xref: /petsc/src/dm/impls/plex/plexcreate.c (revision f0226e147a14668be1d895da7b56f3083575c06b)
1 #define PETSCDM_DLL
2 #include <petsc-private/dmpleximpl.h>    /*I   "petscdmplex.h"   I*/
3 #include <petscdmda.h>
4 #include <petscsf.h>
5 
6 #undef __FUNCT__
7 #define __FUNCT__ "DMPlexCreateDoublet"
8 /*@
9   DMPlexCreateDoublet - Creates a mesh of two cells of the specified type, optionally with later refinement.
10 
11   Collective on MPI_Comm
12 
13   Input Parameters:
14 + comm - The communicator for the DM object
15 . dim - The spatial dimension
16 . simplex - Flag for simplicial cells, otherwise they are tensor product cells
17 . interpolate - Flag to create intermediate mesh pieces (edges, faces)
18 . refinementUniform - Flag for uniform parallel refinement
19 - refinementLimit - A nonzero number indicates the largest admissible volume for a refined cell
20 
21   Output Parameter:
22 . dm  - The DM object
23 
24   Level: beginner
25 
26 .keywords: DM, create
27 .seealso: DMSetType(), DMCreate()
28 @*/
29 PetscErrorCode DMPlexCreateDoublet(MPI_Comm comm, PetscInt dim, PetscBool simplex, PetscBool interpolate, PetscBool refinementUniform, PetscReal refinementLimit, DM *newdm)
30 {
31   DM             dm;
32   PetscInt       p;
33   PetscMPIInt    rank;
34   PetscErrorCode ierr;
35 
36   PetscFunctionBegin;
37   ierr = DMCreate(comm, &dm);CHKERRQ(ierr);
38   ierr = DMSetType(dm, DMPLEX);CHKERRQ(ierr);
39   ierr = DMSetDimension(dm, dim);CHKERRQ(ierr);
40   ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
41   switch (dim) {
42   case 2:
43     if (simplex) {ierr = PetscObjectSetName((PetscObject) dm, "triangular");CHKERRQ(ierr);}
44     else         {ierr = PetscObjectSetName((PetscObject) dm, "quadrilateral");CHKERRQ(ierr);}
45     break;
46   case 3:
47     if (simplex) {ierr = PetscObjectSetName((PetscObject) dm, "tetrahedral");CHKERRQ(ierr);}
48     else         {ierr = PetscObjectSetName((PetscObject) dm, "hexahedral");CHKERRQ(ierr);}
49     break;
50   default:
51     SETERRQ1(comm, PETSC_ERR_ARG_OUTOFRANGE, "Cannot make meshes for dimension %d", dim);
52   }
53   if (rank) {
54     PetscInt numPoints[2] = {0, 0};
55     ierr = DMPlexCreateFromDAG(dm, 1, numPoints, NULL, NULL, NULL, NULL);CHKERRQ(ierr);
56   } else {
57     switch (dim) {
58     case 2:
59       if (simplex) {
60         PetscInt    numPoints[2]        = {4, 2};
61         PetscInt    coneSize[6]         = {3, 3, 0, 0, 0, 0};
62         PetscInt    cones[6]            = {2, 3, 4,  5, 4, 3};
63         PetscInt    coneOrientations[6] = {0, 0, 0,  0, 0, 0};
64         PetscScalar vertexCoords[8]     = {-0.5, 0.5, 0.0, 0.0, 0.0, 1.0, 0.5, 0.5};
65         PetscInt    markerPoints[8]     = {2, 1, 3, 1, 4, 1, 5, 1};
66 
67         ierr = DMPlexCreateFromDAG(dm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
68         for (p = 0; p < 4; ++p) {ierr = DMPlexSetLabelValue(dm, "marker", markerPoints[p*2], markerPoints[p*2+1]);CHKERRQ(ierr);}
69       } else {
70         PetscInt    numPoints[2]        = {6, 2};
71         PetscInt    coneSize[8]         = {4, 4, 0, 0, 0, 0, 0, 0};
72         PetscInt    cones[8]            = {2, 3, 4, 5,  3, 6, 7, 4};
73         PetscInt    coneOrientations[8] = {0, 0, 0, 0,  0, 0, 0, 0};
74         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};
75 
76         ierr = DMPlexCreateFromDAG(dm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
77       }
78       break;
79     case 3:
80       if (simplex) {
81         PetscInt    numPoints[2]        = {5, 2};
82         PetscInt    coneSize[7]         = {4, 4, 0, 0, 0, 0, 0};
83         PetscInt    cones[8]            = {4, 3, 5, 2,  5, 3, 4, 6};
84         PetscInt    coneOrientations[8] = {0, 0, 0, 0,  0, 0, 0, 0};
85         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};
86         PetscInt    markerPoints[10]    = {2, 1, 3, 1, 4, 1, 5, 1, 6, 1};
87 
88         ierr = DMPlexCreateFromDAG(dm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
89         for (p = 0; p < 5; ++p) {ierr = DMPlexSetLabelValue(dm, "marker", markerPoints[p*2], markerPoints[p*2+1]);CHKERRQ(ierr);}
90       } else {
91         PetscInt    numPoints[2]         = {12, 2};
92         PetscInt    coneSize[14]         = {8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0};
93         PetscInt    cones[16]            = {2, 3, 4, 5, 6, 7, 8, 9,  5, 4, 10, 11, 7, 12, 13, 8};
94         PetscInt    coneOrientations[16] = {0, 0, 0, 0, 0, 0, 0, 0,  0, 0,  0,  0, 0,  0,  0, 0};
95         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,
96                                             -1.0, -0.5,  0.5,   0.0, -0.5,  0.5,  0.0,  0.5,  0.5,  -1.0,  0.5,  0.5,
97                                              1.0,  0.5, -0.5,   1.0, -0.5, -0.5,  1.0, -0.5,  0.5,   1.0,  0.5,  0.5};
98 
99         ierr = DMPlexCreateFromDAG(dm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
100       }
101       break;
102     default:
103       SETERRQ1(comm, PETSC_ERR_ARG_OUTOFRANGE, "Cannot make meshes for dimension %d", dim);
104     }
105   }
106   *newdm = dm;
107   if (refinementLimit > 0.0) {
108     DM rdm;
109     const char *name;
110 
111     ierr = DMPlexSetRefinementUniform(*newdm, PETSC_FALSE);CHKERRQ(ierr);
112     ierr = DMPlexSetRefinementLimit(*newdm, refinementLimit);CHKERRQ(ierr);
113     ierr = DMRefine(*newdm, comm, &rdm);CHKERRQ(ierr);
114     ierr = PetscObjectGetName((PetscObject) *newdm, &name);CHKERRQ(ierr);
115     ierr = PetscObjectSetName((PetscObject)    rdm,  name);CHKERRQ(ierr);
116     ierr = DMDestroy(newdm);CHKERRQ(ierr);
117     *newdm = rdm;
118   }
119   if (interpolate) {
120     DM idm = NULL;
121     const char *name;
122 
123     ierr = DMPlexInterpolate(*newdm, &idm);CHKERRQ(ierr);
124     ierr = PetscObjectGetName((PetscObject) *newdm, &name);CHKERRQ(ierr);
125     ierr = PetscObjectSetName((PetscObject)    idm,  name);CHKERRQ(ierr);
126     ierr = DMPlexCopyCoordinates(*newdm, idm);CHKERRQ(ierr);
127     ierr = DMPlexCopyLabels(*newdm, idm);CHKERRQ(ierr);
128     ierr = DMDestroy(newdm);CHKERRQ(ierr);
129     *newdm = idm;
130   }
131   {
132     DM refinedMesh     = NULL;
133     DM distributedMesh = NULL;
134 
135     /* Distribute mesh over processes */
136     ierr = DMPlexDistribute(*newdm, NULL, 0, NULL, &distributedMesh);CHKERRQ(ierr);
137     if (distributedMesh) {
138       ierr = DMDestroy(newdm);CHKERRQ(ierr);
139       *newdm = distributedMesh;
140     }
141     if (refinementUniform) {
142       ierr = DMPlexSetRefinementUniform(*newdm, refinementUniform);CHKERRQ(ierr);
143       ierr = DMRefine(*newdm, comm, &refinedMesh);CHKERRQ(ierr);
144       if (refinedMesh) {
145         ierr = DMDestroy(newdm);CHKERRQ(ierr);
146         *newdm = refinedMesh;
147       }
148     }
149   }
150   PetscFunctionReturn(0);
151 }
152 
153 #undef __FUNCT__
154 #define __FUNCT__ "DMPlexCreateSquareBoundary"
