Actual source code: plexgeometry.c

petsc-master 2019-08-15
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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: .seealso: DMPlexCreate(), DMGetCoordinates()
 32: @*/
 33: PetscErrorCode DMPlexFindVertices(DM dm, PetscInt npoints, const PetscReal coord[], PetscReal eps, PetscInt dagPoints[])
 34: {
 35:   PetscInt          c, dim, i, j, ndof, o, p, vStart, vEnd;
 36:   PetscSection      cs;
 37:   Vec               allCoordsVec;
 38:   const PetscScalar *allCoords;
 39:   PetscReal         norm;
 40:   PetscErrorCode    ierr;

 43:   if (eps < 0) eps = PETSC_SQRT_MACHINE_EPSILON;
 44:   DMGetDimension(dm, &dim);
 45:   DMGetCoordinateSection(dm, &cs);
 46:   DMGetCoordinatesLocal(dm, &allCoordsVec);
 47:   VecGetArrayRead(allCoordsVec, &allCoords);
 48:   DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);
 49:   for (i=0,j=0; i < npoints; i++,j+=dim) {
 50:     dagPoints[i] = -1;
 51:     for (p = vStart; p < vEnd; p++) {
 52:       PetscSectionGetOffset(cs, p, &o);
 53:       PetscSectionGetDof(cs, p, &ndof);
 54:       if (PetscUnlikely(ndof != dim)) SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_PLIB, "point %D: ndof = %D != %D = dim", p, ndof, dim);
 55:       norm = 0.0;
 56:       for (c = 0; c < dim; c++) {
 57:         norm += PetscSqr(coord[j+c] - PetscRealPart(allCoords[o+c]));
 58:       }
 59:       norm = PetscSqrtReal(norm);
 60:       if (norm <= eps) {
 61:         dagPoints[i] = p;
 62:         break;
 63:       }
 64:     }
 65:   }
 66:   VecRestoreArrayRead(allCoordsVec, &allCoords);
 67:   return(0);
 68: }

 70: static PetscErrorCode DMPlexGetLineIntersection_2D_Internal(const PetscReal segmentA[], const PetscReal segmentB[], PetscReal intersection[], PetscBool *hasIntersection)
 71: {
 72:   const PetscReal p0_x  = segmentA[0*2+0];
 73:   const PetscReal p0_y  = segmentA[0*2+1];
 74:   const PetscReal p1_x  = segmentA[1*2+0];
 75:   const PetscReal p1_y  = segmentA[1*2+1];
 76:   const PetscReal p2_x  = segmentB[0*2+0];
 77:   const PetscReal p2_y  = segmentB[0*2+1];
 78:   const PetscReal p3_x  = segmentB[1*2+0];
 79:   const PetscReal p3_y  = segmentB[1*2+1];
 80:   const PetscReal s1_x  = p1_x - p0_x;
 81:   const PetscReal s1_y  = p1_y - p0_y;
 82:   const PetscReal s2_x  = p3_x - p2_x;
 83:   const PetscReal s2_y  = p3_y - p2_y;
 84:   const PetscReal denom = (-s2_x * s1_y + s1_x * s2_y);

 87:   *hasIntersection = PETSC_FALSE;
 88:   /* Non-parallel lines */
 89:   if (denom != 0.0) {
 90:     const PetscReal s = (-s1_y * (p0_x - p2_x) + s1_x * (p0_y - p2_y)) / denom;
 91:     const PetscReal t = ( s2_x * (p0_y - p2_y) - s2_y * (p0_x - p2_x)) / denom;

 93:     if (s >= 0 && s <= 1 && t >= 0 && t <= 1) {
 94:       *hasIntersection = PETSC_TRUE;
 95:       if (intersection) {
 96:         intersection[0] = p0_x + (t * s1_x);
 97:         intersection[1] = p0_y + (t * s1_y);
 98:       }
 99:     }
100:   }
101:   return(0);
102: }

104: static PetscErrorCode DMPlexLocatePoint_Simplex_2D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
105: {
106:   const PetscInt  embedDim = 2;
107:   const PetscReal eps      = PETSC_SQRT_MACHINE_EPSILON;
108:   PetscReal       x        = PetscRealPart(point[0]);
109:   PetscReal       y        = PetscRealPart(point[1]);
110:   PetscReal       v0[2], J[4], invJ[4], detJ;
111:   PetscReal       xi, eta;
112:   PetscErrorCode  ierr;

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

119:   if ((xi >= -eps) && (eta >= -eps) && (xi + eta <= 2.0+eps)) *cell = c;
120:   else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
121:   return(0);
122: }

124: static PetscErrorCode DMPlexClosestPoint_Simplex_2D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscReal cpoint[])
125: {
126:   const PetscInt  embedDim = 2;
127:   PetscReal       x        = PetscRealPart(point[0]);
128:   PetscReal       y        = PetscRealPart(point[1]);
129:   PetscReal       v0[2], J[4], invJ[4], detJ;
130:   PetscReal       xi, eta, r;
131:   PetscErrorCode  ierr;

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

138:   xi  = PetscMax(xi,  0.0);
139:   eta = PetscMax(eta, 0.0);
140:   if (xi + eta > 2.0) {
141:     r    = (xi + eta)/2.0;
142:     xi  /= r;
143:     eta /= r;
144:   }
145:   cpoint[0] = J[0*embedDim+0]*xi + J[0*embedDim+1]*eta + v0[0];
146:   cpoint[1] = J[1*embedDim+0]*xi + J[1*embedDim+1]*eta + v0[1];
147:   return(0);
148: }

150: static PetscErrorCode DMPlexLocatePoint_General_2D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
151: {
152:   PetscSection       coordSection;
153:   Vec             coordsLocal;
154:   PetscScalar    *coords = NULL;
155:   const PetscInt  faces[8]  = {0, 1, 1, 2, 2, 3, 3, 0};
156:   PetscReal       x         = PetscRealPart(point[0]);
157:   PetscReal       y         = PetscRealPart(point[1]);
158:   PetscInt        crossings = 0, f;
159:   PetscErrorCode  ierr;

162:   DMGetCoordinatesLocal(dm, &coordsLocal);
163:   DMGetCoordinateSection(dm, &coordSection);
164:   DMPlexVecGetClosure(dm, coordSection, coordsLocal, c, NULL, &coords);
165:   for (f = 0; f < 4; ++f) {
166:     PetscReal x_i   = PetscRealPart(coords[faces[2*f+0]*2+0]);
167:     PetscReal y_i   = PetscRealPart(coords[faces[2*f+0]*2+1]);
168:     PetscReal x_j   = PetscRealPart(coords[faces[2*f+1]*2+0]);
169:     PetscReal y_j   = PetscRealPart(coords[faces[2*f+1]*2+1]);
170:     PetscReal slope = (y_j - y_i) / (x_j - x_i);
171:     PetscBool cond1 = (x_i <= x) && (x < x_j) ? PETSC_TRUE : PETSC_FALSE;
172:     PetscBool cond2 = (x_j <= x) && (x < x_i) ? PETSC_TRUE : PETSC_FALSE;
173:     PetscBool above = (y < slope * (x - x_i) + y_i) ? PETSC_TRUE : PETSC_FALSE;
174:     if ((cond1 || cond2)  && above) ++crossings;
175:   }
176:   if (crossings % 2) *cell = c;
177:   else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
178:   DMPlexVecRestoreClosure(dm, coordSection, coordsLocal, c, NULL, &coords);
179:   return(0);
180: }

182: static PetscErrorCode DMPlexLocatePoint_Simplex_3D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
183: {
184:   const PetscInt embedDim = 3;
185:   PetscReal      v0[3], J[9], invJ[9], detJ;
186:   PetscReal      x = PetscRealPart(point[0]);
187:   PetscReal      y = PetscRealPart(point[1]);
188:   PetscReal      z = PetscRealPart(point[2]);
189:   PetscReal      xi, eta, zeta;

193:   DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ);
194:   xi   = invJ[0*embedDim+0]*(x - v0[0]) + invJ[0*embedDim+1]*(y - v0[1]) + invJ[0*embedDim+2]*(z - v0[2]);
195:   eta  = invJ[1*embedDim+0]*(x - v0[0]) + invJ[1*embedDim+1]*(y - v0[1]) + invJ[1*embedDim+2]*(z - v0[2]);
196:   zeta = invJ[2*embedDim+0]*(x - v0[0]) + invJ[2*embedDim+1]*(y - v0[1]) + invJ[2*embedDim+2]*(z - v0[2]);

198:   if ((xi >= 0.0) && (eta >= 0.0) && (zeta >= 0.0) && (xi + eta + zeta <= 2.0)) *cell = c;
199:   else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
200:   return(0);
201: }

203: static PetscErrorCode DMPlexLocatePoint_General_3D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
204: {
205:   PetscSection   coordSection;
206:   Vec            coordsLocal;
207:   PetscScalar   *coords = NULL;
208:   const PetscInt faces[24] = {0, 3, 2, 1,  5, 4, 7, 6,  3, 0, 4, 5,
209:                               1, 2, 6, 7,  3, 5, 6, 2,  0, 1, 7, 4};
210:   PetscBool      found = PETSC_TRUE;
211:   PetscInt       f;

215:   DMGetCoordinatesLocal(dm, &coordsLocal);
216:   DMGetCoordinateSection(dm, &coordSection);
217:   DMPlexVecGetClosure(dm, coordSection, coordsLocal, c, NULL, &coords);
218:   for (f = 0; f < 6; ++f) {
219:     /* Check the point is under plane */
220:     /*   Get face normal */
221:     PetscReal v_i[3];
222:     PetscReal v_j[3];
223:     PetscReal normal[3];
224:     PetscReal pp[3];
225:     PetscReal dot;

227:     v_i[0]    = PetscRealPart(coords[faces[f*4+3]*3+0]-coords[faces[f*4+0]*3+0]);
228:     v_i[1]    = PetscRealPart(coords[faces[f*4+3]*3+1]-coords[faces[f*4+0]*3+1]);
229:     v_i[2]    = PetscRealPart(coords[faces[f*4+3]*3+2]-coords[faces[f*4+0]*3+2]);
230:     v_j[0]    = PetscRealPart(coords[faces[f*4+1]*3+0]-coords[faces[f*4+0]*3+0]);
231:     v_j[1]    = PetscRealPart(coords[faces[f*4+1]*3+1]-coords[faces[f*4+0]*3+1]);
232:     v_j[2]    = PetscRealPart(coords[faces[f*4+1]*3+2]-coords[faces[f*4+0]*3+2]);
233:     normal[0] = v_i[1]*v_j[2] - v_i[2]*v_j[1];
234:     normal[1] = v_i[2]*v_j[0] - v_i[0]*v_j[2];
235:     normal[2] = v_i[0]*v_j[1] - v_i[1]*v_j[0];
236:     pp[0]     = PetscRealPart(coords[faces[f*4+0]*3+0] - point[0]);
237:     pp[1]     = PetscRealPart(coords[faces[f*4+0]*3+1] - point[1]);
238:     pp[2]     = PetscRealPart(coords[faces[f*4+0]*3+2] - point[2]);
239:     dot       = normal[0]*pp[0] + normal[1]*pp[1] + normal[2]*pp[2];

241:     /* Check that projected point is in face (2D location problem) */
242:     if (dot < 0.0) {
243:       found = PETSC_FALSE;
244:       break;
245:     }
246:   }
247:   if (found) *cell = c;
248:   else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
249:   DMPlexVecRestoreClosure(dm, coordSection, coordsLocal, c, NULL, &coords);
250:   return(0);
251: }

253: static PetscErrorCode PetscGridHashInitialize_Internal(PetscGridHash box, PetscInt dim, const PetscScalar point[])
254: {
255:   PetscInt d;

258:   box->dim = dim;
259:   for (d = 0; d < dim; ++d) box->lower[d] = box->upper[d] = PetscRealPart(point[d]);
260:   return(0);
261: }

263: PetscErrorCode PetscGridHashCreate(MPI_Comm comm, PetscInt dim, const PetscScalar point[], PetscGridHash *box)
264: {

268:   PetscMalloc1(1, box);
269:   PetscGridHashInitialize_Internal(*box, dim, point);
270:   return(0);
271: }

273: PetscErrorCode PetscGridHashEnlarge(PetscGridHash box, const PetscScalar point[])
274: {
275:   PetscInt d;

278:   for (d = 0; d < box->dim; ++d) {
279:     box->lower[d] = PetscMin(box->lower[d], PetscRealPart(point[d]));
280:     box->upper[d] = PetscMax(box->upper[d], PetscRealPart(point[d]));
281:   }
282:   return(0);
283: }

285: /*
286:   PetscGridHashSetGrid - Divide the grid into boxes

288:   Not collective

290:   Input Parameters:
291: + box - The grid hash object
292: . n   - The number of boxes in each dimension, or PETSC_DETERMINE
293: - h   - The box size in each dimension, only used if n[d] == PETSC_DETERMINE

295:   Level: developer

297: .seealso: PetscGridHashCreate()
298: */
299: PetscErrorCode PetscGridHashSetGrid(PetscGridHash box, const PetscInt n[], const PetscReal h[])
300: {
301:   PetscInt d;

304:   for (d = 0; d < box->dim; ++d) {
305:     box->extent[d] = box->upper[d] - box->lower[d];
306:     if (n[d] == PETSC_DETERMINE) {
307:       box->h[d] = h[d];
308:       box->n[d] = PetscCeilReal(box->extent[d]/h[d]);
309:     } else {
310:       box->n[d] = n[d];
311:       box->h[d] = box->extent[d]/n[d];
312:     }
313:   }
314:   return(0);
315: }

317: /*
318:   PetscGridHashGetEnclosingBox - Find the grid boxes containing each input point

320:   Not collective

322:   Input Parameters:
323: + box       - The grid hash object
324: . numPoints - The number of input points
325: - points    - The input point coordinates

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

331:   Level: developer

333: .seealso: PetscGridHashCreate()
334: */
335: PetscErrorCode PetscGridHashGetEnclosingBox(PetscGridHash box, PetscInt numPoints, const PetscScalar points[], PetscInt dboxes[], PetscInt boxes[])
336: {
337:   const PetscReal *lower = box->lower;
338:   const PetscReal *upper = box->upper;
339:   const PetscReal *h     = box->h;
340:   const PetscInt  *n     = box->n;
341:   const PetscInt   dim   = box->dim;
342:   PetscInt         d, p;

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

349:       if (dbox == n[d] && PetscAbsReal(PetscRealPart(points[p*dim+d]) - upper[d]) < 1.0e-9) dbox = n[d]-1;
350:       if (dbox == -1   && PetscAbsReal(PetscRealPart(points[p*dim+d]) - lower[d]) < 1.0e-9) dbox = 0;
351:       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",
352:                                              p, PetscRealPart(points[p*dim+0]), dim > 1 ? PetscRealPart(points[p*dim+1]) : 0.0, dim > 2 ? PetscRealPart(points[p*dim+2]) : 0.0);
353:       dboxes[p*dim+d] = dbox;
354:     }
355:     if (boxes) for (d = 1, boxes[p] = dboxes[p*dim]; d < dim; ++d) boxes[p] += dboxes[p*dim+d]*n[d-1];
356:   }
357:   return(0);
358: }

360: /*
361:  PetscGridHashGetEnclosingBoxQuery - Find the grid boxes containing each input point

363:  Not collective

365:   Input Parameters:
366: + box       - The grid hash object
367: . numPoints - The number of input points
368: - points    - The input point coordinates

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

375:   Level: developer

377: .seealso: PetscGridHashGetEnclosingBox()
378: */
379: PetscErrorCode PetscGridHashGetEnclosingBoxQuery(PetscGridHash box, PetscInt numPoints, const PetscScalar points[], PetscInt dboxes[], PetscInt boxes[],PetscBool *found)
380: {
381:   const PetscReal *lower = box->lower;
382:   const PetscReal *upper = box->upper;
383:   const PetscReal *h     = box->h;
384:   const PetscInt  *n     = box->n;
385:   const PetscInt   dim   = box->dim;
386:   PetscInt         d, p;

389:   *found = PETSC_FALSE;
390:   for (p = 0; p < numPoints; ++p) {
391:     for (d = 0; d < dim; ++d) {
392:       PetscInt dbox = PetscFloorReal((PetscRealPart(points[p*dim+d]) - lower[d])/h[d]);

394:       if (dbox == n[d] && PetscAbsReal(PetscRealPart(points[p*dim+d]) - upper[d]) < 1.0e-9) dbox = n[d]-1;
395:       if (dbox < 0 || dbox >= n[d]) {
396:         return(0);
397:       }
398:       dboxes[p*dim+d] = dbox;
399:     }
400:     if (boxes) for (d = 1, boxes[p] = dboxes[p*dim]; d < dim; ++d) boxes[p] += dboxes[p*dim+d]*n[d-1];
401:   }
402:   *found = PETSC_TRUE;
403:   return(0);
404: }

406: PetscErrorCode PetscGridHashDestroy(PetscGridHash *box)
407: {

411:   if (*box) {
412:     PetscSectionDestroy(&(*box)->cellSection);
413:     ISDestroy(&(*box)->cells);
414:     DMLabelDestroy(&(*box)->cellsSparse);
415:   }
416:   PetscFree(*box);
417:   return(0);
418: }

420: PetscErrorCode DMPlexLocatePoint_Internal(DM dm, PetscInt dim, const PetscScalar point[], PetscInt cellStart, PetscInt *cell)
421: {
422:   PetscInt       coneSize;

426:   switch (dim) {
427:   case 2:
428:     DMPlexGetConeSize(dm, cellStart, &coneSize);
429:     switch (coneSize) {
430:     case 3:
431:       DMPlexLocatePoint_Simplex_2D_Internal(dm, point, cellStart, cell);
432:       break;
433:     case 4:
434:       DMPlexLocatePoint_General_2D_Internal(dm, point, cellStart, cell);
435:       break;
436:     default:
437:       SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No point location for cell with cone size %D", coneSize);
438:     }
439:     break;
440:   case 3:
441:     DMPlexGetConeSize(dm, cellStart, &coneSize);
442:     switch (coneSize) {
443:     case 4:
444:       DMPlexLocatePoint_Simplex_3D_Internal(dm, point, cellStart, cell);
445:       break;
446:     case 6:
447:       DMPlexLocatePoint_General_3D_Internal(dm, point, cellStart, cell);
448:       break;
449:     default:
450:       SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No point location for cell with cone size %D", coneSize);
451:     }
452:     break;
453:   default:
454:     SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No point location for mesh dimension %D", dim);
455:   }
456:   return(0);
457: }

