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_Linear_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_Quad_2D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
523: {
524:   DM           cdm;
525:   PetscInt     degree, dimR, dimC;
526:   PetscFE      fe;
527:   PetscClassId id;
528:   PetscSpace   sp;
529:   PetscReal    pointR[3], ref[3], error;
530:   Vec          coords;
531:   PetscBool    found = PETSC_FALSE;

533:   PetscFunctionBegin;
534:   PetscCall(DMGetDimension(dm, &dimR));
535:   PetscCall(DMGetCoordinateDM(dm, &cdm));
536:   PetscCall(DMGetDimension(cdm, &dimC));
537:   PetscCall(DMGetField(cdm, 0, NULL, (PetscObject *)&fe));
538:   PetscCall(PetscObjectGetClassId((PetscObject)fe, &id));
539:   if (id != PETSCFE_CLASSID) degree = 1;
540:   else {
541:     PetscCall(PetscFEGetBasisSpace(fe, &sp));
542:     PetscCall(PetscSpaceGetDegree(sp, &degree, NULL));
543:   }
544:   if (degree == 1) {
545:     /* Use simple location method for linear elements*/
546:     PetscCall(DMPlexLocatePoint_Quad_2D_Linear_Internal(dm, point, c, cell));
547:     PetscFunctionReturn(PETSC_SUCCESS);
548:   }
549:   /* Otherwise, we have to solve for the real to reference coordinates */
550:   PetscCall(DMGetCoordinatesLocal(dm, &coords));
551:   error = PETSC_SQRT_MACHINE_EPSILON;
552:   for (PetscInt d = 0; d < dimC; d++) pointR[d] = PetscRealPart(point[d]);
553:   PetscCall(DMPlexCoordinatesToReference_FE(cdm, fe, c, 1, pointR, ref, coords, dimC, dimR, 10, &error));
554:   if (error < PETSC_SQRT_MACHINE_EPSILON) found = PETSC_TRUE;
555:   if ((ref[0] > 1.0 + PETSC_SMALL) || (ref[0] < -1.0 - PETSC_SMALL) || (ref[1] > 1.0 + PETSC_SMALL) || (ref[1] < -1.0 - PETSC_SMALL)) found = PETSC_FALSE;
556:   if (PetscDefined(USE_DEBUG) && found) {
557:     PetscReal real[3], inverseError = 0, normPoint = DMPlex_NormD_Internal(dimC, pointR);

559:     normPoint = normPoint > PETSC_SMALL ? normPoint : 1.0;
560:     PetscCall(DMPlexReferenceToCoordinates_FE(cdm, fe, c, 1, ref, real, coords, dimC, dimR));
561:     inverseError = DMPlex_DistRealD_Internal(dimC, real, pointR);
562:     if (inverseError > PETSC_SQRT_MACHINE_EPSILON * normPoint) found = PETSC_FALSE;
563:     if (!found) PetscCall(PetscInfo(dm, "Point (%g, %g, %g) != Mapped Ref Coords (%g, %g, %g) with error %g\n", (double)pointR[0], (double)pointR[1], (double)pointR[2], (double)real[0], (double)real[1], (double)real[2], (double)inverseError));
564:   }
565:   if (found) *cell = c;
566:   else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
567:   PetscFunctionReturn(PETSC_SUCCESS);
568: }

570: static PetscErrorCode DMPlexLocatePoint_Simplex_3D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
571: {
572:   const PetscInt  embedDim = 3;
573:   const PetscReal eps      = PETSC_SQRT_MACHINE_EPSILON;
574:   PetscReal       v0[3], J[9], invJ[9], detJ;
575:   PetscReal       x = PetscRealPart(point[0]);
576:   PetscReal       y = PetscRealPart(point[1]);
577:   PetscReal       z = PetscRealPart(point[2]);
578:   PetscReal       xi, eta, zeta;

580:   PetscFunctionBegin;
581:   PetscCall(DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ));
582:   xi   = invJ[0 * embedDim + 0] * (x - v0[0]) + invJ[0 * embedDim + 1] * (y - v0[1]) + invJ[0 * embedDim + 2] * (z - v0[2]);
583:   eta  = invJ[1 * embedDim + 0] * (x - v0[0]) + invJ[1 * embedDim + 1] * (y - v0[1]) + invJ[1 * embedDim + 2] * (z - v0[2]);
584:   zeta = invJ[2 * embedDim + 0] * (x - v0[0]) + invJ[2 * embedDim + 1] * (y - v0[1]) + invJ[2 * embedDim + 2] * (z - v0[2]);

586:   if ((xi >= -eps) && (eta >= -eps) && (zeta >= -eps) && (xi + eta + zeta <= 2.0 + eps)) *cell = c;
587:   else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
588:   PetscFunctionReturn(PETSC_SUCCESS);
589: }

591: static PetscErrorCode DMPlexLocatePoint_Hex_3D_Linear_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
592: {
593:   const PetscScalar *array;
594:   PetscScalar       *coords    = NULL;
595:   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};
596:   PetscBool          found     = PETSC_TRUE;
597:   PetscInt           numCoords, f;
598:   PetscBool          isDG;

600:   PetscFunctionBegin;
601:   PetscCall(DMPlexGetCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
602:   PetscCheck(numCoords == 24, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Quadrilateral should have 8 coordinates, not %" PetscInt_FMT, numCoords);
603:   for (f = 0; f < 6; ++f) {
604:     /* Check the point is under plane */
605:     /*   Get face normal */
606:     PetscReal v_i[3];
607:     PetscReal v_j[3];
608:     PetscReal normal[3];
609:     PetscReal pp[3];
610:     PetscReal dot;

612:     v_i[0]    = PetscRealPart(coords[faces[f * 4 + 3] * 3 + 0] - coords[faces[f * 4 + 0] * 3 + 0]);
613:     v_i[1]    = PetscRealPart(coords[faces[f * 4 + 3] * 3 + 1] - coords[faces[f * 4 + 0] * 3 + 1]);
614:     v_i[2]    = PetscRealPart(coords[faces[f * 4 + 3] * 3 + 2] - coords[faces[f * 4 + 0] * 3 + 2]);
615:     v_j[0]    = PetscRealPart(coords[faces[f * 4 + 1] * 3 + 0] - coords[faces[f * 4 + 0] * 3 + 0]);
616:     v_j[1]    = PetscRealPart(coords[faces[f * 4 + 1] * 3 + 1] - coords[faces[f * 4 + 0] * 3 + 1]);
617:     v_j[2]    = PetscRealPart(coords[faces[f * 4 + 1] * 3 + 2] - coords[faces[f * 4 + 0] * 3 + 2]);
618:     normal[0] = v_i[1] * v_j[2] - v_i[2] * v_j[1];
619:     normal[1] = v_i[2] * v_j[0] - v_i[0] * v_j[2];
620:     normal[2] = v_i[0] * v_j[1] - v_i[1] * v_j[0];
621:     pp[0]     = PetscRealPart(coords[faces[f * 4 + 0] * 3 + 0] - point[0]);
622:     pp[1]     = PetscRealPart(coords[faces[f * 4 + 0] * 3 + 1] - point[1]);
623:     pp[2]     = PetscRealPart(coords[faces[f * 4 + 0] * 3 + 2] - point[2]);
624:     dot       = normal[0] * pp[0] + normal[1] * pp[1] + normal[2] * pp[2];

626:     /* Check that projected point is in face (2D location problem) */
627:     if (dot < 0.0) {
628:       found = PETSC_FALSE;
629:       break;
630:     }
631:   }
632:   if (found) *cell = c;
633:   else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
634:   PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
635:   PetscFunctionReturn(PETSC_SUCCESS);
636: }

638: static PetscErrorCode DMPlexLocatePoint_Hex_3D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
639: {
640:   DM           cdm;
641:   PetscInt     degree, dimR, dimC;
642:   PetscFE      fe;
643:   PetscClassId id;
644:   PetscSpace   sp;
645:   PetscReal    pointR[3], ref[3], error;
646:   Vec          coords;
647:   PetscBool    found = PETSC_FALSE;

649:   PetscFunctionBegin;
650:   PetscCall(DMGetDimension(dm, &dimR));
651:   PetscCall(DMGetCoordinateDM(dm, &cdm));
652:   PetscCall(DMGetDimension(cdm, &dimC));
653:   PetscCall(DMGetField(cdm, 0, NULL, (PetscObject *)&fe));
654:   PetscCall(PetscObjectGetClassId((PetscObject)fe, &id));
655:   if (id != PETSCFE_CLASSID) degree = 1;
656:   else {
657:     PetscCall(PetscFEGetBasisSpace(fe, &sp));
658:     PetscCall(PetscSpaceGetDegree(sp, &degree, NULL));
659:   }
660:   if (degree == 1) {
661:     /* Use simple location method for linear elements*/
662:     PetscCall(DMPlexLocatePoint_Hex_3D_Linear_Internal(dm, point, c, cell));
663:     PetscFunctionReturn(PETSC_SUCCESS);
664:   }
665:   /* Otherwise, we have to solve for the real to reference coordinates */
666:   PetscCall(DMGetCoordinatesLocal(dm, &coords));
667:   error = PETSC_SQRT_MACHINE_EPSILON;
668:   for (PetscInt d = 0; d < dimC; d++) pointR[d] = PetscRealPart(point[d]);
669:   PetscCall(DMPlexCoordinatesToReference_FE(cdm, fe, c, 1, pointR, ref, coords, dimC, dimR, 10, &error));
670:   if (error < PETSC_SQRT_MACHINE_EPSILON) found = PETSC_TRUE;
671:   if ((ref[0] > 1.0 + PETSC_SMALL) || (ref[0] < -1.0 - PETSC_SMALL) || (ref[1] > 1.0 + PETSC_SMALL) || (ref[1] < -1.0 - PETSC_SMALL) || (ref[2] > 1.0 + PETSC_SMALL) || (ref[2] < -1.0 - PETSC_SMALL)) found = PETSC_FALSE;
672:   if (PetscDefined(USE_DEBUG) && found) {
673:     PetscReal real[3], inverseError = 0, normPoint = DMPlex_NormD_Internal(dimC, pointR);

675:     normPoint = normPoint > PETSC_SMALL ? normPoint : 1.0;
676:     PetscCall(DMPlexReferenceToCoordinates_FE(cdm, fe, c, 1, ref, real, coords, dimC, dimR));
677:     inverseError = DMPlex_DistRealD_Internal(dimC, real, pointR);
678:     if (inverseError > PETSC_SQRT_MACHINE_EPSILON * normPoint) found = PETSC_FALSE;
679:     if (!found) PetscCall(PetscInfo(dm, "Point (%g, %g, %g) != Mapped Ref Coords (%g, %g, %g) with error %g\n", (double)pointR[0], (double)pointR[1], (double)pointR[2], (double)real[0], (double)real[1], (double)real[2], (double)inverseError));
680:   }
681:   if (found) *cell = c;
682:   else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
683:   PetscFunctionReturn(PETSC_SUCCESS);
684: }

686: static PetscErrorCode PetscGridHashInitialize_Internal(PetscGridHash box, PetscInt dim, const PetscScalar point[])
687: {
688:   PetscInt d;

690:   PetscFunctionBegin;
691:   box->dim = dim;
692:   for (d = 0; d < dim; ++d) box->lower[d] = box->upper[d] = point ? PetscRealPart(point[d]) : 0.;
693:   PetscFunctionReturn(PETSC_SUCCESS);
694: }

696: PetscErrorCode PetscGridHashCreate(MPI_Comm comm, PetscInt dim, const PetscScalar point[], PetscGridHash *box)
697: {
698:   PetscFunctionBegin;
699:   PetscCall(PetscCalloc1(1, box));
700:   PetscCall(PetscGridHashInitialize_Internal(*box, dim, point));
701:   PetscFunctionReturn(PETSC_SUCCESS);
702: }

704: PetscErrorCode PetscGridHashEnlarge(PetscGridHash box, const PetscScalar point[])
705: {
706:   PetscInt d;

708:   PetscFunctionBegin;
709:   for (d = 0; d < box->dim; ++d) {
710:     box->lower[d] = PetscMin(box->lower[d], PetscRealPart(point[d]));
711:     box->upper[d] = PetscMax(box->upper[d], PetscRealPart(point[d]));
712:   }
713:   PetscFunctionReturn(PETSC_SUCCESS);
714: }

716: static PetscErrorCode DMPlexCreateGridHash(DM dm, PetscGridHash *box)
717: {
718:   Vec                coordinates;
719:   const PetscScalar *a;
720:   PetscInt           cdim, cStart, cEnd;

722:   PetscFunctionBegin;
723:   PetscCall(DMGetCoordinateDim(dm, &cdim));
724:   PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
725:   PetscCall(DMGetCoordinatesLocal(dm, &coordinates));

727:   PetscCall(VecGetArrayRead(coordinates, &a));
728:   PetscCall(PetscGridHashCreate(PetscObjectComm((PetscObject)dm), cdim, a, box));
729:   PetscCall(VecRestoreArrayRead(coordinates, &a));
730:   for (PetscInt c = cStart; c < cEnd; ++c) {
731:     const PetscScalar *array;
732:     PetscScalar       *coords = NULL;
733:     PetscInt           numCoords;
734:     PetscBool          isDG;

736:     PetscCall(DMPlexGetCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
737:     for (PetscInt i = 0; i < numCoords / cdim; ++i) PetscCall(PetscGridHashEnlarge(*box, &coords[i * cdim]));
738:     PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
739:   }
740:   PetscFunctionReturn(PETSC_SUCCESS);
741: }

743: /*@C
744:   PetscGridHashSetGrid - Divide the grid into boxes

746:   Not Collective

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

753:   Level: developer

755: .seealso: `DMPLEX`, `PetscGridHashCreate()`
756: @*/
757: PetscErrorCode PetscGridHashSetGrid(PetscGridHash box, const PetscInt n[], const PetscReal h[])
758: {
759:   PetscInt d;

761:   PetscFunctionBegin;
762:   PetscAssertPointer(n, 2);
763:   if (h) PetscAssertPointer(h, 3);
764:   for (d = 0; d < box->dim; ++d) {
765:     box->extent[d] = box->upper[d] - box->lower[d];
766:     if (n[d] == PETSC_DETERMINE) {
767:       PetscCheck(h, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Missing h");
768:       box->h[d] = h[d];
769:       box->n[d] = PetscCeilReal(box->extent[d] / h[d]);
770:     } else {
771:       box->n[d] = n[d];
772:       box->h[d] = box->extent[d] / n[d];
773:     }
774:   }
775:   PetscFunctionReturn(PETSC_SUCCESS);
776: }

778: /*@C
779:   PetscGridHashGetEnclosingBox - Find the grid boxes containing each input point

781:   Not Collective

783:   Input Parameters:
784: + box       - The grid hash object
785: . numPoints - The number of input points
786: - points    - The input point coordinates

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

792:   Level: developer

794:   Note:
795:   This only guarantees that a box contains a point, not that a cell does.

797: .seealso: `DMPLEX`, `PetscGridHashCreate()`
798: @*/
799: PetscErrorCode PetscGridHashGetEnclosingBox(PetscGridHash box, PetscInt numPoints, const PetscScalar points[], PetscInt dboxes[], PetscInt boxes[])
800: {
801:   const PetscReal *lower = box->lower;
802:   const PetscReal *upper = box->upper;
803:   const PetscReal *h     = box->h;
804:   const PetscInt  *n     = box->n;
805:   const PetscInt   dim   = box->dim;
806:   PetscInt         d, p;

808:   PetscFunctionBegin;
809:   for (p = 0; p < numPoints; ++p) {
810:     for (d = 0; d < dim; ++d) {
811:       PetscInt dbox = PetscFloorReal((PetscRealPart(points[p * dim + d]) - lower[d]) / h[d]);

813:       if (dbox == n[d] && PetscAbsReal(PetscRealPart(points[p * dim + d]) - upper[d]) < 1.0e-9) dbox = n[d] - 1;
814:       if (dbox == -1 && PetscAbsReal(PetscRealPart(points[p * dim + d]) - lower[d]) < 1.0e-9) dbox = 0;
815:       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]);
816:       dboxes[p * dim + d] = dbox;
817:     }
818:     if (boxes)
819:       for (d = dim - 2, boxes[p] = dboxes[p * dim + dim - 1]; d >= 0; --d) boxes[p] = boxes[p] * n[d] + dboxes[p * dim + d];
820:   }
821:   PetscFunctionReturn(PETSC_SUCCESS);
822: }

824: /*
825:   PetscGridHashGetEnclosingBoxQuery - Find the grid boxes containing each input point

827:   Not Collective

829:   Input Parameters:
830: + box         - The grid hash object
831: . cellSection - The PetscSection mapping cells to boxes
832: . numPoints   - The number of input points
833: - points      - The input point coordinates

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

840:   Level: developer

842:   Note:
843:   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.

845: .seealso: `DMPLEX`, `PetscGridHashGetEnclosingBox()`
846: */
847: static PetscErrorCode PetscGridHashGetEnclosingBoxQuery(PetscGridHash box, PetscSection cellSection, PetscInt numPoints, const PetscScalar points[], PetscInt dboxes[], PetscInt boxes[], PetscBool *found)
848: {
849:   const PetscReal *lower = box->lower;
850:   const PetscReal *upper = box->upper;
851:   const PetscReal *h     = box->h;
852:   const PetscInt  *n     = box->n;
853:   const PetscInt   dim   = box->dim;
854:   PetscInt         bStart, bEnd, d, p;

856:   PetscFunctionBegin;
858:   *found = PETSC_FALSE;
859:   PetscCall(PetscSectionGetChart(box->cellSection, &bStart, &bEnd));
860:   for (p = 0; p < numPoints; ++p) {
861:     for (d = 0; d < dim; ++d) {
862:       PetscInt dbox = PetscFloorReal((PetscRealPart(points[p * dim + d]) - lower[d]) / h[d]);

864:       if (dbox == n[d] && PetscAbsReal(PetscRealPart(points[p * dim + d]) - upper[d]) < 1.0e-9) dbox = n[d] - 1;
865:       if (dbox < 0 || dbox >= n[d]) PetscFunctionReturn(PETSC_SUCCESS);
866:       dboxes[p * dim + d] = dbox;
867:     }
868:     if (boxes)
869:       for (d = dim - 2, boxes[p] = dboxes[p * dim + dim - 1]; d >= 0; --d) boxes[p] = boxes[p] * n[d] + dboxes[p * dim + d];
870:     // It is possible for a box to overlap no grid cells
871:     if (boxes[p] < bStart || boxes[p] >= bEnd) PetscFunctionReturn(PETSC_SUCCESS);
872:   }
873:   *found = PETSC_TRUE;
874:   PetscFunctionReturn(PETSC_SUCCESS);
875: }

877: PetscErrorCode PetscGridHashDestroy(PetscGridHash *box)
878: {
879:   PetscFunctionBegin;
880:   if (*box) {
881:     PetscCall(PetscSectionDestroy(&(*box)->cellSection));
882:     PetscCall(ISDestroy(&(*box)->cells));
883:     PetscCall(DMLabelDestroy(&(*box)->cellsSparse));
884:   }
885:   PetscCall(PetscFree(*box));
886:   PetscFunctionReturn(PETSC_SUCCESS);
887: }

889: PetscErrorCode DMPlexLocatePoint_Internal(DM dm, PetscInt dim, const PetscScalar point[], PetscInt cellStart, PetscInt *cell)
890: {
891:   DMPolytopeType ct;

893:   PetscFunctionBegin;
894:   PetscCall(DMPlexGetCellType(dm, cellStart, &ct));
895:   switch (ct) {
896:   case DM_POLYTOPE_SEGMENT:
897:     PetscCall(DMPlexLocatePoint_Simplex_1D_Internal(dm, point, cellStart, cell));
898:     break;
899:   case DM_POLYTOPE_TRIANGLE:
900:     PetscCall(DMPlexLocatePoint_Simplex_2D_Internal(dm, point, cellStart, cell));
901:     break;
902:   case DM_POLYTOPE_QUADRILATERAL:
903:     PetscCall(DMPlexLocatePoint_Quad_2D_Internal(dm, point, cellStart, cell));
904:     break;
905:   case DM_POLYTOPE_TETRAHEDRON:
906:     PetscCall(DMPlexLocatePoint_Simplex_3D_Internal(dm, point, cellStart, cell));
907:     break;
908:   case DM_POLYTOPE_HEXAHEDRON:
909:     PetscCall(DMPlexLocatePoint_Hex_3D_Internal(dm, point, cellStart, cell));
910:     break;
911:   default:
912:     SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No point location for cell %" PetscInt_FMT " with type %s", cellStart, DMPolytopeTypes[ct]);
913:   }
914:   PetscFunctionReturn(PETSC_SUCCESS);
915: }

917: /*
918:   DMPlexClosestPoint_Internal - Returns the closest point in the cell to the given point
919: */
920: static PetscErrorCode DMPlexClosestPoint_Internal(DM dm, PetscInt dim, const PetscScalar point[], PetscInt cell, PetscReal cpoint[])
921: {
922:   DMPolytopeType ct;

924:   PetscFunctionBegin;
925:   PetscCall(DMPlexGetCellType(dm, cell, &ct));
926:   switch (ct) {
927:   case DM_POLYTOPE_TRIANGLE:
928:     PetscCall(DMPlexClosestPoint_Simplex_2D_Internal(dm, point, cell, cpoint));
929:     break;
930: #if 0
931:     case DM_POLYTOPE_QUADRILATERAL:
932:     PetscCall(DMPlexClosestPoint_General_2D_Internal(dm, point, cell, cpoint));break;
933:     case DM_POLYTOPE_TETRAHEDRON:
934:     PetscCall(DMPlexClosestPoint_Simplex_3D_Internal(dm, point, cell, cpoint));break;
935:     case DM_POLYTOPE_HEXAHEDRON:
936:     PetscCall(DMPlexClosestPoint_General_3D_Internal(dm, point, cell, cpoint));break;
937: #endif
938:   default:
939:     SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No closest point location for cell %" PetscInt_FMT " with type %s", cell, DMPolytopeTypes[ct]);
940:   }
941:   PetscFunctionReturn(PETSC_SUCCESS);
942: }

944: /*
945:   DMPlexComputeGridHash_Internal - Create a grid hash structure covering the `DMPLEX`

947:   Collective

949:   Input Parameter:
950: . dm - The `DMPLEX`

952:   Output Parameter:
953: . localBox - The grid hash object

955:   Level: developer

957:   Notes:
958:   How do we determine all boxes intersecting a given cell?

