Actual source code: plexgeometry.c

petsc-master 2020-12-03
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  1: #include <petsc/private/dmpleximpl.h>
  2: #include <petsc/private/petscfeimpl.h>
  3: #include <petscblaslapack.h>
  4: #include <petsctime.h>

  6: /*@
  7:   DMPlexFindVertices - Try to find DAG points based on their coordinates.

  9:   Not Collective (provided DMGetCoordinatesLocalSetUp() has been called already)

 11:   Input Parameters:
 12: + dm - The DMPlex object
 13: . npoints - The number of sought points
 14: . coords - The array of coordinates of the sought points
 15: - eps - The tolerance or PETSC_DEFAULT

 17:   Output Parameters:
 18: . dagPoints - The array of found DAG points, or -1 if not found

 20:   Level: intermediate

 22:   Notes:
 23:   The length of the array coords must be npoints * dim where dim is the spatial dimension returned by DMGetDimension().

 25:   The output array dagPoints is NOT newly allocated; the user must pass an array of length npoints.

 27:   Each rank does the search independently; a nonnegative value is returned only if this rank's local DMPlex portion contains the point.

 29:   The tolerance is interpreted as the maximum Euclidean (L2) distance of the sought point from the specified coordinates.

 31:   Complexity of this function is currently O(mn) with m number of vertices to find and n number of vertices in the local mesh. This could probably be improved.

 33: .seealso: DMPlexCreate(), DMGetCoordinatesLocal()
 34: @*/
 35: PetscErrorCode DMPlexFindVertices(DM dm, PetscInt npoints, const PetscReal coord[], PetscReal eps, PetscInt dagPoints[])
 36: {
 37:   PetscInt          c, cdim, i, j, o, p, vStart, vEnd;
 38:   Vec               allCoordsVec;
 39:   const PetscScalar *allCoords;
 40:   PetscReal         norm;
 41:   PetscErrorCode    ierr;

 44:   if (eps < 0) eps = PETSC_SQRT_MACHINE_EPSILON;
 45:   DMGetCoordinateDim(dm, &cdim);
 46:   DMGetCoordinatesLocal(dm, &allCoordsVec);
 47:   VecGetArrayRead(allCoordsVec, &allCoords);
 48:   DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);
 49:   if (PetscDefined(USE_DEBUG)) {
 50:     /* check coordinate section is consistent with DM dimension */
 51:     PetscSection      cs;
 52:     PetscInt          ndof;

 54:     DMGetCoordinateSection(dm, &cs);
 55:     for (p = vStart; p < vEnd; p++) {
 56:       PetscSectionGetDof(cs, p, &ndof);
 57:       if (PetscUnlikely(ndof != cdim)) SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_PLIB, "point %D: ndof = %D != %D = cdim", p, ndof, cdim);
 58:     }
 59:   }
 60:   if (eps == 0.0) {
 61:     for (i=0,j=0; i < npoints; i++,j+=cdim) {
 62:       dagPoints[i] = -1;
 63:       for (p = vStart,o=0; p < vEnd; p++,o+=cdim) {
 64:         for (c = 0; c < cdim; c++) {
 65:           if (coord[j+c] != PetscRealPart(allCoords[o+c])) break;
 66:         }
 67:         if (c == cdim) {
 68:           dagPoints[i] = p;
 69:           break;
 70:         }
 71:       }
 72:     }
 73:     VecRestoreArrayRead(allCoordsVec, &allCoords);
 74:     return(0);
 75:   }
 76:   for (i=0,j=0; i < npoints; i++,j+=cdim) {
 77:     dagPoints[i] = -1;
 78:     for (p = vStart,o=0; p < vEnd; p++,o+=cdim) {
 79:       norm = 0.0;
 80:       for (c = 0; c < cdim; c++) {
 81:         norm += PetscSqr(coord[j+c] - PetscRealPart(allCoords[o+c]));
 82:       }
 83:       norm = PetscSqrtReal(norm);
 84:       if (norm <= eps) {
 85:         dagPoints[i] = p;
 86:         break;
 87:       }
 88:     }
 89:   }
 90:   VecRestoreArrayRead(allCoordsVec, &allCoords);
 91:   return(0);
 92: }

 94: static PetscErrorCode DMPlexGetLineIntersection_2D_Internal(const PetscReal segmentA[], const PetscReal segmentB[], PetscReal intersection[], PetscBool *hasIntersection)
 95: {
 96:   const PetscReal p0_x  = segmentA[0*2+0];
 97:   const PetscReal p0_y  = segmentA[0*2+1];
 98:   const PetscReal p1_x  = segmentA[1*2+0];
 99:   const PetscReal p1_y  = segmentA[1*2+1];
100:   const PetscReal p2_x  = segmentB[0*2+0];
101:   const PetscReal p2_y  = segmentB[0*2+1];
102:   const PetscReal p3_x  = segmentB[1*2+0];
103:   const PetscReal p3_y  = segmentB[1*2+1];
104:   const PetscReal s1_x  = p1_x - p0_x;
105:   const PetscReal s1_y  = p1_y - p0_y;
106:   const PetscReal s2_x  = p3_x - p2_x;
107:   const PetscReal s2_y  = p3_y - p2_y;
108:   const PetscReal denom = (-s2_x * s1_y + s1_x * s2_y);

111:   *hasIntersection = PETSC_FALSE;
112:   /* Non-parallel lines */
113:   if (denom != 0.0) {
114:     const PetscReal s = (-s1_y * (p0_x - p2_x) + s1_x * (p0_y - p2_y)) / denom;
115:     const PetscReal t = ( s2_x * (p0_y - p2_y) - s2_y * (p0_x - p2_x)) / denom;

117:     if (s >= 0 && s <= 1 && t >= 0 && t <= 1) {
118:       *hasIntersection = PETSC_TRUE;
119:       if (intersection) {
120:         intersection[0] = p0_x + (t * s1_x);
121:         intersection[1] = p0_y + (t * s1_y);
122:       }
123:     }
124:   }
125:   return(0);
126: }

128: static PetscErrorCode DMPlexLocatePoint_Simplex_2D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
129: {
130:   const PetscInt  embedDim = 2;
131:   const PetscReal eps      = PETSC_SQRT_MACHINE_EPSILON;
132:   PetscReal       x        = PetscRealPart(point[0]);
133:   PetscReal       y        = PetscRealPart(point[1]);
134:   PetscReal       v0[2], J[4], invJ[4], detJ;
135:   PetscReal       xi, eta;
136:   PetscErrorCode  ierr;

139:   DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ);
140:   xi  = invJ[0*embedDim+0]*(x - v0[0]) + invJ[0*embedDim+1]*(y - v0[1]);
141:   eta = invJ[1*embedDim+0]*(x - v0[0]) + invJ[1*embedDim+1]*(y - v0[1]);

143:   if ((xi >= -eps) && (eta >= -eps) && (xi + eta <= 2.0+eps)) *cell = c;
144:   else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
145:   return(0);
146: }

148: static PetscErrorCode DMPlexClosestPoint_Simplex_2D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscReal cpoint[])
149: {
150:   const PetscInt  embedDim = 2;
151:   PetscReal       x        = PetscRealPart(point[0]);
152:   PetscReal       y        = PetscRealPart(point[1]);
153:   PetscReal       v0[2], J[4], invJ[4], detJ;
154:   PetscReal       xi, eta, r;
155:   PetscErrorCode  ierr;

158:   DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ);
159:   xi  = invJ[0*embedDim+0]*(x - v0[0]) + invJ[0*embedDim+1]*(y - v0[1]);
160:   eta = invJ[1*embedDim+0]*(x - v0[0]) + invJ[1*embedDim+1]*(y - v0[1]);

162:   xi  = PetscMax(xi,  0.0);
163:   eta = PetscMax(eta, 0.0);
164:   if (xi + eta > 2.0) {
165:     r    = (xi + eta)/2.0;
166:     xi  /= r;
167:     eta /= r;
168:   }
169:   cpoint[0] = J[0*embedDim+0]*xi + J[0*embedDim+1]*eta + v0[0];
170:   cpoint[1] = J[1*embedDim+0]*xi + J[1*embedDim+1]*eta + v0[1];
171:   return(0);
172: }

174: static PetscErrorCode DMPlexLocatePoint_Quad_2D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
175: {
176:   PetscSection       coordSection;
177:   Vec             coordsLocal;
178:   PetscScalar    *coords = NULL;
179:   const PetscInt  faces[8]  = {0, 1, 1, 2, 2, 3, 3, 0};
180:   PetscReal       x         = PetscRealPart(point[0]);
181:   PetscReal       y         = PetscRealPart(point[1]);
182:   PetscInt        crossings = 0, f;
183:   PetscErrorCode  ierr;

186:   DMGetCoordinatesLocal(dm, &coordsLocal);
187:   DMGetCoordinateSection(dm, &coordSection);
188:   DMPlexVecGetClosure(dm, coordSection, coordsLocal, c, NULL, &coords);
189:   for (f = 0; f < 4; ++f) {
190:     PetscReal x_i   = PetscRealPart(coords[faces[2*f+0]*2+0]);
191:     PetscReal y_i   = PetscRealPart(coords[faces[2*f+0]*2+1]);
192:     PetscReal x_j   = PetscRealPart(coords[faces[2*f+1]*2+0]);
193:     PetscReal y_j   = PetscRealPart(coords[faces[2*f+1]*2+1]);
194:     PetscReal slope = (y_j - y_i) / (x_j - x_i);
195:     PetscBool cond1 = (x_i <= x) && (x < x_j) ? PETSC_TRUE : PETSC_FALSE;
196:     PetscBool cond2 = (x_j <= x) && (x < x_i) ? PETSC_TRUE : PETSC_FALSE;
197:     PetscBool above = (y < slope * (x - x_i) + y_i) ? PETSC_TRUE : PETSC_FALSE;
198:     if ((cond1 || cond2)  && above) ++crossings;
199:   }
200:   if (crossings % 2) *cell = c;
201:   else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
202:   DMPlexVecRestoreClosure(dm, coordSection, coordsLocal, c, NULL, &coords);
203:   return(0);
204: }

206: static PetscErrorCode DMPlexLocatePoint_Simplex_3D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
207: {
208:   const PetscInt  embedDim = 3;
209:   const PetscReal eps      = PETSC_SQRT_MACHINE_EPSILON;
210:   PetscReal       v0[3], J[9], invJ[9], detJ;
211:   PetscReal       x = PetscRealPart(point[0]);
212:   PetscReal       y = PetscRealPart(point[1]);
213:   PetscReal       z = PetscRealPart(point[2]);
214:   PetscReal       xi, eta, zeta;
215:   PetscErrorCode  ierr;

218:   DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ);
219:   xi   = invJ[0*embedDim+0]*(x - v0[0]) + invJ[0*embedDim+1]*(y - v0[1]) + invJ[0*embedDim+2]*(z - v0[2]);
220:   eta  = invJ[1*embedDim+0]*(x - v0[0]) + invJ[1*embedDim+1]*(y - v0[1]) + invJ[1*embedDim+2]*(z - v0[2]);
221:   zeta = invJ[2*embedDim+0]*(x - v0[0]) + invJ[2*embedDim+1]*(y - v0[1]) + invJ[2*embedDim+2]*(z - v0[2]);

223:   if ((xi >= -eps) && (eta >= -eps) && (zeta >= -eps) && (xi + eta + zeta <= 2.0+eps)) *cell = c;
224:   else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
225:   return(0);
226: }

228: static PetscErrorCode DMPlexLocatePoint_General_3D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
229: {
230:   PetscSection   coordSection;
231:   Vec            coordsLocal;
232:   PetscScalar   *coords = NULL;
233:   const PetscInt faces[24] = {0, 3, 2, 1,  5, 4, 7, 6,  3, 0, 4, 5,
234:                               1, 2, 6, 7,  3, 5, 6, 2,  0, 1, 7, 4};
235:   PetscBool      found = PETSC_TRUE;
236:   PetscInt       f;

240:   DMGetCoordinatesLocal(dm, &coordsLocal);
241:   DMGetCoordinateSection(dm, &coordSection);
242:   DMPlexVecGetClosure(dm, coordSection, coordsLocal, c, NULL, &coords);
243:   for (f = 0; f < 6; ++f) {
244:     /* Check the point is under plane */
245:     /*   Get face normal */
246:     PetscReal v_i[3];
247:     PetscReal v_j[3];
248:     PetscReal normal[3];
249:     PetscReal pp[3];
250:     PetscReal dot;

252:     v_i[0]    = PetscRealPart(coords[faces[f*4+3]*3+0]-coords[faces[f*4+0]*3+0]);
253:     v_i[1]    = PetscRealPart(coords[faces[f*4+3]*3+1]-coords[faces[f*4+0]*3+1]);
254:     v_i[2]    = PetscRealPart(coords[faces[f*4+3]*3+2]-coords[faces[f*4+0]*3+2]);
255:     v_j[0]    = PetscRealPart(coords[faces[f*4+1]*3+0]-coords[faces[f*4+0]*3+0]);
256:     v_j[1]    = PetscRealPart(coords[faces[f*4+1]*3+1]-coords[faces[f*4+0]*3+1]);
257:     v_j[2]    = PetscRealPart(coords[faces[f*4+1]*3+2]-coords[faces[f*4+0]*3+2]);
258:     normal[0] = v_i[1]*v_j[2] - v_i[2]*v_j[1];
259:     normal[1] = v_i[2]*v_j[0] - v_i[0]*v_j[2];
260:     normal[2] = v_i[0]*v_j[1] - v_i[1]*v_j[0];
261:     pp[0]     = PetscRealPart(coords[faces[f*4+0]*3+0] - point[0]);
262:     pp[1]     = PetscRealPart(coords[faces[f*4+0]*3+1] - point[1]);
263:     pp[2]     = PetscRealPart(coords[faces[f*4+0]*3+2] - point[2]);
264:     dot       = normal[0]*pp[0] + normal[1]*pp[1] + normal[2]*pp[2];

266:     /* Check that projected point is in face (2D location problem) */
267:     if (dot < 0.0) {
268:       found = PETSC_FALSE;
269:       break;
270:     }
271:   }
272:   if (found) *cell = c;
273:   else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
274:   DMPlexVecRestoreClosure(dm, coordSection, coordsLocal, c, NULL, &coords);
275:   return(0);
276: }

278: static PetscErrorCode PetscGridHashInitialize_Internal(PetscGridHash box, PetscInt dim, const PetscScalar point[])
279: {
280:   PetscInt d;

283:   box->dim = dim;
284:   for (d = 0; d < dim; ++d) box->lower[d] = box->upper[d] = PetscRealPart(point[d]);
285:   return(0);
286: }

288: PetscErrorCode PetscGridHashCreate(MPI_Comm comm, PetscInt dim, const PetscScalar point[], PetscGridHash *box)
289: {

293:   PetscMalloc1(1, box);
294:   PetscGridHashInitialize_Internal(*box, dim, point);
295:   return(0);
296: }

298: PetscErrorCode PetscGridHashEnlarge(PetscGridHash box, const PetscScalar point[])
299: {
300:   PetscInt d;

303:   for (d = 0; d < box->dim; ++d) {
304:     box->lower[d] = PetscMin(box->lower[d], PetscRealPart(point[d]));
305:     box->upper[d] = PetscMax(box->upper[d], PetscRealPart(point[d]));
306:   }
307:   return(0);
308: }

310: /*
311:   PetscGridHashSetGrid - Divide the grid into boxes

313:   Not collective

315:   Input Parameters:
316: + box - The grid hash object
317: . n   - The number of boxes in each dimension, or PETSC_DETERMINE
318: - h   - The box size in each dimension, only used if n[d] == PETSC_DETERMINE

320:   Level: developer

322: .seealso: PetscGridHashCreate()
323: */
324: PetscErrorCode PetscGridHashSetGrid(PetscGridHash box, const PetscInt n[], const PetscReal h[])
325: {
326:   PetscInt d;

329:   for (d = 0; d < box->dim; ++d) {
330:     box->extent[d] = box->upper[d] - box->lower[d];
331:     if (n[d] == PETSC_DETERMINE) {
332:       box->h[d] = h[d];
333:       box->n[d] = PetscCeilReal(box->extent[d]/h[d]);
334:     } else {
335:       box->n[d] = n[d];
336:       box->h[d] = box->extent[d]/n[d];
337:     }
338:   }
339:   return(0);
340: }

342: /*
343:   PetscGridHashGetEnclosingBox - Find the grid boxes containing each input point

345:   Not collective

347:   Input Parameters:
348: + box       - The grid hash object
349: . numPoints - The number of input points
350: - points    - The input point coordinates

352:   Output Parameters:
353: + dboxes    - An array of numPoints*dim integers expressing the enclosing box as (i_0, i_1, ..., i_dim)
354: - boxes     - An array of numPoints integers expressing the enclosing box as single number, or NULL

356:   Level: developer

358: .seealso: PetscGridHashCreate()
359: */
360: PetscErrorCode PetscGridHashGetEnclosingBox(PetscGridHash box, PetscInt numPoints, const PetscScalar points[], PetscInt dboxes[], PetscInt boxes[])
361: {
362:   const PetscReal *lower = box->lower;
363:   const PetscReal *upper = box->upper;
364:   const PetscReal *h     = box->h;
365:   const PetscInt  *n     = box->n;
366:   const PetscInt   dim   = box->dim;
367:   PetscInt         d, p;

370:   for (p = 0; p < numPoints; ++p) {
371:     for (d = 0; d < dim; ++d) {
372:       PetscInt dbox = PetscFloorReal((PetscRealPart(points[p*dim+d]) - lower[d])/h[d]);

374:       if (dbox == n[d] && PetscAbsReal(PetscRealPart(points[p*dim+d]) - upper[d]) < 1.0e-9) dbox = n[d]-1;
375:       if (dbox == -1   && PetscAbsReal(PetscRealPart(points[p*dim+d]) - lower[d]) < 1.0e-9) dbox = 0;
376:       if (dbox < 0 || dbox >= n[d]) SETERRQ4(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Input point %d (%g, %g, %g) is outside of our bounding box",
377:                                              p, (double) PetscRealPart(points[p*dim+0]), dim > 1 ? (double) PetscRealPart(points[p*dim+1]) : 0.0, dim > 2 ? (double) PetscRealPart(points[p*dim+2]) : 0.0);
378:       dboxes[p*dim+d] = dbox;
379:     }
380:     if (boxes) for (d = 1, boxes[p] = dboxes[p*dim]; d < dim; ++d) boxes[p] += dboxes[p*dim+d]*n[d-1];
381:   }
382:   return(0);
383: }

385: /*
386:  PetscGridHashGetEnclosingBoxQuery - Find the grid boxes containing each input point

388:  Not collective

390:   Input Parameters:
391: + box       - The grid hash object
392: . numPoints - The number of input points
393: - points    - The input point coordinates

395:   Output Parameters:
396: + dboxes    - An array of numPoints*dim integers expressing the enclosing box as (i_0, i_1, ..., i_dim)
397: . boxes     - An array of numPoints integers expressing the enclosing box as single number, or NULL
398: - found     - Flag indicating if point was located within a box

400:   Level: developer

402: .seealso: PetscGridHashGetEnclosingBox()
403: */
404: PetscErrorCode PetscGridHashGetEnclosingBoxQuery(PetscGridHash box, PetscInt numPoints, const PetscScalar points[], PetscInt dboxes[], PetscInt boxes[],PetscBool *found)
405: {
406:   const PetscReal *lower = box->lower;
407:   const PetscReal *upper = box->upper;
408:   const PetscReal *h     = box->h;
409:   const PetscInt  *n     = box->n;
410:   const PetscInt   dim   = box->dim;
411:   PetscInt         d, p;

414:   *found = PETSC_FALSE;
415:   for (p = 0; p < numPoints; ++p) {
416:     for (d = 0; d < dim; ++d) {
417:       PetscInt dbox = PetscFloorReal((PetscRealPart(points[p*dim+d]) - lower[d])/h[d]);

