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", "rotate", "shear", "flare", "annulus", "shell", "sinusoid", "torus", "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 PetscDefined(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 PetscReal eps   = PETSC_SQRT_MACHINE_EPSILON;
440:   PetscReal       xi[2] = {0., 0.};
441:   PetscReal       x[3], v0[3], J[9], invJ[9], detJ;
442:   PetscInt        embedDim;

444:   PetscFunctionBegin;
445:   PetscCall(DMGetCoordinateDim(dm, &embedDim));
446:   PetscCall(DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ));
447:   for (PetscInt j = 0; j < embedDim; ++j) x[j] = PetscRealPart(point[j]);
448:   for (PetscInt i = 0; i < 2; ++i) {
449:     for (PetscInt j = 0; j < embedDim; ++j) xi[i] += invJ[i * embedDim + j] * (x[j] - v0[j]);
450:   }
451:   if ((xi[0] >= -eps) && (xi[1] >= -eps) && (xi[0] + xi[1] <= 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, embedDim;
490:   PetscBool          isDG;

492:   PetscFunctionBegin;
493:   PetscCall(DMPlexGetCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
494:   embedDim = numCoords / 4;
495:   PetscCheck(!(numCoords % 4), PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Quadrilateral should have 8 coordinates, not %" PetscInt_FMT, numCoords);
496:   // Treat linear quads as Monge surfaces, so we just locate on the projection to x-y (could instead project to 2D)
497:   for (PetscInt f = 0; f < 4; ++f) {
498:     PetscReal x_i = PetscRealPart(coords[faces[2 * f + 0] * embedDim + 0]);
499:     PetscReal y_i = PetscRealPart(coords[faces[2 * f + 0] * embedDim + 1]);
500:     PetscReal x_j = PetscRealPart(coords[faces[2 * f + 1] * embedDim + 0]);
501:     PetscReal y_j = PetscRealPart(coords[faces[2 * f + 1] * embedDim + 1]);

503:     if ((x == x_j) && (y == y_j)) {
504:       // point is a corner
505:       crossings = 1;
506:       break;
507:     }
508:     if ((y_j > y) != (y_i > y)) {
509:       PetscReal slope = (x - x_j) * (y_i - y_j) - (x_i - x_j) * (y - y_j);
510:       if (slope == 0) {
511:         // point is a corner
512:         crossings = 1;
513:         break;
514:       }
515:       if ((slope < 0) != (y_i < y_j)) ++crossings;
516:     }
517:   }
518:   if (crossings % 2) *cell = c;
519:   else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
520:   PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
521:   PetscFunctionReturn(PETSC_SUCCESS);
522: }

524: static PetscErrorCode DMPlexLocatePoint_Quad_2D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
525: {
526:   DM           cdm;
527:   PetscInt     degree, dimR, dimC;
528:   PetscFE      fe;
529:   PetscClassId id;
530:   PetscSpace   sp;
531:   PetscReal    pointR[3], ref[3], error;
532:   Vec          coords;
533:   PetscBool    found = PETSC_FALSE;

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

561:     normPoint = normPoint > PETSC_SMALL ? normPoint : 1.0;
562:     PetscCall(DMPlexReferenceToCoordinates_FE(cdm, fe, c, 1, ref, real, coords, dimC, dimR));
563:     inverseError = DMPlex_DistRealD_Internal(dimC, real, pointR);
564:     if (inverseError > PETSC_SQRT_MACHINE_EPSILON * normPoint) found = PETSC_FALSE;
565:     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));
566:   }
567:   if (found) *cell = c;
568:   else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
569:   PetscFunctionReturn(PETSC_SUCCESS);
570: }

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

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

588:   if ((xi >= -eps) && (eta >= -eps) && (zeta >= -eps) && (xi + eta + zeta <= 2.0 + eps)) *cell = c;
589:   else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
590:   PetscFunctionReturn(PETSC_SUCCESS);
591: }

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

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

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

628:     /* Check that projected point is in face (2D location problem) */
629:     if (dot < 0.0) {
630:       found = PETSC_FALSE;
631:       break;
632:     }
633:   }
634:   if (found) *cell = c;
635:   else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
636:   PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
637:   PetscFunctionReturn(PETSC_SUCCESS);
638: }

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

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

677:     normPoint = normPoint > PETSC_SMALL ? normPoint : 1.0;
678:     PetscCall(DMPlexReferenceToCoordinates_FE(cdm, fe, c, 1, ref, real, coords, dimC, dimR));
679:     inverseError = DMPlex_DistRealD_Internal(dimC, real, pointR);
680:     if (inverseError > PETSC_SQRT_MACHINE_EPSILON * normPoint) found = PETSC_FALSE;
681:     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));
682:   }
683:   if (found) *cell = c;
684:   else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
685:   PetscFunctionReturn(PETSC_SUCCESS);
686: }

688: static PetscErrorCode PetscGridHashInitialize_Internal(PetscGridHash box, PetscInt dim, const PetscScalar point[])
689: {
690:   PetscInt d;

692:   PetscFunctionBegin;
693:   box->dim = dim;
694:   for (d = 0; d < dim; ++d) box->lower[d] = box->upper[d] = point ? PetscRealPart(point[d]) : 0.;
695:   PetscFunctionReturn(PETSC_SUCCESS);
696: }

698: /*@
699:   PetscGridHashCreate - Create a `PetscGridHash` for spatially locating points in a mesh.

701:   Collective

703:   Input Parameters:
704: + comm  - the MPI communicator
705: . dim   - the spatial dimension
706: - point - an initial point used to seed the bounding box, or `NULL` for a zero-initialized box

708:   Output Parameter:
709: . box - the newly created `PetscGridHash`

711:   Level: developer

713: .seealso: `DMPLEX`, `PetscGridHash`, `PetscGridHashEnlarge()`, `PetscGridHashDestroy()`
714: @*/
715: PetscErrorCode PetscGridHashCreate(MPI_Comm comm, PetscInt dim, const PetscScalar point[], PetscGridHash *box)
716: {
717:   PetscFunctionBegin;
718:   PetscCall(PetscCalloc1(1, box));
719:   PetscCall(PetscGridHashInitialize_Internal(*box, dim, point));
720:   PetscFunctionReturn(PETSC_SUCCESS);
721: }

723: /*@
724:   PetscGridHashEnlarge - Enlarge the bounding box of a `PetscGridHash` to include a new point.

726:   Not Collective

728:   Input Parameters:
729: + box   - the `PetscGridHash`
730: - point - the point whose coordinates extend the box's lower and upper bounds

732:   Level: developer

734: .seealso: `DMPLEX`, `PetscGridHash`, `PetscGridHashCreate()`, `PetscGridHashDestroy()`
735: @*/
736: PetscErrorCode PetscGridHashEnlarge(PetscGridHash box, const PetscScalar point[])
737: {
738:   PetscInt d;

740:   PetscFunctionBegin;
741:   for (d = 0; d < box->dim; ++d) {
742:     box->lower[d] = PetscMin(box->lower[d], PetscRealPart(point[d]));
743:     box->upper[d] = PetscMax(box->upper[d], PetscRealPart(point[d]));
744:   }
745:   PetscFunctionReturn(PETSC_SUCCESS);
746: }

748: static PetscErrorCode DMPlexCreateGridHash(DM dm, PetscGridHash *box)
749: {
750:   Vec                coordinates;
751:   const PetscScalar *a;
752:   PetscInt           cdim, cStart, cEnd;

754:   PetscFunctionBegin;
755:   PetscCall(DMGetCoordinateDim(dm, &cdim));
756:   PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
757:   PetscCall(DMGetCoordinatesLocal(dm, &coordinates));

759:   PetscCall(VecGetArrayRead(coordinates, &a));
760:   PetscCall(PetscGridHashCreate(PetscObjectComm((PetscObject)dm), cdim, a, box));
761:   PetscCall(VecRestoreArrayRead(coordinates, &a));
762:   for (PetscInt c = cStart; c < cEnd; ++c) {
763:     const PetscScalar *array;
764:     PetscScalar       *coords = NULL;
765:     PetscInt           numCoords;
766:     PetscBool          isDG;

768:     PetscCall(DMPlexGetCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
769:     for (PetscInt i = 0; i < numCoords / cdim; ++i) PetscCall(PetscGridHashEnlarge(*box, &coords[i * cdim]));
770:     PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
771:   }
772:   PetscFunctionReturn(PETSC_SUCCESS);
773: }

775: /*@C
776:   PetscGridHashSetGrid - Divide the grid into boxes

778:   Not Collective

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

785:   Level: developer

787: .seealso: `DMPLEX`, `PetscGridHashCreate()`
788: @*/
789: PetscErrorCode PetscGridHashSetGrid(PetscGridHash box, const PetscInt n[], const PetscReal h[])
790: {
791:   PetscInt d;

793:   PetscFunctionBegin;
794:   PetscAssertPointer(n, 2);
795:   if (h) PetscAssertPointer(h, 3);
796:   for (d = 0; d < box->dim; ++d) {
797:     box->extent[d] = box->upper[d] - box->lower[d];
798:     if (n[d] == PETSC_DETERMINE) {
799:       PetscCheck(h, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Missing h");
800:       box->h[d] = h[d];
801:       box->n[d] = PetscCeilReal(box->extent[d] / h[d]);
802:     } else {
803:       box->n[d] = n[d];
804:       box->h[d] = box->extent[d] / n[d];
805:     }
806:   }
807:   PetscFunctionReturn(PETSC_SUCCESS);
808: }

810: /*@C
811:   PetscGridHashGetEnclosingBox - Find the grid boxes containing each input point

813:   Not Collective

815:   Input Parameters:
816: + box       - The grid hash object
817: . numPoints - The number of input points
818: - points    - The input point coordinates

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

824:   Level: developer

826:   Note:
827:   This only guarantees that a box contains a point, not that a cell does.

829: .seealso: `DMPLEX`, `PetscGridHashCreate()`
830: @*/
831: PetscErrorCode PetscGridHashGetEnclosingBox(PetscGridHash box, PetscInt numPoints, const PetscScalar points[], PetscInt dboxes[], PetscInt boxes[])
832: {
833:   const PetscReal *lower = box->lower;
834:   const PetscReal *upper = box->upper;
835:   const PetscReal *h     = box->h;
836:   const PetscInt  *n     = box->n;
837:   const PetscInt   dim   = box->dim;
838:   PetscInt         d, p;

840:   PetscFunctionBegin;
841:   for (p = 0; p < numPoints; ++p) {
842:     for (d = 0; d < dim; ++d) {
843:       PetscInt dbox = PetscFloorReal((PetscRealPart(points[p * dim + d]) - lower[d]) / h[d]);

845:       if (dbox == n[d] && PetscAbsReal(PetscRealPart(points[p * dim + d]) - upper[d]) < 1.0e-9) dbox = n[d] - 1;
846:       if (dbox == -1 && PetscAbsReal(PetscRealPart(points[p * dim + d]) - lower[d]) < 1.0e-9) dbox = 0;
847:       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]);
848:       dboxes[p * dim + d] = dbox;
849:     }
850:     if (boxes)
851:       for (d = dim - 2, boxes[p] = dboxes[p * dim + dim - 1]; d >= 0; --d) boxes[p] = boxes[p] * n[d] + dboxes[p * dim + d];
852:   }
853:   PetscFunctionReturn(PETSC_SUCCESS);
854: }

856: /*
857:   PetscGridHashGetEnclosingBoxQuery - Find the grid boxes containing each input point

859:   Not Collective

861:   Input Parameters:
862: + box         - The grid hash object
863: . cellSection - The PetscSection mapping cells to boxes
864: . numPoints   - The number of input points
865: - points      - The input point coordinates

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

872:   Level: developer

874:   Note:
875:   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.

877: .seealso: `DMPLEX`, `PetscGridHashGetEnclosingBox()`
878: */
879: static PetscErrorCode PetscGridHashGetEnclosingBoxQuery(PetscGridHash box, PetscSection cellSection, PetscInt numPoints, const PetscScalar points[], PetscInt dboxes[], PetscInt boxes[], PetscBool *found)
880: {
881:   const PetscReal *lower = box->lower;
882:   const PetscReal *upper = box->upper;
883:   const PetscReal *h     = box->h;
884:   const PetscInt  *n     = box->n;
885:   const PetscInt   dim   = box->dim;
886:   PetscInt         bStart, bEnd, d, p;

888:   PetscFunctionBegin;
890:   *found = PETSC_FALSE;
891:   PetscCall(PetscSectionGetChart(box->cellSection, &bStart, &bEnd));
892:   for (p = 0; p < numPoints; ++p) {
893:     for (d = 0; d < dim; ++d) {
894:       PetscInt dbox = PetscFloorReal((PetscRealPart(points[p * dim + d]) - lower[d]) / h[d]);

896:       if (dbox == n[d] && PetscAbsReal(PetscRealPart(points[p * dim + d]) - upper[d]) < 1.0e-9) dbox = n[d] - 1;
897:       if (dbox < 0 || dbox >= n[d]) PetscFunctionReturn(PETSC_SUCCESS);
898:       dboxes[p * dim + d] = dbox;
899:     }
900:     if (boxes)
901:       for (d = dim - 2, boxes[p] = dboxes[p * dim + dim - 1]; d >= 0; --d) boxes[p] = boxes[p] * n[d] + dboxes[p * dim + d];
902:     // It is possible for a box to overlap no grid cells
903:     if (boxes[p] < bStart || boxes[p] >= bEnd) PetscFunctionReturn(PETSC_SUCCESS);
904:   }
905:   *found = PETSC_TRUE;
906:   PetscFunctionReturn(PETSC_SUCCESS);
907: }

909: /*@
910:   PetscGridHashDestroy - Destroy a `PetscGridHash` and free its resources.

912:   Collective

914:   Input Parameter:
915: . box - the `PetscGridHash` to destroy; set to `NULL` on return

917:   Level: developer

919: .seealso: `DMPLEX`, `PetscGridHash`, `PetscGridHashCreate()`, `PetscGridHashEnlarge()`
920: @*/
921: PetscErrorCode PetscGridHashDestroy(PetscGridHash *box)
922: {
923:   PetscFunctionBegin;
924:   if (*box) {
925:     PetscCall(PetscSectionDestroy(&(*box)->cellSection));
926:     PetscCall(ISDestroy(&(*box)->cells));
927:     PetscCall(DMLabelDestroy(&(*box)->cellsSparse));
928:   }
929:   PetscCall(PetscFree(*box));
930:   PetscFunctionReturn(PETSC_SUCCESS);
931: }

933: PetscErrorCode DMPlexLocatePoint_Internal(DM dm, PetscInt dim, const PetscScalar point[], PetscInt cellStart, PetscInt *cell)
934: {
935:   DMPolytopeType ct;

937:   PetscFunctionBegin;
938:   PetscCall(DMPlexGetCellType(dm, cellStart, &ct));
939:   switch (ct) {
940:   case DM_POLYTOPE_SEGMENT:
941:     PetscCall(DMPlexLocatePoint_Simplex_1D_Internal(dm, point, cellStart, cell));
942:     break;
943:   case DM_POLYTOPE_TRIANGLE:
944:     PetscCall(DMPlexLocatePoint_Simplex_2D_Internal(dm, point, cellStart, cell));
945:     break;
946:   case DM_POLYTOPE_QUADRILATERAL:
947:     PetscCall(DMPlexLocatePoint_Quad_2D_Internal(dm, point, cellStart, cell));
948:     break;
949:   case DM_POLYTOPE_TETRAHEDRON:
950:     PetscCall(DMPlexLocatePoint_Simplex_3D_Internal(dm, point, cellStart, cell));
951:     break;
952:   case DM_POLYTOPE_HEXAHEDRON:
953:     PetscCall(DMPlexLocatePoint_Hex_3D_Internal(dm, point, cellStart, cell));
954:     break;
955:   default:
956:     SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No point location for cell %" PetscInt_FMT " with type %s", cellStart, DMPolytopeTypes[ct]);
957:   }
958:   PetscFunctionReturn(PETSC_SUCCESS);
959: }

961: /*
962:   DMPlexClosestPoint_Internal - Returns the closest point in the cell to the given point
963: */
964: static PetscErrorCode DMPlexClosestPoint_Internal(DM dm, PetscInt dim, const PetscScalar point[], PetscInt cell, PetscReal cpoint[])
965: {
966:   DMPolytopeType ct;

968:   PetscFunctionBegin;
969:   PetscCall(DMPlexGetCellType(dm, cell, &ct));
970:   switch (ct) {
971:   case DM_POLYTOPE_TRIANGLE:
972:     PetscCall(DMPlexClosestPoint_Simplex_2D_Internal(dm, point, cell, cpoint));
973:     break;
974: #if 0
975:     case DM_POLYTOPE_QUADRILATERAL:
976:     PetscCall(DMPlexClosestPoint_General_2D_Internal(dm, point, cell, cpoint));break;
977:     case DM_POLYTOPE_TETRAHEDRON:
978:     PetscCall(DMPlexClosestPoint_Simplex_3D_Internal(dm, point, cell, cpoint));break;
979:     case DM_POLYTOPE_HEXAHEDRON:
980:     PetscCall(DMPlexClosestPoint_General_3D_Internal(dm, point, cell, cpoint));break;
981: #endif
982:   default:
983:     SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No closest point location for cell %" PetscInt_FMT " with type %s", cell, DMPolytopeTypes[ct]);
984:   }
985:   PetscFunctionReturn(PETSC_SUCCESS);
986: }

988: /*
989:   DMPlexComputeGridHash_Internal - Create a grid hash structure covering the `DMPLEX`

991:   Collective

993:   Input Parameter:
994: . dm - The `DMPLEX`

996:   Output Parameter:
997: . localBox - The grid hash object

999:   Level: developer

1001:   Notes:
1002:   How do we determine all boxes intersecting a given cell?

1004:   1) Get convex body enclosing cell. We will use a box called the box-hull.

1006:   2) Get smallest brick of boxes enclosing the box-hull

1008:   3) Each box is composed of 6 planes, 3 lower and 3 upper. We loop over dimensions, and
1009:      for each new plane determine whether the cell is on the negative side, positive side, or intersects it.

1011:      a) If the cell is on the negative side of the lower planes, it is not in the box

1013:      b) If the cell is on the positive side of the upper planes, it is not in the box

1015:      c) If there is no intersection, it is in the box

1017:      d) If any intersection point is within the box limits, it is in the box

1019: .seealso: `DMPLEX`, `PetscGridHashCreate()`, `PetscGridHashGetEnclosingBox()`
1020: */
1021: static PetscErrorCode DMPlexComputeGridHash_Internal(DM dm, PetscGridHash *localBox)
1022: {
1023:   PetscInt        debug = ((DM_Plex *)dm->data)->printLocate;
1024:   PetscGridHash   lbox;
1025:   PetscSF         sf;
1026:   const PetscInt *leaves;
1027:   PetscInt       *dboxes, *boxes;
1028:   PetscInt        cdim, cStart, cEnd, Nl = -1;
1029:   PetscBool       flg;

1031:   PetscFunctionBegin;
1032:   PetscCall(DMGetCoordinateDim(dm, &cdim));
1033:   PetscCall(DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd));
1034:   PetscCall(DMPlexCreateGridHash(dm, &lbox));
1035:   {
1036:     PetscInt n[3], d = 3;

1038:     PetscCall(PetscOptionsGetIntArray(NULL, ((PetscObject)dm)->prefix, "-dm_plex_hash_box_faces", n, &d, &flg));
1039:     if (flg) {
1040:       for (PetscInt i = d; i < cdim; ++i) n[i] = n[d - 1];
1041:     } else {
1042:       for (PetscInt i = 0; i < cdim; ++i) n[i] = PetscMax(2, PetscFloorReal(PetscPowReal((PetscReal)(cEnd - cStart), 1.0 / cdim) * 0.8));
1043:     }
1044:     PetscCall(PetscGridHashSetGrid(lbox, n, NULL));
1045:     if (debug)
1046:       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.,
1047:                             (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.));
1048:   }

1050:   PetscCall(DMGetPointSF(dm, &sf));
1051:   if (sf) PetscCall(PetscSFGetGraph(sf, NULL, &Nl, &leaves, NULL));
1052:   Nl = PetscMax(Nl, 0);
1053:   PetscCall(PetscCalloc2(16 * cdim, &dboxes, 16, &boxes));

1055:   PetscCall(DMLabelCreate(PETSC_COMM_SELF, "cells", &lbox->cellsSparse));
1056:   PetscCall(DMLabelCreateIndex(lbox->cellsSparse, cStart, cEnd));
1057:   for (PetscInt c = cStart; c < cEnd; ++c) {
1058:     PetscReal          intPoints[6 * 6 * 6 * 3];
1059:     const PetscScalar *array;
1060:     PetscScalar       *coords            = NULL;
1061:     const PetscReal   *h                 = lbox->h;
1062:     PetscReal          normal[9]         = {1., 0., 0., 0., 1., 0., 0., 0., 1.};
1063:     PetscReal         *lowerIntPoints[3] = {&intPoints[0 * 6 * 6 * 3], &intPoints[1 * 6 * 6 * 3], &intPoints[2 * 6 * 6 * 3]};
1064:     PetscReal         *upperIntPoints[3] = {&intPoints[3 * 6 * 6 * 3], &intPoints[4 * 6 * 6 * 3], &intPoints[5 * 6 * 6 * 3]};
1065:     PetscReal          lp[3], up[3], *tmp;
1066:     PetscInt           numCoords, idx, dlim[6], lowerInt[3], upperInt[3];
1067:     PetscBool          isDG, lower[3], upper[3];

1069:     PetscCall(PetscFindInt(c, Nl, leaves, &idx));
1070:     if (idx >= 0) continue;
1071:     // Get grid of boxes containing the cell
1072:     PetscCall(DMPlexGetCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
1073:     PetscCall(PetscGridHashGetEnclosingBox(lbox, numCoords / cdim, coords, dboxes, boxes));
1074:     PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
1075:     for (PetscInt d = 0; d < cdim; ++d) dlim[d * 2 + 0] = dlim[d * 2 + 1] = dboxes[d];
1076:     for (PetscInt d = cdim; d < 3; ++d) dlim[d * 2 + 0] = dlim[d * 2 + 1] = 0;
1077:     for (PetscInt e = 1; e < numCoords / cdim; ++e) {
1078:       for (PetscInt d = 0; d < cdim; ++d) {
1079:         dlim[d * 2 + 0] = PetscMin(dlim[d * 2 + 0], dboxes[e * cdim + d]);
1080:         dlim[d * 2 + 1] = PetscMax(dlim[d * 2 + 1], dboxes[e * cdim + d]);
1081:       }
1082:     }
1083:     if (debug > 4) {
1084:       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]));
1085:     }
1086:     // Initialize with lower planes for first box
1087:     for (PetscInt d = 0; d < cdim; ++d) {
1088:       lp[d] = lbox->lower[d] + dlim[d * 2 + 0] * h[d];
1089:       up[d] = lp[d] + h[d];
1090:     }
1091:     for (PetscInt d = 0; d < cdim; ++d) {
1092:       PetscCall(DMPlexGetPlaneCellIntersection_Internal(dm, c, lp, &normal[d * 3], &lower[d], &lowerInt[d], lowerIntPoints[d]));
1093:       if (debug > 4) {
1094:         if (!lowerInt[d])
1095:           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"));
1096:         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]));
1097:       }
1098:     }
1099:     // Loop over grid
1100:     for (PetscInt k = dlim[2 * 2 + 0]; k <= dlim[2 * 2 + 1]; ++k, lp[2] = up[2], up[2] += h[2]) {
1101:       if (cdim > 2) PetscCall(DMPlexGetPlaneCellIntersection_Internal(dm, c, up, &normal[3 * 2], &upper[2], &upperInt[2], upperIntPoints[2]));
1102:       if (cdim > 2 && debug > 4) {
1103:         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"));
1104:         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]));
1105:       }
1106:       for (PetscInt j = dlim[1 * 2 + 0]; j <= dlim[1 * 2 + 1]; ++j, lp[1] = up[1], up[1] += h[1]) {
1107:         if (cdim > 1) PetscCall(DMPlexGetPlaneCellIntersection_Internal(dm, c, up, &normal[3 * 1], &upper[1], &upperInt[1], upperIntPoints[1]));
1108:         if (cdim > 1 && debug > 4) {
1109:           if (!upperInt[1])
1110:             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"));
1111:           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]));
1112:         }
1113:         for (PetscInt i = dlim[0 * 2 + 0]; i <= dlim[0 * 2 + 1]; ++i, lp[0] = up[0], up[0] += h[0]) {
1114:           const PetscInt box    = (k * lbox->n[1] + j) * lbox->n[0] + i;
1115:           PetscBool      excNeg = PETSC_TRUE;
1116:           PetscBool      excPos = PETSC_TRUE;
1117:           PetscInt       NlInt  = 0;
1118:           PetscInt       NuInt  = 0;

