630       ierr = DMPlexSetConeOrientation(*dm, 2, ornt);CHKERRQ(ierr);
1631       /* Cell 3 */
1632       cone[0] = 19; cone[1] = 22; cone[2] = 24; cone[3] = 15;
1633       ierr = DMPlexSetCone(*dm, 3, cone);CHKERRQ(ierr);
1634       ornt[0] = -2; ornt[1] = -2; ornt[2] = 0; ornt[3] = -2;
1635       ierr = DMPlexSetConeOrientation(*dm, 3, ornt);CHKERRQ(ierr);
1636       /* Cell 4 */
1637       cone[0] = 16; cone[1] = 24; cone[2] = 21; cone[3] = 25;
1638       ierr = DMPlexSetCone(*dm, 4, cone);CHKERRQ(ierr);
1639       ornt[0] = -2; ornt[1] = -2; ornt[2] = -2; ornt[3] = 0;
1640       ierr = DMPlexSetConeOrientation(*dm, 4, ornt);CHKERRQ(ierr);
1641       /* Cell 5 */
1642       cone[0] = 20; cone[1] = 17; cone[2] = 25; cone[3] = 23;
1643       ierr = DMPlexSetCone(*dm, 5, cone);CHKERRQ(ierr);
1644       ornt[0] = -2; ornt[1] = -2; ornt[2] = -2; ornt[3] = -2;
1645       ierr = DMPlexSetConeOrientation(*dm, 5, ornt);CHKERRQ(ierr);
1646       /* Edges */
1647       cone[0] =  6; cone[1] =  7;
1648       ierr = DMPlexSetCone(*dm, 14, cone);CHKERRQ(ierr);
1649       cone[0] =  7; cone[1] =  8;
1650       ierr = DMPlexSetCone(*dm, 15, cone);CHKERRQ(ierr);
1651       cone[0] =  8; cone[1] =  9;
1652       ierr = DMPlexSetCone(*dm, 16, cone);CHKERRQ(ierr);
1653       cone[0] =  9; cone[1] =  6;
1654       ierr = DMPlexSetCone(*dm, 17, cone);CHKERRQ(ierr);
1655       cone[0] = 10; cone[1] = 11;
1656       ierr = DMPlexSetCone(*dm, 18, cone);CHKERRQ(ierr);
1657       cone[0] = 11; cone[1] =  7;
1658       ierr = DMPlexSetCone(*dm, 19, cone);CHKERRQ(ierr);
1659       cone[0] =  6; cone[1] = 10;
1660       ierr = DMPlexSetCone(*dm, 20, cone);CHKERRQ(ierr);
1661       cone[0] = 12; cone[1] = 13;
1662       ierr = DMPlexSetCone(*dm, 21, cone);CHKERRQ(ierr);
1663       cone[0] = 13; cone[1] = 11;
1664       ierr = DMPlexSetCone(*dm, 22, cone);CHKERRQ(ierr);
1665       cone[0] = 10; cone[1] = 12;
1666       ierr = DMPlexSetCone(*dm, 23, cone);CHKERRQ(ierr);
1667       cone[0] = 13; cone[1] =  8;
1668       ierr = DMPlexSetCone(*dm, 24, cone);CHKERRQ(ierr);
1669       cone[0] = 12; cone[1] =  9;
1670       ierr = DMPlexSetCone(*dm, 25, cone);CHKERRQ(ierr);
1671       ierr = DMPlexSymmetrize(*dm);CHKERRQ(ierr);
1672       ierr = DMPlexStratify(*dm);CHKERRQ(ierr);
1673       /* Build coordinates */
1674       ierr = PetscCalloc1(numVerts * embedDim, &coordsIn);CHKERRQ(ierr);
1675       coordsIn[0*embedDim+0] = -dist; coordsIn[0*embedDim+1] =  dist; coordsIn[0*embedDim+2] = -dist;
1676       coordsIn[1*embedDim+0] =  dist; coordsIn[1*embedDim+1] =  dist; coordsIn[1*embedDim+2] = -dist;
1677       coordsIn[2*embedDim+0] =  dist; coordsIn[2*embedDim+1] = -dist; coordsIn[2*embedDim+2] = -dist;
1678       coordsIn[3*embedDim+0] = -dist; coordsIn[3*embedDim+1] = -dist; coordsIn[3*embedDim+2] = -dist;
1679       coordsIn[4*embedDim+0] = -dist; coordsIn[4*embedDim+1] =  dist; coordsIn[4*embedDim+2] =  dist;
1680       coordsIn[5*embedDim+0] =  dist; coordsIn[5*embedDim+1] =  dist; coordsIn[5*embedDim+2] =  dist;
1681       coordsIn[6*embedDim+0] = -dist; coordsIn[6*embedDim+1] = -dist; coordsIn[6*embedDim+2] =  dist;
1682       coordsIn[7*embedDim+0] =  dist; coordsIn[7*embedDim+1] = -dist; coordsIn[7*embedDim+2] =  dist;
1683     }
1684     break;
1685   case 3:
1686     if (simplex) {
1687       DM              idm;
1688       const PetscReal edgeLen         = 1.0/PETSC_PHI;
1689       const PetscReal vertexA[4]      = {0.5, 0.5, 0.5, 0.5};
1690       const PetscReal vertexB[4]      = {1.0, 0.0, 0.0, 0.0};
1691       const PetscReal vertexC[4]      = {0.5, 0.5*PETSC_PHI, 0.5/PETSC_PHI, 0.0};
1692       const PetscInt  degree          = 12;
1693       PetscInt        s[4]            = {1, 1, 1};
1694       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},
1695                                          {2, 0, 1, 3}, {2, 1, 3, 0}, {2, 3, 0, 1}, {3, 0, 2, 1}, {3, 1, 0, 2}, {3, 2, 1, 0}};
1696       PetscInt        cone[4];
1697       PetscInt       *graph, p, i, j, k, l;
1698 
1699       numCells    = !rank ? 600 : 0;
1700       numVerts    = !rank ? 120 : 0;
1701       firstVertex = numCells;
1702       /* Use the 600-cell, which for a unit sphere has coordinates which are
1703 
1704            1/2 (\pm 1, \pm 1,    \pm 1, \pm 1)                          16
1705                (\pm 1,    0,       0,      0)  all cyclic permutations   8
1706            1/2 (\pm 1, \pm phi, \pm 1/phi, 0)  all even permutations    96
1707 
1708          where \phi^2 - \phi - 1 = 0, meaning \phi is the golden ratio \frac{1 + \sqrt{5}}{2}. The edge
1709          length is then given by 1/\phi = 2.73606.
1710 
1711          http://buzzard.pugetsound.edu/sage-practice/ch03s03.html
1712          http://mathworld.wolfram.com/600-Cell.html
1713        */
1714       /* Construct vertices */
1715       ierr = PetscCalloc1(numVerts * embedDim, &coordsIn);CHKERRQ(ierr);
1716       i    = 0;
1717       for (s[0] = -1; s[0] < 2; s[0] += 2) {
1718         for (s[1] = -1; s[1] < 2; s[1] += 2) {
1719           for (s[2] = -1; s[2] < 2; s[2] += 2) {
1720             for (s[3] = -1; s[3] < 2; s[3] += 2) {
1721               for (d = 0; d < embedDim; ++d) coordsIn[i*embedDim+d] = s[d]*vertexA[d];
1722               ++i;
1723             }
1724           }
1725         }
1726       }
1727       for (p = 0; p < embedDim; ++p) {
1728         s[1] = s[2] = s[3] = 1;
1729         for (s[0] = -1; s[0] < 2; s[0] += 2) {
1730           for (d = 0; d < embedDim; ++d) coordsIn[i*embedDim+d] = s[(d+p)%embedDim]*vertexB[(d+p)%embedDim];
1731           ++i;
1732         }
1733       }
1734       for (p = 0; p < 12; ++p) {
1735         s[3] = 1;
1736         for (s[0] = -1; s[0] < 2; s[0] += 2) {
1737           for (s[1] = -1; s[1] < 2; s[1] += 2) {
1738             for (s[2] = -1; s[2] < 2; s[2] += 2) {
1739               for (d = 0; d < embedDim; ++d) coordsIn[i*embedDim+d] = s[evenPerm[p][d]]*vertexC[evenPerm[p][d]];
1740               ++i;
1741             }
1742           }
1743         }
1744       }
1745       if (i != numVerts) SETERRQ2(comm, PETSC_ERR_PLIB, "Invalid 600-cell, vertices %D != %D", i, numVerts);
1746       /* Construct graph */
1747       ierr = PetscCalloc1(numVerts * numVerts, &graph);CHKERRQ(ierr);
1748       for (i = 0; i < numVerts; ++i) {
1749         for (j = 0, k = 0; j < numVerts; ++j) {
1750           if (PetscAbsReal(DiffNormReal(embedDim, &coordsIn[i*embedDim], &coordsIn[j*embedDim]) - edgeLen) < PETSC_SMALL) {graph[i*numVerts+j] = 1; ++k;}
1751         }
1752         if (k != degree) SETERRQ3(comm, PETSC_ERR_PLIB, "Invalid 600-cell, vertex %D degree %D != %D", i, k, degree);
1753       }
1754       /* Build Topology */
1755       ierr = DMPlexSetChart(*dm, 0, numCells+numVerts);CHKERRQ(ierr);
1756       for (c = 0; c < numCells; c++) {
1757         ierr = DMPlexSetConeSize(*dm, c, embedDim);CHKERRQ(ierr);
1758       }
1759       ierr = DMSetUp(*dm);CHKERRQ(ierr); /* Allocate space for cones */
1760       /* Cells */
1761       for (i = 0, c = 0; i < numVerts; ++i) {
1762         for (j = 0; j < i; ++j) {
1763           for (k = 0; k < j; ++k) {
1764             for (l = 0; l < k; ++l) {
1765               if (graph[i*numVerts+j] && graph[j*numVerts+k] && graph[k*numVerts+i] &&
1766                   graph[l*numVerts+i] && graph[l*numVerts+j] && graph[l*numVerts+k]) {
1767                 cone[0] = firstVertex+i; cone[1] = firstVertex+j; cone[2] = firstVertex+k; cone[3] = firstVertex+l;