419:       if (dbox == n[d] && PetscAbsReal(PetscRealPart(points[p*dim+d]) - upper[d]) < 1.0e-9) dbox = n[d]-1;
420:       if (dbox < 0 || dbox >= n[d]) {
421:         return(0);
422:       }
423:       dboxes[p*dim+d] = dbox;
424:     }
425:     if (boxes) for (d = 1, boxes[p] = dboxes[p*dim]; d < dim; ++d) boxes[p] += dboxes[p*dim+d]*n[d-1];
426:   }
427:   *found = PETSC_TRUE;
428:   return(0);
429: }

431: PetscErrorCode PetscGridHashDestroy(PetscGridHash *box)
432: {

436:   if (*box) {
437:     PetscSectionDestroy(&(*box)->cellSection);
438:     ISDestroy(&(*box)->cells);
439:     DMLabelDestroy(&(*box)->cellsSparse);
440:   }
441:   PetscFree(*box);
442:   return(0);
443: }

445: PetscErrorCode DMPlexLocatePoint_Internal(DM dm, PetscInt dim, const PetscScalar point[], PetscInt cellStart, PetscInt *cell)
446: {
447:   DMPolytopeType ct;

451:   DMPlexGetCellType(dm, cellStart, &ct);
452:   switch (ct) {
453:     case DM_POLYTOPE_TRIANGLE:
454:     DMPlexLocatePoint_Simplex_2D_Internal(dm, point, cellStart, cell);break;
455:     case DM_POLYTOPE_QUADRILATERAL:
456:     DMPlexLocatePoint_Quad_2D_Internal(dm, point, cellStart, cell);break;
457:     case DM_POLYTOPE_TETRAHEDRON:
458:     DMPlexLocatePoint_Simplex_3D_Internal(dm, point, cellStart, cell);break;
459:     case DM_POLYTOPE_HEXAHEDRON:
460:     DMPlexLocatePoint_General_3D_Internal(dm, point, cellStart, cell);break;
461:     default: SETERRQ2(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_OUTOFRANGE, "No point location for cell %D with type %s", cellStart, DMPolytopeTypes[ct]);
462:   }
463:   return(0);
464: }

466: /*
467:   DMPlexClosestPoint_Internal - Returns the closest point in the cell to the given point
468: */
469: PetscErrorCode DMPlexClosestPoint_Internal(DM dm, PetscInt dim, const PetscScalar point[], PetscInt cell, PetscReal cpoint[])
470: {
471:   DMPolytopeType ct;

475:   DMPlexGetCellType(dm, cell, &ct);
476:   switch (ct) {
477:     case DM_POLYTOPE_TRIANGLE:
478:     DMPlexClosestPoint_Simplex_2D_Internal(dm, point, cell, cpoint);break;
479: #if 0
480:     case DM_POLYTOPE_QUADRILATERAL:
481:     DMPlexClosestPoint_General_2D_Internal(dm, point, cell, cpoint);break;
482:     case DM_POLYTOPE_TETRAHEDRON:
483:     DMPlexClosestPoint_Simplex_3D_Internal(dm, point, cell, cpoint);break;
484:     case DM_POLYTOPE_HEXAHEDRON:
485:     DMPlexClosestPoint_General_3D_Internal(dm, point, cell, cpoint);break;
486: #endif
487:     default: SETERRQ2(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_OUTOFRANGE, "No closest point location for cell %D with type %s", cell, DMPolytopeTypes[ct]);
488:   }
489:   return(0);
490: }

492: /*
493:   DMPlexComputeGridHash_Internal - Create a grid hash structure covering the Plex

495:   Collective on dm

497:   Input Parameter:
498: . dm - The Plex

500:   Output Parameter:
501: . localBox - The grid hash object

503:   Level: developer

505: .seealso: PetscGridHashCreate(), PetscGridHashGetEnclosingBox()
506: */
507: PetscErrorCode DMPlexComputeGridHash_Internal(DM dm, PetscGridHash *localBox)
508: {
509:   MPI_Comm           comm;
510:   PetscGridHash      lbox;
511:   Vec                coordinates;
512:   PetscSection       coordSection;
513:   Vec                coordsLocal;
514:   const PetscScalar *coords;
515:   PetscInt          *dboxes, *boxes;
516:   PetscInt           n[3] = {10, 10, 10};
517:   PetscInt           dim, N, cStart, cEnd, c, i;
518:   PetscErrorCode     ierr;

521:   PetscObjectGetComm((PetscObject) dm, &comm);
522:   DMGetCoordinatesLocal(dm, &coordinates);
523:   DMGetCoordinateDim(dm, &dim);
524:   if (dim != 2) SETERRQ(comm, PETSC_ERR_SUP, "I have only coded this for 2D");
525:   VecGetLocalSize(coordinates, &N);
526:   VecGetArrayRead(coordinates, &coords);
527:   PetscGridHashCreate(comm, dim, coords, &lbox);
528:   for (i = 0; i < N; i += dim) {PetscGridHashEnlarge(lbox, &coords[i]);}
529:   VecRestoreArrayRead(coordinates, &coords);
530:   PetscOptionsGetInt(NULL,NULL,"-dm_plex_hash_box_nijk",&n[0],NULL);
531:   n[1] = n[0];
532:   n[2] = n[0];
533:   PetscGridHashSetGrid(lbox, n, NULL);
534: #if 0
535:   /* Could define a custom reduction to merge these */
536:   MPIU_Allreduce(lbox->lower, gbox->lower, 3, MPIU_REAL, MPI_MIN, comm);
537:   MPIU_Allreduce(lbox->upper, gbox->upper, 3, MPIU_REAL, MPI_MAX, comm);
538: #endif
539:   /* Is there a reason to snap the local bounding box to a division of the global box? */
540:   /* Should we compute all overlaps of local boxes? We could do this with a rendevouz scheme partitioning the global box */
541:   /* Create label */
542:   DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd);
543:   DMLabelCreate(PETSC_COMM_SELF, "cells", &lbox->cellsSparse);
544:   DMLabelCreateIndex(lbox->cellsSparse, cStart, cEnd);
545:   /* Compute boxes which overlap each cell: https://stackoverflow.com/questions/13790208/triangle-square-intersection-test-in-2d */
546:   DMGetCoordinatesLocal(dm, &coordsLocal);
547:   DMGetCoordinateSection(dm, &coordSection);
548:   PetscCalloc2(16 * dim, &dboxes, 16, &boxes);
549:   for (c = cStart; c < cEnd; ++c) {
550:     const PetscReal *h       = lbox->h;
551:     PetscScalar     *ccoords = NULL;
552:     PetscInt         csize   = 0;
553:     PetscScalar      point[3];
554:     PetscInt         dlim[6], d, e, i, j, k;

556:     /* Find boxes enclosing each vertex */
557:     DMPlexVecGetClosure(dm, coordSection, coordsLocal, c, &csize, &ccoords);
558:     PetscGridHashGetEnclosingBox(lbox, csize/dim, ccoords, dboxes, boxes);
559:     /* Mark cells containing the vertices */
560:     for (e = 0; e < csize/dim; ++e) {DMLabelSetValue(lbox->cellsSparse, c, boxes[e]);}
561:     /* Get grid of boxes containing these */
562:     for (d = 0;   d < dim; ++d) {dlim[d*2+0] = dlim[d*2+1] = dboxes[d];}
563:     for (d = dim; d < 3;   ++d) {dlim[d*2+0] = dlim[d*2+1] = 0;}
564:     for (e = 1; e < dim+1; ++e) {
565:       for (d = 0; d < dim; ++d) {
566:         dlim[d*2+0] = PetscMin(dlim[d*2+0], dboxes[e*dim+d]);
567:         dlim[d*2+1] = PetscMax(dlim[d*2+1], dboxes[e*dim+d]);
568:       }
569:     }
570:     /* Check for intersection of box with cell */
571:     for (k = dlim[2*2+0], point[2] = lbox->lower[2] + k*h[2]; k <= dlim[2*2+1]; ++k, point[2] += h[2]) {
572:       for (j = dlim[1*2+0], point[1] = lbox->lower[1] + j*h[1]; j <= dlim[1*2+1]; ++j, point[1] += h[1]) {
573:         for (i = dlim[0*2+0], point[0] = lbox->lower[0] + i*h[0]; i <= dlim[0*2+1]; ++i, point[0] += h[0]) {
574:           const PetscInt box = (k*lbox->n[1] + j)*lbox->n[0] + i;
575:           PetscScalar    cpoint[3];
576:           PetscInt       cell, edge, ii, jj, kk;

578:           /* Check whether cell contains any vertex of these subboxes TODO vectorize this */
579:           for (kk = 0, cpoint[2] = point[2]; kk < (dim > 2 ? 2 : 1); ++kk, cpoint[2] += h[2]) {
580:             for (jj = 0, cpoint[1] = point[1]; jj < (dim > 1 ? 2 : 1); ++jj, cpoint[1] += h[1]) {
581:               for (ii = 0, cpoint[0] = point[0]; ii < 2; ++ii, cpoint[0] += h[0]) {

583:                 DMPlexLocatePoint_Internal(dm, dim, cpoint, c, &cell);
584:                 if (cell >= 0) { DMLabelSetValue(lbox->cellsSparse, c, box); ii = jj = kk = 2;}
585:               }
586:             }
587:           }
588:           /* Check whether cell edge intersects any edge of these subboxes TODO vectorize this */
589:           for (edge = 0; edge < dim+1; ++edge) {
590:             PetscReal segA[6], segB[6];

592:             if (PetscUnlikely(dim > 3)) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Unexpected dim %d > 3",dim);
593:             for (d = 0; d < dim; ++d) {segA[d] = PetscRealPart(ccoords[edge*dim+d]); segA[dim+d] = PetscRealPart(ccoords[((edge+1)%(dim+1))*dim+d]);}
594:             for (kk = 0; kk < (dim > 2 ? 2 : 1); ++kk) {
595:               if (dim > 2) {segB[2]     = PetscRealPart(point[2]);
596:                             segB[dim+2] = PetscRealPart(point[2]) + kk*h[2];}
597:               for (jj = 0; jj < (dim > 1 ? 2 : 1); ++jj) {
598:                 if (dim > 1) {segB[1]     = PetscRealPart(point[1]);
599:                               segB[dim+1] = PetscRealPart(point[1]) + jj*h[1];}
600:                 for (ii = 0; ii < 2; ++ii) {
601:                   PetscBool intersects;

603:                   segB[0]     = PetscRealPart(point[0]);
604:                   segB[dim+0] = PetscRealPart(point[0]) + ii*h[0];
605:                   DMPlexGetLineIntersection_2D_Internal(segA, segB, NULL, &intersects);
606:                   if (intersects) { DMLabelSetValue(lbox->cellsSparse, c, box); edge = ii = jj = kk = dim+1;}
607:                 }
608:               }
609:             }
610:           }
611:         }
612:       }
613:     }
614:     DMPlexVecRestoreClosure(dm, coordSection, coordsLocal, c, NULL, &ccoords);
615:   }
616:   PetscFree2(dboxes, boxes);
617:   DMLabelConvertToSection(lbox->cellsSparse, &lbox->cellSection, &lbox->cells);
618:   DMLabelDestroy(&lbox->cellsSparse);
619:   *localBox = lbox;
620:   return(0);
621: }

623: PetscErrorCode DMLocatePoints_Plex(DM dm, Vec v, DMPointLocationType ltype, PetscSF cellSF)
624: {
625:   DM_Plex        *mesh = (DM_Plex *) dm->data;
626:   PetscBool       hash = mesh->useHashLocation, reuse = PETSC_FALSE;
627:   PetscInt        bs, numPoints, p, numFound, *found = NULL;
628:   PetscInt        dim, cStart, cEnd, numCells, c, d;
629:   const PetscInt *boxCells;
630:   PetscSFNode    *cells;
631:   PetscScalar    *a;
632:   PetscMPIInt     result;
633:   PetscLogDouble  t0,t1;
634:   PetscReal       gmin[3],gmax[3];
635:   PetscInt        terminating_query_type[] = { 0, 0, 0 };
636:   PetscErrorCode  ierr;

639:   PetscLogEventBegin(DMPLEX_LocatePoints,0,0,0,0);
640:   PetscTime(&t0);
641:   if (ltype == DM_POINTLOCATION_NEAREST && !hash) SETERRQ(PetscObjectComm((PetscObject) dm), PETSC_ERR_SUP, "Nearest point location only supported with grid hashing. Use -dm_plex_hash_location to enable it.");
642:   DMGetCoordinateDim(dm, &dim);
643:   VecGetBlockSize(v, &bs);
644:   MPI_Comm_compare(PetscObjectComm((PetscObject)cellSF),PETSC_COMM_SELF,&result);
645:   if (result != MPI_IDENT && result != MPI_CONGRUENT) SETERRQ(PetscObjectComm((PetscObject)cellSF),PETSC_ERR_SUP, "Trying parallel point location: only local point location supported");
646:   if (bs != dim) SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Block size for point vector %D must be the mesh coordinate dimension %D", bs, dim);
647:   DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd);
648:   VecGetLocalSize(v, &numPoints);
649:   VecGetArray(v, &a);
650:   numPoints /= bs;
651:   {
652:     const PetscSFNode *sf_cells;

654:     PetscSFGetGraph(cellSF,NULL,NULL,NULL,&sf_cells);
655:     if (sf_cells) {
656:       PetscInfo(dm,"[DMLocatePoints_Plex] Re-using existing StarForest node list\n");
657:       cells = (PetscSFNode*)sf_cells;
658:       reuse = PETSC_TRUE;
659:     } else {
660:       PetscInfo(dm,"[DMLocatePoints_Plex] Creating and initializing new StarForest node list\n");
661:       PetscMalloc1(numPoints, &cells);
662:       /* initialize cells if created */
663:       for (p=0; p<numPoints; p++) {
664:         cells[p].rank  = 0;
665:         cells[p].index = DMLOCATEPOINT_POINT_NOT_FOUND;
666:       }
667:     }
668:   }
669:   /* define domain bounding box */
670:   {
671:     Vec coorglobal;

673:     DMGetCoordinates(dm,&coorglobal);
674:     VecStrideMaxAll(coorglobal,NULL,gmax);
675:     VecStrideMinAll(coorglobal,NULL,gmin);
676:   }
677:   if (hash) {
678:     if (!mesh->lbox) {PetscInfo(dm, "Initializing grid hashing");DMPlexComputeGridHash_Internal(dm, &mesh->lbox);}
679:     /* Designate the local box for each point */
680:     /* Send points to correct process */
681:     /* Search cells that lie in each subbox */
682:     /*   Should we bin points before doing search? */
683:     ISGetIndices(mesh->lbox->cells, &boxCells);
684:   }
685:   for (p = 0, numFound = 0; p < numPoints; ++p) {
686:     const PetscScalar *point = &a[p*bs];
687:     PetscInt           dbin[3] = {-1,-1,-1}, bin, cell = -1, cellOffset;
688:     PetscBool          point_outside_domain = PETSC_FALSE;

690:     /* check bounding box of domain */
691:     for (d=0; d<dim; d++) {
692:       if (PetscRealPart(point[d]) < gmin[d]) { point_outside_domain = PETSC_TRUE; break; }
693:       if (PetscRealPart(point[d]) > gmax[d]) { point_outside_domain = PETSC_TRUE; break; }
694:     }
695:     if (point_outside_domain) {
696:       cells[p].rank = 0;
697:       cells[p].index = DMLOCATEPOINT_POINT_NOT_FOUND;
698:       terminating_query_type[0]++;
699:       continue;
700:     }

702:     /* check initial values in cells[].index - abort early if found */
703:     if (cells[p].index != DMLOCATEPOINT_POINT_NOT_FOUND) {
704:       c = cells[p].index;
705:       cells[p].index = DMLOCATEPOINT_POINT_NOT_FOUND;
706:       DMPlexLocatePoint_Internal(dm, dim, point, c, &cell);
707:       if (cell >= 0) {
708:         cells[p].rank = 0;
709:         cells[p].index = cell;
710:         numFound++;
711:       }
712:     }
713:     if (cells[p].index != DMLOCATEPOINT_POINT_NOT_FOUND) {
714:       terminating_query_type[1]++;
715:       continue;
716:     }

718:     if (hash) {
719:       PetscBool found_box;

721:       /* allow for case that point is outside box - abort early */
722:       PetscGridHashGetEnclosingBoxQuery(mesh->lbox, 1, point, dbin, &bin,&found_box);
723:       if (found_box) {
724:         /* TODO Lay an interface over this so we can switch between Section (dense) and Label (sparse) */
725:         PetscSectionGetDof(mesh->lbox->cellSection, bin, &numCells);
726:         PetscSectionGetOffset(mesh->lbox->cellSection, bin, &cellOffset);
727:         for (c = cellOffset; c < cellOffset + numCells; ++c) {
728:           DMPlexLocatePoint_Internal(dm, dim, point, boxCells[c], &cell);
729:           if (cell >= 0) {
730:             cells[p].rank = 0;
731:             cells[p].index = cell;
732:             numFound++;
733:             terminating_query_type[2]++;
734:             break;
735:           }
736:         }
737:       }
738:     } else {
739:       for (c = cStart; c < cEnd; ++c) {
740:         DMPlexLocatePoint_Internal(dm, dim, point, c, &cell);
741:         if (cell >= 0) {
742:           cells[p].rank = 0;
743:           cells[p].index = cell;
744:           numFound++;
745:           terminating_query_type[2]++;
746:           break;
747:         }
748:       }
749:     }
750:   }
751:   if (hash) {ISRestoreIndices(mesh->lbox->cells, &boxCells);}
752:   if (ltype == DM_POINTLOCATION_NEAREST && hash && numFound < numPoints) {
753:     for (p = 0; p < numPoints; p++) {
754:       const PetscScalar *point = &a[p*bs];
755:       PetscReal          cpoint[3], diff[3], dist, distMax = PETSC_MAX_REAL;
756:       PetscInt           dbin[3] = {-1,-1,-1}, bin, cellOffset, d;

758:       if (cells[p].index < 0) {
759:         ++numFound;
760:         PetscGridHashGetEnclosingBox(mesh->lbox, 1, point, dbin, &bin);
761:         PetscSectionGetDof(mesh->lbox->cellSection, bin, &numCells);
762:         PetscSectionGetOffset(mesh->lbox->cellSection, bin, &cellOffset);
763:         for (c = cellOffset; c < cellOffset + numCells; ++c) {
764:           DMPlexClosestPoint_Internal(dm, dim, point, boxCells[c], cpoint);
765:           for (d = 0; d < dim; ++d) diff[d] = cpoint[d] - PetscRealPart(point[d]);
766:           dist = DMPlex_NormD_Internal(dim, diff);
767:           if (dist < distMax) {
768:             for (d = 0; d < dim; ++d) a[p*bs+d] = cpoint[d];
769:             cells[p].rank  = 0;
770:             cells[p].index = boxCells[c];
771:             distMax = dist;
772:             break;
773:           }
774:         }
775:       }
776:     }
777:   }
778:   /* This code is only be relevant when interfaced to parallel point location */
779:   /* Check for highest numbered proc that claims a point (do we care?) */
780:   if (ltype == DM_POINTLOCATION_REMOVE && numFound < numPoints) {
781:     PetscMalloc1(numFound,&found);
782:     for (p = 0, numFound = 0; p < numPoints; p++) {
783:       if (cells[p].rank >= 0 && cells[p].index >= 0) {
784:         if (numFound < p) {
785:           cells[numFound] = cells[p];
786:         }
787:         found[numFound++] = p;
788:       }
789:     }
790:   }
791:   VecRestoreArray(v, &a);
792:   if (!reuse) {
793:     PetscSFSetGraph(cellSF, cEnd - cStart, numFound, found, PETSC_OWN_POINTER, cells, PETSC_OWN_POINTER);
794:   }
795:   PetscTime(&t1);
796:   if (hash) {
797:     PetscInfo3(dm,"[DMLocatePoints_Plex] terminating_query_type : %D [outside domain] : %D [inside initial cell] : %D [hash]\n",terminating_query_type[0],terminating_query_type[1],terminating_query_type[2]);
798:   } else {
799:     PetscInfo3(dm,"[DMLocatePoints_Plex] terminating_query_type : %D [outside domain] : %D [inside initial cell] : %D [brute-force]\n",terminating_query_type[0],terminating_query_type[1],terminating_query_type[2]);
800:   }
801:   PetscInfo3(dm,"[DMLocatePoints_Plex] npoints %D : time(rank0) %1.2e (sec): points/sec %1.4e\n",numPoints,t1-t0,(double)((double)numPoints/(t1-t0)));
802:   PetscLogEventEnd(DMPLEX_LocatePoints,0,0,0,0);
803:   return(0);
804: }