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

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

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

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

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

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

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

975: .seealso: `DMPLEX`, `PetscGridHashCreate()`, `PetscGridHashGetEnclosingBox()`
976: */
977: static PetscErrorCode DMPlexComputeGridHash_Internal(DM dm, PetscGridHash *localBox)
978: {
979:   PetscInt        debug = ((DM_Plex *)dm->data)->printLocate;
980:   PetscGridHash   lbox;
981:   PetscSF         sf;
982:   const PetscInt *leaves;
983:   PetscInt       *dboxes, *boxes;
984:   PetscInt        cdim, cStart, cEnd, Nl = -1;
985:   PetscBool       flg;

987:   PetscFunctionBegin;
988:   PetscCall(DMGetCoordinateDim(dm, &cdim));
989:   PetscCall(DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd));
990:   PetscCall(DMPlexCreateGridHash(dm, &lbox));
991:   {
992:     PetscInt n[3], d;

994:     PetscCall(PetscOptionsGetIntArray(NULL, ((PetscObject)dm)->prefix, "-dm_plex_hash_box_faces", n, &d, &flg));
995:     if (flg) {
996:       for (PetscInt i = d; i < cdim; ++i) n[i] = n[d - 1];
997:     } else {
998:       for (PetscInt i = 0; i < cdim; ++i) n[i] = PetscMax(2, PetscFloorReal(PetscPowReal((PetscReal)(cEnd - cStart), 1.0 / cdim) * 0.8));
999:     }
1000:     PetscCall(PetscGridHashSetGrid(lbox, n, NULL));
1001:     if (debug)
1002:       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.,
1003:                             (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.));
1004:   }

1006:   PetscCall(DMGetPointSF(dm, &sf));
1007:   if (sf) PetscCall(PetscSFGetGraph(sf, NULL, &Nl, &leaves, NULL));
1008:   Nl = PetscMax(Nl, 0);
1009:   PetscCall(PetscCalloc2(16 * cdim, &dboxes, 16, &boxes));

1011:   PetscCall(DMLabelCreate(PETSC_COMM_SELF, "cells", &lbox->cellsSparse));
1012:   PetscCall(DMLabelCreateIndex(lbox->cellsSparse, cStart, cEnd));
1013:   for (PetscInt c = cStart; c < cEnd; ++c) {
1014:     PetscReal          intPoints[6 * 6 * 6 * 3];
1015:     const PetscScalar *array;
1016:     PetscScalar       *coords            = NULL;
1017:     const PetscReal   *h                 = lbox->h;
1018:     PetscReal          normal[9]         = {1., 0., 0., 0., 1., 0., 0., 0., 1.};
1019:     PetscReal         *lowerIntPoints[3] = {&intPoints[0 * 6 * 6 * 3], &intPoints[1 * 6 * 6 * 3], &intPoints[2 * 6 * 6 * 3]};
1020:     PetscReal         *upperIntPoints[3] = {&intPoints[3 * 6 * 6 * 3], &intPoints[4 * 6 * 6 * 3], &intPoints[5 * 6 * 6 * 3]};
1021:     PetscReal          lp[3], up[3], *tmp;
1022:     PetscInt           numCoords, idx, dlim[6], lowerInt[3], upperInt[3];
1023:     PetscBool          isDG, lower[3], upper[3];

1025:     PetscCall(PetscFindInt(c, Nl, leaves, &idx));
1026:     if (idx >= 0) continue;
1027:     // Get grid of boxes containing the cell
1028:     PetscCall(DMPlexGetCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
1029:     PetscCall(PetscGridHashGetEnclosingBox(lbox, numCoords / cdim, coords, dboxes, boxes));
1030:     PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
1031:     for (PetscInt d = 0; d < cdim; ++d) dlim[d * 2 + 0] = dlim[d * 2 + 1] = dboxes[d];
1032:     for (PetscInt d = cdim; d < 3; ++d) dlim[d * 2 + 0] = dlim[d * 2 + 1] = 0;
1033:     for (PetscInt e = 1; e < numCoords / cdim; ++e) {
1034:       for (PetscInt d = 0; d < cdim; ++d) {
1035:         dlim[d * 2 + 0] = PetscMin(dlim[d * 2 + 0], dboxes[e * cdim + d]);
1036:         dlim[d * 2 + 1] = PetscMax(dlim[d * 2 + 1], dboxes[e * cdim + d]);
1037:       }
1038:     }
1039:     if (debug > 4) {
1040:       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]));
1041:     }
1042:     // Initialize with lower planes for first box
1043:     for (PetscInt d = 0; d < cdim; ++d) {
1044:       lp[d] = lbox->lower[d] + dlim[d * 2 + 0] * h[d];
1045:       up[d] = lp[d] + h[d];
1046:     }
1047:     for (PetscInt d = 0; d < cdim; ++d) {
1048:       PetscCall(DMPlexGetPlaneCellIntersection_Internal(dm, c, lp, &normal[d * 3], &lower[d], &lowerInt[d], lowerIntPoints[d]));
1049:       if (debug > 4) {
1050:         if (!lowerInt[d])
1051:           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"));
1052:         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]));
1053:       }
1054:     }
1055:     // Loop over grid
1056:     for (PetscInt k = dlim[2 * 2 + 0]; k <= dlim[2 * 2 + 1]; ++k, lp[2] = up[2], up[2] += h[2]) {
1057:       if (cdim > 2) PetscCall(DMPlexGetPlaneCellIntersection_Internal(dm, c, up, &normal[3 * 2], &upper[2], &upperInt[2], upperIntPoints[2]));
1058:       if (cdim > 2 && debug > 4) {
1059:         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"));
1060:         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]));
1061:       }
1062:       for (PetscInt j = dlim[1 * 2 + 0]; j <= dlim[1 * 2 + 1]; ++j, lp[1] = up[1], up[1] += h[1]) {
1063:         if (cdim > 1) PetscCall(DMPlexGetPlaneCellIntersection_Internal(dm, c, up, &normal[3 * 1], &upper[1], &upperInt[1], upperIntPoints[1]));
1064:         if (cdim > 1 && debug > 4) {
1065:           if (!upperInt[1])
1066:             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"));
1067:           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]));
1068:         }
1069:         for (PetscInt i = dlim[0 * 2 + 0]; i <= dlim[0 * 2 + 1]; ++i, lp[0] = up[0], up[0] += h[0]) {
1070:           const PetscInt box    = (k * lbox->n[1] + j) * lbox->n[0] + i;
1071:           PetscBool      excNeg = PETSC_TRUE;
1072:           PetscBool      excPos = PETSC_TRUE;
1073:           PetscInt       NlInt  = 0;
1074:           PetscInt       NuInt  = 0;

1076:           PetscCall(DMPlexGetPlaneCellIntersection_Internal(dm, c, up, &normal[3 * 0], &upper[0], &upperInt[0], upperIntPoints[0]));
1077:           if (debug > 4) {
1078:             if (!upperInt[0])
1079:               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"));
1080:             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]));
1081:           }
1082:           for (PetscInt d = 0; d < cdim; ++d) {
1083:             NlInt += lowerInt[d];
1084:             NuInt += upperInt[d];
1085:           }
1086:           // If there is no intersection...
1087:           if (!NlInt && !NuInt) {
1088:             // If the cell is on the negative side of the lower planes, it is not in the box
1089:             for (PetscInt d = 0; d < cdim; ++d)
1090:               if (lower[d]) {
1091:                 excNeg = PETSC_FALSE;
1092:                 break;
1093:               }
1094:             // If the cell is on the positive side of the upper planes, it is not in the box
1095:             for (PetscInt d = 0; d < cdim; ++d)
1096:               if (!upper[d]) {
1097:                 excPos = PETSC_FALSE;
1098:                 break;
1099:               }
1100:             if (excNeg || excPos) {
1101:               if (debug && excNeg) PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Cell %" PetscInt_FMT " is on the negative side of the lower plane\n", c));
1102:               if (debug && excPos) PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Cell %" PetscInt_FMT " is on the positive side of the upper plane\n", c));
1103:               continue;
1104:             }
1105:             // Otherwise it is in the box
1106:             if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Cell %" PetscInt_FMT " is contained in box %" PetscInt_FMT "\n", c, box));
1107:             PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
1108:             continue;
1109:           }
1110:           /*
1111:             If any intersection point is within the box limits, it is in the box
1112:             We need to have tolerances here since intersection point calculations can introduce errors
1113:             Initialize a count to track which planes have intersection outside the box.
1114:             if two adjacent planes have intersection points upper and lower all outside the box, look
1115:             first at if another plane has intersection points outside the box, if so, it is inside the cell
1116:             look next if no intersection points exist on the other planes, and check if the planes are on the
1117:             outside of the intersection points but on opposite ends. If so, the box cuts through the cell.
1118:           */
1119:           PetscInt outsideCount[6] = {0, 0, 0, 0, 0, 0};
1120:           for (PetscInt plane = 0; plane < cdim; ++plane) {
1121:             for (PetscInt ip = 0; ip < lowerInt[plane]; ++ip) {
1122:               PetscInt d;

1124:               for (d = 0; d < cdim; ++d) {
1125:                 if ((lowerIntPoints[plane][ip * cdim + d] < (lp[d] - PETSC_SMALL)) || (lowerIntPoints[plane][ip * cdim + d] > (up[d] + PETSC_SMALL))) {
1126:                   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
1127:                   break;
1128:                 }
1129:               }
1130:               if (d == cdim) {
1131:                 if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Cell %" PetscInt_FMT " intersected lower plane %" PetscInt_FMT " of box %" PetscInt_FMT "\n", c, plane, box));
1132:                 PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
1133:                 goto end;
1134:               }
1135:             }
1136:             for (PetscInt ip = 0; ip < upperInt[plane]; ++ip) {
1137:               PetscInt d;

1139:               for (d = 0; d < cdim; ++d) {
1140:                 if ((upperIntPoints[plane][ip * cdim + d] < (lp[d] - PETSC_SMALL)) || (upperIntPoints[plane][ip * cdim + d] > (up[d] + PETSC_SMALL))) {
1141:                   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
1142:                   break;
1143:                 }
1144:               }
1145:               if (d == cdim) {
1146:                 if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Cell %" PetscInt_FMT " intersected upper plane %" PetscInt_FMT " of box %" PetscInt_FMT "\n", c, plane, box));
1147:                 PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
1148:                 goto end;
1149:               }
1150:             }
1151:           }
1152:           /*
1153:              Check the planes with intersections
1154:              in 2D, check if the square falls in the middle of a cell
1155:              ie all four planes have intersection points outside of the box
1156:              You do not want to be doing this, because it means your grid hashing is finer than your grid,
1157:              but we should still support it I guess
1158:           */
1159:           if (cdim == 2) {
1160:             PetscInt nIntersects = 0;
1161:             for (PetscInt d = 0; d < cdim; ++d) nIntersects += (outsideCount[d] + outsideCount[d + cdim]);
1162:             // if the count adds up to 8, that means each plane has 2 external intersections and thus it is in the cell
1163:             if (nIntersects == 8) {
1164:               PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
1165:               goto end;
1166:             }
1167:           }
1168:           /*
1169:              In 3 dimensions, if two adjacent planes have at least 3 intersections outside the cell in the appropriate direction,
1170:              we then check the 3rd planar dimension. If a plane falls between intersection points, the cell belongs to that box.
1171:              If the planes are on opposite sides of the intersection points, the cell belongs to that box and it passes through the cell.
1172:           */
1173:           if (cdim == 3) {
1174:             PetscInt faces[3] = {0, 0, 0}, checkInternalFace = 0;
1175:             // Find two adjacent planes with at least 3 intersection points in the upper and lower
1176:             // if the third plane has 3 intersection points or more, a pyramid base is formed on that plane and it is in the cell
1177:             for (PetscInt d = 0; d < cdim; ++d)
1178:               if (outsideCount[d] >= 3 && outsideCount[cdim + d] >= 3) {
1179:                 faces[d]++;
1180:                 checkInternalFace++;
1181:               }
1182:             if (checkInternalFace == 3) {
1183:               // All planes have 3 intersection points, add it.
1184:               PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
1185:               goto end;
1186:             }
1187:             // Gross, figure out which adjacent faces have at least 3 points
1188:             PetscInt nonIntersectingFace = -1;
1189:             if (faces[0] == faces[1]) nonIntersectingFace = 2;
1190:             if (faces[0] == faces[2]) nonIntersectingFace = 1;
1191:             if (faces[1] == faces[2]) nonIntersectingFace = 0;
1192:             if (nonIntersectingFace >= 0) {
1193:               for (PetscInt plane = 0; plane < cdim; ++plane) {
1194:                 if (!lowerInt[nonIntersectingFace] && !upperInt[nonIntersectingFace]) continue;
1195:                 // 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.
1196:                 for (PetscInt ip = 0; ip < lowerInt[nonIntersectingFace]; ++ip) {
1197:                   if (lowerIntPoints[plane][ip * cdim + nonIntersectingFace] > lp[nonIntersectingFace] - PETSC_SMALL || lowerIntPoints[plane][ip * cdim + nonIntersectingFace] < up[nonIntersectingFace] + PETSC_SMALL) goto setpoint;
1198:                 }
1199:                 for (PetscInt ip = 0; ip < upperInt[nonIntersectingFace]; ++ip) {
1200:                   if (upperIntPoints[plane][ip * cdim + nonIntersectingFace] > lp[nonIntersectingFace] - PETSC_SMALL || upperIntPoints[plane][ip * cdim + nonIntersectingFace] < up[nonIntersectingFace] + PETSC_SMALL) goto setpoint;
1201:                 }
1202:                 goto end;
1203:               }
1204:               // The points are within the bonds of the non intersecting planes, add it.
1205:             setpoint:
1206:               PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
1207:               goto end;
1208:             }
1209:           }
1210:         end:
1211:           lower[0]          = upper[0];
1212:           lowerInt[0]       = upperInt[0];
1213:           tmp               = lowerIntPoints[0];
1214:           lowerIntPoints[0] = upperIntPoints[0];
1215:           upperIntPoints[0] = tmp;
1216:         }
1217:         lp[0]             = lbox->lower[0] + dlim[0 * 2 + 0] * h[0];
1218:         up[0]             = lp[0] + h[0];
1219:         lower[1]          = upper[1];
1220:         lowerInt[1]       = upperInt[1];
1221:         tmp               = lowerIntPoints[1];
1222:         lowerIntPoints[1] = upperIntPoints[1];
1223:         upperIntPoints[1] = tmp;
1224:       }
1225:       lp[1]             = lbox->lower[1] + dlim[1 * 2 + 0] * h[1];
1226:       up[1]             = lp[1] + h[1];
1227:       lower[2]          = upper[2];
1228:       lowerInt[2]       = upperInt[2];
1229:       tmp               = lowerIntPoints[2];
1230:       lowerIntPoints[2] = upperIntPoints[2];
1231:       upperIntPoints[2] = tmp;
1232:     }
1233:   }
1234:   PetscCall(PetscFree2(dboxes, boxes));

1236:   if (debug) PetscCall(DMLabelView(lbox->cellsSparse, PETSC_VIEWER_STDOUT_SELF));
1237:   PetscCall(DMLabelConvertToSection(lbox->cellsSparse, &lbox->cellSection, &lbox->cells));
1238:   PetscCall(DMLabelDestroy(&lbox->cellsSparse));
1239:   *localBox = lbox;
1240:   PetscFunctionReturn(PETSC_SUCCESS);
1241: }

1243: PetscErrorCode DMLocatePoints_Plex(DM dm, Vec v, DMPointLocationType ltype, PetscSF cellSF)
1244: {
1245:   PetscInt        debug = ((DM_Plex *)dm->data)->printLocate;
1246:   DM_Plex        *mesh  = (DM_Plex *)dm->data;
1247:   PetscBool       hash = mesh->useHashLocation, reuse = PETSC_FALSE;
1248:   PetscInt        bs, numPoints, p, numFound, *found = NULL;
1249:   PetscInt        dim, Nl = 0, cStart, cEnd, numCells, c, d;
1250:   PetscSF         sf;
1251:   const PetscInt *leaves;
1252:   const PetscInt *boxCells;
1253:   PetscSFNode    *cells;
1254:   PetscScalar    *a;
1255:   PetscMPIInt     result;
1256:   PetscLogDouble  t0, t1;
1257:   PetscReal       gmin[3], gmax[3];
1258:   PetscInt        terminating_query_type[] = {0, 0, 0};
1259:   PetscMPIInt     rank;

1261:   PetscFunctionBegin;
1262:   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank));
1263:   PetscCall(PetscLogEventBegin(DMPLEX_LocatePoints, 0, 0, 0, 0));
1264:   PetscCall(PetscTime(&t0));
1265:   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.");
1266:   PetscCall(DMGetCoordinateDim(dm, &dim));
1267:   PetscCall(VecGetBlockSize(v, &bs));
1268:   PetscCallMPI(MPI_Comm_compare(PetscObjectComm((PetscObject)cellSF), PETSC_COMM_SELF, &result));
1269:   PetscCheck(result == MPI_IDENT || result == MPI_CONGRUENT, PetscObjectComm((PetscObject)cellSF), PETSC_ERR_SUP, "Trying parallel point location: only local point location supported");
1270:   // We ignore extra coordinates
1271:   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);
1272:   PetscCall(DMGetCoordinatesLocalSetUp(dm));
1273:   PetscCall(DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd));
1274:   PetscCall(DMGetPointSF(dm, &sf));
1275:   if (sf) PetscCall(PetscSFGetGraph(sf, NULL, &Nl, &leaves, NULL));
1276:   Nl = PetscMax(Nl, 0);
1277:   PetscCall(VecGetLocalSize(v, &numPoints));
1278:   PetscCall(VecGetArray(v, &a));
1279:   numPoints /= bs;
1280:   {
1281:     const PetscSFNode *sf_cells;

1283:     PetscCall(PetscSFGetGraph(cellSF, NULL, NULL, NULL, &sf_cells));
1284:     if (sf_cells) {
1285:       PetscCall(PetscInfo(dm, "[DMLocatePoints_Plex] Re-using existing StarForest node list\n"));
1286:       cells = (PetscSFNode *)sf_cells;
1287:       reuse = PETSC_TRUE;
1288:     } else {
1289:       PetscCall(PetscInfo(dm, "[DMLocatePoints_Plex] Creating and initializing new StarForest node list\n"));
1290:       PetscCall(PetscMalloc1(numPoints, &cells));
1291:       /* initialize cells if created */
1292:       for (p = 0; p < numPoints; p++) {
1293:         cells[p].rank  = 0;
1294:         cells[p].index = DMLOCATEPOINT_POINT_NOT_FOUND;
1295:       }
1296:     }
1297:   }
1298:   PetscCall(DMGetBoundingBox(dm, gmin, gmax));
1299:   if (hash) {
1300:     if (!mesh->lbox) {
1301:       PetscCall(PetscInfo(dm, "Initializing grid hashing\n"));
1302:       PetscCall(DMPlexComputeGridHash_Internal(dm, &mesh->lbox));
1303:     }
1304:     /* Designate the local box for each point */
1305:     /* Send points to correct process */
1306:     /* Search cells that lie in each subbox */
1307:     /*   Should we bin points before doing search? */
1308:     PetscCall(ISGetIndices(mesh->lbox->cells, &boxCells));
1309:   }
1310:   for (p = 0, numFound = 0; p < numPoints; ++p) {
1311:     const PetscScalar *point   = &a[p * bs];
1312:     PetscInt           dbin[3] = {-1, -1, -1}, bin, cell = -1, cellOffset;
1313:     PetscBool          point_outside_domain = PETSC_FALSE;

1315:     /* check bounding box of domain */
1316:     for (d = 0; d < dim; d++) {
1317:       if (PetscRealPart(point[d]) < gmin[d]) {
1318:         point_outside_domain = PETSC_TRUE;
1319:         break;
1320:       }
1321:       if (PetscRealPart(point[d]) > gmax[d]) {
1322:         point_outside_domain = PETSC_TRUE;
1323:         break;
1324:       }
1325:     }
1326:     if (point_outside_domain) {
1327:       cells[p].rank  = 0;
1328:       cells[p].index = DMLOCATEPOINT_POINT_NOT_FOUND;
1329:       terminating_query_type[0]++;
1330:       continue;
1331:     }

1333:     /* check initial values in cells[].index - abort early if found */
1334:     if (cells[p].index != DMLOCATEPOINT_POINT_NOT_FOUND) {
1335:       c              = cells[p].index;
1336:       cells[p].index = DMLOCATEPOINT_POINT_NOT_FOUND;
1337:       PetscCall(DMPlexLocatePoint_Internal(dm, dim, point, c, &cell));
1338:       if (cell >= 0) {
1339:         cells[p].rank  = 0;
1340:         cells[p].index = cell;
1341:         numFound++;
1342:       }
1343:     }
1344:     if (cells[p].index != DMLOCATEPOINT_POINT_NOT_FOUND) {
1345:       terminating_query_type[1]++;
1346:       continue;
1347:     }

1349:     if (hash) {
1350:       PetscBool found_box;

1352:       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.));
1353:       /* allow for case that point is outside box - abort early */
1354:       PetscCall(PetscGridHashGetEnclosingBoxQuery(mesh->lbox, mesh->lbox->cellSection, 1, point, dbin, &bin, &found_box));
1355:       if (found_box) {
1356:         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));
1357:         /* TODO Lay an interface over this so we can switch between Section (dense) and Label (sparse) */
1358:         PetscCall(PetscSectionGetDof(mesh->lbox->cellSection, bin, &numCells));
1359:         PetscCall(PetscSectionGetOffset(mesh->lbox->cellSection, bin, &cellOffset));
1360:         for (c = cellOffset; c < cellOffset + numCells; ++c) {
1361:           if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, "[%d]    Checking for point in cell %" PetscInt_FMT "\n", rank, boxCells[c]));
1362:           PetscCall(DMPlexLocatePoint_Internal(dm, dim, point, boxCells[c], &cell));
1363:           if (cell >= 0) {
1364:             if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, "[%d]      FOUND in cell %" PetscInt_FMT "\n", rank, cell));
1365:             cells[p].rank  = 0;
1366:             cells[p].index = cell;
1367:             numFound++;
1368:             terminating_query_type[2]++;
1369:             break;
1370:           }
1371:         }
1372:       }
1373:     } else {
1374:       PetscBool found = PETSC_FALSE;
1375:       for (c = cStart; c < cEnd; ++c) {
1376:         PetscInt idx;

1378:         PetscCall(PetscFindInt(c, Nl, leaves, &idx));
1379:         if (idx >= 0) continue;
1380:         PetscCall(DMPlexLocatePoint_Internal(dm, dim, point, c, &cell));
1381:         if (cell >= 0) {
1382:           cells[p].rank  = 0;
1383:           cells[p].index = cell;
1384:           numFound++;
1385:           terminating_query_type[2]++;
1386:           found = PETSC_TRUE;
1387:           break;
1388:         }
1389:       }
1390:       if (!found) terminating_query_type[0]++;
1391:     }
1392:   }
1393:   if (hash) PetscCall(ISRestoreIndices(mesh->lbox->cells, &boxCells));
1394:   if (ltype == DM_POINTLOCATION_NEAREST && hash && numFound < numPoints) {
1395:     for (p = 0; p < numPoints; p++) {
1396:       const PetscScalar *point     = &a[p * bs];
1397:       PetscReal          cpoint[3] = {0, 0, 0}, diff[3], best[3] = {PETSC_MAX_REAL, PETSC_MAX_REAL, PETSC_MAX_REAL}, dist, distMax = PETSC_MAX_REAL;
1398:       PetscInt           dbin[3] = {-1, -1, -1}, bin, cellOffset, d, bestc = -1;