1768                 /* Check orientation: https://ef.gy/linear-algebra:normal-vectors-in-higher-dimensional-spaces */
1769                 {
1770                   const PetscInt epsilon[4][4][4][4] = {{{{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}},
1771                                                          {{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  1}, { 0,  0, -1, 0}},
1772                                                          {{0,  0,  0,  0}, { 0, 0,  0, -1}, { 0,  0, 0,  0}, { 0,  1,  0, 0}},
1773                                                          {{0,  0,  0,  0}, { 0, 0,  1,  0}, { 0, -1, 0,  0}, { 0,  0,  0, 0}}},
1774 
1775                                                         {{{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0, -1}, { 0,  0,  1, 0}},
1776                                                          {{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}},
1777                                                          {{0,  0,  0,  1}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, {-1,  0,  0, 0}},
1778                                                          {{0,  0, -1,  0}, { 0, 0,  0,  0}, { 1,  0, 0,  0}, { 0,  0,  0, 0}}},
1779 
1780                                                         {{{0,  0,  0,  0}, { 0, 0,  0,  1}, { 0,  0, 0,  0}, { 0, -1,  0, 0}},
1781                                                          {{0,  0,  0, -1}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 1,  0,  0, 0}},
1782                                                          {{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}},
1783                                                          {{0,  1,  0,  0}, {-1, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}}},
1784 
1785                                                         {{{0,  0,  0,  0}, { 0, 0, -1,  0}, { 0,  1, 0,  0}, { 0,  0,  0, 0}},
1786                                                          {{0,  0,  1,  0}, { 0, 0,  0,  0}, {-1,  0, 0,  0}, { 0,  0,  0, 0}},
1787                                                          {{0, -1,  0,  0}, { 1, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}},
1788                                                          {{0,  0,  0,  0}, { 0, 0,  0,  0}, { 0,  0, 0,  0}, { 0,  0,  0, 0}}}};
1789                   PetscReal normal[4];
1790                   PetscInt  e, f, g;
1791 
1792                   for (d = 0; d < embedDim; ++d) {
1793                     normal[d] = 0.0;
1794                     for (e = 0; e < embedDim; ++e) {
1795                       for (f = 0; f < embedDim; ++f) {
1796                         for (g = 0; g < embedDim; ++g) {
1797                           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]);
1798                         }
1799                       }
1800                     }
1801                   }
1802                   if (DotReal(embedDim, normal, &coordsIn[i*embedDim]) < 0) {PetscInt tmp = cone[1]; cone[1] = cone[2]; cone[2] = tmp;}
1803                 }
1804                 ierr = DMPlexSetCone(*dm, c++, cone);CHKERRQ(ierr);
1805               }
1806             }
1807           }
1808         }
1809       }
1810       ierr = DMPlexSymmetrize(*dm);CHKERRQ(ierr);
1811       ierr = DMPlexStratify(*dm);CHKERRQ(ierr);
1812       ierr = PetscFree(graph);CHKERRQ(ierr);
1813       /* Interpolate mesh */
1814       ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
1815       ierr = DMDestroy(dm);CHKERRQ(ierr);
1816       *dm  = idm;
1817       break;
1818     }
1819   default: SETERRQ1(comm, PETSC_ERR_SUP, "Unsupported dimension for sphere: %D", dim);
1820   }
1821   /* Create coordinates */
1822   ierr = DMGetCoordinateSection(*dm, &coordSection);CHKERRQ(ierr);
1823   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
1824   ierr = PetscSectionSetFieldComponents(coordSection, 0, embedDim);CHKERRQ(ierr);
1825   ierr = PetscSectionSetChart(coordSection, firstVertex, firstVertex+numVerts);CHKERRQ(ierr);
1826   for (v = firstVertex; v < firstVertex+numVerts; ++v) {
1827     ierr = PetscSectionSetDof(coordSection, v, embedDim);CHKERRQ(ierr);
1828     ierr = PetscSectionSetFieldDof(coordSection, v, 0, embedDim);CHKERRQ(ierr);
1829   }
1830   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
1831   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
1832   ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
1833   ierr = VecSetBlockSize(coordinates, embedDim);CHKERRQ(ierr);
1834   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
1835   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
1836   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
1837   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
1838   for (v = 0; v < numVerts; ++v) for (d = 0; d < embedDim; ++d) {coords[v*embedDim+d] = coordsIn[v*embedDim+d];}
1839   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
1840   ierr = DMSetCoordinatesLocal(*dm, coordinates);CHKERRQ(ierr);
1841   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
1842   ierr = PetscFree(coordsIn);CHKERRQ(ierr);
1843   PetscFunctionReturn(0);
1844 }
1845 
1846 /* External function declarations here */
1847 extern PetscErrorCode DMCreateInterpolation_Plex(DM dmCoarse, DM dmFine, Mat *interpolation, Vec *scaling);
1848 extern PetscErrorCode DMCreateInjection_Plex(DM dmCoarse, DM dmFine, Mat *mat);
1849 extern PetscErrorCode DMCreateMassMatrix_Plex(DM dmCoarse, DM dmFine, Mat *mat);
1850 extern PetscErrorCode DMCreateDefaultSection_Plex(DM dm);
1851 extern PetscErrorCode DMCreateDefaultConstraints_Plex(DM dm);
1852 extern PetscErrorCode DMCreateMatrix_Plex(DM dm,  Mat *J);
1853 extern PetscErrorCode DMCreateCoordinateDM_Plex(DM dm, DM *cdm);
1854 PETSC_INTERN PetscErrorCode DMClone_Plex(DM dm, DM *newdm);
1855 extern PetscErrorCode DMSetUp_Plex(DM dm);
1856 extern PetscErrorCode DMDestroy_Plex(DM dm);
1857 extern PetscErrorCode DMView_Plex(DM dm, PetscViewer viewer);
1858 extern PetscErrorCode DMLoad_Plex(DM dm, PetscViewer viewer);
1859 extern PetscErrorCode DMCreateSubDM_Plex(DM dm, PetscInt numFields, const PetscInt fields[], IS *is, DM *subdm);
1860 extern PetscErrorCode DMCreateSuperDM_Plex(DM dms[], PetscInt len, IS **is, DM *superdm);
1861 static PetscErrorCode DMInitialize_Plex(DM dm);
1862 
1863 /* Replace dm with the contents of dmNew
1864    - Share the DM_Plex structure
1865    - Share the coordinates
1866    - Share the SF
1867 */
1868 static PetscErrorCode DMPlexReplace_Static(DM dm, DM dmNew)
1869 {
1870   PetscSF               sf;
1871   DM                    coordDM, coarseDM;
1872   Vec                   coords;
1873   PetscBool             isper;
1874   const PetscReal      *maxCell, *L;
1875   const DMBoundaryType *bd;
1876   PetscErrorCode        ierr;
1877 
1878   PetscFunctionBegin;
1879   ierr = DMGetPointSF(dmNew, &sf);CHKERRQ(ierr);
1880   ierr = DMSetPointSF(dm, sf);CHKERRQ(ierr);
1881   ierr = DMGetCoordinateDM(dmNew, &coordDM);CHKERRQ(ierr);
1882   ierr = DMGetCoordinatesLocal(dmNew, &coords);CHKERRQ(ierr);
1883   ierr = DMSetCoordinateDM(dm, coordDM);CHKERRQ(ierr);
1884   ierr = DMSetCoordinatesLocal(dm, coords);CHKERRQ(ierr);
1885   ierr = DMGetPeriodicity(dm, &isper, &maxCell, &L, &bd);CHKERRQ(ierr);
1886   ierr = DMSetPeriodicity(dmNew, isper, maxCell, L, bd);CHKERRQ(ierr);
1887   ierr = DMDestroy_Plex(dm);CHKERRQ(ierr);
1888   ierr = DMInitialize_Plex(dm);CHKERRQ(ierr);
1889   dm->data = dmNew->data;
1890   ((DM_Plex *) dmNew->data)->refct++;