155 /*@
156   DMPlexCreateSquareBoundary - Creates a 1D mesh the is the boundary of a square lattice.
157 
158   Collective on MPI_Comm
159 
160   Input Parameters:
161 + comm  - The communicator for the DM object
162 . lower - The lower left corner coordinates
163 . upper - The upper right corner coordinates
164 - edges - The number of cells in each direction
165 
166   Output Parameter:
167 . dm  - The DM object
168 
169   Note: Here is the numbering returned for 2 cells in each direction:
170 $ 18--5-17--4--16
171 $  |     |     |
172 $  6    10     3
173 $  |     |     |
174 $ 19-11-20--9--15
175 $  |     |     |
176 $  7     8     2
177 $  |     |     |
178 $ 12--0-13--1--14
179 
180   Level: beginner
181 
182 .keywords: DM, create
183 .seealso: DMPlexCreateBoxMesh(), DMPlexCreateCubeBoundary(), DMSetType(), DMCreate()
184 @*/
185 PetscErrorCode DMPlexCreateSquareBoundary(DM dm, const PetscReal lower[], const PetscReal upper[], const PetscInt edges[])
186 {
187   PetscInt       numVertices    = (edges[0]+1)*(edges[1]+1);
188   PetscInt       numEdges       = edges[0]*(edges[1]+1) + (edges[0]+1)*edges[1];
189   PetscInt       markerTop      = 1;
190   PetscInt       markerBottom   = 1;
191   PetscInt       markerRight    = 1;
192   PetscInt       markerLeft     = 1;
193   PetscBool      markerSeparate = PETSC_FALSE;
194   Vec            coordinates;
195   PetscSection   coordSection;
196   PetscScalar    *coords;
197   PetscInt       coordSize;
198   PetscMPIInt    rank;
199   PetscInt       v, vx, vy;
200   PetscErrorCode ierr;
201 
202   PetscFunctionBegin;
203   ierr = PetscOptionsGetBool(((PetscObject) dm)->prefix, "-dm_plex_separate_marker", &markerSeparate, NULL);CHKERRQ(ierr);
204   if (markerSeparate) {
205     markerTop    = 1;
206     markerBottom = 0;
207     markerRight  = 0;
208     markerLeft   = 0;
209   }
210   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);CHKERRQ(ierr);
211   if (!rank) {
212     PetscInt e, ex, ey;
213 
214     ierr = DMPlexSetChart(dm, 0, numEdges+numVertices);CHKERRQ(ierr);
215     for (e = 0; e < numEdges; ++e) {
216       ierr = DMPlexSetConeSize(dm, e, 2);CHKERRQ(ierr);
217     }
218     ierr = DMSetUp(dm);CHKERRQ(ierr); /* Allocate space for cones */
219     for (vx = 0; vx <= edges[0]; vx++) {
220       for (ey = 0; ey < edges[1]; ey++) {
221         PetscInt edge   = vx*edges[1] + ey + edges[0]*(edges[1]+1);
222         PetscInt vertex = ey*(edges[0]+1) + vx + numEdges;
223         PetscInt cone[2];
224 
225         cone[0] = vertex; cone[1] = vertex+edges[0]+1;
226         ierr    = DMPlexSetCone(dm, edge, cone);CHKERRQ(ierr);
227         if (vx == edges[0]) {
228           ierr = DMPlexSetLabelValue(dm, "marker", edge,    markerRight);CHKERRQ(ierr);
229           ierr = DMPlexSetLabelValue(dm, "marker", cone[0], markerRight);CHKERRQ(ierr);
230           if (ey == edges[1]-1) {
231             ierr = DMPlexSetLabelValue(dm, "marker", cone[1], markerRight);CHKERRQ(ierr);
232           }
233         } else if (vx == 0) {
234           ierr = DMPlexSetLabelValue(dm, "marker", edge,    markerLeft);CHKERRQ(ierr);
235           ierr = DMPlexSetLabelValue(dm, "marker", cone[0], markerLeft);CHKERRQ(ierr);
236           if (ey == edges[1]-1) {
237             ierr = DMPlexSetLabelValue(dm, "marker", cone[1], markerLeft);CHKERRQ(ierr);
238           }
239         }
240       }
241     }
242     for (vy = 0; vy <= edges[1]; vy++) {
243       for (ex = 0; ex < edges[0]; ex++) {
244         PetscInt edge   = vy*edges[0]     + ex;
245         PetscInt vertex = vy*(edges[0]+1) + ex + numEdges;
246         PetscInt cone[2];
247 
248         cone[0] = vertex; cone[1] = vertex+1;
249         ierr    = DMPlexSetCone(dm, edge, cone);CHKERRQ(ierr);
250         if (vy == edges[1]) {
251           ierr = DMPlexSetLabelValue(dm, "marker", edge,    markerTop);CHKERRQ(ierr);
252           ierr = DMPlexSetLabelValue(dm, "marker", cone[0], markerTop);CHKERRQ(ierr);
253           if (ex == edges[0]-1) {
254             ierr = DMPlexSetLabelValue(dm, "marker", cone[1], markerTop);CHKERRQ(ierr);
255           }
256         } else if (vy == 0) {
257           ierr = DMPlexSetLabelValue(dm, "marker", edge,    markerBottom);CHKERRQ(ierr);
258           ierr = DMPlexSetLabelValue(dm, "marker", cone[0], markerBottom);CHKERRQ(ierr);
259           if (ex == edges[0]-1) {
260             ierr = DMPlexSetLabelValue(dm, "marker", cone[1], markerBottom);CHKERRQ(ierr);
261           }
262         }
263       }
264     }
265   }
266   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
267   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
268   /* Build coordinates */
269   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
270   ierr = PetscSectionSetChart(coordSection, numEdges, numEdges + numVertices);CHKERRQ(ierr);
271   for (v = numEdges; v < numEdges+numVertices; ++v) {
272     ierr = PetscSectionSetDof(coordSection, v, 2);CHKERRQ(ierr);
273   }
274   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
275   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
276   ierr = VecCreate(PetscObjectComm((PetscObject)dm), &coordinates);CHKERRQ(ierr);
277   ierr = VecSetBlockSize(coordinates, 2);CHKERRQ(ierr);
278   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);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 #undef __FUNCT__
294 #define __FUNCT__ "DMPlexCreateCubeBoundary"
295 /*@
296   DMPlexCreateCubeBoundary - Creates a 2D mesh the is the boundary of a cubic lattice.
297 
298   Collective on MPI_Comm
299 
300   Input Parameters:
301 + comm  - The communicator for the DM object
302 . lower - The lower left front corner coordinates
303 . upper - The upper right back corner coordinates
304 - edges - The number of cells in each direction
305 
306   Output Parameter:
307 . dm  - The DM object
308 
309   Level: beginner
310 
311 .keywords: DM, create
312 .seealso: DMPlexCreateBoxMesh(), DMPlexCreateSquareBoundary(), DMSetType(), DMCreate()
313 @*/
314 PetscErrorCode DMPlexCreateCubeBoundary(DM dm, const PetscReal lower[], const PetscReal upper[], const PetscInt faces[])
315 {
316   PetscInt       vertices[3], numVertices;
317   PetscInt       numFaces    = 2*faces[0]*faces[1] + 2*faces[1]*faces[2] + 2*faces[0]*faces[2];
318   Vec            coordinates;
319   PetscSection   coordSection;
320   PetscScalar    *coords;
321   PetscInt       coordSize;
322   PetscMPIInt    rank;
323   PetscInt       v, vx, vy, vz;
324   PetscInt       voffset, iface=0, cone[4];
325   PetscErrorCode ierr;
326 
327   PetscFunctionBegin;
328   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");
329   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);CHKERRQ(ierr);
330   vertices[0] = faces[0]+1; vertices[1] = faces[1]+1; vertices[2] = faces[2]+1;
331   numVertices = vertices[0]*vertices[1]*vertices[2];
332   if (!rank) {
333     PetscInt f;
334 
335     ierr = DMPlexSetChart(dm, 0, numFaces+numVertices);CHKERRQ(ierr);
336     for (f = 0; f < numFaces; ++f) {
337       ierr = DMPlexSetConeSize(dm, f, 4);CHKERRQ(ierr);
338     }
339     ierr = DMSetUp(dm);CHKERRQ(ierr); /* Allocate space for cones */
340     for (v = 0; v < numFaces+numVertices; ++v) {
341       ierr = DMPlexSetLabelValue(dm, "marker", v, 1);CHKERRQ(ierr);
342     }
343 
344     /* Side 0 (Top) */
345     for (vy = 0; vy < faces[1]; vy++) {
346       for (vx = 0; vx < faces[0]; vx++) {
347         voffset = numFaces + vertices[0]*vertices[1]*(vertices[2]-1) + vy*vertices[0] + vx;
348         cone[0] = voffset; cone[1] = voffset+1; cone[2] = voffset+vertices[0]+1; cone[3] = voffset+vertices[0];
349         ierr    = DMPlexSetCone(dm, iface, cone);CHKERRQ(ierr);
350         iface++;
351       }
352     }
353 
354     /* Side 1 (Bottom) */
355     for (vy = 0; vy < faces[1]; vy++) {
356       for (vx = 0; vx < faces[0]; vx++) {
357         voffset = numFaces + vy*(faces[0]+1) + vx;
358         cone[0] = voffset+1; cone[1] = voffset; cone[2] = voffset+vertices[0]; cone[3] = voffset+vertices[0]+1;
359         ierr    = DMPlexSetCone(dm, iface, cone);CHKERRQ(ierr);
360         iface++;
361       }
362     }
363 
364     /* Side 2 (Front) */
365     for (vz = 0; vz < faces[2]; vz++) {
366       for (vx = 0; vx < faces[0]; vx++) {
367         voffset = numFaces + vz*vertices[0]*vertices[1] + vx;
368         cone[0] = voffset; cone[1] = voffset+1; cone[2] = voffset+vertices[0]*vertices[1]+1; cone[3] = voffset+vertices[0]*vertices[1];
369         ierr    = DMPlexSetCone(dm, iface, cone);CHKERRQ(ierr);
370         iface++;
371       }
372     }
373 
374     /* Side 3 (Back) */
375     for (vz = 0; vz < faces[2]; vz++) {
376       for (vx = 0; vx < faces[0]; vx++) {
377         voffset = numFaces + vz*vertices[0]*vertices[1] + vertices[0]*(vertices[1]-1) + vx;
378         cone[0] = voffset+vertices[0]*vertices[1]; cone[1] = voffset+vertices[0]*vertices[1]+1;
379         cone[2] = voffset+1; cone[3] = voffset;
380         ierr    = DMPlexSetCone(dm, iface, cone);CHKERRQ(ierr);
381         iface++;
382       }
383     }
384 
385     /* Side 4 (Left) */
386     for (vz = 0; vz < faces[2]; vz++) {
387       for (vy = 0; vy < faces[1]; vy++) {
388         voffset = numFaces + vz*vertices[0]*vertices[1] + vy*vertices[0];
389         cone[0] = voffset; cone[1] = voffset+vertices[0]*vertices[1];
390         cone[2] = voffset+vertices[0]*vertices[1]+vertices[0]; cone[3] = voffset+vertices[0];
391         ierr    = DMPlexSetCone(dm, iface, cone);CHKERRQ(ierr);
392         iface++;
393       }
394     }
395 
396     /* Side 5 (Right) */
397     for (vz = 0; vz < faces[2]; vz++) {
398       for (vy = 0; vy < faces[1]; vy++) {
399         voffset = numFaces + vz*vertices[0]*vertices[1] + vy*vertices[0] + vx;
400         cone[0] = voffset+vertices[0]*vertices[1]; cone[1] = voffset;
401         cone[2] = voffset+vertices[0]; cone[3] = voffset+vertices[0]*vertices[1]+vertices[0];
402         ierr    = DMPlexSetCone(dm, iface, cone);CHKERRQ(ierr);
403         iface++;
404       }
405     }
406   }
407   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
408   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
409   /* Build coordinates */
