Actual source code: plexgeometry.c
1: #include <petsc/private/dmpleximpl.h>
2: #include <petsc/private/petscfeimpl.h>
3: #include <petscblaslapack.h>
4: #include <petsctime.h>
6: const char *const DMPlexCoordMaps[] = {"none", "shear", "flare", "annulus", "shell", "unknown", "DMPlexCoordMap", "DM_COORD_MAP_", NULL};
8: /*@
9: DMPlexFindVertices - Try to find DAG points based on their coordinates.
11: Not Collective (provided `DMGetCoordinatesLocalSetUp()` has been already called)
13: Input Parameters:
14: + dm - The `DMPLEX` object
15: . coordinates - The `Vec` of coordinates of the sought points
16: - eps - The tolerance or `PETSC_DEFAULT`
18: Output Parameter:
19: . points - The `IS` of found DAG points or -1
21: Level: intermediate
23: Notes:
24: The length of `Vec` coordinates must be npoints * dim where dim is the spatial dimension returned by `DMGetCoordinateDim()` and npoints is the number of sought points.
26: The output `IS` is living on `PETSC_COMM_SELF` and its length is npoints.
27: Each rank does the search independently.
28: If this rank's local `DMPLEX` portion contains the DAG point corresponding to the i-th tuple of coordinates, the i-th entry of the output `IS` is set to that DAG point, otherwise to -1.
30: The output `IS` must be destroyed by user.
32: The tolerance is interpreted as the maximum Euclidean (L2) distance of the sought point from the specified coordinates.
34: Complexity of this function is currently O(mn) with m number of vertices to find and n number of vertices in the local mesh. This could probably be improved if needed.
36: .seealso: `DMPLEX`, `DMPlexCreate()`, `DMGetCoordinatesLocal()`
37: @*/
38: PetscErrorCode DMPlexFindVertices(DM dm, Vec coordinates, PetscReal eps, IS *points)
39: {
40: PetscInt c, cdim, i, j, o, p, vStart, vEnd;
41: PetscInt npoints;
42: const PetscScalar *coord;
43: Vec allCoordsVec;
44: const PetscScalar *allCoords;
45: PetscInt *dagPoints;
47: PetscFunctionBegin;
48: if (eps < 0) eps = PETSC_SQRT_MACHINE_EPSILON;
49: PetscCall(DMGetCoordinateDim(dm, &cdim));
50: {
51: PetscInt n;
53: PetscCall(VecGetLocalSize(coordinates, &n));
54: PetscCheck(n % cdim == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Given coordinates Vec has local length %" PetscInt_FMT " not divisible by coordinate dimension %" PetscInt_FMT " of given DM", n, cdim);
55: npoints = n / cdim;
56: }
57: PetscCall(DMGetCoordinatesLocal(dm, &allCoordsVec));
58: PetscCall(VecGetArrayRead(allCoordsVec, &allCoords));
59: PetscCall(VecGetArrayRead(coordinates, &coord));
60: PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
61: if (PetscDefined(USE_DEBUG)) {
62: /* check coordinate section is consistent with DM dimension */
63: PetscSection cs;
64: PetscInt ndof;
66: PetscCall(DMGetCoordinateSection(dm, &cs));
67: for (p = vStart; p < vEnd; p++) {
68: PetscCall(PetscSectionGetDof(cs, p, &ndof));
69: PetscCheck(ndof == cdim, PETSC_COMM_SELF, PETSC_ERR_PLIB, "point %" PetscInt_FMT ": ndof = %" PetscInt_FMT " != %" PetscInt_FMT " = cdim", p, ndof, cdim);
70: }
71: }
72: PetscCall(PetscMalloc1(npoints, &dagPoints));
73: if (eps == 0.0) {
74: for (i = 0, j = 0; i < npoints; i++, j += cdim) {
75: dagPoints[i] = -1;
76: for (p = vStart, o = 0; p < vEnd; p++, o += cdim) {
77: for (c = 0; c < cdim; c++) {
78: if (coord[j + c] != allCoords[o + c]) break;
79: }
80: if (c == cdim) {
81: dagPoints[i] = p;
82: break;
83: }
84: }
85: }
86: } else {
87: for (i = 0, j = 0; i < npoints; i++, j += cdim) {
88: PetscReal norm;
90: dagPoints[i] = -1;
91: for (p = vStart, o = 0; p < vEnd; p++, o += cdim) {
92: norm = 0.0;
93: for (c = 0; c < cdim; c++) norm += PetscRealPart(PetscSqr(coord[j + c] - allCoords[o + c]));
94: norm = PetscSqrtReal(norm);
95: if (norm <= eps) {
96: dagPoints[i] = p;
97: break;
98: }
99: }
100: }
101: }
102: PetscCall(VecRestoreArrayRead(allCoordsVec, &allCoords));
103: PetscCall(VecRestoreArrayRead(coordinates, &coord));
104: PetscCall(ISCreateGeneral(PETSC_COMM_SELF, npoints, dagPoints, PETSC_OWN_POINTER, points));
105: PetscFunctionReturn(PETSC_SUCCESS);
106: }
108: #if 0
109: static PetscErrorCode DMPlexGetLineIntersection_2D_Internal(const PetscReal segmentA[], const PetscReal segmentB[], PetscReal intersection[], PetscBool *hasIntersection)
110: {
111: const PetscReal p0_x = segmentA[0 * 2 + 0];
112: const PetscReal p0_y = segmentA[0 * 2 + 1];
113: const PetscReal p1_x = segmentA[1 * 2 + 0];
114: const PetscReal p1_y = segmentA[1 * 2 + 1];
115: const PetscReal p2_x = segmentB[0 * 2 + 0];
116: const PetscReal p2_y = segmentB[0 * 2 + 1];
117: const PetscReal p3_x = segmentB[1 * 2 + 0];
118: const PetscReal p3_y = segmentB[1 * 2 + 1];
119: const PetscReal s1_x = p1_x - p0_x;
120: const PetscReal s1_y = p1_y - p0_y;
121: const PetscReal s2_x = p3_x - p2_x;
122: const PetscReal s2_y = p3_y - p2_y;
123: const PetscReal denom = (-s2_x * s1_y + s1_x * s2_y);
125: PetscFunctionBegin;
126: *hasIntersection = PETSC_FALSE;
127: /* Non-parallel lines */
128: if (denom != 0.0) {
129: const PetscReal s = (-s1_y * (p0_x - p2_x) + s1_x * (p0_y - p2_y)) / denom;
130: const PetscReal t = (s2_x * (p0_y - p2_y) - s2_y * (p0_x - p2_x)) / denom;
132: if (s >= 0 && s <= 1 && t >= 0 && t <= 1) {
133: *hasIntersection = PETSC_TRUE;
134: if (intersection) {
135: intersection[0] = p0_x + (t * s1_x);
136: intersection[1] = p0_y + (t * s1_y);
137: }
138: }
139: }
140: PetscFunctionReturn(PETSC_SUCCESS);
141: }
143: /* The plane is segmentB x segmentC: https://en.wikipedia.org/wiki/Line%E2%80%93plane_intersection */
144: static PetscErrorCode DMPlexGetLinePlaneIntersection_3D_Internal(const PetscReal segmentA[], const PetscReal segmentB[], const PetscReal segmentC[], PetscReal intersection[], PetscBool *hasIntersection)
145: {
146: const PetscReal p0_x = segmentA[0 * 3 + 0];
147: const PetscReal p0_y = segmentA[0 * 3 + 1];
148: const PetscReal p0_z = segmentA[0 * 3 + 2];
149: const PetscReal p1_x = segmentA[1 * 3 + 0];
150: const PetscReal p1_y = segmentA[1 * 3 + 1];
151: const PetscReal p1_z = segmentA[1 * 3 + 2];
152: const PetscReal q0_x = segmentB[0 * 3 + 0];
153: const PetscReal q0_y = segmentB[0 * 3 + 1];
154: const PetscReal q0_z = segmentB[0 * 3 + 2];
155: const PetscReal q1_x = segmentB[1 * 3 + 0];
156: const PetscReal q1_y = segmentB[1 * 3 + 1];
157: const PetscReal q1_z = segmentB[1 * 3 + 2];
158: const PetscReal r0_x = segmentC[0 * 3 + 0];
159: const PetscReal r0_y = segmentC[0 * 3 + 1];
160: const PetscReal r0_z = segmentC[0 * 3 + 2];
161: const PetscReal r1_x = segmentC[1 * 3 + 0];
162: const PetscReal r1_y = segmentC[1 * 3 + 1];
163: const PetscReal r1_z = segmentC[1 * 3 + 2];
164: const PetscReal s0_x = p1_x - p0_x;
165: const PetscReal s0_y = p1_y - p0_y;
166: const PetscReal s0_z = p1_z - p0_z;
167: const PetscReal s1_x = q1_x - q0_x;
168: const PetscReal s1_y = q1_y - q0_y;
169: const PetscReal s1_z = q1_z - q0_z;
170: const PetscReal s2_x = r1_x - r0_x;
171: const PetscReal s2_y = r1_y - r0_y;
172: const PetscReal s2_z = r1_z - r0_z;
173: const PetscReal s3_x = s1_y * s2_z - s1_z * s2_y; /* s1 x s2 */
174: const PetscReal s3_y = s1_z * s2_x - s1_x * s2_z;
175: const PetscReal s3_z = s1_x * s2_y - s1_y * s2_x;
176: const PetscReal s4_x = s0_y * s2_z - s0_z * s2_y; /* s0 x s2 */
177: const PetscReal s4_y = s0_z * s2_x - s0_x * s2_z;
178: const PetscReal s4_z = s0_x * s2_y - s0_y * s2_x;
179: const PetscReal s5_x = s1_y * s0_z - s1_z * s0_y; /* s1 x s0 */
180: const PetscReal s5_y = s1_z * s0_x - s1_x * s0_z;
181: const PetscReal s5_z = s1_x * s0_y - s1_y * s0_x;
182: const PetscReal denom = -(s0_x * s3_x + s0_y * s3_y + s0_z * s3_z); /* -s0 . (s1 x s2) */
184: PetscFunctionBegin;
185: *hasIntersection = PETSC_FALSE;
186: /* Line not parallel to plane */
187: if (denom != 0.0) {
188: const PetscReal t = (s3_x * (p0_x - q0_x) + s3_y * (p0_y - q0_y) + s3_z * (p0_z - q0_z)) / denom;
189: const PetscReal u = (s4_x * (p0_x - q0_x) + s4_y * (p0_y - q0_y) + s4_z * (p0_z - q0_z)) / denom;
190: const PetscReal v = (s5_x * (p0_x - q0_x) + s5_y * (p0_y - q0_y) + s5_z * (p0_z - q0_z)) / denom;
192: if (t >= 0 && t <= 1 && u >= 0 && u <= 1 && v >= 0 && v <= 1) {
193: *hasIntersection = PETSC_TRUE;
194: if (intersection) {
195: intersection[0] = p0_x + (t * s0_x);
196: intersection[1] = p0_y + (t * s0_y);
197: intersection[2] = p0_z + (t * s0_z);
198: }
199: }
200: }
201: PetscFunctionReturn(PETSC_SUCCESS);
202: }
203: #endif
205: static PetscErrorCode DMPlexGetPlaneSimplexIntersection_Coords_Internal(DM dm, PetscInt dim, PetscInt cdim, const PetscScalar coords[], const PetscReal p[], const PetscReal normal[], PetscBool *pos, PetscInt *Nint, PetscReal intPoints[])
206: {
207: PetscReal d[4]; // distance of vertices to the plane
208: PetscReal dp; // distance from origin to the plane
209: PetscInt n = 0;
211: PetscFunctionBegin;
212: if (pos) *pos = PETSC_FALSE;
213: if (Nint) *Nint = 0;
214: if (PetscDefined(USE_DEBUG)) {
215: PetscReal mag = DMPlex_NormD_Internal(cdim, normal);
216: PetscCheck(PetscAbsReal(mag - (PetscReal)1.0) < PETSC_SMALL, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Normal vector is not normalized: %g", (double)mag);
217: }
219: dp = DMPlex_DotRealD_Internal(cdim, normal, p);
220: for (PetscInt v = 0; v < dim + 1; ++v) {
221: // d[v] is positive, zero, or negative if vertex i is above, on, or below the plane
222: #if defined(PETSC_USE_COMPLEX)
223: PetscReal c[4];
224: for (PetscInt i = 0; i < cdim; ++i) c[i] = PetscRealPart(coords[v * cdim + i]);
225: d[v] = DMPlex_DotRealD_Internal(cdim, normal, c);
226: #else
227: d[v] = DMPlex_DotRealD_Internal(cdim, normal, &coords[v * cdim]);
228: #endif
229: d[v] -= dp;
230: }
232: // If all d are positive or negative, no intersection
233: {
234: PetscInt v;
235: for (v = 0; v < dim + 1; ++v)
236: if (d[v] >= 0.) break;
237: if (v == dim + 1) PetscFunctionReturn(PETSC_SUCCESS);
238: for (v = 0; v < dim + 1; ++v)
239: if (d[v] <= 0.) break;
240: if (v == dim + 1) {
241: if (pos) *pos = PETSC_TRUE;
242: PetscFunctionReturn(PETSC_SUCCESS);
243: }
244: }
246: for (PetscInt v = 0; v < dim + 1; ++v) {
247: // Points with zero distance are automatically added to the list.
