Actual source code: plexgeometry.c

  1: #include <petsc/private/dmpleximpl.h>
  2: #include <petsc/private/petscfeimpl.h>
  3: #include <petscblaslapack.h>
  4: #include <petsctime.h>

  6: const char *const DMPlexCoordMaps[] = {"none", "shear", "flare", "annulus", "shell", "unknown", "DMPlexCoordMap", "DM_COORD_MAP_", NULL};

  8: /*@
  9:   DMPlexFindVertices - Try to find DAG points based on their coordinates.

 11:   Not Collective (provided `DMGetCoordinatesLocalSetUp()` has been already called)

 13:   Input Parameters:
 14: + dm          - The `DMPLEX` object
 15: . coordinates - The `Vec` of coordinates of the sought points
 16: - eps         - The tolerance or `PETSC_DEFAULT`

 18:   Output Parameter:
 19: . points - The `IS` of found DAG points or -1

 21:   Level: intermediate

 23:   Notes:
 24:   The length of `Vec` coordinates must be npoints * dim where dim is the spatial dimension returned by `DMGetCoordinateDim()` and npoints is the number of sought points.

 26:   The output `IS` is living on `PETSC_COMM_SELF` and its length is npoints.
 27:   Each rank does the search independently.
 28:   If this rank's local `DMPLEX` portion contains the DAG point corresponding to the i-th tuple of coordinates, the i-th entry of the output `IS` is set to that DAG point, otherwise to -1.

 30:   The output `IS` must be destroyed by user.

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

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

 36: .seealso: `DMPLEX`, `DMPlexCreate()`, `DMGetCoordinatesLocal()`
 37: @*/
 38: PetscErrorCode DMPlexFindVertices(DM dm, Vec coordinates, PetscReal eps, IS *points)
 39: {
 40:   PetscInt           c, cdim, i, j, o, p, vStart, vEnd;
 41:   PetscInt           npoints;
 42:   const PetscScalar *coord;
 43:   Vec                allCoordsVec;
 44:   const PetscScalar *allCoords;
 45:   PetscInt          *dagPoints;

 47:   PetscFunctionBegin;
 48:   if (eps < 0) eps = PETSC_SQRT_MACHINE_EPSILON;
 49:   PetscCall(DMGetCoordinateDim(dm, &cdim));
 50:   {
 51:     PetscInt n;

 53:     PetscCall(VecGetLocalSize(coordinates, &n));
 54:     PetscCheck(n % cdim == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Given coordinates Vec has local length %" PetscInt_FMT " not divisible by coordinate dimension %" PetscInt_FMT " of given DM", n, cdim);
 55:     npoints = n / cdim;
 56:   }
 57:   PetscCall(DMGetCoordinatesLocal(dm, &allCoordsVec));
 58:   PetscCall(VecGetArrayRead(allCoordsVec, &allCoords));
 59:   PetscCall(VecGetArrayRead(coordinates, &coord));
 60:   PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
 61:   if (PetscDefined(USE_DEBUG)) {
 62:     /* check coordinate section is consistent with DM dimension */
 63:     PetscSection cs;
 64:     PetscInt     ndof;

 66:     PetscCall(DMGetCoordinateSection(dm, &cs));
 67:     for (p = vStart; p < vEnd; p++) {
 68:       PetscCall(PetscSectionGetDof(cs, p, &ndof));
 69:       PetscCheck(ndof == cdim, PETSC_COMM_SELF, PETSC_ERR_PLIB, "point %" PetscInt_FMT ": ndof = %" PetscInt_FMT " != %" PetscInt_FMT " = cdim", p, ndof, cdim);
 70:     }
 71:   }
 72:   PetscCall(PetscMalloc1(npoints, &dagPoints));
 73:   if (eps == 0.0) {
 74:     for (i = 0, j = 0; i < npoints; i++, j += cdim) {
 75:       dagPoints[i] = -1;
 76:       for (p = vStart, o = 0; p < vEnd; p++, o += cdim) {
 77:         for (c = 0; c < cdim; c++) {
 78:           if (coord[j + c] != allCoords[o + c]) break;
 79:         }
 80:         if (c == cdim) {
 81:           dagPoints[i] = p;
 82:           break;
 83:         }
 84:       }
 85:     }
 86:   } else {
 87:     for (i = 0, j = 0; i < npoints; i++, j += cdim) {
 88:       PetscReal norm;

 90:       dagPoints[i] = -1;
 91:       for (p = vStart, o = 0; p < vEnd; p++, o += cdim) {
 92:         norm = 0.0;
 93:         for (c = 0; c < cdim; c++) norm += PetscRealPart(PetscSqr(coord[j + c] - allCoords[o + c]));
 94:         norm = PetscSqrtReal(norm);
 95:         if (norm <= eps) {
 96:           dagPoints[i] = p;
 97:           break;
 98:         }
 99:       }
100:     }
101:   }
102:   PetscCall(VecRestoreArrayRead(allCoordsVec, &allCoords));
103:   PetscCall(VecRestoreArrayRead(coordinates, &coord));
104:   PetscCall(ISCreateGeneral(PETSC_COMM_SELF, npoints, dagPoints, PETSC_OWN_POINTER, points));
105:   PetscFunctionReturn(PETSC_SUCCESS);
106: }

108: #if 0
109: static PetscErrorCode DMPlexGetLineIntersection_2D_Internal(const PetscReal segmentA[], const PetscReal segmentB[], PetscReal intersection[], PetscBool *hasIntersection)
110: {
111:   const PetscReal p0_x  = segmentA[0 * 2 + 0];
112:   const PetscReal p0_y  = segmentA[0 * 2 + 1];
113:   const PetscReal p1_x  = segmentA[1 * 2 + 0];
114:   const PetscReal p1_y  = segmentA[1 * 2 + 1];
115:   const PetscReal p2_x  = segmentB[0 * 2 + 0];
116:   const PetscReal p2_y  = segmentB[0 * 2 + 1];
117:   const PetscReal p3_x  = segmentB[1 * 2 + 0];
118:   const PetscReal p3_y  = segmentB[1 * 2 + 1];
119:   const PetscReal s1_x  = p1_x - p0_x;
120:   const PetscReal s1_y  = p1_y - p0_y;
121:   const PetscReal s2_x  = p3_x - p2_x;
122:   const PetscReal s2_y  = p3_y - p2_y;
123:   const PetscReal denom = (-s2_x * s1_y + s1_x * s2_y);

125:   PetscFunctionBegin;
126:   *hasIntersection = PETSC_FALSE;
127:   /* Non-parallel lines */
128:   if (denom != 0.0) {
129:     const PetscReal s = (-s1_y * (p0_x - p2_x) + s1_x * (p0_y - p2_y)) / denom;
130:     const PetscReal t = (s2_x * (p0_y - p2_y) - s2_y * (p0_x - p2_x)) / denom;

132:     if (s >= 0 && s <= 1 && t >= 0 && t <= 1) {
133:       *hasIntersection = PETSC_TRUE;
134:       if (intersection) {
135:         intersection[0] = p0_x + (t * s1_x);
136:         intersection[1] = p0_y + (t * s1_y);
137:       }
138:     }
139:   }
140:   PetscFunctionReturn(PETSC_SUCCESS);
141: }

143: /* The plane is segmentB x segmentC: https://en.wikipedia.org/wiki/Line%E2%80%93plane_intersection */
144: static PetscErrorCode DMPlexGetLinePlaneIntersection_3D_Internal(const PetscReal segmentA[], const PetscReal segmentB[], const PetscReal segmentC[], PetscReal intersection[], PetscBool *hasIntersection)
145: {
146:   const PetscReal p0_x  = segmentA[0 * 3 + 0];
147:   const PetscReal p0_y  = segmentA[0 * 3 + 1];
148:   const PetscReal p0_z  = segmentA[0 * 3 + 2];
149:   const PetscReal p1_x  = segmentA[1 * 3 + 0];
150:   const PetscReal p1_y  = segmentA[1 * 3 + 1];
151:   const PetscReal p1_z  = segmentA[1 * 3 + 2];
152:   const PetscReal q0_x  = segmentB[0 * 3 + 0];
153:   const PetscReal q0_y  = segmentB[0 * 3 + 1];
154:   const PetscReal q0_z  = segmentB[0 * 3 + 2];
155:   const PetscReal q1_x  = segmentB[1 * 3 + 0];
156:   const PetscReal q1_y  = segmentB[1 * 3 + 1];
157:   const PetscReal q1_z  = segmentB[1 * 3 + 2];
158:   const PetscReal r0_x  = segmentC[0 * 3 + 0];
159:   const PetscReal r0_y  = segmentC[0 * 3 + 1];
160:   const PetscReal r0_z  = segmentC[0 * 3 + 2];
161:   const PetscReal r1_x  = segmentC[1 * 3 + 0];
162:   const PetscReal r1_y  = segmentC[1 * 3 + 1];
163:   const PetscReal r1_z  = segmentC[1 * 3 + 2];
164:   const PetscReal s0_x  = p1_x - p0_x;
165:   const PetscReal s0_y  = p1_y - p0_y;
166:   const PetscReal s0_z  = p1_z - p0_z;
167:   const PetscReal s1_x  = q1_x - q0_x;
168:   const PetscReal s1_y  = q1_y - q0_y;
169:   const PetscReal s1_z  = q1_z - q0_z;
170:   const PetscReal s2_x  = r1_x - r0_x;
171:   const PetscReal s2_y  = r1_y - r0_y;
172:   const PetscReal s2_z  = r1_z - r0_z;
173:   const PetscReal s3_x  = s1_y * s2_z - s1_z * s2_y; /* s1 x s2 */
174:   const PetscReal s3_y  = s1_z * s2_x - s1_x * s2_z;
175:   const PetscReal s3_z  = s1_x * s2_y - s1_y * s2_x;
176:   const PetscReal s4_x  = s0_y * s2_z - s0_z * s2_y; /* s0 x s2 */
177:   const PetscReal s4_y  = s0_z * s2_x - s0_x * s2_z;
178:   const PetscReal s4_z  = s0_x * s2_y - s0_y * s2_x;
179:   const PetscReal s5_x  = s1_y * s0_z - s1_z * s0_y; /* s1 x s0 */
180:   const PetscReal s5_y  = s1_z * s0_x - s1_x * s0_z;
181:   const PetscReal s5_z  = s1_x * s0_y - s1_y * s0_x;
182:   const PetscReal denom = -(s0_x * s3_x + s0_y * s3_y + s0_z * s3_z); /* -s0 . (s1 x s2) */

184:   PetscFunctionBegin;
185:   *hasIntersection = PETSC_FALSE;
186:   /* Line not parallel to plane */
187:   if (denom != 0.0) {
188:     const PetscReal t = (s3_x * (p0_x - q0_x) + s3_y * (p0_y - q0_y) + s3_z * (p0_z - q0_z)) / denom;
189:     const PetscReal u = (s4_x * (p0_x - q0_x) + s4_y * (p0_y - q0_y) + s4_z * (p0_z - q0_z)) / denom;
190:     const PetscReal v = (s5_x * (p0_x - q0_x) + s5_y * (p0_y - q0_y) + s5_z * (p0_z - q0_z)) / denom;

192:     if (t >= 0 && t <= 1 && u >= 0 && u <= 1 && v >= 0 && v <= 1) {
193:       *hasIntersection = PETSC_TRUE;
194:       if (intersection) {
195:         intersection[0] = p0_x + (t * s0_x);
196:         intersection[1] = p0_y + (t * s0_y);
197:         intersection[2] = p0_z + (t * s0_z);
198:       }
199:     }
200:   }
201:   PetscFunctionReturn(PETSC_SUCCESS);
202: }
203: #endif

205: static PetscErrorCode DMPlexGetPlaneSimplexIntersection_Coords_Internal(DM dm, PetscInt dim, PetscInt cdim, const PetscScalar coords[], const PetscReal p[], const PetscReal normal[], PetscBool *pos, PetscInt *Nint, PetscReal intPoints[])
206: {
207:   PetscReal d[4]; // distance of vertices to the plane
208:   PetscReal dp;   // distance from origin to the plane
209:   PetscInt  n = 0;

211:   PetscFunctionBegin;
212:   if (pos) *pos = PETSC_FALSE;
213:   if (Nint) *Nint = 0;
214:   if (PetscDefined(USE_DEBUG)) {
215:     PetscReal mag = DMPlex_NormD_Internal(cdim, normal);
216:     PetscCheck(PetscAbsReal(mag - (PetscReal)1.0) < PETSC_SMALL, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Normal vector is not normalized: %g", (double)mag);
217:   }

219:   dp = DMPlex_DotRealD_Internal(cdim, normal, p);
220:   for (PetscInt v = 0; v < dim + 1; ++v) {
221:     // d[v] is positive, zero, or negative if vertex i is above, on, or below the plane
222: #if defined(PETSC_USE_COMPLEX)
223:     PetscReal c[4];
224:     for (PetscInt i = 0; i < cdim; ++i) c[i] = PetscRealPart(coords[v * cdim + i]);
225:     d[v] = DMPlex_DotRealD_Internal(cdim, normal, c);
226: #else
227:     d[v] = DMPlex_DotRealD_Internal(cdim, normal, &coords[v * cdim]);
228: #endif
229:     d[v] -= dp;
230:   }

232:   // If all d are positive or negative, no intersection
233:   {
234:     PetscInt v;
235:     for (v = 0; v < dim + 1; ++v)
236:       if (d[v] >= 0.) break;
237:     if (v == dim + 1) PetscFunctionReturn(PETSC_SUCCESS);
238:     for (v = 0; v < dim + 1; ++v)
239:       if (d[v] <= 0.) break;
240:     if (v == dim + 1) {
241:       if (pos) *pos = PETSC_TRUE;
242:       PetscFunctionReturn(PETSC_SUCCESS);
243:     }
244:   }

246:   for (PetscInt v = 0; v < dim + 1; ++v) {
247:     // Points with zero distance are automatically added to the list.
248:     if (PetscAbsReal(d[v]) < PETSC_MACHINE_EPSILON) {
249:       for (PetscInt i = 0; i < cdim; ++i) intPoints[n * cdim + i] = PetscRealPart(coords[v * cdim + i]);
250:       ++n;
251:     } else {
252:       // For each point with nonzero distance, seek another point with opposite sign
253:       // and higher index, and compute the intersection of the line between those
254:       // points and the plane.
255:       for (PetscInt w = v + 1; w < dim + 1; ++w) {
256:         if (d[v] * d[w] < 0.) {
257:           PetscReal inv_dist = 1. / (d[v] - d[w]);
258:           for (PetscInt i = 0; i < cdim; ++i) intPoints[n * cdim + i] = (d[v] * PetscRealPart(coords[w * cdim + i]) - d[w] * PetscRealPart(coords[v * cdim + i])) * inv_dist;
259:           ++n;
260:         }
261:       }
262:     }
263:   }
264:   // TODO order output points if there are 4
265:   *Nint = n;
266:   PetscFunctionReturn(PETSC_SUCCESS);
267: }

269: static PetscErrorCode DMPlexGetPlaneSimplexIntersection_Internal(DM dm, PetscInt dim, PetscInt c, const PetscReal p[], const PetscReal normal[], PetscBool *pos, PetscInt *Nint, PetscReal intPoints[])
270: {
271:   const PetscScalar *array;
272:   PetscScalar       *coords = NULL;
273:   PetscInt           numCoords;
274:   PetscBool          isDG;
275:   PetscInt           cdim;

277:   PetscFunctionBegin;
278:   PetscCall(DMGetCoordinateDim(dm, &cdim));
279:   PetscCheck(cdim == dim, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "DM has coordinates in %" PetscInt_FMT "D instead of %" PetscInt_FMT "D", cdim, dim);
280:   PetscCall(DMPlexGetCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
281:   PetscCheck(numCoords == dim * (dim + 1), PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Tetrahedron should have %" PetscInt_FMT " coordinates, not %" PetscInt_FMT, dim * (dim + 1), numCoords);
282:   PetscCall(PetscArrayzero(intPoints, dim * (dim + 1)));

284:   PetscCall(DMPlexGetPlaneSimplexIntersection_Coords_Internal(dm, dim, cdim, coords, p, normal, pos, Nint, intPoints));

286:   PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
287:   PetscFunctionReturn(PETSC_SUCCESS);
288: }

290: static PetscErrorCode DMPlexGetPlaneQuadIntersection_Internal(DM dm, PetscInt dim, PetscInt c, const PetscReal p[], const PetscReal normal[], PetscBool *pos, PetscInt *Nint, PetscReal intPoints[])
291: {
292:   const PetscScalar *array;
293:   PetscScalar       *coords = NULL;
294:   PetscInt           numCoords;
295:   PetscBool          isDG;
296:   PetscInt           cdim;
297:   PetscScalar        tcoords[6] = {0., 0., 0., 0., 0., 0.};
298:   const PetscInt     vertsA[3]  = {0, 1, 3};
299:   const PetscInt     vertsB[3]  = {1, 2, 3};
300:   PetscInt           NintA, NintB;

302:   PetscFunctionBegin;
303:   PetscCall(DMGetCoordinateDim(dm, &cdim));
304:   PetscCheck(cdim == dim, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "DM has coordinates in %" PetscInt_FMT "D instead of %" PetscInt_FMT "D", cdim, dim);
305:   PetscCall(DMPlexGetCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
306:   PetscCheck(numCoords == dim * 4, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Quadrilateral should have %" PetscInt_FMT " coordinates, not %" PetscInt_FMT, dim * 4, numCoords);
307:   PetscCall(PetscArrayzero(intPoints, dim * 4));

309:   for (PetscInt v = 0; v < 3; ++v)
310:     for (PetscInt d = 0; d < cdim; ++d) tcoords[v * cdim + d] = coords[vertsA[v] * cdim + d];
311:   PetscCall(DMPlexGetPlaneSimplexIntersection_Coords_Internal(dm, dim, cdim, tcoords, p, normal, pos, &NintA, intPoints));
312:   for (PetscInt v = 0; v < 3; ++v)
313:     for (PetscInt d = 0; d < cdim; ++d) tcoords[v * cdim + d] = coords[vertsB[v] * cdim + d];
314:   PetscCall(DMPlexGetPlaneSimplexIntersection_Coords_Internal(dm, dim, cdim, tcoords, p, normal, pos, &NintB, &intPoints[NintA * cdim]));
315:   *Nint = NintA + NintB;

317:   PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
318:   PetscFunctionReturn(PETSC_SUCCESS);
319: }

321: static PetscErrorCode DMPlexGetPlaneHexIntersection_Internal(DM dm, PetscInt dim, PetscInt c, const PetscReal p[], const PetscReal normal[], PetscBool *pos, PetscInt *Nint, PetscReal intPoints[])
322: {
323:   const PetscScalar *array;
324:   PetscScalar       *coords = NULL;
325:   PetscInt           numCoords;
326:   PetscBool          isDG;
327:   PetscInt           cdim;
328:   PetscScalar        tcoords[12] = {0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.};
329:   // We split using the (2, 4) main diagonal, so all tets contain those vertices
330:   const PetscInt vertsA[4] = {0, 1, 2, 4};
331:   const PetscInt vertsB[4] = {0, 2, 3, 4};
332:   const PetscInt vertsC[4] = {1, 7, 2, 4};
333:   const PetscInt vertsD[4] = {2, 7, 6, 4};
334:   const PetscInt vertsE[4] = {3, 5, 4, 2};
335:   const PetscInt vertsF[4] = {4, 5, 6, 2};
336:   PetscInt       NintA, NintB, NintC, NintD, NintE, NintF, Nsum = 0;

338:   PetscFunctionBegin;
339:   PetscCall(DMGetCoordinateDim(dm, &cdim));
340:   PetscCheck(cdim == dim, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "DM has coordinates in %" PetscInt_FMT "D instead of %" PetscInt_FMT "D", cdim, dim);
341:   PetscCall(DMPlexGetCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
342:   PetscCheck(numCoords == dim * 8, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Hexahedron should have %" PetscInt_FMT " coordinates, not %" PetscInt_FMT, dim * 8, numCoords);
343:   PetscCall(PetscArrayzero(intPoints, dim * 18));

345:   for (PetscInt v = 0; v < 4; ++v)
346:     for (PetscInt d = 0; d < cdim; ++d) tcoords[v * cdim + d] = coords[vertsA[v] * cdim + d];
347:   PetscCall(DMPlexGetPlaneSimplexIntersection_Coords_Internal(dm, dim, cdim, tcoords, p, normal, pos, &NintA, &intPoints[Nsum * cdim]));
348:   Nsum += NintA;
349:   for (PetscInt v = 0; v < 4; ++v)
350:     for (PetscInt d = 0; d < cdim; ++d) tcoords[v * cdim + d] = coords[vertsB[v] * cdim + d];
351:   PetscCall(DMPlexGetPlaneSimplexIntersection_Coords_Internal(dm, dim, cdim, tcoords, p, normal, pos, &NintB, &intPoints[Nsum * cdim]));
352:   Nsum += NintB;
353:   for (PetscInt v = 0; v < 4; ++v)
354:     for (PetscInt d = 0; d < cdim; ++d) tcoords[v * cdim + d] = coords[vertsC[v] * cdim + d];
355:   PetscCall(DMPlexGetPlaneSimplexIntersection_Coords_Internal(dm, dim, cdim, tcoords, p, normal, pos, &NintC, &intPoints[Nsum * cdim]));
356:   Nsum += NintC;
357:   for (PetscInt v = 0; v < 4; ++v)
358:     for (PetscInt d = 0; d < cdim; ++d) tcoords[v * cdim + d] = coords[vertsD[v] * cdim + d];
359:   PetscCall(DMPlexGetPlaneSimplexIntersection_Coords_Internal(dm, dim, cdim, tcoords, p, normal, pos, &NintD, &intPoints[Nsum * cdim]));
360:   Nsum += NintD;
361:   for (PetscInt v = 0; v < 4; ++v)
362:     for (PetscInt d = 0; d < cdim; ++d) tcoords[v * cdim + d] = coords[vertsE[v] * cdim + d];
363:   PetscCall(DMPlexGetPlaneSimplexIntersection_Coords_Internal(dm, dim, cdim, tcoords, p, normal, pos, &NintE, &intPoints[Nsum * cdim]));
364:   Nsum += NintE;
365:   for (PetscInt v = 0; v < 4; ++v)
366:     for (PetscInt d = 0; d < cdim; ++d) tcoords[v * cdim + d] = coords[vertsF[v] * cdim + d];
367:   PetscCall(DMPlexGetPlaneSimplexIntersection_Coords_Internal(dm, dim, cdim, tcoords, p, normal, pos, &NintF, &intPoints[Nsum * cdim]));
368:   Nsum += NintF;
369:   *Nint = Nsum;

371:   PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
372:   PetscFunctionReturn(PETSC_SUCCESS);
373: }

375: /*
376:   DMPlexGetPlaneCellIntersection_Internal - Finds the intersection of a plane with a cell

378:   Not collective

380:   Input Parameters:
381: + dm     - the DM
382: . c      - the mesh point
383: . p      - a point on the plane.
384: - normal - a normal vector to the plane, must be normalized

386:   Output Parameters:
387: . pos       - `PETSC_TRUE` is the cell is on the positive side of the plane, `PETSC_FALSE` on the negative side
388: + Nint      - the number of intersection points, in [0, 4]
389: - intPoints - the coordinates of the intersection points, should be length at least 12

391:   Note: The `pos` argument is only meaningful if the number of intersections is 0. The algorithmic idea comes from https://github.com/chrisk314/tet-plane-intersection.

