Actual source code: plexgeometry.c

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

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

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

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

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

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

 21:   Level: intermediate

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

378:   Not collective

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

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

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

393:   Level: developer

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

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

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

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

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

437: static PetscErrorCode DMPlexLocatePoint_Simplex_2D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
438: {
439:   const 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, f;
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 (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: PetscErrorCode PetscGridHashCreate(MPI_Comm comm, PetscInt dim, const PetscScalar point[], PetscGridHash *box)
699: {
700:   PetscFunctionBegin;
701:   PetscCall(PetscCalloc1(1, box));
702:   PetscCall(PetscGridHashInitialize_Internal(*box, dim, point));
703:   PetscFunctionReturn(PETSC_SUCCESS);
704: }

706: PetscErrorCode PetscGridHashEnlarge(PetscGridHash box, const PetscScalar point[])
707: {
708:   PetscInt d;

710:   PetscFunctionBegin;
711:   for (d = 0; d < box->dim; ++d) {
712:     box->lower[d] = PetscMin(box->lower[d], PetscRealPart(point[d]));
713:     box->upper[d] = PetscMax(box->upper[d], PetscRealPart(point[d]));
714:   }
715:   PetscFunctionReturn(PETSC_SUCCESS);
716: }

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

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

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

738:     PetscCall(DMPlexGetCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
739:     for (PetscInt i = 0; i < numCoords / cdim; ++i) PetscCall(PetscGridHashEnlarge(*box, &coords[i * cdim]));
740:     PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
741:   }
742:   PetscFunctionReturn(PETSC_SUCCESS);
743: }

745: /*@C
746:   PetscGridHashSetGrid - Divide the grid into boxes

748:   Not Collective

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

755:   Level: developer

757: .seealso: `DMPLEX`, `PetscGridHashCreate()`
758: @*/
759: PetscErrorCode PetscGridHashSetGrid(PetscGridHash box, const PetscInt n[], const PetscReal h[])
760: {
761:   PetscInt d;

763:   PetscFunctionBegin;
764:   PetscAssertPointer(n, 2);
765:   if (h) PetscAssertPointer(h, 3);
766:   for (d = 0; d < box->dim; ++d) {
767:     box->extent[d] = box->upper[d] - box->lower[d];
768:     if (n[d] == PETSC_DETERMINE) {
769:       PetscCheck(h, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Missing h");
770:       box->h[d] = h[d];
771:       box->n[d] = PetscCeilReal(box->extent[d] / h[d]);
772:     } else {
773:       box->n[d] = n[d];
774:       box->h[d] = box->extent[d] / n[d];
775:     }
776:   }
777:   PetscFunctionReturn(PETSC_SUCCESS);
778: }

780: /*@C
781:   PetscGridHashGetEnclosingBox - Find the grid boxes containing each input point

783:   Not Collective

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

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

794:   Level: developer

796:   Note:
797:   This only guarantees that a box contains a point, not that a cell does.

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

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

815:       if (dbox == n[d] && PetscAbsReal(PetscRealPart(points[p * dim + d]) - upper[d]) < 1.0e-9) dbox = n[d] - 1;
816:       if (dbox == -1 && PetscAbsReal(PetscRealPart(points[p * dim + d]) - lower[d]) < 1.0e-9) dbox = 0;
817:       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]);
818:       dboxes[p * dim + d] = dbox;
819:     }
820:     if (boxes)
821:       for (d = dim - 2, boxes[p] = dboxes[p * dim + dim - 1]; d >= 0; --d) boxes[p] = boxes[p] * n[d] + dboxes[p * dim + d];
822:   }
823:   PetscFunctionReturn(PETSC_SUCCESS);
824: }

826: /*
827:   PetscGridHashGetEnclosingBoxQuery - Find the grid boxes containing each input point

829:   Not Collective

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

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

842:   Level: developer

844:   Note:
845:   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.

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

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

866:       if (dbox == n[d] && PetscAbsReal(PetscRealPart(points[p * dim + d]) - upper[d]) < 1.0e-9) dbox = n[d] - 1;
867:       if (dbox < 0 || dbox >= n[d]) PetscFunctionReturn(PETSC_SUCCESS);
868:       dboxes[p * dim + d] = dbox;
869:     }
870:     if (boxes)
871:       for (d = dim - 2, boxes[p] = dboxes[p * dim + dim - 1]; d >= 0; --d) boxes[p] = boxes[p] * n[d] + dboxes[p * dim + d];
872:     // It is possible for a box to overlap no grid cells
873:     if (boxes[p] < bStart || boxes[p] >= bEnd) PetscFunctionReturn(PETSC_SUCCESS);
874:   }
875:   *found = PETSC_TRUE;
876:   PetscFunctionReturn(PETSC_SUCCESS);
877: }

879: PetscErrorCode PetscGridHashDestroy(PetscGridHash *box)
880: {
881:   PetscFunctionBegin;
882:   if (*box) {
883:     PetscCall(PetscSectionDestroy(&(*box)->cellSection));
884:     PetscCall(ISDestroy(&(*box)->cells));
885:     PetscCall(DMLabelDestroy(&(*box)->cellsSparse));
886:   }
887:   PetscCall(PetscFree(*box));
888:   PetscFunctionReturn(PETSC_SUCCESS);
889: }

891: PetscErrorCode DMPlexLocatePoint_Internal(DM dm, PetscInt dim, const PetscScalar point[], PetscInt cellStart, PetscInt *cell)
892: {
893:   DMPolytopeType ct;

895:   PetscFunctionBegin;
896:   PetscCall(DMPlexGetCellType(dm, cellStart, &ct));
897:   switch (ct) {
898:   case DM_POLYTOPE_SEGMENT:
899:     PetscCall(DMPlexLocatePoint_Simplex_1D_Internal(dm, point, cellStart, cell));
900:     break;
901:   case DM_POLYTOPE_TRIANGLE:
902:     PetscCall(DMPlexLocatePoint_Simplex_2D_Internal(dm, point, cellStart, cell));
903:     break;
904:   case DM_POLYTOPE_QUADRILATERAL:
905:     PetscCall(DMPlexLocatePoint_Quad_2D_Internal(dm, point, cellStart, cell));
906:     break;
907:   case DM_POLYTOPE_TETRAHEDRON:
908:     PetscCall(DMPlexLocatePoint_Simplex_3D_Internal(dm, point, cellStart, cell));
909:     break;
910:   case DM_POLYTOPE_HEXAHEDRON:
911:     PetscCall(DMPlexLocatePoint_Hex_3D_Internal(dm, point, cellStart, cell));
912:     break;
913:   default:
914:     SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No point location for cell %" PetscInt_FMT " with type %s", cellStart, DMPolytopeTypes[ct]);
915:   }
916:   PetscFunctionReturn(PETSC_SUCCESS);
917: }

919: /*
920:   DMPlexClosestPoint_Internal - Returns the closest point in the cell to the given point
921: */
922: static PetscErrorCode DMPlexClosestPoint_Internal(DM dm, PetscInt dim, const PetscScalar point[], PetscInt cell, PetscReal cpoint[])
923: {
924:   DMPolytopeType ct;

926:   PetscFunctionBegin;
927:   PetscCall(DMPlexGetCellType(dm, cell, &ct));
928:   switch (ct) {
929:   case DM_POLYTOPE_TRIANGLE:
930:     PetscCall(DMPlexClosestPoint_Simplex_2D_Internal(dm, point, cell, cpoint));
931:     break;
932: #if 0
933:     case DM_POLYTOPE_QUADRILATERAL:
934:     PetscCall(DMPlexClosestPoint_General_2D_Internal(dm, point, cell, cpoint));break;
935:     case DM_POLYTOPE_TETRAHEDRON:
936:     PetscCall(DMPlexClosestPoint_Simplex_3D_Internal(dm, point, cell, cpoint));break;
937:     case DM_POLYTOPE_HEXAHEDRON:
938:     PetscCall(DMPlexClosestPoint_General_3D_Internal(dm, point, cell, cpoint));break;
939: #endif
940:   default:
941:     SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No closest point location for cell %" PetscInt_FMT " with type %s", cell, DMPolytopeTypes[ct]);
942:   }
943:   PetscFunctionReturn(PETSC_SUCCESS);
944: }

946: /*
947:   DMPlexComputeGridHash_Internal - Create a grid hash structure covering the `DMPLEX`

949:   Collective

951:   Input Parameter:
952: . dm - The `DMPLEX`

954:   Output Parameter:
955: . localBox - The grid hash object

957:   Level: developer

959:   Notes:
960:   How do we determine all boxes intersecting a given cell?

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

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

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

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

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

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

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

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

989:   PetscFunctionBegin;
990:   PetscCall(DMGetCoordinateDim(dm, &cdim));
991:   PetscCall(DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd));
992:   PetscCall(DMPlexCreateGridHash(dm, &lbox));
993:   {
994:     PetscInt n[3], d;

996:     PetscCall(PetscOptionsGetIntArray(NULL, ((PetscObject)dm)->prefix, "-dm_plex_hash_box_faces", n, &d, &flg));
997:     if (flg) {
998:       for (PetscInt i = d; i < cdim; ++i) n[i] = n[d - 1];
999:     } else {
1000:       for (PetscInt i = 0; i < cdim; ++i) n[i] = PetscMax(2, PetscFloorReal(PetscPowReal((PetscReal)(cEnd - cStart), 1.0 / cdim) * 0.8));
1001:     }
1002:     PetscCall(PetscGridHashSetGrid(lbox, n, NULL));
1003:     if (debug)
1004:       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.,
1005:                             (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.));
1006:   }

1008:   PetscCall(DMGetPointSF(dm, &sf));
1009:   if (sf) PetscCall(PetscSFGetGraph(sf, NULL, &Nl, &leaves, NULL));
1010:   Nl = PetscMax(Nl, 0);
1011:   PetscCall(PetscCalloc2(16 * cdim, &dboxes, 16, &boxes));

1013:   PetscCall(DMLabelCreate(PETSC_COMM_SELF, "cells", &lbox->cellsSparse));
1014:   PetscCall(DMLabelCreateIndex(lbox->cellsSparse, cStart, cEnd));
1015:   for (PetscInt c = cStart; c < cEnd; ++c) {
1016:     PetscReal          intPoints[6 * 6 * 6 * 3];
1017:     const PetscScalar *array;
1018:     PetscScalar       *coords            = NULL;
1019:     const PetscReal   *h                 = lbox->h;
1020:     PetscReal          normal[9]         = {1., 0., 0., 0., 1., 0., 0., 0., 1.};
1021:     PetscReal         *lowerIntPoints[3] = {&intPoints[0 * 6 * 6 * 3], &intPoints[1 * 6 * 6 * 3], &intPoints[2 * 6 * 6 * 3]};
1022:     PetscReal         *upperIntPoints[3] = {&intPoints[3 * 6 * 6 * 3], &intPoints[4 * 6 * 6 * 3], &intPoints[5 * 6 * 6 * 3]};
1023:     PetscReal          lp[3], up[3], *tmp;
1024:     PetscInt           numCoords, idx, dlim[6], lowerInt[3], upperInt[3];
1025:     PetscBool          isDG, lower[3], upper[3];

1027:     PetscCall(PetscFindInt(c, Nl, leaves, &idx));
1028:     if (idx >= 0) continue;
1029:     // Get grid of boxes containing the cell
1030:     PetscCall(DMPlexGetCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
1031:     PetscCall(PetscGridHashGetEnclosingBox(lbox, numCoords / cdim, coords, dboxes, boxes));
1032:     PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
1033:     for (PetscInt d = 0; d < cdim; ++d) dlim[d * 2 + 0] = dlim[d * 2 + 1] = dboxes[d];
1034:     for (PetscInt d = cdim; d < 3; ++d) dlim[d * 2 + 0] = dlim[d * 2 + 1] = 0;
1035:     for (PetscInt e = 1; e < numCoords / cdim; ++e) {
1036:       for (PetscInt d = 0; d < cdim; ++d) {
1037:         dlim[d * 2 + 0] = PetscMin(dlim[d * 2 + 0], dboxes[e * cdim + d]);
1038:         dlim[d * 2 + 1] = PetscMax(dlim[d * 2 + 1], dboxes[e * cdim + d]);
1039:       }
1040:     }
1041:     if (debug > 4) {
1042:       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]));
1043:     }
1044:     // Initialize with lower planes for first box
1045:     for (PetscInt d = 0; d < cdim; ++d) {
1046:       lp[d] = lbox->lower[d] + dlim[d * 2 + 0] * h[d];
1047:       up[d] = lp[d] + h[d];
1048:     }
1049:     for (PetscInt d = 0; d < cdim; ++d) {
1050:       PetscCall(DMPlexGetPlaneCellIntersection_Internal(dm, c, lp, &normal[d * 3], &lower[d], &lowerInt[d], lowerIntPoints[d]));
1051:       if (debug > 4) {
1052:         if (!lowerInt[d])
1053:           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"));
1054:         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]));
1055:       }
1056:     }
1057:     // Loop over grid
1058:     for (PetscInt k = dlim[2 * 2 + 0]; k <= dlim[2 * 2 + 1]; ++k, lp[2] = up[2], up[2] += h[2]) {
1059:       if (cdim > 2) PetscCall(DMPlexGetPlaneCellIntersection_Internal(dm, c, up, &normal[3 * 2], &upper[2], &upperInt[2], upperIntPoints[2]));
1060:       if (cdim > 2 && debug > 4) {
1061:         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"));
1062:         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]));
1063:       }
1064:       for (PetscInt j = dlim[1 * 2 + 0]; j <= dlim[1 * 2 + 1]; ++j, lp[1] = up[1], up[1] += h[1]) {
1065:         if (cdim > 1) PetscCall(DMPlexGetPlaneCellIntersection_Internal(dm, c, up, &normal[3 * 1], &upper[1], &upperInt[1], upperIntPoints[1]));
1066:         if (cdim > 1 && debug > 4) {
1067:           if (!upperInt[1])
1068:             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"));
1069:           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]));
1070:         }
1071:         for (PetscInt i = dlim[0 * 2 + 0]; i <= dlim[0 * 2 + 1]; ++i, lp[0] = up[0], up[0] += h[0]) {
1072:           const PetscInt box    = (k * lbox->n[1] + j) * lbox->n[0] + i;
1073:           PetscBool      excNeg = PETSC_TRUE;
1074:           PetscBool      excPos = PETSC_TRUE;
1075:           PetscInt       NlInt  = 0;
1076:           PetscInt       NuInt  = 0;

1078:           PetscCall(DMPlexGetPlaneCellIntersection_Internal(dm, c, up, &normal[3 * 0], &upper[0], &upperInt[0], upperIntPoints[0]));
1079:           if (debug > 4) {
1080:             if (!upperInt[0])
1081:               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"));
1082:             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]));
1083:           }
1084:           for (PetscInt d = 0; d < cdim; ++d) {
1085:             NlInt += lowerInt[d];
1086:             NuInt += upperInt[d];
1087:           }
1088:           // If there is no intersection...
1089:           if (!NlInt && !NuInt) {
1090:             // If the cell is on the negative side of the lower planes, it is not in the box
1091:             for (PetscInt d = 0; d < cdim; ++d)
1092:               if (lower[d]) {
1093:                 excNeg = PETSC_FALSE;
1094:                 break;
1095:               }
1096:             // If the cell is on the positive side of the upper planes, it is not in the box
1097:             for (PetscInt d = 0; d < cdim; ++d)
1098:               if (!upper[d]) {
1099:                 excPos = PETSC_FALSE;
1100:                 break;
1101:               }
1102:             if (excNeg || excPos) {
1103:               if (debug && excNeg) PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Cell %" PetscInt_FMT " is on the negative side of the lower plane\n", c));
1104:               if (debug && excPos) PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Cell %" PetscInt_FMT " is on the positive side of the upper plane\n", c));
1105:               continue;
1106:             }
1107:             // Otherwise it is in the box
1108:             if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Cell %" PetscInt_FMT " is contained in box %" PetscInt_FMT "\n", c, box));
1109:             PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
1110:             continue;
1111:           }
1112:           /*
1113:             If any intersection point is within the box limits, it is in the box
1114:             We need to have tolerances here since intersection point calculations can introduce errors
1115:             Initialize a count to track which planes have intersection outside the box.
1116:             if two adjacent planes have intersection points upper and lower all outside the box, look
1117:             first at if another plane has intersection points outside the box, if so, it is inside the cell
1118:             look next if no intersection points exist on the other planes, and check if the planes are on the
1119:             outside of the intersection points but on opposite ends. If so, the box cuts through the cell.
1120:           */
1121:           PetscInt outsideCount[6] = {0, 0, 0, 0, 0, 0};
1122:           for (PetscInt plane = 0; plane < cdim; ++plane) {
1123:             for (PetscInt ip = 0; ip < lowerInt[plane]; ++ip) {
1124:               PetscInt d;

1126:               for (d = 0; d < cdim; ++d) {
1127:                 if ((lowerIntPoints[plane][ip * cdim + d] < (lp[d] - PETSC_SMALL)) || (lowerIntPoints[plane][ip * cdim + d] > (up[d] + PETSC_SMALL))) {
1128:                   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
1129:                   break;
1130:                 }
1131:               }
1132:               if (d == cdim) {
1133:                 if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Cell %" PetscInt_FMT " intersected lower plane %" PetscInt_FMT " of box %" PetscInt_FMT "\n", c, plane, box));
1134:                 PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
1135:                 goto end;
1136:               }
1137:             }
1138:             for (PetscInt ip = 0; ip < upperInt[plane]; ++ip) {
1139:               PetscInt d;

1141:               for (d = 0; d < cdim; ++d) {
1142:                 if ((upperIntPoints[plane][ip * cdim + d] < (lp[d] - PETSC_SMALL)) || (upperIntPoints[plane][ip * cdim + d] > (up[d] + PETSC_SMALL))) {
1143:                   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
1144:                   break;
1145:                 }
1146:               }
1147:               if (d == cdim) {
1148:                 if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, "  Cell %" PetscInt_FMT " intersected upper plane %" PetscInt_FMT " of box %" PetscInt_FMT "\n", c, plane, box));
1149:                 PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
1150:                 goto end;
1151:               }
1152:             }
1153:           }
1154:           /*
1155:              Check the planes with intersections
1156:              in 2D, check if the square falls in the middle of a cell
1157:              ie all four planes have intersection points outside of the box
1158:              You do not want to be doing this, because it means your grid hashing is finer than your grid,
1159:              but we should still support it I guess
1160:           */
1161:           if (cdim == 2) {
1162:             PetscInt nIntersects = 0;
1163:             for (PetscInt d = 0; d < cdim; ++d) nIntersects += (outsideCount[d] + outsideCount[d + cdim]);
1164:             // if the count adds up to 8, that means each plane has 2 external intersections and thus it is in the cell
1165:             if (nIntersects == 8) {
1166:               PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
1167:               goto end;
1168:             }
1169:           }
1170:           /*
1171:              In 3 dimensions, if two adjacent planes have at least 3 intersections outside the cell in the appropriate direction,
1172:              we then check the 3rd planar dimension. If a plane falls between intersection points, the cell belongs to that box.
1173:              If the planes are on opposite sides of the intersection points, the cell belongs to that box and it passes through the cell.
1174:           */
1175:           if (cdim == 3) {
1176:             PetscInt faces[3] = {0, 0, 0}, checkInternalFace = 0;
1177:             // Find two adjacent planes with at least 3 intersection points in the upper and lower
1178:             // if the third plane has 3 intersection points or more, a pyramid base is formed on that plane and it is in the cell
1179:             for (PetscInt d = 0; d < cdim; ++d)
1180:               if (outsideCount[d] >= 3 && outsideCount[cdim + d] >= 3) {
1181:                 faces[d]++;
1182:                 checkInternalFace++;
1183:               }
1184:             if (checkInternalFace == 3) {
1185:               // All planes have 3 intersection points, add it.
1186:               PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
1187:               goto end;
1188:             }
1189:             // Gross, figure out which adjacent faces have at least 3 points
1190:             PetscInt nonIntersectingFace = -1;
1191:             if (faces[0] == faces[1]) nonIntersectingFace = 2;
1192:             if (faces[0] == faces[2]) nonIntersectingFace = 1;
1193:             if (faces[1] == faces[2]) nonIntersectingFace = 0;
1194:             if (nonIntersectingFace >= 0) {
1195:               for (PetscInt plane = 0; plane < cdim; ++plane) {
1196:                 if (!lowerInt[nonIntersectingFace] && !upperInt[nonIntersectingFace]) continue;
1197:                 // 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.
1198:                 for (PetscInt ip = 0; ip < lowerInt[nonIntersectingFace]; ++ip) {
1199:                   if (lowerIntPoints[plane][ip * cdim + nonIntersectingFace] > lp[nonIntersectingFace] - PETSC_SMALL || lowerIntPoints[plane][ip * cdim + nonIntersectingFace] < up[nonIntersectingFace] + PETSC_SMALL) goto setpoint;
1200:                 }
1201:                 for (PetscInt ip = 0; ip < upperInt[nonIntersectingFace]; ++ip) {
1202:                   if (upperIntPoints[plane][ip * cdim + nonIntersectingFace] > lp[nonIntersectingFace] - PETSC_SMALL || upperIntPoints[plane][ip * cdim + nonIntersectingFace] < up[nonIntersectingFace] + PETSC_SMALL) goto setpoint;
1203:                 }
1204:                 goto end;
1205:               }
1206:               // The points are within the bonds of the non intersecting planes, add it.
1207:             setpoint:
1208:               PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
1209:               goto end;
1210:             }
1211:           }
1212:         end:
1213:           lower[0]          = upper[0];
1214:           lowerInt[0]       = upperInt[0];
1215:           tmp               = lowerIntPoints[0];
1216:           lowerIntPoints[0] = upperIntPoints[0];
1217:           upperIntPoints[0] = tmp;
1218:         }
1219:         lp[0]             = lbox->lower[0] + dlim[0 * 2 + 0] * h[0];
1220:         up[0]             = lp[0] + h[0];
1221:         lower[1]          = upper[1];
1222:         lowerInt[1]       = upperInt[1];
1223:         tmp               = lowerIntPoints[1];
1224:         lowerIntPoints[1] = upperIntPoints[1];
1225:         upperIntPoints[1] = tmp;
1226:       }
1227:       lp[1]             = lbox->lower[1] + dlim[1 * 2 + 0] * h[1];
1228:       up[1]             = lp[1] + h[1];
1229:       lower[2]          = upper[2];
1230:       lowerInt[2]       = upperInt[2];
1231:       tmp               = lowerIntPoints[2];
1232:       lowerIntPoints[2] = upperIntPoints[2];
1233:       upperIntPoints[2] = tmp;
1234:     }
1235:   }
1236:   PetscCall(PetscFree2(dboxes, boxes));