248: if (PetscAbsReal(d[v]) < PETSC_MACHINE_EPSILON) {
249: for (PetscInt i = 0; i < cdim; ++i) intPoints[n * cdim + i] = PetscRealPart(coords[v * cdim + i]);
250: ++n;
251: } else {
252: // For each point with nonzero distance, seek another point with opposite sign
253: // and higher index, and compute the intersection of the line between those
254: // points and the plane.
255: for (PetscInt w = v + 1; w < dim + 1; ++w) {
256: if (d[v] * d[w] < 0.) {
257: PetscReal inv_dist = 1. / (d[v] - d[w]);
258: for (PetscInt i = 0; i < cdim; ++i) intPoints[n * cdim + i] = (d[v] * PetscRealPart(coords[w * cdim + i]) - d[w] * PetscRealPart(coords[v * cdim + i])) * inv_dist;
259: ++n;
260: }
261: }
262: }
263: }
264: // TODO order output points if there are 4
265: *Nint = n;
266: PetscFunctionReturn(PETSC_SUCCESS);
267: }
269: static PetscErrorCode DMPlexGetPlaneSimplexIntersection_Internal(DM dm, PetscInt dim, PetscInt c, const PetscReal p[], const PetscReal normal[], PetscBool *pos, PetscInt *Nint, PetscReal intPoints[])
270: {
271: const PetscScalar *array;
272: PetscScalar *coords = NULL;
273: PetscInt numCoords;
274: PetscBool isDG;
275: PetscInt cdim;
277: PetscFunctionBegin;
278: PetscCall(DMGetCoordinateDim(dm, &cdim));
279: PetscCheck(cdim == dim, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "DM has coordinates in %" PetscInt_FMT "D instead of %" PetscInt_FMT "D", cdim, dim);
280: PetscCall(DMPlexGetCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
281: PetscCheck(numCoords == dim * (dim + 1), PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Tetrahedron should have %" PetscInt_FMT " coordinates, not %" PetscInt_FMT, dim * (dim + 1), numCoords);
282: PetscCall(PetscArrayzero(intPoints, dim * (dim + 1)));
284: PetscCall(DMPlexGetPlaneSimplexIntersection_Coords_Internal(dm, dim, cdim, coords, p, normal, pos, Nint, intPoints));
286: PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
287: PetscFunctionReturn(PETSC_SUCCESS);
288: }
290: static PetscErrorCode DMPlexGetPlaneQuadIntersection_Internal(DM dm, PetscInt dim, PetscInt c, const PetscReal p[], const PetscReal normal[], PetscBool *pos, PetscInt *Nint, PetscReal intPoints[])
291: {
292: const PetscScalar *array;
293: PetscScalar *coords = NULL;
294: PetscInt numCoords;
295: PetscBool isDG;
296: PetscInt cdim;
297: PetscScalar tcoords[6] = {0., 0., 0., 0., 0., 0.};
298: const PetscInt vertsA[3] = {0, 1, 3};
299: const PetscInt vertsB[3] = {1, 2, 3};
300: PetscInt NintA, NintB;
302: PetscFunctionBegin;
303: PetscCall(DMGetCoordinateDim(dm, &cdim));
304: PetscCheck(cdim == dim, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "DM has coordinates in %" PetscInt_FMT "D instead of %" PetscInt_FMT "D", cdim, dim);
305: PetscCall(DMPlexGetCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
306: PetscCheck(numCoords == dim * 4, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Quadrilateral should have %" PetscInt_FMT " coordinates, not %" PetscInt_FMT, dim * 4, numCoords);
307: PetscCall(PetscArrayzero(intPoints, dim * 4));
309: for (PetscInt v = 0; v < 3; ++v)
310: for (PetscInt d = 0; d < cdim; ++d) tcoords[v * cdim + d] = coords[vertsA[v] * cdim + d];
311: PetscCall(DMPlexGetPlaneSimplexIntersection_Coords_Internal(dm, dim, cdim, tcoords, p, normal, pos, &NintA, intPoints));
312: for (PetscInt v = 0; v < 3; ++v)
313: for (PetscInt d = 0; d < cdim; ++d) tcoords[v * cdim + d] = coords[vertsB[v] * cdim + d];
314: PetscCall(DMPlexGetPlaneSimplexIntersection_Coords_Internal(dm, dim, cdim, tcoords, p, normal, pos, &NintB, &intPoints[NintA * cdim]));
315: *Nint = NintA + NintB;
317: PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
318: PetscFunctionReturn(PETSC_SUCCESS);
319: }
321: static PetscErrorCode DMPlexGetPlaneHexIntersection_Internal(DM dm, PetscInt dim, PetscInt c, const PetscReal p[], const PetscReal normal[], PetscBool *pos, PetscInt *Nint, PetscReal intPoints[])
322: {
323: const PetscScalar *array;
324: PetscScalar *coords = NULL;
325: PetscInt numCoords;
326: PetscBool isDG;
327: PetscInt cdim;
328: PetscScalar tcoords[12] = {0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.};
329: // We split using the (2, 4) main diagonal, so all tets contain those vertices
330: const PetscInt vertsA[4] = {0, 1, 2, 4};
331: const PetscInt vertsB[4] = {0, 2, 3, 4};
332: const PetscInt vertsC[4] = {1, 7, 2, 4};
333: const PetscInt vertsD[4] = {2, 7, 6, 4};
334: const PetscInt vertsE[4] = {3, 5, 4, 2};
335: const PetscInt vertsF[4] = {4, 5, 6, 2};
336: PetscInt NintA, NintB, NintC, NintD, NintE, NintF, Nsum = 0;
338: PetscFunctionBegin;
339: PetscCall(DMGetCoordinateDim(dm, &cdim));
340: PetscCheck(cdim == dim, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "DM has coordinates in %" PetscInt_FMT "D instead of %" PetscInt_FMT "D", cdim, dim);
341: PetscCall(DMPlexGetCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
342: PetscCheck(numCoords == dim * 8, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Hexahedron should have %" PetscInt_FMT " coordinates, not %" PetscInt_FMT, dim * 8, numCoords);
343: PetscCall(PetscArrayzero(intPoints, dim * 18));
345: for (PetscInt v = 0; v < 4; ++v)
346: for (PetscInt d = 0; d < cdim; ++d) tcoords[v * cdim + d] = coords[vertsA[v] * cdim + d];
347: PetscCall(DMPlexGetPlaneSimplexIntersection_Coords_Internal(dm, dim, cdim, tcoords, p, normal, pos, &NintA, &intPoints[Nsum * cdim]));
348: Nsum += NintA;
349: for (PetscInt v = 0; v < 4; ++v)
350: for (PetscInt d = 0; d < cdim; ++d) tcoords[v * cdim + d] = coords[vertsB[v] * cdim + d];
351: PetscCall(DMPlexGetPlaneSimplexIntersection_Coords_Internal(dm, dim, cdim, tcoords, p, normal, pos, &NintB, &intPoints[Nsum * cdim]));
352: Nsum += NintB;
353: for (PetscInt v = 0; v < 4; ++v)
354: for (PetscInt d = 0; d < cdim; ++d) tcoords[v * cdim + d] = coords[vertsC[v] * cdim + d];
355: PetscCall(DMPlexGetPlaneSimplexIntersection_Coords_Internal(dm, dim, cdim, tcoords, p, normal, pos, &NintC, &intPoints[Nsum * cdim]));
356: Nsum += NintC;
357: for (PetscInt v = 0; v < 4; ++v)
358: for (PetscInt d = 0; d < cdim; ++d) tcoords[v * cdim + d] = coords[vertsD[v] * cdim + d];
359: PetscCall(DMPlexGetPlaneSimplexIntersection_Coords_Internal(dm, dim, cdim, tcoords, p, normal, pos, &NintD, &intPoints[Nsum * cdim]));
360: Nsum += NintD;
361: for (PetscInt v = 0; v < 4; ++v)
362: for (PetscInt d = 0; d < cdim; ++d) tcoords[v * cdim + d] = coords[vertsE[v] * cdim + d];
363: PetscCall(DMPlexGetPlaneSimplexIntersection_Coords_Internal(dm, dim, cdim, tcoords, p, normal, pos, &NintE, &intPoints[Nsum * cdim]));
364: Nsum += NintE;
365: for (PetscInt v = 0; v < 4; ++v)
366: for (PetscInt d = 0; d < cdim; ++d) tcoords[v * cdim + d] = coords[vertsF[v] * cdim + d];
367: PetscCall(DMPlexGetPlaneSimplexIntersection_Coords_Internal(dm, dim, cdim, tcoords, p, normal, pos, &NintF, &intPoints[Nsum * cdim]));
368: Nsum += NintF;
369: *Nint = Nsum;
371: PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
372: PetscFunctionReturn(PETSC_SUCCESS);
373: }
375: /*
376: DMPlexGetPlaneCellIntersection_Internal - Finds the intersection of a plane with a cell
378: Not collective
380: Input Parameters:
381: + dm - the DM
382: . c - the mesh point
383: . p - a point on the plane.
384: - normal - a normal vector to the plane, must be normalized
386: Output Parameters:
387: . pos - `PETSC_TRUE` is the cell is on the positive side of the plane, `PETSC_FALSE` on the negative side
388: + Nint - the number of intersection points, in [0, 4]
389: - intPoints - the coordinates of the intersection points, should be length at least 12
391: Note: The `pos` argument is only meaningful if the number of intersections is 0. The algorithmic idea comes from https://github.com/chrisk314/tet-plane-intersection.