393:   Level: developer

395: .seealso:
396: @*/
397: static PetscErrorCode DMPlexGetPlaneCellIntersection_Internal(DM dm, PetscInt c, const PetscReal p[], const PetscReal normal[], PetscBool *pos, PetscInt *Nint, PetscReal intPoints[])
398: {
399:   DMPolytopeType ct;

401:   PetscFunctionBegin;
402:   PetscCall(DMPlexGetCellType(dm, c, &ct));
403:   switch (ct) {
404:   case DM_POLYTOPE_SEGMENT:
405:   case DM_POLYTOPE_TRIANGLE:
406:   case DM_POLYTOPE_TETRAHEDRON:
407:     PetscCall(DMPlexGetPlaneSimplexIntersection_Internal(dm, DMPolytopeTypeGetDim(ct), c, p, normal, pos, Nint, intPoints));
408:     break;
409:   case DM_POLYTOPE_QUADRILATERAL:
410:     PetscCall(DMPlexGetPlaneQuadIntersection_Internal(dm, DMPolytopeTypeGetDim(ct), c, p, normal, pos, Nint, intPoints));
411:     break;
412:   case DM_POLYTOPE_HEXAHEDRON:
413:     PetscCall(DMPlexGetPlaneHexIntersection_Internal(dm, DMPolytopeTypeGetDim(ct), c, p, normal, pos, Nint, intPoints));
414:     break;
415:   default:
416:     SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No plane intersection for cell %" PetscInt_FMT " with type %s", c, DMPolytopeTypes[ct]);
417:   }
418:   PetscFunctionReturn(PETSC_SUCCESS);
419: }

421: static PetscErrorCode DMPlexLocatePoint_Simplex_1D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
422: {
423:   const PetscReal eps = PETSC_SQRT_MACHINE_EPSILON;
424:   const PetscReal x   = PetscRealPart(point[0]);
425:   PetscReal       v0, J, invJ, detJ;
426:   PetscReal       xi;

428:   PetscFunctionBegin;
429:   PetscCall(DMPlexComputeCellGeometryFEM(dm, c, NULL, &v0, &J, &invJ, &detJ));
430:   xi = invJ * (x - v0);

432:   if ((xi >= -eps) && (xi <= 2. + eps)) *cell = c;
433:   else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
434:   PetscFunctionReturn(PETSC_SUCCESS);
435: }

437: static PetscErrorCode DMPlexLocatePoint_Simplex_2D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
438: {
439:   const PetscInt  embedDim = 2;
440:   const PetscReal eps      = PETSC_SQRT_MACHINE_EPSILON;
441:   PetscReal       x        = PetscRealPart(point[0]);
442:   PetscReal       y        = PetscRealPart(point[1]);
443:   PetscReal       v0[2], J[4], invJ[4], detJ;
444:   PetscReal       xi, eta;

446:   PetscFunctionBegin;
447:   PetscCall(DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ));
448:   xi  = invJ[0 * embedDim + 0] * (x - v0[0]) + invJ[0 * embedDim + 1] * (y - v0[1]);
449:   eta = invJ[1 * embedDim + 0] * (x - v0[0]) + invJ[1 * embedDim + 1] * (y - v0[1]);

451:   if ((xi >= -eps) && (eta >= -eps) && (xi + eta <= 2.0 + eps)) *cell = c;
452:   else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
453:   PetscFunctionReturn(PETSC_SUCCESS);
454: }

456: static PetscErrorCode DMPlexClosestPoint_Simplex_2D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscReal cpoint[])
457: {
458:   const PetscInt embedDim = 2;
459:   PetscReal      x        = PetscRealPart(point[0]);
460:   PetscReal      y        = PetscRealPart(point[1]);
461:   PetscReal      v0[2], J[4], invJ[4], detJ;
462:   PetscReal      xi, eta, r;

464:   PetscFunctionBegin;
465:   PetscCall(DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ));
466:   xi  = invJ[0 * embedDim + 0] * (x - v0[0]) + invJ[0 * embedDim + 1] * (y - v0[1]);
467:   eta = invJ[1 * embedDim + 0] * (x - v0[0]) + invJ[1 * embedDim + 1] * (y - v0[1]);

469:   xi  = PetscMax(xi, 0.0);
470:   eta = PetscMax(eta, 0.0);
471:   if (xi + eta > 2.0) {
472:     r = (xi + eta) / 2.0;
473:     xi /= r;
474:     eta /= r;
475:   }
476:   cpoint[0] = J[0 * embedDim + 0] * xi + J[0 * embedDim + 1] * eta + v0[0];
477:   cpoint[1] = J[1 * embedDim + 0] * xi + J[1 * embedDim + 1] * eta + v0[1];
478:   PetscFunctionReturn(PETSC_SUCCESS);
479: }

481: // This is the ray-casting, or even-odd algorithm: https://en.wikipedia.org/wiki/Even%E2%80%93odd_rule
482: static PetscErrorCode DMPlexLocatePoint_Quad_2D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
483: {
484:   const PetscScalar *array;
485:   PetscScalar       *coords    = NULL;
486:   const PetscInt     faces[8]  = {0, 1, 1, 2, 2, 3, 3, 0};
487:   PetscReal          x         = PetscRealPart(point[0]);
488:   PetscReal          y         = PetscRealPart(point[1]);
489:   PetscInt           crossings = 0, numCoords, f;
490:   PetscBool          isDG;

492:   PetscFunctionBegin;
493:   PetscCall(DMPlexGetCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
494:   PetscCheck(numCoords == 8, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Quadrilateral should have 8 coordinates, not %" PetscInt_FMT, numCoords);
495:   for (f = 0; f < 4; ++f) {
496:     PetscReal x_i = PetscRealPart(coords[faces[2 * f + 0] * 2 + 0]);
497:     PetscReal y_i = PetscRealPart(coords[faces[2 * f + 0] * 2 + 1]);
498:     PetscReal x_j = PetscRealPart(coords[faces[2 * f + 1] * 2 + 0]);
499:     PetscReal y_j = PetscRealPart(coords[faces[2 * f + 1] * 2 + 1]);

501:     if ((x == x_j) && (y == y_j)) {
502:       // point is a corner
503:       crossings = 1;
504:       break;
505:     }
506:     if ((y_j > y) != (y_i > y)) {
507:       PetscReal slope = (x - x_j) * (y_i - y_j) - (x_i - x_j) * (y - y_j);
508:       if (slope == 0) {
509:         // point is a corner
510:         crossings = 1;
511:         break;
512:       }
513:       if ((slope < 0) != (y_i < y_j)) ++crossings;
514:     }
515:   }
516:   if (crossings % 2) *cell = c;
517:   else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
518:   PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
519:   PetscFunctionReturn(PETSC_SUCCESS);
520: }

522: static PetscErrorCode DMPlexLocatePoint_Simplex_3D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
523: {
524:   const PetscInt  embedDim = 3;
525:   const PetscReal eps      = PETSC_SQRT_MACHINE_EPSILON;
526:   PetscReal       v0[3], J[9], invJ[9], detJ;
527:   PetscReal       x = PetscRealPart(point[0]);
528:   PetscReal       y = PetscRealPart(point[1]);
529:   PetscReal       z = PetscRealPart(point[2]);
530:   PetscReal       xi, eta, zeta;

532:   PetscFunctionBegin;
533:   PetscCall(DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ));
534:   xi   = invJ[0 * embedDim + 0] * (x - v0[0]) + invJ[0 * embedDim + 1] * (y - v0[1]) + invJ[0 * embedDim + 2] * (z - v0[2]);
535:   eta  = invJ[1 * embedDim + 0] * (x - v0[0]) + invJ[1 * embedDim + 1] * (y - v0[1]) + invJ[1 * embedDim + 2] * (z - v0[2]);
536:   zeta = invJ[2 * embedDim + 0] * (x - v0[0]) + invJ[2 * embedDim + 1] * (y - v0[1]) + invJ[2 * embedDim + 2] * (z - v0[2]);

538:   if ((xi >= -eps) && (eta >= -eps) && (zeta >= -eps) && (xi + eta + zeta <= 2.0 + eps)) *cell = c;
539:   else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
540:   PetscFunctionReturn(PETSC_SUCCESS);
541: }

543: static PetscErrorCode DMPlexLocatePoint_General_3D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
544: {
545:   const PetscScalar *array;
546:   PetscScalar       *coords    = NULL;
547:   const PetscInt     faces[24] = {0, 3, 2, 1, 5, 4, 7, 6, 3, 0, 4, 5, 1, 2, 6, 7, 3, 5, 6, 2, 0, 1, 7, 4};
548:   PetscBool          found     = PETSC_TRUE;
549:   PetscInt           numCoords, f;
550:   PetscBool          isDG;

552:   PetscFunctionBegin;
553:   PetscCall(DMPlexGetCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
554:   PetscCheck(numCoords == 24, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Quadrilateral should have 8 coordinates, not %" PetscInt_FMT, numCoords);
555:   for (f = 0; f < 6; ++f) {
556:     /* Check the point is under plane */
557:     /*   Get face normal */
558:     PetscReal v_i[3];
559:     PetscReal v_j[3];
560:     PetscReal normal[3];
561:     PetscReal pp[3];
562:     PetscReal dot;

564:     v_i[0]    = PetscRealPart(coords[faces[f * 4 + 3] * 3 + 0] - coords[faces[f * 4 + 0] * 3 + 0]);
565:     v_i[1]    = PetscRealPart(coords[faces[f * 4 + 3] * 3 + 1] - coords[faces[f * 4 + 0] * 3 + 1]);
566:     v_i[2]    = PetscRealPart(coords[faces[f * 4 + 3] * 3 + 2] - coords[faces[f * 4 + 0] * 3 + 2]);
567:     v_j[0]    = PetscRealPart(coords[faces[f * 4 + 1] * 3 + 0] - coords[faces[f * 4 + 0] * 3 + 0]);
568:     v_j[1]    = PetscRealPart(coords[faces[f * 4 + 1] * 3 + 1] - coords[faces[f * 4 + 0] * 3 + 1]);
569:     v_j[2]    = PetscRealPart(coords[faces[f * 4 + 1] * 3 + 2] - coords[faces[f * 4 + 0] * 3 + 2]);
570:     normal[0] = v_i[1] * v_j[2] - v_i[2] * v_j[1];
571:     normal[1] = v_i[2] * v_j[0] - v_i[0] * v_j[2];
572:     normal[2] = v_i[0] * v_j[1] - v_i[1] * v_j[0];
573:     pp[0]     = PetscRealPart(coords[faces[f * 4 + 0] * 3 + 0] - point[0]);
574:     pp[1]     = PetscRealPart(coords[faces[f * 4 + 0] * 3 + 1] - point[1]);
575:     pp[2]     = PetscRealPart(coords[faces[f * 4 + 0] * 3 + 2] - point[2]);
576:     dot       = normal[0] * pp[0] + normal[1] * pp[1] + normal[2] * pp[2];

578:     /* Check that projected point is in face (2D location problem) */
579:     if (dot < 0.0) {
580:       found = PETSC_FALSE;
581:       break;
582:     }
583:   }
584:   if (found) *cell = c;
585:   else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
586:   PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
587:   PetscFunctionReturn(PETSC_SUCCESS);
588: }

590: static PetscErrorCode PetscGridHashInitialize_Internal(PetscGridHash box, PetscInt dim, const PetscScalar point[])
591: {
592:   PetscInt d;

594:   PetscFunctionBegin;
595:   box->dim = dim;
596:   for (d = 0; d < dim; ++d) box->lower[d] = box->upper[d] = point ? PetscRealPart(point[d]) : 0.;
597:   PetscFunctionReturn(PETSC_SUCCESS);
598: }

600: PetscErrorCode PetscGridHashCreate(MPI_Comm comm, PetscInt dim, const PetscScalar point[], PetscGridHash *box)
601: {
602:   PetscFunctionBegin;
603:   PetscCall(PetscCalloc1(1, box));
604:   PetscCall(PetscGridHashInitialize_Internal(*box, dim, point));
605:   PetscFunctionReturn(PETSC_SUCCESS);
606: }

608: PetscErrorCode PetscGridHashEnlarge(PetscGridHash box, const PetscScalar point[])
609: {
610:   PetscInt d;

612:   PetscFunctionBegin;
613:   for (d = 0; d < box->dim; ++d) {
614:     box->lower[d] = PetscMin(box->lower[d], PetscRealPart(point[d]));
615:     box->upper[d] = PetscMax(box->upper[d], PetscRealPart(point[d]));
616:   }
617:   PetscFunctionReturn(PETSC_SUCCESS);
618: }

620: static PetscErrorCode DMPlexCreateGridHash(DM dm, PetscGridHash *box)
621: {
622:   Vec                coordinates;
623:   const PetscScalar *a;
624:   PetscInt           cdim, cStart, cEnd;

626:   PetscFunctionBegin;
627:   PetscCall(DMGetCoordinateDim(dm, &cdim));
628:   PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
629:   PetscCall(DMGetCoordinatesLocal(dm, &coordinates));

631:   PetscCall(VecGetArrayRead(coordinates, &a));
632:   PetscCall(PetscGridHashCreate(PetscObjectComm((PetscObject)dm), cdim, a, box));
633:   PetscCall(VecRestoreArrayRead(coordinates, &a));
634:   for (PetscInt c = cStart; c < cEnd; ++c) {
635:     const PetscScalar *array;
636:     PetscScalar       *coords = NULL;
637:     PetscInt           numCoords;
638:     PetscBool          isDG;

640:     PetscCall(DMPlexGetCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
641:     for (PetscInt i = 0; i < numCoords / cdim; ++i) PetscCall(PetscGridHashEnlarge(*box, &coords[i * cdim]));
642:     PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
643:   }
644:   PetscFunctionReturn(PETSC_SUCCESS);
645: }

647: /*@C
648:   PetscGridHashSetGrid - Divide the grid into boxes

650:   Not Collective

652:   Input Parameters:
653: + box - The grid hash object
654: . n   - The number of boxes in each dimension, may use `PETSC_DETERMINE` for the entries
655: - h   - The box size in each dimension, only used if n[d] == `PETSC_DETERMINE`, if not needed you can pass in `NULL`

657:   Level: developer

659: .seealso: `DMPLEX`, `PetscGridHashCreate()`
660: @*/
661: PetscErrorCode PetscGridHashSetGrid(PetscGridHash box, const PetscInt n[], const PetscReal h[])
662: {
663:   PetscInt d;

665:   PetscFunctionBegin;
666:   PetscAssertPointer(n, 2);
667:   if (h) PetscAssertPointer(h, 3);
668:   for (d = 0; d < box->dim; ++d) {
669:     box->extent[d] = box->upper[d] - box->lower[d];
670:     if (n[d] == PETSC_DETERMINE) {
671:       PetscCheck(h, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Missing h");
672:       box->h[d] = h[d];
673:       box->n[d] = PetscCeilReal(box->extent[d] / h[d]);
674:     } else {
675:       box->n[d] = n[d];
676:       box->h[d] = box->extent[d] / n[d];
677:     }
678:   }
679:   PetscFunctionReturn(PETSC_SUCCESS);
680: }

682: /*@C
683:   PetscGridHashGetEnclosingBox - Find the grid boxes containing each input point

685:   Not Collective

687:   Input Parameters:
688: + box       - The grid hash object
689: . numPoints - The number of input points
690: - points    - The input point coordinates

692:   Output Parameters:
693: + dboxes - An array of `numPoints` x `dim` integers expressing the enclosing box as (i_0, i_1, ..., i_dim)
694: - boxes  - An array of `numPoints` integers expressing the enclosing box as single number, or `NULL`

696:   Level: developer

698:   Note:
699:   This only guarantees that a box contains a point, not that a cell does.

701: .seealso: `DMPLEX`, `PetscGridHashCreate()`
702: @*/
703: PetscErrorCode PetscGridHashGetEnclosingBox(PetscGridHash box, PetscInt numPoints, const PetscScalar points[], PetscInt dboxes[], PetscInt boxes[])
704: {
705:   const PetscReal *lower = box->lower;
706:   const PetscReal *upper = box->upper;
707:   const PetscReal *h     = box->h;
708:   const PetscInt  *n     = box->n;
709:   const PetscInt   dim   = box->dim;
710:   PetscInt         d, p;

712:   PetscFunctionBegin;
713:   for (p = 0; p < numPoints; ++p) {
714:     for (d = 0; d < dim; ++d) {
715:       PetscInt dbox = PetscFloorReal((PetscRealPart(points[p * dim + d]) - lower[d]) / h[d]);

717:       if (dbox == n[d] && PetscAbsReal(PetscRealPart(points[p * dim + d]) - upper[d]) < 1.0e-9) dbox = n[d] - 1;
718:       if (dbox == -1 && PetscAbsReal(PetscRealPart(points[p * dim + d]) - lower[d]) < 1.0e-9) dbox = 0;
719:       PetscCheck(dbox >= 0 && dbox < n[d], PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Input point %" PetscInt_FMT " (%g, %g, %g) is outside of our bounding box (%g, %g, %g) - (%g, %g, %g)", p, (double)PetscRealPart(points[p * dim + 0]), dim > 1 ? (double)PetscRealPart(points[p * dim + 1]) : 0.0, dim > 2 ? (double)PetscRealPart(points[p * dim + 2]) : 0.0, (double)lower[0], (double)lower[1], (double)lower[2], (double)upper[0], (double)upper[1], (double)upper[2]);
720:       dboxes[p * dim + d] = dbox;
721:     }
722:     if (boxes)
723:       for (d = dim - 2, boxes[p] = dboxes[p * dim + dim - 1]; d >= 0; --d) boxes[p] = boxes[p] * n[d] + dboxes[p * dim + d];
724:   }
725:   PetscFunctionReturn(PETSC_SUCCESS);
726: }

728: /*
729:   PetscGridHashGetEnclosingBoxQuery - Find the grid boxes containing each input point

731:   Not Collective

733:   Input Parameters:
734: + box         - The grid hash object
735: . cellSection - The PetscSection mapping cells to boxes
736: . numPoints   - The number of input points
737: - points      - The input point coordinates

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

744:   Level: developer

746:   Note:
747:   This does an additional check that a cell actually contains the point, and found is `PETSC_FALSE` if no cell does. Thus, this function requires that `cellSection` is already constructed.

749: .seealso: `DMPLEX`, `PetscGridHashGetEnclosingBox()`
750: */
751: static PetscErrorCode PetscGridHashGetEnclosingBoxQuery(PetscGridHash box, PetscSection cellSection, PetscInt numPoints, const PetscScalar points[], PetscInt dboxes[], PetscInt boxes[], PetscBool *found)
752: {
753:   const PetscReal *lower = box->lower;
754:   const PetscReal *upper = box->upper;
755:   const PetscReal *h     = box->h;
756:   const PetscInt  *n     = box->n;
757:   const PetscInt   dim   = box->dim;
758:   PetscInt         bStart, bEnd, d, p;

760:   PetscFunctionBegin;
762:   *found = PETSC_FALSE;
763:   PetscCall(PetscSectionGetChart(box->cellSection, &bStart, &bEnd));
764:   for (p = 0; p < numPoints; ++p) {
765:     for (d = 0; d < dim; ++d) {
766:       PetscInt dbox = PetscFloorReal((PetscRealPart(points[p * dim + d]) - lower[d]) / h[d]);

768:       if (dbox == n[d] && PetscAbsReal(PetscRealPart(points[p * dim + d]) - upper[d]) < 1.0e-9) dbox = n[d] - 1;
769:       if (dbox < 0 || dbox >= n[d]) PetscFunctionReturn(PETSC_SUCCESS);
770:       dboxes[p * dim + d] = dbox;
771:     }
772:     if (boxes)
773:       for (d = dim - 2, boxes[p] = dboxes[p * dim + dim - 1]; d >= 0; --d) boxes[p] = boxes[p] * n[d] + dboxes[p * dim + d];
774:     // It is possible for a box to overlap no grid cells
775:     if (boxes[p] < bStart || boxes[p] >= bEnd) PetscFunctionReturn(PETSC_SUCCESS);
776:   }
777:   *found = PETSC_TRUE;
778:   PetscFunctionReturn(PETSC_SUCCESS);
779: }

781: PetscErrorCode PetscGridHashDestroy(PetscGridHash *box)
782: {
783:   PetscFunctionBegin;
784:   if (*box) {
785:     PetscCall(PetscSectionDestroy(&(*box)->cellSection));
786:     PetscCall(ISDestroy(&(*box)->cells));
787:     PetscCall(DMLabelDestroy(&(*box)->cellsSparse));
788:   }
789:   PetscCall(PetscFree(*box));
790:   PetscFunctionReturn(PETSC_SUCCESS);
791: }

793: PetscErrorCode DMPlexLocatePoint_Internal(DM dm, PetscInt dim, const PetscScalar point[], PetscInt cellStart, PetscInt *cell)
794: {
795:   DMPolytopeType ct;

797:   PetscFunctionBegin;
798:   PetscCall(DMPlexGetCellType(dm, cellStart, &ct));
799:   switch (ct) {
800:   case DM_POLYTOPE_SEGMENT:
801:     PetscCall(DMPlexLocatePoint_Simplex_1D_Internal(dm, point, cellStart, cell));
802:     break;
803:   case DM_POLYTOPE_TRIANGLE:
804:     PetscCall(DMPlexLocatePoint_Simplex_2D_Internal(dm, point, cellStart, cell));
805:     break;
806:   case DM_POLYTOPE_QUADRILATERAL:
807:     PetscCall(DMPlexLocatePoint_Quad_2D_Internal(dm, point, cellStart, cell));
808:     break;
809:   case DM_POLYTOPE_TETRAHEDRON:
810:     PetscCall(DMPlexLocatePoint_Simplex_3D_Internal(dm, point, cellStart, cell));
811:     break;
812:   case DM_POLYTOPE_HEXAHEDRON:
813:     PetscCall(DMPlexLocatePoint_General_3D_Internal(dm, point, cellStart, cell));
814:     break;
815:   default:
816:     SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No point location for cell %" PetscInt_FMT " with type %s", cellStart, DMPolytopeTypes[ct]);
817:   }
818:   PetscFunctionReturn(PETSC_SUCCESS);
819: }

821: /*
822:   DMPlexClosestPoint_Internal - Returns the closest point in the cell to the given point
823: */
824: static PetscErrorCode DMPlexClosestPoint_Internal(DM dm, PetscInt dim, const PetscScalar point[], PetscInt cell, PetscReal cpoint[])
825: {
826:   DMPolytopeType ct;

828:   PetscFunctionBegin;
829:   PetscCall(DMPlexGetCellType(dm, cell, &ct));
830:   switch (ct) {
831:   case DM_POLYTOPE_TRIANGLE:
832:     PetscCall(DMPlexClosestPoint_Simplex_2D_Internal(dm, point, cell, cpoint));
833:     break;
834: #if 0
835:     case DM_POLYTOPE_QUADRILATERAL:
836:     PetscCall(DMPlexClosestPoint_General_2D_Internal(dm, point, cell, cpoint));break;
837:     case DM_POLYTOPE_TETRAHEDRON:
838:     PetscCall(DMPlexClosestPoint_Simplex_3D_Internal(dm, point, cell, cpoint));break;
839:     case DM_POLYTOPE_HEXAHEDRON:
840:     PetscCall(DMPlexClosestPoint_General_3D_Internal(dm, point, cell, cpoint));break;
841: #endif
842:   default:
843:     SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No closest point location for cell %" PetscInt_FMT " with type %s", cell, DMPolytopeTypes[ct]);
844:   }
845:   PetscFunctionReturn(PETSC_SUCCESS);
846: }

848: /*
849:   DMPlexComputeGridHash_Internal - Create a grid hash structure covering the `DMPLEX`

851:   Collective

853:   Input Parameter:
854: . dm - The `DMPLEX`

856:   Output Parameter:
857: . localBox - The grid hash object

859:   Level: developer

861:   Notes:
862:   How do we determine all boxes intersecting a given cell?

864:   1) Get convex body enclosing cell. We will use a box called the box-hull.

866:   2) Get smallest brick of boxes enclosing the box-hull

868:   3) Each box is composed of 6 planes, 3 lower and 3 upper. We loop over dimensions, and
869:      for each new plane determine whether the cell is on the negative side, positive side, or intersects it.

871:      a) If the cell is on the negative side of the lower planes, it is not in the box

873:      b) If the cell is on the positive side of the upper planes, it is not in the box

875:      c) If there is no intersection, it is in the box

877:      d) If any intersection point is within the box limits, it is in the box

879: .seealso: `DMPLEX`, `PetscGridHashCreate()`, `PetscGridHashGetEnclosingBox()`
880: */
881: static PetscErrorCode DMPlexComputeGridHash_Internal(DM dm, PetscGridHash *localBox)
882: {
883:   PetscInt        debug = ((DM_Plex *)dm->data)->printLocate;
884:   PetscGridHash   lbox;
885:   PetscSF         sf;
886:   const PetscInt *leaves;
887:   PetscInt       *dboxes, *boxes;
888:   PetscInt        cdim, cStart, cEnd, Nl = -1;
889:   PetscBool       flg;

891:   PetscFunctionBegin;
892:   PetscCall(DMGetCoordinateDim(dm, &cdim));
893:   PetscCall(DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd));
894:   PetscCall(DMPlexCreateGridHash(dm, &lbox));
895:   {
896:     PetscInt n[3], d;

898:     PetscCall(PetscOptionsGetIntArray(NULL, ((PetscObject)dm)->prefix, "-dm_plex_hash_box_faces", n, &d, &flg));
899:     if (flg) {
900:       for (PetscInt i = d; i < cdim; ++i) n[i] = n[d - 1];
901:     } else {
902:       for (PetscInt i = 0; i < cdim; ++i) n[i] = PetscMax(2, PetscFloorReal(PetscPowReal((PetscReal)(cEnd - cStart), 1.0 / cdim) * 0.8));
903:     }
904:     PetscCall(PetscGridHashSetGrid(lbox, n, NULL));
905:     if (debug)
906:       PetscCall(PetscPrintf(PETSC_COMM_SELF, "GridHash:\n  (%g, %g, %g) -- (%g, %g, %g)\n  n %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT "\n  h %g %g %g\n", (double)lbox->lower[0], (double)lbox->lower[1], cdim > 2 ? (double)lbox->lower[2] : 0.,
907:                             (double)lbox->upper[0], (double)lbox->upper[1], cdim > 2 ? (double)lbox->upper[2] : 0, n[0], n[1], cdim > 2 ? n[2] : 0, (double)lbox->h[0], (double)lbox->h[1], cdim > 2 ? (double)lbox->h[2] : 0.));
908:   }

910:   PetscCall(DMGetPointSF(dm, &sf));
911:   if (sf) PetscCall(PetscSFGetGraph(sf, NULL, &Nl, &leaves, NULL));
912:   Nl = PetscMax(Nl, 0);
913:   PetscCall(PetscCalloc2(16 * cdim, &dboxes, 16, &boxes));

915:   PetscCall(DMLabelCreate(PETSC_COMM_SELF, "cells", &lbox->cellsSparse));
916:   PetscCall(DMLabelCreateIndex(lbox->cellsSparse, cStart, cEnd));
917:   for (PetscInt c = cStart; c < cEnd; ++c) {
918:     PetscReal          intPoints[6 * 6 * 6 * 3];
919:     const PetscScalar *array;
920:     PetscScalar       *coords            = NULL;
921:     const PetscReal   *h                 = lbox->h;
922:     PetscReal          normal[9]         = {1., 0., 0., 0., 1., 0., 0., 0., 1.};
923:     PetscReal         *lowerIntPoints[3] = {&intPoints[0 * 6 * 6 * 3], &intPoints[1 * 6 * 6 * 3], &intPoints[2 * 6 * 6 * 3]};
924:     PetscReal         *upperIntPoints[3] = {&intPoints[3 * 6 * 6 * 3], &intPoints[4 * 6 * 6 * 3], &intPoints[5 * 6 * 6 * 3]};
925:     PetscReal          lp[3], up[3], *tmp;
926:     PetscInt           numCoords, idx, dlim[6], lowerInt[3], upperInt[3];
927:     PetscBool          isDG, lower[3], upper[3];

929:     PetscCall(PetscFindInt(c, Nl, leaves, &idx));
930:     if (idx >= 0) continue;
931:     // Get grid of boxes containing the cell
932:     PetscCall(DMPlexGetCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
933:     PetscCall(PetscGridHashGetEnclosingBox(lbox, numCoords / cdim, coords, dboxes, boxes));
934:     PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
935:     for (PetscInt d = 0; d < cdim; ++d) dlim[d * 2 + 0] = dlim[d * 2 + 1] = dboxes[d];
936:     for (PetscInt d = cdim; d < 3; ++d) dlim[d * 2 + 0] = dlim[d * 2 + 1] = 0;
937:     for (PetscInt e = 1; e < numCoords / cdim; ++e) {
938:       for (PetscInt d = 0; d < cdim; ++d) {
939:         dlim[d * 2 + 0] = PetscMin(dlim[d * 2 + 0], dboxes[e * cdim + d]);
940:         dlim[d * 2 + 1] = PetscMax(dlim[d * 2 + 1], dboxes[e * cdim + d]);
941:       }
942:     }
943:     if (debug > 4) {
944:       for (PetscInt d = 0; d < cdim; ++d) PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Cell %" PetscInt_FMT " direction %" PetscInt_FMT " box limits %" PetscInt_FMT "--%" PetscInt_FMT "\n", c, d, dlim[d * 2 + 0], dlim[d * 2 + 1]));
945:     }
946:     // Initialize with lower planes for first box
947:     for (PetscInt d = 0; d < cdim; ++d) {
948:       lp[d] = lbox->lower[d] + dlim[d * 2 + 0] * h[d];
949:       up[d] = lp[d] + h[d];
950:     }
951:     for (PetscInt d = 0; d < cdim; ++d) {
952:       PetscCall(DMPlexGetPlaneCellIntersection_Internal(dm, c, lp, &normal[d * 3], &lower[d], &lowerInt[d], lowerIntPoints[d]));
953:       if (debug > 4) {
954:         if (!lowerInt[d])
955:           PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Cell %" PetscInt_FMT " lower direction %" PetscInt_FMT " (%g, %g, %g) does not intersect %s\n", c, d, (double)lp[0], (double)lp[1], cdim > 2 ? (double)lp[2] : 0., lower[d] ? "positive" : "negative"));
956:         else PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Cell %" PetscInt_FMT " lower direction %" PetscInt_FMT " (%g, %g, %g) intersects %" PetscInt_FMT " times\n", c, d, (double)lp[0], (double)lp[1], cdim > 2 ? (double)lp[2] : 0., lowerInt[d]));
957:       }
958:     }
959:     // Loop over grid
960:     for (PetscInt k = dlim[2 * 2 + 0]; k <= dlim[2 * 2 + 1]; ++k, lp[2] = up[2], up[2] += h[2]) {
961:       if (cdim > 2) PetscCall(DMPlexGetPlaneCellIntersection_Internal(dm, c, up, &normal[3 * 2], &upper[2], &upperInt[2], upperIntPoints[2]));
962:       if (cdim > 2 && debug > 4) {
963:         if (!upperInt[2]) PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Cell %" PetscInt_FMT " upper direction 2 (%g, %g, %g) does not intersect %s\n", c, (double)up[0], (double)up[1], cdim > 2 ? (double)up[2] : 0., upper[2] ? "positive" : "negative"));
964:         else PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Cell %" PetscInt_FMT " upper direction 2 (%g, %g, %g) intersects %" PetscInt_FMT " times\n", c, (double)up[0], (double)up[1], cdim > 2 ? (double)up[2] : 0., upperInt[2]));
965:       }
966:       for (PetscInt j = dlim[1 * 2 + 0]; j <= dlim[1 * 2 + 1]; ++j, lp[1] = up[1], up[1] += h[1]) {
967:         if (cdim > 1) PetscCall(DMPlexGetPlaneCellIntersection_Internal(dm, c, up, &normal[3 * 1], &upper[1], &upperInt[1], upperIntPoints[1]));
968:         if (cdim > 1 && debug > 4) {
969:           if (!upperInt[1])
970:             PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Cell %" PetscInt_FMT " upper direction 1 (%g, %g, %g) does not intersect %s\n", c, (double)up[0], (double)up[1], cdim > 2 ? (double)up[2] : 0., upper[1] ? "positive" : "negative"));
971:           else PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Cell %" PetscInt_FMT " upper direction 1 (%g, %g, %g) intersects %" PetscInt_FMT " times\n", c, (double)up[0], (double)up[1], cdim > 2 ? (double)up[2] : 0., upperInt[1]));
972:         }
973:         for (PetscInt i = dlim[0 * 2 + 0]; i <= dlim[0 * 2 + 1]; ++i, lp[0] = up[0], up[0] += h[0]) {
974:           const PetscInt box    = (k * lbox->n[1] + j) * lbox->n[0] + i;
975:           PetscBool      excNeg = PETSC_TRUE;
976:           PetscBool      excPos = PETSC_TRUE;
977:           PetscInt       NlInt  = 0;
978:           PetscInt       NuInt  = 0;