1238:   if (debug) PetscCall(DMLabelView(lbox->cellsSparse, PETSC_VIEWER_STDOUT_SELF));
1239:   PetscCall(DMLabelConvertToSection(lbox->cellsSparse, &lbox->cellSection, &lbox->cells));
1240:   PetscCall(DMLabelDestroy(&lbox->cellsSparse));
1241:   *localBox = lbox;
1242:   PetscFunctionReturn(PETSC_SUCCESS);
1243: }

1245: PetscErrorCode DMLocatePoints_Plex(DM dm, Vec v, DMPointLocationType ltype, PetscSF cellSF)
1246: {
1247:   PetscInt        debug = ((DM_Plex *)dm->data)->printLocate;
1248:   DM_Plex        *mesh  = (DM_Plex *)dm->data;
1249:   PetscBool       hash = mesh->useHashLocation, reuse = PETSC_FALSE;
1250:   PetscInt        bs, numPoints, numFound, *found = NULL;
1251:   PetscInt        cdim, Nl = 0, cStart, cEnd, numCells;
1252:   PetscSF         sf;
1253:   const PetscInt *leaves;
1254:   const PetscInt *boxCells;
1255:   PetscSFNode    *cells;
1256:   PetscScalar    *a;
1257:   PetscMPIInt     result;
1258:   PetscLogDouble  t0, t1;
1259:   PetscReal       gmin[3], gmax[3];
1260:   PetscInt        terminating_query_type[] = {0, 0, 0};
1261:   PetscMPIInt     rank;

1263:   PetscFunctionBegin;
1264:   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank));
1265:   PetscCall(PetscLogEventBegin(DMPLEX_LocatePoints, 0, 0, 0, 0));
1266:   PetscCall(PetscTime(&t0));
1267:   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.");
1268:   PetscCall(DMGetCoordinateDim(dm, &cdim));
1269:   PetscCall(VecGetBlockSize(v, &bs));
1270:   PetscCallMPI(MPI_Comm_compare(PetscObjectComm((PetscObject)cellSF), PETSC_COMM_SELF, &result));
1271:   PetscCheck(result == MPI_IDENT || result == MPI_CONGRUENT, PetscObjectComm((PetscObject)cellSF), PETSC_ERR_SUP, "Trying parallel point location: only local point location supported");
1272:   // We ignore extra coordinates
1273:   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);
1274:   PetscCall(DMGetCoordinatesLocalSetUp(dm));
1275:   PetscCall(DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd));
1276:   PetscCall(DMGetPointSF(dm, &sf));
1277:   if (sf) PetscCall(PetscSFGetGraph(sf, NULL, &Nl, &leaves, NULL));
1278:   Nl = PetscMax(Nl, 0);
1279:   PetscCall(VecGetLocalSize(v, &numPoints));
1280:   PetscCall(VecGetArray(v, &a));
1281:   numPoints /= bs;
1282:   {
1283:     const PetscSFNode *sf_cells;

1285:     PetscCall(PetscSFGetGraph(cellSF, NULL, NULL, NULL, &sf_cells));
1286:     if (sf_cells) {
1287:       PetscCall(PetscInfo(dm, "[DMLocatePoints_Plex] Re-using existing StarForest node list\n"));
1288:       cells = (PetscSFNode *)sf_cells;
1289:       reuse = PETSC_TRUE;
1290:     } else {
1291:       PetscCall(PetscInfo(dm, "[DMLocatePoints_Plex] Creating and initializing new StarForest node list\n"));
1292:       PetscCall(PetscMalloc1(numPoints, &cells));
1293:       /* initialize cells if created */
1294:       for (PetscInt p = 0; p < numPoints; p++) {
1295:         cells[p].rank  = 0;
1296:         cells[p].index = DMLOCATEPOINT_POINT_NOT_FOUND;
1297:       }
1298:     }
1299:   }
1300:   PetscCall(DMGetBoundingBox(dm, gmin, gmax));
1301:   if (hash) {
1302:     if (!mesh->lbox) {
1303:       PetscCall(PetscInfo(dm, "Initializing grid hashing\n"));
1304:       PetscCall(DMPlexComputeGridHash_Internal(dm, &mesh->lbox));
1305:     }
1306:     /* Designate the local box for each point */
1307:     /* Send points to correct process */
1308:     /* Search cells that lie in each subbox */
1309:     /*   Should we bin points before doing search? */
1310:     PetscCall(ISGetIndices(mesh->lbox->cells, &boxCells));
1311:   }
1312:   numFound = 0;
1313:   for (PetscInt p = 0; p < numPoints; ++p) {
1314:     const PetscScalar *point   = &a[p * bs];
1315:     PetscInt           dbin[3] = {-1, -1, -1}, bin, cell = -1, cellOffset;
1316:     PetscBool          point_outside_domain = PETSC_FALSE;

1318:     /* check bounding box of domain */
1319:     for (PetscInt d = 0; d < cdim; d++) {
1320:       if (PetscRealPart(point[d]) < gmin[d]) {
1321:         point_outside_domain = PETSC_TRUE;
1322:         break;
1323:       }
1324:       if (PetscRealPart(point[d]) > gmax[d]) {
1325:         point_outside_domain = PETSC_TRUE;
1326:         break;
1327:       }
1328:     }
1329:     if (point_outside_domain) {
1330:       cells[p].rank  = 0;
1331:       cells[p].index = DMLOCATEPOINT_POINT_NOT_FOUND;
1332:       terminating_query_type[0]++;
1333:       continue;
1334:     }

1336:     /* check initial values in cells[].index - abort early if found */
1337:     if (cells[p].index != DMLOCATEPOINT_POINT_NOT_FOUND) {
1338:       PetscInt c = cells[p].index;

1340:       cells[p].index = DMLOCATEPOINT_POINT_NOT_FOUND;
1341:       PetscCall(DMPlexLocatePoint_Internal(dm, cdim, point, c, &cell));
1342:       if (cell >= 0) {
1343:         cells[p].rank  = 0;
1344:         cells[p].index = cell;
1345:         numFound++;
1346:       }
1347:     }
1348:     if (cells[p].index != DMLOCATEPOINT_POINT_NOT_FOUND) {
1349:       terminating_query_type[1]++;
1350:       continue;
1351:     }

1353:     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.));
1354:     if (hash) {
1355:       PetscBool found_box;

1357:       /* allow for case that point is outside box - abort early */
1358:       PetscCall(PetscGridHashGetEnclosingBoxQuery(mesh->lbox, mesh->lbox->cellSection, 1, point, dbin, &bin, &found_box));
1359:       if (found_box) {
1360:         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));
1361:         /* TODO Lay an interface over this so we can switch between Section (dense) and Label (sparse) */
1362:         PetscCall(PetscSectionGetDof(mesh->lbox->cellSection, bin, &numCells));
1363:         PetscCall(PetscSectionGetOffset(mesh->lbox->cellSection, bin, &cellOffset));
1364:         for (PetscInt c = cellOffset; c < cellOffset + numCells; ++c) {
1365:           if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, "[%d]    Checking for point in cell %" PetscInt_FMT "\n", rank, boxCells[c]));
1366:           PetscCall(DMPlexLocatePoint_Internal(dm, cdim, point, boxCells[c], &cell));
1367:           if (cell >= 0) {
1368:             if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, "[%d]      FOUND in cell %" PetscInt_FMT "\n", rank, cell));
1369:             cells[p].rank  = 0;
1370:             cells[p].index = cell;
1371:             numFound++;
1372:             terminating_query_type[2]++;
1373:             break;
1374:           }
1375:         }
1376:       }
1377:     } else {
1378:       PetscBool found = PETSC_FALSE;
1379:       for (PetscInt c = cStart; c < cEnd; ++c) {
1380:         PetscInt idx;

1382:         PetscCall(PetscFindInt(c, Nl, leaves, &idx));
1383:         if (idx >= 0) continue;
1384:         PetscCall(DMPlexLocatePoint_Internal(dm, cdim, point, c, &cell));
1385:         if (cell >= 0) {
1386:           cells[p].rank  = 0;
1387:           cells[p].index = cell;
1388:           numFound++;
1389:           terminating_query_type[2]++;
1390:           found = PETSC_TRUE;
1391:           break;
1392:         }
1393:       }
1394:       if (!found) terminating_query_type[0]++;
1395:     }
1396:   }
1397:   if (hash) PetscCall(ISRestoreIndices(mesh->lbox->cells, &boxCells));
1398:   if (ltype == DM_POINTLOCATION_NEAREST && hash && numFound < numPoints) {
1399:     for (PetscInt p = 0; p < numPoints; p++) {
1400:       const PetscScalar *point     = &a[p * bs];
1401:       PetscReal          cpoint[3] = {0, 0, 0}, diff[3], best[3] = {PETSC_MAX_REAL, PETSC_MAX_REAL, PETSC_MAX_REAL}, dist, distMax = PETSC_MAX_REAL;
1402:       PetscInt           dbin[3] = {-1, -1, -1}, bin, cellOffset, bestc = -1;

1404:       if (cells[p].index < 0) {
1405:         PetscCall(PetscGridHashGetEnclosingBox(mesh->lbox, 1, point, dbin, &bin));
1406:         PetscCall(PetscSectionGetDof(mesh->lbox->cellSection, bin, &numCells));
1407:         PetscCall(PetscSectionGetOffset(mesh->lbox->cellSection, bin, &cellOffset));
1408:         for (PetscInt c = cellOffset; c < cellOffset + numCells; ++c) {
1409:           PetscCall(DMPlexClosestPoint_Internal(dm, cdim, point, boxCells[c], cpoint));
1410:           for (PetscInt d = 0; d < cdim; ++d) diff[d] = cpoint[d] - PetscRealPart(point[d]);
1411:           dist = DMPlex_NormD_Internal(cdim, diff);
1412:           if (dist < distMax) {
1413:             for (PetscInt d = 0; d < cdim; ++d) best[d] = cpoint[d];
1414:             bestc   = boxCells[c];
1415:             distMax = dist;
1416:           }
1417:         }
1418:         if (distMax < PETSC_MAX_REAL) {
1419:           ++numFound;
1420:           cells[p].rank  = 0;
1421:           cells[p].index = bestc;
1422:           for (PetscInt d = 0; d < cdim; ++d) a[p * bs + d] = best[d];
1423:         }
1424:       }
1425:     }
1426:   }
1427:   /* This code is only be relevant when interfaced to parallel point location */
1428:   /* Check for highest numbered proc that claims a point (do we care?) */
1429:   if (ltype == DM_POINTLOCATION_REMOVE && numFound < numPoints) {
1430:     PetscCall(PetscMalloc1(numFound, &found));
1431:     numFound = 0;
1432:     for (PetscInt p = 0; p < numPoints; p++) {
1433:       if (cells[p].rank >= 0 && cells[p].index >= 0) {
1434:         if (numFound < p) cells[numFound] = cells[p];
1435:         found[numFound++] = p;
1436:       }
1437:     }
1438:   }
1439:   PetscCall(VecRestoreArray(v, &a));
1440:   if (!reuse) PetscCall(PetscSFSetGraph(cellSF, cEnd - cStart, numFound, found, PETSC_OWN_POINTER, cells, PETSC_OWN_POINTER));
1441:   PetscCall(PetscTime(&t1));
1442:   if (hash) {
1443:     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]));
1444:   } else {
1445:     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]));
1446:   }
1447:   PetscCall(PetscInfo(dm, "[DMLocatePoints_Plex] npoints %" PetscInt_FMT " : time(rank0) %1.2e (sec): points/sec %1.4e\n", numPoints, t1 - t0, numPoints / (t1 - t0)));
1448:   PetscCall(PetscLogEventEnd(DMPLEX_LocatePoints, 0, 0, 0, 0));
1449:   PetscFunctionReturn(PETSC_SUCCESS);
1450: }

1452: /*@
1453:   DMPlexComputeProjection2Dto1D - Rewrite coordinates to be the 1D projection of the 2D coordinates

1455:   Not Collective

1457:   Input/Output Parameter:
1458: . 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

1460:   Output Parameter:
1461: . R - The rotation which accomplishes the projection, array of size 4

1463:   Level: developer

1465: .seealso: `DMPLEX`, `DMPlexComputeProjection3Dto1D()`, `DMPlexComputeProjection3Dto2D()`
1466: @*/
1467: PetscErrorCode DMPlexComputeProjection2Dto1D(PetscScalar coords[], PetscReal R[])
1468: {
1469:   const PetscReal x = PetscRealPart(coords[2] - coords[0]);
1470:   const PetscReal y = PetscRealPart(coords[3] - coords[1]);
1471:   const PetscReal r = PetscSqrtReal(x * x + y * y), c = x / r, s = y / r;

1473:   PetscFunctionBegin;
1474:   R[0]      = c;
1475:   R[1]      = -s;
1476:   R[2]      = s;
1477:   R[3]      = c;
1478:   coords[0] = 0.0;
1479:   coords[1] = r;
1480:   PetscFunctionReturn(PETSC_SUCCESS);
1481: }

1483: /*@
1484:   DMPlexComputeProjection3Dto1D - Rewrite coordinates to be the 1D projection of the 3D coordinates

1486:   Not Collective

1488:   Input/Output Parameter:
1489: . 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

1491:   Output Parameter:
1492: . R - The rotation which accomplishes the projection, an array of size 9

1494:   Level: developer

1496:   Note:
1497:   This uses the basis completion described by Frisvad {cite}`frisvad2012building`

1499: .seealso: `DMPLEX`, `DMPlexComputeProjection2Dto1D()`, `DMPlexComputeProjection3Dto2D()`
1500: @*/
1501: PetscErrorCode DMPlexComputeProjection3Dto1D(PetscScalar coords[], PetscReal R[])
1502: {
1503:   PetscReal x    = PetscRealPart(coords[3] - coords[0]);
1504:   PetscReal y    = PetscRealPart(coords[4] - coords[1]);
1505:   PetscReal z    = PetscRealPart(coords[5] - coords[2]);
1506:   PetscReal r    = PetscSqrtReal(x * x + y * y + z * z);
1507:   PetscReal rinv = 1. / r;

1509:   PetscFunctionBegin;
1510:   x *= rinv;
1511:   y *= rinv;
1512:   z *= rinv;
1513:   if (x > 0.) {
1514:     PetscReal inv1pX = 1. / (1. + x);

1516:     R[0] = x;
1517:     R[1] = -y;
1518:     R[2] = -z;
1519:     R[3] = y;
1520:     R[4] = 1. - y * y * inv1pX;
1521:     R[5] = -y * z * inv1pX;
1522:     R[6] = z;
1523:     R[7] = -y * z * inv1pX;
1524:     R[8] = 1. - z * z * inv1pX;
1525:   } else {
1526:     PetscReal inv1mX = 1. / (1. - x);

1528:     R[0] = x;
1529:     R[1] = z;
1530:     R[2] = y;
1531:     R[3] = y;
1532:     R[4] = -y * z * inv1mX;
1533:     R[5] = 1. - y * y * inv1mX;
1534:     R[6] = z;
1535:     R[7] = 1. - z * z * inv1mX;
1536:     R[8] = -y * z * inv1mX;
1537:   }
1538:   coords[0] = 0.0;
1539:   coords[1] = r;
1540:   coords[2] = 0.0;
1541:   PetscFunctionReturn(PETSC_SUCCESS);
1542: }

1544: /*@
1545:   DMPlexComputeProjection3Dto2D - Rewrite coordinates of 3 or more coplanar 3D points to a common 2D basis for the
1546:   plane.  The normal is defined by positive orientation of the first 3 points.

1548:   Not Collective

1550:   Input Parameter:
1551: . coordSize - Length of coordinate array (3x number of points); must be at least 9 (3 points)

1553:   Input/Output Parameter:
1554: . coords - The interlaced coordinates of each coplanar 3D point; on output the first
1555:            2*coordSize/3 entries contain interlaced 2D points, with the rest undefined

1557:   Output Parameter:
1558: . 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.

1560:   Level: developer

1562: .seealso: `DMPLEX`, `DMPlexComputeProjection2Dto1D()`, `DMPlexComputeProjection3Dto1D()`
1563: @*/
1564: PetscErrorCode DMPlexComputeProjection3Dto2D(PetscInt coordSize, PetscScalar coords[], PetscReal R[])
1565: {
1566:   PetscReal      x1[3], x2[3], n[3], c[3], norm;
1567:   const PetscInt dim = 3;
1568:   PetscInt       d, p;

1570:   PetscFunctionBegin;
1571:   /* 0) Calculate normal vector */
1572:   for (d = 0; d < dim; ++d) {
1573:     x1[d] = PetscRealPart(coords[1 * dim + d] - coords[0 * dim + d]);
1574:     x2[d] = PetscRealPart(coords[2 * dim + d] - coords[0 * dim + d]);
1575:   }
1576:   // n = x1 \otimes x2
1577:   n[0] = x1[1] * x2[2] - x1[2] * x2[1];
1578:   n[1] = x1[2] * x2[0] - x1[0] * x2[2];
1579:   n[2] = x1[0] * x2[1] - x1[1] * x2[0];
1580:   norm = PetscSqrtReal(n[0] * n[0] + n[1] * n[1] + n[2] * n[2]);
1581:   for (d = 0; d < dim; d++) n[d] /= norm;
1582:   norm = PetscSqrtReal(x1[0] * x1[0] + x1[1] * x1[1] + x1[2] * x1[2]);
1583:   for (d = 0; d < dim; d++) x1[d] /= norm;
1584:   // x2 = n \otimes x1
1585:   x2[0] = n[1] * x1[2] - n[2] * x1[1];
1586:   x2[1] = n[2] * x1[0] - n[0] * x1[2];
1587:   x2[2] = n[0] * x1[1] - n[1] * x1[0];
1588:   for (d = 0; d < dim; d++) {
1589:     R[d * dim + 0] = x1[d];
1590:     R[d * dim + 1] = x2[d];
1591:     R[d * dim + 2] = n[d];
1592:     c[d]           = PetscRealPart(coords[0 * dim + d]);
1593:   }
1594:   for (p = 0; p < coordSize / dim; p++) {
1595:     PetscReal y[3];
1596:     for (d = 0; d < dim; d++) y[d] = PetscRealPart(coords[p * dim + d]) - c[d];
1597:     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];
1598:   }
1599:   PetscFunctionReturn(PETSC_SUCCESS);
1600: }

1602: PETSC_UNUSED static inline void Volume_Triangle_Internal(PetscReal *vol, PetscReal coords[])
1603: {
1604:   /* Signed volume is 1/2 the determinant

1606:    |  1  1  1 |
1607:    | x0 x1 x2 |
1608:    | y0 y1 y2 |

1610:      but if x0,y0 is the origin, we have

1612:    | x1 x2 |
1613:    | y1 y2 |
1614:   */
1615:   const PetscReal x1 = coords[2] - coords[0], y1 = coords[3] - coords[1];
1616:   const PetscReal x2 = coords[4] - coords[0], y2 = coords[5] - coords[1];
1617:   PetscReal       M[4], detM;
1618:   M[0] = x1;
1619:   M[1] = x2;
1620:   M[2] = y1;
1621:   M[3] = y2;
1622:   DMPlex_Det2D_Internal(&detM, M);
1623:   *vol = 0.5 * detM;
1624:   (void)PetscLogFlops(5.0);
1625: }

1627: PETSC_UNUSED static inline void Volume_Tetrahedron_Internal(PetscReal *vol, PetscReal coords[])
1628: {
1629:   /* Signed volume is 1/6th of the determinant

1631:    |  1  1  1  1 |
1632:    | x0 x1 x2 x3 |
1633:    | y0 y1 y2 y3 |
1634:    | z0 z1 z2 z3 |

1636:      but if x0,y0,z0 is the origin, we have

1638:    | x1 x2 x3 |
1639:    | y1 y2 y3 |
1640:    | z1 z2 z3 |
1641:   */
1642:   const PetscReal x1 = coords[3] - coords[0], y1 = coords[4] - coords[1], z1 = coords[5] - coords[2];
1643:   const PetscReal x2 = coords[6] - coords[0], y2 = coords[7] - coords[1], z2 = coords[8] - coords[2];
1644:   const PetscReal x3 = coords[9] - coords[0], y3 = coords[10] - coords[1], z3 = coords[11] - coords[2];
1645:   const PetscReal onesixth = ((PetscReal)1. / (PetscReal)6.);
1646:   PetscReal       M[9], detM;
1647:   M[0] = x1;
1648:   M[1] = x2;
1649:   M[2] = x3;
1650:   M[3] = y1;
1651:   M[4] = y2;
1652:   M[5] = y3;
1653:   M[6] = z1;
1654:   M[7] = z2;
1655:   M[8] = z3;
1656:   DMPlex_Det3D_Internal(&detM, M);
1657:   *vol = -onesixth * detM;
1658:   (void)PetscLogFlops(10.0);
1659: }

1661: static inline void Volume_Tetrahedron_Origin_Internal(PetscReal *vol, PetscReal coords[])
1662: {
1663:   const PetscReal onesixth = ((PetscReal)1. / (PetscReal)6.);
1664:   DMPlex_Det3D_Internal(vol, coords);
1665:   *vol *= -onesixth;
1666: }