393: Level: developer
395: .seealso:
396: @*/
397: static PetscErrorCode DMPlexGetPlaneCellIntersection_Internal(DM dm, PetscInt c, const PetscReal p[], const PetscReal normal[], PetscBool *pos, PetscInt *Nint, PetscReal intPoints[])
398: {
399: DMPolytopeType ct;
401: PetscFunctionBegin;
402: PetscCall(DMPlexGetCellType(dm, c, &ct));
403: switch (ct) {
404: case DM_POLYTOPE_SEGMENT:
405: case DM_POLYTOPE_TRIANGLE:
406: case DM_POLYTOPE_TETRAHEDRON:
407: PetscCall(DMPlexGetPlaneSimplexIntersection_Internal(dm, DMPolytopeTypeGetDim(ct), c, p, normal, pos, Nint, intPoints));
408: break;
409: case DM_POLYTOPE_QUADRILATERAL:
410: PetscCall(DMPlexGetPlaneQuadIntersection_Internal(dm, DMPolytopeTypeGetDim(ct), c, p, normal, pos, Nint, intPoints));
411: break;
412: case DM_POLYTOPE_HEXAHEDRON:
413: PetscCall(DMPlexGetPlaneHexIntersection_Internal(dm, DMPolytopeTypeGetDim(ct), c, p, normal, pos, Nint, intPoints));
414: break;
415: default:
416: SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No plane intersection for cell %" PetscInt_FMT " with type %s", c, DMPolytopeTypes[ct]);
417: }
418: PetscFunctionReturn(PETSC_SUCCESS);
419: }
421: static PetscErrorCode DMPlexLocatePoint_Simplex_1D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
422: {
423: const PetscReal eps = PETSC_SQRT_MACHINE_EPSILON;
424: const PetscReal x = PetscRealPart(point[0]);
425: PetscReal v0, J, invJ, detJ;
426: PetscReal xi;
428: PetscFunctionBegin;
429: PetscCall(DMPlexComputeCellGeometryFEM(dm, c, NULL, &v0, &J, &invJ, &detJ));
430: xi = invJ * (x - v0);
432: if ((xi >= -eps) && (xi <= 2. + eps)) *cell = c;
433: else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
434: PetscFunctionReturn(PETSC_SUCCESS);
435: }
437: static PetscErrorCode DMPlexLocatePoint_Simplex_2D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
438: {
439: const PetscInt embedDim = 2;
440: const PetscReal eps = PETSC_SQRT_MACHINE_EPSILON;
441: PetscReal x = PetscRealPart(point[0]);
442: PetscReal y = PetscRealPart(point[1]);
443: PetscReal v0[2], J[4], invJ[4], detJ;
444: PetscReal xi, eta;
446: PetscFunctionBegin;
447: PetscCall(DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ));
448: xi = invJ[0 * embedDim + 0] * (x - v0[0]) + invJ[0 * embedDim + 1] * (y - v0[1]);
449: eta = invJ[1 * embedDim + 0] * (x - v0[0]) + invJ[1 * embedDim + 1] * (y - v0[1]);
451: if ((xi >= -eps) && (eta >= -eps) && (xi + eta <= 2.0 + eps)) *cell = c;
452: else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
453: PetscFunctionReturn(PETSC_SUCCESS);
454: }
456: static PetscErrorCode DMPlexClosestPoint_Simplex_2D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscReal cpoint[])
457: {
458: const PetscInt embedDim = 2;
459: PetscReal x = PetscRealPart(point[0]);
460: PetscReal y = PetscRealPart(point[1]);
461: PetscReal v0[2], J[4], invJ[4], detJ;
462: PetscReal xi, eta, r;
464: PetscFunctionBegin;
465: PetscCall(DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ));
466: xi = invJ[0 * embedDim + 0] * (x - v0[0]) + invJ[0 * embedDim + 1] * (y - v0[1]);
467: eta = invJ[1 * embedDim + 0] * (x - v0[0]) + invJ[1 * embedDim + 1] * (y - v0[1]);
469: xi = PetscMax(xi, 0.0);
470: eta = PetscMax(eta, 0.0);
471: if (xi + eta > 2.0) {
472: r = (xi + eta) / 2.0;
473: xi /= r;
474: eta /= r;
475: }
476: cpoint[0] = J[0 * embedDim + 0] * xi + J[0 * embedDim + 1] * eta + v0[0];
477: cpoint[1] = J[1 * embedDim + 0] * xi + J[1 * embedDim + 1] * eta + v0[1];
478: PetscFunctionReturn(PETSC_SUCCESS);
479: }
481: // This is the ray-casting, or even-odd algorithm: https://en.wikipedia.org/wiki/Even%E2%80%93odd_rule
482: static PetscErrorCode DMPlexLocatePoint_Quad_2D_Linear_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
483: {
484: const PetscScalar *array;
485: PetscScalar *coords = NULL;
486: const PetscInt faces[8] = {0, 1, 1, 2, 2, 3, 3, 0};
487: PetscReal x = PetscRealPart(point[0]);
488: PetscReal y = PetscRealPart(point[1]);
489: PetscInt crossings = 0, numCoords, f;
490: PetscBool isDG;
492: PetscFunctionBegin;
493: PetscCall(DMPlexGetCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
494: PetscCheck(numCoords == 8, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Quadrilateral should have 8 coordinates, not %" PetscInt_FMT, numCoords);
495: for (f = 0; f < 4; ++f) {
496: PetscReal x_i = PetscRealPart(coords[faces[2 * f + 0] * 2 + 0]);
497: PetscReal y_i = PetscRealPart(coords[faces[2 * f + 0] * 2 + 1]);
498: PetscReal x_j = PetscRealPart(coords[faces[2 * f + 1] * 2 + 0]);
499: PetscReal y_j = PetscRealPart(coords[faces[2 * f + 1] * 2 + 1]);
501: if ((x == x_j) && (y == y_j)) {
502: // point is a corner
503: crossings = 1;
504: break;
505: }
506: if ((y_j > y) != (y_i > y)) {
507: PetscReal slope = (x - x_j) * (y_i - y_j) - (x_i - x_j) * (y - y_j);
508: if (slope == 0) {
509: // point is a corner
510: crossings = 1;
511: break;
512: }
513: if ((slope < 0) != (y_i < y_j)) ++crossings;
514: }
515: }
516: if (crossings % 2) *cell = c;
517: else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
518: PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
519: PetscFunctionReturn(PETSC_SUCCESS);
520: }
522: static PetscErrorCode DMPlexLocatePoint_Quad_2D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
523: {
524: DM cdm;
525: PetscInt degree, dimR, dimC;
526: PetscFE fe;
527: PetscClassId id;
528: PetscSpace sp;
529: PetscReal pointR[3], ref[3], error;
530: Vec coords;
531: PetscBool found = PETSC_FALSE;
533: PetscFunctionBegin;
534: PetscCall(DMGetDimension(dm, &dimR));
535: PetscCall(DMGetCoordinateDM(dm, &cdm));
536: PetscCall(DMGetDimension(cdm, &dimC));
537: PetscCall(DMGetField(cdm, 0, NULL, (PetscObject *)&fe));
538: PetscCall(PetscObjectGetClassId((PetscObject)fe, &id));
539: if (id != PETSCFE_CLASSID) degree = 1;
540: else {
541: PetscCall(PetscFEGetBasisSpace(fe, &sp));
542: PetscCall(PetscSpaceGetDegree(sp, °ree, NULL));
543: }
544: if (degree == 1) {
545: /* Use simple location method for linear elements*/
546: PetscCall(DMPlexLocatePoint_Quad_2D_Linear_Internal(dm, point, c, cell));
547: PetscFunctionReturn(PETSC_SUCCESS);
548: }
549: /* Otherwise, we have to solve for the real to reference coordinates */
550: PetscCall(DMGetCoordinatesLocal(dm, &coords));
551: error = PETSC_SQRT_MACHINE_EPSILON;
552: for (PetscInt d = 0; d < dimC; d++) pointR[d] = PetscRealPart(point[d]);
553: PetscCall(DMPlexCoordinatesToReference_FE(cdm, fe, c, 1, pointR, ref, coords, dimC, dimR, 10, &error));
554: if (error < PETSC_SQRT_MACHINE_EPSILON) found = PETSC_TRUE;
555: if ((ref[0] > 1.0 + PETSC_SMALL) || (ref[0] < -1.0 - PETSC_SMALL) || (ref[1] > 1.0 + PETSC_SMALL) || (ref[1] < -1.0 - PETSC_SMALL)) found = PETSC_FALSE;
556: if (PetscDefined(USE_DEBUG) && found) {
557: PetscReal real[3], inverseError = 0, normPoint = DMPlex_NormD_Internal(dimC, pointR);
559: normPoint = normPoint > PETSC_SMALL ? normPoint : 1.0;
560: PetscCall(DMPlexReferenceToCoordinates_FE(cdm, fe, c, 1, ref, real, coords, dimC, dimR));
561: inverseError = DMPlex_DistRealD_Internal(dimC, real, pointR);
562: if (inverseError > PETSC_SQRT_MACHINE_EPSILON * normPoint) found = PETSC_FALSE;
563: if (!found) PetscCall(PetscInfo(dm, "Point (%g, %g, %g) != Mapped Ref Coords (%g, %g, %g) with error %g\n", (double)pointR[0], (double)pointR[1], (double)pointR[2], (double)real[0], (double)real[1], (double)real[2], (double)inverseError));
564: }
565: if (found) *cell = c;
566: else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
567: PetscFunctionReturn(PETSC_SUCCESS);
568: }
570: static PetscErrorCode DMPlexLocatePoint_Simplex_3D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
571: {
572: const PetscInt embedDim = 3;
573: const PetscReal eps = PETSC_SQRT_MACHINE_EPSILON;
574: PetscReal v0[3], J[9], invJ[9], detJ;
575: PetscReal x = PetscRealPart(point[0]);
576: PetscReal y = PetscRealPart(point[1]);
577: PetscReal z = PetscRealPart(point[2]);
578: PetscReal xi, eta, zeta;
580: PetscFunctionBegin;
581: PetscCall(DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ));
582: xi = invJ[0 * embedDim + 0] * (x - v0[0]) + invJ[0 * embedDim + 1] * (y - v0[1]) + invJ[0 * embedDim + 2] * (z - v0[2]);
583: eta = invJ[1 * embedDim + 0] * (x - v0[0]) + invJ[1 * embedDim + 1] * (y - v0[1]) + invJ[1 * embedDim + 2] * (z - v0[2]);
584: zeta = invJ[2 * embedDim + 0] * (x - v0[0]) + invJ[2 * embedDim + 1] * (y - v0[1]) + invJ[2 * embedDim + 2] * (z - v0[2]);
586: if ((xi >= -eps) && (eta >= -eps) && (zeta >= -eps) && (xi + eta + zeta <= 2.0 + eps)) *cell = c;
587: else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
588: PetscFunctionReturn(PETSC_SUCCESS);
589: }
591: static PetscErrorCode DMPlexLocatePoint_Hex_3D_Linear_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
592: {
593: const PetscScalar *array;
594: PetscScalar *coords = NULL;
595: const PetscInt faces[24] = {0, 3, 2, 1, 5, 4, 7, 6, 3, 0, 4, 5, 1, 2, 6, 7, 3, 5, 6, 2, 0, 1, 7, 4};
596: PetscBool found = PETSC_TRUE;
597: PetscInt numCoords, f;
598: PetscBool isDG;
600: PetscFunctionBegin;
601: PetscCall(DMPlexGetCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
602: PetscCheck(numCoords == 24, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Quadrilateral should have 8 coordinates, not %" PetscInt_FMT, numCoords);
603: for (f = 0; f < 6; ++f) {
604: /* Check the point is under plane */
605: /* Get face normal */
606: PetscReal v_i[3];
607: PetscReal v_j[3];
608: PetscReal normal[3];
609: PetscReal pp[3];
610: PetscReal dot;
612: v_i[0] = PetscRealPart(coords[faces[f * 4 + 3] * 3 + 0] - coords[faces[f * 4 + 0] * 3 + 0]);
613: v_i[1] = PetscRealPart(coords[faces[f * 4 + 3] * 3 + 1] - coords[faces[f * 4 + 0] * 3 + 1]);
614: v_i[2] = PetscRealPart(coords[faces[f * 4 + 3] * 3 + 2] - coords[faces[f * 4 + 0] * 3 + 2]);
615: v_j[0] = PetscRealPart(coords[faces[f * 4 + 1] * 3 + 0] - coords[faces[f * 4 + 0] * 3 + 0]);
616: v_j[1] = PetscRealPart(coords[faces[f * 4 + 1] * 3 + 1] - coords[faces[f * 4 + 0] * 3 + 1]);
617: v_j[2] = PetscRealPart(coords[faces[f * 4 + 1] * 3 + 2] - coords[faces[f * 4 + 0] * 3 + 2]);
618: normal[0] = v_i[1] * v_j[2] - v_i[2] * v_j[1];
619: normal[1] = v_i[2] * v_j[0] - v_i[0] * v_j[2];
620: normal[2] = v_i[0] * v_j[1] - v_i[1] * v_j[0];
621: pp[0] = PetscRealPart(coords[faces[f * 4 + 0] * 3 + 0] - point[0]);
622: pp[1] = PetscRealPart(coords[faces[f * 4 + 0] * 3 + 1] - point[1]);
623: pp[2] = PetscRealPart(coords[faces[f * 4 + 0] * 3 + 2] - point[2]);
624: dot = normal[0] * pp[0] + normal[1] * pp[1] + normal[2] * pp[2];
626: /* Check that projected point is in face (2D location problem) */
627: if (dot < 0.0) {
628: found = PETSC_FALSE;
629: break;
630: }
631: }
632: if (found) *cell = c;
633: else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
634: PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
635: PetscFunctionReturn(PETSC_SUCCESS);
636: }
638: static PetscErrorCode DMPlexLocatePoint_Hex_3D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
639: {
640: DM cdm;
641: PetscInt degree, dimR, dimC;
642: PetscFE fe;
643: PetscClassId id;
644: PetscSpace sp;
645: PetscReal pointR[3], ref[3], error;
646: Vec coords;
647: PetscBool found = PETSC_FALSE;
649: PetscFunctionBegin;
650: PetscCall(DMGetDimension(dm, &dimR));
651: PetscCall(DMGetCoordinateDM(dm, &cdm));
652: PetscCall(DMGetDimension(cdm, &dimC));
653: PetscCall(DMGetField(cdm, 0, NULL, (PetscObject *)&fe));
654: PetscCall(PetscObjectGetClassId((PetscObject)fe, &id));
655: if (id != PETSCFE_CLASSID) degree = 1;
656: else {
657: PetscCall(PetscFEGetBasisSpace(fe, &sp));
658: PetscCall(PetscSpaceGetDegree(sp, °ree, NULL));
659: }
660: if (degree == 1) {
661: /* Use simple location method for linear elements*/
662: PetscCall(DMPlexLocatePoint_Hex_3D_Linear_Internal(dm, point, c, cell));
663: PetscFunctionReturn(PETSC_SUCCESS);
664: }
665: /* Otherwise, we have to solve for the real to reference coordinates */
666: PetscCall(DMGetCoordinatesLocal(dm, &coords));
667: error = PETSC_SQRT_MACHINE_EPSILON;
