xref: /petsc/src/dm/impls/plex/plexcreate.c (revision 5b6bfdb9644f185dbf5e5a09b808ec241507e1e7)
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 DMHasCreateInjection_Plex(DM dm, PetscBool *flg)
2121 {
2122   PetscFunctionBegin;
2123   PetscValidHeaderSpecific(dm,DM_CLASSID,1);
2124   PetscValidPointer(flg,2);
2125   *flg = PETSC_TRUE;
2126   PetscFunctionReturn(0);
2127 }
2128 
2129 static PetscErrorCode DMInitialize_Plex(DM dm)
2130 {
2131   PetscErrorCode ierr;
2132 
2133   PetscFunctionBegin;
2134   dm->ops->view                            = DMView_Plex;
2135   dm->ops->load                            = DMLoad_Plex;
2136   dm->ops->setfromoptions                  = DMSetFromOptions_Plex;
2137   dm->ops->clone                           = DMClone_Plex;
2138   dm->ops->setup                           = DMSetUp_Plex;
2139   dm->ops->createdefaultsection            = DMCreateDefaultSection_Plex;
2140   dm->ops->createdefaultconstraints        = DMCreateDefaultConstraints_Plex;
2141   dm->ops->createglobalvector              = DMCreateGlobalVector_Plex;
2142   dm->ops->createlocalvector               = DMCreateLocalVector_Plex;
2143   dm->ops->getlocaltoglobalmapping         = NULL;
2144   dm->ops->createfieldis                   = NULL;
2145   dm->ops->createcoordinatedm              = DMCreateCoordinateDM_Plex;
2146   dm->ops->getcoloring                     = NULL;
2147   dm->ops->creatematrix                    = DMCreateMatrix_Plex;
2148   dm->ops->createinterpolation             = DMCreateInterpolation_Plex;
2149   dm->ops->createmassmatrix                = DMCreateMassMatrix_Plex;
2150   dm->ops->getaggregates                   = NULL;
2151   dm->ops->getinjection                    = DMCreateInjection_Plex;
2152   dm->ops->hascreateinjection              = DMHasCreateInjection_Plex;
2153   dm->ops->refine                          = DMRefine_Plex;
2154   dm->ops->coarsen                         = DMCoarsen_Plex;
2155   dm->ops->refinehierarchy                 = DMRefineHierarchy_Plex;
2156   dm->ops->coarsenhierarchy                = DMCoarsenHierarchy_Plex;
2157   dm->ops->adaptlabel                      = DMAdaptLabel_Plex;
2158   dm->ops->adaptmetric                     = DMAdaptMetric_Plex;
2159   dm->ops->globaltolocalbegin              = NULL;
2160   dm->ops->globaltolocalend                = NULL;
2161   dm->ops->localtoglobalbegin              = NULL;
2162   dm->ops->localtoglobalend                = NULL;
2163   dm->ops->destroy                         = DMDestroy_Plex;
2164   dm->ops->createsubdm                     = DMCreateSubDM_Plex;
2165   dm->ops->createsuperdm                   = DMCreateSuperDM_Plex;
2166   dm->ops->getdimpoints                    = DMGetDimPoints_Plex;
2167   dm->ops->locatepoints                    = DMLocatePoints_Plex;
2168   dm->ops->projectfunctionlocal            = DMProjectFunctionLocal_Plex;
2169   dm->ops->projectfunctionlabellocal       = DMProjectFunctionLabelLocal_Plex;
2170   dm->ops->projectfieldlocal               = DMProjectFieldLocal_Plex;
2171   dm->ops->projectfieldlabellocal          = DMProjectFieldLabelLocal_Plex;
2172   dm->ops->computel2diff                   = DMComputeL2Diff_Plex;
2173   dm->ops->computel2gradientdiff           = DMComputeL2GradientDiff_Plex;
2174   dm->ops->computel2fielddiff              = DMComputeL2FieldDiff_Plex;
2175   dm->ops->getneighbors                    = DMGetNeighors_Plex;
2176   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMPlexInsertBoundaryValues_C",DMPlexInsertBoundaryValues_Plex);CHKERRQ(ierr);
2177   ierr = PetscObjectComposeFunction((PetscObject)dm,"DMSetUpGLVisViewer_C",DMSetUpGLVisViewer_Plex);CHKERRQ(ierr);
2178   PetscFunctionReturn(0);
2179 }
2180 
2181 PETSC_INTERN PetscErrorCode DMClone_Plex(DM dm, DM *newdm)
2182 {
2183   DM_Plex        *mesh = (DM_Plex *) dm->data;
2184   PetscErrorCode ierr;
2185 
2186   PetscFunctionBegin;
2187   mesh->refct++;
2188   (*newdm)->data = mesh;
2189   ierr = PetscObjectChangeTypeName((PetscObject) *newdm, DMPLEX);CHKERRQ(ierr);
2190   ierr = DMInitialize_Plex(*newdm);CHKERRQ(ierr);
2191   PetscFunctionReturn(0);
2192 }
2193 
2194 /*MC
2195   DMPLEX = "plex" - A DM object that encapsulates an unstructured mesh, or CW Complex, which can be expressed using a Hasse Diagram.
2196                     In the local representation, Vecs contain all unknowns in the interior and shared boundary. This is
2197                     specified by a PetscSection object. Ownership in the global representation is determined by
2198                     ownership of the underlying DMPlex points. This is specified by another PetscSection object.