1668: static PetscErrorCode DMPlexComputePointGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1669: {
1670:   PetscSection       coordSection;
1671:   Vec                coordinates;
1672:   const PetscScalar *coords;
1673:   PetscInt           dim, d, off;

1675:   PetscFunctionBegin;
1676:   PetscCall(DMGetCoordinatesLocal(dm, &coordinates));
1677:   PetscCall(DMGetCoordinateSection(dm, &coordSection));
1678:   PetscCall(PetscSectionGetDof(coordSection, e, &dim));
1679:   if (!dim) PetscFunctionReturn(PETSC_SUCCESS);
1680:   PetscCall(PetscSectionGetOffset(coordSection, e, &off));
1681:   PetscCall(VecGetArrayRead(coordinates, &coords));
1682:   if (v0) {
1683:     for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[off + d]);
1684:   }
1685:   PetscCall(VecRestoreArrayRead(coordinates, &coords));
1686:   *detJ = 1.;
1687:   if (J) {
1688:     for (d = 0; d < dim * dim; d++) J[d] = 0.;
1689:     for (d = 0; d < dim; d++) J[d * dim + d] = 1.;
1690:     if (invJ) {
1691:       for (d = 0; d < dim * dim; d++) invJ[d] = 0.;
1692:       for (d = 0; d < dim; d++) invJ[d * dim + d] = 1.;
1693:     }
1694:   }
1695:   PetscFunctionReturn(PETSC_SUCCESS);
1696: }

1698: /*@C
1699:   DMPlexGetCellCoordinates - Get coordinates for a cell, taking into account periodicity

1701:   Not Collective

1703:   Input Parameters:
1704: + dm   - The `DMPLEX`
1705: - cell - The cell number

1707:   Output Parameters:
1708: + isDG   - Using cellwise coordinates
1709: . Nc     - The number of coordinates
1710: . array  - The coordinate array
1711: - coords - The cell coordinates

1713:   Level: developer

1715: .seealso: `DMPLEX`, `DMPlexRestoreCellCoordinates()`, `DMGetCoordinatesLocal()`, `DMGetCellCoordinatesLocal()`
1716: @*/
1717: PetscErrorCode DMPlexGetCellCoordinates(DM dm, PetscInt cell, PetscBool *isDG, PetscInt *Nc, const PetscScalar *array[], PetscScalar *coords[])
1718: {
1719:   DM                 cdm;
1720:   Vec                coordinates;
1721:   PetscSection       cs;
1722:   const PetscScalar *ccoords;
1723:   PetscInt           pStart, pEnd;

1725:   PetscFunctionBeginHot;
1726:   *isDG   = PETSC_FALSE;
1727:   *Nc     = 0;
1728:   *array  = NULL;
1729:   *coords = NULL;
1730:   /* Check for cellwise coordinates */
1731:   PetscCall(DMGetCellCoordinateSection(dm, &cs));
1732:   if (!cs) goto cg;
1733:   /* Check that the cell exists in the cellwise section */
1734:   PetscCall(PetscSectionGetChart(cs, &pStart, &pEnd));
1735:   if (cell < pStart || cell >= pEnd) goto cg;
1736:   /* Check for cellwise coordinates for this cell */
1737:   PetscCall(PetscSectionGetDof(cs, cell, Nc));
1738:   if (!*Nc) goto cg;
1739:   /* Check for cellwise coordinates */
1740:   PetscCall(DMGetCellCoordinatesLocalNoncollective(dm, &coordinates));
1741:   if (!coordinates) goto cg;
1742:   /* Get cellwise coordinates */
1743:   PetscCall(DMGetCellCoordinateDM(dm, &cdm));
1744:   PetscCall(VecGetArrayRead(coordinates, array));
1745:   PetscCall(DMPlexPointLocalRead(cdm, cell, *array, &ccoords));
1746:   PetscCall(DMGetWorkArray(cdm, *Nc, MPIU_SCALAR, coords));
1747:   PetscCall(PetscArraycpy(*coords, ccoords, *Nc));
1748:   PetscCall(VecRestoreArrayRead(coordinates, array));
1749:   *isDG = PETSC_TRUE;
1750:   PetscFunctionReturn(PETSC_SUCCESS);
1751: cg:
1752:   /* Use continuous coordinates */
1753:   PetscCall(DMGetCoordinateDM(dm, &cdm));
1754:   PetscCall(DMGetCoordinateSection(dm, &cs));
1755:   PetscCall(DMGetCoordinatesLocalNoncollective(dm, &coordinates));
1756:   PetscCall(DMPlexVecGetOrientedClosure_Internal(cdm, cs, PETSC_FALSE, coordinates, cell, 0, Nc, coords));
1757:   PetscFunctionReturn(PETSC_SUCCESS);
1758: }

1760: /*@C
1761:   DMPlexRestoreCellCoordinates - Get coordinates for a cell, taking into account periodicity

1763:   Not Collective

1765:   Input Parameters:
1766: + dm   - The `DMPLEX`
1767: - cell - The cell number

1769:   Output Parameters:
1770: + isDG   - Using cellwise coordinates
1771: . Nc     - The number of coordinates
1772: . array  - The coordinate array
1773: - coords - The cell coordinates

1775:   Level: developer

1777: .seealso: `DMPLEX`, `DMPlexGetCellCoordinates()`, `DMGetCoordinatesLocal()`, `DMGetCellCoordinatesLocal()`
1778: @*/
1779: PetscErrorCode DMPlexRestoreCellCoordinates(DM dm, PetscInt cell, PetscBool *isDG, PetscInt *Nc, const PetscScalar *array[], PetscScalar *coords[])
1780: {
1781:   DM           cdm;
1782:   PetscSection cs;
1783:   Vec          coordinates;

1785:   PetscFunctionBeginHot;
1786:   if (*isDG) {
1787:     PetscCall(DMGetCellCoordinateDM(dm, &cdm));
1788:     PetscCall(DMRestoreWorkArray(cdm, *Nc, MPIU_SCALAR, coords));
1789:   } else {
1790:     PetscCall(DMGetCoordinateDM(dm, &cdm));
1791:     PetscCall(DMGetCoordinateSection(dm, &cs));
1792:     PetscCall(DMGetCoordinatesLocalNoncollective(dm, &coordinates));
1793:     PetscCall(DMPlexVecRestoreClosure(cdm, cs, coordinates, cell, Nc, coords));
1794:   }
1795:   PetscFunctionReturn(PETSC_SUCCESS);
1796: }

1798: static PetscErrorCode DMPlexComputeLineGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1799: {
1800:   const PetscScalar *array;
1801:   PetscScalar       *coords = NULL;
1802:   PetscInt           numCoords, d;
1803:   PetscBool          isDG;

1805:   PetscFunctionBegin;
1806:   PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
1807:   PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
1808:   *detJ = 0.0;
1809:   if (numCoords == 6) {
1810:     const PetscInt dim = 3;
1811:     PetscReal      R[9], J0;

1813:     if (v0) {
1814:       for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
1815:     }
1816:     PetscCall(DMPlexComputeProjection3Dto1D(coords, R));
1817:     if (J) {
1818:       J0   = 0.5 * PetscRealPart(coords[1]);
1819:       J[0] = R[0] * J0;
1820:       J[1] = R[1];
1821:       J[2] = R[2];
1822:       J[3] = R[3] * J0;
1823:       J[4] = R[4];
1824:       J[5] = R[5];
1825:       J[6] = R[6] * J0;
1826:       J[7] = R[7];
1827:       J[8] = R[8];
1828:       DMPlex_Det3D_Internal(detJ, J);
1829:       if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
1830:     }
1831:   } else if (numCoords == 4) {
1832:     const PetscInt dim = 2;
1833:     PetscReal      R[4], J0;

1835:     if (v0) {
1836:       for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
1837:     }
1838:     PetscCall(DMPlexComputeProjection2Dto1D(coords, R));
1839:     if (J) {
1840:       J0   = 0.5 * PetscRealPart(coords[1]);
1841:       J[0] = R[0] * J0;
1842:       J[1] = R[1];
1843:       J[2] = R[2] * J0;
1844:       J[3] = R[3];
1845:       DMPlex_Det2D_Internal(detJ, J);
1846:       if (invJ) DMPlex_Invert2D_Internal(invJ, J, *detJ);
1847:     }
1848:   } else if (numCoords == 2) {
1849:     const PetscInt dim = 1;

1851:     if (v0) {
1852:       for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
1853:     }
1854:     if (J) {
1855:       J[0]  = 0.5 * (PetscRealPart(coords[1]) - PetscRealPart(coords[0]));
1856:       *detJ = J[0];
1857:       PetscCall(PetscLogFlops(2.0));
1858:       if (invJ) {
1859:         invJ[0] = 1.0 / J[0];
1860:         PetscCall(PetscLogFlops(1.0));
1861:       }
1862:     }
1863:   } 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);
1864:   PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
1865:   PetscFunctionReturn(PETSC_SUCCESS);
1866: }

1868: static PetscErrorCode DMPlexComputeTriangleGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1869: {
1870:   const PetscScalar *array;
1871:   PetscScalar       *coords = NULL;
1872:   PetscInt           numCoords, d;
1873:   PetscBool          isDG;

1875:   PetscFunctionBegin;
1876:   PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
1877:   PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
1878:   *detJ = 0.0;
1879:   if (numCoords == 9) {
1880:     const PetscInt dim = 3;
1881:     PetscReal      R[9], J0[9] = {1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0};

1883:     if (v0) {
1884:       for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
1885:     }
1886:     PetscCall(DMPlexComputeProjection3Dto2D(numCoords, coords, R));
1887:     if (J) {
1888:       const PetscInt pdim = 2;

1890:       for (d = 0; d < pdim; d++) {
1891:         for (PetscInt f = 0; f < pdim; f++) J0[d * dim + f] = 0.5 * (PetscRealPart(coords[(f + 1) * pdim + d]) - PetscRealPart(coords[0 * pdim + d]));
1892:       }
1893:       PetscCall(PetscLogFlops(8.0));
1894:       DMPlex_Det3D_Internal(detJ, J0);
1895:       for (d = 0; d < dim; d++) {
1896:         for (PetscInt f = 0; f < dim; f++) {
1897:           J[d * dim + f] = 0.0;
1898:           for (PetscInt g = 0; g < dim; g++) J[d * dim + f] += R[d * dim + g] * J0[g * dim + f];
1899:         }
1900:       }
1901:       PetscCall(PetscLogFlops(18.0));
1902:     }
1903:     if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
1904:   } else if (numCoords == 6) {
1905:     const PetscInt dim = 2;

1907:     if (v0) {
1908:       for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
1909:     }
1910:     if (J) {
1911:       for (d = 0; d < dim; d++) {
1912:         for (PetscInt f = 0; f < dim; f++) J[d * dim + f] = 0.5 * (PetscRealPart(coords[(f + 1) * dim + d]) - PetscRealPart(coords[0 * dim + d]));
1913:       }
1914:       PetscCall(PetscLogFlops(8.0));
1915:       DMPlex_Det2D_Internal(detJ, J);
1916:     }
1917:     if (invJ) DMPlex_Invert2D_Internal(invJ, J, *detJ);
1918:   } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this triangle is %" PetscInt_FMT " != 6 or 9", numCoords);
1919:   PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
1920:   PetscFunctionReturn(PETSC_SUCCESS);
1921: }

1923: static PetscErrorCode DMPlexComputeRectangleGeometry_Internal(DM dm, PetscInt e, PetscBool isTensor, PetscInt Nq, const PetscReal points[], PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1924: {
1925:   const PetscScalar *array;
1926:   PetscScalar       *coords = NULL;
1927:   PetscInt           numCoords, d;
1928:   PetscBool          isDG;

1930:   PetscFunctionBegin;
1931:   PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
1932:   PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
1933:   if (!Nq) {
1934:     PetscInt vorder[4] = {0, 1, 2, 3};

1936:     if (isTensor) {
1937:       vorder[2] = 3;
1938:       vorder[3] = 2;
1939:     }
1940:     *detJ = 0.0;
1941:     if (numCoords == 12) {
1942:       const PetscInt dim = 3;
1943:       PetscReal      R[9], J0[9] = {1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0};

1945:       if (v) {
1946:         for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);
1947:       }
1948:       PetscCall(DMPlexComputeProjection3Dto2D(numCoords, coords, R));
1949:       if (J) {
1950:         const PetscInt pdim = 2;

1952:         for (d = 0; d < pdim; d++) {
1953:           J0[d * dim + 0] = 0.5 * (PetscRealPart(coords[vorder[1] * pdim + d]) - PetscRealPart(coords[vorder[0] * pdim + d]));
1954:           J0[d * dim + 1] = 0.5 * (PetscRealPart(coords[vorder[2] * pdim + d]) - PetscRealPart(coords[vorder[1] * pdim + d]));
1955:         }
1956:         PetscCall(PetscLogFlops(8.0));
1957:         DMPlex_Det3D_Internal(detJ, J0);
1958:         for (d = 0; d < dim; d++) {
1959:           for (PetscInt f = 0; f < dim; f++) {
1960:             J[d * dim + f] = 0.0;
1961:             for (PetscInt g = 0; g < dim; g++) J[d * dim + f] += R[d * dim + g] * J0[g * dim + f];
1962:           }
1963:         }
1964:         PetscCall(PetscLogFlops(18.0));
1965:       }
1966:       if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
1967:     } else if (numCoords == 8) {
1968:       const PetscInt dim = 2;

1970:       if (v) {
1971:         for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);
1972:       }
1973:       if (J) {
1974:         for (d = 0; d < dim; d++) {
1975:           J[d * dim + 0] = 0.5 * (PetscRealPart(coords[vorder[1] * dim + d]) - PetscRealPart(coords[vorder[0] * dim + d]));
1976:           J[d * dim + 1] = 0.5 * (PetscRealPart(coords[vorder[3] * dim + d]) - PetscRealPart(coords[vorder[0] * dim + d]));
1977:         }
1978:         PetscCall(PetscLogFlops(8.0));
1979:         DMPlex_Det2D_Internal(detJ, J);
1980:       }
1981:       if (invJ) DMPlex_Invert2D_Internal(invJ, J, *detJ);
1982:     } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this quadrilateral is %" PetscInt_FMT " != 8 or 12", numCoords);
1983:   } else {
1984:     const PetscInt Nv         = 4;
1985:     const PetscInt dimR       = 2;
1986:     PetscInt       zToPlex[4] = {0, 1, 3, 2};
1987:     PetscReal      zOrder[12];
1988:     PetscReal      zCoeff[12];
1989:     PetscInt       i, j, k, l, dim;

1991:     if (isTensor) {
1992:       zToPlex[2] = 2;
1993:       zToPlex[3] = 3;
1994:     }
1995:     if (numCoords == 12) {
1996:       dim = 3;
1997:     } else if (numCoords == 8) {
1998:       dim = 2;
1999:     } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this quadrilateral is %" PetscInt_FMT " != 8 or 12", numCoords);
2000:     for (i = 0; i < Nv; i++) {
2001:       PetscInt zi = zToPlex[i];

2003:       for (j = 0; j < dim; j++) zOrder[dim * i + j] = PetscRealPart(coords[dim * zi + j]);
2004:     }
2005:     for (j = 0; j < dim; j++) {
2006:       /* Nodal basis for evaluation at the vertices: (1 \mp xi) (1 \mp eta):
2007:            \phi^0 = (1 - xi - eta + xi eta) --> 1      = 1/4 ( \phi^0 + \phi^1 + \phi^2 + \phi^3)
2008:            \phi^1 = (1 + xi - eta - xi eta) --> xi     = 1/4 (-\phi^0 + \phi^1 - \phi^2 + \phi^3)
2009:            \phi^2 = (1 - xi + eta - xi eta) --> eta    = 1/4 (-\phi^0 - \phi^1 + \phi^2 + \phi^3)
2010:            \phi^3 = (1 + xi + eta + xi eta) --> xi eta = 1/4 ( \phi^0 - \phi^1 - \phi^2 + \phi^3)
2011:       */
2012:       zCoeff[dim * 0 + j] = 0.25 * (zOrder[dim * 0 + j] + zOrder[dim * 1 + j] + zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
2013:       zCoeff[dim * 1 + j] = 0.25 * (-zOrder[dim * 0 + j] + zOrder[dim * 1 + j] - zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
2014:       zCoeff[dim * 2 + j] = 0.25 * (-zOrder[dim * 0 + j] - zOrder[dim * 1 + j] + zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
2015:       zCoeff[dim * 3 + j] = 0.25 * (zOrder[dim * 0 + j] - zOrder[dim * 1 + j] - zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
2016:     }
2017:     for (i = 0; i < Nq; i++) {
2018:       PetscReal xi = points[dimR * i], eta = points[dimR * i + 1];

2020:       if (v) {
2021:         PetscReal extPoint[4];

2023:         extPoint[0] = 1.;
2024:         extPoint[1] = xi;
2025:         extPoint[2] = eta;
2026:         extPoint[3] = xi * eta;
2027:         for (j = 0; j < dim; j++) {
2028:           PetscReal val = 0.;

2030:           for (k = 0; k < Nv; k++) val += extPoint[k] * zCoeff[dim * k + j];
2031:           v[i * dim + j] = val;
2032:         }
2033:       }
2034:       if (J) {
2035:         PetscReal extJ[8];

2037:         extJ[0] = 0.;
2038:         extJ[1] = 0.;
2039:         extJ[2] = 1.;
2040:         extJ[3] = 0.;
2041:         extJ[4] = 0.;
2042:         extJ[5] = 1.;
2043:         extJ[6] = eta;
2044:         extJ[7] = xi;
2045:         for (j = 0; j < dim; j++) {
2046:           for (k = 0; k < dimR; k++) {
2047:             PetscReal val = 0.;

2049:             for (l = 0; l < Nv; l++) val += zCoeff[dim * l + j] * extJ[dimR * l + k];
2050:             J[i * dim * dim + dim * j + k] = val;
2051:           }
2052:         }
2053:         if (dim == 3) { /* put the cross product in the third component of the Jacobian */
2054:           PetscReal  x, y, z;
2055:           PetscReal *iJ = &J[i * dim * dim];
2056:           PetscReal  norm;

2058:           x     = iJ[1 * dim + 0] * iJ[2 * dim + 1] - iJ[1 * dim + 1] * iJ[2 * dim + 0];
2059:           y     = iJ[0 * dim + 1] * iJ[2 * dim + 0] - iJ[0 * dim + 0] * iJ[2 * dim + 1];
2060:           z     = iJ[0 * dim + 0] * iJ[1 * dim + 1] - iJ[0 * dim + 1] * iJ[1 * dim + 0];
2061:           norm  = PetscSqrtReal(x * x + y * y + z * z);
2062:           iJ[2] = x / norm;
2063:           iJ[5] = y / norm;
2064:           iJ[8] = z / norm;
2065:           DMPlex_Det3D_Internal(&detJ[i], &J[i * dim * dim]);
2066:           if (invJ) DMPlex_Invert3D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);
2067:         } else {
2068:           DMPlex_Det2D_Internal(&detJ[i], &J[i * dim * dim]);
2069:           if (invJ) DMPlex_Invert2D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);
2070:         }
2071:       }
2072:     }
2073:   }
2074:   PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
2075:   PetscFunctionReturn(PETSC_SUCCESS);
2076: }

2078: static PetscErrorCode DMPlexComputeTetrahedronGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
2079: {
2080:   const PetscScalar *array;
2081:   PetscScalar       *coords = NULL;
2082:   const PetscInt     dim    = 3;
2083:   PetscInt           numCoords, d;
2084:   PetscBool          isDG;

2086:   PetscFunctionBegin;
2087:   PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
2088:   PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
2089:   *detJ = 0.0;
2090:   if (v0) {
2091:     for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
2092:   }
2093:   if (J) {
2094:     for (d = 0; d < dim; d++) {
2095:       /* I orient with outward face normals */
2096:       J[d * dim + 0] = 0.5 * (PetscRealPart(coords[2 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2097:       J[d * dim + 1] = 0.5 * (PetscRealPart(coords[1 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2098:       J[d * dim + 2] = 0.5 * (PetscRealPart(coords[3 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2099:     }
2100:     PetscCall(PetscLogFlops(18.0));
2101:     DMPlex_Det3D_Internal(detJ, J);
2102:   }
2103:   if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
2104:   PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
2105:   PetscFunctionReturn(PETSC_SUCCESS);
2106: }

2108: static PetscErrorCode DMPlexComputeHexahedronGeometry_Internal(DM dm, PetscInt e, PetscInt Nq, const PetscReal points[], PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
2109: {
2110:   const PetscScalar *array;
2111:   PetscScalar       *coords = NULL;
2112:   const PetscInt     dim    = 3;
2113:   PetscInt           numCoords, d;
2114:   PetscBool          isDG;

2116:   PetscFunctionBegin;
2117:   PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
2118:   PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
2119:   if (!Nq) {
2120:     *detJ = 0.0;
2121:     if (v) {
2122:       for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);
2123:     }
2124:     if (J) {
2125:       for (d = 0; d < dim; d++) {
2126:         J[d * dim + 0] = 0.5 * (PetscRealPart(coords[3 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2127:         J[d * dim + 1] = 0.5 * (PetscRealPart(coords[1 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2128:         J[d * dim + 2] = 0.5 * (PetscRealPart(coords[4 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2129:       }
2130:       PetscCall(PetscLogFlops(18.0));
2131:       DMPlex_Det3D_Internal(detJ, J);
2132:     }
2133:     if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
2134:   } else {
2135:     const PetscInt Nv         = 8;
2136:     const PetscInt zToPlex[8] = {0, 3, 1, 2, 4, 5, 7, 6};
2137:     const PetscInt dim        = 3;
2138:     const PetscInt dimR       = 3;
2139:     PetscReal      zOrder[24];
2140:     PetscReal      zCoeff[24];
2141:     PetscInt       i, j, k, l;

2143:     for (i = 0; i < Nv; i++) {
2144:       PetscInt zi = zToPlex[i];