459: /*
460:   DMPlexClosestPoint_Internal - Returns the closest point in the cell to the given point
461: */
462: PetscErrorCode DMPlexClosestPoint_Internal(DM dm, PetscInt dim, const PetscScalar point[], PetscInt cell, PetscReal cpoint[])
463: {
464:   PetscInt       coneSize;

468:   switch (dim) {
469:   case 2:
470:     DMPlexGetConeSize(dm, cell, &coneSize);
471:     switch (coneSize) {
472:     case 3:
473:       DMPlexClosestPoint_Simplex_2D_Internal(dm, point, cell, cpoint);
474:       break;
475: #if 0
476:     case 4:
477:       DMPlexClosestPoint_General_2D_Internal(dm, point, cell, cpoint);
478:       break;
479: #endif
480:     default:
481:       SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No closest point location for cell with cone size %D", coneSize);
482:     }
483:     break;
484: #if 0
485:   case 3:
486:     DMPlexGetConeSize(dm, cell, &coneSize);
487:     switch (coneSize) {
488:     case 4:
489:       DMPlexClosestPoint_Simplex_3D_Internal(dm, point, cell, cpoint);
490:       break;
491:     case 6:
492:       DMPlexClosestPoint_General_3D_Internal(dm, point, cell, cpoint);
493:       break;
494:     default:
495:       SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No closest point location for cell with cone size %D", coneSize);
496:     }
497:     break;
498: #endif
499:   default:
500:     SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No closest point location for mesh dimension %D", dim);
501:   }
502:   return(0);
503: }

505: /*
506:   DMPlexComputeGridHash_Internal - Create a grid hash structure covering the Plex

508:   Collective on dm

510:   Input Parameter:
511: . dm - The Plex

513:   Output Parameter:
514: . localBox - The grid hash object

516:   Level: developer

518: .seealso: PetscGridHashCreate(), PetscGridHashGetEnclosingBox()
519: */
520: PetscErrorCode DMPlexComputeGridHash_Internal(DM dm, PetscGridHash *localBox)
521: {
522:   MPI_Comm           comm;
523:   PetscGridHash      lbox;
524:   Vec                coordinates;
525:   PetscSection       coordSection;
526:   Vec                coordsLocal;
527:   const PetscScalar *coords;
528:   PetscInt          *dboxes, *boxes;
529:   PetscInt           n[3] = {10, 10, 10};
530:   PetscInt           dim, N, cStart, cEnd, cMax, c, i;
531:   PetscErrorCode     ierr;

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

571:     /* Find boxes enclosing each vertex */
572:     DMPlexVecGetClosure(dm, coordSection, coordsLocal, c, &csize, &ccoords);
573:     PetscGridHashGetEnclosingBox(lbox, csize/dim, ccoords, dboxes, boxes);
574:     /* Mark cells containing the vertices */
575:     for (e = 0; e < csize/dim; ++e) {DMLabelSetValue(lbox->cellsSparse, c, boxes[e]);}
576:     /* Get grid of boxes containing these */
577:     for (d = 0;   d < dim; ++d) {dlim[d*2+0] = dlim[d*2+1] = dboxes[d];}
578:     for (d = dim; d < 3;   ++d) {dlim[d*2+0] = dlim[d*2+1] = 0;}
579:     for (e = 1; e < dim+1; ++e) {
580:       for (d = 0; d < dim; ++d) {
581:         dlim[d*2+0] = PetscMin(dlim[d*2+0], dboxes[e*dim+d]);
582:         dlim[d*2+1] = PetscMax(dlim[d*2+1], dboxes[e*dim+d]);
583:       }
584:     }
585:     /* Check for intersection of box with cell */
586:     for (k = dlim[2*2+0], point[2] = lbox->lower[2] + k*h[2]; k <= dlim[2*2+1]; ++k, point[2] += h[2]) {
587:       for (j = dlim[1*2+0], point[1] = lbox->lower[1] + j*h[1]; j <= dlim[1*2+1]; ++j, point[1] += h[1]) {
588:         for (i = dlim[0*2+0], point[0] = lbox->lower[0] + i*h[0]; i <= dlim[0*2+1]; ++i, point[0] += h[0]) {
589:           const PetscInt box = (k*lbox->n[1] + j)*lbox->n[0] + i;
590:           PetscScalar    cpoint[3];
591:           PetscInt       cell, edge, ii, jj, kk;

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

598:                 DMPlexLocatePoint_Internal(dm, dim, cpoint, c, &cell);
599:                 if (cell >= 0) { DMLabelSetValue(lbox->cellsSparse, c, box); ii = jj = kk = 2;}
600:               }
601:             }
602:           }
603:           /* Check whether cell edge intersects any edge of these subboxes TODO vectorize this */
604:           for (edge = 0; edge < dim+1; ++edge) {
605:             PetscReal segA[6], segB[6];

607:             if (PetscUnlikely(dim > 3)) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Unexpected dim %d > 3",dim);
608:             for (d = 0; d < dim; ++d) {segA[d] = PetscRealPart(ccoords[edge*dim+d]); segA[dim+d] = PetscRealPart(ccoords[((edge+1)%(dim+1))*dim+d]);}
609:             for (kk = 0; kk < (dim > 2 ? 2 : 1); ++kk) {
610:               if (dim > 2) {segB[2]     = PetscRealPart(point[2]);
611:                             segB[dim+2] = PetscRealPart(point[2]) + kk*h[2];}
612:               for (jj = 0; jj < (dim > 1 ? 2 : 1); ++jj) {
613:                 if (dim > 1) {segB[1]     = PetscRealPart(point[1]);
614:                               segB[dim+1] = PetscRealPart(point[1]) + jj*h[1];}
615:                 for (ii = 0; ii < 2; ++ii) {
616:                   PetscBool intersects;

618:                   segB[0]     = PetscRealPart(point[0]);
619:                   segB[dim+0] = PetscRealPart(point[0]) + ii*h[0];
620:                   DMPlexGetLineIntersection_2D_Internal(segA, segB, NULL, &intersects);
621:                   if (intersects) { DMLabelSetValue(lbox->cellsSparse, c, box); edge = ii = jj = kk = dim+1;}
622:                 }
623:               }
624:             }
625:           }
626:         }
627:       }
628:     }
629:     DMPlexVecRestoreClosure(dm, coordSection, coordsLocal, c, NULL, &ccoords);
630:   }
631:   PetscFree2(dboxes, boxes);
632:   DMLabelConvertToSection(lbox->cellsSparse, &lbox->cellSection, &lbox->cells);
633:   DMLabelDestroy(&lbox->cellsSparse);
634:   *localBox = lbox;
635:   return(0);
636: }

638: PetscErrorCode DMLocatePoints_Plex(DM dm, Vec v, DMPointLocationType ltype, PetscSF cellSF)
639: {
640:   DM_Plex        *mesh = (DM_Plex *) dm->data;
641:   PetscBool       hash = mesh->useHashLocation, reuse = PETSC_FALSE;
642:   PetscInt        bs, numPoints, p, numFound, *found = NULL;
643:   PetscInt        dim, cStart, cEnd, cMax, numCells, c, d;
644:   const PetscInt *boxCells;
645:   PetscSFNode    *cells;
646:   PetscScalar    *a;
647:   PetscMPIInt     result;
648:   PetscLogDouble  t0,t1;
649:   PetscReal       gmin[3],gmax[3];
650:   PetscInt        terminating_query_type[] = { 0, 0, 0 };
651:   PetscErrorCode  ierr;

654:   PetscTime(&t0);
655:   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.");
656:   DMGetCoordinateDim(dm, &dim);
657:   VecGetBlockSize(v, &bs);
658:   MPI_Comm_compare(PetscObjectComm((PetscObject)cellSF),PETSC_COMM_SELF,&result);
659:   if (result != MPI_IDENT && result != MPI_CONGRUENT) SETERRQ(PetscObjectComm((PetscObject)cellSF),PETSC_ERR_SUP, "Trying parallel point location: only local point location supported");
660:   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);
661:   DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);
662:   DMPlexGetHybridBounds(dm, &cMax, NULL, NULL, NULL);
663:   if (cMax >= 0) cEnd = PetscMin(cEnd, cMax);
664:   VecGetLocalSize(v, &numPoints);
665:   VecGetArray(v, &a);
666:   numPoints /= bs;
667:   {
668:     const PetscSFNode *sf_cells;

670:     PetscSFGetGraph(cellSF,NULL,NULL,NULL,&sf_cells);
671:     if (sf_cells) {
672:       PetscInfo(dm,"[DMLocatePoints_Plex] Re-using existing StarForest node list\n");
673:       cells = (PetscSFNode*)sf_cells;
674:       reuse = PETSC_TRUE;
675:     } else {
676:       PetscInfo(dm,"[DMLocatePoints_Plex] Creating and initializing new StarForest node list\n");
677:       PetscMalloc1(numPoints, &cells);
678:       /* initialize cells if created */
679:       for (p=0; p<numPoints; p++) {
680:         cells[p].rank  = 0;
681:         cells[p].index = DMLOCATEPOINT_POINT_NOT_FOUND;
682:       }
683:     }
684:   }
685:   /* define domain bounding box */
686:   {
687:     Vec coorglobal;

689:     DMGetCoordinates(dm,&coorglobal);
690:     VecStrideMaxAll(coorglobal,NULL,gmax);
691:     VecStrideMinAll(coorglobal,NULL,gmin);
692:   }
693:   if (hash) {
694:     if (!mesh->lbox) {PetscInfo(dm, "Initializing grid hashing");DMPlexComputeGridHash_Internal(dm, &mesh->lbox);}
695:     /* Designate the local box for each point */
696:     /* Send points to correct process */
697:     /* Search cells that lie in each subbox */
698:     /*   Should we bin points before doing search? */
699:     ISGetIndices(mesh->lbox->cells, &boxCells);
700:   }
701:   for (p = 0, numFound = 0; p < numPoints; ++p) {
702:     const PetscScalar *point = &a[p*bs];
703:     PetscInt           dbin[3] = {-1,-1,-1}, bin, cell = -1, cellOffset;
704:     PetscBool          point_outside_domain = PETSC_FALSE;

706:     /* check bounding box of domain */
707:     for (d=0; d<dim; d++) {
708:       if (PetscRealPart(point[d]) < gmin[d]) { point_outside_domain = PETSC_TRUE; break; }
709:       if (PetscRealPart(point[d]) > gmax[d]) { point_outside_domain = PETSC_TRUE; break; }
710:     }
711:     if (point_outside_domain) {
712:       cells[p].rank = 0;
713:       cells[p].index = DMLOCATEPOINT_POINT_NOT_FOUND;
714:       terminating_query_type[0]++;
715:       continue;
716:     }

718:     /* check initial values in cells[].index - abort early if found */
719:     if (cells[p].index != DMLOCATEPOINT_POINT_NOT_FOUND) {
720:       c = cells[p].index;
721:       cells[p].index = DMLOCATEPOINT_POINT_NOT_FOUND;
722:       DMPlexLocatePoint_Internal(dm, dim, point, c, &cell);
723:       if (cell >= 0) {
724:         cells[p].rank = 0;
725:         cells[p].index = cell;
726:         numFound++;
727:       }
728:     }
729:     if (cells[p].index != DMLOCATEPOINT_POINT_NOT_FOUND) {
730:       terminating_query_type[1]++;
731:       continue;
732:     }

734:     if (hash) {
735:       PetscBool found_box;

737:       /* allow for case that point is outside box - abort early */
738:       PetscGridHashGetEnclosingBoxQuery(mesh->lbox, 1, point, dbin, &bin,&found_box);
739:       if (found_box) {
740:         /* TODO Lay an interface over this so we can switch between Section (dense) and Label (sparse) */
741:         PetscSectionGetDof(mesh->lbox->cellSection, bin, &numCells);
742:         PetscSectionGetOffset(mesh->lbox->cellSection, bin, &cellOffset);
743:         for (c = cellOffset; c < cellOffset + numCells; ++c) {
744:           DMPlexLocatePoint_Internal(dm, dim, point, boxCells[c], &cell);
745:           if (cell >= 0) {
746:             cells[p].rank = 0;
747:             cells[p].index = cell;
748:             numFound++;
749:             terminating_query_type[2]++;
750:             break;
751:           }
752:         }
753:       }
754:     } else {
755:       for (c = cStart; c < cEnd; ++c) {
756:         DMPlexLocatePoint_Internal(dm, dim, point, c, &cell);
757:         if (cell >= 0) {
758:           cells[p].rank = 0;
759:           cells[p].index = cell;
760:           numFound++;
761:           terminating_query_type[2]++;
762:           break;
763:         }
764:       }
765:     }
766:   }
767:   if (hash) {ISRestoreIndices(mesh->lbox->cells, &boxCells);}
768:   if (ltype == DM_POINTLOCATION_NEAREST && hash && numFound < numPoints) {
769:     for (p = 0; p < numPoints; p++) {
770:       const PetscScalar *point = &a[p*bs];
771:       PetscReal          cpoint[3], diff[3], dist, distMax = PETSC_MAX_REAL;
772:       PetscInt           dbin[3] = {-1,-1,-1}, bin, cellOffset, d;

774:       if (cells[p].index < 0) {
775:         ++numFound;
776:         PetscGridHashGetEnclosingBox(mesh->lbox, 1, point, dbin, &bin);
777:         PetscSectionGetDof(mesh->lbox->cellSection, bin, &numCells);
778:         PetscSectionGetOffset(mesh->lbox->cellSection, bin, &cellOffset);
779:         for (c = cellOffset; c < cellOffset + numCells; ++c) {
780:           DMPlexClosestPoint_Internal(dm, dim, point, boxCells[c], cpoint);
781:           for (d = 0; d < dim; ++d) diff[d] = cpoint[d] - PetscRealPart(point[d]);
782:           dist = DMPlex_NormD_Internal(dim, diff);
783:           if (dist < distMax) {
784:             for (d = 0; d < dim; ++d) a[p*bs+d] = cpoint[d];
785:             cells[p].rank  = 0;
786:             cells[p].index = boxCells[c];
787:             distMax = dist;
788:             break;
789:           }
790:         }
791:       }
792:     }
793:   }
794:   /* This code is only be relevant when interfaced to parallel point location */
795:   /* Check for highest numbered proc that claims a point (do we care?) */
796:   if (ltype == DM_POINTLOCATION_REMOVE && numFound < numPoints) {
797:     PetscMalloc1(numFound,&found);
798:     for (p = 0, numFound = 0; p < numPoints; p++) {
799:       if (cells[p].rank >= 0 && cells[p].index >= 0) {
800:         if (numFound < p) {
801:           cells[numFound] = cells[p];
802:         }
803:         found[numFound++] = p;
804:       }
805:     }
806:   }
807:   VecRestoreArray(v, &a);
808:   if (!reuse) {
809:     PetscSFSetGraph(cellSF, cEnd - cStart, numFound, found, PETSC_OWN_POINTER, cells, PETSC_OWN_POINTER);
810:   }
811:   PetscTime(&t1);
812:   if (hash) {
813:     PetscInfo3(dm,"[DMLocatePoints_Plex] terminating_query_type : %D [outside domain] : %D [inside intial cell] : %D [hash]\n",terminating_query_type[0],terminating_query_type[1],terminating_query_type[2]);
814:   } else {
815:     PetscInfo3(dm,"[DMLocatePoints_Plex] terminating_query_type : %D [outside domain] : %D [inside intial cell] : %D [brute-force]\n",terminating_query_type[0],terminating_query_type[1],terminating_query_type[2]);
816:   }
817:   PetscInfo3(dm,"[DMLocatePoints_Plex] npoints %D : time(rank0) %1.2e (sec): points/sec %1.4e\n",numPoints,t1-t0,(double)((double)numPoints/(t1-t0)));
818:   return(0);
819: }

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

824:   Not collective

826:   Input Parameter:
827: . coords - The coordinates of a segment

829:   Output Parameters:
830: + coords - The new y-coordinate, and 0 for x
831: - R - The rotation which accomplishes the projection

833:   Level: developer

835: .seealso: DMPlexComputeProjection3Dto1D(), DMPlexComputeProjection3Dto2D()
836: @*/
837: PetscErrorCode DMPlexComputeProjection2Dto1D(PetscScalar coords[], PetscReal R[])
838: {
839:   const PetscReal x = PetscRealPart(coords[2] - coords[0]);
840:   const PetscReal y = PetscRealPart(coords[3] - coords[1]);
841:   const PetscReal r = PetscSqrtReal(x*x + y*y), c = x/r, s = y/r;

844:   R[0] = c; R[1] = -s;
845:   R[2] = s; R[3] =  c;
846:   coords[0] = 0.0;
847:   coords[1] = r;
848:   return(0);
849: }

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

854:   Not collective

856:   Input Parameter:
857: . coords - The coordinates of a segment

859:   Output Parameters:
860: + coords - The new y-coordinate, and 0 for x and z
861: - R - The rotation which accomplishes the projection

863:   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

865:   Level: developer

867: .seealso: DMPlexComputeProjection2Dto1D(), DMPlexComputeProjection3Dto2D()
868: @*/
869: PetscErrorCode DMPlexComputeProjection3Dto1D(PetscScalar coords[], PetscReal R[])
870: {
871:   PetscReal      x    = PetscRealPart(coords[3] - coords[0]);
872:   PetscReal      y    = PetscRealPart(coords[4] - coords[1]);
873:   PetscReal      z    = PetscRealPart(coords[5] - coords[2]);
874:   PetscReal      r    = PetscSqrtReal(x*x + y*y + z*z);
875:   PetscReal      rinv = 1. / r;

878:   x *= rinv; y *= rinv; z *= rinv;
879:   if (x > 0.) {
880:     PetscReal inv1pX   = 1./ (1. + x);

882:     R[0] = x; R[1] = -y;              R[2] = -z;
883:     R[3] = y; R[4] = 1. - y*y*inv1pX; R[5] =     -y*z*inv1pX;
884:     R[6] = z; R[7] =     -y*z*inv1pX; R[8] = 1. - z*z*inv1pX;
885:   }
886:   else {
887:     PetscReal inv1mX   = 1./ (1. - x);