1891   dmNew->labels->refct++;
1892   if (!--(dm->labels->refct)) {
1893     DMLabelLink next = dm->labels->next;
1894 
1895     /* destroy the labels */
1896     while (next) {
1897       DMLabelLink tmp = next->next;
1898 
1899       ierr = DMLabelDestroy(&next->label);CHKERRQ(ierr);
1900       ierr = PetscFree(next);CHKERRQ(ierr);
1901       next = tmp;
1902     }
1903     ierr = PetscFree(dm->labels);CHKERRQ(ierr);
1904   }
1905   dm->labels = dmNew->labels;
1906   dm->depthLabel = dmNew->depthLabel;
1907   ierr = DMGetCoarseDM(dmNew,&coarseDM);CHKERRQ(ierr);
1908   ierr = DMSetCoarseDM(dm,coarseDM);CHKERRQ(ierr);
1909   PetscFunctionReturn(0);
1910 }
1911 
1912 /* Swap dm with the contents of dmNew
1913    - Swap the DM_Plex structure
1914    - Swap the coordinates
1915    - Swap the point PetscSF
1916 */
1917 static PetscErrorCode DMPlexSwap_Static(DM dmA, DM dmB)
1918 {
1919   DM              coordDMA, coordDMB;
1920   Vec             coordsA,  coordsB;
1921   PetscSF         sfA,      sfB;
1922   void            *tmp;
1923   DMLabelLinkList listTmp;
1924   DMLabel         depthTmp;
1925   PetscErrorCode  ierr;
1926 
1927   PetscFunctionBegin;
1928   ierr = DMGetPointSF(dmA, &sfA);CHKERRQ(ierr);
1929   ierr = DMGetPointSF(dmB, &sfB);CHKERRQ(ierr);
1930   ierr = PetscObjectReference((PetscObject) sfA);CHKERRQ(ierr);
1931   ierr = DMSetPointSF(dmA, sfB);CHKERRQ(ierr);
1932   ierr = DMSetPointSF(dmB, sfA);CHKERRQ(ierr);
1933   ierr = PetscObjectDereference((PetscObject) sfA);CHKERRQ(ierr);
1934 
1935   ierr = DMGetCoordinateDM(dmA, &coordDMA);CHKERRQ(ierr);
1936   ierr = DMGetCoordinateDM(dmB, &coordDMB);CHKERRQ(ierr);
1937   ierr = PetscObjectReference((PetscObject) coordDMA);CHKERRQ(ierr);
1938   ierr = DMSetCoordinateDM(dmA, coordDMB);CHKERRQ(ierr);
1939   ierr = DMSetCoordinateDM(dmB, coordDMA);CHKERRQ(ierr);
1940   ierr = PetscObjectDereference((PetscObject) coordDMA);CHKERRQ(ierr);
1941 
1942   ierr = DMGetCoordinatesLocal(dmA, &coordsA);CHKERRQ(ierr);
1943   ierr = DMGetCoordinatesLocal(dmB, &coordsB);CHKERRQ(ierr);
1944   ierr = PetscObjectReference((PetscObject) coordsA);CHKERRQ(ierr);
1945   ierr = DMSetCoordinatesLocal(dmA, coordsB);CHKERRQ(ierr);
1946   ierr = DMSetCoordinatesLocal(dmB, coordsA);CHKERRQ(ierr);
1947   ierr = PetscObjectDereference((PetscObject) coordsA);CHKERRQ(ierr);
1948 
1949   tmp       = dmA->data;
1950   dmA->data = dmB->data;
1951   dmB->data = tmp;
1952   listTmp   = dmA->labels;
1953   dmA->labels = dmB->labels;
1954   dmB->labels = listTmp;
1955   depthTmp  = dmA->depthLabel;
1956   dmA->depthLabel = dmB->depthLabel;
1957   dmB->depthLabel = depthTmp;
1958   PetscFunctionReturn(0);
1959 }
1960 
1961 PetscErrorCode DMSetFromOptions_NonRefinement_Plex(PetscOptionItems *PetscOptionsObject,DM dm)
1962 {
1963   DM_Plex       *mesh = (DM_Plex*) dm->data;
1964   PetscErrorCode ierr;
1965 
1966   PetscFunctionBegin;
1967   /* Handle viewing */
1968   ierr = PetscOptionsBool("-dm_plex_print_set_values", "Output all set values info", "DMView", PETSC_FALSE, &mesh->printSetValues, NULL);CHKERRQ(ierr);
1969   ierr = PetscOptionsInt("-dm_plex_print_fem", "Debug output level all fem computations", "DMView", 0, &mesh->printFEM, NULL);CHKERRQ(ierr);
1970   ierr = PetscOptionsReal("-dm_plex_print_tol", "Tolerance for FEM output", "DMView", mesh->printTol, &mesh->printTol, NULL);CHKERRQ(ierr);
1971   /* Point Location */
1972   ierr = PetscOptionsBool("-dm_plex_hash_location", "Use grid hashing for point location", "DMView", PETSC_FALSE, &mesh->useHashLocation, NULL);CHKERRQ(ierr);
1973   /* Generation and remeshing */
1974   ierr = PetscOptionsBool("-dm_plex_remesh_bd", "Allow changes to the boundary on remeshing", "DMView", PETSC_FALSE, &mesh->remeshBd, NULL);CHKERRQ(ierr);
1975   /* Projection behavior */
1976   ierr = PetscOptionsInt("-dm_plex_max_projection_height", "Maxmimum mesh point height used to project locally", "DMPlexSetMaxProjectionHeight", 0, &mesh->maxProjectionHeight, NULL);CHKERRQ(ierr);
1977   ierr = PetscOptionsBool("-dm_plex_regular_refinement", "Use special nested projection algorithm for regular refinement", "DMPlexSetRegularRefinement", mesh->regularRefinement, &mesh->regularRefinement, NULL);CHKERRQ(ierr);
1978 
1979   ierr = PetscPartitionerSetFromOptions(mesh->partitioner);CHKERRQ(ierr);
1980   PetscFunctionReturn(0);
1981 }
1982 
1983 static PetscErrorCode DMSetFromOptions_Plex(PetscOptionItems *PetscOptionsObject,DM dm)
1984 {
1985   PetscInt       refine = 0, coarsen = 0, r;
1986   PetscBool      isHierarchy;
1987   PetscErrorCode ierr;
1988 
1989   PetscFunctionBegin;
1990   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1991   ierr = PetscOptionsHead(PetscOptionsObject,"DMPlex Options");CHKERRQ(ierr);
1992   /* Handle DMPlex refinement */
1993   ierr = PetscOptionsInt("-dm_refine", "The number of uniform refinements", "DMCreate", refine, &refine, NULL);CHKERRQ(ierr);
1994   ierr = PetscOptionsInt("-dm_refine_hierarchy", "The number of uniform refinements", "DMCreate", refine, &refine, &isHierarchy);CHKERRQ(ierr);
1995   if (refine) {ierr = DMPlexSetRefinementUniform(dm, PETSC_TRUE);CHKERRQ(ierr);}
1996   if (refine && isHierarchy) {
1997     DM *dms, coarseDM;
1998 
1999     ierr = DMGetCoarseDM(dm, &coarseDM);CHKERRQ(ierr);
2000     ierr = PetscObjectReference((PetscObject)coarseDM);CHKERRQ(ierr);
2001     ierr = PetscMalloc1(refine,&dms);CHKERRQ(ierr);
2002     ierr = DMRefineHierarchy(dm, refine, dms);CHKERRQ(ierr);
2003     /* Total hack since we do not pass in a pointer */
2004     ierr = DMPlexSwap_Static(dm, dms[refine-1]);CHKERRQ(ierr);
2005     if (refine == 1) {
2006       ierr = DMSetCoarseDM(dm, dms[0]);CHKERRQ(ierr);
2007       ierr = DMPlexSetRegularRefinement(dm, PETSC_TRUE);CHKERRQ(ierr);
2008     } else {
2009       ierr = DMSetCoarseDM(dm, dms[refine-2]);CHKERRQ(ierr);
2010       ierr = DMPlexSetRegularRefinement(dm, PETSC_TRUE);CHKERRQ(ierr);
2011       ierr = DMSetCoarseDM(dms[0], dms[refine-1]);CHKERRQ(ierr);
2012       ierr = DMPlexSetRegularRefinement(dms[0], PETSC_TRUE);CHKERRQ(ierr);
2013     }
2014     ierr = DMSetCoarseDM(dms[refine-1], coarseDM);CHKERRQ(ierr);
2015     ierr = PetscObjectDereference((PetscObject)coarseDM);CHKERRQ(ierr);
2016     /* Free DMs */
2017     for (r = 0; r < refine; ++r) {
2018       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dms[r]);CHKERRQ(ierr);
2019       ierr = DMDestroy(&dms[r]);CHKERRQ(ierr);
2020     }
2021     ierr = PetscFree(dms);CHKERRQ(ierr);
2022   } else {
2023     for (r = 0; r < refine; ++r) {
2024       DM refinedMesh;
2025 
2026       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2027       ierr = DMRefine(dm, PetscObjectComm((PetscObject) dm), &refinedMesh);CHKERRQ(ierr);
2028       /* Total hack since we do not pass in a pointer */
2029       ierr = DMPlexReplace_Static(dm, refinedMesh);CHKERRQ(ierr);
2030       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2031       ierr = DMDestroy(&refinedMesh);CHKERRQ(ierr);
2032     }
2033   }
2034   /* Handle DMPlex coarsening */
2035   ierr = PetscOptionsInt("-dm_coarsen", "Coarsen the mesh", "DMCreate", coarsen, &coarsen, NULL);CHKERRQ(ierr);
2036   ierr = PetscOptionsInt("-dm_coarsen_hierarchy", "The number of coarsenings", "DMCreate", coarsen, &coarsen, &isHierarchy);CHKERRQ(ierr);
2037   if (coarsen && isHierarchy) {
2038     DM *dms;
2039 
2040     ierr = PetscMalloc1(coarsen, &dms);CHKERRQ(ierr);
2041     ierr = DMCoarsenHierarchy(dm, coarsen, dms);CHKERRQ(ierr);