806: /*@C
807:   DMPlexComputeProjection2Dto1D - Rewrite coordinates to be the 1D projection of the 2D coordinates

809:   Not collective

811:   Input Parameter:
812: . coords - The coordinates of a segment

814:   Output Parameters:
815: + coords - The new y-coordinate, and 0 for x
816: - R - The rotation which accomplishes the projection

818:   Level: developer

820: .seealso: DMPlexComputeProjection3Dto1D(), DMPlexComputeProjection3Dto2D()
821: @*/
822: PetscErrorCode DMPlexComputeProjection2Dto1D(PetscScalar coords[], PetscReal R[])
823: {
824:   const PetscReal x = PetscRealPart(coords[2] - coords[0]);
825:   const PetscReal y = PetscRealPart(coords[3] - coords[1]);
826:   const PetscReal r = PetscSqrtReal(x*x + y*y), c = x/r, s = y/r;

829:   R[0] = c; R[1] = -s;
830:   R[2] = s; R[3] =  c;
831:   coords[0] = 0.0;
832:   coords[1] = r;
833:   return(0);
834: }

836: /*@C
837:   DMPlexComputeProjection3Dto1D - Rewrite coordinates to be the 1D projection of the 3D coordinates

839:   Not collective

841:   Input Parameter:
842: . coords - The coordinates of a segment

844:   Output Parameters:
845: + coords - The new y-coordinate, and 0 for x and z
846: - R - The rotation which accomplishes the projection

848:   Note: This uses the basis completion described by Frisvad in http://www.imm.dtu.dk/~jerf/papers/abstracts/onb.html, DOI:10.1080/2165347X.2012.689606

850:   Level: developer

852: .seealso: DMPlexComputeProjection2Dto1D(), DMPlexComputeProjection3Dto2D()
853: @*/
854: PetscErrorCode DMPlexComputeProjection3Dto1D(PetscScalar coords[], PetscReal R[])
855: {
856:   PetscReal      x    = PetscRealPart(coords[3] - coords[0]);
857:   PetscReal      y    = PetscRealPart(coords[4] - coords[1]);
858:   PetscReal      z    = PetscRealPart(coords[5] - coords[2]);
859:   PetscReal      r    = PetscSqrtReal(x*x + y*y + z*z);
860:   PetscReal      rinv = 1. / r;

863:   x *= rinv; y *= rinv; z *= rinv;
864:   if (x > 0.) {
865:     PetscReal inv1pX   = 1./ (1. + x);

867:     R[0] = x; R[1] = -y;              R[2] = -z;
868:     R[3] = y; R[4] = 1. - y*y*inv1pX; R[5] =     -y*z*inv1pX;
869:     R[6] = z; R[7] =     -y*z*inv1pX; R[8] = 1. - z*z*inv1pX;
870:   }
871:   else {
872:     PetscReal inv1mX   = 1./ (1. - x);

874:     R[0] = x; R[1] = z;               R[2] = y;
875:     R[3] = y; R[4] =     -y*z*inv1mX; R[5] = 1. - y*y*inv1mX;
876:     R[6] = z; R[7] = 1. - z*z*inv1mX; R[8] =     -y*z*inv1mX;
877:   }
878:   coords[0] = 0.0;
879:   coords[1] = r;
880:   return(0);
881: }

883: /*@
884:   DMPlexComputeProjection3Dto2D - Rewrite coordinates of 3 or more coplanar 3D points to a common 2D basis for the
885:     plane.  The normal is defined by positive orientation of the first 3 points.

887:   Not collective

889:   Input Parameter:
890: + coordSize - Length of coordinate array (3x number of points); must be at least 9 (3 points)
891: - coords - The interlaced coordinates of each coplanar 3D point

893:   Output Parameters:
894: + coords - The first 2*coordSize/3 entries contain interlaced 2D points, with the rest undefined
895: - R - 3x3 row-major rotation matrix whose columns are the tangent basis [t1, t2, n].  Multiplying by R^T transforms from original frame to tangent frame.

897:   Level: developer

899: .seealso: DMPlexComputeProjection2Dto1D(), DMPlexComputeProjection3Dto1D()
900: @*/
901: PetscErrorCode DMPlexComputeProjection3Dto2D(PetscInt coordSize, PetscScalar coords[], PetscReal R[])
902: {
903:   PetscReal x1[3], x2[3], n[3], c[3], norm;
904:   const PetscInt dim = 3;
905:   PetscInt       d, p;

908:   /* 0) Calculate normal vector */
909:   for (d = 0; d < dim; ++d) {
910:     x1[d] = PetscRealPart(coords[1*dim+d] - coords[0*dim+d]);
911:     x2[d] = PetscRealPart(coords[2*dim+d] - coords[0*dim+d]);
912:   }
913:   // n = x1 \otimes x2
914:   n[0] = x1[1]*x2[2] - x1[2]*x2[1];
915:   n[1] = x1[2]*x2[0] - x1[0]*x2[2];
916:   n[2] = x1[0]*x2[1] - x1[1]*x2[0];
917:   norm = PetscSqrtReal(n[0]*n[0] + n[1]*n[1] + n[2]*n[2]);
918:   for (d = 0; d < dim; d++) n[d] /= norm;
919:   norm = PetscSqrtReal(x1[0] * x1[0] + x1[1] * x1[1] + x1[2] * x1[2]);
920:   for (d = 0; d < dim; d++) x1[d] /= norm;
921:   // x2 = n \otimes x1
922:   x2[0] = n[1] * x1[2] - n[2] * x1[1];
923:   x2[1] = n[2] * x1[0] - n[0] * x1[2];
924:   x2[2] = n[0] * x1[1] - n[1] * x1[0];
925:   for (d=0; d<dim; d++) {
926:     R[d * dim + 0] = x1[d];
927:     R[d * dim + 1] = x2[d];
928:     R[d * dim + 2] = n[d];
929:     c[d] = PetscRealPart(coords[0*dim + d]);
930:   }
931:   for (p=0; p<coordSize/dim; p++) {
932:     PetscReal y[3];
933:     for (d=0; d<dim; d++) y[d] = PetscRealPart(coords[p*dim + d]) - c[d];
934:     for (d=0; d<2; d++) coords[p*2+d] = R[0*dim + d] * y[0] + R[1*dim + d] * y[1] + R[2*dim + d] * y[2];
935:   }
936:   return(0);
937: }

939: PETSC_UNUSED
940: PETSC_STATIC_INLINE void Volume_Triangle_Internal(PetscReal *vol, PetscReal coords[])
941: {
942:   /* Signed volume is 1/2 the determinant

944:    |  1  1  1 |
945:    | x0 x1 x2 |
946:    | y0 y1 y2 |

948:      but if x0,y0 is the origin, we have

950:    | x1 x2 |
951:    | y1 y2 |
952:   */
953:   const PetscReal x1 = coords[2] - coords[0], y1 = coords[3] - coords[1];
954:   const PetscReal x2 = coords[4] - coords[0], y2 = coords[5] - coords[1];
955:   PetscReal       M[4], detM;
956:   M[0] = x1; M[1] = x2;
957:   M[2] = y1; M[3] = y2;
958:   DMPlex_Det2D_Internal(&detM, M);
959:   *vol = 0.5*detM;
960:   (void)PetscLogFlops(5.0);
961: }

963: PETSC_STATIC_INLINE void Volume_Triangle_Origin_Internal(PetscReal *vol, PetscReal coords[])
964: {
965:   DMPlex_Det2D_Internal(vol, coords);
966:   *vol *= 0.5;
967: }

969: PETSC_UNUSED
970: PETSC_STATIC_INLINE void Volume_Tetrahedron_Internal(PetscReal *vol, PetscReal coords[])
971: {
972:   /* Signed volume is 1/6th of the determinant

974:    |  1  1  1  1 |
975:    | x0 x1 x2 x3 |
976:    | y0 y1 y2 y3 |
977:    | z0 z1 z2 z3 |

979:      but if x0,y0,z0 is the origin, we have

981:    | x1 x2 x3 |
982:    | y1 y2 y3 |
983:    | z1 z2 z3 |
984:   */
985:   const PetscReal x1 = coords[3] - coords[0], y1 = coords[4]  - coords[1], z1 = coords[5]  - coords[2];
986:   const PetscReal x2 = coords[6] - coords[0], y2 = coords[7]  - coords[1], z2 = coords[8]  - coords[2];
987:   const PetscReal x3 = coords[9] - coords[0], y3 = coords[10] - coords[1], z3 = coords[11] - coords[2];
988:   const PetscReal onesixth = ((PetscReal)1./(PetscReal)6.);
989:   PetscReal       M[9], detM;
990:   M[0] = x1; M[1] = x2; M[2] = x3;
991:   M[3] = y1; M[4] = y2; M[5] = y3;
992:   M[6] = z1; M[7] = z2; M[8] = z3;
993:   DMPlex_Det3D_Internal(&detM, M);
994:   *vol = -onesixth*detM;
995:   (void)PetscLogFlops(10.0);
996: }

998: PETSC_STATIC_INLINE void Volume_Tetrahedron_Origin_Internal(PetscReal *vol, PetscReal coords[])
999: {
1000:   const PetscReal onesixth = ((PetscReal)1./(PetscReal)6.);
1001:   DMPlex_Det3D_Internal(vol, coords);
1002:   *vol *= -onesixth;
1003: }

1005: static PetscErrorCode DMPlexComputePointGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1006: {
1007:   PetscSection   coordSection;
1008:   Vec            coordinates;
1009:   const PetscScalar *coords;
1010:   PetscInt       dim, d, off;

1014:   DMGetCoordinatesLocal(dm, &coordinates);
1015:   DMGetCoordinateSection(dm, &coordSection);
1016:   PetscSectionGetDof(coordSection,e,&dim);
1017:   if (!dim) return(0);
1018:   PetscSectionGetOffset(coordSection,e,&off);
1019:   VecGetArrayRead(coordinates,&coords);
1020:   if (v0) {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[off + d]);}
1021:   VecRestoreArrayRead(coordinates,&coords);
1022:   *detJ = 1.;
1023:   if (J) {
1024:     for (d = 0; d < dim * dim; d++) J[d] = 0.;
1025:     for (d = 0; d < dim; d++) J[d * dim + d] = 1.;
1026:     if (invJ) {
1027:       for (d = 0; d < dim * dim; d++) invJ[d] = 0.;
1028:       for (d = 0; d < dim; d++) invJ[d * dim + d] = 1.;
1029:     }
1030:   }
1031:   return(0);
1032: }

1034: static PetscErrorCode DMPlexComputeLineGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1035: {
1036:   PetscSection   coordSection;
1037:   Vec            coordinates;
1038:   PetscScalar   *coords = NULL;
1039:   PetscInt       numCoords, d, pStart, pEnd, numSelfCoords = 0;

1043:   DMGetCoordinatesLocal(dm, &coordinates);
1044:   DMGetCoordinateSection(dm, &coordSection);
1045:   PetscSectionGetChart(coordSection,&pStart,&pEnd);
1046:   if (e >= pStart && e < pEnd) {PetscSectionGetDof(coordSection,e,&numSelfCoords);}
1047:   DMPlexVecGetClosure(dm, coordSection, coordinates, e, &numCoords, &coords);
1048:   numCoords = numSelfCoords ? numSelfCoords : numCoords;
1049:   if (invJ && !J) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
1050:   *detJ = 0.0;
1051:   if (numCoords == 6) {
1052:     const PetscInt dim = 3;
1053:     PetscReal      R[9], J0;

1055:     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
1056:     DMPlexComputeProjection3Dto1D(coords, R);
1057:     if (J)    {
1058:       J0   = 0.5*PetscRealPart(coords[1]);
1059:       J[0] = R[0]*J0; J[1] = R[1]; J[2] = R[2];
1060:       J[3] = R[3]*J0; J[4] = R[4]; J[5] = R[5];
1061:       J[6] = R[6]*J0; J[7] = R[7]; J[8] = R[8];
1062:       DMPlex_Det3D_Internal(detJ, J);
1063:       if (invJ) {DMPlex_Invert2D_Internal(invJ, J, *detJ);}
1064:     }
1065:   } else if (numCoords == 4) {
1066:     const PetscInt dim = 2;
1067:     PetscReal      R[4], J0;

1069:     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
1070:     DMPlexComputeProjection2Dto1D(coords, R);
1071:     if (J)    {
1072:       J0   = 0.5*PetscRealPart(coords[1]);
1073:       J[0] = R[0]*J0; J[1] = R[1];
1074:       J[2] = R[2]*J0; J[3] = R[3];
1075:       DMPlex_Det2D_Internal(detJ, J);
1076:       if (invJ) {DMPlex_Invert2D_Internal(invJ, J, *detJ);}
1077:     }
1078:   } else if (numCoords == 2) {
1079:     const PetscInt dim = 1;

1081:     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
1082:     if (J)    {
1083:       J[0]  = 0.5*(PetscRealPart(coords[1]) - PetscRealPart(coords[0]));
1084:       *detJ = J[0];
1085:       PetscLogFlops(2.0);
1086:       if (invJ) {invJ[0] = 1.0/J[0]; PetscLogFlops(1.0);}
1087:     }
1088:   } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this segment is %D != 2", numCoords);
1089:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, &numCoords, &coords);
1090:   return(0);
1091: }

1093: static PetscErrorCode DMPlexComputeTriangleGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1094: {
1095:   PetscSection   coordSection;
1096:   Vec            coordinates;
1097:   PetscScalar   *coords = NULL;
1098:   PetscInt       numCoords, numSelfCoords = 0, d, f, g, pStart, pEnd;

1102:   DMGetCoordinatesLocal(dm, &coordinates);
1103:   DMGetCoordinateSection(dm, &coordSection);
1104:   PetscSectionGetChart(coordSection,&pStart,&pEnd);
1105:   if (e >= pStart && e < pEnd) {PetscSectionGetDof(coordSection,e,&numSelfCoords);}
1106:   DMPlexVecGetClosure(dm, coordSection, coordinates, e, &numCoords, &coords);
1107:   numCoords = numSelfCoords ? numSelfCoords : numCoords;
1108:   *detJ = 0.0;
1109:   if (numCoords == 9) {
1110:     const PetscInt dim = 3;
1111:     PetscReal      R[9], J0[9] = {1.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,1.0};

1113:     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
1114:     DMPlexComputeProjection3Dto2D(numCoords, coords, R);
1115:     if (J)    {
1116:       const PetscInt pdim = 2;

1118:       for (d = 0; d < pdim; d++) {
1119:         for (f = 0; f < pdim; f++) {
1120:           J0[d*dim+f] = 0.5*(PetscRealPart(coords[(f+1)*pdim+d]) - PetscRealPart(coords[0*pdim+d]));
1121:         }
1122:       }
1123:       PetscLogFlops(8.0);
1124:       DMPlex_Det3D_Internal(detJ, J0);
1125:       for (d = 0; d < dim; d++) {
1126:         for (f = 0; f < dim; f++) {
1127:           J[d*dim+f] = 0.0;
1128:           for (g = 0; g < dim; g++) {
1129:             J[d*dim+f] += R[d*dim+g]*J0[g*dim+f];
1130:           }
1131:         }
1132:       }
1133:       PetscLogFlops(18.0);
1134:     }
1135:     if (invJ) {DMPlex_Invert3D_Internal(invJ, J, *detJ);}
1136:   } else if (numCoords == 6) {
1137:     const PetscInt dim = 2;

1139:     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
1140:     if (J)    {
1141:       for (d = 0; d < dim; d++) {
1142:         for (f = 0; f < dim; f++) {
1143:           J[d*dim+f] = 0.5*(PetscRealPart(coords[(f+1)*dim+d]) - PetscRealPart(coords[0*dim+d]));
1144:         }
1145:       }
1146:       PetscLogFlops(8.0);
1147:       DMPlex_Det2D_Internal(detJ, J);
1148:     }
1149:     if (invJ) {DMPlex_Invert2D_Internal(invJ, J, *detJ);}
1150:   } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this triangle is %D != 6 or 9", numCoords);
1151:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, &numCoords, &coords);
1152:   return(0);
1153: }

1155: static PetscErrorCode DMPlexComputeRectangleGeometry_Internal(DM dm, PetscInt e, PetscBool isTensor, PetscInt Nq, const PetscReal points[], PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1156: {
1157:   PetscSection   coordSection;
1158:   Vec            coordinates;
1159:   PetscScalar   *coords = NULL;
1160:   PetscInt       numCoords, numSelfCoords = 0, d, f, g, pStart, pEnd;

1164:   DMGetCoordinatesLocal(dm, &coordinates);
1165:   DMGetCoordinateSection(dm, &coordSection);
1166:   PetscSectionGetChart(coordSection,&pStart,&pEnd);
1167:   if (e >= pStart && e < pEnd) {PetscSectionGetDof(coordSection,e,&numSelfCoords);}
1168:   DMPlexVecGetClosure(dm, coordSection, coordinates, e, &numCoords, &coords);
1169:   numCoords = numSelfCoords ? numSelfCoords : numCoords;
1170:   if (!Nq) {
1171:     PetscInt vorder[4] = {0, 1, 2, 3};

1173:     if (isTensor) {vorder[2] = 3; vorder[3] = 2;}
1174:     *detJ = 0.0;
1175:     if (numCoords == 12) {
1176:       const PetscInt dim = 3;
1177:       PetscReal      R[9], J0[9] = {1.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,1.0};

1179:       if (v)   {for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);}
1180:       DMPlexComputeProjection3Dto2D(numCoords, coords, R);
1181:       if (J)    {
1182:         const PetscInt pdim = 2;

1184:         for (d = 0; d < pdim; d++) {
1185:           J0[d*dim+0] = 0.5*(PetscRealPart(coords[vorder[1]*pdim+d]) - PetscRealPart(coords[vorder[0]*pdim+d]));
1186:           J0[d*dim+1] = 0.5*(PetscRealPart(coords[vorder[2]*pdim+d]) - PetscRealPart(coords[vorder[1]*pdim+d]));
1187:         }
1188:         PetscLogFlops(8.0);
1189:         DMPlex_Det3D_Internal(detJ, J0);
1190:         for (d = 0; d < dim; d++) {
1191:           for (f = 0; f < dim; f++) {
1192:             J[d*dim+f] = 0.0;
1193:             for (g = 0; g < dim; g++) {
1194:               J[d*dim+f] += R[d*dim+g]*J0[g*dim+f];
1195:             }
1196:           }
1197:         }
1198:         PetscLogFlops(18.0);
1199:       }
1200:       if (invJ) {DMPlex_Invert3D_Internal(invJ, J, *detJ);}
1201:     } else if (numCoords == 8) {
1202:       const PetscInt dim = 2;

1204:       if (v)   {for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);}
1205:       if (J)    {
1206:         for (d = 0; d < dim; d++) {
1207:           J[d*dim+0] = 0.5*(PetscRealPart(coords[vorder[1]*dim+d]) - PetscRealPart(coords[vorder[0]*dim+d]));
1208:           J[d*dim+1] = 0.5*(PetscRealPart(coords[vorder[3]*dim+d]) - PetscRealPart(coords[vorder[0]*dim+d]));
1209:         }
1210:         PetscLogFlops(8.0);
1211:         DMPlex_Det2D_Internal(detJ, J);
1212:       }
1213:       if (invJ) {DMPlex_Invert2D_Internal(invJ, J, *detJ);}
1214:     } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this quadrilateral is %D != 8 or 12", numCoords);
1215:   } else {
1216:     const PetscInt Nv = 4;
1217:     const PetscInt dimR = 2;
1218:     PetscInt  zToPlex[4] = {0, 1, 3, 2};
1219:     PetscReal zOrder[12];
1220:     PetscReal zCoeff[12];
1221:     PetscInt  i, j, k, l, dim;

