Actual source code: plexrefregular.c

  1: #include <petsc/private/dmplextransformimpl.h>

  3: /*
  4:    Regular Refinement of Hybrid Meshes

  6:    We would like to express regular refinement as a small set of rules that can be applied on every point of the Plex
  7:    to automatically generate a refined Plex. In fact, we would like these rules to be general enough to encompass other
  8:    transformations, such as changing from one type of cell to another, as simplex to hex.

 10:    To start, we can create a function that takes an original cell type and returns the number of new cells replacing it
 11:    and the types of the new cells.

 13:    We need the group multiplication table for group actions from the dihedral group for each cell type.

 15:    We need an operator which takes in a cell, and produces a new set of cells with new faces and correct orientations. I think
 16:    we can just write this operator for faces with identity, and then compose the face orientation actions to get the actual
 17:    (face, orient) pairs for each subcell.
 18: */

 20: /*@
 21:   DMPlexRefineRegularGetAffineFaceTransforms - Gets the affine map from the reference face cell to each face in the given cell

 23:   Input Parameters:
 24: + tr - The `DMPlexTransform` object
 25: - ct - The cell type

 27:   Output Parameters:
 28: + Nf   - The number of faces for this cell type
 29: . v0   - The translation of the first vertex for each face
 30: . J    - The Jacobian for each face (map from original cell to subcell)
 31: . invJ - The inverse Jacobian for each face
 32: - detJ - The determinant of the Jacobian for each face

 34:   Level: developer

 36:   Note:
 37:   The Jacobian and inverse Jacobian will be rectangular, and the inverse is really a generalized inverse.
 38: .vb
 39:     v0 + j x_face = x_cell
 40:     invj (x_cell - v0) = x_face
 41: .ve

 43: .seealso: `DMPLEX`, `DM`, `DMPlexTransform`, `DMPolytopeType`, `DMPlexCellRefinerGetAffineTransforms()`
 44: @*/
 45: PetscErrorCode DMPlexRefineRegularGetAffineFaceTransforms(DMPlexTransform tr, DMPolytopeType ct, PetscInt *Nf, PetscReal *v0[], PetscReal *J[], PetscReal *invJ[], PetscReal *detJ[])
 46: {
 47:   /*
 48:    2
 49:    |\
 50:    | \
 51:    |  \
 52:    |   \
 53:    |    \
 54:    |     \
 55:    |      \
 56:    2       1
 57:    |        \
 58:    |         \
 59:    |          \
 60:    0---0-------1
 61:    v0[Nf][dc]:       3 x 2
 62:    J[Nf][df][dc]:    3 x 1 x 2
 63:    invJ[Nf][dc][df]: 3 x 2 x 1
 64:    detJ[Nf]:         3
 65:    */
 66:   static PetscReal tri_v0[]   = {0.0, -1.0, 0.0, 0.0, -1.0, 0.0};
 67:   static PetscReal tri_J[]    = {1.0, 0.0, -1.0, 1.0, 0.0, -1.0};
 68:   static PetscReal tri_invJ[] = {1.0, 0.0, -0.5, 0.5, 0.0, -1.0};
 69:   static PetscReal tri_detJ[] = {1.0, 1.414213562373095, 1.0};
 70:   /*
 71:    3---------2---------2
 72:    |                   |
 73:    |                   |
 74:    |                   |
 75:    3                   1
 76:    |                   |
 77:    |                   |
 78:    |                   |
 79:    0---------0---------1

 81:    v0[Nf][dc]:       4 x 2
 82:    J[Nf][df][dc]:    4 x 1 x 2
 83:    invJ[Nf][dc][df]: 4 x 2 x 1
 84:    detJ[Nf]:         4
 85:    */
 86:   static PetscReal quad_v0[]   = {0.0, -1.0, 1.0, 0.0, 0.0, 1.0, -1.0, 0.0};
 87:   static PetscReal quad_J[]    = {1.0, 0.0, 0.0, 1.0, -1.0, 0.0, 0.0, -1.0};
 88:   static PetscReal quad_invJ[] = {1.0, 0.0, 0.0, 1.0, -1.0, 0.0, 0.0, -1.0};
 89:   static PetscReal quad_detJ[] = {1.0, 1.0, 1.0, 1.0};

 91:   PetscFunctionBegin;
 92:   switch (ct) {
 93:   case DM_POLYTOPE_TRIANGLE:
 94:     if (Nf) *Nf = 3;
 95:     if (v0) *v0 = tri_v0;
 96:     if (J) *J = tri_J;
 97:     if (invJ) *invJ = tri_invJ;
 98:     if (detJ) *detJ = tri_detJ;
 99:     break;
100:   case DM_POLYTOPE_QUADRILATERAL:
101:     if (Nf) *Nf = 4;
102:     if (v0) *v0 = quad_v0;
103:     if (J) *J = quad_J;
104:     if (invJ) *invJ = quad_invJ;
105:     if (detJ) *detJ = quad_detJ;
106:     break;
107:   default:
108:     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unsupported polytope type %s", DMPolytopeTypes[ct]);
109:   }
110:   PetscFunctionReturn(PETSC_SUCCESS);
111: }

113: /*@
114:   DMPlexRefineRegularGetAffineTransforms - Gets the affine map from the reference cell to each subcell

116:   Input Parameters:
117: + tr - The `DMPlexTransform` object
118: - ct - The cell type

120:   Output Parameters:
121: + Nc   - The number of subcells produced from this cell type
122: . v0   - The translation of the first vertex for each subcell, an array of length $dim * Nc$. Pass `NULL` to ignore.
123: . J    - The Jacobian for each subcell (map from reference cell to subcell), an array of length $dim^2 * Nc$. Pass `NULL` to ignore.
124: - invJ - The inverse Jacobian for each subcell, an array of length $dim^2 * Nc$. Pass `NULL` to ignore.

126:   Level: developer

128:   Note:
129:   Do not free these output arrays

131: .seealso: `DMPLEX`, `DM`, `DMPlexTransform`, `DMPolytopeType`, `DMPlexRefineRegularGetAffineFaceTransforms()`, `DMPLEXREFINEREGULAR`
132: @*/
133: PetscErrorCode DMPlexRefineRegularGetAffineTransforms(DMPlexTransform tr, DMPolytopeType ct, PetscInt *Nc, PetscReal *v0[], PetscReal *J[], PetscReal *invJ[])
134: {
135:   /* 0--A--0--B--1 */
136:   static PetscReal seg_v0[]   = {-1.0, 0.0};
137:   static PetscReal seg_J[]    = {0.5, 0.5};
138:   static PetscReal seg_invJ[] = {2.0, 2.0};
139:   /*
140:    2
141:    |\
142:    | \
143:    |  \
144:    |   \
145:    | C  \
146:    |     \
147:    |      \
148:    2---1---1
149:    |\  D  / \
150:    | 2   0   \
151:    |A \ /  B  \
152:    0---0-------1
153:    */
154:   static PetscReal tri_v0[]   = {-1.0, -1.0, 0.0, -1.0, -1.0, 0.0, 0.0, -1.0};
155:   static PetscReal tri_J[]    = {0.5, 0.0,  0.0, 0.5,

157:                                  0.5, 0.0,  0.0, 0.5,

159:                                  0.5, 0.0,  0.0, 0.5,

161:                                  0.0, -0.5, 0.5, 0.5};
162:   static PetscReal tri_invJ[] = {2.0, 0.0, 0.0,  2.0,

164:                                  2.0, 0.0, 0.0,  2.0,

166:                                  2.0, 0.0, 0.0,  2.0,

168:                                  2.0, 2.0, -2.0, 0.0};
169:   static PetscReal tet_v0[]   = {-1.0, -1.0, -1.0, -1.0, 0.0, -1.0, 0.0, -1.0, -1.0, -1.0, -1.0, 0.0, 0.0, -1.0, -1.0, -1.0, 0.0, 0.0, 0.0, -1.0, 0.0, 0.0, -1.0, 0.0};
170:   static PetscReal tet_J[]    = {0.5,  0.0,  0.0,  0.0, 0.5, 0.0,  0.0,  0.0,  0.5,

172:                                  0.5,  0.0,  0.0,  0.0, 0.5, 0.0,  0.0,  0.0,  0.5,

174:                                  0.5,  0.0,  0.0,  0.0, 0.5, 0.0,  0.0,  0.0,  0.5,

176:                                  0.5,  0.0,  0.0,  0.0, 0.5, 0.0,  0.0,  0.0,  0.5,

178:                                  -0.5, -0.5, 0.0,  0.5, 0.0, 0.0,  0.0,  0.5,  0.5,

180:                                  0.0,  0.5,  0.5,  0.0, 0.0, -0.5, -0.5, -0.5, 0.0,

182:                                  -0.5, 0.0,  0.0,  0.5, 0.0, 0.5,  -0.5, -0.5, -0.5,

184:                                  -0.5, -0.5, -0.5, 0.5, 0.5, 0.0,  0.0,  -0.5, 0.0};
185:   static PetscReal tet_invJ[] = {2.0,  0.0,  0.0,  0.0,  2.0,  0.0,  0.0,  0.0,  2.0,

187:                                  2.0,  0.0,  0.0,  0.0,  2.0,  0.0,  0.0,  0.0,  2.0,

189:                                  2.0,  0.0,  0.0,  0.0,  2.0,  0.0,  0.0,  0.0,  2.0,

191:                                  2.0,  0.0,  0.0,  0.0,  2.0,  0.0,  0.0,  0.0,  2.0,

193:                                  0.0,  2.0,  0.0,  -2.0, -2.0, 0.0,  2.0,  2.0,  2.0,

195:                                  -2.0, -2.0, -2.0, 2.0,  2.0,  0.0,  0.0,  -2.0, 0.0,

197:                                  -2.0, 0.0,  0.0,  0.0,  -2.0, -2.0, 2.0,  2.0,  0.0,

199:                                  0.0,  2.0,  2.0,  0.0,  0.0,  -2.0, -2.0, -2.0, 0.0};
200:   /*
201:      3---------2---------2
202:      |         |         |
203:      |    D    2    C    |
204:      |         |         |
205:      3----3----0----1----1
206:      |         |         |
207:      |    A    0    B    |
208:      |         |         |
209:      0---------0---------1
210:      */
211:   static PetscReal quad_v0[]   = {-1.0, -1.0, 0.0, -1.0, 0.0, 0.0, -1.0, 0.0};
212:   static PetscReal quad_J[]    = {0.5, 0.0, 0.0, 0.5,

214:                                   0.5, 0.0, 0.0, 0.5,

216:                                   0.5, 0.0, 0.0, 0.5,

218:                                   0.5, 0.0, 0.0, 0.5};
219:   static PetscReal quad_invJ[] = {2.0, 0.0, 0.0, 2.0,

221:                                   2.0, 0.0, 0.0, 2.0,

223:                                   2.0, 0.0, 0.0, 2.0,

225:                                   2.0, 0.0, 0.0, 2.0};
226:   /*
227:      Bottom (viewed from top)    Top
228:      1---------2---------2       7---------2---------6
229:      |         |         |       |         |         |
230:      |    B    2    C    |       |    H    2    G    |
231:      |         |         |       |         |         |
232:      3----3----0----1----1       3----3----0----1----1
233:      |         |         |       |         |         |
234:      |    A    0    D    |       |    E    0    F    |
235:      |         |         |       |         |         |
236:      0---------0---------3       4---------0---------5
237:      */
238:   static PetscReal hex_v0[]   = {-1.0, -1.0, -1.0, -1.0, 0.0, -1.0, 0.0, 0.0, -1.0, 0.0, -1.0, -1.0, -1.0, -1.0, 0.0, 0.0, -1.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0, 0.0};
239:   static PetscReal hex_J[]    = {0.5, 0.0, 0.0, 0.0, 0.5, 0.0, 0.0, 0.0, 0.5,

241:                                  0.5, 0.0, 0.0, 0.0, 0.5, 0.0, 0.0, 0.0, 0.5,

243:                                  0.5, 0.0, 0.0, 0.0, 0.5, 0.0, 0.0, 0.0, 0.5,

245:                                  0.5, 0.0, 0.0, 0.0, 0.5, 0.0, 0.0, 0.0, 0.5,

247:                                  0.5, 0.0, 0.0, 0.0, 0.5, 0.0, 0.0, 0.0, 0.5,

249:                                  0.5, 0.0, 0.0, 0.0, 0.5, 0.0, 0.0, 0.0, 0.5,

251:                                  0.5, 0.0, 0.0, 0.0, 0.5, 0.0, 0.0, 0.0, 0.5,

253:                                  0.5, 0.0, 0.0, 0.0, 0.5, 0.0, 0.0, 0.0, 0.5};
254:   static PetscReal hex_invJ[] = {2.0, 0.0, 0.0, 0.0, 2.0, 0.0, 0.0, 0.0, 2.0,

256:                                  2.0, 0.0, 0.0, 0.0, 2.0, 0.0, 0.0, 0.0, 2.0,

258:                                  2.0, 0.0, 0.0, 0.0, 2.0, 0.0, 0.0, 0.0, 2.0,

260:                                  2.0, 0.0, 0.0, 0.0, 2.0, 0.0, 0.0, 0.0, 2.0,

262:                                  2.0, 0.0, 0.0, 0.0, 2.0, 0.0, 0.0, 0.0, 2.0,

264:                                  2.0, 0.0, 0.0, 0.0, 2.0, 0.0, 0.0, 0.0, 2.0,

266:                                  2.0, 0.0, 0.0, 0.0, 2.0, 0.0, 0.0, 0.0, 2.0,

268:                                  2.0, 0.0, 0.0, 0.0, 2.0, 0.0, 0.0, 0.0, 2.0};

270:   PetscFunctionBegin;
271:   switch (ct) {
272:   case DM_POLYTOPE_SEGMENT:
273:     if (Nc) *Nc = 2;
274:     if (v0) *v0 = seg_v0;
275:     if (J) *J = seg_J;
276:     if (invJ) *invJ = seg_invJ;
277:     break;
278:   case DM_POLYTOPE_TRIANGLE:
279:     if (Nc) *Nc = 4;
280:     if (v0) *v0 = tri_v0;
281:     if (J) *J = tri_J;
282:     if (invJ) *invJ = tri_invJ;
283:     break;
284:   case DM_POLYTOPE_QUADRILATERAL:
285:     if (Nc) *Nc = 4;
286:     if (v0) *v0 = quad_v0;
287:     if (J) *J = quad_J;
288:     if (invJ) *invJ = quad_invJ;
289:     break;
290:   case DM_POLYTOPE_TETRAHEDRON:
291:     if (Nc) *Nc = 8;
292:     if (v0) *v0 = tet_v0;
293:     if (J) *J = tet_J;
294:     if (invJ) *invJ = tet_invJ;
295:     break;
296:   case DM_POLYTOPE_HEXAHEDRON:
297:     if (Nc) *Nc = 8;
298:     if (v0) *v0 = hex_v0;
299:     if (J) *J = hex_J;
300:     if (invJ) *invJ = hex_invJ;
301:     break;
302:   default:
303:     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unsupported polytope type %s", DMPolytopeTypes[ct]);
304:   }
305:   PetscFunctionReturn(PETSC_SUCCESS);
306: }