668: for (PetscInt d = 0; d < dimC; d++) pointR[d] = PetscRealPart(point[d]);
669: PetscCall(DMPlexCoordinatesToReference_FE(cdm, fe, c, 1, pointR, ref, coords, dimC, dimR, 10, &error));
670: if (error < PETSC_SQRT_MACHINE_EPSILON) found = PETSC_TRUE;
671: if ((ref[0] > 1.0 + PETSC_SMALL) || (ref[0] < -1.0 - PETSC_SMALL) || (ref[1] > 1.0 + PETSC_SMALL) || (ref[1] < -1.0 - PETSC_SMALL) || (ref[2] > 1.0 + PETSC_SMALL) || (ref[2] < -1.0 - PETSC_SMALL)) found = PETSC_FALSE;
672: if (PetscDefined(USE_DEBUG) && found) {
673: PetscReal real[3], inverseError = 0, normPoint = DMPlex_NormD_Internal(dimC, pointR);
675: normPoint = normPoint > PETSC_SMALL ? normPoint : 1.0;
676: PetscCall(DMPlexReferenceToCoordinates_FE(cdm, fe, c, 1, ref, real, coords, dimC, dimR));
677: inverseError = DMPlex_DistRealD_Internal(dimC, real, pointR);
678: if (inverseError > PETSC_SQRT_MACHINE_EPSILON * normPoint) found = PETSC_FALSE;
679: if (!found) PetscCall(PetscInfo(dm, "Point (%g, %g, %g) != Mapped Ref Coords (%g, %g, %g) with error %g\n", (double)pointR[0], (double)pointR[1], (double)pointR[2], (double)real[0], (double)real[1], (double)real[2], (double)inverseError));
680: }
681: if (found) *cell = c;
682: else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
683: PetscFunctionReturn(PETSC_SUCCESS);
684: }
686: static PetscErrorCode PetscGridHashInitialize_Internal(PetscGridHash box, PetscInt dim, const PetscScalar point[])
687: {
688: PetscInt d;
690: PetscFunctionBegin;
691: box->dim = dim;
692: for (d = 0; d < dim; ++d) box->lower[d] = box->upper[d] = point ? PetscRealPart(point[d]) : 0.;
693: PetscFunctionReturn(PETSC_SUCCESS);
694: }
696: PetscErrorCode PetscGridHashCreate(MPI_Comm comm, PetscInt dim, const PetscScalar point[], PetscGridHash *box)
697: {
698: PetscFunctionBegin;
699: PetscCall(PetscCalloc1(1, box));
700: PetscCall(PetscGridHashInitialize_Internal(*box, dim, point));
701: PetscFunctionReturn(PETSC_SUCCESS);
702: }
704: PetscErrorCode PetscGridHashEnlarge(PetscGridHash box, const PetscScalar point[])
705: {
706: PetscInt d;
708: PetscFunctionBegin;
709: for (d = 0; d < box->dim; ++d) {
710: box->lower[d] = PetscMin(box->lower[d], PetscRealPart(point[d]));
711: box->upper[d] = PetscMax(box->upper[d], PetscRealPart(point[d]));
712: }
713: PetscFunctionReturn(PETSC_SUCCESS);
714: }
716: static PetscErrorCode DMPlexCreateGridHash(DM dm, PetscGridHash *box)
717: {
718: Vec coordinates;
719: const PetscScalar *a;
720: PetscInt cdim, cStart, cEnd;
722: PetscFunctionBegin;
723: PetscCall(DMGetCoordinateDim(dm, &cdim));
724: PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
725: PetscCall(DMGetCoordinatesLocal(dm, &coordinates));
727: PetscCall(VecGetArrayRead(coordinates, &a));
728: PetscCall(PetscGridHashCreate(PetscObjectComm((PetscObject)dm), cdim, a, box));
729: PetscCall(VecRestoreArrayRead(coordinates, &a));
730: for (PetscInt c = cStart; c < cEnd; ++c) {
731: const PetscScalar *array;
732: PetscScalar *coords = NULL;
733: PetscInt numCoords;
734: PetscBool isDG;
736: PetscCall(DMPlexGetCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
737: for (PetscInt i = 0; i < numCoords / cdim; ++i) PetscCall(PetscGridHashEnlarge(*box, &coords[i * cdim]));
738: PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
739: }
740: PetscFunctionReturn(PETSC_SUCCESS);
741: }
743: /*@C
744: PetscGridHashSetGrid - Divide the grid into boxes
746: Not Collective
748: Input Parameters:
749: + box - The grid hash object
750: . n - The number of boxes in each dimension, may use `PETSC_DETERMINE` for the entries
751: - h - The box size in each dimension, only used if n[d] == `PETSC_DETERMINE`, if not needed you can pass in `NULL`
753: Level: developer
755: .seealso: `DMPLEX`, `PetscGridHashCreate()`
756: @*/
757: PetscErrorCode PetscGridHashSetGrid(PetscGridHash box, const PetscInt n[], const PetscReal h[])
758: {
759: PetscInt d;
761: PetscFunctionBegin;
762: PetscAssertPointer(n, 2);
763: if (h) PetscAssertPointer(h, 3);
764: for (d = 0; d < box->dim; ++d) {
765: box->extent[d] = box->upper[d] - box->lower[d];
766: if (n[d] == PETSC_DETERMINE) {
767: PetscCheck(h, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Missing h");
768: box->h[d] = h[d];
769: box->n[d] = PetscCeilReal(box->extent[d] / h[d]);
770: } else {
771: box->n[d] = n[d];
772: box->h[d] = box->extent[d] / n[d];
773: }
774: }
775: PetscFunctionReturn(PETSC_SUCCESS);
776: }
778: /*@C
779: PetscGridHashGetEnclosingBox - Find the grid boxes containing each input point
781: Not Collective
783: Input Parameters:
784: + box - The grid hash object
785: . numPoints - The number of input points
786: - points - The input point coordinates
788: Output Parameters:
789: + dboxes - An array of `numPoints` x `dim` integers expressing the enclosing box as (i_0, i_1, ..., i_dim)
790: - boxes - An array of `numPoints` integers expressing the enclosing box as single number, or `NULL`
792: Level: developer
794: Note:
795: This only guarantees that a box contains a point, not that a cell does.
797: .seealso: `DMPLEX`, `PetscGridHashCreate()`
798: @*/
799: PetscErrorCode PetscGridHashGetEnclosingBox(PetscGridHash box, PetscInt numPoints, const PetscScalar points[], PetscInt dboxes[], PetscInt boxes[])
800: {
801: const PetscReal *lower = box->lower;
802: const PetscReal *upper = box->upper;
803: const PetscReal *h = box->h;
804: const PetscInt *n = box->n;
805: const PetscInt dim = box->dim;
806: PetscInt d, p;
808: PetscFunctionBegin;
809: for (p = 0; p < numPoints; ++p) {
810: for (d = 0; d < dim; ++d) {
811: PetscInt dbox = PetscFloorReal((PetscRealPart(points[p * dim + d]) - lower[d]) / h[d]);
813: if (dbox == n[d] && PetscAbsReal(PetscRealPart(points[p * dim + d]) - upper[d]) < 1.0e-9) dbox = n[d] - 1;
814: if (dbox == -1 && PetscAbsReal(PetscRealPart(points[p * dim + d]) - lower[d]) < 1.0e-9) dbox = 0;
815: PetscCheck(dbox >= 0 && dbox < n[d], PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Input point %" PetscInt_FMT " (%g, %g, %g) is outside of our bounding box (%g, %g, %g) - (%g, %g, %g)", p, (double)PetscRealPart(points[p * dim + 0]), dim > 1 ? (double)PetscRealPart(points[p * dim + 1]) : 0.0, dim > 2 ? (double)PetscRealPart(points[p * dim + 2]) : 0.0, (double)lower[0], (double)lower[1], (double)lower[2], (double)upper[0], (double)upper[1], (double)upper[2]);
816: dboxes[p * dim + d] = dbox;
817: }
818: if (boxes)
819: for (d = dim - 2, boxes[p] = dboxes[p * dim + dim - 1]; d >= 0; --d) boxes[p] = boxes[p] * n[d] + dboxes[p * dim + d];
820: }
821: PetscFunctionReturn(PETSC_SUCCESS);
822: }
824: /*
825: PetscGridHashGetEnclosingBoxQuery - Find the grid boxes containing each input point
827: Not Collective
829: Input Parameters:
830: + box - The grid hash object
831: . cellSection - The PetscSection mapping cells to boxes
832: . numPoints - The number of input points
833: - points - The input point coordinates
835: Output Parameters:
836: + dboxes - An array of `numPoints`*`dim` integers expressing the enclosing box as (i_0, i_1, ..., i_dim)
837: . boxes - An array of `numPoints` integers expressing the enclosing box as single number, or `NULL`
838: - found - Flag indicating if point was located within a box
840: Level: developer
842: Note:
843: This does an additional check that a cell actually contains the point, and found is `PETSC_FALSE` if no cell does. Thus, this function requires that `cellSection` is already constructed.
845: .seealso: `DMPLEX`, `PetscGridHashGetEnclosingBox()`
846: */
847: static PetscErrorCode PetscGridHashGetEnclosingBoxQuery(PetscGridHash box, PetscSection cellSection, PetscInt numPoints, const PetscScalar points[], PetscInt dboxes[], PetscInt boxes[], PetscBool *found)
848: {
849: const PetscReal *lower = box->lower;
850: const PetscReal *upper = box->upper;
851: const PetscReal *h = box->h;
852: const PetscInt *n = box->n;
853: const PetscInt dim = box->dim;
854: PetscInt bStart, bEnd, d, p;
856: PetscFunctionBegin;
858: *found = PETSC_FALSE;
859: PetscCall(PetscSectionGetChart(box->cellSection, &bStart, &bEnd));
860: for (p = 0; p < numPoints; ++p) {
861: for (d = 0; d < dim; ++d) {
862: PetscInt dbox = PetscFloorReal((PetscRealPart(points[p * dim + d]) - lower[d]) / h[d]);
864: if (dbox == n[d] && PetscAbsReal(PetscRealPart(points[p * dim + d]) - upper[d]) < 1.0e-9) dbox = n[d] - 1;
865: if (dbox < 0 || dbox >= n[d]) PetscFunctionReturn(PETSC_SUCCESS);
866: dboxes[p * dim + d] = dbox;
867: }
868: if (boxes)
869: for (d = dim - 2, boxes[p] = dboxes[p * dim + dim - 1]; d >= 0; --d) boxes[p] = boxes[p] * n[d] + dboxes[p * dim + d];
870: // It is possible for a box to overlap no grid cells
871: if (boxes[p] < bStart || boxes[p] >= bEnd) PetscFunctionReturn(PETSC_SUCCESS);
872: }
873: *found = PETSC_TRUE;
874: PetscFunctionReturn(PETSC_SUCCESS);
875: }
877: PetscErrorCode PetscGridHashDestroy(PetscGridHash *box)
878: {
879: PetscFunctionBegin;
880: if (*box) {
881: PetscCall(PetscSectionDestroy(&(*box)->cellSection));
882: PetscCall(ISDestroy(&(*box)->cells));
883: PetscCall(DMLabelDestroy(&(*box)->cellsSparse));
884: }
885: PetscCall(PetscFree(*box));
886: PetscFunctionReturn(PETSC_SUCCESS);
887: }
889: PetscErrorCode DMPlexLocatePoint_Internal(DM dm, PetscInt dim, const PetscScalar point[], PetscInt cellStart, PetscInt *cell)
890: {
891: DMPolytopeType ct;
893: PetscFunctionBegin;
894: PetscCall(DMPlexGetCellType(dm, cellStart, &ct));
895: switch (ct) {
896: case DM_POLYTOPE_SEGMENT:
897: PetscCall(DMPlexLocatePoint_Simplex_1D_Internal(dm, point, cellStart, cell));
898: break;
899: case DM_POLYTOPE_TRIANGLE:
900: PetscCall(DMPlexLocatePoint_Simplex_2D_Internal(dm, point, cellStart, cell));
901: break;
902: case DM_POLYTOPE_QUADRILATERAL:
903: PetscCall(DMPlexLocatePoint_Quad_2D_Internal(dm, point, cellStart, cell));
904: break;
905: case DM_POLYTOPE_TETRAHEDRON:
906: PetscCall(DMPlexLocatePoint_Simplex_3D_Internal(dm, point, cellStart, cell));
907: break;
908: case DM_POLYTOPE_HEXAHEDRON:
909: PetscCall(DMPlexLocatePoint_Hex_3D_Internal(dm, point, cellStart, cell));
910: break;
911: default:
912: SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No point location for cell %" PetscInt_FMT " with type %s", cellStart, DMPolytopeTypes[ct]);
913: }
914: PetscFunctionReturn(PETSC_SUCCESS);
915: }
917: /*
918: DMPlexClosestPoint_Internal - Returns the closest point in the cell to the given point
919: */
920: static PetscErrorCode DMPlexClosestPoint_Internal(DM dm, PetscInt dim, const PetscScalar point[], PetscInt cell, PetscReal cpoint[])
921: {
922: DMPolytopeType ct;
924: PetscFunctionBegin;
925: PetscCall(DMPlexGetCellType(dm, cell, &ct));
926: switch (ct) {
927: case DM_POLYTOPE_TRIANGLE:
928: PetscCall(DMPlexClosestPoint_Simplex_2D_Internal(dm, point, cell, cpoint));
929: break;
930: #if 0
931: case DM_POLYTOPE_QUADRILATERAL:
932: PetscCall(DMPlexClosestPoint_General_2D_Internal(dm, point, cell, cpoint));break;
933: case DM_POLYTOPE_TETRAHEDRON:
934: PetscCall(DMPlexClosestPoint_Simplex_3D_Internal(dm, point, cell, cpoint));break;
935: case DM_POLYTOPE_HEXAHEDRON:
936: PetscCall(DMPlexClosestPoint_General_3D_Internal(dm, point, cell, cpoint));break;
937: #endif
938: default:
939: SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No closest point location for cell %" PetscInt_FMT " with type %s", cell, DMPolytopeTypes[ct]);
940: }
941: PetscFunctionReturn(PETSC_SUCCESS);
942: }
944: /*
945: DMPlexComputeGridHash_Internal - Create a grid hash structure covering the `DMPLEX`
947: Collective
949: Input Parameter:
950: . dm - The `DMPLEX`
952: Output Parameter:
953: . localBox - The grid hash object
955: Level: developer
957: Notes:
958: How do we determine all boxes intersecting a given cell?
960: 1) Get convex body enclosing cell. We will use a box called the box-hull.
962: 2) Get smallest brick of boxes enclosing the box-hull
964: 3) Each box is composed of 6 planes, 3 lower and 3 upper. We loop over dimensions, and
965: for each new plane determine whether the cell is on the negative side, positive side, or intersects it.