1400:       if (cells[p].index < 0) {
1401:         PetscCall(PetscGridHashGetEnclosingBox(mesh->lbox, 1, point, dbin, &bin));
1402:         PetscCall(PetscSectionGetDof(mesh->lbox->cellSection, bin, &numCells));
1403:         PetscCall(PetscSectionGetOffset(mesh->lbox->cellSection, bin, &cellOffset));
1404:         for (c = cellOffset; c < cellOffset + numCells; ++c) {
1405:           PetscCall(DMPlexClosestPoint_Internal(dm, dim, point, boxCells[c], cpoint));
1406:           for (d = 0; d < dim; ++d) diff[d] = cpoint[d] - PetscRealPart(point[d]);
1407:           dist = DMPlex_NormD_Internal(dim, diff);
1408:           if (dist < distMax) {
1409:             for (d = 0; d < dim; ++d) best[d] = cpoint[d];
1410:             bestc   = boxCells[c];
1411:             distMax = dist;
1412:           }
1413:         }
1414:         if (distMax < PETSC_MAX_REAL) {
1415:           ++numFound;
1416:           cells[p].rank  = 0;
1417:           cells[p].index = bestc;
1418:           for (d = 0; d < dim; ++d) a[p * bs + d] = best[d];
1419:         }
1420:       }
1421:     }
1422:   }
1423:   /* This code is only be relevant when interfaced to parallel point location */
1424:   /* Check for highest numbered proc that claims a point (do we care?) */
1425:   if (ltype == DM_POINTLOCATION_REMOVE && numFound < numPoints) {
1426:     PetscCall(PetscMalloc1(numFound, &found));
1427:     for (p = 0, numFound = 0; p < numPoints; p++) {
1428:       if (cells[p].rank >= 0 && cells[p].index >= 0) {
1429:         if (numFound < p) cells[numFound] = cells[p];
1430:         found[numFound++] = p;
1431:       }
1432:     }
1433:   }
1434:   PetscCall(VecRestoreArray(v, &a));
1435:   if (!reuse) PetscCall(PetscSFSetGraph(cellSF, cEnd - cStart, numFound, found, PETSC_OWN_POINTER, cells, PETSC_OWN_POINTER));
1436:   PetscCall(PetscTime(&t1));
1437:   if (hash) {
1438:     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]));
1439:   } else {
1440:     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]));
1441:   }
1442:   PetscCall(PetscInfo(dm, "[DMLocatePoints_Plex] npoints %" PetscInt_FMT " : time(rank0) %1.2e (sec): points/sec %1.4e\n", numPoints, t1 - t0, numPoints / (t1 - t0)));
1443:   PetscCall(PetscLogEventEnd(DMPLEX_LocatePoints, 0, 0, 0, 0));
1444:   PetscFunctionReturn(PETSC_SUCCESS);
1445: }

1447: /*@
1448:   DMPlexComputeProjection2Dto1D - Rewrite coordinates to be the 1D projection of the 2D coordinates

1450:   Not Collective

1452:   Input/Output Parameter:
1453: . 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

1455:   Output Parameter:
1456: . R - The rotation which accomplishes the projection, array of size 4

1458:   Level: developer

1460: .seealso: `DMPLEX`, `DMPlexComputeProjection3Dto1D()`, `DMPlexComputeProjection3Dto2D()`
1461: @*/
1462: PetscErrorCode DMPlexComputeProjection2Dto1D(PetscScalar coords[], PetscReal R[])
1463: {
1464:   const PetscReal x = PetscRealPart(coords[2] - coords[0]);
1465:   const PetscReal y = PetscRealPart(coords[3] - coords[1]);
1466:   const PetscReal r = PetscSqrtReal(x * x + y * y), c = x / r, s = y / r;

1468:   PetscFunctionBegin;
1469:   R[0]      = c;
1470:   R[1]      = -s;
1471:   R[2]      = s;
1472:   R[3]      = c;
1473:   coords[0] = 0.0;
1474:   coords[1] = r;
1475:   PetscFunctionReturn(PETSC_SUCCESS);
1476: }

1478: /*@
1479:   DMPlexComputeProjection3Dto1D - Rewrite coordinates to be the 1D projection of the 3D coordinates

1481:   Not Collective

1483:   Input/Output Parameter:
1484: . 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

1486:   Output Parameter:
1487: . R - The rotation which accomplishes the projection, an array of size 9

1489:   Level: developer

1491:   Note:
1492:   This uses the basis completion described by Frisvad {cite}`frisvad2012building`

1494: .seealso: `DMPLEX`, `DMPlexComputeProjection2Dto1D()`, `DMPlexComputeProjection3Dto2D()`
1495: @*/
1496: PetscErrorCode DMPlexComputeProjection3Dto1D(PetscScalar coords[], PetscReal R[])
1497: {
1498:   PetscReal x    = PetscRealPart(coords[3] - coords[0]);
1499:   PetscReal y    = PetscRealPart(coords[4] - coords[1]);
1500:   PetscReal z    = PetscRealPart(coords[5] - coords[2]);
1501:   PetscReal r    = PetscSqrtReal(x * x + y * y + z * z);
1502:   PetscReal rinv = 1. / r;

1504:   PetscFunctionBegin;
1505:   x *= rinv;
1506:   y *= rinv;
1507:   z *= rinv;
1508:   if (x > 0.) {
1509:     PetscReal inv1pX = 1. / (1. + x);

1511:     R[0] = x;
1512:     R[1] = -y;
1513:     R[2] = -z;
1514:     R[3] = y;
1515:     R[4] = 1. - y * y * inv1pX;
1516:     R[5] = -y * z * inv1pX;
1517:     R[6] = z;
1518:     R[7] = -y * z * inv1pX;
1519:     R[8] = 1. - z * z * inv1pX;
1520:   } else {
1521:     PetscReal inv1mX = 1. / (1. - x);

1523:     R[0] = x;
1524:     R[1] = z;
1525:     R[2] = y;
1526:     R[3] = y;
1527:     R[4] = -y * z * inv1mX;
1528:     R[5] = 1. - y * y * inv1mX;
1529:     R[6] = z;
1530:     R[7] = 1. - z * z * inv1mX;
1531:     R[8] = -y * z * inv1mX;
1532:   }
1533:   coords[0] = 0.0;
1534:   coords[1] = r;
1535:   coords[2] = 0.0;
1536:   PetscFunctionReturn(PETSC_SUCCESS);
1537: }

1539: /*@
1540:   DMPlexComputeProjection3Dto2D - Rewrite coordinates of 3 or more coplanar 3D points to a common 2D basis for the
1541:   plane.  The normal is defined by positive orientation of the first 3 points.

1543:   Not Collective

1545:   Input Parameter:
1546: . coordSize - Length of coordinate array (3x number of points); must be at least 9 (3 points)

1548:   Input/Output Parameter:
1549: . coords - The interlaced coordinates of each coplanar 3D point; on output the first
1550:            2*coordSize/3 entries contain interlaced 2D points, with the rest undefined

1552:   Output Parameter:
1553: . 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.

1555:   Level: developer

1557: .seealso: `DMPLEX`, `DMPlexComputeProjection2Dto1D()`, `DMPlexComputeProjection3Dto1D()`
1558: @*/
1559: PetscErrorCode DMPlexComputeProjection3Dto2D(PetscInt coordSize, PetscScalar coords[], PetscReal R[])
1560: {
1561:   PetscReal      x1[3], x2[3], n[3], c[3], norm;
1562:   const PetscInt dim = 3;
1563:   PetscInt       d, p;

1565:   PetscFunctionBegin;
1566:   /* 0) Calculate normal vector */
1567:   for (d = 0; d < dim; ++d) {
1568:     x1[d] = PetscRealPart(coords[1 * dim + d] - coords[0 * dim + d]);
1569:     x2[d] = PetscRealPart(coords[2 * dim + d] - coords[0 * dim + d]);
1570:   }
1571:   // n = x1 \otimes x2
1572:   n[0] = x1[1] * x2[2] - x1[2] * x2[1];
1573:   n[1] = x1[2] * x2[0] - x1[0] * x2[2];
1574:   n[2] = x1[0] * x2[1] - x1[1] * x2[0];
1575:   norm = PetscSqrtReal(n[0] * n[0] + n[1] * n[1] + n[2] * n[2]);
1576:   for (d = 0; d < dim; d++) n[d] /= norm;
1577:   norm = PetscSqrtReal(x1[0] * x1[0] + x1[1] * x1[1] + x1[2] * x1[2]);
1578:   for (d = 0; d < dim; d++) x1[d] /= norm;
1579:   // x2 = n \otimes x1
1580:   x2[0] = n[1] * x1[2] - n[2] * x1[1];
1581:   x2[1] = n[2] * x1[0] - n[0] * x1[2];
1582:   x2[2] = n[0] * x1[1] - n[1] * x1[0];
1583:   for (d = 0; d < dim; d++) {
1584:     R[d * dim + 0] = x1[d];
1585:     R[d * dim + 1] = x2[d];
1586:     R[d * dim + 2] = n[d];
1587:     c[d]           = PetscRealPart(coords[0 * dim + d]);
1588:   }
1589:   for (p = 0; p < coordSize / dim; p++) {
1590:     PetscReal y[3];
1591:     for (d = 0; d < dim; d++) y[d] = PetscRealPart(coords[p * dim + d]) - c[d];
1592:     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];
1593:   }
1594:   PetscFunctionReturn(PETSC_SUCCESS);
1595: }

1597: PETSC_UNUSED static inline void Volume_Triangle_Internal(PetscReal *vol, PetscReal coords[])
1598: {
1599:   /* Signed volume is 1/2 the determinant

1601:    |  1  1  1 |
1602:    | x0 x1 x2 |
1603:    | y0 y1 y2 |

1605:      but if x0,y0 is the origin, we have

1607:    | x1 x2 |
1608:    | y1 y2 |
1609:   */
1610:   const PetscReal x1 = coords[2] - coords[0], y1 = coords[3] - coords[1];
1611:   const PetscReal x2 = coords[4] - coords[0], y2 = coords[5] - coords[1];
1612:   PetscReal       M[4], detM;
1613:   M[0] = x1;
1614:   M[1] = x2;
1615:   M[2] = y1;
1616:   M[3] = y2;
1617:   DMPlex_Det2D_Internal(&detM, M);
1618:   *vol = 0.5 * detM;
1619:   (void)PetscLogFlops(5.0);
1620: }

1622: PETSC_UNUSED static inline void Volume_Tetrahedron_Internal(PetscReal *vol, PetscReal coords[])
1623: {
1624:   /* Signed volume is 1/6th of the determinant

1626:    |  1  1  1  1 |
1627:    | x0 x1 x2 x3 |
1628:    | y0 y1 y2 y3 |
1629:    | z0 z1 z2 z3 |

1631:      but if x0,y0,z0 is the origin, we have

1633:    | x1 x2 x3 |
1634:    | y1 y2 y3 |
1635:    | z1 z2 z3 |
1636:   */
1637:   const PetscReal x1 = coords[3] - coords[0], y1 = coords[4] - coords[1], z1 = coords[5] - coords[2];
1638:   const PetscReal x2 = coords[6] - coords[0], y2 = coords[7] - coords[1], z2 = coords[8] - coords[2];
1639:   const PetscReal x3 = coords[9] - coords[0], y3 = coords[10] - coords[1], z3 = coords[11] - coords[2];
1640:   const PetscReal onesixth = ((PetscReal)1. / (PetscReal)6.);
1641:   PetscReal       M[9], detM;
1642:   M[0] = x1;
1643:   M[1] = x2;
1644:   M[2] = x3;
1645:   M[3] = y1;
1646:   M[4] = y2;
1647:   M[5] = y3;
1648:   M[6] = z1;
1649:   M[7] = z2;
1650:   M[8] = z3;
1651:   DMPlex_Det3D_Internal(&detM, M);
1652:   *vol = -onesixth * detM;
1653:   (void)PetscLogFlops(10.0);
1654: }

1656: static inline void Volume_Tetrahedron_Origin_Internal(PetscReal *vol, PetscReal coords[])
1657: {
1658:   const PetscReal onesixth = ((PetscReal)1. / (PetscReal)6.);
1659:   DMPlex_Det3D_Internal(vol, coords);
1660:   *vol *= -onesixth;
1661: }

1663: static PetscErrorCode DMPlexComputePointGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1664: {
1665:   PetscSection       coordSection;
1666:   Vec                coordinates;
1667:   const PetscScalar *coords;
1668:   PetscInt           dim, d, off;

1670:   PetscFunctionBegin;
1671:   PetscCall(DMGetCoordinatesLocal(dm, &coordinates));
1672:   PetscCall(DMGetCoordinateSection(dm, &coordSection));
1673:   PetscCall(PetscSectionGetDof(coordSection, e, &dim));
1674:   if (!dim) PetscFunctionReturn(PETSC_SUCCESS);
1675:   PetscCall(PetscSectionGetOffset(coordSection, e, &off));
1676:   PetscCall(VecGetArrayRead(coordinates, &coords));
1677:   if (v0) {
1678:     for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[off + d]);
1679:   }
1680:   PetscCall(VecRestoreArrayRead(coordinates, &coords));
1681:   *detJ = 1.;
1682:   if (J) {
1683:     for (d = 0; d < dim * dim; d++) J[d] = 0.;
1684:     for (d = 0; d < dim; d++) J[d * dim + d] = 1.;
1685:     if (invJ) {
1686:       for (d = 0; d < dim * dim; d++) invJ[d] = 0.;
1687:       for (d = 0; d < dim; d++) invJ[d * dim + d] = 1.;
1688:     }
1689:   }
1690:   PetscFunctionReturn(PETSC_SUCCESS);
1691: }

1693: /*@C
1694:   DMPlexGetCellCoordinates - Get coordinates for a cell, taking into account periodicity

1696:   Not Collective

1698:   Input Parameters:
1699: + dm   - The `DMPLEX`
1700: - cell - The cell number

1702:   Output Parameters:
1703: + isDG   - Using cellwise coordinates
1704: . Nc     - The number of coordinates
1705: . array  - The coordinate array
1706: - coords - The cell coordinates

1708:   Level: developer

1710: .seealso: `DMPLEX`, `DMPlexRestoreCellCoordinates()`, `DMGetCoordinatesLocal()`, `DMGetCellCoordinatesLocal()`
1711: @*/
1712: PetscErrorCode DMPlexGetCellCoordinates(DM dm, PetscInt cell, PetscBool *isDG, PetscInt *Nc, const PetscScalar *array[], PetscScalar *coords[])
1713: {
1714:   DM                 cdm;
1715:   Vec                coordinates;
1716:   PetscSection       cs;
1717:   const PetscScalar *ccoords;
1718:   PetscInt           pStart, pEnd;

1720:   PetscFunctionBeginHot;
1721:   *isDG   = PETSC_FALSE;
1722:   *Nc     = 0;
1723:   *array  = NULL;
1724:   *coords = NULL;
1725:   /* Check for cellwise coordinates */
1726:   PetscCall(DMGetCellCoordinateSection(dm, &cs));
1727:   if (!cs) goto cg;
1728:   /* Check that the cell exists in the cellwise section */
1729:   PetscCall(PetscSectionGetChart(cs, &pStart, &pEnd));
1730:   if (cell < pStart || cell >= pEnd) goto cg;
1731:   /* Check for cellwise coordinates for this cell */
1732:   PetscCall(PetscSectionGetDof(cs, cell, Nc));
1733:   if (!*Nc) goto cg;
1734:   /* Check for cellwise coordinates */
1735:   PetscCall(DMGetCellCoordinatesLocalNoncollective(dm, &coordinates));
1736:   if (!coordinates) goto cg;
1737:   /* Get cellwise coordinates */
1738:   PetscCall(DMGetCellCoordinateDM(dm, &cdm));
1739:   PetscCall(VecGetArrayRead(coordinates, array));
1740:   PetscCall(DMPlexPointLocalRead(cdm, cell, *array, &ccoords));
1741:   PetscCall(DMGetWorkArray(cdm, *Nc, MPIU_SCALAR, coords));
1742:   PetscCall(PetscArraycpy(*coords, ccoords, *Nc));
1743:   PetscCall(VecRestoreArrayRead(coordinates, array));
1744:   *isDG = PETSC_TRUE;
1745:   PetscFunctionReturn(PETSC_SUCCESS);
1746: cg:
1747:   /* Use continuous coordinates */
1748:   PetscCall(DMGetCoordinateDM(dm, &cdm));
1749:   PetscCall(DMGetCoordinateSection(dm, &cs));
1750:   PetscCall(DMGetCoordinatesLocalNoncollective(dm, &coordinates));
1751:   PetscCall(DMPlexVecGetOrientedClosure_Internal(cdm, cs, PETSC_FALSE, coordinates, cell, 0, Nc, coords));
1752:   PetscFunctionReturn(PETSC_SUCCESS);
1753: }

1755: /*@C
1756:   DMPlexRestoreCellCoordinates - Get coordinates for a cell, taking into account periodicity

1758:   Not Collective

1760:   Input Parameters:
1761: + dm   - The `DMPLEX`
1762: - cell - The cell number

1764:   Output Parameters:
1765: + isDG   - Using cellwise coordinates
1766: . Nc     - The number of coordinates
1767: . array  - The coordinate array
1768: - coords - The cell coordinates

1770:   Level: developer

1772: .seealso: `DMPLEX`, `DMPlexGetCellCoordinates()`, `DMGetCoordinatesLocal()`, `DMGetCellCoordinatesLocal()`
1773: @*/
1774: PetscErrorCode DMPlexRestoreCellCoordinates(DM dm, PetscInt cell, PetscBool *isDG, PetscInt *Nc, const PetscScalar *array[], PetscScalar *coords[])
1775: {
1776:   DM           cdm;
1777:   PetscSection cs;
1778:   Vec          coordinates;

1780:   PetscFunctionBeginHot;
1781:   if (*isDG) {
1782:     PetscCall(DMGetCellCoordinateDM(dm, &cdm));
1783:     PetscCall(DMRestoreWorkArray(cdm, *Nc, MPIU_SCALAR, coords));
1784:   } else {
1785:     PetscCall(DMGetCoordinateDM(dm, &cdm));
1786:     PetscCall(DMGetCoordinateSection(dm, &cs));
1787:     PetscCall(DMGetCoordinatesLocalNoncollective(dm, &coordinates));
1788:     PetscCall(DMPlexVecRestoreClosure(cdm, cs, coordinates, cell, Nc, coords));
1789:   }
1790:   PetscFunctionReturn(PETSC_SUCCESS);
1791: }

1793: static PetscErrorCode DMPlexComputeLineGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1794: {
1795:   const PetscScalar *array;
1796:   PetscScalar       *coords = NULL;
1797:   PetscInt           numCoords, d;
1798:   PetscBool          isDG;

1800:   PetscFunctionBegin;
1801:   PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
1802:   PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
1803:   *detJ = 0.0;
1804:   if (numCoords == 6) {
1805:     const PetscInt dim = 3;
1806:     PetscReal      R[9], J0;

1808:     if (v0) {
1809:       for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
1810:     }
1811:     PetscCall(DMPlexComputeProjection3Dto1D(coords, R));
1812:     if (J) {
1813:       J0   = 0.5 * PetscRealPart(coords[1]);
1814:       J[0] = R[0] * J0;
1815:       J[1] = R[1];
1816:       J[2] = R[2];
1817:       J[3] = R[3] * J0;
1818:       J[4] = R[4];
1819:       J[5] = R[5];
1820:       J[6] = R[6] * J0;
1821:       J[7] = R[7];
1822:       J[8] = R[8];
1823:       DMPlex_Det3D_Internal(detJ, J);
1824:       if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
1825:     }
1826:   } else if (numCoords == 4) {
1827:     const PetscInt dim = 2;
1828:     PetscReal      R[4], J0;

1830:     if (v0) {
1831:       for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
1832:     }
1833:     PetscCall(DMPlexComputeProjection2Dto1D(coords, R));
1834:     if (J) {
1835:       J0   = 0.5 * PetscRealPart(coords[1]);
1836:       J[0] = R[0] * J0;
1837:       J[1] = R[1];
1838:       J[2] = R[2] * J0;
1839:       J[3] = R[3];
1840:       DMPlex_Det2D_Internal(detJ, J);
1841:       if (invJ) DMPlex_Invert2D_Internal(invJ, J, *detJ);
1842:     }
1843:   } else if (numCoords == 2) {
1844:     const PetscInt dim = 1;

1846:     if (v0) {
1847:       for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
1848:     }
1849:     if (J) {
1850:       J[0]  = 0.5 * (PetscRealPart(coords[1]) - PetscRealPart(coords[0]));
1851:       *detJ = J[0];
1852:       PetscCall(PetscLogFlops(2.0));
1853:       if (invJ) {
1854:         invJ[0] = 1.0 / J[0];
1855:         PetscCall(PetscLogFlops(1.0));
1856:       }
1857:     }
1858:   } 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);
1859:   PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
1860:   PetscFunctionReturn(PETSC_SUCCESS);
1861: }

1863: static PetscErrorCode DMPlexComputeTriangleGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1864: {
1865:   const PetscScalar *array;
1866:   PetscScalar       *coords = NULL;
1867:   PetscInt           numCoords, d;
1868:   PetscBool          isDG;

1870:   PetscFunctionBegin;
1871:   PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
1872:   PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
1873:   *detJ = 0.0;
1874:   if (numCoords == 9) {
1875:     const PetscInt dim = 3;
1876:     PetscReal      R[9], J0[9] = {1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0};

1878:     if (v0) {
1879:       for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
1880:     }
1881:     PetscCall(DMPlexComputeProjection3Dto2D(numCoords, coords, R));
1882:     if (J) {
1883:       const PetscInt pdim = 2;

1885:       for (d = 0; d < pdim; d++) {
1886:         for (PetscInt f = 0; f < pdim; f++) J0[d * dim + f] = 0.5 * (PetscRealPart(coords[(f + 1) * pdim + d]) - PetscRealPart(coords[0 * pdim + d]));
1887:       }
1888:       PetscCall(PetscLogFlops(8.0));
1889:       DMPlex_Det3D_Internal(detJ, J0);
1890:       for (d = 0; d < dim; d++) {
1891:         for (PetscInt f = 0; f < dim; f++) {
1892:           J[d * dim + f] = 0.0;
1893:           for (PetscInt g = 0; g < dim; g++) J[d * dim + f] += R[d * dim + g] * J0[g * dim + f];
1894:         }
1895:       }
1896:       PetscCall(PetscLogFlops(18.0));
1897:     }
1898:     if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
1899:   } else if (numCoords == 6) {
1900:     const PetscInt dim = 2;

1902:     if (v0) {
1903:       for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
1904:     }
1905:     if (J) {
1906:       for (d = 0; d < dim; d++) {
1907:         for (PetscInt f = 0; f < dim; f++) J[d * dim + f] = 0.5 * (PetscRealPart(coords[(f + 1) * dim + d]) - PetscRealPart(coords[0 * dim + d]));
1908:       }
1909:       PetscCall(PetscLogFlops(8.0));
1910:       DMPlex_Det2D_Internal(detJ, J);
1911:     }
1912:     if (invJ) DMPlex_Invert2D_Internal(invJ, J, *detJ);
1913:   } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this triangle is %" PetscInt_FMT " != 6 or 9", numCoords);
1914:   PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
1915:   PetscFunctionReturn(PETSC_SUCCESS);
1916: }

1918: static PetscErrorCode DMPlexComputeRectangleGeometry_Internal(DM dm, PetscInt e, PetscBool isTensor, PetscInt Nq, const PetscReal points[], PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1919: {
1920:   const PetscScalar *array;
1921:   PetscScalar       *coords = NULL;
1922:   PetscInt           numCoords, d;
1923:   PetscBool          isDG;

1925:   PetscFunctionBegin;
1926:   PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
1927:   PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
1928:   if (!Nq) {
1929:     PetscInt vorder[4] = {0, 1, 2, 3};

1931:     if (isTensor) {
1932:       vorder[2] = 3;
1933:       vorder[3] = 2;
1934:     }
1935:     *detJ = 0.0;
1936:     if (numCoords == 12) {
1937:       const PetscInt dim = 3;
1938:       PetscReal      R[9], J0[9] = {1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0};