1223:     if (isTensor) {zToPlex[2] = 2; zToPlex[3] = 3;}
1224:     if (numCoords == 12) {
1225:       dim = 3;
1226:     } else if (numCoords == 8) {
1227:       dim = 2;
1228:     } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this quadrilateral is %D != 8 or 12", numCoords);
1229:     for (i = 0; i < Nv; i++) {
1230:       PetscInt zi = zToPlex[i];

1232:       for (j = 0; j < dim; j++) {
1233:         zOrder[dim * i + j] = PetscRealPart(coords[dim * zi + j]);
1234:       }
1235:     }
1236:     for (j = 0; j < dim; j++) {
1237:       zCoeff[dim * 0 + j] = 0.25 * (  zOrder[dim * 0 + j] + zOrder[dim * 1 + j] + zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
1238:       zCoeff[dim * 1 + j] = 0.25 * (- zOrder[dim * 0 + j] + zOrder[dim * 1 + j] - zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
1239:       zCoeff[dim * 2 + j] = 0.25 * (- zOrder[dim * 0 + j] - zOrder[dim * 1 + j] + zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
1240:       zCoeff[dim * 3 + j] = 0.25 * (  zOrder[dim * 0 + j] - zOrder[dim * 1 + j] - zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
1241:     }
1242:     for (i = 0; i < Nq; i++) {
1243:       PetscReal xi = points[dimR * i], eta = points[dimR * i + 1];

1245:       if (v) {
1246:         PetscReal extPoint[4];

1248:         extPoint[0] = 1.;
1249:         extPoint[1] = xi;
1250:         extPoint[2] = eta;
1251:         extPoint[3] = xi * eta;
1252:         for (j = 0; j < dim; j++) {
1253:           PetscReal val = 0.;

1255:           for (k = 0; k < Nv; k++) {
1256:             val += extPoint[k] * zCoeff[dim * k + j];
1257:           }
1258:           v[i * dim + j] = val;
1259:         }
1260:       }
1261:       if (J) {
1262:         PetscReal extJ[8];

1264:         extJ[0] = 0.;
1265:         extJ[1] = 0.;
1266:         extJ[2] = 1.;
1267:         extJ[3] = 0.;
1268:         extJ[4] = 0.;
1269:         extJ[5] = 1.;
1270:         extJ[6] = eta;
1271:         extJ[7] = xi;
1272:         for (j = 0; j < dim; j++) {
1273:           for (k = 0; k < dimR; k++) {
1274:             PetscReal val = 0.;

1276:             for (l = 0; l < Nv; l++) {
1277:               val += zCoeff[dim * l + j] * extJ[dimR * l + k];
1278:             }
1279:             J[i * dim * dim + dim * j + k] = val;
1280:           }
1281:         }
1282:         if (dim == 3) { /* put the cross product in the third component of the Jacobian */
1283:           PetscReal x, y, z;
1284:           PetscReal *iJ = &J[i * dim * dim];
1285:           PetscReal norm;

1287:           x = iJ[1 * dim + 0] * iJ[2 * dim + 1] - iJ[1 * dim + 1] * iJ[2 * dim + 0];
1288:           y = iJ[0 * dim + 1] * iJ[2 * dim + 0] - iJ[0 * dim + 0] * iJ[2 * dim + 1];
1289:           z = iJ[0 * dim + 0] * iJ[1 * dim + 1] - iJ[0 * dim + 1] * iJ[1 * dim + 0];
1290:           norm = PetscSqrtReal(x * x + y * y + z * z);
1291:           iJ[2] = x / norm;
1292:           iJ[5] = y / norm;
1293:           iJ[8] = z / norm;
1294:           DMPlex_Det3D_Internal(&detJ[i], &J[i * dim * dim]);
1295:           if (invJ) {DMPlex_Invert3D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);}
1296:         } else {
1297:           DMPlex_Det2D_Internal(&detJ[i], &J[i * dim * dim]);
1298:           if (invJ) {DMPlex_Invert2D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);}
1299:         }
1300:       }
1301:     }
1302:   }
1303:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, &numCoords, &coords);
1304:   return(0);
1305: }

1307: static PetscErrorCode DMPlexComputeTetrahedronGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1308: {
1309:   PetscSection   coordSection;
1310:   Vec            coordinates;
1311:   PetscScalar   *coords = NULL;
1312:   const PetscInt dim = 3;
1313:   PetscInt       d;

1317:   DMGetCoordinatesLocal(dm, &coordinates);
1318:   DMGetCoordinateSection(dm, &coordSection);
1319:   DMPlexVecGetClosure(dm, coordSection, coordinates, e, NULL, &coords);
1320:   *detJ = 0.0;
1321:   if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
1322:   if (J)    {
1323:     for (d = 0; d < dim; d++) {
1324:       /* I orient with outward face normals */
1325:       J[d*dim+0] = 0.5*(PetscRealPart(coords[2*dim+d]) - PetscRealPart(coords[0*dim+d]));
1326:       J[d*dim+1] = 0.5*(PetscRealPart(coords[1*dim+d]) - PetscRealPart(coords[0*dim+d]));
1327:       J[d*dim+2] = 0.5*(PetscRealPart(coords[3*dim+d]) - PetscRealPart(coords[0*dim+d]));
1328:     }
1329:     PetscLogFlops(18.0);
1330:     DMPlex_Det3D_Internal(detJ, J);
1331:   }
1332:   if (invJ) {DMPlex_Invert3D_Internal(invJ, J, *detJ);}
1333:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, NULL, &coords);
1334:   return(0);
1335: }

1337: static PetscErrorCode DMPlexComputeHexahedronGeometry_Internal(DM dm, PetscInt e, PetscInt Nq, const PetscReal points[], PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1338: {
1339:   PetscSection   coordSection;
1340:   Vec            coordinates;
1341:   PetscScalar   *coords = NULL;
1342:   const PetscInt dim = 3;
1343:   PetscInt       d;

1347:   DMGetCoordinatesLocal(dm, &coordinates);
1348:   DMGetCoordinateSection(dm, &coordSection);
1349:   DMPlexVecGetClosure(dm, coordSection, coordinates, e, NULL, &coords);
1350:   if (!Nq) {
1351:     *detJ = 0.0;
1352:     if (v)   {for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);}
1353:     if (J)    {
1354:       for (d = 0; d < dim; d++) {
1355:         J[d*dim+0] = 0.5*(PetscRealPart(coords[3*dim+d]) - PetscRealPart(coords[0*dim+d]));
1356:         J[d*dim+1] = 0.5*(PetscRealPart(coords[1*dim+d]) - PetscRealPart(coords[0*dim+d]));
1357:         J[d*dim+2] = 0.5*(PetscRealPart(coords[4*dim+d]) - PetscRealPart(coords[0*dim+d]));
1358:       }
1359:       PetscLogFlops(18.0);
1360:       DMPlex_Det3D_Internal(detJ, J);
1361:     }
1362:     if (invJ) {DMPlex_Invert3D_Internal(invJ, J, *detJ);}
1363:   } else {
1364:     const PetscInt Nv = 8;
1365:     const PetscInt zToPlex[8] = {0, 3, 1, 2, 4, 5, 7, 6};
1366:     const PetscInt dim = 3;
1367:     const PetscInt dimR = 3;
1368:     PetscReal zOrder[24];
1369:     PetscReal zCoeff[24];
1370:     PetscInt  i, j, k, l;

1372:     for (i = 0; i < Nv; i++) {
1373:       PetscInt zi = zToPlex[i];

1375:       for (j = 0; j < dim; j++) {
1376:         zOrder[dim * i + j] = PetscRealPart(coords[dim * zi + j]);
1377:       }
1378:     }
1379:     for (j = 0; j < dim; j++) {
1380:       zCoeff[dim * 0 + j] = 0.125 * (  zOrder[dim * 0 + j] + zOrder[dim * 1 + j] + zOrder[dim * 2 + j] + zOrder[dim * 3 + j] + zOrder[dim * 4 + j] + zOrder[dim * 5 + j] + zOrder[dim * 6 + j] + zOrder[dim * 7 + j]);
1381:       zCoeff[dim * 1 + j] = 0.125 * (- zOrder[dim * 0 + j] + zOrder[dim * 1 + j] - zOrder[dim * 2 + j] + zOrder[dim * 3 + j] - zOrder[dim * 4 + j] + zOrder[dim * 5 + j] - zOrder[dim * 6 + j] + zOrder[dim * 7 + j]);
1382:       zCoeff[dim * 2 + j] = 0.125 * (- zOrder[dim * 0 + j] - zOrder[dim * 1 + j] + zOrder[dim * 2 + j] + zOrder[dim * 3 + j] - zOrder[dim * 4 + j] - zOrder[dim * 5 + j] + zOrder[dim * 6 + j] + zOrder[dim * 7 + j]);
1383:       zCoeff[dim * 3 + j] = 0.125 * (  zOrder[dim * 0 + j] - zOrder[dim * 1 + j] - zOrder[dim * 2 + j] + zOrder[dim * 3 + j] + zOrder[dim * 4 + j] - zOrder[dim * 5 + j] - zOrder[dim * 6 + j] + zOrder[dim * 7 + j]);
1384:       zCoeff[dim * 4 + j] = 0.125 * (- zOrder[dim * 0 + j] - zOrder[dim * 1 + j] - zOrder[dim * 2 + j] - zOrder[dim * 3 + j] + zOrder[dim * 4 + j] + zOrder[dim * 5 + j] + zOrder[dim * 6 + j] + zOrder[dim * 7 + j]);
1385:       zCoeff[dim * 5 + j] = 0.125 * (+ zOrder[dim * 0 + j] - zOrder[dim * 1 + j] + zOrder[dim * 2 + j] - zOrder[dim * 3 + j] - zOrder[dim * 4 + j] + zOrder[dim * 5 + j] - zOrder[dim * 6 + j] + zOrder[dim * 7 + j]);
1386:       zCoeff[dim * 6 + j] = 0.125 * (+ zOrder[dim * 0 + j] + zOrder[dim * 1 + j] - zOrder[dim * 2 + j] - zOrder[dim * 3 + j] - zOrder[dim * 4 + j] - zOrder[dim * 5 + j] + zOrder[dim * 6 + j] + zOrder[dim * 7 + j]);
1387:       zCoeff[dim * 7 + j] = 0.125 * (- zOrder[dim * 0 + j] + zOrder[dim * 1 + j] + zOrder[dim * 2 + j] - zOrder[dim * 3 + j] + zOrder[dim * 4 + j] - zOrder[dim * 5 + j] - zOrder[dim * 6 + j] + zOrder[dim * 7 + j]);
1388:     }
1389:     for (i = 0; i < Nq; i++) {
1390:       PetscReal xi = points[dimR * i], eta = points[dimR * i + 1], theta = points[dimR * i + 2];

1392:       if (v) {
1393:         PetscReal extPoint[8];

1395:         extPoint[0] = 1.;
1396:         extPoint[1] = xi;
1397:         extPoint[2] = eta;
1398:         extPoint[3] = xi * eta;
1399:         extPoint[4] = theta;
1400:         extPoint[5] = theta * xi;
1401:         extPoint[6] = theta * eta;
1402:         extPoint[7] = theta * eta * xi;
1403:         for (j = 0; j < dim; j++) {
1404:           PetscReal val = 0.;

1406:           for (k = 0; k < Nv; k++) {
1407:             val += extPoint[k] * zCoeff[dim * k + j];
1408:           }
1409:           v[i * dim + j] = val;
1410:         }
1411:       }
1412:       if (J) {
1413:         PetscReal extJ[24];

1415:         extJ[0]  = 0.         ; extJ[1]  = 0.        ; extJ[2]  = 0.      ;
1416:         extJ[3]  = 1.         ; extJ[4]  = 0.        ; extJ[5]  = 0.      ;
1417:         extJ[6]  = 0.         ; extJ[7]  = 1.        ; extJ[8]  = 0.      ;
1418:         extJ[9]  = eta        ; extJ[10] = xi        ; extJ[11] = 0.      ;
1419:         extJ[12] = 0.         ; extJ[13] = 0.        ; extJ[14] = 1.      ;
1420:         extJ[15] = theta      ; extJ[16] = 0.        ; extJ[17] = xi      ;
1421:         extJ[18] = 0.         ; extJ[19] = theta     ; extJ[20] = eta     ;
1422:         extJ[21] = theta * eta; extJ[22] = theta * xi; extJ[23] = eta * xi;

1424:         for (j = 0; j < dim; j++) {
1425:           for (k = 0; k < dimR; k++) {
1426:             PetscReal val = 0.;

1428:             for (l = 0; l < Nv; l++) {
1429:               val += zCoeff[dim * l + j] * extJ[dimR * l + k];
1430:             }
1431:             J[i * dim * dim + dim * j + k] = val;
1432:           }
1433:         }
1434:         DMPlex_Det3D_Internal(&detJ[i], &J[i * dim * dim]);
1435:         if (invJ) {DMPlex_Invert3D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);}
1436:       }
1437:     }
1438:   }
1439:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, NULL, &coords);
1440:   return(0);
1441: }

1443: static PetscErrorCode DMPlexComputeCellGeometryFEM_Implicit(DM dm, PetscInt cell, PetscQuadrature quad, PetscReal *v, PetscReal *J, PetscReal *invJ, PetscReal *detJ)
1444: {
1445:   DMPolytopeType  ct;
1446:   PetscInt        depth, dim, coordDim, coneSize, i;
1447:   PetscInt        Nq = 0;
1448:   const PetscReal *points = NULL;
1449:   DMLabel         depthLabel;
1450:   PetscReal       xi0[3] = {-1.,-1.,-1.}, v0[3], J0[9], detJ0;
1451:   PetscBool       isAffine = PETSC_TRUE;
1452:   PetscErrorCode  ierr;

1455:   DMPlexGetDepth(dm, &depth);
1456:   DMPlexGetConeSize(dm, cell, &coneSize);
1457:   DMPlexGetDepthLabel(dm, &depthLabel);
1458:   DMLabelGetValue(depthLabel, cell, &dim);
1459:   if (depth == 1 && dim == 1) {
1460:     DMGetDimension(dm, &dim);
1461:   }
1462:   DMGetCoordinateDim(dm, &coordDim);
1463:   if (coordDim > 3) SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported coordinate dimension %D > 3", coordDim);
1464:   if (quad) {PetscQuadratureGetData(quad, NULL, NULL, &Nq, &points, NULL);}
1465:   DMPlexGetCellType(dm, cell, &ct);
1466:   switch (ct) {
1467:     case DM_POLYTOPE_POINT:
1468:     DMPlexComputePointGeometry_Internal(dm, cell, v, J, invJ, detJ);
1469:     isAffine = PETSC_FALSE;
1470:     break;
1471:     case DM_POLYTOPE_SEGMENT:
1472:     case DM_POLYTOPE_POINT_PRISM_TENSOR:
1473:     if (Nq) {DMPlexComputeLineGeometry_Internal(dm, cell, v0, J0, NULL, &detJ0);}
1474:     else    {DMPlexComputeLineGeometry_Internal(dm, cell, v,  J,  invJ,  detJ);}
1475:     break;
1476:     case DM_POLYTOPE_TRIANGLE:
1477:     if (Nq) {DMPlexComputeTriangleGeometry_Internal(dm, cell, v0, J0, NULL, &detJ0);}
1478:     else    {DMPlexComputeTriangleGeometry_Internal(dm, cell, v,  J,  invJ,  detJ);}
1479:     break;
1480:     case DM_POLYTOPE_QUADRILATERAL:
1481:     DMPlexComputeRectangleGeometry_Internal(dm, cell, PETSC_FALSE, Nq, points, v, J, invJ, detJ);
1482:     isAffine = PETSC_FALSE;
1483:     break;
1484:     case DM_POLYTOPE_SEG_PRISM_TENSOR:
1485:     DMPlexComputeRectangleGeometry_Internal(dm, cell, PETSC_TRUE, Nq, points, v, J, invJ, detJ);
1486:     isAffine = PETSC_FALSE;
1487:     break;
1488:     case DM_POLYTOPE_TETRAHEDRON:
1489:     if (Nq) {DMPlexComputeTetrahedronGeometry_Internal(dm, cell, v0, J0, NULL, &detJ0);}
1490:     else    {DMPlexComputeTetrahedronGeometry_Internal(dm, cell, v,  J,  invJ,  detJ);}
1491:     break;
1492:     case DM_POLYTOPE_HEXAHEDRON:
1493:     DMPlexComputeHexahedronGeometry_Internal(dm, cell, Nq, points, v, J, invJ, detJ);
1494:     isAffine = PETSC_FALSE;
1495:     break;
1496:     default: SETERRQ2(PetscObjectComm((PetscObject) dm), PETSC_ERR_ARG_OUTOFRANGE, "No element geometry for cell %D with type %s", cell, DMPolytopeTypes[ct]);
1497:   }
1498:   if (isAffine && Nq) {
1499:     if (v) {
1500:       for (i = 0; i < Nq; i++) {
1501:         CoordinatesRefToReal(coordDim, dim, xi0, v0, J0, &points[dim * i], &v[coordDim * i]);
1502:       }
1503:     }
1504:     if (detJ) {
1505:       for (i = 0; i < Nq; i++) {
1506:         detJ[i] = detJ0;
1507:       }
1508:     }
1509:     if (J) {
1510:       PetscInt k;

1512:       for (i = 0, k = 0; i < Nq; i++) {
1513:         PetscInt j;

1515:         for (j = 0; j < coordDim * coordDim; j++, k++) {
1516:           J[k] = J0[j];
1517:         }
1518:       }
1519:     }
1520:     if (invJ) {
1521:       PetscInt k;
1522:       switch (coordDim) {
1523:       case 0:
1524:         break;
1525:       case 1:
1526:         invJ[0] = 1./J0[0];
1527:         break;
1528:       case 2:
1529:         DMPlex_Invert2D_Internal(invJ, J0, detJ0);
1530:         break;
1531:       case 3:
1532:         DMPlex_Invert3D_Internal(invJ, J0, detJ0);
1533:         break;
1534:       }
1535:       for (i = 1, k = coordDim * coordDim; i < Nq; i++) {
1536:         PetscInt j;

1538:         for (j = 0; j < coordDim * coordDim; j++, k++) {
1539:           invJ[k] = invJ[j];
1540:         }
1541:       }
1542:     }
1543:   }
1544:   return(0);
1545: }

1547: /*@C
1548:   DMPlexComputeCellGeometryAffineFEM - Assuming an affine map, compute the Jacobian, inverse Jacobian, and Jacobian determinant for a given cell

1550:   Collective on dm

1552:   Input Arguments:
1553: + dm   - the DM
1554: - cell - the cell

1556:   Output Arguments:
1557: + v0   - the translation part of this affine transform
1558: . J    - the Jacobian of the transform from the reference element
1559: . invJ - the inverse of the Jacobian
1560: - detJ - the Jacobian determinant

1562:   Level: advanced

1564:   Fortran Notes:
1565:   Since it returns arrays, this routine is only available in Fortran 90, and you must
1566:   include petsc.h90 in your code.