308: #if 0
309: static PetscErrorCode DMPlexCellRefinerGetCellVertices_Regular(DMPlexCellRefiner cr, DMPolytopeType ct, PetscInt *Nv, PetscReal *subcellV[])
310: {
311:   static PetscReal seg_v[]  = {-1.0,  0.0,  1.0};
312:   static PetscReal tri_v[]  = {-1.0, -1.0,  1.0, -1.0,  -1.0, 1.0,  0.0, -1.0,  0.0, 0.0,  -1.0, 0.0};
313:   static PetscReal quad_v[] = {-1.0, -1.0,  1.0, -1.0,   1.0, 1.0,  -1.0, 1.0,  0.0, -1.0,  1.0, 0.0,   0.0, 1.0,  -1.0, 0.0,  0.0, 0.0};
314:   static PetscReal tet_v[]  = {-1.0, -1.0, -1.0,   0.0, -1.0, -1.0,   1.0, -1.0, -1.0,
315:                                -1.0,  0.0, -1.0,   0.0,  0.0, -1.0,  -1.0,  1.0, -1.0,
316:                                -1.0, -1.0,  0.0,   0.0, -1.0,  0.0,  -1.0,  0.0,  0.0,  -1.0, -1.0,  1.0};
317:   static PetscReal hex_v[]  = {-1.0, -1.0, -1.0,   0.0, -1.0, -1.0,   1.0, -1.0, -1.0,
318:                                -1.0,  0.0, -1.0,   0.0,  0.0, -1.0,   1.0,  0.0, -1.0,
319:                                -1.0,  1.0, -1.0,   0.0,  1.0, -1.0,   1.0,  1.0, -1.0,
320:                                -1.0, -1.0,  0.0,   0.0, -1.0,  0.0,   1.0, -1.0,  0.0,
321:                                -1.0,  0.0,  0.0,   0.0,  0.0,  0.0,   1.0,  0.0,  0.0,
322:                                -1.0,  1.0,  0.0,   0.0,  1.0,  0.0,   1.0,  1.0,  0.0,
323:                                -1.0, -1.0,  1.0,   0.0, -1.0,  1.0,   1.0, -1.0,  1.0,
324:                                -1.0,  0.0,  1.0,   0.0,  0.0,  1.0,   1.0,  0.0,  1.0,
325:                                -1.0,  1.0,  1.0,   0.0,  1.0,  1.0,   1.0,  1.0,  1.0};

327:   PetscFunctionBegin;
328:   switch (ct) {
329:     case DM_POLYTOPE_SEGMENT:       *Nv =  3; *subcellV = seg_v;  break;
330:     case DM_POLYTOPE_TRIANGLE:      *Nv =  6; *subcellV = tri_v;  break;
331:     case DM_POLYTOPE_QUADRILATERAL: *Nv =  9; *subcellV = quad_v; break;
332:     case DM_POLYTOPE_TETRAHEDRON:   *Nv = 10; *subcellV = tet_v;  break;
333:     case DM_POLYTOPE_HEXAHEDRON:    *Nv = 27; *subcellV = hex_v;  break;
334:     default: SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "No subcell vertices for cell type %s", DMPolytopeTypes[ct]);
335:   }
336:   PetscFunctionReturn(PETSC_SUCCESS);
337: }

339: static PetscErrorCode DMPlexCellRefinerGetSubcellVertices_Regular(DMPlexCellRefiner cr, DMPolytopeType ct, DMPolytopeType rct, PetscInt r, PetscInt *Nv, PetscInt *subcellV[])
340: {
341:   static PetscInt seg_v[]  = {0, 1, 1, 2};
342:   static PetscInt tri_v[]  = {0, 3, 5,  3, 1, 4,  5, 4, 2,  3, 4, 5};
343:   static PetscInt quad_v[] = {0, 4, 8, 7,  4, 1, 5, 8,  8, 5, 2, 6,  7, 8, 6, 3};
344:   static PetscInt tet_v[]  = {0, 3, 1, 6,  3, 2, 4, 8,  1, 4, 5, 7,  6, 8, 7, 9,
345:                               1, 6, 3, 7,  8, 4, 3, 7,  7, 3, 1, 4,  7, 3, 8, 6};
346:   static PetscInt hex_v[]  = {0,  3,  4,  1,  9, 10, 13, 12,   3,  6,  7,  4, 12, 13, 16, 15,   4,  7,  8,  5, 13, 14, 17, 16,   1,  4 , 5 , 2, 10, 11, 14, 13,
347:                               9, 12, 13, 10, 18, 19, 22, 21,  10, 13, 14, 11, 19, 20, 23, 22,  13, 16, 17, 14, 22, 23, 26, 25,  12, 15, 16, 13, 21, 22, 25, 24};

349:   PetscFunctionBegin;
350:   PetscCheck(ct == rct,PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Cell type %s does not produce %s", DMPolytopeTypes[ct], DMPolytopeTypes[rct]);
351:   switch (ct) {
352:     case DM_POLYTOPE_SEGMENT:       *Nv = 2; *subcellV = &seg_v[r*(*Nv)];  break;
353:     case DM_POLYTOPE_TRIANGLE:      *Nv = 3; *subcellV = &tri_v[r*(*Nv)];  break;
354:     case DM_POLYTOPE_QUADRILATERAL: *Nv = 4; *subcellV = &quad_v[r*(*Nv)]; break;
355:     case DM_POLYTOPE_TETRAHEDRON:   *Nv = 4; *subcellV = &tet_v[r*(*Nv)];  break;
356:     case DM_POLYTOPE_HEXAHEDRON:    *Nv = 8; *subcellV = &hex_v[r*(*Nv)];  break;
357:     default: SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "No subcell vertices for cell type %s", DMPolytopeTypes[ct]);
358:   }
359:   PetscFunctionReturn(PETSC_SUCCESS);
360: }
361: #endif

363: static PetscErrorCode DMPlexTransformView_Regular(DMPlexTransform tr, PetscViewer viewer)
364: {
365:   PetscBool isascii;

367:   PetscFunctionBegin;
370:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
371:   if (isascii) {
372:     const char *name;

374:     PetscCall(PetscObjectGetName((PetscObject)tr, &name));
375:     PetscCall(PetscViewerASCIIPrintf(viewer, "Regular refinement %s\n", name ? name : ""));
376:   } else {
377:     SETERRQ(PetscObjectComm((PetscObject)tr), PETSC_ERR_SUP, "Viewer type %s not yet supported for DMPlexTransform writing", ((PetscObject)viewer)->type_name);
378:   }
379:   PetscFunctionReturn(PETSC_SUCCESS);
380: }

382: static PetscErrorCode DMPlexTransformDestroy_Regular(DMPlexTransform tr)
383: {
384:   DMPlexRefine_Regular *f = (DMPlexRefine_Regular *)tr->data;

386:   PetscFunctionBegin;
387:   PetscCall(PetscFree(f));
388:   PetscFunctionReturn(PETSC_SUCCESS);
389: }