889:     R[0] = x; R[1] = z;               R[2] = y;
890:     R[3] = y; R[4] =     -y*z*inv1mX; R[5] = 1. - y*y*inv1mX;
891:     R[6] = z; R[7] = 1. - z*z*inv1mX; R[8] =     -y*z*inv1mX;
892:   }
893:   coords[0] = 0.0;
894:   coords[1] = r;
895:   return(0);
896: }

898: /*@
899:   DMPlexComputeProjection3Dto2D - Rewrite coordinates to be the 2D projection of the 3D coordinates

901:   Not collective

903:   Input Parameter:
904: . coords - The coordinates of a segment

906:   Output Parameters:
907: + coords - The new y- and z-coordinates, and 0 for x
908: - R - The rotation which accomplishes the projection

910:   Level: developer

912: .seealso: DMPlexComputeProjection2Dto1D(), DMPlexComputeProjection3Dto1D()
913: @*/
914: PetscErrorCode DMPlexComputeProjection3Dto2D(PetscInt coordSize, PetscScalar coords[], PetscReal R[])
915: {
916:   PetscReal      x1[3],  x2[3], n[3], norm;
917:   PetscReal      x1p[3], x2p[3], xnp[3];
918:   PetscReal      sqrtz, alpha;
919:   const PetscInt dim = 3;
920:   PetscInt       d, e, p;

923:   /* 0) Calculate normal vector */
924:   for (d = 0; d < dim; ++d) {
925:     x1[d] = PetscRealPart(coords[1*dim+d] - coords[0*dim+d]);
926:     x2[d] = PetscRealPart(coords[2*dim+d] - coords[0*dim+d]);
927:   }
928:   n[0] = x1[1]*x2[2] - x1[2]*x2[1];
929:   n[1] = x1[2]*x2[0] - x1[0]*x2[2];
930:   n[2] = x1[0]*x2[1] - x1[1]*x2[0];
931:   norm = PetscSqrtReal(n[0]*n[0] + n[1]*n[1] + n[2]*n[2]);
932:   n[0] /= norm;
933:   n[1] /= norm;
934:   n[2] /= norm;
935:   /* 1) Take the normal vector and rotate until it is \hat z

937:     Let the normal vector be <nx, ny, nz> and alpha = 1/sqrt(1 - nz^2), then

939:     R = /  alpha nx nz  alpha ny nz -1/alpha \
940:         | -alpha ny     alpha nx        0    |
941:         \     nx            ny         nz    /

943:     will rotate the normal vector to \hat z
944:   */
945:   sqrtz = PetscSqrtReal(1.0 - n[2]*n[2]);
946:   /* Check for n = z */
947:   if (sqrtz < 1.0e-10) {
948:     const PetscInt s = PetscSign(n[2]);
949:     /* If nz < 0, rotate 180 degrees around x-axis */
950:     for (p = 3; p < coordSize/3; ++p) {
951:       coords[p*2+0] = PetscRealPart(coords[p*dim+0] - coords[0*dim+0]);
952:       coords[p*2+1] = (PetscRealPart(coords[p*dim+1] - coords[0*dim+1])) * s;
953:     }
954:     coords[0] = 0.0;
955:     coords[1] = 0.0;
956:     coords[2] = x1[0];
957:     coords[3] = x1[1] * s;
958:     coords[4] = x2[0];
959:     coords[5] = x2[1] * s;
960:     R[0] = 1.0;     R[1] = 0.0;     R[2] = 0.0;
961:     R[3] = 0.0;     R[4] = 1.0 * s; R[5] = 0.0;
962:     R[6] = 0.0;     R[7] = 0.0;     R[8] = 1.0 * s;
963:     return(0);
964:   }
965:   alpha = 1.0/sqrtz;
966:   R[0] =  alpha*n[0]*n[2]; R[1] = alpha*n[1]*n[2]; R[2] = -sqrtz;
967:   R[3] = -alpha*n[1];      R[4] = alpha*n[0];      R[5] = 0.0;
968:   R[6] =  n[0];            R[7] = n[1];            R[8] = n[2];
969:   for (d = 0; d < dim; ++d) {
970:     x1p[d] = 0.0;
971:     x2p[d] = 0.0;
972:     for (e = 0; e < dim; ++e) {
973:       x1p[d] += R[d*dim+e]*x1[e];
974:       x2p[d] += R[d*dim+e]*x2[e];
975:     }
976:   }
977:   if (PetscAbsReal(x1p[2]) > 10. * PETSC_SMALL) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid rotation calculated");
978:   if (PetscAbsReal(x2p[2]) > 10. * PETSC_SMALL) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid rotation calculated");
979:   /* 2) Project to (x, y) */
980:   for (p = 3; p < coordSize/3; ++p) {
981:     for (d = 0; d < dim; ++d) {
982:       xnp[d] = 0.0;
983:       for (e = 0; e < dim; ++e) {
984:         xnp[d] += R[d*dim+e]*PetscRealPart(coords[p*dim+e] - coords[0*dim+e]);
985:       }
986:       if (d < dim-1) coords[p*2+d] = xnp[d];
987:     }
988:   }
989:   coords[0] = 0.0;
990:   coords[1] = 0.0;
991:   coords[2] = x1p[0];
992:   coords[3] = x1p[1];
993:   coords[4] = x2p[0];
994:   coords[5] = x2p[1];
995:   /* Output R^T which rotates \hat z to the input normal */
996:   for (d = 0; d < dim; ++d) {
997:     for (e = d+1; e < dim; ++e) {
998:       PetscReal tmp;

1000:       tmp        = R[d*dim+e];
1001:       R[d*dim+e] = R[e*dim+d];
1002:       R[e*dim+d] = tmp;
1003:     }
1004:   }
1005:   return(0);
1006: }

1008: PETSC_UNUSED
1009: PETSC_STATIC_INLINE void Volume_Triangle_Internal(PetscReal *vol, PetscReal coords[])
1010: {
1011:   /* Signed volume is 1/2 the determinant

1013:    |  1  1  1 |
1014:    | x0 x1 x2 |
1015:    | y0 y1 y2 |

1017:      but if x0,y0 is the origin, we have

1019:    | x1 x2 |
1020:    | y1 y2 |
1021:   */
1022:   const PetscReal x1 = coords[2] - coords[0], y1 = coords[3] - coords[1];
1023:   const PetscReal x2 = coords[4] - coords[0], y2 = coords[5] - coords[1];
1024:   PetscReal       M[4], detM;
1025:   M[0] = x1; M[1] = x2;
1026:   M[2] = y1; M[3] = y2;
1027:   DMPlex_Det2D_Internal(&detM, M);
1028:   *vol = 0.5*detM;
1029:   (void)PetscLogFlops(5.0);
1030: }

1032: PETSC_STATIC_INLINE void Volume_Triangle_Origin_Internal(PetscReal *vol, PetscReal coords[])
1033: {
1034:   DMPlex_Det2D_Internal(vol, coords);
1035:   *vol *= 0.5;
1036: }

1038: PETSC_UNUSED
1039: PETSC_STATIC_INLINE void Volume_Tetrahedron_Internal(PetscReal *vol, PetscReal coords[])
1040: {
1041:   /* Signed volume is 1/6th of the determinant

1043:    |  1  1  1  1 |
1044:    | x0 x1 x2 x3 |
1045:    | y0 y1 y2 y3 |
1046:    | z0 z1 z2 z3 |

1048:      but if x0,y0,z0 is the origin, we have

1050:    | x1 x2 x3 |
1051:    | y1 y2 y3 |
1052:    | z1 z2 z3 |
1053:   */
1054:   const PetscReal x1 = coords[3] - coords[0], y1 = coords[4]  - coords[1], z1 = coords[5]  - coords[2];
1055:   const PetscReal x2 = coords[6] - coords[0], y2 = coords[7]  - coords[1], z2 = coords[8]  - coords[2];
1056:   const PetscReal x3 = coords[9] - coords[0], y3 = coords[10] - coords[1], z3 = coords[11] - coords[2];
1057:   const PetscReal onesixth = ((PetscReal)1./(PetscReal)6.);
1058:   PetscReal       M[9], detM;
1059:   M[0] = x1; M[1] = x2; M[2] = x3;
1060:   M[3] = y1; M[4] = y2; M[5] = y3;
1061:   M[6] = z1; M[7] = z2; M[8] = z3;
1062:   DMPlex_Det3D_Internal(&detM, M);
1063:   *vol = -onesixth*detM;
1064:   (void)PetscLogFlops(10.0);
1065: }

1067: PETSC_STATIC_INLINE void Volume_Tetrahedron_Origin_Internal(PetscReal *vol, PetscReal coords[])
1068: {
1069:   const PetscReal onesixth = ((PetscReal)1./(PetscReal)6.);
1070:   DMPlex_Det3D_Internal(vol, coords);
1071:   *vol *= -onesixth;
1072: }

1074: static PetscErrorCode DMPlexComputePointGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1075: {
1076:   PetscSection   coordSection;
1077:   Vec            coordinates;
1078:   const PetscScalar *coords;
1079:   PetscInt       dim, d, off;

1083:   DMGetCoordinatesLocal(dm, &coordinates);
1084:   DMGetCoordinateSection(dm, &coordSection);
1085:   PetscSectionGetDof(coordSection,e,&dim);
1086:   if (!dim) return(0);
1087:   PetscSectionGetOffset(coordSection,e,&off);
1088:   VecGetArrayRead(coordinates,&coords);
1089:   if (v0) {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[off + d]);}
1090:   VecRestoreArrayRead(coordinates,&coords);
1091:   *detJ = 1.;
1092:   if (J) {
1093:     for (d = 0; d < dim * dim; d++) J[d] = 0.;
1094:     for (d = 0; d < dim; d++) J[d * dim + d] = 1.;
1095:     if (invJ) {
1096:       for (d = 0; d < dim * dim; d++) invJ[d] = 0.;
1097:       for (d = 0; d < dim; d++) invJ[d * dim + d] = 1.;
1098:     }
1099:   }
1100:   return(0);
1101: }

1103: static PetscErrorCode DMPlexComputeLineGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1104: {
1105:   PetscSection   coordSection;
1106:   Vec            coordinates;
1107:   PetscScalar   *coords = NULL;
1108:   PetscInt       numCoords, d, pStart, pEnd, numSelfCoords = 0;

1112:   DMGetCoordinatesLocal(dm, &coordinates);
1113:   DMGetCoordinateSection(dm, &coordSection);
1114:   PetscSectionGetChart(coordSection,&pStart,&pEnd);
1115:   if (e >= pStart && e < pEnd) {PetscSectionGetDof(coordSection,e,&numSelfCoords);}
1116:   DMPlexVecGetClosure(dm, coordSection, coordinates, e, &numCoords, &coords);
1117:   numCoords = numSelfCoords ? numSelfCoords : numCoords;
1118:   if (invJ && !J) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
1119:   *detJ = 0.0;
1120:   if (numCoords == 6) {
1121:     const PetscInt dim = 3;
1122:     PetscReal      R[9], J0;

1124:     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
1125:     DMPlexComputeProjection3Dto1D(coords, R);
1126:     if (J)    {
1127:       J0   = 0.5*PetscRealPart(coords[1]);
1128:       J[0] = R[0]*J0; J[1] = R[1]; J[2] = R[2];
1129:       J[3] = R[3]*J0; J[4] = R[4]; J[5] = R[5];
1130:       J[6] = R[6]*J0; J[7] = R[7]; J[8] = R[8];
1131:       DMPlex_Det3D_Internal(detJ, J);
1132:       if (invJ) {DMPlex_Invert2D_Internal(invJ, J, *detJ);}
1133:     }
1134:   } else if (numCoords == 4) {
1135:     const PetscInt dim = 2;
1136:     PetscReal      R[4], J0;

1138:     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
1139:     DMPlexComputeProjection2Dto1D(coords, R);
1140:     if (J)    {
1141:       J0   = 0.5*PetscRealPart(coords[1]);
1142:       J[0] = R[0]*J0; J[1] = R[1];
1143:       J[2] = R[2]*J0; J[3] = R[3];
1144:       DMPlex_Det2D_Internal(detJ, J);
1145:       if (invJ) {DMPlex_Invert2D_Internal(invJ, J, *detJ);}
1146:     }
1147:   } else if (numCoords == 2) {
1148:     const PetscInt dim = 1;

1150:     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
1151:     if (J)    {
1152:       J[0]  = 0.5*(PetscRealPart(coords[1]) - PetscRealPart(coords[0]));
1153:       *detJ = J[0];
1154:       PetscLogFlops(2.0);
1155:       if (invJ) {invJ[0] = 1.0/J[0]; PetscLogFlops(1.0);}
1156:     }
1157:   } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this segment is %D != 2", numCoords);
1158:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, &numCoords, &coords);
1159:   return(0);
1160: }

1162: static PetscErrorCode DMPlexComputeTriangleGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1163: {
1164:   PetscSection   coordSection;
1165:   Vec            coordinates;
1166:   PetscScalar   *coords = NULL;
1167:   PetscInt       numCoords, numSelfCoords = 0, d, f, g, pStart, pEnd;

1171:   DMGetCoordinatesLocal(dm, &coordinates);
1172:   DMGetCoordinateSection(dm, &coordSection);
1173:   PetscSectionGetChart(coordSection,&pStart,&pEnd);
1174:   if (e >= pStart && e < pEnd) {PetscSectionGetDof(coordSection,e,&numSelfCoords);}
1175:   DMPlexVecGetClosure(dm, coordSection, coordinates, e, &numCoords, &coords);
1176:   numCoords = numSelfCoords ? numSelfCoords : numCoords;
1177:   *detJ = 0.0;
1178:   if (numCoords == 9) {
1179:     const PetscInt dim = 3;
1180:     PetscReal      R[9], J0[9] = {1.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,1.0};

1182:     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
1183:     DMPlexComputeProjection3Dto2D(numCoords, coords, R);
1184:     if (J)    {
1185:       const PetscInt pdim = 2;

1187:       for (d = 0; d < pdim; d++) {
1188:         for (f = 0; f < pdim; f++) {
1189:           J0[d*dim+f] = 0.5*(PetscRealPart(coords[(f+1)*pdim+d]) - PetscRealPart(coords[0*pdim+d]));
1190:         }
1191:       }
1192:       PetscLogFlops(8.0);
1193:       DMPlex_Det3D_Internal(detJ, J0);
1194:       for (d = 0; d < dim; d++) {
1195:         for (f = 0; f < dim; f++) {
1196:           J[d*dim+f] = 0.0;
1197:           for (g = 0; g < dim; g++) {
1198:             J[d*dim+f] += R[d*dim+g]*J0[g*dim+f];
1199:           }
1200:         }
1201:       }
1202:       PetscLogFlops(18.0);
1203:     }
1204:     if (invJ) {DMPlex_Invert3D_Internal(invJ, J, *detJ);}
1205:   } else if (numCoords == 6) {
1206:     const PetscInt dim = 2;

1208:     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
1209:     if (J)    {
1210:       for (d = 0; d < dim; d++) {
1211:         for (f = 0; f < dim; f++) {
1212:           J[d*dim+f] = 0.5*(PetscRealPart(coords[(f+1)*dim+d]) - PetscRealPart(coords[0*dim+d]));
1213:         }
1214:       }
1215:       PetscLogFlops(8.0);
1216:       DMPlex_Det2D_Internal(detJ, J);
1217:     }
1218:     if (invJ) {DMPlex_Invert2D_Internal(invJ, J, *detJ);}
1219:   } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this triangle is %D != 6 or 9", numCoords);
1220:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, &numCoords, &coords);
1221:   return(0);
1222: }

1224: static PetscErrorCode DMPlexComputeRectangleGeometry_Internal(DM dm, PetscInt e, PetscInt Nq, const PetscReal points[], PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1225: {
1226:   PetscSection   coordSection;
1227:   Vec            coordinates;
1228:   PetscScalar   *coords = NULL;
1229:   PetscInt       numCoords, numSelfCoords = 0, d, f, g, pStart, pEnd;

1233:   DMGetCoordinatesLocal(dm, &coordinates);
1234:   DMGetCoordinateSection(dm, &coordSection);
1235:   PetscSectionGetChart(coordSection,&pStart,&pEnd);
1236:   if (e >= pStart && e < pEnd) {PetscSectionGetDof(coordSection,e,&numSelfCoords);}
1237:   DMPlexVecGetClosure(dm, coordSection, coordinates, e, &numCoords, &coords);
1238:   numCoords = numSelfCoords ? numSelfCoords : numCoords;
1239:   if (!Nq) {
1240:     *detJ = 0.0;
1241:     if (numCoords == 12) {
1242:       const PetscInt dim = 3;
1243:       PetscReal      R[9], J0[9] = {1.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,1.0};

1245:       if (v)   {for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);}
1246:       DMPlexComputeProjection3Dto2D(numCoords, coords, R);
1247:       if (J)    {
1248:         const PetscInt pdim = 2;

1250:         for (d = 0; d < pdim; d++) {
1251:           J0[d*dim+0] = 0.5*(PetscRealPart(coords[1*pdim+d]) - PetscRealPart(coords[0*pdim+d]));
1252:           J0[d*dim+1] = 0.5*(PetscRealPart(coords[2*pdim+d]) - PetscRealPart(coords[1*pdim+d]));
1253:         }
1254:         PetscLogFlops(8.0);
1255:         DMPlex_Det3D_Internal(detJ, J0);
1256:         for (d = 0; d < dim; d++) {
1257:           for (f = 0; f < dim; f++) {
1258:             J[d*dim+f] = 0.0;
1259:             for (g = 0; g < dim; g++) {
1260:               J[d*dim+f] += R[d*dim+g]*J0[g*dim+f];
1261:             }
1262:           }
1263:         }
1264:         PetscLogFlops(18.0);
1265:       }
1266:       if (invJ) {DMPlex_Invert3D_Internal(invJ, J, *detJ);}
1267:     } else if (numCoords == 8) {
1268:       const PetscInt dim = 2;