1568: .seealso: DMPlexComputeCellGeometryFEM(), DMGetCoordinateSection(), DMGetCoordinates()
1569: @*/
1570: PetscErrorCode DMPlexComputeCellGeometryAffineFEM(DM dm, PetscInt cell, PetscReal *v0, PetscReal *J, PetscReal *invJ, PetscReal *detJ)
1571: {

1575:   DMPlexComputeCellGeometryFEM_Implicit(dm,cell,NULL,v0,J,invJ,detJ);
1576:   return(0);
1577: }

1579: static PetscErrorCode DMPlexComputeCellGeometryFEM_FE(DM dm, PetscFE fe, PetscInt point, PetscQuadrature quad, PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1580: {
1581:   PetscQuadrature   feQuad;
1582:   PetscSection      coordSection;
1583:   Vec               coordinates;
1584:   PetscScalar      *coords = NULL;
1585:   const PetscReal  *quadPoints;
1586:   PetscTabulation T;
1587:   PetscInt          dim, cdim, pdim, qdim, Nq, numCoords, q;
1588:   PetscErrorCode    ierr;

1591:   DMGetCoordinatesLocal(dm, &coordinates);
1592:   DMGetCoordinateSection(dm, &coordSection);
1593:   DMPlexVecGetClosure(dm, coordSection, coordinates, point, &numCoords, &coords);
1594:   DMGetDimension(dm, &dim);
1595:   DMGetCoordinateDim(dm, &cdim);
1596:   if (!quad) { /* use the first point of the first functional of the dual space */
1597:     PetscDualSpace dsp;

1599:     PetscFEGetDualSpace(fe, &dsp);
1600:     PetscDualSpaceGetFunctional(dsp, 0, &quad);
1601:     PetscQuadratureGetData(quad, &qdim, NULL, &Nq, &quadPoints, NULL);
1602:     Nq = 1;
1603:   } else {
1604:     PetscQuadratureGetData(quad, &qdim, NULL, &Nq, &quadPoints, NULL);
1605:   }
1606:   PetscFEGetDimension(fe, &pdim);
1607:   PetscFEGetQuadrature(fe, &feQuad);
1608:   if (feQuad == quad) {
1609:     PetscFEGetCellTabulation(fe, &T);
1610:     if (numCoords != pdim*cdim) SETERRQ4(PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "There are %d coordinates for point %d != %d*%d", numCoords, point, pdim, cdim);
1611:   } else {
1612:     PetscFECreateTabulation(fe, 1, Nq, quadPoints, J ? 1 : 0, &T);
1613:   }
1614:   if (qdim != dim) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Point dimension %d != quadrature dimension %d", dim, qdim);
1615:   {
1616:     const PetscReal *basis    = T->T[0];
1617:     const PetscReal *basisDer = T->T[1];
1618:     PetscReal        detJt;

1620:     if (v) {
1621:       PetscArrayzero(v, Nq*cdim);
1622:       for (q = 0; q < Nq; ++q) {
1623:         PetscInt i, k;

1625:         for (k = 0; k < pdim; ++k) {
1626:           const PetscInt vertex = k/cdim;
1627:           for (i = 0; i < cdim; ++i) {
1628:             v[q*cdim + i] += basis[(q*pdim + k)*cdim + i] * PetscRealPart(coords[vertex*cdim + i]);
1629:           }
1630:         }
1631:         PetscLogFlops(2.0*pdim*cdim);
1632:       }
1633:     }
1634:     if (J) {
1635:       PetscArrayzero(J, Nq*cdim*cdim);
1636:       for (q = 0; q < Nq; ++q) {
1637:         PetscInt i, j, k, c, r;

1639:         /* J = dx_i/d\xi_j = sum[k=0,n-1] dN_k/d\xi_j * x_i(k) */
1640:         for (k = 0; k < pdim; ++k) {
1641:           const PetscInt vertex = k/cdim;
1642:           for (j = 0; j < dim; ++j) {
1643:             for (i = 0; i < cdim; ++i) {
1644:               J[(q*cdim + i)*cdim + j] += basisDer[((q*pdim + k)*cdim + i)*dim + j] * PetscRealPart(coords[vertex*cdim + i]);
1645:             }
1646:           }
1647:         }
1648:         PetscLogFlops(2.0*pdim*dim*cdim);
1649:         if (cdim > dim) {
1650:           for (c = dim; c < cdim; ++c)
1651:             for (r = 0; r < cdim; ++r)
1652:               J[r*cdim+c] = r == c ? 1.0 : 0.0;
1653:         }
1654:         if (!detJ && !invJ) continue;
1655:         detJt = 0.;
1656:         switch (cdim) {
1657:         case 3:
1658:           DMPlex_Det3D_Internal(&detJt, &J[q*cdim*dim]);
1659:           if (invJ) {DMPlex_Invert3D_Internal(&invJ[q*cdim*dim], &J[q*cdim*dim], detJt);}
1660:           break;
1661:         case 2:
1662:           DMPlex_Det2D_Internal(&detJt, &J[q*cdim*dim]);
1663:           if (invJ) {DMPlex_Invert2D_Internal(&invJ[q*cdim*dim], &J[q*cdim*dim], detJt);}
1664:           break;
1665:         case 1:
1666:           detJt = J[q*cdim*dim];
1667:           if (invJ) invJ[q*cdim*dim] = 1.0/detJt;
1668:         }
1669:         if (detJ) detJ[q] = detJt;
1670:       }
1671:     } else if (detJ || invJ) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Need J to compute invJ or detJ");
1672:   }
1673:   if (feQuad != quad) {PetscTabulationDestroy(&T);}
1674:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, point, &numCoords, &coords);
1675:   return(0);
1676: }

1678: /*@C
1679:   DMPlexComputeCellGeometryFEM - Compute the Jacobian, inverse Jacobian, and Jacobian determinant at each quadrature point in the given cell

1681:   Collective on dm

1683:   Input Arguments:
1684: + dm   - the DM
1685: . cell - the cell
1686: - quad - the quadrature containing the points in the reference element where the geometry will be evaluated.  If quad == NULL, geometry will be
1687:          evaluated at the first vertex of the reference element

1689:   Output Arguments:
1690: + v    - the image of the transformed quadrature points, otherwise the image of the first vertex in the closure of the reference element
1691: . J    - the Jacobian of the transform from the reference element at each quadrature point
1692: . invJ - the inverse of the Jacobian at each quadrature point
1693: - detJ - the Jacobian determinant at each quadrature point

1695:   Level: advanced

1697:   Fortran Notes:
1698:   Since it returns arrays, this routine is only available in Fortran 90, and you must
1699:   include petsc.h90 in your code.

1701: .seealso: DMGetCoordinateSection(), DMGetCoordinates()
1702: @*/
1703: PetscErrorCode DMPlexComputeCellGeometryFEM(DM dm, PetscInt cell, PetscQuadrature quad, PetscReal *v, PetscReal *J, PetscReal *invJ, PetscReal *detJ)
1704: {
1705:   DM             cdm;
1706:   PetscFE        fe = NULL;

1711:   DMGetCoordinateDM(dm, &cdm);
1712:   if (cdm) {
1713:     PetscClassId id;
1714:     PetscInt     numFields;
1715:     PetscDS      prob;
1716:     PetscObject  disc;

1718:     DMGetNumFields(cdm, &numFields);
1719:     if (numFields) {
1720:       DMGetDS(cdm, &prob);
1721:       PetscDSGetDiscretization(prob,0,&disc);
1722:       PetscObjectGetClassId(disc,&id);
1723:       if (id == PETSCFE_CLASSID) {
1724:         fe = (PetscFE) disc;
1725:       }
1726:     }
1727:   }
1728:   if (!fe) {DMPlexComputeCellGeometryFEM_Implicit(dm, cell, quad, v, J, invJ, detJ);}
1729:   else     {DMPlexComputeCellGeometryFEM_FE(dm, fe, cell, quad, v, J, invJ, detJ);}
1730:   return(0);
1731: }

1733: static PetscErrorCode DMPlexComputeGeometryFVM_1D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
1734: {
1735:   PetscSection   coordSection;
1736:   Vec            coordinates;
1737:   PetscScalar   *coords = NULL;
1738:   PetscScalar    tmp[2];
1739:   PetscInt       coordSize, d;

1743:   DMGetCoordinatesLocal(dm, &coordinates);
1744:   DMGetCoordinateSection(dm, &coordSection);
1745:   DMPlexVecGetClosure(dm, coordSection, coordinates, cell, &coordSize, &coords);
1746:   DMLocalizeCoordinate_Internal(dm, dim, coords, &coords[dim], tmp);
1747:   if (centroid) {
1748:     for (d = 0; d < dim; ++d) centroid[d] = 0.5*PetscRealPart(coords[d] + tmp[d]);
1749:   }
1750:   if (normal) {
1751:     PetscReal norm;

1753:     if (dim != 2) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "We only support 2D edges right now");
1754:     normal[0]  = -PetscRealPart(coords[1] - tmp[1]);
1755:     normal[1]  =  PetscRealPart(coords[0] - tmp[0]);
1756:     norm       = DMPlex_NormD_Internal(dim, normal);
1757:     for (d = 0; d < dim; ++d) normal[d] /= norm;
1758:   }
1759:   if (vol) {
1760:     *vol = 0.0;
1761:     for (d = 0; d < dim; ++d) *vol += PetscSqr(PetscRealPart(coords[d] - tmp[d]));
1762:     *vol = PetscSqrtReal(*vol);
1763:   }
1764:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, cell, &coordSize, &coords);
1765:   return(0);
1766: }

1768: /* Centroid_i = (\sum_n A_n Cn_i) / A */
1769: static PetscErrorCode DMPlexComputeGeometryFVM_2D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
1770: {
1771:   DMPolytopeType ct;
1772:   PetscSection   coordSection;
1773:   Vec            coordinates;
1774:   PetscScalar   *coords = NULL;
1775:   PetscReal      vsum = 0.0, csum[3] = {0.0, 0.0, 0.0}, vtmp, ctmp[4], v0[3], R[9];
1776:   PetscBool      isHybrid = PETSC_FALSE;
1777:   PetscInt       fv[4] = {0, 1, 2, 3};
1778:   PetscInt       tdim = 2, coordSize, numCorners, p, d, e;

1782:   /* Must check for hybrid cells because prisms have a different orientation scheme */
1783:   DMPlexGetCellType(dm, cell, &ct);
1784:   switch (ct) {
1785:     case DM_POLYTOPE_POINT_PRISM_TENSOR:
1786:     case DM_POLYTOPE_SEG_PRISM_TENSOR:
1787:     case DM_POLYTOPE_TRI_PRISM_TENSOR:
1788:     case DM_POLYTOPE_QUAD_PRISM_TENSOR:
1789:       isHybrid = PETSC_TRUE;
1790:     default: break;
1791:   }
1792:   DMGetCoordinatesLocal(dm, &coordinates);
1793:   DMPlexGetConeSize(dm, cell, &numCorners);
1794:   DMGetCoordinateSection(dm, &coordSection);
1795:   DMPlexVecGetClosure(dm, coordSection, coordinates, cell, &coordSize, &coords);
1796:   DMGetCoordinateDim(dm, &dim);
1797:   /* Side faces for hybrid cells are are stored as tensor products */
1798:   if (isHybrid && numCorners == 4) {fv[2] = 3; fv[3] = 2;}

1800:   if (dim > 2 && centroid) {
1801:     v0[0] = PetscRealPart(coords[0]);
1802:     v0[1] = PetscRealPart(coords[1]);
1803:     v0[2] = PetscRealPart(coords[2]);
1804:   }
1805:   if (normal) {
1806:     if (dim > 2) {
1807:       const PetscReal x0 = PetscRealPart(coords[dim*fv[1]+0] - coords[0]), x1 = PetscRealPart(coords[dim*fv[2]+0] - coords[0]);
1808:       const PetscReal y0 = PetscRealPart(coords[dim*fv[1]+1] - coords[1]), y1 = PetscRealPart(coords[dim*fv[2]+1] - coords[1]);
1809:       const PetscReal z0 = PetscRealPart(coords[dim*fv[1]+2] - coords[2]), z1 = PetscRealPart(coords[dim*fv[2]+2] - coords[2]);
1810:       PetscReal       norm;

1812:       normal[0] = y0*z1 - z0*y1;
1813:       normal[1] = z0*x1 - x0*z1;
1814:       normal[2] = x0*y1 - y0*x1;
1815:       norm = PetscSqrtReal(normal[0]*normal[0] + normal[1]*normal[1] + normal[2]*normal[2]);
1816:       normal[0] /= norm;
1817:       normal[1] /= norm;
1818:       normal[2] /= norm;
1819:     } else {
1820:       for (d = 0; d < dim; ++d) normal[d] = 0.0;
1821:     }
1822:   }
1823:   if (dim == 3) {DMPlexComputeProjection3Dto2D(coordSize, coords, R);}
1824:   for (p = 0; p < numCorners; ++p) {
1825:     const PetscInt pi  = p < 4 ? fv[p] : p;
1826:     const PetscInt pin = p < 3 ? fv[(p+1)%numCorners] : (p+1)%numCorners;
1827:     /* Need to do this copy to get types right */
1828:     for (d = 0; d < tdim; ++d) {
1829:       ctmp[d]      = PetscRealPart(coords[pi*tdim+d]);
1830:       ctmp[tdim+d] = PetscRealPart(coords[pin*tdim+d]);
1831:     }
1832:     Volume_Triangle_Origin_Internal(&vtmp, ctmp);
1833:     vsum += vtmp;
1834:     for (d = 0; d < tdim; ++d) {
1835:       csum[d] += (ctmp[d] + ctmp[tdim+d])*vtmp;
1836:     }
1837:   }
1838:   for (d = 0; d < tdim; ++d) {
1839:     csum[d] /= (tdim+1)*vsum;
1840:   }
1841:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, cell, &coordSize, &coords);
1842:   if (vol) *vol = PetscAbsReal(vsum);
1843:   if (centroid) {
1844:     if (dim > 2) {
1845:       for (d = 0; d < dim; ++d) {
1846:         centroid[d] = v0[d];
1847:         for (e = 0; e < dim; ++e) {
1848:           centroid[d] += R[d*dim+e]*csum[e];
1849:         }
1850:       }
1851:     } else for (d = 0; d < dim; ++d) centroid[d] = csum[d];
1852:   }
1853:   return(0);
1854: }

1856: /* Centroid_i = (\sum_n V_n Cn_i) / V */
1857: static PetscErrorCode DMPlexComputeGeometryFVM_3D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
1858: {
1859:   DMPolytopeType  ct;
1860:   PetscSection    coordSection;
1861:   Vec             coordinates;
1862:   PetscScalar    *coords = NULL;
1863:   PetscReal       vsum = 0.0, vtmp, coordsTmp[3*3];
1864:   const PetscInt *faces, *facesO;
1865:   PetscBool       isHybrid = PETSC_FALSE;
1866:   PetscInt        numFaces, f, coordSize, p, d;
1867:   PetscErrorCode  ierr;

1870:   if (PetscUnlikely(dim > 3)) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"No support for dim %D > 3",dim);
1871:   /* Must check for hybrid cells because prisms have a different orientation scheme */
1872:   DMPlexGetCellType(dm, cell, &ct);
1873:   switch (ct) {
1874:     case DM_POLYTOPE_POINT_PRISM_TENSOR:
1875:     case DM_POLYTOPE_SEG_PRISM_TENSOR:
1876:     case DM_POLYTOPE_TRI_PRISM_TENSOR:
1877:     case DM_POLYTOPE_QUAD_PRISM_TENSOR:
1878:       isHybrid = PETSC_TRUE;
1879:     default: break;
1880:   }

1882:   DMGetCoordinatesLocal(dm, &coordinates);
1883:   DMGetCoordinateSection(dm, &coordSection);

1885:   if (centroid) for (d = 0; d < dim; ++d) centroid[d] = 0.0;
1886:   DMPlexGetConeSize(dm, cell, &numFaces);
1887:   DMPlexGetCone(dm, cell, &faces);
1888:   DMPlexGetConeOrientation(dm, cell, &facesO);
1889:   for (f = 0; f < numFaces; ++f) {
1890:     PetscBool      flip = isHybrid && f == 0 ? PETSC_TRUE : PETSC_FALSE; /* The first hybrid face is reversed */
1891:     DMPolytopeType ct;

1893:     DMPlexVecGetClosure(dm, coordSection, coordinates, faces[f], &coordSize, &coords);
1894:     DMPlexGetCellType(dm, faces[f], &ct);
1895:     switch (ct) {
1896:     case DM_POLYTOPE_TRIANGLE:
1897:       for (d = 0; d < dim; ++d) {
1898:         coordsTmp[0*dim+d] = PetscRealPart(coords[0*dim+d]);
1899:         coordsTmp[1*dim+d] = PetscRealPart(coords[1*dim+d]);
1900:         coordsTmp[2*dim+d] = PetscRealPart(coords[2*dim+d]);
1901:       }
1902:       Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
1903:       if (facesO[f] < 0 || flip) vtmp = -vtmp;
1904:       vsum += vtmp;
1905:       if (centroid) {           /* Centroid of OABC = (a+b+c)/4 */
1906:         for (d = 0; d < dim; ++d) {
1907:           for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p*dim+d]*vtmp;
1908:         }
1909:       }
1910:       break;
1911:     case DM_POLYTOPE_QUADRILATERAL:
1912:     case DM_POLYTOPE_SEG_PRISM_TENSOR:
1913:     {
1914:       PetscInt fv[4] = {0, 1, 2, 3};

1916:       /* Side faces for hybrid cells are are stored as tensor products */
1917:       if (isHybrid && f > 1) {fv[2] = 3; fv[3] = 2;}
1918:       /* DO FOR PYRAMID */
1919:       /* First tet */
1920:       for (d = 0; d < dim; ++d) {
1921:         coordsTmp[0*dim+d] = PetscRealPart(coords[fv[0]*dim+d]);
1922:         coordsTmp[1*dim+d] = PetscRealPart(coords[fv[1]*dim+d]);
1923:         coordsTmp[2*dim+d] = PetscRealPart(coords[fv[3]*dim+d]);
1924:       }
1925:       Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
1926:       if (facesO[f] < 0 || flip) vtmp = -vtmp;
1927:       vsum += vtmp;
1928:       if (centroid) {
1929:         for (d = 0; d < dim; ++d) {
1930:           for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p*dim+d]*vtmp;
1931:         }
1932:       }
1933:       /* Second tet */
1934:       for (d = 0; d < dim; ++d) {
1935:         coordsTmp[0*dim+d] = PetscRealPart(coords[fv[1]*dim+d]);
1936:         coordsTmp[1*dim+d] = PetscRealPart(coords[fv[2]*dim+d]);
1937:         coordsTmp[2*dim+d] = PetscRealPart(coords[fv[3]*dim+d]);
1938:       }
1939:       Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
1940:       if (facesO[f] < 0 || flip) vtmp = -vtmp;
1941:       vsum += vtmp;
1942:       if (centroid) {
1943:         for (d = 0; d < dim; ++d) {
1944:           for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p*dim+d]*vtmp;
1945:         }
1946:       }
1947:       break;
1948:     }
1949:     default:
1950:       SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Cannot handle face %D of type %s", faces[f], DMPolytopeTypes[ct]);
1951:     }
1952:     DMPlexVecRestoreClosure(dm, coordSection, coordinates, faces[f], &coordSize, &coords);
1953:   }
1954:   if (vol)     *vol = PetscAbsReal(vsum);
1955:   if (normal)   for (d = 0; d < dim; ++d) normal[d]    = 0.0;
1956:   if (centroid) for (d = 0; d < dim; ++d) centroid[d] /= (vsum*4);
1957:   return(0);
1958: }

1960: /*@C
1961:   DMPlexComputeCellGeometryFVM - Compute the volume for a given cell

1963:   Collective on dm

1965:   Input Arguments:
1966: + dm   - the DM
1967: - cell - the cell

1969:   Output Arguments:
1970: + volume   - the cell volume
1971: . centroid - the cell centroid
1972: - normal - the cell normal, if appropriate

1974:   Level: advanced

1976:   Fortran Notes:
1977:   Since it returns arrays, this routine is only available in Fortran 90, and you must
1978:   include petsc.h90 in your code.