391: PetscErrorCode DMPlexTransformGetSubcellOrientation_Regular(DMPlexTransform tr, DMPolytopeType sct, PetscInt sp, PetscInt so, DMPolytopeType tct, PetscInt r, PetscInt o, PetscInt *rnew, PetscInt *onew)
392: {
393:   static PetscInt seg_seg[]   = {1, -1, 0, -1, 0, 0, 1, 0};
394:   static PetscInt tri_seg[]   = {2, -1, 1, -1, 0, -1, 1, -1, 0, -1, 2, -1, 0, -1, 2, -1, 1, -1, 0, 0, 1, 0, 2, 0, 1, 0, 2, 0, 0, 0, 2, 0, 0, 0, 1, 0};
395:   static PetscInt tri_tri[]   = {1, -3, 0, -3, 2, -3, 3, -2, 0, -2, 2, -2, 1, -2, 3, -1, 2, -1, 1, -1, 0, -1, 3, -3, 0, 0, 1, 0, 2, 0, 3, 0, 1, 1, 2, 1, 0, 1, 3, 1, 2, 2, 0, 2, 1, 2, 3, 2};
396:   static PetscInt quad_seg[]  = {1, 0, 0, 0, 3, 0, 2, 0, 0, 0, 3, 0, 2, 0, 1, 0, 3, 0, 2, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 3, 0, 0, 0, 1, 0, 2, 0, 3, 0, 1, 0, 2, 0, 3, 0, 0, 0, 2, 0, 3, 0, 0, 0, 1, 0, 3, 0, 0, 0, 1, 0, 2, 0};
397:   static PetscInt quad_quad[] = {2, -4, 1, -4, 0, -4, 3, -4, 1, -3, 0, -3, 3, -3, 2, -3, 0, -2, 3, -2, 2, -2, 1, -2, 3, -1, 2, -1, 1, -1, 0, -1, 0, 0, 1, 0, 2, 0, 3, 0, 1, 1, 2, 1, 3, 1, 0, 1, 2, 2, 3, 2, 0, 2, 1, 2, 3, 3, 0, 3, 1, 3, 2, 3};
398:   static PetscInt tseg_seg[]  = {0, -1, 0, 0, 0, 0, 0, -1};
399:   static PetscInt tseg_tseg[] = {1, -2, 0, -2, 1, -1, 0, -1, 0, 0, 1, 0, 0, 1, 1, 1};
400:   static PetscInt tet_seg[]   = {0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0};
401:   static PetscInt tet_tri[] = {2, -1, 3, -1, 1, -3, 0, -2, 6, 1, 7, -3, 5, 2, 4, -3, 3, -1, 1, -1, 2, -3, 0, -1, 4, 0,  5, 0,  6, 0,  7, 0,  1, -1, 2, -1, 3, -3, 0, -3, 4, 0,  5, 0,  6, 0,  7, 0, 3, -2, 2, -3, 0, -1, 1, -1, 7, -3, 6, 1, 4, 2,  5, -3,
402:                                2, -3, 0, -2, 3, -1, 1, -3, 4, 0, 5, 0,  6, 0, 7, 0,  0, -2, 3, -2, 2, -2, 1, -2, 4, 0,  5, 0,  6, 0,  7, 0,  0, -1, 1, -2, 3, -2, 2, -2, 7, 1,  6, -3, 5, -3, 4, 2, 1, -2, 3, -3, 0, -3, 2, -1, 4, 0,  5, 0, 6, 0,  7, 0,
403:                                3, -3, 0, -1, 1, -1, 2, -3, 4, 0, 5, 0,  6, 0, 7, 0,  1, -3, 0, -3, 2, -1, 3, -3, 6, -3, 7, 1,  4, -3, 5, 2,  0, -3, 2, -2, 1, -2, 3, -2, 4, 0,  5, 0,  6, 0,  7, 0, 2, -2, 1, -3, 0, -2, 3, -1, 4, 0,  5, 0, 6, 0,  7, 0,
404:                                0, 0,  1, 0,  2, 0,  3, 0,  4, 0, 5, 0,  6, 0, 7, 0,  1, 0,  2, 2,  0, 1,  3, 1,  4, 0,  5, 0,  6, 0,  7, 0,  2, 2,  0, 0,  1, 1,  3, 2,  4, 0,  5, 0,  6, 0,  7, 0, 1, 2,  0, 1,  3, 1,  2, 2,  5, 0,  4, 0, 7, -1, 6, -1,
405:                                0, 1,  3, 0,  1, 0,  2, 0,  4, 0, 5, 0,  6, 0, 7, 0,  3, 0,  1, 2,  0, 2,  2, 1,  4, 0,  5, 0,  6, 0,  7, 0,  2, 0,  3, 2,  0, 0,  1, 1,  4, -2, 5, -2, 7, 0,  6, 0, 3, 2,  0, 2,  2, 1,  1, 2,  4, 0,  5, 0, 6, 0,  7, 0,
406:                                0, 2,  2, 0,  3, 0,  1, 0,  4, 0, 5, 0,  6, 0, 7, 0,  3, 1,  2, 1,  1, 2,  0, 2,  5, -2, 4, -2, 6, -1, 7, -1, 2, 1,  1, 1,  3, 2,  0, 0,  4, 0,  5, 0,  6, 0,  7, 0, 1, 1,  3, 1,  2, 2,  0, 1,  4, 0,  5, 0, 6, 0,  7, 0};
407:   static PetscInt tet_tet[] = {2, -12, 3, -12, 1, -12, 0, -12, 6, -9, 7, -9, 5, -12, 4, -12, 3, -11, 1, -11, 2, -11, 0, -11, 4, 0,  5, 0,  6, 0,  7, 0,  1, -10, 2, -10, 3, -10, 0, -10, 4, 0,  5, 0,  6, 0,  7, 0,  3, -9, 2, -9, 0, -9, 1, -9,
408:                                7, -9,  6, -9,  4, -12, 5, -12, 2, -8, 0, -8, 3, -8,  1, -8,  4, 0,   5, 0,   6, 0,   7, 0,   0, -7, 3, -7, 2, -7, 1, -7, 4, 0,   5, 0,   6, 0,   7, 0,   0, -6, 1, -6, 3, -6, 2, -6, 4, -3, 5, -3, 7, -6, 6, -6,
409:                                1, -5,  3, -5,  0, -5,  2, -5,  4, 0,  5, 0,  6, 0,   7, 0,   3, -4,  0, -4,  1, -4,  2, -4,  4, 0,  5, 0,  6, 0,  7, 0,  1, -3,  0, -3,  2, -3,  3, -3,  5, -3, 4, -3, 6, -6, 7, -6, 0, -2, 2, -2, 1, -2, 3, -2,
410:                                4, 0,   5, 0,   6, 0,   7, 0,   2, -1, 1, -1, 0, -1,  3, -1,  4, 0,   5, 0,   6, 0,   7, 0,   0, 0,  1, 0,  2, 0,  3, 0,  4, 0,   5, 0,   6, 0,   7, 0,   1, 1,  2, 1,  0, 1,  3, 1,  4, 0,  5, 0,  6, 0,  7, 0,
411:                                2, 2,   0, 2,   1, 2,   3, 2,   4, 0,  5, 0,  6, 0,   7, 0,   1, 3,   0, 3,   3, 3,   2, 3,   5, 0,  4, 0,  7, 0,  6, 0,  0, 4,   3, 4,   1, 4,   2, 4,   4, 0,  5, 0,  6, 0,  7, 0,  3, 5,  1, 5,  0, 5,  2, 5,
412:                                4, 0,   5, 0,   6, 0,   7, 0,   2, 6,  3, 6,  0, 6,   1, 6,   6, 6,   7, 6,   4, 6,   5, 6,   3, 7,  0, 7,  2, 7,  1, 7,  4, 0,   5, 0,   6, 0,   7, 0,   0, 8,  2, 8,  3, 8,  1, 8,  4, 0,  5, 0,  6, 0,  7, 0,
413:                                3, 9,   2, 9,   1, 9,   0, 9,   7, 6,  6, 6,  5, 6,   4, 6,   2, 10,  1, 10,  3, 10,  0, 10,  4, 0,  5, 0,  6, 0,  7, 0,  1, 11,  3, 11,  2, 11,  0, 11,  4, 0,  5, 0,  6, 0,  7, 0};
414:   static PetscInt hex_seg[] = {2, 0, 3, 0, 4, 0, 5, 0, 1, 0, 0, 0, 4, 0, 5, 0, 0, 0, 1, 0, 3, 0, 2, 0, 5, 0, 4, 0, 1, 0, 0, 0, 3, 0, 2, 0, 3, 0, 2, 0, 4, 0, 5, 0, 0, 0, 1, 0, 3, 0, 2, 0, 5, 0, 4, 0, 1, 0, 0, 0, 4, 0, 5, 0, 1, 0, 0, 0, 2, 0, 3, 0,
415:                                2, 0, 3, 0, 5, 0, 4, 0, 0, 0, 1, 0, 5, 0, 4, 0, 0, 0, 1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 3, 0, 2, 0, 1, 0, 0, 0, 5, 0, 4, 0, 3, 0, 2, 0, 0, 0, 1, 0, 3, 0, 2, 0, 1, 0, 0, 0, 4, 0, 5, 0, 2, 0, 3, 0, 0, 0, 1, 0, 4, 0, 5, 0,
416:                                1, 0, 0, 0, 4, 0, 5, 0, 3, 0, 2, 0, 1, 0, 0, 0, 5, 0, 4, 0, 2, 0, 3, 0, 5, 0, 4, 0, 2, 0, 3, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 3, 0, 4, 0, 5, 0, 4, 0, 5, 0, 2, 0, 3, 0, 0, 0, 1, 0, 3, 0, 2, 0, 0, 0, 1, 0, 5, 0, 4, 0,
417:                                1, 0, 0, 0, 3, 0, 2, 0, 5, 0, 4, 0, 2, 0, 3, 0, 1, 0, 0, 0, 5, 0, 4, 0, 0, 0, 1, 0, 4, 0, 5, 0, 2, 0, 3, 0, 0, 0, 1, 0, 3, 0, 2, 0, 4, 0, 5, 0, 0, 0, 1, 0, 5, 0, 4, 0, 3, 0, 2, 0, 0, 0, 1, 0, 2, 0, 3, 0, 5, 0, 4, 0,
418:                                0, 0, 1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 0, 0, 1, 0, 5, 0, 4, 0, 2, 0, 3, 0, 0, 0, 1, 0, 3, 0, 2, 0, 5, 0, 4, 0, 0, 0, 1, 0, 4, 0, 5, 0, 3, 0, 2, 0, 2, 0, 3, 0, 1, 0, 0, 0, 4, 0, 5, 0, 1, 0, 0, 0, 3, 0, 2, 0, 4, 0, 5, 0,
419:                                3, 0, 2, 0, 0, 0, 1, 0, 4, 0, 5, 0, 4, 0, 5, 0, 2, 0, 3, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 3, 0, 5, 0, 4, 0, 5, 0, 4, 0, 2, 0, 3, 0, 0, 0, 1, 0, 1, 0, 0, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1, 0, 0, 0, 4, 0, 5, 0, 2, 0, 3, 0,
420:                                2, 0, 3, 0, 0, 0, 1, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1, 0, 0, 0, 5, 0, 4, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1, 0, 0, 0, 4, 0, 5, 0, 3, 0, 2, 0, 0, 0, 1, 0, 5, 0, 4, 0, 0, 0, 1, 0, 3, 0, 2, 0, 2, 0, 3, 0, 5, 0, 4, 0, 1, 0, 0, 0,
421:                                4, 0, 5, 0, 1, 0, 0, 0, 3, 0, 2, 0, 3, 0, 2, 0, 5, 0, 4, 0, 0, 0, 1, 0, 3, 0, 2, 0, 4, 0, 5, 0, 1, 0, 0, 0, 5, 0, 4, 0, 1, 0, 0, 0, 2, 0, 3, 0, 4, 0, 5, 0, 0, 0, 1, 0, 2, 0, 3, 0, 2, 0, 3, 0, 4, 0, 5, 0, 0, 0, 1, 0};
422:   static PetscInt hex_quad[]    = {7,  -2, 4,  -2, 5,  -2, 6,  -2, 8,  -3, 11, -3, 10, -3, 9,  -3, 3,  1,  2,  1,  1,  1,  0,  1,  8,  -2, 9,  -2, 10, -2, 11, -2, 3,  -4, 0,  -4, 1,  -4, 2,  -4, 7,  0,  4,  0,  5,  0,  6,  0,  9,  1,  8,  1,  11,
423:                                    1,  10, 1,  0,  3,  3,  3,  2,  3,  1,  3,  5,  2,  6,  2,  7,  2,  4,  2,  6,  3,  5,  3,  4,  3,  7,  3,  10, -1, 9,  -1, 8,  -1, 11, -1, 2,  -4, 3,  -4, 0,  -4, 1,  -4, 4,  1,  7,  1,  6,  1,  5,  1,  11, 2,
424:                                    8,  2,  9,  2,  10, 2,  1,  3,  0,  3,  3,  3,  2,  3,  10, -4, 11, -4, 8,  -4, 9,  -4, 2,  1,  1,  1,  0,  1,  3,  1,  6,  -1, 5,  -1, 4,  -1, 7,  -1, 5,  -4, 6,  -4, 7,  -4, 4,  -4, 9,  0,  10, 0,  11, 0,  8,
425:                                    0,  0,  -2, 1,  -2, 2,  -2, 3,  -2, 11, 3,  10, 3,  9,  3,  8,  3,  1,  -2, 2,  -2, 3,  -2, 0,  -2, 4,  -3, 7,  -3, 6,  -3, 5,  -3, 11, -1, 8,  -1, 9,  -1, 10, -1, 7,  3,  4,  3,  5,  3,  6,  3,  2,  2,  1,  2,
426:                                    0,  2,  3,  2,  10, 2,  9,  2,  8,  2,  11, 2,  5,  1,  6,  1,  7,  1,  4,  1,  1,  -1, 2,  -1, 3,  -1, 0,  -1, 5,  2,  4,  2,  7,  2,  6,  2,  1,  2,  0,  2,  3,  2,  2,  2,  10, -4, 9,  -4, 8,  -4, 11, -4, 4,
427:                                    -3, 5,  -3, 6,  -3, 7,  -3, 0,  -3, 1,  -3, 2,  -3, 3,  -3, 8,  -2, 11, -2, 10, -2, 9,  -2, 3,  1,  0,  1,  1,  1,  2,  1,  9,  -4, 8,  -4, 11, -4, 10, -4, 6,  3,  7,  3,  4,  3,  5,  3,  1,  3,  2,  3,  3,  3,
428:                                    0,  3,  10, 1,  11, 1,  8,  1,  9,  1,  5,  -4, 4,  -4, 7,  -4, 6,  -4, 8,  0,  11, 0,  10, 0,  9,  0,  4,  -4, 7,  -4, 6,  -4, 5,  -4, 0,  0,  3,  0,  2,  0,  1,  0,  0,  0,  1,  0,  2,  0,  3,  0,  5,  -1, 4,
429:                                    -1, 7,  -1, 6,  -1, 9,  -3, 8,  -3, 11, -3, 10, -3, 9,  -3, 10, -3, 11, -3, 8,  -3, 6,  -2, 5,  -2, 4,  -2, 7,  -2, 3,  -3, 0,  -3, 1,  -3, 2,  -3, 7,  0,  6,  0,  5,  0,  4,  0,  2,  -1, 3,  -1, 0,  -1, 1,  -1,
430:                                    11, 3,  8,  3,  9,  3,  10, 3,  2,  2,  3,  2,  0,  2,  1,  2,  6,  2,  7,  2,  4,  2,  5,  2,  10, 2,  11, 2,  8,  2,  9,  2,  6,  -1, 7,  -1, 4,  -1, 5,  -1, 3,  0,  2,  0,  1,  0,  0,  0,  9,  1,  10, 1,  11,
431:                                    1,  8,  1,  2,  -4, 1,  -4, 0,  -4, 3,  -4, 11, -2, 10, -2, 9,  -2, 8,  -2, 7,  -2, 6,  -2, 5,  -2, 4,  -2, 1,  -1, 0,  -1, 3,  -1, 2,  -1, 4,  0,  5,  0,  6,  0,  7,  0,  11, -1, 10, -1, 9,  -1, 8,  -1, 0,  -2,
432:                                    3,  -2, 2,  -2, 1,  -2, 8,  3,  9,  3,  10, 3,  11, 3,  4,  1,  5,  1,  6,  1,  7,  1,  3,  -3, 2,  -3, 1,  -3, 0,  -3, 7,  -3, 6,  -3, 5,  -3, 4,  -3, 8,  0,  9,  0,  10, 0,  11, 0,  0,  0,  1,  0,  2,  0,  3,
433:                                    0,  4,  0,  5,  0,  6,  0,  7,  0,  8,  0,  9,  0,  10, 0,  11, 0,  1,  3,  2,  3,  3,  3,  0,  3,  11, -2, 10, -2, 9,  -2, 8,  -2, 4,  1,  5,  1,  6,  1,  7,  1,  2,  2,  3,  2,  0,  2,  1,  2,  7,  -3, 6,  -3,
434:                                    5,  -3, 4,  -3, 11, -1, 10, -1, 9,  -1, 8,  -1, 3,  1,  0,  1,  1,  1,  2,  1,  8,  3,  9,  3,  10, 3,  11, 3,  7,  -2, 6,  -2, 5,  -2, 4,  -2, 5,  2,  4,  2,  7,  2,  6,  2,  0,  -3, 1,  -3, 2,  -3, 3,  -3, 9,