1270:       if (v)   {for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);}
1271:       if (J)    {
1272:         for (d = 0; d < dim; d++) {
1273:           J[d*dim+0] = 0.5*(PetscRealPart(coords[1*dim+d]) - PetscRealPart(coords[0*dim+d]));
1274:           J[d*dim+1] = 0.5*(PetscRealPart(coords[3*dim+d]) - PetscRealPart(coords[0*dim+d]));
1275:         }
1276:         PetscLogFlops(8.0);
1277:         DMPlex_Det2D_Internal(detJ, J);
1278:       }
1279:       if (invJ) {DMPlex_Invert2D_Internal(invJ, J, *detJ);}
1280:     } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this quadrilateral is %D != 8 or 12", numCoords);
1281:   } else {
1282:     const PetscInt Nv = 4;
1283:     const PetscInt dimR = 2;
1284:     const PetscInt zToPlex[4] = {0, 1, 3, 2};
1285:     PetscReal zOrder[12];
1286:     PetscReal zCoeff[12];
1287:     PetscInt  i, j, k, l, dim;

1289:     if (numCoords == 12) {
1290:       dim = 3;
1291:     } else if (numCoords == 8) {
1292:       dim = 2;
1293:     } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this quadrilateral is %D != 8 or 12", numCoords);
1294:     for (i = 0; i < Nv; i++) {
1295:       PetscInt zi = zToPlex[i];

1297:       for (j = 0; j < dim; j++) {
1298:         zOrder[dim * i + j] = PetscRealPart(coords[dim * zi + j]);
1299:       }
1300:     }
1301:     for (j = 0; j < dim; j++) {
1302:       zCoeff[dim * 0 + j] = 0.25 * (  zOrder[dim * 0 + j] + zOrder[dim * 1 + j] + zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
1303:       zCoeff[dim * 1 + j] = 0.25 * (- zOrder[dim * 0 + j] + zOrder[dim * 1 + j] - zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
1304:       zCoeff[dim * 2 + j] = 0.25 * (- zOrder[dim * 0 + j] - zOrder[dim * 1 + j] + zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
1305:       zCoeff[dim * 3 + j] = 0.25 * (  zOrder[dim * 0 + j] - zOrder[dim * 1 + j] - zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
1306:     }
1307:     for (i = 0; i < Nq; i++) {
1308:       PetscReal xi = points[dimR * i], eta = points[dimR * i + 1];

1310:       if (v) {
1311:         PetscReal extPoint[4];

1313:         extPoint[0] = 1.;
1314:         extPoint[1] = xi;
1315:         extPoint[2] = eta;
1316:         extPoint[3] = xi * eta;
1317:         for (j = 0; j < dim; j++) {
1318:           PetscReal val = 0.;

1320:           for (k = 0; k < Nv; k++) {
1321:             val += extPoint[k] * zCoeff[dim * k + j];
1322:           }
1323:           v[i * dim + j] = val;
1324:         }
1325:       }
1326:       if (J) {
1327:         PetscReal extJ[8];

1329:         extJ[0] = 0.;
1330:         extJ[1] = 0.;
1331:         extJ[2] = 1.;
1332:         extJ[3] = 0.;
1333:         extJ[4] = 0.;
1334:         extJ[5] = 1.;
1335:         extJ[6] = eta;
1336:         extJ[7] = xi;
1337:         for (j = 0; j < dim; j++) {
1338:           for (k = 0; k < dimR; k++) {
1339:             PetscReal val = 0.;

1341:             for (l = 0; l < Nv; l++) {
1342:               val += zCoeff[dim * l + j] * extJ[dimR * l + k];
1343:             }
1344:             J[i * dim * dim + dim * j + k] = val;
1345:           }
1346:         }
1347:         if (dim == 3) { /* put the cross product in the third component of the Jacobian */
1348:           PetscReal x, y, z;
1349:           PetscReal *iJ = &J[i * dim * dim];
1350:           PetscReal norm;

1352:           x = iJ[1 * dim + 0] * iJ[2 * dim + 1] - iJ[1 * dim + 1] * iJ[2 * dim + 0];
1353:           y = iJ[0 * dim + 1] * iJ[2 * dim + 0] - iJ[0 * dim + 0] * iJ[2 * dim + 1];
1354:           z = iJ[0 * dim + 0] * iJ[1 * dim + 1] - iJ[0 * dim + 1] * iJ[1 * dim + 0];
1355:           norm = PetscSqrtReal(x * x + y * y + z * z);
1356:           iJ[2] = x / norm;
1357:           iJ[5] = y / norm;
1358:           iJ[8] = z / norm;
1359:           DMPlex_Det3D_Internal(&detJ[i], &J[i * dim * dim]);
1360:           if (invJ) {DMPlex_Invert3D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);}
1361:         } else {
1362:           DMPlex_Det2D_Internal(&detJ[i], &J[i * dim * dim]);
1363:           if (invJ) {DMPlex_Invert2D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);}
1364:         }
1365:       }
1366:     }
1367:   }
1368:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, &numCoords, &coords);
1369:   return(0);
1370: }

1372: static PetscErrorCode DMPlexComputeTetrahedronGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1373: {
1374:   PetscSection   coordSection;
1375:   Vec            coordinates;
1376:   PetscScalar   *coords = NULL;
1377:   const PetscInt dim = 3;
1378:   PetscInt       d;

1382:   DMGetCoordinatesLocal(dm, &coordinates);
1383:   DMGetCoordinateSection(dm, &coordSection);
1384:   DMPlexVecGetClosure(dm, coordSection, coordinates, e, NULL, &coords);
1385:   *detJ = 0.0;
1386:   if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
1387:   if (J)    {
1388:     for (d = 0; d < dim; d++) {
1389:       /* I orient with outward face normals */
1390:       J[d*dim+0] = 0.5*(PetscRealPart(coords[2*dim+d]) - PetscRealPart(coords[0*dim+d]));
1391:       J[d*dim+1] = 0.5*(PetscRealPart(coords[1*dim+d]) - PetscRealPart(coords[0*dim+d]));
1392:       J[d*dim+2] = 0.5*(PetscRealPart(coords[3*dim+d]) - PetscRealPart(coords[0*dim+d]));
1393:     }
1394:     PetscLogFlops(18.0);
1395:     DMPlex_Det3D_Internal(detJ, J);
1396:   }
1397:   if (invJ) {DMPlex_Invert3D_Internal(invJ, J, *detJ);}
1398:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, NULL, &coords);
1399:   return(0);
1400: }

1402: static PetscErrorCode DMPlexComputeHexahedronGeometry_Internal(DM dm, PetscInt e, PetscInt Nq, const PetscReal points[], PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1403: {
1404:   PetscSection   coordSection;
1405:   Vec            coordinates;
1406:   PetscScalar   *coords = NULL;
1407:   const PetscInt dim = 3;
1408:   PetscInt       d;

1412:   DMGetCoordinatesLocal(dm, &coordinates);
1413:   DMGetCoordinateSection(dm, &coordSection);
1414:   DMPlexVecGetClosure(dm, coordSection, coordinates, e, NULL, &coords);
1415:   if (!Nq) {
1416:     *detJ = 0.0;
1417:     if (v)   {for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);}
1418:     if (J)    {
1419:       for (d = 0; d < dim; d++) {
1420:         J[d*dim+0] = 0.5*(PetscRealPart(coords[3*dim+d]) - PetscRealPart(coords[0*dim+d]));
1421:         J[d*dim+1] = 0.5*(PetscRealPart(coords[1*dim+d]) - PetscRealPart(coords[0*dim+d]));
1422:         J[d*dim+2] = 0.5*(PetscRealPart(coords[4*dim+d]) - PetscRealPart(coords[0*dim+d]));
1423:       }
1424:       PetscLogFlops(18.0);
1425:       DMPlex_Det3D_Internal(detJ, J);
1426:     }
1427:     if (invJ) {DMPlex_Invert3D_Internal(invJ, J, *detJ);}
1428:   } else {
1429:     const PetscInt Nv = 8;
1430:     const PetscInt zToPlex[8] = {0, 3, 1, 2, 4, 5, 7, 6};
1431:     const PetscInt dim = 3;
1432:     const PetscInt dimR = 3;
1433:     PetscReal zOrder[24];
1434:     PetscReal zCoeff[24];
1435:     PetscInt  i, j, k, l;

1437:     for (i = 0; i < Nv; i++) {
1438:       PetscInt zi = zToPlex[i];

1440:       for (j = 0; j < dim; j++) {
1441:         zOrder[dim * i + j] = PetscRealPart(coords[dim * zi + j]);
1442:       }
1443:     }
1444:     for (j = 0; j < dim; j++) {
1445:       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]);
1446:       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]);
1447:       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]);
1448:       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]);
1449:       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]);
1450:       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]);
1451:       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]);
1452:       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]);
1453:     }
1454:     for (i = 0; i < Nq; i++) {
1455:       PetscReal xi = points[dimR * i], eta = points[dimR * i + 1], theta = points[dimR * i + 2];

1457:       if (v) {
1458:         PetscReal extPoint[8];

1460:         extPoint[0] = 1.;
1461:         extPoint[1] = xi;
1462:         extPoint[2] = eta;
1463:         extPoint[3] = xi * eta;
1464:         extPoint[4] = theta;
1465:         extPoint[5] = theta * xi;
1466:         extPoint[6] = theta * eta;
1467:         extPoint[7] = theta * eta * xi;
1468:         for (j = 0; j < dim; j++) {
1469:           PetscReal val = 0.;

1471:           for (k = 0; k < Nv; k++) {
1472:             val += extPoint[k] * zCoeff[dim * k + j];
1473:           }
1474:           v[i * dim + j] = val;
1475:         }
1476:       }
1477:       if (J) {
1478:         PetscReal extJ[24];

1480:         extJ[0]  = 0.         ; extJ[1]  = 0.        ; extJ[2]  = 0.      ;
1481:         extJ[3]  = 1.         ; extJ[4]  = 0.        ; extJ[5]  = 0.      ;
1482:         extJ[6]  = 0.         ; extJ[7]  = 1.        ; extJ[8]  = 0.      ;
1483:         extJ[9]  = eta        ; extJ[10] = xi        ; extJ[11] = 0.      ;
1484:         extJ[12] = 0.         ; extJ[13] = 0.        ; extJ[14] = 1.      ;
1485:         extJ[15] = theta      ; extJ[16] = 0.        ; extJ[17] = xi      ;
1486:         extJ[18] = 0.         ; extJ[19] = theta     ; extJ[20] = eta     ;
1487:         extJ[21] = theta * eta; extJ[22] = theta * xi; extJ[23] = eta * xi;

1489:         for (j = 0; j < dim; j++) {
1490:           for (k = 0; k < dimR; k++) {
1491:             PetscReal val = 0.;

1493:             for (l = 0; l < Nv; l++) {
1494:               val += zCoeff[dim * l + j] * extJ[dimR * l + k];
1495:             }
1496:             J[i * dim * dim + dim * j + k] = val;
1497:           }
1498:         }
1499:         DMPlex_Det3D_Internal(&detJ[i], &J[i * dim * dim]);
1500:         if (invJ) {DMPlex_Invert3D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);}
1501:       }
1502:     }
1503:   }
1504:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, NULL, &coords);
1505:   return(0);
1506: }

1508: static PetscErrorCode DMPlexComputeCellGeometryFEM_Implicit(DM dm, PetscInt cell, PetscQuadrature quad, PetscReal *v, PetscReal *J, PetscReal *invJ, PetscReal *detJ)
1509: {
1510:   PetscInt        depth, dim, coordDim, coneSize, i;
1511:   PetscInt        Nq = 0;
1512:   const PetscReal *points = NULL;
1513:   DMLabel         depthLabel;
1514:   PetscReal       xi0[3] = {-1.,-1.,-1.}, v0[3], J0[9], detJ0;
1515:   PetscBool       isAffine = PETSC_TRUE;
1516:   PetscErrorCode  ierr;

1519:   DMPlexGetDepth(dm, &depth);
1520:   DMPlexGetConeSize(dm, cell, &coneSize);
1521:   DMPlexGetDepthLabel(dm, &depthLabel);
1522:   DMLabelGetValue(depthLabel, cell, &dim);
1523:   if (depth == 1 && dim == 1) {
1524:     DMGetDimension(dm, &dim);
1525:   }
1526:   DMGetCoordinateDim(dm, &coordDim);
1527:   if (coordDim > 3) SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported coordinate dimension %D > 3", coordDim);
1528:   if (quad) {PetscQuadratureGetData(quad, NULL, NULL, &Nq, &points, NULL);}
1529:   switch (dim) {
1530:   case 0:
1531:     DMPlexComputePointGeometry_Internal(dm, cell, v, J, invJ, detJ);
1532:     isAffine = PETSC_FALSE;
1533:     break;
1534:   case 1:
1535:     if (Nq) {
1536:       DMPlexComputeLineGeometry_Internal(dm, cell, v0, J0, NULL, &detJ0);
1537:     } else {
1538:       DMPlexComputeLineGeometry_Internal(dm, cell, v, J, invJ, detJ);
1539:     }
1540:     break;
1541:   case 2:
1542:     switch (coneSize) {
1543:     case 3:
1544:       if (Nq) {
1545:         DMPlexComputeTriangleGeometry_Internal(dm, cell, v0, J0, NULL, &detJ0);
1546:       } else {
1547:         DMPlexComputeTriangleGeometry_Internal(dm, cell, v, J, invJ, detJ);
1548:       }
1549:       break;
1550:     case 4:
1551:       DMPlexComputeRectangleGeometry_Internal(dm, cell, Nq, points, v, J, invJ, detJ);
1552:       isAffine = PETSC_FALSE;
1553:       break;
1554:     default:
1555:       SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported number of faces %D in cell %D for element geometry computation", coneSize, cell);
1556:     }
1557:     break;
1558:   case 3:
1559:     switch (coneSize) {
1560:     case 4:
1561:       if (Nq) {
1562:         DMPlexComputeTetrahedronGeometry_Internal(dm, cell, v0, J0, NULL, &detJ0);
1563:       } else {
1564:         DMPlexComputeTetrahedronGeometry_Internal(dm, cell, v, J, invJ, detJ);
1565:       }
1566:       break;
1567:     case 6: /* Faces */
1568:     case 8: /* Vertices */
1569:       DMPlexComputeHexahedronGeometry_Internal(dm, cell, Nq, points, v, J, invJ, detJ);
1570:       isAffine = PETSC_FALSE;
1571:       break;
1572:     default:
1573:       SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported number of faces %D in cell %D for element geometry computation", coneSize, cell);
1574:     }
1575:     break;
1576:   default:
1577:     SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported dimension %D for element geometry computation", dim);
1578:   }
1579:   if (isAffine && Nq) {
1580:     if (v) {
1581:       for (i = 0; i < Nq; i++) {
1582:         CoordinatesRefToReal(coordDim, dim, xi0, v0, J0, &points[dim * i], &v[coordDim * i]);
1583:       }
1584:     }
1585:     if (detJ) {
1586:       for (i = 0; i < Nq; i++) {
1587:         detJ[i] = detJ0;
1588:       }
1589:     }
1590:     if (J) {
1591:       PetscInt k;

1593:       for (i = 0, k = 0; i < Nq; i++) {
1594:         PetscInt j;

1596:         for (j = 0; j < coordDim * coordDim; j++, k++) {
1597:           J[k] = J0[j];
1598:         }
1599:       }
1600:     }
1601:     if (invJ) {
1602:       PetscInt k;
1603:       switch (coordDim) {
1604:       case 0:
1605:         break;
1606:       case 1:
1607:         invJ[0] = 1./J0[0];
1608:         break;
1609:       case 2:
1610:         DMPlex_Invert2D_Internal(invJ, J0, detJ0);
1611:         break;
1612:       case 3:
1613:         DMPlex_Invert3D_Internal(invJ, J0, detJ0);
1614:         break;
1615:       }
1616:       for (i = 1, k = coordDim * coordDim; i < Nq; i++) {
1617:         PetscInt j;

1619:         for (j = 0; j < coordDim * coordDim; j++, k++) {
1620:           invJ[k] = invJ[j];
1621:         }
1622:       }
1623:     }
1624:   }
1625:   return(0);
1626: }

1628: /*@C
1629:   DMPlexComputeCellGeometryAffineFEM - Assuming an affine map, compute the Jacobian, inverse Jacobian, and Jacobian determinant for a given cell

1631:   Collective on dm

1633:   Input Arguments:
1634: + dm   - the DM
1635: - cell - the cell

1637:   Output Arguments:
1638: + v0   - the translation part of this affine transform
1639: . J    - the Jacobian of the transform from the reference element
1640: . invJ - the inverse of the Jacobian
1641: - detJ - the Jacobian determinant

1643:   Level: advanced

1645:   Fortran Notes:
1646:   Since it returns arrays, this routine is only available in Fortran 90, and you must
1647:   include petsc.h90 in your code.