1940:       if (v) {
1941:         for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);
1942:       }
1943:       PetscCall(DMPlexComputeProjection3Dto2D(numCoords, coords, R));
1944:       if (J) {
1945:         const PetscInt pdim = 2;

1947:         for (d = 0; d < pdim; d++) {
1948:           J0[d * dim + 0] = 0.5 * (PetscRealPart(coords[vorder[1] * pdim + d]) - PetscRealPart(coords[vorder[0] * pdim + d]));
1949:           J0[d * dim + 1] = 0.5 * (PetscRealPart(coords[vorder[2] * pdim + d]) - PetscRealPart(coords[vorder[1] * pdim + d]));
1950:         }
1951:         PetscCall(PetscLogFlops(8.0));
1952:         DMPlex_Det3D_Internal(detJ, J0);
1953:         for (d = 0; d < dim; d++) {
1954:           for (PetscInt f = 0; f < dim; f++) {
1955:             J[d * dim + f] = 0.0;
1956:             for (PetscInt g = 0; g < dim; g++) J[d * dim + f] += R[d * dim + g] * J0[g * dim + f];
1957:           }
1958:         }
1959:         PetscCall(PetscLogFlops(18.0));
1960:       }
1961:       if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
1962:     } else if (numCoords == 8) {
1963:       const PetscInt dim = 2;

1965:       if (v) {
1966:         for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);
1967:       }
1968:       if (J) {
1969:         for (d = 0; d < dim; d++) {
1970:           J[d * dim + 0] = 0.5 * (PetscRealPart(coords[vorder[1] * dim + d]) - PetscRealPart(coords[vorder[0] * dim + d]));
1971:           J[d * dim + 1] = 0.5 * (PetscRealPart(coords[vorder[3] * dim + d]) - PetscRealPart(coords[vorder[0] * dim + d]));
1972:         }
1973:         PetscCall(PetscLogFlops(8.0));
1974:         DMPlex_Det2D_Internal(detJ, J);
1975:       }
1976:       if (invJ) DMPlex_Invert2D_Internal(invJ, J, *detJ);
1977:     } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this quadrilateral is %" PetscInt_FMT " != 8 or 12", numCoords);
1978:   } else {
1979:     const PetscInt Nv         = 4;
1980:     const PetscInt dimR       = 2;
1981:     PetscInt       zToPlex[4] = {0, 1, 3, 2};
1982:     PetscReal      zOrder[12];
1983:     PetscReal      zCoeff[12];
1984:     PetscInt       i, j, k, l, dim;

1986:     if (isTensor) {
1987:       zToPlex[2] = 2;
1988:       zToPlex[3] = 3;
1989:     }
1990:     if (numCoords == 12) {
1991:       dim = 3;
1992:     } else if (numCoords == 8) {
1993:       dim = 2;
1994:     } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this quadrilateral is %" PetscInt_FMT " != 8 or 12", numCoords);
1995:     for (i = 0; i < Nv; i++) {
1996:       PetscInt zi = zToPlex[i];

1998:       for (j = 0; j < dim; j++) zOrder[dim * i + j] = PetscRealPart(coords[dim * zi + j]);
1999:     }
2000:     for (j = 0; j < dim; j++) {
2001:       /* Nodal basis for evaluation at the vertices: (1 \mp xi) (1 \mp eta):
2002:            \phi^0 = (1 - xi - eta + xi eta) --> 1      = 1/4 ( \phi^0 + \phi^1 + \phi^2 + \phi^3)
2003:            \phi^1 = (1 + xi - eta - xi eta) --> xi     = 1/4 (-\phi^0 + \phi^1 - \phi^2 + \phi^3)
2004:            \phi^2 = (1 - xi + eta - xi eta) --> eta    = 1/4 (-\phi^0 - \phi^1 + \phi^2 + \phi^3)
2005:            \phi^3 = (1 + xi + eta + xi eta) --> xi eta = 1/4 ( \phi^0 - \phi^1 - \phi^2 + \phi^3)
2006:       */
2007:       zCoeff[dim * 0 + j] = 0.25 * (zOrder[dim * 0 + j] + zOrder[dim * 1 + j] + zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
2008:       zCoeff[dim * 1 + j] = 0.25 * (-zOrder[dim * 0 + j] + zOrder[dim * 1 + j] - zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
2009:       zCoeff[dim * 2 + j] = 0.25 * (-zOrder[dim * 0 + j] - zOrder[dim * 1 + j] + zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
2010:       zCoeff[dim * 3 + j] = 0.25 * (zOrder[dim * 0 + j] - zOrder[dim * 1 + j] - zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
2011:     }
2012:     for (i = 0; i < Nq; i++) {
2013:       PetscReal xi = points[dimR * i], eta = points[dimR * i + 1];

2015:       if (v) {
2016:         PetscReal extPoint[4];

2018:         extPoint[0] = 1.;
2019:         extPoint[1] = xi;
2020:         extPoint[2] = eta;
2021:         extPoint[3] = xi * eta;
2022:         for (j = 0; j < dim; j++) {
2023:           PetscReal val = 0.;

2025:           for (k = 0; k < Nv; k++) val += extPoint[k] * zCoeff[dim * k + j];
2026:           v[i * dim + j] = val;
2027:         }
2028:       }
2029:       if (J) {
2030:         PetscReal extJ[8];

2032:         extJ[0] = 0.;
2033:         extJ[1] = 0.;
2034:         extJ[2] = 1.;
2035:         extJ[3] = 0.;
2036:         extJ[4] = 0.;
2037:         extJ[5] = 1.;
2038:         extJ[6] = eta;
2039:         extJ[7] = xi;
2040:         for (j = 0; j < dim; j++) {
2041:           for (k = 0; k < dimR; k++) {
2042:             PetscReal val = 0.;

2044:             for (l = 0; l < Nv; l++) val += zCoeff[dim * l + j] * extJ[dimR * l + k];
2045:             J[i * dim * dim + dim * j + k] = val;
2046:           }
2047:         }
2048:         if (dim == 3) { /* put the cross product in the third component of the Jacobian */
2049:           PetscReal  x, y, z;
2050:           PetscReal *iJ = &J[i * dim * dim];
2051:           PetscReal  norm;

2053:           x     = iJ[1 * dim + 0] * iJ[2 * dim + 1] - iJ[1 * dim + 1] * iJ[2 * dim + 0];
2054:           y     = iJ[0 * dim + 1] * iJ[2 * dim + 0] - iJ[0 * dim + 0] * iJ[2 * dim + 1];
2055:           z     = iJ[0 * dim + 0] * iJ[1 * dim + 1] - iJ[0 * dim + 1] * iJ[1 * dim + 0];
2056:           norm  = PetscSqrtReal(x * x + y * y + z * z);
2057:           iJ[2] = x / norm;
2058:           iJ[5] = y / norm;
2059:           iJ[8] = z / norm;
2060:           DMPlex_Det3D_Internal(&detJ[i], &J[i * dim * dim]);
2061:           if (invJ) DMPlex_Invert3D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);
2062:         } else {
2063:           DMPlex_Det2D_Internal(&detJ[i], &J[i * dim * dim]);
2064:           if (invJ) DMPlex_Invert2D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);
2065:         }
2066:       }
2067:     }
2068:   }
2069:   PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
2070:   PetscFunctionReturn(PETSC_SUCCESS);
2071: }

2073: static PetscErrorCode DMPlexComputeTetrahedronGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
2074: {
2075:   const PetscScalar *array;
2076:   PetscScalar       *coords = NULL;
2077:   const PetscInt     dim    = 3;
2078:   PetscInt           numCoords, d;
2079:   PetscBool          isDG;

2081:   PetscFunctionBegin;
2082:   PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
2083:   PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
2084:   *detJ = 0.0;
2085:   if (v0) {
2086:     for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
2087:   }
2088:   if (J) {
2089:     for (d = 0; d < dim; d++) {
2090:       /* I orient with outward face normals */
2091:       J[d * dim + 0] = 0.5 * (PetscRealPart(coords[2 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2092:       J[d * dim + 1] = 0.5 * (PetscRealPart(coords[1 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2093:       J[d * dim + 2] = 0.5 * (PetscRealPart(coords[3 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2094:     }
2095:     PetscCall(PetscLogFlops(18.0));
2096:     DMPlex_Det3D_Internal(detJ, J);
2097:   }
2098:   if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
2099:   PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
2100:   PetscFunctionReturn(PETSC_SUCCESS);
2101: }

2103: static PetscErrorCode DMPlexComputeHexahedronGeometry_Internal(DM dm, PetscInt e, PetscInt Nq, const PetscReal points[], PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
2104: {
2105:   const PetscScalar *array;
2106:   PetscScalar       *coords = NULL;
2107:   const PetscInt     dim    = 3;
2108:   PetscInt           numCoords, d;
2109:   PetscBool          isDG;

2111:   PetscFunctionBegin;
2112:   PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
2113:   PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
2114:   if (!Nq) {
2115:     *detJ = 0.0;
2116:     if (v) {
2117:       for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);
2118:     }
2119:     if (J) {
2120:       for (d = 0; d < dim; d++) {
2121:         J[d * dim + 0] = 0.5 * (PetscRealPart(coords[3 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2122:         J[d * dim + 1] = 0.5 * (PetscRealPart(coords[1 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2123:         J[d * dim + 2] = 0.5 * (PetscRealPart(coords[4 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2124:       }
2125:       PetscCall(PetscLogFlops(18.0));
2126:       DMPlex_Det3D_Internal(detJ, J);
2127:     }
2128:     if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
2129:   } else {
2130:     const PetscInt Nv         = 8;
2131:     const PetscInt zToPlex[8] = {0, 3, 1, 2, 4, 5, 7, 6};
2132:     const PetscInt dim        = 3;
2133:     const PetscInt dimR       = 3;
2134:     PetscReal      zOrder[24];
2135:     PetscReal      zCoeff[24];
2136:     PetscInt       i, j, k, l;

2138:     for (i = 0; i < Nv; i++) {
2139:       PetscInt zi = zToPlex[i];

2141:       for (j = 0; j < dim; j++) zOrder[dim * i + j] = PetscRealPart(coords[dim * zi + j]);
2142:     }
2143:     for (j = 0; j < dim; j++) {
2144:       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]);
2145:       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]);
2146:       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]);
2147:       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]);
2148:       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]);
2149:       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]);
2150:       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]);
2151:       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]);
2152:     }
2153:     for (i = 0; i < Nq; i++) {
2154:       PetscReal xi = points[dimR * i], eta = points[dimR * i + 1], theta = points[dimR * i + 2];

2156:       if (v) {
2157:         PetscReal extPoint[8];

2159:         extPoint[0] = 1.;
2160:         extPoint[1] = xi;
2161:         extPoint[2] = eta;
2162:         extPoint[3] = xi * eta;
2163:         extPoint[4] = theta;
2164:         extPoint[5] = theta * xi;
2165:         extPoint[6] = theta * eta;
2166:         extPoint[7] = theta * eta * xi;
2167:         for (j = 0; j < dim; j++) {
2168:           PetscReal val = 0.;

2170:           for (k = 0; k < Nv; k++) val += extPoint[k] * zCoeff[dim * k + j];
2171:           v[i * dim + j] = val;
2172:         }
2173:       }
2174:       if (J) {
2175:         PetscReal extJ[24];

2177:         extJ[0]  = 0.;
2178:         extJ[1]  = 0.;
2179:         extJ[2]  = 0.;
2180:         extJ[3]  = 1.;
2181:         extJ[4]  = 0.;
2182:         extJ[5]  = 0.;
2183:         extJ[6]  = 0.;
2184:         extJ[7]  = 1.;
2185:         extJ[8]  = 0.;
2186:         extJ[9]  = eta;
2187:         extJ[10] = xi;
2188:         extJ[11] = 0.;
2189:         extJ[12] = 0.;
2190:         extJ[13] = 0.;
2191:         extJ[14] = 1.;
2192:         extJ[15] = theta;
2193:         extJ[16] = 0.;
2194:         extJ[17] = xi;
2195:         extJ[18] = 0.;
2196:         extJ[19] = theta;
2197:         extJ[20] = eta;
2198:         extJ[21] = theta * eta;
2199:         extJ[22] = theta * xi;
2200:         extJ[23] = eta * xi;

2202:         for (j = 0; j < dim; j++) {
2203:           for (k = 0; k < dimR; k++) {
2204:             PetscReal val = 0.;

2206:             for (l = 0; l < Nv; l++) val += zCoeff[dim * l + j] * extJ[dimR * l + k];
2207:             J[i * dim * dim + dim * j + k] = val;
2208:           }
2209:         }
2210:         DMPlex_Det3D_Internal(&detJ[i], &J[i * dim * dim]);
2211:         if (invJ) DMPlex_Invert3D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);
2212:       }
2213:     }
2214:   }
2215:   PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
2216:   PetscFunctionReturn(PETSC_SUCCESS);
2217: }

2219: static PetscErrorCode DMPlexComputeTriangularPrismGeometry_Internal(DM dm, PetscInt e, PetscInt Nq, const PetscReal points[], PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
2220: {
2221:   const PetscScalar *array;
2222:   PetscScalar       *coords = NULL;
2223:   const PetscInt     dim    = 3;
2224:   PetscInt           numCoords, d;
2225:   PetscBool          isDG;

2227:   PetscFunctionBegin;
2228:   PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
2229:   PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
2230:   if (!Nq) {
2231:     /* Assume that the map to the reference is affine */
2232:     *detJ = 0.0;
2233:     if (v) {
2234:       for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);
2235:     }
2236:     if (J) {
2237:       for (d = 0; d < dim; d++) {
2238:         J[d * dim + 0] = 0.5 * (PetscRealPart(coords[2 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2239:         J[d * dim + 1] = 0.5 * (PetscRealPart(coords[1 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2240:         J[d * dim + 2] = 0.5 * (PetscRealPart(coords[4 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2241:       }
2242:       PetscCall(PetscLogFlops(18.0));
2243:       DMPlex_Det3D_Internal(detJ, J);
2244:     }
2245:     if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
2246:   } else {
2247:     const PetscInt dim  = 3;
2248:     const PetscInt dimR = 3;
2249:     const PetscInt Nv   = 6;
2250:     PetscReal      verts[18];
2251:     PetscReal      coeff[18];
2252:     PetscInt       i, j, k, l;

2254:     for (i = 0; i < Nv; ++i)
2255:       for (j = 0; j < dim; ++j) verts[dim * i + j] = PetscRealPart(coords[dim * i + j]);
2256:     for (j = 0; j < dim; ++j) {
2257:       /* Check for triangle,
2258:            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)
2259:            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)
2260:            phi^2 =  1/2 (1 + eta)   chi^2 = delta(-1,  1)

2262:            phi^0 + phi^1 + phi^2 = 1    coef_1   = 1/2 (         chi^1 + chi^2)
2263:           -phi^0 + phi^1 - phi^2 = xi   coef_xi  = 1/2 (-chi^0 + chi^1)
2264:           -phi^0 - phi^1 + phi^2 = eta  coef_eta = 1/2 (-chi^0         + chi^2)

2266:           < chi_0 chi_1 chi_2> A /  1  1  1 \ / phi_0 \   <chi> I <phi>^T  so we need the inverse transpose
2267:                                  | -1  1 -1 | | phi_1 | =
2268:                                  \ -1 -1  1 / \ phi_2 /

2270:           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
2271:       */
2272:       /* Nodal basis for evaluation at the vertices: {-xi - eta, 1 + xi, 1 + eta} (1 \mp zeta):
2273:            \phi^0 = 1/4 (   -xi - eta        + xi zeta + eta zeta) --> /  1  1  1  1  1  1 \ 1
2274:            \phi^1 = 1/4 (1      + eta - zeta           - eta zeta) --> | -1  1 -1 -1 -1  1 | eta
2275:            \phi^2 = 1/4 (1 + xi       - zeta - xi zeta)            --> | -1 -1  1 -1  1 -1 | xi
2276:            \phi^3 = 1/4 (   -xi - eta        - xi zeta - eta zeta) --> | -1 -1 -1  1  1  1 | zeta
2277:            \phi^4 = 1/4 (1 + xi       + zeta + xi zeta)            --> |  1  1 -1 -1  1 -1 | xi zeta
2278:            \phi^5 = 1/4 (1      + eta + zeta           + eta zeta) --> \  1 -1  1 -1 -1  1 / eta zeta
2279:            1/4 /  0  1  1  0  1  1 \
2280:                | -1  1  0 -1  0  1 |
2281:                | -1  0  1 -1  1  0 |
2282:                |  0 -1 -1  0  1  1 |
2283:                |  1  0 -1 -1  1  0 |
2284:                \  1 -1  0 -1  0  1 /
2285:       */
2286:       coeff[dim * 0 + j] = (1. / 4.) * (verts[dim * 1 + j] + verts[dim * 2 + j] + verts[dim * 4 + j] + verts[dim * 5 + j]);
2287:       coeff[dim * 1 + j] = (1. / 4.) * (-verts[dim * 0 + j] + verts[dim * 1 + j] - verts[dim * 3 + j] + verts[dim * 5 + j]);
2288:       coeff[dim * 2 + j] = (1. / 4.) * (-verts[dim * 0 + j] + verts[dim * 2 + j] - verts[dim * 3 + j] + verts[dim * 4 + j]);
2289:       coeff[dim * 3 + j] = (1. / 4.) * (-verts[dim * 1 + j] - verts[dim * 2 + j] + verts[dim * 4 + j] + verts[dim * 5 + j]);
2290:       coeff[dim * 4 + j] = (1. / 4.) * (verts[dim * 0 + j] - verts[dim * 2 + j] - verts[dim * 3 + j] + verts[dim * 4 + j]);
2291:       coeff[dim * 5 + j] = (1. / 4.) * (verts[dim * 0 + j] - verts[dim * 1 + j] - verts[dim * 3 + j] + verts[dim * 5 + j]);
2292:       /* For reference prism:
2293:       {0, 0, 0}
2294:       {0, 1, 0}
2295:       {1, 0, 0}
2296:       {0, 0, 1}
2297:       {0, 0, 0}
2298:       {0, 0, 0}
2299:       */
2300:     }
2301:     for (i = 0; i < Nq; ++i) {
2302:       const PetscReal xi = points[dimR * i], eta = points[dimR * i + 1], zeta = points[dimR * i + 2];

2304:       if (v) {
2305:         PetscReal extPoint[6];
2306:         PetscInt  c;

2308:         extPoint[0] = 1.;
2309:         extPoint[1] = eta;
2310:         extPoint[2] = xi;
2311:         extPoint[3] = zeta;
2312:         extPoint[4] = xi * zeta;
2313:         extPoint[5] = eta * zeta;
2314:         for (c = 0; c < dim; ++c) {
2315:           PetscReal val = 0.;

2317:           for (k = 0; k < Nv; ++k) val += extPoint[k] * coeff[k * dim + c];
2318:           v[i * dim + c] = val;
2319:         }
2320:       }
2321:       if (J) {
2322:         PetscReal extJ[18];

2324:         extJ[0]  = 0.;
2325:         extJ[1]  = 0.;
2326:         extJ[2]  = 0.;
2327:         extJ[3]  = 0.;
2328:         extJ[4]  = 1.;
2329:         extJ[5]  = 0.;
2330:         extJ[6]  = 1.;
2331:         extJ[7]  = 0.;
2332:         extJ[8]  = 0.;
2333:         extJ[9]  = 0.;
2334:         extJ[10] = 0.;
2335:         extJ[11] = 1.;
2336:         extJ[12] = zeta;
2337:         extJ[13] = 0.;
2338:         extJ[14] = xi;
2339:         extJ[15] = 0.;
2340:         extJ[16] = zeta;
2341:         extJ[17] = eta;

2343:         for (j = 0; j < dim; j++) {
2344:           for (k = 0; k < dimR; k++) {
2345:             PetscReal val = 0.;

2347:             for (l = 0; l < Nv; l++) val += coeff[dim * l + j] * extJ[dimR * l + k];
2348:             J[i * dim * dim + dim * j + k] = val;
2349:           }
2350:         }
2351:         DMPlex_Det3D_Internal(&detJ[i], &J[i * dim * dim]);
2352:         if (invJ) DMPlex_Invert3D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);
2353:       }
2354:     }
2355:   }
2356:   PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
2357:   PetscFunctionReturn(PETSC_SUCCESS);
2358: }

2360: static PetscErrorCode DMPlexComputeCellGeometryFEM_Implicit(DM dm, PetscInt cell, PetscQuadrature quad, PetscReal *v, PetscReal *J, PetscReal *invJ, PetscReal *detJ)
2361: {
2362:   DMPolytopeType   ct;
2363:   PetscInt         depth, dim, coordDim, coneSize, i;
2364:   PetscInt         Nq     = 0;
2365:   const PetscReal *points = NULL;
2366:   DMLabel          depthLabel;
2367:   PetscReal        xi0[3]   = {-1., -1., -1.}, v0[3], J0[9], detJ0;
2368:   PetscBool        isAffine = PETSC_TRUE;

2370:   PetscFunctionBegin;
2371:   PetscCall(DMPlexGetDepth(dm, &depth));
2372:   PetscCall(DMPlexGetConeSize(dm, cell, &coneSize));
2373:   PetscCall(DMPlexGetDepthLabel(dm, &depthLabel));
2374:   PetscCall(DMLabelGetValue(depthLabel, cell, &dim));
2375:   if (depth == 1 && dim == 1) PetscCall(DMGetDimension(dm, &dim));
2376:   PetscCall(DMGetCoordinateDim(dm, &coordDim));
2377:   PetscCheck(coordDim <= 3, PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported coordinate dimension %" PetscInt_FMT " > 3", coordDim);
2378:   if (quad) PetscCall(PetscQuadratureGetData(quad, NULL, NULL, &Nq, &points, NULL));
2379:   PetscCall(DMPlexGetCellType(dm, cell, &ct));
2380:   switch (ct) {
2381:   case DM_POLYTOPE_POINT:
2382:     PetscCall(DMPlexComputePointGeometry_Internal(dm, cell, v, J, invJ, detJ));
2383:     isAffine = PETSC_FALSE;
2384:     break;
2385:   case DM_POLYTOPE_SEGMENT:
2386:   case DM_POLYTOPE_POINT_PRISM_TENSOR:
2387:     if (Nq) PetscCall(DMPlexComputeLineGeometry_Internal(dm, cell, v0, J0, NULL, &detJ0));
2388:     else PetscCall(DMPlexComputeLineGeometry_Internal(dm, cell, v, J, invJ, detJ));
2389:     break;
2390:   case DM_POLYTOPE_TRIANGLE:
2391:     if (Nq) PetscCall(DMPlexComputeTriangleGeometry_Internal(dm, cell, v0, J0, NULL, &detJ0));
2392:     else PetscCall(DMPlexComputeTriangleGeometry_Internal(dm, cell, v, J, invJ, detJ));
2393:     break;
2394:   case DM_POLYTOPE_QUADRILATERAL:
2395:     PetscCall(DMPlexComputeRectangleGeometry_Internal(dm, cell, PETSC_FALSE, Nq, points, v, J, invJ, detJ));
2396:     isAffine = PETSC_FALSE;
2397:     break;
2398:   case DM_POLYTOPE_SEG_PRISM_TENSOR:
2399:     PetscCall(DMPlexComputeRectangleGeometry_Internal(dm, cell, PETSC_TRUE, Nq, points, v, J, invJ, detJ));
2400:     isAffine = PETSC_FALSE;
2401:     break;
2402:   case DM_POLYTOPE_TETRAHEDRON:
2403:     if (Nq) PetscCall(DMPlexComputeTetrahedronGeometry_Internal(dm, cell, v0, J0, NULL, &detJ0));
2404:     else PetscCall(DMPlexComputeTetrahedronGeometry_Internal(dm, cell, v, J, invJ, detJ));
2405:     break;
2406:   case DM_POLYTOPE_HEXAHEDRON:
2407:     PetscCall(DMPlexComputeHexahedronGeometry_Internal(dm, cell, Nq, points, v, J, invJ, detJ));
2408:     isAffine = PETSC_FALSE;
2409:     break;
2410:   case DM_POLYTOPE_TRI_PRISM:
2411:     PetscCall(DMPlexComputeTriangularPrismGeometry_Internal(dm, cell, Nq, points, v, J, invJ, detJ));
2412:     isAffine = PETSC_FALSE;
2413:     break;
2414:   default:
2415:     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))]);
2416:   }
2417:   if (isAffine && Nq) {
2418:     if (v) {
2419:       for (i = 0; i < Nq; i++) CoordinatesRefToReal(coordDim, dim, xi0, v0, J0, &points[dim * i], &v[coordDim * i]);
2420:     }
2421:     if (detJ) {
2422:       for (i = 0; i < Nq; i++) detJ[i] = detJ0;
2423:     }
2424:     if (J) {
2425:       PetscInt k;