2042     /* Free DMs */
2043     for (r = 0; r < coarsen; ++r) {
2044       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dms[r]);CHKERRQ(ierr);
2045       ierr = DMDestroy(&dms[r]);CHKERRQ(ierr);
2046     }
2047     ierr = PetscFree(dms);CHKERRQ(ierr);
2048   } else {
2049     for (r = 0; r < coarsen; ++r) {
2050       DM coarseMesh;
2051 
2052       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2053       ierr = DMCoarsen(dm, PetscObjectComm((PetscObject) dm), &coarseMesh);CHKERRQ(ierr);
2054       /* Total hack since we do not pass in a pointer */
2055       ierr = DMPlexReplace_Static(dm, coarseMesh);CHKERRQ(ierr);
2056       ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2057       ierr = DMDestroy(&coarseMesh);CHKERRQ(ierr);
2058     }
2059   }
2060   /* Handle */
2061   ierr = DMSetFromOptions_NonRefinement_Plex(PetscOptionsObject, dm);CHKERRQ(ierr);
2062   ierr = PetscOptionsTail();CHKERRQ(ierr);
2063   PetscFunctionReturn(0);
2064 }
2065 
2066 static PetscErrorCode DMCreateGlobalVector_Plex(DM dm,Vec *vec)
2067 {
2068   PetscErrorCode ierr;
2069 
2070   PetscFunctionBegin;
2071   ierr = DMCreateGlobalVector_Section_Private(dm,vec);CHKERRQ(ierr);
2072   /* ierr = VecSetOperation(*vec, VECOP_DUPLICATE, (void(*)(void)) VecDuplicate_MPI_DM);CHKERRQ(ierr); */
2073   ierr = VecSetOperation(*vec, VECOP_VIEW, (void (*)(void)) VecView_Plex);CHKERRQ(ierr);
2074   ierr = VecSetOperation(*vec, VECOP_VIEWNATIVE, (void (*)(void)) VecView_Plex_Native);CHKERRQ(ierr);
2075   ierr = VecSetOperation(*vec, VECOP_LOAD, (void (*)(void)) VecLoad_Plex);CHKERRQ(ierr);
2076   ierr = VecSetOperation(*vec, VECOP_LOADNATIVE, (void (*)(void)) VecLoad_Plex_Native);CHKERRQ(ierr);
2077   PetscFunctionReturn(0);
2078 }
2079 
2080 static PetscErrorCode DMCreateLocalVector_Plex(DM dm,Vec *vec)
2081 {
2082   PetscErrorCode ierr;
2083 
2084   PetscFunctionBegin;
2085   ierr = DMCreateLocalVector_Section_Private(dm,vec);CHKERRQ(ierr);
2086   ierr = VecSetOperation(*vec, VECOP_VIEW, (void (*)(void)) VecView_Plex_Local);CHKERRQ(ierr);
2087   ierr = VecSetOperation(*vec, VECOP_LOAD, (void (*)(void)) VecLoad_Plex_Local);CHKERRQ(ierr);
2088   PetscFunctionReturn(0);
2089 }
2090 
2091 static PetscErrorCode DMGetDimPoints_Plex(DM dm, PetscInt dim, PetscInt *pStart, PetscInt *pEnd)
2092 {
2093   PetscInt       depth, d;
2094   PetscErrorCode ierr;
2095 
2096   PetscFunctionBegin;
2097   ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
2098   if (depth == 1) {
2099     ierr = DMGetDimension(dm, &d);CHKERRQ(ierr);
2100     if (dim == 0)      {ierr = DMPlexGetDepthStratum(dm, dim, pStart, pEnd);CHKERRQ(ierr);}
2101     else if (dim == d) {ierr = DMPlexGetDepthStratum(dm, 1, pStart, pEnd);CHKERRQ(ierr);}
2102     else               {*pStart = 0; *pEnd = 0;}
2103   } else {
2104     ierr = DMPlexGetDepthStratum(dm, dim, pStart, pEnd);CHKERRQ(ierr);
2105   }
2106   PetscFunctionReturn(0);
2107 }
2108 
2109 static PetscErrorCode DMGetNeighors_Plex(DM dm, PetscInt *nranks, const PetscMPIInt *ranks[])
2110 {
2111   PetscSF        sf;
2112   PetscErrorCode ierr;
2113 
2114   PetscFunctionBegin;
2115   ierr = DMGetPointSF(dm, &sf);CHKERRQ(ierr);
2116   ierr = PetscSFGetRanks(sf, nranks, ranks, NULL, NULL, NULL);CHKERRQ(ierr);
2117   PetscFunctionReturn(0);
2118 }
2119 
2120 static PetscErrorCode DMInitialize_Plex(DM dm)
2121 {
2122   PetscErrorCode ierr;
2123 
2124   PetscFunctionBegin;
2125   dm->ops->view                            = DMView_Plex;
2126   dm->ops->load                            = DMLoad_Plex;
2127   dm->ops->setfromoptions                  = DMSetFromOptions_Plex;
2128   dm->ops->clone                           = DMClone_Plex;
2129   dm->ops->setup                           = DMSetUp_Plex;
2130   dm->ops->createdefaultsection            = DMCreateDefaultSection_Plex;
2131   dm->ops->createdefaultconstraints        = DMCreateDefaultConstraints_Plex;
2132   dm->ops->createglobalvector              = DMCreateGlobalVector_Plex;
2133   dm->ops->createlocalvector               = DMCreateLocalVector_Plex;
2134   dm->ops->getlocaltoglobalmapping         = NULL;
2135   dm->ops->createfieldis                   = NULL;
2136   dm->ops->createcoordinatedm              = DMCreateCoordinateDM_Plex;
2137   dm->ops->getcoloring                     = NULL;
2138   dm->ops->creatematrix                    = DMCreateMatrix_Plex;
2139   dm->ops->createinterpolation             = DMCreateInterpolation_Plex;
2140   dm->ops->createmassmatrix                = DMCreateMassMatrix_Plex;
2141   dm->ops->getaggregates                   = NULL;
2142   dm->ops->getinjection                    = DMCreateInjection_Plex;
2143   dm->ops->refine                          = DMRefine_Plex;
2144   dm->ops->coarsen                         = DMCoarsen_Plex;
2145   dm->ops->refinehierarchy                 = DMRefineHierarchy_Plex;
2146   dm->ops->coarsenhierarchy                = DMCoarsenHierarchy_Plex;
2147   dm->ops->adaptlabel                      = DMAdaptLabel_Plex;
2148   dm->ops->adaptmetric                     = DMAdaptMetric_Plex;
2149   dm->ops->globaltolocalbegin              = NULL;
2150   dm->ops->globaltolocalend                = NULL;
2151   dm->ops->localtoglobalbegin              = NULL;
2152   dm->ops->localtoglobalend                = NULL;
2153   dm->ops->destroy                         = DMDestroy_Plex;
2154   dm->ops->createsubdm                     = DMCreateSubDM_Plex;
2155   dm->ops->createsuperdm                   = DMCreateSuperDM_Plex;
2156   dm->ops->getdimpoints                    = DMGetDimPoints_Plex;
2157   dm->ops->locatepoints                    = DMLocatePoints_Plex;
2158   dm->ops->projectfunctionlocal            = DMProjectFunctionLocal_Plex;
2159   dm->ops->projectfunctionlabellocal       = DMProjectFunctionLabelLocal_Plex;
2160   dm->ops->projectfieldlocal               = DMProjectFieldLocal_Plex;
2161   dm->ops->projectfieldlabellocal          = DMProjectFieldLabelLocal_Plex;
2162   dm->ops->computel2diff                   = DMComputeL2Diff_Plex;
2163   dm->ops->computel2gradientdiff           = DMComputeL2GradientDiff_Plex;
2164   dm->ops->computel2fielddiff              = DMComputeL2FieldDiff_Plex;
2165   dm->ops->getneighbors                    = DMGetNeighors_Plex;
2166   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMPlexInsertBoundaryValues_C",DMPlexInsertBoundaryValues_Plex);CHKERRQ(ierr);
2167   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMSetUpGLVisViewer_C",DMSetUpGLVisViewer_Plex);CHKERRQ(ierr);
2168   PetscFunctionReturn(0);
2169 }
2170 
2171 PETSC_INTERN PetscErrorCode DMClone_Plex(DM dm, DM *newdm)
2172 {
2173   DM_Plex        *mesh = (DM_Plex *) dm->data;
2174   PetscErrorCode ierr;
2175 
2176   PetscFunctionBegin;
2177   mesh->refct++;
2178   (*newdm)->data = mesh;
2179   ierr = PetscObjectChangeTypeName((PetscObject) *newdm, DMPLEX);CHKERRQ(ierr);
2180   ierr = DMInitialize_Plex(*newdm);CHKERRQ(ierr);
2181   PetscFunctionReturn(0);
2182 }
2183 
2184 /*MC
2185   DMPLEX = "plex" - A DM object that encapsulates an unstructured mesh, or CW Complex, which can be expressed using a Hasse Diagram.
2186                     In the local representation, Vecs contain all unknowns in the interior and shared boundary. This is
2187                     specified by a PetscSection object. Ownership in the global representation is determined by
2188                     ownership of the underlying DMPlex points. This is specified by another PetscSection object.