1649: .seealso: DMPlexComputeCellGeometryFEM(), DMGetCoordinateSection(), DMGetCoordinates()
1650: @*/
1651: PetscErrorCode DMPlexComputeCellGeometryAffineFEM(DM dm, PetscInt cell, PetscReal *v0, PetscReal *J, PetscReal *invJ, PetscReal *detJ)
1652: {

1656:   DMPlexComputeCellGeometryFEM_Implicit(dm,cell,NULL,v0,J,invJ,detJ);
1657:   return(0);
1658: }

1660: static PetscErrorCode DMPlexComputeCellGeometryFEM_FE(DM dm, PetscFE fe, PetscInt point, PetscQuadrature quad, PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1661: {
1662:   PetscQuadrature  feQuad;
1663:   PetscSection     coordSection;
1664:   Vec              coordinates;
1665:   PetscScalar     *coords = NULL;
1666:   const PetscReal *quadPoints;
1667:   PetscReal       *basisDer, *basis, detJt;
1668:   PetscInt         dim, cdim, pdim, qdim, Nq, numCoords, q;
1669:   PetscErrorCode   ierr;

1672:   DMGetCoordinatesLocal(dm, &coordinates);
1673:   DMGetCoordinateSection(dm, &coordSection);
1674:   DMPlexVecGetClosure(dm, coordSection, coordinates, point, &numCoords, &coords);
1675:   DMGetDimension(dm, &dim);
1676:   DMGetCoordinateDim(dm, &cdim);
1677:   if (!quad) { /* use the first point of the first functional of the dual space */
1678:     PetscDualSpace dsp;

1680:     PetscFEGetDualSpace(fe, &dsp);
1681:     PetscDualSpaceGetFunctional(dsp, 0, &quad);
1682:     PetscQuadratureGetData(quad, &qdim, NULL, &Nq, &quadPoints, NULL);
1683:     Nq = 1;
1684:   } else {
1685:     PetscQuadratureGetData(quad, &qdim, NULL, &Nq, &quadPoints, NULL);
1686:   }
1687:   PetscFEGetDimension(fe, &pdim);
1688:   PetscFEGetQuadrature(fe, &feQuad);
1689:   if (feQuad == quad) {
1690:     PetscFEGetDefaultTabulation(fe, &basis, J ? &basisDer : NULL, NULL);
1691:     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);
1692:   } else {
1693:     PetscFEGetTabulation(fe, Nq, quadPoints, &basis, J ? &basisDer : NULL, NULL);
1694:   }
1695:   if (qdim != dim) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Point dimension %d != quadrature dimension %d", dim, qdim);
1696:   if (v) {
1697:     PetscArrayzero(v, Nq*cdim);
1698:     for (q = 0; q < Nq; ++q) {
1699:       PetscInt i, k;

1701:       for (k = 0; k < pdim; ++k)
1702:         for (i = 0; i < cdim; ++i)
1703:           v[q*cdim + i] += basis[q*pdim + k] * PetscRealPart(coords[k*cdim + i]);
1704:       PetscLogFlops(2.0*pdim*cdim);
1705:     }
1706:   }
1707:   if (J) {
1708:     PetscArrayzero(J, Nq*cdim*cdim);
1709:     for (q = 0; q < Nq; ++q) {
1710:       PetscInt i, j, k, c, r;

1712:       /* J = dx_i/d\xi_j = sum[k=0,n-1] dN_k/d\xi_j * x_i(k) */
1713:       for (k = 0; k < pdim; ++k)
1714:         for (j = 0; j < dim; ++j)
1715:           for (i = 0; i < cdim; ++i)
1716:             J[(q*cdim + i)*cdim + j] += basisDer[(q*pdim + k)*dim + j] * PetscRealPart(coords[k*cdim + i]);
1717:       PetscLogFlops(2.0*pdim*dim*cdim);
1718:       if (cdim > dim) {
1719:         for (c = dim; c < cdim; ++c)
1720:           for (r = 0; r < cdim; ++r)
1721:             J[r*cdim+c] = r == c ? 1.0 : 0.0;
1722:       }
1723:       if (!detJ && !invJ) continue;
1724:       detJt = 0.;
1725:       switch (cdim) {
1726:       case 3:
1727:         DMPlex_Det3D_Internal(&detJt, &J[q*cdim*dim]);
1728:         if (invJ) {DMPlex_Invert3D_Internal(&invJ[q*cdim*dim], &J[q*cdim*dim], detJt);}
1729:         break;
1730:       case 2:
1731:         DMPlex_Det2D_Internal(&detJt, &J[q*cdim*dim]);
1732:         if (invJ) {DMPlex_Invert2D_Internal(&invJ[q*cdim*dim], &J[q*cdim*dim], detJt);}
1733:         break;
1734:       case 1:
1735:         detJt = J[q*cdim*dim];
1736:         if (invJ) invJ[q*cdim*dim] = 1.0/detJt;
1737:       }
1738:       if (detJ) detJ[q] = detJt;
1739:     }
1740:   }
1741:   else if (detJ || invJ) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Need J to compute invJ or detJ");
1742:   if (feQuad != quad) {
1743:     PetscFERestoreTabulation(fe, Nq, quadPoints, &basis, J ? &basisDer : NULL, NULL);
1744:   }
1745:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, point, &numCoords, &coords);
1746:   return(0);
1747: }

1749: /*@C
1750:   DMPlexComputeCellGeometryFEM - Compute the Jacobian, inverse Jacobian, and Jacobian determinant at each quadrature point in the given cell

1752:   Collective on dm

1754:   Input Arguments:
1755: + dm   - the DM
1756: . cell - the cell
1757: - quad - the quadrature containing the points in the reference element where the geometry will be evaluated.  If quad == NULL, geometry will be
1758:          evaluated at the first vertex of the reference element

1760:   Output Arguments:
1761: + v    - the image of the transformed quadrature points, otherwise the image of the first vertex in the closure of the reference element
1762: . J    - the Jacobian of the transform from the reference element at each quadrature point
1763: . invJ - the inverse of the Jacobian at each quadrature point
1764: - detJ - the Jacobian determinant at each quadrature point

1766:   Level: advanced

1768:   Fortran Notes:
1769:   Since it returns arrays, this routine is only available in Fortran 90, and you must
1770:   include petsc.h90 in your code.

1772: .seealso: DMGetCoordinateSection(), DMGetCoordinates()
1773: @*/
1774: PetscErrorCode DMPlexComputeCellGeometryFEM(DM dm, PetscInt cell, PetscQuadrature quad, PetscReal *v, PetscReal *J, PetscReal *invJ, PetscReal *detJ)
1775: {
1776:   DM             cdm;
1777:   PetscFE        fe = NULL;

1782:   DMGetCoordinateDM(dm, &cdm);
1783:   if (cdm) {
1784:     PetscClassId id;
1785:     PetscInt     numFields;
1786:     PetscDS      prob;
1787:     PetscObject  disc;

1789:     DMGetNumFields(cdm, &numFields);
1790:     if (numFields) {
1791:       DMGetDS(cdm, &prob);
1792:       PetscDSGetDiscretization(prob,0,&disc);
1793:       PetscObjectGetClassId(disc,&id);
1794:       if (id == PETSCFE_CLASSID) {
1795:         fe = (PetscFE) disc;
1796:       }
1797:     }
1798:   }
1799:   if (!fe) {DMPlexComputeCellGeometryFEM_Implicit(dm, cell, quad, v, J, invJ, detJ);}
1800:   else     {DMPlexComputeCellGeometryFEM_FE(dm, fe, cell, quad, v, J, invJ, detJ);}
1801:   return(0);
1802: }

1804: static PetscErrorCode DMPlexComputeGeometryFVM_1D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
1805: {
1806:   PetscSection   coordSection;
1807:   Vec            coordinates;
1808:   PetscScalar   *coords = NULL;
1809:   PetscScalar    tmp[2];
1810:   PetscInt       coordSize;

1814:   DMGetCoordinatesLocal(dm, &coordinates);
1815:   DMGetCoordinateSection(dm, &coordSection);
1816:   DMPlexVecGetClosure(dm, coordSection, coordinates, cell, &coordSize, &coords);
1817:   if (dim != 2) SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "We only support 2D edges right now");
1818:   DMLocalizeCoordinate_Internal(dm, dim, coords, &coords[dim], tmp);
1819:   if (centroid) {
1820:     centroid[0] = 0.5*PetscRealPart(coords[0] + tmp[0]);
1821:     centroid[1] = 0.5*PetscRealPart(coords[1] + tmp[1]);
1822:   }
1823:   if (normal) {
1824:     PetscReal norm;

1826:     normal[0]  = -PetscRealPart(coords[1] - tmp[1]);
1827:     normal[1]  =  PetscRealPart(coords[0] - tmp[0]);
1828:     norm       = PetscSqrtReal(normal[0]*normal[0] + normal[1]*normal[1]);
1829:     normal[0] /= norm;
1830:     normal[1] /= norm;
1831:   }
1832:   if (vol) {
1833:     *vol = PetscSqrtReal(PetscSqr(PetscRealPart(coords[0] - tmp[0])) + PetscSqr(PetscRealPart(coords[1] - tmp[1])));
1834:   }
1835:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, cell, &coordSize, &coords);
1836:   return(0);
1837: }

1839: /* Centroid_i = (\sum_n A_n Cn_i ) / A */
1840: static PetscErrorCode DMPlexComputeGeometryFVM_2D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
1841: {
1842:   DMLabel        depth;
1843:   PetscSection   coordSection;
1844:   Vec            coordinates;
1845:   PetscScalar   *coords = NULL;
1846:   PetscReal      vsum = 0.0, csum[3] = {0.0, 0.0, 0.0}, vtmp, ctmp[4], v0[3], R[9];
1847:   PetscBool      isHybrid = PETSC_FALSE;
1848:   PetscInt       fv[4] = {0, 1, 2, 3};
1849:   PetscInt       cdepth, pEndInterior[4], tdim = 2, coordSize, numCorners, p, d, e;

1853:   /* Must check for hybrid cells because prisms have a different orientation scheme */
1854:   DMPlexGetDepthLabel(dm, &depth);
1855:   DMLabelGetValue(depth, cell, &cdepth);
1856:   DMPlexGetHybridBounds(dm, &pEndInterior[3], &pEndInterior[2], &pEndInterior[1], &pEndInterior[0]);
1857:   if ((pEndInterior[cdepth]) >=0 && (cell >= pEndInterior[cdepth])) isHybrid = PETSC_TRUE;

1859:   DMGetCoordinatesLocal(dm, &coordinates);
1860:   DMPlexGetConeSize(dm, cell, &numCorners);
1861:   DMGetCoordinateSection(dm, &coordSection);
1862:   DMPlexVecGetClosure(dm, coordSection, coordinates, cell, &coordSize, &coords);
1863:   DMGetCoordinateDim(dm, &dim);
1864:   /* Side faces for hybrid cells are are stored as tensor products */
1865:   if (isHybrid && numCorners == 4) {fv[2] = 3; fv[3] = 2;}

1867:   if (dim > 2 && centroid) {
1868:     v0[0] = PetscRealPart(coords[0]);
1869:     v0[1] = PetscRealPart(coords[1]);
1870:     v0[2] = PetscRealPart(coords[2]);
1871:   }
1872:   if (normal) {
1873:     if (dim > 2) {
1874:       const PetscReal x0 = PetscRealPart(coords[dim*fv[1]+0] - coords[0]), x1 = PetscRealPart(coords[dim*fv[2]+0] - coords[0]);
1875:       const PetscReal y0 = PetscRealPart(coords[dim*fv[1]+1] - coords[1]), y1 = PetscRealPart(coords[dim*fv[2]+1] - coords[1]);
1876:       const PetscReal z0 = PetscRealPart(coords[dim*fv[1]+2] - coords[2]), z1 = PetscRealPart(coords[dim*fv[2]+2] - coords[2]);
1877:       PetscReal       norm;

1879:       normal[0] = y0*z1 - z0*y1;
1880:       normal[1] = z0*x1 - x0*z1;
1881:       normal[2] = x0*y1 - y0*x1;
1882:       norm = PetscSqrtReal(normal[0]*normal[0] + normal[1]*normal[1] + normal[2]*normal[2]);
1883:       normal[0] /= norm;
1884:       normal[1] /= norm;
1885:       normal[2] /= norm;
1886:     } else {
1887:       for (d = 0; d < dim; ++d) normal[d] = 0.0;
1888:     }
1889:   }
1890:   if (dim == 3) {DMPlexComputeProjection3Dto2D(coordSize, coords, R);}
1891:   for (p = 0; p < numCorners; ++p) {
1892:     const PetscInt pi  = p < 4 ? fv[p] : p;
1893:     const PetscInt pin = p < 3 ? fv[(p+1)%numCorners] : (p+1)%numCorners;
1894:     /* Need to do this copy to get types right */
1895:     for (d = 0; d < tdim; ++d) {
1896:       ctmp[d]      = PetscRealPart(coords[pi*tdim+d]);
1897:       ctmp[tdim+d] = PetscRealPart(coords[pin*tdim+d]);
1898:     }
1899:     Volume_Triangle_Origin_Internal(&vtmp, ctmp);
1900:     vsum += vtmp;
1901:     for (d = 0; d < tdim; ++d) {
1902:       csum[d] += (ctmp[d] + ctmp[tdim+d])*vtmp;
1903:     }
1904:   }
1905:   for (d = 0; d < tdim; ++d) {
1906:     csum[d] /= (tdim+1)*vsum;
1907:   }
1908:   DMPlexVecRestoreClosure(dm, coordSection, coordinates, cell, &coordSize, &coords);
1909:   if (vol) *vol = PetscAbsReal(vsum);
1910:   if (centroid) {
1911:     if (dim > 2) {
1912:       for (d = 0; d < dim; ++d) {
1913:         centroid[d] = v0[d];
1914:         for (e = 0; e < dim; ++e) {
1915:           centroid[d] += R[d*dim+e]*csum[e];
1916:         }
1917:       }
1918:     } else for (d = 0; d < dim; ++d) centroid[d] = csum[d];
1919:   }
1920:   return(0);
1921: }

1923: /* Centroid_i = (\sum_n V_n Cn_i ) / V */
1924: static PetscErrorCode DMPlexComputeGeometryFVM_3D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
1925: {
1926:   DMLabel         depth;
1927:   PetscSection    coordSection;
1928:   Vec             coordinates;
1929:   PetscScalar    *coords = NULL;
1930:   PetscReal       vsum = 0.0, vtmp, coordsTmp[3*3];
1931:   const PetscInt *faces, *facesO;
1932:   PetscBool       isHybrid = PETSC_FALSE;
1933:   PetscInt        pEndInterior[4], cdepth, numFaces, f, coordSize, numCorners, p, d;
1934:   PetscErrorCode  ierr;

1937:   if (PetscUnlikely(dim > 3)) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"No support for dim %D > 3",dim);
1938:   /* Must check for hybrid cells because prisms have a different orientation scheme */
1939:   DMPlexGetDepthLabel(dm, &depth);
1940:   DMLabelGetValue(depth, cell, &cdepth);
1941:   DMPlexGetHybridBounds(dm, &pEndInterior[3], &pEndInterior[2], &pEndInterior[1], &pEndInterior[0]);
1942:   if ((pEndInterior[cdepth]) >=0 && (cell >= pEndInterior[cdepth])) isHybrid = PETSC_TRUE;

1944:   DMGetCoordinatesLocal(dm, &coordinates);
1945:   DMGetCoordinateSection(dm, &coordSection);

1947:   if (centroid) for (d = 0; d < dim; ++d) centroid[d] = 0.0;
1948:   DMPlexGetConeSize(dm, cell, &numFaces);
1949:   DMPlexGetCone(dm, cell, &faces);
1950:   DMPlexGetConeOrientation(dm, cell, &facesO);
1951:   for (f = 0; f < numFaces; ++f) {
1952:     PetscBool flip = isHybrid && f == 0 ? PETSC_TRUE : PETSC_FALSE; /* The first hybrid face is reversed */

1954:     DMPlexVecGetClosure(dm, coordSection, coordinates, faces[f], &coordSize, &coords);
1955:     numCorners = coordSize/dim;
1956:     switch (numCorners) {
1957:     case 3:
1958:       for (d = 0; d < dim; ++d) {
1959:         coordsTmp[0*dim+d] = PetscRealPart(coords[0*dim+d]);
1960:         coordsTmp[1*dim+d] = PetscRealPart(coords[1*dim+d]);
1961:         coordsTmp[2*dim+d] = PetscRealPart(coords[2*dim+d]);
1962:       }
1963:       Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
1964:       if (facesO[f] < 0 || flip) vtmp = -vtmp;
1965:       vsum += vtmp;
1966:       if (centroid) {           /* Centroid of OABC = (a+b+c)/4 */
1967:         for (d = 0; d < dim; ++d) {
1968:           for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p*dim+d]*vtmp;
1969:         }
1970:       }
1971:       break;
1972:     case 4:
1973:     {
1974:       PetscInt fv[4] = {0, 1, 2, 3};

1976:       /* Side faces for hybrid cells are are stored as tensor products */
1977:       if (isHybrid && f > 1) {fv[2] = 3; fv[3] = 2;}
1978:       /* DO FOR PYRAMID */
1979:       /* First tet */
1980:       for (d = 0; d < dim; ++d) {
1981:         coordsTmp[0*dim+d] = PetscRealPart(coords[fv[0]*dim+d]);
1982:         coordsTmp[1*dim+d] = PetscRealPart(coords[fv[1]*dim+d]);
1983:         coordsTmp[2*dim+d] = PetscRealPart(coords[fv[3]*dim+d]);
1984:       }
1985:       Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
1986:       if (facesO[f] < 0 || flip) vtmp = -vtmp;
1987:       vsum += vtmp;
1988:       if (centroid) {
1989:         for (d = 0; d < dim; ++d) {
1990:           for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p*dim+d]*vtmp;
1991:         }
1992:       }
1993:       /* Second tet */
1994:       for (d = 0; d < dim; ++d) {
1995:         coordsTmp[0*dim+d] = PetscRealPart(coords[fv[1]*dim+d]);
1996:         coordsTmp[1*dim+d] = PetscRealPart(coords[fv[2]*dim+d]);
1997:         coordsTmp[2*dim+d] = PetscRealPart(coords[fv[3]*dim+d]);
1998:       }
1999:       Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
2000:       if (facesO[f] < 0 || flip) vtmp = -vtmp;
2001:       vsum += vtmp;
2002:       if (centroid) {
2003:         for (d = 0; d < dim; ++d) {
2004:           for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p*dim+d]*vtmp;
2005:         }
2006:       }
2007:       break;
2008:     }
2009:     default:
2010:       SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Cannot handle faces with %D vertices", numCorners);
2011:     }
2012:     DMPlexVecRestoreClosure(dm, coordSection, coordinates, faces[f], &coordSize, &coords);
2013:   }
2014:   if (vol)     *vol = PetscAbsReal(vsum);
2015:   if (normal)   for (d = 0; d < dim; ++d) normal[d]    = 0.0;
2016:   if (centroid) for (d = 0; d < dim; ++d) centroid[d] /= (vsum*4);
2017:   return(0);
2018: }

2020: /*@C
2021:   DMPlexComputeCellGeometryFVM - Compute the volume for a given cell

2023:   Collective on dm

2025:   Input Arguments:
2026: + dm   - the DM
2027: - cell - the cell

2029:   Output Arguments:
2030: + volume   - the cell volume
2031: . centroid - the cell centroid
2032: - normal - the cell normal, if appropriate

2034:   Level: advanced

2036:   Fortran Notes:
2037:   Since it returns arrays, this routine is only available in Fortran 90, and you must
2038:   include petsc.h90 in your code.