2427:       for (i = 0, k = 0; i < Nq; i++) {
2428:         PetscInt j;

2430:         for (j = 0; j < coordDim * coordDim; j++, k++) J[k] = J0[j];
2431:       }
2432:     }
2433:     if (invJ) {
2434:       PetscInt k;
2435:       switch (coordDim) {
2436:       case 0:
2437:         break;
2438:       case 1:
2439:         invJ[0] = 1. / J0[0];
2440:         break;
2441:       case 2:
2442:         DMPlex_Invert2D_Internal(invJ, J0, detJ0);
2443:         break;
2444:       case 3:
2445:         DMPlex_Invert3D_Internal(invJ, J0, detJ0);
2446:         break;
2447:       }
2448:       for (i = 1, k = coordDim * coordDim; i < Nq; i++) {
2449:         PetscInt j;

2451:         for (j = 0; j < coordDim * coordDim; j++, k++) invJ[k] = invJ[j];
2452:       }
2453:     }
2454:   }
2455:   PetscFunctionReturn(PETSC_SUCCESS);
2456: }

2458: /*@C
2459:   DMPlexComputeCellGeometryAffineFEM - Assuming an affine map, compute the Jacobian, inverse Jacobian, and Jacobian determinant for a given cell

2461:   Collective

2463:   Input Parameters:
2464: + dm   - the `DMPLEX`
2465: - cell - the cell

2467:   Output Parameters:
2468: + v0   - the translation part of this affine transform, meaning the translation to the origin (not the first vertex of the reference cell)
2469: . J    - the Jacobian of the transform from the reference element
2470: . invJ - the inverse of the Jacobian
2471: - detJ - the Jacobian determinant

2473:   Level: advanced

2475: .seealso: `DMPLEX`, `DMPlexComputeCellGeometryFEM()`, `DMGetCoordinateSection()`, `DMGetCoordinates()`
2476: @*/
2477: PetscErrorCode DMPlexComputeCellGeometryAffineFEM(DM dm, PetscInt cell, PetscReal *v0, PetscReal *J, PetscReal *invJ, PetscReal *detJ)
2478: {
2479:   PetscFunctionBegin;
2480:   PetscCall(DMPlexComputeCellGeometryFEM_Implicit(dm, cell, NULL, v0, J, invJ, detJ));
2481:   PetscFunctionReturn(PETSC_SUCCESS);
2482: }

2484: static PetscErrorCode DMPlexComputeCellGeometryFEM_FE(DM dm, PetscFE fe, PetscInt point, PetscQuadrature quad, PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
2485: {
2486:   const PetscScalar *array;
2487:   PetscScalar       *coords = NULL;
2488:   PetscInt           numCoords;
2489:   PetscBool          isDG;
2490:   PetscQuadrature    feQuad;
2491:   const PetscReal   *quadPoints;
2492:   PetscTabulation    T;
2493:   PetscInt           dim, cdim, pdim, qdim, Nq, q;

2495:   PetscFunctionBegin;
2496:   PetscCall(DMGetDimension(dm, &dim));
2497:   PetscCall(DMGetCoordinateDim(dm, &cdim));
2498:   PetscCall(DMPlexGetCellCoordinates(dm, point, &isDG, &numCoords, &array, &coords));
2499:   if (!quad) { /* use the first point of the first functional of the dual space */
2500:     PetscDualSpace dsp;

2502:     PetscCall(PetscFEGetDualSpace(fe, &dsp));
2503:     PetscCall(PetscDualSpaceGetFunctional(dsp, 0, &quad));
2504:     PetscCall(PetscQuadratureGetData(quad, &qdim, NULL, &Nq, &quadPoints, NULL));
2505:     Nq = 1;
2506:   } else {
2507:     PetscCall(PetscQuadratureGetData(quad, &qdim, NULL, &Nq, &quadPoints, NULL));
2508:   }
2509:   PetscCall(PetscFEGetDimension(fe, &pdim));
2510:   PetscCall(PetscFEGetQuadrature(fe, &feQuad));
2511:   if (feQuad == quad) {
2512:     PetscCall(PetscFEGetCellTabulation(fe, J ? 1 : 0, &T));
2513:     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);
2514:   } else {
2515:     PetscCall(PetscFECreateTabulation(fe, 1, Nq, quadPoints, J ? 1 : 0, &T));
2516:   }
2517:   PetscCheck(qdim == dim, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Point dimension %" PetscInt_FMT " != quadrature dimension %" PetscInt_FMT, dim, qdim);
2518:   {
2519:     const PetscReal *basis    = T->T[0];
2520:     const PetscReal *basisDer = T->T[1];
2521:     PetscReal        detJt;

2523:     PetscAssert(Nq == T->Np, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Np %" PetscInt_FMT " != %" PetscInt_FMT, Nq, T->Np);
2524:     PetscAssert(pdim == T->Nb, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Nb %" PetscInt_FMT " != %" PetscInt_FMT, pdim, T->Nb);
2525:     PetscAssert(dim == T->Nc, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Nc %" PetscInt_FMT " != %" PetscInt_FMT, dim, T->Nc);
2526:     PetscAssert(cdim == T->cdim, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "cdim %" PetscInt_FMT " != %" PetscInt_FMT, cdim, T->cdim);
2527:     if (v) {
2528:       PetscCall(PetscArrayzero(v, Nq * cdim));
2529:       for (q = 0; q < Nq; ++q) {
2530:         PetscInt i, k;

2532:         for (k = 0; k < pdim; ++k) {
2533:           const PetscInt vertex = k / cdim;
2534:           for (i = 0; i < cdim; ++i) v[q * cdim + i] += basis[(q * pdim + k) * cdim + i] * PetscRealPart(coords[vertex * cdim + i]);
2535:         }
2536:         PetscCall(PetscLogFlops(2.0 * pdim * cdim));
2537:       }
2538:     }
2539:     if (J) {
2540:       PetscCall(PetscArrayzero(J, Nq * cdim * cdim));
2541:       for (q = 0; q < Nq; ++q) {
2542:         PetscInt i, j, k, c, r;

2544:         /* J = dx_i/d\xi_j = sum[k=0,n-1] dN_k/d\xi_j * x_i(k) */
2545:         for (k = 0; k < pdim; ++k) {
2546:           const PetscInt vertex = k / cdim;
2547:           for (j = 0; j < dim; ++j) {
2548:             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]);
2549:           }
2550:         }
2551:         PetscCall(PetscLogFlops(2.0 * pdim * dim * cdim));
2552:         if (cdim > dim) {
2553:           for (c = dim; c < cdim; ++c)
2554:             for (r = 0; r < cdim; ++r) J[r * cdim + c] = r == c ? 1.0 : 0.0;
2555:         }
2556:         if (!detJ && !invJ) continue;
2557:         detJt = 0.;
2558:         switch (cdim) {
2559:         case 3:
2560:           DMPlex_Det3D_Internal(&detJt, &J[q * cdim * dim]);
2561:           if (invJ) DMPlex_Invert3D_Internal(&invJ[q * cdim * dim], &J[q * cdim * dim], detJt);
2562:           break;
2563:         case 2:
2564:           DMPlex_Det2D_Internal(&detJt, &J[q * cdim * dim]);
2565:           if (invJ) DMPlex_Invert2D_Internal(&invJ[q * cdim * dim], &J[q * cdim * dim], detJt);
2566:           break;
2567:         case 1:
2568:           detJt = J[q * cdim * dim];
2569:           if (invJ) invJ[q * cdim * dim] = 1.0 / detJt;
2570:         }
2571:         if (detJ) detJ[q] = detJt;
2572:       }
2573:     } else PetscCheck(!detJ && !invJ, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Need J to compute invJ or detJ");
2574:   }
2575:   if (feQuad != quad) PetscCall(PetscTabulationDestroy(&T));
2576:   PetscCall(DMPlexRestoreCellCoordinates(dm, point, &isDG, &numCoords, &array, &coords));
2577:   PetscFunctionReturn(PETSC_SUCCESS);
2578: }

2580: /*@C
2581:   DMPlexComputeCellGeometryFEM - Compute the Jacobian, inverse Jacobian, and Jacobian determinant at each quadrature point in the given cell

2583:   Collective

2585:   Input Parameters:
2586: + dm   - the `DMPLEX`
2587: . cell - the cell
2588: - quad - the quadrature containing the points in the reference element where the geometry will be evaluated.  If `quad` is `NULL`, geometry will be
2589:          evaluated at the first vertex of the reference element

2591:   Output Parameters:
2592: + v    - the image of the transformed quadrature points, otherwise the image of the first vertex in the closure of the reference element
2593: . J    - the Jacobian of the transform from the reference element at each quadrature point
2594: . invJ - the inverse of the Jacobian at each quadrature point
2595: - detJ - the Jacobian determinant at each quadrature point

2597:   Level: advanced

2599: .seealso: `DMPLEX`, `DMGetCoordinateSection()`, `DMGetCoordinates()`
2600: @*/
2601: PetscErrorCode DMPlexComputeCellGeometryFEM(DM dm, PetscInt cell, PetscQuadrature quad, PetscReal *v, PetscReal *J, PetscReal *invJ, PetscReal *detJ)
2602: {
2603:   DM      cdm;
2604:   PetscFE fe = NULL;

2606:   PetscFunctionBegin;
2607:   PetscAssertPointer(detJ, 7);
2608:   PetscCall(DMGetCoordinateDM(dm, &cdm));
2609:   if (cdm) {
2610:     PetscClassId id;
2611:     PetscInt     numFields;
2612:     PetscDS      prob;
2613:     PetscObject  disc;

2615:     PetscCall(DMGetNumFields(cdm, &numFields));
2616:     if (numFields) {
2617:       PetscCall(DMGetDS(cdm, &prob));
2618:       PetscCall(PetscDSGetDiscretization(prob, 0, &disc));
2619:       PetscCall(PetscObjectGetClassId(disc, &id));
2620:       if (id == PETSCFE_CLASSID) fe = (PetscFE)disc;
2621:     }
2622:   }
2623:   if (!fe) PetscCall(DMPlexComputeCellGeometryFEM_Implicit(dm, cell, quad, v, J, invJ, detJ));
2624:   else PetscCall(DMPlexComputeCellGeometryFEM_FE(dm, fe, cell, quad, v, J, invJ, detJ));
2625:   PetscFunctionReturn(PETSC_SUCCESS);
2626: }

2628: static PetscErrorCode DMPlexComputeGeometryFVM_0D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
2629: {
2630:   PetscSection       coordSection;
2631:   Vec                coordinates;
2632:   const PetscScalar *coords = NULL;
2633:   PetscInt           d, dof, off;

2635:   PetscFunctionBegin;
2636:   PetscCall(DMGetCoordinatesLocal(dm, &coordinates));
2637:   PetscCall(DMGetCoordinateSection(dm, &coordSection));
2638:   PetscCall(VecGetArrayRead(coordinates, &coords));

2640:   /* for a point the centroid is just the coord */
2641:   if (centroid) {
2642:     PetscCall(PetscSectionGetDof(coordSection, cell, &dof));
2643:     PetscCall(PetscSectionGetOffset(coordSection, cell, &off));
2644:     for (d = 0; d < dof; d++) centroid[d] = PetscRealPart(coords[off + d]);
2645:   }
2646:   if (normal) {
2647:     const PetscInt *support, *cones;
2648:     PetscInt        supportSize;
2649:     PetscReal       norm, sign;

2651:     /* compute the norm based upon the support centroids */
2652:     PetscCall(DMPlexGetSupportSize(dm, cell, &supportSize));
2653:     PetscCall(DMPlexGetSupport(dm, cell, &support));
2654:     PetscCall(DMPlexComputeCellGeometryFVM(dm, support[0], NULL, normal, NULL));

2656:     /* Take the normal from the centroid of the support to the vertex*/
2657:     PetscCall(PetscSectionGetDof(coordSection, cell, &dof));
2658:     PetscCall(PetscSectionGetOffset(coordSection, cell, &off));
2659:     for (d = 0; d < dof; d++) normal[d] -= PetscRealPart(coords[off + d]);

2661:     /* Determine the sign of the normal based upon its location in the support */
2662:     PetscCall(DMPlexGetCone(dm, support[0], &cones));
2663:     sign = cones[0] == cell ? 1.0 : -1.0;

2665:     norm = DMPlex_NormD_Internal(dim, normal);
2666:     for (d = 0; d < dim; ++d) normal[d] /= (norm * sign);
2667:   }
2668:   if (vol) *vol = 1.0;
2669:   PetscCall(VecRestoreArrayRead(coordinates, &coords));
2670:   PetscFunctionReturn(PETSC_SUCCESS);
2671: }

2673: static PetscErrorCode DMPlexComputeGeometryFVM_1D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
2674: {
2675:   const PetscScalar *array;
2676:   PetscScalar       *coords = NULL;
2677:   PetscInt           cdim, coordSize, d;
2678:   PetscBool          isDG;

2680:   PetscFunctionBegin;
2681:   PetscCall(DMGetCoordinateDim(dm, &cdim));
2682:   PetscCall(DMPlexGetCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
2683:   PetscCheck(coordSize == cdim * 2, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Edge has %" PetscInt_FMT " coordinates != %" PetscInt_FMT, coordSize, cdim * 2);
2684:   if (centroid) {
2685:     for (d = 0; d < cdim; ++d) centroid[d] = 0.5 * PetscRealPart(coords[d] + coords[cdim + d]);
2686:   }
2687:   if (normal) {
2688:     PetscReal norm;

2690:     switch (cdim) {
2691:     case 3:
2692:       normal[2] = 0.; /* fall through */
2693:     case 2:
2694:       normal[0] = -PetscRealPart(coords[1] - coords[cdim + 1]);
2695:       normal[1] = PetscRealPart(coords[0] - coords[cdim + 0]);
2696:       break;
2697:     case 1:
2698:       normal[0] = 1.0;
2699:       break;
2700:     default:
2701:       SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Dimension %" PetscInt_FMT " not supported", cdim);
2702:     }
2703:     norm = DMPlex_NormD_Internal(cdim, normal);
2704:     for (d = 0; d < cdim; ++d) normal[d] /= norm;
2705:   }
2706:   if (vol) {
2707:     *vol = 0.0;
2708:     for (d = 0; d < cdim; ++d) *vol += PetscSqr(PetscRealPart(coords[d] - coords[cdim + d]));
2709:     *vol = PetscSqrtReal(*vol);
2710:   }
2711:   PetscCall(DMPlexRestoreCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
2712:   PetscFunctionReturn(PETSC_SUCCESS);
2713: }

2715: /* Centroid_i = (\sum_n A_n Cn_i) / A */
2716: static PetscErrorCode DMPlexComputeGeometryFVM_2D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
2717: {
2718:   DMPolytopeType     ct;
2719:   const PetscScalar *array;
2720:   PetscScalar       *coords = NULL;
2721:   PetscInt           coordSize;
2722:   PetscBool          isDG;
2723:   PetscInt           fv[4] = {0, 1, 2, 3};
2724:   PetscInt           cdim, numCorners, p, d;

2726:   PetscFunctionBegin;
2727:   /* Must check for hybrid cells because prisms have a different orientation scheme */
2728:   PetscCall(DMPlexGetCellType(dm, cell, &ct));
2729:   switch (ct) {
2730:   case DM_POLYTOPE_SEG_PRISM_TENSOR:
2731:     fv[2] = 3;
2732:     fv[3] = 2;
2733:     break;
2734:   default:
2735:     break;
2736:   }
2737:   PetscCall(DMGetCoordinateDim(dm, &cdim));
2738:   PetscCall(DMPlexGetConeSize(dm, cell, &numCorners));
2739:   PetscCall(DMPlexGetCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
2740:   {
2741:     PetscReal c[3] = {0., 0., 0.}, n[3] = {0., 0., 0.}, origin[3] = {0., 0., 0.}, norm;

2743:     for (d = 0; d < cdim; d++) origin[d] = PetscRealPart(coords[d]);
2744:     for (p = 0; p < numCorners - 2; ++p) {
2745:       PetscReal e0[3] = {0., 0., 0.}, e1[3] = {0., 0., 0.};
2746:       for (d = 0; d < cdim; d++) {
2747:         e0[d] = PetscRealPart(coords[cdim * fv[p + 1] + d]) - origin[d];
2748:         e1[d] = PetscRealPart(coords[cdim * fv[p + 2] + d]) - origin[d];
2749:       }
2750:       const PetscReal dx = e0[1] * e1[2] - e0[2] * e1[1];
2751:       const PetscReal dy = e0[2] * e1[0] - e0[0] * e1[2];
2752:       const PetscReal dz = e0[0] * e1[1] - e0[1] * e1[0];
2753:       const PetscReal a  = PetscSqrtReal(dx * dx + dy * dy + dz * dz);

2755:       n[0] += dx;
2756:       n[1] += dy;
2757:       n[2] += dz;
2758:       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.;
2759:     }
2760:     norm = PetscSqrtReal(n[0] * n[0] + n[1] * n[1] + n[2] * n[2]);
2761:     // Allow zero volume cells
2762:     if (norm != 0) {
2763:       n[0] /= norm;
2764:       n[1] /= norm;
2765:       n[2] /= norm;
2766:       c[0] /= norm;
2767:       c[1] /= norm;
2768:       c[2] /= norm;
2769:     }
2770:     if (vol) *vol = 0.5 * norm;
2771:     if (centroid)
2772:       for (d = 0; d < cdim; ++d) centroid[d] = c[d];
2773:     if (normal)
2774:       for (d = 0; d < cdim; ++d) normal[d] = n[d];
2775:   }
2776:   PetscCall(DMPlexRestoreCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
2777:   PetscFunctionReturn(PETSC_SUCCESS);
2778: }

2780: /* Centroid_i = (\sum_n V_n Cn_i) / V */
2781: static PetscErrorCode DMPlexComputeGeometryFVM_3D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
2782: {
2783:   DMPolytopeType        ct;
2784:   const PetscScalar    *array;
2785:   PetscScalar          *coords = NULL;
2786:   PetscInt              coordSize;
2787:   PetscBool             isDG;
2788:   PetscReal             vsum      = 0.0, vtmp, coordsTmp[3 * 3], origin[3];
2789:   const PetscInt        order[16] = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15};
2790:   const PetscInt       *cone, *faceSizes, *faces;
2791:   const DMPolytopeType *faceTypes;
2792:   PetscBool             isHybrid = PETSC_FALSE;
2793:   PetscInt              numFaces, f, fOff = 0, p, d;

2795:   PetscFunctionBegin;
2796:   PetscCheck(dim <= 3, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "No support for dim %" PetscInt_FMT " > 3", dim);
2797:   /* Must check for hybrid cells because prisms have a different orientation scheme */
2798:   PetscCall(DMPlexGetCellType(dm, cell, &ct));
2799:   switch (ct) {
2800:   case DM_POLYTOPE_POINT_PRISM_TENSOR:
2801:   case DM_POLYTOPE_SEG_PRISM_TENSOR:
2802:   case DM_POLYTOPE_TRI_PRISM_TENSOR:
2803:   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
2804:     isHybrid = PETSC_TRUE;
2805:   default:
2806:     break;
2807:   }

2809:   if (centroid)
2810:     for (d = 0; d < dim; ++d) centroid[d] = 0.0;
2811:   PetscCall(DMPlexGetCone(dm, cell, &cone));

2813:   // Using the closure of faces for coordinates does not work in periodic geometries, so we index into the cell coordinates
2814:   PetscCall(DMPlexGetRawFaces_Internal(dm, ct, order, &numFaces, &faceTypes, &faceSizes, &faces));
2815:   PetscCall(DMPlexGetCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
2816:   for (f = 0; f < numFaces; ++f) {
2817:     PetscBool flip = isHybrid && f == 0 ? PETSC_TRUE : PETSC_FALSE; /* The first hybrid face is reversed */

2819:     // If using zero as the origin vertex for each tetrahedron, an element far from the origin will have positive and
2820:     // negative volumes that nearly cancel, thus incurring rounding error. Here we define origin[] as the first vertex
2821:     // so that all tetrahedra have positive volume.
2822:     if (f == 0)
2823:       for (d = 0; d < dim; d++) origin[d] = PetscRealPart(coords[d]);
2824:     switch (faceTypes[f]) {
2825:     case DM_POLYTOPE_TRIANGLE:
2826:       for (d = 0; d < dim; ++d) {
2827:         coordsTmp[0 * dim + d] = PetscRealPart(coords[faces[fOff + 0] * dim + d]) - origin[d];
2828:         coordsTmp[1 * dim + d] = PetscRealPart(coords[faces[fOff + 1] * dim + d]) - origin[d];
2829:         coordsTmp[2 * dim + d] = PetscRealPart(coords[faces[fOff + 2] * dim + d]) - origin[d];
2830:       }
2831:       Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
2832:       if (flip) vtmp = -vtmp;
2833:       vsum += vtmp;
2834:       if (centroid) { /* Centroid of OABC = (a+b+c)/4 */
2835:         for (d = 0; d < dim; ++d) {
2836:           for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p * dim + d] * vtmp;
2837:         }
2838:       }
2839:       break;
2840:     case DM_POLYTOPE_QUADRILATERAL:
2841:     case DM_POLYTOPE_SEG_PRISM_TENSOR: {
2842:       PetscInt fv[4] = {0, 1, 2, 3};