1980: .seealso: DMGetCoordinateSection(), DMGetCoordinates()
1981: @*/
1982: PetscErrorCode DMPlexComputeCellGeometryFVM(DM dm, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
1983: {
1984:   PetscInt       depth, dim;

1988:   DMPlexGetDepth(dm, &depth);
1989:   DMGetDimension(dm, &dim);
1990:   if (depth != dim) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Mesh must be interpolated");
1991:   DMPlexGetPointDepth(dm, cell, &depth);
1992:   switch (depth) {
1993:   case 1:
1994:     DMPlexComputeGeometryFVM_1D_Internal(dm, dim, cell, vol, centroid, normal);
1995:     break;
1996:   case 2:
1997:     DMPlexComputeGeometryFVM_2D_Internal(dm, dim, cell, vol, centroid, normal);
1998:     break;
1999:   case 3:
2000:     DMPlexComputeGeometryFVM_3D_Internal(dm, dim, cell, vol, centroid, normal);
2001:     break;
2002:   default:
2003:     SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported dimension %D (depth %D) for element geometry computation", dim, depth);
2004:   }
2005:   return(0);
2006: }

2008: /*@
2009:   DMPlexComputeGeometryFEM - Precompute cell geometry for the entire mesh

2011:   Collective on dm

2013:   Input Parameter:
2014: . dm - The DMPlex

2016:   Output Parameter:
2017: . cellgeom - A vector with the cell geometry data for each cell

2019:   Level: beginner

2021: @*/
2022: PetscErrorCode DMPlexComputeGeometryFEM(DM dm, Vec *cellgeom)
2023: {
2024:   DM             dmCell;
2025:   Vec            coordinates;
2026:   PetscSection   coordSection, sectionCell;
2027:   PetscScalar   *cgeom;
2028:   PetscInt       cStart, cEnd, c;

2032:   DMClone(dm, &dmCell);
2033:   DMGetCoordinateSection(dm, &coordSection);
2034:   DMGetCoordinatesLocal(dm, &coordinates);
2035:   DMSetCoordinateSection(dmCell, PETSC_DETERMINE, coordSection);
2036:   DMSetCoordinatesLocal(dmCell, coordinates);
2037:   PetscSectionCreate(PetscObjectComm((PetscObject) dm), &sectionCell);
2038:   DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd);
2039:   PetscSectionSetChart(sectionCell, cStart, cEnd);
2040:   /* TODO This needs to be multiplied by Nq for non-affine */
2041:   for (c = cStart; c < cEnd; ++c) {PetscSectionSetDof(sectionCell, c, (PetscInt) PetscCeilReal(((PetscReal) sizeof(PetscFEGeom))/sizeof(PetscScalar)));}
2042:   PetscSectionSetUp(sectionCell);
2043:   DMSetLocalSection(dmCell, sectionCell);
2044:   PetscSectionDestroy(&sectionCell);
2045:   DMCreateLocalVector(dmCell, cellgeom);
2046:   VecGetArray(*cellgeom, &cgeom);
2047:   for (c = cStart; c < cEnd; ++c) {
2048:     PetscFEGeom *cg;

2050:     DMPlexPointLocalRef(dmCell, c, cgeom, &cg);
2051:     PetscArrayzero(cg, 1);
2052:     DMPlexComputeCellGeometryFEM(dmCell, c, NULL, cg->v, cg->J, cg->invJ, cg->detJ);
2053:     if (*cg->detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %D", (double) *cg->detJ, c);
2054:   }
2055:   return(0);
2056: }

2058: /*@
2059:   DMPlexComputeGeometryFVM - Computes the cell and face geometry for a finite volume method

2061:   Input Parameter:
2062: . dm - The DM

2064:   Output Parameters:
2065: + cellgeom - A Vec of PetscFVCellGeom data
2066: - facegeom - A Vec of PetscFVFaceGeom data

2068:   Level: developer

2070: .seealso: PetscFVFaceGeom, PetscFVCellGeom, DMPlexComputeGeometryFEM()
2071: @*/
2072: PetscErrorCode DMPlexComputeGeometryFVM(DM dm, Vec *cellgeom, Vec *facegeom)
2073: {
2074:   DM             dmFace, dmCell;
2075:   DMLabel        ghostLabel;
2076:   PetscSection   sectionFace, sectionCell;
2077:   PetscSection   coordSection;
2078:   Vec            coordinates;
2079:   PetscScalar   *fgeom, *cgeom;
2080:   PetscReal      minradius, gminradius;
2081:   PetscInt       dim, cStart, cEnd, cEndInterior, c, fStart, fEnd, f;

2085:   DMGetDimension(dm, &dim);
2086:   DMGetCoordinateSection(dm, &coordSection);
2087:   DMGetCoordinatesLocal(dm, &coordinates);
2088:   /* Make cell centroids and volumes */
2089:   DMClone(dm, &dmCell);
2090:   DMSetCoordinateSection(dmCell, PETSC_DETERMINE, coordSection);
2091:   DMSetCoordinatesLocal(dmCell, coordinates);
2092:   PetscSectionCreate(PetscObjectComm((PetscObject) dm), &sectionCell);
2093:   DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);
2094:   DMPlexGetGhostCellStratum(dm, &cEndInterior, NULL);
2095:   PetscSectionSetChart(sectionCell, cStart, cEnd);
2096:   for (c = cStart; c < cEnd; ++c) {PetscSectionSetDof(sectionCell, c, (PetscInt) PetscCeilReal(((PetscReal) sizeof(PetscFVCellGeom))/sizeof(PetscScalar)));}
2097:   PetscSectionSetUp(sectionCell);
2098:   DMSetLocalSection(dmCell, sectionCell);
2099:   PetscSectionDestroy(&sectionCell);
2100:   DMCreateLocalVector(dmCell, cellgeom);
2101:   if (cEndInterior < 0) cEndInterior = cEnd;
2102:   VecGetArray(*cellgeom, &cgeom);
2103:   for (c = cStart; c < cEndInterior; ++c) {
2104:     PetscFVCellGeom *cg;

2106:     DMPlexPointLocalRef(dmCell, c, cgeom, &cg);
2107:     PetscArrayzero(cg, 1);
2108:     DMPlexComputeCellGeometryFVM(dmCell, c, &cg->volume, cg->centroid, NULL);
2109:   }
2110:   /* Compute face normals and minimum cell radius */
2111:   DMClone(dm, &dmFace);
2112:   PetscSectionCreate(PetscObjectComm((PetscObject) dm), &sectionFace);
2113:   DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);
2114:   PetscSectionSetChart(sectionFace, fStart, fEnd);
2115:   for (f = fStart; f < fEnd; ++f) {PetscSectionSetDof(sectionFace, f, (PetscInt) PetscCeilReal(((PetscReal) sizeof(PetscFVFaceGeom))/sizeof(PetscScalar)));}
2116:   PetscSectionSetUp(sectionFace);
2117:   DMSetLocalSection(dmFace, sectionFace);
2118:   PetscSectionDestroy(&sectionFace);
2119:   DMCreateLocalVector(dmFace, facegeom);
2120:   VecGetArray(*facegeom, &fgeom);
2121:   DMGetLabel(dm, "ghost", &ghostLabel);
2122:   minradius = PETSC_MAX_REAL;
2123:   for (f = fStart; f < fEnd; ++f) {
2124:     PetscFVFaceGeom *fg;
2125:     PetscReal        area;
2126:     const PetscInt  *cells;
2127:     PetscInt         ncells, ghost = -1, d, numChildren;

2129:     if (ghostLabel) {DMLabelGetValue(ghostLabel, f, &ghost);}
2130:     DMPlexGetTreeChildren(dm,f,&numChildren,NULL);
2131:     DMPlexGetSupport(dm, f, &cells);
2132:     DMPlexGetSupportSize(dm, f, &ncells);
2133:     /* It is possible to get a face with no support when using partition overlap */
2134:     if (!ncells || ghost >= 0 || numChildren) continue;
2135:     DMPlexPointLocalRef(dmFace, f, fgeom, &fg);
2136:     DMPlexComputeCellGeometryFVM(dm, f, &area, fg->centroid, fg->normal);
2137:     for (d = 0; d < dim; ++d) fg->normal[d] *= area;
2138:     /* Flip face orientation if necessary to match ordering in support, and Update minimum radius */
2139:     {
2140:       PetscFVCellGeom *cL, *cR;
2141:       PetscReal       *lcentroid, *rcentroid;
2142:       PetscReal        l[3], r[3], v[3];

2144:       DMPlexPointLocalRead(dmCell, cells[0], cgeom, &cL);
2145:       lcentroid = cells[0] >= cEndInterior ? fg->centroid : cL->centroid;
2146:       if (ncells > 1) {
2147:         DMPlexPointLocalRead(dmCell, cells[1], cgeom, &cR);
2148:         rcentroid = cells[1] >= cEndInterior ? fg->centroid : cR->centroid;
2149:       }
2150:       else {
2151:         rcentroid = fg->centroid;
2152:       }
2153:       DMLocalizeCoordinateReal_Internal(dm, dim, fg->centroid, lcentroid, l);
2154:       DMLocalizeCoordinateReal_Internal(dm, dim, fg->centroid, rcentroid, r);
2155:       DMPlex_WaxpyD_Internal(dim, -1, l, r, v);
2156:       if (DMPlex_DotRealD_Internal(dim, fg->normal, v) < 0) {
2157:         for (d = 0; d < dim; ++d) fg->normal[d] = -fg->normal[d];
2158:       }
2159:       if (DMPlex_DotRealD_Internal(dim, fg->normal, v) <= 0) {
2160:         if (dim == 2) SETERRQ5(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Direction for face %d could not be fixed, normal (%g,%g) v (%g,%g)", f, (double) fg->normal[0], (double) fg->normal[1], (double) v[0], (double) v[1]);
2161:         if (dim == 3) SETERRQ7(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Direction for face %d could not be fixed, normal (%g,%g,%g) v (%g,%g,%g)", f, (double) fg->normal[0], (double) fg->normal[1], (double) fg->normal[2], (double) v[0], (double) v[1], (double) v[2]);
2162:         SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Direction for face %d could not be fixed", f);
2163:       }
2164:       if (cells[0] < cEndInterior) {
2165:         DMPlex_WaxpyD_Internal(dim, -1, fg->centroid, cL->centroid, v);
2166:         minradius = PetscMin(minradius, DMPlex_NormD_Internal(dim, v));
2167:       }
2168:       if (ncells > 1 && cells[1] < cEndInterior) {
2169:         DMPlex_WaxpyD_Internal(dim, -1, fg->centroid, cR->centroid, v);
2170:         minradius = PetscMin(minradius, DMPlex_NormD_Internal(dim, v));
2171:       }
2172:     }
2173:   }
2174:   MPIU_Allreduce(&minradius, &gminradius, 1, MPIU_REAL, MPIU_MIN, PetscObjectComm((PetscObject)dm));
2175:   DMPlexSetMinRadius(dm, gminradius);
2176:   /* Compute centroids of ghost cells */
2177:   for (c = cEndInterior; c < cEnd; ++c) {
2178:     PetscFVFaceGeom *fg;
2179:     const PetscInt  *cone,    *support;
2180:     PetscInt         coneSize, supportSize, s;

2182:     DMPlexGetConeSize(dmCell, c, &coneSize);
2183:     if (coneSize != 1) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Ghost cell %d has cone size %d != 1", c, coneSize);
2184:     DMPlexGetCone(dmCell, c, &cone);
2185:     DMPlexGetSupportSize(dmCell, cone[0], &supportSize);
2186:     if (supportSize != 2) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Face %d has support size %d != 2", cone[0], supportSize);
2187:     DMPlexGetSupport(dmCell, cone[0], &support);
2188:     DMPlexPointLocalRef(dmFace, cone[0], fgeom, &fg);
2189:     for (s = 0; s < 2; ++s) {
2190:       /* Reflect ghost centroid across plane of face */
2191:       if (support[s] == c) {
2192:         PetscFVCellGeom       *ci;
2193:         PetscFVCellGeom       *cg;
2194:         PetscReal              c2f[3], a;

2196:         DMPlexPointLocalRead(dmCell, support[(s+1)%2], cgeom, &ci);
2197:         DMPlex_WaxpyD_Internal(dim, -1, ci->centroid, fg->centroid, c2f); /* cell to face centroid */
2198:         a    = DMPlex_DotRealD_Internal(dim, c2f, fg->normal)/DMPlex_DotRealD_Internal(dim, fg->normal, fg->normal);
2199:         DMPlexPointLocalRef(dmCell, support[s], cgeom, &cg);
2200:         DMPlex_WaxpyD_Internal(dim, 2*a, fg->normal, ci->centroid, cg->centroid);
2201:         cg->volume = ci->volume;
2202:       }
2203:     }
2204:   }
2205:   VecRestoreArray(*facegeom, &fgeom);
2206:   VecRestoreArray(*cellgeom, &cgeom);
2207:   DMDestroy(&dmCell);
2208:   DMDestroy(&dmFace);
2209:   return(0);
2210: }

2212: /*@C
2213:   DMPlexGetMinRadius - Returns the minimum distance from any cell centroid to a face

2215:   Not collective

2217:   Input Argument:
2218: . dm - the DM

2220:   Output Argument:
2221: . minradius - the minium cell radius

2223:   Level: developer

2225: .seealso: DMGetCoordinates()
2226: @*/
2227: PetscErrorCode DMPlexGetMinRadius(DM dm, PetscReal *minradius)
2228: {
2232:   *minradius = ((DM_Plex*) dm->data)->minradius;
2233:   return(0);
2234: }

2236: /*@C
2237:   DMPlexSetMinRadius - Sets the minimum distance from the cell centroid to a face

2239:   Logically collective

2241:   Input Arguments:
2242: + dm - the DM
2243: - minradius - the minium cell radius

2245:   Level: developer

2247: .seealso: DMSetCoordinates()
2248: @*/
2249: PetscErrorCode DMPlexSetMinRadius(DM dm, PetscReal minradius)
2250: {
2253:   ((DM_Plex*) dm->data)->minradius = minradius;
2254:   return(0);
2255: }

2257: static PetscErrorCode BuildGradientReconstruction_Internal(DM dm, PetscFV fvm, DM dmFace, PetscScalar *fgeom, DM dmCell, PetscScalar *cgeom)
2258: {
2259:   DMLabel        ghostLabel;
2260:   PetscScalar   *dx, *grad, **gref;
2261:   PetscInt       dim, cStart, cEnd, c, cEndInterior, maxNumFaces;

2265:   DMGetDimension(dm, &dim);
2266:   DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);
2267:   DMPlexGetGhostCellStratum(dm, &cEndInterior, NULL);
2268:   DMPlexGetMaxSizes(dm, &maxNumFaces, NULL);
2269:   PetscFVLeastSquaresSetMaxFaces(fvm, maxNumFaces);
2270:   DMGetLabel(dm, "ghost", &ghostLabel);
2271:   PetscMalloc3(maxNumFaces*dim, &dx, maxNumFaces*dim, &grad, maxNumFaces, &gref);
2272:   for (c = cStart; c < cEndInterior; c++) {
2273:     const PetscInt        *faces;
2274:     PetscInt               numFaces, usedFaces, f, d;
2275:     PetscFVCellGeom        *cg;
2276:     PetscBool              boundary;
2277:     PetscInt               ghost;

2279:     DMPlexPointLocalRead(dmCell, c, cgeom, &cg);
2280:     DMPlexGetConeSize(dm, c, &numFaces);
2281:     DMPlexGetCone(dm, c, &faces);
2282:     if (numFaces < dim) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Cell %D has only %D faces, not enough for gradient reconstruction", c, numFaces);
2283:     for (f = 0, usedFaces = 0; f < numFaces; ++f) {
2284:       PetscFVCellGeom       *cg1;
2285:       PetscFVFaceGeom       *fg;
2286:       const PetscInt        *fcells;
2287:       PetscInt               ncell, side;

2289:       DMLabelGetValue(ghostLabel, faces[f], &ghost);
2290:       DMIsBoundaryPoint(dm, faces[f], &boundary);
2291:       if ((ghost >= 0) || boundary) continue;
2292:       DMPlexGetSupport(dm, faces[f], &fcells);
2293:       side  = (c != fcells[0]); /* c is on left=0 or right=1 of face */
2294:       ncell = fcells[!side];    /* the neighbor */
2295:       DMPlexPointLocalRef(dmFace, faces[f], fgeom, &fg);
2296:       DMPlexPointLocalRead(dmCell, ncell, cgeom, &cg1);
2297:       for (d = 0; d < dim; ++d) dx[usedFaces*dim+d] = cg1->centroid[d] - cg->centroid[d];
2298:       gref[usedFaces++] = fg->grad[side];  /* Gradient reconstruction term will go here */
2299:     }
2300:     if (!usedFaces) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_USER, "Mesh contains isolated cell (no neighbors). Is it intentional?");
2301:     PetscFVComputeGradient(fvm, usedFaces, dx, grad);
2302:     for (f = 0, usedFaces = 0; f < numFaces; ++f) {
2303:       DMLabelGetValue(ghostLabel, faces[f], &ghost);
2304:       DMIsBoundaryPoint(dm, faces[f], &boundary);
2305:       if ((ghost >= 0) || boundary) continue;
2306:       for (d = 0; d < dim; ++d) gref[usedFaces][d] = grad[usedFaces*dim+d];
2307:       ++usedFaces;
2308:     }
2309:   }
2310:   PetscFree3(dx, grad, gref);
2311:   return(0);
2312: }

2314: static PetscErrorCode BuildGradientReconstruction_Internal_Tree(DM dm, PetscFV fvm, DM dmFace, PetscScalar *fgeom, DM dmCell, PetscScalar *cgeom)
2315: {
2316:   DMLabel        ghostLabel;
2317:   PetscScalar   *dx, *grad, **gref;
2318:   PetscInt       dim, cStart, cEnd, c, cEndInterior, fStart, fEnd, f, nStart, nEnd, maxNumFaces = 0;
2319:   PetscSection   neighSec;
2320:   PetscInt     (*neighbors)[2];
2321:   PetscInt      *counter;

2325:   DMGetDimension(dm, &dim);
2326:   DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);
2327:   DMPlexGetGhostCellStratum(dm, &cEndInterior, NULL);
2328:   if (cEndInterior < 0) cEndInterior = cEnd;
2329:   PetscSectionCreate(PetscObjectComm((PetscObject)dm),&neighSec);
2330:   PetscSectionSetChart(neighSec,cStart,cEndInterior);
2331:   DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);
2332:   DMGetLabel(dm, "ghost", &ghostLabel);
2333:   for (f = fStart; f < fEnd; f++) {
2334:     const PetscInt        *fcells;
2335:     PetscBool              boundary;
2336:     PetscInt               ghost = -1;
2337:     PetscInt               numChildren, numCells, c;

2339:     if (ghostLabel) {DMLabelGetValue(ghostLabel, f, &ghost);}
2340:     DMIsBoundaryPoint(dm, f, &boundary);
2341:     DMPlexGetTreeChildren(dm, f, &numChildren, NULL);
2342:     if ((ghost >= 0) || boundary || numChildren) continue;
2343:     DMPlexGetSupportSize(dm, f, &numCells);
2344:     if (numCells == 2) {
2345:       DMPlexGetSupport(dm, f, &fcells);
2346:       for (c = 0; c < 2; c++) {
2347:         PetscInt cell = fcells[c];

2349:         if (cell >= cStart && cell < cEndInterior) {
2350:           PetscSectionAddDof(neighSec,cell,1);
2351:         }
2352:       }
2353:     }
2354:   }
2355:   PetscSectionSetUp(neighSec);
2356:   PetscSectionGetMaxDof(neighSec,&maxNumFaces);
2357:   PetscFVLeastSquaresSetMaxFaces(fvm, maxNumFaces);
2358:   nStart = 0;
2359:   PetscSectionGetStorageSize(neighSec,&nEnd);
2360:   PetscMalloc1((nEnd-nStart),&neighbors);
2361:   PetscCalloc1((cEndInterior-cStart),&counter);
2362:   for (f = fStart; f < fEnd; f++) {
2363:     const PetscInt        *fcells;
2364:     PetscBool              boundary;
2365:     PetscInt               ghost = -1;
2366:     PetscInt               numChildren, numCells, c;

2368:     if (ghostLabel) {DMLabelGetValue(ghostLabel, f, &ghost);}
2369:     DMIsBoundaryPoint(dm, f, &boundary);
2370:     DMPlexGetTreeChildren(dm, f, &numChildren, NULL);
2371:     if ((ghost >= 0) || boundary || numChildren) continue;
2372:     DMPlexGetSupportSize(dm, f, &numCells);
2373:     if (numCells == 2) {
2374:       DMPlexGetSupport(dm, f, &fcells);
2375:       for (c = 0; c < 2; c++) {
2376:         PetscInt cell = fcells[c], off;