2040: .seealso: DMGetCoordinateSection(), DMGetCoordinates()
2041: @*/
2042: PetscErrorCode DMPlexComputeCellGeometryFVM(DM dm, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
2043: {
2044:   PetscInt       depth, dim;

2048:   DMPlexGetDepth(dm, &depth);
2049:   DMGetDimension(dm, &dim);
2050:   if (depth != dim) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Mesh must be interpolated");
2051:   /* We need to keep a pointer to the depth label */
2052:   DMGetLabelValue(dm, "depth", cell, &depth);
2053:   /* Cone size is now the number of faces */
2054:   switch (depth) {
2055:   case 1:
2056:     DMPlexComputeGeometryFVM_1D_Internal(dm, dim, cell, vol, centroid, normal);
2057:     break;
2058:   case 2:
2059:     DMPlexComputeGeometryFVM_2D_Internal(dm, dim, cell, vol, centroid, normal);
2060:     break;
2061:   case 3:
2062:     DMPlexComputeGeometryFVM_3D_Internal(dm, dim, cell, vol, centroid, normal);
2063:     break;
2064:   default:
2065:     SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported dimension %D (depth %D) for element geometry computation", dim, depth);
2066:   }
2067:   return(0);
2068: }

2070: /*@
2071:   DMPlexComputeGeometryFEM - Precompute cell geometry for the entire mesh

2073:   Collective on dm

2075:   Input Parameter:
2076: . dm - The DMPlex

2078:   Output Parameter:
2079: . cellgeom - A vector with the cell geometry data for each cell

2081:   Level: beginner

2083: @*/
2084: PetscErrorCode DMPlexComputeGeometryFEM(DM dm, Vec *cellgeom)
2085: {
2086:   DM             dmCell;
2087:   Vec            coordinates;
2088:   PetscSection   coordSection, sectionCell;
2089:   PetscScalar   *cgeom;
2090:   PetscInt       cStart, cEnd, cMax, c;

2094:   DMClone(dm, &dmCell);
2095:   DMGetCoordinateSection(dm, &coordSection);
2096:   DMGetCoordinatesLocal(dm, &coordinates);
2097:   DMSetCoordinateSection(dmCell, PETSC_DETERMINE, coordSection);
2098:   DMSetCoordinatesLocal(dmCell, coordinates);
2099:   PetscSectionCreate(PetscObjectComm((PetscObject) dm), &sectionCell);
2100:   DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);
2101:   DMPlexGetHybridBounds(dm, &cMax, NULL, NULL, NULL);
2102:   cEnd = cMax < 0 ? cEnd : cMax;
2103:   PetscSectionSetChart(sectionCell, cStart, cEnd);
2104:   /* TODO This needs to be multiplied by Nq for non-affine */
2105:   for (c = cStart; c < cEnd; ++c) {PetscSectionSetDof(sectionCell, c, (PetscInt) PetscCeilReal(((PetscReal) sizeof(PetscFEGeom))/sizeof(PetscScalar)));}
2106:   PetscSectionSetUp(sectionCell);
2107:   DMSetLocalSection(dmCell, sectionCell);
2108:   PetscSectionDestroy(&sectionCell);
2109:   DMCreateLocalVector(dmCell, cellgeom);
2110:   VecGetArray(*cellgeom, &cgeom);
2111:   for (c = cStart; c < cEnd; ++c) {
2112:     PetscFEGeom *cg;

2114:     DMPlexPointLocalRef(dmCell, c, cgeom, &cg);
2115:     PetscArrayzero(cg, 1);
2116:     DMPlexComputeCellGeometryFEM(dmCell, c, NULL, cg->v, cg->J, cg->invJ, cg->detJ);
2117:     if (*cg->detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", cg->detJ, c);
2118:   }
2119:   return(0);
2120: }

2122: /*@
2123:   DMPlexComputeGeometryFVM - Computes the cell and face geometry for a finite volume method

2125:   Input Parameter:
2126: . dm - The DM

2128:   Output Parameters:
2129: + cellgeom - A Vec of PetscFVCellGeom data
2130: - facegeom - A Vec of PetscFVFaceGeom data

2132:   Level: developer

2134: .seealso: PetscFVFaceGeom, PetscFVCellGeom, DMPlexComputeGeometryFEM()
2135: @*/
2136: PetscErrorCode DMPlexComputeGeometryFVM(DM dm, Vec *cellgeom, Vec *facegeom)
2137: {
2138:   DM             dmFace, dmCell;
2139:   DMLabel        ghostLabel;
2140:   PetscSection   sectionFace, sectionCell;
2141:   PetscSection   coordSection;
2142:   Vec            coordinates;
2143:   PetscScalar   *fgeom, *cgeom;
2144:   PetscReal      minradius, gminradius;
2145:   PetscInt       dim, cStart, cEnd, cEndInterior, c, fStart, fEnd, f;

2149:   DMGetDimension(dm, &dim);
2150:   DMGetCoordinateSection(dm, &coordSection);
2151:   DMGetCoordinatesLocal(dm, &coordinates);
2152:   /* Make cell centroids and volumes */
2153:   DMClone(dm, &dmCell);
2154:   DMSetCoordinateSection(dmCell, PETSC_DETERMINE, coordSection);
2155:   DMSetCoordinatesLocal(dmCell, coordinates);
2156:   PetscSectionCreate(PetscObjectComm((PetscObject) dm), &sectionCell);
2157:   DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);
2158:   DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);
2159:   PetscSectionSetChart(sectionCell, cStart, cEnd);
2160:   for (c = cStart; c < cEnd; ++c) {PetscSectionSetDof(sectionCell, c, (PetscInt) PetscCeilReal(((PetscReal) sizeof(PetscFVCellGeom))/sizeof(PetscScalar)));}
2161:   PetscSectionSetUp(sectionCell);
2162:   DMSetLocalSection(dmCell, sectionCell);
2163:   PetscSectionDestroy(&sectionCell);
2164:   DMCreateLocalVector(dmCell, cellgeom);
2165:   if (cEndInterior < 0) {
2166:     cEndInterior = cEnd;
2167:   }
2168:   VecGetArray(*cellgeom, &cgeom);
2169:   for (c = cStart; c < cEndInterior; ++c) {
2170:     PetscFVCellGeom *cg;

2172:     DMPlexPointLocalRef(dmCell, c, cgeom, &cg);
2173:     PetscArrayzero(cg, 1);
2174:     DMPlexComputeCellGeometryFVM(dmCell, c, &cg->volume, cg->centroid, NULL);
2175:   }
2176:   /* Compute face normals and minimum cell radius */
2177:   DMClone(dm, &dmFace);
2178:   PetscSectionCreate(PetscObjectComm((PetscObject) dm), &sectionFace);
2179:   DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);
2180:   PetscSectionSetChart(sectionFace, fStart, fEnd);
2181:   for (f = fStart; f < fEnd; ++f) {PetscSectionSetDof(sectionFace, f, (PetscInt) PetscCeilReal(((PetscReal) sizeof(PetscFVFaceGeom))/sizeof(PetscScalar)));}
2182:   PetscSectionSetUp(sectionFace);
2183:   DMSetLocalSection(dmFace, sectionFace);
2184:   PetscSectionDestroy(&sectionFace);
2185:   DMCreateLocalVector(dmFace, facegeom);
2186:   VecGetArray(*facegeom, &fgeom);
2187:   DMGetLabel(dm, "ghost", &ghostLabel);
2188:   minradius = PETSC_MAX_REAL;
2189:   for (f = fStart; f < fEnd; ++f) {
2190:     PetscFVFaceGeom *fg;
2191:     PetscReal        area;
2192:     PetscInt         ghost = -1, d, numChildren;

2194:     if (ghostLabel) {DMLabelGetValue(ghostLabel, f, &ghost);}
2195:     DMPlexGetTreeChildren(dm,f,&numChildren,NULL);
2196:     if (ghost >= 0 || numChildren) continue;
2197:     DMPlexPointLocalRef(dmFace, f, fgeom, &fg);
2198:     DMPlexComputeCellGeometryFVM(dm, f, &area, fg->centroid, fg->normal);
2199:     for (d = 0; d < dim; ++d) fg->normal[d] *= area;
2200:     /* Flip face orientation if necessary to match ordering in support, and Update minimum radius */
2201:     {
2202:       PetscFVCellGeom *cL, *cR;
2203:       PetscInt         ncells;
2204:       const PetscInt  *cells;
2205:       PetscReal       *lcentroid, *rcentroid;
2206:       PetscReal        l[3], r[3], v[3];

2208:       DMPlexGetSupport(dm, f, &cells);
2209:       DMPlexGetSupportSize(dm, f, &ncells);
2210:       DMPlexPointLocalRead(dmCell, cells[0], cgeom, &cL);
2211:       lcentroid = cells[0] >= cEndInterior ? fg->centroid : cL->centroid;
2212:       if (ncells > 1) {
2213:         DMPlexPointLocalRead(dmCell, cells[1], cgeom, &cR);
2214:         rcentroid = cells[1] >= cEndInterior ? fg->centroid : cR->centroid;
2215:       }
2216:       else {
2217:         rcentroid = fg->centroid;
2218:       }
2219:       DMLocalizeCoordinateReal_Internal(dm, dim, fg->centroid, lcentroid, l);
2220:       DMLocalizeCoordinateReal_Internal(dm, dim, fg->centroid, rcentroid, r);
2221:       DMPlex_WaxpyD_Internal(dim, -1, l, r, v);
2222:       if (DMPlex_DotRealD_Internal(dim, fg->normal, v) < 0) {
2223:         for (d = 0; d < dim; ++d) fg->normal[d] = -fg->normal[d];
2224:       }
2225:       if (DMPlex_DotRealD_Internal(dim, fg->normal, v) <= 0) {
2226:         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]);
2227:         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]);
2228:         SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Direction for face %d could not be fixed", f);
2229:       }
2230:       if (cells[0] < cEndInterior) {
2231:         DMPlex_WaxpyD_Internal(dim, -1, fg->centroid, cL->centroid, v);
2232:         minradius = PetscMin(minradius, DMPlex_NormD_Internal(dim, v));
2233:       }
2234:       if (ncells > 1 && cells[1] < cEndInterior) {
2235:         DMPlex_WaxpyD_Internal(dim, -1, fg->centroid, cR->centroid, v);
2236:         minradius = PetscMin(minradius, DMPlex_NormD_Internal(dim, v));
2237:       }
2238:     }
2239:   }
2240:   MPIU_Allreduce(&minradius, &gminradius, 1, MPIU_REAL, MPIU_MIN, PetscObjectComm((PetscObject)dm));
2241:   DMPlexSetMinRadius(dm, gminradius);
2242:   /* Compute centroids of ghost cells */
2243:   for (c = cEndInterior; c < cEnd; ++c) {
2244:     PetscFVFaceGeom *fg;
2245:     const PetscInt  *cone,    *support;
2246:     PetscInt         coneSize, supportSize, s;

2248:     DMPlexGetConeSize(dmCell, c, &coneSize);
2249:     if (coneSize != 1) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Ghost cell %d has cone size %d != 1", c, coneSize);
2250:     DMPlexGetCone(dmCell, c, &cone);
2251:     DMPlexGetSupportSize(dmCell, cone[0], &supportSize);
2252:     if (supportSize != 2) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Face %d has support size %d != 2", cone[0], supportSize);
2253:     DMPlexGetSupport(dmCell, cone[0], &support);
2254:     DMPlexPointLocalRef(dmFace, cone[0], fgeom, &fg);
2255:     for (s = 0; s < 2; ++s) {
2256:       /* Reflect ghost centroid across plane of face */
2257:       if (support[s] == c) {
2258:         PetscFVCellGeom       *ci;
2259:         PetscFVCellGeom       *cg;
2260:         PetscReal              c2f[3], a;

2262:         DMPlexPointLocalRead(dmCell, support[(s+1)%2], cgeom, &ci);
2263:         DMPlex_WaxpyD_Internal(dim, -1, ci->centroid, fg->centroid, c2f); /* cell to face centroid */
2264:         a    = DMPlex_DotRealD_Internal(dim, c2f, fg->normal)/DMPlex_DotRealD_Internal(dim, fg->normal, fg->normal);
2265:         DMPlexPointLocalRef(dmCell, support[s], cgeom, &cg);
2266:         DMPlex_WaxpyD_Internal(dim, 2*a, fg->normal, ci->centroid, cg->centroid);
2267:         cg->volume = ci->volume;
2268:       }
2269:     }
2270:   }
2271:   VecRestoreArray(*facegeom, &fgeom);
2272:   VecRestoreArray(*cellgeom, &cgeom);
2273:   DMDestroy(&dmCell);
2274:   DMDestroy(&dmFace);
2275:   return(0);
2276: }

2278: /*@C
2279:   DMPlexGetMinRadius - Returns the minimum distance from any cell centroid to a face

2281:   Not collective

2283:   Input Argument:
2284: . dm - the DM

2286:   Output Argument:
2287: . minradius - the minium cell radius

2289:   Level: developer

2291: .seealso: DMGetCoordinates()
2292: @*/
2293: PetscErrorCode DMPlexGetMinRadius(DM dm, PetscReal *minradius)
2294: {
2298:   *minradius = ((DM_Plex*) dm->data)->minradius;
2299:   return(0);
2300: }

2302: /*@C
2303:   DMPlexSetMinRadius - Sets the minimum distance from the cell centroid to a face

2305:   Logically collective

2307:   Input Arguments:
2308: + dm - the DM
2309: - minradius - the minium cell radius

2311:   Level: developer

2313: .seealso: DMSetCoordinates()
2314: @*/
2315: PetscErrorCode DMPlexSetMinRadius(DM dm, PetscReal minradius)
2316: {
2319:   ((DM_Plex*) dm->data)->minradius = minradius;
2320:   return(0);
2321: }

2323: static PetscErrorCode BuildGradientReconstruction_Internal(DM dm, PetscFV fvm, DM dmFace, PetscScalar *fgeom, DM dmCell, PetscScalar *cgeom)
2324: {
2325:   DMLabel        ghostLabel;
2326:   PetscScalar   *dx, *grad, **gref;
2327:   PetscInt       dim, cStart, cEnd, c, cEndInterior, maxNumFaces;

2331:   DMGetDimension(dm, &dim);
2332:   DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);
2333:   DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);
2334:   DMPlexGetMaxSizes(dm, &maxNumFaces, NULL);
2335:   PetscFVLeastSquaresSetMaxFaces(fvm, maxNumFaces);
2336:   DMGetLabel(dm, "ghost", &ghostLabel);
2337:   PetscMalloc3(maxNumFaces*dim, &dx, maxNumFaces*dim, &grad, maxNumFaces, &gref);
2338:   for (c = cStart; c < cEndInterior; c++) {
2339:     const PetscInt        *faces;
2340:     PetscInt               numFaces, usedFaces, f, d;
2341:     PetscFVCellGeom        *cg;
2342:     PetscBool              boundary;
2343:     PetscInt               ghost;

2345:     DMPlexPointLocalRead(dmCell, c, cgeom, &cg);
2346:     DMPlexGetConeSize(dm, c, &numFaces);
2347:     DMPlexGetCone(dm, c, &faces);
2348:     if (numFaces < dim) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Cell %D has only %D faces, not enough for gradient reconstruction", c, numFaces);
2349:     for (f = 0, usedFaces = 0; f < numFaces; ++f) {
2350:       PetscFVCellGeom       *cg1;
2351:       PetscFVFaceGeom       *fg;
2352:       const PetscInt        *fcells;
2353:       PetscInt               ncell, side;

2355:       DMLabelGetValue(ghostLabel, faces[f], &ghost);
2356:       DMIsBoundaryPoint(dm, faces[f], &boundary);
2357:       if ((ghost >= 0) || boundary) continue;
2358:       DMPlexGetSupport(dm, faces[f], &fcells);
2359:       side  = (c != fcells[0]); /* c is on left=0 or right=1 of face */
2360:       ncell = fcells[!side];    /* the neighbor */
2361:       DMPlexPointLocalRef(dmFace, faces[f], fgeom, &fg);
2362:       DMPlexPointLocalRead(dmCell, ncell, cgeom, &cg1);
2363:       for (d = 0; d < dim; ++d) dx[usedFaces*dim+d] = cg1->centroid[d] - cg->centroid[d];
2364:       gref[usedFaces++] = fg->grad[side];  /* Gradient reconstruction term will go here */
2365:     }
2366:     if (!usedFaces) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_USER, "Mesh contains isolated cell (no neighbors). Is it intentional?");
2367:     PetscFVComputeGradient(fvm, usedFaces, dx, grad);
2368:     for (f = 0, usedFaces = 0; f < numFaces; ++f) {
2369:       DMLabelGetValue(ghostLabel, faces[f], &ghost);
2370:       DMIsBoundaryPoint(dm, faces[f], &boundary);
2371:       if ((ghost >= 0) || boundary) continue;
2372:       for (d = 0; d < dim; ++d) gref[usedFaces][d] = grad[usedFaces*dim+d];
2373:       ++usedFaces;
2374:     }
2375:   }
2376:   PetscFree3(dx, grad, gref);
2377:   return(0);
2378: }

2380: static PetscErrorCode BuildGradientReconstruction_Internal_Tree(DM dm, PetscFV fvm, DM dmFace, PetscScalar *fgeom, DM dmCell, PetscScalar *cgeom)
2381: {
2382:   DMLabel        ghostLabel;
2383:   PetscScalar   *dx, *grad, **gref;
2384:   PetscInt       dim, cStart, cEnd, c, cEndInterior, fStart, fEnd, f, nStart, nEnd, maxNumFaces = 0;
2385:   PetscSection   neighSec;
2386:   PetscInt     (*neighbors)[2];
2387:   PetscInt      *counter;

2391:   DMGetDimension(dm, &dim);
2392:   DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);
2393:   DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);
2394:   if (cEndInterior < 0) {
2395:     cEndInterior = cEnd;
2396:   }
2397:   PetscSectionCreate(PetscObjectComm((PetscObject)dm),&neighSec);
2398:   PetscSectionSetChart(neighSec,cStart,cEndInterior);
2399:   DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd);
2400:   DMGetLabel(dm, "ghost", &ghostLabel);
2401:   for (f = fStart; f < fEnd; f++) {
2402:     const PetscInt        *fcells;
2403:     PetscBool              boundary;
2404:     PetscInt               ghost = -1;
2405:     PetscInt               numChildren, numCells, c;