2189 
2190   Level: intermediate
2191 
2192 .seealso: DMType, DMPlexCreate(), DMCreate(), DMSetType()
2193 M*/
2194 
2195 PETSC_EXTERN PetscErrorCode DMCreate_Plex(DM dm)
2196 {
2197   DM_Plex        *mesh;
2198   PetscInt       unit, d;
2199   PetscErrorCode ierr;
2200 
2201   PetscFunctionBegin;
2202   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
2203   ierr     = PetscNewLog(dm,&mesh);CHKERRQ(ierr);
2204   dm->dim  = 0;
2205   dm->data = mesh;
2206 
2207   mesh->refct             = 1;
2208   ierr                    = PetscSectionCreate(PetscObjectComm((PetscObject)dm), &mesh->coneSection);CHKERRQ(ierr);
2209   mesh->maxConeSize       = 0;
2210   mesh->cones             = NULL;
2211   mesh->coneOrientations  = NULL;
2212   ierr                    = PetscSectionCreate(PetscObjectComm((PetscObject)dm), &mesh->supportSection);CHKERRQ(ierr);
2213   mesh->maxSupportSize    = 0;
2214   mesh->supports          = NULL;
2215   mesh->refinementUniform = PETSC_TRUE;
2216   mesh->refinementLimit   = -1.0;
2217 
2218   mesh->facesTmp = NULL;
2219 
2220   mesh->tetgenOpts   = NULL;
2221   mesh->triangleOpts = NULL;
2222   ierr = PetscPartitionerCreate(PetscObjectComm((PetscObject)dm), &mesh->partitioner);CHKERRQ(ierr);
2223   mesh->remeshBd     = PETSC_FALSE;
2224 
2225   mesh->subpointMap = NULL;
2226 
2227   for (unit = 0; unit < NUM_PETSC_UNITS; ++unit) mesh->scale[unit] = 1.0;
2228 
2229   mesh->regularRefinement   = PETSC_FALSE;
2230   mesh->depthState          = -1;
2231   mesh->globalVertexNumbers = NULL;
2232   mesh->globalCellNumbers   = NULL;
2233   mesh->anchorSection       = NULL;
2234   mesh->anchorIS            = NULL;
2235   mesh->createanchors       = NULL;
2236   mesh->computeanchormatrix = NULL;
2237   mesh->parentSection       = NULL;
2238   mesh->parents             = NULL;
2239   mesh->childIDs            = NULL;
2240   mesh->childSection        = NULL;
2241   mesh->children            = NULL;
2242   mesh->referenceTree       = NULL;
2243   mesh->getchildsymmetry    = NULL;
2244   for (d = 0; d < 8; ++d) mesh->hybridPointMax[d] = PETSC_DETERMINE;
2245   mesh->vtkCellHeight       = 0;
2246   mesh->useAnchors          = PETSC_FALSE;
2247 
2248   mesh->maxProjectionHeight = 0;
2249 
2250   mesh->printSetValues = PETSC_FALSE;
2251   mesh->printFEM       = 0;
2252   mesh->printTol       = 1.0e-10;
2253 
2254   ierr = DMInitialize_Plex(dm);CHKERRQ(ierr);
2255   PetscFunctionReturn(0);
2256 }
2257 
2258 /*@
2259   DMPlexCreate - Creates a DMPlex object, which encapsulates an unstructured mesh, or CW complex, which can be expressed using a Hasse Diagram.
2260 
2261   Collective on MPI_Comm
2262 
2263   Input Parameter:
2264 . comm - The communicator for the DMPlex object
2265 
2266   Output Parameter:
2267 . mesh  - The DMPlex object
2268 
2269   Level: beginner
2270 
2271 .keywords: DMPlex, create
2272 @*/
2273 PetscErrorCode DMPlexCreate(MPI_Comm comm, DM *mesh)
2274 {
2275   PetscErrorCode ierr;
2276 
2277   PetscFunctionBegin;
2278   PetscValidPointer(mesh,2);
2279   ierr = DMCreate(comm, mesh);CHKERRQ(ierr);
2280   ierr = DMSetType(*mesh, DMPLEX);CHKERRQ(ierr);
2281   PetscFunctionReturn(0);
2282 }
2283 
2284 /*
2285   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
2286 */
2287 static PetscErrorCode DMPlexBuildFromCellList_Parallel_Private(DM dm, PetscInt numCells, PetscInt numVertices, PetscInt numCorners, const int cells[], PetscSF *sfVert)
2288 {
2289   PetscSF         sfPoint;
2290   PetscLayout     vLayout;
2291   PetscHashI      vhash;
2292   PetscSFNode    *remoteVerticesAdj, *vertexLocal, *vertexOwner, *remoteVertex;
2293   const PetscInt *vrange;
2294   PetscInt        numVerticesAdj, off, *verticesAdj, numVerticesGhost = 0, *localVertex, *cone, c, p, v, g;
2295   PETSC_UNUSED PetscHashIIter ret, iter;
2296   PetscMPIInt     rank, size;
2297   PetscErrorCode  ierr;
2298 
2299   PetscFunctionBegin;
2300   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject) dm), &rank);CHKERRQ(ierr);
2301   ierr = MPI_Comm_size(PetscObjectComm((PetscObject) dm), &size);CHKERRQ(ierr);
2302   /* Partition vertices */
2303   ierr = PetscLayoutCreate(PetscObjectComm((PetscObject) dm), &vLayout);CHKERRQ(ierr);
2304   ierr = PetscLayoutSetLocalSize(vLayout, numVertices);CHKERRQ(ierr);
2305   ierr = PetscLayoutSetBlockSize(vLayout, 1);CHKERRQ(ierr);
2306   ierr = PetscLayoutSetUp(vLayout);CHKERRQ(ierr);
2307   ierr = PetscLayoutGetRanges(vLayout, &vrange);CHKERRQ(ierr);
2308   /* Count vertices and map them to procs */
2309   PetscHashICreate(vhash);
2310   for (c = 0; c < numCells; ++c) {
2311     for (p = 0; p < numCorners; ++p) {
2312       PetscHashIPut(vhash, cells[c*numCorners+p], ret, iter);
2313     }
2314   }
2315   PetscHashISize(vhash, numVerticesAdj);
2316   ierr = PetscMalloc1(numVerticesAdj, &verticesAdj);CHKERRQ(ierr);
2317   off = 0; ierr = PetscHashIGetKeys(vhash, &off, verticesAdj);CHKERRQ(ierr);
2318   if (off != numVerticesAdj) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Invalid number of local vertices %D should be %D", off, numVerticesAdj);
2319   ierr = PetscSortInt(numVerticesAdj, verticesAdj);CHKERRQ(ierr);
2320   ierr = PetscMalloc1(numVerticesAdj, &remoteVerticesAdj);CHKERRQ(ierr);
2321   for (v = 0; v < numVerticesAdj; ++v) {
2322     const PetscInt gv = verticesAdj[v];
2323     PetscInt       vrank;
2324 
2325     ierr = PetscFindInt(gv, size+1, vrange, &vrank);CHKERRQ(ierr);
2326     vrank = vrank < 0 ? -(vrank+2) : vrank;
2327     remoteVerticesAdj[v].index = gv - vrange[vrank];
2328     remoteVerticesAdj[v].rank  = vrank;
2329   }
2330   /* Create cones */
2331   ierr = DMPlexSetChart(dm, 0, numCells+numVerticesAdj);CHKERRQ(ierr);
2332   for (c = 0; c < numCells; ++c) {ierr = DMPlexSetConeSize(dm, c, numCorners);CHKERRQ(ierr);}
2333   ierr = DMSetUp(dm);CHKERRQ(ierr);
2334   ierr = DMGetWorkArray(dm, numCorners, MPIU_INT, &cone);CHKERRQ(ierr);
2335   for (c = 0; c < numCells; ++c) {
2336     for (p = 0; p < numCorners; ++p) {
2337       const PetscInt gv = cells[c*numCorners+p];
2338       PetscInt       lv;
2339 
2340       ierr = PetscFindInt(gv, numVerticesAdj, verticesAdj, &lv);CHKERRQ(ierr);
2341       if (lv < 0) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Could not find global vertex %D in local connectivity", gv);
2342       cone[p] = lv+numCells;
2343     }
2344     ierr = DMPlexSetCone(dm, c, cone);CHKERRQ(ierr);
2345   }
2346   ierr = DMRestoreWorkArray(dm, numCorners, MPIU_INT, &cone);CHKERRQ(ierr);
2347   /* Create SF for vertices */
2348   ierr = PetscSFCreate(PetscObjectComm((PetscObject)dm), sfVert);CHKERRQ(ierr);
2349   ierr = PetscObjectSetName((PetscObject) *sfVert, "Vertex Ownership SF");CHKERRQ(ierr);
2350   ierr = PetscSFSetFromOptions(*sfVert);CHKERRQ(ierr);
2351   ierr = PetscSFSetGraph(*sfVert, numVertices, numVerticesAdj, NULL, PETSC_OWN_POINTER, remoteVerticesAdj, PETSC_OWN_POINTER);CHKERRQ(ierr);
2352   ierr = PetscFree(verticesAdj);CHKERRQ(ierr);
2353   /* Build pointSF */
2354   ierr = PetscMalloc2(numVerticesAdj, &vertexLocal, numVertices, &vertexOwner);CHKERRQ(ierr);
2355   for (v = 0; v < numVerticesAdj; ++v) {vertexLocal[v].index = v+numCells; vertexLocal[v].rank = rank;}
2356   for (v = 0; v < numVertices;    ++v) {vertexOwner[v].index = -1;         vertexOwner[v].rank = -1;}
2357   ierr = PetscSFReduceBegin(*sfVert, MPIU_2INT, vertexLocal, vertexOwner, MPI_MAXLOC);CHKERRQ(ierr);
2358   ierr = PetscSFReduceEnd(*sfVert, MPIU_2INT, vertexLocal, vertexOwner, MPI_MAXLOC);CHKERRQ(ierr);
2359   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);
2360   ierr = PetscSFBcastBegin(*sfVert, MPIU_2INT, vertexOwner, vertexLocal);CHKERRQ(ierr);
2361   ierr = PetscSFBcastEnd(*sfVert, MPIU_2INT, vertexOwner, vertexLocal);CHKERRQ(ierr);
2362   for (v = 0; v < numVerticesAdj; ++v) if (vertexLocal[v].rank != rank) ++numVerticesGhost;
2363   ierr = PetscMalloc1(numVerticesGhost, &localVertex);CHKERRQ(ierr);
2364   ierr = PetscMalloc1(numVerticesGhost, &remoteVertex);CHKERRQ(ierr);
2365   for (v = 0, g = 0; v < numVerticesAdj; ++v) {
2366     if (vertexLocal[v].rank != rank) {
2367       localVertex[g]        = v+numCells;
2368       remoteVertex[g].index = vertexLocal[v].index;
2369       remoteVertex[g].rank  = vertexLocal[v].rank;