435:                                    1,  10, 1,  11, 1,  8,  1,  1,  -1, 0,  -1, 3,  -1, 2,  -1, 5,  -1, 4,  -1, 7,  -1, 6,  -1, 10, 2,  11, 2,  8,  2,  9,  2,  4,  -3, 5,  -3, 6,  -3, 7,  -3, 1,  2,  0,  2,  3,  2,  2,  2,  11, 3,  8,  3,  9,  3,
436:                                    10, 3,  8,  0,  11, 0,  10, 0,  9,  0,  7,  3,  4,  3,  5,  3,  6,  3,  3,  -3, 0,  -3, 1,  -3, 2,  -3, 3,  -3, 2,  -3, 1,  -3, 0,  -3, 6,  2,  7,  2,  4,  2,  5,  2,  9,  -3, 8,  -3, 11, -3, 10, -3, 9,  -3, 10,
437:                                    -3, 11, -3, 8,  -3, 5,  1,  6,  1,  7,  1,  4,  1,  0,  0,  3,  0,  2,  0,  1,  0,  0,  -2, 3,  -2, 2,  -2, 1,  -2, 9,  -4, 8,  -4, 11, -4, 10, -4, 5,  -4, 4,  -4, 7,  -4, 6,  -4, 2,  -4, 1,  -4, 0,  -4, 3,  -4,
438:                                    10, 1,  11, 1,  8,  1,  9,  1,  6,  3,  7,  3,  4,  3,  5,  3,  7,  0,  6,  0,  5,  0,  4,  0,  3,  0,  2,  0,  1,  0,  0,  0,  8,  -2, 11, -2, 10, -2, 9,  -2, 6,  -1, 7,  -1, 4,  -1, 5,  -1, 2,  -1, 3,  -1, 0,
439:                                    -1, 1,  -1, 10, -4, 9,  -4, 8,  -4, 11, -4, 11, -1, 8,  -1, 9,  -1, 10, -1, 4,  -4, 7,  -4, 6,  -4, 5,  -4, 1,  -1, 2,  -1, 3,  -1, 0,  -1, 10, 2,  9,  2,  8,  2,  11, 2,  6,  -2, 5,  -2, 4,  -2, 7,  -2, 2,  2,
440:                                    1,  2,  0,  2,  3,  2,  8,  -2, 9,  -2, 10, -2, 11, -2, 0,  3,  3,  3,  2,  3,  1,  3,  4,  -3, 7,  -3, 6,  -3, 5,  -3, 4,  1,  7,  1,  6,  1,  5,  1,  8,  -3, 11, -3, 10, -3, 9,  -3, 0,  -2, 1,  -2, 2,  -2, 3,
441:                                    -2, 9,  1,  8,  1,  11, 1,  10, 1,  3,  -4, 0,  -4, 1,  -4, 2,  -4, 6,  -1, 5,  -1, 4,  -1, 7,  -1, 5,  -4, 6,  -4, 7,  -4, 4,  -4, 10, -1, 9,  -1, 8,  -1, 11, -1, 1,  3,  0,  3,  3,  3,  2,  3,  7,  -2, 4,  -2,
442:                                    5,  -2, 6,  -2, 11, 2,  8,  2,  9,  2,  10, 2,  2,  -4, 3,  -4, 0,  -4, 1,  -4, 10, -4, 11, -4, 8,  -4, 9,  -4, 1,  -2, 2,  -2, 3,  -2, 0,  -2, 5,  2,  6,  2,  7,  2,  4,  2,  11, 3,  10, 3,  9,  3,  8,  3,  2,
443:                                    1,  1,  1,  0,  1,  3,  1,  7,  0,  4,  0,  5,  0,  6,  0,  6,  3,  5,  3,  4,  3,  7,  3,  9,  0,  10, 0,  11, 0,  8,  0,  3,  1,  2,  1,  1,  1,  0,  1};
444:   static PetscInt hex_hex[]     = {3, -24, 0, -24, 4, -24, 5, -24, 2, -24, 6, -24, 7, -24, 1, -24, 3, -23, 5, -23, 6, -23, 2, -23, 0, -23, 1, -23, 7, -23, 4, -23, 4, -22, 0, -22, 1, -22, 7, -22, 5, -22, 6, -22, 2, -22, 3, -22, 6, -21, 7, -21,
445:                                    1, -21, 2, -21, 5, -21, 3, -21, 0, -21, 4, -21, 1, -20, 2, -20, 6, -20, 7, -20, 0, -20, 4, -20, 5, -20, 3, -20, 6, -19, 2, -19, 3, -19, 5, -19, 7, -19, 4, -19, 0, -19, 1, -19, 4, -18, 5, -18, 3, -18, 0, -18,
446:                                    7, -18, 1, -18, 2, -18, 6, -18, 1, -17, 7, -17, 4, -17, 0, -17, 2, -17, 3, -17, 5, -17, 6, -17, 2, -16, 3, -16, 5, -16, 6, -16, 1, -16, 7, -16, 4, -16, 0, -16, 7, -15, 4, -15, 0, -15, 1, -15, 6, -15, 2, -15,
447:                                    3, -15, 5, -15, 7, -14, 1, -14, 2, -14, 6, -14, 4, -14, 5, -14, 3, -14, 0, -14, 0, -13, 4, -13, 5, -13, 3, -13, 1, -13, 2, -13, 6, -13, 7, -13, 5, -12, 4, -12, 7, -12, 6, -12, 3, -12, 2, -12, 1, -12, 0, -12,
448:                                    7, -11, 6, -11, 5, -11, 4, -11, 1, -11, 0, -11, 3, -11, 2, -11, 0, -10, 1, -10, 7, -10, 4, -10, 3, -10, 5, -10, 6, -10, 2, -10, 4, -9,  7, -9,  6, -9,  5, -9,  0, -9,  3, -9,  2, -9,  1, -9,  5, -8,  6, -8,
449:                                    2, -8,  3, -8,  4, -8,  0, -8,  1, -8,  7, -8,  2, -7,  6, -7,  7, -7,  1, -7,  3, -7,  0, -7,  4, -7,  5, -7,  6, -6,  5, -6,  4, -6,  7, -6,  2, -6,  1, -6,  0, -6,  3, -6,  5, -5,  3, -5,  0, -5,  4, -5,
450:                                    6, -5,  7, -5,  1, -5,  2, -5,  2, -4,  1, -4,  0, -4,  3, -4,  6, -4,  5, -4,  4, -4,  7, -4,  1, -3,  0, -3,  3, -3,  2, -3,  7, -3,  6, -3,  5, -3,  4, -3,  0, -2,  3, -2,  2, -2,  1, -2,  4, -2,  7, -2,
451:                                    6, -2,  5, -2,  3, -1,  2, -1,  1, -1,  0, -1,  5, -1,  4, -1,  7, -1,  6, -1,  0, 0,   1, 0,   2, 0,   3, 0,   4, 0,   5, 0,   6, 0,   7, 0,   1, 1,   2, 1,   3, 1,   0, 1,   7, 1,   4, 1,   5, 1,   6, 1,
452:                                    2, 2,   3, 2,   0, 2,   1, 2,   6, 2,   7, 2,   4, 2,   5, 2,   3, 3,   0, 3,   1, 3,   2, 3,   5, 3,   6, 3,   7, 3,   4, 3,   4, 4,   0, 4,   3, 4,   5, 4,   7, 4,   6, 4,   2, 4,   1, 4,   7, 5,   4, 5,
453:                                    5, 5,   6, 5,   1, 5,   2, 5,   3, 5,   0, 5,   1, 6,   7, 6,   6, 6,   2, 6,   0, 6,   3, 6,   5, 6,   4, 6,   3, 7,   2, 7,   6, 7,   5, 7,   0, 7,   4, 7,   7, 7,   1, 7,   5, 8,   6, 8,   7, 8,   4, 8,
454:                                    3, 8,   0, 8,   1, 8,   2, 8,   4, 9,   7, 9,   1, 9,   0, 9,   5, 9,   3, 9,   2, 9,   6, 9,   4, 10,  5, 10,  6, 10,  7, 10,  0, 10,  1, 10,  2, 10,  3, 10,  6, 11,  7, 11,  4, 11,  5, 11,  2, 11,  3, 11,
455:                                    0, 11,  1, 11,  3, 12,  5, 12,  4, 12,  0, 12,  2, 12,  1, 12,  7, 12,  6, 12,  6, 13,  2, 13,  1, 13,  7, 13,  5, 13,  4, 13,  0, 13,  3, 13,  1, 14,  0, 14,  4, 14,  7, 14,  2, 14,  6, 14,  5, 14,  3, 14,
456:                                    6, 15,  5, 15,  3, 15,  2, 15,  7, 15,  1, 15,  0, 15,  4, 15,  0, 16,  4, 16,  7, 16,  1, 16,  3, 16,  2, 16,  6, 16,  5, 16,  0, 17,  3, 17,  5, 17,  4, 17,  1, 17,  7, 17,  6, 17,  2, 17,  5, 18,  3, 18,
457:                                    2, 18,  6, 18,  4, 18,  7, 18,  1, 18,  0, 18,  7, 19,  6, 19,  2, 19,  1, 19,  4, 19,  0, 19,  3, 19,  5, 19,  2, 20,  1, 20,  7, 20,  6, 20,  3, 20,  5, 20,  4, 20,  0, 20,  7, 21,  1, 21,  0, 21,  4, 21,
458:                                    6, 21,  5, 21,  3, 21,  2, 21,  2, 22,  6, 22,  5, 22,  3, 22,  1, 22,  0, 22,  4, 22,  7, 22,  5, 23,  4, 23,  0, 23,  3, 23,  6, 23,  2, 23,  1, 23,  7, 23};
459:   static PetscInt trip_seg[]    = {1, 0, 2, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, -1, 2, -1, 1, -1, 1, -1, 0, -1, 2, -1, 2, -1, 1, -1, 0, -1,
460:                                    0, 0, 1, 0, 2, 0, 2, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 0, 2, -1, 1, -1, 0, -1, 1, -1, 0, -1, 2, -1, 0, -1, 2, -1, 1, -1};
461:   static PetscInt trip_tri[]    = {1, 1, 2, 1, 0, 1, 3, 1, 2, 2, 0, 2, 1, 2, 3, 2, 0, 0, 1, 0, 2, 0, 3, 0, 2, -1, 1, -1, 0, -1, 3, -3, 0, -2, 2, -2, 1, -2, 3, -1, 1, -3, 0, -3, 2, -3, 3, -2,
462:                                    0, 0, 1, 0, 2, 0, 3, 0, 2, 2, 0, 2, 1, 2, 3, 2, 1, 1, 2, 1, 0, 1, 3, 1, 1, -3, 0, -3, 2, -3, 3, -2, 0, -2, 2, -2, 1, -2, 3, -1, 2, -1, 1, -1, 0, -1, 3, -3};
463:   static PetscInt trip_quad[]   = {4, -1, 5, -1, 3, -1, 1, -1, 2, -1, 0, -1, 5, -1, 3, -1, 4, -1, 2, -1, 0, -1, 1, -1, 3, -1, 4, -1, 5, -1, 0, -1, 1, -1, 2, -1, 0, -3, 2, -3, 1, -3, 3, -3, 5, -3, 4, -3,
464:                                    1, -3, 0, -3, 2, -3, 4, -3, 3, -3, 5, -3, 2, -3, 1, -3, 0, -3, 5, -3, 4, -3, 3, -3, 0, 0,  1, 0,  2, 0,  3, 0,  4, 0,  5, 0,  2, 0,  0, 0,  1, 0,  5, 0,  3, 0,  4, 0,
465:                                    1, 0,  2, 0,  0, 0,  4, 0,  5, 0,  3, 0,  5, 2,  4, 2,  3, 2,  2, 2,  1, 2,  0, 2,  4, 2,  3, 2,  5, 2,  1, 2,  0, 2,  2, 2,  3, 2,  5, 2,  4, 2,  0, 2,  2, 2,  1, 2};
466:   static PetscInt trip_trip[]   = {5, -6, 6, -6, 4, -6, 7, -6, 1, -6, 2, -6, 0, -6, 3, -6, 6, -5, 4, -5, 5, -5, 7, -5, 2, -5, 0, -5, 1, -5, 3, -5, 4, -4, 5, -4, 6, -4, 7, -4, 0, -4, 1, -4, 2, -4, 3, -4,
467:                                    2, -3, 1, -3, 0, -3, 3, -1, 6, -3, 5, -3, 4, -3, 7, -1, 0, -2, 2, -2, 1, -2, 3, -3, 4, -2, 6, -2, 5, -2, 7, -3, 1, -1, 0, -1, 2, -1, 3, -2, 5, -1, 4, -1, 6, -1, 7, -2,
468:                                    0, 0,  1, 0,  2, 0,  3, 0,  4, 0,  5, 0,  6, 0,  7, 0,  2, 1,  0, 1,  1, 1,  3, 1,  6, 1,  4, 1,  5, 1,  7, 1,  1, 2,  2, 2,  0, 2,  3, 2,  5, 2,  6, 2,  4, 2,  7, 2,
469:                                    5, 3,  4, 3,  6, 3,  7, 4,  1, 3,  0, 3,  2, 3,  3, 4,  4, 4,  6, 4,  5, 4,  7, 5,  0, 4,  2, 4,  1, 4,  3, 5,  6, 5,  5, 5,  4, 5,  7, 3,  2, 5,  1, 5,  0, 5,  3, 3};
470:   static PetscInt ttri_tseg[]   = {2, -2, 1, -2, 0, -2, 1, -2, 0, -2, 2, -2, 0, -2, 2, -2, 1, -2, 2, -1, 1, -1, 0, -1, 1, -1, 0, -1, 2, -1, 0, -1, 2, -1, 1, -1,
471:                                    0, 0,  1, 0,  2, 0,  1, 0,  2, 0,  0, 0,  2, 0,  0, 0,  1, 0,  0, 1,  1, 1,  2, 1,  1, 1,  2, 1,  0, 1,  2, 1,  0, 1,  1, 1};
472:   static PetscInt ttri_ttri[]   = {1, -6, 0, -6, 2, -6, 3, -5, 0, -5, 2, -5, 1, -5, 3, -4, 2, -4, 1, -4, 0, -4, 3, -6, 1, -3, 0, -3, 2, -3, 3, -2, 0, -2, 2, -2, 1, -2, 3, -1, 2, -1, 1, -1, 0, -1, 3, -3,
473:                                    0, 0,  1, 0,  2, 0,  3, 0,  1, 1,  2, 1,  0, 1,  3, 1,  2, 2,  0, 2,  1, 2,  3, 2,  0, 3,  1, 3,  2, 3,  3, 3,  1, 4,  2, 4,  0, 4,  3, 4,  2, 5,  0, 5,  1, 5,  3, 5};
474:   static PetscInt tquad_tvert[] = {0, -1, 0, -1, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, -1, 0, -1};
475:   static PetscInt tquad_tseg[]  = {1, 1, 0, 1, 3, 1, 2, 1, 0, 1, 3, 1, 2, 1, 1, 1, 3, 1, 2, 1, 1, 1, 0, 1, 2, 1, 1, 1, 0, 1, 3, 1, 1, 0, 0, 0, 3, 0, 2, 0, 0, 0, 3, 0, 2, 0, 1, 0, 3, 0, 2, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 3, 0,
476:                                    0, 0, 1, 0, 2, 0, 3, 0, 1, 0, 2, 0, 3, 0, 0, 0, 2, 0, 3, 0, 0, 0, 1, 0, 3, 0, 0, 0, 1, 0, 2, 0, 0, 1, 1, 1, 2, 1, 3, 1, 1, 1, 2, 1, 3, 1, 0, 1, 2, 1, 3, 1, 0, 1, 1, 1, 3, 1, 0, 1, 1, 1, 2, 1};
477:   static PetscInt tquad_tquad[] = {2,  -8, 1,  -8, 0,  -8, 3,  -8, 1,  -7, 0,  -7, 3,  -7, 2,  -7, 0,  -6, 3,  -6, 2,  -6, 1, -6, 3, -5, 2, -5, 1, -5, 0, -5, 2, -4, 1, -4, 0, -4, 3, -4, 1, -3, 0,
478:                                    -3, 3,  -3, 2,  -3, 0,  -2, 3,  -2, 2,  -2, 1,  -2, 3,  -1, 2,  -1, 1,  -1, 0,  -1, 0,  0, 1,  0, 2,  0, 3,  0, 1,  1, 2,  1, 3,  1, 0,  1, 2,  2, 3,  2, 0,  2,
479:                                    1,  2,  3,  3,  0,  3,  1,  3,  2,  3,  0,  4,  1,  4,  2,  4,  3,  4,  1,  5,  2,  5,  3, 5,  0, 5,  2, 6,  3, 6,  0, 6,  1, 6,  3, 7,  0, 7,  1, 7,  2, 7};