967: a) If the cell is on the negative side of the lower planes, it is not in the box
969: b) If the cell is on the positive side of the upper planes, it is not in the box
971: c) If there is no intersection, it is in the box
973: d) If any intersection point is within the box limits, it is in the box
975: .seealso: `DMPLEX`, `PetscGridHashCreate()`, `PetscGridHashGetEnclosingBox()`
976: */
977: static PetscErrorCode DMPlexComputeGridHash_Internal(DM dm, PetscGridHash *localBox)
978: {
979: PetscInt debug = ((DM_Plex *)dm->data)->printLocate;
980: PetscGridHash lbox;
981: PetscSF sf;
982: const PetscInt *leaves;
983: PetscInt *dboxes, *boxes;
984: PetscInt cdim, cStart, cEnd, Nl = -1;
985: PetscBool flg;
987: PetscFunctionBegin;
988: PetscCall(DMGetCoordinateDim(dm, &cdim));
989: PetscCall(DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd));
990: PetscCall(DMPlexCreateGridHash(dm, &lbox));
991: {
992: PetscInt n[3], d;
994: PetscCall(PetscOptionsGetIntArray(NULL, ((PetscObject)dm)->prefix, "-dm_plex_hash_box_faces", n, &d, &flg));
995: if (flg) {
996: for (PetscInt i = d; i < cdim; ++i) n[i] = n[d - 1];
997: } else {
998: for (PetscInt i = 0; i < cdim; ++i) n[i] = PetscMax(2, PetscFloorReal(PetscPowReal((PetscReal)(cEnd - cStart), 1.0 / cdim) * 0.8));
999: }
1000: PetscCall(PetscGridHashSetGrid(lbox, n, NULL));
1001: if (debug)
1002: PetscCall(PetscPrintf(PETSC_COMM_SELF, "GridHash:\n (%g, %g, %g) -- (%g, %g, %g)\n n %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT "\n h %g %g %g\n", (double)lbox->lower[0], (double)lbox->lower[1], cdim > 2 ? (double)lbox->lower[2] : 0.,
1003: (double)lbox->upper[0], (double)lbox->upper[1], cdim > 2 ? (double)lbox->upper[2] : 0, n[0], n[1], cdim > 2 ? n[2] : 0, (double)lbox->h[0], (double)lbox->h[1], cdim > 2 ? (double)lbox->h[2] : 0.));
1004: }
1006: PetscCall(DMGetPointSF(dm, &sf));
1007: if (sf) PetscCall(PetscSFGetGraph(sf, NULL, &Nl, &leaves, NULL));
1008: Nl = PetscMax(Nl, 0);
1009: PetscCall(PetscCalloc2(16 * cdim, &dboxes, 16, &boxes));
1011: PetscCall(DMLabelCreate(PETSC_COMM_SELF, "cells", &lbox->cellsSparse));
1012: PetscCall(DMLabelCreateIndex(lbox->cellsSparse, cStart, cEnd));
1013: for (PetscInt c = cStart; c < cEnd; ++c) {
1014: PetscReal intPoints[6 * 6 * 6 * 3];
1015: const PetscScalar *array;
1016: PetscScalar *coords = NULL;
1017: const PetscReal *h = lbox->h;
1018: PetscReal normal[9] = {1., 0., 0., 0., 1., 0., 0., 0., 1.};
1019: PetscReal *lowerIntPoints[3] = {&intPoints[0 * 6 * 6 * 3], &intPoints[1 * 6 * 6 * 3], &intPoints[2 * 6 * 6 * 3]};
1020: PetscReal *upperIntPoints[3] = {&intPoints[3 * 6 * 6 * 3], &intPoints[4 * 6 * 6 * 3], &intPoints[5 * 6 * 6 * 3]};
1021: PetscReal lp[3], up[3], *tmp;
1022: PetscInt numCoords, idx, dlim[6], lowerInt[3], upperInt[3];
1023: PetscBool isDG, lower[3], upper[3];
1025: PetscCall(PetscFindInt(c, Nl, leaves, &idx));
1026: if (idx >= 0) continue;
1027: // Get grid of boxes containing the cell
1028: PetscCall(DMPlexGetCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
1029: PetscCall(PetscGridHashGetEnclosingBox(lbox, numCoords / cdim, coords, dboxes, boxes));
1030: PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
1031: for (PetscInt d = 0; d < cdim; ++d) dlim[d * 2 + 0] = dlim[d * 2 + 1] = dboxes[d];
1032: for (PetscInt d = cdim; d < 3; ++d) dlim[d * 2 + 0] = dlim[d * 2 + 1] = 0;
1033: for (PetscInt e = 1; e < numCoords / cdim; ++e) {
1034: for (PetscInt d = 0; d < cdim; ++d) {
1035: dlim[d * 2 + 0] = PetscMin(dlim[d * 2 + 0], dboxes[e * cdim + d]);
1036: dlim[d * 2 + 1] = PetscMax(dlim[d * 2 + 1], dboxes[e * cdim + d]);
1037: }
1038: }
1039: if (debug > 4) {
1040: for (PetscInt d = 0; d < cdim; ++d) PetscCall(PetscPrintf(PETSC_COMM_SELF, " Cell %" PetscInt_FMT " direction %" PetscInt_FMT " box limits %" PetscInt_FMT "--%" PetscInt_FMT "\n", c, d, dlim[d * 2 + 0], dlim[d * 2 + 1]));
1041: }
1042: // Initialize with lower planes for first box
1043: for (PetscInt d = 0; d < cdim; ++d) {
1044: lp[d] = lbox->lower[d] + dlim[d * 2 + 0] * h[d];
1045: up[d] = lp[d] + h[d];
1046: }
1047: for (PetscInt d = 0; d < cdim; ++d) {
1048: PetscCall(DMPlexGetPlaneCellIntersection_Internal(dm, c, lp, &normal[d * 3], &lower[d], &lowerInt[d], lowerIntPoints[d]));
1049: if (debug > 4) {
1050: if (!lowerInt[d])
1051: PetscCall(PetscPrintf(PETSC_COMM_SELF, " Cell %" PetscInt_FMT " lower direction %" PetscInt_FMT " (%g, %g, %g) does not intersect %s\n", c, d, (double)lp[0], (double)lp[1], cdim > 2 ? (double)lp[2] : 0., lower[d] ? "positive" : "negative"));
1052: else PetscCall(PetscPrintf(PETSC_COMM_SELF, " Cell %" PetscInt_FMT " lower direction %" PetscInt_FMT " (%g, %g, %g) intersects %" PetscInt_FMT " times\n", c, d, (double)lp[0], (double)lp[1], cdim > 2 ? (double)lp[2] : 0., lowerInt[d]));
1053: }
1054: }
1055: // Loop over grid
1056: for (PetscInt k = dlim[2 * 2 + 0]; k <= dlim[2 * 2 + 1]; ++k, lp[2] = up[2], up[2] += h[2]) {
1057: if (cdim > 2) PetscCall(DMPlexGetPlaneCellIntersection_Internal(dm, c, up, &normal[3 * 2], &upper[2], &upperInt[2], upperIntPoints[2]));
1058: if (cdim > 2 && debug > 4) {
1059: if (!upperInt[2]) PetscCall(PetscPrintf(PETSC_COMM_SELF, " Cell %" PetscInt_FMT " upper direction 2 (%g, %g, %g) does not intersect %s\n", c, (double)up[0], (double)up[1], cdim > 2 ? (double)up[2] : 0., upper[2] ? "positive" : "negative"));
1060: else PetscCall(PetscPrintf(PETSC_COMM_SELF, " Cell %" PetscInt_FMT " upper direction 2 (%g, %g, %g) intersects %" PetscInt_FMT " times\n", c, (double)up[0], (double)up[1], cdim > 2 ? (double)up[2] : 0., upperInt[2]));
1061: }
1062: for (PetscInt j = dlim[1 * 2 + 0]; j <= dlim[1 * 2 + 1]; ++j, lp[1] = up[1], up[1] += h[1]) {
1063: if (cdim > 1) PetscCall(DMPlexGetPlaneCellIntersection_Internal(dm, c, up, &normal[3 * 1], &upper[1], &upperInt[1], upperIntPoints[1]));
1064: if (cdim > 1 && debug > 4) {
1065: if (!upperInt[1])
1066: PetscCall(PetscPrintf(PETSC_COMM_SELF, " Cell %" PetscInt_FMT " upper direction 1 (%g, %g, %g) does not intersect %s\n", c, (double)up[0], (double)up[1], cdim > 2 ? (double)up[2] : 0., upper[1] ? "positive" : "negative"));
1067: else PetscCall(PetscPrintf(PETSC_COMM_SELF, " Cell %" PetscInt_FMT " upper direction 1 (%g, %g, %g) intersects %" PetscInt_FMT " times\n", c, (double)up[0], (double)up[1], cdim > 2 ? (double)up[2] : 0., upperInt[1]));
1068: }
1069: for (PetscInt i = dlim[0 * 2 + 0]; i <= dlim[0 * 2 + 1]; ++i, lp[0] = up[0], up[0] += h[0]) {
1070: const PetscInt box = (k * lbox->n[1] + j) * lbox->n[0] + i;
1071: PetscBool excNeg = PETSC_TRUE;
1072: PetscBool excPos = PETSC_TRUE;
1073: PetscInt NlInt = 0;
1074: PetscInt NuInt = 0;
1076: PetscCall(DMPlexGetPlaneCellIntersection_Internal(dm, c, up, &normal[3 * 0], &upper[0], &upperInt[0], upperIntPoints[0]));
1077: if (debug > 4) {
1078: if (!upperInt[0])
1079: PetscCall(PetscPrintf(PETSC_COMM_SELF, " Cell %" PetscInt_FMT " upper direction 0 (%g, %g, %g) does not intersect %s\n", c, (double)up[0], (double)up[1], cdim > 2 ? (double)up[2] : 0., upper[0] ? "positive" : "negative"));
1080: else PetscCall(PetscPrintf(PETSC_COMM_SELF, " Cell %" PetscInt_FMT " upper direction 0 (%g, %g, %g) intersects %" PetscInt_FMT " times\n", c, (double)up[0], (double)up[1], cdim > 2 ? (double)up[2] : 0., upperInt[0]));
1081: }
1082: for (PetscInt d = 0; d < cdim; ++d) {
1083: NlInt += lowerInt[d];
1084: NuInt += upperInt[d];
1085: }
1086: // If there is no intersection...
1087: if (!NlInt && !NuInt) {
1088: // If the cell is on the negative side of the lower planes, it is not in the box
1089: for (PetscInt d = 0; d < cdim; ++d)
1090: if (lower[d]) {
1091: excNeg = PETSC_FALSE;
1092: break;
1093: }
1094: // If the cell is on the positive side of the upper planes, it is not in the box
1095: for (PetscInt d = 0; d < cdim; ++d)
1096: if (!upper[d]) {
1097: excPos = PETSC_FALSE;
1098: break;
1099: }
1100: if (excNeg || excPos) {
1101: if (debug && excNeg) PetscCall(PetscPrintf(PETSC_COMM_SELF, " Cell %" PetscInt_FMT " is on the negative side of the lower plane\n", c));
1102: if (debug && excPos) PetscCall(PetscPrintf(PETSC_COMM_SELF, " Cell %" PetscInt_FMT " is on the positive side of the upper plane\n", c));
1103: continue;
1104: }
1105: // Otherwise it is in the box
1106: if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, " Cell %" PetscInt_FMT " is contained in box %" PetscInt_FMT "\n", c, box));
1107: PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
1108: continue;
1109: }
1110: /*
1111: If any intersection point is within the box limits, it is in the box
1112: We need to have tolerances here since intersection point calculations can introduce errors
1113: Initialize a count to track which planes have intersection outside the box.
1114: if two adjacent planes have intersection points upper and lower all outside the box, look
1115: first at if another plane has intersection points outside the box, if so, it is inside the cell
1116: look next if no intersection points exist on the other planes, and check if the planes are on the
1117: outside of the intersection points but on opposite ends. If so, the box cuts through the cell.