2370       ++g;
2371     }
2372   }
2373   ierr = PetscFree2(vertexLocal, vertexOwner);CHKERRQ(ierr);
2374   if (g != numVerticesGhost) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid number of vertex ghosts %D should be %D", g, numVerticesGhost);
2375   ierr = DMGetPointSF(dm, &sfPoint);CHKERRQ(ierr);
2376   ierr = PetscObjectSetName((PetscObject) sfPoint, "point SF");CHKERRQ(ierr);
2377   ierr = PetscSFSetGraph(sfPoint, numCells+numVerticesAdj, numVerticesGhost, localVertex, PETSC_OWN_POINTER, remoteVertex, PETSC_OWN_POINTER);CHKERRQ(ierr);
2378   ierr = PetscLayoutDestroy(&vLayout);CHKERRQ(ierr);
2379   PetscHashIDestroy(vhash);
2380   /* Fill in the rest of the topology structure */
2381   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
2382   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
2383   PetscFunctionReturn(0);
2384 }
2385 
2386 /*
2387   This takes as input the coordinates for each owned vertex
2388 */
2389 static PetscErrorCode DMPlexBuildCoordinates_Parallel_Private(DM dm, PetscInt spaceDim, PetscInt numCells, PetscInt numV, PetscSF sfVert, const PetscReal vertexCoords[])
2390 {
2391   PetscSection   coordSection;
2392   Vec            coordinates;
2393   PetscScalar   *coords;
2394   PetscInt       numVertices, numVerticesAdj, coordSize, v;
2395   PetscErrorCode ierr;
2396 
2397   PetscFunctionBegin;
2398   ierr = DMSetCoordinateDim(dm, spaceDim);CHKERRQ(ierr);
2399   ierr = PetscSFGetGraph(sfVert, &numVertices, &numVerticesAdj, NULL, NULL);CHKERRQ(ierr);
2400   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
2401   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
2402   ierr = PetscSectionSetFieldComponents(coordSection, 0, spaceDim);CHKERRQ(ierr);
2403   ierr = PetscSectionSetChart(coordSection, numCells, numCells + numVerticesAdj);CHKERRQ(ierr);
2404   for (v = numCells; v < numCells+numVerticesAdj; ++v) {
2405     ierr = PetscSectionSetDof(coordSection, v, spaceDim);CHKERRQ(ierr);
2406     ierr = PetscSectionSetFieldDof(coordSection, v, 0, spaceDim);CHKERRQ(ierr);
2407   }
2408   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
2409   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
2410   ierr = VecCreate(PetscObjectComm((PetscObject)dm), &coordinates);CHKERRQ(ierr);
2411   ierr = VecSetBlockSize(coordinates, spaceDim);CHKERRQ(ierr);
2412   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
2413   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
2414   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
2415   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
2416   {
2417     MPI_Datatype coordtype;
2418 
2419     /* Need a temp buffer for coords if we have complex/single */
2420     ierr = MPI_Type_contiguous(spaceDim, MPIU_SCALAR, &coordtype);CHKERRQ(ierr);
2421     ierr = MPI_Type_commit(&coordtype);CHKERRQ(ierr);
2422 #if defined(PETSC_USE_COMPLEX)
2423     {
2424     PetscScalar *svertexCoords;
2425     PetscInt    i;
2426     ierr = PetscMalloc1(numV*spaceDim,&svertexCoords);CHKERRQ(ierr);
2427     for (i=0; i<numV*spaceDim; i++) svertexCoords[i] = vertexCoords[i];
2428     ierr = PetscSFBcastBegin(sfVert, coordtype, svertexCoords, coords);CHKERRQ(ierr);
2429     ierr = PetscSFBcastEnd(sfVert, coordtype, svertexCoords, coords);CHKERRQ(ierr);
2430     ierr = PetscFree(svertexCoords);CHKERRQ(ierr);
2431     }
2432 #else
2433     ierr = PetscSFBcastBegin(sfVert, coordtype, vertexCoords, coords);CHKERRQ(ierr);
2434     ierr = PetscSFBcastEnd(sfVert, coordtype, vertexCoords, coords);CHKERRQ(ierr);
2435 #endif
2436     ierr = MPI_Type_free(&coordtype);CHKERRQ(ierr);
2437   }
2438   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
2439   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
2440   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
2441   PetscFunctionReturn(0);
2442 }
2443 
2444 /*@C
2445   DMPlexCreateFromCellListParallel - This takes as input common mesh generator output, a list of the vertices for each cell, and produces a DM
2446 
2447   Input Parameters:
2448 + comm - The communicator
2449 . dim - The topological dimension of the mesh
2450 . numCells - The number of cells owned by this process
2451 . numVertices - The number of vertices owned by this process
2452 . numCorners - The number of vertices for each cell
2453 . interpolate - Flag indicating that intermediate mesh entities (faces, edges) should be created automatically
2454 . cells - An array of numCells*numCorners numbers, the global vertex numbers for each cell
2455 . spaceDim - The spatial dimension used for coordinates
2456 - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex
2457 
2458   Output Parameter:
2459 + dm - The DM
2460 - vertexSF - Optional, SF describing complete vertex ownership
2461 
2462   Note: Two triangles sharing a face
2463 $
2464 $        2
2465 $      / | \
2466 $     /  |  \
2467 $    /   |   \
2468 $   0  0 | 1  3
2469 $    \   |   /
2470 $     \  |  /
2471 $      \ | /
2472 $        1
2473 would have input
2474 $  numCells = 2, numVertices = 4
2475 $  cells = [0 1 2  1 3 2]
2476 $
2477 which would result in the DMPlex
2478 $
2479 $        4
2480 $      / | \
2481 $     /  |  \
2482 $    /   |   \
2483 $   2  0 | 1  5
2484 $    \   |   /
2485 $     \  |  /
2486 $      \ | /
2487 $        3
2488 
2489   Level: beginner
2490 
2491 .seealso: DMPlexCreateFromCellList(), DMPlexCreateFromDAG(), DMPlexCreate()
2492 @*/
2493 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)
2494 {
2495   PetscSF        sfVert;
2496   PetscErrorCode ierr;
2497 
2498   PetscFunctionBegin;
2499   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
2500   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
2501   PetscValidLogicalCollectiveInt(*dm, dim, 2);
2502   PetscValidLogicalCollectiveInt(*dm, spaceDim, 8);
2503   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
2504   ierr = DMPlexBuildFromCellList_Parallel_Private(*dm, numCells, numVertices, numCorners, cells, &sfVert);CHKERRQ(ierr);
2505   if (interpolate) {
2506     DM idm;
2507 
2508     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
2509     ierr = DMDestroy(dm);CHKERRQ(ierr);
2510     *dm  = idm;
2511   }
2512   ierr = DMPlexBuildCoordinates_Parallel_Private(*dm, spaceDim, numCells, numVertices,sfVert, vertexCoords);CHKERRQ(ierr);
2513   if (vertexSF) *vertexSF = sfVert;
2514   else {ierr = PetscSFDestroy(&sfVert);CHKERRQ(ierr);}
2515   PetscFunctionReturn(0);
2516 }
2517 
2518 /*
2519   This takes as input the common mesh generator output, a list of the vertices for each cell
2520 */
2521 static PetscErrorCode DMPlexBuildFromCellList_Private(DM dm, PetscInt numCells, PetscInt numVertices, PetscInt numCorners, const int cells[])
2522 {
2523   PetscInt      *cone, c, p;
2524   PetscErrorCode ierr;
2525 
2526   PetscFunctionBegin;
2527   ierr = DMPlexSetChart(dm, 0, numCells+numVertices);CHKERRQ(ierr);
2528   for (c = 0; c < numCells; ++c) {
2529     ierr = DMPlexSetConeSize(dm, c, numCorners);CHKERRQ(ierr);
2530   }
2531   ierr = DMSetUp(dm);CHKERRQ(ierr);
2532   ierr = DMGetWorkArray(dm, numCorners, MPIU_INT, &cone);CHKERRQ(ierr);
2533   for (c = 0; c < numCells; ++c) {
2534     for (p = 0; p < numCorners; ++p) {
2535       cone[p] = cells[c*numCorners+p]+numCells;
2536     }
2537     ierr = DMPlexSetCone(dm, c, cone);CHKERRQ(ierr);
2538   }
2539   ierr = DMRestoreWorkArray(dm, numCorners, MPIU_INT, &cone);CHKERRQ(ierr);
2540   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
2541   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
2542   PetscFunctionReturn(0);
2543 }
2544 
2545 /*
2546   This takes as input the coordinates for each vertex
2547 */
2548 static PetscErrorCode DMPlexBuildCoordinates_Private(DM dm, PetscInt spaceDim, PetscInt numCells, PetscInt numVertices, const double vertexCoords[])
2549 {
2550   PetscSection   coordSection;
2551   Vec            coordinates;
2552   DM             cdm;
2553   PetscScalar   *coords;
2554   PetscInt       v, d;
2555   PetscErrorCode ierr;
2556 
2557   PetscFunctionBegin;
2558   ierr = DMSetCoordinateDim(dm, spaceDim);CHKERRQ(ierr);
2559   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
2560   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