1120:           PetscCall(DMPlexGetPlaneCellIntersection_Internal(dm, c, up, &normal[3 * 0], &upper[0], &upperInt[0], upperIntPoints[0]));
1121:           if (debug > 4) {
1122:             if (!upperInt[0])
1123:               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"));
1124:             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]));
1125:           }
1126:           for (PetscInt d = 0; d < cdim; ++d) {
1127:             NlInt += lowerInt[d];
1128:             NuInt += upperInt[d];
1129:           }
1130:           // If there is no intersection...
1131:           if (!NlInt && !NuInt) {
1132:             // If the cell is on the negative side of the lower planes, it is not in the box
1133:             for (PetscInt d = 0; d < cdim; ++d)
1134:               if (lower[d]) {
1135:                 excNeg = PETSC_FALSE;
1136:                 break;
1137:               }
1138:             // If the cell is on the positive side of the upper planes, it is not in the box
1139:             for (PetscInt d = 0; d < cdim; ++d)
1140:               if (!upper[d]) {
1141:                 excPos = PETSC_FALSE;
1142:                 break;
1143:               }
1144:             if (excNeg || excPos) {
1145:               if (debug && excNeg) PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Cell %" PetscInt_FMT " is on the negative side of the lower plane\n", c));
1146:               if (debug && excPos) PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Cell %" PetscInt_FMT " is on the positive side of the upper plane\n", c));
1147:               continue;
1148:             }
1149:             // Otherwise it is in the box
1150:             if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Cell %" PetscInt_FMT " is contained in box %" PetscInt_FMT "\n", c, box));
1151:             PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
1152:             continue;
1153:           }
1154:           /*
1155:             If any intersection point is within the box limits, it is in the box
1156:             We need to have tolerances here since intersection point calculations can introduce errors
1157:             Initialize a count to track which planes have intersection outside the box.
1158:             if two adjacent planes have intersection points upper and lower all outside the box, look
1159:             first at if another plane has intersection points outside the box, if so, it is inside the cell
1160:             look next if no intersection points exist on the other planes, and check if the planes are on the
1161:             outside of the intersection points but on opposite ends. If so, the box cuts through the cell.
1162:           */
1163:           PetscInt outsideCount[6] = {0, 0, 0, 0, 0, 0};
1164:           for (PetscInt plane = 0; plane < cdim; ++plane) {
1165:             for (PetscInt ip = 0; ip < lowerInt[plane]; ++ip) {
1166:               PetscInt d;

1168:               for (d = 0; d < cdim; ++d) {
1169:                 if ((lowerIntPoints[plane][ip * cdim + d] < (lp[d] - PETSC_SMALL)) || (lowerIntPoints[plane][ip * cdim + d] > (up[d] + PETSC_SMALL))) {
1170:                   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
1171:                   break;
1172:                 }
1173:               }
1174:               if (d == cdim) {
1175:                 if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Cell %" PetscInt_FMT " intersected lower plane %" PetscInt_FMT " of box %" PetscInt_FMT "\n", c, plane, box));
1176:                 PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
1177:                 goto end;
1178:               }
1179:             }
1180:             for (PetscInt ip = 0; ip < upperInt[plane]; ++ip) {
1181:               PetscInt d;

1183:               for (d = 0; d < cdim; ++d) {
1184:                 if ((upperIntPoints[plane][ip * cdim + d] < (lp[d] - PETSC_SMALL)) || (upperIntPoints[plane][ip * cdim + d] > (up[d] + PETSC_SMALL))) {
1185:                   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
1186:                   break;
1187:                 }
1188:               }
1189:               if (d == cdim) {
1190:                 if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Cell %" PetscInt_FMT " intersected upper plane %" PetscInt_FMT " of box %" PetscInt_FMT "\n", c, plane, box));
1191:                 PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
1192:                 goto end;
1193:               }
1194:             }
1195:           }
1196:           /*
1197:              Check the planes with intersections
1198:              in 2D, check if the square falls in the middle of a cell
1199:              ie all four planes have intersection points outside of the box
1200:              You do not want to be doing this, because it means your grid hashing is finer than your grid,
1201:              but we should still support it I guess
1202:           */
1203:           if (cdim == 2) {
1204:             PetscInt nIntersects = 0;
1205:             for (PetscInt d = 0; d < cdim; ++d) nIntersects += (outsideCount[d] + outsideCount[d + cdim]);
1206:             // if the count adds up to 8, that means each plane has 2 external intersections and thus it is in the cell
1207:             if (nIntersects == 8) {
1208:               PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
1209:               goto end;
1210:             }
1211:           }
1212:           /*
1213:              In 3 dimensions, if two adjacent planes have at least 3 intersections outside the cell in the appropriate direction,
1214:              we then check the 3rd planar dimension. If a plane falls between intersection points, the cell belongs to that box.
1215:              If the planes are on opposite sides of the intersection points, the cell belongs to that box and it passes through the cell.
1216:           */
1217:           if (cdim == 3) {
1218:             PetscInt faces[3] = {0, 0, 0}, checkInternalFace = 0;
1219:             // Find two adjacent planes with at least 3 intersection points in the upper and lower
1220:             // if the third plane has 3 intersection points or more, a pyramid base is formed on that plane and it is in the cell
1221:             for (PetscInt d = 0; d < cdim; ++d)
1222:               if (outsideCount[d] >= 3 && outsideCount[cdim + d] >= 3) {
1223:                 faces[d]++;
1224:                 checkInternalFace++;
1225:               }
1226:             if (checkInternalFace == 3) {
1227:               // All planes have 3 intersection points, add it.
1228:               PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
1229:               goto end;
1230:             }
1231:             // Gross, figure out which adjacent faces have at least 3 points
1232:             PetscInt nonIntersectingFace = -1;
1233:             if (faces[0] == faces[1]) nonIntersectingFace = 2;
1234:             if (faces[0] == faces[2]) nonIntersectingFace = 1;
1235:             if (faces[1] == faces[2]) nonIntersectingFace = 0;
1236:             if (nonIntersectingFace >= 0) {
1237:               for (PetscInt plane = 0; plane < cdim; ++plane) {
1238:                 if (!lowerInt[nonIntersectingFace] && !upperInt[nonIntersectingFace]) continue;
1239:                 // 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.
1240:                 for (PetscInt ip = 0; ip < lowerInt[nonIntersectingFace]; ++ip) {
1241:                   if (lowerIntPoints[plane][ip * cdim + nonIntersectingFace] > lp[nonIntersectingFace] - PETSC_SMALL || lowerIntPoints[plane][ip * cdim + nonIntersectingFace] < up[nonIntersectingFace] + PETSC_SMALL) goto setpoint;
1242:                 }
1243:                 for (PetscInt ip = 0; ip < upperInt[nonIntersectingFace]; ++ip) {
1244:                   if (upperIntPoints[plane][ip * cdim + nonIntersectingFace] > lp[nonIntersectingFace] - PETSC_SMALL || upperIntPoints[plane][ip * cdim + nonIntersectingFace] < up[nonIntersectingFace] + PETSC_SMALL) goto setpoint;
1245:                 }
1246:                 goto end;
1247:               }
1248:               // The points are within the bonds of the non intersecting planes, add it.
1249:             setpoint:
1250:               PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
1251:               goto end;
1252:             }
1253:           }
1254:         end:
1255:           lower[0]          = upper[0];
1256:           lowerInt[0]       = upperInt[0];
1257:           tmp               = lowerIntPoints[0];
1258:           lowerIntPoints[0] = upperIntPoints[0];
1259:           upperIntPoints[0] = tmp;
1260:         }
1261:         lp[0]             = lbox->lower[0] + dlim[0 * 2 + 0] * h[0];
1262:         up[0]             = lp[0] + h[0];
1263:         lower[1]          = upper[1];
1264:         lowerInt[1]       = upperInt[1];
1265:         tmp               = lowerIntPoints[1];
1266:         lowerIntPoints[1] = upperIntPoints[1];
1267:         upperIntPoints[1] = tmp;
1268:       }
1269:       lp[1]             = lbox->lower[1] + dlim[1 * 2 + 0] * h[1];
1270:       up[1]             = lp[1] + h[1];
1271:       lower[2]          = upper[2];
1272:       lowerInt[2]       = upperInt[2];
1273:       tmp               = lowerIntPoints[2];
1274:       lowerIntPoints[2] = upperIntPoints[2];
1275:       upperIntPoints[2] = tmp;
1276:     }
1277:   }
1278:   PetscCall(PetscFree2(dboxes, boxes));

1280:   if (debug) PetscCall(DMLabelView(lbox->cellsSparse, PETSC_VIEWER_STDOUT_SELF));
1281:   PetscCall(DMLabelConvertToSection(lbox->cellsSparse, &lbox->cellSection, &lbox->cells));
1282:   PetscCall(DMLabelDestroy(&lbox->cellsSparse));
1283:   *localBox = lbox;
1284:   PetscFunctionReturn(PETSC_SUCCESS);
1285: }

1287: PetscErrorCode DMLocatePoints_Plex(DM dm, Vec v, DMPointLocationType ltype, PetscSF cellSF)
1288: {
1289:   PetscInt        debug = ((DM_Plex *)dm->data)->printLocate;
1290:   DM_Plex        *mesh  = (DM_Plex *)dm->data;
1291:   PetscBool       hash = mesh->useHashLocation, reuse = PETSC_FALSE;
1292:   PetscInt        bs, numPoints, numFound, *found = NULL;
1293:   PetscInt        cdim, Nl = 0, cStart, cEnd, numCells;
1294:   PetscSF         sf;
1295:   const PetscInt *leaves;
1296:   const PetscInt *boxCells;
1297:   PetscSFNode    *cells;
1298:   PetscScalar    *a;
1299:   PetscMPIInt     result;
1300:   PetscLogDouble  t0, t1;
1301:   PetscReal       gmin[3], gmax[3];
1302:   PetscInt        terminating_query_type[] = {0, 0, 0};
1303:   PetscMPIInt     rank;

1305:   PetscFunctionBegin;
1306:   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank));
1307:   PetscCall(PetscLogEventBegin(DMPLEX_LocatePoints, 0, 0, 0, 0));
1308:   PetscCall(PetscTime(&t0));
1309:   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.");
1310:   PetscCall(DMGetCoordinateDim(dm, &cdim));
1311:   PetscCall(VecGetBlockSize(v, &bs));
1312:   PetscCallMPI(MPI_Comm_compare(PetscObjectComm((PetscObject)cellSF), PETSC_COMM_SELF, &result));
1313:   PetscCheck(result == MPI_IDENT || result == MPI_CONGRUENT, PetscObjectComm((PetscObject)cellSF), PETSC_ERR_SUP, "Trying parallel point location: only local point location supported");
1314:   // We ignore extra coordinates
1315:   PetscCheck(bs >= cdim, PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Block size for point vector %" PetscInt_FMT " must be the mesh coordinate dimension %" PetscInt_FMT, bs, cdim);
1316:   PetscCall(DMGetCoordinatesLocalSetUp(dm));
1317:   PetscCall(DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd));
1318:   PetscCall(DMGetPointSF(dm, &sf));
1319:   if (sf) PetscCall(PetscSFGetGraph(sf, NULL, &Nl, &leaves, NULL));
1320:   Nl = PetscMax(Nl, 0);
1321:   PetscCall(VecGetLocalSize(v, &numPoints));
1322:   PetscCall(VecGetArray(v, &a));
1323:   numPoints /= bs;
1324:   {
1325:     const PetscSFNode *sf_cells;

1327:     PetscCall(PetscSFGetGraph(cellSF, NULL, NULL, NULL, &sf_cells));
1328:     if (sf_cells) {
1329:       PetscCall(PetscInfo(dm, "[DMLocatePoints_Plex] Re-using existing StarForest node list\n"));
1330:       cells = (PetscSFNode *)sf_cells;
1331:       reuse = PETSC_TRUE;
1332:     } else {
1333:       PetscCall(PetscInfo(dm, "[DMLocatePoints_Plex] Creating and initializing new StarForest node list\n"));
1334:       PetscCall(PetscMalloc1(numPoints, &cells));
1335:       /* initialize cells if created */
1336:       for (PetscInt p = 0; p < numPoints; p++) {
1337:         cells[p].rank  = 0;
1338:         cells[p].index = DMLOCATEPOINT_POINT_NOT_FOUND;
1339:       }
1340:     }
1341:   }
1342:   PetscCall(DMGetBoundingBox(dm, gmin, gmax));
1343:   if (hash) {
1344:     if (!mesh->lbox) {
1345:       PetscCall(PetscInfo(dm, "Initializing grid hashing\n"));
1346:       PetscCall(DMPlexComputeGridHash_Internal(dm, &mesh->lbox));
1347:     }
1348:     /* Designate the local box for each point */
1349:     /* Send points to correct process */
1350:     /* Search cells that lie in each subbox */
1351:     /*   Should we bin points before doing search? */
1352:     PetscCall(ISGetIndices(mesh->lbox->cells, &boxCells));
1353:   }
1354:   numFound = 0;
1355:   for (PetscInt p = 0; p < numPoints; ++p) {
1356:     const PetscScalar *point   = &a[p * bs];
1357:     PetscInt           dbin[3] = {-1, -1, -1}, bin, cell = -1, cellOffset;
1358:     PetscBool          point_outside_domain = PETSC_FALSE;

1360:     /* check bounding box of domain */
1361:     for (PetscInt d = 0; d < cdim; d++) {
1362:       if (PetscRealPart(point[d]) < gmin[d]) {
1363:         point_outside_domain = PETSC_TRUE;
1364:         break;
1365:       }
1366:       if (PetscRealPart(point[d]) > gmax[d]) {
1367:         point_outside_domain = PETSC_TRUE;
1368:         break;
1369:       }
1370:     }
1371:     if (point_outside_domain) {
1372:       cells[p].rank  = 0;
1373:       cells[p].index = DMLOCATEPOINT_POINT_NOT_FOUND;
1374:       terminating_query_type[0]++;
1375:       continue;
1376:     }

1378:     /* check initial values in cells[].index - abort early if found */
1379:     if (cells[p].index != DMLOCATEPOINT_POINT_NOT_FOUND) {
1380:       PetscInt c = cells[p].index;

1382:       cells[p].index = DMLOCATEPOINT_POINT_NOT_FOUND;
1383:       PetscCall(DMPlexLocatePoint_Internal(dm, cdim, point, c, &cell));
1384:       if (cell >= 0) {
1385:         cells[p].rank  = 0;
1386:         cells[p].index = cell;
1387:         numFound++;
1388:       }
1389:     }
1390:     if (cells[p].index != DMLOCATEPOINT_POINT_NOT_FOUND) {
1391:       terminating_query_type[1]++;
1392:       continue;
1393:     }

1395:     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]), cdim > 2 ? (double)PetscRealPart(point[2]) : 0.));
1396:     if (hash) {
1397:       PetscBool found_box;

1399:       /* allow for case that point is outside box - abort early */
1400:       PetscCall(PetscGridHashGetEnclosingBoxQuery(mesh->lbox, mesh->lbox->cellSection, 1, point, dbin, &bin, &found_box));
1401:       if (found_box) {
1402:         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], cdim > 2 ? dbin[2] : 0));
1403:         /* TODO Lay an interface over this so we can switch between Section (dense) and Label (sparse) */
1404:         PetscCall(PetscSectionGetDof(mesh->lbox->cellSection, bin, &numCells));
1405:         PetscCall(PetscSectionGetOffset(mesh->lbox->cellSection, bin, &cellOffset));
1406:         for (PetscInt c = cellOffset; c < cellOffset + numCells; ++c) {
1407:           if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, "[%d]    Checking for point in cell %" PetscInt_FMT "\n", rank, boxCells[c]));
1408:           PetscCall(DMPlexLocatePoint_Internal(dm, cdim, point, boxCells[c], &cell));
1409:           if (cell >= 0) {
1410:             if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, "[%d]      FOUND in cell %" PetscInt_FMT "\n", rank, cell));
1411:             cells[p].rank  = 0;
1412:             cells[p].index = cell;
1413:             numFound++;
1414:             terminating_query_type[2]++;
1415:             break;
1416:           }
1417:         }
1418:       }
1419:     } else {
1420:       PetscBool found = PETSC_FALSE;
1421:       for (PetscInt c = cStart; c < cEnd; ++c) {
1422:         PetscInt idx;

1424:         PetscCall(PetscFindInt(c, Nl, leaves, &idx));
1425:         if (idx >= 0) continue;
1426:         PetscCall(DMPlexLocatePoint_Internal(dm, cdim, point, c, &cell));
1427:         if (cell >= 0) {
1428:           cells[p].rank  = 0;
1429:           cells[p].index = cell;
1430:           numFound++;
1431:           terminating_query_type[2]++;
1432:           found = PETSC_TRUE;
1433:           break;
1434:         }
1435:       }
1436:       if (!found) terminating_query_type[0]++;
1437:     }
1438:   }
1439:   if (hash) PetscCall(ISRestoreIndices(mesh->lbox->cells, &boxCells));
1440:   if (ltype == DM_POINTLOCATION_NEAREST && hash && numFound < numPoints) {
1441:     for (PetscInt p = 0; p < numPoints; p++) {
1442:       const PetscScalar *point     = &a[p * bs];
1443:       PetscReal          cpoint[3] = {0, 0, 0}, diff[3], best[3] = {PETSC_MAX_REAL, PETSC_MAX_REAL, PETSC_MAX_REAL}, dist, distMax = PETSC_MAX_REAL;
1444:       PetscInt           dbin[3] = {-1, -1, -1}, bin, cellOffset, bestc = -1;

1446:       if (cells[p].index < 0) {
1447:         PetscCall(PetscGridHashGetEnclosingBox(mesh->lbox, 1, point, dbin, &bin));
1448:         PetscCall(PetscSectionGetDof(mesh->lbox->cellSection, bin, &numCells));
1449:         PetscCall(PetscSectionGetOffset(mesh->lbox->cellSection, bin, &cellOffset));
1450:         for (PetscInt c = cellOffset; c < cellOffset + numCells; ++c) {
1451:           PetscCall(DMPlexClosestPoint_Internal(dm, cdim, point, boxCells[c], cpoint));
1452:           for (PetscInt d = 0; d < cdim; ++d) diff[d] = cpoint[d] - PetscRealPart(point[d]);
1453:           dist = DMPlex_NormD_Internal(cdim, diff);
1454:           if (dist < distMax) {
1455:             for (PetscInt d = 0; d < cdim; ++d) best[d] = cpoint[d];
1456:             bestc   = boxCells[c];
1457:             distMax = dist;
1458:           }
1459:         }
1460:         if (distMax < PETSC_MAX_REAL) {
1461:           ++numFound;
1462:           cells[p].rank  = 0;
1463:           cells[p].index = bestc;
1464:           for (PetscInt d = 0; d < cdim; ++d) a[p * bs + d] = best[d];
1465:         }
1466:       }
1467:     }
1468:   }
1469:   /* This code is only be relevant when interfaced to parallel point location */
1470:   /* Check for highest numbered proc that claims a point (do we care?) */
1471:   if (ltype == DM_POINTLOCATION_REMOVE && numFound < numPoints) {
1472:     PetscCall(PetscMalloc1(numFound, &found));
1473:     numFound = 0;
1474:     for (PetscInt p = 0; p < numPoints; p++) {
1475:       if (cells[p].rank >= 0 && cells[p].index >= 0) {
1476:         if (numFound < p) cells[numFound] = cells[p];
1477:         found[numFound++] = p;
1478:       }
1479:     }
1480:   }
1481:   PetscCall(VecRestoreArray(v, &a));
1482:   if (!reuse) PetscCall(PetscSFSetGraph(cellSF, cEnd - cStart, numFound, found, PETSC_OWN_POINTER, cells, PETSC_OWN_POINTER));
1483:   PetscCall(PetscTime(&t1));
1484:   if (hash) {
1485:     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]));
1486:   } else {
1487:     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]));
1488:   }
1489:   PetscCall(PetscInfo(dm, "[DMLocatePoints_Plex] npoints %" PetscInt_FMT " : time(rank0) %1.2e (sec): points/sec %1.4e\n", numPoints, t1 - t0, numPoints / (t1 - t0)));
1490:   PetscCall(PetscLogEventEnd(DMPLEX_LocatePoints, 0, 0, 0, 0));
1491:   PetscFunctionReturn(PETSC_SUCCESS);
1492: }

1494: /*@
1495:   DMPlexComputeProjection2Dto1D - Rewrite coordinates to be the 1D projection of the 2D coordinates

1497:   Not Collective

1499:   Input/Output Parameter:
1500: . 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

1502:   Output Parameter:
1503: . R - The rotation which accomplishes the projection, array of size 4

1505:   Level: developer

1507: .seealso: `DMPLEX`, `DMPlexComputeProjection3Dto1D()`, `DMPlexComputeProjection3Dto2D()`
1508: @*/
1509: PetscErrorCode DMPlexComputeProjection2Dto1D(PetscScalar coords[], PetscReal R[])
1510: {
1511:   const PetscReal x = PetscRealPart(coords[2] - coords[0]);
1512:   const PetscReal y = PetscRealPart(coords[3] - coords[1]);
1513:   const PetscReal r = PetscSqrtReal(x * x + y * y), c = x / r, s = y / r;

1515:   PetscFunctionBegin;
1516:   R[0]      = c;
1517:   R[1]      = -s;
1518:   R[2]      = s;
1519:   R[3]      = c;
1520:   coords[0] = 0.0;
1521:   coords[1] = r;
1522:   PetscFunctionReturn(PETSC_SUCCESS);
1523: }

1525: /*@
1526:   DMPlexComputeProjection3Dto1D - Rewrite coordinates to be the 1D projection of the 3D coordinates

1528:   Not Collective

1530:   Input/Output Parameter:
1531: . 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

1533:   Output Parameter:
1534: . R - The rotation which accomplishes the projection, an array of size 9

1536:   Level: developer

1538:   Note:
1539:   This uses the basis completion described by Frisvad {cite}`frisvad2012building`

1541: .seealso: `DMPLEX`, `DMPlexComputeProjection2Dto1D()`, `DMPlexComputeProjection3Dto2D()`
1542: @*/
1543: PetscErrorCode DMPlexComputeProjection3Dto1D(PetscScalar coords[], PetscReal R[])
1544: {
1545:   PetscReal x    = PetscRealPart(coords[3] - coords[0]);
1546:   PetscReal y    = PetscRealPart(coords[4] - coords[1]);
1547:   PetscReal z    = PetscRealPart(coords[5] - coords[2]);
1548:   PetscReal r    = PetscSqrtReal(x * x + y * y + z * z);
1549:   PetscReal rinv = 1. / r;

1551:   PetscFunctionBegin;
1552:   x *= rinv;
1553:   y *= rinv;
1554:   z *= rinv;
1555:   if (x > 0.) {
1556:     PetscReal inv1pX = 1. / (1. + x);

1558:     R[0] = x;
1559:     R[1] = -y;
1560:     R[2] = -z;
1561:     R[3] = y;
1562:     R[4] = 1. - y * y * inv1pX;
1563:     R[5] = -y * z * inv1pX;
1564:     R[6] = z;
1565:     R[7] = -y * z * inv1pX;
1566:     R[8] = 1. - z * z * inv1pX;
1567:   } else {
1568:     PetscReal inv1mX = 1. / (1. - x);

1570:     R[0] = x;
1571:     R[1] = z;
1572:     R[2] = y;
1573:     R[3] = y;
1574:     R[4] = -y * z * inv1mX;
1575:     R[5] = 1. - y * y * inv1mX;
1576:     R[6] = z;
1577:     R[7] = 1. - z * z * inv1mX;
1578:     R[8] = -y * z * inv1mX;
1579:   }
1580:   coords[0] = 0.0;
1581:   coords[1] = r;
1582:   coords[2] = 0.0;
1583:   PetscFunctionReturn(PETSC_SUCCESS);
1584: }

1586: /*@
1587:   DMPlexComputeProjection3Dto2D - Rewrite coordinates of 3 or more coplanar 3D points to a common 2D basis for the
1588:   plane.  The normal is defined by positive orientation of the first 3 points.