410   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
411   ierr = PetscSectionSetChart(coordSection, numFaces, numFaces + numVertices);CHKERRQ(ierr);
412   for (v = numFaces; v < numFaces+numVertices; ++v) {
413     ierr = PetscSectionSetDof(coordSection, v, 3);CHKERRQ(ierr);
414   }
415   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
416   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
417   ierr = VecCreate(PetscObjectComm((PetscObject)dm), &coordinates);CHKERRQ(ierr);
418   ierr = VecSetBlockSize(coordinates, 3);CHKERRQ(ierr);
419   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
420   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
421   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
422   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
423   for (vz = 0; vz <= faces[2]; ++vz) {
424     for (vy = 0; vy <= faces[1]; ++vy) {
425       for (vx = 0; vx <= faces[0]; ++vx) {
426         coords[((vz*(faces[1]+1)+vy)*(faces[0]+1)+vx)*3+0] = lower[0] + ((upper[0] - lower[0])/faces[0])*vx;
427         coords[((vz*(faces[1]+1)+vy)*(faces[0]+1)+vx)*3+1] = lower[1] + ((upper[1] - lower[1])/faces[1])*vy;
428         coords[((vz*(faces[1]+1)+vy)*(faces[0]+1)+vx)*3+2] = lower[2] + ((upper[2] - lower[2])/faces[2])*vz;
429       }
430     }
431   }
432   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
433   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
434   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
435   PetscFunctionReturn(0);
436 }
437 
438 #undef __FUNCT__
439 #define __FUNCT__ "DMPlexCreateCubeMesh_Internal"
440 static PetscErrorCode DMPlexCreateCubeMesh_Internal(DM dm, const PetscReal lower[], const PetscReal upper[], const PetscInt edges[], DMBoundaryType bdX, DMBoundaryType bdY, DMBoundaryType bdZ)
441 {
442   PetscInt       markerTop      = 1;
443   PetscInt       markerBottom   = 1;
444   PetscInt       markerFront    = 1;
445   PetscInt       markerBack     = 1;
446   PetscInt       markerRight    = 1;
447   PetscInt       markerLeft     = 1;
448   PetscInt       dim;
449   PetscBool      markerSeparate = PETSC_FALSE;
450   PetscMPIInt    rank;
451   PetscErrorCode ierr;
452 
453   PetscFunctionBegin;
454   ierr = DMGetDimension(dm,&dim);CHKERRQ(ierr);
455   ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);CHKERRQ(ierr);
456   ierr = PetscOptionsGetBool(((PetscObject) dm)->prefix, "-dm_plex_separate_marker", &markerSeparate, NULL);CHKERRQ(ierr);
457   if (markerSeparate) {
458     switch (dim) {
459     case 2:
460       markerTop    = 3;
461       markerBottom = 1;
462       markerRight  = 2;
463       markerLeft   = 4;
464       break;
465     case 3:
466       markerBottom = 1;
467       markerTop    = 2;
468       markerFront  = 3;
469       markerBack   = 4;
470       markerRight  = 5;
471       markerLeft   = 6;
472       break;
473     default:
474       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Dimension %d not supported",dim);
475       break;
476     }
477   }
478   {
479     const PetscInt numXEdges    = !rank ? edges[0]   : 0;
480     const PetscInt numYEdges    = !rank ? edges[1]   : 0;
481     const PetscInt numZEdges    = !rank ? edges[2]   : 0;
482     const PetscInt numXVertices = !rank ? (bdX == DM_BOUNDARY_PERIODIC || bdX == DM_BOUNDARY_TWIST ? edges[0] : edges[0]+1) : 0;
483     const PetscInt numYVertices = !rank ? (bdY == DM_BOUNDARY_PERIODIC || bdY == DM_BOUNDARY_TWIST ? edges[1] : edges[1]+1) : 0;
484     const PetscInt numZVertices = !rank ? (bdZ == DM_BOUNDARY_PERIODIC || bdY == DM_BOUNDARY_TWIST ? edges[2] : edges[2]+1) : 0;
485     const PetscInt numCells     = numXEdges*numYEdges*numZEdges;
486     const PetscInt numXFaces    = numYEdges*numZEdges;
487     const PetscInt numYFaces    = numXEdges*numZEdges;
488     const PetscInt numZFaces    = numXEdges*numYEdges;
489     const PetscInt numTotXFaces = numXVertices*numXFaces;
490     const PetscInt numTotYFaces = numYVertices*numYFaces;
491     const PetscInt numTotZFaces = numZVertices*numZFaces;
492     const PetscInt numFaces     = numTotXFaces + numTotYFaces + numTotZFaces;
493     const PetscInt numTotXEdges = numXEdges*numYVertices*numZVertices;
494     const PetscInt numTotYEdges = numYEdges*numXVertices*numZVertices;
495     const PetscInt numTotZEdges = numZEdges*numXVertices*numYVertices;
496     const PetscInt numVertices  = numXVertices*numYVertices*numZVertices;
497     const PetscInt numEdges     = numTotXEdges + numTotYEdges + numTotZEdges;
498     const PetscInt firstVertex  = (dim == 2) ? numFaces : numCells;
499     const PetscInt firstXFace   = (dim == 2) ? 0 : numCells + numVertices;
500     const PetscInt firstYFace   = firstXFace + numTotXFaces;
501     const PetscInt firstZFace   = firstYFace + numTotYFaces;
502     const PetscInt firstXEdge   = numCells + numFaces + numVertices;
503     const PetscInt firstYEdge   = firstXEdge + numTotXEdges;
504     const PetscInt firstZEdge   = firstYEdge + numTotYEdges;
505     Vec            coordinates;
506     PetscSection   coordSection;
507     PetscScalar   *coords;
508     PetscInt       coordSize;
509     PetscInt       v, vx, vy, vz;
510     PetscInt       c, f, fx, fy, fz, e, ex, ey, ez;
511 
512     ierr = DMPlexSetChart(dm, 0, numCells+numFaces+numEdges+numVertices);CHKERRQ(ierr);
513     for (c = 0; c < numCells; c++) {
514       ierr = DMPlexSetConeSize(dm, c, 6);CHKERRQ(ierr);
515     }
516     for (f = firstXFace; f < firstXFace+numFaces; ++f) {
517       ierr = DMPlexSetConeSize(dm, f, 4);CHKERRQ(ierr);
518     }
519     for (e = firstXEdge; e < firstXEdge+numEdges; ++e) {
520       ierr = DMPlexSetConeSize(dm, e, 2);CHKERRQ(ierr);
521     }
522     ierr = DMSetUp(dm);CHKERRQ(ierr); /* Allocate space for cones */
523     /* Build cells */
524     for (fz = 0; fz < numZEdges; ++fz) {
525       for (fy = 0; fy < numYEdges; ++fy) {
526         for (fx = 0; fx < numXEdges; ++fx) {
527           PetscInt cell    = (fz*numYEdges + fy)*numXEdges + fx;
528           PetscInt faceB   = firstZFace + (fy*numXEdges+fx)*numZVertices +   fz;
529           PetscInt faceT   = firstZFace + (fy*numXEdges+fx)*numZVertices + ((fz+1)%numZVertices);
530           PetscInt faceF   = firstYFace + (fz*numXEdges+fx)*numYVertices +   fy;
531           PetscInt faceK   = firstYFace + (fz*numXEdges+fx)*numYVertices + ((fy+1)%numYVertices);
532           PetscInt faceL   = firstXFace + (fz*numYEdges+fy)*numXVertices +   fx;
533           PetscInt faceR   = firstXFace + (fz*numYEdges+fy)*numXVertices + ((fx+1)%numXVertices);
534                             /* B,  T,  F,  K,  R,  L */
535           PetscInt ornt[8] = {-4,  0,  0, -1,  0, -4}; /* ??? */
536           PetscInt cone[8];
537 
538           /* no boundary twisting in 3D */
539           cone[0] = faceB; cone[1] = faceT; cone[2] = faceF; cone[3] = faceK; cone[4] = faceR; cone[5] = faceL;
540           ierr    = DMPlexSetCone(dm, cell, cone);CHKERRQ(ierr);
541           ierr    = DMPlexSetConeOrientation(dm, cell, ornt);CHKERRQ(ierr);
542         }
543       }
544     }
545     /* Build x faces */
546     for (fz = 0; fz < numZEdges; ++fz) {
547       for (fy = 0; fy < numYEdges; ++fy) {
548         for (fx = 0; fx < numXVertices; ++fx) {
549           PetscInt face    = firstXFace + (fz*numYEdges+fy)*numXVertices + fx;
550           PetscInt edgeL   = firstZEdge + (  fy*                 numXVertices+fx)*numZEdges + fz;
551           PetscInt edgeR   = firstZEdge + (((fy+1)%numYVertices)*numXVertices+fx)*numZEdges + fz;
552           PetscInt edgeB   = firstYEdge + (  fz*                 numXVertices+fx)*numYEdges + fy;
553           PetscInt edgeT   = firstYEdge + (((fz+1)%numZVertices)*numXVertices+fx)*numYEdges + fy;
554           PetscInt ornt[4] = {0, 0, -2, -2};
555           PetscInt cone[4];
556 
557           if (dim == 3) {
558             /* markers */
559             if (bdX != DM_BOUNDARY_PERIODIC) {
560               if (fx == numXVertices-1) {
561                 ierr = DMPlexSetLabelValue(dm, "marker", face, markerRight);CHKERRQ(ierr);
562               }
563               else if (fx == 0) {
564                 ierr = DMPlexSetLabelValue(dm, "marker", face, markerLeft);CHKERRQ(ierr);
565               }
566             }
567           }
568           cone[0] = edgeB; cone[1] = edgeR; cone[2] = edgeT; cone[3] = edgeL;
569           ierr    = DMPlexSetCone(dm, face, cone);CHKERRQ(ierr);
570           ierr    = DMPlexSetConeOrientation(dm, face, ornt);CHKERRQ(ierr);
571         }
572       }
573     }
574     /* Build y faces */
575     for (fz = 0; fz < numZEdges; ++fz) {
576       for (fx = 0; fx < numYEdges; ++fx) {
577         for (fy = 0; fy < numYVertices; ++fy) {
578           PetscInt face    = firstYFace + (fz*numXEdges+fx)*numYVertices + fy;
579           PetscInt edgeL   = firstZEdge + (fy*numXVertices+  fx                 )*numZEdges + fz;
580           PetscInt edgeR   = firstZEdge + (fy*numXVertices+((fx+1)%numXVertices))*numZEdges + fz;
581           PetscInt edgeB   = firstXEdge + (  fz                 *numYVertices+fy)*numXEdges + fx;
582           PetscInt edgeT   = firstXEdge + (((fz+1)%numZVertices)*numYVertices+fy)*numXEdges + fx;
583           PetscInt ornt[4] = {0, 0, -2, -2};
584           PetscInt cone[4];
585 
586           if (dim == 3) {
587             /* markers */
588             if (bdY != DM_BOUNDARY_PERIODIC) {
589               if (fy == numYVertices-1) {
590                 ierr = DMPlexSetLabelValue(dm, "marker", face, markerBack);CHKERRQ(ierr);
591               }
592               else if (fy == 0) {
593                 ierr = DMPlexSetLabelValue(dm, "marker", face, markerFront);CHKERRQ(ierr);
594               }
595             }
596           }
597           cone[0] = edgeB; cone[1] = edgeR; cone[2] = edgeT; cone[3] = edgeL;
598           ierr    = DMPlexSetCone(dm, face, cone);CHKERRQ(ierr);
599           ierr    = DMPlexSetConeOrientation(dm, face, ornt);CHKERRQ(ierr);
600         }
601       }
602     }
603     /* Build z faces */
604     for (fy = 0; fy < numYEdges; ++fy) {
605       for (fx = 0; fx < numXEdges; ++fx) {
606         for (fz = 0; fz < numZVertices; fz++) {
607           PetscInt face    = firstZFace + (fy*numXEdges+fx)*numZVertices + fz;