2561   ierr = PetscSectionSetFieldComponents(coordSection, 0, spaceDim);CHKERRQ(ierr);
2562   ierr = PetscSectionSetChart(coordSection, numCells, numCells + numVertices);CHKERRQ(ierr);
2563   for (v = numCells; v < numCells+numVertices; ++v) {
2564     ierr = PetscSectionSetDof(coordSection, v, spaceDim);CHKERRQ(ierr);
2565     ierr = PetscSectionSetFieldDof(coordSection, v, 0, spaceDim);CHKERRQ(ierr);
2566   }
2567   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
2568 
2569   ierr = DMGetCoordinateDM(dm, &cdm);CHKERRQ(ierr);
2570   ierr = DMCreateLocalVector(cdm, &coordinates);CHKERRQ(ierr);
2571   ierr = VecSetBlockSize(coordinates, spaceDim);CHKERRQ(ierr);
2572   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
2573   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
2574   for (v = 0; v < numVertices; ++v) {
2575     for (d = 0; d < spaceDim; ++d) {
2576       coords[v*spaceDim+d] = vertexCoords[v*spaceDim+d];
2577     }
2578   }
2579   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
2580   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
2581   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
2582   PetscFunctionReturn(0);
2583 }
2584 
2585 /*@C
2586   DMPlexCreateFromCellList - This takes as input common mesh generator output, a list of the vertices for each cell, and produces a DM
2587 
2588   Input Parameters:
2589 + comm - The communicator
2590 . dim - The topological dimension of the mesh
2591 . numCells - The number of cells
2592 . numVertices - The number of vertices
2593 . numCorners - The number of vertices for each cell
2594 . interpolate - Flag indicating that intermediate mesh entities (faces, edges) should be created automatically
2595 . cells - An array of numCells*numCorners numbers, the vertices for each cell
2596 . spaceDim - The spatial dimension used for coordinates
2597 - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex
2598 
2599   Output Parameter:
2600 . dm - The DM
2601 
2602   Note: Two triangles sharing a face
2603 $
2604 $        2
2605 $      / | \
2606 $     /  |  \
2607 $    /   |   \
2608 $   0  0 | 1  3
2609 $    \   |   /
2610 $     \  |  /
2611 $      \ | /
2612 $        1
2613 would have input
2614 $  numCells = 2, numVertices = 4
2615 $  cells = [0 1 2  1 3 2]
2616 $
2617 which would result in the DMPlex
2618 $
2619 $        4
2620 $      / | \
2621 $     /  |  \
2622 $    /   |   \
2623 $   2  0 | 1  5
2624 $    \   |   /
2625 $     \  |  /
2626 $      \ | /
2627 $        3
2628 
2629   Level: beginner
2630 
2631 .seealso: DMPlexCreateFromDAG(), DMPlexCreate()
2632 @*/
2633 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)
2634 {
2635   PetscErrorCode ierr;
2636 
2637   PetscFunctionBegin;
2638   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
2639   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
2640   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
2641   ierr = DMPlexBuildFromCellList_Private(*dm, numCells, numVertices, numCorners, cells);CHKERRQ(ierr);
2642   if (interpolate) {
2643     DM idm;
2644 
2645     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
2646     ierr = DMDestroy(dm);CHKERRQ(ierr);
2647     *dm  = idm;
2648   }
2649   ierr = DMPlexBuildCoordinates_Private(*dm, spaceDim, numCells, numVertices, vertexCoords);CHKERRQ(ierr);
2650   PetscFunctionReturn(0);
2651 }
2652 
2653 /*@
2654   DMPlexCreateFromDAG - This takes as input the adjacency-list representation of the Directed Acyclic Graph (Hasse Diagram) encoding a mesh, and produces a DM
2655 
2656   Input Parameters:
2657 + dm - The empty DM object, usually from DMCreate() and DMSetDimension()
2658 . depth - The depth of the DAG
2659 . numPoints - The number of points at each depth
2660 . coneSize - The cone size of each point
2661 . cones - The concatenation of the cone points for each point, the cone list must be oriented correctly for each point
2662 . coneOrientations - The orientation of each cone point
2663 - vertexCoords - An array of numVertices*dim numbers, the coordinates of each vertex
2664 
2665   Output Parameter:
2666 . dm - The DM
2667 
2668   Note: Two triangles sharing a face would have input
2669 $  depth = 1, numPoints = [4 2], coneSize = [3 3 0 0 0 0]
2670 $  cones = [2 3 4  3 5 4], coneOrientations = [0 0 0  0 0 0]
2671 $ vertexCoords = [-1.0 0.0  0.0 -1.0  0.0 1.0  1.0 0.0]
2672 $
2673 which would result in the DMPlex
2674 $
2675 $        4
2676 $      / | \
2677 $     /  |  \
2678 $    /   |   \
2679 $   2  0 | 1  5
2680 $    \   |   /
2681 $     \  |  /
2682 $      \ | /
2683 $        3
2684 $
2685 $ Notice that all points are numbered consecutively, unlikely DMPlexCreateFromCellList()
2686 
2687   Level: advanced
2688 
2689 .seealso: DMPlexCreateFromCellList(), DMPlexCreate()
2690 @*/
2691 PetscErrorCode DMPlexCreateFromDAG(DM dm, PetscInt depth, const PetscInt numPoints[], const PetscInt coneSize[], const PetscInt cones[], const PetscInt coneOrientations[], const PetscScalar vertexCoords[])
2692 {
2693   Vec            coordinates;
2694   PetscSection   coordSection;
2695   PetscScalar    *coords;
2696   PetscInt       coordSize, firstVertex = -1, pStart = 0, pEnd = 0, p, v, dim, dimEmbed, d, off;
2697   PetscErrorCode ierr;
2698 
2699   PetscFunctionBegin;
2700   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
2701   ierr = DMGetCoordinateDim(dm, &dimEmbed);CHKERRQ(ierr);
2702   if (dimEmbed < dim) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Embedding dimension %d cannot be less than intrinsic dimension %d",dimEmbed,dim);
2703   for (d = 0; d <= depth; ++d) pEnd += numPoints[d];
2704   ierr = DMPlexSetChart(dm, pStart, pEnd);CHKERRQ(ierr);
2705   for (p = pStart; p < pEnd; ++p) {
2706     ierr = DMPlexSetConeSize(dm, p, coneSize[p-pStart]);CHKERRQ(ierr);
2707     if (firstVertex < 0 && !coneSize[p - pStart]) {
2708       firstVertex = p - pStart;
2709     }
2710   }
2711   if (firstVertex < 0 && numPoints[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Expected %d vertices but could not find any", numPoints[0]);
2712   ierr = DMSetUp(dm);CHKERRQ(ierr); /* Allocate space for cones */
2713   for (p = pStart, off = 0; p < pEnd; off += coneSize[p-pStart], ++p) {
2714     ierr = DMPlexSetCone(dm, p, &cones[off]);CHKERRQ(ierr);
2715     ierr = DMPlexSetConeOrientation(dm, p, &coneOrientations[off]);CHKERRQ(ierr);
2716   }
2717   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
2718   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
2719   /* Build coordinates */
2720   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
2721   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
2722   ierr = PetscSectionSetFieldComponents(coordSection, 0, dimEmbed);CHKERRQ(ierr);
2723   ierr = PetscSectionSetChart(coordSection, firstVertex, firstVertex+numPoints[0]);CHKERRQ(ierr);
2724   for (v = firstVertex; v < firstVertex+numPoints[0]; ++v) {
2725     ierr = PetscSectionSetDof(coordSection, v, dimEmbed);CHKERRQ(ierr);
2726     ierr = PetscSectionSetFieldDof(coordSection, v, 0, dimEmbed);CHKERRQ(ierr);
2727   }
2728   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
2729   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
2730   ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
2731   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
2732   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
2733   ierr = VecSetBlockSize(coordinates, dimEmbed);CHKERRQ(ierr);
2734   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
2735   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
2736   for (v = 0; v < numPoints[0]; ++v) {
2737     PetscInt off;
2738 
2739     ierr = PetscSectionGetOffset(coordSection, v+firstVertex, &off);CHKERRQ(ierr);
2740     for (d = 0; d < dimEmbed; ++d) {
2741       coords[off+d] = vertexCoords[v*dimEmbed+d];
2742     }
2743   }
2744   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
2745   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
2746   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
2747   PetscFunctionReturn(0);
2748 }
2749 
2750 /*@C
2751   DMPlexCreateFromFile - This takes a filename and produces a DM
2752 
2753   Input Parameters:
2754 + comm - The communicator
2755 . filename - A file name