1118: */
1119: PetscInt outsideCount[6] = {0, 0, 0, 0, 0, 0};
1120: for (PetscInt plane = 0; plane < cdim; ++plane) {
1121: for (PetscInt ip = 0; ip < lowerInt[plane]; ++ip) {
1122: PetscInt d;
1124: for (d = 0; d < cdim; ++d) {
1125: if ((lowerIntPoints[plane][ip * cdim + d] < (lp[d] - PETSC_SMALL)) || (lowerIntPoints[plane][ip * cdim + d] > (up[d] + PETSC_SMALL))) {
1126: if (lowerIntPoints[plane][ip * cdim + d] < (lp[d] - PETSC_SMALL)) outsideCount[d]++; // The lower point is to the left of this box, and we count it
1127: break;
1128: }
1129: }
1130: if (d == cdim) {
1131: if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, " Cell %" PetscInt_FMT " intersected lower plane %" PetscInt_FMT " of box %" PetscInt_FMT "\n", c, plane, box));
1132: PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
1133: goto end;
1134: }
1135: }
1136: for (PetscInt ip = 0; ip < upperInt[plane]; ++ip) {
1137: PetscInt d;
1139: for (d = 0; d < cdim; ++d) {
1140: if ((upperIntPoints[plane][ip * cdim + d] < (lp[d] - PETSC_SMALL)) || (upperIntPoints[plane][ip * cdim + d] > (up[d] + PETSC_SMALL))) {
1141: if (upperIntPoints[plane][ip * cdim + d] > (up[d] + PETSC_SMALL)) outsideCount[cdim + d]++; // The upper point is to the right of this box, and we count it
1142: break;
1143: }
1144: }
1145: if (d == cdim) {
1146: if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, " Cell %" PetscInt_FMT " intersected upper plane %" PetscInt_FMT " of box %" PetscInt_FMT "\n", c, plane, box));
1147: PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
1148: goto end;
1149: }
1150: }
1151: }
1152: /*
1153: Check the planes with intersections
1154: in 2D, check if the square falls in the middle of a cell
1155: ie all four planes have intersection points outside of the box
1156: You do not want to be doing this, because it means your grid hashing is finer than your grid,
1157: but we should still support it I guess
1158: */
1159: if (cdim == 2) {
1160: PetscInt nIntersects = 0;
1161: for (PetscInt d = 0; d < cdim; ++d) nIntersects += (outsideCount[d] + outsideCount[d + cdim]);
1162: // if the count adds up to 8, that means each plane has 2 external intersections and thus it is in the cell
1163: if (nIntersects == 8) {
1164: PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
1165: goto end;
1166: }
1167: }
1168: /*
1169: In 3 dimensions, if two adjacent planes have at least 3 intersections outside the cell in the appropriate direction,
1170: we then check the 3rd planar dimension. If a plane falls between intersection points, the cell belongs to that box.
1171: If the planes are on opposite sides of the intersection points, the cell belongs to that box and it passes through the cell.
1172: */
1173: if (cdim == 3) {
1174: PetscInt faces[3] = {0, 0, 0}, checkInternalFace = 0;
1175: // Find two adjacent planes with at least 3 intersection points in the upper and lower
1176: // if the third plane has 3 intersection points or more, a pyramid base is formed on that plane and it is in the cell
1177: for (PetscInt d = 0; d < cdim; ++d)
1178: if (outsideCount[d] >= 3 && outsideCount[cdim + d] >= 3) {
1179: faces[d]++;
1180: checkInternalFace++;
1181: }
1182: if (checkInternalFace == 3) {
1183: // All planes have 3 intersection points, add it.
1184: PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
1185: goto end;
1186: }
1187: // Gross, figure out which adjacent faces have at least 3 points
1188: PetscInt nonIntersectingFace = -1;
1189: if (faces[0] == faces[1]) nonIntersectingFace = 2;
1190: if (faces[0] == faces[2]) nonIntersectingFace = 1;
1191: if (faces[1] == faces[2]) nonIntersectingFace = 0;
1192: if (nonIntersectingFace >= 0) {
1193: for (PetscInt plane = 0; plane < cdim; ++plane) {
1194: if (!lowerInt[nonIntersectingFace] && !upperInt[nonIntersectingFace]) continue;
1195: // If we have 2 adjacent sides with pyramids of intersection outside of them, and there is a point between the end caps at all, it must be between the two non intersecting ends, and the box is inside the cell.
1196: for (PetscInt ip = 0; ip < lowerInt[nonIntersectingFace]; ++ip) {
1197: if (lowerIntPoints[plane][ip * cdim + nonIntersectingFace] > lp[nonIntersectingFace] - PETSC_SMALL || lowerIntPoints[plane][ip * cdim + nonIntersectingFace] < up[nonIntersectingFace] + PETSC_SMALL) goto setpoint;
1198: }
1199: for (PetscInt ip = 0; ip < upperInt[nonIntersectingFace]; ++ip) {
1200: if (upperIntPoints[plane][ip * cdim + nonIntersectingFace] > lp[nonIntersectingFace] - PETSC_SMALL || upperIntPoints[plane][ip * cdim + nonIntersectingFace] < up[nonIntersectingFace] + PETSC_SMALL) goto setpoint;
1201: }
1202: goto end;
1203: }
1204: // The points are within the bonds of the non intersecting planes, add it.
1205: setpoint:
1206: PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
1207: goto end;
1208: }
1209: }
1210: end:
1211: lower[0] = upper[0];
1212: lowerInt[0] = upperInt[0];
1213: tmp = lowerIntPoints[0];
1214: lowerIntPoints[0] = upperIntPoints[0];
1215: upperIntPoints[0] = tmp;
1216: }
1217: lp[0] = lbox->lower[0] + dlim[0 * 2 + 0] * h[0];
1218: up[0] = lp[0] + h[0];
1219: lower[1] = upper[1];
1220: lowerInt[1] = upperInt[1];
1221: tmp = lowerIntPoints[1];
1222: lowerIntPoints[1] = upperIntPoints[1];
1223: upperIntPoints[1] = tmp;
1224: }
1225: lp[1] = lbox->lower[1] + dlim[1 * 2 + 0] * h[1];
1226: up[1] = lp[1] + h[1];
1227: lower[2] = upper[2];
1228: lowerInt[2] = upperInt[2];
1229: tmp = lowerIntPoints[2];
1230: lowerIntPoints[2] = upperIntPoints[2];
1231: upperIntPoints[2] = tmp;
1232: }
1233: }
1234: PetscCall(PetscFree2(dboxes, boxes));
1236: if (debug) PetscCall(DMLabelView(lbox->cellsSparse, PETSC_VIEWER_STDOUT_SELF));
1237: PetscCall(DMLabelConvertToSection(lbox->cellsSparse, &lbox->cellSection, &lbox->cells));
1238: PetscCall(DMLabelDestroy(&lbox->cellsSparse));
1239: *localBox = lbox;
1240: PetscFunctionReturn(PETSC_SUCCESS);
1241: }
1243: PetscErrorCode DMLocatePoints_Plex(DM dm, Vec v, DMPointLocationType ltype, PetscSF cellSF)
1244: {
1245: PetscInt debug = ((DM_Plex *)dm->data)->printLocate;
1246: DM_Plex *mesh = (DM_Plex *)dm->data;
1247: PetscBool hash = mesh->useHashLocation, reuse = PETSC_FALSE;
1248: PetscInt bs, numPoints, p, numFound, *found = NULL;
1249: PetscInt dim, Nl = 0, cStart, cEnd, numCells, c, d;
1250: PetscSF sf;
1251: const PetscInt *leaves;
1252: const PetscInt *boxCells;
1253: PetscSFNode *cells;
1254: PetscScalar *a;
1255: PetscMPIInt result;
1256: PetscLogDouble t0, t1;
1257: PetscReal gmin[3], gmax[3];
1258: PetscInt terminating_query_type[] = {0, 0, 0};
1259: PetscMPIInt rank;
1261: PetscFunctionBegin;
1262: PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank));
1263: PetscCall(PetscLogEventBegin(DMPLEX_LocatePoints, 0, 0, 0, 0));
1264: PetscCall(PetscTime(&t0));
1265: PetscCheck(ltype != DM_POINTLOCATION_NEAREST || hash, PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Nearest point location only supported with grid hashing. Use -dm_plex_hash_location to enable it.");
1266: PetscCall(DMGetCoordinateDim(dm, &dim));
1267: PetscCall(VecGetBlockSize(v, &bs));
1268: PetscCallMPI(MPI_Comm_compare(PetscObjectComm((PetscObject)cellSF), PETSC_COMM_SELF, &result));
1269: PetscCheck(result == MPI_IDENT || result == MPI_CONGRUENT, PetscObjectComm((PetscObject)cellSF), PETSC_ERR_SUP, "Trying parallel point location: only local point location supported");
1270: // We ignore extra coordinates
1271: PetscCheck(bs >= dim, PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Block size for point vector %" PetscInt_FMT " must be the mesh coordinate dimension %" PetscInt_FMT, bs, dim);
1272: PetscCall(DMGetCoordinatesLocalSetUp(dm));
1273: PetscCall(DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd));
1274: PetscCall(DMGetPointSF(dm, &sf));
1275: if (sf) PetscCall(PetscSFGetGraph(sf, NULL, &Nl, &leaves, NULL));
1276: Nl = PetscMax(Nl, 0);
1277: PetscCall(VecGetLocalSize(v, &numPoints));
1278: PetscCall(VecGetArray(v, &a));
1279: numPoints /= bs;
1280: {
1281: const PetscSFNode *sf_cells;
1283: PetscCall(PetscSFGetGraph(cellSF, NULL, NULL, NULL, &sf_cells));
1284: if (sf_cells) {
1285: PetscCall(PetscInfo(dm, "[DMLocatePoints_Plex] Re-using existing StarForest node list\n"));
1286: cells = (PetscSFNode *)sf_cells;
1287: reuse = PETSC_TRUE;
1288: } else {
1289: PetscCall(PetscInfo(dm, "[DMLocatePoints_Plex] Creating and initializing new StarForest node list\n"));
1290: PetscCall(PetscMalloc1(numPoints, &cells));
1291: /* initialize cells if created */
1292: for (p = 0; p < numPoints; p++) {
1293: cells[p].rank = 0;
1294: cells[p].index = DMLOCATEPOINT_POINT_NOT_FOUND;
1295: }
1296: }
1297: }
1298: PetscCall(DMGetBoundingBox(dm, gmin, gmax));
1299: if (hash) {
1300: if (!mesh->lbox) {
1301: PetscCall(PetscInfo(dm, "Initializing grid hashing\n"));
1302: PetscCall(DMPlexComputeGridHash_Internal(dm, &mesh->lbox));
1303: }
1304: /* Designate the local box for each point */
1305: /* Send points to correct process */
1306: /* Search cells that lie in each subbox */
1307: /* Should we bin points before doing search? */
1308: PetscCall(ISGetIndices(mesh->lbox->cells, &boxCells));
1309: }
1310: for (p = 0, numFound = 0; p < numPoints; ++p) {
1311: const PetscScalar *point = &a[p * bs];
1312: PetscInt dbin[3] = {-1, -1, -1}, bin, cell = -1, cellOffset;
1313: PetscBool point_outside_domain = PETSC_FALSE;
1315: /* check bounding box of domain */
1316: for (d = 0; d < dim; d++) {
1317: if (PetscRealPart(point[d]) < gmin[d]) {
1318: point_outside_domain = PETSC_TRUE;
1319: break;
1320: }
1321: if (PetscRealPart(point[d]) > gmax[d]) {
1322: point_outside_domain = PETSC_TRUE;
1323: break;
1324: }
1325: }
1326: if (point_outside_domain) {
1327: cells[p].rank = 0;
1328: cells[p].index = DMLOCATEPOINT_POINT_NOT_FOUND;
1329: terminating_query_type[0]++;
1330: continue;
1331: }
1333: /* check initial values in cells[].index - abort early if found */
1334: if (cells[p].index != DMLOCATEPOINT_POINT_NOT_FOUND) {
1335: c = cells[p].index;
1336: cells[p].index = DMLOCATEPOINT_POINT_NOT_FOUND;
1337: PetscCall(DMPlexLocatePoint_Internal(dm, dim, point, c, &cell));
1338: if (cell >= 0) {
1339: cells[p].rank = 0;
1340: cells[p].index = cell;
1341: numFound++;
1342: }
1343: }
1344: if (cells[p].index != DMLOCATEPOINT_POINT_NOT_FOUND) {
1345: terminating_query_type[1]++;
1346: continue;
1347: }
1349: if (hash) {
1350: PetscBool found_box;
1352: if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, "[%d]Checking point %" PetscInt_FMT " (%.2g, %.2g, %.2g)\n", rank, p, (double)PetscRealPart(point[0]), (double)PetscRealPart(point[1]), dim > 2 ? (double)PetscRealPart(point[2]) : 0.));
1353: /* allow for case that point is outside box - abort early */
1354: PetscCall(PetscGridHashGetEnclosingBoxQuery(mesh->lbox, mesh->lbox->cellSection, 1, point, dbin, &bin, &found_box));
1355: if (found_box) {