608           PetscInt edgeL   = firstYEdge + (fz*numXVertices+  fx                 )*numYEdges + fy;
609           PetscInt edgeR   = firstYEdge + (fz*numXVertices+((fx+1)%numXVertices))*numYEdges + fy;
610           PetscInt edgeB   = firstXEdge + (fz*numYVertices+  fy                 )*numXEdges + fx;
611           PetscInt edgeT   = firstXEdge + (fz*numYVertices+((fy+1)%numYVertices))*numXEdges + fx;
612           PetscInt ornt[4] = {0, 0, -2, -2};
613           PetscInt cone[4];
614 
615           if (dim == 2) {
616             if (bdX == DM_BOUNDARY_TWIST && fx == numXEdges-1) {edgeR += numYEdges-1-2*fy; ornt[1] = -2;}
617             if (bdY == DM_BOUNDARY_TWIST && fy == numYEdges-1) {edgeT += numXEdges-1-2*fx; ornt[2] =  0;}
618           }
619           else {
620             /* markers */
621             if (bdZ != DM_BOUNDARY_PERIODIC) {
622               if (fz == numZVertices-1) {
623                 ierr = DMPlexSetLabelValue(dm, "marker", face, markerTop);CHKERRQ(ierr);
624               }
625               else if (fz == 0) {
626                 ierr = DMPlexSetLabelValue(dm, "marker", face, markerBottom);CHKERRQ(ierr);
627               }
628             }
629           }
630           cone[0] = edgeB; cone[1] = edgeR; cone[2] = edgeT; cone[3] = edgeL;
631           ierr    = DMPlexSetCone(dm, face, cone);CHKERRQ(ierr);
632           ierr    = DMPlexSetConeOrientation(dm, face, ornt);CHKERRQ(ierr);
633         }
634       }
635     }
636     /* Build Z edges*/
637     for (vy = 0; vy < numYVertices; vy++) {
638       for (vx = 0; vx < numXVertices; vx++) {
639         for (ez = 0; ez < numZEdges; ez++) {
640           const PetscInt edge    = firstZEdge  + (vy*numXVertices+vx)*numZEdges + ez;
641           const PetscInt vertexB = firstVertex + (  ez                 *numYVertices+vy)*numXVertices + vx;
642           const PetscInt vertexT = firstVertex + (((ez+1)%numZVertices)*numYVertices+vy)*numXVertices + vx;
643           PetscInt       cone[2];
644 
645           if (dim == 3) {
646             if (bdX != DM_BOUNDARY_PERIODIC) {
647               if (vx == numXVertices-1) {
648                 ierr = DMPlexSetLabelValue(dm, "marker", edge, markerRight);CHKERRQ(ierr);
649               }
650               else if (vx == 0) {
651                 ierr = DMPlexSetLabelValue(dm, "marker", edge, markerLeft);CHKERRQ(ierr);
652               }
653             }
654             if (bdY != DM_BOUNDARY_PERIODIC) {
655               if (vy == numYVertices-1) {
656                 ierr = DMPlexSetLabelValue(dm, "marker", edge, markerBack);CHKERRQ(ierr);
657               }
658               else if (vy == 0) {
659                 ierr = DMPlexSetLabelValue(dm, "marker", edge, markerFront);CHKERRQ(ierr);
660               }
661             }
662           }
663           cone[0] = vertexB; cone[1] = vertexT;
664           ierr = DMPlexSetCone(dm, edge, cone);CHKERRQ(ierr);
665         }
666       }
667     }
668     /* Build Y edges*/
669     for (vz = 0; vz < numZVertices; vz++) {
670       for (vx = 0; vx < numXVertices; vx++) {
671         for (ey = 0; ey < numYEdges; ey++) {
672           const PetscInt nextv   = (dim == 2 && bdY == DM_BOUNDARY_TWIST && ey == numYEdges-1) ? (numXVertices-vx-1) : (vz*numYVertices+((ey+1)%numYVertices))*numXVertices + vx;
673           const PetscInt edge    = firstYEdge  + (vz*numXVertices+vx)*numYEdges + ey;
674           const PetscInt vertexF = firstVertex + (vz*numYVertices+ey)*numXVertices + vx;
675           const PetscInt vertexK = firstVertex + nextv;
676           PetscInt       cone[2];
677 
678           cone[0] = vertexF; cone[1] = vertexK;
679           ierr = DMPlexSetCone(dm, edge, cone);CHKERRQ(ierr);
680           if (dim == 2) {
681             if ((bdX != DM_BOUNDARY_PERIODIC) && (bdX != DM_BOUNDARY_TWIST)) {
682               if (vx == numXVertices-1) {
683                 ierr = DMPlexSetLabelValue(dm, "marker", edge,    markerRight);CHKERRQ(ierr);
684                 ierr = DMPlexSetLabelValue(dm, "marker", cone[0], markerRight);CHKERRQ(ierr);
685                 if (ey == numYEdges-1) {
686                   ierr = DMPlexSetLabelValue(dm, "marker", cone[1], markerRight);CHKERRQ(ierr);
687                 }
688               }
689               else if (vx == 0) {
690                 ierr = DMPlexSetLabelValue(dm, "marker", edge,    markerLeft);CHKERRQ(ierr);
691                 ierr = DMPlexSetLabelValue(dm, "marker", cone[0], markerLeft);CHKERRQ(ierr);
692                 if (ey == numYEdges-1) {
693                   ierr = DMPlexSetLabelValue(dm, "marker", cone[1], markerLeft);CHKERRQ(ierr);
694                 }
695               }
696             }
697           }
698           else {
699             if (bdX != DM_BOUNDARY_PERIODIC) {
700               if (vx == numXVertices-1) {
701                 ierr = DMPlexSetLabelValue(dm, "marker", edge, markerRight);CHKERRQ(ierr);
702               }
703               else if (vx == 0) {
704                 ierr = DMPlexSetLabelValue(dm, "marker", edge, markerLeft);CHKERRQ(ierr);
705               }
706             }
707             if (bdZ != DM_BOUNDARY_PERIODIC) {
708               if (vz == numZVertices-1) {
709                 ierr = DMPlexSetLabelValue(dm, "marker", edge, markerTop);CHKERRQ(ierr);
710               }
711               else if (vz == 0) {
712                 ierr = DMPlexSetLabelValue(dm, "marker", edge, markerBottom);CHKERRQ(ierr);
713               }
714             }
715           }
716         }
717       }
718     }
719     /* Build X edges*/
720     for (vz = 0; vz < numZVertices; vz++) {
721       for (vy = 0; vy < numYVertices; vy++) {
722         for (ex = 0; ex < numXEdges; ex++) {
723           const PetscInt nextv   = (dim == 2 && bdX == DM_BOUNDARY_TWIST && ex == numXEdges-1) ? (numYVertices-vy-1)*numXVertices : (vz*numYVertices+vy)*numXVertices + (ex+1)%numXVertices;
724           const PetscInt edge    = firstXEdge  + (vz*numYVertices+vy)*numXEdges + ex;
725           const PetscInt vertexL = firstVertex + (vz*numYVertices+vy)*numXVertices + ex;
726           const PetscInt vertexR = firstVertex + nextv;
727           PetscInt       cone[2];
728 
729           cone[0] = vertexL; cone[1] = vertexR;
730           ierr = DMPlexSetCone(dm, edge, cone);CHKERRQ(ierr);
731           if (dim == 2) {
732             if ((bdY != DM_BOUNDARY_PERIODIC) && (bdY != DM_BOUNDARY_TWIST)) {
733               if (vy == numYVertices-1) {
734                 ierr = DMPlexSetLabelValue(dm, "marker", edge,    markerTop);CHKERRQ(ierr);
735                 ierr = DMPlexSetLabelValue(dm, "marker", cone[0], markerTop);CHKERRQ(ierr);
736                 if (ex == numXEdges-1) {
737                   ierr = DMPlexSetLabelValue(dm, "marker", cone[1], markerTop);CHKERRQ(ierr);
738                 }
739               }
740               else if (vy == 0) {
741                 ierr = DMPlexSetLabelValue(dm, "marker", edge,    markerBottom);CHKERRQ(ierr);
742                 ierr = DMPlexSetLabelValue(dm, "marker", cone[0], markerBottom);CHKERRQ(ierr);
743                 if (ex == numXEdges-1) {
744                   ierr = DMPlexSetLabelValue(dm, "marker", cone[1], markerBottom);CHKERRQ(ierr);
745                 }
746               }
747             }
748           }
749           else {
750             if (bdY != DM_BOUNDARY_PERIODIC) {
751               if (vy == numYVertices-1) {
752                 ierr = DMPlexSetLabelValue(dm, "marker", edge, markerBack);CHKERRQ(ierr);
753               }
754               else if (vy == 0) {
755                 ierr = DMPlexSetLabelValue(dm, "marker", edge, markerFront);CHKERRQ(ierr);
756               }
757             }
758             if (bdZ != DM_BOUNDARY_PERIODIC) {
759               if (vz == numZVertices-1) {
760                 ierr = DMPlexSetLabelValue(dm, "marker", edge, markerTop);CHKERRQ(ierr);
761               }
762               else if (vz == 0) {
763                 ierr = DMPlexSetLabelValue(dm, "marker", edge, markerBottom);CHKERRQ(ierr);
764               }
765             }
766           }
767         }
768       }
769     }
770     ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
771     ierr = DMPlexStratify(dm);CHKERRQ(ierr);
772     /* Build coordinates */
773     ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
774     ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
775     ierr = PetscSectionSetFieldComponents(coordSection, 0, dim);CHKERRQ(ierr);
776     ierr = PetscSectionSetChart(coordSection, firstVertex, firstVertex+numVertices);CHKERRQ(ierr);
777     for (v = firstVertex; v < firstVertex+numVertices; ++v) {
778       ierr = PetscSectionSetDof(coordSection, v, dim);CHKERRQ(ierr);
779       ierr = PetscSectionSetFieldDof(coordSection, v, 0, dim);CHKERRQ(ierr);
780     }
781     ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
782     ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
783     ierr = VecCreate(PetscObjectComm((PetscObject)dm), &coordinates);CHKERRQ(ierr);
784     ierr = VecSetBlockSize(coordinates, dim);CHKERRQ(ierr);
785     ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
786     ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
787     ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
788     for (vz = 0; vz < numZVertices; ++vz) {
789       for (vy = 0; vy < numYVertices; ++vy) {
790         for (vx = 0; vx < numXVertices; ++vx) {
791           coords[((vz*numYVertices+vy)*numXVertices+vx)*dim+0] = lower[0] + ((upper[0] - lower[0])/numXEdges)*vx;
792           coords[((vz*numYVertices+vy)*numXVertices+vx)*dim+1] = lower[1] + ((upper[1] - lower[1])/numYEdges)*vy;
793           if (dim == 3) {
794             coords[((vz*numYVertices+vy)*numXVertices+vx)*dim+2] = lower[2] + ((upper[2] - lower[2])/numZEdges)*vz;
795           }
796         }
797       }
798     }
799     ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
800     ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
801     ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
802   }
803   PetscFunctionReturn(0);
804 }
805 
806 #undef __FUNCT__
807 #define __FUNCT__ "DMPlexCreateSquareMesh"