2844:       /* Side faces for hybrid cells are stored as tensor products */
2845:       if (isHybrid && f > 1) {
2846:         fv[2] = 3;
2847:         fv[3] = 2;
2848:       }
2849:       /* DO FOR PYRAMID */
2850:       /* First tet */
2851:       for (d = 0; d < dim; ++d) {
2852:         coordsTmp[0 * dim + d] = PetscRealPart(coords[faces[fOff + fv[0]] * dim + d]) - origin[d];
2853:         coordsTmp[1 * dim + d] = PetscRealPart(coords[faces[fOff + fv[1]] * dim + d]) - origin[d];
2854:         coordsTmp[2 * dim + d] = PetscRealPart(coords[faces[fOff + fv[3]] * dim + d]) - origin[d];
2855:       }
2856:       Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
2857:       if (flip) vtmp = -vtmp;
2858:       vsum += vtmp;
2859:       if (centroid) {
2860:         for (d = 0; d < dim; ++d) {
2861:           for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p * dim + d] * vtmp;
2862:         }
2863:       }
2864:       /* Second tet */
2865:       for (d = 0; d < dim; ++d) {
2866:         coordsTmp[0 * dim + d] = PetscRealPart(coords[faces[fOff + fv[1]] * dim + d]) - origin[d];
2867:         coordsTmp[1 * dim + d] = PetscRealPart(coords[faces[fOff + fv[2]] * dim + d]) - origin[d];
2868:         coordsTmp[2 * dim + d] = PetscRealPart(coords[faces[fOff + fv[3]] * dim + d]) - origin[d];
2869:       }
2870:       Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
2871:       if (flip) vtmp = -vtmp;
2872:       vsum += vtmp;
2873:       if (centroid) {
2874:         for (d = 0; d < dim; ++d) {
2875:           for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p * dim + d] * vtmp;
2876:         }
2877:       }
2878:       break;
2879:     }
2880:     default:
2881:       SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Cannot handle face %" PetscInt_FMT " of type %s", cone[f], DMPolytopeTypes[ct]);
2882:     }
2883:     fOff += faceSizes[f];
2884:   }
2885:   PetscCall(DMPlexRestoreRawFaces_Internal(dm, ct, order, &numFaces, &faceTypes, &faceSizes, &faces));
2886:   PetscCall(DMPlexRestoreCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
2887:   if (vol) *vol = PetscAbsReal(vsum);
2888:   if (normal)
2889:     for (d = 0; d < dim; ++d) normal[d] = 0.0;
2890:   if (centroid)
2891:     for (d = 0; d < dim; ++d) centroid[d] = centroid[d] / (vsum * 4) + origin[d];
2892:   PetscFunctionReturn(PETSC_SUCCESS);
2893: }

2895: /*@C
2896:   DMPlexComputeCellGeometryFVM - Compute the volume for a given cell

2898:   Collective

2900:   Input Parameters:
2901: + dm   - the `DMPLEX`
2902: - cell - the cell

2904:   Output Parameters:
2905: + vol      - the cell volume
2906: . centroid - the cell centroid
2907: - normal   - the cell normal, if appropriate

2909:   Level: advanced

2911: .seealso: `DMPLEX`, `DMGetCoordinateSection()`, `DMGetCoordinates()`
2912: @*/
2913: PetscErrorCode DMPlexComputeCellGeometryFVM(DM dm, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
2914: {
2915:   PetscInt depth, dim;

2917:   PetscFunctionBegin;
2918:   PetscCall(DMPlexGetDepth(dm, &depth));
2919:   PetscCall(DMGetDimension(dm, &dim));
2920:   PetscCheck(depth == dim, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Mesh must be interpolated");
2921:   PetscCall(DMPlexGetPointDepth(dm, cell, &depth));
2922:   switch (depth) {
2923:   case 0:
2924:     PetscCall(DMPlexComputeGeometryFVM_0D_Internal(dm, dim, cell, vol, centroid, normal));
2925:     break;
2926:   case 1:
2927:     PetscCall(DMPlexComputeGeometryFVM_1D_Internal(dm, dim, cell, vol, centroid, normal));
2928:     break;
2929:   case 2:
2930:     PetscCall(DMPlexComputeGeometryFVM_2D_Internal(dm, dim, cell, vol, centroid, normal));
2931:     break;
2932:   case 3:
2933:     PetscCall(DMPlexComputeGeometryFVM_3D_Internal(dm, dim, cell, vol, centroid, normal));
2934:     break;
2935:   default:
2936:     SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported dimension %" PetscInt_FMT " (depth %" PetscInt_FMT ") for element geometry computation", dim, depth);
2937:   }
2938:   PetscFunctionReturn(PETSC_SUCCESS);
2939: }

2941: /*@
2942:   DMPlexComputeGeometryFVM - Computes the cell and face geometry for a finite volume method

2944:   Input Parameter:
2945: . dm - The `DMPLEX`

2947:   Output Parameters:
2948: + cellgeom - A `Vec` of `PetscFVCellGeom` data
2949: - facegeom - A `Vec` of `PetscFVFaceGeom` data

2951:   Level: developer

2953: .seealso: `DMPLEX`, `PetscFVFaceGeom`, `PetscFVCellGeom`
2954: @*/
2955: PetscErrorCode DMPlexComputeGeometryFVM(DM dm, Vec *cellgeom, Vec *facegeom)
2956: {
2957:   DM           dmFace, dmCell;
2958:   DMLabel      ghostLabel;
2959:   PetscSection sectionFace, sectionCell;
2960:   PetscSection coordSection;
2961:   Vec          coordinates;
2962:   PetscScalar *fgeom, *cgeom;
2963:   PetscReal    minradius, gminradius;
2964:   PetscInt     dim, cStart, cEnd, cEndInterior, c, fStart, fEnd, f;

2966:   PetscFunctionBegin;
2967:   PetscCall(DMGetDimension(dm, &dim));
2968:   PetscCall(DMGetCoordinateSection(dm, &coordSection));
2969:   PetscCall(DMGetCoordinatesLocal(dm, &coordinates));
2970:   /* Make cell centroids and volumes */
2971:   PetscCall(DMClone(dm, &dmCell));
2972:   PetscCall(DMSetCoordinateSection(dmCell, PETSC_DETERMINE, coordSection));
2973:   PetscCall(DMSetCoordinatesLocal(dmCell, coordinates));
2974:   PetscCall(PetscSectionCreate(PetscObjectComm((PetscObject)dm), &sectionCell));
2975:   PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
2976:   PetscCall(DMPlexGetCellTypeStratum(dm, DM_POLYTOPE_FV_GHOST, &cEndInterior, NULL));
2977:   PetscCall(PetscSectionSetChart(sectionCell, cStart, cEnd));
2978:   for (c = cStart; c < cEnd; ++c) PetscCall(PetscSectionSetDof(sectionCell, c, (PetscInt)PetscCeilReal(((PetscReal)sizeof(PetscFVCellGeom)) / sizeof(PetscScalar))));
2979:   PetscCall(PetscSectionSetUp(sectionCell));
2980:   PetscCall(DMSetLocalSection(dmCell, sectionCell));
2981:   PetscCall(PetscSectionDestroy(&sectionCell));
2982:   PetscCall(DMCreateLocalVector(dmCell, cellgeom));
2983:   if (cEndInterior < 0) cEndInterior = cEnd;
2984:   PetscCall(VecGetArray(*cellgeom, &cgeom));
2985:   for (c = cStart; c < cEndInterior; ++c) {
2986:     PetscFVCellGeom *cg;

2988:     PetscCall(DMPlexPointLocalRef(dmCell, c, cgeom, &cg));
2989:     PetscCall(PetscArrayzero(cg, 1));
2990:     PetscCall(DMPlexComputeCellGeometryFVM(dmCell, c, &cg->volume, cg->centroid, NULL));
2991:   }
2992:   /* Compute face normals and minimum cell radius */
2993:   PetscCall(DMClone(dm, &dmFace));
2994:   PetscCall(PetscSectionCreate(PetscObjectComm((PetscObject)dm), &sectionFace));
2995:   PetscCall(DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd));
2996:   PetscCall(PetscSectionSetChart(sectionFace, fStart, fEnd));
2997:   for (f = fStart; f < fEnd; ++f) PetscCall(PetscSectionSetDof(sectionFace, f, (PetscInt)PetscCeilReal(((PetscReal)sizeof(PetscFVFaceGeom)) / sizeof(PetscScalar))));
2998:   PetscCall(PetscSectionSetUp(sectionFace));
2999:   PetscCall(DMSetLocalSection(dmFace, sectionFace));
3000:   PetscCall(PetscSectionDestroy(&sectionFace));
3001:   PetscCall(DMCreateLocalVector(dmFace, facegeom));
3002:   PetscCall(VecGetArray(*facegeom, &fgeom));
3003:   PetscCall(DMGetLabel(dm, "ghost", &ghostLabel));
3004:   minradius = PETSC_MAX_REAL;
3005:   for (f = fStart; f < fEnd; ++f) {
3006:     PetscFVFaceGeom *fg;
3007:     PetscReal        area;
3008:     const PetscInt  *cells;
3009:     PetscInt         ncells, ghost = -1, d, numChildren;

3011:     if (ghostLabel) PetscCall(DMLabelGetValue(ghostLabel, f, &ghost));
3012:     PetscCall(DMPlexGetTreeChildren(dm, f, &numChildren, NULL));
3013:     PetscCall(DMPlexGetSupport(dm, f, &cells));
3014:     PetscCall(DMPlexGetSupportSize(dm, f, &ncells));
3015:     /* It is possible to get a face with no support when using partition overlap */
3016:     if (!ncells || ghost >= 0 || numChildren) continue;
3017:     PetscCall(DMPlexPointLocalRef(dmFace, f, fgeom, &fg));
3018:     PetscCall(DMPlexComputeCellGeometryFVM(dm, f, &area, fg->centroid, fg->normal));
3019:     for (d = 0; d < dim; ++d) fg->normal[d] *= area;
3020:     /* Flip face orientation if necessary to match ordering in support, and Update minimum radius */
3021:     {
3022:       PetscFVCellGeom *cL, *cR;
3023:       PetscReal       *lcentroid, *rcentroid;
3024:       PetscReal        l[3], r[3], v[3];

3026:       PetscCall(DMPlexPointLocalRead(dmCell, cells[0], cgeom, &cL));
3027:       lcentroid = cells[0] >= cEndInterior ? fg->centroid : cL->centroid;
3028:       if (ncells > 1) {
3029:         PetscCall(DMPlexPointLocalRead(dmCell, cells[1], cgeom, &cR));
3030:         rcentroid = cells[1] >= cEndInterior ? fg->centroid : cR->centroid;
3031:       } else {
3032:         rcentroid = fg->centroid;
3033:       }
3034:       PetscCall(DMLocalizeCoordinateReal_Internal(dm, dim, fg->centroid, lcentroid, l));
3035:       PetscCall(DMLocalizeCoordinateReal_Internal(dm, dim, fg->centroid, rcentroid, r));
3036:       DMPlex_WaxpyD_Internal(dim, -1, l, r, v);
3037:       if (DMPlex_DotRealD_Internal(dim, fg->normal, v) < 0) {
3038:         for (d = 0; d < dim; ++d) fg->normal[d] = -fg->normal[d];
3039:       }
3040:       if (DMPlex_DotRealD_Internal(dim, fg->normal, v) <= 0) {
3041:         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]);
3042:         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]);
3043:         SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Direction for face %" PetscInt_FMT " could not be fixed", f);
3044:       }
3045:       if (cells[0] < cEndInterior) {
3046:         DMPlex_WaxpyD_Internal(dim, -1, fg->centroid, cL->centroid, v);
3047:         minradius = PetscMin(minradius, DMPlex_NormD_Internal(dim, v));
3048:       }
3049:       if (ncells > 1 && cells[1] < cEndInterior) {
3050:         DMPlex_WaxpyD_Internal(dim, -1, fg->centroid, cR->centroid, v);
3051:         minradius = PetscMin(minradius, DMPlex_NormD_Internal(dim, v));
3052:       }
3053:     }
3054:   }
3055:   PetscCallMPI(MPIU_Allreduce(&minradius, &gminradius, 1, MPIU_REAL, MPIU_MIN, PetscObjectComm((PetscObject)dm)));
3056:   PetscCall(DMPlexSetMinRadius(dm, gminradius));
3057:   /* Compute centroids of ghost cells */
3058:   for (c = cEndInterior; c < cEnd; ++c) {
3059:     PetscFVFaceGeom *fg;
3060:     const PetscInt  *cone, *support;
3061:     PetscInt         coneSize, supportSize, s;

3063:     PetscCall(DMPlexGetConeSize(dmCell, c, &coneSize));
3064:     PetscCheck(coneSize == 1, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Ghost cell %" PetscInt_FMT " has cone size %" PetscInt_FMT " != 1", c, coneSize);
3065:     PetscCall(DMPlexGetCone(dmCell, c, &cone));
3066:     PetscCall(DMPlexGetSupportSize(dmCell, cone[0], &supportSize));
3067:     PetscCheck(supportSize == 2, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Face %" PetscInt_FMT " has support size %" PetscInt_FMT " != 2", cone[0], supportSize);
3068:     PetscCall(DMPlexGetSupport(dmCell, cone[0], &support));
3069:     PetscCall(DMPlexPointLocalRef(dmFace, cone[0], fgeom, &fg));
3070:     for (s = 0; s < 2; ++s) {
3071:       /* Reflect ghost centroid across plane of face */
3072:       if (support[s] == c) {
3073:         PetscFVCellGeom *ci;
3074:         PetscFVCellGeom *cg;
3075:         PetscReal        c2f[3], a;

3077:         PetscCall(DMPlexPointLocalRead(dmCell, support[(s + 1) % 2], cgeom, &ci));
3078:         DMPlex_WaxpyD_Internal(dim, -1, ci->centroid, fg->centroid, c2f); /* cell to face centroid */
3079:         a = DMPlex_DotRealD_Internal(dim, c2f, fg->normal) / DMPlex_DotRealD_Internal(dim, fg->normal, fg->normal);
3080:         PetscCall(DMPlexPointLocalRef(dmCell, support[s], cgeom, &cg));
3081:         DMPlex_WaxpyD_Internal(dim, 2 * a, fg->normal, ci->centroid, cg->centroid);
3082:         cg->volume = ci->volume;
3083:       }
3084:     }
3085:   }
3086:   PetscCall(VecRestoreArray(*facegeom, &fgeom));
3087:   PetscCall(VecRestoreArray(*cellgeom, &cgeom));
3088:   PetscCall(DMDestroy(&dmCell));
3089:   PetscCall(DMDestroy(&dmFace));
3090:   PetscFunctionReturn(PETSC_SUCCESS);
3091: }

3093: /*@
3094:   DMPlexGetMinRadius - Returns the minimum distance from any cell centroid to a face

3096:   Not Collective

3098:   Input Parameter:
3099: . dm - the `DMPLEX`

3101:   Output Parameter:
3102: . minradius - the minimum cell radius

3104:   Level: developer

3106: .seealso: `DMPLEX`, `DMGetCoordinates()`
3107: @*/
3108: PetscErrorCode DMPlexGetMinRadius(DM dm, PetscReal *minradius)
3109: {
3110:   PetscFunctionBegin;
3112:   PetscAssertPointer(minradius, 2);
3113:   *minradius = ((DM_Plex *)dm->data)->minradius;
3114:   PetscFunctionReturn(PETSC_SUCCESS);
3115: }

3117: /*@
3118:   DMPlexSetMinRadius - Sets the minimum distance from the cell centroid to a face

3120:   Logically Collective

3122:   Input Parameters:
3123: + dm        - the `DMPLEX`
3124: - minradius - the minimum cell radius

3126:   Level: developer

3128: .seealso: `DMPLEX`, `DMSetCoordinates()`
3129: @*/
3130: PetscErrorCode DMPlexSetMinRadius(DM dm, PetscReal minradius)
3131: {
3132:   PetscFunctionBegin;
3134:   ((DM_Plex *)dm->data)->minradius = minradius;
3135:   PetscFunctionReturn(PETSC_SUCCESS);
3136: }

3138: static PetscErrorCode BuildGradientReconstruction_Internal(DM dm, PetscFV fvm, DM dmFace, PetscScalar *fgeom, DM dmCell, PetscScalar *cgeom)
3139: {
3140:   DMLabel      ghostLabel;
3141:   PetscScalar *dx, *grad, **gref;
3142:   PetscInt     dim, cStart, cEnd, c, cEndInterior, maxNumFaces;

3144:   PetscFunctionBegin;
3145:   PetscCall(DMGetDimension(dm, &dim));
3146:   PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
3147:   PetscCall(DMPlexGetCellTypeStratum(dm, DM_POLYTOPE_FV_GHOST, &cEndInterior, NULL));
3148:   cEndInterior = cEndInterior < 0 ? cEnd : cEndInterior;
3149:   PetscCall(DMPlexGetMaxSizes(dm, &maxNumFaces, NULL));
3150:   PetscCall(PetscFVLeastSquaresSetMaxFaces(fvm, maxNumFaces));
3151:   PetscCall(DMGetLabel(dm, "ghost", &ghostLabel));
3152:   PetscCall(PetscMalloc3(maxNumFaces * dim, &dx, maxNumFaces * dim, &grad, maxNumFaces, &gref));
3153:   for (c = cStart; c < cEndInterior; c++) {
3154:     const PetscInt  *faces;
3155:     PetscInt         numFaces, usedFaces, f, d;
3156:     PetscFVCellGeom *cg;
3157:     PetscBool        boundary;
3158:     PetscInt         ghost;

3160:     // do not attempt to compute a gradient reconstruction stencil in a ghost cell.  It will never be used
3161:     PetscCall(DMLabelGetValue(ghostLabel, c, &ghost));
3162:     if (ghost >= 0) continue;

3164:     PetscCall(DMPlexPointLocalRead(dmCell, c, cgeom, &cg));
3165:     PetscCall(DMPlexGetConeSize(dm, c, &numFaces));
3166:     PetscCall(DMPlexGetCone(dm, c, &faces));
3167:     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);
3168:     for (f = 0, usedFaces = 0; f < numFaces; ++f) {
3169:       PetscFVCellGeom *cg1;
3170:       PetscFVFaceGeom *fg;
3171:       const PetscInt  *fcells;
3172:       PetscInt         ncell, side;

3174:       PetscCall(DMLabelGetValue(ghostLabel, faces[f], &ghost));
3175:       PetscCall(DMIsBoundaryPoint(dm, faces[f], &boundary));
3176:       if ((ghost >= 0) || boundary) continue;
3177:       PetscCall(DMPlexGetSupport(dm, faces[f], &fcells));
3178:       side  = (c != fcells[0]); /* c is on left=0 or right=1 of face */
3179:       ncell = fcells[!side];    /* the neighbor */
3180:       PetscCall(DMPlexPointLocalRef(dmFace, faces[f], fgeom, &fg));
3181:       PetscCall(DMPlexPointLocalRead(dmCell, ncell, cgeom, &cg1));
3182:       for (d = 0; d < dim; ++d) dx[usedFaces * dim + d] = cg1->centroid[d] - cg->centroid[d];
3183:       gref[usedFaces++] = fg->grad[side]; /* Gradient reconstruction term will go here */
3184:     }
3185:     PetscCheck(usedFaces, PETSC_COMM_SELF, PETSC_ERR_USER, "Mesh contains isolated cell (no neighbors). Is it intentional?");
3186:     PetscCall(PetscFVComputeGradient(fvm, usedFaces, dx, grad));
3187:     for (f = 0, usedFaces = 0; f < numFaces; ++f) {
3188:       PetscCall(DMLabelGetValue(ghostLabel, faces[f], &ghost));
3189:       PetscCall(DMIsBoundaryPoint(dm, faces[f], &boundary));
3190:       if ((ghost >= 0) || boundary) continue;
3191:       for (d = 0; d < dim; ++d) gref[usedFaces][d] = grad[usedFaces * dim + d];
3192:       ++usedFaces;
3193:     }
3194:   }
3195:   PetscCall(PetscFree3(dx, grad, gref));
3196:   PetscFunctionReturn(PETSC_SUCCESS);
3197: }

3199: static PetscErrorCode BuildGradientReconstruction_Internal_Tree(DM dm, PetscFV fvm, DM dmFace, PetscScalar *fgeom, DM dmCell, PetscScalar *cgeom)
3200: {
3201:   DMLabel      ghostLabel;
3202:   PetscScalar *dx, *grad, **gref;
3203:   PetscInt     dim, cStart, cEnd, c, cEndInterior, fStart, fEnd, f, nStart, nEnd, maxNumFaces = 0;
3204:   PetscSection neighSec;
3205:   PetscInt(*neighbors)[2];
3206:   PetscInt *counter;

3208:   PetscFunctionBegin;
3209:   PetscCall(DMGetDimension(dm, &dim));
3210:   PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
3211:   PetscCall(DMPlexGetCellTypeStratum(dm, DM_POLYTOPE_FV_GHOST, &cEndInterior, NULL));
3212:   if (cEndInterior < 0) cEndInterior = cEnd;
3213:   PetscCall(PetscSectionCreate(PetscObjectComm((PetscObject)dm), &neighSec));
3214:   PetscCall(PetscSectionSetChart(neighSec, cStart, cEndInterior));
3215:   PetscCall(DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd));
3216:   PetscCall(DMGetLabel(dm, "ghost", &ghostLabel));
3217:   for (f = fStart; f < fEnd; f++) {
3218:     const PetscInt *fcells;
3219:     PetscBool       boundary;
3220:     PetscInt        ghost = -1;
3221:     PetscInt        numChildren, numCells, c;

3223:     if (ghostLabel) PetscCall(DMLabelGetValue(ghostLabel, f, &ghost));
3224:     PetscCall(DMIsBoundaryPoint(dm, f, &boundary));
3225:     PetscCall(DMPlexGetTreeChildren(dm, f, &numChildren, NULL));
3226:     if ((ghost >= 0) || boundary || numChildren) continue;
3227:     PetscCall(DMPlexGetSupportSize(dm, f, &numCells));
3228:     if (numCells == 2) {
3229:       PetscCall(DMPlexGetSupport(dm, f, &fcells));
3230:       for (c = 0; c < 2; c++) {
3231:         PetscInt cell = fcells[c];

3233:         if (cell >= cStart && cell < cEndInterior) PetscCall(PetscSectionAddDof(neighSec, cell, 1));
3234:       }
3235:     }
3236:   }
3237:   PetscCall(PetscSectionSetUp(neighSec));
3238:   PetscCall(PetscSectionGetMaxDof(neighSec, &maxNumFaces));
3239:   PetscCall(PetscFVLeastSquaresSetMaxFaces(fvm, maxNumFaces));
3240:   nStart = 0;
3241:   PetscCall(PetscSectionGetStorageSize(neighSec, &nEnd));
3242:   PetscCall(PetscMalloc1(nEnd - nStart, &neighbors));
3243:   PetscCall(PetscCalloc1(cEndInterior - cStart, &counter));
3244:   for (f = fStart; f < fEnd; f++) {
3245:     const PetscInt *fcells;
3246:     PetscBool       boundary;
3247:     PetscInt        ghost = -1;
3248:     PetscInt        numChildren, numCells, c;

3250:     if (ghostLabel) PetscCall(DMLabelGetValue(ghostLabel, f, &ghost));
3251:     PetscCall(DMIsBoundaryPoint(dm, f, &boundary));
3252:     PetscCall(DMPlexGetTreeChildren(dm, f, &numChildren, NULL));
3253:     if ((ghost >= 0) || boundary || numChildren) continue;
3254:     PetscCall(DMPlexGetSupportSize(dm, f, &numCells));
3255:     if (numCells == 2) {
3256:       PetscCall(DMPlexGetSupport(dm, f, &fcells));
3257:       for (c = 0; c < 2; c++) {
3258:         PetscInt cell = fcells[c], off;