1590:   Not Collective

1592:   Input Parameter:
1593: . coordSize - Length of coordinate array (3x number of points); must be at least 9 (3 points)

1595:   Input/Output Parameter:
1596: . coords - The interlaced coordinates of each coplanar 3D point; on output the first
1597:            2*coordSize/3 entries contain interlaced 2D points, with the rest undefined

1599:   Output Parameter:
1600: . 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.

1602:   Level: developer

1604: .seealso: `DMPLEX`, `DMPlexComputeProjection2Dto1D()`, `DMPlexComputeProjection3Dto1D()`
1605: @*/
1606: PetscErrorCode DMPlexComputeProjection3Dto2D(PetscInt coordSize, PetscScalar coords[], PetscReal R[])
1607: {
1608:   PetscReal      x1[3], x2[3], n[3], c[3], norm;
1609:   const PetscInt dim = 3;
1610:   PetscInt       d;

1612:   PetscFunctionBegin;
1613:   /* 0) Calculate normal vector */
1614:   for (d = 0; d < dim; ++d) {
1615:     x1[d] = PetscRealPart(coords[1 * dim + d] - coords[0 * dim + d]);
1616:     x2[d] = PetscRealPart(coords[2 * dim + d] - coords[0 * dim + d]);
1617:   }
1618:   // n = x1 \otimes x2
1619:   n[0] = x1[1] * x2[2] - x1[2] * x2[1];
1620:   n[1] = x1[2] * x2[0] - x1[0] * x2[2];
1621:   n[2] = x1[0] * x2[1] - x1[1] * x2[0];
1622:   norm = PetscSqrtReal(n[0] * n[0] + n[1] * n[1] + n[2] * n[2]);
1623:   for (d = 0; d < dim; d++) n[d] /= norm;
1624:   norm = PetscSqrtReal(x1[0] * x1[0] + x1[1] * x1[1] + x1[2] * x1[2]);
1625:   for (d = 0; d < dim; d++) x1[d] /= norm;
1626:   // x2 = n \otimes x1
1627:   x2[0] = n[1] * x1[2] - n[2] * x1[1];
1628:   x2[1] = n[2] * x1[0] - n[0] * x1[2];
1629:   x2[2] = n[0] * x1[1] - n[1] * x1[0];
1630:   for (d = 0; d < dim; d++) {
1631:     R[d * dim + 0] = x1[d];
1632:     R[d * dim + 1] = x2[d];
1633:     R[d * dim + 2] = n[d];
1634:     c[d]           = PetscRealPart(coords[0 * dim + d]);
1635:   }
1636:   for (PetscInt p = 0; p < coordSize / dim; p++) {
1637:     PetscReal y[3];
1638:     for (d = 0; d < dim; d++) y[d] = PetscRealPart(coords[p * dim + d]) - c[d];
1639:     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];
1640:   }
1641:   PetscFunctionReturn(PETSC_SUCCESS);
1642: }

1644: PETSC_UNUSED static inline void Volume_Triangle_Internal(PetscReal *vol, PetscReal coords[])
1645: {
1646:   /* Signed volume is 1/2 the determinant

1648:    |  1  1  1 |
1649:    | x0 x1 x2 |
1650:    | y0 y1 y2 |

1652:      but if x0,y0 is the origin, we have

1654:    | x1 x2 |
1655:    | y1 y2 |
1656:   */
1657:   const PetscReal x1 = coords[2] - coords[0], y1 = coords[3] - coords[1];
1658:   const PetscReal x2 = coords[4] - coords[0], y2 = coords[5] - coords[1];
1659:   PetscReal       M[4], detM;
1660:   M[0] = x1;
1661:   M[1] = x2;
1662:   M[2] = y1;
1663:   M[3] = y2;
1664:   DMPlex_Det2D_Internal(&detM, M);
1665:   *vol = 0.5 * detM;
1666:   (void)PetscLogFlops(5.0);
1667: }

1669: PETSC_UNUSED static inline void Volume_Tetrahedron_Internal(PetscReal *vol, PetscReal coords[])
1670: {
1671:   /* Signed volume is 1/6th of the determinant

1673:    |  1  1  1  1 |
1674:    | x0 x1 x2 x3 |
1675:    | y0 y1 y2 y3 |
1676:    | z0 z1 z2 z3 |

1678:      but if x0,y0,z0 is the origin, we have

1680:    | x1 x2 x3 |
1681:    | y1 y2 y3 |
1682:    | z1 z2 z3 |
1683:   */
1684:   const PetscReal x1 = coords[3] - coords[0], y1 = coords[4] - coords[1], z1 = coords[5] - coords[2];
1685:   const PetscReal x2 = coords[6] - coords[0], y2 = coords[7] - coords[1], z2 = coords[8] - coords[2];
1686:   const PetscReal x3 = coords[9] - coords[0], y3 = coords[10] - coords[1], z3 = coords[11] - coords[2];
1687:   const PetscReal onesixth = ((PetscReal)1. / (PetscReal)6.);
1688:   PetscReal       M[9], detM;
1689:   M[0] = x1;
1690:   M[1] = x2;
1691:   M[2] = x3;
1692:   M[3] = y1;
1693:   M[4] = y2;
1694:   M[5] = y3;
1695:   M[6] = z1;
1696:   M[7] = z2;
1697:   M[8] = z3;
1698:   DMPlex_Det3D_Internal(&detM, M);
1699:   *vol = -onesixth * detM;
1700:   (void)PetscLogFlops(10.0);
1701: }

1703: static inline void Volume_Tetrahedron_Origin_Internal(PetscReal *vol, PetscReal coords[])
1704: {
1705:   const PetscReal onesixth = ((PetscReal)1. / (PetscReal)6.);
1706:   DMPlex_Det3D_Internal(vol, coords);
1707:   *vol *= -onesixth;
1708: }

1710: static PetscErrorCode DMPlexComputePointGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1711: {
1712:   PetscSection       coordSection;
1713:   Vec                coordinates;
1714:   const PetscScalar *coords;
1715:   PetscInt           dim, d, off;

1717:   PetscFunctionBegin;
1718:   PetscCall(DMGetCoordinatesLocal(dm, &coordinates));
1719:   PetscCall(DMGetCoordinateSection(dm, &coordSection));
1720:   PetscCall(PetscSectionGetDof(coordSection, e, &dim));
1721:   if (!dim) PetscFunctionReturn(PETSC_SUCCESS);
1722:   PetscCall(PetscSectionGetOffset(coordSection, e, &off));
1723:   PetscCall(VecGetArrayRead(coordinates, &coords));
1724:   if (v0) {
1725:     for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[off + d]);
1726:   }
1727:   PetscCall(VecRestoreArrayRead(coordinates, &coords));
1728:   *detJ = 1.;
1729:   if (J) {
1730:     for (d = 0; d < dim * dim; d++) J[d] = 0.;
1731:     for (d = 0; d < dim; d++) J[d * dim + d] = 1.;
1732:     if (invJ) {
1733:       for (d = 0; d < dim * dim; d++) invJ[d] = 0.;
1734:       for (d = 0; d < dim; d++) invJ[d * dim + d] = 1.;
1735:     }
1736:   }
1737:   PetscFunctionReturn(PETSC_SUCCESS);
1738: }

1740: /*@C
1741:   DMPlexGetCellCoordinates - Get coordinates for a cell, taking into account periodicity

1743:   Not Collective

1745:   Input Parameters:
1746: + dm   - The `DMPLEX`
1747: - cell - The cell number

1749:   Output Parameters:
1750: + isDG   - Using cellwise coordinates
1751: . Nc     - The number of coordinates
1752: . array  - The coordinate array
1753: - coords - The cell coordinates

1755:   Level: developer

1757: .seealso: `DMPLEX`, `DMPlexRestoreCellCoordinates()`, `DMGetCoordinatesLocal()`, `DMGetCellCoordinatesLocal()`
1758: @*/
1759: PetscErrorCode DMPlexGetCellCoordinates(DM dm, PetscInt cell, PetscBool *isDG, PetscInt *Nc, const PetscScalar *array[], PetscScalar *coords[])
1760: {
1761:   DM                 cdm;
1762:   Vec                coordinates;
1763:   PetscSection       cs;
1764:   const PetscScalar *ccoords;
1765:   PetscInt           pStart, pEnd;

1767:   PetscFunctionBeginHot;
1768:   *isDG   = PETSC_FALSE;
1769:   *Nc     = 0;
1770:   *array  = NULL;
1771:   *coords = NULL;
1772:   /* Check for cellwise coordinates */
1773:   PetscCall(DMGetCellCoordinateSection(dm, &cs));
1774:   if (!cs) goto cg;
1775:   /* Check that the cell exists in the cellwise section */
1776:   PetscCall(PetscSectionGetChart(cs, &pStart, &pEnd));
1777:   if (cell < pStart || cell >= pEnd) goto cg;
1778:   /* Check for cellwise coordinates for this cell */
1779:   PetscCall(PetscSectionGetDof(cs, cell, Nc));
1780:   if (!*Nc) goto cg;
1781:   /* Check for cellwise coordinates */
1782:   PetscCall(DMGetCellCoordinatesLocalNoncollective(dm, &coordinates));
1783:   if (!coordinates) goto cg;
1784:   /* Get cellwise coordinates */
1785:   PetscCall(DMGetCellCoordinateDM(dm, &cdm));
1786:   PetscCall(VecGetArrayRead(coordinates, array));
1787:   PetscCall(DMPlexPointLocalRead(cdm, cell, *array, &ccoords));
1788:   PetscCall(DMGetWorkArray(cdm, *Nc, MPIU_SCALAR, coords));
1789:   PetscCall(PetscArraycpy(*coords, ccoords, *Nc));
1790:   PetscCall(VecRestoreArrayRead(coordinates, array));
1791:   *isDG = PETSC_TRUE;
1792:   PetscFunctionReturn(PETSC_SUCCESS);
1793: cg:
1794:   /* Use continuous coordinates */
1795:   PetscCall(DMGetCoordinateDM(dm, &cdm));
1796:   PetscCall(DMGetCoordinateSection(dm, &cs));
1797:   PetscCall(DMGetCoordinatesLocalNoncollective(dm, &coordinates));
1798:   PetscCall(DMPlexVecGetOrientedClosure(cdm, cs, PETSC_FALSE, coordinates, cell, 0, Nc, coords));
1799:   PetscFunctionReturn(PETSC_SUCCESS);
1800: }

1802: /*@C
1803:   DMPlexRestoreCellCoordinates - Get coordinates for a cell, taking into account periodicity

1805:   Not Collective

1807:   Input Parameters:
1808: + dm   - The `DMPLEX`
1809: - cell - The cell number

1811:   Output Parameters:
1812: + isDG   - Using cellwise coordinates
1813: . Nc     - The number of coordinates
1814: . array  - The coordinate array
1815: - coords - The cell coordinates

1817:   Level: developer

1819: .seealso: `DMPLEX`, `DMPlexGetCellCoordinates()`, `DMGetCoordinatesLocal()`, `DMGetCellCoordinatesLocal()`
1820: @*/
1821: PetscErrorCode DMPlexRestoreCellCoordinates(DM dm, PetscInt cell, PetscBool *isDG, PetscInt *Nc, const PetscScalar *array[], PetscScalar *coords[])
1822: {
1823:   DM           cdm;
1824:   PetscSection cs;
1825:   Vec          coordinates;

1827:   PetscFunctionBeginHot;
1828:   if (*isDG) {
1829:     PetscCall(DMGetCellCoordinateDM(dm, &cdm));
1830:     PetscCall(DMRestoreWorkArray(cdm, *Nc, MPIU_SCALAR, coords));
1831:   } else {
1832:     PetscCall(DMGetCoordinateDM(dm, &cdm));
1833:     PetscCall(DMGetCoordinateSection(dm, &cs));
1834:     PetscCall(DMGetCoordinatesLocalNoncollective(dm, &coordinates));
1835:     PetscCall(DMPlexVecRestoreClosure(cdm, cs, coordinates, cell, Nc, coords));
1836:   }
1837:   PetscFunctionReturn(PETSC_SUCCESS);
1838: }

1840: static PetscErrorCode DMPlexComputeLineGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1841: {
1842:   const PetscScalar *array;
1843:   PetscScalar       *coords = NULL;
1844:   PetscInt           numCoords, d;
1845:   PetscBool          isDG;

1847:   PetscFunctionBegin;
1848:   PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
1849:   PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
1850:   *detJ = 0.0;
1851:   if (numCoords == 6) {
1852:     const PetscInt dim = 3;
1853:     PetscReal      R[9], J0;

1855:     if (v0) {
1856:       for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
1857:     }
1858:     PetscCall(DMPlexComputeProjection3Dto1D(coords, R));
1859:     if (J) {
1860:       J0   = 0.5 * PetscRealPart(coords[1]);
1861:       J[0] = R[0] * J0;
1862:       J[1] = R[1];
1863:       J[2] = R[2];
1864:       J[3] = R[3] * J0;
1865:       J[4] = R[4];
1866:       J[5] = R[5];
1867:       J[6] = R[6] * J0;
1868:       J[7] = R[7];
1869:       J[8] = R[8];
1870:       DMPlex_Det3D_Internal(detJ, J);
1871:       if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
1872:     }
1873:   } else if (numCoords == 4) {
1874:     const PetscInt dim = 2;
1875:     PetscReal      R[4], J0;

1877:     if (v0) {
1878:       for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
1879:     }
1880:     PetscCall(DMPlexComputeProjection2Dto1D(coords, R));
1881:     if (J) {
1882:       J0   = 0.5 * PetscRealPart(coords[1]);
1883:       J[0] = R[0] * J0;
1884:       J[1] = R[1];
1885:       J[2] = R[2] * J0;
1886:       J[3] = R[3];
1887:       DMPlex_Det2D_Internal(detJ, J);
1888:       if (invJ) DMPlex_Invert2D_Internal(invJ, J, *detJ);
1889:     }
1890:   } else if (numCoords == 2) {
1891:     const PetscInt dim = 1;

1893:     if (v0) {
1894:       for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
1895:     }
1896:     if (J) {
1897:       J[0]  = 0.5 * (PetscRealPart(coords[1]) - PetscRealPart(coords[0]));
1898:       *detJ = J[0];
1899:       PetscCall(PetscLogFlops(2.0));
1900:       if (invJ) {
1901:         invJ[0] = 1.0 / J[0];
1902:         PetscCall(PetscLogFlops(1.0));
1903:       }
1904:     }
1905:   } 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);
1906:   PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
1907:   PetscFunctionReturn(PETSC_SUCCESS);
1908: }

1910: static PetscErrorCode DMPlexComputeTriangleGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1911: {
1912:   const PetscScalar *array;
1913:   PetscScalar       *coords = NULL;
1914:   PetscInt           numCoords, d;
1915:   PetscBool          isDG;

1917:   PetscFunctionBegin;
1918:   PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
1919:   PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
1920:   *detJ = 0.0;
1921:   if (numCoords == 9) {
1922:     const PetscInt dim = 3;
1923:     PetscReal      R[9], J0[9] = {1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0};

1925:     if (v0) {
1926:       for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
1927:     }
1928:     PetscCall(DMPlexComputeProjection3Dto2D(numCoords, coords, R));
1929:     if (J) {
1930:       const PetscInt pdim = 2;

1932:       for (d = 0; d < pdim; d++) {
1933:         for (PetscInt f = 0; f < pdim; f++) J0[d * dim + f] = 0.5 * (PetscRealPart(coords[(f + 1) * pdim + d]) - PetscRealPart(coords[0 * pdim + d]));
1934:       }
1935:       PetscCall(PetscLogFlops(8.0));
1936:       DMPlex_Det3D_Internal(detJ, J0);
1937:       for (d = 0; d < dim; d++) {
1938:         for (PetscInt f = 0; f < dim; f++) {
1939:           J[d * dim + f] = 0.0;
1940:           for (PetscInt g = 0; g < dim; g++) J[d * dim + f] += R[d * dim + g] * J0[g * dim + f];
1941:         }
1942:       }
1943:       PetscCall(PetscLogFlops(18.0));
1944:     }
1945:     if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
1946:   } else if (numCoords == 6) {
1947:     const PetscInt dim = 2;

1949:     if (v0) {
1950:       for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
1951:     }
1952:     if (J) {
1953:       for (d = 0; d < dim; d++) {
1954:         for (PetscInt f = 0; f < dim; f++) J[d * dim + f] = 0.5 * (PetscRealPart(coords[(f + 1) * dim + d]) - PetscRealPart(coords[0 * dim + d]));
1955:       }
1956:       PetscCall(PetscLogFlops(8.0));
1957:       DMPlex_Det2D_Internal(detJ, J);
1958:     }
1959:     if (invJ) DMPlex_Invert2D_Internal(invJ, J, *detJ);
1960:   } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this triangle is %" PetscInt_FMT " != 6 or 9", numCoords);
1961:   PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
1962:   PetscFunctionReturn(PETSC_SUCCESS);
1963: }

1965: static PetscErrorCode DMPlexComputeRectangleGeometry_Internal(DM dm, PetscInt e, PetscBool isTensor, PetscInt Nq, const PetscReal points[], PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1966: {
1967:   const PetscScalar *array;
1968:   PetscScalar       *coords = NULL;
1969:   PetscInt           numCoords, d;
1970:   PetscBool          isDG;

1972:   PetscFunctionBegin;
1973:   PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
1974:   PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
1975:   if (!Nq) {
1976:     PetscInt vorder[4] = {0, 1, 2, 3};

1978:     if (isTensor) {
1979:       vorder[2] = 3;
1980:       vorder[3] = 2;
1981:     }
1982:     *detJ = 0.0;
1983:     if (numCoords == 12) {
1984:       const PetscInt dim = 3;
1985:       PetscReal      R[9], J0[9] = {1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0};

1987:       if (v) {
1988:         for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);
1989:       }
1990:       PetscCall(DMPlexComputeProjection3Dto2D(numCoords, coords, R));
1991:       if (J) {
1992:         const PetscInt pdim = 2;

1994:         for (d = 0; d < pdim; d++) {
1995:           J0[d * dim + 0] = 0.5 * (PetscRealPart(coords[vorder[1] * pdim + d]) - PetscRealPart(coords[vorder[0] * pdim + d]));
1996:           J0[d * dim + 1] = 0.5 * (PetscRealPart(coords[vorder[2] * pdim + d]) - PetscRealPart(coords[vorder[1] * pdim + d]));
1997:         }
1998:         PetscCall(PetscLogFlops(8.0));
1999:         DMPlex_Det3D_Internal(detJ, J0);
2000:         for (d = 0; d < dim; d++) {
2001:           for (PetscInt f = 0; f < dim; f++) {
2002:             J[d * dim + f] = 0.0;
2003:             for (PetscInt g = 0; g < dim; g++) J[d * dim + f] += R[d * dim + g] * J0[g * dim + f];
2004:           }
2005:         }
2006:         PetscCall(PetscLogFlops(18.0));
2007:       }
2008:       if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
2009:     } else if (numCoords == 8) {
2010:       const PetscInt dim = 2;

2012:       if (v) {
2013:         for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);
2014:       }
2015:       if (J) {
2016:         for (d = 0; d < dim; d++) {
2017:           J[d * dim + 0] = 0.5 * (PetscRealPart(coords[vorder[1] * dim + d]) - PetscRealPart(coords[vorder[0] * dim + d]));
2018:           J[d * dim + 1] = 0.5 * (PetscRealPart(coords[vorder[3] * dim + d]) - PetscRealPart(coords[vorder[0] * dim + d]));
2019:         }
2020:         PetscCall(PetscLogFlops(8.0));
2021:         DMPlex_Det2D_Internal(detJ, J);
2022:       }
2023:       if (invJ) DMPlex_Invert2D_Internal(invJ, J, *detJ);
2024:     } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this quadrilateral is %" PetscInt_FMT " != 8 or 12", numCoords);
2025:   } else {
2026:     const PetscInt Nv         = 4;
2027:     const PetscInt dimR       = 2;
2028:     PetscInt       zToPlex[4] = {0, 1, 3, 2};
2029:     PetscReal      zOrder[12];
2030:     PetscReal      zCoeff[12];
2031:     PetscInt       i, j, k, l, dim;

2033:     if (isTensor) {
2034:       zToPlex[2] = 2;
2035:       zToPlex[3] = 3;
2036:     }
2037:     if (numCoords == 12) {
2038:       dim = 3;
2039:     } else if (numCoords == 8) {
2040:       dim = 2;
2041:     } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this quadrilateral is %" PetscInt_FMT " != 8 or 12", numCoords);
2042:     for (i = 0; i < Nv; i++) {
2043:       PetscInt zi = zToPlex[i];

2045:       for (j = 0; j < dim; j++) zOrder[dim * i + j] = PetscRealPart(coords[dim * zi + j]);
2046:     }
2047:     for (j = 0; j < dim; j++) {
2048:       /* Nodal basis for evaluation at the vertices: (1 \mp xi) (1 \mp eta):
2049:            \phi^0 = (1 - xi - eta + xi eta) --> 1      = 1/4 ( \phi^0 + \phi^1 + \phi^2 + \phi^3)
2050:            \phi^1 = (1 + xi - eta - xi eta) --> xi     = 1/4 (-\phi^0 + \phi^1 - \phi^2 + \phi^3)
2051:            \phi^2 = (1 - xi + eta - xi eta) --> eta    = 1/4 (-\phi^0 - \phi^1 + \phi^2 + \phi^3)
2052:            \phi^3 = (1 + xi + eta + xi eta) --> xi eta = 1/4 ( \phi^0 - \phi^1 - \phi^2 + \phi^3)
2053:       */
2054:       zCoeff[dim * 0 + j] = 0.25 * (zOrder[dim * 0 + j] + zOrder[dim * 1 + j] + zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
2055:       zCoeff[dim * 1 + j] = 0.25 * (-zOrder[dim * 0 + j] + zOrder[dim * 1 + j] - zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
2056:       zCoeff[dim * 2 + j] = 0.25 * (-zOrder[dim * 0 + j] - zOrder[dim * 1 + j] + zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
2057:       zCoeff[dim * 3 + j] = 0.25 * (zOrder[dim * 0 + j] - zOrder[dim * 1 + j] - zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
2058:     }
2059:     for (i = 0; i < Nq; i++) {
2060:       PetscReal xi = points[dimR * i], eta = points[dimR * i + 1];

2062:       if (v) {
2063:         PetscReal extPoint[4];

2065:         extPoint[0] = 1.;
2066:         extPoint[1] = xi;
2067:         extPoint[2] = eta;
2068:         extPoint[3] = xi * eta;
2069:         for (j = 0; j < dim; j++) {
2070:           PetscReal val = 0.;