808 /*@
809   DMPlexCreateSquareMesh - Creates a 2D mesh for a square lattice.
810 
811   Collective on MPI_Comm
812 
813   Input Parameters:
814 + comm  - The communicator for the DM object
815 . lower - The lower left corner coordinates
816 . upper - The upper right corner coordinates
817 . edges - The number of cells in each direction
818 . bdX   - The boundary type for the X direction
819 - bdY   - The boundary type for the Y direction
820 
821   Output Parameter:
822 . dm  - The DM object
823 
824   Note: Here is the numbering returned for 2 cells in each direction:
825 $ 22--8-23--9--24
826 $  |     |     |
827 $ 13  2 14  3  15
828 $  |     |     |
829 $ 19--6-20--7--21
830 $  |     |     |
831 $ 10  0 11  1 12
832 $  |     |     |
833 $ 16--4-17--5--18
834 
835   Level: beginner
836 
837 .keywords: DM, create
838 .seealso: DMPlexCreateBoxMesh(), DMPlexCreateSquareBoundary(), DMPlexCreateCubeBoundary(), DMSetType(), DMCreate()
839 @*/
840 PetscErrorCode DMPlexCreateSquareMesh(DM dm, const PetscReal lower[], const PetscReal upper[], const PetscInt edges[], DMBoundaryType bdX, DMBoundaryType bdY)
841 {
842   PetscReal      lower3[3], upper3[3];
843   PetscInt       edges3[3];
844   PetscErrorCode ierr;
845 
846   PetscFunctionBegin;
847   lower3[0] = lower[0]; lower3[1] = lower[1]; lower3[2] = 0.;
848   upper3[0] = upper[0]; upper3[1] = upper[1]; upper3[2] = 0.;
849   edges3[0] = edges[0]; edges3[1] = edges[1]; edges3[2] = 0;
850   ierr = DMPlexCreateCubeMesh_Internal(dm, lower3, upper3, edges3, bdX, bdY, DM_BOUNDARY_NONE);CHKERRQ(ierr);
851   PetscFunctionReturn(0);
852 }
853 
854 #undef __FUNCT__
855 #define __FUNCT__ "DMPlexCreateBoxMesh"
856 /*@
857   DMPlexCreateBoxMesh - Creates a mesh on the tensor product of unit intervals (box) using simplices.
858 
859   Collective on MPI_Comm
860 
861   Input Parameters:
862 + comm - The communicator for the DM object
863 . dim - The spatial dimension
864 - interpolate - Flag to create intermediate mesh pieces (edges, faces)
865 
866   Output Parameter:
867 . dm  - The DM object
868 
869   Level: beginner
870 
871 .keywords: DM, create
872 .seealso: DMPlexCreateHexBoxMesh(), DMSetType(), DMCreate()
873 @*/
874 PetscErrorCode DMPlexCreateBoxMesh(MPI_Comm comm, PetscInt dim, PetscBool interpolate, DM *dm)
875 {
876   DM             boundary;
877   PetscErrorCode ierr;
878 
879   PetscFunctionBegin;
880   PetscValidPointer(dm, 4);
881   ierr = DMCreate(comm, &boundary);CHKERRQ(ierr);
882   PetscValidLogicalCollectiveInt(boundary,dim,2);
883   ierr = DMSetType(boundary, DMPLEX);CHKERRQ(ierr);
884   ierr = DMSetDimension(boundary, dim-1);CHKERRQ(ierr);
885   switch (dim) {
886   case 2:
887   {
888     PetscReal lower[2] = {0.0, 0.0};
889     PetscReal upper[2] = {1.0, 1.0};
890     PetscInt  edges[2] = {2, 2};
891 
892     ierr = DMPlexCreateSquareBoundary(boundary, lower, upper, edges);CHKERRQ(ierr);
893     break;
894   }
895   case 3:
896   {
897     PetscReal lower[3] = {0.0, 0.0, 0.0};
898     PetscReal upper[3] = {1.0, 1.0, 1.0};
899     PetscInt  faces[3] = {1, 1, 1};
900 
901     ierr = DMPlexCreateCubeBoundary(boundary, lower, upper, faces);CHKERRQ(ierr);
902     break;
903   }
904   default:
905     SETERRQ1(comm, PETSC_ERR_SUP, "Dimension not supported: %d", dim);
906   }
907   ierr = DMPlexGenerate(boundary, NULL, interpolate, dm);CHKERRQ(ierr);
908   ierr = DMDestroy(&boundary);CHKERRQ(ierr);
909   PetscFunctionReturn(0);
910 }
911 
912 #undef __FUNCT__
913 #define __FUNCT__ "DMPlexCreateHexBoxMesh"
914 /*@
915   DMPlexCreateHexBoxMesh - Creates a mesh on the tensor product of unit intervals (box) using hexahedra.
916 
917   Collective on MPI_Comm
918 
919   Input Parameters:
920 + comm  - The communicator for the DM object
921 . dim   - The spatial dimension
922 . periodicX - The boundary type for the X direction
923 . periodicY - The boundary type for the Y direction
924 . periodicZ - The boundary type for the Z direction
925 - cells - The number of cells in each direction
926 
927   Output Parameter:
928 . dm  - The DM object
929 
930   Level: beginner
931 
932 .keywords: DM, create
933 .seealso: DMPlexCreateBoxMesh(), DMSetType(), DMCreate()
934 @*/
935 PetscErrorCode DMPlexCreateHexBoxMesh(MPI_Comm comm, PetscInt dim, const PetscInt cells[], DMBoundaryType periodicX, DMBoundaryType periodicY, DMBoundaryType periodicZ, DM *dm)
936 {
937   PetscErrorCode ierr;
938 
939   PetscFunctionBegin;
940   PetscValidPointer(dm, 4);
941   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
942   PetscValidLogicalCollectiveInt(*dm,dim,2);
943   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
944   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
945   switch (dim) {
946   case 2:
947   {
948     PetscReal lower[2] = {0.0, 0.0};
949     PetscReal upper[2] = {1.0, 1.0};
950 
951     ierr = DMPlexCreateSquareMesh(*dm, lower, upper, cells, periodicX, periodicY);CHKERRQ(ierr);
952     break;
953   }
954   case 3:
955   {
956     PetscReal lower[3] = {0.0, 0.0, 0.0};
957     PetscReal upper[3] = {1.0, 1.0, 1.0};
958 
959     ierr = DMPlexCreateCubeMesh_Internal(*dm, lower, upper, cells, periodicX, periodicY, periodicZ);CHKERRQ(ierr);
960     break;
961   }
962   default:
963     SETERRQ1(comm, PETSC_ERR_SUP, "Dimension not supported: %d", dim);
964   }
965   PetscFunctionReturn(0);
966 }
967 
968 /* External function declarations here */
969 extern PetscErrorCode DMCreateInterpolation_Plex(DM dmCoarse, DM dmFine, Mat *interpolation, Vec *scaling);
970 extern PetscErrorCode DMCreateInjection_Plex(DM dmCoarse, DM dmFine, VecScatter *ctx);
971 extern PetscErrorCode DMCreateDefaultSection_Plex(DM dm);
972 extern PetscErrorCode DMCreateMatrix_Plex(DM dm,  Mat *J);
973 extern PetscErrorCode DMCreateCoordinateDM_Plex(DM dm, DM *cdm);
974 extern PetscErrorCode DMRefine_Plex(DM dm, MPI_Comm comm, DM *dmRefined);
975 extern PetscErrorCode DMCoarsen_Plex(DM dm, MPI_Comm comm, DM *dmCoarsened);
976 extern PetscErrorCode DMRefineHierarchy_Plex(DM dm, PetscInt nlevels, DM dmRefined[]);
977 extern PetscErrorCode DMClone_Plex(DM dm, DM *newdm);
978 extern PetscErrorCode DMSetUp_Plex(DM dm);
979 extern PetscErrorCode DMDestroy_Plex(DM dm);
980 extern PetscErrorCode DMView_Plex(DM dm, PetscViewer viewer);
981 extern PetscErrorCode DMLoad_Plex(DM dm, PetscViewer viewer);
982 extern PetscErrorCode DMCreateSubDM_Plex(DM dm, PetscInt numFields, PetscInt fields[], IS *is, DM *subdm);
983 extern PetscErrorCode DMLocatePoints_Plex(DM dm, Vec v, IS *cellIS);
984 
985 #undef __FUNCT__
986 #define __FUNCT__ "DMPlexReplace_Static"
987 /* Replace dm with the contents of dmNew
988    - Share the DM_Plex structure
989    - Share the coordinates
990    - Share the SF
991 */
992 static PetscErrorCode DMPlexReplace_Static(DM dm, DM dmNew)
993 {
994   PetscSF          sf;
995   DM               coordDM;
996   Vec              coords;
997   const PetscReal *maxCell, *L;
998   PetscErrorCode   ierr;
999 
1000   PetscFunctionBegin;
1001   ierr = DMGetPointSF(dmNew, &sf);CHKERRQ(ierr);
1002   ierr = DMSetPointSF(dm, sf);CHKERRQ(ierr);
1003   ierr = DMGetCoordinateDM(dmNew, &coordDM);CHKERRQ(ierr);
1004   ierr = DMGetCoordinatesLocal(dmNew, &coords);CHKERRQ(ierr);
1005   ierr = DMSetCoordinateDM(dm, coordDM);CHKERRQ(ierr);
1006   ierr = DMSetCoordinatesLocal(dm, coords);CHKERRQ(ierr);
1007   ierr = DMGetPeriodicity(dm, &maxCell, &L);CHKERRQ(ierr);
1008   if (L) {ierr = DMSetPeriodicity(dmNew, maxCell, L);CHKERRQ(ierr);}
1009   ierr = DMDestroy_Plex(dm);CHKERRQ(ierr);
1010   dm->data = dmNew->data;
1011   ((DM_Plex *) dmNew->data)->refct++;
1012   PetscFunctionReturn(0);
1013 }
1014 
1015 #undef __FUNCT__
1016 #define __FUNCT__ "DMPlexSwap_Static"
1017 /* Swap dm with the contents of dmNew
1018    - Swap the DM_Plex structure
1019    - Swap the coordinates
1020 */
1021 static PetscErrorCode DMPlexSwap_Static(DM dmA, DM dmB)
1022 {
1023   DM             coordDMA, coordDMB;
1024   Vec            coordsA,  coordsB;
1025   void          *tmp;
1026   PetscErrorCode ierr;
1027 
1028   PetscFunctionBegin;
1029   ierr = DMGetCoordinateDM(dmA, &coordDMA);CHKERRQ(ierr);
1030   ierr = DMGetCoordinateDM(dmB, &coordDMB);CHKERRQ(ierr);
1031   ierr = PetscObjectReference((PetscObject) coordDMA);CHKERRQ(ierr);
1032   ierr = DMSetCoordinateDM(dmA, coordDMB);CHKERRQ(ierr);
1033   ierr = DMSetCoordinateDM(dmB, coordDMA);CHKERRQ(ierr);
1034   ierr = PetscObjectDereference((PetscObject) coordDMA);CHKERRQ(ierr);
1035 
1036   ierr = DMGetCoordinatesLocal(dmA, &coordsA);CHKERRQ(ierr);
1037   ierr = DMGetCoordinatesLocal(dmB, &coordsB);CHKERRQ(ierr);
1038   ierr = PetscObjectReference((PetscObject) coordsA);CHKERRQ(ierr);
1039   ierr = DMSetCoordinatesLocal(dmA, coordsB);CHKERRQ(ierr);
1040   ierr = DMSetCoordinatesLocal(dmB, coordsA);CHKERRQ(ierr);
1041   ierr = PetscObjectDereference((PetscObject) coordsA);CHKERRQ(ierr);
1042   tmp       = dmA->data;
1043   dmA->data = dmB->data;
1044   dmB->data = tmp;