3260:         if (cell >= cStart && cell < cEndInterior) {
3261:           PetscCall(PetscSectionGetOffset(neighSec, cell, &off));
3262:           off += counter[cell - cStart]++;
3263:           neighbors[off][0] = f;
3264:           neighbors[off][1] = fcells[1 - c];
3265:         }
3266:       }
3267:     }
3268:   }
3269:   PetscCall(PetscFree(counter));
3270:   PetscCall(PetscMalloc3(maxNumFaces * dim, &dx, maxNumFaces * dim, &grad, maxNumFaces, &gref));
3271:   for (c = cStart; c < cEndInterior; c++) {
3272:     PetscInt         numFaces, f, d, off, ghost = -1;
3273:     PetscFVCellGeom *cg;

3275:     PetscCall(DMPlexPointLocalRead(dmCell, c, cgeom, &cg));
3276:     PetscCall(PetscSectionGetDof(neighSec, c, &numFaces));
3277:     PetscCall(PetscSectionGetOffset(neighSec, c, &off));

3279:     // do not attempt to compute a gradient reconstruction stencil in a ghost cell.  It will never be used
3280:     if (ghostLabel) PetscCall(DMLabelGetValue(ghostLabel, c, &ghost));
3281:     if (ghost >= 0) continue;

3283:     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);
3284:     for (f = 0; f < numFaces; ++f) {
3285:       PetscFVCellGeom *cg1;
3286:       PetscFVFaceGeom *fg;
3287:       const PetscInt  *fcells;
3288:       PetscInt         ncell, side, nface;

3290:       nface = neighbors[off + f][0];
3291:       ncell = neighbors[off + f][1];
3292:       PetscCall(DMPlexGetSupport(dm, nface, &fcells));
3293:       side = (c != fcells[0]);
3294:       PetscCall(DMPlexPointLocalRef(dmFace, nface, fgeom, &fg));
3295:       PetscCall(DMPlexPointLocalRead(dmCell, ncell, cgeom, &cg1));
3296:       for (d = 0; d < dim; ++d) dx[f * dim + d] = cg1->centroid[d] - cg->centroid[d];
3297:       gref[f] = fg->grad[side]; /* Gradient reconstruction term will go here */
3298:     }
3299:     PetscCall(PetscFVComputeGradient(fvm, numFaces, dx, grad));
3300:     for (f = 0; f < numFaces; ++f) {
3301:       for (d = 0; d < dim; ++d) gref[f][d] = grad[f * dim + d];
3302:     }
3303:   }
3304:   PetscCall(PetscFree3(dx, grad, gref));
3305:   PetscCall(PetscSectionDestroy(&neighSec));
3306:   PetscCall(PetscFree(neighbors));
3307:   PetscFunctionReturn(PETSC_SUCCESS);
3308: }

3310: /*@
3311:   DMPlexComputeGradientFVM - Compute geometric factors for gradient reconstruction, which are stored in the geometry data, and compute layout for gradient data

3313:   Collective

3315:   Input Parameters:
3316: + dm           - The `DMPLEX`
3317: . fvm          - The `PetscFV`
3318: - cellGeometry - The face geometry from `DMPlexComputeCellGeometryFVM()`

3320:   Input/Output Parameter:
3321: . faceGeometry - The face geometry from `DMPlexComputeFaceGeometryFVM()`; on output
3322:                  the geometric factors for gradient calculation are inserted

3324:   Output Parameter:
3325: . dmGrad - The `DM` describing the layout of gradient data

3327:   Level: developer

3329: .seealso: `DMPLEX`, `DMPlexGetFaceGeometryFVM()`, `DMPlexGetCellGeometryFVM()`
3330: @*/
3331: PetscErrorCode DMPlexComputeGradientFVM(DM dm, PetscFV fvm, Vec faceGeometry, Vec cellGeometry, DM *dmGrad)
3332: {
3333:   DM           dmFace, dmCell;
3334:   PetscScalar *fgeom, *cgeom;
3335:   PetscSection sectionGrad, parentSection;
3336:   PetscInt     dim, pdim, cStart, cEnd, cEndInterior, c;

3338:   PetscFunctionBegin;
3339:   PetscCall(DMGetDimension(dm, &dim));
3340:   PetscCall(PetscFVGetNumComponents(fvm, &pdim));
3341:   PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
3342:   PetscCall(DMPlexGetCellTypeStratum(dm, DM_POLYTOPE_FV_GHOST, &cEndInterior, NULL));
3343:   /* Construct the interpolant corresponding to each face from the least-square solution over the cell neighborhood */
3344:   PetscCall(VecGetDM(faceGeometry, &dmFace));
3345:   PetscCall(VecGetDM(cellGeometry, &dmCell));
3346:   PetscCall(VecGetArray(faceGeometry, &fgeom));
3347:   PetscCall(VecGetArray(cellGeometry, &cgeom));
3348:   PetscCall(DMPlexGetTree(dm, &parentSection, NULL, NULL, NULL, NULL));
3349:   if (!parentSection) {
3350:     PetscCall(BuildGradientReconstruction_Internal(dm, fvm, dmFace, fgeom, dmCell, cgeom));
3351:   } else {
3352:     PetscCall(BuildGradientReconstruction_Internal_Tree(dm, fvm, dmFace, fgeom, dmCell, cgeom));
3353:   }
3354:   PetscCall(VecRestoreArray(faceGeometry, &fgeom));
3355:   PetscCall(VecRestoreArray(cellGeometry, &cgeom));
3356:   /* Create storage for gradients */
3357:   PetscCall(DMClone(dm, dmGrad));
3358:   PetscCall(PetscSectionCreate(PetscObjectComm((PetscObject)dm), &sectionGrad));
3359:   PetscCall(PetscSectionSetChart(sectionGrad, cStart, cEnd));
3360:   for (c = cStart; c < cEnd; ++c) PetscCall(PetscSectionSetDof(sectionGrad, c, pdim * dim));
3361:   PetscCall(PetscSectionSetUp(sectionGrad));
3362:   PetscCall(DMSetLocalSection(*dmGrad, sectionGrad));
3363:   PetscCall(PetscSectionDestroy(&sectionGrad));
3364:   PetscFunctionReturn(PETSC_SUCCESS);
3365: }

3367: /*@
3368:   DMPlexGetDataFVM - Retrieve precomputed cell geometry

3370:   Collective

3372:   Input Parameters:
3373: + dm - The `DM`
3374: - fv - The `PetscFV`

3376:   Output Parameters:
3377: + cellgeom - The cell geometry
3378: . facegeom - The face geometry
3379: - gradDM   - The gradient matrices

3381:   Level: developer

3383: .seealso: `DMPLEX`, `DMPlexComputeGeometryFVM()`
3384: @*/
3385: PetscErrorCode DMPlexGetDataFVM(DM dm, PetscFV fv, Vec *cellgeom, Vec *facegeom, DM *gradDM)
3386: {
3387:   PetscObject cellgeomobj, facegeomobj;

3389:   PetscFunctionBegin;
3390:   PetscCall(PetscObjectQuery((PetscObject)dm, "DMPlex_cellgeom_fvm", &cellgeomobj));
3391:   if (!cellgeomobj) {
3392:     Vec cellgeomInt, facegeomInt;

3394:     PetscCall(DMPlexComputeGeometryFVM(dm, &cellgeomInt, &facegeomInt));
3395:     PetscCall(PetscObjectCompose((PetscObject)dm, "DMPlex_cellgeom_fvm", (PetscObject)cellgeomInt));
3396:     PetscCall(PetscObjectCompose((PetscObject)dm, "DMPlex_facegeom_fvm", (PetscObject)facegeomInt));
3397:     PetscCall(VecDestroy(&cellgeomInt));
3398:     PetscCall(VecDestroy(&facegeomInt));
3399:     PetscCall(PetscObjectQuery((PetscObject)dm, "DMPlex_cellgeom_fvm", &cellgeomobj));
3400:   }
3401:   PetscCall(PetscObjectQuery((PetscObject)dm, "DMPlex_facegeom_fvm", &facegeomobj));
3402:   if (cellgeom) *cellgeom = (Vec)cellgeomobj;
3403:   if (facegeom) *facegeom = (Vec)facegeomobj;
3404:   if (gradDM) {
3405:     PetscObject gradobj;
3406:     PetscBool   computeGradients;

3408:     PetscCall(PetscFVGetComputeGradients(fv, &computeGradients));
3409:     if (!computeGradients) {
3410:       *gradDM = NULL;
3411:       PetscFunctionReturn(PETSC_SUCCESS);
3412:     }
3413:     PetscCall(PetscObjectQuery((PetscObject)dm, "DMPlex_dmgrad_fvm", &gradobj));
3414:     if (!gradobj) {
3415:       DM dmGradInt;

3417:       PetscCall(DMPlexComputeGradientFVM(dm, fv, (Vec)facegeomobj, (Vec)cellgeomobj, &dmGradInt));
3418:       PetscCall(PetscObjectCompose((PetscObject)dm, "DMPlex_dmgrad_fvm", (PetscObject)dmGradInt));
3419:       PetscCall(DMDestroy(&dmGradInt));
3420:       PetscCall(PetscObjectQuery((PetscObject)dm, "DMPlex_dmgrad_fvm", &gradobj));
3421:     }
3422:     *gradDM = (DM)gradobj;
3423:   }
3424:   PetscFunctionReturn(PETSC_SUCCESS);
3425: }

3427: static PetscErrorCode DMPlexCoordinatesToReference_NewtonUpdate(PetscInt dimC, PetscInt dimR, PetscScalar *J, PetscScalar *invJ, PetscScalar *work, PetscReal *resNeg, PetscReal *guess)
3428: {
3429:   PetscInt l, m;

3431:   PetscFunctionBeginHot;
3432:   if (dimC == dimR && dimR <= 3) {
3433:     /* invert Jacobian, multiply */
3434:     PetscScalar det, idet;

3436:     switch (dimR) {
3437:     case 1:
3438:       invJ[0] = 1. / J[0];
3439:       break;
3440:     case 2:
3441:       det     = J[0] * J[3] - J[1] * J[2];
3442:       idet    = 1. / det;
3443:       invJ[0] = J[3] * idet;
3444:       invJ[1] = -J[1] * idet;
3445:       invJ[2] = -J[2] * idet;
3446:       invJ[3] = J[0] * idet;
3447:       break;
3448:     case 3: {
3449:       invJ[0] = J[4] * J[8] - J[5] * J[7];
3450:       invJ[1] = J[2] * J[7] - J[1] * J[8];
3451:       invJ[2] = J[1] * J[5] - J[2] * J[4];
3452:       det     = invJ[0] * J[0] + invJ[1] * J[3] + invJ[2] * J[6];
3453:       idet    = 1. / det;
3454:       invJ[0] *= idet;
3455:       invJ[1] *= idet;
3456:       invJ[2] *= idet;
3457:       invJ[3] = idet * (J[5] * J[6] - J[3] * J[8]);
3458:       invJ[4] = idet * (J[0] * J[8] - J[2] * J[6]);
3459:       invJ[5] = idet * (J[2] * J[3] - J[0] * J[5]);
3460:       invJ[6] = idet * (J[3] * J[7] - J[4] * J[6]);
3461:       invJ[7] = idet * (J[1] * J[6] - J[0] * J[7]);
3462:       invJ[8] = idet * (J[0] * J[4] - J[1] * J[3]);
3463:     } break;
3464:     }
3465:     for (l = 0; l < dimR; l++) {
3466:       for (m = 0; m < dimC; m++) guess[l] += PetscRealPart(invJ[l * dimC + m]) * resNeg[m];
3467:     }
3468:   } else {
3469: #if defined(PETSC_USE_COMPLEX)
3470:     char transpose = 'C';
3471: #else
3472:     char transpose = 'T';
3473: #endif
3474:     PetscBLASInt m, n, one = 1, worksize, info;

3476:     PetscCall(PetscBLASIntCast(dimR, &m));
3477:     PetscCall(PetscBLASIntCast(dimC, &n));
3478:     PetscCall(PetscBLASIntCast(dimC * dimC, &worksize));
3479:     for (l = 0; l < dimC; l++) invJ[l] = resNeg[l];

3481:     PetscCallBLAS("LAPACKgels", LAPACKgels_(&transpose, &m, &n, &one, J, &m, invJ, &n, work, &worksize, &info));
3482:     PetscCheck(info == 0, PETSC_COMM_SELF, PETSC_ERR_LIB, "Bad argument to GELS %" PetscBLASInt_FMT, info);

3484:     for (l = 0; l < dimR; l++) guess[l] += PetscRealPart(invJ[l]);
3485:   }
3486:   PetscFunctionReturn(PETSC_SUCCESS);
3487: }

3489: static PetscErrorCode DMPlexCoordinatesToReference_Tensor(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal realCoords[], PetscReal refCoords[], Vec coords, PetscInt dimC, PetscInt dimR)
3490: {
3491:   PetscInt     coordSize, i, j, k, l, m, maxIts = 7, numV = (1 << dimR);
3492:   PetscScalar *coordsScalar = NULL;
3493:   PetscReal   *cellData, *cellCoords, *cellCoeffs, *extJ, *resNeg;
3494:   PetscScalar *J, *invJ, *work;

3496:   PetscFunctionBegin;
3498:   PetscCall(DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar));
3499:   PetscCheck(coordSize >= dimC * numV, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Expecting at least %" PetscInt_FMT " coordinates, got %" PetscInt_FMT, dimC * (1 << dimR), coordSize);
3500:   PetscCall(DMGetWorkArray(dm, 2 * coordSize + dimR + dimC, MPIU_REAL, &cellData));
3501:   PetscCall(DMGetWorkArray(dm, 3 * dimR * dimC, MPIU_SCALAR, &J));
3502:   cellCoords = &cellData[0];
3503:   cellCoeffs = &cellData[coordSize];
3504:   extJ       = &cellData[2 * coordSize];
3505:   resNeg     = &cellData[2 * coordSize + dimR];
3506:   invJ       = &J[dimR * dimC];
3507:   work       = &J[2 * dimR * dimC];
3508:   if (dimR == 2) {
3509:     const PetscInt zToPlex[4] = {0, 1, 3, 2};

3511:     for (i = 0; i < 4; i++) {
3512:       PetscInt plexI = zToPlex[i];

3514:       for (j = 0; j < dimC; j++) cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
3515:     }
3516:   } else if (dimR == 3) {
3517:     const PetscInt zToPlex[8] = {0, 3, 1, 2, 4, 5, 7, 6};

3519:     for (i = 0; i < 8; i++) {
3520:       PetscInt plexI = zToPlex[i];

3522:       for (j = 0; j < dimC; j++) cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
3523:     }
3524:   } else {
3525:     for (i = 0; i < coordSize; i++) cellCoords[i] = PetscRealPart(coordsScalar[i]);
3526:   }
3527:   /* Perform the shuffling transform that converts values at the corners of [-1,1]^d to coefficients */
3528:   for (i = 0; i < dimR; i++) {
3529:     PetscReal *swap;

3531:     for (j = 0; j < (numV / 2); j++) {
3532:       for (k = 0; k < dimC; k++) {
3533:         cellCoeffs[dimC * j + k]                = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] + cellCoords[dimC * 2 * j + k]);
3534:         cellCoeffs[dimC * (j + (numV / 2)) + k] = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] - cellCoords[dimC * 2 * j + k]);
3535:       }
3536:     }

3538:     if (i < dimR - 1) {
3539:       swap       = cellCoeffs;
3540:       cellCoeffs = cellCoords;
3541:       cellCoords = swap;
3542:     }
3543:   }
3544:   PetscCall(PetscArrayzero(refCoords, numPoints * dimR));
3545:   for (j = 0; j < numPoints; j++) {
3546:     for (i = 0; i < maxIts; i++) {
3547:       PetscReal *guess = &refCoords[dimR * j];

3549:       /* compute -residual and Jacobian */
3550:       for (k = 0; k < dimC; k++) resNeg[k] = realCoords[dimC * j + k];
3551:       for (k = 0; k < dimC * dimR; k++) J[k] = 0.;
3552:       for (k = 0; k < numV; k++) {
3553:         PetscReal extCoord = 1.;
3554:         for (l = 0; l < dimR; l++) {
3555:           PetscReal coord = guess[l];
3556:           PetscInt  dep   = (k & (1 << l)) >> l;

3558:           extCoord *= dep * coord + !dep;
3559:           extJ[l] = dep;

3561:           for (m = 0; m < dimR; m++) {
3562:             PetscReal coord = guess[m];
3563:             PetscInt  dep   = ((k & (1 << m)) >> m) && (m != l);
3564:             PetscReal mult  = dep * coord + !dep;

3566:             extJ[l] *= mult;
3567:           }
3568:         }
3569:         for (l = 0; l < dimC; l++) {
3570:           PetscReal coeff = cellCoeffs[dimC * k + l];

3572:           resNeg[l] -= coeff * extCoord;
3573:           for (m = 0; m < dimR; m++) J[dimR * l + m] += coeff * extJ[m];
3574:         }
3575:       }
3576:       if (0 && PetscDefined(USE_DEBUG)) {
3577:         PetscReal maxAbs = 0.;

3579:         for (l = 0; l < dimC; l++) maxAbs = PetscMax(maxAbs, PetscAbsReal(resNeg[l]));
3580:         PetscCall(PetscInfo(dm, "cell %" PetscInt_FMT ", point %" PetscInt_FMT ", iter %" PetscInt_FMT ": res %g\n", cell, j, i, (double)maxAbs));
3581:       }

3583:       PetscCall(DMPlexCoordinatesToReference_NewtonUpdate(dimC, dimR, J, invJ, work, resNeg, guess));
3584:     }
3585:   }
3586:   PetscCall(DMRestoreWorkArray(dm, 3 * dimR * dimC, MPIU_SCALAR, &J));
3587:   PetscCall(DMRestoreWorkArray(dm, 2 * coordSize + dimR + dimC, MPIU_REAL, &cellData));
3588:   PetscCall(DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar));
3589:   PetscFunctionReturn(PETSC_SUCCESS);
3590: }

3592: static PetscErrorCode DMPlexReferenceToCoordinates_Tensor(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal refCoords[], PetscReal realCoords[], Vec coords, PetscInt dimC, PetscInt dimR)
3593: {
3594:   PetscInt     coordSize, i, j, k, l, numV = (1 << dimR);
3595:   PetscScalar *coordsScalar = NULL;
3596:   PetscReal   *cellData, *cellCoords, *cellCoeffs;

3598:   PetscFunctionBegin;
3600:   PetscCall(DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar));
3601:   PetscCheck(coordSize >= dimC * numV, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Expecting at least %" PetscInt_FMT " coordinates, got %" PetscInt_FMT, dimC * (1 << dimR), coordSize);
3602:   PetscCall(DMGetWorkArray(dm, 2 * coordSize, MPIU_REAL, &cellData));
3603:   cellCoords = &cellData[0];
3604:   cellCoeffs = &cellData[coordSize];
3605:   if (dimR == 2) {
3606:     const PetscInt zToPlex[4] = {0, 1, 3, 2};

3608:     for (i = 0; i < 4; i++) {
3609:       PetscInt plexI = zToPlex[i];

3611:       for (j = 0; j < dimC; j++) cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
3612:     }
3613:   } else if (dimR == 3) {
3614:     const PetscInt zToPlex[8] = {0, 3, 1, 2, 4, 5, 7, 6};

3616:     for (i = 0; i < 8; i++) {
3617:       PetscInt plexI = zToPlex[i];

3619:       for (j = 0; j < dimC; j++) cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
3620:     }
3621:   } else {
3622:     for (i = 0; i < coordSize; i++) cellCoords[i] = PetscRealPart(coordsScalar[i]);
3623:   }
3624:   /* Perform the shuffling transform that converts values at the corners of [-1,1]^d to coefficients */
3625:   for (i = 0; i < dimR; i++) {
3626:     PetscReal *swap;

3628:     for (j = 0; j < (numV / 2); j++) {
3629:       for (k = 0; k < dimC; k++) {
3630:         cellCoeffs[dimC * j + k]                = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] + cellCoords[dimC * 2 * j + k]);
3631:         cellCoeffs[dimC * (j + (numV / 2)) + k] = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] - cellCoords[dimC * 2 * j + k]);
3632:       }
3633:     }

3635:     if (i < dimR - 1) {
3636:       swap       = cellCoeffs;
3637:       cellCoeffs = cellCoords;
3638:       cellCoords = swap;
3639:     }
3640:   }
3641:   PetscCall(PetscArrayzero(realCoords, numPoints * dimC));
3642:   for (j = 0; j < numPoints; j++) {
3643:     const PetscReal *guess  = &refCoords[dimR * j];
3644:     PetscReal       *mapped = &realCoords[dimC * j];

3646:     for (k = 0; k < numV; k++) {
3647:       PetscReal extCoord = 1.;
3648:       for (l = 0; l < dimR; l++) {
3649:         PetscReal coord = guess[l];
3650:         PetscInt  dep   = (k & (1 << l)) >> l;

3652:         extCoord *= dep * coord + !dep;
3653:       }
3654:       for (l = 0; l < dimC; l++) {
3655:         PetscReal coeff = cellCoeffs[dimC * k + l];

3657:         mapped[l] += coeff * extCoord;
3658:       }
3659:     }
3660:   }
3661:   PetscCall(DMRestoreWorkArray(dm, 2 * coordSize, MPIU_REAL, &cellData));
3662:   PetscCall(DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar));
3663:   PetscFunctionReturn(PETSC_SUCCESS);
3664: }

3666: PetscErrorCode DMPlexCoordinatesToReference_FE(DM dm, PetscFE fe, PetscInt cell, PetscInt numPoints, const PetscReal realCoords[], PetscReal refCoords[], Vec coords, PetscInt Nc, PetscInt dimR, PetscInt maxIter, PetscReal *tol)
3667: {
3668:   PetscInt     numComp, pdim, i, j, k, l, m, coordSize;
3669:   PetscScalar *nodes = NULL;
3670:   PetscReal   *invV, *modes;
3671:   PetscReal   *B, *D, *resNeg;
3672:   PetscScalar *J, *invJ, *work;
3673:   PetscReal    tolerance = tol == NULL ? 0.0 : *tol;

3675:   PetscFunctionBegin;
3676:   PetscCall(PetscFEGetDimension(fe, &pdim));
3677:   PetscCall(PetscFEGetNumComponents(fe, &numComp));
3678:   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);
3679:   /* we shouldn't apply inverse closure permutation, if one exists */
3680:   PetscCall(DMPlexVecGetOrientedClosure_Internal(dm, NULL, PETSC_FALSE, coords, cell, 0, &coordSize, &nodes));
3681:   /* convert nodes to values in the stable evaluation basis */
3682:   PetscCall(DMGetWorkArray(dm, pdim, MPIU_REAL, &modes));
3683:   invV = fe->invV;
3684:   for (i = 0; i < pdim; ++i) {
3685:     modes[i] = 0.;
3686:     for (j = 0; j < pdim; ++j) modes[i] += invV[i * pdim + j] * PetscRealPart(nodes[j]);
3687:   }
3688:   PetscCall(DMGetWorkArray(dm, pdim * Nc + pdim * Nc * dimR + Nc, MPIU_REAL, &B));
3689:   D      = &B[pdim * Nc];
3690:   resNeg = &D[pdim * Nc * dimR];
3691:   PetscCall(DMGetWorkArray(dm, 3 * Nc * dimR, MPIU_SCALAR, &J));
3692:   invJ = &J[Nc * dimR];
3693:   work = &invJ[Nc * dimR];
3694:   for (i = 0; i < numPoints * dimR; i++) refCoords[i] = 0.;
3695:   for (j = 0; j < numPoints; j++) {
3696:     PetscReal normPoint = DMPlex_NormD_Internal(Nc, &realCoords[j * Nc]);
3697:     normPoint           = normPoint > PETSC_SMALL ? normPoint : 1.0;
3698:     for (i = 0; i < maxIter; i++) { /* we could batch this so that we're not making big B and D arrays all the time */
3699:       PetscReal *guess = &refCoords[j * dimR], error = 0;
3700:       PetscCall(PetscSpaceEvaluate(fe->basisSpace, 1, guess, B, D, NULL));
3701:       for (k = 0; k < Nc; k++) resNeg[k] = realCoords[j * Nc + k];
3702:       for (k = 0; k < Nc * dimR; k++) J[k] = 0.;
3703:       for (k = 0; k < pdim; k++) {
3704:         for (l = 0; l < Nc; l++) {
3705:           resNeg[l] -= modes[k] * B[k * Nc + l];
3706:           for (m = 0; m < dimR; m++) J[l * dimR + m] += modes[k] * D[(k * Nc + l) * dimR + m];
3707:         }
3708:       }
3709:       if (0 && PetscDefined(USE_DEBUG)) {
3710:         PetscReal maxAbs = 0.;