2072:           for (k = 0; k < Nv; k++) val += extPoint[k] * zCoeff[dim * k + j];
2073:           v[i * dim + j] = val;
2074:         }
2075:       }
2076:       if (J) {
2077:         PetscReal extJ[8];

2079:         extJ[0] = 0.;
2080:         extJ[1] = 0.;
2081:         extJ[2] = 1.;
2082:         extJ[3] = 0.;
2083:         extJ[4] = 0.;
2084:         extJ[5] = 1.;
2085:         extJ[6] = eta;
2086:         extJ[7] = xi;
2087:         for (j = 0; j < dim; j++) {
2088:           for (k = 0; k < dimR; k++) {
2089:             PetscReal val = 0.;

2091:             for (l = 0; l < Nv; l++) val += zCoeff[dim * l + j] * extJ[dimR * l + k];
2092:             J[i * dim * dim + dim * j + k] = val;
2093:           }
2094:         }
2095:         if (dim == 3) { /* put the cross product in the third component of the Jacobian */
2096:           PetscReal  x, y, z;
2097:           PetscReal *iJ = &J[i * dim * dim];
2098:           PetscReal  norm;

2100:           x     = iJ[1 * dim + 0] * iJ[2 * dim + 1] - iJ[1 * dim + 1] * iJ[2 * dim + 0];
2101:           y     = iJ[0 * dim + 1] * iJ[2 * dim + 0] - iJ[0 * dim + 0] * iJ[2 * dim + 1];
2102:           z     = iJ[0 * dim + 0] * iJ[1 * dim + 1] - iJ[0 * dim + 1] * iJ[1 * dim + 0];
2103:           norm  = PetscSqrtReal(x * x + y * y + z * z);
2104:           iJ[2] = x / norm;
2105:           iJ[5] = y / norm;
2106:           iJ[8] = z / norm;
2107:           DMPlex_Det3D_Internal(&detJ[i], &J[i * dim * dim]);
2108:           if (invJ) DMPlex_Invert3D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);
2109:         } else {
2110:           DMPlex_Det2D_Internal(&detJ[i], &J[i * dim * dim]);
2111:           if (invJ) DMPlex_Invert2D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);
2112:         }
2113:       }
2114:     }
2115:   }
2116:   PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
2117:   PetscFunctionReturn(PETSC_SUCCESS);
2118: }

2120: static PetscErrorCode DMPlexComputeTetrahedronGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
2121: {
2122:   const PetscScalar *array;
2123:   PetscScalar       *coords = NULL;
2124:   const PetscInt     dim    = 3;
2125:   PetscInt           numCoords, d;
2126:   PetscBool          isDG;

2128:   PetscFunctionBegin;
2129:   PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
2130:   PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
2131:   *detJ = 0.0;
2132:   if (v0) {
2133:     for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
2134:   }
2135:   if (J) {
2136:     for (d = 0; d < dim; d++) {
2137:       /* I orient with outward face normals */
2138:       J[d * dim + 0] = 0.5 * (PetscRealPart(coords[2 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2139:       J[d * dim + 1] = 0.5 * (PetscRealPart(coords[1 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2140:       J[d * dim + 2] = 0.5 * (PetscRealPart(coords[3 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2141:     }
2142:     PetscCall(PetscLogFlops(18.0));
2143:     DMPlex_Det3D_Internal(detJ, J);
2144:   }
2145:   if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
2146:   PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
2147:   PetscFunctionReturn(PETSC_SUCCESS);
2148: }

2150: static PetscErrorCode DMPlexComputeHexahedronGeometry_Internal(DM dm, PetscInt e, PetscInt Nq, const PetscReal points[], PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
2151: {
2152:   const PetscScalar *array;
2153:   PetscScalar       *coords = NULL;
2154:   const PetscInt     dim    = 3;
2155:   PetscInt           numCoords;
2156:   PetscBool          isDG;

2158:   PetscFunctionBegin;
2159:   PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
2160:   PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
2161:   if (!Nq) {
2162:     *detJ = 0.0;
2163:     if (v) {
2164:       for (PetscInt d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);
2165:     }
2166:     if (J) {
2167:       for (PetscInt d = 0; d < dim; d++) {
2168:         J[d * dim + 0] = 0.5 * (PetscRealPart(coords[3 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2169:         J[d * dim + 1] = 0.5 * (PetscRealPart(coords[1 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2170:         J[d * dim + 2] = 0.5 * (PetscRealPart(coords[4 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2171:       }
2172:       PetscCall(PetscLogFlops(18.0));
2173:       DMPlex_Det3D_Internal(detJ, J);
2174:     }
2175:     if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
2176:   } else {
2177:     const PetscInt Nv         = 8;
2178:     const PetscInt zToPlex[8] = {0, 3, 1, 2, 4, 5, 7, 6};
2179:     const PetscInt dim        = 3;
2180:     const PetscInt dimR       = 3;
2181:     PetscReal      zOrder[24];
2182:     PetscReal      zCoeff[24];
2183:     PetscInt       i, j, k, l;

2185:     for (i = 0; i < Nv; i++) {
2186:       PetscInt zi = zToPlex[i];

2188:       for (j = 0; j < dim; j++) zOrder[dim * i + j] = PetscRealPart(coords[dim * zi + j]);
2189:     }
2190:     for (j = 0; j < dim; j++) {
2191:       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]);
2192:       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]);
2193:       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]);
2194:       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]);
2195:       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]);
2196:       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]);
2197:       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]);
2198:       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]);
2199:     }
2200:     for (i = 0; i < Nq; i++) {
2201:       PetscReal xi = points[dimR * i], eta = points[dimR * i + 1], theta = points[dimR * i + 2];

2203:       if (v) {
2204:         PetscReal extPoint[8];

2206:         extPoint[0] = 1.;
2207:         extPoint[1] = xi;
2208:         extPoint[2] = eta;
2209:         extPoint[3] = xi * eta;
2210:         extPoint[4] = theta;
2211:         extPoint[5] = theta * xi;
2212:         extPoint[6] = theta * eta;
2213:         extPoint[7] = theta * eta * xi;
2214:         for (j = 0; j < dim; j++) {
2215:           PetscReal val = 0.;

2217:           for (k = 0; k < Nv; k++) val += extPoint[k] * zCoeff[dim * k + j];
2218:           v[i * dim + j] = val;
2219:         }
2220:       }
2221:       if (J) {
2222:         PetscReal extJ[24];

2224:         extJ[0]  = 0.;
2225:         extJ[1]  = 0.;
2226:         extJ[2]  = 0.;
2227:         extJ[3]  = 1.;
2228:         extJ[4]  = 0.;
2229:         extJ[5]  = 0.;
2230:         extJ[6]  = 0.;
2231:         extJ[7]  = 1.;
2232:         extJ[8]  = 0.;
2233:         extJ[9]  = eta;
2234:         extJ[10] = xi;
2235:         extJ[11] = 0.;
2236:         extJ[12] = 0.;
2237:         extJ[13] = 0.;
2238:         extJ[14] = 1.;
2239:         extJ[15] = theta;
2240:         extJ[16] = 0.;
2241:         extJ[17] = xi;
2242:         extJ[18] = 0.;
2243:         extJ[19] = theta;
2244:         extJ[20] = eta;
2245:         extJ[21] = theta * eta;
2246:         extJ[22] = theta * xi;
2247:         extJ[23] = eta * xi;

2249:         for (j = 0; j < dim; j++) {
2250:           for (k = 0; k < dimR; k++) {
2251:             PetscReal val = 0.;

2253:             for (l = 0; l < Nv; l++) val += zCoeff[dim * l + j] * extJ[dimR * l + k];
2254:             J[i * dim * dim + dim * j + k] = val;
2255:           }
2256:         }
2257:         DMPlex_Det3D_Internal(&detJ[i], &J[i * dim * dim]);
2258:         if (invJ) DMPlex_Invert3D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);
2259:       }
2260:     }
2261:   }
2262:   PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
2263:   PetscFunctionReturn(PETSC_SUCCESS);
2264: }

2266: static PetscErrorCode DMPlexComputeTriangularPrismGeometry_Internal(DM dm, PetscInt e, PetscInt Nq, const PetscReal points[], PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
2267: {
2268:   const PetscScalar *array;
2269:   PetscScalar       *coords = NULL;
2270:   const PetscInt     dim    = 3;
2271:   PetscInt           numCoords;
2272:   PetscBool          isDG;

2274:   PetscFunctionBegin;
2275:   PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
2276:   PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
2277:   if (!Nq) {
2278:     /* Assume that the map to the reference is affine */
2279:     *detJ = 0.0;
2280:     if (v) {
2281:       for (PetscInt d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);
2282:     }
2283:     if (J) {
2284:       for (PetscInt d = 0; d < dim; d++) {
2285:         J[d * dim + 0] = 0.5 * (PetscRealPart(coords[2 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2286:         J[d * dim + 1] = 0.5 * (PetscRealPart(coords[1 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2287:         J[d * dim + 2] = 0.5 * (PetscRealPart(coords[4 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2288:       }
2289:       PetscCall(PetscLogFlops(18.0));
2290:       DMPlex_Det3D_Internal(detJ, J);
2291:     }
2292:     if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
2293:   } else {
2294:     const PetscInt dim  = 3;
2295:     const PetscInt dimR = 3;
2296:     const PetscInt Nv   = 6;
2297:     PetscReal      verts[18];
2298:     PetscReal      coeff[18];
2299:     PetscInt       i, j, k, l;

2301:     for (i = 0; i < Nv; ++i)
2302:       for (j = 0; j < dim; ++j) verts[dim * i + j] = PetscRealPart(coords[dim * i + j]);
2303:     for (j = 0; j < dim; ++j) {
2304:       /* Check for triangle,
2305:            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)
2306:            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)
2307:            phi^2 =  1/2 (1 + eta)   chi^2 = delta(-1,  1)

2309:            phi^0 + phi^1 + phi^2 = 1    coef_1   = 1/2 (         chi^1 + chi^2)
2310:           -phi^0 + phi^1 - phi^2 = xi   coef_xi  = 1/2 (-chi^0 + chi^1)
2311:           -phi^0 - phi^1 + phi^2 = eta  coef_eta = 1/2 (-chi^0         + chi^2)

2313:           < chi_0 chi_1 chi_2> A /  1  1  1 \ / phi_0 \   <chi> I <phi>^T  so we need the inverse transpose
2314:                                  | -1  1 -1 | | phi_1 | =
2315:                                  \ -1 -1  1 / \ phi_2 /

2317:           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
2318:       */
2319:       /* Nodal basis for evaluation at the vertices: {-xi - eta, 1 + xi, 1 + eta} (1 \mp zeta):
2320:            \phi^0 = 1/4 (   -xi - eta        + xi zeta + eta zeta) --> /  1  1  1  1  1  1 \ 1
2321:            \phi^1 = 1/4 (1      + eta - zeta           - eta zeta) --> | -1  1 -1 -1 -1  1 | eta
2322:            \phi^2 = 1/4 (1 + xi       - zeta - xi zeta)            --> | -1 -1  1 -1  1 -1 | xi
2323:            \phi^3 = 1/4 (   -xi - eta        - xi zeta - eta zeta) --> | -1 -1 -1  1  1  1 | zeta
2324:            \phi^4 = 1/4 (1 + xi       + zeta + xi zeta)            --> |  1  1 -1 -1  1 -1 | xi zeta
2325:            \phi^5 = 1/4 (1      + eta + zeta           + eta zeta) --> \  1 -1  1 -1 -1  1 / eta zeta
2326:            1/4 /  0  1  1  0  1  1 \
2327:                | -1  1  0 -1  0  1 |
2328:                | -1  0  1 -1  1  0 |
2329:                |  0 -1 -1  0  1  1 |
2330:                |  1  0 -1 -1  1  0 |
2331:                \  1 -1  0 -1  0  1 /
2332:       */
2333:       coeff[dim * 0 + j] = (1. / 4.) * (verts[dim * 1 + j] + verts[dim * 2 + j] + verts[dim * 4 + j] + verts[dim * 5 + j]);
2334:       coeff[dim * 1 + j] = (1. / 4.) * (-verts[dim * 0 + j] + verts[dim * 1 + j] - verts[dim * 3 + j] + verts[dim * 5 + j]);
2335:       coeff[dim * 2 + j] = (1. / 4.) * (-verts[dim * 0 + j] + verts[dim * 2 + j] - verts[dim * 3 + j] + verts[dim * 4 + j]);
2336:       coeff[dim * 3 + j] = (1. / 4.) * (-verts[dim * 1 + j] - verts[dim * 2 + j] + verts[dim * 4 + j] + verts[dim * 5 + j]);
2337:       coeff[dim * 4 + j] = (1. / 4.) * (verts[dim * 0 + j] - verts[dim * 2 + j] - verts[dim * 3 + j] + verts[dim * 4 + j]);
2338:       coeff[dim * 5 + j] = (1. / 4.) * (verts[dim * 0 + j] - verts[dim * 1 + j] - verts[dim * 3 + j] + verts[dim * 5 + j]);
2339:       /* For reference prism:
2340:       {0, 0, 0}
2341:       {0, 1, 0}
2342:       {1, 0, 0}
2343:       {0, 0, 1}
2344:       {0, 0, 0}
2345:       {0, 0, 0}
2346:       */
2347:     }
2348:     for (i = 0; i < Nq; ++i) {
2349:       const PetscReal xi = points[dimR * i], eta = points[dimR * i + 1], zeta = points[dimR * i + 2];

2351:       if (v) {
2352:         PetscReal extPoint[6];

2354:         extPoint[0] = 1.;
2355:         extPoint[1] = eta;
2356:         extPoint[2] = xi;
2357:         extPoint[3] = zeta;
2358:         extPoint[4] = xi * zeta;
2359:         extPoint[5] = eta * zeta;
2360:         for (PetscInt c = 0; c < dim; ++c) {
2361:           PetscReal val = 0.;

2363:           for (k = 0; k < Nv; ++k) val += extPoint[k] * coeff[k * dim + c];
2364:           v[i * dim + c] = val;
2365:         }
2366:       }
2367:       if (J) {
2368:         PetscReal extJ[18];

2370:         extJ[0]  = 0.;
2371:         extJ[1]  = 0.;
2372:         extJ[2]  = 0.;
2373:         extJ[3]  = 0.;
2374:         extJ[4]  = 1.;
2375:         extJ[5]  = 0.;
2376:         extJ[6]  = 1.;
2377:         extJ[7]  = 0.;
2378:         extJ[8]  = 0.;
2379:         extJ[9]  = 0.;
2380:         extJ[10] = 0.;
2381:         extJ[11] = 1.;
2382:         extJ[12] = zeta;
2383:         extJ[13] = 0.;
2384:         extJ[14] = xi;
2385:         extJ[15] = 0.;
2386:         extJ[16] = zeta;
2387:         extJ[17] = eta;

2389:         for (j = 0; j < dim; j++) {
2390:           for (k = 0; k < dimR; k++) {
2391:             PetscReal val = 0.;

2393:             for (l = 0; l < Nv; l++) val += coeff[dim * l + j] * extJ[dimR * l + k];
2394:             J[i * dim * dim + dim * j + k] = val;
2395:           }
2396:         }
2397:         DMPlex_Det3D_Internal(&detJ[i], &J[i * dim * dim]);
2398:         if (invJ) DMPlex_Invert3D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);
2399:       }
2400:     }
2401:   }
2402:   PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
2403:   PetscFunctionReturn(PETSC_SUCCESS);
2404: }

2406: static PetscErrorCode DMPlexComputeCellGeometryFEM_Implicit(DM dm, PetscInt cell, PetscQuadrature quad, PetscReal *v, PetscReal *J, PetscReal *invJ, PetscReal *detJ)
2407: {
2408:   DMPolytopeType   ct;
2409:   PetscInt         depth, dim, coordDim, coneSize, i;
2410:   PetscInt         Nq     = 0;
2411:   const PetscReal *points = NULL;
2412:   DMLabel          depthLabel;
2413:   PetscReal        xi0[3]   = {-1., -1., -1.}, v0[3], J0[9], detJ0;
2414:   PetscBool        isAffine = PETSC_TRUE;

2416:   PetscFunctionBegin;
2417:   PetscCall(DMPlexGetDepth(dm, &depth));
2418:   PetscCall(DMPlexGetConeSize(dm, cell, &coneSize));
2419:   PetscCall(DMPlexGetDepthLabel(dm, &depthLabel));
2420:   PetscCall(DMLabelGetValue(depthLabel, cell, &dim));
2421:   if (depth == 1 && dim == 1) PetscCall(DMGetDimension(dm, &dim));
2422:   PetscCall(DMGetCoordinateDim(dm, &coordDim));
2423:   PetscCheck(coordDim <= 3, PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported coordinate dimension %" PetscInt_FMT " > 3", coordDim);
2424:   if (quad) PetscCall(PetscQuadratureGetData(quad, NULL, NULL, &Nq, &points, NULL));
2425:   PetscCall(DMPlexGetCellType(dm, cell, &ct));
2426:   switch (ct) {
2427:   case DM_POLYTOPE_POINT:
2428:     PetscCall(DMPlexComputePointGeometry_Internal(dm, cell, v, J, invJ, detJ));
2429:     isAffine = PETSC_FALSE;
2430:     break;
2431:   case DM_POLYTOPE_SEGMENT:
2432:   case DM_POLYTOPE_POINT_PRISM_TENSOR:
2433:     if (Nq) PetscCall(DMPlexComputeLineGeometry_Internal(dm, cell, v0, J0, NULL, &detJ0));
2434:     else PetscCall(DMPlexComputeLineGeometry_Internal(dm, cell, v, J, invJ, detJ));
2435:     break;
2436:   case DM_POLYTOPE_TRIANGLE:
2437:     if (Nq) PetscCall(DMPlexComputeTriangleGeometry_Internal(dm, cell, v0, J0, NULL, &detJ0));
2438:     else PetscCall(DMPlexComputeTriangleGeometry_Internal(dm, cell, v, J, invJ, detJ));
2439:     break;
2440:   case DM_POLYTOPE_QUADRILATERAL:
2441:     PetscCall(DMPlexComputeRectangleGeometry_Internal(dm, cell, PETSC_FALSE, Nq, points, v, J, invJ, detJ));
2442:     isAffine = PETSC_FALSE;
2443:     break;
2444:   case DM_POLYTOPE_SEG_PRISM_TENSOR:
2445:     PetscCall(DMPlexComputeRectangleGeometry_Internal(dm, cell, PETSC_TRUE, Nq, points, v, J, invJ, detJ));
2446:     isAffine = PETSC_FALSE;
2447:     break;
2448:   case DM_POLYTOPE_TETRAHEDRON:
2449:     if (Nq) PetscCall(DMPlexComputeTetrahedronGeometry_Internal(dm, cell, v0, J0, NULL, &detJ0));
2450:     else PetscCall(DMPlexComputeTetrahedronGeometry_Internal(dm, cell, v, J, invJ, detJ));
2451:     break;
2452:   case DM_POLYTOPE_HEXAHEDRON:
2453:     PetscCall(DMPlexComputeHexahedronGeometry_Internal(dm, cell, Nq, points, v, J, invJ, detJ));
2454:     isAffine = PETSC_FALSE;
2455:     break;
2456:   case DM_POLYTOPE_TRI_PRISM:
2457:     PetscCall(DMPlexComputeTriangularPrismGeometry_Internal(dm, cell, Nq, points, v, J, invJ, detJ));
2458:     isAffine = PETSC_FALSE;
2459:     break;
2460:   default:
2461:     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))]);
2462:   }
2463:   if (isAffine && Nq) {
2464:     if (v) {
2465:       for (i = 0; i < Nq; i++) CoordinatesRefToReal(coordDim, dim, xi0, v0, J0, &points[dim * i], &v[coordDim * i]);
2466:     }
2467:     if (detJ) {
2468:       for (i = 0; i < Nq; i++) detJ[i] = detJ0;
2469:     }
2470:     if (J) {
2471:       PetscInt k;

2473:       for (i = 0, k = 0; i < Nq; i++) {
2474:         for (PetscInt j = 0; j < coordDim * coordDim; j++, k++) J[k] = J0[j];
2475:       }
2476:     }
2477:     if (invJ) {
2478:       PetscInt k;
2479:       switch (coordDim) {
2480:       case 0:
2481:         break;
2482:       case 1:
2483:         invJ[0] = 1. / J0[0];
2484:         break;
2485:       case 2:
2486:         DMPlex_Invert2D_Internal(invJ, J0, detJ0);
2487:         break;
2488:       case 3:
2489:         DMPlex_Invert3D_Internal(invJ, J0, detJ0);
2490:         break;
2491:       }
2492:       for (i = 1, k = coordDim * coordDim; i < Nq; i++) {
2493:         for (PetscInt j = 0; j < coordDim * coordDim; j++, k++) invJ[k] = invJ[j];
2494:       }
2495:     }
2496:   }
2497:   PetscFunctionReturn(PETSC_SUCCESS);
2498: }

2500: /*@C
2501:   DMPlexComputeCellGeometryAffineFEM - Assuming an affine map, compute the Jacobian, inverse Jacobian, and Jacobian determinant for a given cell

2503:   Collective

2505:   Input Parameters:
2506: + dm   - the `DMPLEX`
2507: - cell - the cell

2509:   Output Parameters:
2510: + v0   - the translation part of this affine transform, meaning the translation to the origin (not the first vertex of the reference cell)
2511: . J    - the Jacobian of the transform from the reference element
2512: . invJ - the inverse of the Jacobian
2513: - detJ - the Jacobian determinant

2515:   Level: advanced

2517: .seealso: `DMPLEX`, `DMPlexComputeCellGeometryFEM()`, `DMGetCoordinateSection()`, `DMGetCoordinates()`
2518: @*/
2519: PetscErrorCode DMPlexComputeCellGeometryAffineFEM(DM dm, PetscInt cell, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
2520: {
2521:   PetscFunctionBegin;
2522:   PetscCall(DMPlexComputeCellGeometryFEM_Implicit(dm, cell, NULL, v0, J, invJ, detJ));
2523:   PetscFunctionReturn(PETSC_SUCCESS);
2524: }

2526: static PetscErrorCode DMPlexComputeCellGeometryFEM_FE(DM dm, PetscFE fe, PetscInt point, PetscQuadrature quad, PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
2527: {
2528:   const PetscScalar *array;
2529:   PetscScalar       *coords = NULL;
2530:   PetscInt           numCoords;
2531:   PetscBool          isDG;
2532:   PetscQuadrature    feQuad;
2533:   const PetscReal   *quadPoints;
2534:   PetscTabulation    T;
2535:   PetscInt           dim, cdim, pdim, qdim, Nq, q;

2537:   PetscFunctionBegin;
2538:   PetscCall(DMGetDimension(dm, &dim));
2539:   PetscCall(DMGetCoordinateDim(dm, &cdim));
2540:   PetscCall(DMPlexGetCellCoordinates(dm, point, &isDG, &numCoords, &array, &coords));
2541:   if (!quad) { /* use the first point of the first functional of the dual space */
2542:     PetscDualSpace dsp;

2544:     PetscCall(PetscFEGetDualSpace(fe, &dsp));
2545:     PetscCall(PetscDualSpaceGetFunctional(dsp, 0, &quad));
2546:     PetscCall(PetscQuadratureGetData(quad, &qdim, NULL, &Nq, &quadPoints, NULL));
2547:     Nq = 1;
2548:   } else {
2549:     PetscCall(PetscQuadratureGetData(quad, &qdim, NULL, &Nq, &quadPoints, NULL));
2550:   }
2551:   PetscCheck(qdim == dim, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Point dimension %" PetscInt_FMT " != quadrature dimension %" PetscInt_FMT, dim, qdim);
2552:   PetscCall(PetscFEGetDimension(fe, &pdim));
2553:   PetscCall(PetscFEGetQuadrature(fe, &feQuad));
2554:   if (feQuad == quad) {
2555:     PetscCall(PetscFEGetCellTabulation(fe, J ? 1 : 0, &T));
2556:     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);
2557:   } else {
2558:     PetscCall(PetscFECreateTabulation(fe, 1, Nq, quadPoints, J ? 1 : 0, &T));
2559:   }
2560:   {
2561:     const PetscReal *basis    = T->T[0];
2562:     const PetscReal *basisDer = T->T[1];
2563:     PetscReal        detJt;