1045   PetscFunctionReturn(0);
1046 }
1047 
1048 #undef __FUNCT__
1049 #define __FUNCT__ "DMSetFromOptions_NonRefinement_Plex"
1050 PetscErrorCode  DMSetFromOptions_NonRefinement_Plex(DM dm)
1051 {
1052   DM_Plex       *mesh = (DM_Plex*) dm->data;
1053   DMBoundary     b;
1054   PetscErrorCode ierr;
1055 
1056   PetscFunctionBegin;
1057   /* Handle boundary conditions */
1058   ierr = PetscOptionsBegin(PetscObjectComm((PetscObject) dm), NULL, "Boundary condition options", "");CHKERRQ(ierr);
1059   for (b = mesh->boundary; b; b = b->next) {
1060     char      optname[1024];
1061     PetscInt  ids[1024], len = 1024, i;
1062     PetscBool flg;
1063 
1064     ierr = PetscSNPrintf(optname, sizeof(optname), "-bc_%s", b->name);CHKERRQ(ierr);
1065     ierr = PetscMemzero(ids, sizeof(ids));CHKERRQ(ierr);
1066     ierr = PetscOptionsIntArray(optname, "List of boundary IDs", "", ids, &len, &flg);CHKERRQ(ierr);
1067     if (flg) {
1068       DMLabel label;
1069 
1070       ierr = DMPlexGetLabel(dm, b->labelname, &label);CHKERRQ(ierr);
1071       for (i = 0; i < len; ++i) {
1072         PetscBool has;
1073 
1074         ierr = DMLabelHasValue(label, ids[i], &has);CHKERRQ(ierr);
1075         if (!has) SETERRQ2(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_WRONG, "Boundary id %D is not present in the label %s", ids[i], b->name);
1076       }
1077       b->numids = len;
1078       ierr = PetscFree(b->ids);CHKERRQ(ierr);
1079       ierr = PetscMalloc1(len, &b->ids);CHKERRQ(ierr);
1080       ierr = PetscMemcpy(b->ids, ids, len*sizeof(PetscInt));CHKERRQ(ierr);
1081     }
1082   }
1083   ierr = PetscOptionsEnd();CHKERRQ(ierr);
1084   /* Handle viewing */
1085   ierr = PetscOptionsBool("-dm_plex_print_set_values", "Output all set values info", "DMView", PETSC_FALSE, &mesh->printSetValues, NULL);CHKERRQ(ierr);
1086   ierr = PetscOptionsInt("-dm_plex_print_fem", "Debug output level all fem computations", "DMView", 0, &mesh->printFEM, NULL);CHKERRQ(ierr);
1087   ierr = PetscOptionsReal("-dm_plex_print_tol", "Tolerance for FEM output", "DMView", PETSC_FALSE, &mesh->printTol, NULL);CHKERRQ(ierr);
1088   PetscFunctionReturn(0);
1089 }
1090 
1091 #undef __FUNCT__
1092 #define __FUNCT__ "DMSetFromOptions_Plex"
1093 PetscErrorCode  DMSetFromOptions_Plex(DM dm)
1094 {
1095   PetscInt       refine = 0, r;
1096   PetscBool      isHierarchy;
1097   PetscErrorCode ierr;
1098 
1099   PetscFunctionBegin;
1100   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1101   ierr = PetscOptionsHead("DMPlex Options");CHKERRQ(ierr);
1102   /* Handle DMPlex refinement */
1103   ierr = PetscOptionsInt("-dm_refine", "The number of uniform refinements", "DMCreate", refine, &refine, NULL);CHKERRQ(ierr);
1104   ierr = PetscOptionsInt("-dm_refine_hierarchy", "The number of uniform refinements", "DMCreate", refine, &refine, &isHierarchy);CHKERRQ(ierr);
1105   if (refine) {ierr = DMPlexSetRefinementUniform(dm, PETSC_TRUE);CHKERRQ(ierr);}
1106   if (refine && isHierarchy) {
1107     DM *dms;
1108 
1109     ierr = PetscMalloc1(refine,&dms);CHKERRQ(ierr);
1110     ierr = DMRefineHierarchy(dm, refine, dms);CHKERRQ(ierr);
1111     /* Total hack since we do not pass in a pointer */
1112     ierr = DMPlexSwap_Static(dm, dms[refine-1]);CHKERRQ(ierr);
1113     if (refine == 1) {
1114       ierr = DMPlexSetCoarseDM(dm, dms[0]);CHKERRQ(ierr);
1115     } else {
1116       ierr = DMPlexSetCoarseDM(dm, dms[refine-2]);CHKERRQ(ierr);
1117       ierr = DMPlexSetCoarseDM(dms[0], dms[refine-1]);CHKERRQ(ierr);
1118     }
1119     /* Free DMs */
1120     for (r = 0; r < refine; ++r) {
1121       ierr = DMSetFromOptions_NonRefinement_Plex(dm);CHKERRQ(ierr);
1122       ierr = DMDestroy(&dms[r]);CHKERRQ(ierr);
1123     }
1124     ierr = PetscFree(dms);CHKERRQ(ierr);
1125   } else {
1126     for (r = 0; r < refine; ++r) {
1127       DM refinedMesh;
1128 
1129       ierr = DMSetFromOptions_NonRefinement_Plex(dm);CHKERRQ(ierr);
1130       ierr = DMRefine(dm, PetscObjectComm((PetscObject) dm), &refinedMesh);CHKERRQ(ierr);
1131       /* Total hack since we do not pass in a pointer */
1132       ierr = DMPlexReplace_Static(dm, refinedMesh);CHKERRQ(ierr);
1133       ierr = DMDestroy(&refinedMesh);CHKERRQ(ierr);
1134     }
1135   }
1136   ierr = DMSetFromOptions_NonRefinement_Plex(dm);CHKERRQ(ierr);
1137   ierr = PetscOptionsTail();CHKERRQ(ierr);
1138   PetscFunctionReturn(0);
1139 }
1140 
1141 #undef __FUNCT__
1142 #define __FUNCT__ "DMCreateGlobalVector_Plex"
1143 static PetscErrorCode DMCreateGlobalVector_Plex(DM dm,Vec *vec)
1144 {
1145   PetscErrorCode ierr;
1146 
1147   PetscFunctionBegin;
1148   ierr = DMCreateGlobalVector_Section_Private(dm,vec);CHKERRQ(ierr);
1149   /* ierr = VecSetOperation(*vec, VECOP_DUPLICATE, (void(*)(void)) VecDuplicate_MPI_DM);CHKERRQ(ierr); */
1150   ierr = VecSetOperation(*vec, VECOP_VIEW, (void (*)(void)) VecView_Plex);CHKERRQ(ierr);
1151   ierr = VecSetOperation(*vec, VECOP_LOAD, (void (*)(void)) VecLoad_Plex);CHKERRQ(ierr);
1152   PetscFunctionReturn(0);
1153 }
1154 
1155 #undef __FUNCT__
1156 #define __FUNCT__ "DMCreateLocalVector_Plex"
1157 static PetscErrorCode DMCreateLocalVector_Plex(DM dm,Vec *vec)
1158 {
1159   PetscErrorCode ierr;
1160 
1161   PetscFunctionBegin;
1162   ierr = DMCreateLocalVector_Section_Private(dm,vec);CHKERRQ(ierr);
1163   ierr = VecSetOperation(*vec, VECOP_VIEW, (void (*)(void)) VecView_Plex_Local);CHKERRQ(ierr);
1164   ierr = VecSetOperation(*vec, VECOP_LOAD, (void (*)(void)) VecLoad_Plex_Local);CHKERRQ(ierr);
1165   PetscFunctionReturn(0);
1166 }
1167 
1168 #undef __FUNCT__
1169 #define __FUNCT__ "DMGetDimPoints_Plex"
1170 static PetscErrorCode DMGetDimPoints_Plex(DM dm, PetscInt dim, PetscInt *pStart, PetscInt *pEnd)
1171 {
1172   PetscInt       depth, d;
1173   PetscErrorCode ierr;
1174 
1175   PetscFunctionBegin;
1176   ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
1177   if (depth == 1) {
1178     ierr = DMGetDimension(dm, &d);CHKERRQ(ierr);
1179     if (dim == 0)      {ierr = DMPlexGetDepthStratum(dm, dim, pStart, pEnd);CHKERRQ(ierr);}
1180     else if (dim == d) {ierr = DMPlexGetDepthStratum(dm, 1, pStart, pEnd);CHKERRQ(ierr);}
1181     else               {*pStart = 0; *pEnd = 0;}
1182   } else {
1183     ierr = DMPlexGetDepthStratum(dm, dim, pStart, pEnd);CHKERRQ(ierr);
1184   }
1185   PetscFunctionReturn(0);
1186 }
1187 
1188 #undef __FUNCT__
1189 #define __FUNCT__ "DMInitialize_Plex"
1190 PetscErrorCode DMInitialize_Plex(DM dm)
1191 {
1192   PetscFunctionBegin;
1193   dm->ops->view                            = DMView_Plex;
1194   dm->ops->load                            = DMLoad_Plex;
1195   dm->ops->setfromoptions                  = DMSetFromOptions_Plex;
1196   dm->ops->clone                           = DMClone_Plex;
1197   dm->ops->setup                           = DMSetUp_Plex;
1198   dm->ops->createdefaultsection            = DMCreateDefaultSection_Plex;
1199   dm->ops->createglobalvector              = DMCreateGlobalVector_Plex;
1200   dm->ops->createlocalvector               = DMCreateLocalVector_Plex;
1201   dm->ops->getlocaltoglobalmapping         = NULL;
1202   dm->ops->createfieldis                   = NULL;
1203   dm->ops->createcoordinatedm              = DMCreateCoordinateDM_Plex;
1204   dm->ops->getcoloring                     = NULL;
1205   dm->ops->creatematrix                    = DMCreateMatrix_Plex;
1206   dm->ops->createinterpolation             = DMCreateInterpolation_Plex;
1207   dm->ops->getaggregates                   = NULL;
1208   dm->ops->getinjection                    = DMCreateInjection_Plex;
1209   dm->ops->refine                          = DMRefine_Plex;
1210   dm->ops->coarsen                         = DMCoarsen_Plex;
1211   dm->ops->refinehierarchy                 = DMRefineHierarchy_Plex;
1212   dm->ops->coarsenhierarchy                = NULL;
1213   dm->ops->globaltolocalbegin              = NULL;
1214   dm->ops->globaltolocalend                = NULL;
1215   dm->ops->localtoglobalbegin              = NULL;
1216   dm->ops->localtoglobalend                = NULL;
1217   dm->ops->destroy                         = DMDestroy_Plex;
1218   dm->ops->createsubdm                     = DMCreateSubDM_Plex;
1219   dm->ops->getdimpoints                    = DMGetDimPoints_Plex;
1220   dm->ops->locatepoints                    = DMLocatePoints_Plex;
1221   PetscFunctionReturn(0);
1222 }
1223 
1224 #undef __FUNCT__
1225 #define __FUNCT__ "DMClone_Plex"
1226 PetscErrorCode DMClone_Plex(DM dm, DM *newdm)
1227 {
1228   DM_Plex        *mesh = (DM_Plex *) dm->data;
1229   PetscErrorCode ierr;
1230 
1231   PetscFunctionBegin;
1232   mesh->refct++;
1233   (*newdm)->data = mesh;
1234   ierr = PetscObjectChangeTypeName((PetscObject) *newdm, DMPLEX);CHKERRQ(ierr);
1235   ierr = DMInitialize_Plex(*newdm);CHKERRQ(ierr);
1236   PetscFunctionReturn(0);
1237 }
1238 
1239 /*MC
1240   DMPLEX = "plex" - A DM object that encapsulates an unstructured mesh, or CW Complex, which can be expressed using a Hasse Diagram.