3712:         for (l = 0; l < Nc; l++) maxAbs = PetscMax(maxAbs, PetscAbsReal(resNeg[l]));
3713:         PetscCall(PetscInfo(dm, "cell %" PetscInt_FMT ", point %" PetscInt_FMT ", iter %" PetscInt_FMT ": res %g\n", cell, j, i, (double)maxAbs));
3714:       }
3715:       error = DMPlex_NormD_Internal(Nc, resNeg);
3716:       if (error < tolerance * normPoint) {
3717:         if (tol) *tol = error / normPoint;
3718:         break;
3719:       }
3720:       PetscCall(DMPlexCoordinatesToReference_NewtonUpdate(Nc, dimR, J, invJ, work, resNeg, guess));
3721:     }
3722:   }
3723:   PetscCall(DMRestoreWorkArray(dm, 3 * Nc * dimR, MPIU_SCALAR, &J));
3724:   PetscCall(DMRestoreWorkArray(dm, pdim * Nc + pdim * Nc * dimR + Nc, MPIU_REAL, &B));
3725:   PetscCall(DMRestoreWorkArray(dm, pdim, MPIU_REAL, &modes));
3726:   PetscCall(DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &nodes));
3727:   PetscFunctionReturn(PETSC_SUCCESS);
3728: }

3730: /* TODO: TOBY please fix this for Nc > 1 */
3731: PetscErrorCode DMPlexReferenceToCoordinates_FE(DM dm, PetscFE fe, PetscInt cell, PetscInt numPoints, const PetscReal refCoords[], PetscReal realCoords[], Vec coords, PetscInt Nc, PetscInt dimR)
3732: {
3733:   PetscInt     numComp, pdim, i, j, k, l, coordSize;
3734:   PetscScalar *nodes = NULL;
3735:   PetscReal   *invV, *modes;
3736:   PetscReal   *B;

3738:   PetscFunctionBegin;
3739:   PetscCall(PetscFEGetDimension(fe, &pdim));
3740:   PetscCall(PetscFEGetNumComponents(fe, &numComp));
3741:   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);
3742:   /* we shouldn't apply inverse closure permutation, if one exists */
3743:   PetscCall(DMPlexVecGetOrientedClosure_Internal(dm, NULL, PETSC_FALSE, coords, cell, 0, &coordSize, &nodes));
3744:   /* convert nodes to values in the stable evaluation basis */
3745:   PetscCall(DMGetWorkArray(dm, pdim, MPIU_REAL, &modes));
3746:   invV = fe->invV;
3747:   for (i = 0; i < pdim; ++i) {
3748:     modes[i] = 0.;
3749:     for (j = 0; j < pdim; ++j) modes[i] += invV[i * pdim + j] * PetscRealPart(nodes[j]);
3750:   }
3751:   PetscCall(DMGetWorkArray(dm, numPoints * pdim * Nc, MPIU_REAL, &B));
3752:   PetscCall(PetscSpaceEvaluate(fe->basisSpace, numPoints, refCoords, B, NULL, NULL));
3753:   for (i = 0; i < numPoints * Nc; i++) realCoords[i] = 0.;
3754:   for (j = 0; j < numPoints; j++) {
3755:     PetscReal *mapped = &realCoords[j * Nc];

3757:     for (k = 0; k < pdim; k++) {
3758:       for (l = 0; l < Nc; l++) mapped[l] += modes[k] * B[(j * pdim + k) * Nc + l];
3759:     }
3760:   }
3761:   PetscCall(DMRestoreWorkArray(dm, numPoints * pdim * Nc, MPIU_REAL, &B));
3762:   PetscCall(DMRestoreWorkArray(dm, pdim, MPIU_REAL, &modes));
3763:   PetscCall(DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &nodes));
3764:   PetscFunctionReturn(PETSC_SUCCESS);
3765: }

3767: /*@
3768:   DMPlexCoordinatesToReference - Pull coordinates back from the mesh to the reference element
3769:   using a single element map.

3771:   Not Collective

3773:   Input Parameters:
3774: + dm         - The mesh, with coordinate maps defined either by a `PetscDS` for the coordinate `DM` (see `DMGetCoordinateDM()`) or
3775:                implicitly by the coordinates of the corner vertices of the cell: as an affine map for simplicial elements, or
3776:                as a multilinear map for tensor-product elements
3777: . cell       - the cell whose map is used.
3778: . numPoints  - the number of points to locate
3779: - realCoords - (numPoints x coordinate dimension) array of coordinates (see `DMGetCoordinateDim()`)

3781:   Output Parameter:
3782: . refCoords - (`numPoints` x `dimension`) array of reference coordinates (see `DMGetDimension()`)

3784:   Level: intermediate

3786:   Notes:
3787:   This inversion will be accurate inside the reference element, but may be inaccurate for
3788:   mappings that do not extend uniquely outside the reference cell (e.g, most non-affine maps)

3790: .seealso: `DMPLEX`, `DMPlexReferenceToCoordinates()`
3791: @*/
3792: PetscErrorCode DMPlexCoordinatesToReference(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal realCoords[], PetscReal refCoords[])
3793: {
3794:   PetscInt dimC, dimR, depth, cStart, cEnd, i;
3795:   DM       coordDM = NULL;
3796:   Vec      coords;
3797:   PetscFE  fe = NULL;

3799:   PetscFunctionBegin;
3801:   PetscCall(DMGetDimension(dm, &dimR));
3802:   PetscCall(DMGetCoordinateDim(dm, &dimC));
3803:   if (dimR <= 0 || dimC <= 0 || numPoints <= 0) PetscFunctionReturn(PETSC_SUCCESS);
3804:   PetscCall(DMPlexGetDepth(dm, &depth));
3805:   PetscCall(DMGetCoordinatesLocal(dm, &coords));
3806:   PetscCall(DMGetCoordinateDM(dm, &coordDM));
3807:   if (coordDM) {
3808:     PetscInt coordFields;

3810:     PetscCall(DMGetNumFields(coordDM, &coordFields));
3811:     if (coordFields) {
3812:       PetscClassId id;
3813:       PetscObject  disc;

3815:       PetscCall(DMGetField(coordDM, 0, NULL, &disc));
3816:       PetscCall(PetscObjectGetClassId(disc, &id));
3817:       if (id == PETSCFE_CLASSID) fe = (PetscFE)disc;
3818:     }
3819:   }
3820:   PetscCall(DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd));
3821:   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);
3822:   if (!fe) { /* implicit discretization: affine or multilinear */
3823:     PetscInt  coneSize;
3824:     PetscBool isSimplex, isTensor;

3826:     PetscCall(DMPlexGetConeSize(dm, cell, &coneSize));
3827:     isSimplex = (coneSize == (dimR + 1)) ? PETSC_TRUE : PETSC_FALSE;
3828:     isTensor  = (coneSize == ((depth == 1) ? (1 << dimR) : (2 * dimR))) ? PETSC_TRUE : PETSC_FALSE;
3829:     if (isSimplex) {
3830:       PetscReal detJ, *v0, *J, *invJ;

3832:       PetscCall(DMGetWorkArray(dm, dimC + 2 * dimC * dimC, MPIU_REAL, &v0));
3833:       J    = &v0[dimC];
3834:       invJ = &J[dimC * dimC];
3835:       PetscCall(DMPlexComputeCellGeometryAffineFEM(dm, cell, v0, J, invJ, &detJ));
3836:       for (i = 0; i < numPoints; i++) { /* Apply the inverse affine transformation for each point */
3837:         const PetscReal x0[3] = {-1., -1., -1.};

3839:         CoordinatesRealToRef(dimC, dimR, x0, v0, invJ, &realCoords[dimC * i], &refCoords[dimR * i]);
3840:       }
3841:       PetscCall(DMRestoreWorkArray(dm, dimC + 2 * dimC * dimC, MPIU_REAL, &v0));
3842:     } else if (isTensor) {
3843:       PetscCall(DMPlexCoordinatesToReference_Tensor(coordDM, cell, numPoints, realCoords, refCoords, coords, dimC, dimR));
3844:     } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Unrecognized cone size %" PetscInt_FMT, coneSize);
3845:   } else {
3846:     PetscCall(DMPlexCoordinatesToReference_FE(coordDM, fe, cell, numPoints, realCoords, refCoords, coords, dimC, dimR, 7, NULL));
3847:   }
3848:   PetscFunctionReturn(PETSC_SUCCESS);
3849: }

3851: /*@
3852:   DMPlexReferenceToCoordinates - Map references coordinates to coordinates in the mesh for a single element map.

3854:   Not Collective

3856:   Input Parameters:
3857: + dm        - The mesh, with coordinate maps defined either by a PetscDS for the coordinate `DM` (see `DMGetCoordinateDM()`) or
3858:                implicitly by the coordinates of the corner vertices of the cell: as an affine map for simplicial elements, or
3859:                as a multilinear map for tensor-product elements
3860: . cell      - the cell whose map is used.
3861: . numPoints - the number of points to locate
3862: - refCoords - (numPoints x dimension) array of reference coordinates (see `DMGetDimension()`)

3864:   Output Parameter:
3865: . realCoords - (numPoints x coordinate dimension) array of coordinates (see `DMGetCoordinateDim()`)

3867:   Level: intermediate

3869: .seealso: `DMPLEX`, `DMPlexCoordinatesToReference()`
3870: @*/
3871: PetscErrorCode DMPlexReferenceToCoordinates(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal refCoords[], PetscReal realCoords[])
3872: {
3873:   PetscInt dimC, dimR, depth, cStart, cEnd, i;
3874:   DM       coordDM = NULL;
3875:   Vec      coords;
3876:   PetscFE  fe = NULL;

3878:   PetscFunctionBegin;
3880:   PetscCall(DMGetDimension(dm, &dimR));
3881:   PetscCall(DMGetCoordinateDim(dm, &dimC));
3882:   if (dimR <= 0 || dimC <= 0 || numPoints <= 0) PetscFunctionReturn(PETSC_SUCCESS);
3883:   PetscCall(DMPlexGetDepth(dm, &depth));
3884:   PetscCall(DMGetCoordinatesLocal(dm, &coords));
3885:   PetscCall(DMGetCoordinateDM(dm, &coordDM));
3886:   if (coordDM) {
3887:     PetscInt coordFields;

3889:     PetscCall(DMGetNumFields(coordDM, &coordFields));
3890:     if (coordFields) {
3891:       PetscClassId id;
3892:       PetscObject  disc;

3894:       PetscCall(DMGetField(coordDM, 0, NULL, &disc));
3895:       PetscCall(PetscObjectGetClassId(disc, &id));
3896:       if (id == PETSCFE_CLASSID) fe = (PetscFE)disc;
3897:     }
3898:   }
3899:   PetscCall(DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd));
3900:   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);
3901:   if (!fe) { /* implicit discretization: affine or multilinear */
3902:     PetscInt  coneSize;
3903:     PetscBool isSimplex, isTensor;

3905:     PetscCall(DMPlexGetConeSize(dm, cell, &coneSize));
3906:     isSimplex = (coneSize == (dimR + 1)) ? PETSC_TRUE : PETSC_FALSE;
3907:     isTensor  = (coneSize == ((depth == 1) ? (1 << dimR) : (2 * dimR))) ? PETSC_TRUE : PETSC_FALSE;
3908:     if (isSimplex) {
3909:       PetscReal detJ, *v0, *J;

3911:       PetscCall(DMGetWorkArray(dm, dimC + 2 * dimC * dimC, MPIU_REAL, &v0));
3912:       J = &v0[dimC];
3913:       PetscCall(DMPlexComputeCellGeometryAffineFEM(dm, cell, v0, J, NULL, &detJ));
3914:       for (i = 0; i < numPoints; i++) { /* Apply the affine transformation for each point */
3915:         const PetscReal xi0[3] = {-1., -1., -1.};

3917:         CoordinatesRefToReal(dimC, dimR, xi0, v0, J, &refCoords[dimR * i], &realCoords[dimC * i]);
3918:       }
3919:       PetscCall(DMRestoreWorkArray(dm, dimC + 2 * dimC * dimC, MPIU_REAL, &v0));
3920:     } else if (isTensor) {
3921:       PetscCall(DMPlexReferenceToCoordinates_Tensor(coordDM, cell, numPoints, refCoords, realCoords, coords, dimC, dimR));
3922:     } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Unrecognized cone size %" PetscInt_FMT, coneSize);
3923:   } else {
3924:     PetscCall(DMPlexReferenceToCoordinates_FE(coordDM, fe, cell, numPoints, refCoords, realCoords, coords, dimC, dimR));
3925:   }
3926:   PetscFunctionReturn(PETSC_SUCCESS);
3927: }

3929: 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[])
3930: {
3931:   const PetscInt Nc = uOff[1] - uOff[0];
3932:   PetscInt       c;

3934:   for (c = 0; c < Nc; ++c) f0[c] = u[c];
3935: }

3937: /* Shear applies the transformation, assuming we fix z,
3938:   / 1  0  m_0 \
3939:   | 0  1  m_1 |
3940:   \ 0  0   1  /
3941: */
3942: 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[])
3943: {
3944:   const PetscInt Nc = uOff[1] - uOff[0];
3945:   const PetscInt ax = (PetscInt)PetscRealPart(constants[0]);
3946:   PetscInt       c;

3948:   for (c = 0; c < Nc; ++c) coords[c] = u[c] + constants[c + 1] * u[ax];
3949: }

3951: /* Flare applies the transformation, assuming we fix x_f,

3953:    x_i = x_i * alpha_i x_f
3954: */
3955: 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[])
3956: {
3957:   const PetscInt Nc = uOff[1] - uOff[0];
3958:   const PetscInt cf = (PetscInt)PetscRealPart(constants[0]);
3959:   PetscInt       c;

3961:   for (c = 0; c < Nc; ++c) coords[c] = u[c] * (c == cf ? 1.0 : constants[c + 1] * u[cf]);
3962: }

3964: /*
3965:   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
3966:   will correspond to the top and bottom of our square. So

3968:     (0,0)--(1,0)  ==>  (1,0)--(2,0)      Just a shift of (1,0)
3969:     (0,1)--(1,1)  ==>  (0,1)--(0,2)      Switch x and y

3971:   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:

3973:     (x, y)  ==>  (x+1, \pi/2 y)                           in (r', \theta') space
3974:             ==>  ((x+1) cos(\pi/2 y), (x+1) sin(\pi/2 y)) in (x', y') space
3975: */
3976: 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[])
3977: {
3978:   const PetscReal ri = PetscRealPart(constants[0]);
3979:   const PetscReal ro = PetscRealPart(constants[1]);

3981:   xp[0] = (x[0] * (ro - ri) + ri) * PetscCosReal(0.5 * PETSC_PI * x[1]);
3982:   xp[1] = (x[0] * (ro - ri) + ri) * PetscSinReal(0.5 * PETSC_PI * x[1]);
3983: }

3985: /*
3986:   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
3987:   lower hemisphere and the upper surface onto the top, letting z be the radius.

3989:     (x, y)  ==>  ((z+3)/2, \pi/2 (|x| or |y|), arctan y/x)                                                  in (r', \theta', \phi') space
3990:             ==>  ((z+3)/2 \cos(\theta') cos(\phi'), (z+3)/2 \cos(\theta') sin(\phi'), (z+3)/2 sin(\theta')) in (x', y', z') space
3991: */
3992: 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[])
3993: {
3994:   const PetscReal pi4    = PETSC_PI / 4.0;
3995:   const PetscReal ri     = PetscRealPart(constants[0]);
3996:   const PetscReal ro     = PetscRealPart(constants[1]);
3997:   const PetscReal rp     = (x[2] + 1) * 0.5 * (ro - ri) + ri;
3998:   const PetscReal phip   = PetscAtan2Real(x[1], x[0]);
3999:   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])));

4001:   xp[0] = rp * PetscCosReal(thetap) * PetscCosReal(phip);
4002:   xp[1] = rp * PetscCosReal(thetap) * PetscSinReal(phip);
4003:   xp[2] = rp * PetscSinReal(thetap);
4004: }

4006: /*@C
4007:   DMPlexRemapGeometry - This function maps the original `DM` coordinates to new coordinates.

4009:   Not Collective

4011:   Input Parameters:
4012: + dm   - The `DM`
4013: . time - The time
4014: - func - The function transforming current coordinates to new coordinates

4016:   Calling sequence of `func`:
4017: + dim          - The spatial dimension
4018: . Nf           - The number of input fields (here 1)
4019: . NfAux        - The number of input auxiliary fields
4020: . uOff         - The offset of the coordinates in u[] (here 0)
4021: . uOff_x       - The offset of the coordinates in u_x[] (here 0)
4022: . u            - The coordinate values at this point in space
4023: . u_t          - The coordinate time derivative at this point in space (here `NULL`)
4024: . u_x          - The coordinate derivatives at this point in space
4025: . aOff         - The offset of each auxiliary field in u[]
4026: . aOff_x       - The offset of each auxiliary field in u_x[]
4027: . a            - The auxiliary field values at this point in space
4028: . a_t          - The auxiliary field time derivative at this point in space (or `NULL`)
4029: . a_x          - The auxiliary field derivatives at this point in space
4030: . t            - The current time
4031: . x            - The coordinates of this point (here not used)
4032: . numConstants - The number of constants
4033: . constants    - The value of each constant
4034: - f            - The new coordinates at this point in space

4036:   Level: intermediate

4038: .seealso: `DMPLEX`, `DMGetCoordinates()`, `DMGetCoordinatesLocal()`, `DMGetCoordinateDM()`, `DMProjectFieldLocal()`, `DMProjectFieldLabelLocal()`
4039: @*/
4040: 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[]))
4041: {
4042:   DM           cdm;
4043:   PetscDS      cds;
4044:   DMField      cf;
4045:   PetscObject  obj;
4046:   PetscClassId id;
4047:   Vec          lCoords, tmpCoords;

4049:   PetscFunctionBegin;
4050:   PetscCall(DMGetCoordinateDM(dm, &cdm));
4051:   PetscCall(DMGetCoordinatesLocal(dm, &lCoords));
4052:   PetscCall(DMGetDS(cdm, &cds));
4053:   PetscCall(PetscDSGetDiscretization(cds, 0, &obj));
4054:   PetscCall(PetscObjectGetClassId(obj, &id));
4055:   if (id != PETSCFE_CLASSID) {
4056:     PetscSection       cSection;
4057:     const PetscScalar *constants;
4058:     PetscScalar       *coords, f[16];
4059:     PetscInt           dim, cdim, Nc, vStart, vEnd;

4061:     PetscCall(DMGetDimension(dm, &dim));
4062:     PetscCall(DMGetCoordinateDim(dm, &cdim));
4063:     PetscCheck(cdim <= 16, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Affine version of DMPlexRemapGeometry is currently limited to dimensions <= 16, not %" PetscInt_FMT, cdim);
4064:     PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
4065:     PetscCall(DMGetCoordinateSection(dm, &cSection));
4066:     PetscCall(PetscDSGetConstants(cds, &Nc, &constants));
4067:     PetscCall(VecGetArrayWrite(lCoords, &coords));
4068:     for (PetscInt v = vStart; v < vEnd; ++v) {
4069:       PetscInt uOff[2] = {0, cdim};
4070:       PetscInt off, c;

4072:       PetscCall(PetscSectionGetOffset(cSection, v, &off));
4073:       (*func)(dim, 1, 0, uOff, NULL, &coords[off], NULL, NULL, NULL, NULL, NULL, NULL, NULL, 0.0, NULL, Nc, constants, f);
4074:       for (c = 0; c < cdim; ++c) coords[off + c] = f[c];
4075:     }
4076:     PetscCall(VecRestoreArrayWrite(lCoords, &coords));
4077:   } else {
4078:     PetscCall(DMGetLocalVector(cdm, &tmpCoords));
4079:     PetscCall(VecCopy(lCoords, tmpCoords));
4080:     /* We have to do the coordinate field manually right now since the coordinate DM will not have its own */
4081:     PetscCall(DMGetCoordinateField(dm, &cf));
4082:     cdm->coordinates[0].field = cf;
4083:     PetscCall(DMProjectFieldLocal(cdm, time, tmpCoords, &func, INSERT_VALUES, lCoords));
4084:     cdm->coordinates[0].field = NULL;
4085:     PetscCall(DMRestoreLocalVector(cdm, &tmpCoords));
4086:     PetscCall(DMSetCoordinatesLocal(dm, lCoords));
4087:   }
4088:   PetscFunctionReturn(PETSC_SUCCESS);
4089: }

4091: /*@
4092:   DMPlexShearGeometry - This shears the domain, meaning adds a multiple of the shear coordinate to all other coordinates.

4094:   Not Collective

4096:   Input Parameters:
4097: + dm          - The `DMPLEX`
4098: . direction   - The shear coordinate direction, e.g. `DM_X` is the x-axis
4099: - multipliers - The multiplier m for each direction which is not the shear direction

4101:   Level: intermediate

4103: .seealso: `DMPLEX`, `DMPlexRemapGeometry()`, `DMDirection`, `DM_X`, `DM_Y`, `DM_Z`
4104: @*/
4105: PetscErrorCode DMPlexShearGeometry(DM dm, DMDirection direction, PetscReal multipliers[])
4106: {
4107:   DM             cdm;
4108:   PetscDS        cds;
4109:   PetscScalar   *moduli;
4110:   const PetscInt dir = (PetscInt)direction;
4111:   PetscInt       dE, d, e;

4113:   PetscFunctionBegin;
4114:   PetscCall(DMGetCoordinateDM(dm, &cdm));
4115:   PetscCall(DMGetCoordinateDim(dm, &dE));
4116:   PetscCall(PetscMalloc1(dE + 1, &moduli));
4117:   moduli[0] = dir;
4118:   for (d = 0, e = 0; d < dE; ++d) moduli[d + 1] = d == dir ? 0.0 : (multipliers ? multipliers[e++] : 1.0);
4119:   PetscCall(DMGetDS(cdm, &cds));
4120:   PetscCall(PetscDSSetConstants(cds, dE + 1, moduli));
4121:   PetscCall(DMPlexRemapGeometry(dm, 0.0, coordMap_shear));
4122:   PetscCall(PetscFree(moduli));
4123:   PetscFunctionReturn(PETSC_SUCCESS);
4124: }