980:           PetscCall(DMPlexGetPlaneCellIntersection_Internal(dm, c, up, &normal[3 * 0], &upper[0], &upperInt[0], upperIntPoints[0]));
981:           if (debug > 4) {
982:             if (!upperInt[0])
983:               PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Cell %" PetscInt_FMT " upper direction 0 (%g, %g, %g) does not intersect %s\n", c, (double)up[0], (double)up[1], cdim > 2 ? (double)up[2] : 0., upper[0] ? "positive" : "negative"));
984:             else PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Cell %" PetscInt_FMT " upper direction 0 (%g, %g, %g) intersects %" PetscInt_FMT " times\n", c, (double)up[0], (double)up[1], cdim > 2 ? (double)up[2] : 0., upperInt[0]));
985:           }
986:           for (PetscInt d = 0; d < cdim; ++d) {
987:             NlInt += lowerInt[d];
988:             NuInt += upperInt[d];
989:           }
990:           // If there is no intersection...
991:           if (!NlInt && !NuInt) {
992:             // If the cell is on the negative side of the lower planes, it is not in the box
993:             for (PetscInt d = 0; d < cdim; ++d)
994:               if (lower[d]) {
995:                 excNeg = PETSC_FALSE;
996:                 break;
997:               }
998:             // If the cell is on the positive side of the upper planes, it is not in the box
999:             for (PetscInt d = 0; d < cdim; ++d)
1000:               if (!upper[d]) {
1001:                 excPos = PETSC_FALSE;
1002:                 break;
1003:               }
1004:             if (excNeg || excPos) {
1005:               if (debug && excNeg) PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Cell %" PetscInt_FMT " is on the negative side of the lower plane\n", c));
1006:               if (debug && excPos) PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Cell %" PetscInt_FMT " is on the positive side of the upper plane\n", c));
1007:               continue;
1008:             }
1009:             // Otherwise it is in the box
1010:             if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Cell %" PetscInt_FMT " is contained in box %" PetscInt_FMT "\n", c, box));
1011:             PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
1012:             continue;
1013:           }
1014:           /*
1015:             If any intersection point is within the box limits, it is in the box
1016:             We need to have tolerances here since intersection point calculations can introduce errors
1017:             Initialize a count to track which planes have intersection outside the box.
1018:             if two adjacent planes have intersection points upper and lower all outside the box, look
1019:             first at if another plane has intersection points outside the box, if so, it is inside the cell
1020:             look next if no intersection points exist on the other planes, and check if the planes are on the
1021:             outside of the intersection points but on opposite ends. If so, the box cuts through the cell.
1022:           */
1023:           PetscInt outsideCount[6] = {0, 0, 0, 0, 0, 0};
1024:           for (PetscInt plane = 0; plane < cdim; ++plane) {
1025:             for (PetscInt ip = 0; ip < lowerInt[plane]; ++ip) {
1026:               PetscInt d;

1028:               for (d = 0; d < cdim; ++d) {
1029:                 if ((lowerIntPoints[plane][ip * cdim + d] < (lp[d] - PETSC_SMALL)) || (lowerIntPoints[plane][ip * cdim + d] > (up[d] + PETSC_SMALL))) {
1030:                   if (lowerIntPoints[plane][ip * cdim + d] < (lp[d] - PETSC_SMALL)) outsideCount[d]++; // The lower point is to the left of this box, and we count it
1031:                   break;
1032:                 }
1033:               }
1034:               if (d == cdim) {
1035:                 if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Cell %" PetscInt_FMT " intersected lower plane %" PetscInt_FMT " of box %" PetscInt_FMT "\n", c, plane, box));
1036:                 PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
1037:                 goto end;
1038:               }
1039:             }
1040:             for (PetscInt ip = 0; ip < upperInt[plane]; ++ip) {
1041:               PetscInt d;

1043:               for (d = 0; d < cdim; ++d) {
1044:                 if ((upperIntPoints[plane][ip * cdim + d] < (lp[d] - PETSC_SMALL)) || (upperIntPoints[plane][ip * cdim + d] > (up[d] + PETSC_SMALL))) {
1045:                   if (upperIntPoints[plane][ip * cdim + d] > (up[d] + PETSC_SMALL)) outsideCount[cdim + d]++; // The upper point is to the right of this box, and we count it
1046:                   break;
1047:                 }
1048:               }
1049:               if (d == cdim) {
1050:                 if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Cell %" PetscInt_FMT " intersected upper plane %" PetscInt_FMT " of box %" PetscInt_FMT "\n", c, plane, box));
1051:                 PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
1052:                 goto end;
1053:               }
1054:             }
1055:           }
1056:           /*
1057:              Check the planes with intersections
1058:              in 2D, check if the square falls in the middle of a cell
1059:              ie all four planes have intersection points outside of the box
1060:              You do not want to be doing this, because it means your grid hashing is finer than your grid,
1061:              but we should still support it I guess
1062:           */
1063:           if (cdim == 2) {
1064:             PetscInt nIntersects = 0;
1065:             for (PetscInt d = 0; d < cdim; ++d) nIntersects += (outsideCount[d] + outsideCount[d + cdim]);
1066:             // if the count adds up to 8, that means each plane has 2 external intersections and thus it is in the cell
1067:             if (nIntersects == 8) {
1068:               PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
1069:               goto end;
1070:             }
1071:           }
1072:           /*
1073:              In 3 dimensions, if two adjacent planes have at least 3 intersections outside the cell in the appropriate direction,
1074:              we then check the 3rd planar dimension. If a plane falls between intersection points, the cell belongs to that box.
1075:              If the planes are on opposite sides of the intersection points, the cell belongs to that box and it passes through the cell.
1076:           */
1077:           if (cdim == 3) {
1078:             PetscInt faces[3] = {0, 0, 0}, checkInternalFace = 0;
1079:             // Find two adjacent planes with at least 3 intersection points in the upper and lower
1080:             // if the third plane has 3 intersection points or more, a pyramid base is formed on that plane and it is in the cell
1081:             for (PetscInt d = 0; d < cdim; ++d)
1082:               if (outsideCount[d] >= 3 && outsideCount[cdim + d] >= 3) {
1083:                 faces[d]++;
1084:                 checkInternalFace++;
1085:               }
1086:             if (checkInternalFace == 3) {
1087:               // All planes have 3 intersection points, add it.
1088:               PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
1089:               goto end;
1090:             }
1091:             // Gross, figure out which adjacent faces have at least 3 points
1092:             PetscInt nonIntersectingFace = -1;
1093:             if (faces[0] == faces[1]) nonIntersectingFace = 2;
1094:             if (faces[0] == faces[2]) nonIntersectingFace = 1;
1095:             if (faces[1] == faces[2]) nonIntersectingFace = 0;
1096:             if (nonIntersectingFace >= 0) {
1097:               for (PetscInt plane = 0; plane < cdim; ++plane) {
1098:                 if (!lowerInt[nonIntersectingFace] && !upperInt[nonIntersectingFace]) continue;
1099:                 // If we have 2 adjacent sides with pyramids of intersection outside of them, and there is a point between the end caps at all, it must be between the two non intersecting ends, and the box is inside the cell.
1100:                 for (PetscInt ip = 0; ip < lowerInt[nonIntersectingFace]; ++ip) {
1101:                   if (lowerIntPoints[plane][ip * cdim + nonIntersectingFace] > lp[nonIntersectingFace] - PETSC_SMALL || lowerIntPoints[plane][ip * cdim + nonIntersectingFace] < up[nonIntersectingFace] + PETSC_SMALL) goto setpoint;
1102:                 }
1103:                 for (PetscInt ip = 0; ip < upperInt[nonIntersectingFace]; ++ip) {
1104:                   if (upperIntPoints[plane][ip * cdim + nonIntersectingFace] > lp[nonIntersectingFace] - PETSC_SMALL || upperIntPoints[plane][ip * cdim + nonIntersectingFace] < up[nonIntersectingFace] + PETSC_SMALL) goto setpoint;
1105:                 }
1106:                 goto end;
1107:               }
1108:               // The points are within the bonds of the non intersecting planes, add it.
1109:             setpoint:
1110:               PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
1111:               goto end;
1112:             }
1113:           }
1114:         end:
1115:           lower[0]          = upper[0];
1116:           lowerInt[0]       = upperInt[0];
1117:           tmp               = lowerIntPoints[0];
1118:           lowerIntPoints[0] = upperIntPoints[0];
1119:           upperIntPoints[0] = tmp;
1120:         }
1121:         lp[0]             = lbox->lower[0] + dlim[0 * 2 + 0] * h[0];
1122:         up[0]             = lp[0] + h[0];
1123:         lower[1]          = upper[1];
1124:         lowerInt[1]       = upperInt[1];
1125:         tmp               = lowerIntPoints[1];
1126:         lowerIntPoints[1] = upperIntPoints[1];
1127:         upperIntPoints[1] = tmp;
1128:       }
1129:       lp[1]             = lbox->lower[1] + dlim[1 * 2 + 0] * h[1];
1130:       up[1]             = lp[1] + h[1];
1131:       lower[2]          = upper[2];
1132:       lowerInt[2]       = upperInt[2];
1133:       tmp               = lowerIntPoints[2];
1134:       lowerIntPoints[2] = upperIntPoints[2];
1135:       upperIntPoints[2] = tmp;
1136:     }
1137:   }
1138:   PetscCall(PetscFree2(dboxes, boxes));

1140:   if (debug) PetscCall(DMLabelView(lbox->cellsSparse, PETSC_VIEWER_STDOUT_SELF));
1141:   PetscCall(DMLabelConvertToSection(lbox->cellsSparse, &lbox->cellSection, &lbox->cells));
1142:   PetscCall(DMLabelDestroy(&lbox->cellsSparse));
1143:   *localBox = lbox;
1144:   PetscFunctionReturn(PETSC_SUCCESS);
1145: }

1147: PetscErrorCode DMLocatePoints_Plex(DM dm, Vec v, DMPointLocationType ltype, PetscSF cellSF)
1148: {
1149:   PetscInt        debug = ((DM_Plex *)dm->data)->printLocate;
1150:   DM_Plex        *mesh  = (DM_Plex *)dm->data;
1151:   PetscBool       hash = mesh->useHashLocation, reuse = PETSC_FALSE;
1152:   PetscInt        bs, numPoints, p, numFound, *found = NULL;
1153:   PetscInt        dim, Nl = 0, cStart, cEnd, numCells, c, d;
1154:   PetscSF         sf;
1155:   const PetscInt *leaves;
1156:   const PetscInt *boxCells;
1157:   PetscSFNode    *cells;
1158:   PetscScalar    *a;
1159:   PetscMPIInt     result;
1160:   PetscLogDouble  t0, t1;
1161:   PetscReal       gmin[3], gmax[3];
1162:   PetscInt        terminating_query_type[] = {0, 0, 0};
1163:   PetscMPIInt     rank;

1165:   PetscFunctionBegin;
1166:   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank));
1167:   PetscCall(PetscLogEventBegin(DMPLEX_LocatePoints, 0, 0, 0, 0));
1168:   PetscCall(PetscTime(&t0));
1169:   PetscCheck(ltype != DM_POINTLOCATION_NEAREST || hash, PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Nearest point location only supported with grid hashing. Use -dm_plex_hash_location to enable it.");
1170:   PetscCall(DMGetCoordinateDim(dm, &dim));
1171:   PetscCall(VecGetBlockSize(v, &bs));
1172:   PetscCallMPI(MPI_Comm_compare(PetscObjectComm((PetscObject)cellSF), PETSC_COMM_SELF, &result));
1173:   PetscCheck(result == MPI_IDENT || result == MPI_CONGRUENT, PetscObjectComm((PetscObject)cellSF), PETSC_ERR_SUP, "Trying parallel point location: only local point location supported");
1174:   PetscCheck(bs == dim, PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Block size for point vector %" PetscInt_FMT " must be the mesh coordinate dimension %" PetscInt_FMT, bs, dim);
1175:   PetscCall(DMGetCoordinatesLocalSetUp(dm));
1176:   PetscCall(DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd));
1177:   PetscCall(DMGetPointSF(dm, &sf));
1178:   if (sf) PetscCall(PetscSFGetGraph(sf, NULL, &Nl, &leaves, NULL));
1179:   Nl = PetscMax(Nl, 0);
1180:   PetscCall(VecGetLocalSize(v, &numPoints));
1181:   PetscCall(VecGetArray(v, &a));
1182:   numPoints /= bs;
1183:   {
1184:     const PetscSFNode *sf_cells;

1186:     PetscCall(PetscSFGetGraph(cellSF, NULL, NULL, NULL, &sf_cells));
1187:     if (sf_cells) {
1188:       PetscCall(PetscInfo(dm, "[DMLocatePoints_Plex] Re-using existing StarForest node list\n"));
1189:       cells = (PetscSFNode *)sf_cells;
1190:       reuse = PETSC_TRUE;
1191:     } else {
1192:       PetscCall(PetscInfo(dm, "[DMLocatePoints_Plex] Creating and initializing new StarForest node list\n"));
1193:       PetscCall(PetscMalloc1(numPoints, &cells));
1194:       /* initialize cells if created */
1195:       for (p = 0; p < numPoints; p++) {
1196:         cells[p].rank  = 0;
1197:         cells[p].index = DMLOCATEPOINT_POINT_NOT_FOUND;
1198:       }
1199:     }
1200:   }
1201:   PetscCall(DMGetBoundingBox(dm, gmin, gmax));
1202:   if (hash) {
1203:     if (!mesh->lbox) {
1204:       PetscCall(PetscInfo(dm, "Initializing grid hashing\n"));
1205:       PetscCall(DMPlexComputeGridHash_Internal(dm, &mesh->lbox));
1206:     }
1207:     /* Designate the local box for each point */
1208:     /* Send points to correct process */
1209:     /* Search cells that lie in each subbox */
1210:     /*   Should we bin points before doing search? */
1211:     PetscCall(ISGetIndices(mesh->lbox->cells, &boxCells));
1212:   }
1213:   for (p = 0, numFound = 0; p < numPoints; ++p) {
1214:     const PetscScalar *point   = &a[p * bs];
1215:     PetscInt           dbin[3] = {-1, -1, -1}, bin, cell = -1, cellOffset;
1216:     PetscBool          point_outside_domain = PETSC_FALSE;

1218:     /* check bounding box of domain */
1219:     for (d = 0; d < dim; d++) {
1220:       if (PetscRealPart(point[d]) < gmin[d]) {
1221:         point_outside_domain = PETSC_TRUE;
1222:         break;
1223:       }
1224:       if (PetscRealPart(point[d]) > gmax[d]) {
1225:         point_outside_domain = PETSC_TRUE;
1226:         break;
1227:       }
1228:     }
1229:     if (point_outside_domain) {
1230:       cells[p].rank  = 0;
1231:       cells[p].index = DMLOCATEPOINT_POINT_NOT_FOUND;
1232:       terminating_query_type[0]++;
1233:       continue;
1234:     }

1236:     /* check initial values in cells[].index - abort early if found */
1237:     if (cells[p].index != DMLOCATEPOINT_POINT_NOT_FOUND) {
1238:       c              = cells[p].index;
1239:       cells[p].index = DMLOCATEPOINT_POINT_NOT_FOUND;
1240:       PetscCall(DMPlexLocatePoint_Internal(dm, dim, point, c, &cell));
1241:       if (cell >= 0) {
1242:         cells[p].rank  = 0;
1243:         cells[p].index = cell;
1244:         numFound++;
1245:       }
1246:     }
1247:     if (cells[p].index != DMLOCATEPOINT_POINT_NOT_FOUND) {
1248:       terminating_query_type[1]++;
1249:       continue;
1250:     }

1252:     if (hash) {
1253:       PetscBool found_box;

1255:       if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, "[%d]Checking point %" PetscInt_FMT " (%.2g, %.2g, %.2g)\n", rank, p, (double)PetscRealPart(point[0]), (double)PetscRealPart(point[1]), dim > 2 ? (double)PetscRealPart(point[2]) : 0.));
1256:       /* allow for case that point is outside box - abort early */
1257:       PetscCall(PetscGridHashGetEnclosingBoxQuery(mesh->lbox, mesh->lbox->cellSection, 1, point, dbin, &bin, &found_box));
1258:       if (found_box) {
1259:         if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, "[%d]  Found point in box %" PetscInt_FMT " (%" PetscInt_FMT ", %" PetscInt_FMT ", %" PetscInt_FMT ")\n", rank, bin, dbin[0], dbin[1], dim > 2 ? dbin[2] : 0));
1260:         /* TODO Lay an interface over this so we can switch between Section (dense) and Label (sparse) */
1261:         PetscCall(PetscSectionGetDof(mesh->lbox->cellSection, bin, &numCells));
1262:         PetscCall(PetscSectionGetOffset(mesh->lbox->cellSection, bin, &cellOffset));
1263:         for (c = cellOffset; c < cellOffset + numCells; ++c) {
1264:           if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, "[%d]    Checking for point in cell %" PetscInt_FMT "\n", rank, boxCells[c]));
1265:           PetscCall(DMPlexLocatePoint_Internal(dm, dim, point, boxCells[c], &cell));
1266:           if (cell >= 0) {
1267:             if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, "[%d]      FOUND in cell %" PetscInt_FMT "\n", rank, cell));
1268:             cells[p].rank  = 0;
1269:             cells[p].index = cell;
1270:             numFound++;
1271:             terminating_query_type[2]++;
1272:             break;
1273:           }
1274:         }
1275:       }
1276:     } else {
1277:       for (c = cStart; c < cEnd; ++c) {
1278:         PetscInt idx;

1280:         PetscCall(PetscFindInt(c, Nl, leaves, &idx));
1281:         if (idx >= 0) continue;
1282:         PetscCall(DMPlexLocatePoint_Internal(dm, dim, point, c, &cell));
1283:         if (cell >= 0) {
1284:           cells[p].rank  = 0;
1285:           cells[p].index = cell;
1286:           numFound++;
1287:           terminating_query_type[2]++;
1288:           break;
1289:         }
1290:       }
1291:     }
1292:   }
1293:   if (hash) PetscCall(ISRestoreIndices(mesh->lbox->cells, &boxCells));
1294:   if (ltype == DM_POINTLOCATION_NEAREST && hash && numFound < numPoints) {
1295:     for (p = 0; p < numPoints; p++) {
1296:       const PetscScalar *point     = &a[p * bs];
1297:       PetscReal          cpoint[3] = {0, 0, 0}, diff[3], best[3] = {PETSC_MAX_REAL, PETSC_MAX_REAL, PETSC_MAX_REAL}, dist, distMax = PETSC_MAX_REAL;
1298:       PetscInt           dbin[3] = {-1, -1, -1}, bin, cellOffset, d, bestc = -1;

1300:       if (cells[p].index < 0) {
1301:         PetscCall(PetscGridHashGetEnclosingBox(mesh->lbox, 1, point, dbin, &bin));
1302:         PetscCall(PetscSectionGetDof(mesh->lbox->cellSection, bin, &numCells));
1303:         PetscCall(PetscSectionGetOffset(mesh->lbox->cellSection, bin, &cellOffset));
1304:         for (c = cellOffset; c < cellOffset + numCells; ++c) {
1305:           PetscCall(DMPlexClosestPoint_Internal(dm, dim, point, boxCells[c], cpoint));
1306:           for (d = 0; d < dim; ++d) diff[d] = cpoint[d] - PetscRealPart(point[d]);
1307:           dist = DMPlex_NormD_Internal(dim, diff);
1308:           if (dist < distMax) {
1309:             for (d = 0; d < dim; ++d) best[d] = cpoint[d];
1310:             bestc   = boxCells[c];
1311:             distMax = dist;
1312:           }
1313:         }
1314:         if (distMax < PETSC_MAX_REAL) {
1315:           ++numFound;
1316:           cells[p].rank  = 0;
1317:           cells[p].index = bestc;
1318:           for (d = 0; d < dim; ++d) a[p * bs + d] = best[d];
1319:         }
1320:       }
1321:     }
1322:   }
1323:   /* This code is only be relevant when interfaced to parallel point location */
1324:   /* Check for highest numbered proc that claims a point (do we care?) */
1325:   if (ltype == DM_POINTLOCATION_REMOVE && numFound < numPoints) {
1326:     PetscCall(PetscMalloc1(numFound, &found));
1327:     for (p = 0, numFound = 0; p < numPoints; p++) {
1328:       if (cells[p].rank >= 0 && cells[p].index >= 0) {
1329:         if (numFound < p) cells[numFound] = cells[p];
1330:         found[numFound++] = p;
1331:       }
1332:     }
1333:   }
1334:   PetscCall(VecRestoreArray(v, &a));
1335:   if (!reuse) PetscCall(PetscSFSetGraph(cellSF, cEnd - cStart, numFound, found, PETSC_OWN_POINTER, cells, PETSC_OWN_POINTER));
1336:   PetscCall(PetscTime(&t1));
1337:   if (hash) {
1338:     PetscCall(PetscInfo(dm, "[DMLocatePoints_Plex] terminating_query_type : %" PetscInt_FMT " [outside domain] : %" PetscInt_FMT " [inside initial cell] : %" PetscInt_FMT " [hash]\n", terminating_query_type[0], terminating_query_type[1], terminating_query_type[2]));
1339:   } else {
1340:     PetscCall(PetscInfo(dm, "[DMLocatePoints_Plex] terminating_query_type : %" PetscInt_FMT " [outside domain] : %" PetscInt_FMT " [inside initial cell] : %" PetscInt_FMT " [brute-force]\n", terminating_query_type[0], terminating_query_type[1], terminating_query_type[2]));
1341:   }
1342:   PetscCall(PetscInfo(dm, "[DMLocatePoints_Plex] npoints %" PetscInt_FMT " : time(rank0) %1.2e (sec): points/sec %1.4e\n", numPoints, t1 - t0, (double)((double)numPoints / (t1 - t0))));
1343:   PetscCall(PetscLogEventEnd(DMPLEX_LocatePoints, 0, 0, 0, 0));
1344:   PetscFunctionReturn(PETSC_SUCCESS);
1345: }

1347: /*@
1348:   DMPlexComputeProjection2Dto1D - Rewrite coordinates to be the 1D projection of the 2D coordinates

1350:   Not Collective

1352:   Input/Output Parameter:
1353: . coords - The coordinates of a segment, on output the new y-coordinate, and 0 for x, an array of size 4, last two entries are unchanged

1355:   Output Parameter:
1356: . R - The rotation which accomplishes the projection, array of size 4

1358:   Level: developer

1360: .seealso: `DMPLEX`, `DMPlexComputeProjection3Dto1D()`, `DMPlexComputeProjection3Dto2D()`
1361: @*/
1362: PetscErrorCode DMPlexComputeProjection2Dto1D(PetscScalar coords[], PetscReal R[])
1363: {
1364:   const PetscReal x = PetscRealPart(coords[2] - coords[0]);
1365:   const PetscReal y = PetscRealPart(coords[3] - coords[1]);
1366:   const PetscReal r = PetscSqrtReal(x * x + y * y), c = x / r, s = y / r;

1368:   PetscFunctionBegin;
1369:   R[0]      = c;
1370:   R[1]      = -s;
1371:   R[2]      = s;
1372:   R[3]      = c;
1373:   coords[0] = 0.0;
1374:   coords[1] = r;
1375:   PetscFunctionReturn(PETSC_SUCCESS);
1376: }

1378: /*@
1379:   DMPlexComputeProjection3Dto1D - Rewrite coordinates to be the 1D projection of the 3D coordinates

1381:   Not Collective

1383:   Input/Output Parameter:
1384: . coords - The coordinates of a segment; on output, the new y-coordinate, and 0 for x and z, an array of size 6, the other entries are unchanged

1386:   Output Parameter:
1387: . R - The rotation which accomplishes the projection, an array of size 9

1389:   Level: developer

1391:   Note:
1392:   This uses the basis completion described by Frisvad {cite}`frisvad2012building`

1394: .seealso: `DMPLEX`, `DMPlexComputeProjection2Dto1D()`, `DMPlexComputeProjection3Dto2D()`
1395: @*/
1396: PetscErrorCode DMPlexComputeProjection3Dto1D(PetscScalar coords[], PetscReal R[])
1397: {
1398:   PetscReal x    = PetscRealPart(coords[3] - coords[0]);
1399:   PetscReal y    = PetscRealPart(coords[4] - coords[1]);
1400:   PetscReal z    = PetscRealPart(coords[5] - coords[2]);
1401:   PetscReal r    = PetscSqrtReal(x * x + y * y + z * z);
1402:   PetscReal rinv = 1. / r;

1404:   PetscFunctionBegin;
1405:   x *= rinv;
1406:   y *= rinv;
1407:   z *= rinv;
1408:   if (x > 0.) {
1409:     PetscReal inv1pX = 1. / (1. + x);

1411:     R[0] = x;
1412:     R[1] = -y;
1413:     R[2] = -z;
1414:     R[3] = y;
1415:     R[4] = 1. - y * y * inv1pX;
1416:     R[5] = -y * z * inv1pX;
1417:     R[6] = z;
1418:     R[7] = -y * z * inv1pX;
1419:     R[8] = 1. - z * z * inv1pX;
1420:   } else {
1421:     PetscReal inv1mX = 1. / (1. - x);

1423:     R[0] = x;
1424:     R[1] = z;
1425:     R[2] = y;
1426:     R[3] = y;
1427:     R[4] = -y * z * inv1mX;
1428:     R[5] = 1. - y * y * inv1mX;
1429:     R[6] = z;
1430:     R[7] = 1. - z * z * inv1mX;
1431:     R[8] = -y * z * inv1mX;
1432:   }
1433:   coords[0] = 0.0;
1434:   coords[1] = r;
1435:   coords[2] = 0.0;
1436:   PetscFunctionReturn(PETSC_SUCCESS);
1437: }

1439: /*@
1440:   DMPlexComputeProjection3Dto2D - Rewrite coordinates of 3 or more coplanar 3D points to a common 2D basis for the
1441:   plane.  The normal is defined by positive orientation of the first 3 points.