1241                     In the local representation, Vecs contain all unknowns in the interior and shared boundary. This is
1242                     specified by a PetscSection object. Ownership in the global representation is determined by
1243                     ownership of the underlying DMPlex points. This is specified by another PetscSection object.
1244 
1245   Level: intermediate
1246 
1247 .seealso: DMType, DMPlexCreate(), DMCreate(), DMSetType()
1248 M*/
1249 
1250 #undef __FUNCT__
1251 #define __FUNCT__ "DMCreate_Plex"
1252 PETSC_EXTERN PetscErrorCode DMCreate_Plex(DM dm)
1253 {
1254   DM_Plex        *mesh;
1255   PetscInt       unit, d;
1256   PetscErrorCode ierr;
1257 
1258   PetscFunctionBegin;
1259   PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
1260   ierr     = PetscNewLog(dm,&mesh);CHKERRQ(ierr);
1261   dm->dim  = 0;
1262   dm->data = mesh;
1263 
1264   mesh->refct             = 1;
1265   ierr                    = PetscSectionCreate(PetscObjectComm((PetscObject)dm), &mesh->coneSection);CHKERRQ(ierr);
1266   mesh->maxConeSize       = 0;
1267   mesh->cones             = NULL;
1268   mesh->coneOrientations  = NULL;
1269   ierr                    = PetscSectionCreate(PetscObjectComm((PetscObject)dm), &mesh->supportSection);CHKERRQ(ierr);
1270   mesh->maxSupportSize    = 0;
1271   mesh->supports          = NULL;
1272   mesh->refinementUniform = PETSC_TRUE;
1273   mesh->refinementLimit   = -1.0;
1274 
1275   mesh->facesTmp = NULL;
1276 
1277   mesh->subpointMap = NULL;
1278 
1279   for (unit = 0; unit < NUM_PETSC_UNITS; ++unit) mesh->scale[unit] = 1.0;
1280 
1281   mesh->labels              = NULL;
1282   mesh->depthLabel          = NULL;
1283   mesh->globalVertexNumbers = NULL;
1284   mesh->globalCellNumbers   = NULL;
1285   mesh->anchorSection       = NULL;
1286   mesh->anchorIS            = NULL;
1287   mesh->constraintSection   = NULL;
1288   mesh->constraintMat       = NULL;
1289   mesh->parentSection       = NULL;
1290   mesh->parents             = NULL;
1291   mesh->childIDs            = NULL;
1292   mesh->childSection        = NULL;
1293   mesh->children            = NULL;
1294   mesh->referenceTree       = NULL;
1295   mesh->getchildsymmetry    = NULL;
1296   for (d = 0; d < 8; ++d) mesh->hybridPointMax[d] = PETSC_DETERMINE;
1297   mesh->vtkCellHeight       = 0;
1298   mesh->useCone             = PETSC_FALSE;
1299   mesh->useClosure          = PETSC_TRUE;
1300   mesh->useConstraints      = PETSC_FALSE;
1301 
1302   mesh->printSetValues = PETSC_FALSE;
1303   mesh->printFEM       = 0;
1304   mesh->printTol       = 1.0e-10;
1305 
1306   ierr = DMInitialize_Plex(dm);CHKERRQ(ierr);
1307   PetscFunctionReturn(0);
1308 }
1309 
1310 #undef __FUNCT__
1311 #define __FUNCT__ "DMPlexCreate"
1312 /*@
1313   DMPlexCreate - Creates a DMPlex object, which encapsulates an unstructured mesh, or CW complex, which can be expressed using a Hasse Diagram.
1314 
1315   Collective on MPI_Comm
1316 
1317   Input Parameter:
1318 . comm - The communicator for the DMPlex object
1319 
1320   Output Parameter:
1321 . mesh  - The DMPlex object
1322 
1323   Level: beginner
1324 
1325 .keywords: DMPlex, create
1326 @*/
1327 PetscErrorCode DMPlexCreate(MPI_Comm comm, DM *mesh)
1328 {
1329   PetscErrorCode ierr;
1330 
1331   PetscFunctionBegin;
1332   PetscValidPointer(mesh,2);
1333   ierr = DMCreate(comm, mesh);CHKERRQ(ierr);
1334   ierr = DMSetType(*mesh, DMPLEX);CHKERRQ(ierr);
1335   PetscFunctionReturn(0);
1336 }
1337 
1338 #undef __FUNCT__
1339 #define __FUNCT__ "DMPlexBuildFromCellList_Private"
1340 /*
1341   This takes as input the common mesh generator output, a list of the vertices for each cell
1342 */
1343 PetscErrorCode DMPlexBuildFromCellList_Private(DM dm, PetscInt numCells, PetscInt numVertices, PetscInt numCorners, const int cells[])
1344 {
1345   PetscInt      *cone, c, p;
1346   PetscErrorCode ierr;
1347 
1348   PetscFunctionBegin;
1349   ierr = DMPlexSetChart(dm, 0, numCells+numVertices);CHKERRQ(ierr);
1350   for (c = 0; c < numCells; ++c) {
1351     ierr = DMPlexSetConeSize(dm, c, numCorners);CHKERRQ(ierr);
1352   }
1353   ierr = DMSetUp(dm);CHKERRQ(ierr);
1354   ierr = DMGetWorkArray(dm, numCorners, PETSC_INT, &cone);CHKERRQ(ierr);
1355   for (c = 0; c < numCells; ++c) {
1356     for (p = 0; p < numCorners; ++p) {
1357       cone[p] = cells[c*numCorners+p]+numCells;
1358     }
1359     ierr = DMPlexSetCone(dm, c, cone);CHKERRQ(ierr);
1360   }
1361   ierr = DMRestoreWorkArray(dm, numCorners, PETSC_INT, &cone);CHKERRQ(ierr);
1362   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
1363   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
1364   PetscFunctionReturn(0);
1365 }
1366 
1367 #undef __FUNCT__
1368 #define __FUNCT__ "DMPlexBuildCoordinates_Private"
1369 /*
1370   This takes as input the coordinates for each vertex
1371 */
1372 PetscErrorCode DMPlexBuildCoordinates_Private(DM dm, PetscInt spaceDim, PetscInt numCells, PetscInt numVertices, const double vertexCoords[])
1373 {
1374   PetscSection   coordSection;
1375   Vec            coordinates;
1376   PetscScalar   *coords;
1377   PetscInt       coordSize, v, d;
1378   PetscErrorCode ierr;
1379 
1380   PetscFunctionBegin;
1381   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
1382   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
1383   ierr = PetscSectionSetFieldComponents(coordSection, 0, spaceDim);CHKERRQ(ierr);
1384   ierr = PetscSectionSetChart(coordSection, numCells, numCells + numVertices);CHKERRQ(ierr);
1385   for (v = numCells; v < numCells+numVertices; ++v) {
1386     ierr = PetscSectionSetDof(coordSection, v, spaceDim);CHKERRQ(ierr);
1387     ierr = PetscSectionSetFieldDof(coordSection, v, 0, spaceDim);CHKERRQ(ierr);
1388   }
1389   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
1390   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
1391   ierr = VecCreate(PetscObjectComm((PetscObject)dm), &coordinates);CHKERRQ(ierr);
1392   ierr = VecSetBlockSize(coordinates, spaceDim);CHKERRQ(ierr);
1393   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
1394   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
1395   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
1396   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
1397   for (v = 0; v < numVertices; ++v) {
1398     for (d = 0; d < spaceDim; ++d) {
1399       coords[v*spaceDim+d] = vertexCoords[v*spaceDim+d];
1400     }
1401   }
1402   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
1403   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
1404   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
1405   PetscFunctionReturn(0);
1406 }
1407 
1408 #undef __FUNCT__
1409 #define __FUNCT__ "DMPlexCreateFromCellList"
1410 /*@C
1411   DMPlexCreateFromCellList - This takes as input common mesh generator output, a list of the vertices for each cell, and produces a DM
1412 
1413   Input Parameters:
1414 + comm - The communicator
1415 . dim - The topological dimension of the mesh
1416 . numCells - The number of cells
1417 . numVertices - The number of vertices
1418 . numCorners - The number of vertices for each cell
1419 . interpolate - Flag indicating that intermediate mesh entities (faces, edges) should be created automatically
1420 . cells - An array of numCells*numCorners numbers, the vertices for each cell
1421 . spaceDim - The spatial dimension used for coordinates
1422 - vertexCoords - An array of numVertices*spaceDim numbers, the coordinates of each vertex
1423 
1424   Output Parameter:
1425 . dm - The DM
1426 
1427   Note: Two triangles sharing a face
1428 $
1429 $        2
1430 $      / | \
1431 $     /  |  \
1432 $    /   |   \
1433 $   0  0 | 1  3
1434 $    \   |   /
1435 $     \  |  /
1436 $      \ | /
1437 $        1
1438 would have input
1439 $  numCells = 2, numVertices = 4
1440 $  cells = [0 1 2  1 3 2]
1441 $
1442 which would result in the DMPlex
1443 $
1444 $        4
1445 $      / | \
1446 $     /  |  \
1447 $    /   |   \
1448 $   2  0 | 1  5
1449 $    \   |   /
1450 $     \  |  /
1451 $      \ | /
1452 $        3
1453 
1454   Level: beginner
1455 
1456 .seealso: DMPlexCreateFromDAG(), DMPlexCreate()
1457 @*/
1458 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)
1459 {
1460   PetscErrorCode ierr;
1461 
1462   PetscFunctionBegin;
1463   ierr = DMCreate(comm, dm);CHKERRQ(ierr);
1464   ierr = DMSetType(*dm, DMPLEX);CHKERRQ(ierr);
1465   ierr = DMSetDimension(*dm, dim);CHKERRQ(ierr);
1466   ierr = DMPlexBuildFromCellList_Private(*dm, numCells, numVertices, numCorners, cells);CHKERRQ(ierr);
1467   if (interpolate) {
1468     DM idm = NULL;
1469 
1470     ierr = DMPlexInterpolate(*dm, &idm);CHKERRQ(ierr);
1471     ierr = DMDestroy(dm);CHKERRQ(ierr);