2565:     PetscAssert(Nq == T->Np, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Np %" PetscInt_FMT " != %" PetscInt_FMT, Nq, T->Np);
2566:     PetscAssert(pdim == T->Nb, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Nb %" PetscInt_FMT " != %" PetscInt_FMT, pdim, T->Nb);
2567:     PetscAssert(cdim == T->Nc, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Nc %" PetscInt_FMT " != %" PetscInt_FMT, cdim, T->Nc);
2568:     PetscAssert(dim == T->cdim, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "cdim %" PetscInt_FMT " != %" PetscInt_FMT, dim, T->cdim);
2569:     if (v) {
2570:       PetscCall(PetscArrayzero(v, Nq * cdim));
2571:       for (q = 0; q < Nq; ++q) {
2572:         PetscInt i, k;

2574:         for (k = 0; k < pdim; ++k) {
2575:           const PetscInt vertex = k / cdim;
2576:           for (i = 0; i < cdim; ++i) v[q * cdim + i] += basis[(q * pdim + k) * cdim + i] * PetscRealPart(coords[vertex * cdim + i]);
2577:         }
2578:         PetscCall(PetscLogFlops(2.0 * pdim * cdim));
2579:       }
2580:     }
2581:     if (J) {
2582:       PetscCall(PetscArrayzero(J, Nq * cdim * cdim));
2583:       for (q = 0; q < Nq; ++q) {
2584:         PetscInt i, j, k, c, r;

2586:         /* J = dx_i/d\xi_j = sum[k=0,n-1] dN_k/d\xi_j * x_i(k) */
2587:         for (k = 0; k < pdim; ++k) {
2588:           const PetscInt vertex = k / cdim;
2589:           for (j = 0; j < dim; ++j) {
2590:             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]);
2591:           }
2592:         }
2593:         PetscCall(PetscLogFlops(2.0 * pdim * dim * cdim));
2594:         if (cdim > dim) {
2595:           for (c = dim; c < cdim; ++c)
2596:             for (r = 0; r < cdim; ++r) J[r * cdim + c] = r == c ? 1.0 : 0.0;
2597:         }
2598:         if (!detJ && !invJ) continue;
2599:         detJt = 0.;
2600:         switch (cdim) {
2601:         case 3:
2602:           DMPlex_Det3D_Internal(&detJt, &J[q * cdim * dim]);
2603:           if (invJ) DMPlex_Invert3D_Internal(&invJ[q * cdim * dim], &J[q * cdim * dim], detJt);
2604:           break;
2605:         case 2:
2606:           DMPlex_Det2D_Internal(&detJt, &J[q * cdim * dim]);
2607:           if (invJ) DMPlex_Invert2D_Internal(&invJ[q * cdim * dim], &J[q * cdim * dim], detJt);
2608:           break;
2609:         case 1:
2610:           detJt = J[q * cdim * dim];
2611:           if (invJ) invJ[q * cdim * dim] = 1.0 / detJt;
2612:         }
2613:         if (detJ) detJ[q] = detJt;
2614:       }
2615:     } else PetscCheck(!detJ && !invJ, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Need J to compute invJ or detJ");
2616:   }
2617:   if (feQuad != quad) PetscCall(PetscTabulationDestroy(&T));
2618:   PetscCall(DMPlexRestoreCellCoordinates(dm, point, &isDG, &numCoords, &array, &coords));
2619:   PetscFunctionReturn(PETSC_SUCCESS);
2620: }

2622: /*@C
2623:   DMPlexComputeCellGeometryFEM - Compute the Jacobian, inverse Jacobian, and Jacobian determinant at each quadrature point in the given cell

2625:   Collective

2627:   Input Parameters:
2628: + dm   - the `DMPLEX`
2629: . cell - the cell
2630: - quad - the quadrature containing the points in the reference element where the geometry will be evaluated.  If `quad` is `NULL`, geometry will be
2631:          evaluated at the first vertex of the reference element

2633:   Output Parameters:
2634: + v    - the image of the transformed quadrature points, otherwise the image of the first vertex in the closure of the reference element. This is a
2635:          one-dimensional array of size $cdim * Nq$ where $cdim$ is the dimension of the `DM` coordinate space and $Nq$ is the number of quadrature points
2636: . J    - the Jacobian of the transform from the reference element at each quadrature point. This is a one-dimensional array of size $Nq * cdim * cdim$ containing
2637:          each Jacobian in column-major order.
2638: . invJ - the inverse of the Jacobian at each quadrature point. This is a one-dimensional array of size $Nq * cdim * cdim$ containing
2639:          each inverse Jacobian in column-major order.
2640: - detJ - the Jacobian determinant at each quadrature point. This is a one-dimensional array of size $Nq$.

2642:   Level: advanced

2644:   Note:
2645:   Implicit cell geometry must be used when the topological mesh dimension is not equal to the coordinate dimension, for instance for embedded manifolds.

2647: .seealso: `DMPLEX`, `DMGetCoordinateSection()`, `DMGetCoordinates()`
2648: @*/
2649: PetscErrorCode DMPlexComputeCellGeometryFEM(DM dm, PetscInt cell, PetscQuadrature quad, PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal detJ[])
2650: {
2651:   DM       cdm;
2652:   PetscFE  fe = NULL;
2653:   PetscInt dim, cdim;

2655:   PetscFunctionBegin;
2656:   PetscAssertPointer(detJ, 7);
2657:   PetscCall(DMGetDimension(dm, &dim));
2658:   PetscCall(DMGetCoordinateDim(dm, &cdim));
2659:   PetscCall(DMGetCoordinateDM(dm, &cdm));
2660:   if (cdm) {
2661:     PetscSpace   sp;
2662:     PetscClassId id;
2663:     PetscDS      prob;
2664:     PetscObject  disc;
2665:     PetscInt     Nf, spdim, qdim;

2667:     PetscCall(DMGetNumFields(cdm, &Nf));
2668:     if (Nf) {
2669:       PetscCall(DMGetDS(cdm, &prob));
2670:       PetscCall(PetscDSGetDiscretization(prob, 0, &disc));
2671:       PetscCall(PetscObjectGetClassId(disc, &id));
2672:       if (id == PETSCFE_CLASSID) fe = (PetscFE)disc;
2673:       if (fe && quad) {
2674:         PetscCall(PetscQuadratureGetData(quad, &qdim, NULL, NULL, NULL, NULL));
2675:         PetscCall(PetscFEGetBasisSpace(fe, &sp));
2676:         PetscCall(PetscSpaceGetNumVariables(sp, &spdim));
2677:         if (qdim != spdim) fe = NULL;
2678:       }
2679:     }
2680:   }
2681:   if (!fe || (dim != cdim)) PetscCall(DMPlexComputeCellGeometryFEM_Implicit(dm, cell, quad, v, J, invJ, detJ));
2682:   else PetscCall(DMPlexComputeCellGeometryFEM_FE(dm, fe, cell, quad, v, J, invJ, detJ));
2683:   PetscFunctionReturn(PETSC_SUCCESS);
2684: }

2686: static PetscErrorCode DMPlexComputeGeometryFVM_0D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
2687: {
2688:   PetscSection       coordSection;
2689:   Vec                coordinates;
2690:   const PetscScalar *coords = NULL;
2691:   PetscInt           d, dof, off;

2693:   PetscFunctionBegin;
2694:   PetscCall(DMGetCoordinatesLocal(dm, &coordinates));
2695:   PetscCall(DMGetCoordinateSection(dm, &coordSection));
2696:   PetscCall(VecGetArrayRead(coordinates, &coords));

2698:   /* for a point the centroid is just the coord */
2699:   if (centroid) {
2700:     PetscCall(PetscSectionGetDof(coordSection, cell, &dof));
2701:     PetscCall(PetscSectionGetOffset(coordSection, cell, &off));
2702:     for (d = 0; d < dof; d++) centroid[d] = PetscRealPart(coords[off + d]);
2703:   }
2704:   if (normal) {
2705:     const PetscInt *support, *cones;
2706:     PetscInt        supportSize;
2707:     PetscReal       norm, sign;

2709:     /* compute the norm based upon the support centroids */
2710:     PetscCall(DMPlexGetSupportSize(dm, cell, &supportSize));
2711:     PetscCall(DMPlexGetSupport(dm, cell, &support));
2712:     PetscCall(DMPlexComputeCellGeometryFVM(dm, support[0], NULL, normal, NULL));

2714:     /* Take the normal from the centroid of the support to the vertex*/
2715:     PetscCall(PetscSectionGetDof(coordSection, cell, &dof));
2716:     PetscCall(PetscSectionGetOffset(coordSection, cell, &off));
2717:     for (d = 0; d < dof; d++) normal[d] -= PetscRealPart(coords[off + d]);

2719:     /* Determine the sign of the normal based upon its location in the support */
2720:     PetscCall(DMPlexGetCone(dm, support[0], &cones));
2721:     sign = cones[0] == cell ? 1.0 : -1.0;

2723:     norm = DMPlex_NormD_Internal(dim, normal);
2724:     for (d = 0; d < dim; ++d) normal[d] /= (norm * sign);
2725:   }
2726:   if (vol) *vol = 1.0;
2727:   PetscCall(VecRestoreArrayRead(coordinates, &coords));
2728:   PetscFunctionReturn(PETSC_SUCCESS);
2729: }

2731: static PetscErrorCode DMPlexComputeGeometryFVM_1D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
2732: {
2733:   const PetscScalar *array;
2734:   PetscScalar       *coords = NULL;
2735:   PetscInt           cdim, coordSize, d;
2736:   PetscBool          isDG;

2738:   PetscFunctionBegin;
2739:   PetscCall(DMGetCoordinateDim(dm, &cdim));
2740:   PetscCall(DMPlexGetCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
2741:   PetscCheck(coordSize == cdim * 2, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Edge has %" PetscInt_FMT " coordinates != %" PetscInt_FMT, coordSize, cdim * 2);
2742:   if (centroid) {
2743:     for (d = 0; d < cdim; ++d) centroid[d] = 0.5 * PetscRealPart(coords[d] + coords[cdim + d]);
2744:   }
2745:   if (normal) {
2746:     PetscReal norm;

2748:     switch (cdim) {
2749:     case 3:
2750:       normal[2] = 0.; /* fall through */
2751:     case 2:
2752:       normal[0] = -PetscRealPart(coords[1] - coords[cdim + 1]);
2753:       normal[1] = PetscRealPart(coords[0] - coords[cdim + 0]);
2754:       break;
2755:     case 1:
2756:       normal[0] = 1.0;
2757:       break;
2758:     default:
2759:       SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Dimension %" PetscInt_FMT " not supported", cdim);
2760:     }
2761:     norm = DMPlex_NormD_Internal(cdim, normal);
2762:     for (d = 0; d < cdim; ++d) normal[d] /= norm;
2763:   }
2764:   if (vol) {
2765:     *vol = 0.0;
2766:     for (d = 0; d < cdim; ++d) *vol += PetscSqr(PetscRealPart(coords[d] - coords[cdim + d]));
2767:     *vol = PetscSqrtReal(*vol);
2768:   }
2769:   PetscCall(DMPlexRestoreCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
2770:   PetscFunctionReturn(PETSC_SUCCESS);
2771: }

2773: /* Centroid_i = (\sum_n A_n Cn_i) / A */
2774: static PetscErrorCode DMPlexComputeGeometryFVM_2D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
2775: {
2776:   DMPolytopeType     ct;
2777:   const PetscScalar *array;
2778:   PetscScalar       *coords = NULL;
2779:   PetscInt           coordSize;
2780:   PetscBool          isDG;
2781:   PetscInt           fv[4] = {0, 1, 2, 3};
2782:   PetscInt           cdim, numCorners, p, d;

2784:   PetscFunctionBegin;
2785:   /* Must check for hybrid cells because prisms have a different orientation scheme */
2786:   PetscCall(DMPlexGetCellType(dm, cell, &ct));
2787:   switch (ct) {
2788:   case DM_POLYTOPE_SEG_PRISM_TENSOR:
2789:     fv[2] = 3;
2790:     fv[3] = 2;
2791:     break;
2792:   default:
2793:     break;
2794:   }
2795:   PetscCall(DMGetCoordinateDim(dm, &cdim));
2796:   PetscCall(DMPlexGetConeSize(dm, cell, &numCorners));
2797:   PetscCall(DMPlexGetCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
2798:   {
2799:     PetscReal c[3] = {0., 0., 0.}, n[3] = {0., 0., 0.}, origin[3] = {0., 0., 0.}, norm;

2801:     for (d = 0; d < cdim; d++) origin[d] = PetscRealPart(coords[d]);
2802:     for (p = 0; p < numCorners - 2; ++p) {
2803:       PetscReal e0[3] = {0., 0., 0.}, e1[3] = {0., 0., 0.};
2804:       for (d = 0; d < cdim; d++) {
2805:         e0[d] = PetscRealPart(coords[cdim * fv[p + 1] + d]) - origin[d];
2806:         e1[d] = PetscRealPart(coords[cdim * fv[p + 2] + d]) - origin[d];
2807:       }
2808:       const PetscReal dx = e0[1] * e1[2] - e0[2] * e1[1];
2809:       const PetscReal dy = e0[2] * e1[0] - e0[0] * e1[2];
2810:       const PetscReal dz = e0[0] * e1[1] - e0[1] * e1[0];
2811:       const PetscReal a  = PetscSqrtReal(dx * dx + dy * dy + dz * dz);

2813:       n[0] += dx;
2814:       n[1] += dy;
2815:       n[2] += dz;
2816:       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.;
2817:     }
2818:     norm = PetscSqrtReal(n[0] * n[0] + n[1] * n[1] + n[2] * n[2]);
2819:     // Allow zero volume cells
2820:     if (norm != 0) {
2821:       n[0] /= norm;
2822:       n[1] /= norm;
2823:       n[2] /= norm;
2824:       c[0] /= norm;
2825:       c[1] /= norm;
2826:       c[2] /= norm;
2827:     }
2828:     if (vol) *vol = 0.5 * norm;
2829:     if (centroid)
2830:       for (d = 0; d < cdim; ++d) centroid[d] = c[d];
2831:     if (normal)
2832:       for (d = 0; d < cdim; ++d) normal[d] = n[d];
2833:   }
2834:   PetscCall(DMPlexRestoreCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
2835:   PetscFunctionReturn(PETSC_SUCCESS);
2836: }

2838: /* Centroid_i = (\sum_n V_n Cn_i) / V */
2839: static PetscErrorCode DMPlexComputeGeometryFVM_3D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
2840: {
2841:   DMPolytopeType        ct;
2842:   const PetscScalar    *array;
2843:   PetscScalar          *coords = NULL;
2844:   PetscInt              coordSize;
2845:   PetscBool             isDG;
2846:   PetscReal             vsum      = 0.0, vtmp, coordsTmp[3 * 3], origin[3];
2847:   const PetscInt        order[16] = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15};
2848:   const PetscInt       *cone, *faceSizes, *faces;
2849:   const DMPolytopeType *faceTypes;
2850:   PetscBool             isHybrid = PETSC_FALSE;
2851:   PetscInt              numFaces, f, fOff = 0, p, d;

2853:   PetscFunctionBegin;
2854:   PetscCheck(dim <= 3, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "No support for dim %" PetscInt_FMT " > 3", dim);
2855:   /* Must check for hybrid cells because prisms have a different orientation scheme */
2856:   PetscCall(DMPlexGetCellType(dm, cell, &ct));
2857:   switch (ct) {
2858:   case DM_POLYTOPE_POINT_PRISM_TENSOR:
2859:   case DM_POLYTOPE_SEG_PRISM_TENSOR:
2860:   case DM_POLYTOPE_TRI_PRISM_TENSOR:
2861:   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
2862:     isHybrid = PETSC_TRUE;
2863:   default:
2864:     break;
2865:   }

2867:   if (centroid)
2868:     for (d = 0; d < dim; ++d) centroid[d] = 0.0;
2869:   PetscCall(DMPlexGetCone(dm, cell, &cone));

2871:   // Using the closure of faces for coordinates does not work in periodic geometries, so we index into the cell coordinates
2872:   PetscCall(DMPlexGetRawFaces_Internal(dm, ct, order, &numFaces, &faceTypes, &faceSizes, &faces));
2873:   PetscCall(DMPlexGetCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
2874:   for (f = 0; f < numFaces; ++f) {
2875:     PetscBool flip = isHybrid && f == 0 ? PETSC_TRUE : PETSC_FALSE; /* The first hybrid face is reversed */

2877:     // If using zero as the origin vertex for each tetrahedron, an element far from the origin will have positive and
2878:     // negative volumes that nearly cancel, thus incurring rounding error. Here we define origin[] as the first vertex
2879:     // so that all tetrahedra have positive volume.
2880:     if (f == 0)
2881:       for (d = 0; d < dim; d++) origin[d] = PetscRealPart(coords[d]);
2882:     switch (faceTypes[f]) {
2883:     case DM_POLYTOPE_TRIANGLE:
2884:       for (d = 0; d < dim; ++d) {
2885:         coordsTmp[0 * dim + d] = PetscRealPart(coords[faces[fOff + 0] * dim + d]) - origin[d];
2886:         coordsTmp[1 * dim + d] = PetscRealPart(coords[faces[fOff + 1] * dim + d]) - origin[d];
2887:         coordsTmp[2 * dim + d] = PetscRealPart(coords[faces[fOff + 2] * dim + d]) - origin[d];
2888:       }
2889:       Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
2890:       if (flip) vtmp = -vtmp;
2891:       vsum += vtmp;
2892:       if (centroid) { /* Centroid of OABC = (a+b+c)/4 */
2893:         for (d = 0; d < dim; ++d) {
2894:           for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p * dim + d] * vtmp;
2895:         }
2896:       }
2897:       break;
2898:     case DM_POLYTOPE_QUADRILATERAL:
2899:     case DM_POLYTOPE_SEG_PRISM_TENSOR: {
2900:       PetscInt fv[4] = {0, 1, 2, 3};

2902:       /* Side faces for hybrid cells are stored as tensor products */
2903:       if (isHybrid && f > 1) {
2904:         fv[2] = 3;
2905:         fv[3] = 2;
2906:       }
2907:       /* DO FOR PYRAMID */
2908:       /* First tet */
2909:       for (d = 0; d < dim; ++d) {
2910:         coordsTmp[0 * dim + d] = PetscRealPart(coords[faces[fOff + fv[0]] * dim + d]) - origin[d];
2911:         coordsTmp[1 * dim + d] = PetscRealPart(coords[faces[fOff + fv[1]] * dim + d]) - origin[d];
2912:         coordsTmp[2 * dim + d] = PetscRealPart(coords[faces[fOff + fv[3]] * dim + d]) - origin[d];
2913:       }
2914:       Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
2915:       if (flip) vtmp = -vtmp;
2916:       vsum += vtmp;
2917:       if (centroid) {
2918:         for (d = 0; d < dim; ++d) {
2919:           for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p * dim + d] * vtmp;
2920:         }
2921:       }
2922:       /* Second tet */
2923:       for (d = 0; d < dim; ++d) {
2924:         coordsTmp[0 * dim + d] = PetscRealPart(coords[faces[fOff + fv[1]] * dim + d]) - origin[d];
2925:         coordsTmp[1 * dim + d] = PetscRealPart(coords[faces[fOff + fv[2]] * dim + d]) - origin[d];
2926:         coordsTmp[2 * dim + d] = PetscRealPart(coords[faces[fOff + fv[3]] * dim + d]) - origin[d];
2927:       }
2928:       Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
2929:       if (flip) vtmp = -vtmp;
2930:       vsum += vtmp;
2931:       if (centroid) {
2932:         for (d = 0; d < dim; ++d) {
2933:           for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p * dim + d] * vtmp;
2934:         }
2935:       }
2936:       break;
2937:     }
2938:     default:
2939:       SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Cannot handle face %" PetscInt_FMT " of type %s", cone[f], DMPolytopeTypes[ct]);
2940:     }
2941:     fOff += faceSizes[f];
2942:   }
2943:   PetscCall(DMPlexRestoreRawFaces_Internal(dm, ct, order, &numFaces, &faceTypes, &faceSizes, &faces));
2944:   PetscCall(DMPlexRestoreCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
2945:   if (vol) *vol = PetscAbsReal(vsum);
2946:   if (normal)
2947:     for (d = 0; d < dim; ++d) normal[d] = 0.0;
2948:   if (centroid)
2949:     for (d = 0; d < dim; ++d) centroid[d] = centroid[d] / (vsum * 4) + origin[d];
2950:   PetscFunctionReturn(PETSC_SUCCESS);
2951: }

2953: /*@C
2954:   DMPlexComputeCellGeometryFVM - Compute the volume for a given cell

2956:   Collective

2958:   Input Parameters:
2959: + dm   - the `DMPLEX`
2960: - cell - the cell

2962:   Output Parameters:
2963: + vol      - the cell volume
2964: . centroid - the cell centroid
2965: - normal   - the cell normal, if appropriate

2967:   Level: advanced

2969: .seealso: `DMPLEX`, `DMGetCoordinateSection()`, `DMGetCoordinates()`
2970: @*/
2971: PetscErrorCode DMPlexComputeCellGeometryFVM(DM dm, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
2972: {
2973:   PetscInt depth, dim;

2975:   PetscFunctionBegin;
2976:   PetscCall(DMPlexGetDepth(dm, &depth));
2977:   PetscCall(DMGetDimension(dm, &dim));
2978:   PetscCall(DMPlexGetPointDepth(dm, cell, &depth));
2979:   switch (depth) {
2980:   case 0:
2981:     PetscCall(DMPlexComputeGeometryFVM_0D_Internal(dm, dim, cell, vol, centroid, normal));
2982:     break;
2983:   case 1:
2984:     PetscCall(DMPlexComputeGeometryFVM_1D_Internal(dm, dim, cell, vol, centroid, normal));
2985:     break;
2986:   case 2:
2987:     PetscCall(DMPlexComputeGeometryFVM_2D_Internal(dm, dim, cell, vol, centroid, normal));
2988:     break;
2989:   case 3:
2990:     PetscCall(DMPlexComputeGeometryFVM_3D_Internal(dm, dim, cell, vol, centroid, normal));
2991:     break;
2992:   default:
2993:     SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported dimension %" PetscInt_FMT " (depth %" PetscInt_FMT ") for element geometry computation", dim, depth);
2994:   }
2995:   PetscFunctionReturn(PETSC_SUCCESS);
2996: }

2998: /*@
2999:   DMPlexComputeGeometryFVM - Computes the cell and face geometry for a finite volume method

3001:   Input Parameter:
3002: . dm - The `DMPLEX`

3004:   Output Parameters:
3005: + cellgeom - A `Vec` of `PetscFVCellGeom` data
3006: - facegeom - A `Vec` of `PetscFVFaceGeom` data

3008:   Level: developer

3010: .seealso: `DMPLEX`, `PetscFVFaceGeom`, `PetscFVCellGeom`
3011: @*/
3012: PetscErrorCode DMPlexComputeGeometryFVM(DM dm, Vec *cellgeom, Vec *facegeom)
3013: {
3014:   DM           dmFace, dmCell;
3015:   DMLabel      ghostLabel;
3016:   PetscSection sectionFace, sectionCell;
3017:   PetscSection coordSection;
3018:   Vec          coordinates;
3019:   PetscScalar *fgeom, *cgeom;
3020:   PetscReal    minradius;
3021:   PetscInt     dim, cStart, cEnd, cEndInterior, c, fStart, fEnd, f;