1443:   Not Collective

1445:   Input Parameter:
1446: . coordSize - Length of coordinate array (3x number of points); must be at least 9 (3 points)

1448:   Input/Output Parameter:
1449: . coords - The interlaced coordinates of each coplanar 3D point; on output the first
1450:            2*coordSize/3 entries contain interlaced 2D points, with the rest undefined

1452:   Output Parameter:
1453: . R - 3x3 row-major rotation matrix whose columns are the tangent basis [t1, t2, n].  Multiplying by R^T transforms from original frame to tangent frame.

1455:   Level: developer

1457: .seealso: `DMPLEX`, `DMPlexComputeProjection2Dto1D()`, `DMPlexComputeProjection3Dto1D()`
1458: @*/
1459: PetscErrorCode DMPlexComputeProjection3Dto2D(PetscInt coordSize, PetscScalar coords[], PetscReal R[])
1460: {
1461:   PetscReal      x1[3], x2[3], n[3], c[3], norm;
1462:   const PetscInt dim = 3;
1463:   PetscInt       d, p;

1465:   PetscFunctionBegin;
1466:   /* 0) Calculate normal vector */
1467:   for (d = 0; d < dim; ++d) {
1468:     x1[d] = PetscRealPart(coords[1 * dim + d] - coords[0 * dim + d]);
1469:     x2[d] = PetscRealPart(coords[2 * dim + d] - coords[0 * dim + d]);
1470:   }
1471:   // n = x1 \otimes x2
1472:   n[0] = x1[1] * x2[2] - x1[2] * x2[1];
1473:   n[1] = x1[2] * x2[0] - x1[0] * x2[2];
1474:   n[2] = x1[0] * x2[1] - x1[1] * x2[0];
1475:   norm = PetscSqrtReal(n[0] * n[0] + n[1] * n[1] + n[2] * n[2]);
1476:   for (d = 0; d < dim; d++) n[d] /= norm;
1477:   norm = PetscSqrtReal(x1[0] * x1[0] + x1[1] * x1[1] + x1[2] * x1[2]);
1478:   for (d = 0; d < dim; d++) x1[d] /= norm;
1479:   // x2 = n \otimes x1
1480:   x2[0] = n[1] * x1[2] - n[2] * x1[1];
1481:   x2[1] = n[2] * x1[0] - n[0] * x1[2];
1482:   x2[2] = n[0] * x1[1] - n[1] * x1[0];
1483:   for (d = 0; d < dim; d++) {
1484:     R[d * dim + 0] = x1[d];
1485:     R[d * dim + 1] = x2[d];
1486:     R[d * dim + 2] = n[d];
1487:     c[d]           = PetscRealPart(coords[0 * dim + d]);
1488:   }
1489:   for (p = 0; p < coordSize / dim; p++) {
1490:     PetscReal y[3];
1491:     for (d = 0; d < dim; d++) y[d] = PetscRealPart(coords[p * dim + d]) - c[d];
1492:     for (d = 0; d < 2; d++) coords[p * 2 + d] = R[0 * dim + d] * y[0] + R[1 * dim + d] * y[1] + R[2 * dim + d] * y[2];
1493:   }
1494:   PetscFunctionReturn(PETSC_SUCCESS);
1495: }

1497: PETSC_UNUSED static inline void Volume_Triangle_Internal(PetscReal *vol, PetscReal coords[])
1498: {
1499:   /* Signed volume is 1/2 the determinant

1501:    |  1  1  1 |
1502:    | x0 x1 x2 |
1503:    | y0 y1 y2 |

1505:      but if x0,y0 is the origin, we have

1507:    | x1 x2 |
1508:    | y1 y2 |
1509:   */
1510:   const PetscReal x1 = coords[2] - coords[0], y1 = coords[3] - coords[1];
1511:   const PetscReal x2 = coords[4] - coords[0], y2 = coords[5] - coords[1];
1512:   PetscReal       M[4], detM;
1513:   M[0] = x1;
1514:   M[1] = x2;
1515:   M[2] = y1;
1516:   M[3] = y2;
1517:   DMPlex_Det2D_Internal(&detM, M);
1518:   *vol = 0.5 * detM;
1519:   (void)PetscLogFlops(5.0);
1520: }

1522: PETSC_UNUSED static inline void Volume_Tetrahedron_Internal(PetscReal *vol, PetscReal coords[])
1523: {
1524:   /* Signed volume is 1/6th of the determinant

1526:    |  1  1  1  1 |
1527:    | x0 x1 x2 x3 |
1528:    | y0 y1 y2 y3 |
1529:    | z0 z1 z2 z3 |

1531:      but if x0,y0,z0 is the origin, we have

1533:    | x1 x2 x3 |
1534:    | y1 y2 y3 |
1535:    | z1 z2 z3 |
1536:   */
1537:   const PetscReal x1 = coords[3] - coords[0], y1 = coords[4] - coords[1], z1 = coords[5] - coords[2];
1538:   const PetscReal x2 = coords[6] - coords[0], y2 = coords[7] - coords[1], z2 = coords[8] - coords[2];
1539:   const PetscReal x3 = coords[9] - coords[0], y3 = coords[10] - coords[1], z3 = coords[11] - coords[2];
1540:   const PetscReal onesixth = ((PetscReal)1. / (PetscReal)6.);
1541:   PetscReal       M[9], detM;
1542:   M[0] = x1;
1543:   M[1] = x2;
1544:   M[2] = x3;
1545:   M[3] = y1;
1546:   M[4] = y2;
1547:   M[5] = y3;
1548:   M[6] = z1;
1549:   M[7] = z2;
1550:   M[8] = z3;
1551:   DMPlex_Det3D_Internal(&detM, M);
1552:   *vol = -onesixth * detM;
1553:   (void)PetscLogFlops(10.0);
1554: }

1556: static inline void Volume_Tetrahedron_Origin_Internal(PetscReal *vol, PetscReal coords[])
1557: {
1558:   const PetscReal onesixth = ((PetscReal)1. / (PetscReal)6.);
1559:   DMPlex_Det3D_Internal(vol, coords);
1560:   *vol *= -onesixth;
1561: }

1563: static PetscErrorCode DMPlexComputePointGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1564: {
1565:   PetscSection       coordSection;
1566:   Vec                coordinates;
1567:   const PetscScalar *coords;
1568:   PetscInt           dim, d, off;

1570:   PetscFunctionBegin;
1571:   PetscCall(DMGetCoordinatesLocal(dm, &coordinates));
1572:   PetscCall(DMGetCoordinateSection(dm, &coordSection));
1573:   PetscCall(PetscSectionGetDof(coordSection, e, &dim));
1574:   if (!dim) PetscFunctionReturn(PETSC_SUCCESS);
1575:   PetscCall(PetscSectionGetOffset(coordSection, e, &off));
1576:   PetscCall(VecGetArrayRead(coordinates, &coords));
1577:   if (v0) {
1578:     for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[off + d]);
1579:   }
1580:   PetscCall(VecRestoreArrayRead(coordinates, &coords));
1581:   *detJ = 1.;
1582:   if (J) {
1583:     for (d = 0; d < dim * dim; d++) J[d] = 0.;
1584:     for (d = 0; d < dim; d++) J[d * dim + d] = 1.;
1585:     if (invJ) {
1586:       for (d = 0; d < dim * dim; d++) invJ[d] = 0.;
1587:       for (d = 0; d < dim; d++) invJ[d * dim + d] = 1.;
1588:     }
1589:   }
1590:   PetscFunctionReturn(PETSC_SUCCESS);
1591: }

1593: /*@C
1594:   DMPlexGetCellCoordinates - Get coordinates for a cell, taking into account periodicity

1596:   Not Collective

1598:   Input Parameters:
1599: + dm   - The `DMPLEX`
1600: - cell - The cell number

1602:   Output Parameters:
1603: + isDG   - Using cellwise coordinates
1604: . Nc     - The number of coordinates
1605: . array  - The coordinate array
1606: - coords - The cell coordinates

1608:   Level: developer

1610: .seealso: `DMPLEX`, `DMPlexRestoreCellCoordinates()`, `DMGetCoordinatesLocal()`, `DMGetCellCoordinatesLocal()`
1611: @*/
1612: PetscErrorCode DMPlexGetCellCoordinates(DM dm, PetscInt cell, PetscBool *isDG, PetscInt *Nc, const PetscScalar *array[], PetscScalar *coords[])
1613: {
1614:   DM                 cdm;
1615:   Vec                coordinates;
1616:   PetscSection       cs;
1617:   const PetscScalar *ccoords;
1618:   PetscInt           pStart, pEnd;

1620:   PetscFunctionBeginHot;
1621:   *isDG   = PETSC_FALSE;
1622:   *Nc     = 0;
1623:   *array  = NULL;
1624:   *coords = NULL;
1625:   /* Check for cellwise coordinates */
1626:   PetscCall(DMGetCellCoordinateSection(dm, &cs));
1627:   if (!cs) goto cg;
1628:   /* Check that the cell exists in the cellwise section */
1629:   PetscCall(PetscSectionGetChart(cs, &pStart, &pEnd));
1630:   if (cell < pStart || cell >= pEnd) goto cg;
1631:   /* Check for cellwise coordinates for this cell */
1632:   PetscCall(PetscSectionGetDof(cs, cell, Nc));
1633:   if (!*Nc) goto cg;
1634:   /* Check for cellwise coordinates */
1635:   PetscCall(DMGetCellCoordinatesLocalNoncollective(dm, &coordinates));
1636:   if (!coordinates) goto cg;
1637:   /* Get cellwise coordinates */
1638:   PetscCall(DMGetCellCoordinateDM(dm, &cdm));
1639:   PetscCall(VecGetArrayRead(coordinates, array));
1640:   PetscCall(DMPlexPointLocalRead(cdm, cell, *array, &ccoords));
1641:   PetscCall(DMGetWorkArray(cdm, *Nc, MPIU_SCALAR, coords));
1642:   PetscCall(PetscArraycpy(*coords, ccoords, *Nc));
1643:   PetscCall(VecRestoreArrayRead(coordinates, array));
1644:   *isDG = PETSC_TRUE;
1645:   PetscFunctionReturn(PETSC_SUCCESS);
1646: cg:
1647:   /* Use continuous coordinates */
1648:   PetscCall(DMGetCoordinateDM(dm, &cdm));
1649:   PetscCall(DMGetCoordinateSection(dm, &cs));
1650:   PetscCall(DMGetCoordinatesLocalNoncollective(dm, &coordinates));
1651:   PetscCall(DMPlexVecGetOrientedClosure_Internal(cdm, cs, PETSC_FALSE, coordinates, cell, 0, Nc, coords));
1652:   PetscFunctionReturn(PETSC_SUCCESS);
1653: }

1655: /*@C
1656:   DMPlexRestoreCellCoordinates - Get coordinates for a cell, taking into account periodicity

1658:   Not Collective

1660:   Input Parameters:
1661: + dm   - The `DMPLEX`
1662: - cell - The cell number

1664:   Output Parameters:
1665: + isDG   - Using cellwise coordinates
1666: . Nc     - The number of coordinates
1667: . array  - The coordinate array
1668: - coords - The cell coordinates

1670:   Level: developer

1672: .seealso: `DMPLEX`, `DMPlexGetCellCoordinates()`, `DMGetCoordinatesLocal()`, `DMGetCellCoordinatesLocal()`
1673: @*/
1674: PetscErrorCode DMPlexRestoreCellCoordinates(DM dm, PetscInt cell, PetscBool *isDG, PetscInt *Nc, const PetscScalar *array[], PetscScalar *coords[])
1675: {
1676:   DM           cdm;
1677:   PetscSection cs;
1678:   Vec          coordinates;

1680:   PetscFunctionBeginHot;
1681:   if (*isDG) {
1682:     PetscCall(DMGetCellCoordinateDM(dm, &cdm));
1683:     PetscCall(DMRestoreWorkArray(cdm, *Nc, MPIU_SCALAR, coords));
1684:   } else {
1685:     PetscCall(DMGetCoordinateDM(dm, &cdm));
1686:     PetscCall(DMGetCoordinateSection(dm, &cs));
1687:     PetscCall(DMGetCoordinatesLocalNoncollective(dm, &coordinates));
1688:     PetscCall(DMPlexVecRestoreClosure(cdm, cs, coordinates, cell, Nc, (PetscScalar **)coords));
1689:   }
1690:   PetscFunctionReturn(PETSC_SUCCESS);
1691: }

1693: static PetscErrorCode DMPlexComputeLineGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1694: {
1695:   const PetscScalar *array;
1696:   PetscScalar       *coords = NULL;
1697:   PetscInt           numCoords, d;
1698:   PetscBool          isDG;

1700:   PetscFunctionBegin;
1701:   PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
1702:   PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
1703:   *detJ = 0.0;
1704:   if (numCoords == 6) {
1705:     const PetscInt dim = 3;
1706:     PetscReal      R[9], J0;

1708:     if (v0) {
1709:       for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
1710:     }
1711:     PetscCall(DMPlexComputeProjection3Dto1D(coords, R));
1712:     if (J) {
1713:       J0   = 0.5 * PetscRealPart(coords[1]);
1714:       J[0] = R[0] * J0;
1715:       J[1] = R[1];
1716:       J[2] = R[2];
1717:       J[3] = R[3] * J0;
1718:       J[4] = R[4];
1719:       J[5] = R[5];
1720:       J[6] = R[6] * J0;
1721:       J[7] = R[7];
1722:       J[8] = R[8];
1723:       DMPlex_Det3D_Internal(detJ, J);
1724:       if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
1725:     }
1726:   } else if (numCoords == 4) {
1727:     const PetscInt dim = 2;
1728:     PetscReal      R[4], J0;

1730:     if (v0) {
1731:       for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
1732:     }
1733:     PetscCall(DMPlexComputeProjection2Dto1D(coords, R));
1734:     if (J) {
1735:       J0   = 0.5 * PetscRealPart(coords[1]);
1736:       J[0] = R[0] * J0;
1737:       J[1] = R[1];
1738:       J[2] = R[2] * J0;
1739:       J[3] = R[3];
1740:       DMPlex_Det2D_Internal(detJ, J);
1741:       if (invJ) DMPlex_Invert2D_Internal(invJ, J, *detJ);
1742:     }
1743:   } else if (numCoords == 2) {
1744:     const PetscInt dim = 1;

1746:     if (v0) {
1747:       for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
1748:     }
1749:     if (J) {
1750:       J[0]  = 0.5 * (PetscRealPart(coords[1]) - PetscRealPart(coords[0]));
1751:       *detJ = J[0];
1752:       PetscCall(PetscLogFlops(2.0));
1753:       if (invJ) {
1754:         invJ[0] = 1.0 / J[0];
1755:         PetscCall(PetscLogFlops(1.0));
1756:       }
1757:     }
1758:   } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for segment %" PetscInt_FMT " is %" PetscInt_FMT " != 2 or 4 or 6", e, numCoords);
1759:   PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
1760:   PetscFunctionReturn(PETSC_SUCCESS);
1761: }

1763: static PetscErrorCode DMPlexComputeTriangleGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1764: {
1765:   const PetscScalar *array;
1766:   PetscScalar       *coords = NULL;
1767:   PetscInt           numCoords, d;
1768:   PetscBool          isDG;

1770:   PetscFunctionBegin;
1771:   PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
1772:   PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
1773:   *detJ = 0.0;
1774:   if (numCoords == 9) {
1775:     const PetscInt dim = 3;
1776:     PetscReal      R[9], J0[9] = {1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0};

1778:     if (v0) {
1779:       for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
1780:     }
1781:     PetscCall(DMPlexComputeProjection3Dto2D(numCoords, coords, R));
1782:     if (J) {
1783:       const PetscInt pdim = 2;

1785:       for (d = 0; d < pdim; d++) {
1786:         for (PetscInt f = 0; f < pdim; f++) J0[d * dim + f] = 0.5 * (PetscRealPart(coords[(f + 1) * pdim + d]) - PetscRealPart(coords[0 * pdim + d]));
1787:       }
1788:       PetscCall(PetscLogFlops(8.0));
1789:       DMPlex_Det3D_Internal(detJ, J0);
1790:       for (d = 0; d < dim; d++) {
1791:         for (PetscInt f = 0; f < dim; f++) {
1792:           J[d * dim + f] = 0.0;
1793:           for (PetscInt g = 0; g < dim; g++) J[d * dim + f] += R[d * dim + g] * J0[g * dim + f];
1794:         }
1795:       }
1796:       PetscCall(PetscLogFlops(18.0));
1797:     }
1798:     if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
1799:   } else if (numCoords == 6) {
1800:     const PetscInt dim = 2;

1802:     if (v0) {
1803:       for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
1804:     }
1805:     if (J) {
1806:       for (d = 0; d < dim; d++) {
1807:         for (PetscInt f = 0; f < dim; f++) J[d * dim + f] = 0.5 * (PetscRealPart(coords[(f + 1) * dim + d]) - PetscRealPart(coords[0 * dim + d]));
1808:       }
1809:       PetscCall(PetscLogFlops(8.0));
1810:       DMPlex_Det2D_Internal(detJ, J);
1811:     }
1812:     if (invJ) DMPlex_Invert2D_Internal(invJ, J, *detJ);
1813:   } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this triangle is %" PetscInt_FMT " != 6 or 9", numCoords);
1814:   PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
1815:   PetscFunctionReturn(PETSC_SUCCESS);
1816: }

1818: static PetscErrorCode DMPlexComputeRectangleGeometry_Internal(DM dm, PetscInt e, PetscBool isTensor, PetscInt Nq, const PetscReal points[], PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1819: {
1820:   const PetscScalar *array;
1821:   PetscScalar       *coords = NULL;
1822:   PetscInt           numCoords, d;
1823:   PetscBool          isDG;

1825:   PetscFunctionBegin;
1826:   PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
1827:   PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
1828:   if (!Nq) {
1829:     PetscInt vorder[4] = {0, 1, 2, 3};

1831:     if (isTensor) {
1832:       vorder[2] = 3;
1833:       vorder[3] = 2;
1834:     }
1835:     *detJ = 0.0;
1836:     if (numCoords == 12) {
1837:       const PetscInt dim = 3;
1838:       PetscReal      R[9], J0[9] = {1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0};

1840:       if (v) {
1841:         for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);
1842:       }
1843:       PetscCall(DMPlexComputeProjection3Dto2D(numCoords, coords, R));
1844:       if (J) {
1845:         const PetscInt pdim = 2;

1847:         for (d = 0; d < pdim; d++) {
1848:           J0[d * dim + 0] = 0.5 * (PetscRealPart(coords[vorder[1] * pdim + d]) - PetscRealPart(coords[vorder[0] * pdim + d]));
1849:           J0[d * dim + 1] = 0.5 * (PetscRealPart(coords[vorder[2] * pdim + d]) - PetscRealPart(coords[vorder[1] * pdim + d]));
1850:         }
1851:         PetscCall(PetscLogFlops(8.0));
1852:         DMPlex_Det3D_Internal(detJ, J0);
1853:         for (d = 0; d < dim; d++) {
1854:           for (PetscInt f = 0; f < dim; f++) {
1855:             J[d * dim + f] = 0.0;
1856:             for (PetscInt g = 0; g < dim; g++) J[d * dim + f] += R[d * dim + g] * J0[g * dim + f];
1857:           }
1858:         }
1859:         PetscCall(PetscLogFlops(18.0));
1860:       }
1861:       if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
1862:     } else if (numCoords == 8) {
1863:       const PetscInt dim = 2;

1865:       if (v) {
1866:         for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);
1867:       }
1868:       if (J) {
1869:         for (d = 0; d < dim; d++) {
1870:           J[d * dim + 0] = 0.5 * (PetscRealPart(coords[vorder[1] * dim + d]) - PetscRealPart(coords[vorder[0] * dim + d]));
1871:           J[d * dim + 1] = 0.5 * (PetscRealPart(coords[vorder[3] * dim + d]) - PetscRealPart(coords[vorder[0] * dim + d]));
1872:         }
1873:         PetscCall(PetscLogFlops(8.0));
1874:         DMPlex_Det2D_Internal(detJ, J);
1875:       }
1876:       if (invJ) DMPlex_Invert2D_Internal(invJ, J, *detJ);
1877:     } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this quadrilateral is %" PetscInt_FMT " != 8 or 12", numCoords);
1878:   } else {
1879:     const PetscInt Nv         = 4;
1880:     const PetscInt dimR       = 2;
1881:     PetscInt       zToPlex[4] = {0, 1, 3, 2};
1882:     PetscReal      zOrder[12];
1883:     PetscReal      zCoeff[12];
1884:     PetscInt       i, j, k, l, dim;

1886:     if (isTensor) {
1887:       zToPlex[2] = 2;
1888:       zToPlex[3] = 3;
1889:     }
1890:     if (numCoords == 12) {
1891:       dim = 3;
1892:     } else if (numCoords == 8) {
1893:       dim = 2;
1894:     } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this quadrilateral is %" PetscInt_FMT " != 8 or 12", numCoords);
1895:     for (i = 0; i < Nv; i++) {
1896:       PetscInt zi = zToPlex[i];

1898:       for (j = 0; j < dim; j++) zOrder[dim * i + j] = PetscRealPart(coords[dim * zi + j]);
1899:     }
1900:     for (j = 0; j < dim; j++) {
1901:       /* Nodal basis for evaluation at the vertices: (1 \mp xi) (1 \mp eta):
1902:            \phi^0 = (1 - xi - eta + xi eta) --> 1      = 1/4 ( \phi^0 + \phi^1 + \phi^2 + \phi^3)
1903:            \phi^1 = (1 + xi - eta - xi eta) --> xi     = 1/4 (-\phi^0 + \phi^1 - \phi^2 + \phi^3)
1904:            \phi^2 = (1 - xi + eta - xi eta) --> eta    = 1/4 (-\phi^0 - \phi^1 + \phi^2 + \phi^3)
1905:            \phi^3 = (1 + xi + eta + xi eta) --> xi eta = 1/4 ( \phi^0 - \phi^1 - \phi^2 + \phi^3)
1906:       */
1907:       zCoeff[dim * 0 + j] = 0.25 * (zOrder[dim * 0 + j] + zOrder[dim * 1 + j] + zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
1908:       zCoeff[dim * 1 + j] = 0.25 * (-zOrder[dim * 0 + j] + zOrder[dim * 1 + j] - zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
1909:       zCoeff[dim * 2 + j] = 0.25 * (-zOrder[dim * 0 + j] - zOrder[dim * 1 + j] + zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
1910:       zCoeff[dim * 3 + j] = 0.25 * (zOrder[dim * 0 + j] - zOrder[dim * 1 + j] - zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
1911:     }
1912:     for (i = 0; i < Nq; i++) {
1913:       PetscReal xi = points[dimR * i], eta = points[dimR * i + 1];

1915:       if (v) {
1916:         PetscReal extPoint[4];

1918:         extPoint[0] = 1.;
1919:         extPoint[1] = xi;
1920:         extPoint[2] = eta;
1921:         extPoint[3] = xi * eta;
1922:         for (j = 0; j < dim; j++) {
1923:           PetscReal val = 0.;

1925:           for (k = 0; k < Nv; k++) val += extPoint[k] * zCoeff[dim * k + j];
1926:           v[i * dim + j] = val;
1927:         }
1928:       }
1929:       if (J) {
1930:         PetscReal extJ[8];

1932:         extJ[0] = 0.;
1933:         extJ[1] = 0.;
1934:         extJ[2] = 1.;
1935:         extJ[3] = 0.;
1936:         extJ[4] = 0.;
1937:         extJ[5] = 1.;
1938:         extJ[6] = eta;
1939:         extJ[7] = xi;
1940:         for (j = 0; j < dim; j++) {
1941:           for (k = 0; k < dimR; k++) {
1942:             PetscReal val = 0.;

1944:             for (l = 0; l < Nv; l++) val += zCoeff[dim * l + j] * extJ[dimR * l + k];
1945:             J[i * dim * dim + dim * j + k] = val;
1946:           }
1947:         }
1948:         if (dim == 3) { /* put the cross product in the third component of the Jacobian */
1949:           PetscReal  x, y, z;
1950:           PetscReal *iJ = &J[i * dim * dim];
1951:           PetscReal  norm;

1953:           x     = iJ[1 * dim + 0] * iJ[2 * dim + 1] - iJ[1 * dim + 1] * iJ[2 * dim + 0];
1954:           y     = iJ[0 * dim + 1] * iJ[2 * dim + 0] - iJ[0 * dim + 0] * iJ[2 * dim + 1];
1955:           z     = iJ[0 * dim + 0] * iJ[1 * dim + 1] - iJ[0 * dim + 1] * iJ[1 * dim + 0];
1956:           norm  = PetscSqrtReal(x * x + y * y + z * z);
1957:           iJ[2] = x / norm;
1958:           iJ[5] = y / norm;
1959:           iJ[8] = z / norm;
1960:           DMPlex_Det3D_Internal(&detJ[i], &J[i * dim * dim]);
1961:           if (invJ) DMPlex_Invert3D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);
1962:         } else {
1963:           DMPlex_Det2D_Internal(&detJ[i], &J[i * dim * dim]);
1964:           if (invJ) DMPlex_Invert2D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);
1965:         }
1966:       }
1967:     }
1968:   }
1969:   PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
1970:   PetscFunctionReturn(PETSC_SUCCESS);
1971: }

1973: static PetscErrorCode DMPlexComputeTetrahedronGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1974: {
1975:   const PetscScalar *array;
1976:   PetscScalar       *coords = NULL;
1977:   const PetscInt     dim    = 3;
1978:   PetscInt           numCoords, d;
1979:   PetscBool          isDG;

1981:   PetscFunctionBegin;
1982:   PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
1983:   PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
1984:   *detJ = 0.0;
1985:   if (v0) {
1986:     for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
1987:   }
1988:   if (J) {
1989:     for (d = 0; d < dim; d++) {
1990:       /* I orient with outward face normals */
1991:       J[d * dim + 0] = 0.5 * (PetscRealPart(coords[2 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
1992:       J[d * dim + 1] = 0.5 * (PetscRealPart(coords[1 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
1993:       J[d * dim + 2] = 0.5 * (PetscRealPart(coords[3 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
1994:     }
1995:     PetscCall(PetscLogFlops(18.0));
1996:     DMPlex_Det3D_Internal(detJ, J);
1997:   }
1998:   if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
1999:   PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
2000:   PetscFunctionReturn(PETSC_SUCCESS);
2001: }

2003: static PetscErrorCode DMPlexComputeHexahedronGeometry_Internal(DM dm, PetscInt e, PetscInt Nq, const PetscReal points[], PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
2004: {
2005:   const PetscScalar *array;
2006:   PetscScalar       *coords = NULL;
2007:   const PetscInt     dim    = 3;
2008:   PetscInt           numCoords, d;
2009:   PetscBool          isDG;

2011:   PetscFunctionBegin;
2012:   PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
2013:   PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
2014:   if (!Nq) {
2015:     *detJ = 0.0;
2016:     if (v) {
2017:       for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);
2018:     }
2019:     if (J) {
2020:       for (d = 0; d < dim; d++) {
2021:         J[d * dim + 0] = 0.5 * (PetscRealPart(coords[3 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2022:         J[d * dim + 1] = 0.5 * (PetscRealPart(coords[1 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2023:         J[d * dim + 2] = 0.5 * (PetscRealPart(coords[4 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2024:       }
2025:       PetscCall(PetscLogFlops(18.0));
2026:       DMPlex_Det3D_Internal(detJ, J);
2027:     }
2028:     if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
2029:   } else {
2030:     const PetscInt Nv         = 8;
2031:     const PetscInt zToPlex[8] = {0, 3, 1, 2, 4, 5, 7, 6};
2032:     const PetscInt dim        = 3;
2033:     const PetscInt dimR       = 3;
2034:     PetscReal      zOrder[24];
2035:     PetscReal      zCoeff[24];
2036:     PetscInt       i, j, k, l;