1472     *dm  = idm;
1473   }
1474   ierr = DMPlexBuildCoordinates_Private(*dm, spaceDim, numCells, numVertices, vertexCoords);CHKERRQ(ierr);
1475   PetscFunctionReturn(0);
1476 }
1477 
1478 #undef __FUNCT__
1479 #define __FUNCT__ "DMPlexCreateFromDAG"
1480 /*@
1481   DMPlexCreateFromDAG - This takes as input the adjacency-list representation of the Directed Acyclic Graph (Hasse Diagram) encoding a mesh, and produces a DM
1482 
1483   Input Parameters:
1484 + dm - The empty DM object, usually from DMCreate() and DMSetDimension()
1485 . depth - The depth of the DAG
1486 . numPoints - The number of points at each depth
1487 . coneSize - The cone size of each point
1488 . cones - The concatenation of the cone points for each point, the cone list must be oriented correctly for each point
1489 . coneOrientations - The orientation of each cone point
1490 - vertexCoords - An array of numVertices*dim numbers, the coordinates of each vertex
1491 
1492   Output Parameter:
1493 . dm - The DM
1494 
1495   Note: Two triangles sharing a face would have input
1496 $  depth = 1, numPoints = [4 2], coneSize = [3 3 0 0 0 0]
1497 $  cones = [2 3 4  3 5 4], coneOrientations = [0 0 0  0 0 0]
1498 $ vertexCoords = [-1.0 0.0  0.0 -1.0  0.0 1.0  1.0 0.0]
1499 $
1500 which would result in the DMPlex
1501 $
1502 $        4
1503 $      / | \
1504 $     /  |  \
1505 $    /   |   \
1506 $   2  0 | 1  5
1507 $    \   |   /
1508 $     \  |  /
1509 $      \ | /
1510 $        3
1511 $
1512 $ Notice that all points are numbered consecutively, unlikely DMPlexCreateFromCellList()
1513 
1514   Level: advanced
1515 
1516 .seealso: DMPlexCreateFromCellList(), DMPlexCreate()
1517 @*/
1518 PetscErrorCode DMPlexCreateFromDAG(DM dm, PetscInt depth, const PetscInt numPoints[], const PetscInt coneSize[], const PetscInt cones[], const PetscInt coneOrientations[], const PetscScalar vertexCoords[])
1519 {
1520   Vec            coordinates;
1521   PetscSection   coordSection;
1522   PetscScalar    *coords;
1523   PetscInt       coordSize, firstVertex = -1, pStart = 0, pEnd = 0, p, v, dim, d, off;
1524   PetscErrorCode ierr;
1525 
1526   PetscFunctionBegin;
1527   ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
1528   for (d = 0; d <= depth; ++d) pEnd += numPoints[d];
1529   ierr = DMPlexSetChart(dm, pStart, pEnd);CHKERRQ(ierr);
1530   for (p = pStart; p < pEnd; ++p) {
1531     ierr = DMPlexSetConeSize(dm, p, coneSize[p-pStart]);CHKERRQ(ierr);
1532     if (firstVertex < 0 && !coneSize[p - pStart]) {
1533       firstVertex = p - pStart;
1534     }
1535   }
1536   if (firstVertex < 0 && numPoints[0]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Expected %d vertices but could not find any", numPoints[0]);
1537   ierr = DMSetUp(dm);CHKERRQ(ierr); /* Allocate space for cones */
1538   for (p = pStart, off = 0; p < pEnd; off += coneSize[p-pStart], ++p) {
1539     ierr = DMPlexSetCone(dm, p, &cones[off]);CHKERRQ(ierr);
1540     ierr = DMPlexSetConeOrientation(dm, p, &coneOrientations[off]);CHKERRQ(ierr);
1541   }
1542   ierr = DMPlexSymmetrize(dm);CHKERRQ(ierr);
1543   ierr = DMPlexStratify(dm);CHKERRQ(ierr);
1544   /* Build coordinates */
1545   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
1546   ierr = PetscSectionSetNumFields(coordSection, 1);CHKERRQ(ierr);
1547   ierr = PetscSectionSetFieldComponents(coordSection, 0, dim);CHKERRQ(ierr);
1548   ierr = PetscSectionSetChart(coordSection, firstVertex, firstVertex+numPoints[0]);CHKERRQ(ierr);
1549   for (v = firstVertex; v < firstVertex+numPoints[0]; ++v) {
1550     ierr = PetscSectionSetDof(coordSection, v, dim);CHKERRQ(ierr);
1551     ierr = PetscSectionSetFieldDof(coordSection, v, 0, dim);CHKERRQ(ierr);
1552   }
1553   ierr = PetscSectionSetUp(coordSection);CHKERRQ(ierr);
1554   ierr = PetscSectionGetStorageSize(coordSection, &coordSize);CHKERRQ(ierr);
1555   ierr = VecCreate(PetscObjectComm((PetscObject)dm), &coordinates);CHKERRQ(ierr);
1556   ierr = VecSetBlockSize(coordinates, dim);CHKERRQ(ierr);
1557   ierr = PetscObjectSetName((PetscObject) coordinates, "coordinates");CHKERRQ(ierr);
1558   ierr = VecSetSizes(coordinates, coordSize, PETSC_DETERMINE);CHKERRQ(ierr);
1559   ierr = VecSetType(coordinates,VECSTANDARD);CHKERRQ(ierr);
1560   ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
1561   for (v = 0; v < numPoints[0]; ++v) {
1562     PetscInt off;
1563 
1564     ierr = PetscSectionGetOffset(coordSection, v+firstVertex, &off);CHKERRQ(ierr);
1565     for (d = 0; d < dim; ++d) {
1566       coords[off+d] = vertexCoords[v*dim+d];
1567     }
1568   }
1569   ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
1570   ierr = DMSetCoordinatesLocal(dm, coordinates);CHKERRQ(ierr);
1571   ierr = VecDestroy(&coordinates);CHKERRQ(ierr);
1572   PetscFunctionReturn(0);
1573 }
1574 
1575 #undef __FUNCT__
1576 #define __FUNCT__ "DMPlexCreateReferenceCell"
1577 /*@
1578   DMPlexCreateReferenceCell - Create a DMPLEX with the appropriate FEM reference cell
1579 
1580   Collective on comm
1581 
1582   Input Parameters:
1583 + comm    - The communicator
1584 . dim     - The spatial dimension
1585 - simplex - Flag for simplex, otherwise use a tensor-product cell
1586 
1587   Output Parameter:
1588 . refdm - The reference cell
1589 
1590   Level: intermediate
1591 
1592 .keywords: reference cell
1593 .seealso:
1594 @*/
1595 PetscErrorCode DMPlexCreateReferenceCell(MPI_Comm comm, PetscInt dim, PetscBool simplex, DM *refdm)
1596 {
1597   DM             rdm;
1598   PetscErrorCode ierr;
1599 
1600   PetscFunctionBeginUser;
1601   ierr = DMCreate(comm, &rdm);CHKERRQ(ierr);
1602   ierr = DMSetType(rdm, DMPLEX);CHKERRQ(ierr);
1603   ierr = DMSetDimension(rdm, dim);CHKERRQ(ierr);
1604   switch (dim) {
1605   case 0:
1606   {
1607     PetscInt    numPoints[1]        = {1};
1608     PetscInt    coneSize[1]         = {0};
1609     PetscInt    cones[1]            = {0};
1610     PetscInt    coneOrientations[1] = {0};
1611     PetscScalar vertexCoords[1]     = {0.0};
1612 
1613     ierr = DMPlexCreateFromDAG(rdm, 0, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
1614   }
1615   break;
1616   case 1:
1617   {
1618     PetscInt    numPoints[2]        = {2, 1};
1619     PetscInt    coneSize[3]         = {2, 0, 0};
1620     PetscInt    cones[2]            = {1, 2};
1621     PetscInt    coneOrientations[2] = {0, 0};
1622     PetscScalar vertexCoords[2]     = {-1.0,  1.0};
1623 
1624     ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
1625   }
1626   break;
1627   case 2:
1628     if (simplex) {
1629       PetscInt    numPoints[2]        = {3, 1};
1630       PetscInt    coneSize[4]         = {3, 0, 0, 0};
1631       PetscInt    cones[3]            = {1, 2, 3};
1632       PetscInt    coneOrientations[3] = {0, 0, 0};
1633       PetscScalar vertexCoords[6]     = {-1.0, -1.0,  1.0, -1.0,  -1.0, 1.0};
1634 
1635       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
1636     } else {
1637       PetscInt    numPoints[2]        = {4, 1};
1638       PetscInt    coneSize[5]         = {4, 0, 0, 0, 0};
1639       PetscInt    cones[4]            = {1, 2, 3, 4};
1640       PetscInt    coneOrientations[4] = {0, 0, 0, 0};
1641       PetscScalar vertexCoords[8]     = {-1.0, -1.0,  1.0, -1.0,  1.0, 1.0,  -1.0, 1.0};
1642 
1643       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
1644     }
1645   break;
1646   case 3:
1647     if (simplex) {
1648       PetscInt    numPoints[2]        = {4, 1};
1649       PetscInt    coneSize[5]         = {4, 0, 0, 0, 0};
1650       PetscInt    cones[4]            = {1, 3, 2, 4};
1651       PetscInt    coneOrientations[4] = {0, 0, 0, 0};
1652       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};
1653 
1654       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
1655     } else {
1656       PetscInt    numPoints[2]        = {8, 1};
1657       PetscInt    coneSize[9]         = {8, 0, 0, 0, 0, 0, 0, 0, 0};
1658       PetscInt    cones[8]            = {1, 4, 3, 2, 5, 6, 7, 8};
1659       PetscInt    coneOrientations[8] = {0, 0, 0, 0, 0, 0, 0, 0};
1660       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,
1661                                          -1.0, -1.0,  1.0,  1.0, -1.0,  1.0,  1.0, 1.0,  1.0,  -1.0, 1.0,  1.0};
1662 
1663       ierr = DMPlexCreateFromDAG(rdm, 1, numPoints, coneSize, cones, coneOrientations, vertexCoords);CHKERRQ(ierr);
1664     }
1665   break;
1666   default:
1667     SETERRQ1(comm, PETSC_ERR_ARG_WRONG, "Cannot create reference cell for dimension %d", dim);
1668   }
1669   *refdm = NULL;
1670   ierr = DMPlexInterpolate(rdm, refdm);CHKERRQ(ierr);
1671   ierr = DMPlexCopyCoordinates(rdm, *refdm);CHKERRQ(ierr);
1672   ierr = DMDestroy(&rdm);CHKERRQ(ierr);
1673   PetscFunctionReturn(0);
1674 }
1675