3023:   PetscFunctionBegin;
3024:   PetscCall(DMGetDimension(dm, &dim));
3025:   PetscCall(DMGetCoordinateSection(dm, &coordSection));
3026:   PetscCall(DMGetCoordinatesLocal(dm, &coordinates));
3027:   /* Make cell centroids and volumes */
3028:   PetscCall(DMClone(dm, &dmCell));
3029:   PetscCall(DMSetCoordinateSection(dmCell, PETSC_DETERMINE, coordSection));
3030:   PetscCall(DMSetCoordinatesLocal(dmCell, coordinates));
3031:   PetscCall(PetscSectionCreate(PetscObjectComm((PetscObject)dm), &sectionCell));
3032:   PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
3033:   PetscCall(DMPlexGetCellTypeStratum(dm, DM_POLYTOPE_FV_GHOST, &cEndInterior, NULL));
3034:   PetscCall(PetscSectionSetChart(sectionCell, cStart, cEnd));
3035:   for (c = cStart; c < cEnd; ++c) PetscCall(PetscSectionSetDof(sectionCell, c, (PetscInt)PetscCeilReal(((PetscReal)sizeof(PetscFVCellGeom)) / sizeof(PetscScalar))));
3036:   PetscCall(PetscSectionSetUp(sectionCell));
3037:   PetscCall(DMSetLocalSection(dmCell, sectionCell));
3038:   PetscCall(PetscSectionDestroy(&sectionCell));
3039:   PetscCall(DMCreateLocalVector(dmCell, cellgeom));
3040:   if (cEndInterior < 0) cEndInterior = cEnd;
3041:   PetscCall(VecGetArray(*cellgeom, &cgeom));
3042:   for (c = cStart; c < cEndInterior; ++c) {
3043:     PetscFVCellGeom *cg;

3045:     PetscCall(DMPlexPointLocalRef(dmCell, c, cgeom, &cg));
3046:     PetscCall(PetscArrayzero(cg, 1));
3047:     PetscCall(DMPlexComputeCellGeometryFVM(dmCell, c, &cg->volume, cg->centroid, NULL));
3048:   }
3049:   /* Compute face normals and minimum cell radius */
3050:   PetscCall(DMClone(dm, &dmFace));
3051:   PetscCall(PetscSectionCreate(PetscObjectComm((PetscObject)dm), &sectionFace));
3052:   PetscCall(DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd));
3053:   PetscCall(PetscSectionSetChart(sectionFace, fStart, fEnd));
3054:   for (f = fStart; f < fEnd; ++f) PetscCall(PetscSectionSetDof(sectionFace, f, (PetscInt)PetscCeilReal(((PetscReal)sizeof(PetscFVFaceGeom)) / sizeof(PetscScalar))));
3055:   PetscCall(PetscSectionSetUp(sectionFace));
3056:   PetscCall(DMSetLocalSection(dmFace, sectionFace));
3057:   PetscCall(PetscSectionDestroy(&sectionFace));
3058:   PetscCall(DMCreateLocalVector(dmFace, facegeom));
3059:   PetscCall(VecGetArray(*facegeom, &fgeom));
3060:   PetscCall(DMGetLabel(dm, "ghost", &ghostLabel));
3061:   minradius = PETSC_MAX_REAL;
3062:   for (f = fStart; f < fEnd; ++f) {
3063:     PetscFVFaceGeom *fg;
3064:     PetscReal        area;
3065:     const PetscInt  *cells;
3066:     PetscInt         ncells, ghost = -1, d, numChildren;

3068:     if (ghostLabel) PetscCall(DMLabelGetValue(ghostLabel, f, &ghost));
3069:     PetscCall(DMPlexGetTreeChildren(dm, f, &numChildren, NULL));
3070:     PetscCall(DMPlexGetSupport(dm, f, &cells));
3071:     PetscCall(DMPlexGetSupportSize(dm, f, &ncells));
3072:     /* It is possible to get a face with no support when using partition overlap */
3073:     if (!ncells || ghost >= 0 || numChildren) continue;
3074:     PetscCall(DMPlexPointLocalRef(dmFace, f, fgeom, &fg));
3075:     PetscCall(DMPlexComputeCellGeometryFVM(dm, f, &area, fg->centroid, fg->normal));
3076:     for (d = 0; d < dim; ++d) fg->normal[d] *= area;
3077:     /* Flip face orientation if necessary to match ordering in support, and Update minimum radius */
3078:     {
3079:       PetscFVCellGeom *cL, *cR;
3080:       PetscReal       *lcentroid, *rcentroid;
3081:       PetscReal        l[3], r[3], v[3];

3083:       PetscCall(DMPlexPointLocalRead(dmCell, cells[0], cgeom, &cL));
3084:       lcentroid = cells[0] >= cEndInterior ? fg->centroid : cL->centroid;
3085:       if (ncells > 1) {
3086:         PetscCall(DMPlexPointLocalRead(dmCell, cells[1], cgeom, &cR));
3087:         rcentroid = cells[1] >= cEndInterior ? fg->centroid : cR->centroid;
3088:       } else {
3089:         rcentroid = fg->centroid;
3090:       }
3091:       PetscCall(DMLocalizeCoordinateReal_Internal(dm, dim, fg->centroid, lcentroid, l));
3092:       PetscCall(DMLocalizeCoordinateReal_Internal(dm, dim, fg->centroid, rcentroid, r));
3093:       DMPlex_WaxpyD_Internal(dim, -1, l, r, v);
3094:       if (DMPlex_DotRealD_Internal(dim, fg->normal, v) < 0) {
3095:         for (d = 0; d < dim; ++d) fg->normal[d] = -fg->normal[d];
3096:       }
3097:       if (DMPlex_DotRealD_Internal(dim, fg->normal, v) <= 0) {
3098:         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]);
3099:         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]);
3100:         SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Direction for face %" PetscInt_FMT " could not be fixed", f);
3101:       }
3102:       if (cells[0] < cEndInterior) {
3103:         DMPlex_WaxpyD_Internal(dim, -1, fg->centroid, cL->centroid, v);
3104:         minradius = PetscMin(minradius, DMPlex_NormD_Internal(dim, v));
3105:       }
3106:       if (ncells > 1 && cells[1] < cEndInterior) {
3107:         DMPlex_WaxpyD_Internal(dim, -1, fg->centroid, cR->centroid, v);
3108:         minradius = PetscMin(minradius, DMPlex_NormD_Internal(dim, v));
3109:       }
3110:     }
3111:   }
3112:   PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, &minradius, 1, MPIU_REAL, MPIU_MIN, PetscObjectComm((PetscObject)dm)));
3113:   PetscCall(DMPlexSetMinRadius(dm, minradius));
3114:   /* Compute centroids of ghost cells */
3115:   for (c = cEndInterior; c < cEnd; ++c) {
3116:     PetscFVFaceGeom *fg;
3117:     const PetscInt  *cone, *support;
3118:     PetscInt         coneSize, supportSize, s;

3120:     PetscCall(DMPlexGetConeSize(dmCell, c, &coneSize));
3121:     PetscCheck(coneSize == 1, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Ghost cell %" PetscInt_FMT " has cone size %" PetscInt_FMT " != 1", c, coneSize);
3122:     PetscCall(DMPlexGetCone(dmCell, c, &cone));
3123:     PetscCall(DMPlexGetSupportSize(dmCell, cone[0], &supportSize));
3124:     PetscCheck(supportSize == 2, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Face %" PetscInt_FMT " has support size %" PetscInt_FMT " != 2", cone[0], supportSize);
3125:     PetscCall(DMPlexGetSupport(dmCell, cone[0], &support));
3126:     PetscCall(DMPlexPointLocalRef(dmFace, cone[0], fgeom, &fg));
3127:     for (s = 0; s < 2; ++s) {
3128:       /* Reflect ghost centroid across plane of face */
3129:       if (support[s] == c) {
3130:         PetscFVCellGeom *ci;
3131:         PetscFVCellGeom *cg;
3132:         PetscReal        c2f[3], a;

3134:         PetscCall(DMPlexPointLocalRead(dmCell, support[(s + 1) % 2], cgeom, &ci));
3135:         DMPlex_WaxpyD_Internal(dim, -1, ci->centroid, fg->centroid, c2f); /* cell to face centroid */
3136:         a = DMPlex_DotRealD_Internal(dim, c2f, fg->normal) / DMPlex_DotRealD_Internal(dim, fg->normal, fg->normal);
3137:         PetscCall(DMPlexPointLocalRef(dmCell, support[s], cgeom, &cg));
3138:         DMPlex_WaxpyD_Internal(dim, 2 * a, fg->normal, ci->centroid, cg->centroid);
3139:         cg->volume = ci->volume;
3140:       }
3141:     }
3142:   }
3143:   PetscCall(VecRestoreArray(*facegeom, &fgeom));
3144:   PetscCall(VecRestoreArray(*cellgeom, &cgeom));
3145:   PetscCall(DMDestroy(&dmCell));
3146:   PetscCall(DMDestroy(&dmFace));
3147:   PetscFunctionReturn(PETSC_SUCCESS);
3148: }

3150: /*@
3151:   DMPlexGetMinRadius - Returns the minimum distance from any cell centroid to a face

3153:   Not Collective

3155:   Input Parameter:
3156: . dm - the `DMPLEX`

3158:   Output Parameter:
3159: . minradius - the minimum cell radius

3161:   Level: developer

3163: .seealso: `DMPLEX`, `DMGetCoordinates()`
3164: @*/
3165: PetscErrorCode DMPlexGetMinRadius(DM dm, PetscReal *minradius)
3166: {
3167:   PetscFunctionBegin;
3169:   PetscAssertPointer(minradius, 2);
3170:   *minradius = ((DM_Plex *)dm->data)->minradius;
3171:   PetscFunctionReturn(PETSC_SUCCESS);
3172: }

3174: /*@
3175:   DMPlexSetMinRadius - Sets the minimum distance from the cell centroid to a face

3177:   Logically Collective

3179:   Input Parameters:
3180: + dm        - the `DMPLEX`
3181: - minradius - the minimum cell radius

3183:   Level: developer

3185: .seealso: `DMPLEX`, `DMSetCoordinates()`
3186: @*/
3187: PetscErrorCode DMPlexSetMinRadius(DM dm, PetscReal minradius)
3188: {
3189:   PetscFunctionBegin;
3191:   ((DM_Plex *)dm->data)->minradius = minradius;
3192:   PetscFunctionReturn(PETSC_SUCCESS);
3193: }

3195: /*@C
3196:   DMPlexGetCoordinateMap - Returns the function used to map coordinates of newly generated mesh points

3198:   Not Collective

3200:   Input Parameter:
3201: . dm - the `DMPLEX`

3203:   Output Parameter:
3204: . coordFunc - the mapping function

3206:   Level: developer

3208:   Note:
3209:   This function maps from the generated coordinate for the new point to the actual coordinate. Thus it is only practical for manifolds with a nice analytical definition that you can get to from any starting point, like a sphere,

3211: .seealso: `DMPLEX`, `DMGetCoordinates()`, `DMPlexSetCoordinateMap()`, `PetscPointFn`
3212: @*/
3213: PetscErrorCode DMPlexGetCoordinateMap(DM dm, PetscPointFn **coordFunc)
3214: {
3215:   PetscFunctionBegin;
3217:   PetscAssertPointer(coordFunc, 2);
3218:   *coordFunc = ((DM_Plex *)dm->data)->coordFunc;
3219:   PetscFunctionReturn(PETSC_SUCCESS);
3220: }

3222: /*@C
3223:   DMPlexSetCoordinateMap - Sets the function used to map coordinates of newly generated mesh points

3225:   Logically Collective

3227:   Input Parameters:
3228: + dm        - the `DMPLEX`
3229: - coordFunc - the mapping function

3231:   Level: developer

3233:   Note:
3234:   This function maps from the generated coordinate for the new point to the actual coordinate. Thus it is only practical for manifolds with a nice analytical definition that you can get to from any starting point, like a sphere,

3236: .seealso: `DMPLEX`, `DMSetCoordinates()`, `DMPlexGetCoordinateMap()`, `PetscPointFn`
3237: @*/
3238: PetscErrorCode DMPlexSetCoordinateMap(DM dm, PetscPointFn *coordFunc)
3239: {
3240:   PetscFunctionBegin;
3242:   ((DM_Plex *)dm->data)->coordFunc = coordFunc;
3243:   PetscFunctionReturn(PETSC_SUCCESS);
3244: }

3246: static PetscErrorCode BuildGradientReconstruction_Internal(DM dm, PetscFV fvm, DM dmFace, PetscScalar *fgeom, DM dmCell, PetscScalar *cgeom)
3247: {
3248:   DMLabel      ghostLabel;
3249:   PetscScalar *dx, *grad, **gref;
3250:   PetscInt     dim, cStart, cEnd, c, cEndInterior, maxNumFaces;

3252:   PetscFunctionBegin;
3253:   PetscCall(DMGetDimension(dm, &dim));
3254:   PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
3255:   PetscCall(DMPlexGetCellTypeStratum(dm, DM_POLYTOPE_FV_GHOST, &cEndInterior, NULL));
3256:   cEndInterior = cEndInterior < 0 ? cEnd : cEndInterior;
3257:   PetscCall(DMPlexGetMaxSizes(dm, &maxNumFaces, NULL));
3258:   PetscCall(PetscFVLeastSquaresSetMaxFaces(fvm, maxNumFaces));
3259:   PetscCall(DMGetLabel(dm, "ghost", &ghostLabel));
3260:   PetscCall(PetscMalloc3(maxNumFaces * dim, &dx, maxNumFaces * dim, &grad, maxNumFaces, &gref));
3261:   for (c = cStart; c < cEndInterior; c++) {
3262:     const PetscInt  *faces;
3263:     PetscInt         numFaces, usedFaces, f, d;
3264:     PetscFVCellGeom *cg;
3265:     PetscBool        boundary;
3266:     PetscInt         ghost;

3268:     // do not attempt to compute a gradient reconstruction stencil in a ghost cell.  It will never be used
3269:     PetscCall(DMLabelGetValue(ghostLabel, c, &ghost));
3270:     if (ghost >= 0) continue;

3272:     PetscCall(DMPlexPointLocalRead(dmCell, c, cgeom, &cg));
3273:     PetscCall(DMPlexGetConeSize(dm, c, &numFaces));
3274:     PetscCall(DMPlexGetCone(dm, c, &faces));
3275:     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);
3276:     for (f = 0, usedFaces = 0; f < numFaces; ++f) {
3277:       PetscFVCellGeom *cg1;
3278:       PetscFVFaceGeom *fg;
3279:       const PetscInt  *fcells;
3280:       PetscInt         ncell, side;

3282:       PetscCall(DMLabelGetValue(ghostLabel, faces[f], &ghost));
3283:       PetscCall(DMIsBoundaryPoint(dm, faces[f], &boundary));
3284:       if ((ghost >= 0) || boundary) continue;
3285:       PetscCall(DMPlexGetSupport(dm, faces[f], &fcells));
3286:       side  = (c != fcells[0]); /* c is on left=0 or right=1 of face */
3287:       ncell = fcells[!side];    /* the neighbor */
3288:       PetscCall(DMPlexPointLocalRef(dmFace, faces[f], fgeom, &fg));
3289:       PetscCall(DMPlexPointLocalRead(dmCell, ncell, cgeom, &cg1));
3290:       for (d = 0; d < dim; ++d) dx[usedFaces * dim + d] = cg1->centroid[d] - cg->centroid[d];
3291:       gref[usedFaces++] = fg->grad[side]; /* Gradient reconstruction term will go here */
3292:     }
3293:     PetscCheck(usedFaces, PETSC_COMM_SELF, PETSC_ERR_USER, "Mesh contains isolated cell (no neighbors). Is it intentional?");
3294:     PetscCall(PetscFVComputeGradient(fvm, usedFaces, dx, grad));
3295:     for (f = 0, usedFaces = 0; f < numFaces; ++f) {
3296:       PetscCall(DMLabelGetValue(ghostLabel, faces[f], &ghost));
3297:       PetscCall(DMIsBoundaryPoint(dm, faces[f], &boundary));
3298:       if ((ghost >= 0) || boundary) continue;
3299:       for (d = 0; d < dim; ++d) gref[usedFaces][d] = grad[usedFaces * dim + d];
3300:       ++usedFaces;
3301:     }
3302:   }
3303:   PetscCall(PetscFree3(dx, grad, gref));
3304:   PetscFunctionReturn(PETSC_SUCCESS);
3305: }

3307: static PetscErrorCode BuildGradientReconstruction_Internal_Tree(DM dm, PetscFV fvm, DM dmFace, PetscScalar *fgeom, DM dmCell, PetscScalar *cgeom)
3308: {
3309:   DMLabel      ghostLabel;
3310:   PetscScalar *dx, *grad, **gref;
3311:   PetscInt     dim, cStart, cEnd, c, cEndInterior, fStart, fEnd, f, nStart, nEnd, maxNumFaces = 0;
3312:   PetscSection neighSec;
3313:   PetscInt (*neighbors)[2];
3314:   PetscInt *counter;

3316:   PetscFunctionBegin;
3317:   PetscCall(DMGetDimension(dm, &dim));
3318:   PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
3319:   PetscCall(DMPlexGetCellTypeStratum(dm, DM_POLYTOPE_FV_GHOST, &cEndInterior, NULL));
3320:   if (cEndInterior < 0) cEndInterior = cEnd;
3321:   PetscCall(PetscSectionCreate(PetscObjectComm((PetscObject)dm), &neighSec));
3322:   PetscCall(PetscSectionSetChart(neighSec, cStart, cEndInterior));
3323:   PetscCall(DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd));
3324:   PetscCall(DMGetLabel(dm, "ghost", &ghostLabel));
3325:   for (f = fStart; f < fEnd; f++) {
3326:     const PetscInt *fcells;
3327:     PetscBool       boundary;
3328:     PetscInt        ghost = -1;
3329:     PetscInt        numChildren, numCells, c;

3331:     if (ghostLabel) PetscCall(DMLabelGetValue(ghostLabel, f, &ghost));
3332:     PetscCall(DMIsBoundaryPoint(dm, f, &boundary));
3333:     PetscCall(DMPlexGetTreeChildren(dm, f, &numChildren, NULL));
3334:     if ((ghost >= 0) || boundary || numChildren) continue;
3335:     PetscCall(DMPlexGetSupportSize(dm, f, &numCells));
3336:     if (numCells == 2) {
3337:       PetscCall(DMPlexGetSupport(dm, f, &fcells));
3338:       for (c = 0; c < 2; c++) {
3339:         PetscInt cell = fcells[c];

3341:         if (cell >= cStart && cell < cEndInterior) PetscCall(PetscSectionAddDof(neighSec, cell, 1));
3342:       }
3343:     }
3344:   }
3345:   PetscCall(PetscSectionSetUp(neighSec));
3346:   PetscCall(PetscSectionGetMaxDof(neighSec, &maxNumFaces));
3347:   PetscCall(PetscFVLeastSquaresSetMaxFaces(fvm, maxNumFaces));
3348:   nStart = 0;
3349:   PetscCall(PetscSectionGetStorageSize(neighSec, &nEnd));
3350:   PetscCall(PetscMalloc1(nEnd - nStart, &neighbors));
3351:   PetscCall(PetscCalloc1(cEndInterior - cStart, &counter));
3352:   for (f = fStart; f < fEnd; f++) {
3353:     const PetscInt *fcells;
3354:     PetscBool       boundary;
3355:     PetscInt        ghost = -1;
3356:     PetscInt        numChildren, numCells, c;

3358:     if (ghostLabel) PetscCall(DMLabelGetValue(ghostLabel, f, &ghost));
3359:     PetscCall(DMIsBoundaryPoint(dm, f, &boundary));
3360:     PetscCall(DMPlexGetTreeChildren(dm, f, &numChildren, NULL));
3361:     if ((ghost >= 0) || boundary || numChildren) continue;
3362:     PetscCall(DMPlexGetSupportSize(dm, f, &numCells));
3363:     if (numCells == 2) {
3364:       PetscCall(DMPlexGetSupport(dm, f, &fcells));
3365:       for (c = 0; c < 2; c++) {
3366:         PetscInt cell = fcells[c], off;

3368:         if (cell >= cStart && cell < cEndInterior) {
3369:           PetscCall(PetscSectionGetOffset(neighSec, cell, &off));
3370:           off += counter[cell - cStart]++;
3371:           neighbors[off][0] = f;
3372:           neighbors[off][1] = fcells[1 - c];
3373:         }
3374:       }
3375:     }
3376:   }
3377:   PetscCall(PetscFree(counter));
3378:   PetscCall(PetscMalloc3(maxNumFaces * dim, &dx, maxNumFaces * dim, &grad, maxNumFaces, &gref));
3379:   for (c = cStart; c < cEndInterior; c++) {
3380:     PetscInt         numFaces, f, d, off, ghost = -1;
3381:     PetscFVCellGeom *cg;

3383:     PetscCall(DMPlexPointLocalRead(dmCell, c, cgeom, &cg));
3384:     PetscCall(PetscSectionGetDof(neighSec, c, &numFaces));
3385:     PetscCall(PetscSectionGetOffset(neighSec, c, &off));

3387:     // do not attempt to compute a gradient reconstruction stencil in a ghost cell.  It will never be used
3388:     if (ghostLabel) PetscCall(DMLabelGetValue(ghostLabel, c, &ghost));
3389:     if (ghost >= 0) continue;

3391:     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);
3392:     for (f = 0; f < numFaces; ++f) {
3393:       PetscFVCellGeom *cg1;
3394:       PetscFVFaceGeom *fg;
3395:       const PetscInt  *fcells;
3396:       PetscInt         ncell, side, nface;

3398:       nface = neighbors[off + f][0];
3399:       ncell = neighbors[off + f][1];
3400:       PetscCall(DMPlexGetSupport(dm, nface, &fcells));
3401:       side = (c != fcells[0]);
3402:       PetscCall(DMPlexPointLocalRef(dmFace, nface, fgeom, &fg));
3403:       PetscCall(DMPlexPointLocalRead(dmCell, ncell, cgeom, &cg1));
3404:       for (d = 0; d < dim; ++d) dx[f * dim + d] = cg1->centroid[d] - cg->centroid[d];
3405:       gref[f] = fg->grad[side]; /* Gradient reconstruction term will go here */
3406:     }
3407:     PetscCall(PetscFVComputeGradient(fvm, numFaces, dx, grad));
3408:     for (f = 0; f < numFaces; ++f) {
3409:       for (d = 0; d < dim; ++d) gref[f][d] = grad[f * dim + d];
3410:     }
3411:   }
3412:   PetscCall(PetscFree3(dx, grad, gref));
3413:   PetscCall(PetscSectionDestroy(&neighSec));
3414:   PetscCall(PetscFree(neighbors));
3415:   PetscFunctionReturn(PETSC_SUCCESS);
3416: }

3418: /*@
3419:   DMPlexComputeGradientFVM - Compute geometric factors for gradient reconstruction, which are stored in the geometry data, and compute layout for gradient data

3421:   Collective

3423:   Input Parameters:
3424: + dm           - The `DMPLEX`
3425: . fvm          - The `PetscFV`
3426: - cellGeometry - The face geometry from `DMPlexComputeCellGeometryFVM()`

3428:   Input/Output Parameter:
3429: . faceGeometry - The face geometry from `DMPlexComputeFaceGeometryFVM()`; on output
3430:                  the geometric factors for gradient calculation are inserted

3432:   Output Parameter:
3433: . dmGrad - The `DM` describing the layout of gradient data