2038:     for (i = 0; i < Nv; i++) {
2039:       PetscInt zi = zToPlex[i];

2041:       for (j = 0; j < dim; j++) zOrder[dim * i + j] = PetscRealPart(coords[dim * zi + j]);
2042:     }
2043:     for (j = 0; j < dim; j++) {
2044:       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]);
2045:       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]);
2046:       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]);
2047:       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]);
2048:       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]);
2049:       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]);
2050:       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]);
2051:       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]);
2052:     }
2053:     for (i = 0; i < Nq; i++) {
2054:       PetscReal xi = points[dimR * i], eta = points[dimR * i + 1], theta = points[dimR * i + 2];

2056:       if (v) {
2057:         PetscReal extPoint[8];

2059:         extPoint[0] = 1.;
2060:         extPoint[1] = xi;
2061:         extPoint[2] = eta;
2062:         extPoint[3] = xi * eta;
2063:         extPoint[4] = theta;
2064:         extPoint[5] = theta * xi;
2065:         extPoint[6] = theta * eta;
2066:         extPoint[7] = theta * eta * xi;
2067:         for (j = 0; j < dim; j++) {
2068:           PetscReal val = 0.;

2070:           for (k = 0; k < Nv; k++) val += extPoint[k] * zCoeff[dim * k + j];
2071:           v[i * dim + j] = val;
2072:         }
2073:       }
2074:       if (J) {
2075:         PetscReal extJ[24];

2077:         extJ[0]  = 0.;
2078:         extJ[1]  = 0.;
2079:         extJ[2]  = 0.;
2080:         extJ[3]  = 1.;
2081:         extJ[4]  = 0.;
2082:         extJ[5]  = 0.;
2083:         extJ[6]  = 0.;
2084:         extJ[7]  = 1.;
2085:         extJ[8]  = 0.;
2086:         extJ[9]  = eta;
2087:         extJ[10] = xi;
2088:         extJ[11] = 0.;
2089:         extJ[12] = 0.;
2090:         extJ[13] = 0.;
2091:         extJ[14] = 1.;
2092:         extJ[15] = theta;
2093:         extJ[16] = 0.;
2094:         extJ[17] = xi;
2095:         extJ[18] = 0.;
2096:         extJ[19] = theta;
2097:         extJ[20] = eta;
2098:         extJ[21] = theta * eta;
2099:         extJ[22] = theta * xi;
2100:         extJ[23] = eta * xi;

2102:         for (j = 0; j < dim; j++) {
2103:           for (k = 0; k < dimR; k++) {
2104:             PetscReal val = 0.;

2106:             for (l = 0; l < Nv; l++) val += zCoeff[dim * l + j] * extJ[dimR * l + k];
2107:             J[i * dim * dim + dim * j + k] = val;
2108:           }
2109:         }
2110:         DMPlex_Det3D_Internal(&detJ[i], &J[i * dim * dim]);
2111:         if (invJ) DMPlex_Invert3D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);
2112:       }
2113:     }
2114:   }
2115:   PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
2116:   PetscFunctionReturn(PETSC_SUCCESS);
2117: }

2119: static PetscErrorCode DMPlexComputeTriangularPrismGeometry_Internal(DM dm, PetscInt e, PetscInt Nq, const PetscReal points[], PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
2120: {
2121:   const PetscScalar *array;
2122:   PetscScalar       *coords = NULL;
2123:   const PetscInt     dim    = 3;
2124:   PetscInt           numCoords, d;
2125:   PetscBool          isDG;

2127:   PetscFunctionBegin;
2128:   PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
2129:   PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
2130:   if (!Nq) {
2131:     /* Assume that the map to the reference is affine */
2132:     *detJ = 0.0;
2133:     if (v) {
2134:       for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);
2135:     }
2136:     if (J) {
2137:       for (d = 0; d < dim; d++) {
2138:         J[d * dim + 0] = 0.5 * (PetscRealPart(coords[2 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2139:         J[d * dim + 1] = 0.5 * (PetscRealPart(coords[1 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2140:         J[d * dim + 2] = 0.5 * (PetscRealPart(coords[4 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2141:       }
2142:       PetscCall(PetscLogFlops(18.0));
2143:       DMPlex_Det3D_Internal(detJ, J);
2144:     }
2145:     if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
2146:   } else {
2147:     const PetscInt dim  = 3;
2148:     const PetscInt dimR = 3;
2149:     const PetscInt Nv   = 6;
2150:     PetscReal      verts[18];
2151:     PetscReal      coeff[18];
2152:     PetscInt       i, j, k, l;

2154:     for (i = 0; i < Nv; ++i)
2155:       for (j = 0; j < dim; ++j) verts[dim * i + j] = PetscRealPart(coords[dim * i + j]);
2156:     for (j = 0; j < dim; ++j) {
2157:       /* Check for triangle,
2158:            phi^0 = -1/2 (xi + eta)  chi^0 = delta(-1, -1)   x(xi) = \sum_k x_k phi^k(xi) = \sum_k chi^k(x) phi^k(xi)
2159:            phi^1 =  1/2 (1 + xi)    chi^1 = delta( 1, -1)   y(xi) = \sum_k y_k phi^k(xi) = \sum_k chi^k(y) phi^k(xi)
2160:            phi^2 =  1/2 (1 + eta)   chi^2 = delta(-1,  1)

2162:            phi^0 + phi^1 + phi^2 = 1    coef_1   = 1/2 (         chi^1 + chi^2)
2163:           -phi^0 + phi^1 - phi^2 = xi   coef_xi  = 1/2 (-chi^0 + chi^1)
2164:           -phi^0 - phi^1 + phi^2 = eta  coef_eta = 1/2 (-chi^0         + chi^2)

2166:           < chi_0 chi_1 chi_2> A /  1  1  1 \ / phi_0 \   <chi> I <phi>^T  so we need the inverse transpose
2167:                                  | -1  1 -1 | | phi_1 | =
2168:                                  \ -1 -1  1 / \ phi_2 /

2170:           Check phi^0: 1/2 (phi^0 chi^1 + phi^0 chi^2 + phi^0 chi^0 - phi^0 chi^1 + phi^0 chi^0 - phi^0 chi^2) = phi^0 chi^0
2171:       */
2172:       /* Nodal basis for evaluation at the vertices: {-xi - eta, 1 + xi, 1 + eta} (1 \mp zeta):
2173:            \phi^0 = 1/4 (   -xi - eta        + xi zeta + eta zeta) --> /  1  1  1  1  1  1 \ 1
2174:            \phi^1 = 1/4 (1      + eta - zeta           - eta zeta) --> | -1  1 -1 -1 -1  1 | eta
2175:            \phi^2 = 1/4 (1 + xi       - zeta - xi zeta)            --> | -1 -1  1 -1  1 -1 | xi
2176:            \phi^3 = 1/4 (   -xi - eta        - xi zeta - eta zeta) --> | -1 -1 -1  1  1  1 | zeta
2177:            \phi^4 = 1/4 (1 + xi       + zeta + xi zeta)            --> |  1  1 -1 -1  1 -1 | xi zeta
2178:            \phi^5 = 1/4 (1      + eta + zeta           + eta zeta) --> \  1 -1  1 -1 -1  1 / eta zeta
2179:            1/4 /  0  1  1  0  1  1 \
2180:                | -1  1  0 -1  0  1 |
2181:                | -1  0  1 -1  1  0 |
2182:                |  0 -1 -1  0  1  1 |
2183:                |  1  0 -1 -1  1  0 |
2184:                \  1 -1  0 -1  0  1 /
2185:       */
2186:       coeff[dim * 0 + j] = (1. / 4.) * (verts[dim * 1 + j] + verts[dim * 2 + j] + verts[dim * 4 + j] + verts[dim * 5 + j]);
2187:       coeff[dim * 1 + j] = (1. / 4.) * (-verts[dim * 0 + j] + verts[dim * 1 + j] - verts[dim * 3 + j] + verts[dim * 5 + j]);
2188:       coeff[dim * 2 + j] = (1. / 4.) * (-verts[dim * 0 + j] + verts[dim * 2 + j] - verts[dim * 3 + j] + verts[dim * 4 + j]);
2189:       coeff[dim * 3 + j] = (1. / 4.) * (-verts[dim * 1 + j] - verts[dim * 2 + j] + verts[dim * 4 + j] + verts[dim * 5 + j]);
2190:       coeff[dim * 4 + j] = (1. / 4.) * (verts[dim * 0 + j] - verts[dim * 2 + j] - verts[dim * 3 + j] + verts[dim * 4 + j]);
2191:       coeff[dim * 5 + j] = (1. / 4.) * (verts[dim * 0 + j] - verts[dim * 1 + j] - verts[dim * 3 + j] + verts[dim * 5 + j]);
2192:       /* For reference prism:
2193:       {0, 0, 0}
2194:       {0, 1, 0}
2195:       {1, 0, 0}
2196:       {0, 0, 1}
2197:       {0, 0, 0}
2198:       {0, 0, 0}
2199:       */
2200:     }
2201:     for (i = 0; i < Nq; ++i) {
2202:       const PetscReal xi = points[dimR * i], eta = points[dimR * i + 1], zeta = points[dimR * i + 2];

2204:       if (v) {
2205:         PetscReal extPoint[6];
2206:         PetscInt  c;

2208:         extPoint[0] = 1.;
2209:         extPoint[1] = eta;
2210:         extPoint[2] = xi;
2211:         extPoint[3] = zeta;
2212:         extPoint[4] = xi * zeta;
2213:         extPoint[5] = eta * zeta;
2214:         for (c = 0; c < dim; ++c) {
2215:           PetscReal val = 0.;

2217:           for (k = 0; k < Nv; ++k) val += extPoint[k] * coeff[k * dim + c];
2218:           v[i * dim + c] = val;
2219:         }
2220:       }
2221:       if (J) {
2222:         PetscReal extJ[18];

2224:         extJ[0]  = 0.;
2225:         extJ[1]  = 0.;
2226:         extJ[2]  = 0.;
2227:         extJ[3]  = 0.;
2228:         extJ[4]  = 1.;
2229:         extJ[5]  = 0.;
2230:         extJ[6]  = 1.;
2231:         extJ[7]  = 0.;
2232:         extJ[8]  = 0.;
2233:         extJ[9]  = 0.;
2234:         extJ[10] = 0.;
2235:         extJ[11] = 1.;
2236:         extJ[12] = zeta;
2237:         extJ[13] = 0.;
2238:         extJ[14] = xi;
2239:         extJ[15] = 0.;
2240:         extJ[16] = zeta;
2241:         extJ[17] = eta;

2243:         for (j = 0; j < dim; j++) {
2244:           for (k = 0; k < dimR; k++) {
2245:             PetscReal val = 0.;

2247:             for (l = 0; l < Nv; l++) val += coeff[dim * l + j] * extJ[dimR * l + k];
2248:             J[i * dim * dim + dim * j + k] = val;
2249:           }
2250:         }
2251:         DMPlex_Det3D_Internal(&detJ[i], &J[i * dim * dim]);
2252:         if (invJ) DMPlex_Invert3D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);
2253:       }
2254:     }
2255:   }
2256:   PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
2257:   PetscFunctionReturn(PETSC_SUCCESS);
2258: }

2260: static PetscErrorCode DMPlexComputeCellGeometryFEM_Implicit(DM dm, PetscInt cell, PetscQuadrature quad, PetscReal *v, PetscReal *J, PetscReal *invJ, PetscReal *detJ)
2261: {
2262:   DMPolytopeType   ct;
2263:   PetscInt         depth, dim, coordDim, coneSize, i;
2264:   PetscInt         Nq     = 0;
2265:   const PetscReal *points = NULL;
2266:   DMLabel          depthLabel;
2267:   PetscReal        xi0[3]   = {-1., -1., -1.}, v0[3], J0[9], detJ0;
2268:   PetscBool        isAffine = PETSC_TRUE;

2270:   PetscFunctionBegin;
2271:   PetscCall(DMPlexGetDepth(dm, &depth));
2272:   PetscCall(DMPlexGetConeSize(dm, cell, &coneSize));
2273:   PetscCall(DMPlexGetDepthLabel(dm, &depthLabel));
2274:   PetscCall(DMLabelGetValue(depthLabel, cell, &dim));
2275:   if (depth == 1 && dim == 1) PetscCall(DMGetDimension(dm, &dim));
2276:   PetscCall(DMGetCoordinateDim(dm, &coordDim));
2277:   PetscCheck(coordDim <= 3, PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported coordinate dimension %" PetscInt_FMT " > 3", coordDim);
2278:   if (quad) PetscCall(PetscQuadratureGetData(quad, NULL, NULL, &Nq, &points, NULL));
2279:   PetscCall(DMPlexGetCellType(dm, cell, &ct));
2280:   switch (ct) {
2281:   case DM_POLYTOPE_POINT:
2282:     PetscCall(DMPlexComputePointGeometry_Internal(dm, cell, v, J, invJ, detJ));
2283:     isAffine = PETSC_FALSE;
2284:     break;
2285:   case DM_POLYTOPE_SEGMENT:
2286:   case DM_POLYTOPE_POINT_PRISM_TENSOR:
2287:     if (Nq) PetscCall(DMPlexComputeLineGeometry_Internal(dm, cell, v0, J0, NULL, &detJ0));
2288:     else PetscCall(DMPlexComputeLineGeometry_Internal(dm, cell, v, J, invJ, detJ));
2289:     break;
2290:   case DM_POLYTOPE_TRIANGLE:
2291:     if (Nq) PetscCall(DMPlexComputeTriangleGeometry_Internal(dm, cell, v0, J0, NULL, &detJ0));
2292:     else PetscCall(DMPlexComputeTriangleGeometry_Internal(dm, cell, v, J, invJ, detJ));
2293:     break;
2294:   case DM_POLYTOPE_QUADRILATERAL:
2295:     PetscCall(DMPlexComputeRectangleGeometry_Internal(dm, cell, PETSC_FALSE, Nq, points, v, J, invJ, detJ));
2296:     isAffine = PETSC_FALSE;
2297:     break;
2298:   case DM_POLYTOPE_SEG_PRISM_TENSOR:
2299:     PetscCall(DMPlexComputeRectangleGeometry_Internal(dm, cell, PETSC_TRUE, Nq, points, v, J, invJ, detJ));
2300:     isAffine = PETSC_FALSE;
2301:     break;
2302:   case DM_POLYTOPE_TETRAHEDRON:
2303:     if (Nq) PetscCall(DMPlexComputeTetrahedronGeometry_Internal(dm, cell, v0, J0, NULL, &detJ0));
2304:     else PetscCall(DMPlexComputeTetrahedronGeometry_Internal(dm, cell, v, J, invJ, detJ));
2305:     break;
2306:   case DM_POLYTOPE_HEXAHEDRON:
2307:     PetscCall(DMPlexComputeHexahedronGeometry_Internal(dm, cell, Nq, points, v, J, invJ, detJ));
2308:     isAffine = PETSC_FALSE;
2309:     break;
2310:   case DM_POLYTOPE_TRI_PRISM:
2311:     PetscCall(DMPlexComputeTriangularPrismGeometry_Internal(dm, cell, Nq, points, v, J, invJ, detJ));
2312:     isAffine = PETSC_FALSE;
2313:     break;
2314:   default:
2315:     SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No element geometry for cell %" PetscInt_FMT " with type %s", cell, DMPolytopeTypes[PetscMax(0, PetscMin(ct, DM_NUM_POLYTOPES))]);
2316:   }
2317:   if (isAffine && Nq) {
2318:     if (v) {
2319:       for (i = 0; i < Nq; i++) CoordinatesRefToReal(coordDim, dim, xi0, v0, J0, &points[dim * i], &v[coordDim * i]);
2320:     }
2321:     if (detJ) {
2322:       for (i = 0; i < Nq; i++) detJ[i] = detJ0;
2323:     }
2324:     if (J) {
2325:       PetscInt k;

2327:       for (i = 0, k = 0; i < Nq; i++) {
2328:         PetscInt j;

2330:         for (j = 0; j < coordDim * coordDim; j++, k++) J[k] = J0[j];
2331:       }
2332:     }
2333:     if (invJ) {
2334:       PetscInt k;
2335:       switch (coordDim) {
2336:       case 0:
2337:         break;
2338:       case 1:
2339:         invJ[0] = 1. / J0[0];
2340:         break;
2341:       case 2:
2342:         DMPlex_Invert2D_Internal(invJ, J0, detJ0);
2343:         break;
2344:       case 3:
2345:         DMPlex_Invert3D_Internal(invJ, J0, detJ0);
2346:         break;
2347:       }
2348:       for (i = 1, k = coordDim * coordDim; i < Nq; i++) {
2349:         PetscInt j;

2351:         for (j = 0; j < coordDim * coordDim; j++, k++) invJ[k] = invJ[j];
2352:       }
2353:     }
2354:   }
2355:   PetscFunctionReturn(PETSC_SUCCESS);
2356: }

2358: /*@C
2359:   DMPlexComputeCellGeometryAffineFEM - Assuming an affine map, compute the Jacobian, inverse Jacobian, and Jacobian determinant for a given cell

2361:   Collective

2363:   Input Parameters:
2364: + dm   - the `DMPLEX`
2365: - cell - the cell

2367:   Output Parameters:
2368: + v0   - the translation part of this affine transform, meaning the translation to the origin (not the first vertex of the reference cell)
2369: . J    - the Jacobian of the transform from the reference element
2370: . invJ - the inverse of the Jacobian
2371: - detJ - the Jacobian determinant

2373:   Level: advanced

2375: .seealso: `DMPLEX`, `DMPlexComputeCellGeometryFEM()`, `DMGetCoordinateSection()`, `DMGetCoordinates()`
2376: @*/
2377: PetscErrorCode DMPlexComputeCellGeometryAffineFEM(DM dm, PetscInt cell, PetscReal *v0, PetscReal *J, PetscReal *invJ, PetscReal *detJ)
2378: {
2379:   PetscFunctionBegin;
2380:   PetscCall(DMPlexComputeCellGeometryFEM_Implicit(dm, cell, NULL, v0, J, invJ, detJ));
2381:   PetscFunctionReturn(PETSC_SUCCESS);
2382: }

2384: static PetscErrorCode DMPlexComputeCellGeometryFEM_FE(DM dm, PetscFE fe, PetscInt point, PetscQuadrature quad, PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
2385: {
2386:   const PetscScalar *array;
2387:   PetscScalar       *coords = NULL;
2388:   PetscInt           numCoords;
2389:   PetscBool          isDG;
2390:   PetscQuadrature    feQuad;
2391:   const PetscReal   *quadPoints;
2392:   PetscTabulation    T;
2393:   PetscInt           dim, cdim, pdim, qdim, Nq, q;

2395:   PetscFunctionBegin;
2396:   PetscCall(DMGetDimension(dm, &dim));
2397:   PetscCall(DMGetCoordinateDim(dm, &cdim));
2398:   PetscCall(DMPlexGetCellCoordinates(dm, point, &isDG, &numCoords, &array, &coords));
2399:   if (!quad) { /* use the first point of the first functional of the dual space */
2400:     PetscDualSpace dsp;

2402:     PetscCall(PetscFEGetDualSpace(fe, &dsp));
2403:     PetscCall(PetscDualSpaceGetFunctional(dsp, 0, &quad));
2404:     PetscCall(PetscQuadratureGetData(quad, &qdim, NULL, &Nq, &quadPoints, NULL));
2405:     Nq = 1;
2406:   } else {
2407:     PetscCall(PetscQuadratureGetData(quad, &qdim, NULL, &Nq, &quadPoints, NULL));
2408:   }
2409:   PetscCall(PetscFEGetDimension(fe, &pdim));
2410:   PetscCall(PetscFEGetQuadrature(fe, &feQuad));
2411:   if (feQuad == quad) {
2412:     PetscCall(PetscFEGetCellTabulation(fe, J ? 1 : 0, &T));
2413:     PetscCheck(numCoords == pdim * cdim, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "There are %" PetscInt_FMT " coordinates for point %" PetscInt_FMT " != %" PetscInt_FMT "*%" PetscInt_FMT, numCoords, point, pdim, cdim);
2414:   } else {
2415:     PetscCall(PetscFECreateTabulation(fe, 1, Nq, quadPoints, J ? 1 : 0, &T));
2416:   }
2417:   PetscCheck(qdim == dim, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Point dimension %" PetscInt_FMT " != quadrature dimension %" PetscInt_FMT, dim, qdim);
2418:   {
2419:     const PetscReal *basis    = T->T[0];
2420:     const PetscReal *basisDer = T->T[1];
2421:     PetscReal        detJt;

2423:     PetscAssert(Nq == T->Np, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Np %" PetscInt_FMT " != %" PetscInt_FMT, Nq, T->Np);
2424:     PetscAssert(pdim == T->Nb, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Nb %" PetscInt_FMT " != %" PetscInt_FMT, pdim, T->Nb);
2425:     PetscAssert(dim == T->Nc, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Nc %" PetscInt_FMT " != %" PetscInt_FMT, dim, T->Nc);
2426:     PetscAssert(cdim == T->cdim, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "cdim %" PetscInt_FMT " != %" PetscInt_FMT, cdim, T->cdim);
2427:     if (v) {
2428:       PetscCall(PetscArrayzero(v, Nq * cdim));
2429:       for (q = 0; q < Nq; ++q) {
2430:         PetscInt i, k;

2432:         for (k = 0; k < pdim; ++k) {
2433:           const PetscInt vertex = k / cdim;
2434:           for (i = 0; i < cdim; ++i) v[q * cdim + i] += basis[(q * pdim + k) * cdim + i] * PetscRealPart(coords[vertex * cdim + i]);
2435:         }
2436:         PetscCall(PetscLogFlops(2.0 * pdim * cdim));
2437:       }
2438:     }
2439:     if (J) {
2440:       PetscCall(PetscArrayzero(J, Nq * cdim * cdim));
2441:       for (q = 0; q < Nq; ++q) {
2442:         PetscInt i, j, k, c, r;

2444:         /* J = dx_i/d\xi_j = sum[k=0,n-1] dN_k/d\xi_j * x_i(k) */
2445:         for (k = 0; k < pdim; ++k) {
2446:           const PetscInt vertex = k / cdim;
2447:           for (j = 0; j < dim; ++j) {
2448:             for (i = 0; i < cdim; ++i) J[(q * cdim + i) * cdim + j] += basisDer[((q * pdim + k) * cdim + i) * dim + j] * PetscRealPart(coords[vertex * cdim + i]);
2449:           }
2450:         }
2451:         PetscCall(PetscLogFlops(2.0 * pdim * dim * cdim));
2452:         if (cdim > dim) {
2453:           for (c = dim; c < cdim; ++c)
2454:             for (r = 0; r < cdim; ++r) J[r * cdim + c] = r == c ? 1.0 : 0.0;
2455:         }
2456:         if (!detJ && !invJ) continue;
2457:         detJt = 0.;
2458:         switch (cdim) {
2459:         case 3:
2460:           DMPlex_Det3D_Internal(&detJt, &J[q * cdim * dim]);
2461:           if (invJ) DMPlex_Invert3D_Internal(&invJ[q * cdim * dim], &J[q * cdim * dim], detJt);
2462:           break;
2463:         case 2:
2464:           DMPlex_Det2D_Internal(&detJt, &J[q * cdim * dim]);
2465:           if (invJ) DMPlex_Invert2D_Internal(&invJ[q * cdim * dim], &J[q * cdim * dim], detJt);
2466:           break;
2467:         case 1:
2468:           detJt = J[q * cdim * dim];
2469:           if (invJ) invJ[q * cdim * dim] = 1.0 / detJt;
2470:         }
2471:         if (detJ) detJ[q] = detJt;
2472:       }
2473:     } else PetscCheck(!detJ && !invJ, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Need J to compute invJ or detJ");
2474:   }
2475:   if (feQuad != quad) PetscCall(PetscTabulationDestroy(&T));
2476:   PetscCall(DMPlexRestoreCellCoordinates(dm, point, &isDG, &numCoords, &array, &coords));
2477:   PetscFunctionReturn(PETSC_SUCCESS);
2478: }

2480: /*@C
2481:   DMPlexComputeCellGeometryFEM - Compute the Jacobian, inverse Jacobian, and Jacobian determinant at each quadrature point in the given cell

2483:   Collective

2485:   Input Parameters:
2486: + dm   - the `DMPLEX`
2487: . cell - the cell
2488: - quad - the quadrature containing the points in the reference element where the geometry will be evaluated.  If `quad` is `NULL`, geometry will be
2489:          evaluated at the first vertex of the reference element

2491:   Output Parameters:
2492: + v    - the image of the transformed quadrature points, otherwise the image of the first vertex in the closure of the reference element
2493: . J    - the Jacobian of the transform from the reference element at each quadrature point
2494: . invJ - the inverse of the Jacobian at each quadrature point
2495: - detJ - the Jacobian determinant at each quadrature point

2497:   Level: advanced

2499: .seealso: `DMPLEX`, `DMGetCoordinateSection()`, `DMGetCoordinates()`
2500: @*/
2501: PetscErrorCode DMPlexComputeCellGeometryFEM(DM dm, PetscInt cell, PetscQuadrature quad, PetscReal *v, PetscReal *J, PetscReal *invJ, PetscReal *detJ)
2502: {
2503:   DM      cdm;
2504:   PetscFE fe = NULL;

2506:   PetscFunctionBegin;
2507:   PetscAssertPointer(detJ, 7);
2508:   PetscCall(DMGetCoordinateDM(dm, &cdm));
2509:   if (cdm) {
2510:     PetscClassId id;
2511:     PetscInt     numFields;
2512:     PetscDS      prob;
2513:     PetscObject  disc;

2515:     PetscCall(DMGetNumFields(cdm, &numFields));
2516:     if (numFields) {
2517:       PetscCall(DMGetDS(cdm, &prob));
2518:       PetscCall(PetscDSGetDiscretization(prob, 0, &disc));
2519:       PetscCall(PetscObjectGetClassId(disc, &id));
2520:       if (id == PETSCFE_CLASSID) fe = (PetscFE)disc;
2521:     }
2522:   }
2523:   if (!fe) PetscCall(DMPlexComputeCellGeometryFEM_Implicit(dm, cell, quad, v, J, invJ, detJ));
2524:   else PetscCall(DMPlexComputeCellGeometryFEM_FE(dm, fe, cell, quad, v, J, invJ, detJ));
2525:   PetscFunctionReturn(PETSC_SUCCESS);
2526: }

2528: static PetscErrorCode DMPlexComputeGeometryFVM_0D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
2529: {
2530:   PetscSection       coordSection;
2531:   Vec                coordinates;
2532:   const PetscScalar *coords = NULL;
2533:   PetscInt           d, dof, off;

2535:   PetscFunctionBegin;
2536:   PetscCall(DMGetCoordinatesLocal(dm, &coordinates));
2537:   PetscCall(DMGetCoordinateSection(dm, &coordSection));
2538:   PetscCall(VecGetArrayRead(coordinates, &coords));