481:   PetscFunctionBeginHot;
482:   *rnew = r;
483:   *onew = o;
484:   if (!so) PetscFunctionReturn(PETSC_SUCCESS);
485:   switch (sct) {
486:   case DM_POLYTOPE_POINT:
487:     break;
488:   case DM_POLYTOPE_POINT_PRISM_TENSOR:
489:     *onew = so < 0 ? -(o + 1) : o;
490:     break;
491:   case DM_POLYTOPE_SEGMENT:
492:     switch (tct) {
493:     case DM_POLYTOPE_POINT:
494:       break;
495:     case DM_POLYTOPE_SEGMENT:
496:       *rnew = seg_seg[(so + 1) * 4 + r * 2];
497:       *onew = DMPolytopeTypeComposeOrientation(tct, o, seg_seg[(so + 1) * 4 + r * 2 + 1]);
498:       break;
499:     default:
500:       SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cell type %s is not produced by %s", DMPolytopeTypes[tct], DMPolytopeTypes[sct]);
501:     }
502:     break;
503:   case DM_POLYTOPE_TRIANGLE:
504:     switch (tct) {
505:     case DM_POLYTOPE_SEGMENT:
506:       *rnew = tri_seg[(so + 3) * 6 + r * 2];
507:       *onew = DMPolytopeTypeComposeOrientation(tct, o, tri_seg[(so + 3) * 6 + r * 2 + 1]);
508:       break;
509:     case DM_POLYTOPE_TRIANGLE:
510:       *rnew = tri_tri[(so + 3) * 8 + r * 2];
511:       *onew = DMPolytopeTypeComposeOrientation(tct, o, tri_tri[(so + 3) * 8 + r * 2 + 1]);
512:       break;
513:     default:
514:       SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cell type %s is not produced by %s", DMPolytopeTypes[tct], DMPolytopeTypes[sct]);
515:     }
516:     break;
517:   case DM_POLYTOPE_QUADRILATERAL:
518:     switch (tct) {
519:     case DM_POLYTOPE_POINT:
520:       break;
521:     case DM_POLYTOPE_SEGMENT:
522:       *rnew = quad_seg[(so + 4) * 8 + r * 2];
523:       *onew = DMPolytopeTypeComposeOrientation(tct, o, quad_seg[(so + 4) * 8 + r * 2 + 1]);
524:       break;
525:     case DM_POLYTOPE_QUADRILATERAL:
526:       *rnew = quad_quad[(so + 4) * 8 + r * 2];
527:       *onew = DMPolytopeTypeComposeOrientation(tct, o, quad_quad[(so + 4) * 8 + r * 2 + 1]);
528:       break;
529:     default:
530:       SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cell type %s is not produced by %s", DMPolytopeTypes[tct], DMPolytopeTypes[sct]);
531:     }
532:     break;
533:   case DM_POLYTOPE_SEG_PRISM_TENSOR:
534:     switch (tct) {
535:     case DM_POLYTOPE_POINT_PRISM_TENSOR:
536:       *rnew = tseg_seg[(so + 2) * 2 + r * 2];
537:       *onew = DMPolytopeTypeComposeOrientation(tct, o, tseg_seg[(so + 2) * 2 + r * 2 + 1]);
538:       break;
539:     case DM_POLYTOPE_SEG_PRISM_TENSOR:
540:       *rnew = tseg_tseg[(so + 2) * 4 + r * 2];
541:       *onew = DMPolytopeTypeComposeOrientation(tct, o, tseg_tseg[(so + 2) * 4 + r * 2 + 1]);
542:       break;
543:     default:
544:       SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cell type %s is not produced by %s", DMPolytopeTypes[tct], DMPolytopeTypes[sct]);
545:     }
546:     break;
547:   case DM_POLYTOPE_TETRAHEDRON:
548:     switch (tct) {
549:     case DM_POLYTOPE_SEGMENT:
550:       *rnew = tet_seg[(so + 12) * 2 + r * 2];
551:       *onew = DMPolytopeTypeComposeOrientation(tct, o, tet_seg[(so + 12) * 2 + r * 2 + 1]);
552:       break;
553:     case DM_POLYTOPE_TRIANGLE:
554:       *rnew = tet_tri[(so + 12) * 16 + r * 2];
555:       *onew = DMPolytopeTypeComposeOrientation(tct, o, tet_tri[(so + 12) * 16 + r * 2 + 1]);
556:       break;
557:     case DM_POLYTOPE_TETRAHEDRON:
558:       *rnew = tet_tet[(so + 12) * 16 + r * 2];
559:       *onew = DMPolytopeTypeComposeOrientation(tct, o, tet_tet[(so + 12) * 16 + r * 2 + 1]);
560:       break;
561:     default:
562:       SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cell type %s is not produced by %s", DMPolytopeTypes[tct], DMPolytopeTypes[sct]);
563:     }
564:     break;
565:   case DM_POLYTOPE_HEXAHEDRON:
566:     switch (tct) {
567:     case DM_POLYTOPE_POINT:
568:       break;
569:     case DM_POLYTOPE_SEGMENT:
570:       *rnew = hex_seg[(so + 24) * 12 + r * 2];
571:       *onew = DMPolytopeTypeComposeOrientation(tct, o, hex_seg[(so + 24) * 12 + r * 2 + 1]);
572:       break;
573:     case DM_POLYTOPE_QUADRILATERAL:
574:       *rnew = hex_quad[(so + 24) * 24 + r * 2];
575:       *onew = DMPolytopeTypeComposeOrientation(tct, o, hex_quad[(so + 24) * 24 + r * 2 + 1]);
576:       break;
577:     case DM_POLYTOPE_HEXAHEDRON:
578:       *rnew = hex_hex[(so + 24) * 16 + r * 2];
579:       *onew = DMPolytopeTypeComposeOrientation(tct, o, hex_hex[(so + 24) * 16 + r * 2 + 1]);
580:       break;
581:     default:
582:       SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cell type %s is not produced by %s", DMPolytopeTypes[tct], DMPolytopeTypes[sct]);
583:     }
584:     break;
585:   case DM_POLYTOPE_TRI_PRISM:
586:     switch (tct) {
587:     case DM_POLYTOPE_SEGMENT:
588:       *rnew = trip_seg[(so + 6) * 6 + r * 2];
589:       *onew = DMPolytopeTypeComposeOrientation(tct, o, trip_seg[(so + 6) * 6 + r * 2 + 1]);
590:       break;
591:     case DM_POLYTOPE_TRIANGLE:
592:       *rnew = trip_tri[(so + 6) * 8 + r * 2];
593:       *onew = DMPolytopeTypeComposeOrientation(tct, o, trip_tri[(so + 6) * 8 + r * 2 + 1]);
594:       break;
595:     case DM_POLYTOPE_QUADRILATERAL:
596:       *rnew = trip_quad[(so + 6) * 12 + r * 2];
597:       *onew = DMPolytopeTypeComposeOrientation(tct, o, trip_quad[(so + 6) * 12 + r * 2 + 1]);
598:       break;
599:     case DM_POLYTOPE_TRI_PRISM:
600:       *rnew = trip_trip[(so + 6) * 16 + r * 2];
601:       *onew = DMPolytopeTypeComposeOrientation(tct, o, trip_trip[(so + 6) * 16 + r * 2 + 1]);
602:       break;
603:     default:
604:       SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cell type %s is not produced by %s", DMPolytopeTypes[tct], DMPolytopeTypes[sct]);
605:     }
606:     break;
607:   case DM_POLYTOPE_TRI_PRISM_TENSOR:
608:     switch (tct) {
609:     case DM_POLYTOPE_SEG_PRISM_TENSOR:
610:       *rnew = ttri_tseg[(so + 6) * 6 + r * 2];
611:       *onew = DMPolytopeTypeComposeOrientation(tct, o, ttri_tseg[(so + 6) * 6 + r * 2 + 1]);
612:       break;
613:     case DM_POLYTOPE_TRI_PRISM_TENSOR:
614:       *rnew = ttri_ttri[(so + 6) * 8 + r * 2];
615:       *onew = DMPolytopeTypeComposeOrientation(tct, o, ttri_ttri[(so + 6) * 8 + r * 2 + 1]);
616:       break;
617:     default:
618:       SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cell type %s is not produced by %s", DMPolytopeTypes[tct], DMPolytopeTypes[sct]);
619:     }
620:     break;
621:   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
622:     switch (tct) {
623:     case DM_POLYTOPE_POINT_PRISM_TENSOR:
624:       *rnew = tquad_tvert[(so + 8) * 2 + r * 2];
625:       *onew = DMPolytopeTypeComposeOrientation(tct, o, tquad_tvert[(so + 8) * 2 + r * 2 + 1]);
626:       break;
627:     case DM_POLYTOPE_SEG_PRISM_TENSOR:
628:       *rnew = tquad_tseg[(so + 8) * 8 + r * 2];
629:       *onew = DMPolytopeTypeComposeOrientation(tct, o, tquad_tseg[(so + 8) * 8 + r * 2 + 1]);
630:       break;
631:     case DM_POLYTOPE_QUAD_PRISM_TENSOR:
632:       *rnew = tquad_tquad[(so + 8) * 8 + r * 2];
633:       *onew = DMPolytopeTypeComposeOrientation(tct, o, tquad_tquad[(so + 8) * 8 + r * 2 + 1]);
634:       break;
635:     default:
636:       SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cell type %s is not produced by %s", DMPolytopeTypes[tct], DMPolytopeTypes[sct]);
637:     }
638:     break;
639:   default:
640:     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Unsupported cell type %s", DMPolytopeTypes[sct]);
641:   }
642:   PetscFunctionReturn(PETSC_SUCCESS);
643: }