2199 
2200   Level: intermediate
2201 
2202 .seealso: DMType, DMPlexCreate(), DMCreate(), DMSetType()
2203 M*/
2204 
2205 PETSC_EXTERN PetscErrorCode DMCreate_Plex(DM dm)
2206 {
2207   DM_Plex        *mesh;
2208   PetscInt       unit, d;
2209   PetscErrorCode ierr;
2210 
2211   PetscFunctionBegin;
2212   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
2213   ierr     = PetscNewLog(dm,&mesh);CHKERRQ(ierr);
2214   dm->dim  = 0;
2215   dm->data = mesh;
2216 
2217   mesh->refct             = 1;
2218   ierr                    = PetscSectionCreate(PetscObjectComm((PetscObject)dm), &mesh->coneSection);CHKERRQ(ierr);
2219   mesh->maxConeSize       = 0;
2220   mesh->cones             = NULL;
2221   mesh->coneOrientations  = NULL;
2222   ierr                    = PetscSectionCreate(PetscObjectComm((PetscObject)dm), &mesh->supportSection);CHKERRQ(ierr);
2223   mesh->maxSupportSize    = 0;
2224   mesh->supports          = NULL;
2225   mesh->refinementUniform = PETSC_TRUE;
2226   mesh->refinementLimit   = -1.0;
2227 
2228   mesh->facesTmp = NULL;
2229 
2230   mesh->tetgenOpts   = NULL;
2231   mesh->triangleOpts = NULL;
2232   ierr = PetscPartitionerCreate(PetscObjectComm((PetscObject)dm), &mesh->partitioner);CHKERRQ(ierr);
2233   mesh->remeshBd     = PETSC_FALSE;
2234 
2235   mesh->subpointMap = NULL;
2236 
2237   for (unit = 0; unit < NUM_PETSC_UNITS; ++unit) mesh->scale[unit] = 1.0;
2238 
2239   mesh->regularRefinement   = PETSC_FALSE;
2240   mesh->depthState          = -1;
2241   mesh->globalVertexNumbers = NULL;
2242   mesh->globalCellNumbers   = NULL;
2243   mesh->anchorSection       = NULL;
2244   mesh->anchorIS            = NULL;
2245   mesh->createanchors       = NULL;
2246   mesh->computeanchormatrix = NULL;
2247   mesh->parentSection       = NULL;
2248   mesh->parents             = NULL;
2249   mesh->childIDs            = NULL;
2250   mesh->childSection        = NULL;
2251   mesh->children            = NULL;
2252   mesh->referenceTree       = NULL;
2253   mesh->getchildsymmetry    = NULL;
2254   for (d = 0; d < 8; ++d) mesh->hybridPointMax[d] = PETSC_DETERMINE;
2255   mesh->vtkCellHeight       = 0;
2256   mesh->useAnchors          = PETSC_FALSE;
2257 
2258   mesh->maxProjectionHeight = 0;
2259 
2260   mesh->printSetValues = PETSC_FALSE;
2261   mesh->printFEM       = 0;
2262   mesh->printTol       = 1.0e-10;
2263 
2264   ierr = DMInitialize_Plex(dm);CHKERRQ(ierr);
2265   PetscFunctionReturn(0);
2266 }
2267 
2268 /*@
2269   DMPlexCreate - Creates a DMPlex object, which encapsulates an unstructured mesh, or CW complex, which can be expressed using a Hasse Diagram.
2270 
2271   Collective on MPI_Comm
2272 
2273   Input Parameter:
2274 . comm - The communicator for the DMPlex object
2275 
2276   Output Parameter:
2277 . mesh  - The DMPlex object
2278 
2279   Level: beginner
2280 
2281 .keywords: DMPlex, create
2282 @*/
2283 PetscErrorCode DMPlexCreate(MPI_Comm comm, DM *mesh)
2284 {
2285   PetscErrorCode ierr;
2286 
2287   PetscFunctionBegin;
2288   PetscValidPointer(mesh,2);
2289   ierr = DMCreate(comm, mesh);CHKERRQ(ierr);
2290   ierr = DMSetType(*mesh, DMPLEX);CHKERRQ(ierr);
2291   PetscFunctionReturn(0);
2292 }
2293 
2294 /*
2295   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
2296 */
2297 static PetscErrorCode DMPlexBuildFromCellList_Parallel_Private(DM dm, PetscInt numCells, PetscInt numVertices, PetscInt numCorners, const int cells[], PetscSF *sfVert)
2298 {
2299   PetscSF         sfPoint;
2300   PetscLayout     vLayout;
2301   PetscHashI      vhash;
2302   PetscSFNode    *remoteVerticesAdj, *vertexLocal, *vertexOwner, *remoteVertex;
2303   const PetscInt *vrange;
2304   PetscInt        numVerticesAdj, off, *verticesAdj, numVerticesGhost = 0, *localVertex, *cone, c, p, v, g;
2305   PETSC_UNUSED PetscHashIIter ret, iter;
2306   PetscMPIInt     rank, size;
2307   PetscErrorCode  ierr;
2308 
2309   PetscFunctionBegin;
2310   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject) dm), &rank);CHKERRQ(ierr);
2311   ierr = MPI_Comm_size(PetscObjectComm((PetscObject) dm), &size);CHKERRQ(ierr);
2312   /* Partition vertices */
2313   ierr = PetscLayoutCreate(PetscObjectComm((PetscObject) dm), &vLayout);CHKERRQ(ierr);
2314   ierr = PetscLayoutSetLocalSize(vLayout, numVertices);CHKERRQ(ierr);
2315   ierr = PetscLayoutSetBlockSize(vLayout, 1);CHKERRQ(ierr);
2316   ierr = PetscLayoutSetUp(vLayout);CHKERRQ(ierr);
2317   ierr = PetscLayoutGetRanges(vLayout, &vrange);CHKERRQ(ierr);
2318   /* Count vertices and map them to procs */
2319   PetscHashICreate(vhash);
2320   for (c = 0; c < numCells; ++c) {
2321     for (p = 0; p < numCorners; ++p) {
2322       PetscHashIPut(vhash, cells[c*numCorners+p], ret, iter);
2323     }
2324   }
2325   PetscHashISize(vhash, numVerticesAdj);
2326   ierr = PetscMalloc1(numVerticesAdj, &verticesAdj);CHKERRQ(ierr);
2327   off = 0; ierr = PetscHashIGetKeys(vhash, &off, verticesAdj);CHKERRQ(ierr);
2328   if (off != numVerticesAdj) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Invalid number of local vertices %D should be %D", off, numVerticesAdj);
2329   ierr = PetscSortInt(numVerticesAdj, verticesAdj);CHKERRQ(ierr);
2330   ierr = PetscMalloc1(numVerticesAdj, &remoteVerticesAdj);CHKERRQ(ierr);
2331   for (v = 0; v < numVerticesAdj; ++v) {
2332     const PetscInt gv = verticesAdj[v];
2333     PetscInt       vrank;
2334 
2335     ierr = PetscFindInt(gv, size+1, vrange, &vrank);CHKERRQ(ierr);
2336     vrank = vrank < 0 ? -(vrank+2) : vrank;
2337     remoteVerticesAdj[v].index = gv - vrange[vrank];