1356: if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, "[%d] Found point in box %" PetscInt_FMT " (%" PetscInt_FMT ", %" PetscInt_FMT ", %" PetscInt_FMT ")\n", rank, bin, dbin[0], dbin[1], dim > 2 ? dbin[2] : 0));
1357: /* TODO Lay an interface over this so we can switch between Section (dense) and Label (sparse) */
1358: PetscCall(PetscSectionGetDof(mesh->lbox->cellSection, bin, &numCells));
1359: PetscCall(PetscSectionGetOffset(mesh->lbox->cellSection, bin, &cellOffset));
1360: for (c = cellOffset; c < cellOffset + numCells; ++c) {
1361: if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, "[%d] Checking for point in cell %" PetscInt_FMT "\n", rank, boxCells[c]));
1362: PetscCall(DMPlexLocatePoint_Internal(dm, dim, point, boxCells[c], &cell));
1363: if (cell >= 0) {
1364: if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, "[%d] FOUND in cell %" PetscInt_FMT "\n", rank, cell));
1365: cells[p].rank = 0;
1366: cells[p].index = cell;
1367: numFound++;
1368: terminating_query_type[2]++;
1369: break;
1370: }
1371: }
1372: }
1373: } else {
1374: PetscBool found = PETSC_FALSE;
1375: for (c = cStart; c < cEnd; ++c) {
1376: PetscInt idx;
1378: PetscCall(PetscFindInt(c, Nl, leaves, &idx));
1379: if (idx >= 0) continue;
1380: PetscCall(DMPlexLocatePoint_Internal(dm, dim, point, c, &cell));
1381: if (cell >= 0) {
1382: cells[p].rank = 0;
1383: cells[p].index = cell;
1384: numFound++;
1385: terminating_query_type[2]++;
1386: found = PETSC_TRUE;
1387: break;
1388: }
1389: }
1390: if (!found) terminating_query_type[0]++;
1391: }
1392: }
1393: if (hash) PetscCall(ISRestoreIndices(mesh->lbox->cells, &boxCells));
1394: if (ltype == DM_POINTLOCATION_NEAREST && hash && numFound < numPoints) {
1395: for (p = 0; p < numPoints; p++) {
1396: const PetscScalar *point = &a[p * bs];
1397: PetscReal cpoint[3] = {0, 0, 0}, diff[3], best[3] = {PETSC_MAX_REAL, PETSC_MAX_REAL, PETSC_MAX_REAL}, dist, distMax = PETSC_MAX_REAL;
1398: PetscInt dbin[3] = {-1, -1, -1}, bin, cellOffset, d, bestc = -1;
1400: if (cells[p].index < 0) {
1401: PetscCall(PetscGridHashGetEnclosingBox(mesh->lbox, 1, point, dbin, &bin));
1402: PetscCall(PetscSectionGetDof(mesh->lbox->cellSection, bin, &numCells));
1403: PetscCall(PetscSectionGetOffset(mesh->lbox->cellSection, bin, &cellOffset));
1404: for (c = cellOffset; c < cellOffset + numCells; ++c) {
1405: PetscCall(DMPlexClosestPoint_Internal(dm, dim, point, boxCells[c], cpoint));
1406: for (d = 0; d < dim; ++d) diff[d] = cpoint[d] - PetscRealPart(point[d]);
1407: dist = DMPlex_NormD_Internal(dim, diff);
1408: if (dist < distMax) {
1409: for (d = 0; d < dim; ++d) best[d] = cpoint[d];
1410: bestc = boxCells[c];
1411: distMax = dist;
1412: }
1413: }
1414: if (distMax < PETSC_MAX_REAL) {
1415: ++numFound;
1416: cells[p].rank = 0;
1417: cells[p].index = bestc;
1418: for (d = 0; d < dim; ++d) a[p * bs + d] = best[d];
1419: }
1420: }
1421: }
1422: }
1423: /* This code is only be relevant when interfaced to parallel point location */
1424: /* Check for highest numbered proc that claims a point (do we care?) */
1425: if (ltype == DM_POINTLOCATION_REMOVE && numFound < numPoints) {
1426: PetscCall(PetscMalloc1(numFound, &found));
1427: for (p = 0, numFound = 0; p < numPoints; p++) {
1428: if (cells[p].rank >= 0 && cells[p].index >= 0) {
1429: if (numFound < p) cells[numFound] = cells[p];
1430: found[numFound++] = p;
1431: }
1432: }
1433: }
1434: PetscCall(VecRestoreArray(v, &a));
1435: if (!reuse) PetscCall(PetscSFSetGraph(cellSF, cEnd - cStart, numFound, found, PETSC_OWN_POINTER, cells, PETSC_OWN_POINTER));
1436: PetscCall(PetscTime(&t1));
1437: if (hash) {
1438: PetscCall(PetscInfo(dm, "[DMLocatePoints_Plex] terminating_query_type : %" PetscInt_FMT " [outside domain] : %" PetscInt_FMT " [inside initial cell] : %" PetscInt_FMT " [hash]\n", terminating_query_type[0], terminating_query_type[1], terminating_query_type[2]));
1439: } else {
1440: PetscCall(PetscInfo(dm, "[DMLocatePoints_Plex] terminating_query_type : %" PetscInt_FMT " [outside domain] : %" PetscInt_FMT " [inside initial cell] : %" PetscInt_FMT " [brute-force]\n", terminating_query_type[0], terminating_query_type[1], terminating_query_type[2]));
1441: }
1442: PetscCall(PetscInfo(dm, "[DMLocatePoints_Plex] npoints %" PetscInt_FMT " : time(rank0) %1.2e (sec): points/sec %1.4e\n", numPoints, t1 - t0, numPoints / (t1 - t0)));
1443: PetscCall(PetscLogEventEnd(DMPLEX_LocatePoints, 0, 0, 0, 0));
1444: PetscFunctionReturn(PETSC_SUCCESS);
1445: }
1447: /*@
1448: DMPlexComputeProjection2Dto1D - Rewrite coordinates to be the 1D projection of the 2D coordinates
1450: Not Collective
1452: Input/Output Parameter:
1453: . coords - The coordinates of a segment, on output the new y-coordinate, and 0 for x, an array of size 4, last two entries are unchanged
1455: Output Parameter:
1456: . R - The rotation which accomplishes the projection, array of size 4
1458: Level: developer
1460: .seealso: `DMPLEX`, `DMPlexComputeProjection3Dto1D()`, `DMPlexComputeProjection3Dto2D()`
1461: @*/
1462: PetscErrorCode DMPlexComputeProjection2Dto1D(PetscScalar coords[], PetscReal R[])
1463: {
1464: const PetscReal x = PetscRealPart(coords[2] - coords[0]);
1465: const PetscReal y = PetscRealPart(coords[3] - coords[1]);
1466: const PetscReal r = PetscSqrtReal(x * x + y * y), c = x / r, s = y / r;
1468: PetscFunctionBegin;
1469: R[0] = c;
1470: R[1] = -s;
1471: R[2] = s;
1472: R[3] = c;
1473: coords[0] = 0.0;
1474: coords[1] = r;
1475: PetscFunctionReturn(PETSC_SUCCESS);
1476: }
1478: /*@
1479: DMPlexComputeProjection3Dto1D - Rewrite coordinates to be the 1D projection of the 3D coordinates
1481: Not Collective
1483: Input/Output Parameter:
1484: . coords - The coordinates of a segment; on output, the new y-coordinate, and 0 for x and z, an array of size 6, the other entries are unchanged
1486: Output Parameter:
1487: . R - The rotation which accomplishes the projection, an array of size 9
1489: Level: developer
1491: Note:
1492: This uses the basis completion described by Frisvad {cite}`frisvad2012building`
1494: .seealso: `DMPLEX`, `DMPlexComputeProjection2Dto1D()`, `DMPlexComputeProjection3Dto2D()`
1495: @*/
1496: PetscErrorCode DMPlexComputeProjection3Dto1D(PetscScalar coords[], PetscReal R[])
1497: {
1498: PetscReal x = PetscRealPart(coords[3] - coords[0]);
1499: PetscReal y = PetscRealPart(coords[4] - coords[1]);
1500: PetscReal z = PetscRealPart(coords[5] - coords[2]);
1501: PetscReal r = PetscSqrtReal(x * x + y * y + z * z);
1502: PetscReal rinv = 1. / r;
1504: PetscFunctionBegin;
1505: x *= rinv;
1506: y *= rinv;
1507: z *= rinv;
1508: if (x > 0.) {
1509: PetscReal inv1pX = 1. / (1. + x);
1511: R[0] = x;
1512: R[1] = -y;
1513: R[2] = -z;
1514: R[3] = y;
1515: R[4] = 1. - y * y * inv1pX;
1516: R[5] = -y * z * inv1pX;
1517: R[6] = z;
1518: R[7] = -y * z * inv1pX;
1519: R[8] = 1. - z * z * inv1pX;
1520: } else {
1521: PetscReal inv1mX = 1. / (1. - x);
1523: R[0] = x;
1524: R[1] = z;
1525: R[2] = y;
1526: R[3] = y;
1527: R[4] = -y * z * inv1mX;
1528: R[5] = 1. - y * y * inv1mX;
1529: R[6] = z;
1530: R[7] = 1. - z * z * inv1mX;
1531: R[8] = -y * z * inv1mX;
1532: }
1533: coords[0] = 0.0;
1534: coords[1] = r;
1535: coords[2] = 0.0;
1536: PetscFunctionReturn(PETSC_SUCCESS);
1537: }
1539: /*@
1540: DMPlexComputeProjection3Dto2D - Rewrite coordinates of 3 or more coplanar 3D points to a common 2D basis for the
1541: plane. The normal is defined by positive orientation of the first 3 points.
1543: Not Collective
1545: Input Parameter:
1546: . coordSize - Length of coordinate array (3x number of points); must be at least 9 (3 points)
1548: Input/Output Parameter:
1549: . coords - The interlaced coordinates of each coplanar 3D point; on output the first
1550: 2*coordSize/3 entries contain interlaced 2D points, with the rest undefined
1552: Output Parameter:
1553: . R - 3x3 row-major rotation matrix whose columns are the tangent basis [t1, t2, n]. Multiplying by R^T transforms from original frame to tangent frame.
1555: Level: developer
1557: .seealso: `DMPLEX`, `DMPlexComputeProjection2Dto1D()`, `DMPlexComputeProjection3Dto1D()`
1558: @*/
1559: PetscErrorCode DMPlexComputeProjection3Dto2D(PetscInt coordSize, PetscScalar coords[], PetscReal R[])
1560: {
1561: PetscReal x1[3], x2[3], n[3], c[3], norm;
1562: const PetscInt dim = 3;
1563: PetscInt d, p;
1565: PetscFunctionBegin;
1566: /* 0) Calculate normal vector */
1567: for (d = 0; d < dim; ++d) {
1568: x1[d] = PetscRealPart(coords[1 * dim + d] - coords[0 * dim + d]);
1569: x2[d] = PetscRealPart(coords[2 * dim + d] - coords[0 * dim + d]);
1570: }
1571: // n = x1 \otimes x2
1572: n[0] = x1[1] * x2[2] - x1[2] * x2[1];
1573: n[1] = x1[2] * x2[0] - x1[0] * x2[2];
1574: n[2] = x1[0] * x2[1] - x1[1] * x2[0];
1575: norm = PetscSqrtReal(n[0] * n[0] + n[1] * n[1] + n[2] * n[2]);
1576: for (d = 0; d < dim; d++) n[d] /= norm;
1577: norm = PetscSqrtReal(x1[0] * x1[0] + x1[1] * x1[1] + x1[2] * x1[2]);
1578: for (d = 0; d < dim; d++) x1[d] /= norm;
1579: // x2 = n \otimes x1
1580: x2[0] = n[1] * x1[2] - n[2] * x1[1];
1581: x2[1] = n[2] * x1[0] - n[0] * x1[2];
1582: x2[2] = n[0] * x1[1] - n[1] * x1[0];
1583: for (d = 0; d < dim; d++) {
1584: R[d * dim + 0] = x1[d];
1585: R[d * dim + 1] = x2[d];
1586: R[d * dim + 2] = n[d];
1587: c[d] = PetscRealPart(coords[0 * dim + d]);
1588: }
1589: for (p = 0; p < coordSize / dim; p++) {
1590: PetscReal y[3];
1591: for (d = 0; d < dim; d++) y[d] = PetscRealPart(coords[p * dim + d]) - c[d];
1592: for (d = 0; d < 2; d++) coords[p * 2 + d] = R[0 * dim + d] * y[0] + R[1 * dim + d] * y[1] + R[2 * dim + d] * y[2];
1593: }
1594: PetscFunctionReturn(PETSC_SUCCESS);
1595: }
1597: PETSC_UNUSED static inline void Volume_Triangle_Internal(PetscReal *vol, PetscReal coords[])
1598: {
1599: /* Signed volume is 1/2 the determinant
1601: | 1 1 1 |
1602: | x0 x1 x2 |
1603: | y0 y1 y2 |
1605: but if x0,y0 is the origin, we have
1607: | x1 x2 |
1608: | y1 y2 |
1609: */
1610: const PetscReal x1 = coords[2] - coords[0], y1 = coords[3] - coords[1];
1611: const PetscReal x2 = coords[4] - coords[0], y2 = coords[5] - coords[1];
1612: PetscReal M[4], detM;
1613: M[0] = x1;
1614: M[1] = x2;
1615: M[2] = y1;
1616: M[3] = y2;
1617: DMPlex_Det2D_Internal(&detM, M);
1618: *vol = 0.5 * detM;
1619: (void)PetscLogFlops(5.0);
1620: }
1622: PETSC_UNUSED static inline void Volume_Tetrahedron_Internal(PetscReal *vol, PetscReal coords[])
1623: {
1624: /* Signed volume is 1/6th of the determinant
1626: | 1 1 1 1 |
1627: | x0 x1 x2 x3 |
1628: | y0 y1 y2 y3 |
1629: | z0 z1 z2 z3 |
1631: but if x0,y0,z0 is the origin, we have
1633: | x1 x2 x3 |
1634: | y1 y2 y3 |
1635: | z1 z2 z3 |
1636: */
1637: const PetscReal x1 = coords[3] - coords[0], y1 = coords[4] - coords[1], z1 = coords[5] - coords[2];
1638: const PetscReal x2 = coords[6] - coords[0], y2 = coords[7] - coords[1], z2 = coords[8] - coords[2];
1639: const PetscReal x3 = coords[9] - coords[0], y3 = coords[10] - coords[1], z3 = coords[11] - coords[2];