2756 - interpolate - Flag to create intermediate mesh pieces (edges, faces)
2757 
2758   Output Parameter:
2759 . dm - The DM
2760 
2761   Level: beginner
2762 
2763 .seealso: DMPlexCreateFromDAG(), DMPlexCreateFromCellList(), DMPlexCreate()
2764 @*/
2765 PetscErrorCode DMPlexCreateFromFile(MPI_Comm comm, const char filename[], PetscBool interpolate, DM *dm)
2766 {
2767   const char    *extGmsh    = ".msh";
2768   const char    *extCGNS    = ".cgns";
2769   const char    *extExodus  = ".exo";
2770   const char    *extGenesis = ".gen";
2771   const char    *extFluent  = ".cas";
2772   const char    *extHDF5    = ".h5";
2773   const char    *extMed     = ".med";
2774   const char    *extPLY     = ".ply";
2775   size_t         len;
2776   PetscBool      isGmsh, isCGNS, isExodus, isGenesis, isFluent, isHDF5, isMed, isPLY;
2777   PetscMPIInt    rank;
2778   PetscErrorCode ierr;
2779 
2780   PetscFunctionBegin;
2781   PetscValidPointer(filename, 2);
2782   PetscValidPointer(dm, 4);
2783   ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
2784   ierr = PetscStrlen(filename, &len);CHKERRQ(ierr);
2785   if (!len) SETERRQ(comm, PETSC_ERR_ARG_WRONG, "Filename must be a valid path");
2786   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extGmsh,    4, &isGmsh);CHKERRQ(ierr);
2787   ierr = PetscStrncmp(&filename[PetscMax(0,len-5)], extCGNS,    5, &isCGNS);CHKERRQ(ierr);
2788   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extExodus,  4, &isExodus);CHKERRQ(ierr);
2789   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extGenesis, 4, &isGenesis);CHKERRQ(ierr);
2790   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extFluent,  4, &isFluent);CHKERRQ(ierr);
2791   ierr = PetscStrncmp(&filename[PetscMax(0,len-3)], extHDF5,    3, &isHDF5);CHKERRQ(ierr);
2792   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extMed,     4, &isMed);CHKERRQ(ierr);
2793   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extPLY,     4, &isPLY);CHKERRQ(ierr);
2794   if (isGmsh) {
2795     ierr = DMPlexCreateGmshFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
2796   } else if (isCGNS) {
2797     ierr = DMPlexCreateCGNSFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
2798   } else if (isExodus || isGenesis) {
2799     ierr = DMPlexCreateExodusFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
2800   } else if (isFluent) {
2801     ierr = DMPlexCreateFluentFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
2802   } else if (isHDF5) {
2803     PetscViewer viewer;
2804 
2805     ierr = PetscViewerCreate(comm, &viewer);CHKERRQ(ierr);
2806     ierr = PetscViewerSetType(viewer, PETSCVIEWERHDF5);CHKERRQ(ierr);
2807     ierr = PetscViewerFileSetMode(viewer, FILE_MODE_READ);CHKERRQ(ierr);
2808     ierr = PetscViewerFileSetName(viewer, filename);CHKERRQ(ierr);
2809     ierr = DMCreate(comm, dm);CHKERRQ(ierr);
2810     ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
2811     ierr = DMLoad(*dm, viewer);CHKERRQ(ierr);
2812     ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
2813 
2814     if (interpolate) {
2815       DM idm;
2816 
2817       ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
2818       ierr = DMDestroy(dm);CHKERRQ(ierr);
2819       *dm  = idm;
2820     }
2821   } else if (isMed) {
2822     ierr = DMPlexCreateMedFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
2823   } else if (isPLY) {
2824     ierr = DMPlexCreatePLYFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
2825   } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cannot load file %s: unrecognized extension", filename);
2826   PetscFunctionReturn(0);
2827 }
2828 
2829 /*@
2830   DMPlexCreateReferenceCell - Create a DMPLEX with the appropriate FEM reference cell
2831 
2832   Collective on comm
2833 
2834   Input Parameters:
2835 + comm    - The communicator
2836 . dim     - The spatial dimension
2837 - simplex - Flag for simplex, otherwise use a tensor-product cell
2838 
2839   Output Parameter:
2840 . refdm - The reference cell
2841 
2842   Level: intermediate
2843 
2844 .keywords: reference cell
2845 .seealso:
2846 @*/
2847 PetscErrorCode DMPlexCreateReferenceCell(MPI_Comm comm, PetscInt dim, PetscBool simplex, DM *refdm)
2848 {
2849   DM             rdm;
2850   Vec            coords;
2851   PetscErrorCode ierr;
2852 
2853   PetscFunctionBeginUser;
2854   ierr = DMCreate(comm, &rdm);CHKERRQ(ierr);
2855   ierr = DMSetType(rdm, DMPLEX);CHKERRQ(ierr);
2856   ierr = DMSetDimension(rdm, dim);CHKERRQ(ierr);
2857   switch (dim) {
2858   case 0:
2859   {
2860     PetscInt    numPoints[1]        = {1};
2861     PetscInt    coneSize[1]         = {0};
2862     PetscInt    cones[1]            = {0};
2863     PetscInt    coneOrientations[1] = {0};
2864     PetscScalar vertexCoords[1]     = {0.0};
2865 
2866     ierr = DMPlexCreateFromDAG(rdm, 0, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2867   }
2868   break;
2869   case 1:
2870   {
2871     PetscInt    numPoints[2]        = {2, 1};
2872     PetscInt    coneSize[3]         = {2, 0, 0};
2873     PetscInt    cones[2]            = {1, 2};
2874     PetscInt    coneOrientations[2] = {0, 0};
2875     PetscScalar vertexCoords[2]     = {-1.0,  1.0};
2876 
2877     ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2878   }
2879   break;
2880   case 2:
2881     if (simplex) {
2882       PetscInt    numPoints[2]        = {3, 1};
2883       PetscInt    coneSize[4]         = {3, 0, 0, 0};
2884       PetscInt    cones[3]            = {1, 2, 3};
2885       PetscInt    coneOrientations[3] = {0, 0, 0};
2886       PetscScalar vertexCoords[6]     = {-1.0, -1.0,  1.0, -1.0,  -1.0, 1.0};
2887 
2888       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2889     } else {
2890       PetscInt    numPoints[2]        = {4, 1};
2891       PetscInt    coneSize[5]         = {4, 0, 0, 0, 0};
2892       PetscInt    cones[4]            = {1, 2, 3, 4};
2893       PetscInt    coneOrientations[4] = {0, 0, 0, 0};
2894       PetscScalar vertexCoords[8]     = {-1.0, -1.0,  1.0, -1.0,  1.0, 1.0,  -1.0, 1.0};
2895 
2896       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2897     }
2898   break;
2899   case 3:
2900     if (simplex) {
2901       PetscInt    numPoints[2]        = {4, 1};
2902       PetscInt    coneSize[5]         = {4, 0, 0, 0, 0};
2903       PetscInt    cones[4]            = {1, 3, 2, 4};
2904       PetscInt    coneOrientations[4] = {0, 0, 0, 0};
2905       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};
2906 
2907       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2908     } else {
2909       PetscInt    numPoints[2]        = {8, 1};
2910       PetscInt    coneSize[9]         = {8, 0, 0, 0, 0, 0, 0, 0, 0};
2911       PetscInt    cones[8]            = {1, 4, 3, 2, 5, 6, 7, 8};
2912       PetscInt    coneOrientations[8] = {0, 0, 0, 0, 0, 0, 0, 0};
2913       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,
2914                                          -1.0, -1.0,  1.0,  1.0, -1.0,  1.0,  1.0, 1.0,  1.0,  -1.0, 1.0,  1.0};
2915 
2916       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
2917     }
2918   break;
2919   default:
2920     SETERRQ1(comm, PETSC_ERR_ARG_WRONG, "Cannot create reference cell for dimension %d", dim);
2921   }
2922   ierr = DMPlexInterpolate(rdm, refdm);CHKERRQ(ierr);
2923   if (rdm->coordinateDM) {
2924     DM           ncdm;
2925     PetscSection cs;
2926     PetscInt     pEnd = -1;
2927 
2928     ierr = DMGetDefaultSection(rdm->coordinateDM, &cs);CHKERRQ(ierr);
2929     if (cs) {ierr = PetscSectionGetChart(cs, NULL, &pEnd);CHKERRQ(ierr);}
2930     if (pEnd >= 0) {
2931       ierr = DMClone(rdm->coordinateDM, &ncdm);CHKERRQ(ierr);
2932       ierr = DMSetDefaultSection(ncdm, cs);CHKERRQ(ierr);
2933       ierr = DMSetCoordinateDM(*refdm, ncdm);CHKERRQ(ierr);
2934       ierr = DMDestroy(&ncdm);CHKERRQ(ierr);
2935     }
2936   }
2937   ierr = DMGetCoordinatesLocal(rdm, &coords);CHKERRQ(ierr);
2938   if (coords) {
2939     ierr = DMSetCoordinatesLocal(*refdm, coords);CHKERRQ(ierr);
2940   } else {
2941     ierr = DMGetCoordinates(rdm, &coords);CHKERRQ(ierr);
2942     if (coords) {ierr = DMSetCoordinates(*refdm, coords);CHKERRQ(ierr);}
2943   }
2944   ierr = DMDestroy(&rdm);CHKERRQ(ierr);
2945   PetscFunctionReturn(0);
2946 }
2947