2338     remoteVerticesAdj[v].rank  = vrank;
2339   }
2340   /* Create cones */
2341   ierr = DMPlexSetChart(dm, 0, numCells+numVerticesAdj);CHKERRQ(ierr);
2342   for (c = 0; c < numCells; ++c) {ierr = DMPlexSetConeSize(dm, c, numCorners);CHKERRQ(ierr);}
2343   ierr = DMSetUp(dm);CHKERRQ(ierr);
2344   ierr = DMGetWorkArray(dm, numCorners, MPIU_INT, &cone);CHKERRQ(ierr);
2345   for (c = 0; c < numCells; ++c) {
2346     for (p = 0; p < numCorners; ++p) {
2347       const PetscInt gv = cells[c*numCorners+p];
2348       PetscInt       lv;
2349 
2350       ierr = PetscFindInt(gv, numVerticesAdj, verticesAdj, &lv);CHKERRQ(ierr);
2351       if (lv < 0) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Could not find global vertex %D in local connectivity", gv);
2352       cone[p] = lv+numCells;
2353     }
2354     ierr = DMPlexSetCone(dm, c, cone);CHKERRQ(ierr);
2355   }
2356   ierr = DMRestoreWorkArray(dm, numCorners, MPIU_INT, &cone);CHKERRQ(ierr);
2357   /* Create SF for vertices */
2358   ierr = PetscSFCreate(PetscObjectComm((PetscObject)dm), sfVert);CHKERRQ(ierr);
2359   ierr = PetscObjectSetName((PetscObject) *sfVert, "Vertex Ownership SF");CHKERRQ(ierr);
2360   ierr = PetscSFSetFromOptions(*sfVert);CHKERRQ(ierr);
2361   ierr = PetscSFSetGraph(*sfVert, numVertices, numVerticesAdj, NULL, PETSC_OWN_POINTER, remoteVerticesAdj, PETSC_OWN_POINTER);CHKERRQ(ierr);
2362   ierr = PetscFree(verticesAdj);CHKERRQ(ierr);
2363   /* Build pointSF */
2364   ierr = PetscMalloc2(numVerticesAdj, &vertexLocal, numVertices, &vertexOwner);CHKERRQ(ierr);
2365   for (v = 0; v < numVerticesAdj; ++v) {vertexLocal[v].index = v+numCells; vertexLocal[v].rank = rank;}
2366   for (v = 0; v < numVertices;    ++v) {vertexOwner[v].index = -1;         vertexOwner[v].rank = -1;}
2367   ierr = PetscSFReduceBegin(*sfVert, MPIU_2INT, vertexLocal, vertexOwner, MPI_MAXLOC);CHKERRQ(ierr);
2368   ierr = PetscSFReduceEnd(*sfVert, MPIU_2INT, vertexLocal, vertexOwner, MPI_MAXLOC);CHKERRQ(ierr);
2369   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);
2370   ierr = PetscSFBcastBegin(*sfVert, MPIU_2INT, vertexOwner, vertexLocal);CHKERRQ(ierr);
2371   ierr = PetscSFBcastEnd(*sfVert, MPIU_2INT, vertexOwner, vertexLocal);CHKERRQ(ierr);
2372   for (v = 0; v < numVerticesAdj; ++v) if (vertexLocal[v].rank != rank) ++numVerticesGhost;
2373   ierr = PetscMalloc1(numVerticesGhost, &localVertex);CHKERRQ(ierr);
2374   ierr = PetscMalloc1(numVerticesGhost, &remoteVertex);CHKERRQ(ierr);
2375   for (v = 0, g = 0; v < numVerticesAdj; ++v) {
2376     if (vertexLocal[v].rank != rank) {
2377       localVertex[g]        = v+numCells;
2378       remoteVertex[g].index = vertexLocal[v].index;
2379       remoteVertex[g].rank  = vertexLocal[v].rank;
2380       ++g;
2381     }
2382   }
2383   ierr = PetscFree2(vertexLocal, vertexOwner);CHKERRQ(ierr);
2384   if (g != numVerticesGhost) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid number of vertex ghosts %D should be %D", g, numVerticesGhost);
2385   ierr = DMGetPointSF(dm, &sfPoint);CHKERRQ(ierr);
2386   ierr = PetscObjectSetName((PetscObject) sfPoint, "point SF");CHKERRQ(ierr);
2387   ierr = PetscSFSetGraph(sfPoint, numCells+numVerticesAdj, numVerticesGhost, localVertex, PETSC_OWN_POINTER, remoteVertex, PETSC_OWN_POINTER);CHKERRQ(ierr);
2388   ierr = PetscLayoutDestroy(&vLayout);CHKERRQ(ierr);
2389   PetscHashIDestroy(vhash);
2390   /* Fill in the rest of the topology structure */
2391   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
2392   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
2393   PetscFunctionReturn(0);
2394 }
2395 
2396 /*
2397   This takes as input the coordinates for each owned vertex
2398 */
2399 static PetscErrorCode DMPlexBuildCoordinates_Parallel_Private(DM dm, PetscInt spaceDim, PetscInt numCells, PetscInt numV, PetscSF sfVert, const PetscReal vertexCoords[])
2400 {
2401   PetscSection   coordSection;
2402   Vec            coordinates;
2403   PetscScalar   *coords;
2404   PetscInt       numVertices, numVerticesAdj, coordSize, v;
2405   PetscErrorCode ierr;
2406 
2407   PetscFunctionBegin;
2408   ierr = DMSetCoordinateDim(dm, spaceDim);CHKERRQ(ierr);
2409   ierr = PetscSFGetGraph(sfVert, &numVertices, &numVerticesAdj, NULL, NULL);CHKERRQ(ierr);
2410   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
2411   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
2412   ierr = PetscSectionSetFieldComponents(coordSection, 0, spaceDim);CHKERRQ(ierr);
2413   ierr = PetscSectionSetChart(coordSection, numCells, numCells + numVerticesAdj);CHKERRQ(ierr);
2414   for (v = numCells; v < numCells+numVerticesAdj; ++v) {
2415     ierr = PetscSectionSetDof(coordSection, v, spaceDim);CHKERRQ(ierr);
2416     ierr = PetscSectionSetFieldDof(coordSection, v, 0, spaceDim);CHKERRQ(ierr);
2417   }
2418   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
2419   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
2420   ierr = VecCreate(PetscObjectComm((PetscObject)dm), &coordinates);CHKERRQ(ierr);
2421   ierr = VecSetBlockSize(coordinates, spaceDim);CHKERRQ(ierr);
2422   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
2423   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
2424   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
2425   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
2426   {
2427     MPI_Datatype coordtype;
2428 
2429     /* Need a temp buffer for coords if we have complex/single */
2430     ierr = MPI_Type_contiguous(spaceDim, MPIU_SCALAR, &coordtype);CHKERRQ(ierr);
2431     ierr = MPI_Type_commit(&coordtype);CHKERRQ(ierr);