2378:         if (cell >= cStart && cell < cEndInterior) {
2379:           PetscSectionGetOffset(neighSec,cell,&off);
2380:           off += counter[cell - cStart]++;
2381:           neighbors[off][0] = f;
2382:           neighbors[off][1] = fcells[1 - c];
2383:         }
2384:       }
2385:     }
2386:   }
2387:   PetscFree(counter);
2388:   PetscMalloc3(maxNumFaces*dim, &dx, maxNumFaces*dim, &grad, maxNumFaces, &gref);
2389:   for (c = cStart; c < cEndInterior; c++) {
2390:     PetscInt               numFaces, f, d, off, ghost = -1;
2391:     PetscFVCellGeom        *cg;

2393:     DMPlexPointLocalRead(dmCell, c, cgeom, &cg);
2394:     PetscSectionGetDof(neighSec, c, &numFaces);
2395:     PetscSectionGetOffset(neighSec, c, &off);
2396:     if (ghostLabel) {DMLabelGetValue(ghostLabel, c, &ghost);}
2397:     if (ghost < 0 && numFaces < dim) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Cell %D has only %D faces, not enough for gradient reconstruction", c, numFaces);
2398:     for (f = 0; f < numFaces; ++f) {
2399:       PetscFVCellGeom       *cg1;
2400:       PetscFVFaceGeom       *fg;
2401:       const PetscInt        *fcells;
2402:       PetscInt               ncell, side, nface;

2404:       nface = neighbors[off + f][0];
2405:       ncell = neighbors[off + f][1];
2406:       DMPlexGetSupport(dm,nface,&fcells);
2407:       side  = (c != fcells[0]);
2408:       DMPlexPointLocalRef(dmFace, nface, fgeom, &fg);
2409:       DMPlexPointLocalRead(dmCell, ncell, cgeom, &cg1);
2410:       for (d = 0; d < dim; ++d) dx[f*dim+d] = cg1->centroid[d] - cg->centroid[d];
2411:       gref[f] = fg->grad[side];  /* Gradient reconstruction term will go here */
2412:     }
2413:     PetscFVComputeGradient(fvm, numFaces, dx, grad);
2414:     for (f = 0; f < numFaces; ++f) {
2415:       for (d = 0; d < dim; ++d) gref[f][d] = grad[f*dim+d];
2416:     }
2417:   }
2418:   PetscFree3(dx, grad, gref);
2419:   PetscSectionDestroy(&neighSec);
2420:   PetscFree(neighbors);
2421:   return(0);
2422: }

2424: /*@
2425:   DMPlexComputeGradientFVM - Compute geometric factors for gradient reconstruction, which are stored in the geometry data, and compute layout for gradient data

2427:   Collective on dm

2429:   Input Arguments:
2430: + dm  - The DM
2431: . fvm - The PetscFV
2432: . faceGeometry - The face geometry from DMPlexComputeFaceGeometryFVM()
2433: - cellGeometry - The face geometry from DMPlexComputeCellGeometryFVM()

2435:   Output Parameters:
2436: + faceGeometry - The geometric factors for gradient calculation are inserted
2437: - dmGrad - The DM describing the layout of gradient data

2439:   Level: developer

2441: .seealso: DMPlexGetFaceGeometryFVM(), DMPlexGetCellGeometryFVM()
2442: @*/
2443: PetscErrorCode DMPlexComputeGradientFVM(DM dm, PetscFV fvm, Vec faceGeometry, Vec cellGeometry, DM *dmGrad)
2444: {
2445:   DM             dmFace, dmCell;
2446:   PetscScalar   *fgeom, *cgeom;
2447:   PetscSection   sectionGrad, parentSection;
2448:   PetscInt       dim, pdim, cStart, cEnd, cEndInterior, c;

2452:   DMGetDimension(dm, &dim);
2453:   PetscFVGetNumComponents(fvm, &pdim);
2454:   DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);
2455:   DMPlexGetGhostCellStratum(dm, &cEndInterior, NULL);
2456:   /* Construct the interpolant corresponding to each face from the least-square solution over the cell neighborhood */
2457:   VecGetDM(faceGeometry, &dmFace);
2458:   VecGetDM(cellGeometry, &dmCell);
2459:   VecGetArray(faceGeometry, &fgeom);
2460:   VecGetArray(cellGeometry, &cgeom);
2461:   DMPlexGetTree(dm,&parentSection,NULL,NULL,NULL,NULL);
2462:   if (!parentSection) {
2463:     BuildGradientReconstruction_Internal(dm, fvm, dmFace, fgeom, dmCell, cgeom);
2464:   } else {
2465:     BuildGradientReconstruction_Internal_Tree(dm, fvm, dmFace, fgeom, dmCell, cgeom);
2466:   }
2467:   VecRestoreArray(faceGeometry, &fgeom);
2468:   VecRestoreArray(cellGeometry, &cgeom);
2469:   /* Create storage for gradients */
2470:   DMClone(dm, dmGrad);
2471:   PetscSectionCreate(PetscObjectComm((PetscObject) dm), &sectionGrad);
2472:   PetscSectionSetChart(sectionGrad, cStart, cEnd);
2473:   for (c = cStart; c < cEnd; ++c) {PetscSectionSetDof(sectionGrad, c, pdim*dim);}
2474:   PetscSectionSetUp(sectionGrad);
2475:   DMSetLocalSection(*dmGrad, sectionGrad);
2476:   PetscSectionDestroy(&sectionGrad);
2477:   return(0);
2478: }

2480: /*@
2481:   DMPlexGetDataFVM - Retrieve precomputed cell geometry

2483:   Collective on dm

2485:   Input Arguments:
2486: + dm  - The DM
2487: - fvm - The PetscFV

2489:   Output Parameters:
2490: + cellGeometry - The cell geometry
2491: . faceGeometry - The face geometry
2492: - dmGrad       - The gradient matrices

2494:   Level: developer

2496: .seealso: DMPlexComputeGeometryFVM()
2497: @*/
2498: PetscErrorCode DMPlexGetDataFVM(DM dm, PetscFV fv, Vec *cellgeom, Vec *facegeom, DM *gradDM)
2499: {
2500:   PetscObject    cellgeomobj, facegeomobj;

2504:   PetscObjectQuery((PetscObject) dm, "DMPlex_cellgeom_fvm", &cellgeomobj);
2505:   if (!cellgeomobj) {
2506:     Vec cellgeomInt, facegeomInt;

2508:     DMPlexComputeGeometryFVM(dm, &cellgeomInt, &facegeomInt);
2509:     PetscObjectCompose((PetscObject) dm, "DMPlex_cellgeom_fvm",(PetscObject)cellgeomInt);
2510:     PetscObjectCompose((PetscObject) dm, "DMPlex_facegeom_fvm",(PetscObject)facegeomInt);
2511:     VecDestroy(&cellgeomInt);
2512:     VecDestroy(&facegeomInt);
2513:     PetscObjectQuery((PetscObject) dm, "DMPlex_cellgeom_fvm", &cellgeomobj);
2514:   }
2515:   PetscObjectQuery((PetscObject) dm, "DMPlex_facegeom_fvm", &facegeomobj);
2516:   if (cellgeom) *cellgeom = (Vec) cellgeomobj;
2517:   if (facegeom) *facegeom = (Vec) facegeomobj;
2518:   if (gradDM) {
2519:     PetscObject gradobj;
2520:     PetscBool   computeGradients;

2522:     PetscFVGetComputeGradients(fv,&computeGradients);
2523:     if (!computeGradients) {
2524:       *gradDM = NULL;
2525:       return(0);
2526:     }
2527:     PetscObjectQuery((PetscObject) dm, "DMPlex_dmgrad_fvm", &gradobj);
2528:     if (!gradobj) {
2529:       DM dmGradInt;

2531:       DMPlexComputeGradientFVM(dm,fv,(Vec) facegeomobj,(Vec) cellgeomobj,&dmGradInt);
2532:       PetscObjectCompose((PetscObject) dm, "DMPlex_dmgrad_fvm", (PetscObject)dmGradInt);
2533:       DMDestroy(&dmGradInt);
2534:       PetscObjectQuery((PetscObject) dm, "DMPlex_dmgrad_fvm", &gradobj);
2535:     }
2536:     *gradDM = (DM) gradobj;
2537:   }
2538:   return(0);
2539: }

2541: static PetscErrorCode DMPlexCoordinatesToReference_NewtonUpdate(PetscInt dimC, PetscInt dimR, PetscScalar *J, PetscScalar *invJ, PetscScalar *work,  PetscReal *resNeg, PetscReal *guess)
2542: {
2543:   PetscInt l, m;

2546:   if (dimC == dimR && dimR <= 3) {
2547:     /* invert Jacobian, multiply */
2548:     PetscScalar det, idet;

2550:     switch (dimR) {
2551:     case 1:
2552:       invJ[0] = 1./ J[0];
2553:       break;
2554:     case 2:
2555:       det = J[0] * J[3] - J[1] * J[2];
2556:       idet = 1./det;
2557:       invJ[0] =  J[3] * idet;
2558:       invJ[1] = -J[1] * idet;
2559:       invJ[2] = -J[2] * idet;
2560:       invJ[3] =  J[0] * idet;
2561:       break;
2562:     case 3:
2563:       {
2564:         invJ[0] = J[4] * J[8] - J[5] * J[7];
2565:         invJ[1] = J[2] * J[7] - J[1] * J[8];
2566:         invJ[2] = J[1] * J[5] - J[2] * J[4];
2567:         det = invJ[0] * J[0] + invJ[1] * J[3] + invJ[2] * J[6];
2568:         idet = 1./det;
2569:         invJ[0] *= idet;
2570:         invJ[1] *= idet;
2571:         invJ[2] *= idet;
2572:         invJ[3]  = idet * (J[5] * J[6] - J[3] * J[8]);
2573:         invJ[4]  = idet * (J[0] * J[8] - J[2] * J[6]);
2574:         invJ[5]  = idet * (J[2] * J[3] - J[0] * J[5]);
2575:         invJ[6]  = idet * (J[3] * J[7] - J[4] * J[6]);
2576:         invJ[7]  = idet * (J[1] * J[6] - J[0] * J[7]);
2577:         invJ[8]  = idet * (J[0] * J[4] - J[1] * J[3]);
2578:       }
2579:       break;
2580:     }
2581:     for (l = 0; l < dimR; l++) {
2582:       for (m = 0; m < dimC; m++) {
2583:         guess[l] += PetscRealPart(invJ[l * dimC + m]) * resNeg[m];
2584:       }
2585:     }
2586:   } else {
2587: #if defined(PETSC_USE_COMPLEX)
2588:     char transpose = 'C';
2589: #else
2590:     char transpose = 'T';
2591: #endif
2592:     PetscBLASInt m = dimR;
2593:     PetscBLASInt n = dimC;
2594:     PetscBLASInt one = 1;
2595:     PetscBLASInt worksize = dimR * dimC, info;

2597:     for (l = 0; l < dimC; l++) {invJ[l] = resNeg[l];}

2599:     PetscStackCallBLAS("LAPACKgels",LAPACKgels_(&transpose,&m,&n,&one,J,&m,invJ,&n,work,&worksize, &info));
2600:     if (info != 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"Bad argument to GELS");

2602:     for (l = 0; l < dimR; l++) {guess[l] += PetscRealPart(invJ[l]);}
2603:   }
2604:   return(0);
2605: }

2607: static PetscErrorCode DMPlexCoordinatesToReference_Tensor(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal realCoords[], PetscReal refCoords[], Vec coords, PetscInt dimC, PetscInt dimR)
2608: {
2609:   PetscInt       coordSize, i, j, k, l, m, maxIts = 7, numV = (1 << dimR);
2610:   PetscScalar    *coordsScalar = NULL;
2611:   PetscReal      *cellData, *cellCoords, *cellCoeffs, *extJ, *resNeg;
2612:   PetscScalar    *J, *invJ, *work;

2617:   DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar);
2618:   if (coordSize < dimC * numV) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Expecting at least %D coordinates, got %D",dimC * (1 << dimR), coordSize);
2619:   DMGetWorkArray(dm, 2 * coordSize + dimR + dimC, MPIU_REAL, &cellData);
2620:   DMGetWorkArray(dm, 3 * dimR * dimC, MPIU_SCALAR, &J);
2621:   cellCoords = &cellData[0];
2622:   cellCoeffs = &cellData[coordSize];
2623:   extJ       = &cellData[2 * coordSize];
2624:   resNeg     = &cellData[2 * coordSize + dimR];
2625:   invJ       = &J[dimR * dimC];
2626:   work       = &J[2 * dimR * dimC];
2627:   if (dimR == 2) {
2628:     const PetscInt zToPlex[4] = {0, 1, 3, 2};

2630:     for (i = 0; i < 4; i++) {
2631:       PetscInt plexI = zToPlex[i];

2633:       for (j = 0; j < dimC; j++) {
2634:         cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
2635:       }
2636:     }
2637:   } else if (dimR == 3) {
2638:     const PetscInt zToPlex[8] = {0, 3, 1, 2, 4, 5, 7, 6};

2640:     for (i = 0; i < 8; i++) {
2641:       PetscInt plexI = zToPlex[i];

2643:       for (j = 0; j < dimC; j++) {
2644:         cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
2645:       }
2646:     }
2647:   } else {
2648:     for (i = 0; i < coordSize; i++) {cellCoords[i] = PetscRealPart(coordsScalar[i]);}
2649:   }
2650:   /* Perform the shuffling transform that converts values at the corners of [-1,1]^d to coefficients */
2651:   for (i = 0; i < dimR; i++) {
2652:     PetscReal *swap;

2654:     for (j = 0; j < (numV / 2); j++) {
2655:       for (k = 0; k < dimC; k++) {
2656:         cellCoeffs[dimC * j + k]                = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] + cellCoords[dimC * 2 * j + k]);
2657:         cellCoeffs[dimC * (j + (numV / 2)) + k] = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] - cellCoords[dimC * 2 * j + k]);
2658:       }
2659:     }

2661:     if (i < dimR - 1) {
2662:       swap = cellCoeffs;
2663:       cellCoeffs = cellCoords;
2664:       cellCoords = swap;
2665:     }
2666:   }
2667:   PetscArrayzero(refCoords,numPoints * dimR);
2668:   for (j = 0; j < numPoints; j++) {
2669:     for (i = 0; i < maxIts; i++) {
2670:       PetscReal *guess = &refCoords[dimR * j];

2672:       /* compute -residual and Jacobian */
2673:       for (k = 0; k < dimC; k++) {resNeg[k] = realCoords[dimC * j + k];}
2674:       for (k = 0; k < dimC * dimR; k++) {J[k] = 0.;}
2675:       for (k = 0; k < numV; k++) {
2676:         PetscReal extCoord = 1.;
2677:         for (l = 0; l < dimR; l++) {
2678:           PetscReal coord = guess[l];
2679:           PetscInt  dep   = (k & (1 << l)) >> l;

2681:           extCoord *= dep * coord + !dep;
2682:           extJ[l] = dep;

2684:           for (m = 0; m < dimR; m++) {
2685:             PetscReal coord = guess[m];
2686:             PetscInt  dep   = ((k & (1 << m)) >> m) && (m != l);
2687:             PetscReal mult  = dep * coord + !dep;

2689:             extJ[l] *= mult;
2690:           }
2691:         }
2692:         for (l = 0; l < dimC; l++) {
2693:           PetscReal coeff = cellCoeffs[dimC * k + l];

2695:           resNeg[l] -= coeff * extCoord;
2696:           for (m = 0; m < dimR; m++) {
2697:             J[dimR * l + m] += coeff * extJ[m];
2698:           }
2699:         }
2700:       }
2701:       if (0 && PetscDefined(USE_DEBUG)) {
2702:         PetscReal maxAbs = 0.;

2704:         for (l = 0; l < dimC; l++) {
2705:           maxAbs = PetscMax(maxAbs,PetscAbsReal(resNeg[l]));
2706:         }
2707:         PetscInfo4(dm,"cell %D, point %D, iter %D: res %g\n",cell,j,i,(double) maxAbs);
2708:       }

2710:       DMPlexCoordinatesToReference_NewtonUpdate(dimC,dimR,J,invJ,work,resNeg,guess);
2711:     }
2712:   }
2713:   DMRestoreWorkArray(dm, 3 * dimR * dimC, MPIU_SCALAR, &J);
2714:   DMRestoreWorkArray(dm, 2 * coordSize + dimR + dimC, MPIU_REAL, &cellData);
2715:   DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar);
2716:   return(0);
2717: }

2719: static PetscErrorCode DMPlexReferenceToCoordinates_Tensor(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal refCoords[], PetscReal realCoords[], Vec coords, PetscInt dimC, PetscInt dimR)
2720: {
2721:   PetscInt       coordSize, i, j, k, l, numV = (1 << dimR);
2722:   PetscScalar    *coordsScalar = NULL;
2723:   PetscReal      *cellData, *cellCoords, *cellCoeffs;

2728:   DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar);
2729:   if (coordSize < dimC * numV) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Expecting at least %D coordinates, got %D",dimC * (1 << dimR), coordSize);
2730:   DMGetWorkArray(dm, 2 * coordSize, MPIU_REAL, &cellData);
2731:   cellCoords = &cellData[0];
2732:   cellCoeffs = &cellData[coordSize];
2733:   if (dimR == 2) {
2734:     const PetscInt zToPlex[4] = {0, 1, 3, 2};

2736:     for (i = 0; i < 4; i++) {
2737:       PetscInt plexI = zToPlex[i];

2739:       for (j = 0; j < dimC; j++) {
2740:         cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
2741:       }
2742:     }
2743:   } else if (dimR == 3) {
2744:     const PetscInt zToPlex[8] = {0, 3, 1, 2, 4, 5, 7, 6};

2746:     for (i = 0; i < 8; i++) {
2747:       PetscInt plexI = zToPlex[i];

2749:       for (j = 0; j < dimC; j++) {
2750:         cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
2751:       }
2752:     }
2753:   } else {
2754:     for (i = 0; i < coordSize; i++) {cellCoords[i] = PetscRealPart(coordsScalar[i]);}
2755:   }
2756:   /* Perform the shuffling transform that converts values at the corners of [-1,1]^d to coefficients */
2757:   for (i = 0; i < dimR; i++) {
2758:     PetscReal *swap;

2760:     for (j = 0; j < (numV / 2); j++) {
2761:       for (k = 0; k < dimC; k++) {
2762:         cellCoeffs[dimC * j + k]                = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] + cellCoords[dimC * 2 * j + k]);
2763:         cellCoeffs[dimC * (j + (numV / 2)) + k] = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] - cellCoords[dimC * 2 * j + k]);
2764:       }
2765:     }

2767:     if (i < dimR - 1) {
2768:       swap = cellCoeffs;
2769:       cellCoeffs = cellCoords;
2770:       cellCoords = swap;
2771:     }
2772:   }
2773:   PetscArrayzero(realCoords,numPoints * dimC);
2774:   for (j = 0; j < numPoints; j++) {
2775:     const PetscReal *guess  = &refCoords[dimR * j];
2776:     PetscReal       *mapped = &realCoords[dimC * j];

2778:     for (k = 0; k < numV; k++) {
2779:       PetscReal extCoord = 1.;
2780:       for (l = 0; l < dimR; l++) {
2781:         PetscReal coord = guess[l];
2782:         PetscInt  dep   = (k & (1 << l)) >> l;

2784:         extCoord *= dep * coord + !dep;
2785:       }
2786:       for (l = 0; l < dimC; l++) {
2787:         PetscReal coeff = cellCoeffs[dimC * k + l];

2789:         mapped[l] += coeff * extCoord;
2790:       }
2791:     }
2792:   }
2793:   DMRestoreWorkArray(dm, 2 * coordSize, MPIU_REAL, &cellData);
2794:   DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar);
2795:   return(0);
2796: }

2798: /* TODO: TOBY please fix this for Nc > 1 */
2799: static PetscErrorCode DMPlexCoordinatesToReference_FE(DM dm, PetscFE fe, PetscInt cell, PetscInt numPoints, const PetscReal realCoords[], PetscReal refCoords[], Vec coords, PetscInt Nc, PetscInt dimR)
2800: {
2801:   PetscInt       numComp, pdim, i, j, k, l, m, maxIter = 7, coordSize;
2802:   PetscScalar    *nodes = NULL;
2803:   PetscReal      *invV, *modes;
2804:   PetscReal      *B, *D, *resNeg;
2805:   PetscScalar    *J, *invJ, *work;