645: PetscErrorCode DMPlexTransformCellRefine_Regular(DMPlexTransform tr, DMPolytopeType source, PetscInt p, PetscInt *rt, PetscInt *Nt, DMPolytopeType *target[], PetscInt *size[], PetscInt *cone[], PetscInt *ornt[])
646: {
647:   /* All vertices remain in the refined mesh */
648:   static DMPolytopeType vertexT[] = {DM_POLYTOPE_POINT};
649:   static PetscInt       vertexS[] = {1};
650:   static PetscInt       vertexC[] = {0};
651:   static PetscInt       vertexO[] = {0};
652:   /* Split all edges with a new vertex, making two new 2 edges
653:      0--0--0--1--1
654:   */
655:   static DMPolytopeType segT[] = {DM_POLYTOPE_POINT, DM_POLYTOPE_SEGMENT};
656:   static PetscInt       segS[] = {1, 2};
657:   static PetscInt       segC[] = {DM_POLYTOPE_POINT, 1, 0, 0, DM_POLYTOPE_POINT, 0, 0, DM_POLYTOPE_POINT, 0, 0, DM_POLYTOPE_POINT, 1, 1, 0};
658:   static PetscInt       segO[] = {0, 0, 0, 0};
659:   /* Do not split tensor edges */
660:   static DMPolytopeType tvertT[] = {DM_POLYTOPE_POINT_PRISM_TENSOR};
661:   static PetscInt       tvertS[] = {1};
662:   static PetscInt       tvertC[] = {DM_POLYTOPE_POINT, 1, 0, 0, DM_POLYTOPE_POINT, 1, 1, 0};
663:   static PetscInt       tvertO[] = {0, 0};
664:   /* Add 3 edges inside every triangle, making 4 new triangles.
665:    2
666:    |\
667:    | \
668:    |  \
669:    0   1
670:    | C  \
671:    |     \
672:    |      \
673:    2---1---1
674:    |\  D  / \
675:    1 2   0   0
676:    |A \ /  B  \
677:    0-0-0---1---1
678:   */
679:   static DMPolytopeType triT[] = {DM_POLYTOPE_SEGMENT, DM_POLYTOPE_TRIANGLE};
680:   static PetscInt       triS[] = {3, 4};
681:   static PetscInt triC[] = {DM_POLYTOPE_POINT, 1, 0, 0, DM_POLYTOPE_POINT, 1, 1, 0, DM_POLYTOPE_POINT, 1, 1, 0, DM_POLYTOPE_POINT, 1, 2, 0, DM_POLYTOPE_POINT, 1, 2, 0, DM_POLYTOPE_POINT, 1, 0, 0, DM_POLYTOPE_SEGMENT, 1, 0, 0, DM_POLYTOPE_SEGMENT, 0, 2, DM_POLYTOPE_SEGMENT, 1, 2, 1, DM_POLYTOPE_SEGMENT, 1, 0, 1, DM_POLYTOPE_SEGMENT, 1, 1, 0, DM_POLYTOPE_SEGMENT, 0, 0, DM_POLYTOPE_SEGMENT, 0, 1, DM_POLYTOPE_SEGMENT, 1, 1, 1, DM_POLYTOPE_SEGMENT, 1, 2, 0, DM_POLYTOPE_SEGMENT, 0, 0, DM_POLYTOPE_SEGMENT, 0, 1, DM_POLYTOPE_SEGMENT, 0, 2};
682:   static PetscInt triO[] = {0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0};
683:   /* Add a vertex in the center of each quadrilateral, and 4 edges inside, making 4 new quads.
684:      3----1----2----0----2
685:      |         |         |
686:      0    D    2    C    1
687:      |         |         |
688:      3----3----0----1----1
689:      |         |         |
690:      1    A    0    B    0
691:      |         |         |
692:      0----0----0----1----1
693:   */
694:   static DMPolytopeType quadT[] = {DM_POLYTOPE_POINT, DM_POLYTOPE_SEGMENT, DM_POLYTOPE_QUADRILATERAL};
695:   static PetscInt       quadS[] = {1, 4, 4};
696:   static PetscInt quadC[] = {DM_POLYTOPE_POINT, 1, 0, 0, DM_POLYTOPE_POINT, 0, 0, DM_POLYTOPE_POINT, 1, 1, 0, DM_POLYTOPE_POINT, 0, 0, DM_POLYTOPE_POINT, 1, 2, 0, DM_POLYTOPE_POINT, 0, 0, DM_POLYTOPE_POINT, 1, 3, 0, DM_POLYTOPE_POINT, 0, 0, DM_POLYTOPE_SEGMENT, 1, 0, 0, DM_POLYTOPE_SEGMENT, 0, 0, DM_POLYTOPE_SEGMENT, 0, 3, DM_POLYTOPE_SEGMENT, 1, 3, 1, DM_POLYTOPE_SEGMENT, 1, 0, 1, DM_POLYTOPE_SEGMENT, 1, 1, 0, DM_POLYTOPE_SEGMENT, 0, 1, DM_POLYTOPE_SEGMENT, 0, 0, DM_POLYTOPE_SEGMENT, 0, 1, DM_POLYTOPE_SEGMENT, 1, 1, 1, DM_POLYTOPE_SEGMENT, 1, 2, 0, DM_POLYTOPE_SEGMENT, 0, 2, DM_POLYTOPE_SEGMENT, 0, 3, DM_POLYTOPE_SEGMENT, 0, 2, DM_POLYTOPE_SEGMENT, 1, 2, 1, DM_POLYTOPE_SEGMENT, 1, 3, 0};
697:   static PetscInt quadO[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, -1, 0, 0};
698:   /* Add 1 edge inside every tensor quad, making 2 new tensor quads
699:      2----2----1----3----3
700:      |         |         |
701:      |         |         |
702:      |         |         |
703:      4    A    6    B    5
704:      |         |         |
705:      |         |         |
706:      |         |         |
707:      0----0----0----1----1
708:   */
709:   static DMPolytopeType tsegT[] = {DM_POLYTOPE_POINT_PRISM_TENSOR, DM_POLYTOPE_SEG_PRISM_TENSOR};
710:   static PetscInt       tsegS[] = {1, 2};
711:   static PetscInt tsegC[] = {DM_POLYTOPE_POINT, 1, 0, 0, DM_POLYTOPE_POINT, 1, 1, 0, DM_POLYTOPE_SEGMENT, 1, 0, 0, DM_POLYTOPE_SEGMENT, 1, 1, 0, DM_POLYTOPE_POINT_PRISM_TENSOR, 1, 2, 0, DM_POLYTOPE_POINT_PRISM_TENSOR, 0, 0, DM_POLYTOPE_SEGMENT, 1, 0, 1, DM_POLYTOPE_SEGMENT, 1, 1, 1, DM_POLYTOPE_POINT_PRISM_TENSOR, 0, 0, DM_POLYTOPE_POINT_PRISM_TENSOR, 1, 3, 0};
712:   static PetscInt tsegO[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0};
713:   /* Add 1 edge and 8 triangles inside every cell, making 8 new tets
714:      The vertices of our reference tet are [(-1, -1, -1), (-1, 1, -1), (1, -1, -1), (-1, -1, 1)], which we call [v0, v1, v2, v3]. The first
715:      three edges are [v0, v1], [v1, v2], [v2, v0] called e0, e1, and e2, and then three edges to the top point [v0, v3], [v1, v3], [v2, v3]
716:      called e3, e4, and e5. The faces of a tet, given in DMPlexGetRawFaces_Internal() are
717:        [v0, v1, v2], [v0, v3, v1], [v0, v2, v3], [v2, v1, v3]
718:      The first four tets just cut off the corners, using the replica notation for new vertices,
719:        [v0,      (e0, 0), (e2, 0), (e3, 0)]
720:        [(e0, 0), v1,      (e1, 0), (e4, 0)]
721:        [(e2, 0), (e1, 0), v2,      (e5, 0)]
722:        [(e3, 0), (e4, 0), (e5, 0), v3     ]
723:      The next four tets match a vertex to the newly created faces from cutting off those first tets.
724:        [(e2, 0), (e3, 0), (e0, 0), (e5, 0)]
725:        [(e4, 0), (e1, 0), (e0, 0), (e5, 0)]
726:        [(e5, 0), (e0, 0), (e2, 0), (e1, 0)]
727:        [(e5, 0), (e0, 0), (e4, 0), (e3, 0)]
728:      We can see that a new edge is introduced in the cell [(e0, 0), (e5, 0)] which we call (-1, 0). The first four faces created are
729:        [(e2, 0), (e0, 0), (e3, 0)]
730:        [(e0, 0), (e1, 0), (e4, 0)]
731:        [(e2, 0), (e5, 0), (e1, 0)]
732:        [(e3, 0), (e4, 0), (e5, 0)]
733:      The next four, from the second group of tets, are
734:        [(e2, 0), (e0, 0), (e5, 0)]
735:        [(e4, 0), (e0, 0), (e5, 0)]
736:        [(e0, 0), (e1, 0), (e5, 0)]
737:        [(e5, 0), (e3, 0), (e0, 0)]
738:      I could write a program to generate these orientations by comparing the faces from GetRawFaces() with my existing table.
739:    */
740:   static DMPolytopeType tetT[] = {DM_POLYTOPE_SEGMENT, DM_POLYTOPE_TRIANGLE, DM_POLYTOPE_TETRAHEDRON};
741:   static PetscInt       tetS[] = {1, 8, 8};
742:   static PetscInt tetC[] = {DM_POLYTOPE_POINT, 2, 0, 0, 0, DM_POLYTOPE_POINT, 2, 2, 1, 0, DM_POLYTOPE_SEGMENT, 1, 0, 2, DM_POLYTOPE_SEGMENT, 1, 1, 2, DM_POLYTOPE_SEGMENT, 1, 2, 2, DM_POLYTOPE_SEGMENT, 1, 0, 0, DM_POLYTOPE_SEGMENT, 1, 3, 0, DM_POLYTOPE_SEGMENT, 1, 1, 1, DM_POLYTOPE_SEGMENT, 1, 2, 0, DM_POLYTOPE_SEGMENT, 1, 3, 2, DM_POLYTOPE_SEGMENT, 1, 0, 1, DM_POLYTOPE_SEGMENT, 1, 1, 0, DM_POLYTOPE_SEGMENT, 1, 3, 1, DM_POLYTOPE_SEGMENT, 1, 2, 1, DM_POLYTOPE_SEGMENT, 1, 0, 2, DM_POLYTOPE_SEGMENT, 0, 0, DM_POLYTOPE_SEGMENT, 1, 2, 0, DM_POLYTOPE_SEGMENT, 1, 1, 1, DM_POLYTOPE_SEGMENT, 0, 0, DM_POLYTOPE_SEGMENT, 1, 3, 1, DM_POLYTOPE_SEGMENT, 1, 0, 0, DM_POLYTOPE_SEGMENT, 1, 3, 2, DM_POLYTOPE_SEGMENT, 0, 0, DM_POLYTOPE_SEGMENT, 1, 2, 1, DM_POLYTOPE_SEGMENT, 1, 1, 2, DM_POLYTOPE_SEGMENT, 0, 0, DM_POLYTOPE_TRIANGLE, 1, 0, 0, DM_POLYTOPE_TRIANGLE, 1, 1, 0, DM_POLYTOPE_TRIANGLE, 1, 2, 0, DM_POLYTOPE_TRIANGLE, 0, 0, DM_POLYTOPE_TRIANGLE, 1, 0, 1, DM_POLYTOPE_TRIANGLE, 1, 1, 2, DM_POLYTOPE_TRIANGLE, 0, 1, DM_POLYTOPE_TRIANGLE, 1, 3, 1, DM_POLYTOPE_TRIANGLE, 1, 0, 2, DM_POLYTOPE_TRIANGLE, 0, 2, DM_POLYTOPE_TRIANGLE, 1, 2, 1, DM_POLYTOPE_TRIANGLE, 1, 3, 0, DM_POLYTOPE_TRIANGLE, 0, 3, DM_POLYTOPE_TRIANGLE, 1, 1, 1, DM_POLYTOPE_TRIANGLE, 1, 2, 2, DM_POLYTOPE_TRIANGLE, 1, 3, 2, DM_POLYTOPE_TRIANGLE, 0, 0, DM_POLYTOPE_TRIANGLE, 1, 2, 3, DM_POLYTOPE_TRIANGLE, 0, 4, DM_POLYTOPE_TRIANGLE, 0, 7, DM_POLYTOPE_TRIANGLE, 0, 1, DM_POLYTOPE_TRIANGLE, 1, 3, 3, DM_POLYTOPE_TRIANGLE, 0, 5, DM_POLYTOPE_TRIANGLE, 0, 6, DM_POLYTOPE_TRIANGLE, 0, 4, DM_POLYTOPE_TRIANGLE, 0, 6, DM_POLYTOPE_TRIANGLE, 0, 2, DM_POLYTOPE_TRIANGLE, 1, 0, 3, DM_POLYTOPE_TRIANGLE, 0, 5, DM_POLYTOPE_TRIANGLE, 0, 7, DM_POLYTOPE_TRIANGLE, 0, 3, DM_POLYTOPE_TRIANGLE, 1, 1, 3};
743:   static PetscInt tetO[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, -1, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -1, -1, 1, 0, 0, -1, -1, -3, 2, -1, 0, -1, 1};
744:   /* Add a vertex in the center of each cell, add 6 edges and 12 quads inside every cell, making 8 new hexes
745:      The vertices of our reference hex are (-1, -1, -1), (-1, 1, -1), (1, 1, -1), (1, -1, -1), (-1, -1, 1), (1, -1, 1), (1, 1, 1), (-1, 1, 1) which we call [v0, v1, v2, v3, v4, v5, v6, v7]. The fours edges around the bottom [v0, v1], [v1, v2], [v2, v3], [v3, v0] are [e0, e1, e2, e3], and likewise around the top [v4, v5], [v5, v6], [v6, v7], [v7, v4] are [e4, e5, e6, e7]. Finally [v0, v4], [v1, v7], [v2, v6], [v3, v5] are [e9, e10, e11, e8]. The faces of a hex, given in DMPlexGetRawFaces_Internal(), oriented with outward normals, are
746:        [v0, v1, v2, v3] f0 bottom
747:        [v4, v5, v6, v7] f1 top