2146:       for (j = 0; j < dim; j++) zOrder[dim * i + j] = PetscRealPart(coords[dim * zi + j]);
2147:     }
2148:     for (j = 0; j < dim; j++) {
2149:       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]);
2150:       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]);
2151:       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]);
2152:       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]);
2153:       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]);
2154:       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]);
2155:       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]);
2156:       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]);
2157:     }
2158:     for (i = 0; i < Nq; i++) {
2159:       PetscReal xi = points[dimR * i], eta = points[dimR * i + 1], theta = points[dimR * i + 2];

2161:       if (v) {
2162:         PetscReal extPoint[8];

2164:         extPoint[0] = 1.;
2165:         extPoint[1] = xi;
2166:         extPoint[2] = eta;
2167:         extPoint[3] = xi * eta;
2168:         extPoint[4] = theta;
2169:         extPoint[5] = theta * xi;
2170:         extPoint[6] = theta * eta;
2171:         extPoint[7] = theta * eta * xi;
2172:         for (j = 0; j < dim; j++) {
2173:           PetscReal val = 0.;

2175:           for (k = 0; k < Nv; k++) val += extPoint[k] * zCoeff[dim * k + j];
2176:           v[i * dim + j] = val;
2177:         }
2178:       }
2179:       if (J) {
2180:         PetscReal extJ[24];

2182:         extJ[0]  = 0.;
2183:         extJ[1]  = 0.;
2184:         extJ[2]  = 0.;
2185:         extJ[3]  = 1.;
2186:         extJ[4]  = 0.;
2187:         extJ[5]  = 0.;
2188:         extJ[6]  = 0.;
2189:         extJ[7]  = 1.;
2190:         extJ[8]  = 0.;
2191:         extJ[9]  = eta;
2192:         extJ[10] = xi;
2193:         extJ[11] = 0.;
2194:         extJ[12] = 0.;
2195:         extJ[13] = 0.;
2196:         extJ[14] = 1.;
2197:         extJ[15] = theta;
2198:         extJ[16] = 0.;
2199:         extJ[17] = xi;
2200:         extJ[18] = 0.;
2201:         extJ[19] = theta;
2202:         extJ[20] = eta;
2203:         extJ[21] = theta * eta;
2204:         extJ[22] = theta * xi;
2205:         extJ[23] = eta * xi;

2207:         for (j = 0; j < dim; j++) {
2208:           for (k = 0; k < dimR; k++) {
2209:             PetscReal val = 0.;

2211:             for (l = 0; l < Nv; l++) val += zCoeff[dim * l + j] * extJ[dimR * l + k];
2212:             J[i * dim * dim + dim * j + k] = val;
2213:           }
2214:         }
2215:         DMPlex_Det3D_Internal(&detJ[i], &J[i * dim * dim]);
2216:         if (invJ) DMPlex_Invert3D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);
2217:       }
2218:     }
2219:   }
2220:   PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
2221:   PetscFunctionReturn(PETSC_SUCCESS);
2222: }

2224: static PetscErrorCode DMPlexComputeTriangularPrismGeometry_Internal(DM dm, PetscInt e, PetscInt Nq, const PetscReal points[], PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
2225: {
2226:   const PetscScalar *array;
2227:   PetscScalar       *coords = NULL;
2228:   const PetscInt     dim    = 3;
2229:   PetscInt           numCoords, d;
2230:   PetscBool          isDG;

2232:   PetscFunctionBegin;
2233:   PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
2234:   PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
2235:   if (!Nq) {
2236:     /* Assume that the map to the reference is affine */
2237:     *detJ = 0.0;
2238:     if (v) {
2239:       for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);
2240:     }
2241:     if (J) {
2242:       for (d = 0; d < dim; d++) {
2243:         J[d * dim + 0] = 0.5 * (PetscRealPart(coords[2 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2244:         J[d * dim + 1] = 0.5 * (PetscRealPart(coords[1 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2245:         J[d * dim + 2] = 0.5 * (PetscRealPart(coords[4 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2246:       }
2247:       PetscCall(PetscLogFlops(18.0));
2248:       DMPlex_Det3D_Internal(detJ, J);
2249:     }
2250:     if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
2251:   } else {
2252:     const PetscInt dim  = 3;
2253:     const PetscInt dimR = 3;
2254:     const PetscInt Nv   = 6;
2255:     PetscReal      verts[18];
2256:     PetscReal      coeff[18];
2257:     PetscInt       i, j, k, l;

2259:     for (i = 0; i < Nv; ++i)
2260:       for (j = 0; j < dim; ++j) verts[dim * i + j] = PetscRealPart(coords[dim * i + j]);
2261:     for (j = 0; j < dim; ++j) {
2262:       /* Check for triangle,
2263:            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)
2264:            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)
2265:            phi^2 =  1/2 (1 + eta)   chi^2 = delta(-1,  1)

2267:            phi^0 + phi^1 + phi^2 = 1    coef_1   = 1/2 (         chi^1 + chi^2)
2268:           -phi^0 + phi^1 - phi^2 = xi   coef_xi  = 1/2 (-chi^0 + chi^1)
2269:           -phi^0 - phi^1 + phi^2 = eta  coef_eta = 1/2 (-chi^0         + chi^2)

2271:           < chi_0 chi_1 chi_2> A /  1  1  1 \ / phi_0 \   <chi> I <phi>^T  so we need the inverse transpose
2272:                                  | -1  1 -1 | | phi_1 | =
2273:                                  \ -1 -1  1 / \ phi_2 /

2275:           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
2276:       */
2277:       /* Nodal basis for evaluation at the vertices: {-xi - eta, 1 + xi, 1 + eta} (1 \mp zeta):
2278:            \phi^0 = 1/4 (   -xi - eta        + xi zeta + eta zeta) --> /  1  1  1  1  1  1 \ 1
2279:            \phi^1 = 1/4 (1      + eta - zeta           - eta zeta) --> | -1  1 -1 -1 -1  1 | eta
2280:            \phi^2 = 1/4 (1 + xi       - zeta - xi zeta)            --> | -1 -1  1 -1  1 -1 | xi
2281:            \phi^3 = 1/4 (   -xi - eta        - xi zeta - eta zeta) --> | -1 -1 -1  1  1  1 | zeta
2282:            \phi^4 = 1/4 (1 + xi       + zeta + xi zeta)            --> |  1  1 -1 -1  1 -1 | xi zeta
2283:            \phi^5 = 1/4 (1      + eta + zeta           + eta zeta) --> \  1 -1  1 -1 -1  1 / eta zeta
2284:            1/4 /  0  1  1  0  1  1 \
2285:                | -1  1  0 -1  0  1 |
2286:                | -1  0  1 -1  1  0 |
2287:                |  0 -1 -1  0  1  1 |
2288:                |  1  0 -1 -1  1  0 |
2289:                \  1 -1  0 -1  0  1 /
2290:       */
2291:       coeff[dim * 0 + j] = (1. / 4.) * (verts[dim * 1 + j] + verts[dim * 2 + j] + verts[dim * 4 + j] + verts[dim * 5 + j]);
2292:       coeff[dim * 1 + j] = (1. / 4.) * (-verts[dim * 0 + j] + verts[dim * 1 + j] - verts[dim * 3 + j] + verts[dim * 5 + j]);
2293:       coeff[dim * 2 + j] = (1. / 4.) * (-verts[dim * 0 + j] + verts[dim * 2 + j] - verts[dim * 3 + j] + verts[dim * 4 + j]);
2294:       coeff[dim * 3 + j] = (1. / 4.) * (-verts[dim * 1 + j] - verts[dim * 2 + j] + verts[dim * 4 + j] + verts[dim * 5 + j]);
2295:       coeff[dim * 4 + j] = (1. / 4.) * (verts[dim * 0 + j] - verts[dim * 2 + j] - verts[dim * 3 + j] + verts[dim * 4 + j]);
2296:       coeff[dim * 5 + j] = (1. / 4.) * (verts[dim * 0 + j] - verts[dim * 1 + j] - verts[dim * 3 + j] + verts[dim * 5 + j]);
2297:       /* For reference prism:
2298:       {0, 0, 0}
2299:       {0, 1, 0}
2300:       {1, 0, 0}
2301:       {0, 0, 1}
2302:       {0, 0, 0}
2303:       {0, 0, 0}
2304:       */
2305:     }
2306:     for (i = 0; i < Nq; ++i) {
2307:       const PetscReal xi = points[dimR * i], eta = points[dimR * i + 1], zeta = points[dimR * i + 2];

2309:       if (v) {
2310:         PetscReal extPoint[6];
2311:         PetscInt  c;

2313:         extPoint[0] = 1.;
2314:         extPoint[1] = eta;
2315:         extPoint[2] = xi;
2316:         extPoint[3] = zeta;
2317:         extPoint[4] = xi * zeta;
2318:         extPoint[5] = eta * zeta;
2319:         for (c = 0; c < dim; ++c) {
2320:           PetscReal val = 0.;

2322:           for (k = 0; k < Nv; ++k) val += extPoint[k] * coeff[k * dim + c];
2323:           v[i * dim + c] = val;
2324:         }
2325:       }
2326:       if (J) {
2327:         PetscReal extJ[18];

2329:         extJ[0]  = 0.;
2330:         extJ[1]  = 0.;
2331:         extJ[2]  = 0.;
2332:         extJ[3]  = 0.;
2333:         extJ[4]  = 1.;
2334:         extJ[5]  = 0.;
2335:         extJ[6]  = 1.;
2336:         extJ[7]  = 0.;
2337:         extJ[8]  = 0.;
2338:         extJ[9]  = 0.;
2339:         extJ[10] = 0.;
2340:         extJ[11] = 1.;
2341:         extJ[12] = zeta;
2342:         extJ[13] = 0.;
2343:         extJ[14] = xi;
2344:         extJ[15] = 0.;
2345:         extJ[16] = zeta;
2346:         extJ[17] = eta;

2348:         for (j = 0; j < dim; j++) {
2349:           for (k = 0; k < dimR; k++) {
2350:             PetscReal val = 0.;

2352:             for (l = 0; l < Nv; l++) val += coeff[dim * l + j] * extJ[dimR * l + k];
2353:             J[i * dim * dim + dim * j + k] = val;
2354:           }
2355:         }
2356:         DMPlex_Det3D_Internal(&detJ[i], &J[i * dim * dim]);
2357:         if (invJ) DMPlex_Invert3D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);
2358:       }
2359:     }
2360:   }
2361:   PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
2362:   PetscFunctionReturn(PETSC_SUCCESS);
2363: }

2365: static PetscErrorCode DMPlexComputeCellGeometryFEM_Implicit(DM dm, PetscInt cell, PetscQuadrature quad, PetscReal *v, PetscReal *J, PetscReal *invJ, PetscReal *detJ)
2366: {
2367:   DMPolytopeType   ct;
2368:   PetscInt         depth, dim, coordDim, coneSize, i;
2369:   PetscInt         Nq     = 0;
2370:   const PetscReal *points = NULL;
2371:   DMLabel          depthLabel;
2372:   PetscReal        xi0[3]   = {-1., -1., -1.}, v0[3], J0[9], detJ0;
2373:   PetscBool        isAffine = PETSC_TRUE;

2375:   PetscFunctionBegin;
2376:   PetscCall(DMPlexGetDepth(dm, &depth));
2377:   PetscCall(DMPlexGetConeSize(dm, cell, &coneSize));
2378:   PetscCall(DMPlexGetDepthLabel(dm, &depthLabel));
2379:   PetscCall(DMLabelGetValue(depthLabel, cell, &dim));
2380:   if (depth == 1 && dim == 1) PetscCall(DMGetDimension(dm, &dim));
2381:   PetscCall(DMGetCoordinateDim(dm, &coordDim));
2382:   PetscCheck(coordDim <= 3, PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported coordinate dimension %" PetscInt_FMT " > 3", coordDim);
2383:   if (quad) PetscCall(PetscQuadratureGetData(quad, NULL, NULL, &Nq, &points, NULL));
2384:   PetscCall(DMPlexGetCellType(dm, cell, &ct));
2385:   switch (ct) {
2386:   case DM_POLYTOPE_POINT:
2387:     PetscCall(DMPlexComputePointGeometry_Internal(dm, cell, v, J, invJ, detJ));
2388:     isAffine = PETSC_FALSE;
2389:     break;
2390:   case DM_POLYTOPE_SEGMENT:
2391:   case DM_POLYTOPE_POINT_PRISM_TENSOR:
2392:     if (Nq) PetscCall(DMPlexComputeLineGeometry_Internal(dm, cell, v0, J0, NULL, &detJ0));
2393:     else PetscCall(DMPlexComputeLineGeometry_Internal(dm, cell, v, J, invJ, detJ));
2394:     break;
2395:   case DM_POLYTOPE_TRIANGLE:
2396:     if (Nq) PetscCall(DMPlexComputeTriangleGeometry_Internal(dm, cell, v0, J0, NULL, &detJ0));
2397:     else PetscCall(DMPlexComputeTriangleGeometry_Internal(dm, cell, v, J, invJ, detJ));
2398:     break;
2399:   case DM_POLYTOPE_QUADRILATERAL:
2400:     PetscCall(DMPlexComputeRectangleGeometry_Internal(dm, cell, PETSC_FALSE, Nq, points, v, J, invJ, detJ));
2401:     isAffine = PETSC_FALSE;
2402:     break;
2403:   case DM_POLYTOPE_SEG_PRISM_TENSOR:
2404:     PetscCall(DMPlexComputeRectangleGeometry_Internal(dm, cell, PETSC_TRUE, Nq, points, v, J, invJ, detJ));
2405:     isAffine = PETSC_FALSE;
2406:     break;
2407:   case DM_POLYTOPE_TETRAHEDRON:
2408:     if (Nq) PetscCall(DMPlexComputeTetrahedronGeometry_Internal(dm, cell, v0, J0, NULL, &detJ0));
2409:     else PetscCall(DMPlexComputeTetrahedronGeometry_Internal(dm, cell, v, J, invJ, detJ));
2410:     break;
2411:   case DM_POLYTOPE_HEXAHEDRON:
2412:     PetscCall(DMPlexComputeHexahedronGeometry_Internal(dm, cell, Nq, points, v, J, invJ, detJ));
2413:     isAffine = PETSC_FALSE;
2414:     break;
2415:   case DM_POLYTOPE_TRI_PRISM:
2416:     PetscCall(DMPlexComputeTriangularPrismGeometry_Internal(dm, cell, Nq, points, v, J, invJ, detJ));
2417:     isAffine = PETSC_FALSE;
2418:     break;
2419:   default:
2420:     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))]);
2421:   }
2422:   if (isAffine && Nq) {
2423:     if (v) {
2424:       for (i = 0; i < Nq; i++) CoordinatesRefToReal(coordDim, dim, xi0, v0, J0, &points[dim * i], &v[coordDim * i]);
2425:     }
2426:     if (detJ) {
2427:       for (i = 0; i < Nq; i++) detJ[i] = detJ0;
2428:     }
2429:     if (J) {
2430:       PetscInt k;

2432:       for (i = 0, k = 0; i < Nq; i++) {
2433:         PetscInt j;

2435:         for (j = 0; j < coordDim * coordDim; j++, k++) J[k] = J0[j];
2436:       }
2437:     }
2438:     if (invJ) {
2439:       PetscInt k;
2440:       switch (coordDim) {
2441:       case 0:
2442:         break;
2443:       case 1:
2444:         invJ[0] = 1. / J0[0];
2445:         break;
2446:       case 2:
2447:         DMPlex_Invert2D_Internal(invJ, J0, detJ0);
2448:         break;
2449:       case 3:
2450:         DMPlex_Invert3D_Internal(invJ, J0, detJ0);
2451:         break;
2452:       }
2453:       for (i = 1, k = coordDim * coordDim; i < Nq; i++) {
2454:         PetscInt j;

2456:         for (j = 0; j < coordDim * coordDim; j++, k++) invJ[k] = invJ[j];
2457:       }
2458:     }
2459:   }
2460:   PetscFunctionReturn(PETSC_SUCCESS);
2461: }

2463: /*@C
2464:   DMPlexComputeCellGeometryAffineFEM - Assuming an affine map, compute the Jacobian, inverse Jacobian, and Jacobian determinant for a given cell

2466:   Collective

2468:   Input Parameters:
2469: + dm   - the `DMPLEX`
2470: - cell - the cell

2472:   Output Parameters:
2473: + v0   - the translation part of this affine transform, meaning the translation to the origin (not the first vertex of the reference cell)
2474: . J    - the Jacobian of the transform from the reference element
2475: . invJ - the inverse of the Jacobian
2476: - detJ - the Jacobian determinant

2478:   Level: advanced

2480: .seealso: `DMPLEX`, `DMPlexComputeCellGeometryFEM()`, `DMGetCoordinateSection()`, `DMGetCoordinates()`
2481: @*/
2482: PetscErrorCode DMPlexComputeCellGeometryAffineFEM(DM dm, PetscInt cell, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
2483: {
2484:   PetscFunctionBegin;
2485:   PetscCall(DMPlexComputeCellGeometryFEM_Implicit(dm, cell, NULL, v0, J, invJ, detJ));
2486:   PetscFunctionReturn(PETSC_SUCCESS);
2487: }

2489: static PetscErrorCode DMPlexComputeCellGeometryFEM_FE(DM dm, PetscFE fe, PetscInt point, PetscQuadrature quad, PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
2490: {
2491:   const PetscScalar *array;
2492:   PetscScalar       *coords = NULL;
2493:   PetscInt           numCoords;
2494:   PetscBool          isDG;
2495:   PetscQuadrature    feQuad;
2496:   const PetscReal   *quadPoints;
2497:   PetscTabulation    T;
2498:   PetscInt           dim, cdim, pdim, qdim, Nq, q;

2500:   PetscFunctionBegin;
2501:   PetscCall(DMGetDimension(dm, &dim));
2502:   PetscCall(DMGetCoordinateDim(dm, &cdim));
2503:   PetscCall(DMPlexGetCellCoordinates(dm, point, &isDG, &numCoords, &array, &coords));
2504:   if (!quad) { /* use the first point of the first functional of the dual space */
2505:     PetscDualSpace dsp;

2507:     PetscCall(PetscFEGetDualSpace(fe, &dsp));
2508:     PetscCall(PetscDualSpaceGetFunctional(dsp, 0, &quad));
2509:     PetscCall(PetscQuadratureGetData(quad, &qdim, NULL, &Nq, &quadPoints, NULL));
2510:     Nq = 1;
2511:   } else {
2512:     PetscCall(PetscQuadratureGetData(quad, &qdim, NULL, &Nq, &quadPoints, NULL));
2513:   }
2514:   PetscCall(PetscFEGetDimension(fe, &pdim));
2515:   PetscCall(PetscFEGetQuadrature(fe, &feQuad));
2516:   if (feQuad == quad) {
2517:     PetscCall(PetscFEGetCellTabulation(fe, J ? 1 : 0, &T));
2518:     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);
2519:   } else {
2520:     PetscCall(PetscFECreateTabulation(fe, 1, Nq, quadPoints, J ? 1 : 0, &T));
2521:   }
2522:   PetscCheck(qdim == dim, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Point dimension %" PetscInt_FMT " != quadrature dimension %" PetscInt_FMT, dim, qdim);
2523:   {
2524:     const PetscReal *basis    = T->T[0];
2525:     const PetscReal *basisDer = T->T[1];
2526:     PetscReal        detJt;

2528:     PetscAssert(Nq == T->Np, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Np %" PetscInt_FMT " != %" PetscInt_FMT, Nq, T->Np);
2529:     PetscAssert(pdim == T->Nb, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Nb %" PetscInt_FMT " != %" PetscInt_FMT, pdim, T->Nb);
2530:     PetscAssert(cdim == T->Nc, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Nc %" PetscInt_FMT " != %" PetscInt_FMT, cdim, T->Nc);
2531:     PetscAssert(dim == T->cdim, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "cdim %" PetscInt_FMT " != %" PetscInt_FMT, dim, T->cdim);
2532:     if (v) {
2533:       PetscCall(PetscArrayzero(v, Nq * cdim));
2534:       for (q = 0; q < Nq; ++q) {
2535:         PetscInt i, k;

2537:         for (k = 0; k < pdim; ++k) {
2538:           const PetscInt vertex = k / cdim;
2539:           for (i = 0; i < cdim; ++i) v[q * cdim + i] += basis[(q * pdim + k) * cdim + i] * PetscRealPart(coords[vertex * cdim + i]);
2540:         }
2541:         PetscCall(PetscLogFlops(2.0 * pdim * cdim));
2542:       }
2543:     }
2544:     if (J) {
2545:       PetscCall(PetscArrayzero(J, Nq * cdim * cdim));
2546:       for (q = 0; q < Nq; ++q) {
2547:         PetscInt i, j, k, c, r;

2549:         /* J = dx_i/d\xi_j = sum[k=0,n-1] dN_k/d\xi_j * x_i(k) */
2550:         for (k = 0; k < pdim; ++k) {
2551:           const PetscInt vertex = k / cdim;
2552:           for (j = 0; j < dim; ++j) {
2553:             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]);
2554:           }
2555:         }
2556:         PetscCall(PetscLogFlops(2.0 * pdim * dim * cdim));
2557:         if (cdim > dim) {
2558:           for (c = dim; c < cdim; ++c)
2559:             for (r = 0; r < cdim; ++r) J[r * cdim + c] = r == c ? 1.0 : 0.0;
2560:         }
2561:         if (!detJ && !invJ) continue;
2562:         detJt = 0.;
2563:         switch (cdim) {
2564:         case 3:
2565:           DMPlex_Det3D_Internal(&detJt, &J[q * cdim * dim]);
2566:           if (invJ) DMPlex_Invert3D_Internal(&invJ[q * cdim * dim], &J[q * cdim * dim], detJt);
2567:           break;
2568:         case 2:
2569:           DMPlex_Det2D_Internal(&detJt, &J[q * cdim * dim]);
2570:           if (invJ) DMPlex_Invert2D_Internal(&invJ[q * cdim * dim], &J[q * cdim * dim], detJt);
2571:           break;
2572:         case 1:
2573:           detJt = J[q * cdim * dim];
2574:           if (invJ) invJ[q * cdim * dim] = 1.0 / detJt;
2575:         }
2576:         if (detJ) detJ[q] = detJt;
2577:       }
2578:     } else PetscCheck(!detJ && !invJ, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Need J to compute invJ or detJ");
2579:   }
2580:   if (feQuad != quad) PetscCall(PetscTabulationDestroy(&T));
2581:   PetscCall(DMPlexRestoreCellCoordinates(dm, point, &isDG, &numCoords, &array, &coords));
2582:   PetscFunctionReturn(PETSC_SUCCESS);
2583: }

2585: /*@C
2586:   DMPlexComputeCellGeometryFEM - Compute the Jacobian, inverse Jacobian, and Jacobian determinant at each quadrature point in the given cell

2588:   Collective

2590:   Input Parameters:
2591: + dm   - the `DMPLEX`
2592: . cell - the cell
2593: - quad - the quadrature containing the points in the reference element where the geometry will be evaluated.  If `quad` is `NULL`, geometry will be
2594:          evaluated at the first vertex of the reference element

2596:   Output Parameters:
2597: + v    - the image of the transformed quadrature points, otherwise the image of the first vertex in the closure of the reference element
2598: . J    - the Jacobian of the transform from the reference element at each quadrature point
2599: . invJ - the inverse of the Jacobian at each quadrature point
2600: - detJ - the Jacobian determinant at each quadrature point

2602:   Level: advanced

2604:   Note:
2605:   Implicit cell geometry must be used when the topological mesh dimension is not equal to the coordinate dimension, for instance for embedded manifolds.