2432 #if defined(PETSC_USE_COMPLEX)
2433     {
2434     PetscScalar *svertexCoords;
2435     PetscInt    i;
2436     ierr = PetscMalloc1(numV*spaceDim,&svertexCoords);CHKERRQ(ierr);
2437     for (i=0; i<numV*spaceDim; i++) svertexCoords[i] = vertexCoords[i];
2438     ierr = PetscSFBcastBegin(sfVert, coordtype, svertexCoords, coords);CHKERRQ(ierr);
2439     ierr = PetscSFBcastEnd(sfVert, coordtype, svertexCoords, coords);CHKERRQ(ierr);
2440     ierr = PetscFree(svertexCoords);CHKERRQ(ierr);
2441     }
2442 #else
2443     ierr = PetscSFBcastBegin(sfVert, coordtype, vertexCoords, coords);CHKERRQ(ierr);
2444     ierr = PetscSFBcastEnd(sfVert, coordtype, vertexCoords, coords);CHKERRQ(ierr);
2445 #endif
2446     ierr = MPI_Type_free(&coordtype);CHKERRQ(ierr);
2447   }
2448   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
2449   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
2450   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
2451   PetscFunctionReturn(0);
2452 }
2453 
2454 /*@C
2455   DMPlexCreateFromCellListParallel - This takes as input common mesh generator output, a list of the vertices for each cell, and produces a DM
2456 
2457   Input Parameters:
2458 + comm - The communicator
2459 . dim - The topological dimension of the mesh
2460 . numCells - The number of cells owned by this process
2461 . numVertices - The number of vertices owned by this process
2462 . numCorners - The number of vertices for each cell
2463 . interpolate - Flag indicating that intermediate mesh entities (faces, edges) should be created automatically
2464 . cells - An array of numCells*numCorners numbers, the global vertex numbers for each cell
2465 . spaceDim - The spatial dimension used for coordinates
2466 - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex
2467 
2468   Output Parameter:
2469 + dm - The DM
2470 - vertexSF - Optional, SF describing complete vertex ownership
2471 
2472   Note: Two triangles sharing a face
2473 $
2474 $        2
2475 $      / | \
2476 $     /  |  \
2477 $    /   |   \
2478 $   0  0 | 1  3
2479 $    \   |   /
2480 $     \  |  /
2481 $      \ | /
2482 $        1
2483 would have input
2484 $  numCells = 2, numVertices = 4
2485 $  cells = [0 1 2  1 3 2]
2486 $
2487 which would result in the DMPlex
2488 $
2489 $        4
2490 $      / | \
2491 $     /  |  \
2492 $    /   |   \
2493 $   2  0 | 1  5
2494 $    \   |   /
2495 $     \  |  /
2496 $      \ | /
2497 $        3
2498 
2499   Level: beginner
2500 
2501 .seealso: DMPlexCreateFromCellList(), DMPlexCreateFromDAG(), DMPlexCreate()
2502 @*/
2503 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)
2504 {
2505   PetscSF        sfVert;
2506   PetscErrorCode ierr;
2507 
2508   PetscFunctionBegin;
2509   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
2510   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
2511   PetscValidLogicalCollectiveInt(*dm, dim, 2);
2512   PetscValidLogicalCollectiveInt(*dm, spaceDim, 8);
2513   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
2514   ierr = DMPlexBuildFromCellList_Parallel_Private(*dm, numCells, numVertices, numCorners, cells, &sfVert);CHKERRQ(ierr);
2515   if (interpolate) {
2516     DM idm;
2517 
2518     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
2519     ierr = DMDestroy(dm);CHKERRQ(ierr);
2520     *dm  = idm;
2521   }
2522   ierr = DMPlexBuildCoordinates_Parallel_Private(*dm, spaceDim, numCells, numVertices,sfVert, vertexCoords);CHKERRQ(ierr);
2523   if (vertexSF) *vertexSF = sfVert;
2524   else {ierr = PetscSFDestroy(&sfVert);CHKERRQ(ierr);}
2525   PetscFunctionReturn(0);
2526 }
2527 
2528 /*
2529   This takes as input the common mesh generator output, a list of the vertices for each cell
2530 */
2531 static PetscErrorCode DMPlexBuildFromCellList_Private(DM dm, PetscInt numCells, PetscInt numVertices, PetscInt numCorners, const int cells[])
2532 {
2533   PetscInt      *cone, c, p;
2534   PetscErrorCode ierr;
2535 
2536   PetscFunctionBegin;
2537   ierr = DMPlexSetChart(dm, 0, numCells+numVertices);CHKERRQ(ierr);
2538   for (c = 0; c < numCells; ++c) {
2539     ierr = DMPlexSetConeSize(dm, c, numCorners);CHKERRQ(ierr);
2540   }
2541   ierr = DMSetUp(dm);CHKERRQ(ierr);
2542   ierr = DMGetWorkArray(dm, numCorners, MPIU_INT, &cone);CHKERRQ(ierr);
2543   for (c = 0; c < numCells; ++c) {
2544     for (p = 0; p < numCorners; ++p) {
2545       cone[p] = cells[c*numCorners+p]+numCells;
2546     }
2547     ierr = DMPlexSetCone(dm, c, cone);CHKERRQ(ierr);
2548   }
2549   ierr = DMRestoreWorkArray(dm, numCorners, MPIU_INT, &cone);CHKERRQ(ierr);
2550   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
2551   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
2552   PetscFunctionReturn(0);
2553 }
2554 
2555 /*
2556   This takes as input the coordinates for each vertex
2557 */
2558 static PetscErrorCode DMPlexBuildCoordinates_Private(DM dm, PetscInt spaceDim, PetscInt numCells, PetscInt numVertices, const double vertexCoords[])
2559 {
2560   PetscSection   coordSection;
2561   Vec            coordinates;
2562   DM             cdm;
2563   PetscScalar   *coords;
2564   PetscInt       v, d;
2565   PetscErrorCode ierr;
2566 
2567   PetscFunctionBegin;
2568   ierr = DMSetCoordinateDim(dm, spaceDim);CHKERRQ(ierr);
2569   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
2570   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
2571   ierr = PetscSectionSetFieldComponents(coordSection, 0, spaceDim);CHKERRQ(ierr);
2572   ierr = PetscSectionSetChart(coordSection, numCells, numCells + numVertices);CHKERRQ(ierr);