2407:     if (ghostLabel) {DMLabelGetValue(ghostLabel, f, &ghost);}
2408:     DMIsBoundaryPoint(dm, f, &boundary);
2409:     DMPlexGetTreeChildren(dm, f, &numChildren, NULL);
2410:     if ((ghost >= 0) || boundary || numChildren) continue;
2411:     DMPlexGetSupportSize(dm, f, &numCells);
2412:     if (numCells == 2) {
2413:       DMPlexGetSupport(dm, f, &fcells);
2414:       for (c = 0; c < 2; c++) {
2415:         PetscInt cell = fcells[c];

2417:         if (cell >= cStart && cell < cEndInterior) {
2418:           PetscSectionAddDof(neighSec,cell,1);
2419:         }
2420:       }
2421:     }
2422:   }
2423:   PetscSectionSetUp(neighSec);
2424:   PetscSectionGetMaxDof(neighSec,&maxNumFaces);
2425:   PetscFVLeastSquaresSetMaxFaces(fvm, maxNumFaces);
2426:   nStart = 0;
2427:   PetscSectionGetStorageSize(neighSec,&nEnd);
2428:   PetscMalloc1((nEnd-nStart),&neighbors);
2429:   PetscCalloc1((cEndInterior-cStart),&counter);
2430:   for (f = fStart; f < fEnd; f++) {
2431:     const PetscInt        *fcells;
2432:     PetscBool              boundary;
2433:     PetscInt               ghost = -1;
2434:     PetscInt               numChildren, numCells, c;

2436:     if (ghostLabel) {DMLabelGetValue(ghostLabel, f, &ghost);}
2437:     DMIsBoundaryPoint(dm, f, &boundary);
2438:     DMPlexGetTreeChildren(dm, f, &numChildren, NULL);
2439:     if ((ghost >= 0) || boundary || numChildren) continue;
2440:     DMPlexGetSupportSize(dm, f, &numCells);
2441:     if (numCells == 2) {
2442:       DMPlexGetSupport(dm, f, &fcells);
2443:       for (c = 0; c < 2; c++) {
2444:         PetscInt cell = fcells[c], off;

2446:         if (cell >= cStart && cell < cEndInterior) {
2447:           PetscSectionGetOffset(neighSec,cell,&off);
2448:           off += counter[cell - cStart]++;
2449:           neighbors[off][0] = f;
2450:           neighbors[off][1] = fcells[1 - c];
2451:         }
2452:       }
2453:     }
2454:   }
2455:   PetscFree(counter);
2456:   PetscMalloc3(maxNumFaces*dim, &dx, maxNumFaces*dim, &grad, maxNumFaces, &gref);
2457:   for (c = cStart; c < cEndInterior; c++) {
2458:     PetscInt               numFaces, f, d, off, ghost = -1;
2459:     PetscFVCellGeom        *cg;

2461:     DMPlexPointLocalRead(dmCell, c, cgeom, &cg);
2462:     PetscSectionGetDof(neighSec, c, &numFaces);
2463:     PetscSectionGetOffset(neighSec, c, &off);
2464:     if (ghostLabel) {DMLabelGetValue(ghostLabel, c, &ghost);}
2465:     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);
2466:     for (f = 0; f < numFaces; ++f) {
2467:       PetscFVCellGeom       *cg1;
2468:       PetscFVFaceGeom       *fg;
2469:       const PetscInt        *fcells;
2470:       PetscInt               ncell, side, nface;

2472:       nface = neighbors[off + f][0];
2473:       ncell = neighbors[off + f][1];
2474:       DMPlexGetSupport(dm,nface,&fcells);
2475:       side  = (c != fcells[0]);
2476:       DMPlexPointLocalRef(dmFace, nface, fgeom, &fg);
2477:       DMPlexPointLocalRead(dmCell, ncell, cgeom, &cg1);
2478:       for (d = 0; d < dim; ++d) dx[f*dim+d] = cg1->centroid[d] - cg->centroid[d];
2479:       gref[f] = fg->grad[side];  /* Gradient reconstruction term will go here */
2480:     }
2481:     PetscFVComputeGradient(fvm, numFaces, dx, grad);
2482:     for (f = 0; f < numFaces; ++f) {
2483:       for (d = 0; d < dim; ++d) gref[f][d] = grad[f*dim+d];
2484:     }
2485:   }
2486:   PetscFree3(dx, grad, gref);
2487:   PetscSectionDestroy(&neighSec);
2488:   PetscFree(neighbors);
2489:   return(0);
2490: }

2492: /*@
2493:   DMPlexComputeGradientFVM - Compute geometric factors for gradient reconstruction, which are stored in the geometry data, and compute layout for gradient data

2495:   Collective on dm

2497:   Input Arguments:
2498: + dm  - The DM
2499: . fvm - The PetscFV
2500: . faceGeometry - The face geometry from DMPlexComputeFaceGeometryFVM()
2501: - cellGeometry - The face geometry from DMPlexComputeCellGeometryFVM()

2503:   Output Parameters:
2504: + faceGeometry - The geometric factors for gradient calculation are inserted
2505: - dmGrad - The DM describing the layout of gradient data

2507:   Level: developer

2509: .seealso: DMPlexGetFaceGeometryFVM(), DMPlexGetCellGeometryFVM()
2510: @*/
2511: PetscErrorCode DMPlexComputeGradientFVM(DM dm, PetscFV fvm, Vec faceGeometry, Vec cellGeometry, DM *dmGrad)
2512: {
2513:   DM             dmFace, dmCell;
2514:   PetscScalar   *fgeom, *cgeom;
2515:   PetscSection   sectionGrad, parentSection;
2516:   PetscInt       dim, pdim, cStart, cEnd, cEndInterior, c;

2520:   DMGetDimension(dm, &dim);
2521:   PetscFVGetNumComponents(fvm, &pdim);
2522:   DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);
2523:   DMPlexGetHybridBounds(dm, &cEndInterior, NULL, NULL, NULL);
2524:   /* Construct the interpolant corresponding to each face from the least-square solution over the cell neighborhood */
2525:   VecGetDM(faceGeometry, &dmFace);
2526:   VecGetDM(cellGeometry, &dmCell);
2527:   VecGetArray(faceGeometry, &fgeom);
2528:   VecGetArray(cellGeometry, &cgeom);
2529:   DMPlexGetTree(dm,&parentSection,NULL,NULL,NULL,NULL);
2530:   if (!parentSection) {
2531:     BuildGradientReconstruction_Internal(dm, fvm, dmFace, fgeom, dmCell, cgeom);
2532:   } else {
2533:     BuildGradientReconstruction_Internal_Tree(dm, fvm, dmFace, fgeom, dmCell, cgeom);
2534:   }
2535:   VecRestoreArray(faceGeometry, &fgeom);
2536:   VecRestoreArray(cellGeometry, &cgeom);
2537:   /* Create storage for gradients */
2538:   DMClone(dm, dmGrad);
2539:   PetscSectionCreate(PetscObjectComm((PetscObject) dm), &sectionGrad);
2540:   PetscSectionSetChart(sectionGrad, cStart, cEnd);
2541:   for (c = cStart; c < cEnd; ++c) {PetscSectionSetDof(sectionGrad, c, pdim*dim);}
2542:   PetscSectionSetUp(sectionGrad);
2543:   DMSetLocalSection(*dmGrad, sectionGrad);
2544:   PetscSectionDestroy(&sectionGrad);
2545:   return(0);
2546: }

2548: /*@
2549:   DMPlexGetDataFVM - Retrieve precomputed cell geometry

2551:   Collective on dm

2553:   Input Arguments:
2554: + dm  - The DM
2555: - fvm - The PetscFV

2557:   Output Parameters:
2558: + cellGeometry - The cell geometry
2559: . faceGeometry - The face geometry
2560: - dmGrad       - The gradient matrices

2562:   Level: developer

2564: .seealso: DMPlexComputeGeometryFVM()
2565: @*/
2566: PetscErrorCode DMPlexGetDataFVM(DM dm, PetscFV fv, Vec *cellgeom, Vec *facegeom, DM *gradDM)
2567: {
2568:   PetscObject    cellgeomobj, facegeomobj;

2572:   PetscObjectQuery((PetscObject) dm, "DMPlex_cellgeom_fvm", &cellgeomobj);
2573:   if (!cellgeomobj) {
2574:     Vec cellgeomInt, facegeomInt;

2576:     DMPlexComputeGeometryFVM(dm, &cellgeomInt, &facegeomInt);
2577:     PetscObjectCompose((PetscObject) dm, "DMPlex_cellgeom_fvm",(PetscObject)cellgeomInt);
2578:     PetscObjectCompose((PetscObject) dm, "DMPlex_facegeom_fvm",(PetscObject)facegeomInt);
2579:     VecDestroy(&cellgeomInt);
2580:     VecDestroy(&facegeomInt);
2581:     PetscObjectQuery((PetscObject) dm, "DMPlex_cellgeom_fvm", &cellgeomobj);
2582:   }
2583:   PetscObjectQuery((PetscObject) dm, "DMPlex_facegeom_fvm", &facegeomobj);
2584:   if (cellgeom) *cellgeom = (Vec) cellgeomobj;
2585:   if (facegeom) *facegeom = (Vec) facegeomobj;
2586:   if (gradDM) {
2587:     PetscObject gradobj;
2588:     PetscBool   computeGradients;

2590:     PetscFVGetComputeGradients(fv,&computeGradients);
2591:     if (!computeGradients) {
2592:       *gradDM = NULL;
2593:       return(0);
2594:     }
2595:     PetscObjectQuery((PetscObject) dm, "DMPlex_dmgrad_fvm", &gradobj);
2596:     if (!gradobj) {
2597:       DM dmGradInt;

2599:       DMPlexComputeGradientFVM(dm,fv,(Vec) facegeomobj,(Vec) cellgeomobj,&dmGradInt);
2600:       PetscObjectCompose((PetscObject) dm, "DMPlex_dmgrad_fvm", (PetscObject)dmGradInt);
2601:       DMDestroy(&dmGradInt);
2602:       PetscObjectQuery((PetscObject) dm, "DMPlex_dmgrad_fvm", &gradobj);
2603:     }
2604:     *gradDM = (DM) gradobj;
2605:   }
2606:   return(0);
2607: }

2609: static PetscErrorCode DMPlexCoordinatesToReference_NewtonUpdate(PetscInt dimC, PetscInt dimR, PetscScalar *J, PetscScalar *invJ, PetscScalar *work,  PetscReal *resNeg, PetscReal *guess)
2610: {
2611:   PetscInt l, m;

2614:   if (dimC == dimR && dimR <= 3) {
2615:     /* invert Jacobian, multiply */
2616:     PetscScalar det, idet;

2618:     switch (dimR) {
2619:     case 1:
2620:       invJ[0] = 1./ J[0];
2621:       break;
2622:     case 2:
2623:       det = J[0] * J[3] - J[1] * J[2];
2624:       idet = 1./det;
2625:       invJ[0] =  J[3] * idet;
2626:       invJ[1] = -J[1] * idet;
2627:       invJ[2] = -J[2] * idet;
2628:       invJ[3] =  J[0] * idet;
2629:       break;
2630:     case 3:
2631:       {
2632:         invJ[0] = J[4] * J[8] - J[5] * J[7];
2633:         invJ[1] = J[2] * J[7] - J[1] * J[8];
2634:         invJ[2] = J[1] * J[5] - J[2] * J[4];
2635:         det = invJ[0] * J[0] + invJ[1] * J[3] + invJ[2] * J[6];
2636:         idet = 1./det;
2637:         invJ[0] *= idet;
2638:         invJ[1] *= idet;
2639:         invJ[2] *= idet;
2640:         invJ[3]  = idet * (J[5] * J[6] - J[3] * J[8]);
2641:         invJ[4]  = idet * (J[0] * J[8] - J[2] * J[6]);
2642:         invJ[5]  = idet * (J[2] * J[3] - J[0] * J[5]);
2643:         invJ[6]  = idet * (J[3] * J[7] - J[4] * J[6]);
2644:         invJ[7]  = idet * (J[1] * J[6] - J[0] * J[7]);
2645:         invJ[8]  = idet * (J[0] * J[4] - J[1] * J[3]);
2646:       }
2647:       break;
2648:     }
2649:     for (l = 0; l < dimR; l++) {
2650:       for (m = 0; m < dimC; m++) {
2651:         guess[l] += PetscRealPart(invJ[l * dimC + m]) * resNeg[m];
2652:       }
2653:     }
2654:   } else {
2655: #if defined(PETSC_USE_COMPLEX)
2656:     char transpose = 'C';
2657: #else
2658:     char transpose = 'T';
2659: #endif
2660:     PetscBLASInt m = dimR;
2661:     PetscBLASInt n = dimC;
2662:     PetscBLASInt one = 1;
2663:     PetscBLASInt worksize = dimR * dimC, info;

2665:     for (l = 0; l < dimC; l++) {invJ[l] = resNeg[l];}

2667:     PetscStackCallBLAS("LAPACKgels",LAPACKgels_(&transpose,&m,&n,&one,J,&m,invJ,&n,work,&worksize, &info));
2668:     if (info != 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"Bad argument to GELS");

2670:     for (l = 0; l < dimR; l++) {guess[l] += PetscRealPart(invJ[l]);}
2671:   }
2672:   return(0);
2673: }

2675: static PetscErrorCode DMPlexCoordinatesToReference_Tensor(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal realCoords[], PetscReal refCoords[], Vec coords, PetscInt dimC, PetscInt dimR)
2676: {
2677:   PetscInt       coordSize, i, j, k, l, m, maxIts = 7, numV = (1 << dimR);
2678:   PetscScalar    *coordsScalar = NULL;
2679:   PetscReal      *cellData, *cellCoords, *cellCoeffs, *extJ, *resNeg;
2680:   PetscScalar    *J, *invJ, *work;

2685:   DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar);
2686:   if (coordSize < dimC * numV) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Expecting at least %D coordinates, got %D",dimC * (1 << dimR), coordSize);
2687:   DMGetWorkArray(dm, 2 * coordSize + dimR + dimC, MPIU_REAL, &cellData);
2688:   DMGetWorkArray(dm, 3 * dimR * dimC, MPIU_SCALAR, &J);
2689:   cellCoords = &cellData[0];
2690:   cellCoeffs = &cellData[coordSize];
2691:   extJ       = &cellData[2 * coordSize];
2692:   resNeg     = &cellData[2 * coordSize + dimR];
2693:   invJ       = &J[dimR * dimC];
2694:   work       = &J[2 * dimR * dimC];
2695:   if (dimR == 2) {
2696:     const PetscInt zToPlex[4] = {0, 1, 3, 2};

2698:     for (i = 0; i < 4; i++) {
2699:       PetscInt plexI = zToPlex[i];

2701:       for (j = 0; j < dimC; j++) {
2702:         cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
2703:       }
2704:     }
2705:   } else if (dimR == 3) {
2706:     const PetscInt zToPlex[8] = {0, 3, 1, 2, 4, 5, 7, 6};

2708:     for (i = 0; i < 8; i++) {
2709:       PetscInt plexI = zToPlex[i];

2711:       for (j = 0; j < dimC; j++) {
2712:         cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
2713:       }
2714:     }
2715:   } else {
2716:     for (i = 0; i < coordSize; i++) {cellCoords[i] = PetscRealPart(coordsScalar[i]);}
2717:   }
2718:   /* Perform the shuffling transform that converts values at the corners of [-1,1]^d to coefficients */
2719:   for (i = 0; i < dimR; i++) {
2720:     PetscReal *swap;

2722:     for (j = 0; j < (numV / 2); j++) {
2723:       for (k = 0; k < dimC; k++) {
2724:         cellCoeffs[dimC * j + k]                = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] + cellCoords[dimC * 2 * j + k]);
2725:         cellCoeffs[dimC * (j + (numV / 2)) + k] = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] - cellCoords[dimC * 2 * j + k]);
2726:       }
2727:     }

2729:     if (i < dimR - 1) {
2730:       swap = cellCoeffs;
2731:       cellCoeffs = cellCoords;
2732:       cellCoords = swap;
2733:     }
2734:   }
2735:   PetscArrayzero(refCoords,numPoints * dimR);
2736:   for (j = 0; j < numPoints; j++) {
2737:     for (i = 0; i < maxIts; i++) {
2738:       PetscReal *guess = &refCoords[dimR * j];

2740:       /* compute -residual and Jacobian */
2741:       for (k = 0; k < dimC; k++) {resNeg[k] = realCoords[dimC * j + k];}
2742:       for (k = 0; k < dimC * dimR; k++) {J[k] = 0.;}
2743:       for (k = 0; k < numV; k++) {
2744:         PetscReal extCoord = 1.;
2745:         for (l = 0; l < dimR; l++) {
2746:           PetscReal coord = guess[l];
2747:           PetscInt  dep   = (k & (1 << l)) >> l;

2749:           extCoord *= dep * coord + !dep;
2750:           extJ[l] = dep;

2752:           for (m = 0; m < dimR; m++) {
2753:             PetscReal coord = guess[m];
2754:             PetscInt  dep   = ((k & (1 << m)) >> m) && (m != l);
2755:             PetscReal mult  = dep * coord + !dep;

2757:             extJ[l] *= mult;
2758:           }
2759:         }
2760:         for (l = 0; l < dimC; l++) {
2761:           PetscReal coeff = cellCoeffs[dimC * k + l];

2763:           resNeg[l] -= coeff * extCoord;
2764:           for (m = 0; m < dimR; m++) {
2765:             J[dimR * l + m] += coeff * extJ[m];
2766:           }
2767:         }
2768:       }
2769: #if 0 && defined(PETSC_USE_DEBUG)
2770:       {
2771:         PetscReal maxAbs = 0.;

2773:         for (l = 0; l < dimC; l++) {
2774:           maxAbs = PetscMax(maxAbs,PetscAbsReal(resNeg[l]));
2775:         }
2776:         PetscInfo4(dm,"cell %D, point %D, iter %D: res %g\n",cell,j,i,maxAbs);
2777:       }
2778: #endif

2780:       DMPlexCoordinatesToReference_NewtonUpdate(dimC,dimR,J,invJ,work,resNeg,guess);
2781:     }
2782:   }
2783:   DMRestoreWorkArray(dm, 3 * dimR * dimC, MPIU_SCALAR, &J);
2784:   DMRestoreWorkArray(dm, 2 * coordSize + dimR + dimC, MPIU_REAL, &cellData);
2785:   DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar);
2786:   return(0);
2787: }