748:        [v0, v3, v5, v4] f2 front
749:        [v2, v1, v7, v6] f3 back
750:        [v3, v2, v6, v5] f4 right
751:        [v0, v4, v7, v1] f5 left
752:      The eight hexes are divided into four on the bottom, and four on the top,
753:        [v0,      (e0, 0),  (f0, 0),  (e3, 0),  (e9, 0), (f2, 0),  (c0, 0),  (f5, 0)]
754:        [(e0, 0), v1,       (e1, 0),  (f0, 0),  (f5, 0), (c0, 0),  (f3, 0),  (e10, 0)]
755:        [(f0, 0), (e1, 0),  v2,       (e2, 0),  (c0, 0), (f4, 0),  (e11, 0), (f3, 0)]
756:        [(e3, 0), (f0, 0),  (e2, 0),  v3,       (f2, 0), (e8, 0),  (f4, 0),  (c0, 0)]
757:        [(e9, 0), (f5, 0),  (c0, 0),  (f2, 0),  v4,      (e4, 0),  (f1, 0),  (e7, 0)]
758:        [(f2, 0), (c0, 0),  (f4, 0),  (e8, 0),  (e4, 0), v5,       (e5, 0),  (f1, 0)]
759:        [(c0, 0), (f3, 0),  (e11, 0), (f4, 0),  (f1, 0), (e5, 0),  v6,       (e6, 0)]
760:        [(f5, 0), (e10, 0), (f3, 0),  (c0, 0),  (e7, 0), (f1, 0),  (e6, 0),  v7]
761:      The 6 internal edges will go from the faces to the central vertex. The 12 internal faces can be divided into groups of 4 by the plane on which they sit. First the faces on the x-y plane are,
762:        [(e9, 0), (f2, 0),  (c0, 0),  (f5, 0)]
763:        [(f5, 0), (c0, 0),  (f3, 0),  (e10, 0)]
764:        [(c0, 0), (f4, 0),  (e11, 0), (f3, 0)]
765:        [(f2, 0), (e8, 0),  (f4, 0),  (c0, 0)]
766:      and on the x-z plane,
767:        [(f0, 0), (e0, 0), (f5, 0), (c0, 0)]
768:        [(c0, 0), (f5, 0), (e7, 0), (f1, 0)]
769:        [(f4, 0), (c0, 0), (f1, 0), (e5, 0)]
770:        [(e2, 0), (f0, 0), (c0, 0), (f4, 0)]
771:      and on the y-z plane,
772:        [(e3, 0), (f2, 0), (c0, 0), (f0, 0)]
773:        [(f2, 0), (e4, 0), (f1, 0), (c0, 0)]
774:        [(c0, 0), (f1, 0), (e6, 0), (f3, 0)]
775:        [(f0, 0), (c0, 0), (f3, 0), (e1, 0)]
776:   */
777:   static DMPolytopeType hexT[] = {DM_POLYTOPE_POINT, DM_POLYTOPE_SEGMENT, DM_POLYTOPE_QUADRILATERAL, DM_POLYTOPE_HEXAHEDRON};
778:   static PetscInt       hexS[] = {1, 6, 12, 8};
779:   static PetscInt hexC[] = {DM_POLYTOPE_POINT, 1, 0, 0, DM_POLYTOPE_POINT, 0, 0, DM_POLYTOPE_POINT, 1, 1, 0, DM_POLYTOPE_POINT, 0, 0, DM_POLYTOPE_POINT, 1, 2, 0, DM_POLYTOPE_POINT, 0, 0, DM_POLYTOPE_POINT, 1, 3, 0, DM_POLYTOPE_POINT, 0, 0, DM_POLYTOPE_POINT, 1, 4, 0, DM_POLYTOPE_POINT, 0, 0, DM_POLYTOPE_POINT, 1, 5, 0, DM_POLYTOPE_POINT, 0, 0, DM_POLYTOPE_SEGMENT, 1, 2, 3, DM_POLYTOPE_SEGMENT, 0, 2, DM_POLYTOPE_SEGMENT, 0, 5, DM_POLYTOPE_SEGMENT, 1, 5, 0, DM_POLYTOPE_SEGMENT, 0, 5, DM_POLYTOPE_SEGMENT, 0, 3, DM_POLYTOPE_SEGMENT, 1, 3, 1, DM_POLYTOPE_SEGMENT, 1, 5, 2, DM_POLYTOPE_SEGMENT, 0, 4, DM_POLYTOPE_SEGMENT, 1, 4, 1, DM_POLYTOPE_SEGMENT, 1, 3, 3, DM_POLYTOPE_SEGMENT, 0, 3, DM_POLYTOPE_SEGMENT, 1, 2, 1, DM_POLYTOPE_SEGMENT, 1, 4, 3, DM_POLYTOPE_SEGMENT, 0, 4, DM_POLYTOPE_SEGMENT, 0, 2, DM_POLYTOPE_SEGMENT, 1, 0, 0, DM_POLYTOPE_SEGMENT, 1, 5, 3, DM_POLYTOPE_SEGMENT, 0, 5, DM_POLYTOPE_SEGMENT, 0, 0, DM_POLYTOPE_SEGMENT, 0, 5, DM_POLYTOPE_SEGMENT, 1, 5, 1, DM_POLYTOPE_SEGMENT, 1, 1, 3, DM_POLYTOPE_SEGMENT, 0, 1, DM_POLYTOPE_SEGMENT, 0, 4, DM_POLYTOPE_SEGMENT, 0, 1, DM_POLYTOPE_SEGMENT, 1, 1, 1, DM_POLYTOPE_SEGMENT, 1, 4, 2, DM_POLYTOPE_SEGMENT, 1, 0, 2, DM_POLYTOPE_SEGMENT, 0, 0, DM_POLYTOPE_SEGMENT, 0, 4, DM_POLYTOPE_SEGMENT, 1, 4, 0, DM_POLYTOPE_SEGMENT, 1, 2, 0, DM_POLYTOPE_SEGMENT, 0, 2, DM_POLYTOPE_SEGMENT, 0, 0, DM_POLYTOPE_SEGMENT, 1, 0, 3, DM_POLYTOPE_SEGMENT, 1, 2, 2, DM_POLYTOPE_SEGMENT, 1, 1, 0, DM_POLYTOPE_SEGMENT, 0, 1, DM_POLYTOPE_SEGMENT, 0, 2, DM_POLYTOPE_SEGMENT, 0, 1, DM_POLYTOPE_SEGMENT, 1, 1, 2, DM_POLYTOPE_SEGMENT, 1, 3, 2, DM_POLYTOPE_SEGMENT, 0, 3, DM_POLYTOPE_SEGMENT, 0, 0, DM_POLYTOPE_SEGMENT, 0, 3, DM_POLYTOPE_SEGMENT, 1, 3, 0, DM_POLYTOPE_SEGMENT, 1, 0, 1, DM_POLYTOPE_QUADRILATERAL, 1, 0, 0, DM_POLYTOPE_QUADRILATERAL, 0, 0, DM_POLYTOPE_QUADRILATERAL, 1, 2, 0, DM_POLYTOPE_QUADRILATERAL, 0, 4, DM_POLYTOPE_QUADRILATERAL, 0, 8, DM_POLYTOPE_QUADRILATERAL, 1, 5, 0, DM_POLYTOPE_QUADRILATERAL, 1, 0, 1, DM_POLYTOPE_QUADRILATERAL, 0, 1, DM_POLYTOPE_QUADRILATERAL, 0, 4, DM_POLYTOPE_QUADRILATERAL, 1, 3, 1, DM_POLYTOPE_QUADRILATERAL, 0, 11, DM_POLYTOPE_QUADRILATERAL, 1, 5, 3, DM_POLYTOPE_QUADRILATERAL, 1, 0, 2, DM_POLYTOPE_QUADRILATERAL, 0, 2, DM_POLYTOPE_QUADRILATERAL, 0, 7, DM_POLYTOPE_QUADRILATERAL, 1, 3, 0, DM_POLYTOPE_QUADRILATERAL, 1, 4, 1, DM_POLYTOPE_QUADRILATERAL, 0, 11, DM_POLYTOPE_QUADRILATERAL, 1, 0, 3, DM_POLYTOPE_QUADRILATERAL, 0, 3, DM_POLYTOPE_QUADRILATERAL, 1, 2, 1, DM_POLYTOPE_QUADRILATERAL, 0, 7, DM_POLYTOPE_QUADRILATERAL, 1, 4, 0, DM_POLYTOPE_QUADRILATERAL, 0, 8, DM_POLYTOPE_QUADRILATERAL, 0, 0, DM_POLYTOPE_QUADRILATERAL, 1, 1, 0, DM_POLYTOPE_QUADRILATERAL, 1, 2, 3, DM_POLYTOPE_QUADRILATERAL, 0, 5, DM_POLYTOPE_QUADRILATERAL, 0, 9, DM_POLYTOPE_QUADRILATERAL, 1, 5, 1, DM_POLYTOPE_QUADRILATERAL, 0, 3, DM_POLYTOPE_QUADRILATERAL, 1, 1, 1, DM_POLYTOPE_QUADRILATERAL, 1, 2, 2, DM_POLYTOPE_QUADRILATERAL, 0, 6, DM_POLYTOPE_QUADRILATERAL, 1, 4, 3, DM_POLYTOPE_QUADRILATERAL, 0, 9, DM_POLYTOPE_QUADRILATERAL, 0, 2, DM_POLYTOPE_QUADRILATERAL, 1, 1, 2, DM_POLYTOPE_QUADRILATERAL, 0, 6, DM_POLYTOPE_QUADRILATERAL, 1, 3, 3, DM_POLYTOPE_QUADRILATERAL, 1, 4, 2, DM_POLYTOPE_QUADRILATERAL, 0, 10, DM_POLYTOPE_QUADRILATERAL, 0, 1, DM_POLYTOPE_QUADRILATERAL, 1, 1, 3, DM_POLYTOPE_QUADRILATERAL, 0, 5, DM_POLYTOPE_QUADRILATERAL, 1, 3, 2, DM_POLYTOPE_QUADRILATERAL, 0, 10, DM_POLYTOPE_QUADRILATERAL, 1, 5, 2};
780:   static PetscInt hexO[] = {0, 0, 0, 0,  0,  0, 0, 0, 0, 0, 0,  0, 0, 0, -1, -1, 0,  -1, -1, 0, -1, -1, 0, 0, -1, 0, 0, -1, -1, 0, 0,  -1, -1, -1, 0,  0, 0,  -1, -1, 0, 0, 0, -1, -1, 0,  0, -1, -1, -1, 0, 0,  -1, -1, -1,
781:                             0, 0, 0, -1, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, -3, 0,  -2, 0,  0,  0, -3, 0,  0, 0, 0,  0, 0, 0,  0,  0, -2, 0,  0,  0,  -2, 0, -2, 0,  0,  0, 0, 0, -2, 0,  -3, 0, 0,  0,  -2, 0, -3, 0,  -2, 0};
782:   /* Add 3 quads inside every triangular prism, making 4 new prisms. */
783:   static DMPolytopeType tripT[] = {DM_POLYTOPE_SEGMENT, DM_POLYTOPE_TRIANGLE, DM_POLYTOPE_QUADRILATERAL, DM_POLYTOPE_TRI_PRISM};
784:   static PetscInt       tripS[] = {3, 4, 6, 8};
785:   static PetscInt tripC[] = {DM_POLYTOPE_POINT, 1, 2, 0, DM_POLYTOPE_POINT, 1, 3, 0, DM_POLYTOPE_POINT, 1, 3, 0, DM_POLYTOPE_POINT, 1, 4, 0, DM_POLYTOPE_POINT, 1, 4, 0, DM_POLYTOPE_POINT, 1, 2, 0, DM_POLYTOPE_SEGMENT, 1, 2, 3, DM_POLYTOPE_SEGMENT, 0, 2, DM_POLYTOPE_SEGMENT, 1, 4, 1, DM_POLYTOPE_SEGMENT, 1, 2, 1, DM_POLYTOPE_SEGMENT, 1, 3, 3, DM_POLYTOPE_SEGMENT, 0, 0, DM_POLYTOPE_SEGMENT, 0, 1, DM_POLYTOPE_SEGMENT, 1, 3, 1, DM_POLYTOPE_SEGMENT, 1, 4, 3, DM_POLYTOPE_SEGMENT, 0, 0, DM_POLYTOPE_SEGMENT, 0, 1, DM_POLYTOPE_SEGMENT, 0, 2, DM_POLYTOPE_SEGMENT, 1, 0, 1, DM_POLYTOPE_SEGMENT, 1, 3, 0, DM_POLYTOPE_SEGMENT, 0, 0, DM_POLYTOPE_SEGMENT, 1, 2, 0, DM_POLYTOPE_SEGMENT, 1, 0, 0, DM_POLYTOPE_SEGMENT, 1, 4, 0, DM_POLYTOPE_SEGMENT, 0, 1, DM_POLYTOPE_SEGMENT, 1, 3, 0, DM_POLYTOPE_SEGMENT, 1, 0, 2, DM_POLYTOPE_SEGMENT, 1, 2, 0, DM_POLYTOPE_SEGMENT, 0, 2, DM_POLYTOPE_SEGMENT, 1, 4, 0, DM_POLYTOPE_SEGMENT, 0, 0, DM_POLYTOPE_SEGMENT, 1, 3, 2, DM_POLYTOPE_SEGMENT, 1, 1, 0, DM_POLYTOPE_SEGMENT, 1, 2, 2, DM_POLYTOPE_SEGMENT, 0, 1, DM_POLYTOPE_SEGMENT, 1, 4, 2, DM_POLYTOPE_SEGMENT, 1, 1, 1, DM_POLYTOPE_SEGMENT, 1, 3, 2, DM_POLYTOPE_SEGMENT, 0, 2, DM_POLYTOPE_SEGMENT, 1, 2, 2, DM_POLYTOPE_SEGMENT, 1, 1, 2, DM_POLYTOPE_SEGMENT, 1, 4, 2, DM_POLYTOPE_TRIANGLE, 1, 0, 0, DM_POLYTOPE_TRIANGLE, 0, 0, DM_POLYTOPE_QUADRILATERAL, 1, 2, 0, DM_POLYTOPE_QUADRILATERAL, 0, 2, DM_POLYTOPE_QUADRILATERAL, 1, 4, 1, DM_POLYTOPE_TRIANGLE, 1, 0, 2, DM_POLYTOPE_TRIANGLE, 0, 1, DM_POLYTOPE_QUADRILATERAL, 1, 2, 1, DM_POLYTOPE_QUADRILATERAL, 1, 3, 0, DM_POLYTOPE_QUADRILATERAL, 0, 0, DM_POLYTOPE_TRIANGLE, 1, 0, 1, DM_POLYTOPE_TRIANGLE, 0, 2, DM_POLYTOPE_QUADRILATERAL, 0, 1, DM_POLYTOPE_QUADRILATERAL, 1, 3, 1, DM_POLYTOPE_QUADRILATERAL, 1, 4, 0, DM_POLYTOPE_TRIANGLE, 1, 0, 3, DM_POLYTOPE_TRIANGLE, 0, 3, DM_POLYTOPE_QUADRILATERAL, 0, 0, DM_POLYTOPE_QUADRILATERAL, 0, 1, DM_POLYTOPE_QUADRILATERAL, 0, 2, DM_POLYTOPE_TRIANGLE, 0, 0, DM_POLYTOPE_TRIANGLE, 1, 1, 0, DM_POLYTOPE_QUADRILATERAL, 1, 2, 3, DM_POLYTOPE_QUADRILATERAL, 0, 5, DM_POLYTOPE_QUADRILATERAL, 1, 4, 2, DM_POLYTOPE_TRIANGLE, 0, 1, DM_POLYTOPE_TRIANGLE, 1, 1, 1, DM_POLYTOPE_QUADRILATERAL, 1, 2, 2, DM_POLYTOPE_QUADRILATERAL, 1, 3, 3, DM_POLYTOPE_QUADRILATERAL, 0, 3, DM_POLYTOPE_TRIANGLE, 0, 2, DM_POLYTOPE_TRIANGLE, 1, 1, 2, DM_POLYTOPE_QUADRILATERAL, 0, 4, DM_POLYTOPE_QUADRILATERAL, 1, 3, 2, DM_POLYTOPE_QUADRILATERAL, 1, 4, 3, DM_POLYTOPE_TRIANGLE, 0, 3, DM_POLYTOPE_TRIANGLE, 1, 1, 3, DM_POLYTOPE_QUADRILATERAL, 0, 3, DM_POLYTOPE_QUADRILATERAL, 0, 4, DM_POLYTOPE_QUADRILATERAL, 0, 5};
786:   static PetscInt tripO[] = {0, 0, 0, 0, 0,  0, 0, -1, -1, -1, 0,  -1, -1, -1, 0, 0, 0, 0, -1, 0, -1, -1, -1, 0, -1, -1, -1, 0, -1, -1, 0,  -1, -1, 0,  0, -1, -1, 0, 0, -1, -1,
787:                              0, 0, 0, 0, -3, 0, 0, 0,  0,  0,  -3, 0,  0,  -3, 0, 0, 2, 0, 0,  0, 0,  -2, 0,  0, -3, 0,  -2, 0, 0,  0,  -3, -2, 0,  -3, 0, 0,  -2, 0, 0, 0,  0};
788:   /* Add 3 tensor quads inside every tensor triangular prism, making 4 new prisms.
789:       2
790:       |\
791:       | \
792:       |  \
793:       0---1