2573   for (v = numCells; v < numCells+numVertices; ++v) {
2574     ierr = PetscSectionSetDof(coordSection, v, spaceDim);CHKERRQ(ierr);
2575     ierr = PetscSectionSetFieldDof(coordSection, v, 0, spaceDim);CHKERRQ(ierr);
2576   }
2577   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
2578 
2579   ierr = DMGetCoordinateDM(dm, &cdm);CHKERRQ(ierr);
2580   ierr = DMCreateLocalVector(cdm, &coordinates);CHKERRQ(ierr);
2581   ierr = VecSetBlockSize(coordinates, spaceDim);CHKERRQ(ierr);
2582   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
2583   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
2584   for (v = 0; v < numVertices; ++v) {
2585     for (d = 0; d < spaceDim; ++d) {
2586       coords[v*spaceDim+d] = vertexCoords[v*spaceDim+d];
2587     }
2588   }
2589   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
2590   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
2591   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
2592   PetscFunctionReturn(0);
2593 }
2594 
2595 /*@C
2596   DMPlexCreateFromCellList - This takes as input common mesh generator output, a list of the vertices for each cell, and produces a DM
2597 
2598   Input Parameters:
2599 + comm - The communicator
2600 . dim - The topological dimension of the mesh
2601 . numCells - The number of cells
2602 . numVertices - The number of vertices
2603 . numCorners - The number of vertices for each cell
2604 . interpolate - Flag indicating that intermediate mesh entities (faces, edges) should be created automatically
2605 . cells - An array of numCells*numCorners numbers, the vertices for each cell
2606 . spaceDim - The spatial dimension used for coordinates
2607 - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex
2608 
2609   Output Parameter:
2610 . dm - The DM
2611 
2612   Note: Two triangles sharing a face
2613 $
2614 $        2
2615 $      / | \
2616 $     /  |  \
2617 $    /   |   \
2618 $   0  0 | 1  3
2619 $    \   |   /
2620 $     \  |  /
2621 $      \ | /
2622 $        1
2623 would have input
2624 $  numCells = 2, numVertices = 4
2625 $  cells = [0 1 2  1 3 2]
2626 $
2627 which would result in the DMPlex
2628 $
2629 $        4
2630 $      / | \
2631 $     /  |  \
2632 $    /   |   \
2633 $   2  0 | 1  5
2634 $    \   |   /
2635 $     \  |  /
2636 $      \ | /
2637 $        3
2638 
2639   Level: beginner
2640 
2641 .seealso: DMPlexCreateFromDAG(), DMPlexCreate()
2642 @*/
2643 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)
2644 {
2645   PetscErrorCode ierr;
2646 
2647   PetscFunctionBegin;
2648   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
2649   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
2650   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
2651   ierr = DMPlexBuildFromCellList_Private(*dm, numCells, numVertices, numCorners, cells);CHKERRQ(ierr);
2652   if (interpolate) {
2653     DM idm;
2654 
2655     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
2656     ierr = DMDestroy(dm);CHKERRQ(ierr);
2657     *dm  = idm;
2658   }
2659   ierr = DMPlexBuildCoordinates_Private(*dm, spaceDim, numCells, numVertices, vertexCoords);CHKERRQ(ierr);
2660   PetscFunctionReturn(0);
2661 }
2662 
2663 /*@
2664   DMPlexCreateFromDAG - This takes as input the adjacency-list representation of the Directed Acyclic Graph (Hasse Diagram) encoding a mesh, and produces a DM
2665 
2666   Input Parameters:
2667 + dm - The empty DM object, usually from DMCreate() and DMSetDimension()
2668 . depth - The depth of the DAG
2669 . numPoints - The number of points at each depth
2670 . coneSize - The cone size of each point
2671 . cones - The concatenation of the cone points for each point, the cone list must be oriented correctly for each point
2672 . coneOrientations - The orientation of each cone point
2673 - vertexCoords - An array of numVertices*dim numbers, the coordinates of each vertex
2674 
2675   Output Parameter:
2676 . dm - The DM
2677 
2678   Note: Two triangles sharing a face would have input
2679 $  depth = 1, numPoints = [4 2], coneSize = [3 3 0 0 0 0]
2680 $  cones = [2 3 4  3 5 4], coneOrientations = [0 0 0  0 0 0]
2681 $ vertexCoords = [-1.0 0.0  0.0 -1.0  0.0 1.0  1.0 0.0]
2682 $
2683 which would result in the DMPlex
2684 $
2685 $        4
2686 $      / | \
2687 $     /  |  \
2688 $    /   |   \
2689 $   2  0 | 1  5
2690 $    \   |   /
2691 $     \  |  /
2692 $      \ | /
2693 $        3
2694 $
2695 $ Notice that all points are numbered consecutively, unlikely DMPlexCreateFromCellList()
2696 
2697   Level: advanced
2698 
2699 .seealso: DMPlexCreateFromCellList(), DMPlexCreate()
2700 @*/
2701 PetscErrorCode DMPlexCreateFromDAG(DM dm, PetscInt depth, const PetscInt numPoints[], const PetscInt coneSize[], const PetscInt cones[], const PetscInt coneOrientations[], const PetscScalar vertexCoords[])
2702 {
2703   Vec            coordinates;
2704   PetscSection   coordSection;
2705   PetscScalar    *coords;
2706   PetscInt       coordSize, firstVertex = -1, pStart = 0, pEnd = 0, p, v, dim, dimEmbed, d, off;
2707   PetscErrorCode ierr;
2708 
2709   PetscFunctionBegin;
2710   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
2711   ierr = DMGetCoordinateDim(dm, &dimEmbed);CHKERRQ(ierr);
2712   if (dimEmbed < dim) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Embedding dimension %d cannot be less than intrinsic dimension %d",dimEmbed,dim);
2713   for (d = 0; d <= depth; ++d) pEnd += numPoints[d];
2714   ierr = DMPlexSetChart(dm, pStart, pEnd);CHKERRQ(ierr);
2715   for (p = pStart; p < pEnd; ++p) {