2607: .seealso: `DMPLEX`, `DMGetCoordinateSection()`, `DMGetCoordinates()`
2608: @*/
2609: PetscErrorCode DMPlexComputeCellGeometryFEM(DM dm, PetscInt cell, PetscQuadrature quad, PetscReal *v, PetscReal J[], PetscReal invJ[], PetscReal *detJ)
2610: {
2611:   DM       cdm;
2612:   PetscFE  fe = NULL;
2613:   PetscInt dim, cdim;

2615:   PetscFunctionBegin;
2616:   PetscAssertPointer(detJ, 7);
2617:   PetscCall(DMGetDimension(dm, &dim));
2618:   PetscCall(DMGetCoordinateDim(dm, &cdim));
2619:   PetscCall(DMGetCoordinateDM(dm, &cdm));
2620:   if (cdm) {
2621:     PetscClassId id;
2622:     PetscInt     numFields;
2623:     PetscDS      prob;
2624:     PetscObject  disc;

2626:     PetscCall(DMGetNumFields(cdm, &numFields));
2627:     if (numFields) {
2628:       PetscCall(DMGetDS(cdm, &prob));
2629:       PetscCall(PetscDSGetDiscretization(prob, 0, &disc));
2630:       PetscCall(PetscObjectGetClassId(disc, &id));
2631:       if (id == PETSCFE_CLASSID) fe = (PetscFE)disc;
2632:     }
2633:   }
2634:   if (!fe || (dim != cdim)) PetscCall(DMPlexComputeCellGeometryFEM_Implicit(dm, cell, quad, v, J, invJ, detJ));
2635:   else PetscCall(DMPlexComputeCellGeometryFEM_FE(dm, fe, cell, quad, v, J, invJ, detJ));
2636:   PetscFunctionReturn(PETSC_SUCCESS);
2637: }

2639: static PetscErrorCode DMPlexComputeGeometryFVM_0D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
2640: {
2641:   PetscSection       coordSection;
2642:   Vec                coordinates;
2643:   const PetscScalar *coords = NULL;
2644:   PetscInt           d, dof, off;

2646:   PetscFunctionBegin;
2647:   PetscCall(DMGetCoordinatesLocal(dm, &coordinates));
2648:   PetscCall(DMGetCoordinateSection(dm, &coordSection));
2649:   PetscCall(VecGetArrayRead(coordinates, &coords));

2651:   /* for a point the centroid is just the coord */
2652:   if (centroid) {
2653:     PetscCall(PetscSectionGetDof(coordSection, cell, &dof));
2654:     PetscCall(PetscSectionGetOffset(coordSection, cell, &off));
2655:     for (d = 0; d < dof; d++) centroid[d] = PetscRealPart(coords[off + d]);
2656:   }
2657:   if (normal) {
2658:     const PetscInt *support, *cones;
2659:     PetscInt        supportSize;
2660:     PetscReal       norm, sign;

2662:     /* compute the norm based upon the support centroids */
2663:     PetscCall(DMPlexGetSupportSize(dm, cell, &supportSize));
2664:     PetscCall(DMPlexGetSupport(dm, cell, &support));
2665:     PetscCall(DMPlexComputeCellGeometryFVM(dm, support[0], NULL, normal, NULL));

2667:     /* Take the normal from the centroid of the support to the vertex*/
2668:     PetscCall(PetscSectionGetDof(coordSection, cell, &dof));
2669:     PetscCall(PetscSectionGetOffset(coordSection, cell, &off));
2670:     for (d = 0; d < dof; d++) normal[d] -= PetscRealPart(coords[off + d]);

2672:     /* Determine the sign of the normal based upon its location in the support */
2673:     PetscCall(DMPlexGetCone(dm, support[0], &cones));
2674:     sign = cones[0] == cell ? 1.0 : -1.0;

2676:     norm = DMPlex_NormD_Internal(dim, normal);
2677:     for (d = 0; d < dim; ++d) normal[d] /= (norm * sign);
2678:   }
2679:   if (vol) *vol = 1.0;
2680:   PetscCall(VecRestoreArrayRead(coordinates, &coords));
2681:   PetscFunctionReturn(PETSC_SUCCESS);
2682: }

2684: static PetscErrorCode DMPlexComputeGeometryFVM_1D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
2685: {
2686:   const PetscScalar *array;
2687:   PetscScalar       *coords = NULL;
2688:   PetscInt           cdim, coordSize, d;
2689:   PetscBool          isDG;

2691:   PetscFunctionBegin;
2692:   PetscCall(DMGetCoordinateDim(dm, &cdim));
2693:   PetscCall(DMPlexGetCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
2694:   PetscCheck(coordSize == cdim * 2, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Edge has %" PetscInt_FMT " coordinates != %" PetscInt_FMT, coordSize, cdim * 2);
2695:   if (centroid) {
2696:     for (d = 0; d < cdim; ++d) centroid[d] = 0.5 * PetscRealPart(coords[d] + coords[cdim + d]);
2697:   }
2698:   if (normal) {
2699:     PetscReal norm;

2701:     switch (cdim) {
2702:     case 3:
2703:       normal[2] = 0.; /* fall through */
2704:     case 2:
2705:       normal[0] = -PetscRealPart(coords[1] - coords[cdim + 1]);
2706:       normal[1] = PetscRealPart(coords[0] - coords[cdim + 0]);
2707:       break;
2708:     case 1:
2709:       normal[0] = 1.0;
2710:       break;
2711:     default:
2712:       SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Dimension %" PetscInt_FMT " not supported", cdim);
2713:     }
2714:     norm = DMPlex_NormD_Internal(cdim, normal);
2715:     for (d = 0; d < cdim; ++d) normal[d] /= norm;
2716:   }
2717:   if (vol) {
2718:     *vol = 0.0;
2719:     for (d = 0; d < cdim; ++d) *vol += PetscSqr(PetscRealPart(coords[d] - coords[cdim + d]));
2720:     *vol = PetscSqrtReal(*vol);
2721:   }
2722:   PetscCall(DMPlexRestoreCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
2723:   PetscFunctionReturn(PETSC_SUCCESS);
2724: }

2726: /* Centroid_i = (\sum_n A_n Cn_i) / A */
2727: static PetscErrorCode DMPlexComputeGeometryFVM_2D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
2728: {
2729:   DMPolytopeType     ct;
2730:   const PetscScalar *array;
2731:   PetscScalar       *coords = NULL;
2732:   PetscInt           coordSize;
2733:   PetscBool          isDG;
2734:   PetscInt           fv[4] = {0, 1, 2, 3};
2735:   PetscInt           cdim, numCorners, p, d;

2737:   PetscFunctionBegin;
2738:   /* Must check for hybrid cells because prisms have a different orientation scheme */
2739:   PetscCall(DMPlexGetCellType(dm, cell, &ct));
2740:   switch (ct) {
2741:   case DM_POLYTOPE_SEG_PRISM_TENSOR:
2742:     fv[2] = 3;
2743:     fv[3] = 2;
2744:     break;
2745:   default:
2746:     break;
2747:   }
2748:   PetscCall(DMGetCoordinateDim(dm, &cdim));
2749:   PetscCall(DMPlexGetConeSize(dm, cell, &numCorners));
2750:   PetscCall(DMPlexGetCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
2751:   {
2752:     PetscReal c[3] = {0., 0., 0.}, n[3] = {0., 0., 0.}, origin[3] = {0., 0., 0.}, norm;

2754:     for (d = 0; d < cdim; d++) origin[d] = PetscRealPart(coords[d]);
2755:     for (p = 0; p < numCorners - 2; ++p) {
2756:       PetscReal e0[3] = {0., 0., 0.}, e1[3] = {0., 0., 0.};
2757:       for (d = 0; d < cdim; d++) {
2758:         e0[d] = PetscRealPart(coords[cdim * fv[p + 1] + d]) - origin[d];
2759:         e1[d] = PetscRealPart(coords[cdim * fv[p + 2] + d]) - origin[d];
2760:       }
2761:       const PetscReal dx = e0[1] * e1[2] - e0[2] * e1[1];
2762:       const PetscReal dy = e0[2] * e1[0] - e0[0] * e1[2];
2763:       const PetscReal dz = e0[0] * e1[1] - e0[1] * e1[0];
2764:       const PetscReal a  = PetscSqrtReal(dx * dx + dy * dy + dz * dz);

2766:       n[0] += dx;
2767:       n[1] += dy;
2768:       n[2] += dz;
2769:       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.;
2770:     }
2771:     norm = PetscSqrtReal(n[0] * n[0] + n[1] * n[1] + n[2] * n[2]);
2772:     // Allow zero volume cells
2773:     if (norm != 0) {
2774:       n[0] /= norm;
2775:       n[1] /= norm;
2776:       n[2] /= norm;
2777:       c[0] /= norm;
2778:       c[1] /= norm;
2779:       c[2] /= norm;
2780:     }
2781:     if (vol) *vol = 0.5 * norm;
2782:     if (centroid)
2783:       for (d = 0; d < cdim; ++d) centroid[d] = c[d];
2784:     if (normal)
2785:       for (d = 0; d < cdim; ++d) normal[d] = n[d];
2786:   }
2787:   PetscCall(DMPlexRestoreCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
2788:   PetscFunctionReturn(PETSC_SUCCESS);
2789: }

2791: /* Centroid_i = (\sum_n V_n Cn_i) / V */
2792: static PetscErrorCode DMPlexComputeGeometryFVM_3D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
2793: {
2794:   DMPolytopeType        ct;
2795:   const PetscScalar    *array;
2796:   PetscScalar          *coords = NULL;
2797:   PetscInt              coordSize;
2798:   PetscBool             isDG;
2799:   PetscReal             vsum      = 0.0, vtmp, coordsTmp[3 * 3], origin[3];
2800:   const PetscInt        order[16] = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15};
2801:   const PetscInt       *cone, *faceSizes, *faces;
2802:   const DMPolytopeType *faceTypes;
2803:   PetscBool             isHybrid = PETSC_FALSE;
2804:   PetscInt              numFaces, f, fOff = 0, p, d;

2806:   PetscFunctionBegin;
2807:   PetscCheck(dim <= 3, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "No support for dim %" PetscInt_FMT " > 3", dim);
2808:   /* Must check for hybrid cells because prisms have a different orientation scheme */
2809:   PetscCall(DMPlexGetCellType(dm, cell, &ct));
2810:   switch (ct) {
2811:   case DM_POLYTOPE_POINT_PRISM_TENSOR:
2812:   case DM_POLYTOPE_SEG_PRISM_TENSOR:
2813:   case DM_POLYTOPE_TRI_PRISM_TENSOR:
2814:   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
2815:     isHybrid = PETSC_TRUE;
2816:   default:
2817:     break;
2818:   }

2820:   if (centroid)
2821:     for (d = 0; d < dim; ++d) centroid[d] = 0.0;
2822:   PetscCall(DMPlexGetCone(dm, cell, &cone));

2824:   // Using the closure of faces for coordinates does not work in periodic geometries, so we index into the cell coordinates
2825:   PetscCall(DMPlexGetRawFaces_Internal(dm, ct, order, &numFaces, &faceTypes, &faceSizes, &faces));
2826:   PetscCall(DMPlexGetCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
2827:   for (f = 0; f < numFaces; ++f) {
2828:     PetscBool flip = isHybrid && f == 0 ? PETSC_TRUE : PETSC_FALSE; /* The first hybrid face is reversed */

2830:     // If using zero as the origin vertex for each tetrahedron, an element far from the origin will have positive and
2831:     // negative volumes that nearly cancel, thus incurring rounding error. Here we define origin[] as the first vertex
2832:     // so that all tetrahedra have positive volume.
2833:     if (f == 0)
2834:       for (d = 0; d < dim; d++) origin[d] = PetscRealPart(coords[d]);
2835:     switch (faceTypes[f]) {
2836:     case DM_POLYTOPE_TRIANGLE:
2837:       for (d = 0; d < dim; ++d) {
2838:         coordsTmp[0 * dim + d] = PetscRealPart(coords[faces[fOff + 0] * dim + d]) - origin[d];
2839:         coordsTmp[1 * dim + d] = PetscRealPart(coords[faces[fOff + 1] * dim + d]) - origin[d];
2840:         coordsTmp[2 * dim + d] = PetscRealPart(coords[faces[fOff + 2] * dim + d]) - origin[d];
2841:       }
2842:       Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
2843:       if (flip) vtmp = -vtmp;
2844:       vsum += vtmp;
2845:       if (centroid) { /* Centroid of OABC = (a+b+c)/4 */
2846:         for (d = 0; d < dim; ++d) {
2847:           for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p * dim + d] * vtmp;
2848:         }
2849:       }
2850:       break;
2851:     case DM_POLYTOPE_QUADRILATERAL:
2852:     case DM_POLYTOPE_SEG_PRISM_TENSOR: {
2853:       PetscInt fv[4] = {0, 1, 2, 3};

2855:       /* Side faces for hybrid cells are stored as tensor products */
2856:       if (isHybrid && f > 1) {
2857:         fv[2] = 3;
2858:         fv[3] = 2;
2859:       }
2860:       /* DO FOR PYRAMID */
2861:       /* First tet */
2862:       for (d = 0; d < dim; ++d) {
2863:         coordsTmp[0 * dim + d] = PetscRealPart(coords[faces[fOff + fv[0]] * dim + d]) - origin[d];
2864:         coordsTmp[1 * dim + d] = PetscRealPart(coords[faces[fOff + fv[1]] * dim + d]) - origin[d];
2865:         coordsTmp[2 * dim + d] = PetscRealPart(coords[faces[fOff + fv[3]] * dim + d]) - origin[d];
2866:       }
2867:       Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
2868:       if (flip) vtmp = -vtmp;
2869:       vsum += vtmp;
2870:       if (centroid) {
2871:         for (d = 0; d < dim; ++d) {
2872:           for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p * dim + d] * vtmp;
2873:         }
2874:       }
2875:       /* Second tet */
2876:       for (d = 0; d < dim; ++d) {
2877:         coordsTmp[0 * dim + d] = PetscRealPart(coords[faces[fOff + fv[1]] * dim + d]) - origin[d];
2878:         coordsTmp[1 * dim + d] = PetscRealPart(coords[faces[fOff + fv[2]] * dim + d]) - origin[d];
2879:         coordsTmp[2 * dim + d] = PetscRealPart(coords[faces[fOff + fv[3]] * dim + d]) - origin[d];
2880:       }
2881:       Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
2882:       if (flip) vtmp = -vtmp;
2883:       vsum += vtmp;
2884:       if (centroid) {
2885:         for (d = 0; d < dim; ++d) {
2886:           for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p * dim + d] * vtmp;
2887:         }
2888:       }
2889:       break;
2890:     }
2891:     default:
2892:       SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Cannot handle face %" PetscInt_FMT " of type %s", cone[f], DMPolytopeTypes[ct]);
2893:     }
2894:     fOff += faceSizes[f];
2895:   }
2896:   PetscCall(DMPlexRestoreRawFaces_Internal(dm, ct, order, &numFaces, &faceTypes, &faceSizes, &faces));
2897:   PetscCall(DMPlexRestoreCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
2898:   if (vol) *vol = PetscAbsReal(vsum);
2899:   if (normal)
2900:     for (d = 0; d < dim; ++d) normal[d] = 0.0;
2901:   if (centroid)
2902:     for (d = 0; d < dim; ++d) centroid[d] = centroid[d] / (vsum * 4) + origin[d];
2903:   PetscFunctionReturn(PETSC_SUCCESS);
2904: }

2906: /*@C
2907:   DMPlexComputeCellGeometryFVM - Compute the volume for a given cell

2909:   Collective

2911:   Input Parameters:
2912: + dm   - the `DMPLEX`
2913: - cell - the cell

2915:   Output Parameters:
2916: + vol      - the cell volume
2917: . centroid - the cell centroid
2918: - normal   - the cell normal, if appropriate

2920:   Level: advanced

2922: .seealso: `DMPLEX`, `DMGetCoordinateSection()`, `DMGetCoordinates()`
2923: @*/
2924: PetscErrorCode DMPlexComputeCellGeometryFVM(DM dm, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
2925: {
2926:   PetscInt depth, dim;

2928:   PetscFunctionBegin;
2929:   PetscCall(DMPlexGetDepth(dm, &depth));
2930:   PetscCall(DMGetDimension(dm, &dim));
2931:   PetscCheck(depth == dim, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Mesh must be interpolated");
2932:   PetscCall(DMPlexGetPointDepth(dm, cell, &depth));
2933:   switch (depth) {
2934:   case 0:
2935:     PetscCall(DMPlexComputeGeometryFVM_0D_Internal(dm, dim, cell, vol, centroid, normal));
2936:     break;
2937:   case 1:
2938:     PetscCall(DMPlexComputeGeometryFVM_1D_Internal(dm, dim, cell, vol, centroid, normal));
2939:     break;
2940:   case 2:
2941:     PetscCall(DMPlexComputeGeometryFVM_2D_Internal(dm, dim, cell, vol, centroid, normal));
2942:     break;
2943:   case 3:
2944:     PetscCall(DMPlexComputeGeometryFVM_3D_Internal(dm, dim, cell, vol, centroid, normal));
2945:     break;
2946:   default:
2947:     SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported dimension %" PetscInt_FMT " (depth %" PetscInt_FMT ") for element geometry computation", dim, depth);
2948:   }
2949:   PetscFunctionReturn(PETSC_SUCCESS);
2950: }

2952: /*@
2953:   DMPlexComputeGeometryFVM - Computes the cell and face geometry for a finite volume method

2955:   Input Parameter:
2956: . dm - The `DMPLEX`

2958:   Output Parameters:
2959: + cellgeom - A `Vec` of `PetscFVCellGeom` data
2960: - facegeom - A `Vec` of `PetscFVFaceGeom` data

2962:   Level: developer

2964: .seealso: `DMPLEX`, `PetscFVFaceGeom`, `PetscFVCellGeom`
2965: @*/
2966: PetscErrorCode DMPlexComputeGeometryFVM(DM dm, Vec *cellgeom, Vec *facegeom)
2967: {
2968:   DM           dmFace, dmCell;
2969:   DMLabel      ghostLabel;
2970:   PetscSection sectionFace, sectionCell;
2971:   PetscSection coordSection;
2972:   Vec          coordinates;
2973:   PetscScalar *fgeom, *cgeom;
2974:   PetscReal    minradius, gminradius;
2975:   PetscInt     dim, cStart, cEnd, cEndInterior, c, fStart, fEnd, f;

2977:   PetscFunctionBegin;
2978:   PetscCall(DMGetDimension(dm, &dim));
2979:   PetscCall(DMGetCoordinateSection(dm, &coordSection));
2980:   PetscCall(DMGetCoordinatesLocal(dm, &coordinates));
2981:   /* Make cell centroids and volumes */
2982:   PetscCall(DMClone(dm, &dmCell));
2983:   PetscCall(DMSetCoordinateSection(dmCell, PETSC_DETERMINE, coordSection));
2984:   PetscCall(DMSetCoordinatesLocal(dmCell, coordinates));
2985:   PetscCall(PetscSectionCreate(PetscObjectComm((PetscObject)dm), &sectionCell));
2986:   PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
2987:   PetscCall(DMPlexGetCellTypeStratum(dm, DM_POLYTOPE_FV_GHOST, &cEndInterior, NULL));
2988:   PetscCall(PetscSectionSetChart(sectionCell, cStart, cEnd));
2989:   for (c = cStart; c < cEnd; ++c) PetscCall(PetscSectionSetDof(sectionCell, c, (PetscInt)PetscCeilReal(((PetscReal)sizeof(PetscFVCellGeom)) / sizeof(PetscScalar))));
2990:   PetscCall(PetscSectionSetUp(sectionCell));
2991:   PetscCall(DMSetLocalSection(dmCell, sectionCell));
2992:   PetscCall(PetscSectionDestroy(&sectionCell));
2993:   PetscCall(DMCreateLocalVector(dmCell, cellgeom));
2994:   if (cEndInterior < 0) cEndInterior = cEnd;
2995:   PetscCall(VecGetArray(*cellgeom, &cgeom));
2996:   for (c = cStart; c < cEndInterior; ++c) {
2997:     PetscFVCellGeom *cg;