795:       2

797:       0   1

799:       2
800:       |\
801:       | \
802:       |  \
803:       0---1
804:   */
805:   static DMPolytopeType ttriT[] = {DM_POLYTOPE_SEG_PRISM_TENSOR, DM_POLYTOPE_TRI_PRISM_TENSOR};
806:   static PetscInt       ttriS[] = {3, 4};
807:   static PetscInt ttriC[] = {DM_POLYTOPE_SEGMENT, 1, 0, 0, DM_POLYTOPE_SEGMENT, 1, 1, 0, DM_POLYTOPE_POINT_PRISM_TENSOR, 1, 2, 0, DM_POLYTOPE_POINT_PRISM_TENSOR, 1, 3, 0, DM_POLYTOPE_SEGMENT, 1, 0, 1, DM_POLYTOPE_SEGMENT, 1, 1, 1, DM_POLYTOPE_POINT_PRISM_TENSOR, 1, 3, 0, DM_POLYTOPE_POINT_PRISM_TENSOR, 1, 4, 0, DM_POLYTOPE_SEGMENT, 1, 0, 2, DM_POLYTOPE_SEGMENT, 1, 1, 2, DM_POLYTOPE_POINT_PRISM_TENSOR, 1, 4, 0, DM_POLYTOPE_POINT_PRISM_TENSOR, 1, 2, 0, DM_POLYTOPE_TRIANGLE, 1, 0, 0, DM_POLYTOPE_TRIANGLE, 1, 1, 0, DM_POLYTOPE_SEG_PRISM_TENSOR, 1, 2, 0, DM_POLYTOPE_SEG_PRISM_TENSOR, 0, 2, DM_POLYTOPE_SEG_PRISM_TENSOR, 1, 4, 1, DM_POLYTOPE_TRIANGLE, 1, 0, 1, DM_POLYTOPE_TRIANGLE, 1, 1, 1, DM_POLYTOPE_SEG_PRISM_TENSOR, 1, 2, 1, DM_POLYTOPE_SEG_PRISM_TENSOR, 1, 3, 0, DM_POLYTOPE_SEG_PRISM_TENSOR, 0, 0, DM_POLYTOPE_TRIANGLE, 1, 0, 2, DM_POLYTOPE_TRIANGLE, 1, 1, 2, DM_POLYTOPE_SEG_PRISM_TENSOR, 0, 1, DM_POLYTOPE_SEG_PRISM_TENSOR, 1, 3, 1, DM_POLYTOPE_SEG_PRISM_TENSOR, 1, 4, 0, DM_POLYTOPE_TRIANGLE, 1, 0, 3, DM_POLYTOPE_TRIANGLE, 1, 1, 3, DM_POLYTOPE_SEG_PRISM_TENSOR, 0, 0, DM_POLYTOPE_SEG_PRISM_TENSOR, 0, 1, DM_POLYTOPE_SEG_PRISM_TENSOR, 0, 2};
808:   static PetscInt ttriO[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0};
809:   /* Add 1 edge and 4 tensor quads inside every tensor quad prism, making 4 new prisms. */
810:   static DMPolytopeType tquadT[] = {DM_POLYTOPE_POINT_PRISM_TENSOR, DM_POLYTOPE_SEG_PRISM_TENSOR, DM_POLYTOPE_QUAD_PRISM_TENSOR};
811:   static PetscInt       tquadS[] = {1, 4, 4};
812:   static PetscInt tquadC[] = {DM_POLYTOPE_POINT, 1, 0, 0, DM_POLYTOPE_POINT, 1, 1, 0, DM_POLYTOPE_SEGMENT, 1, 0, 0, DM_POLYTOPE_SEGMENT, 1, 1, 0, DM_POLYTOPE_POINT_PRISM_TENSOR, 1, 2, 0, DM_POLYTOPE_POINT_PRISM_TENSOR, 0, 0, DM_POLYTOPE_SEGMENT, 1, 0, 1, DM_POLYTOPE_SEGMENT, 1, 1, 1, DM_POLYTOPE_POINT_PRISM_TENSOR, 1, 3, 0, DM_POLYTOPE_POINT_PRISM_TENSOR, 0, 0, DM_POLYTOPE_SEGMENT, 1, 0, 2, DM_POLYTOPE_SEGMENT, 1, 1, 2, DM_POLYTOPE_POINT_PRISM_TENSOR, 1, 4, 0, DM_POLYTOPE_POINT_PRISM_TENSOR, 0, 0, DM_POLYTOPE_SEGMENT, 1, 0, 3, DM_POLYTOPE_SEGMENT, 1, 1, 3, DM_POLYTOPE_POINT_PRISM_TENSOR, 1, 5, 0, DM_POLYTOPE_POINT_PRISM_TENSOR, 0, 0, DM_POLYTOPE_QUADRILATERAL, 1, 0, 0, DM_POLYTOPE_QUADRILATERAL, 1, 1, 0, DM_POLYTOPE_SEG_PRISM_TENSOR, 1, 2, 0, DM_POLYTOPE_SEG_PRISM_TENSOR, 0, 0, DM_POLYTOPE_SEG_PRISM_TENSOR, 0, 3, DM_POLYTOPE_SEG_PRISM_TENSOR, 1, 5, 1, DM_POLYTOPE_QUADRILATERAL, 1, 0, 1, DM_POLYTOPE_QUADRILATERAL, 1, 1, 1, DM_POLYTOPE_SEG_PRISM_TENSOR, 1, 2, 1, DM_POLYTOPE_SEG_PRISM_TENSOR, 1, 3, 0, DM_POLYTOPE_SEG_PRISM_TENSOR, 0, 1, DM_POLYTOPE_SEG_PRISM_TENSOR, 0, 0, DM_POLYTOPE_QUADRILATERAL, 1, 0, 2, DM_POLYTOPE_QUADRILATERAL, 1, 1, 2, DM_POLYTOPE_SEG_PRISM_TENSOR, 0, 1, DM_POLYTOPE_SEG_PRISM_TENSOR, 1, 3, 1, DM_POLYTOPE_SEG_PRISM_TENSOR, 1, 4, 0, DM_POLYTOPE_SEG_PRISM_TENSOR, 0, 2, DM_POLYTOPE_QUADRILATERAL, 1, 0, 3, DM_POLYTOPE_QUADRILATERAL, 1, 1, 3, DM_POLYTOPE_SEG_PRISM_TENSOR, 0, 3, DM_POLYTOPE_SEG_PRISM_TENSOR, 0, 2, DM_POLYTOPE_SEG_PRISM_TENSOR, 1, 4, 1, DM_POLYTOPE_SEG_PRISM_TENSOR, 1, 5, 0};
813:   static PetscInt tquadO[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0};
814:   /* Add 4 edges, 12 triangles, 1 quad, 4 tetrahedra, and 6 pyramids inside every pyramid. */
815:   static DMPolytopeType tpyrT[] = {DM_POLYTOPE_SEGMENT, DM_POLYTOPE_TRIANGLE, DM_POLYTOPE_QUADRILATERAL, DM_POLYTOPE_TETRAHEDRON, DM_POLYTOPE_PYRAMID};
816:   static PetscInt       tpyrS[] = {4, 12, 1, 4, 6};
817:   static PetscInt       tpyrC[] = {
818:     DM_POLYTOPE_POINT,
819:     2,
820:     1,
821:     1,
822:     0,
823:     DM_POLYTOPE_POINT,
824:     1,
825:     0,
826:     0,
827:     DM_POLYTOPE_POINT,
828:     2,
829:     2,
830:     1,
831:     0,
832:     DM_POLYTOPE_POINT,
833:     1,
834:     0,
835:     0,
836:     DM_POLYTOPE_POINT,
837:     2,
838:     3,
839:     1,
840:     0,
841:     DM_POLYTOPE_POINT,
842:     1,
843:     0,
844:     0,
845:     DM_POLYTOPE_POINT,
846:     2,
847:     4,
848:     1,
849:     0,
850:     DM_POLYTOPE_POINT,
851:     1,
852:     0,
853:     0,
854:     /* These four triangle face out of the bottom pyramid */
855:     DM_POLYTOPE_SEGMENT,
856:     1,
857:     1,
858:     1,
859:     DM_POLYTOPE_SEGMENT,
860:     0,
861:     3,
862:     DM_POLYTOPE_SEGMENT,
863:     0,
864:     0,
865:     DM_POLYTOPE_SEGMENT,
866:     1,
867:     2,
868:     1,
869:     DM_POLYTOPE_SEGMENT,
870:     0,
871:     0,
872:     DM_POLYTOPE_SEGMENT,
873:     0,
874:     1,
875:     DM_POLYTOPE_SEGMENT,
876:     1,
877:     3,
878:     1,
879:     DM_POLYTOPE_SEGMENT,
880:     0,
881:     1,
882:     DM_POLYTOPE_SEGMENT,
883:     0,
884:     2,
885:     DM_POLYTOPE_SEGMENT,
886:     1,
887:     4,
888:     1,
889:     DM_POLYTOPE_SEGMENT,
890:     0,
891:     2,
892:     DM_POLYTOPE_SEGMENT,
893:     0,
894:     3,
895:     /* These eight triangles face out of the corner pyramids */
896:     DM_POLYTOPE_SEGMENT,
897:     1,
898:     0,
899:     3,
900:     DM_POLYTOPE_SEGMENT,
901:     0,
902:     3,
903:     DM_POLYTOPE_SEGMENT,
904:     1,
905:     1,
906:     2,
907:     DM_POLYTOPE_SEGMENT,
908:     1,
909:     0,
910:     2,
911:     DM_POLYTOPE_SEGMENT,
912:     0,
913:     0,
914:     DM_POLYTOPE_SEGMENT,
915:     1,
916:     2,
917:     2,
918:     DM_POLYTOPE_SEGMENT,
919:     1,
920:     0,
921:     1,
922:     DM_POLYTOPE_SEGMENT,
923:     0,
924:     1,
925:     DM_POLYTOPE_SEGMENT,
926:     1,
927:     3,
928:     2,
929:     DM_POLYTOPE_SEGMENT,
930:     1,
931:     0,
932:     0,
933:     DM_POLYTOPE_SEGMENT,
934:     0,
935:     2,
936:     DM_POLYTOPE_SEGMENT,
937:     1,
938:     4,
939:     2,
940:     DM_POLYTOPE_SEGMENT,
941:     1,
942:     0,
943:     3,
944:     DM_POLYTOPE_SEGMENT,
945:     1,
946:     1,
947:     0,
948:     DM_POLYTOPE_SEGMENT,
949:     0,
950:     0,
951:     DM_POLYTOPE_SEGMENT,
952:     1,
953:     0,
954:     2,
955:     DM_POLYTOPE_SEGMENT,
956:     1,
957:     2,
958:     0,
959:     DM_POLYTOPE_SEGMENT,
960:     0,
961:     1,
962:     DM_POLYTOPE_SEGMENT,
963:     1,
964:     0,
965:     1,
966:     DM_POLYTOPE_SEGMENT,
967:     1,
968:     3,
969:     0,
970:     DM_POLYTOPE_SEGMENT,
971:     0,
972:     2,
973:     DM_POLYTOPE_SEGMENT,
974:     1,
975:     0,
976:     0,
977:     DM_POLYTOPE_SEGMENT,
978:     1,
979:     4,
980:     0,
981:     DM_POLYTOPE_SEGMENT,
982:     0,
983:     3,
984:     /* This quad faces out of the bottom pyramid */
985:     DM_POLYTOPE_SEGMENT,
986:     1,
987:     1,
988:     1,
989:     DM_POLYTOPE_SEGMENT,
990:     1,
991:     2,
992:     1,
993:     DM_POLYTOPE_SEGMENT,
994:     1,
995:     3,
996:     1,
997:     DM_POLYTOPE_SEGMENT,
998:     1,
999:     4,
1000:     1,
1001:     /* The bottom face of each tet is on the triangular face */
1002:     DM_POLYTOPE_TRIANGLE,
1003:     1,
1004:     1,
1005:     3,
1006:     DM_POLYTOPE_TRIANGLE,
1007:     0,
1008:     8,
1009:     DM_POLYTOPE_TRIANGLE,
1010:     0,
1011:     4,
1012:     DM_POLYTOPE_TRIANGLE,
1013:     0,
1014:     0,
1015:     DM_POLYTOPE_TRIANGLE,
1016:     1,
1017:     2,
1018:     3,
1019:     DM_POLYTOPE_TRIANGLE,
1020:     0,
1021:     9,
1022:     DM_POLYTOPE_TRIANGLE,
1023:     0,
1024:     5,
1025:     DM_POLYTOPE_TRIANGLE,
1026:     0,
1027:     1,
1028:     DM_POLYTOPE_TRIANGLE,
1029:     1,
1030:     3,
1031:     3,
1032:     DM_POLYTOPE_TRIANGLE,
1033:     0,
1034:     10,
1035:     DM_POLYTOPE_TRIANGLE,
1036:     0,
1037:     6,
1038:     DM_POLYTOPE_TRIANGLE,
1039:     0,
1040:     2,
1041:     DM_POLYTOPE_TRIANGLE,
1042:     1,
1043:     4,
1044:     3,
1045:     DM_POLYTOPE_TRIANGLE,
1046:     0,
1047:     11,
1048:     DM_POLYTOPE_TRIANGLE,
1049:     0,
1050:     7,
1051:     DM_POLYTOPE_TRIANGLE,
1052:     0,
1053:     3,
1054:     /* The front face of all pyramids is toward the front */
1055:     DM_POLYTOPE_QUADRILATERAL,
1056:     1,
1057:     0,
1058:     0,
1059:     DM_POLYTOPE_TRIANGLE,
1060:     1,
1061:     1,
1062:     0,
1063:     DM_POLYTOPE_TRIANGLE,
1064:     0,
1065:     4,
1066:     DM_POLYTOPE_TRIANGLE,
1067:     0,
1068:     11,
1069:     DM_POLYTOPE_TRIANGLE,
1070:     1,
1071:     4,
1072:     1,
1073:     DM_POLYTOPE_QUADRILATERAL,
1074:     1,
1075:     0,
1076:     3,
1077:     DM_POLYTOPE_TRIANGLE,
1078:     1,
1079:     1,
1080:     1,
1081:     DM_POLYTOPE_TRIANGLE,
1082:     1,
1083:     2,
1084:     0,
1085:     DM_POLYTOPE_TRIANGLE,
1086:     0,
1087:     5,
1088:     DM_POLYTOPE_TRIANGLE,
1089:     0,
1090:     8,
1091:     DM_POLYTOPE_QUADRILATERAL,
1092:     1,
1093:     0,
1094:     2,
1095:     DM_POLYTOPE_TRIANGLE,
1096:     0,
1097:     9,
1098:     DM_POLYTOPE_TRIANGLE,
1099:     1,
1100:     2,
1101:     1,
1102:     DM_POLYTOPE_TRIANGLE,
1103:     1,
1104:     3,
1105:     0,
1106:     DM_POLYTOPE_TRIANGLE,
1107:     0,
1108:     6,
1109:     DM_POLYTOPE_QUADRILATERAL,
1110:     1,
1111:     0,
1112:     1,
1113:     DM_POLYTOPE_TRIANGLE,
1114:     0,
1115:     7,
1116:     DM_POLYTOPE_TRIANGLE,
1117:     0,
1118:     10,
1119:     DM_POLYTOPE_TRIANGLE,
1120:     1,
1121:     3,
1122:     1,
1123:     DM_POLYTOPE_TRIANGLE,
1124:     1,
1125:     4,
1126:     0,
1127:     DM_POLYTOPE_QUADRILATERAL,
1128:     0,
1129:     0,
1130:     DM_POLYTOPE_TRIANGLE,
1131:     1,
1132:     1,
1133:     2,
1134:     DM_POLYTOPE_TRIANGLE,
1135:     1,
1136:     2,
1137:     2,
1138:     DM_POLYTOPE_TRIANGLE,
1139:     1,
1140:     3,
1141:     2,
1142:     DM_POLYTOPE_TRIANGLE,
1143:     1,
1144:     4,
1145:     2,
1146:     DM_POLYTOPE_QUADRILATERAL,
1147:     0,
1148:     0,
1149:     DM_POLYTOPE_TRIANGLE,
1150:     0,
1151:     0,
1152:     DM_POLYTOPE_TRIANGLE,
1153:     0,
1154:     3,
1155:     DM_POLYTOPE_TRIANGLE,
1156:     0,
1157:     2,
1158:     DM_POLYTOPE_TRIANGLE,
1159:     0,
1160:     1,
1161:   };
1162:   static PetscInt tpyrO[] = {0,  0, 0,  0,  0,  0, 0,  0,  0,  0, -1, 0,  0,  -1, 0,  0,  -1, 0, 0, -1, 0, -1, 0, 0, -1, 0, 0, -1, 0, 0, -1, 0, -1, 0, 0, -1, 0, 0,  -1, 0, 0, -1, 0, 0, -1, -1, -1,
1163:                              -1, 0, -3, -2, -3, 0, -3, -2, -3, 0, -3, -2, -3, 0,  -3, -2, -3, 0, 0, 0,  0, 0,  0, 0, 0,  0, 0, 0,  0, 0, 0,  0, 0,  0, 0, 0,  0, -2, 0,  0, 0, 0,  1, 0, 0,  0,  0};

1165:   PetscFunctionBegin;
1166:   if (rt) *rt = 0;
1167:   switch (source) {
1168:   case DM_POLYTOPE_POINT:
1169:     *Nt     = 1;
1170:     *target = vertexT;
1171:     *size   = vertexS;
1172:     *cone   = vertexC;
1173:     *ornt   = vertexO;
1174:     break;
1175:   case DM_POLYTOPE_SEGMENT:
1176:     *Nt     = 2;
1177:     *target = segT;
1178:     *size   = segS;
1179:     *cone   = segC;
1180:     *ornt   = segO;
1181:     break;
1182:   case DM_POLYTOPE_POINT_PRISM_TENSOR:
1183:     *Nt     = 1;
1184:     *target = tvertT;
1185:     *size   = tvertS;
1186:     *cone   = tvertC;
1187:     *ornt   = tvertO;
1188:     break;
1189:   case DM_POLYTOPE_TRIANGLE:
1190:     *Nt     = 2;
1191:     *target = triT;
1192:     *size   = triS;
1193:     *cone   = triC;
1194:     *ornt   = triO;
1195:     break;
1196:   case DM_POLYTOPE_QUADRILATERAL:
1197:     *Nt     = 3;
1198:     *target = quadT;
1199:     *size   = quadS;
1200:     *cone   = quadC;
1201:     *ornt   = quadO;
1202:     break;
1203:   case DM_POLYTOPE_SEG_PRISM_TENSOR:
1204:     *Nt     = 2;
1205:     *target = tsegT;
1206:     *size   = tsegS;
1207:     *cone   = tsegC;
1208:     *ornt   = tsegO;
1209:     break;
1210:   case DM_POLYTOPE_TETRAHEDRON:
1211:     *Nt     = 3;
1212:     *target = tetT;
1213:     *size   = tetS;
1214:     *cone   = tetC;
1215:     *ornt   = tetO;
1216:     break;
1217:   case DM_POLYTOPE_HEXAHEDRON:
1218:     *Nt     = 4;
1219:     *target = hexT;
1220:     *size   = hexS;
1221:     *cone   = hexC;
1222:     *ornt   = hexO;
1223:     break;
1224:   case DM_POLYTOPE_TRI_PRISM:
1225:     *Nt     = 4;
1226:     *target = tripT;
1227:     *size   = tripS;
1228:     *cone   = tripC;
1229:     *ornt   = tripO;
1230:     break;
1231:   case DM_POLYTOPE_TRI_PRISM_TENSOR:
1232:     *Nt     = 2;
1233:     *target = ttriT;
1234:     *size   = ttriS;
1235:     *cone   = ttriC;
1236:     *ornt   = ttriO;
1237:     break;
1238:   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
1239:     *Nt     = 3;
1240:     *target = tquadT;
1241:     *size   = tquadS;
1242:     *cone   = tquadC;
1243:     *ornt   = tquadO;
1244:     break;
1245:   case DM_POLYTOPE_PYRAMID:
1246:     *Nt     = 5;
1247:     *target = tpyrT;
1248:     *size   = tpyrS;
1249:     *cone   = tpyrC;
1250:     *ornt   = tpyrO;
1251:     break;
1252:   case DM_POLYTOPE_FV_GHOST:
1253:     *Nt     = 0;
1254:     *target = NULL;
1255:     *size   = NULL;
1256:     *cone   = NULL;
1257:     *ornt   = NULL;
1258:     break;
1259:   default:
1260:     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "No refinement strategy for %s", DMPolytopeTypes[source]);
1261:   }
1262:   PetscFunctionReturn(PETSC_SUCCESS);
1263: }

1265: static PetscErrorCode DMPlexTransformInitialize_Regular(DMPlexTransform tr)
1266: {
1267:   PetscFunctionBegin;
1268:   tr->ops->view                  = DMPlexTransformView_Regular;
1269:   tr->ops->destroy               = DMPlexTransformDestroy_Regular;
1270:   tr->ops->setdimensions         = DMPlexTransformSetDimensions_Internal;
1271:   tr->ops->celltransform         = DMPlexTransformCellRefine_Regular;
1272:   tr->ops->getsubcellorientation = DMPlexTransformGetSubcellOrientation_Regular;
1273:   tr->ops->mapcoordinates        = DMPlexTransformMapCoordinatesBarycenter_Internal;
1274:   PetscFunctionReturn(PETSC_SUCCESS);
1275: }

1277: PETSC_EXTERN PetscErrorCode DMPlexTransformCreate_Regular(DMPlexTransform tr)
1278: {
1279:   DMPlexRefine_Regular *f;

1281:   PetscFunctionBegin;
1283:   PetscCall(PetscNew(&f));
1284:   tr->data = f;

1286:   PetscCall(DMPlexTransformInitialize_Regular(tr));
1287:   PetscFunctionReturn(PETSC_SUCCESS);
1288: }