2809:   PetscFEGetDimension(fe, &pdim);
2810:   PetscFEGetNumComponents(fe, &numComp);
2811:   if (numComp != Nc) SETERRQ2(PetscObjectComm((PetscObject)dm),PETSC_ERR_SUP,"coordinate discretization must have as many components (%D) as embedding dimension (!= %D)",numComp,Nc);
2812:   DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &nodes);
2813:   /* convert nodes to values in the stable evaluation basis */
2814:   DMGetWorkArray(dm,pdim,MPIU_REAL,&modes);
2815:   invV = fe->invV;
2816:   for (i = 0; i < pdim; ++i) {
2817:     modes[i] = 0.;
2818:     for (j = 0; j < pdim; ++j) {
2819:       modes[i] += invV[i * pdim + j] * PetscRealPart(nodes[j]);
2820:     }
2821:   }
2822:   DMGetWorkArray(dm,pdim * Nc + pdim * Nc * dimR + Nc,MPIU_REAL,&B);
2823:   D      = &B[pdim*Nc];
2824:   resNeg = &D[pdim*Nc * dimR];
2825:   DMGetWorkArray(dm,3 * Nc * dimR,MPIU_SCALAR,&J);
2826:   invJ = &J[Nc * dimR];
2827:   work = &invJ[Nc * dimR];
2828:   for (i = 0; i < numPoints * dimR; i++) {refCoords[i] = 0.;}
2829:   for (j = 0; j < numPoints; j++) {
2830:       for (i = 0; i < maxIter; i++) { /* we could batch this so that we're not making big B and D arrays all the time */
2831:       PetscReal *guess = &refCoords[j * dimR];
2832:       PetscSpaceEvaluate(fe->basisSpace, 1, guess, B, D, NULL);
2833:       for (k = 0; k < Nc; k++) {resNeg[k] = realCoords[j * Nc + k];}
2834:       for (k = 0; k < Nc * dimR; k++) {J[k] = 0.;}
2835:       for (k = 0; k < pdim; k++) {
2836:         for (l = 0; l < Nc; l++) {
2837:           resNeg[l] -= modes[k] * B[k * Nc + l];
2838:           for (m = 0; m < dimR; m++) {
2839:             J[l * dimR + m] += modes[k] * D[(k * Nc + l) * dimR + m];
2840:           }
2841:         }
2842:       }
2843:       if (0 && PetscDefined(USE_DEBUG)) {
2844:         PetscReal maxAbs = 0.;

2846:         for (l = 0; l < Nc; l++) {
2847:           maxAbs = PetscMax(maxAbs,PetscAbsReal(resNeg[l]));
2848:         }
2849:         PetscInfo4(dm,"cell %D, point %D, iter %D: res %g\n",cell,j,i,(double) maxAbs);
2850:       }
2851:       DMPlexCoordinatesToReference_NewtonUpdate(Nc,dimR,J,invJ,work,resNeg,guess);
2852:     }
2853:   }
2854:   DMRestoreWorkArray(dm,3 * Nc * dimR,MPIU_SCALAR,&J);
2855:   DMRestoreWorkArray(dm,pdim * Nc + pdim * Nc * dimR + Nc,MPIU_REAL,&B);
2856:   DMRestoreWorkArray(dm,pdim,MPIU_REAL,&modes);
2857:   DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &nodes);
2858:   return(0);
2859: }

2861: /* TODO: TOBY please fix this for Nc > 1 */
2862: static PetscErrorCode DMPlexReferenceToCoordinates_FE(DM dm, PetscFE fe, PetscInt cell, PetscInt numPoints, const PetscReal refCoords[], PetscReal realCoords[], Vec coords, PetscInt Nc, PetscInt dimR)
2863: {
2864:   PetscInt       numComp, pdim, i, j, k, l, coordSize;
2865:   PetscScalar    *nodes = NULL;
2866:   PetscReal      *invV, *modes;
2867:   PetscReal      *B;

2871:   PetscFEGetDimension(fe, &pdim);
2872:   PetscFEGetNumComponents(fe, &numComp);
2873:   if (numComp != Nc) SETERRQ2(PetscObjectComm((PetscObject)dm),PETSC_ERR_SUP,"coordinate discretization must have as many components (%D) as embedding dimension (!= %D)",numComp,Nc);
2874:   DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &nodes);
2875:   /* convert nodes to values in the stable evaluation basis */
2876:   DMGetWorkArray(dm,pdim,MPIU_REAL,&modes);
2877:   invV = fe->invV;
2878:   for (i = 0; i < pdim; ++i) {
2879:     modes[i] = 0.;
2880:     for (j = 0; j < pdim; ++j) {
2881:       modes[i] += invV[i * pdim + j] * PetscRealPart(nodes[j]);
2882:     }
2883:   }
2884:   DMGetWorkArray(dm,numPoints * pdim * Nc,MPIU_REAL,&B);
2885:   PetscSpaceEvaluate(fe->basisSpace, numPoints, refCoords, B, NULL, NULL);
2886:   for (i = 0; i < numPoints * Nc; i++) {realCoords[i] = 0.;}
2887:   for (j = 0; j < numPoints; j++) {
2888:     PetscReal *mapped = &realCoords[j * Nc];

2890:     for (k = 0; k < pdim; k++) {
2891:       for (l = 0; l < Nc; l++) {
2892:         mapped[l] += modes[k] * B[(j * pdim + k) * Nc + l];
2893:       }
2894:     }
2895:   }
2896:   DMRestoreWorkArray(dm,numPoints * pdim * Nc,MPIU_REAL,&B);
2897:   DMRestoreWorkArray(dm,pdim,MPIU_REAL,&modes);
2898:   DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &nodes);
2899:   return(0);
2900: }

2902: /*@
2903:   DMPlexCoordinatesToReference - Pull coordinates back from the mesh to the reference element using a single element
2904:   map.  This inversion will be accurate inside the reference element, but may be inaccurate for mappings that do not
2905:   extend uniquely outside the reference cell (e.g, most non-affine maps)

2907:   Not collective

2909:   Input Parameters:
2910: + dm         - The mesh, with coordinate maps defined either by a PetscDS for the coordinate DM (see DMGetCoordinateDM()) or
2911:                implicitly by the coordinates of the corner vertices of the cell: as an affine map for simplicial elements, or
2912:                as a multilinear map for tensor-product elements
2913: . cell       - the cell whose map is used.
2914: . numPoints  - the number of points to locate
2915: - realCoords - (numPoints x coordinate dimension) array of coordinates (see DMGetCoordinateDim())

2917:   Output Parameters:
2918: . refCoords  - (numPoints x dimension) array of reference coordinates (see DMGetDimension())

2920:   Level: intermediate

2922: .seealso: DMPlexReferenceToCoordinates()
2923: @*/
2924: PetscErrorCode DMPlexCoordinatesToReference(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal realCoords[], PetscReal refCoords[])
2925: {
2926:   PetscInt       dimC, dimR, depth, cStart, cEnd, i;
2927:   DM             coordDM = NULL;
2928:   Vec            coords;
2929:   PetscFE        fe = NULL;

2934:   DMGetDimension(dm,&dimR);
2935:   DMGetCoordinateDim(dm,&dimC);
2936:   if (dimR <= 0 || dimC <= 0 || numPoints <= 0) return(0);
2937:   DMPlexGetDepth(dm,&depth);
2938:   DMGetCoordinatesLocal(dm,&coords);
2939:   DMGetCoordinateDM(dm,&coordDM);
2940:   if (coordDM) {
2941:     PetscInt coordFields;

2943:     DMGetNumFields(coordDM,&coordFields);
2944:     if (coordFields) {
2945:       PetscClassId id;
2946:       PetscObject  disc;

2948:       DMGetField(coordDM,0,NULL,&disc);
2949:       PetscObjectGetClassId(disc,&id);
2950:       if (id == PETSCFE_CLASSID) {
2951:         fe = (PetscFE) disc;
2952:       }
2953:     }
2954:   }
2955:   DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd);
2956:   if (cell < cStart || cell >= cEnd) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"point %D not in cell range [%D,%D)",cell,cStart,cEnd);
2957:   if (!fe) { /* implicit discretization: affine or multilinear */
2958:     PetscInt  coneSize;
2959:     PetscBool isSimplex, isTensor;

2961:     DMPlexGetConeSize(dm,cell,&coneSize);
2962:     isSimplex = (coneSize == (dimR + 1)) ? PETSC_TRUE : PETSC_FALSE;
2963:     isTensor  = (coneSize == ((depth == 1) ? (1 << dimR) : (2 * dimR))) ? PETSC_TRUE : PETSC_FALSE;
2964:     if (isSimplex) {
2965:       PetscReal detJ, *v0, *J, *invJ;

2967:       DMGetWorkArray(dm,dimC + 2 * dimC * dimC, MPIU_REAL, &v0);
2968:       J    = &v0[dimC];
2969:       invJ = &J[dimC * dimC];
2970:       DMPlexComputeCellGeometryAffineFEM(dm, cell, v0, J, invJ, &detJ);
2971:       for (i = 0; i < numPoints; i++) { /* Apply the inverse affine transformation for each point */
2972:         const PetscReal x0[3] = {-1.,-1.,-1.};

2974:         CoordinatesRealToRef(dimC, dimR, x0, v0, invJ, &realCoords[dimC * i], &refCoords[dimR * i]);
2975:       }
2976:       DMRestoreWorkArray(dm,dimC + 2 * dimC * dimC, MPIU_REAL, &v0);
2977:     } else if (isTensor) {
2978:       DMPlexCoordinatesToReference_Tensor(coordDM, cell, numPoints, realCoords, refCoords, coords, dimC, dimR);
2979:     } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Unrecognized cone size %D",coneSize);
2980:   } else {
2981:     DMPlexCoordinatesToReference_FE(coordDM, fe, cell, numPoints, realCoords, refCoords, coords, dimC, dimR);
2982:   }
2983:   return(0);
2984: }

2986: /*@
2987:   DMPlexReferenceToCoordinates - Map references coordinates to coordinates in the the mesh for a single element map.

2989:   Not collective

2991:   Input Parameters:
2992: + dm         - The mesh, with coordinate maps defined either by a PetscDS for the coordinate DM (see DMGetCoordinateDM()) or
2993:                implicitly by the coordinates of the corner vertices of the cell: as an affine map for simplicial elements, or
2994:                as a multilinear map for tensor-product elements
2995: . cell       - the cell whose map is used.
2996: . numPoints  - the number of points to locate
2997: - refCoords  - (numPoints x dimension) array of reference coordinates (see DMGetDimension())

2999:   Output Parameters:
3000: . realCoords - (numPoints x coordinate dimension) array of coordinates (see DMGetCoordinateDim())

3002:    Level: intermediate

3004: .seealso: DMPlexCoordinatesToReference()
3005: @*/
3006: PetscErrorCode DMPlexReferenceToCoordinates(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal refCoords[], PetscReal realCoords[])
3007: {
3008:   PetscInt       dimC, dimR, depth, cStart, cEnd, i;
3009:   DM             coordDM = NULL;
3010:   Vec            coords;
3011:   PetscFE        fe = NULL;

3016:   DMGetDimension(dm,&dimR);
3017:   DMGetCoordinateDim(dm,&dimC);
3018:   if (dimR <= 0 || dimC <= 0 || numPoints <= 0) return(0);
3019:   DMPlexGetDepth(dm,&depth);
3020:   DMGetCoordinatesLocal(dm,&coords);
3021:   DMGetCoordinateDM(dm,&coordDM);
3022:   if (coordDM) {
3023:     PetscInt coordFields;

3025:     DMGetNumFields(coordDM,&coordFields);
3026:     if (coordFields) {
3027:       PetscClassId id;
3028:       PetscObject  disc;

3030:       DMGetField(coordDM,0,NULL,&disc);
3031:       PetscObjectGetClassId(disc,&id);
3032:       if (id == PETSCFE_CLASSID) {
3033:         fe = (PetscFE) disc;
3034:       }
3035:     }
3036:   }
3037:   DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd);
3038:   if (cell < cStart || cell >= cEnd) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"point %D not in cell range [%D,%D)",cell,cStart,cEnd);
3039:   if (!fe) { /* implicit discretization: affine or multilinear */
3040:     PetscInt  coneSize;
3041:     PetscBool isSimplex, isTensor;

3043:     DMPlexGetConeSize(dm,cell,&coneSize);
3044:     isSimplex = (coneSize == (dimR + 1)) ? PETSC_TRUE : PETSC_FALSE;
3045:     isTensor  = (coneSize == ((depth == 1) ? (1 << dimR) : (2 * dimR))) ? PETSC_TRUE : PETSC_FALSE;
3046:     if (isSimplex) {
3047:       PetscReal detJ, *v0, *J;

3049:       DMGetWorkArray(dm,dimC + 2 * dimC * dimC, MPIU_REAL, &v0);
3050:       J    = &v0[dimC];
3051:       DMPlexComputeCellGeometryAffineFEM(dm, cell, v0, J, NULL, &detJ);
3052:       for (i = 0; i < numPoints; i++) { /* Apply the affine transformation for each point */
3053:         const PetscReal xi0[3] = {-1.,-1.,-1.};

3055:         CoordinatesRefToReal(dimC, dimR, xi0, v0, J, &refCoords[dimR * i], &realCoords[dimC * i]);
3056:       }
3057:       DMRestoreWorkArray(dm,dimC + 2 * dimC * dimC, MPIU_REAL, &v0);
3058:     } else if (isTensor) {
3059:       DMPlexReferenceToCoordinates_Tensor(coordDM, cell, numPoints, refCoords, realCoords, coords, dimC, dimR);
3060:     } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Unrecognized cone size %D",coneSize);
3061:   } else {
3062:     DMPlexReferenceToCoordinates_FE(coordDM, fe, cell, numPoints, refCoords, realCoords, coords, dimC, dimR);
3063:   }
3064:   return(0);
3065: }

3067: /*@C
3068:   DMPlexRemapGeometry - This function maps the original DM coordinates to new coordinates.

3070:   Not collective

3072:   Input Parameters:
3073: + dm      - The DM
3074: . time    - The time
3075: - func    - The function transforming current coordinates to new coordaintes

3077:    Calling sequence of func:
3078: $    func(PetscInt dim, PetscInt Nf, PetscInt NfAux,
3079: $         const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
3080: $         const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
3081: $         PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f[]);

3083: +  dim          - The spatial dimension
3084: .  Nf           - The number of input fields (here 1)
3085: .  NfAux        - The number of input auxiliary fields
3086: .  uOff         - The offset of the coordinates in u[] (here 0)
3087: .  uOff_x       - The offset of the coordinates in u_x[] (here 0)
3088: .  u            - The coordinate values at this point in space
3089: .  u_t          - The coordinate time derivative at this point in space (here NULL)
3090: .  u_x          - The coordinate derivatives at this point in space
3091: .  aOff         - The offset of each auxiliary field in u[]
3092: .  aOff_x       - The offset of each auxiliary field in u_x[]
3093: .  a            - The auxiliary field values at this point in space
3094: .  a_t          - The auxiliary field time derivative at this point in space (or NULL)
3095: .  a_x          - The auxiliary field derivatives at this point in space
3096: .  t            - The current time
3097: .  x            - The coordinates of this point (here not used)
3098: .  numConstants - The number of constants
3099: .  constants    - The value of each constant
3100: -  f            - The new coordinates at this point in space

3102:   Level: intermediate

3104: .seealso: DMGetCoordinates(), DMGetCoordinatesLocal(), DMGetCoordinateDM(), DMProjectFieldLocal(), DMProjectFieldLabelLocal()
3105: @*/
3106: PetscErrorCode DMPlexRemapGeometry(DM dm, PetscReal time,
3107:                                    void (*func)(PetscInt, PetscInt, PetscInt,
3108:                                                 const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[],
3109:                                                 const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[],
3110:                                                 PetscReal, const PetscReal[], PetscInt, const PetscScalar[], PetscScalar[]))
3111: {
3112:   DM             cdm;
3113:   DMField        cf;
3114:   Vec            lCoords, tmpCoords;

3118:   DMGetCoordinateDM(dm, &cdm);
3119:   DMGetCoordinatesLocal(dm, &lCoords);
3120:   DMGetLocalVector(cdm, &tmpCoords);
3121:   VecCopy(lCoords, tmpCoords);
3122:   /* We have to do the coordinate field manually right now since the coordinate DM will not have its own */
3123:   DMGetCoordinateField(dm, &cf);
3124:   cdm->coordinateField = cf;
3125:   DMProjectFieldLocal(cdm, time, tmpCoords, &func, INSERT_VALUES, lCoords);
3126:   cdm->coordinateField = NULL;
3127:   DMRestoreLocalVector(cdm, &tmpCoords);
3128:   DMSetCoordinatesLocal(dm, lCoords);
3129:   return(0);
3130: }

3132: /* Shear applies the transformation, assuming we fix z,
3133:   / 1  0  m_0 \
3134:   | 0  1  m_1 |
3135:   \ 0  0   1  /
3136: */
3137: static void f0_shear(PetscInt dim, PetscInt Nf, PetscInt NfAux,
3138:                      const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
3139:                      const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
3140:                      PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar coords[])
3141: {
3142:   const PetscInt Nc = uOff[1]-uOff[0];
3143:   const PetscInt ax = (PetscInt) PetscRealPart(constants[0]);
3144:   PetscInt       c;

3146:   for (c = 0; c < Nc; ++c) {
3147:     coords[c] = u[c] + constants[c+1]*u[ax];
3148:   }
3149: }

3151: /*@C
3152:   DMPlexShearGeometry - This shears the domain, meaning adds a multiple of the shear coordinate to all other coordinates.

3154:   Not collective

3156:   Input Parameters:
3157: + dm          - The DM
3158: . direction   - The shear coordinate direction, e.g. 0 is the x-axis
3159: - multipliers - The multiplier m for each direction which is not the shear direction

3161:   Level: intermediate

3163: .seealso: DMPlexRemapGeometry()
3164: @*/
3165: PetscErrorCode DMPlexShearGeometry(DM dm, DMDirection direction, PetscReal multipliers[])
3166: {
3167:   DM             cdm;
3168:   PetscDS        cds;
3169:   PetscObject    obj;
3170:   PetscClassId   id;
3171:   PetscScalar   *moduli;
3172:   const PetscInt dir = (PetscInt) direction;
3173:   PetscInt       dE, d, e;

3177:   DMGetCoordinateDM(dm, &cdm);
3178:   DMGetCoordinateDim(dm, &dE);
3179:   PetscMalloc1(dE+1, &moduli);
3180:   moduli[0] = dir;
3181:   for (d = 0, e = 0; d < dE; ++d) moduli[d+1] = d == dir ? 0.0 : (multipliers ? multipliers[e++] : 1.0);
3182:   DMGetDS(cdm, &cds);
3183:   PetscDSGetDiscretization(cds, 0, &obj);
3184:   PetscObjectGetClassId(obj, &id);
3185:   if (id != PETSCFE_CLASSID) {
3186:     Vec           lCoords;
3187:     PetscSection  cSection;
3188:     PetscScalar  *coords;
3189:     PetscInt      vStart, vEnd, v;

3191:     DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);
3192:     DMGetCoordinateSection(dm, &cSection);
3193:     DMGetCoordinatesLocal(dm, &lCoords);
3194:     VecGetArray(lCoords, &coords);
3195:     for (v = vStart; v < vEnd; ++v) {
3196:       PetscReal ds;
3197:       PetscInt  off, c;

3199:       PetscSectionGetOffset(cSection, v, &off);
3200:       ds   = PetscRealPart(coords[off+dir]);
3201:       for (c = 0; c < dE; ++c) coords[off+c] += moduli[c]*ds;
3202:     }
3203:     VecRestoreArray(lCoords, &coords);
3204:   } else {
3205:     PetscDSSetConstants(cds, dE+1, moduli);
3206:     DMPlexRemapGeometry(dm, 0.0, f0_shear);
3207:   }
3208:   PetscFree(moduli);
3209:   return(0);
3210: }