2999:     PetscCall(DMPlexPointLocalRef(dmCell, c, cgeom, &cg));
3000:     PetscCall(PetscArrayzero(cg, 1));
3001:     PetscCall(DMPlexComputeCellGeometryFVM(dmCell, c, &cg->volume, cg->centroid, NULL));
3002:   }
3003:   /* Compute face normals and minimum cell radius */
3004:   PetscCall(DMClone(dm, &dmFace));
3005:   PetscCall(PetscSectionCreate(PetscObjectComm((PetscObject)dm), &sectionFace));
3006:   PetscCall(DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd));
3007:   PetscCall(PetscSectionSetChart(sectionFace, fStart, fEnd));
3008:   for (f = fStart; f < fEnd; ++f) PetscCall(PetscSectionSetDof(sectionFace, f, (PetscInt)PetscCeilReal(((PetscReal)sizeof(PetscFVFaceGeom)) / sizeof(PetscScalar))));
3009:   PetscCall(PetscSectionSetUp(sectionFace));
3010:   PetscCall(DMSetLocalSection(dmFace, sectionFace));
3011:   PetscCall(PetscSectionDestroy(&sectionFace));
3012:   PetscCall(DMCreateLocalVector(dmFace, facegeom));
3013:   PetscCall(VecGetArray(*facegeom, &fgeom));
3014:   PetscCall(DMGetLabel(dm, "ghost", &ghostLabel));
3015:   minradius = PETSC_MAX_REAL;
3016:   for (f = fStart; f < fEnd; ++f) {
3017:     PetscFVFaceGeom *fg;
3018:     PetscReal        area;
3019:     const PetscInt  *cells;
3020:     PetscInt         ncells, ghost = -1, d, numChildren;

3022:     if (ghostLabel) PetscCall(DMLabelGetValue(ghostLabel, f, &ghost));
3023:     PetscCall(DMPlexGetTreeChildren(dm, f, &numChildren, NULL));
3024:     PetscCall(DMPlexGetSupport(dm, f, &cells));
3025:     PetscCall(DMPlexGetSupportSize(dm, f, &ncells));
3026:     /* It is possible to get a face with no support when using partition overlap */
3027:     if (!ncells || ghost >= 0 || numChildren) continue;
3028:     PetscCall(DMPlexPointLocalRef(dmFace, f, fgeom, &fg));
3029:     PetscCall(DMPlexComputeCellGeometryFVM(dm, f, &area, fg->centroid, fg->normal));
3030:     for (d = 0; d < dim; ++d) fg->normal[d] *= area;
3031:     /* Flip face orientation if necessary to match ordering in support, and Update minimum radius */
3032:     {
3033:       PetscFVCellGeom *cL, *cR;
3034:       PetscReal       *lcentroid, *rcentroid;
3035:       PetscReal        l[3], r[3], v[3];

3037:       PetscCall(DMPlexPointLocalRead(dmCell, cells[0], cgeom, &cL));
3038:       lcentroid = cells[0] >= cEndInterior ? fg->centroid : cL->centroid;
3039:       if (ncells > 1) {
3040:         PetscCall(DMPlexPointLocalRead(dmCell, cells[1], cgeom, &cR));
3041:         rcentroid = cells[1] >= cEndInterior ? fg->centroid : cR->centroid;
3042:       } else {
3043:         rcentroid = fg->centroid;
3044:       }
3045:       PetscCall(DMLocalizeCoordinateReal_Internal(dm, dim, fg->centroid, lcentroid, l));
3046:       PetscCall(DMLocalizeCoordinateReal_Internal(dm, dim, fg->centroid, rcentroid, r));
3047:       DMPlex_WaxpyD_Internal(dim, -1, l, r, v);
3048:       if (DMPlex_DotRealD_Internal(dim, fg->normal, v) < 0) {
3049:         for (d = 0; d < dim; ++d) fg->normal[d] = -fg->normal[d];
3050:       }
3051:       if (DMPlex_DotRealD_Internal(dim, fg->normal, v) <= 0) {
3052:         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]);
3053:         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]);
3054:         SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Direction for face %" PetscInt_FMT " could not be fixed", f);
3055:       }
3056:       if (cells[0] < cEndInterior) {
3057:         DMPlex_WaxpyD_Internal(dim, -1, fg->centroid, cL->centroid, v);
3058:         minradius = PetscMin(minradius, DMPlex_NormD_Internal(dim, v));
3059:       }
3060:       if (ncells > 1 && cells[1] < cEndInterior) {
3061:         DMPlex_WaxpyD_Internal(dim, -1, fg->centroid, cR->centroid, v);
3062:         minradius = PetscMin(minradius, DMPlex_NormD_Internal(dim, v));
3063:       }
3064:     }
3065:   }
3066:   PetscCallMPI(MPIU_Allreduce(&minradius, &gminradius, 1, MPIU_REAL, MPIU_MIN, PetscObjectComm((PetscObject)dm)));
3067:   PetscCall(DMPlexSetMinRadius(dm, gminradius));
3068:   /* Compute centroids of ghost cells */
3069:   for (c = cEndInterior; c < cEnd; ++c) {
3070:     PetscFVFaceGeom *fg;
3071:     const PetscInt  *cone, *support;
3072:     PetscInt         coneSize, supportSize, s;

3074:     PetscCall(DMPlexGetConeSize(dmCell, c, &coneSize));
3075:     PetscCheck(coneSize == 1, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Ghost cell %" PetscInt_FMT " has cone size %" PetscInt_FMT " != 1", c, coneSize);
3076:     PetscCall(DMPlexGetCone(dmCell, c, &cone));
3077:     PetscCall(DMPlexGetSupportSize(dmCell, cone[0], &supportSize));
3078:     PetscCheck(supportSize == 2, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Face %" PetscInt_FMT " has support size %" PetscInt_FMT " != 2", cone[0], supportSize);
3079:     PetscCall(DMPlexGetSupport(dmCell, cone[0], &support));
3080:     PetscCall(DMPlexPointLocalRef(dmFace, cone[0], fgeom, &fg));
3081:     for (s = 0; s < 2; ++s) {
3082:       /* Reflect ghost centroid across plane of face */
3083:       if (support[s] == c) {
3084:         PetscFVCellGeom *ci;
3085:         PetscFVCellGeom *cg;
3086:         PetscReal        c2f[3], a;

3088:         PetscCall(DMPlexPointLocalRead(dmCell, support[(s + 1) % 2], cgeom, &ci));
3089:         DMPlex_WaxpyD_Internal(dim, -1, ci->centroid, fg->centroid, c2f); /* cell to face centroid */
3090:         a = DMPlex_DotRealD_Internal(dim, c2f, fg->normal) / DMPlex_DotRealD_Internal(dim, fg->normal, fg->normal);
3091:         PetscCall(DMPlexPointLocalRef(dmCell, support[s], cgeom, &cg));
3092:         DMPlex_WaxpyD_Internal(dim, 2 * a, fg->normal, ci->centroid, cg->centroid);
3093:         cg->volume = ci->volume;
3094:       }
3095:     }
3096:   }
3097:   PetscCall(VecRestoreArray(*facegeom, &fgeom));
3098:   PetscCall(VecRestoreArray(*cellgeom, &cgeom));
3099:   PetscCall(DMDestroy(&dmCell));
3100:   PetscCall(DMDestroy(&dmFace));
3101:   PetscFunctionReturn(PETSC_SUCCESS);
3102: }

3104: /*@
3105:   DMPlexGetMinRadius - Returns the minimum distance from any cell centroid to a face

3107:   Not Collective

3109:   Input Parameter:
3110: . dm - the `DMPLEX`

3112:   Output Parameter:
3113: . minradius - the minimum cell radius

3115:   Level: developer

3117: .seealso: `DMPLEX`, `DMGetCoordinates()`
3118: @*/
3119: PetscErrorCode DMPlexGetMinRadius(DM dm, PetscReal *minradius)
3120: {
3121:   PetscFunctionBegin;
3123:   PetscAssertPointer(minradius, 2);
3124:   *minradius = ((DM_Plex *)dm->data)->minradius;
3125:   PetscFunctionReturn(PETSC_SUCCESS);
3126: }

3128: /*@
3129:   DMPlexSetMinRadius - Sets the minimum distance from the cell centroid to a face

3131:   Logically Collective

3133:   Input Parameters:
3134: + dm        - the `DMPLEX`
3135: - minradius - the minimum cell radius

3137:   Level: developer

3139: .seealso: `DMPLEX`, `DMSetCoordinates()`
3140: @*/
3141: PetscErrorCode DMPlexSetMinRadius(DM dm, PetscReal minradius)
3142: {
3143:   PetscFunctionBegin;
3145:   ((DM_Plex *)dm->data)->minradius = minradius;
3146:   PetscFunctionReturn(PETSC_SUCCESS);
3147: }

3149: /*@C
3150:   DMPlexGetCoordinateMap - Returns the function used to map coordinates of newly generated mesh points

3152:   Not Collective

3154:   Input Parameter:
3155: . dm - the `DMPLEX`

3157:   Output Parameter:
3158: . coordFunc - the mapping function

3160:   Level: developer

3162:   Note:
3163:   This function maps from the gnerated 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,

3165: .seealso: `DMPLEX`, `DMGetCoordinates()`, `DMPlexSetCoordinateMap()`
3166: @*/
3167: PetscErrorCode DMPlexGetCoordinateMap(DM dm, PetscPointFunc *coordFunc)
3168: {
3169:   PetscFunctionBegin;
3171:   PetscAssertPointer(coordFunc, 2);
3172:   *coordFunc = ((DM_Plex *)dm->data)->coordFunc;
3173:   PetscFunctionReturn(PETSC_SUCCESS);
3174: }

3176: /*@C
3177:   DMPlexSetCoordinateMap - Sets the function used to map coordinates of newly generated mesh points

3179:   Logically Collective

3181:   Input Parameters:
3182: + dm        - the `DMPLEX`
3183: - coordFunc - the mapping function

3185:   Level: developer

3187:   Note:
3188:   This function maps from the gnerated 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,

3190: .seealso: `DMPLEX`, `DMSetCoordinates()`, `DMPlexGetCoordinateMap()`
3191: @*/
3192: PetscErrorCode DMPlexSetCoordinateMap(DM dm, PetscPointFunc coordFunc)
3193: {
3194:   PetscFunctionBegin;
3196:   ((DM_Plex *)dm->data)->coordFunc = coordFunc;
3197:   PetscFunctionReturn(PETSC_SUCCESS);
3198: }

3200: static PetscErrorCode BuildGradientReconstruction_Internal(DM dm, PetscFV fvm, DM dmFace, PetscScalar *fgeom, DM dmCell, PetscScalar *cgeom)
3201: {
3202:   DMLabel      ghostLabel;
3203:   PetscScalar *dx, *grad, **gref;
3204:   PetscInt     dim, cStart, cEnd, c, cEndInterior, maxNumFaces;

3206:   PetscFunctionBegin;
3207:   PetscCall(DMGetDimension(dm, &dim));
3208:   PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
3209:   PetscCall(DMPlexGetCellTypeStratum(dm, DM_POLYTOPE_FV_GHOST, &cEndInterior, NULL));
3210:   cEndInterior = cEndInterior < 0 ? cEnd : cEndInterior;
3211:   PetscCall(DMPlexGetMaxSizes(dm, &maxNumFaces, NULL));
3212:   PetscCall(PetscFVLeastSquaresSetMaxFaces(fvm, maxNumFaces));
3213:   PetscCall(DMGetLabel(dm, "ghost", &ghostLabel));
3214:   PetscCall(PetscMalloc3(maxNumFaces * dim, &dx, maxNumFaces * dim, &grad, maxNumFaces, &gref));
3215:   for (c = cStart; c < cEndInterior; c++) {
3216:     const PetscInt  *faces;
3217:     PetscInt         numFaces, usedFaces, f, d;
3218:     PetscFVCellGeom *cg;
3219:     PetscBool        boundary;
3220:     PetscInt         ghost;

3222:     // do not attempt to compute a gradient reconstruction stencil in a ghost cell.  It will never be used
3223:     PetscCall(DMLabelGetValue(ghostLabel, c, &ghost));
3224:     if (ghost >= 0) continue;

3226:     PetscCall(DMPlexPointLocalRead(dmCell, c, cgeom, &cg));
3227:     PetscCall(DMPlexGetConeSize(dm, c, &numFaces));
3228:     PetscCall(DMPlexGetCone(dm, c, &faces));
3229:     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);
3230:     for (f = 0, usedFaces = 0; f < numFaces; ++f) {
3231:       PetscFVCellGeom *cg1;
3232:       PetscFVFaceGeom *fg;
3233:       const PetscInt  *fcells;
3234:       PetscInt         ncell, side;

3236:       PetscCall(DMLabelGetValue(ghostLabel, faces[f], &ghost));
3237:       PetscCall(DMIsBoundaryPoint(dm, faces[f], &boundary));
3238:       if ((ghost >= 0) || boundary) continue;
3239:       PetscCall(DMPlexGetSupport(dm, faces[f], &fcells));
3240:       side  = (c != fcells[0]); /* c is on left=0 or right=1 of face */
3241:       ncell = fcells[!side];    /* the neighbor */
3242:       PetscCall(DMPlexPointLocalRef(dmFace, faces[f], fgeom, &fg));
3243:       PetscCall(DMPlexPointLocalRead(dmCell, ncell, cgeom, &cg1));
3244:       for (d = 0; d < dim; ++d) dx[usedFaces * dim + d] = cg1->centroid[d] - cg->centroid[d];
3245:       gref[usedFaces++] = fg->grad[side]; /* Gradient reconstruction term will go here */
3246:     }
3247:     PetscCheck(usedFaces, PETSC_COMM_SELF, PETSC_ERR_USER, "Mesh contains isolated cell (no neighbors). Is it intentional?");
3248:     PetscCall(PetscFVComputeGradient(fvm, usedFaces, dx, grad));
3249:     for (f = 0, usedFaces = 0; f < numFaces; ++f) {
3250:       PetscCall(DMLabelGetValue(ghostLabel, faces[f], &ghost));
3251:       PetscCall(DMIsBoundaryPoint(dm, faces[f], &boundary));
3252:       if ((ghost >= 0) || boundary) continue;
3253:       for (d = 0; d < dim; ++d) gref[usedFaces][d] = grad[usedFaces * dim + d];
3254:       ++usedFaces;
3255:     }
3256:   }
3257:   PetscCall(PetscFree3(dx, grad, gref));
3258:   PetscFunctionReturn(PETSC_SUCCESS);
3259: }

3261: static PetscErrorCode BuildGradientReconstruction_Internal_Tree(DM dm, PetscFV fvm, DM dmFace, PetscScalar *fgeom, DM dmCell, PetscScalar *cgeom)
3262: {
3263:   DMLabel      ghostLabel;
3264:   PetscScalar *dx, *grad, **gref;
3265:   PetscInt     dim, cStart, cEnd, c, cEndInterior, fStart, fEnd, f, nStart, nEnd, maxNumFaces = 0;
3266:   PetscSection neighSec;
3267:   PetscInt (*neighbors)[2];
3268:   PetscInt *counter;

3270:   PetscFunctionBegin;
3271:   PetscCall(DMGetDimension(dm, &dim));
3272:   PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
3273:   PetscCall(DMPlexGetCellTypeStratum(dm, DM_POLYTOPE_FV_GHOST, &cEndInterior, NULL));
3274:   if (cEndInterior < 0) cEndInterior = cEnd;
3275:   PetscCall(PetscSectionCreate(PetscObjectComm((PetscObject)dm), &neighSec));
3276:   PetscCall(PetscSectionSetChart(neighSec, cStart, cEndInterior));
3277:   PetscCall(DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd));
3278:   PetscCall(DMGetLabel(dm, "ghost", &ghostLabel));
3279:   for (f = fStart; f < fEnd; f++) {
3280:     const PetscInt *fcells;
3281:     PetscBool       boundary;
3282:     PetscInt        ghost = -1;
3283:     PetscInt        numChildren, numCells, c;

3285:     if (ghostLabel) PetscCall(DMLabelGetValue(ghostLabel, f, &ghost));
3286:     PetscCall(DMIsBoundaryPoint(dm, f, &boundary));
3287:     PetscCall(DMPlexGetTreeChildren(dm, f, &numChildren, NULL));
3288:     if ((ghost >= 0) || boundary || numChildren) continue;
3289:     PetscCall(DMPlexGetSupportSize(dm, f, &numCells));
3290:     if (numCells == 2) {
3291:       PetscCall(DMPlexGetSupport(dm, f, &fcells));
3292:       for (c = 0; c < 2; c++) {
3293:         PetscInt cell = fcells[c];

3295:         if (cell >= cStart && cell < cEndInterior) PetscCall(PetscSectionAddDof(neighSec, cell, 1));
3296:       }
3297:     }
3298:   }
3299:   PetscCall(PetscSectionSetUp(neighSec));
3300:   PetscCall(PetscSectionGetMaxDof(neighSec, &maxNumFaces));
3301:   PetscCall(PetscFVLeastSquaresSetMaxFaces(fvm, maxNumFaces));
3302:   nStart = 0;
3303:   PetscCall(PetscSectionGetStorageSize(neighSec, &nEnd));
3304:   PetscCall(PetscMalloc1(nEnd - nStart, &neighbors));
3305:   PetscCall(PetscCalloc1(cEndInterior - cStart, &counter));
3306:   for (f = fStart; f < fEnd; f++) {
3307:     const PetscInt *fcells;
3308:     PetscBool       boundary;
3309:     PetscInt        ghost = -1;
3310:     PetscInt        numChildren, numCells, c;

3312:     if (ghostLabel) PetscCall(DMLabelGetValue(ghostLabel, f, &ghost));
3313:     PetscCall(DMIsBoundaryPoint(dm, f, &boundary));
3314:     PetscCall(DMPlexGetTreeChildren(dm, f, &numChildren, NULL));
3315:     if ((ghost >= 0) || boundary || numChildren) continue;
3316:     PetscCall(DMPlexGetSupportSize(dm, f, &numCells));
3317:     if (numCells == 2) {
3318:       PetscCall(DMPlexGetSupport(dm, f, &fcells));
3319:       for (c = 0; c < 2; c++) {
3320:         PetscInt cell = fcells[c], off;

3322:         if (cell >= cStart && cell < cEndInterior) {
3323:           PetscCall(PetscSectionGetOffset(neighSec, cell, &off));
3324:           off += counter[cell - cStart]++;
3325:           neighbors[off][0] = f;
3326:           neighbors[off][1] = fcells[1 - c];
3327:         }
3328:       }
3329:     }
3330:   }
3331:   PetscCall(PetscFree(counter));
3332:   PetscCall(PetscMalloc3(maxNumFaces * dim, &dx, maxNumFaces * dim, &grad, maxNumFaces, &gref));
3333:   for (c = cStart; c < cEndInterior; c++) {
3334:     PetscInt         numFaces, f, d, off, ghost = -1;
3335:     PetscFVCellGeom *cg;

3337:     PetscCall(DMPlexPointLocalRead(dmCell, c, cgeom, &cg));
3338:     PetscCall(PetscSectionGetDof(neighSec, c, &numFaces));
3339:     PetscCall(PetscSectionGetOffset(neighSec, c, &off));

3341:     // do not attempt to compute a gradient reconstruction stencil in a ghost cell.  It will never be used
3342:     if (ghostLabel) PetscCall(DMLabelGetValue(ghostLabel, c, &ghost));
3343:     if (ghost >= 0) continue;

3345:     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);
3346:     for (f = 0; f < numFaces; ++f) {
3347:       PetscFVCellGeom *cg1;
3348:       PetscFVFaceGeom *fg;
3349:       const PetscInt  *fcells;
3350:       PetscInt         ncell, side, nface;

3352:       nface = neighbors[off + f][0];
3353:       ncell = neighbors[off + f][1];
3354:       PetscCall(DMPlexGetSupport(dm, nface, &fcells));
3355:       side = (c != fcells[0]);
3356:       PetscCall(DMPlexPointLocalRef(dmFace, nface, fgeom, &fg));
3357:       PetscCall(DMPlexPointLocalRead(dmCell, ncell, cgeom, &cg1));
3358:       for (d = 0; d < dim; ++d) dx[f * dim + d] = cg1->centroid[d] - cg->centroid[d];
3359:       gref[f] = fg->grad[side]; /* Gradient reconstruction term will go here */
3360:     }
3361:     PetscCall(PetscFVComputeGradient(fvm, numFaces, dx, grad));
3362:     for (f = 0; f < numFaces; ++f) {
3363:       for (d = 0; d < dim; ++d) gref[f][d] = grad[f * dim + d];
3364:     }
3365:   }
3366:   PetscCall(PetscFree3(dx, grad, gref));
3367:   PetscCall(PetscSectionDestroy(&neighSec));
3368:   PetscCall(PetscFree(neighbors));
3369:   PetscFunctionReturn(PETSC_SUCCESS);
3370: }

3372: /*@
3373:   DMPlexComputeGradientFVM - Compute geometric factors for gradient reconstruction, which are stored in the geometry data, and compute layout for gradient data

3375:   Collective

3377:   Input Parameters:
3378: + dm           - The `DMPLEX`
3379: . fvm          - The `PetscFV`
3380: - cellGeometry - The face geometry from `DMPlexComputeCellGeometryFVM()`

3382:   Input/Output Parameter:
3383: . faceGeometry - The face geometry from `DMPlexComputeFaceGeometryFVM()`; on output
3384:                  the geometric factors for gradient calculation are inserted

3386:   Output Parameter:
3387: . dmGrad - The `DM` describing the layout of gradient data

3389:   Level: developer

3391: .seealso: `DMPLEX`, `DMPlexGetFaceGeometryFVM()`, `DMPlexGetCellGeometryFVM()`
3392: @*/
3393: PetscErrorCode DMPlexComputeGradientFVM(DM dm, PetscFV fvm, Vec faceGeometry, Vec cellGeometry, DM *dmGrad)
3394: {
3395:   DM           dmFace, dmCell;
3396:   PetscScalar *fgeom, *cgeom;
3397:   PetscSection sectionGrad, parentSection;
3398:   PetscInt     dim, pdim, cStart, cEnd, cEndInterior, c;