2716     ierr = DMPlexSetConeSize(dm, p, coneSize[p-pStart]);CHKERRQ(ierr);
2717     if (firstVertex < 0 && !coneSize[p - pStart]) {
2718       firstVertex = p - pStart;
2719     }
2720   }
2721   if (firstVertex < 0 && numPoints[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Expected %d vertices but could not find any", numPoints[0]);
2722   ierr = DMSetUp(dm);CHKERRQ(ierr); /* Allocate space for cones */
2723   for (p = pStart, off = 0; p < pEnd; off += coneSize[p-pStart], ++p) {
2724     ierr = DMPlexSetCone(dm, p, &cones[off]);CHKERRQ(ierr);
2725     ierr = DMPlexSetConeOrientation(dm, p, &coneOrientations[off]);CHKERRQ(ierr);
2726   }
2727   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
2728   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
2729   /* Build coordinates */
2730   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
2731   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
2732   ierr = PetscSectionSetFieldComponents(coordSection, 0, dimEmbed);CHKERRQ(ierr);
2733   ierr = PetscSectionSetChart(coordSection, firstVertex, firstVertex+numPoints[0]);CHKERRQ(ierr);
2734   for (v = firstVertex; v < firstVertex+numPoints[0]; ++v) {
2735     ierr = PetscSectionSetDof(coordSection, v, dimEmbed);CHKERRQ(ierr);
2736     ierr = PetscSectionSetFieldDof(coordSection, v, 0, dimEmbed);CHKERRQ(ierr);
2737   }
2738   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
2739   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
2740   ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
2741   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
2742   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
2743   ierr = VecSetBlockSize(coordinates, dimEmbed);CHKERRQ(ierr);
2744   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
2745   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
2746   for (v = 0; v < numPoints[0]; ++v) {
2747     PetscInt off;
2748 
2749     ierr = PetscSectionGetOffset(coordSection, v+firstVertex, &off);CHKERRQ(ierr);
2750     for (d = 0; d < dimEmbed; ++d) {
2751       coords[off+d] = vertexCoords[v*dimEmbed+d];
2752     }
2753   }
2754   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
2755   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
2756   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
2757   PetscFunctionReturn(0);
2758 }
2759 
2760 /*@C
2761   DMPlexCreateCellVertexFromFile - Create a DMPlex mesh from a simple cell-vertex file.
2762 
2763 + comm        - The MPI communicator
2764 . filename    - Name of the .dat file
2765 - interpolate - Create faces and edges in the mesh
2766 
2767   Output Parameter:
2768 . dm  - The DM object representing the mesh
2769 
2770   Note: The format is the simplest possible:
2771 $ Ne
2772 $ v0 v1 ... vk
2773 $ Nv
2774 $ x y z marker
2775 
2776   Level: beginner
2777 
2778 .seealso: DMPlexCreateFromFile(), DMPlexCreateMedFromFile(), DMPlexCreateGmsh(), DMPlexCreate()
2779 @*/
2780 PetscErrorCode DMPlexCreateCellVertexFromFile(MPI_Comm comm, const char filename[], PetscBool interpolate, DM *dm)
2781 {
2782   DMLabel         marker;
2783   PetscViewer     viewer;
2784   Vec             coordinates;
2785   PetscSection    coordSection;
2786   PetscScalar    *coords;
2787   char            line[PETSC_MAX_PATH_LEN];
2788   PetscInt        dim = 3, cdim = 3, coordSize, v, c, d;
2789   PetscMPIInt     rank;
2790   int             snum, Nv, Nc;
2791   PetscErrorCode  ierr;
2792 
2793   PetscFunctionBegin;
2794   ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
2795   ierr = PetscViewerCreate(comm, &viewer);CHKERRQ(ierr);
2796   ierr = PetscViewerSetType(viewer, PETSCVIEWERASCII);CHKERRQ(ierr);
2797   ierr = PetscViewerFileSetMode(viewer, FILE_MODE_READ);CHKERRQ(ierr);
2798   ierr = PetscViewerFileSetName(viewer, filename);CHKERRQ(ierr);
2799   if (!rank) {
2800     ierr = PetscViewerRead(viewer, line, 2, NULL, PETSC_STRING);CHKERRQ(ierr);
2801     snum = sscanf(line, "%d %d", &Nc, &Nv);
2802     if (snum != 2) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unable to parse cell-vertex file: %s", line);
2803   } else {
2804     Nc = Nv = 0;
2805   }
2806   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
2807   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
2808   ierr = DMPlexSetChart(*dm, 0, Nc+Nv);CHKERRQ(ierr);
2809   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
2810   ierr = DMSetCoordinateDim(*dm, cdim);CHKERRQ(ierr);
2811   /* Read topology */
2812   if (!rank) {
2813     PetscInt cone[8], corners = 8;
2814     int      vbuf[8], v;
2815 
2816     for (c = 0; c < Nc; ++c) {ierr = DMPlexSetConeSize(*dm, c, corners);CHKERRQ(ierr);}
2817     ierr = DMSetUp(*dm);CHKERRQ(ierr);
2818     for (c = 0; c < Nc; ++c) {
2819       ierr = PetscViewerRead(viewer, line, corners, NULL, PETSC_STRING);CHKERRQ(ierr);
2820       snum = sscanf(line, "%d %d %d %d %d %d %d %d", &vbuf[0], &vbuf[1], &vbuf[2], &vbuf[3], &vbuf[4], &vbuf[5], &vbuf[6], &vbuf[7]);
2821       if (snum != corners) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unable to parse cell-vertex file: %s", line);
2822       for (v = 0; v < corners; ++v) cone[v] = vbuf[v] + Nc;
2823       /* Hexahedra are inverted */
2824       {
2825         PetscInt tmp = cone[1];
2826         cone[1] = cone[3];
2827         cone[3] = tmp;
2828       }
2829       ierr = DMPlexSetCone(*dm, c, cone);CHKERRQ(ierr);
2830     }
2831   }
2832   ierr = DMPlexSymmetrize(*dm);CHKERRQ(ierr);
2833   ierr = DMPlexStratify(*dm);CHKERRQ(ierr);
2834   /* Read coordinates */