3435:   Level: developer

3437: .seealso: `DMPLEX`, `DMPlexGetFaceGeometryFVM()`, `DMPlexGetCellGeometryFVM()`
3438: @*/
3439: PetscErrorCode DMPlexComputeGradientFVM(DM dm, PetscFV fvm, Vec faceGeometry, Vec cellGeometry, DM *dmGrad)
3440: {
3441:   DM           dmFace, dmCell;
3442:   PetscScalar *fgeom, *cgeom;
3443:   PetscSection sectionGrad, parentSection;
3444:   PetscInt     dim, pdim, cStart, cEnd, cEndInterior, c;

3446:   PetscFunctionBegin;
3447:   PetscCall(DMGetDimension(dm, &dim));
3448:   PetscCall(PetscFVGetNumComponents(fvm, &pdim));
3449:   PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
3450:   PetscCall(DMPlexGetCellTypeStratum(dm, DM_POLYTOPE_FV_GHOST, &cEndInterior, NULL));
3451:   /* Construct the interpolant corresponding to each face from the least-square solution over the cell neighborhood */
3452:   PetscCall(VecGetDM(faceGeometry, &dmFace));
3453:   PetscCall(VecGetDM(cellGeometry, &dmCell));
3454:   PetscCall(VecGetArray(faceGeometry, &fgeom));
3455:   PetscCall(VecGetArray(cellGeometry, &cgeom));
3456:   PetscCall(DMPlexGetTree(dm, &parentSection, NULL, NULL, NULL, NULL));
3457:   if (!parentSection) {
3458:     PetscCall(BuildGradientReconstruction_Internal(dm, fvm, dmFace, fgeom, dmCell, cgeom));
3459:   } else {
3460:     PetscCall(BuildGradientReconstruction_Internal_Tree(dm, fvm, dmFace, fgeom, dmCell, cgeom));
3461:   }
3462:   PetscCall(VecRestoreArray(faceGeometry, &fgeom));
3463:   PetscCall(VecRestoreArray(cellGeometry, &cgeom));
3464:   /* Create storage for gradients */
3465:   PetscCall(DMClone(dm, dmGrad));
3466:   PetscCall(PetscSectionCreate(PetscObjectComm((PetscObject)dm), &sectionGrad));
3467:   PetscCall(PetscSectionSetChart(sectionGrad, cStart, cEnd));
3468:   for (c = cStart; c < cEnd; ++c) PetscCall(PetscSectionSetDof(sectionGrad, c, pdim * dim));
3469:   PetscCall(PetscSectionSetUp(sectionGrad));
3470:   PetscCall(DMSetLocalSection(*dmGrad, sectionGrad));
3471:   PetscCall(PetscSectionDestroy(&sectionGrad));
3472:   PetscFunctionReturn(PETSC_SUCCESS);
3473: }

3475: /*@
3476:   DMPlexGetDataFVM - Retrieve precomputed cell geometry

3478:   Collective

3480:   Input Parameters:
3481: + dm - The `DM`
3482: - fv - The `PetscFV`

3484:   Output Parameters:
3485: + cellgeom - The cell geometry
3486: . facegeom - The face geometry
3487: - gradDM   - The gradient matrices

3489:   Level: developer

3491: .seealso: `DMPLEX`, `DMPlexComputeGeometryFVM()`
3492: @*/
3493: PetscErrorCode DMPlexGetDataFVM(DM dm, PetscFV fv, Vec *cellgeom, Vec *facegeom, DM *gradDM)
3494: {
3495:   PetscObject cellgeomobj, facegeomobj;

3497:   PetscFunctionBegin;
3498:   PetscCall(PetscObjectQuery((PetscObject)dm, "DMPlex_cellgeom_fvm", &cellgeomobj));
3499:   if (!cellgeomobj) {
3500:     Vec cellgeomInt, facegeomInt;

3502:     PetscCall(DMPlexComputeGeometryFVM(dm, &cellgeomInt, &facegeomInt));
3503:     PetscCall(PetscObjectCompose((PetscObject)dm, "DMPlex_cellgeom_fvm", (PetscObject)cellgeomInt));
3504:     PetscCall(PetscObjectCompose((PetscObject)dm, "DMPlex_facegeom_fvm", (PetscObject)facegeomInt));
3505:     PetscCall(VecDestroy(&cellgeomInt));
3506:     PetscCall(VecDestroy(&facegeomInt));
3507:     PetscCall(PetscObjectQuery((PetscObject)dm, "DMPlex_cellgeom_fvm", &cellgeomobj));
3508:   }
3509:   PetscCall(PetscObjectQuery((PetscObject)dm, "DMPlex_facegeom_fvm", &facegeomobj));
3510:   if (cellgeom) *cellgeom = (Vec)cellgeomobj;
3511:   if (facegeom) *facegeom = (Vec)facegeomobj;
3512:   if (gradDM) {
3513:     PetscObject gradobj;
3514:     PetscBool   computeGradients;

3516:     PetscCall(PetscFVGetComputeGradients(fv, &computeGradients));
3517:     if (!computeGradients) {
3518:       *gradDM = NULL;
3519:       PetscFunctionReturn(PETSC_SUCCESS);
3520:     }
3521:     PetscCall(PetscObjectQuery((PetscObject)dm, "DMPlex_dmgrad_fvm", &gradobj));
3522:     if (!gradobj) {
3523:       DM dmGradInt;

3525:       PetscCall(DMPlexComputeGradientFVM(dm, fv, (Vec)facegeomobj, (Vec)cellgeomobj, &dmGradInt));
3526:       PetscCall(PetscObjectCompose((PetscObject)dm, "DMPlex_dmgrad_fvm", (PetscObject)dmGradInt));
3527:       PetscCall(DMDestroy(&dmGradInt));
3528:       PetscCall(PetscObjectQuery((PetscObject)dm, "DMPlex_dmgrad_fvm", &gradobj));
3529:     }
3530:     *gradDM = (DM)gradobj;
3531:   }
3532:   PetscFunctionReturn(PETSC_SUCCESS);
3533: }

3535: static PetscErrorCode DMPlexCoordinatesToReference_NewtonUpdate(PetscInt dimC, PetscInt dimR, PetscScalar *J, PetscScalar *invJ, PetscScalar *work, PetscReal *resNeg, PetscReal *guess)
3536: {
3537:   PetscInt l, m;

3539:   PetscFunctionBeginHot;
3540:   if (dimC == dimR && dimR <= 3) {
3541:     /* invert Jacobian, multiply */
3542:     PetscScalar det, idet;

3544:     switch (dimR) {
3545:     case 1:
3546:       invJ[0] = 1. / J[0];
3547:       break;
3548:     case 2:
3549:       det     = J[0] * J[3] - J[1] * J[2];
3550:       idet    = 1. / det;
3551:       invJ[0] = J[3] * idet;
3552:       invJ[1] = -J[1] * idet;
3553:       invJ[2] = -J[2] * idet;
3554:       invJ[3] = J[0] * idet;
3555:       break;
3556:     case 3: {
3557:       invJ[0] = J[4] * J[8] - J[5] * J[7];
3558:       invJ[1] = J[2] * J[7] - J[1] * J[8];
3559:       invJ[2] = J[1] * J[5] - J[2] * J[4];
3560:       det     = invJ[0] * J[0] + invJ[1] * J[3] + invJ[2] * J[6];
3561:       idet    = 1. / det;
3562:       invJ[0] *= idet;
3563:       invJ[1] *= idet;
3564:       invJ[2] *= idet;
3565:       invJ[3] = idet * (J[5] * J[6] - J[3] * J[8]);
3566:       invJ[4] = idet * (J[0] * J[8] - J[2] * J[6]);
3567:       invJ[5] = idet * (J[2] * J[3] - J[0] * J[5]);
3568:       invJ[6] = idet * (J[3] * J[7] - J[4] * J[6]);
3569:       invJ[7] = idet * (J[1] * J[6] - J[0] * J[7]);
3570:       invJ[8] = idet * (J[0] * J[4] - J[1] * J[3]);
3571:     } break;
3572:     }
3573:     for (l = 0; l < dimR; l++) {
3574:       for (m = 0; m < dimC; m++) guess[l] += PetscRealPart(invJ[l * dimC + m]) * resNeg[m];
3575:     }
3576:   } else {
3577:     char         transpose = PetscDefined(USE_COMPLEX) ? 'C' : 'T';
3578:     PetscBLASInt m, n, one = 1, worksize;

3580:     PetscCall(PetscBLASIntCast(dimR, &m));
3581:     PetscCall(PetscBLASIntCast(dimC, &n));
3582:     PetscCall(PetscBLASIntCast(dimC * dimC, &worksize));
3583:     for (l = 0; l < dimC; l++) invJ[l] = resNeg[l];

3585:     PetscCallLAPACKInfo("LAPACKgels", LAPACKgels_(&transpose, &m, &n, &one, J, &m, invJ, &n, work, &worksize, &info));
3586:     for (l = 0; l < dimR; l++) guess[l] += PetscRealPart(invJ[l]);
3587:   }
3588:   PetscFunctionReturn(PETSC_SUCCESS);
3589: }

3591: static PetscErrorCode DMPlexCoordinatesToReference_Tensor(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal realCoords[], PetscReal refCoords[], Vec coords, PetscInt dimC, PetscInt dimR)
3592: {
3593:   PetscInt     coordSize, i, j, k, l, m, maxIts = 7, numV = (1 << dimR);
3594:   PetscScalar *coordsScalar = NULL;
3595:   PetscReal   *cellData, *cellCoords, *cellCoeffs, *extJ, *resNeg;
3596:   PetscScalar *J, *invJ, *work;

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 + dimR + dimC, MPIU_REAL, &cellData));
3603:   PetscCall(DMGetWorkArray(dm, 3 * dimR * dimC, MPIU_SCALAR, &J));
3604:   cellCoords = &cellData[0];
3605:   cellCoeffs = &cellData[coordSize];
3606:   extJ       = &cellData[2 * coordSize];
3607:   resNeg     = &cellData[2 * coordSize + dimR];
3608:   invJ       = &J[dimR * dimC];
3609:   work       = &J[2 * dimR * dimC];
3610:   if (dimR == 2) {
3611:     const PetscInt zToPlex[4] = {0, 1, 3, 2};

3613:     for (i = 0; i < 4; i++) {
3614:       PetscInt plexI = zToPlex[i];

3616:       for (j = 0; j < dimC; j++) cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
3617:     }
3618:   } else if (dimR == 3) {
3619:     const PetscInt zToPlex[8] = {0, 3, 1, 2, 4, 5, 7, 6};

3621:     for (i = 0; i < 8; i++) {
3622:       PetscInt plexI = zToPlex[i];

3624:       for (j = 0; j < dimC; j++) cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
3625:     }
3626:   } else {
3627:     for (i = 0; i < coordSize; i++) cellCoords[i] = PetscRealPart(coordsScalar[i]);
3628:   }
3629:   /* Perform the shuffling transform that converts values at the corners of [-1,1]^d to coefficients */
3630:   for (i = 0; i < dimR; i++) {
3631:     PetscReal *swap;

3633:     for (j = 0; j < (numV / 2); j++) {
3634:       for (k = 0; k < dimC; k++) {
3635:         cellCoeffs[dimC * j + k]                = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] + cellCoords[dimC * 2 * j + k]);
3636:         cellCoeffs[dimC * (j + (numV / 2)) + k] = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] - cellCoords[dimC * 2 * j + k]);
3637:       }
3638:     }

3640:     if (i < dimR - 1) {
3641:       swap       = cellCoeffs;
3642:       cellCoeffs = cellCoords;
3643:       cellCoords = swap;
3644:     }
3645:   }
3646:   PetscCall(PetscArrayzero(refCoords, numPoints * dimR));
3647:   for (j = 0; j < numPoints; j++) {
3648:     for (i = 0; i < maxIts; i++) {
3649:       PetscReal *guess = &refCoords[dimR * j];

3651:       /* compute -residual and Jacobian */
3652:       for (k = 0; k < dimC; k++) resNeg[k] = realCoords[dimC * j + k];
3653:       for (k = 0; k < dimC * dimR; k++) J[k] = 0.;
3654:       for (k = 0; k < numV; k++) {
3655:         PetscReal extCoord = 1.;
3656:         for (l = 0; l < dimR; l++) {
3657:           PetscReal coord = guess[l];
3658:           PetscInt  dep   = (k & (1 << l)) >> l;

3660:           extCoord *= dep * coord + !dep;
3661:           extJ[l] = dep;

3663:           for (m = 0; m < dimR; m++) {
3664:             PetscReal coord = guess[m];
3665:             PetscInt  dep   = ((k & (1 << m)) >> m) && (m != l);
3666:             PetscReal mult  = dep * coord + !dep;

3668:             extJ[l] *= mult;
3669:           }
3670:         }
3671:         for (l = 0; l < dimC; l++) {
3672:           PetscReal coeff = cellCoeffs[dimC * k + l];

3674:           resNeg[l] -= coeff * extCoord;
3675:           for (m = 0; m < dimR; m++) J[dimR * l + m] += coeff * extJ[m];
3676:         }
3677:       }
3678:       if (0 && PetscDefined(USE_DEBUG)) {
3679:         PetscReal maxAbs = 0.;

3681:         for (l = 0; l < dimC; l++) maxAbs = PetscMax(maxAbs, PetscAbsReal(resNeg[l]));
3682:         PetscCall(PetscInfo(dm, "cell %" PetscInt_FMT ", point %" PetscInt_FMT ", iter %" PetscInt_FMT ": res %g\n", cell, j, i, (double)maxAbs));
3683:       }

3685:       PetscCall(DMPlexCoordinatesToReference_NewtonUpdate(dimC, dimR, J, invJ, work, resNeg, guess));
3686:     }
3687:   }
3688:   PetscCall(DMRestoreWorkArray(dm, 3 * dimR * dimC, MPIU_SCALAR, &J));
3689:   PetscCall(DMRestoreWorkArray(dm, 2 * coordSize + dimR + dimC, MPIU_REAL, &cellData));
3690:   PetscCall(DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar));
3691:   PetscFunctionReturn(PETSC_SUCCESS);
3692: }

3694: static PetscErrorCode DMPlexReferenceToCoordinates_Tensor(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal refCoords[], PetscReal realCoords[], Vec coords, PetscInt dimC, PetscInt dimR)
3695: {
3696:   PetscInt     coordSize, i, j, k, l, numV = (1 << dimR);
3697:   PetscScalar *coordsScalar = NULL;
3698:   PetscReal   *cellData, *cellCoords, *cellCoeffs;

3700:   PetscFunctionBegin;
3702:   PetscCall(DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar));
3703:   PetscCheck(coordSize >= dimC * numV, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Expecting at least %" PetscInt_FMT " coordinates, got %" PetscInt_FMT, dimC * (1 << dimR), coordSize);
3704:   PetscCall(DMGetWorkArray(dm, 2 * coordSize, MPIU_REAL, &cellData));
3705:   cellCoords = &cellData[0];
3706:   cellCoeffs = &cellData[coordSize];
3707:   if (dimR == 2) {
3708:     const PetscInt zToPlex[4] = {0, 1, 3, 2};

3710:     for (i = 0; i < 4; i++) {
3711:       PetscInt plexI = zToPlex[i];

3713:       for (j = 0; j < dimC; j++) cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
3714:     }
3715:   } else if (dimR == 3) {
3716:     const PetscInt zToPlex[8] = {0, 3, 1, 2, 4, 5, 7, 6};

3718:     for (i = 0; i < 8; i++) {
3719:       PetscInt plexI = zToPlex[i];

3721:       for (j = 0; j < dimC; j++) cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
3722:     }
3723:   } else {
3724:     for (i = 0; i < coordSize; i++) cellCoords[i] = PetscRealPart(coordsScalar[i]);
3725:   }
3726:   /* Perform the shuffling transform that converts values at the corners of [-1,1]^d to coefficients */
3727:   for (i = 0; i < dimR; i++) {
3728:     PetscReal *swap;

3730:     for (j = 0; j < (numV / 2); j++) {
3731:       for (k = 0; k < dimC; k++) {
3732:         cellCoeffs[dimC * j + k]                = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] + cellCoords[dimC * 2 * j + k]);
3733:         cellCoeffs[dimC * (j + (numV / 2)) + k] = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] - cellCoords[dimC * 2 * j + k]);
3734:       }
3735:     }

3737:     if (i < dimR - 1) {
3738:       swap       = cellCoeffs;
3739:       cellCoeffs = cellCoords;
3740:       cellCoords = swap;
3741:     }
3742:   }
3743:   PETSC_PRAGMA_DIAGNOSTIC_IGNORED_BEGIN("-Warray-bounds")
3744:   PetscCall(PetscArrayzero(realCoords, numPoints * dimC));
3745:   PETSC_PRAGMA_DIAGNOSTIC_IGNORED_END()
3746:   for (j = 0; j < numPoints; j++) {
3747:     const PetscReal *guess  = &refCoords[dimR * j];
3748:     PetscReal       *mapped = &realCoords[dimC * j];

3750:     for (k = 0; k < numV; k++) {
3751:       PetscReal extCoord = 1.;
3752:       for (l = 0; l < dimR; l++) {
3753:         PetscReal coord = guess[l];
3754:         PetscInt  dep   = (k & (1 << l)) >> l;

3756:         extCoord *= dep * coord + !dep;
3757:       }
3758:       for (l = 0; l < dimC; l++) {
3759:         PetscReal coeff = cellCoeffs[dimC * k + l];

3761:         mapped[l] += coeff * extCoord;
3762:       }
3763:     }
3764:   }
3765:   PetscCall(DMRestoreWorkArray(dm, 2 * coordSize, MPIU_REAL, &cellData));
3766:   PetscCall(DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar));
3767:   PetscFunctionReturn(PETSC_SUCCESS);
3768: }

3770: 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)
3771: {
3772:   PetscInt     numComp, pdim, i, j, k, l, m, coordSize;
3773:   PetscScalar *nodes = NULL;
3774:   PetscReal   *invV, *modes;
3775:   PetscReal   *B, *D, *resNeg;
3776:   PetscScalar *J, *invJ, *work;
3777:   PetscReal    tolerance = tol == NULL ? 0.0 : *tol;

3779:   PetscFunctionBegin;
3780:   PetscCall(PetscFEGetDimension(fe, &pdim));
3781:   PetscCall(PetscFEGetNumComponents(fe, &numComp));
3782:   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);
3783:   /* we shouldn't apply inverse closure permutation, if one exists */
3784:   PetscCall(DMPlexVecGetOrientedClosure(dm, NULL, PETSC_FALSE, coords, cell, 0, &coordSize, &nodes));
3785:   /* convert nodes to values in the stable evaluation basis */
3786:   PetscCall(DMGetWorkArray(dm, pdim, MPIU_REAL, &modes));
3787:   invV = fe->invV;
3788:   for (i = 0; i < pdim; ++i) {
3789:     modes[i] = 0.;
3790:     for (j = 0; j < pdim; ++j) modes[i] += invV[i * pdim + j] * PetscRealPart(nodes[j]);
3791:   }
3792:   PetscCall(DMGetWorkArray(dm, pdim * Nc + pdim * Nc * dimR + Nc, MPIU_REAL, &B));
3793:   D      = &B[pdim * Nc];
3794:   resNeg = &D[pdim * Nc * dimR];
3795:   PetscCall(DMGetWorkArray(dm, 3 * Nc * dimR, MPIU_SCALAR, &J));
3796:   invJ = &J[Nc * dimR];
3797:   work = &invJ[Nc * dimR];
3798:   for (i = 0; i < numPoints * dimR; i++) refCoords[i] = 0.;
3799:   for (j = 0; j < numPoints; j++) {
3800:     PetscReal normPoint = DMPlex_NormD_Internal(Nc, &realCoords[j * Nc]);
3801:     normPoint           = normPoint > PETSC_SMALL ? normPoint : 1.0;
3802:     for (i = 0; i < maxIter; i++) { /* we could batch this so that we're not making big B and D arrays all the time */
3803:       PetscReal *guess = &refCoords[j * dimR], error = 0;
3804:       PetscCall(PetscSpaceEvaluate(fe->basisSpace, 1, guess, B, D, NULL));
3805:       for (k = 0; k < Nc; k++) resNeg[k] = realCoords[j * Nc + k];
3806:       for (k = 0; k < Nc * dimR; k++) J[k] = 0.;
3807:       for (k = 0; k < pdim; k++) {
3808:         for (l = 0; l < Nc; l++) {
3809:           resNeg[l] -= modes[k] * B[k * Nc + l];
3810:           for (m = 0; m < dimR; m++) J[l * dimR + m] += modes[k] * D[(k * Nc + l) * dimR + m];
3811:         }
3812:       }
3813:       if (0 && PetscDefined(USE_DEBUG)) {
3814:         PetscReal maxAbs = 0.;

3816:         for (l = 0; l < Nc; l++) maxAbs = PetscMax(maxAbs, PetscAbsReal(resNeg[l]));
3817:         PetscCall(PetscInfo(dm, "cell %" PetscInt_FMT ", point %" PetscInt_FMT ", iter %" PetscInt_FMT ": res %g\n", cell, j, i, (double)maxAbs));
3818:       }
3819:       error = DMPlex_NormD_Internal(Nc, resNeg);
3820:       if (error < tolerance * normPoint) {
3821:         if (tol) *tol = error / normPoint;
3822:         break;
3823:       }
3824:       PetscCall(DMPlexCoordinatesToReference_NewtonUpdate(Nc, dimR, J, invJ, work, resNeg, guess));
3825:     }
3826:   }
3827:   PetscCall(DMRestoreWorkArray(dm, 3 * Nc * dimR, MPIU_SCALAR, &J));
3828:   PetscCall(DMRestoreWorkArray(dm, pdim * Nc + pdim * Nc * dimR + Nc, MPIU_REAL, &B));
3829:   PetscCall(DMRestoreWorkArray(dm, pdim, MPIU_REAL, &modes));
3830:   PetscCall(DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &nodes));
3831:   PetscFunctionReturn(PETSC_SUCCESS);
3832: }

3834: /* TODO: TOBY please fix this for Nc > 1 */
3835: PetscErrorCode DMPlexReferenceToCoordinates_FE(DM dm, PetscFE fe, PetscInt cell, PetscInt numPoints, const PetscReal refCoords[], PetscReal realCoords[], Vec coords, PetscInt Nc, PetscInt dimR)
3836: {
3837:   PetscInt     numComp, pdim, i, j, k, l, coordSize;
3838:   PetscScalar *nodes = NULL;
3839:   PetscReal   *invV, *modes;
3840:   PetscReal   *B;

3842:   PetscFunctionBegin;
3843:   PetscCall(PetscFEGetDimension(fe, &pdim));
3844:   PetscCall(PetscFEGetNumComponents(fe, &numComp));
3845:   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);
3846:   /* we shouldn't apply inverse closure permutation, if one exists */
3847:   PetscCall(DMPlexVecGetOrientedClosure(dm, NULL, PETSC_FALSE, coords, cell, 0, &coordSize, &nodes));
3848:   /* convert nodes to values in the stable evaluation basis */
3849:   PetscCall(DMGetWorkArray(dm, pdim, MPIU_REAL, &modes));
3850:   invV = fe->invV;
3851:   for (i = 0; i < pdim; ++i) {
3852:     modes[i] = 0.;
3853:     for (j = 0; j < pdim; ++j) modes[i] += invV[i * pdim + j] * PetscRealPart(nodes[j]);
3854:   }
3855:   PetscCall(DMGetWorkArray(dm, numPoints * pdim * Nc, MPIU_REAL, &B));
3856:   PetscCall(PetscSpaceEvaluate(fe->basisSpace, numPoints, refCoords, B, NULL, NULL));
3857:   for (i = 0; i < numPoints * Nc; i++) realCoords[i] = 0.;
3858:   for (j = 0; j < numPoints; j++) {
3859:     PetscReal *mapped = &realCoords[j * Nc];

3861:     for (k = 0; k < pdim; k++) {
3862:       for (l = 0; l < Nc; l++) mapped[l] += modes[k] * B[(j * pdim + k) * Nc + l];
3863:     }
3864:   }
3865:   PetscCall(DMRestoreWorkArray(dm, numPoints * pdim * Nc, MPIU_REAL, &B));
3866:   PetscCall(DMRestoreWorkArray(dm, pdim, MPIU_REAL, &modes));
3867:   PetscCall(DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &nodes));
3868:   PetscFunctionReturn(PETSC_SUCCESS);
3869: }

3871: /*@
3872:   DMPlexCoordinatesToReference - Pull coordinates back from the mesh to the reference element
3873:   using a single element map.