2540:   /* for a point the centroid is just the coord */
2541:   if (centroid) {
2542:     PetscCall(PetscSectionGetDof(coordSection, cell, &dof));
2543:     PetscCall(PetscSectionGetOffset(coordSection, cell, &off));
2544:     for (d = 0; d < dof; d++) centroid[d] = PetscRealPart(coords[off + d]);
2545:   }
2546:   if (normal) {
2547:     const PetscInt *support, *cones;
2548:     PetscInt        supportSize;
2549:     PetscReal       norm, sign;

2551:     /* compute the norm based upon the support centroids */
2552:     PetscCall(DMPlexGetSupportSize(dm, cell, &supportSize));
2553:     PetscCall(DMPlexGetSupport(dm, cell, &support));
2554:     PetscCall(DMPlexComputeCellGeometryFVM(dm, support[0], NULL, normal, NULL));

2556:     /* Take the normal from the centroid of the support to the vertex*/
2557:     PetscCall(PetscSectionGetDof(coordSection, cell, &dof));
2558:     PetscCall(PetscSectionGetOffset(coordSection, cell, &off));
2559:     for (d = 0; d < dof; d++) normal[d] -= PetscRealPart(coords[off + d]);

2561:     /* Determine the sign of the normal based upon its location in the support */
2562:     PetscCall(DMPlexGetCone(dm, support[0], &cones));
2563:     sign = cones[0] == cell ? 1.0 : -1.0;

2565:     norm = DMPlex_NormD_Internal(dim, normal);
2566:     for (d = 0; d < dim; ++d) normal[d] /= (norm * sign);
2567:   }
2568:   if (vol) *vol = 1.0;
2569:   PetscCall(VecRestoreArrayRead(coordinates, &coords));
2570:   PetscFunctionReturn(PETSC_SUCCESS);
2571: }

2573: static PetscErrorCode DMPlexComputeGeometryFVM_1D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
2574: {
2575:   const PetscScalar *array;
2576:   PetscScalar       *coords = NULL;
2577:   PetscInt           cdim, coordSize, d;
2578:   PetscBool          isDG;

2580:   PetscFunctionBegin;
2581:   PetscCall(DMGetCoordinateDim(dm, &cdim));
2582:   PetscCall(DMPlexGetCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
2583:   PetscCheck(coordSize == cdim * 2, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Edge has %" PetscInt_FMT " coordinates != %" PetscInt_FMT, coordSize, cdim * 2);
2584:   if (centroid) {
2585:     for (d = 0; d < cdim; ++d) centroid[d] = 0.5 * PetscRealPart(coords[d] + coords[cdim + d]);
2586:   }
2587:   if (normal) {
2588:     PetscReal norm;

2590:     switch (cdim) {
2591:     case 3:
2592:       normal[2] = 0.; /* fall through */
2593:     case 2:
2594:       normal[0] = -PetscRealPart(coords[1] - coords[cdim + 1]);
2595:       normal[1] = PetscRealPart(coords[0] - coords[cdim + 0]);
2596:       break;
2597:     case 1:
2598:       normal[0] = 1.0;
2599:       break;
2600:     default:
2601:       SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Dimension %" PetscInt_FMT " not supported", cdim);
2602:     }
2603:     norm = DMPlex_NormD_Internal(cdim, normal);
2604:     for (d = 0; d < cdim; ++d) normal[d] /= norm;
2605:   }
2606:   if (vol) {
2607:     *vol = 0.0;
2608:     for (d = 0; d < cdim; ++d) *vol += PetscSqr(PetscRealPart(coords[d] - coords[cdim + d]));
2609:     *vol = PetscSqrtReal(*vol);
2610:   }
2611:   PetscCall(DMPlexRestoreCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
2612:   PetscFunctionReturn(PETSC_SUCCESS);
2613: }

2615: /* Centroid_i = (\sum_n A_n Cn_i) / A */
2616: static PetscErrorCode DMPlexComputeGeometryFVM_2D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
2617: {
2618:   DMPolytopeType     ct;
2619:   const PetscScalar *array;
2620:   PetscScalar       *coords = NULL;
2621:   PetscInt           coordSize;
2622:   PetscBool          isDG;
2623:   PetscInt           fv[4] = {0, 1, 2, 3};
2624:   PetscInt           cdim, numCorners, p, d;

2626:   PetscFunctionBegin;
2627:   /* Must check for hybrid cells because prisms have a different orientation scheme */
2628:   PetscCall(DMPlexGetCellType(dm, cell, &ct));
2629:   switch (ct) {
2630:   case DM_POLYTOPE_SEG_PRISM_TENSOR:
2631:     fv[2] = 3;
2632:     fv[3] = 2;
2633:     break;
2634:   default:
2635:     break;
2636:   }
2637:   PetscCall(DMGetCoordinateDim(dm, &cdim));
2638:   PetscCall(DMPlexGetConeSize(dm, cell, &numCorners));
2639:   PetscCall(DMPlexGetCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
2640:   {
2641:     PetscReal c[3] = {0., 0., 0.}, n[3] = {0., 0., 0.}, origin[3] = {0., 0., 0.}, norm;

2643:     for (d = 0; d < cdim; d++) origin[d] = PetscRealPart(coords[d]);
2644:     for (p = 0; p < numCorners - 2; ++p) {
2645:       PetscReal e0[3] = {0., 0., 0.}, e1[3] = {0., 0., 0.};
2646:       for (d = 0; d < cdim; d++) {
2647:         e0[d] = PetscRealPart(coords[cdim * fv[p + 1] + d]) - origin[d];
2648:         e1[d] = PetscRealPart(coords[cdim * fv[p + 2] + d]) - origin[d];
2649:       }
2650:       const PetscReal dx = e0[1] * e1[2] - e0[2] * e1[1];
2651:       const PetscReal dy = e0[2] * e1[0] - e0[0] * e1[2];
2652:       const PetscReal dz = e0[0] * e1[1] - e0[1] * e1[0];
2653:       const PetscReal a  = PetscSqrtReal(dx * dx + dy * dy + dz * dz);

2655:       n[0] += dx;
2656:       n[1] += dy;
2657:       n[2] += dz;
2658:       for (d = 0; d < cdim; d++) c[d] += a * PetscRealPart(origin[d] + coords[cdim * fv[p + 1] + d] + coords[cdim * fv[p + 2] + d]) / 3.;
2659:     }
2660:     norm = PetscSqrtReal(n[0] * n[0] + n[1] * n[1] + n[2] * n[2]);
2661:     // Allow zero volume cells
2662:     if (norm != 0) {
2663:       n[0] /= norm;
2664:       n[1] /= norm;
2665:       n[2] /= norm;
2666:       c[0] /= norm;
2667:       c[1] /= norm;
2668:       c[2] /= norm;
2669:     }
2670:     if (vol) *vol = 0.5 * norm;
2671:     if (centroid)
2672:       for (d = 0; d < cdim; ++d) centroid[d] = c[d];
2673:     if (normal)
2674:       for (d = 0; d < cdim; ++d) normal[d] = n[d];
2675:   }
2676:   PetscCall(DMPlexRestoreCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
2677:   PetscFunctionReturn(PETSC_SUCCESS);
2678: }

2680: /* Centroid_i = (\sum_n V_n Cn_i) / V */
2681: static PetscErrorCode DMPlexComputeGeometryFVM_3D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
2682: {
2683:   DMPolytopeType        ct;
2684:   const PetscScalar    *array;
2685:   PetscScalar          *coords = NULL;
2686:   PetscInt              coordSize;
2687:   PetscBool             isDG;
2688:   PetscReal             vsum      = 0.0, vtmp, coordsTmp[3 * 3], origin[3];
2689:   const PetscInt        order[16] = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15};
2690:   const PetscInt       *cone, *faceSizes, *faces;
2691:   const DMPolytopeType *faceTypes;
2692:   PetscBool             isHybrid = PETSC_FALSE;
2693:   PetscInt              numFaces, f, fOff = 0, p, d;

2695:   PetscFunctionBegin;
2696:   PetscCheck(dim <= 3, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "No support for dim %" PetscInt_FMT " > 3", dim);
2697:   /* Must check for hybrid cells because prisms have a different orientation scheme */
2698:   PetscCall(DMPlexGetCellType(dm, cell, &ct));
2699:   switch (ct) {
2700:   case DM_POLYTOPE_POINT_PRISM_TENSOR:
2701:   case DM_POLYTOPE_SEG_PRISM_TENSOR:
2702:   case DM_POLYTOPE_TRI_PRISM_TENSOR:
2703:   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
2704:     isHybrid = PETSC_TRUE;
2705:   default:
2706:     break;
2707:   }

2709:   if (centroid)
2710:     for (d = 0; d < dim; ++d) centroid[d] = 0.0;
2711:   PetscCall(DMPlexGetCone(dm, cell, &cone));

2713:   // Using the closure of faces for coordinates does not work in periodic geometries, so we index into the cell coordinates
2714:   PetscCall(DMPlexGetRawFaces_Internal(dm, ct, order, &numFaces, &faceTypes, &faceSizes, &faces));
2715:   PetscCall(DMPlexGetCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
2716:   for (f = 0; f < numFaces; ++f) {
2717:     PetscBool flip = isHybrid && f == 0 ? PETSC_TRUE : PETSC_FALSE; /* The first hybrid face is reversed */

2719:     // If using zero as the origin vertex for each tetrahedron, an element far from the origin will have positive and
2720:     // negative volumes that nearly cancel, thus incurring rounding error. Here we define origin[] as the first vertex
2721:     // so that all tetrahedra have positive volume.
2722:     if (f == 0)
2723:       for (d = 0; d < dim; d++) origin[d] = PetscRealPart(coords[d]);
2724:     switch (faceTypes[f]) {
2725:     case DM_POLYTOPE_TRIANGLE:
2726:       for (d = 0; d < dim; ++d) {
2727:         coordsTmp[0 * dim + d] = PetscRealPart(coords[faces[fOff + 0] * dim + d]) - origin[d];
2728:         coordsTmp[1 * dim + d] = PetscRealPart(coords[faces[fOff + 1] * dim + d]) - origin[d];
2729:         coordsTmp[2 * dim + d] = PetscRealPart(coords[faces[fOff + 2] * dim + d]) - origin[d];
2730:       }
2731:       Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
2732:       if (flip) vtmp = -vtmp;
2733:       vsum += vtmp;
2734:       if (centroid) { /* Centroid of OABC = (a+b+c)/4 */
2735:         for (d = 0; d < dim; ++d) {
2736:           for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p * dim + d] * vtmp;
2737:         }
2738:       }
2739:       break;
2740:     case DM_POLYTOPE_QUADRILATERAL:
2741:     case DM_POLYTOPE_SEG_PRISM_TENSOR: {
2742:       PetscInt fv[4] = {0, 1, 2, 3};

2744:       /* Side faces for hybrid cells are stored as tensor products */
2745:       if (isHybrid && f > 1) {
2746:         fv[2] = 3;
2747:         fv[3] = 2;
2748:       }
2749:       /* DO FOR PYRAMID */
2750:       /* First tet */
2751:       for (d = 0; d < dim; ++d) {
2752:         coordsTmp[0 * dim + d] = PetscRealPart(coords[faces[fOff + fv[0]] * dim + d]) - origin[d];
2753:         coordsTmp[1 * dim + d] = PetscRealPart(coords[faces[fOff + fv[1]] * dim + d]) - origin[d];
2754:         coordsTmp[2 * dim + d] = PetscRealPart(coords[faces[fOff + fv[3]] * dim + d]) - origin[d];
2755:       }
2756:       Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
2757:       if (flip) vtmp = -vtmp;
2758:       vsum += vtmp;
2759:       if (centroid) {
2760:         for (d = 0; d < dim; ++d) {
2761:           for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p * dim + d] * vtmp;
2762:         }
2763:       }
2764:       /* Second tet */
2765:       for (d = 0; d < dim; ++d) {
2766:         coordsTmp[0 * dim + d] = PetscRealPart(coords[faces[fOff + fv[1]] * dim + d]) - origin[d];
2767:         coordsTmp[1 * dim + d] = PetscRealPart(coords[faces[fOff + fv[2]] * dim + d]) - origin[d];
2768:         coordsTmp[2 * dim + d] = PetscRealPart(coords[faces[fOff + fv[3]] * dim + d]) - origin[d];
2769:       }
2770:       Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
2771:       if (flip) vtmp = -vtmp;
2772:       vsum += vtmp;
2773:       if (centroid) {
2774:         for (d = 0; d < dim; ++d) {
2775:           for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p * dim + d] * vtmp;
2776:         }
2777:       }
2778:       break;
2779:     }
2780:     default:
2781:       SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Cannot handle face %" PetscInt_FMT " of type %s", cone[f], DMPolytopeTypes[ct]);
2782:     }
2783:     fOff += faceSizes[f];
2784:   }
2785:   PetscCall(DMPlexRestoreRawFaces_Internal(dm, ct, order, &numFaces, &faceTypes, &faceSizes, &faces));
2786:   PetscCall(DMPlexRestoreCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
2787:   if (vol) *vol = PetscAbsReal(vsum);
2788:   if (normal)
2789:     for (d = 0; d < dim; ++d) normal[d] = 0.0;
2790:   if (centroid)
2791:     for (d = 0; d < dim; ++d) centroid[d] = centroid[d] / (vsum * 4) + origin[d];
2792:   PetscFunctionReturn(PETSC_SUCCESS);
2793: }

2795: /*@C
2796:   DMPlexComputeCellGeometryFVM - Compute the volume for a given cell

2798:   Collective

2800:   Input Parameters:
2801: + dm   - the `DMPLEX`
2802: - cell - the cell

2804:   Output Parameters:
2805: + vol      - the cell volume
2806: . centroid - the cell centroid
2807: - normal   - the cell normal, if appropriate

2809:   Level: advanced

2811: .seealso: `DMPLEX`, `DMGetCoordinateSection()`, `DMGetCoordinates()`
2812: @*/
2813: PetscErrorCode DMPlexComputeCellGeometryFVM(DM dm, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
2814: {
2815:   PetscInt depth, dim;

2817:   PetscFunctionBegin;
2818:   PetscCall(DMPlexGetDepth(dm, &depth));
2819:   PetscCall(DMGetDimension(dm, &dim));
2820:   PetscCheck(depth == dim, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Mesh must be interpolated");
2821:   PetscCall(DMPlexGetPointDepth(dm, cell, &depth));
2822:   switch (depth) {
2823:   case 0:
2824:     PetscCall(DMPlexComputeGeometryFVM_0D_Internal(dm, dim, cell, vol, centroid, normal));
2825:     break;
2826:   case 1:
2827:     PetscCall(DMPlexComputeGeometryFVM_1D_Internal(dm, dim, cell, vol, centroid, normal));
2828:     break;
2829:   case 2:
2830:     PetscCall(DMPlexComputeGeometryFVM_2D_Internal(dm, dim, cell, vol, centroid, normal));
2831:     break;
2832:   case 3:
2833:     PetscCall(DMPlexComputeGeometryFVM_3D_Internal(dm, dim, cell, vol, centroid, normal));
2834:     break;
2835:   default:
2836:     SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported dimension %" PetscInt_FMT " (depth %" PetscInt_FMT ") for element geometry computation", dim, depth);
2837:   }
2838:   PetscFunctionReturn(PETSC_SUCCESS);
2839: }

2841: /*@
2842:   DMPlexComputeGeometryFVM - Computes the cell and face geometry for a finite volume method

2844:   Input Parameter:
2845: . dm - The `DMPLEX`

2847:   Output Parameters:
2848: + cellgeom - A `Vec` of `PetscFVCellGeom` data
2849: - facegeom - A `Vec` of `PetscFVFaceGeom` data

2851:   Level: developer

2853: .seealso: `DMPLEX`, `PetscFVFaceGeom`, `PetscFVCellGeom`
2854: @*/
2855: PetscErrorCode DMPlexComputeGeometryFVM(DM dm, Vec *cellgeom, Vec *facegeom)
2856: {
2857:   DM           dmFace, dmCell;
2858:   DMLabel      ghostLabel;
2859:   PetscSection sectionFace, sectionCell;
2860:   PetscSection coordSection;
2861:   Vec          coordinates;
2862:   PetscScalar *fgeom, *cgeom;
2863:   PetscReal    minradius, gminradius;
2864:   PetscInt     dim, cStart, cEnd, cEndInterior, c, fStart, fEnd, f;

2866:   PetscFunctionBegin;
2867:   PetscCall(DMGetDimension(dm, &dim));
2868:   PetscCall(DMGetCoordinateSection(dm, &coordSection));
2869:   PetscCall(DMGetCoordinatesLocal(dm, &coordinates));
2870:   /* Make cell centroids and volumes */
2871:   PetscCall(DMClone(dm, &dmCell));
2872:   PetscCall(DMSetCoordinateSection(dmCell, PETSC_DETERMINE, coordSection));
2873:   PetscCall(DMSetCoordinatesLocal(dmCell, coordinates));
2874:   PetscCall(PetscSectionCreate(PetscObjectComm((PetscObject)dm), &sectionCell));
2875:   PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
2876:   PetscCall(DMPlexGetCellTypeStratum(dm, DM_POLYTOPE_FV_GHOST, &cEndInterior, NULL));
2877:   PetscCall(PetscSectionSetChart(sectionCell, cStart, cEnd));
2878:   for (c = cStart; c < cEnd; ++c) PetscCall(PetscSectionSetDof(sectionCell, c, (PetscInt)PetscCeilReal(((PetscReal)sizeof(PetscFVCellGeom)) / sizeof(PetscScalar))));
2879:   PetscCall(PetscSectionSetUp(sectionCell));
2880:   PetscCall(DMSetLocalSection(dmCell, sectionCell));
2881:   PetscCall(PetscSectionDestroy(&sectionCell));
2882:   PetscCall(DMCreateLocalVector(dmCell, cellgeom));
2883:   if (cEndInterior < 0) cEndInterior = cEnd;
2884:   PetscCall(VecGetArray(*cellgeom, &cgeom));
2885:   for (c = cStart; c < cEndInterior; ++c) {
2886:     PetscFVCellGeom *cg;

2888:     PetscCall(DMPlexPointLocalRef(dmCell, c, cgeom, &cg));
2889:     PetscCall(PetscArrayzero(cg, 1));
2890:     PetscCall(DMPlexComputeCellGeometryFVM(dmCell, c, &cg->volume, cg->centroid, NULL));
2891:   }
2892:   /* Compute face normals and minimum cell radius */
2893:   PetscCall(DMClone(dm, &dmFace));
2894:   PetscCall(PetscSectionCreate(PetscObjectComm((PetscObject)dm), &sectionFace));
2895:   PetscCall(DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd));
2896:   PetscCall(PetscSectionSetChart(sectionFace, fStart, fEnd));
2897:   for (f = fStart; f < fEnd; ++f) PetscCall(PetscSectionSetDof(sectionFace, f, (PetscInt)PetscCeilReal(((PetscReal)sizeof(PetscFVFaceGeom)) / sizeof(PetscScalar))));
2898:   PetscCall(PetscSectionSetUp(sectionFace));
2899:   PetscCall(DMSetLocalSection(dmFace, sectionFace));
2900:   PetscCall(PetscSectionDestroy(&sectionFace));
2901:   PetscCall(DMCreateLocalVector(dmFace, facegeom));
2902:   PetscCall(VecGetArray(*facegeom, &fgeom));
2903:   PetscCall(DMGetLabel(dm, "ghost", &ghostLabel));
2904:   minradius = PETSC_MAX_REAL;
2905:   for (f = fStart; f < fEnd; ++f) {
2906:     PetscFVFaceGeom *fg;
2907:     PetscReal        area;
2908:     const PetscInt  *cells;
2909:     PetscInt         ncells, ghost = -1, d, numChildren;

2911:     if (ghostLabel) PetscCall(DMLabelGetValue(ghostLabel, f, &ghost));
2912:     PetscCall(DMPlexGetTreeChildren(dm, f, &numChildren, NULL));
2913:     PetscCall(DMPlexGetSupport(dm, f, &cells));
2914:     PetscCall(DMPlexGetSupportSize(dm, f, &ncells));
2915:     /* It is possible to get a face with no support when using partition overlap */
2916:     if (!ncells || ghost >= 0 || numChildren) continue;
2917:     PetscCall(DMPlexPointLocalRef(dmFace, f, fgeom, &fg));
2918:     PetscCall(DMPlexComputeCellGeometryFVM(dm, f, &area, fg->centroid, fg->normal));
2919:     for (d = 0; d < dim; ++d) fg->normal[d] *= area;
2920:     /* Flip face orientation if necessary to match ordering in support, and Update minimum radius */
2921:     {
2922:       PetscFVCellGeom *cL, *cR;
2923:       PetscReal       *lcentroid, *rcentroid;
2924:       PetscReal        l[3], r[3], v[3];

2926:       PetscCall(DMPlexPointLocalRead(dmCell, cells[0], cgeom, &cL));
2927:       lcentroid = cells[0] >= cEndInterior ? fg->centroid : cL->centroid;
2928:       if (ncells > 1) {
2929:         PetscCall(DMPlexPointLocalRead(dmCell, cells[1], cgeom, &cR));
2930:         rcentroid = cells[1] >= cEndInterior ? fg->centroid : cR->centroid;
2931:       } else {
2932:         rcentroid = fg->centroid;
2933:       }
2934:       PetscCall(DMLocalizeCoordinateReal_Internal(dm, dim, fg->centroid, lcentroid, l));
2935:       PetscCall(DMLocalizeCoordinateReal_Internal(dm, dim, fg->centroid, rcentroid, r));
2936:       DMPlex_WaxpyD_Internal(dim, -1, l, r, v);
2937:       if (DMPlex_DotRealD_Internal(dim, fg->normal, v) < 0) {
2938:         for (d = 0; d < dim; ++d) fg->normal[d] = -fg->normal[d];
2939:       }
2940:       if (DMPlex_DotRealD_Internal(dim, fg->normal, v) <= 0) {
2941:         PetscCheck(dim != 2, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Direction for face %" PetscInt_FMT " 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]);
2942:         PetscCheck(dim != 3, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Direction for face %" PetscInt_FMT " 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]);
2943:         SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Direction for face %" PetscInt_FMT " could not be fixed", f);
2944:       }
2945:       if (cells[0] < cEndInterior) {
2946:         DMPlex_WaxpyD_Internal(dim, -1, fg->centroid, cL->centroid, v);
2947:         minradius = PetscMin(minradius, DMPlex_NormD_Internal(dim, v));
2948:       }
2949:       if (ncells > 1 && cells[1] < cEndInterior) {
2950:         DMPlex_WaxpyD_Internal(dim, -1, fg->centroid, cR->centroid, v);
2951:         minradius = PetscMin(minradius, DMPlex_NormD_Internal(dim, v));
2952:       }
2953:     }
2954:   }
2955:   PetscCallMPI(MPIU_Allreduce(&minradius, &gminradius, 1, MPIU_REAL, MPIU_MIN, PetscObjectComm((PetscObject)dm)));
2956:   PetscCall(DMPlexSetMinRadius(dm, gminradius));
2957:   /* Compute centroids of ghost cells */
2958:   for (c = cEndInterior; c < cEnd; ++c) {
2959:     PetscFVFaceGeom *fg;
2960:     const PetscInt  *cone, *support;
2961:     PetscInt         coneSize, supportSize, s;

2963:     PetscCall(DMPlexGetConeSize(dmCell, c, &coneSize));
2964:     PetscCheck(coneSize == 1, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Ghost cell %" PetscInt_FMT " has cone size %" PetscInt_FMT " != 1", c, coneSize);
2965:     PetscCall(DMPlexGetCone(dmCell, c, &cone));
2966:     PetscCall(DMPlexGetSupportSize(dmCell, cone[0], &supportSize));
2967:     PetscCheck(supportSize == 2, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Face %" PetscInt_FMT " has support size %" PetscInt_FMT " != 2", cone[0], supportSize);
2968:     PetscCall(DMPlexGetSupport(dmCell, cone[0], &support));
2969:     PetscCall(DMPlexPointLocalRef(dmFace, cone[0], fgeom, &fg));
2970:     for (s = 0; s < 2; ++s) {
2971:       /* Reflect ghost centroid across plane of face */
2972:       if (support[s] == c) {
2973:         PetscFVCellGeom *ci;
2974:         PetscFVCellGeom *cg;
2975:         PetscReal        c2f[3], a;

2977:         PetscCall(DMPlexPointLocalRead(dmCell, support[(s + 1) % 2], cgeom, &ci));
2978:         DMPlex_WaxpyD_Internal(dim, -1, ci->centroid, fg->centroid, c2f); /* cell to face centroid */
2979:         a = DMPlex_DotRealD_Internal(dim, c2f, fg->normal) / DMPlex_DotRealD_Internal(dim, fg->normal, fg->normal);
2980:         PetscCall(DMPlexPointLocalRef(dmCell, support[s], cgeom, &cg));
2981:         DMPlex_WaxpyD_Internal(dim, 2 * a, fg->normal, ci->centroid, cg->centroid);
2982:         cg->volume = ci->volume;
2983:       }
2984:     }
2985:   }
2986:   PetscCall(VecRestoreArray(*facegeom, &fgeom));
2987:   PetscCall(VecRestoreArray(*cellgeom, &cgeom));
2988:   PetscCall(DMDestroy(&dmCell));
2989:   PetscCall(DMDestroy(&dmFace));
2990:   PetscFunctionReturn(PETSC_SUCCESS);
2991: }

2993: /*@
2994:   DMPlexGetMinRadius - Returns the minimum distance from any cell centroid to a face

2996:   Not Collective

2998:   Input Parameter:
2999: . dm - the `DMPLEX`

3001:   Output Parameter:
3002: . minradius - the minimum cell radius

3004:   Level: developer

3006: .seealso: `DMPLEX`, `DMGetCoordinates()`
3007: @*/
3008: PetscErrorCode DMPlexGetMinRadius(DM dm, PetscReal *minradius)
3009: {
3010:   PetscFunctionBegin;
3012:   PetscAssertPointer(minradius, 2);
3013:   *minradius = ((DM_Plex *)dm->data)->minradius;
3014:   PetscFunctionReturn(PETSC_SUCCESS);
3015: }

3017: /*@
3018:   DMPlexSetMinRadius - Sets the minimum distance from the cell centroid to a face

3020:   Logically Collective

3022:   Input Parameters:
3023: + dm        - the `DMPLEX`
3024: - minradius - the minimum cell radius

3026:   Level: developer

3028: .seealso: `DMPLEX`, `DMSetCoordinates()`
3029: @*/
3030: PetscErrorCode DMPlexSetMinRadius(DM dm, PetscReal minradius)
3031: {
3032:   PetscFunctionBegin;
3034:   ((DM_Plex *)dm->data)->minradius = minradius;
3035:   PetscFunctionReturn(PETSC_SUCCESS);
3036: }

3038: static PetscErrorCode BuildGradientReconstruction_Internal(DM dm, PetscFV fvm, DM dmFace, PetscScalar *fgeom, DM dmCell, PetscScalar *cgeom)
3039: {
3040:   DMLabel      ghostLabel;
3041:   PetscScalar *dx, *grad, **gref;
3042:   PetscInt     dim, cStart, cEnd, c, cEndInterior, maxNumFaces;