2835   ierr = DMGetCoordinateSection(*dm, &coordSection);CHKERRQ(ierr);
2836   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
2837   ierr = PetscSectionSetFieldComponents(coordSection, 0, cdim);CHKERRQ(ierr);
2838   ierr = PetscSectionSetChart(coordSection, Nc, Nc + Nv);CHKERRQ(ierr);
2839   for (v = Nc; v < Nc+Nv; ++v) {
2840     ierr = PetscSectionSetDof(coordSection, v, cdim);CHKERRQ(ierr);
2841     ierr = PetscSectionSetFieldDof(coordSection, v, 0, cdim);CHKERRQ(ierr);
2842   }
2843   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
2844   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
2845   ierr = VecCreate(PETSC_COMM_SELF, &coordinates);CHKERRQ(ierr);
2846   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
2847   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
2848   ierr = VecSetBlockSize(coordinates, cdim);CHKERRQ(ierr);
2849   ierr = VecSetType(coordinates, VECSTANDARD);CHKERRQ(ierr);
2850   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
2851   if (!rank) {
2852     double x[3];
2853     int    val;
2854 
2855     ierr = DMCreateLabel(*dm, "marker");CHKERRQ(ierr);
2856     ierr = DMGetLabel(*dm, "marker", &marker);CHKERRQ(ierr);
2857     for (v = 0; v < Nv; ++v) {
2858       ierr = PetscViewerRead(viewer, line, 4, NULL, PETSC_STRING);CHKERRQ(ierr);
2859       snum = sscanf(line, "%lg %lg %lg %d", &x[0], &x[1], &x[2], &val);
2860       if (snum != 4) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unable to parse cell-vertex file: %s", line);
2861       for (d = 0; d < cdim; ++d) coords[v*cdim+d] = x[d];
2862       if (val) {ierr = DMLabelSetValue(marker, v+Nc, val);CHKERRQ(ierr);}
2863     }
2864   }
2865   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
2866   ierr = DMSetCoordinatesLocal(*dm, coordinates);CHKERRQ(ierr);
2867   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
2868   ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
2869   if (interpolate) {
2870     DM      idm;
2871     DMLabel bdlabel;
2872 
2873     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
2874     ierr = DMDestroy(dm);CHKERRQ(ierr);
2875     *dm  = idm;
2876 
2877     ierr = DMGetLabel(*dm, "marker", &bdlabel);CHKERRQ(ierr);
2878     ierr = DMPlexMarkBoundaryFaces(*dm, PETSC_DETERMINE, bdlabel);CHKERRQ(ierr);
2879     ierr = DMPlexLabelComplete(*dm, bdlabel);CHKERRQ(ierr);
2880   }
2881   PetscFunctionReturn(0);
2882 }
2883 
2884 /*@C
2885   DMPlexCreateFromFile - This takes a filename and produces a DM
2886 
2887   Input Parameters:
2888 + comm - The communicator
2889 . filename - A file name
2890 - interpolate - Flag to create intermediate mesh pieces (edges, faces)
2891 
2892   Output Parameter:
2893 . dm - The DM
2894 
2895   Level: beginner
2896 
2897 .seealso: DMPlexCreateFromDAG(), DMPlexCreateFromCellList(), DMPlexCreate()
2898 @*/
2899 PetscErrorCode DMPlexCreateFromFile(MPI_Comm comm, const char filename[], PetscBool interpolate, DM *dm)
2900 {
2901   const char    *extGmsh    = ".msh";
2902   const char    *extCGNS    = ".cgns";
2903   const char    *extExodus  = ".exo";
2904   const char    *extGenesis = ".gen";
2905   const char    *extFluent  = ".cas";
2906   const char    *extHDF5    = ".h5";
2907   const char    *extMed     = ".med";
2908   const char    *extPLY     = ".ply";
2909   const char    *extCV      = ".dat";
2910   size_t         len;
2911   PetscBool      isGmsh, isCGNS, isExodus, isGenesis, isFluent, isHDF5, isMed, isPLY, isCV;
2912   PetscMPIInt    rank;
2913   PetscErrorCode ierr;
2914 
2915   PetscFunctionBegin;
2916   PetscValidPointer(filename, 2);
2917   PetscValidPointer(dm, 4);
2918   ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
2919   ierr = PetscStrlen(filename, &len);CHKERRQ(ierr);
2920   if (!len) SETERRQ(comm, PETSC_ERR_ARG_WRONG, "Filename must be a valid path");
2921   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extGmsh,    4, &isGmsh);CHKERRQ(ierr);
2922   ierr = PetscStrncmp(&filename[PetscMax(0,len-5)], extCGNS,    5, &isCGNS);CHKERRQ(ierr);
2923   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extExodus,  4, &isExodus);CHKERRQ(ierr);
2924   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extGenesis, 4, &isGenesis);CHKERRQ(ierr);
2925   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extFluent,  4, &isFluent);CHKERRQ(ierr);
2926   ierr = PetscStrncmp(&filename[PetscMax(0,len-3)], extHDF5,    3, &isHDF5);CHKERRQ(ierr);
2927   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extMed,     4, &isMed);CHKERRQ(ierr);
2928   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extPLY,     4, &isPLY);CHKERRQ(ierr);
2929   ierr = PetscStrncmp(&filename[PetscMax(0,len-4)], extCV,      4, &isCV);CHKERRQ(ierr);
2930   if (isGmsh) {
2931     ierr = DMPlexCreateGmshFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
2932   } else if (isCGNS) {
2933     ierr = DMPlexCreateCGNSFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
2934   } else if (isExodus || isGenesis) {
2935     ierr = DMPlexCreateExodusFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
2936   } else if (isFluent) {
2937     ierr = DMPlexCreateFluentFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
2938   } else if (isHDF5) {
2939     PetscViewer viewer;
2940 
2941     ierr = PetscViewerCreate(comm, &viewer);CHKERRQ(ierr);
2942     ierr = PetscViewerSetType(viewer, PETSCVIEWERHDF5);CHKERRQ(ierr);
2943     ierr = PetscViewerFileSetMode(viewer, FILE_MODE_READ);CHKERRQ(ierr);
2944     ierr = PetscViewerFileSetName(viewer, filename);CHKERRQ(ierr);
2945     ierr = DMCreate(comm, dm);CHKERRQ(ierr);