3875:   Not Collective

3877:   Input Parameters:
3878: + dm         - The mesh, with coordinate maps defined either by a `PetscDS` for the coordinate `DM` (see `DMGetCoordinateDM()`) or
3879:                implicitly by the coordinates of the corner vertices of the cell: as an affine map for simplicial elements, or
3880:                as a multilinear map for tensor-product elements
3881: . cell       - the cell whose map is used.
3882: . numPoints  - the number of points to locate
3883: - realCoords - (numPoints x coordinate dimension) array of coordinates (see `DMGetCoordinateDim()`)

3885:   Output Parameter:
3886: . refCoords - (`numPoints` x `dimension`) array of reference coordinates (see `DMGetDimension()`)

3888:   Level: intermediate

3890:   Notes:
3891:   This inversion will be accurate inside the reference element, but may be inaccurate for
3892:   mappings that do not extend uniquely outside the reference cell (e.g, most non-affine maps)

3894: .seealso: `DMPLEX`, `DMPlexReferenceToCoordinates()`
3895: @*/
3896: PetscErrorCode DMPlexCoordinatesToReference(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal realCoords[], PetscReal refCoords[])
3897: {
3898:   PetscInt       dimC, dimR, depth, i, cellHeight, height;
3899:   DMPolytopeType ct;
3900:   DM             coordDM = NULL;
3901:   Vec            coords;
3902:   PetscFE        fe = NULL;

3904:   PetscFunctionBegin;
3906:   PetscCall(DMGetDimension(dm, &dimR));
3907:   PetscCall(DMGetCoordinateDim(dm, &dimC));
3908:   if (dimR <= 0 || dimC <= 0 || numPoints <= 0) PetscFunctionReturn(PETSC_SUCCESS);
3909:   PetscCall(DMPlexGetDepth(dm, &depth));
3910:   PetscCall(DMGetCoordinatesLocal(dm, &coords));
3911:   PetscCall(DMGetCoordinateDM(dm, &coordDM));
3912:   PetscCall(DMPlexGetVTKCellHeight(dm, &cellHeight));
3913:   if (coordDM) {
3914:     PetscInt coordFields;

3916:     PetscCall(DMGetNumFields(coordDM, &coordFields));
3917:     if (coordFields) {
3918:       PetscClassId id;
3919:       PetscObject  disc;

3921:       PetscCall(DMGetField(coordDM, 0, NULL, &disc));
3922:       PetscCall(PetscObjectGetClassId(disc, &id));
3923:       if (id == PETSCFE_CLASSID) fe = (PetscFE)disc;
3924:     }
3925:   }
3926:   PetscCall(DMPlexGetCellType(dm, cell, &ct));
3927:   PetscCall(DMPlexGetPointHeight(dm, cell, &height));
3928:   PetscCheck(height == cellHeight, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "point %" PetscInt_FMT " not in a cell, height = %" PetscInt_FMT, cell, height);
3929:   PetscCheck(!DMPolytopeTypeIsHybrid(ct) && ct != DM_POLYTOPE_FV_GHOST, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "point %" PetscInt_FMT " is unsupported cell type %s", cell, DMPolytopeTypes[ct]);
3930:   if (!fe) { /* implicit discretization: affine or multilinear */
3931:     PetscInt  coneSize;
3932:     PetscBool isSimplex, isTensor;

3934:     PetscCall(DMPlexGetConeSize(dm, cell, &coneSize));
3935:     isSimplex = (coneSize == (dimR + 1)) ? PETSC_TRUE : PETSC_FALSE;
3936:     isTensor  = (coneSize == ((depth == 1) ? (1 << dimR) : (2 * dimR))) ? PETSC_TRUE : PETSC_FALSE;
3937:     if (isSimplex) {
3938:       PetscReal detJ, *v0, *J, *invJ;

3940:       PetscCall(DMGetWorkArray(dm, dimC + 2 * dimC * dimC, MPIU_REAL, &v0));
3941:       J    = &v0[dimC];
3942:       invJ = &J[dimC * dimC];
3943:       PetscCall(DMPlexComputeCellGeometryAffineFEM(dm, cell, v0, J, invJ, &detJ));
3944:       for (i = 0; i < numPoints; i++) { /* Apply the inverse affine transformation for each point */
3945:         const PetscReal x0[3] = {-1., -1., -1.};

3947:         CoordinatesRealToRef(dimC, dimR, x0, v0, invJ, &realCoords[dimC * i], &refCoords[dimR * i]);
3948:       }
3949:       PetscCall(DMRestoreWorkArray(dm, dimC + 2 * dimC * dimC, MPIU_REAL, &v0));
3950:     } else if (isTensor) {
3951:       PetscCall(DMPlexCoordinatesToReference_Tensor(coordDM, cell, numPoints, realCoords, refCoords, coords, dimC, dimR));
3952:     } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Unrecognized cone size %" PetscInt_FMT, coneSize);
3953:   } else {
3954:     PetscCall(DMPlexCoordinatesToReference_FE(coordDM, fe, cell, numPoints, realCoords, refCoords, coords, dimC, dimR, 7, NULL));
3955:   }
3956:   PetscFunctionReturn(PETSC_SUCCESS);
3957: }

3959: /*@
3960:   DMPlexReferenceToCoordinates - Map references coordinates to coordinates in the mesh for a single element map.

3962:   Not Collective

3964:   Input Parameters:
3965: + dm        - The mesh, with coordinate maps defined either by a PetscDS for the coordinate `DM` (see `DMGetCoordinateDM()`) or
3966:                implicitly by the coordinates of the corner vertices of the cell: as an affine map for simplicial elements, or
3967:                as a multilinear map for tensor-product elements
3968: . cell      - the cell whose map is used.
3969: . numPoints - the number of points to locate
3970: - refCoords - (numPoints x dimension) array of reference coordinates (see `DMGetDimension()`)

3972:   Output Parameter:
3973: . realCoords - (numPoints x coordinate dimension) array of coordinates (see `DMGetCoordinateDim()`)

3975:   Level: intermediate

3977: .seealso: `DMPLEX`, `DMPlexCoordinatesToReference()`
3978: @*/
3979: PetscErrorCode DMPlexReferenceToCoordinates(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal refCoords[], PetscReal realCoords[])
3980: {
3981:   PetscInt       dimC, dimR, depth, i, cellHeight, height;
3982:   DMPolytopeType ct;
3983:   DM             coordDM = NULL;
3984:   Vec            coords;
3985:   PetscFE        fe = NULL;

3987:   PetscFunctionBegin;
3989:   PetscCall(DMGetDimension(dm, &dimR));
3990:   PetscCall(DMGetCoordinateDim(dm, &dimC));
3991:   if (dimR <= 0 || dimC <= 0 || numPoints <= 0) PetscFunctionReturn(PETSC_SUCCESS);
3992:   PetscCall(DMPlexGetDepth(dm, &depth));
3993:   PetscCall(DMGetCoordinatesLocal(dm, &coords));
3994:   PetscCall(DMGetCoordinateDM(dm, &coordDM));
3995:   PetscCall(DMPlexGetVTKCellHeight(dm, &cellHeight));
3996:   if (coordDM) {
3997:     PetscInt coordFields;

3999:     PetscCall(DMGetNumFields(coordDM, &coordFields));
4000:     if (coordFields) {
4001:       PetscClassId id;
4002:       PetscObject  disc;

4004:       PetscCall(DMGetField(coordDM, 0, NULL, &disc));
4005:       PetscCall(PetscObjectGetClassId(disc, &id));
4006:       if (id == PETSCFE_CLASSID) fe = (PetscFE)disc;
4007:     }
4008:   }
4009:   PetscCall(DMPlexGetCellType(dm, cell, &ct));
4010:   PetscCall(DMPlexGetPointHeight(dm, cell, &height));
4011:   PetscCheck(height == cellHeight, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "point %" PetscInt_FMT " not in a cell, height = %" PetscInt_FMT, cell, height);
4012:   PetscCheck(!DMPolytopeTypeIsHybrid(ct) && ct != DM_POLYTOPE_FV_GHOST, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "point %" PetscInt_FMT " is unsupported cell type %s", cell, DMPolytopeTypes[ct]);
4013:   if (!fe) { /* implicit discretization: affine or multilinear */
4014:     PetscInt  coneSize;
4015:     PetscBool isSimplex, isTensor;

4017:     PetscCall(DMPlexGetConeSize(dm, cell, &coneSize));
4018:     isSimplex = (coneSize == (dimR + 1)) ? PETSC_TRUE : PETSC_FALSE;
4019:     isTensor  = (coneSize == ((depth == 1) ? (1 << dimR) : (2 * dimR))) ? PETSC_TRUE : PETSC_FALSE;
4020:     if (isSimplex) {
4021:       PetscReal detJ, *v0, *J;

4023:       PetscCall(DMGetWorkArray(dm, dimC + 2 * dimC * dimC, MPIU_REAL, &v0));
4024:       J = &v0[dimC];
4025:       PetscCall(DMPlexComputeCellGeometryAffineFEM(dm, cell, v0, J, NULL, &detJ));
4026:       for (i = 0; i < numPoints; i++) { /* Apply the affine transformation for each point */
4027:         const PetscReal xi0[3] = {-1., -1., -1.};

4029:         CoordinatesRefToReal(dimC, dimR, xi0, v0, J, &refCoords[dimR * i], &realCoords[dimC * i]);
4030:       }
4031:       PetscCall(DMRestoreWorkArray(dm, dimC + 2 * dimC * dimC, MPIU_REAL, &v0));
4032:     } else if (isTensor) {
4033:       PetscCall(DMPlexReferenceToCoordinates_Tensor(coordDM, cell, numPoints, refCoords, realCoords, coords, dimC, dimR));
4034:     } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Unrecognized cone size %" PetscInt_FMT, coneSize);
4035:   } else {
4036:     PetscCall(DMPlexReferenceToCoordinates_FE(coordDM, fe, cell, numPoints, refCoords, realCoords, coords, dimC, dimR));
4037:   }
4038:   PetscFunctionReturn(PETSC_SUCCESS);
4039: }

4041: 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[])
4042: {
4043:   const PetscInt Nc = uOff[1] - uOff[0];
4044:   PetscInt       c;

4046:   for (c = 0; c < Nc; ++c) f0[c] = u[c];
4047: }

4049: /* Constants are
4050:      center location
4051:      axis vector
4052:      rotation angle
4053:  */
4054: void coordMap_rotate(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[])
4055: {
4056:   const PetscInt     Nc     = PetscMin(uOff[1] - uOff[0], 3);
4057:   const PetscScalar *center = constants;
4058:   const PetscScalar *k      = &constants[Nc]; // The rotation axis k
4059:   const PetscReal    theta  = PetscRealPart(constants[Nc * 2]);
4060:   const PetscReal    ct     = PetscCosReal(theta);
4061:   const PetscReal    st     = PetscSinReal(theta);
4062:   PetscReal          v[3];

4064:   // Translate to coordinate with center at the origin
4065:   for (PetscInt d = 0; d < Nc; ++d) v[d] = PetscRealPart(u[d] - center[d]);
4066:   switch (dim) {
4067:   case 2:
4068:     /* Rotate point, axis is ignored in 2D
4069:        / ct -st \
4070:        \ st  ct / */
4071:     f0[0] = ct * v[0] - st * v[1];
4072:     f0[1] = st * v[0] + ct * v[1];
4073:     break;
4074:   case 3:
4075:     /* / ct + k_x^2 (1 - ct)       & k_x k_y (1 - ct) - k_z st & k_x k_z (1 - ct) + k_y st \
4076:        | k_y k_x (1 - ct) + k_z st & ct + k_y^2 (1 - ct)       & k_y k_z (1 - ct) - k_x st |
4077:        \ k_z k_x (1 - ct) - k_y st & k_z k_y (1 - ct) + k_x st & ct + k_z^2 (1 - ct)       / */
4078:     f0[0] = (ct + k[0] * k[0] * (1. - ct)) * v[0] + (k[0] * k[1] * (1. - ct) - k[2] * st) * v[1] + (k[0] * k[2] * (1. - ct) + k[1] * st) * v[2];
4079:     f0[1] = (k[1] * k[0] * (1. - ct) + k[2] * st) * v[0] + (ct + k[1] * k[1] * (1. - ct)) * v[1] + (k[1] * k[2] * (1. - ct) - k[0] * st) * v[2];
4080:     f0[2] = (k[2] * k[0] * (1. - ct) - k[1] * st) * v[0] + (k[2] * k[1] * (1. - ct) + k[0] * st) * v[1] + (ct + k[2] * k[2] * (1. - ct)) * v[2];
4081:     break;
4082:   default:
4083:     for (PetscInt d = 0; d < Nc; ++d) f0[d] = v[d];
4084:   }
4085:   // Translate back to original coordinates
4086:   for (PetscInt d = 0; d < Nc; ++d) f0[d] += center[d];
4087: }

4089: /* Shear applies the transformation, assuming we fix z,
4090:   / 1  0  m_0 \
4091:   | 0  1  m_1 |
4092:   \ 0  0   1  /
4093: */
4094: 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[])
4095: {
4096:   const PetscInt Nc = uOff[1] - uOff[0];
4097:   const PetscInt ax = (PetscInt)PetscRealPart(constants[0]);
4098:   PetscInt       c;

4100:   for (c = 0; c < Nc; ++c) coords[c] = u[c] + constants[c + 1] * u[ax];
4101: }

4103: /* Flare applies the transformation, assuming we fix x_f,

4105:    x_i = x_i * alpha_i x_f
4106: */
4107: 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[])
4108: {
4109:   const PetscInt Nc = uOff[1] - uOff[0];
4110:   const PetscInt cf = (PetscInt)PetscRealPart(constants[0]);

4112:   for (PetscInt c = 0; c < Nc; ++c) coords[c] = u[c] * (c == cf ? 1.0 : constants[c + 1] * u[cf]);
4113: }

4115: /*
4116:   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
4117:   will correspond to the top and bottom of our square. So

4119:     (0,0)--(1,0)  ==>  (1,0)--(2,0)      Just a shift of (1,0)
4120:     (0,1)--(1,1)  ==>  (0,1)--(0,2)      Switch x and y

4122:   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:

4124:     (x, y)  ==>  (x+1, \pi/2 y)                           in (r', \theta') space
4125:             ==>  ((x+1) cos(\pi/2 y), (x+1) sin(\pi/2 y)) in (x', y') space
4126: */
4127: 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[])
4128: {
4129:   const PetscReal ri = PetscRealPart(constants[0]);
4130:   const PetscReal ro = PetscRealPart(constants[1]);

4132:   xp[0] = (x[0] * (ro - ri) + ri) * PetscCosReal(0.5 * PETSC_PI * x[1]);
4133:   xp[1] = (x[0] * (ro - ri) + ri) * PetscSinReal(0.5 * PETSC_PI * x[1]);
4134: }

4136: /*
4137:   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
4138:   lower hemisphere and the upper surface onto the top, letting z be the radius.

4140:     (x, y)  ==>  ((z+3)/2, \pi/2 (|x| or |y|), arctan y/x)                                                  in (r', \theta', \phi') space
4141:             ==>  ((z+3)/2 \cos(\theta') cos(\phi'), (z+3)/2 \cos(\theta') sin(\phi'), (z+3)/2 sin(\theta')) in (x', y', z') space
4142: */
4143: 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[])
4144: {
4145:   const PetscReal pi4    = PETSC_PI / 4.0;
4146:   const PetscReal ri     = PetscRealPart(constants[0]);
4147:   const PetscReal ro     = PetscRealPart(constants[1]);
4148:   const PetscReal rp     = (x[2] + 1) * 0.5 * (ro - ri) + ri;
4149:   const PetscReal phip   = PetscAtan2Real(x[1], x[0]);
4150:   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])));

4152:   xp[0] = rp * PetscCosReal(thetap) * PetscCosReal(phip);
4153:   xp[1] = rp * PetscCosReal(thetap) * PetscSinReal(phip);
4154:   xp[2] = rp * PetscSinReal(thetap);
4155: }

4157: void coordMap_sinusoid(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[])
4158: {
4159:   const PetscReal c = PetscRealPart(constants[0]);
4160:   const PetscReal m = PetscRealPart(constants[1]);
4161:   const PetscReal n = PetscRealPart(constants[2]);

4163:   xp[0] = x[0];
4164:   xp[1] = x[1];
4165:   if (dim > 2) xp[2] = c * PetscCosReal(2. * m * PETSC_PI * x[0]) * PetscCosReal(2. * n * PETSC_PI * x[1]);
4166: }

4168: /* This function maps the cylinder [0, r] x [0, 1] along z to the torus revolved around z with radius R,
4169:      x' = (R + y) cos(2 pi z)
4170:      y' = (R + y) sin(2 pi z)
4171:      z' = x
4172: */
4173: void coordMap_torus(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[])
4174: {
4175:   const PetscReal R = PetscRealPart(constants[0]);

4177:   xp[0] = (R + x[1]) * PetscCosReal(2 * PETSC_PI * x[2]);
4178:   xp[1] = (R + x[1]) * PetscSinReal(2 * PETSC_PI * x[2]);
4179:   xp[2] = x[0];
4180: }

4182: /*@C
4183:   DMPlexRemapGeometry - This function maps the original `DM` coordinates to new coordinates.

4185:   Not Collective

4187:   Input Parameters:
4188: + dm   - The `DM`
4189: . time - The time
4190: - func - The function transforming current coordinates to new coordinates

4192:   Calling sequence of `func`:
4193: + dim          - The spatial dimension
4194: . Nf           - The number of input fields (here 1)
4195: . NfAux        - The number of input auxiliary fields
4196: . uOff         - The offset of the coordinates in u[] (here 0)
4197: . uOff_x       - The offset of the coordinates in u_x[] (here 0)
4198: . u            - The coordinate values at this point in space
4199: . u_t          - The coordinate time derivative at this point in space (here `NULL`)
4200: . u_x          - The coordinate derivatives at this point in space
4201: . aOff         - The offset of each auxiliary field in u[]
4202: . aOff_x       - The offset of each auxiliary field in u_x[]
4203: . a            - The auxiliary field values at this point in space
4204: . a_t          - The auxiliary field time derivative at this point in space (or `NULL`)
4205: . a_x          - The auxiliary field derivatives at this point in space
4206: . t            - The current time
4207: . x            - The coordinates of this point (here not used)
4208: . numConstants - The number of constants
4209: . constants    - The value of each constant
4210: - f            - The new coordinates at this point in space

4212:   Level: intermediate

4214: .seealso: `DMPLEX`, `DMGetCoordinates()`, `DMGetCoordinatesLocal()`, `DMGetCoordinateDM()`, `DMProjectFieldLocal()`, `DMProjectFieldLabelLocal()`
4215: @*/
4216: 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[]))
4217: {
4218:   DM           cdm;
4219:   PetscDS      cds;
4220:   DMField      cf;
4221:   PetscObject  obj;
4222:   PetscClassId id;
4223:   Vec          lCoords, tmpCoords;

4225:   PetscFunctionBegin;
4226:   if (!func) PetscCall(DMPlexGetCoordinateMap(dm, &func));
4227:   PetscCall(DMGetCoordinateDM(dm, &cdm));
4228:   PetscCall(DMGetCoordinatesLocal(dm, &lCoords));
4229:   PetscCall(DMGetDS(cdm, &cds));
4230:   PetscCall(PetscDSGetDiscretization(cds, 0, &obj));
4231:   PetscCall(PetscObjectGetClassId(obj, &id));
4232:   if (id != PETSCFE_CLASSID) {
4233:     PetscSection       cSection;
4234:     const PetscScalar *constants;
4235:     PetscScalar       *coords, f[16];
4236:     PetscInt           dim, cdim, Nc, vStart, vEnd;

4238:     PetscCall(DMGetDimension(dm, &dim));
4239:     PetscCall(DMGetCoordinateDim(dm, &cdim));
4240:     PetscCheck(cdim <= 16, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Affine version of DMPlexRemapGeometry is currently limited to dimensions <= 16, not %" PetscInt_FMT, cdim);
4241:     PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
4242:     PetscCall(DMGetCoordinateSection(dm, &cSection));
4243:     PetscCall(PetscDSGetConstants(cds, &Nc, &constants));
4244:     PetscCall(VecGetArrayWrite(lCoords, &coords));
4245:     for (PetscInt v = vStart; v < vEnd; ++v) {
4246:       PetscInt uOff[2] = {0, cdim};
4247:       PetscInt off;

4249:       PetscCall(PetscSectionGetOffset(cSection, v, &off));
4250:       (*func)(dim, 1, 0, uOff, NULL, &coords[off], NULL, NULL, NULL, NULL, NULL, NULL, NULL, 0.0, NULL, Nc, constants, f);
4251:       for (PetscInt c = 0; c < cdim; ++c) coords[off + c] = f[c];
4252:     }
4253:     PetscCall(VecRestoreArrayWrite(lCoords, &coords));
4254:   } else {
4255:     PetscCall(DMGetLocalVector(cdm, &tmpCoords));
4256:     PetscCall(VecCopy(lCoords, tmpCoords));
4257:     /* We have to do the coordinate field manually right now since the coordinate DM will not have its own */
4258:     PetscCall(DMGetCoordinateField(dm, &cf));
4259:     cdm->coordinates[0].field = cf;
4260:     PetscCall(DMProjectFieldLocal(cdm, time, tmpCoords, &func, INSERT_VALUES, lCoords));
4261:     cdm->coordinates[0].field = NULL;
4262:     PetscCall(DMRestoreLocalVector(cdm, &tmpCoords));
4263:     PetscCall(DMSetCoordinatesLocal(dm, lCoords));
4264:   }
4265:   PetscFunctionReturn(PETSC_SUCCESS);
4266: }

4268: /*@
4269:   DMPlexShearGeometry - This shears the domain, meaning adds a multiple of the shear coordinate to all other coordinates.

4271:   Not Collective

4273:   Input Parameters:
4274: + dm          - The `DMPLEX`
4275: . direction   - The shear coordinate direction, e.g. `DM_X` is the x-axis
4276: - multipliers - The multiplier m for each direction which is not the shear direction

4278:   Level: intermediate

4280: .seealso: `DMPLEX`, `DMPlexRemapGeometry()`, `DMDirection`, `DM_X`, `DM_Y`, `DM_Z`
4281: @*/
4282: PetscErrorCode DMPlexShearGeometry(DM dm, DMDirection direction, PetscReal multipliers[])
4283: {
4284:   DM             cdm;
4285:   PetscDS        cds;
4286:   PetscScalar   *moduli;
4287:   const PetscInt dir = (PetscInt)direction;
4288:   PetscInt       dE, d, e;

4290:   PetscFunctionBegin;
4291:   PetscCall(DMGetCoordinateDM(dm, &cdm));
4292:   PetscCall(DMGetCoordinateDim(dm, &dE));
4293:   PetscCall(PetscMalloc1(dE + 1, &moduli));
4294:   moduli[0] = dir;
4295:   for (d = 0, e = 0; d < dE; ++d) moduli[d + 1] = d == dir ? 0.0 : (multipliers ? multipliers[e++] : 1.0);
4296:   PetscCall(DMGetDS(cdm, &cds));
4297:   PetscCall(PetscDSSetConstants(cds, dE + 1, moduli));
4298:   PetscCall(DMPlexRemapGeometry(dm, 0.0, coordMap_shear));
4299:   PetscCall(PetscFree(moduli));
4300:   PetscFunctionReturn(PETSC_SUCCESS);
4301: }