3044:   PetscFunctionBegin;
3045:   PetscCall(DMGetDimension(dm, &dim));
3046:   PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
3047:   PetscCall(DMPlexGetCellTypeStratum(dm, DM_POLYTOPE_FV_GHOST, &cEndInterior, NULL));
3048:   cEndInterior = cEndInterior < 0 ? cEnd : cEndInterior;
3049:   PetscCall(DMPlexGetMaxSizes(dm, &maxNumFaces, NULL));
3050:   PetscCall(PetscFVLeastSquaresSetMaxFaces(fvm, maxNumFaces));
3051:   PetscCall(DMGetLabel(dm, "ghost", &ghostLabel));
3052:   PetscCall(PetscMalloc3(maxNumFaces * dim, &dx, maxNumFaces * dim, &grad, maxNumFaces, &gref));
3053:   for (c = cStart; c < cEndInterior; c++) {
3054:     const PetscInt  *faces;
3055:     PetscInt         numFaces, usedFaces, f, d;
3056:     PetscFVCellGeom *cg;
3057:     PetscBool        boundary;
3058:     PetscInt         ghost;

3060:     // do not attempt to compute a gradient reconstruction stencil in a ghost cell.  It will never be used
3061:     PetscCall(DMLabelGetValue(ghostLabel, c, &ghost));
3062:     if (ghost >= 0) continue;

3064:     PetscCall(DMPlexPointLocalRead(dmCell, c, cgeom, &cg));
3065:     PetscCall(DMPlexGetConeSize(dm, c, &numFaces));
3066:     PetscCall(DMPlexGetCone(dm, c, &faces));
3067:     PetscCheck(numFaces >= dim, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Cell %" PetscInt_FMT " has only %" PetscInt_FMT " faces, not enough for gradient reconstruction", c, numFaces);
3068:     for (f = 0, usedFaces = 0; f < numFaces; ++f) {
3069:       PetscFVCellGeom *cg1;
3070:       PetscFVFaceGeom *fg;
3071:       const PetscInt  *fcells;
3072:       PetscInt         ncell, side;

3074:       PetscCall(DMLabelGetValue(ghostLabel, faces[f], &ghost));
3075:       PetscCall(DMIsBoundaryPoint(dm, faces[f], &boundary));
3076:       if ((ghost >= 0) || boundary) continue;
3077:       PetscCall(DMPlexGetSupport(dm, faces[f], &fcells));
3078:       side  = (c != fcells[0]); /* c is on left=0 or right=1 of face */
3079:       ncell = fcells[!side];    /* the neighbor */
3080:       PetscCall(DMPlexPointLocalRef(dmFace, faces[f], fgeom, &fg));
3081:       PetscCall(DMPlexPointLocalRead(dmCell, ncell, cgeom, &cg1));
3082:       for (d = 0; d < dim; ++d) dx[usedFaces * dim + d] = cg1->centroid[d] - cg->centroid[d];
3083:       gref[usedFaces++] = fg->grad[side]; /* Gradient reconstruction term will go here */
3084:     }
3085:     PetscCheck(usedFaces, PETSC_COMM_SELF, PETSC_ERR_USER, "Mesh contains isolated cell (no neighbors). Is it intentional?");
3086:     PetscCall(PetscFVComputeGradient(fvm, usedFaces, dx, grad));
3087:     for (f = 0, usedFaces = 0; f < numFaces; ++f) {
3088:       PetscCall(DMLabelGetValue(ghostLabel, faces[f], &ghost));
3089:       PetscCall(DMIsBoundaryPoint(dm, faces[f], &boundary));
3090:       if ((ghost >= 0) || boundary) continue;
3091:       for (d = 0; d < dim; ++d) gref[usedFaces][d] = grad[usedFaces * dim + d];
3092:       ++usedFaces;
3093:     }
3094:   }
3095:   PetscCall(PetscFree3(dx, grad, gref));
3096:   PetscFunctionReturn(PETSC_SUCCESS);
3097: }

3099: static PetscErrorCode BuildGradientReconstruction_Internal_Tree(DM dm, PetscFV fvm, DM dmFace, PetscScalar *fgeom, DM dmCell, PetscScalar *cgeom)
3100: {
3101:   DMLabel      ghostLabel;
3102:   PetscScalar *dx, *grad, **gref;
3103:   PetscInt     dim, cStart, cEnd, c, cEndInterior, fStart, fEnd, f, nStart, nEnd, maxNumFaces = 0;
3104:   PetscSection neighSec;
3105:   PetscInt(*neighbors)[2];
3106:   PetscInt *counter;

3108:   PetscFunctionBegin;
3109:   PetscCall(DMGetDimension(dm, &dim));
3110:   PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
3111:   PetscCall(DMPlexGetCellTypeStratum(dm, DM_POLYTOPE_FV_GHOST, &cEndInterior, NULL));
3112:   if (cEndInterior < 0) cEndInterior = cEnd;
3113:   PetscCall(PetscSectionCreate(PetscObjectComm((PetscObject)dm), &neighSec));
3114:   PetscCall(PetscSectionSetChart(neighSec, cStart, cEndInterior));
3115:   PetscCall(DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd));
3116:   PetscCall(DMGetLabel(dm, "ghost", &ghostLabel));
3117:   for (f = fStart; f < fEnd; f++) {
3118:     const PetscInt *fcells;
3119:     PetscBool       boundary;
3120:     PetscInt        ghost = -1;
3121:     PetscInt        numChildren, numCells, c;

3123:     if (ghostLabel) PetscCall(DMLabelGetValue(ghostLabel, f, &ghost));
3124:     PetscCall(DMIsBoundaryPoint(dm, f, &boundary));
3125:     PetscCall(DMPlexGetTreeChildren(dm, f, &numChildren, NULL));
3126:     if ((ghost >= 0) || boundary || numChildren) continue;
3127:     PetscCall(DMPlexGetSupportSize(dm, f, &numCells));
3128:     if (numCells == 2) {
3129:       PetscCall(DMPlexGetSupport(dm, f, &fcells));
3130:       for (c = 0; c < 2; c++) {
3131:         PetscInt cell = fcells[c];

3133:         if (cell >= cStart && cell < cEndInterior) PetscCall(PetscSectionAddDof(neighSec, cell, 1));
3134:       }
3135:     }
3136:   }
3137:   PetscCall(PetscSectionSetUp(neighSec));
3138:   PetscCall(PetscSectionGetMaxDof(neighSec, &maxNumFaces));
3139:   PetscCall(PetscFVLeastSquaresSetMaxFaces(fvm, maxNumFaces));
3140:   nStart = 0;
3141:   PetscCall(PetscSectionGetStorageSize(neighSec, &nEnd));
3142:   PetscCall(PetscMalloc1(nEnd - nStart, &neighbors));
3143:   PetscCall(PetscCalloc1(cEndInterior - cStart, &counter));
3144:   for (f = fStart; f < fEnd; f++) {
3145:     const PetscInt *fcells;
3146:     PetscBool       boundary;
3147:     PetscInt        ghost = -1;
3148:     PetscInt        numChildren, numCells, c;

3150:     if (ghostLabel) PetscCall(DMLabelGetValue(ghostLabel, f, &ghost));
3151:     PetscCall(DMIsBoundaryPoint(dm, f, &boundary));
3152:     PetscCall(DMPlexGetTreeChildren(dm, f, &numChildren, NULL));
3153:     if ((ghost >= 0) || boundary || numChildren) continue;
3154:     PetscCall(DMPlexGetSupportSize(dm, f, &numCells));
3155:     if (numCells == 2) {
3156:       PetscCall(DMPlexGetSupport(dm, f, &fcells));
3157:       for (c = 0; c < 2; c++) {
3158:         PetscInt cell = fcells[c], off;

3160:         if (cell >= cStart && cell < cEndInterior) {
3161:           PetscCall(PetscSectionGetOffset(neighSec, cell, &off));
3162:           off += counter[cell - cStart]++;
3163:           neighbors[off][0] = f;
3164:           neighbors[off][1] = fcells[1 - c];
3165:         }
3166:       }
3167:     }
3168:   }
3169:   PetscCall(PetscFree(counter));
3170:   PetscCall(PetscMalloc3(maxNumFaces * dim, &dx, maxNumFaces * dim, &grad, maxNumFaces, &gref));
3171:   for (c = cStart; c < cEndInterior; c++) {
3172:     PetscInt         numFaces, f, d, off, ghost = -1;
3173:     PetscFVCellGeom *cg;

3175:     PetscCall(DMPlexPointLocalRead(dmCell, c, cgeom, &cg));
3176:     PetscCall(PetscSectionGetDof(neighSec, c, &numFaces));
3177:     PetscCall(PetscSectionGetOffset(neighSec, c, &off));

3179:     // do not attempt to compute a gradient reconstruction stencil in a ghost cell.  It will never be used
3180:     if (ghostLabel) PetscCall(DMLabelGetValue(ghostLabel, c, &ghost));
3181:     if (ghost >= 0) continue;

3183:     PetscCheck(numFaces >= dim, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Cell %" PetscInt_FMT " has only %" PetscInt_FMT " faces, not enough for gradient reconstruction", c, numFaces);
3184:     for (f = 0; f < numFaces; ++f) {
3185:       PetscFVCellGeom *cg1;
3186:       PetscFVFaceGeom *fg;
3187:       const PetscInt  *fcells;
3188:       PetscInt         ncell, side, nface;

3190:       nface = neighbors[off + f][0];
3191:       ncell = neighbors[off + f][1];
3192:       PetscCall(DMPlexGetSupport(dm, nface, &fcells));
3193:       side = (c != fcells[0]);
3194:       PetscCall(DMPlexPointLocalRef(dmFace, nface, fgeom, &fg));
3195:       PetscCall(DMPlexPointLocalRead(dmCell, ncell, cgeom, &cg1));
3196:       for (d = 0; d < dim; ++d) dx[f * dim + d] = cg1->centroid[d] - cg->centroid[d];
3197:       gref[f] = fg->grad[side]; /* Gradient reconstruction term will go here */
3198:     }
3199:     PetscCall(PetscFVComputeGradient(fvm, numFaces, dx, grad));
3200:     for (f = 0; f < numFaces; ++f) {
3201:       for (d = 0; d < dim; ++d) gref[f][d] = grad[f * dim + d];
3202:     }
3203:   }
3204:   PetscCall(PetscFree3(dx, grad, gref));
3205:   PetscCall(PetscSectionDestroy(&neighSec));
3206:   PetscCall(PetscFree(neighbors));
3207:   PetscFunctionReturn(PETSC_SUCCESS);
3208: }

3210: /*@
3211:   DMPlexComputeGradientFVM - Compute geometric factors for gradient reconstruction, which are stored in the geometry data, and compute layout for gradient data

3213:   Collective

3215:   Input Parameters:
3216: + dm           - The `DMPLEX`
3217: . fvm          - The `PetscFV`
3218: - cellGeometry - The face geometry from `DMPlexComputeCellGeometryFVM()`

3220:   Input/Output Parameter:
3221: . faceGeometry - The face geometry from `DMPlexComputeFaceGeometryFVM()`; on output
3222:                  the geometric factors for gradient calculation are inserted

3224:   Output Parameter:
3225: . dmGrad - The `DM` describing the layout of gradient data

3227:   Level: developer

3229: .seealso: `DMPLEX`, `DMPlexGetFaceGeometryFVM()`, `DMPlexGetCellGeometryFVM()`
3230: @*/
3231: PetscErrorCode DMPlexComputeGradientFVM(DM dm, PetscFV fvm, Vec faceGeometry, Vec cellGeometry, DM *dmGrad)
3232: {
3233:   DM           dmFace, dmCell;
3234:   PetscScalar *fgeom, *cgeom;
3235:   PetscSection sectionGrad, parentSection;
3236:   PetscInt     dim, pdim, cStart, cEnd, cEndInterior, c;

3238:   PetscFunctionBegin;
3239:   PetscCall(DMGetDimension(dm, &dim));
3240:   PetscCall(PetscFVGetNumComponents(fvm, &pdim));
3241:   PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
3242:   PetscCall(DMPlexGetCellTypeStratum(dm, DM_POLYTOPE_FV_GHOST, &cEndInterior, NULL));
3243:   /* Construct the interpolant corresponding to each face from the least-square solution over the cell neighborhood */
3244:   PetscCall(VecGetDM(faceGeometry, &dmFace));
3245:   PetscCall(VecGetDM(cellGeometry, &dmCell));
3246:   PetscCall(VecGetArray(faceGeometry, &fgeom));
3247:   PetscCall(VecGetArray(cellGeometry, &cgeom));
3248:   PetscCall(DMPlexGetTree(dm, &parentSection, NULL, NULL, NULL, NULL));
3249:   if (!parentSection) {
3250:     PetscCall(BuildGradientReconstruction_Internal(dm, fvm, dmFace, fgeom, dmCell, cgeom));
3251:   } else {
3252:     PetscCall(BuildGradientReconstruction_Internal_Tree(dm, fvm, dmFace, fgeom, dmCell, cgeom));
3253:   }
3254:   PetscCall(VecRestoreArray(faceGeometry, &fgeom));
3255:   PetscCall(VecRestoreArray(cellGeometry, &cgeom));
3256:   /* Create storage for gradients */
3257:   PetscCall(DMClone(dm, dmGrad));
3258:   PetscCall(PetscSectionCreate(PetscObjectComm((PetscObject)dm), &sectionGrad));
3259:   PetscCall(PetscSectionSetChart(sectionGrad, cStart, cEnd));
3260:   for (c = cStart; c < cEnd; ++c) PetscCall(PetscSectionSetDof(sectionGrad, c, pdim * dim));
3261:   PetscCall(PetscSectionSetUp(sectionGrad));
3262:   PetscCall(DMSetLocalSection(*dmGrad, sectionGrad));
3263:   PetscCall(PetscSectionDestroy(&sectionGrad));
3264:   PetscFunctionReturn(PETSC_SUCCESS);
3265: }

3267: /*@
3268:   DMPlexGetDataFVM - Retrieve precomputed cell geometry

3270:   Collective

3272:   Input Parameters:
3273: + dm - The `DM`
3274: - fv - The `PetscFV`

3276:   Output Parameters:
3277: + cellgeom - The cell geometry
3278: . facegeom - The face geometry
3279: - gradDM   - The gradient matrices

3281:   Level: developer

3283: .seealso: `DMPLEX`, `DMPlexComputeGeometryFVM()`
3284: @*/
3285: PetscErrorCode DMPlexGetDataFVM(DM dm, PetscFV fv, Vec *cellgeom, Vec *facegeom, DM *gradDM)
3286: {
3287:   PetscObject cellgeomobj, facegeomobj;

3289:   PetscFunctionBegin;
3290:   PetscCall(PetscObjectQuery((PetscObject)dm, "DMPlex_cellgeom_fvm", &cellgeomobj));
3291:   if (!cellgeomobj) {
3292:     Vec cellgeomInt, facegeomInt;

3294:     PetscCall(DMPlexComputeGeometryFVM(dm, &cellgeomInt, &facegeomInt));
3295:     PetscCall(PetscObjectCompose((PetscObject)dm, "DMPlex_cellgeom_fvm", (PetscObject)cellgeomInt));
3296:     PetscCall(PetscObjectCompose((PetscObject)dm, "DMPlex_facegeom_fvm", (PetscObject)facegeomInt));
3297:     PetscCall(VecDestroy(&cellgeomInt));
3298:     PetscCall(VecDestroy(&facegeomInt));
3299:     PetscCall(PetscObjectQuery((PetscObject)dm, "DMPlex_cellgeom_fvm", &cellgeomobj));
3300:   }
3301:   PetscCall(PetscObjectQuery((PetscObject)dm, "DMPlex_facegeom_fvm", &facegeomobj));
3302:   if (cellgeom) *cellgeom = (Vec)cellgeomobj;
3303:   if (facegeom) *facegeom = (Vec)facegeomobj;
3304:   if (gradDM) {
3305:     PetscObject gradobj;
3306:     PetscBool   computeGradients;

3308:     PetscCall(PetscFVGetComputeGradients(fv, &computeGradients));
3309:     if (!computeGradients) {
3310:       *gradDM = NULL;
3311:       PetscFunctionReturn(PETSC_SUCCESS);
3312:     }
3313:     PetscCall(PetscObjectQuery((PetscObject)dm, "DMPlex_dmgrad_fvm", &gradobj));
3314:     if (!gradobj) {
3315:       DM dmGradInt;

3317:       PetscCall(DMPlexComputeGradientFVM(dm, fv, (Vec)facegeomobj, (Vec)cellgeomobj, &dmGradInt));
3318:       PetscCall(PetscObjectCompose((PetscObject)dm, "DMPlex_dmgrad_fvm", (PetscObject)dmGradInt));
3319:       PetscCall(DMDestroy(&dmGradInt));
3320:       PetscCall(PetscObjectQuery((PetscObject)dm, "DMPlex_dmgrad_fvm", &gradobj));
3321:     }
3322:     *gradDM = (DM)gradobj;
3323:   }
3324:   PetscFunctionReturn(PETSC_SUCCESS);
3325: }

3327: static PetscErrorCode DMPlexCoordinatesToReference_NewtonUpdate(PetscInt dimC, PetscInt dimR, PetscScalar *J, PetscScalar *invJ, PetscScalar *work, PetscReal *resNeg, PetscReal *guess)
3328: {
3329:   PetscInt l, m;

3331:   PetscFunctionBeginHot;
3332:   if (dimC == dimR && dimR <= 3) {
3333:     /* invert Jacobian, multiply */
3334:     PetscScalar det, idet;

3336:     switch (dimR) {
3337:     case 1:
3338:       invJ[0] = 1. / J[0];
3339:       break;
3340:     case 2:
3341:       det     = J[0] * J[3] - J[1] * J[2];
3342:       idet    = 1. / det;
3343:       invJ[0] = J[3] * idet;
3344:       invJ[1] = -J[1] * idet;
3345:       invJ[2] = -J[2] * idet;
3346:       invJ[3] = J[0] * idet;
3347:       break;
3348:     case 3: {
3349:       invJ[0] = J[4] * J[8] - J[5] * J[7];
3350:       invJ[1] = J[2] * J[7] - J[1] * J[8];
3351:       invJ[2] = J[1] * J[5] - J[2] * J[4];
3352:       det     = invJ[0] * J[0] + invJ[1] * J[3] + invJ[2] * J[6];
3353:       idet    = 1. / det;
3354:       invJ[0] *= idet;
3355:       invJ[1] *= idet;
3356:       invJ[2] *= idet;
3357:       invJ[3] = idet * (J[5] * J[6] - J[3] * J[8]);
3358:       invJ[4] = idet * (J[0] * J[8] - J[2] * J[6]);
3359:       invJ[5] = idet * (J[2] * J[3] - J[0] * J[5]);
3360:       invJ[6] = idet * (J[3] * J[7] - J[4] * J[6]);
3361:       invJ[7] = idet * (J[1] * J[6] - J[0] * J[7]);
3362:       invJ[8] = idet * (J[0] * J[4] - J[1] * J[3]);
3363:     } break;
3364:     }
3365:     for (l = 0; l < dimR; l++) {
3366:       for (m = 0; m < dimC; m++) guess[l] += PetscRealPart(invJ[l * dimC + m]) * resNeg[m];
3367:     }
3368:   } else {
3369: #if defined(PETSC_USE_COMPLEX)
3370:     char transpose = 'C';
3371: #else
3372:     char transpose = 'T';
3373: #endif
3374:     PetscBLASInt m        = (PetscBLASInt)dimR;
3375:     PetscBLASInt n        = (PetscBLASInt)dimC;
3376:     PetscBLASInt one      = 1;
3377:     PetscBLASInt worksize = (PetscBLASInt)(dimR * dimC), info;

3379:     for (l = 0; l < dimC; l++) invJ[l] = resNeg[l];

3381:     PetscCallBLAS("LAPACKgels", LAPACKgels_(&transpose, &m, &n, &one, J, &m, invJ, &n, work, &worksize, &info));
3382:     PetscCheck(info == 0, PETSC_COMM_SELF, PETSC_ERR_LIB, "Bad argument to GELS");

3384:     for (l = 0; l < dimR; l++) guess[l] += PetscRealPart(invJ[l]);
3385:   }
3386:   PetscFunctionReturn(PETSC_SUCCESS);
3387: }

3389: static PetscErrorCode DMPlexCoordinatesToReference_Tensor(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal realCoords[], PetscReal refCoords[], Vec coords, PetscInt dimC, PetscInt dimR)
3390: {
3391:   PetscInt     coordSize, i, j, k, l, m, maxIts = 7, numV = (1 << dimR);
3392:   PetscScalar *coordsScalar = NULL;
3393:   PetscReal   *cellData, *cellCoords, *cellCoeffs, *extJ, *resNeg;
3394:   PetscScalar *J, *invJ, *work;

3396:   PetscFunctionBegin;
3398:   PetscCall(DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar));
3399:   PetscCheck(coordSize >= dimC * numV, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Expecting at least %" PetscInt_FMT " coordinates, got %" PetscInt_FMT, dimC * (1 << dimR), coordSize);
3400:   PetscCall(DMGetWorkArray(dm, 2 * coordSize + dimR + dimC, MPIU_REAL, &cellData));
3401:   PetscCall(DMGetWorkArray(dm, 3 * dimR * dimC, MPIU_SCALAR, &J));
3402:   cellCoords = &cellData[0];
3403:   cellCoeffs = &cellData[coordSize];
3404:   extJ       = &cellData[2 * coordSize];
3405:   resNeg     = &cellData[2 * coordSize + dimR];
3406:   invJ       = &J[dimR * dimC];
3407:   work       = &J[2 * dimR * dimC];
3408:   if (dimR == 2) {
3409:     const PetscInt zToPlex[4] = {0, 1, 3, 2};

3411:     for (i = 0; i < 4; i++) {
3412:       PetscInt plexI = zToPlex[i];

3414:       for (j = 0; j < dimC; j++) cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
3415:     }
3416:   } else if (dimR == 3) {
3417:     const PetscInt zToPlex[8] = {0, 3, 1, 2, 4, 5, 7, 6};

3419:     for (i = 0; i < 8; i++) {
3420:       PetscInt plexI = zToPlex[i];

3422:       for (j = 0; j < dimC; j++) cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
3423:     }
3424:   } else {
3425:     for (i = 0; i < coordSize; i++) cellCoords[i] = PetscRealPart(coordsScalar[i]);
3426:   }
3427:   /* Perform the shuffling transform that converts values at the corners of [-1,1]^d to coefficients */
3428:   for (i = 0; i < dimR; i++) {
3429:     PetscReal *swap;

3431:     for (j = 0; j < (numV / 2); j++) {
3432:       for (k = 0; k < dimC; k++) {
3433:         cellCoeffs[dimC * j + k]                = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] + cellCoords[dimC * 2 * j + k]);
3434:         cellCoeffs[dimC * (j + (numV / 2)) + k] = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] - cellCoords[dimC * 2 * j + k]);
3435:       }
3436:     }

3438:     if (i < dimR - 1) {
3439:       swap       = cellCoeffs;
3440:       cellCoeffs = cellCoords;
3441:       cellCoords = swap;
3442:     }
3443:   }
3444:   PetscCall(PetscArrayzero(refCoords, numPoints * dimR));
3445:   for (j = 0; j < numPoints; j++) {
3446:     for (i = 0; i < maxIts; i++) {
3447:       PetscReal *guess = &refCoords[dimR * j];

3449:       /* compute -residual and Jacobian */
3450:       for (k = 0; k < dimC; k++) resNeg[k] = realCoords[dimC * j + k];
3451:       for (k = 0; k < dimC * dimR; k++) J[k] = 0.;
3452:       for (k = 0; k < numV; k++) {
3453:         PetscReal extCoord = 1.;
3454:         for (l = 0; l < dimR; l++) {
3455:           PetscReal coord = guess[l];
3456:           PetscInt  dep   = (k & (1 << l)) >> l;

3458:           extCoord *= dep * coord + !dep;
3459:           extJ[l] = dep;

3461:           for (m = 0; m < dimR; m++) {
3462:             PetscReal coord = guess[m];
3463:             PetscInt  dep   = ((k & (1 << m)) >> m) && (m != l);
3464:             PetscReal mult  = dep * coord + !dep;

3466:             extJ[l] *= mult;
3467:           }
3468:         }
3469:         for (l = 0; l < dimC; l++) {
3470:           PetscReal coeff = cellCoeffs[dimC * k + l];

3472:           resNeg[l] -= coeff * extCoord;
3473:           for (m = 0; m < dimR; m++) J[dimR * l + m] += coeff * extJ[m];
3474:         }
3475:       }
3476:       if (0 && PetscDefined(USE_DEBUG)) {
3477:         PetscReal maxAbs = 0.;

3479:         for (l = 0; l < dimC; l++) maxAbs = PetscMax(maxAbs, PetscAbsReal(resNeg[l]));
3480:         PetscCall(PetscInfo(dm, "cell %" PetscInt_FMT ", point %" PetscInt_FMT ", iter %" PetscInt_FMT ": res %g\n", cell, j, i, (double)maxAbs));
3481:       }

3483:       PetscCall(DMPlexCoordinatesToReference_NewtonUpdate(dimC, dimR, J, invJ, work, resNeg, guess));
3484:     }
3485:   }
3486:   PetscCall(DMRestoreWorkArray(dm, 3 * dimR * dimC, MPIU_SCALAR, &J));
3487:   PetscCall(DMRestoreWorkArray(dm, 2 * coordSize + dimR + dimC, MPIU_REAL, &cellData));
3488:   PetscCall(DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar));
3489:   PetscFunctionReturn(PETSC_SUCCESS);
3490: }

3492: static PetscErrorCode DMPlexReferenceToCoordinates_Tensor(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal refCoords[], PetscReal realCoords[], Vec coords, PetscInt dimC, PetscInt dimR)
3493: {
3494:   PetscInt     coordSize, i, j, k, l, numV = (1 << dimR);
3495:   PetscScalar *coordsScalar = NULL;
3496:   PetscReal   *cellData, *cellCoords, *cellCoeffs;

3498:   PetscFunctionBegin;
3500:   PetscCall(DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar));
3501:   PetscCheck(coordSize >= dimC * numV, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Expecting at least %" PetscInt_FMT " coordinates, got %" PetscInt_FMT, dimC * (1 << dimR), coordSize);
3502:   PetscCall(DMGetWorkArray(dm, 2 * coordSize, MPIU_REAL, &cellData));
3503:   cellCoords = &cellData[0];
3504:   cellCoeffs = &cellData[coordSize];
3505:   if (dimR == 2) {
3506:     const PetscInt zToPlex[4] = {0, 1, 3, 2};

3508:     for (i = 0; i < 4; i++) {
3509:       PetscInt plexI = zToPlex[i];

3511:       for (j = 0; j < dimC; j++) cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
3512:     }
3513:   } else if (dimR == 3) {
3514:     const PetscInt zToPlex[8] = {0, 3, 1, 2, 4, 5, 7, 6};

3516:     for (i = 0; i < 8; i++) {
3517:       PetscInt plexI = zToPlex[i];

3519:       for (j = 0; j < dimC; j++) cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
3520:     }
3521:   } else {
3522:     for (i = 0; i < coordSize; i++) cellCoords[i] = PetscRealPart(coordsScalar[i]);
3523:   }
3524:   /* Perform the shuffling transform that converts values at the corners of [-1,1]^d to coefficients */
3525:   for (i = 0; i < dimR; i++) {
3526:     PetscReal *swap;

3528:     for (j = 0; j < (numV / 2); j++) {
3529:       for (k = 0; k < dimC; k++) {
3530:         cellCoeffs[dimC * j + k]                = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] + cellCoords[dimC * 2 * j + k]);
3531:         cellCoeffs[dimC * (j + (numV / 2)) + k] = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] - cellCoords[dimC * 2 * j + k]);
3532:       }
3533:     }