3400:   PetscFunctionBegin;
3401:   PetscCall(DMGetDimension(dm, &dim));
3402:   PetscCall(PetscFVGetNumComponents(fvm, &pdim));
3403:   PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
3404:   PetscCall(DMPlexGetCellTypeStratum(dm, DM_POLYTOPE_FV_GHOST, &cEndInterior, NULL));
3405:   /* Construct the interpolant corresponding to each face from the least-square solution over the cell neighborhood */
3406:   PetscCall(VecGetDM(faceGeometry, &dmFace));
3407:   PetscCall(VecGetDM(cellGeometry, &dmCell));
3408:   PetscCall(VecGetArray(faceGeometry, &fgeom));
3409:   PetscCall(VecGetArray(cellGeometry, &cgeom));
3410:   PetscCall(DMPlexGetTree(dm, &parentSection, NULL, NULL, NULL, NULL));
3411:   if (!parentSection) {
3412:     PetscCall(BuildGradientReconstruction_Internal(dm, fvm, dmFace, fgeom, dmCell, cgeom));
3413:   } else {
3414:     PetscCall(BuildGradientReconstruction_Internal_Tree(dm, fvm, dmFace, fgeom, dmCell, cgeom));
3415:   }
3416:   PetscCall(VecRestoreArray(faceGeometry, &fgeom));
3417:   PetscCall(VecRestoreArray(cellGeometry, &cgeom));
3418:   /* Create storage for gradients */
3419:   PetscCall(DMClone(dm, dmGrad));
3420:   PetscCall(PetscSectionCreate(PetscObjectComm((PetscObject)dm), &sectionGrad));
3421:   PetscCall(PetscSectionSetChart(sectionGrad, cStart, cEnd));
3422:   for (c = cStart; c < cEnd; ++c) PetscCall(PetscSectionSetDof(sectionGrad, c, pdim * dim));
3423:   PetscCall(PetscSectionSetUp(sectionGrad));
3424:   PetscCall(DMSetLocalSection(*dmGrad, sectionGrad));
3425:   PetscCall(PetscSectionDestroy(&sectionGrad));
3426:   PetscFunctionReturn(PETSC_SUCCESS);
3427: }

3429: /*@
3430:   DMPlexGetDataFVM - Retrieve precomputed cell geometry

3432:   Collective

3434:   Input Parameters:
3435: + dm - The `DM`
3436: - fv - The `PetscFV`

3438:   Output Parameters:
3439: + cellgeom - The cell geometry
3440: . facegeom - The face geometry
3441: - gradDM   - The gradient matrices

3443:   Level: developer

3445: .seealso: `DMPLEX`, `DMPlexComputeGeometryFVM()`
3446: @*/
3447: PetscErrorCode DMPlexGetDataFVM(DM dm, PetscFV fv, Vec *cellgeom, Vec *facegeom, DM *gradDM)
3448: {
3449:   PetscObject cellgeomobj, facegeomobj;

3451:   PetscFunctionBegin;
3452:   PetscCall(PetscObjectQuery((PetscObject)dm, "DMPlex_cellgeom_fvm", &cellgeomobj));
3453:   if (!cellgeomobj) {
3454:     Vec cellgeomInt, facegeomInt;

3456:     PetscCall(DMPlexComputeGeometryFVM(dm, &cellgeomInt, &facegeomInt));
3457:     PetscCall(PetscObjectCompose((PetscObject)dm, "DMPlex_cellgeom_fvm", (PetscObject)cellgeomInt));
3458:     PetscCall(PetscObjectCompose((PetscObject)dm, "DMPlex_facegeom_fvm", (PetscObject)facegeomInt));
3459:     PetscCall(VecDestroy(&cellgeomInt));
3460:     PetscCall(VecDestroy(&facegeomInt));
3461:     PetscCall(PetscObjectQuery((PetscObject)dm, "DMPlex_cellgeom_fvm", &cellgeomobj));
3462:   }
3463:   PetscCall(PetscObjectQuery((PetscObject)dm, "DMPlex_facegeom_fvm", &facegeomobj));
3464:   if (cellgeom) *cellgeom = (Vec)cellgeomobj;
3465:   if (facegeom) *facegeom = (Vec)facegeomobj;
3466:   if (gradDM) {
3467:     PetscObject gradobj;
3468:     PetscBool   computeGradients;

3470:     PetscCall(PetscFVGetComputeGradients(fv, &computeGradients));
3471:     if (!computeGradients) {
3472:       *gradDM = NULL;
3473:       PetscFunctionReturn(PETSC_SUCCESS);
3474:     }
3475:     PetscCall(PetscObjectQuery((PetscObject)dm, "DMPlex_dmgrad_fvm", &gradobj));
3476:     if (!gradobj) {
3477:       DM dmGradInt;

3479:       PetscCall(DMPlexComputeGradientFVM(dm, fv, (Vec)facegeomobj, (Vec)cellgeomobj, &dmGradInt));
3480:       PetscCall(PetscObjectCompose((PetscObject)dm, "DMPlex_dmgrad_fvm", (PetscObject)dmGradInt));
3481:       PetscCall(DMDestroy(&dmGradInt));
3482:       PetscCall(PetscObjectQuery((PetscObject)dm, "DMPlex_dmgrad_fvm", &gradobj));
3483:     }
3484:     *gradDM = (DM)gradobj;
3485:   }
3486:   PetscFunctionReturn(PETSC_SUCCESS);
3487: }

3489: static PetscErrorCode DMPlexCoordinatesToReference_NewtonUpdate(PetscInt dimC, PetscInt dimR, PetscScalar *J, PetscScalar *invJ, PetscScalar *work, PetscReal *resNeg, PetscReal *guess)
3490: {
3491:   PetscInt l, m;

3493:   PetscFunctionBeginHot;
3494:   if (dimC == dimR && dimR <= 3) {
3495:     /* invert Jacobian, multiply */
3496:     PetscScalar det, idet;

3498:     switch (dimR) {
3499:     case 1:
3500:       invJ[0] = 1. / J[0];
3501:       break;
3502:     case 2:
3503:       det     = J[0] * J[3] - J[1] * J[2];
3504:       idet    = 1. / det;
3505:       invJ[0] = J[3] * idet;
3506:       invJ[1] = -J[1] * idet;
3507:       invJ[2] = -J[2] * idet;
3508:       invJ[3] = J[0] * idet;
3509:       break;
3510:     case 3: {
3511:       invJ[0] = J[4] * J[8] - J[5] * J[7];
3512:       invJ[1] = J[2] * J[7] - J[1] * J[8];
3513:       invJ[2] = J[1] * J[5] - J[2] * J[4];
3514:       det     = invJ[0] * J[0] + invJ[1] * J[3] + invJ[2] * J[6];
3515:       idet    = 1. / det;
3516:       invJ[0] *= idet;
3517:       invJ[1] *= idet;
3518:       invJ[2] *= idet;
3519:       invJ[3] = idet * (J[5] * J[6] - J[3] * J[8]);
3520:       invJ[4] = idet * (J[0] * J[8] - J[2] * J[6]);
3521:       invJ[5] = idet * (J[2] * J[3] - J[0] * J[5]);
3522:       invJ[6] = idet * (J[3] * J[7] - J[4] * J[6]);
3523:       invJ[7] = idet * (J[1] * J[6] - J[0] * J[7]);
3524:       invJ[8] = idet * (J[0] * J[4] - J[1] * J[3]);
3525:     } break;
3526:     }
3527:     for (l = 0; l < dimR; l++) {
3528:       for (m = 0; m < dimC; m++) guess[l] += PetscRealPart(invJ[l * dimC + m]) * resNeg[m];
3529:     }
3530:   } else {
3531: #if defined(PETSC_USE_COMPLEX)
3532:     char transpose = 'C';
3533: #else
3534:     char transpose = 'T';
3535: #endif
3536:     PetscBLASInt m, n, one = 1, worksize, info;

3538:     PetscCall(PetscBLASIntCast(dimR, &m));
3539:     PetscCall(PetscBLASIntCast(dimC, &n));
3540:     PetscCall(PetscBLASIntCast(dimC * dimC, &worksize));
3541:     for (l = 0; l < dimC; l++) invJ[l] = resNeg[l];

3543:     PetscCallBLAS("LAPACKgels", LAPACKgels_(&transpose, &m, &n, &one, J, &m, invJ, &n, work, &worksize, &info));
3544:     PetscCheck(info == 0, PETSC_COMM_SELF, PETSC_ERR_LIB, "Bad argument to GELS %" PetscBLASInt_FMT, info);

3546:     for (l = 0; l < dimR; l++) guess[l] += PetscRealPart(invJ[l]);
3547:   }
3548:   PetscFunctionReturn(PETSC_SUCCESS);
3549: }

3551: static PetscErrorCode DMPlexCoordinatesToReference_Tensor(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal realCoords[], PetscReal refCoords[], Vec coords, PetscInt dimC, PetscInt dimR)
3552: {
3553:   PetscInt     coordSize, i, j, k, l, m, maxIts = 7, numV = (1 << dimR);
3554:   PetscScalar *coordsScalar = NULL;
3555:   PetscReal   *cellData, *cellCoords, *cellCoeffs, *extJ, *resNeg;
3556:   PetscScalar *J, *invJ, *work;

3558:   PetscFunctionBegin;
3560:   PetscCall(DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar));
3561:   PetscCheck(coordSize >= dimC * numV, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Expecting at least %" PetscInt_FMT " coordinates, got %" PetscInt_FMT, dimC * (1 << dimR), coordSize);
3562:   PetscCall(DMGetWorkArray(dm, 2 * coordSize + dimR + dimC, MPIU_REAL, &cellData));
3563:   PetscCall(DMGetWorkArray(dm, 3 * dimR * dimC, MPIU_SCALAR, &J));
3564:   cellCoords = &cellData[0];
3565:   cellCoeffs = &cellData[coordSize];
3566:   extJ       = &cellData[2 * coordSize];
3567:   resNeg     = &cellData[2 * coordSize + dimR];
3568:   invJ       = &J[dimR * dimC];
3569:   work       = &J[2 * dimR * dimC];
3570:   if (dimR == 2) {
3571:     const PetscInt zToPlex[4] = {0, 1, 3, 2};

3573:     for (i = 0; i < 4; i++) {
3574:       PetscInt plexI = zToPlex[i];

3576:       for (j = 0; j < dimC; j++) cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
3577:     }
3578:   } else if (dimR == 3) {
3579:     const PetscInt zToPlex[8] = {0, 3, 1, 2, 4, 5, 7, 6};

3581:     for (i = 0; i < 8; i++) {
3582:       PetscInt plexI = zToPlex[i];

3584:       for (j = 0; j < dimC; j++) cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
3585:     }
3586:   } else {
3587:     for (i = 0; i < coordSize; i++) cellCoords[i] = PetscRealPart(coordsScalar[i]);
3588:   }
3589:   /* Perform the shuffling transform that converts values at the corners of [-1,1]^d to coefficients */
3590:   for (i = 0; i < dimR; i++) {
3591:     PetscReal *swap;

3593:     for (j = 0; j < (numV / 2); j++) {
3594:       for (k = 0; k < dimC; k++) {
3595:         cellCoeffs[dimC * j + k]                = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] + cellCoords[dimC * 2 * j + k]);
3596:         cellCoeffs[dimC * (j + (numV / 2)) + k] = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] - cellCoords[dimC * 2 * j + k]);
3597:       }
3598:     }

3600:     if (i < dimR - 1) {
3601:       swap       = cellCoeffs;
3602:       cellCoeffs = cellCoords;
3603:       cellCoords = swap;
3604:     }
3605:   }
3606:   PetscCall(PetscArrayzero(refCoords, numPoints * dimR));
3607:   for (j = 0; j < numPoints; j++) {
3608:     for (i = 0; i < maxIts; i++) {
3609:       PetscReal *guess = &refCoords[dimR * j];

3611:       /* compute -residual and Jacobian */
3612:       for (k = 0; k < dimC; k++) resNeg[k] = realCoords[dimC * j + k];
3613:       for (k = 0; k < dimC * dimR; k++) J[k] = 0.;
3614:       for (k = 0; k < numV; k++) {
3615:         PetscReal extCoord = 1.;
3616:         for (l = 0; l < dimR; l++) {
3617:           PetscReal coord = guess[l];
3618:           PetscInt  dep   = (k & (1 << l)) >> l;

3620:           extCoord *= dep * coord + !dep;
3621:           extJ[l] = dep;

3623:           for (m = 0; m < dimR; m++) {
3624:             PetscReal coord = guess[m];
3625:             PetscInt  dep   = ((k & (1 << m)) >> m) && (m != l);
3626:             PetscReal mult  = dep * coord + !dep;

3628:             extJ[l] *= mult;
3629:           }
3630:         }
3631:         for (l = 0; l < dimC; l++) {
3632:           PetscReal coeff = cellCoeffs[dimC * k + l];

3634:           resNeg[l] -= coeff * extCoord;
3635:           for (m = 0; m < dimR; m++) J[dimR * l + m] += coeff * extJ[m];
3636:         }
3637:       }
3638:       if (0 && PetscDefined(USE_DEBUG)) {
3639:         PetscReal maxAbs = 0.;

3641:         for (l = 0; l < dimC; l++) maxAbs = PetscMax(maxAbs, PetscAbsReal(resNeg[l]));
3642:         PetscCall(PetscInfo(dm, "cell %" PetscInt_FMT ", point %" PetscInt_FMT ", iter %" PetscInt_FMT ": res %g\n", cell, j, i, (double)maxAbs));
3643:       }

3645:       PetscCall(DMPlexCoordinatesToReference_NewtonUpdate(dimC, dimR, J, invJ, work, resNeg, guess));
3646:     }
3647:   }
3648:   PetscCall(DMRestoreWorkArray(dm, 3 * dimR * dimC, MPIU_SCALAR, &J));
3649:   PetscCall(DMRestoreWorkArray(dm, 2 * coordSize + dimR + dimC, MPIU_REAL, &cellData));
3650:   PetscCall(DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar));
3651:   PetscFunctionReturn(PETSC_SUCCESS);
3652: }

3654: static PetscErrorCode DMPlexReferenceToCoordinates_Tensor(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal refCoords[], PetscReal realCoords[], Vec coords, PetscInt dimC, PetscInt dimR)
3655: {
3656:   PetscInt     coordSize, i, j, k, l, numV = (1 << dimR);
3657:   PetscScalar *coordsScalar = NULL;
3658:   PetscReal   *cellData, *cellCoords, *cellCoeffs;

3660:   PetscFunctionBegin;
3662:   PetscCall(DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar));
3663:   PetscCheck(coordSize >= dimC * numV, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Expecting at least %" PetscInt_FMT " coordinates, got %" PetscInt_FMT, dimC * (1 << dimR), coordSize);
3664:   PetscCall(DMGetWorkArray(dm, 2 * coordSize, MPIU_REAL, &cellData));
3665:   cellCoords = &cellData[0];
3666:   cellCoeffs = &cellData[coordSize];
3667:   if (dimR == 2) {
3668:     const PetscInt zToPlex[4] = {0, 1, 3, 2};

3670:     for (i = 0; i < 4; i++) {
3671:       PetscInt plexI = zToPlex[i];

3673:       for (j = 0; j < dimC; j++) cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
3674:     }
3675:   } else if (dimR == 3) {
3676:     const PetscInt zToPlex[8] = {0, 3, 1, 2, 4, 5, 7, 6};

3678:     for (i = 0; i < 8; i++) {
3679:       PetscInt plexI = zToPlex[i];

3681:       for (j = 0; j < dimC; j++) cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
3682:     }
3683:   } else {
3684:     for (i = 0; i < coordSize; i++) cellCoords[i] = PetscRealPart(coordsScalar[i]);
3685:   }
3686:   /* Perform the shuffling transform that converts values at the corners of [-1,1]^d to coefficients */
3687:   for (i = 0; i < dimR; i++) {
3688:     PetscReal *swap;

3690:     for (j = 0; j < (numV / 2); j++) {
3691:       for (k = 0; k < dimC; k++) {
3692:         cellCoeffs[dimC * j + k]                = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] + cellCoords[dimC * 2 * j + k]);
3693:         cellCoeffs[dimC * (j + (numV / 2)) + k] = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] - cellCoords[dimC * 2 * j + k]);
3694:       }
3695:     }

3697:     if (i < dimR - 1) {
3698:       swap       = cellCoeffs;
3699:       cellCoeffs = cellCoords;
3700:       cellCoords = swap;
3701:     }
3702:   }
3703:   PetscCall(PetscArrayzero(realCoords, numPoints * dimC));
3704:   for (j = 0; j < numPoints; j++) {
3705:     const PetscReal *guess  = &refCoords[dimR * j];
3706:     PetscReal       *mapped = &realCoords[dimC * j];

3708:     for (k = 0; k < numV; k++) {
3709:       PetscReal extCoord = 1.;
3710:       for (l = 0; l < dimR; l++) {
3711:         PetscReal coord = guess[l];
3712:         PetscInt  dep   = (k & (1 << l)) >> l;

3714:         extCoord *= dep * coord + !dep;
3715:       }
3716:       for (l = 0; l < dimC; l++) {
3717:         PetscReal coeff = cellCoeffs[dimC * k + l];

3719:         mapped[l] += coeff * extCoord;
3720:       }
3721:     }
3722:   }
3723:   PetscCall(DMRestoreWorkArray(dm, 2 * coordSize, MPIU_REAL, &cellData));
3724:   PetscCall(DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar));
3725:   PetscFunctionReturn(PETSC_SUCCESS);
3726: }

3728: 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)
3729: {
3730:   PetscInt     numComp, pdim, i, j, k, l, m, coordSize;
3731:   PetscScalar *nodes = NULL;
3732:   PetscReal   *invV, *modes;
3733:   PetscReal   *B, *D, *resNeg;
3734:   PetscScalar *J, *invJ, *work;
3735:   PetscReal    tolerance = tol == NULL ? 0.0 : *tol;

3737:   PetscFunctionBegin;
3738:   PetscCall(PetscFEGetDimension(fe, &pdim));
3739:   PetscCall(PetscFEGetNumComponents(fe, &numComp));
3740:   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);
3741:   /* we shouldn't apply inverse closure permutation, if one exists */
3742:   PetscCall(DMPlexVecGetOrientedClosure_Internal(dm, NULL, PETSC_FALSE, coords, cell, 0, &coordSize, &nodes));
3743:   /* convert nodes to values in the stable evaluation basis */
3744:   PetscCall(DMGetWorkArray(dm, pdim, MPIU_REAL, &modes));
3745:   invV = fe->invV;
3746:   for (i = 0; i < pdim; ++i) {
3747:     modes[i] = 0.;
3748:     for (j = 0; j < pdim; ++j) modes[i] += invV[i * pdim + j] * PetscRealPart(nodes[j]);
3749:   }
3750:   PetscCall(DMGetWorkArray(dm, pdim * Nc + pdim * Nc * dimR + Nc, MPIU_REAL, &B));
3751:   D      = &B[pdim * Nc];
3752:   resNeg = &D[pdim * Nc * dimR];
3753:   PetscCall(DMGetWorkArray(dm, 3 * Nc * dimR, MPIU_SCALAR, &J));
3754:   invJ = &J[Nc * dimR];
3755:   work = &invJ[Nc * dimR];
3756:   for (i = 0; i < numPoints * dimR; i++) refCoords[i] = 0.;
3757:   for (j = 0; j < numPoints; j++) {
3758:     PetscReal normPoint = DMPlex_NormD_Internal(Nc, &realCoords[j * Nc]);
3759:     normPoint           = normPoint > PETSC_SMALL ? normPoint : 1.0;
3760:     for (i = 0; i < maxIter; i++) { /* we could batch this so that we're not making big B and D arrays all the time */
3761:       PetscReal *guess = &refCoords[j * dimR], error = 0;
3762:       PetscCall(PetscSpaceEvaluate(fe->basisSpace, 1, guess, B, D, NULL));
3763:       for (k = 0; k < Nc; k++) resNeg[k] = realCoords[j * Nc + k];
3764:       for (k = 0; k < Nc * dimR; k++) J[k] = 0.;
3765:       for (k = 0; k < pdim; k++) {
3766:         for (l = 0; l < Nc; l++) {
3767:           resNeg[l] -= modes[k] * B[k * Nc + l];
3768:           for (m = 0; m < dimR; m++) J[l * dimR + m] += modes[k] * D[(k * Nc + l) * dimR + m];
3769:         }
3770:       }
3771:       if (0 && PetscDefined(USE_DEBUG)) {
3772:         PetscReal maxAbs = 0.;

3774:         for (l = 0; l < Nc; l++) maxAbs = PetscMax(maxAbs, PetscAbsReal(resNeg[l]));
3775:         PetscCall(PetscInfo(dm, "cell %" PetscInt_FMT ", point %" PetscInt_FMT ", iter %" PetscInt_FMT ": res %g\n", cell, j, i, (double)maxAbs));
3776:       }
3777:       error = DMPlex_NormD_Internal(Nc, resNeg);
3778:       if (error < tolerance * normPoint) {
3779:         if (tol) *tol = error / normPoint;
3780:         break;
3781:       }
3782:       PetscCall(DMPlexCoordinatesToReference_NewtonUpdate(Nc, dimR, J, invJ, work, resNeg, guess));
3783:     }
3784:   }
3785:   PetscCall(DMRestoreWorkArray(dm, 3 * Nc * dimR, MPIU_SCALAR, &J));
3786:   PetscCall(DMRestoreWorkArray(dm, pdim * Nc + pdim * Nc * dimR + Nc, MPIU_REAL, &B));
3787:   PetscCall(DMRestoreWorkArray(dm, pdim, MPIU_REAL, &modes));
3788:   PetscCall(DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &nodes));
3789:   PetscFunctionReturn(PETSC_SUCCESS);
3790: }

3792: /* TODO: TOBY please fix this for Nc > 1 */
3793: PetscErrorCode DMPlexReferenceToCoordinates_FE(DM dm, PetscFE fe, PetscInt cell, PetscInt numPoints, const PetscReal refCoords[], PetscReal realCoords[], Vec coords, PetscInt Nc, PetscInt dimR)
3794: {
3795:   PetscInt     numComp, pdim, i, j, k, l, coordSize;
3796:   PetscScalar *nodes = NULL;
3797:   PetscReal   *invV, *modes;
3798:   PetscReal   *B;

3800:   PetscFunctionBegin;
3801:   PetscCall(PetscFEGetDimension(fe, &pdim));
3802:   PetscCall(PetscFEGetNumComponents(fe, &numComp));
3803:   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);
3804:   /* we shouldn't apply inverse closure permutation, if one exists */
3805:   PetscCall(DMPlexVecGetOrientedClosure_Internal(dm, NULL, PETSC_FALSE, coords, cell, 0, &coordSize, &nodes));
3806:   /* convert nodes to values in the stable evaluation basis */
3807:   PetscCall(DMGetWorkArray(dm, pdim, MPIU_REAL, &modes));
3808:   invV = fe->invV;
3809:   for (i = 0; i < pdim; ++i) {
3810:     modes[i] = 0.;
3811:     for (j = 0; j < pdim; ++j) modes[i] += invV[i * pdim + j] * PetscRealPart(nodes[j]);
3812:   }
3813:   PetscCall(DMGetWorkArray(dm, numPoints * pdim * Nc, MPIU_REAL, &B));
3814:   PetscCall(PetscSpaceEvaluate(fe->basisSpace, numPoints, refCoords, B, NULL, NULL));
3815:   for (i = 0; i < numPoints * Nc; i++) realCoords[i] = 0.;
3816:   for (j = 0; j < numPoints; j++) {
3817:     PetscReal *mapped = &realCoords[j * Nc];

3819:     for (k = 0; k < pdim; k++) {
3820:       for (l = 0; l < Nc; l++) mapped[l] += modes[k] * B[(j * pdim + k) * Nc + l];
3821:     }
3822:   }
3823:   PetscCall(DMRestoreWorkArray(dm, numPoints * pdim * Nc, MPIU_REAL, &B));
3824:   PetscCall(DMRestoreWorkArray(dm, pdim, MPIU_REAL, &modes));
3825:   PetscCall(DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &nodes));
3826:   PetscFunctionReturn(PETSC_SUCCESS);
3827: }

3829: /*@
3830:   DMPlexCoordinatesToReference - Pull coordinates back from the mesh to the reference element
3831:   using a single element map.