2789: static PetscErrorCode DMPlexReferenceToCoordinates_Tensor(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal refCoords[], PetscReal realCoords[], Vec coords, PetscInt dimC, PetscInt dimR)
2790: {
2791:   PetscInt       coordSize, i, j, k, l, numV = (1 << dimR);
2792:   PetscScalar    *coordsScalar = NULL;
2793:   PetscReal      *cellData, *cellCoords, *cellCoeffs;

2798:   DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar);
2799:   if (coordSize < dimC * numV) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Expecting at least %D coordinates, got %D",dimC * (1 << dimR), coordSize);
2800:   DMGetWorkArray(dm, 2 * coordSize, MPIU_REAL, &cellData);
2801:   cellCoords = &cellData[0];
2802:   cellCoeffs = &cellData[coordSize];
2803:   if (dimR == 2) {
2804:     const PetscInt zToPlex[4] = {0, 1, 3, 2};

2806:     for (i = 0; i < 4; i++) {
2807:       PetscInt plexI = zToPlex[i];

2809:       for (j = 0; j < dimC; j++) {
2810:         cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
2811:       }
2812:     }
2813:   } else if (dimR == 3) {
2814:     const PetscInt zToPlex[8] = {0, 3, 1, 2, 4, 5, 7, 6};

2816:     for (i = 0; i < 8; i++) {
2817:       PetscInt plexI = zToPlex[i];

2819:       for (j = 0; j < dimC; j++) {
2820:         cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
2821:       }
2822:     }
2823:   } else {
2824:     for (i = 0; i < coordSize; i++) {cellCoords[i] = PetscRealPart(coordsScalar[i]);}
2825:   }
2826:   /* Perform the shuffling transform that converts values at the corners of [-1,1]^d to coefficients */
2827:   for (i = 0; i < dimR; i++) {
2828:     PetscReal *swap;

2830:     for (j = 0; j < (numV / 2); j++) {
2831:       for (k = 0; k < dimC; k++) {
2832:         cellCoeffs[dimC * j + k]                = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] + cellCoords[dimC * 2 * j + k]);
2833:         cellCoeffs[dimC * (j + (numV / 2)) + k] = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] - cellCoords[dimC * 2 * j + k]);
2834:       }
2835:     }

2837:     if (i < dimR - 1) {
2838:       swap = cellCoeffs;
2839:       cellCoeffs = cellCoords;
2840:       cellCoords = swap;
2841:     }
2842:   }
2843:   PetscArrayzero(realCoords,numPoints * dimC);
2844:   for (j = 0; j < numPoints; j++) {
2845:     const PetscReal *guess  = &refCoords[dimR * j];
2846:     PetscReal       *mapped = &realCoords[dimC * j];

2848:     for (k = 0; k < numV; k++) {
2849:       PetscReal extCoord = 1.;
2850:       for (l = 0; l < dimR; l++) {
2851:         PetscReal coord = guess[l];
2852:         PetscInt  dep   = (k & (1 << l)) >> l;

2854:         extCoord *= dep * coord + !dep;
2855:       }
2856:       for (l = 0; l < dimC; l++) {
2857:         PetscReal coeff = cellCoeffs[dimC * k + l];

2859:         mapped[l] += coeff * extCoord;
2860:       }
2861:     }
2862:   }
2863:   DMRestoreWorkArray(dm, 2 * coordSize, MPIU_REAL, &cellData);
2864:   DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar);
2865:   return(0);
2866: }

2868: /* TODO: TOBY please fix this for Nc > 1 */
2869: static PetscErrorCode DMPlexCoordinatesToReference_FE(DM dm, PetscFE fe, PetscInt cell, PetscInt numPoints, const PetscReal realCoords[], PetscReal refCoords[], Vec coords, PetscInt Nc, PetscInt dimR)
2870: {
2871:   PetscInt       numComp, pdim, i, j, k, l, m, maxIter = 7, coordSize;
2872:   PetscScalar    *nodes = NULL;
2873:   PetscReal      *invV, *modes;
2874:   PetscReal      *B, *D, *resNeg;
2875:   PetscScalar    *J, *invJ, *work;

2879:   PetscFEGetDimension(fe, &pdim);
2880:   PetscFEGetNumComponents(fe, &numComp);
2881:   if (numComp != Nc) SETERRQ2(PetscObjectComm((PetscObject)dm),PETSC_ERR_SUP,"coordinate discretization must have as many components (%D) as embedding dimension (!= %D)",numComp,Nc);
2882:   DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &nodes);
2883:   /* convert nodes to values in the stable evaluation basis */
2884:   DMGetWorkArray(dm,pdim,MPIU_REAL,&modes);
2885:   invV = fe->invV;
2886:   for (i = 0; i < pdim; ++i) {
2887:     modes[i] = 0.;
2888:     for (j = 0; j < pdim; ++j) {
2889:       modes[i] += invV[i * pdim + j] * PetscRealPart(nodes[j]);
2890:     }
2891:   }
2892:   DMGetWorkArray(dm,pdim * Nc + pdim * Nc * dimR + Nc,MPIU_REAL,&B);
2893:   D      = &B[pdim*Nc];
2894:   resNeg = &D[pdim*Nc * dimR];
2895:   DMGetWorkArray(dm,3 * Nc * dimR,MPIU_SCALAR,&J);
2896:   invJ = &J[Nc * dimR];
2897:   work = &invJ[Nc * dimR];
2898:   for (i = 0; i < numPoints * dimR; i++) {refCoords[i] = 0.;}
2899:   for (j = 0; j < numPoints; j++) {
2900:       for (i = 0; i < maxIter; i++) { /* we could batch this so that we're not making big B and D arrays all the time */
2901:       PetscReal *guess = &refCoords[j * dimR];
2902:       PetscSpaceEvaluate(fe->basisSpace, 1, guess, B, D, NULL);
2903:       for (k = 0; k < Nc; k++) {resNeg[k] = realCoords[j * Nc + k];}
2904:       for (k = 0; k < Nc * dimR; k++) {J[k] = 0.;}
2905:       for (k = 0; k < pdim; k++) {
2906:         for (l = 0; l < Nc; l++) {
2907:           resNeg[l] -= modes[k] * B[k * Nc + l];
2908:           for (m = 0; m < dimR; m++) {
2909:             J[l * dimR + m] += modes[k] * D[(k * Nc + l) * dimR + m];
2910:           }
2911:         }
2912:       }
2913: #if 0 && defined(PETSC_USE_DEBUG)
2914:       {
2915:         PetscReal maxAbs = 0.;

2917:         for (l = 0; l < Nc; l++) {
2918:           maxAbs = PetscMax(maxAbs,PetscAbsReal(resNeg[l]));
2919:         }
2920:         PetscInfo4(dm,"cell %D, point %D, iter %D: res %g\n",cell,j,i,maxAbs);
2921:       }
2922: #endif
2923:       DMPlexCoordinatesToReference_NewtonUpdate(Nc,dimR,J,invJ,work,resNeg,guess);
2924:     }
2925:   }
2926:   DMRestoreWorkArray(dm,3 * Nc * dimR,MPIU_SCALAR,&J);
2927:   DMRestoreWorkArray(dm,pdim * Nc + pdim * Nc * dimR + Nc,MPIU_REAL,&B);
2928:   DMRestoreWorkArray(dm,pdim,MPIU_REAL,&modes);
2929:   DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &nodes);
2930:   return(0);
2931: }

2933: /* TODO: TOBY please fix this for Nc > 1 */
2934: static PetscErrorCode DMPlexReferenceToCoordinates_FE(DM dm, PetscFE fe, PetscInt cell, PetscInt numPoints, const PetscReal refCoords[], PetscReal realCoords[], Vec coords, PetscInt Nc, PetscInt dimR)
2935: {
2936:   PetscInt       numComp, pdim, i, j, k, l, coordSize;
2937:   PetscScalar    *nodes = NULL;
2938:   PetscReal      *invV, *modes;
2939:   PetscReal      *B;

2943:   PetscFEGetDimension(fe, &pdim);
2944:   PetscFEGetNumComponents(fe, &numComp);
2945:   if (numComp != Nc) SETERRQ2(PetscObjectComm((PetscObject)dm),PETSC_ERR_SUP,"coordinate discretization must have as many components (%D) as embedding dimension (!= %D)",numComp,Nc);
2946:   DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &nodes);
2947:   /* convert nodes to values in the stable evaluation basis */
2948:   DMGetWorkArray(dm,pdim,MPIU_REAL,&modes);
2949:   invV = fe->invV;
2950:   for (i = 0; i < pdim; ++i) {
2951:     modes[i] = 0.;
2952:     for (j = 0; j < pdim; ++j) {
2953:       modes[i] += invV[i * pdim + j] * PetscRealPart(nodes[j]);
2954:     }
2955:   }
2956:   DMGetWorkArray(dm,numPoints * pdim * Nc,MPIU_REAL,&B);
2957:   PetscSpaceEvaluate(fe->basisSpace, numPoints, refCoords, B, NULL, NULL);
2958:   for (i = 0; i < numPoints * Nc; i++) {realCoords[i] = 0.;}
2959:   for (j = 0; j < numPoints; j++) {
2960:     PetscReal *mapped = &realCoords[j * Nc];

2962:     for (k = 0; k < pdim; k++) {
2963:       for (l = 0; l < Nc; l++) {
2964:         mapped[l] += modes[k] * B[(j * pdim + k) * Nc + l];
2965:       }
2966:     }
2967:   }
2968:   DMRestoreWorkArray(dm,numPoints * pdim * Nc,MPIU_REAL,&B);
2969:   DMRestoreWorkArray(dm,pdim,MPIU_REAL,&modes);
2970:   DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &nodes);
2971:   return(0);
2972: }

2974: /*@
2975:   DMPlexCoordinatesToReference - Pull coordinates back from the mesh to the reference element using a single element
2976:   map.  This inversion will be accurate inside the reference element, but may be inaccurate for mappings that do not
2977:   extend uniquely outside the reference cell (e.g, most non-affine maps)

2979:   Not collective

2981:   Input Parameters:
2982: + dm         - The mesh, with coordinate maps defined either by a PetscDS for the coordinate DM (see DMGetCoordinateDM()) or
2983:                implicitly by the coordinates of the corner vertices of the cell: as an affine map for simplicial elements, or
2984:                as a multilinear map for tensor-product elements
2985: . cell       - the cell whose map is used.
2986: . numPoints  - the number of points to locate
2987: - realCoords - (numPoints x coordinate dimension) array of coordinates (see DMGetCoordinateDim())

2989:   Output Parameters:
2990: . refCoords  - (numPoints x dimension) array of reference coordinates (see DMGetDimension())

2992:   Level: intermediate

2994: .seealso: DMPlexReferenceToCoordinates()
2995: @*/
2996: PetscErrorCode DMPlexCoordinatesToReference(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal realCoords[], PetscReal refCoords[])
2997: {
2998:   PetscInt       dimC, dimR, depth, cStart, cEnd, cEndInterior, i;
2999:   DM             coordDM = NULL;
3000:   Vec            coords;
3001:   PetscFE        fe = NULL;

3006:   DMGetDimension(dm,&dimR);
3007:   DMGetCoordinateDim(dm,&dimC);
3008:   if (dimR <= 0 || dimC <= 0 || numPoints <= 0) return(0);
3009:   DMPlexGetDepth(dm,&depth);
3010:   DMGetCoordinatesLocal(dm,&coords);
3011:   DMGetCoordinateDM(dm,&coordDM);
3012:   if (coordDM) {
3013:     PetscInt coordFields;

3015:     DMGetNumFields(coordDM,&coordFields);
3016:     if (coordFields) {
3017:       PetscClassId id;
3018:       PetscObject  disc;

3020:       DMGetField(coordDM,0,NULL,&disc);
3021:       PetscObjectGetClassId(disc,&id);
3022:       if (id == PETSCFE_CLASSID) {
3023:         fe = (PetscFE) disc;
3024:       }
3025:     }
3026:   }
3027:   DMPlexGetHeightStratum(dm,0,&cStart,&cEnd);
3028:   DMPlexGetHybridBounds(dm,&cEndInterior,NULL,NULL,NULL);
3029:   cEnd = cEndInterior > 0 ? cEndInterior : cEnd;
3030:   if (cell < cStart || cell >= cEnd) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"point %D not in cell range [%D,%D)",cell,cStart,cEnd);
3031:   if (!fe) { /* implicit discretization: affine or multilinear */
3032:     PetscInt  coneSize;
3033:     PetscBool isSimplex, isTensor;

3035:     DMPlexGetConeSize(dm,cell,&coneSize);
3036:     isSimplex = (coneSize == (dimR + 1)) ? PETSC_TRUE : PETSC_FALSE;
3037:     isTensor  = (coneSize == ((depth == 1) ? (1 << dimR) : (2 * dimR))) ? PETSC_TRUE : PETSC_FALSE;
3038:     if (isSimplex) {
3039:       PetscReal detJ, *v0, *J, *invJ;

3041:       DMGetWorkArray(dm,dimC + 2 * dimC * dimC, MPIU_REAL, &v0);
3042:       J    = &v0[dimC];
3043:       invJ = &J[dimC * dimC];
3044:       DMPlexComputeCellGeometryAffineFEM(dm, cell, v0, J, invJ, &detJ);
3045:       for (i = 0; i < numPoints; i++) { /* Apply the inverse affine transformation for each point */
3046:         const PetscReal x0[3] = {-1.,-1.,-1.};

3048:         CoordinatesRealToRef(dimC, dimR, x0, v0, invJ, &realCoords[dimC * i], &refCoords[dimR * i]);
3049:       }
3050:       DMRestoreWorkArray(dm,dimC + 2 * dimC * dimC, MPIU_REAL, &v0);
3051:     } else if (isTensor) {
3052:       DMPlexCoordinatesToReference_Tensor(coordDM, cell, numPoints, realCoords, refCoords, coords, dimC, dimR);
3053:     } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Unrecognized cone size %D",coneSize);
3054:   } else {
3055:     DMPlexCoordinatesToReference_FE(coordDM, fe, cell, numPoints, realCoords, refCoords, coords, dimC, dimR);
3056:   }
3057:   return(0);
3058: }

3060: /*@
3061:   DMPlexReferenceToCoordinates - Map references coordinates to coordinates in the the mesh for a single element map.

3063:   Not collective

3065:   Input Parameters:
3066: + dm         - The mesh, with coordinate maps defined either by a PetscDS for the coordinate DM (see DMGetCoordinateDM()) or
3067:                implicitly by the coordinates of the corner vertices of the cell: as an affine map for simplicial elements, or
3068:                as a multilinear map for tensor-product elements
3069: . cell       - the cell whose map is used.
3070: . numPoints  - the number of points to locate
3071: - refCoords  - (numPoints x dimension) array of reference coordinates (see DMGetDimension())

3073:   Output Parameters:
3074: . realCoords - (numPoints x coordinate dimension) array of coordinates (see DMGetCoordinateDim())

3076:    Level: intermediate
3077:    
3078: .seealso: DMPlexCoordinatesToReference()
3079: @*/
3080: PetscErrorCode DMPlexReferenceToCoordinates(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal refCoords[], PetscReal realCoords[])
3081: {
3082:   PetscInt       dimC, dimR, depth, cStart, cEnd, cEndInterior, i;
3083:   DM             coordDM = NULL;
3084:   Vec            coords;
3085:   PetscFE        fe = NULL;

3090:   DMGetDimension(dm,&dimR);
3091:   DMGetCoordinateDim(dm,&dimC);
3092:   if (dimR <= 0 || dimC <= 0 || numPoints <= 0) return(0);
3093:   DMPlexGetDepth(dm,&depth);
3094:   DMGetCoordinatesLocal(dm,&coords);
3095:   DMGetCoordinateDM(dm,&coordDM);
3096:   if (coordDM) {
3097:     PetscInt coordFields;

3099:     DMGetNumFields(coordDM,&coordFields);
3100:     if (coordFields) {
3101:       PetscClassId id;
3102:       PetscObject  disc;

3104:       DMGetField(coordDM,0,NULL,&disc);
3105:       PetscObjectGetClassId(disc,&id);
3106:       if (id == PETSCFE_CLASSID) {
3107:         fe = (PetscFE) disc;
3108:       }
3109:     }
3110:   }
3111:   DMPlexGetHeightStratum(dm,0,&cStart,&cEnd);
3112:   DMPlexGetHybridBounds(dm,&cEndInterior,NULL,NULL,NULL);
3113:   cEnd = cEndInterior > 0 ? cEndInterior : cEnd;
3114:   if (cell < cStart || cell >= cEnd) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"point %D not in cell range [%D,%D)",cell,cStart,cEnd);
3115:   if (!fe) { /* implicit discretization: affine or multilinear */
3116:     PetscInt  coneSize;
3117:     PetscBool isSimplex, isTensor;

3119:     DMPlexGetConeSize(dm,cell,&coneSize);
3120:     isSimplex = (coneSize == (dimR + 1)) ? PETSC_TRUE : PETSC_FALSE;
3121:     isTensor  = (coneSize == ((depth == 1) ? (1 << dimR) : (2 * dimR))) ? PETSC_TRUE : PETSC_FALSE;
3122:     if (isSimplex) {
3123:       PetscReal detJ, *v0, *J;

3125:       DMGetWorkArray(dm,dimC + 2 * dimC * dimC, MPIU_REAL, &v0);
3126:       J    = &v0[dimC];
3127:       DMPlexComputeCellGeometryAffineFEM(dm, cell, v0, J, NULL, &detJ);
3128:       for (i = 0; i < numPoints; i++) { /* Apply the affine transformation for each point */
3129:         const PetscReal xi0[3] = {-1.,-1.,-1.};

3131:         CoordinatesRefToReal(dimC, dimR, xi0, v0, J, &refCoords[dimR * i], &realCoords[dimC * i]);
3132:       }
3133:       DMRestoreWorkArray(dm,dimC + 2 * dimC * dimC, MPIU_REAL, &v0);
3134:     } else if (isTensor) {
3135:       DMPlexReferenceToCoordinates_Tensor(coordDM, cell, numPoints, refCoords, realCoords, coords, dimC, dimR);
3136:     } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Unrecognized cone size %D",coneSize);
3137:   } else {
3138:     DMPlexReferenceToCoordinates_FE(coordDM, fe, cell, numPoints, refCoords, realCoords, coords, dimC, dimR);
3139:   }
3140:   return(0);
3141: }