3535:     if (i < dimR - 1) {
3536:       swap       = cellCoeffs;
3537:       cellCoeffs = cellCoords;
3538:       cellCoords = swap;
3539:     }
3540:   }
3541:   PetscCall(PetscArrayzero(realCoords, numPoints * dimC));
3542:   for (j = 0; j < numPoints; j++) {
3543:     const PetscReal *guess  = &refCoords[dimR * j];
3544:     PetscReal       *mapped = &realCoords[dimC * j];

3546:     for (k = 0; k < numV; k++) {
3547:       PetscReal extCoord = 1.;
3548:       for (l = 0; l < dimR; l++) {
3549:         PetscReal coord = guess[l];
3550:         PetscInt  dep   = (k & (1 << l)) >> l;

3552:         extCoord *= dep * coord + !dep;
3553:       }
3554:       for (l = 0; l < dimC; l++) {
3555:         PetscReal coeff = cellCoeffs[dimC * k + l];

3557:         mapped[l] += coeff * extCoord;
3558:       }
3559:     }
3560:   }
3561:   PetscCall(DMRestoreWorkArray(dm, 2 * coordSize, MPIU_REAL, &cellData));
3562:   PetscCall(DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar));
3563:   PetscFunctionReturn(PETSC_SUCCESS);
3564: }

3566: /* TODO: TOBY please fix this for Nc > 1 */
3567: static PetscErrorCode DMPlexCoordinatesToReference_FE(DM dm, PetscFE fe, PetscInt cell, PetscInt numPoints, const PetscReal realCoords[], PetscReal refCoords[], Vec coords, PetscInt Nc, PetscInt dimR)
3568: {
3569:   PetscInt     numComp, pdim, i, j, k, l, m, maxIter = 7, coordSize;
3570:   PetscScalar *nodes = NULL;
3571:   PetscReal   *invV, *modes;
3572:   PetscReal   *B, *D, *resNeg;
3573:   PetscScalar *J, *invJ, *work;

3575:   PetscFunctionBegin;
3576:   PetscCall(PetscFEGetDimension(fe, &pdim));
3577:   PetscCall(PetscFEGetNumComponents(fe, &numComp));
3578:   PetscCheck(numComp == Nc, PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "coordinate discretization must have as many components (%" PetscInt_FMT ") as embedding dimension (!= %" PetscInt_FMT ")", numComp, Nc);
3579:   PetscCall(DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &nodes));
3580:   /* convert nodes to values in the stable evaluation basis */
3581:   PetscCall(DMGetWorkArray(dm, pdim, MPIU_REAL, &modes));
3582:   invV = fe->invV;
3583:   for (i = 0; i < pdim; ++i) {
3584:     modes[i] = 0.;
3585:     for (j = 0; j < pdim; ++j) modes[i] += invV[i * pdim + j] * PetscRealPart(nodes[j]);
3586:   }
3587:   PetscCall(DMGetWorkArray(dm, pdim * Nc + pdim * Nc * dimR + Nc, MPIU_REAL, &B));
3588:   D      = &B[pdim * Nc];
3589:   resNeg = &D[pdim * Nc * dimR];
3590:   PetscCall(DMGetWorkArray(dm, 3 * Nc * dimR, MPIU_SCALAR, &J));
3591:   invJ = &J[Nc * dimR];
3592:   work = &invJ[Nc * dimR];
3593:   for (i = 0; i < numPoints * dimR; i++) refCoords[i] = 0.;
3594:   for (j = 0; j < numPoints; j++) {
3595:     for (i = 0; i < maxIter; i++) { /* we could batch this so that we're not making big B and D arrays all the time */
3596:       PetscReal *guess = &refCoords[j * dimR];
3597:       PetscCall(PetscSpaceEvaluate(fe->basisSpace, 1, guess, B, D, NULL));
3598:       for (k = 0; k < Nc; k++) resNeg[k] = realCoords[j * Nc + k];
3599:       for (k = 0; k < Nc * dimR; k++) J[k] = 0.;
3600:       for (k = 0; k < pdim; k++) {
3601:         for (l = 0; l < Nc; l++) {
3602:           resNeg[l] -= modes[k] * B[k * Nc + l];
3603:           for (m = 0; m < dimR; m++) J[l * dimR + m] += modes[k] * D[(k * Nc + l) * dimR + m];
3604:         }
3605:       }
3606:       if (0 && PetscDefined(USE_DEBUG)) {
3607:         PetscReal maxAbs = 0.;

3609:         for (l = 0; l < Nc; l++) maxAbs = PetscMax(maxAbs, PetscAbsReal(resNeg[l]));
3610:         PetscCall(PetscInfo(dm, "cell %" PetscInt_FMT ", point %" PetscInt_FMT ", iter %" PetscInt_FMT ": res %g\n", cell, j, i, (double)maxAbs));
3611:       }
3612:       PetscCall(DMPlexCoordinatesToReference_NewtonUpdate(Nc, dimR, J, invJ, work, resNeg, guess));
3613:     }
3614:   }
3615:   PetscCall(DMRestoreWorkArray(dm, 3 * Nc * dimR, MPIU_SCALAR, &J));
3616:   PetscCall(DMRestoreWorkArray(dm, pdim * Nc + pdim * Nc * dimR + Nc, MPIU_REAL, &B));
3617:   PetscCall(DMRestoreWorkArray(dm, pdim, MPIU_REAL, &modes));
3618:   PetscCall(DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &nodes));
3619:   PetscFunctionReturn(PETSC_SUCCESS);
3620: }

3622: /* TODO: TOBY please fix this for Nc > 1 */
3623: static PetscErrorCode DMPlexReferenceToCoordinates_FE(DM dm, PetscFE fe, PetscInt cell, PetscInt numPoints, const PetscReal refCoords[], PetscReal realCoords[], Vec coords, PetscInt Nc, PetscInt dimR)
3624: {
3625:   PetscInt     numComp, pdim, i, j, k, l, coordSize;
3626:   PetscScalar *nodes = NULL;
3627:   PetscReal   *invV, *modes;
3628:   PetscReal   *B;

3630:   PetscFunctionBegin;
3631:   PetscCall(PetscFEGetDimension(fe, &pdim));
3632:   PetscCall(PetscFEGetNumComponents(fe, &numComp));
3633:   PetscCheck(numComp == Nc, PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "coordinate discretization must have as many components (%" PetscInt_FMT ") as embedding dimension (!= %" PetscInt_FMT ")", numComp, Nc);
3634:   PetscCall(DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &nodes));
3635:   /* convert nodes to values in the stable evaluation basis */
3636:   PetscCall(DMGetWorkArray(dm, pdim, MPIU_REAL, &modes));
3637:   invV = fe->invV;
3638:   for (i = 0; i < pdim; ++i) {
3639:     modes[i] = 0.;
3640:     for (j = 0; j < pdim; ++j) modes[i] += invV[i * pdim + j] * PetscRealPart(nodes[j]);
3641:   }
3642:   PetscCall(DMGetWorkArray(dm, numPoints * pdim * Nc, MPIU_REAL, &B));
3643:   PetscCall(PetscSpaceEvaluate(fe->basisSpace, numPoints, refCoords, B, NULL, NULL));
3644:   for (i = 0; i < numPoints * Nc; i++) realCoords[i] = 0.;
3645:   for (j = 0; j < numPoints; j++) {
3646:     PetscReal *mapped = &realCoords[j * Nc];

3648:     for (k = 0; k < pdim; k++) {
3649:       for (l = 0; l < Nc; l++) mapped[l] += modes[k] * B[(j * pdim + k) * Nc + l];
3650:     }
3651:   }
3652:   PetscCall(DMRestoreWorkArray(dm, numPoints * pdim * Nc, MPIU_REAL, &B));
3653:   PetscCall(DMRestoreWorkArray(dm, pdim, MPIU_REAL, &modes));
3654:   PetscCall(DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &nodes));
3655:   PetscFunctionReturn(PETSC_SUCCESS);
3656: }

3658: /*@
3659:   DMPlexCoordinatesToReference - Pull coordinates back from the mesh to the reference element
3660:   using a single element map.

3662:   Not Collective

3664:   Input Parameters:
3665: + dm         - The mesh, with coordinate maps defined either by a `PetscDS` for the coordinate `DM` (see `DMGetCoordinateDM()`) or
3666:                implicitly by the coordinates of the corner vertices of the cell: as an affine map for simplicial elements, or
3667:                as a multilinear map for tensor-product elements
3668: . cell       - the cell whose map is used.
3669: . numPoints  - the number of points to locate
3670: - realCoords - (numPoints x coordinate dimension) array of coordinates (see `DMGetCoordinateDim()`)

3672:   Output Parameter:
3673: . refCoords - (`numPoints` x `dimension`) array of reference coordinates (see `DMGetDimension()`)

3675:   Level: intermediate

3677:   Notes:
3678:   This inversion will be accurate inside the reference element, but may be inaccurate for
3679:   mappings that do not extend uniquely outside the reference cell (e.g, most non-affine maps)

3681: .seealso: `DMPLEX`, `DMPlexReferenceToCoordinates()`
3682: @*/
3683: PetscErrorCode DMPlexCoordinatesToReference(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal realCoords[], PetscReal refCoords[])
3684: {
3685:   PetscInt dimC, dimR, depth, cStart, cEnd, i;
3686:   DM       coordDM = NULL;
3687:   Vec      coords;
3688:   PetscFE  fe = NULL;

3690:   PetscFunctionBegin;
3692:   PetscCall(DMGetDimension(dm, &dimR));
3693:   PetscCall(DMGetCoordinateDim(dm, &dimC));
3694:   if (dimR <= 0 || dimC <= 0 || numPoints <= 0) PetscFunctionReturn(PETSC_SUCCESS);
3695:   PetscCall(DMPlexGetDepth(dm, &depth));
3696:   PetscCall(DMGetCoordinatesLocal(dm, &coords));
3697:   PetscCall(DMGetCoordinateDM(dm, &coordDM));
3698:   if (coordDM) {
3699:     PetscInt coordFields;

3701:     PetscCall(DMGetNumFields(coordDM, &coordFields));
3702:     if (coordFields) {
3703:       PetscClassId id;
3704:       PetscObject  disc;

3706:       PetscCall(DMGetField(coordDM, 0, NULL, &disc));
3707:       PetscCall(PetscObjectGetClassId(disc, &id));
3708:       if (id == PETSCFE_CLASSID) fe = (PetscFE)disc;
3709:     }
3710:   }
3711:   PetscCall(DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd));
3712:   PetscCheck(cell >= cStart && cell < cEnd, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "point %" PetscInt_FMT " not in cell range [%" PetscInt_FMT ",%" PetscInt_FMT ")", cell, cStart, cEnd);
3713:   if (!fe) { /* implicit discretization: affine or multilinear */
3714:     PetscInt  coneSize;
3715:     PetscBool isSimplex, isTensor;

3717:     PetscCall(DMPlexGetConeSize(dm, cell, &coneSize));
3718:     isSimplex = (coneSize == (dimR + 1)) ? PETSC_TRUE : PETSC_FALSE;
3719:     isTensor  = (coneSize == ((depth == 1) ? (1 << dimR) : (2 * dimR))) ? PETSC_TRUE : PETSC_FALSE;
3720:     if (isSimplex) {
3721:       PetscReal detJ, *v0, *J, *invJ;

3723:       PetscCall(DMGetWorkArray(dm, dimC + 2 * dimC * dimC, MPIU_REAL, &v0));
3724:       J    = &v0[dimC];
3725:       invJ = &J[dimC * dimC];
3726:       PetscCall(DMPlexComputeCellGeometryAffineFEM(dm, cell, v0, J, invJ, &detJ));
3727:       for (i = 0; i < numPoints; i++) { /* Apply the inverse affine transformation for each point */
3728:         const PetscReal x0[3] = {-1., -1., -1.};

3730:         CoordinatesRealToRef(dimC, dimR, x0, v0, invJ, &realCoords[dimC * i], &refCoords[dimR * i]);
3731:       }
3732:       PetscCall(DMRestoreWorkArray(dm, dimC + 2 * dimC * dimC, MPIU_REAL, &v0));
3733:     } else if (isTensor) {
3734:       PetscCall(DMPlexCoordinatesToReference_Tensor(coordDM, cell, numPoints, realCoords, refCoords, coords, dimC, dimR));
3735:     } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Unrecognized cone size %" PetscInt_FMT, coneSize);
3736:   } else {
3737:     PetscCall(DMPlexCoordinatesToReference_FE(coordDM, fe, cell, numPoints, realCoords, refCoords, coords, dimC, dimR));
3738:   }
3739:   PetscFunctionReturn(PETSC_SUCCESS);
3740: }

3742: /*@
3743:   DMPlexReferenceToCoordinates - Map references coordinates to coordinates in the mesh for a single element map.

3745:   Not Collective

3747:   Input Parameters:
3748: + dm        - The mesh, with coordinate maps defined either by a PetscDS for the coordinate `DM` (see `DMGetCoordinateDM()`) or
3749:                implicitly by the coordinates of the corner vertices of the cell: as an affine map for simplicial elements, or
3750:                as a multilinear map for tensor-product elements
3751: . cell      - the cell whose map is used.
3752: . numPoints - the number of points to locate
3753: - refCoords - (numPoints x dimension) array of reference coordinates (see `DMGetDimension()`)

3755:   Output Parameter:
3756: . realCoords - (numPoints x coordinate dimension) array of coordinates (see `DMGetCoordinateDim()`)

3758:   Level: intermediate

3760: .seealso: `DMPLEX`, `DMPlexCoordinatesToReference()`
3761: @*/
3762: PetscErrorCode DMPlexReferenceToCoordinates(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal refCoords[], PetscReal realCoords[])
3763: {
3764:   PetscInt dimC, dimR, depth, cStart, cEnd, i;
3765:   DM       coordDM = NULL;
3766:   Vec      coords;
3767:   PetscFE  fe = NULL;

3769:   PetscFunctionBegin;
3771:   PetscCall(DMGetDimension(dm, &dimR));
3772:   PetscCall(DMGetCoordinateDim(dm, &dimC));
3773:   if (dimR <= 0 || dimC <= 0 || numPoints <= 0) PetscFunctionReturn(PETSC_SUCCESS);
3774:   PetscCall(DMPlexGetDepth(dm, &depth));
3775:   PetscCall(DMGetCoordinatesLocal(dm, &coords));
3776:   PetscCall(DMGetCoordinateDM(dm, &coordDM));
3777:   if (coordDM) {
3778:     PetscInt coordFields;

3780:     PetscCall(DMGetNumFields(coordDM, &coordFields));
3781:     if (coordFields) {
3782:       PetscClassId id;
3783:       PetscObject  disc;

3785:       PetscCall(DMGetField(coordDM, 0, NULL, &disc));
3786:       PetscCall(PetscObjectGetClassId(disc, &id));
3787:       if (id == PETSCFE_CLASSID) fe = (PetscFE)disc;
3788:     }
3789:   }
3790:   PetscCall(DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd));
3791:   PetscCheck(cell >= cStart && cell < cEnd, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "point %" PetscInt_FMT " not in cell range [%" PetscInt_FMT ",%" PetscInt_FMT ")", cell, cStart, cEnd);
3792:   if (!fe) { /* implicit discretization: affine or multilinear */
3793:     PetscInt  coneSize;
3794:     PetscBool isSimplex, isTensor;

3796:     PetscCall(DMPlexGetConeSize(dm, cell, &coneSize));
3797:     isSimplex = (coneSize == (dimR + 1)) ? PETSC_TRUE : PETSC_FALSE;
3798:     isTensor  = (coneSize == ((depth == 1) ? (1 << dimR) : (2 * dimR))) ? PETSC_TRUE : PETSC_FALSE;
3799:     if (isSimplex) {
3800:       PetscReal detJ, *v0, *J;

3802:       PetscCall(DMGetWorkArray(dm, dimC + 2 * dimC * dimC, MPIU_REAL, &v0));
3803:       J = &v0[dimC];
3804:       PetscCall(DMPlexComputeCellGeometryAffineFEM(dm, cell, v0, J, NULL, &detJ));
3805:       for (i = 0; i < numPoints; i++) { /* Apply the affine transformation for each point */
3806:         const PetscReal xi0[3] = {-1., -1., -1.};

3808:         CoordinatesRefToReal(dimC, dimR, xi0, v0, J, &refCoords[dimR * i], &realCoords[dimC * i]);
3809:       }
3810:       PetscCall(DMRestoreWorkArray(dm, dimC + 2 * dimC * dimC, MPIU_REAL, &v0));
3811:     } else if (isTensor) {
3812:       PetscCall(DMPlexReferenceToCoordinates_Tensor(coordDM, cell, numPoints, refCoords, realCoords, coords, dimC, dimR));
3813:     } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Unrecognized cone size %" PetscInt_FMT, coneSize);
3814:   } else {
3815:     PetscCall(DMPlexReferenceToCoordinates_FE(coordDM, fe, cell, numPoints, refCoords, realCoords, coords, dimC, dimR));
3816:   }
3817:   PetscFunctionReturn(PETSC_SUCCESS);
3818: }

3820: void coordMap_identity(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
3821: {
3822:   const PetscInt Nc = uOff[1] - uOff[0];
3823:   PetscInt       c;

3825:   for (c = 0; c < Nc; ++c) f0[c] = u[c];
3826: }

3828: /* Shear applies the transformation, assuming we fix z,
3829:   / 1  0  m_0 \
3830:   | 0  1  m_1 |
3831:   \ 0  0   1  /
3832: */
3833: void coordMap_shear(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar coords[])
3834: {
3835:   const PetscInt Nc = uOff[1] - uOff[0];
3836:   const PetscInt ax = (PetscInt)PetscRealPart(constants[0]);
3837:   PetscInt       c;

3839:   for (c = 0; c < Nc; ++c) coords[c] = u[c] + constants[c + 1] * u[ax];
3840: }

3842: /* Flare applies the transformation, assuming we fix x_f,

3844:    x_i = x_i * alpha_i x_f
3845: */
3846: void coordMap_flare(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar coords[])
3847: {
3848:   const PetscInt Nc = uOff[1] - uOff[0];
3849:   const PetscInt cf = (PetscInt)PetscRealPart(constants[0]);
3850:   PetscInt       c;

3852:   for (c = 0; c < Nc; ++c) coords[c] = u[c] * (c == cf ? 1.0 : constants[c + 1] * u[cf]);
3853: }

3855: /*
3856:   We would like to map the unit square to a quarter of the annulus between circles of radius 1 and 2. We start by mapping the straight sections, which
3857:   will correspond to the top and bottom of our square. So

3859:     (0,0)--(1,0)  ==>  (1,0)--(2,0)      Just a shift of (1,0)
3860:     (0,1)--(1,1)  ==>  (0,1)--(0,2)      Switch x and y

3862:   So it looks like we want to map each layer in y to a ray, so x is the radius and y is the angle:

3864:     (x, y)  ==>  (x+1, \pi/2 y)                           in (r', \theta') space
3865:             ==>  ((x+1) cos(\pi/2 y), (x+1) sin(\pi/2 y)) in (x', y') space
3866: */
3867: void coordMap_annulus(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar xp[])
3868: {
3869:   const PetscReal ri = PetscRealPart(constants[0]);
3870:   const PetscReal ro = PetscRealPart(constants[1]);

3872:   xp[0] = (x[0] * (ro - ri) + ri) * PetscCosReal(0.5 * PETSC_PI * x[1]);
3873:   xp[1] = (x[0] * (ro - ri) + ri) * PetscSinReal(0.5 * PETSC_PI * x[1]);
3874: }

3876: /*
3877:   We would like to map the unit cube to a hemisphere of the spherical shell between balls of radius 1 and 2. We want to map the bottom surface onto the
3878:   lower hemisphere and the upper surface onto the top, letting z be the radius.

3880:     (x, y)  ==>  ((z+3)/2, \pi/2 (|x| or |y|), arctan y/x)                                                  in (r', \theta', \phi') space
3881:             ==>  ((z+3)/2 \cos(\theta') cos(\phi'), (z+3)/2 \cos(\theta') sin(\phi'), (z+3)/2 sin(\theta')) in (x', y', z') space
3882: */
3883: void coordMap_shell(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar xp[])
3884: {
3885:   const PetscReal pi4    = PETSC_PI / 4.0;
3886:   const PetscReal ri     = PetscRealPart(constants[0]);
3887:   const PetscReal ro     = PetscRealPart(constants[1]);
3888:   const PetscReal rp     = (x[2] + 1) * 0.5 * (ro - ri) + ri;
3889:   const PetscReal phip   = PetscAtan2Real(x[1], x[0]);
3890:   const PetscReal thetap = 0.5 * PETSC_PI * (1.0 - ((((phip <= pi4) && (phip >= -pi4)) || ((phip >= 3.0 * pi4) || (phip <= -3.0 * pi4))) ? PetscAbsReal(x[0]) : PetscAbsReal(x[1])));

3892:   xp[0] = rp * PetscCosReal(thetap) * PetscCosReal(phip);
3893:   xp[1] = rp * PetscCosReal(thetap) * PetscSinReal(phip);
3894:   xp[2] = rp * PetscSinReal(thetap);
3895: }

3897: /*@C
3898:   DMPlexRemapGeometry - This function maps the original `DM` coordinates to new coordinates.

3900:   Not Collective

3902:   Input Parameters:
3903: + dm   - The `DM`
3904: . time - The time
3905: - func - The function transforming current coordinates to new coordinates

3907:   Calling sequence of `func`:
3908: + dim          - The spatial dimension
3909: . Nf           - The number of input fields (here 1)
3910: . NfAux        - The number of input auxiliary fields
3911: . uOff         - The offset of the coordinates in u[] (here 0)
3912: . uOff_x       - The offset of the coordinates in u_x[] (here 0)
3913: . u            - The coordinate values at this point in space
3914: . u_t          - The coordinate time derivative at this point in space (here `NULL`)
3915: . u_x          - The coordinate derivatives at this point in space
3916: . aOff         - The offset of each auxiliary field in u[]
3917: . aOff_x       - The offset of each auxiliary field in u_x[]
3918: . a            - The auxiliary field values at this point in space
3919: . a_t          - The auxiliary field time derivative at this point in space (or `NULL`)
3920: . a_x          - The auxiliary field derivatives at this point in space
3921: . t            - The current time
3922: . x            - The coordinates of this point (here not used)
3923: . numConstants - The number of constants
3924: . constants    - The value of each constant
3925: - f            - The new coordinates at this point in space

3927:   Level: intermediate

3929: .seealso: `DMPLEX`, `DMGetCoordinates()`, `DMGetCoordinatesLocal()`, `DMGetCoordinateDM()`, `DMProjectFieldLocal()`, `DMProjectFieldLabelLocal()`
3930: @*/
3931: PetscErrorCode DMPlexRemapGeometry(DM dm, PetscReal time, void (*func)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f[]))
3932: {
3933:   DM           cdm;
3934:   PetscDS      cds;
3935:   DMField      cf;
3936:   PetscObject  obj;
3937:   PetscClassId id;
3938:   Vec          lCoords, tmpCoords;

3940:   PetscFunctionBegin;
3941:   PetscCall(DMGetCoordinateDM(dm, &cdm));
3942:   PetscCall(DMGetCoordinatesLocal(dm, &lCoords));
3943:   PetscCall(DMGetDS(cdm, &cds));
3944:   PetscCall(PetscDSGetDiscretization(cds, 0, &obj));
3945:   PetscCall(PetscObjectGetClassId(obj, &id));
3946:   if (id != PETSCFE_CLASSID) {
3947:     PetscSection       cSection;
3948:     const PetscScalar *constants;
3949:     PetscScalar       *coords, f[16];
3950:     PetscInt           dim, cdim, Nc, vStart, vEnd;

3952:     PetscCall(DMGetDimension(dm, &dim));
3953:     PetscCall(DMGetCoordinateDim(dm, &cdim));
3954:     PetscCheck(cdim <= 16, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Affine version of DMPlexRemapGeometry is currently limited to dimensions <= 16, not %" PetscInt_FMT, cdim);
3955:     PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
3956:     PetscCall(DMGetCoordinateSection(dm, &cSection));
3957:     PetscCall(PetscDSGetConstants(cds, &Nc, &constants));
3958:     PetscCall(VecGetArrayWrite(lCoords, &coords));
3959:     for (PetscInt v = vStart; v < vEnd; ++v) {
3960:       PetscInt uOff[2] = {0, cdim};
3961:       PetscInt off, c;

3963:       PetscCall(PetscSectionGetOffset(cSection, v, &off));
3964:       (*func)(dim, 1, 0, uOff, NULL, &coords[off], NULL, NULL, NULL, NULL, NULL, NULL, NULL, 0.0, NULL, Nc, constants, f);
3965:       for (c = 0; c < cdim; ++c) coords[off + c] = f[c];
3966:     }
3967:     PetscCall(VecRestoreArrayWrite(lCoords, &coords));
3968:   } else {
3969:     PetscCall(DMGetLocalVector(cdm, &tmpCoords));
3970:     PetscCall(VecCopy(lCoords, tmpCoords));
3971:     /* We have to do the coordinate field manually right now since the coordinate DM will not have its own */
3972:     PetscCall(DMGetCoordinateField(dm, &cf));
3973:     cdm->coordinates[0].field = cf;
3974:     PetscCall(DMProjectFieldLocal(cdm, time, tmpCoords, &func, INSERT_VALUES, lCoords));
3975:     cdm->coordinates[0].field = NULL;
3976:     PetscCall(DMRestoreLocalVector(cdm, &tmpCoords));
3977:     PetscCall(DMSetCoordinatesLocal(dm, lCoords));
3978:   }
3979:   PetscFunctionReturn(PETSC_SUCCESS);
3980: }

3982: /*@
3983:   DMPlexShearGeometry - This shears the domain, meaning adds a multiple of the shear coordinate to all other coordinates.

3985:   Not Collective

3987:   Input Parameters:
3988: + dm          - The `DMPLEX`
3989: . direction   - The shear coordinate direction, e.g. `DM_X` is the x-axis
3990: - multipliers - The multiplier m for each direction which is not the shear direction

3992:   Level: intermediate

3994: .seealso: `DMPLEX`, `DMPlexRemapGeometry()`, `DMDirection`, `DM_X`, `DM_Y`, `DM_Z`
3995: @*/
3996: PetscErrorCode DMPlexShearGeometry(DM dm, DMDirection direction, PetscReal multipliers[])
3997: {
3998:   DM             cdm;
3999:   PetscDS        cds;
4000:   PetscScalar   *moduli;
4001:   const PetscInt dir = (PetscInt)direction;
4002:   PetscInt       dE, d, e;

4004:   PetscFunctionBegin;
4005:   PetscCall(DMGetCoordinateDM(dm, &cdm));
4006:   PetscCall(DMGetCoordinateDim(dm, &dE));
4007:   PetscCall(PetscMalloc1(dE + 1, &moduli));
4008:   moduli[0] = dir;
4009:   for (d = 0, e = 0; d < dE; ++d) moduli[d + 1] = d == dir ? 0.0 : (multipliers ? multipliers[e++] : 1.0);
4010:   PetscCall(DMGetDS(cdm, &cds));
4011:   PetscCall(PetscDSSetConstants(cds, dE + 1, moduli));
4012:   PetscCall(DMPlexRemapGeometry(dm, 0.0, coordMap_shear));
4013:   PetscCall(PetscFree(moduli));
4014:   PetscFunctionReturn(PETSC_SUCCESS);
4015: }