3833:   Not Collective

3835:   Input Parameters:
3836: + dm         - The mesh, with coordinate maps defined either by a `PetscDS` for the coordinate `DM` (see `DMGetCoordinateDM()`) or
3837:                implicitly by the coordinates of the corner vertices of the cell: as an affine map for simplicial elements, or
3838:                as a multilinear map for tensor-product elements
3839: . cell       - the cell whose map is used.
3840: . numPoints  - the number of points to locate
3841: - realCoords - (numPoints x coordinate dimension) array of coordinates (see `DMGetCoordinateDim()`)

3843:   Output Parameter:
3844: . refCoords - (`numPoints` x `dimension`) array of reference coordinates (see `DMGetDimension()`)

3846:   Level: intermediate

3848:   Notes:
3849:   This inversion will be accurate inside the reference element, but may be inaccurate for
3850:   mappings that do not extend uniquely outside the reference cell (e.g, most non-affine maps)

3852: .seealso: `DMPLEX`, `DMPlexReferenceToCoordinates()`
3853: @*/
3854: PetscErrorCode DMPlexCoordinatesToReference(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal realCoords[], PetscReal refCoords[])
3855: {
3856:   PetscInt dimC, dimR, depth, cStart, cEnd, i;
3857:   DM       coordDM = NULL;
3858:   Vec      coords;
3859:   PetscFE  fe = NULL;

3861:   PetscFunctionBegin;
3863:   PetscCall(DMGetDimension(dm, &dimR));
3864:   PetscCall(DMGetCoordinateDim(dm, &dimC));
3865:   if (dimR <= 0 || dimC <= 0 || numPoints <= 0) PetscFunctionReturn(PETSC_SUCCESS);
3866:   PetscCall(DMPlexGetDepth(dm, &depth));
3867:   PetscCall(DMGetCoordinatesLocal(dm, &coords));
3868:   PetscCall(DMGetCoordinateDM(dm, &coordDM));
3869:   if (coordDM) {
3870:     PetscInt coordFields;

3872:     PetscCall(DMGetNumFields(coordDM, &coordFields));
3873:     if (coordFields) {
3874:       PetscClassId id;
3875:       PetscObject  disc;

3877:       PetscCall(DMGetField(coordDM, 0, NULL, &disc));
3878:       PetscCall(PetscObjectGetClassId(disc, &id));
3879:       if (id == PETSCFE_CLASSID) fe = (PetscFE)disc;
3880:     }
3881:   }
3882:   PetscCall(DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd));
3883:   PetscCheck(cell >= cStart && cell < cEnd, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "point %" PetscInt_FMT " not in cell range [%" PetscInt_FMT ",%" PetscInt_FMT ")", cell, cStart, cEnd);
3884:   if (!fe) { /* implicit discretization: affine or multilinear */
3885:     PetscInt  coneSize;
3886:     PetscBool isSimplex, isTensor;

3888:     PetscCall(DMPlexGetConeSize(dm, cell, &coneSize));
3889:     isSimplex = (coneSize == (dimR + 1)) ? PETSC_TRUE : PETSC_FALSE;
3890:     isTensor  = (coneSize == ((depth == 1) ? (1 << dimR) : (2 * dimR))) ? PETSC_TRUE : PETSC_FALSE;
3891:     if (isSimplex) {
3892:       PetscReal detJ, *v0, *J, *invJ;

3894:       PetscCall(DMGetWorkArray(dm, dimC + 2 * dimC * dimC, MPIU_REAL, &v0));
3895:       J    = &v0[dimC];
3896:       invJ = &J[dimC * dimC];
3897:       PetscCall(DMPlexComputeCellGeometryAffineFEM(dm, cell, v0, J, invJ, &detJ));
3898:       for (i = 0; i < numPoints; i++) { /* Apply the inverse affine transformation for each point */
3899:         const PetscReal x0[3] = {-1., -1., -1.};

3901:         CoordinatesRealToRef(dimC, dimR, x0, v0, invJ, &realCoords[dimC * i], &refCoords[dimR * i]);
3902:       }
3903:       PetscCall(DMRestoreWorkArray(dm, dimC + 2 * dimC * dimC, MPIU_REAL, &v0));
3904:     } else if (isTensor) {
3905:       PetscCall(DMPlexCoordinatesToReference_Tensor(coordDM, cell, numPoints, realCoords, refCoords, coords, dimC, dimR));
3906:     } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Unrecognized cone size %" PetscInt_FMT, coneSize);
3907:   } else {
3908:     PetscCall(DMPlexCoordinatesToReference_FE(coordDM, fe, cell, numPoints, realCoords, refCoords, coords, dimC, dimR, 7, NULL));
3909:   }
3910:   PetscFunctionReturn(PETSC_SUCCESS);
3911: }

3913: /*@
3914:   DMPlexReferenceToCoordinates - Map references coordinates to coordinates in the mesh for a single element map.

3916:   Not Collective

3918:   Input Parameters:
3919: + dm        - The mesh, with coordinate maps defined either by a PetscDS for the coordinate `DM` (see `DMGetCoordinateDM()`) or
3920:                implicitly by the coordinates of the corner vertices of the cell: as an affine map for simplicial elements, or
3921:                as a multilinear map for tensor-product elements
3922: . cell      - the cell whose map is used.
3923: . numPoints - the number of points to locate
3924: - refCoords - (numPoints x dimension) array of reference coordinates (see `DMGetDimension()`)

3926:   Output Parameter:
3927: . realCoords - (numPoints x coordinate dimension) array of coordinates (see `DMGetCoordinateDim()`)

3929:   Level: intermediate

3931: .seealso: `DMPLEX`, `DMPlexCoordinatesToReference()`
3932: @*/
3933: PetscErrorCode DMPlexReferenceToCoordinates(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal refCoords[], PetscReal realCoords[])
3934: {
3935:   PetscInt dimC, dimR, depth, cStart, cEnd, i;
3936:   DM       coordDM = NULL;
3937:   Vec      coords;
3938:   PetscFE  fe = NULL;

3940:   PetscFunctionBegin;
3942:   PetscCall(DMGetDimension(dm, &dimR));
3943:   PetscCall(DMGetCoordinateDim(dm, &dimC));
3944:   if (dimR <= 0 || dimC <= 0 || numPoints <= 0) PetscFunctionReturn(PETSC_SUCCESS);
3945:   PetscCall(DMPlexGetDepth(dm, &depth));
3946:   PetscCall(DMGetCoordinatesLocal(dm, &coords));
3947:   PetscCall(DMGetCoordinateDM(dm, &coordDM));
3948:   if (coordDM) {
3949:     PetscInt coordFields;

3951:     PetscCall(DMGetNumFields(coordDM, &coordFields));
3952:     if (coordFields) {
3953:       PetscClassId id;
3954:       PetscObject  disc;

3956:       PetscCall(DMGetField(coordDM, 0, NULL, &disc));
3957:       PetscCall(PetscObjectGetClassId(disc, &id));
3958:       if (id == PETSCFE_CLASSID) fe = (PetscFE)disc;
3959:     }
3960:   }
3961:   PetscCall(DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd));
3962:   PetscCheck(cell >= cStart && cell < cEnd, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "point %" PetscInt_FMT " not in cell range [%" PetscInt_FMT ",%" PetscInt_FMT ")", cell, cStart, cEnd);
3963:   if (!fe) { /* implicit discretization: affine or multilinear */
3964:     PetscInt  coneSize;
3965:     PetscBool isSimplex, isTensor;

3967:     PetscCall(DMPlexGetConeSize(dm, cell, &coneSize));
3968:     isSimplex = (coneSize == (dimR + 1)) ? PETSC_TRUE : PETSC_FALSE;
3969:     isTensor  = (coneSize == ((depth == 1) ? (1 << dimR) : (2 * dimR))) ? PETSC_TRUE : PETSC_FALSE;
3970:     if (isSimplex) {
3971:       PetscReal detJ, *v0, *J;

3973:       PetscCall(DMGetWorkArray(dm, dimC + 2 * dimC * dimC, MPIU_REAL, &v0));
3974:       J = &v0[dimC];
3975:       PetscCall(DMPlexComputeCellGeometryAffineFEM(dm, cell, v0, J, NULL, &detJ));
3976:       for (i = 0; i < numPoints; i++) { /* Apply the affine transformation for each point */
3977:         const PetscReal xi0[3] = {-1., -1., -1.};

3979:         CoordinatesRefToReal(dimC, dimR, xi0, v0, J, &refCoords[dimR * i], &realCoords[dimC * i]);
3980:       }
3981:       PetscCall(DMRestoreWorkArray(dm, dimC + 2 * dimC * dimC, MPIU_REAL, &v0));
3982:     } else if (isTensor) {
3983:       PetscCall(DMPlexReferenceToCoordinates_Tensor(coordDM, cell, numPoints, refCoords, realCoords, coords, dimC, dimR));
3984:     } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Unrecognized cone size %" PetscInt_FMT, coneSize);
3985:   } else {
3986:     PetscCall(DMPlexReferenceToCoordinates_FE(coordDM, fe, cell, numPoints, refCoords, realCoords, coords, dimC, dimR));
3987:   }
3988:   PetscFunctionReturn(PETSC_SUCCESS);
3989: }

3991: 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[])
3992: {
3993:   const PetscInt Nc = uOff[1] - uOff[0];
3994:   PetscInt       c;

3996:   for (c = 0; c < Nc; ++c) f0[c] = u[c];
3997: }

3999: /* Shear applies the transformation, assuming we fix z,
4000:   / 1  0  m_0 \
4001:   | 0  1  m_1 |
4002:   \ 0  0   1  /
4003: */
4004: 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[])
4005: {
4006:   const PetscInt Nc = uOff[1] - uOff[0];
4007:   const PetscInt ax = (PetscInt)PetscRealPart(constants[0]);
4008:   PetscInt       c;

4010:   for (c = 0; c < Nc; ++c) coords[c] = u[c] + constants[c + 1] * u[ax];
4011: }

4013: /* Flare applies the transformation, assuming we fix x_f,

4015:    x_i = x_i * alpha_i x_f
4016: */
4017: 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[])
4018: {
4019:   const PetscInt Nc = uOff[1] - uOff[0];
4020:   const PetscInt cf = (PetscInt)PetscRealPart(constants[0]);
4021:   PetscInt       c;

4023:   for (c = 0; c < Nc; ++c) coords[c] = u[c] * (c == cf ? 1.0 : constants[c + 1] * u[cf]);
4024: }

4026: /*
4027:   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
4028:   will correspond to the top and bottom of our square. So

4030:     (0,0)--(1,0)  ==>  (1,0)--(2,0)      Just a shift of (1,0)
4031:     (0,1)--(1,1)  ==>  (0,1)--(0,2)      Switch x and y

4033:   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:

4035:     (x, y)  ==>  (x+1, \pi/2 y)                           in (r', \theta') space
4036:             ==>  ((x+1) cos(\pi/2 y), (x+1) sin(\pi/2 y)) in (x', y') space
4037: */
4038: 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[])
4039: {
4040:   const PetscReal ri = PetscRealPart(constants[0]);
4041:   const PetscReal ro = PetscRealPart(constants[1]);

4043:   xp[0] = (x[0] * (ro - ri) + ri) * PetscCosReal(0.5 * PETSC_PI * x[1]);
4044:   xp[1] = (x[0] * (ro - ri) + ri) * PetscSinReal(0.5 * PETSC_PI * x[1]);
4045: }

4047: /*
4048:   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
4049:   lower hemisphere and the upper surface onto the top, letting z be the radius.

4051:     (x, y)  ==>  ((z+3)/2, \pi/2 (|x| or |y|), arctan y/x)                                                  in (r', \theta', \phi') space
4052:             ==>  ((z+3)/2 \cos(\theta') cos(\phi'), (z+3)/2 \cos(\theta') sin(\phi'), (z+3)/2 sin(\theta')) in (x', y', z') space
4053: */
4054: 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[])
4055: {
4056:   const PetscReal pi4    = PETSC_PI / 4.0;
4057:   const PetscReal ri     = PetscRealPart(constants[0]);
4058:   const PetscReal ro     = PetscRealPart(constants[1]);
4059:   const PetscReal rp     = (x[2] + 1) * 0.5 * (ro - ri) + ri;
4060:   const PetscReal phip   = PetscAtan2Real(x[1], x[0]);
4061:   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])));

4063:   xp[0] = rp * PetscCosReal(thetap) * PetscCosReal(phip);
4064:   xp[1] = rp * PetscCosReal(thetap) * PetscSinReal(phip);
4065:   xp[2] = rp * PetscSinReal(thetap);
4066: }

4068: 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[])
4069: {
4070:   const PetscReal c = PetscRealPart(constants[0]);
4071:   const PetscReal m = PetscRealPart(constants[1]);
4072:   const PetscReal n = PetscRealPart(constants[2]);

4074:   xp[0] = x[0];
4075:   xp[1] = x[1];
4076:   if (dim > 2) xp[2] = c * PetscCosReal(2. * m * PETSC_PI * x[0]) * PetscCosReal(2. * n * PETSC_PI * x[1]);
4077: }

4079: /*@C
4080:   DMPlexRemapGeometry - This function maps the original `DM` coordinates to new coordinates.

4082:   Not Collective

4084:   Input Parameters:
4085: + dm   - The `DM`
4086: . time - The time
4087: - func - The function transforming current coordinates to new coordinates

4089:   Calling sequence of `func`:
4090: + dim          - The spatial dimension
4091: . Nf           - The number of input fields (here 1)
4092: . NfAux        - The number of input auxiliary fields
4093: . uOff         - The offset of the coordinates in u[] (here 0)
4094: . uOff_x       - The offset of the coordinates in u_x[] (here 0)
4095: . u            - The coordinate values at this point in space
4096: . u_t          - The coordinate time derivative at this point in space (here `NULL`)
4097: . u_x          - The coordinate derivatives at this point in space
4098: . aOff         - The offset of each auxiliary field in u[]
4099: . aOff_x       - The offset of each auxiliary field in u_x[]
4100: . a            - The auxiliary field values at this point in space
4101: . a_t          - The auxiliary field time derivative at this point in space (or `NULL`)
4102: . a_x          - The auxiliary field derivatives at this point in space
4103: . t            - The current time
4104: . x            - The coordinates of this point (here not used)
4105: . numConstants - The number of constants
4106: . constants    - The value of each constant
4107: - f            - The new coordinates at this point in space

4109:   Level: intermediate

4111: .seealso: `DMPLEX`, `DMGetCoordinates()`, `DMGetCoordinatesLocal()`, `DMGetCoordinateDM()`, `DMProjectFieldLocal()`, `DMProjectFieldLabelLocal()`
4112: @*/
4113: 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[]))
4114: {
4115:   DM           cdm;
4116:   PetscDS      cds;
4117:   DMField      cf;
4118:   PetscObject  obj;
4119:   PetscClassId id;
4120:   Vec          lCoords, tmpCoords;

4122:   PetscFunctionBegin;
4123:   if (!func) PetscCall(DMPlexGetCoordinateMap(dm, &func));
4124:   PetscCall(DMGetCoordinateDM(dm, &cdm));
4125:   PetscCall(DMGetCoordinatesLocal(dm, &lCoords));
4126:   PetscCall(DMGetDS(cdm, &cds));
4127:   PetscCall(PetscDSGetDiscretization(cds, 0, &obj));
4128:   PetscCall(PetscObjectGetClassId(obj, &id));
4129:   if (id != PETSCFE_CLASSID) {
4130:     PetscSection       cSection;
4131:     const PetscScalar *constants;
4132:     PetscScalar       *coords, f[16];
4133:     PetscInt           dim, cdim, Nc, vStart, vEnd;

4135:     PetscCall(DMGetDimension(dm, &dim));
4136:     PetscCall(DMGetCoordinateDim(dm, &cdim));
4137:     PetscCheck(cdim <= 16, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Affine version of DMPlexRemapGeometry is currently limited to dimensions <= 16, not %" PetscInt_FMT, cdim);
4138:     PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
4139:     PetscCall(DMGetCoordinateSection(dm, &cSection));
4140:     PetscCall(PetscDSGetConstants(cds, &Nc, &constants));
4141:     PetscCall(VecGetArrayWrite(lCoords, &coords));
4142:     for (PetscInt v = vStart; v < vEnd; ++v) {
4143:       PetscInt uOff[2] = {0, cdim};
4144:       PetscInt off, c;

4146:       PetscCall(PetscSectionGetOffset(cSection, v, &off));
4147:       (*func)(dim, 1, 0, uOff, NULL, &coords[off], NULL, NULL, NULL, NULL, NULL, NULL, NULL, 0.0, NULL, Nc, constants, f);
4148:       for (c = 0; c < cdim; ++c) coords[off + c] = f[c];
4149:     }
4150:     PetscCall(VecRestoreArrayWrite(lCoords, &coords));
4151:   } else {
4152:     PetscCall(DMGetLocalVector(cdm, &tmpCoords));
4153:     PetscCall(VecCopy(lCoords, tmpCoords));
4154:     /* We have to do the coordinate field manually right now since the coordinate DM will not have its own */
4155:     PetscCall(DMGetCoordinateField(dm, &cf));
4156:     cdm->coordinates[0].field = cf;
4157:     PetscCall(DMProjectFieldLocal(cdm, time, tmpCoords, &func, INSERT_VALUES, lCoords));
4158:     cdm->coordinates[0].field = NULL;
4159:     PetscCall(DMRestoreLocalVector(cdm, &tmpCoords));
4160:     PetscCall(DMSetCoordinatesLocal(dm, lCoords));
4161:   }
4162:   PetscFunctionReturn(PETSC_SUCCESS);
4163: }

4165: /*@
4166:   DMPlexShearGeometry - This shears the domain, meaning adds a multiple of the shear coordinate to all other coordinates.

4168:   Not Collective

4170:   Input Parameters:
4171: + dm          - The `DMPLEX`
4172: . direction   - The shear coordinate direction, e.g. `DM_X` is the x-axis
4173: - multipliers - The multiplier m for each direction which is not the shear direction

4175:   Level: intermediate

4177: .seealso: `DMPLEX`, `DMPlexRemapGeometry()`, `DMDirection`, `DM_X`, `DM_Y`, `DM_Z`
4178: @*/
4179: PetscErrorCode DMPlexShearGeometry(DM dm, DMDirection direction, PetscReal multipliers[])
4180: {
4181:   DM             cdm;
4182:   PetscDS        cds;
4183:   PetscScalar   *moduli;
4184:   const PetscInt dir = (PetscInt)direction;
4185:   PetscInt       dE, d, e;

4187:   PetscFunctionBegin;
4188:   PetscCall(DMGetCoordinateDM(dm, &cdm));
4189:   PetscCall(DMGetCoordinateDim(dm, &dE));
4190:   PetscCall(PetscMalloc1(dE + 1, &moduli));
4191:   moduli[0] = dir;
4192:   for (d = 0, e = 0; d < dE; ++d) moduli[d + 1] = d == dir ? 0.0 : (multipliers ? multipliers[e++] : 1.0);
4193:   PetscCall(DMGetDS(cdm, &cds));
4194:   PetscCall(PetscDSSetConstants(cds, dE + 1, moduli));
4195:   PetscCall(DMPlexRemapGeometry(dm, 0.0, coordMap_shear));
4196:   PetscCall(PetscFree(moduli));
4197:   PetscFunctionReturn(PETSC_SUCCESS);
4198: }