2946     ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
2947     ierr = DMLoad(*dm, viewer);CHKERRQ(ierr);
2948     ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
2949 
2950     if (interpolate) {
2951       DM idm;
2952 
2953       ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
2954       ierr = DMDestroy(dm);CHKERRQ(ierr);
2955       *dm  = idm;
2956     }
2957   } else if (isMed) {
2958     ierr = DMPlexCreateMedFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
2959   } else if (isPLY) {
2960     ierr = DMPlexCreatePLYFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
2961   } else if (isCV) {
2962     ierr = DMPlexCreateCellVertexFromFile(comm, filename, interpolate, dm);CHKERRQ(ierr);
2963   } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cannot load file %s: unrecognized extension", filename);
2964   PetscFunctionReturn(0);
2965 }
2966 
2967 /*@
2968   DMPlexCreateReferenceCell - Create a DMPLEX with the appropriate FEM reference cell
2969 
2970   Collective on comm
2971 
2972   Input Parameters:
2973 + comm    - The communicator
2974 . dim     - The spatial dimension
2975 - simplex - Flag for simplex, otherwise use a tensor-product cell
2976 
2977   Output Parameter:
2978 . refdm - The reference cell
2979 
2980   Level: intermediate
2981 
2982 .keywords: reference cell
2983 .seealso:
2984 @*/
2985 PetscErrorCode DMPlexCreateReferenceCell(MPI_Comm comm, PetscInt dim, PetscBool simplex, DM *refdm)
2986 {
2987   DM             rdm;
2988   Vec            coords;
2989   PetscErrorCode ierr;
2990 
2991   PetscFunctionBeginUser;
2992   ierr = DMCreate(comm, &rdm);CHKERRQ(ierr);
2993   ierr = DMSetType(rdm, DMPLEX);CHKERRQ(ierr);
2994   ierr = DMSetDimension(rdm, dim);CHKERRQ(ierr);
2995   switch (dim) {
2996   case 0:
2997   {
2998     PetscInt    numPoints[1]        = {1};
2999     PetscInt    coneSize[1]         = {0};
3000     PetscInt    cones[1]            = {0};
3001     PetscInt    coneOrientations[1] = {0};
3002     PetscScalar vertexCoords[1]     = {0.0};
3003 
3004     ierr = DMPlexCreateFromDAG(rdm, 0, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
3005   }
3006   break;
3007   case 1:
3008   {
3009     PetscInt    numPoints[2]        = {2, 1};
3010     PetscInt    coneSize[3]         = {2, 0, 0};
3011     PetscInt    cones[2]            = {1, 2};
3012     PetscInt    coneOrientations[2] = {0, 0};
3013     PetscScalar vertexCoords[2]     = {-1.0,  1.0};
3014 
3015     ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
3016   }
3017   break;
3018   case 2:
3019     if (simplex) {
3020       PetscInt    numPoints[2]        = {3, 1};
3021       PetscInt    coneSize[4]         = {3, 0, 0, 0};
3022       PetscInt    cones[3]            = {1, 2, 3};
3023       PetscInt    coneOrientations[3] = {0, 0, 0};
3024       PetscScalar vertexCoords[6]     = {-1.0, -1.0,  1.0, -1.0,  -1.0, 1.0};
3025 
3026       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
3027     } else {
3028       PetscInt    numPoints[2]        = {4, 1};
3029       PetscInt    coneSize[5]         = {4, 0, 0, 0, 0};
3030       PetscInt    cones[4]            = {1, 2, 3, 4};
3031       PetscInt    coneOrientations[4] = {0, 0, 0, 0};
3032       PetscScalar vertexCoords[8]     = {-1.0, -1.0,  1.0, -1.0,  1.0, 1.0,  -1.0, 1.0};
3033 
3034       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
3035     }
3036   break;
3037   case 3:
3038     if (simplex) {
3039       PetscInt    numPoints[2]        = {4, 1};
3040       PetscInt    coneSize[5]         = {4, 0, 0, 0, 0};
3041       PetscInt    cones[4]            = {1, 3, 2, 4};
3042       PetscInt    coneOrientations[4] = {0, 0, 0, 0};
3043       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};
3044 
3045       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
3046     } else {
3047       PetscInt    numPoints[2]        = {8, 1};
3048       PetscInt    coneSize[9]         = {8, 0, 0, 0, 0, 0, 0, 0, 0};
3049       PetscInt    cones[8]            = {1, 4, 3, 2, 5, 6, 7, 8};
3050       PetscInt    coneOrientations[8] = {0, 0, 0, 0, 0, 0, 0, 0};
3051       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,
3052                                          -1.0, -1.0,  1.0,  1.0, -1.0,  1.0,  1.0, 1.0,  1.0,  -1.0, 1.0,  1.0};
3053 
3054       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
3055     }
3056   break;
3057   default:
3058     SETERRQ1(comm, PETSC_ERR_ARG_WRONG, "Cannot create reference cell for dimension %d", dim);
3059   }
3060   ierr = DMPlexInterpolate(rdm, refdm);CHKERRQ(ierr);
3061   if (rdm->coordinateDM) {
3062     DM           ncdm;
3063     PetscSection cs;
3064     PetscInt     pEnd = -1;
3065 
3066     ierr = DMGetDefaultSection(rdm->coordinateDM, &cs);CHKERRQ(ierr);
3067     if (cs) {ierr = PetscSectionGetChart(cs, NULL, &pEnd);CHKERRQ(ierr);}
3068     if (pEnd >= 0) {
3069       ierr = DMClone(rdm->coordinateDM, &ncdm);CHKERRQ(ierr);
3070       ierr = DMSetDefaultSection(ncdm, cs);CHKERRQ(ierr);
3071       ierr = DMSetCoordinateDM(*refdm, ncdm);CHKERRQ(ierr);
3072       ierr = DMDestroy(&ncdm);CHKERRQ(ierr);
3073     }
3074   }
3075   ierr = DMGetCoordinatesLocal(rdm, &coords);CHKERRQ(ierr);
3076   if (coords) {
3077     ierr = DMSetCoordinatesLocal(*refdm, coords);CHKERRQ(ierr);
3078   } else {
3079     ierr = DMGetCoordinates(rdm, &coords);CHKERRQ(ierr);
3080     if (coords) {ierr = DMSetCoordinates(*refdm, coords);CHKERRQ(ierr);}
3081   }
3082   ierr = DMDestroy(&rdm);CHKERRQ(ierr);
3083   PetscFunctionReturn(0);
3084 }
3085