1640: const PetscReal onesixth = ((PetscReal)1. / (PetscReal)6.);
1641: PetscReal M[9], detM;
1642: M[0] = x1;
1643: M[1] = x2;
1644: M[2] = x3;
1645: M[3] = y1;
1646: M[4] = y2;
1647: M[5] = y3;
1648: M[6] = z1;
1649: M[7] = z2;
1650: M[8] = z3;
1651: DMPlex_Det3D_Internal(&detM, M);
1652: *vol = -onesixth * detM;
1653: (void)PetscLogFlops(10.0);
1654: }
1656: static inline void Volume_Tetrahedron_Origin_Internal(PetscReal *vol, PetscReal coords[])
1657: {
1658: const PetscReal onesixth = ((PetscReal)1. / (PetscReal)6.);
1659: DMPlex_Det3D_Internal(vol, coords);
1660: *vol *= -onesixth;
1661: }
1663: static PetscErrorCode DMPlexComputePointGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1664: {
1665: PetscSection coordSection;
1666: Vec coordinates;
1667: const PetscScalar *coords;
1668: PetscInt dim, d, off;
1670: PetscFunctionBegin;
1671: PetscCall(DMGetCoordinatesLocal(dm, &coordinates));
1672: PetscCall(DMGetCoordinateSection(dm, &coordSection));
1673: PetscCall(PetscSectionGetDof(coordSection, e, &dim));
1674: if (!dim) PetscFunctionReturn(PETSC_SUCCESS);
1675: PetscCall(PetscSectionGetOffset(coordSection, e, &off));
1676: PetscCall(VecGetArrayRead(coordinates, &coords));
1677: if (v0) {
1678: for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[off + d]);
1679: }
1680: PetscCall(VecRestoreArrayRead(coordinates, &coords));
1681: *detJ = 1.;
1682: if (J) {
1683: for (d = 0; d < dim * dim; d++) J[d] = 0.;
1684: for (d = 0; d < dim; d++) J[d * dim + d] = 1.;
1685: if (invJ) {
1686: for (d = 0; d < dim * dim; d++) invJ[d] = 0.;
1687: for (d = 0; d < dim; d++) invJ[d * dim + d] = 1.;
1688: }
1689: }
1690: PetscFunctionReturn(PETSC_SUCCESS);
1691: }
1693: /*@C
1694: DMPlexGetCellCoordinates - Get coordinates for a cell, taking into account periodicity
1696: Not Collective
1698: Input Parameters:
1699: + dm - The `DMPLEX`
1700: - cell - The cell number
1702: Output Parameters:
1703: + isDG - Using cellwise coordinates
1704: . Nc - The number of coordinates
1705: . array - The coordinate array
1706: - coords - The cell coordinates
1708: Level: developer
1710: .seealso: `DMPLEX`, `DMPlexRestoreCellCoordinates()`, `DMGetCoordinatesLocal()`, `DMGetCellCoordinatesLocal()`
1711: @*/
1712: PetscErrorCode DMPlexGetCellCoordinates(DM dm, PetscInt cell, PetscBool *isDG, PetscInt *Nc, const PetscScalar *array[], PetscScalar *coords[])
1713: {
1714: DM cdm;
1715: Vec coordinates;
1716: PetscSection cs;
1717: const PetscScalar *ccoords;
1718: PetscInt pStart, pEnd;
1720: PetscFunctionBeginHot;
1721: *isDG = PETSC_FALSE;
1722: *Nc = 0;
1723: *array = NULL;
1724: *coords = NULL;
1725: /* Check for cellwise coordinates */
1726: PetscCall(DMGetCellCoordinateSection(dm, &cs));
1727: if (!cs) goto cg;
1728: /* Check that the cell exists in the cellwise section */
1729: PetscCall(PetscSectionGetChart(cs, &pStart, &pEnd));
1730: if (cell < pStart || cell >= pEnd) goto cg;
1731: /* Check for cellwise coordinates for this cell */
1732: PetscCall(PetscSectionGetDof(cs, cell, Nc));
1733: if (!*Nc) goto cg;
1734: /* Check for cellwise coordinates */
1735: PetscCall(DMGetCellCoordinatesLocalNoncollective(dm, &coordinates));
1736: if (!coordinates) goto cg;
1737: /* Get cellwise coordinates */
1738: PetscCall(DMGetCellCoordinateDM(dm, &cdm));
1739: PetscCall(VecGetArrayRead(coordinates, array));
1740: PetscCall(DMPlexPointLocalRead(cdm, cell, *array, &ccoords));
1741: PetscCall(DMGetWorkArray(cdm, *Nc, MPIU_SCALAR, coords));
1742: PetscCall(PetscArraycpy(*coords, ccoords, *Nc));
1743: PetscCall(VecRestoreArrayRead(coordinates, array));
1744: *isDG = PETSC_TRUE;
1745: PetscFunctionReturn(PETSC_SUCCESS);
1746: cg:
1747: /* Use continuous coordinates */
1748: PetscCall(DMGetCoordinateDM(dm, &cdm));
1749: PetscCall(DMGetCoordinateSection(dm, &cs));
1750: PetscCall(DMGetCoordinatesLocalNoncollective(dm, &coordinates));
1751: PetscCall(DMPlexVecGetOrientedClosure_Internal(cdm, cs, PETSC_FALSE, coordinates, cell, 0, Nc, coords));
1752: PetscFunctionReturn(PETSC_SUCCESS);
1753: }
1755: /*@C
1756: DMPlexRestoreCellCoordinates - Get coordinates for a cell, taking into account periodicity
1758: Not Collective
1760: Input Parameters:
1761: + dm - The `DMPLEX`
1762: - cell - The cell number
1764: Output Parameters:
1765: + isDG - Using cellwise coordinates
1766: . Nc - The number of coordinates
1767: . array - The coordinate array
1768: - coords - The cell coordinates
1770: Level: developer
1772: .seealso: `DMPLEX`, `DMPlexGetCellCoordinates()`, `DMGetCoordinatesLocal()`, `DMGetCellCoordinatesLocal()`
1773: @*/
1774: PetscErrorCode DMPlexRestoreCellCoordinates(DM dm, PetscInt cell, PetscBool *isDG, PetscInt *Nc, const PetscScalar *array[], PetscScalar *coords[])
1775: {
1776: DM cdm;
1777: PetscSection cs;
1778: Vec coordinates;
1780: PetscFunctionBeginHot;
1781: if (*isDG) {
1782: PetscCall(DMGetCellCoordinateDM(dm, &cdm));
1783: PetscCall(DMRestoreWorkArray(cdm, *Nc, MPIU_SCALAR, coords));
1784: } else {
1785: PetscCall(DMGetCoordinateDM(dm, &cdm));
1786: PetscCall(DMGetCoordinateSection(dm, &cs));
1787: PetscCall(DMGetCoordinatesLocalNoncollective(dm, &coordinates));
1788: PetscCall(DMPlexVecRestoreClosure(cdm, cs, coordinates, cell, Nc, coords));
1789: }
1790: PetscFunctionReturn(PETSC_SUCCESS);
1791: }
1793: static PetscErrorCode DMPlexComputeLineGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1794: {
1795: const PetscScalar *array;
1796: PetscScalar *coords = NULL;
1797: PetscInt numCoords, d;
1798: PetscBool isDG;
1800: PetscFunctionBegin;
1801: PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
1802: PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
1803: *detJ = 0.0;
1804: if (numCoords == 6) {
1805: const PetscInt dim = 3;
1806: PetscReal R[9], J0;
1808: if (v0) {
1809: for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
1810: }
1811: PetscCall(DMPlexComputeProjection3Dto1D(coords, R));
1812: if (J) {
1813: J0 = 0.5 * PetscRealPart(coords[1]);
1814: J[0] = R[0] * J0;
1815: J[1] = R[1];
1816: J[2] = R[2];
1817: J[3] = R[3] * J0;
1818: J[4] = R[4];
1819: J[5] = R[5];
1820: J[6] = R[6] * J0;
1821: J[7] = R[7];
1822: J[8] = R[8];
1823: DMPlex_Det3D_Internal(detJ, J);
1824: if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
1825: }
1826: } else if (numCoords == 4) {
1827: const PetscInt dim = 2;
1828: PetscReal R[4], J0;
1830: if (v0) {
1831: for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
1832: }
1833: PetscCall(DMPlexComputeProjection2Dto1D(coords, R));
1834: if (J) {
1835: J0 = 0.5 * PetscRealPart(coords[1]);
1836: J[0] = R[0] * J0;
1837: J[1] = R[1];
1838: J[2] = R[2] * J0;
1839: J[3] = R[3];
1840: DMPlex_Det2D_Internal(detJ, J);
1841: if (invJ) DMPlex_Invert2D_Internal(invJ, J, *detJ);
1842: }
1843: } else if (numCoords == 2) {
1844: const PetscInt dim = 1;
1846: if (v0) {
1847: for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
1848: }
1849: if (J) {
1850: J[0] = 0.5 * (PetscRealPart(coords[1]) - PetscRealPart(coords[0]));
1851: *detJ = J[0];
1852: PetscCall(PetscLogFlops(2.0));
1853: if (invJ) {
1854: invJ[0] = 1.0 / J[0];
1855: PetscCall(PetscLogFlops(1.0));
1856: }
1857: }
1858: } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for segment %" PetscInt_FMT " is %" PetscInt_FMT " != 2 or 4 or 6", e, numCoords);
1859: PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
1860: PetscFunctionReturn(PETSC_SUCCESS);
1861: }
1863: static PetscErrorCode DMPlexComputeTriangleGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1864: {
1865: const PetscScalar *array;
1866: PetscScalar *coords = NULL;
1867: PetscInt numCoords, d;
1868: PetscBool isDG;
1870: PetscFunctionBegin;
1871: PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
1872: PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
1873: *detJ = 0.0;
1874: if (numCoords == 9) {
1875: const PetscInt dim = 3;
1876: PetscReal R[9], J0[9] = {1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0};
1878: if (v0) {
1879: for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
1880: }
1881: PetscCall(DMPlexComputeProjection3Dto2D(numCoords, coords, R));
1882: if (J) {
1883: const PetscInt pdim = 2;
1885: for (d = 0; d < pdim; d++) {
1886: for (PetscInt f = 0; f < pdim; f++) J0[d * dim + f] = 0.5 * (PetscRealPart(coords[(f + 1) * pdim + d]) - PetscRealPart(coords[0 * pdim + d]));
1887: }
1888: PetscCall(PetscLogFlops(8.0));
1889: DMPlex_Det3D_Internal(detJ, J0);
1890: for (d = 0; d < dim; d++) {
1891: for (PetscInt f = 0; f < dim; f++) {
1892: J[d * dim + f] = 0.0;
1893: for (PetscInt g = 0; g < dim; g++) J[d * dim + f] += R[d * dim + g] * J0[g * dim + f];
1894: }
1895: }
1896: PetscCall(PetscLogFlops(18.0));
1897: }
1898: if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
1899: } else if (numCoords == 6) {
1900: const PetscInt dim = 2;
1902: if (v0) {
1903: for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
1904: }
1905: if (J) {
1906: for (d = 0; d < dim; d++) {
1907: for (PetscInt f = 0; f < dim; f++) J[d * dim + f] = 0.5 * (PetscRealPart(coords[(f + 1) * dim + d]) - PetscRealPart(coords[0 * dim + d]));
1908: }
1909: PetscCall(PetscLogFlops(8.0));
1910: DMPlex_Det2D_Internal(detJ, J);
1911: }
1912: if (invJ) DMPlex_Invert2D_Internal(invJ, J, *detJ);
1913: } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this triangle is %" PetscInt_FMT " != 6 or 9", numCoords);
1914: PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
1915: PetscFunctionReturn(PETSC_SUCCESS);
1916: }
1918: static PetscErrorCode DMPlexComputeRectangleGeometry_Internal(DM dm, PetscInt e, PetscBool isTensor, PetscInt Nq, const PetscReal points[], PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1919: {
1920: const PetscScalar *array;
1921: PetscScalar *coords = NULL;
1922: PetscInt numCoords, d;
1923: PetscBool isDG;
1925: PetscFunctionBegin;
1926: PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
1927: PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
1928: if (!Nq) {
1929: PetscInt vorder[4] = {0, 1, 2, 3};
1931: if (isTensor) {
1932: vorder[2] = 3;
1933: vorder[3] = 2;
1934: }
1935: *detJ = 0.0;
1936: if (numCoords == 12) {
1937: const PetscInt dim = 3;
1938: PetscReal R[9], J0[9] = {1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0};
1940: if (v) {
1941: for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);
1942: }
1943: PetscCall(DMPlexComputeProjection3Dto2D(numCoords, coords, R));
1944: if (J) {
1945: const PetscInt pdim = 2;
1947: for (d = 0; d < pdim; d++) {
1948: J0[d * dim + 0] = 0.5 * (PetscRealPart(coords[vorder[1] * pdim + d]) - PetscRealPart(coords[vorder[0] * pdim + d]));
1949: J0[d * dim + 1] = 0.5 * (PetscRealPart(coords[vorder[2] * pdim + d]) - PetscRealPart(coords[vorder[1] * pdim + d]));
1950: }
1951: PetscCall(PetscLogFlops(8.0));
1952: DMPlex_Det3D_Internal(detJ, J0);
1953: for (d = 0; d < dim; d++) {
1954: for (PetscInt f = 0; f < dim; f++) {
1955: J[d * dim + f] = 0.0;
1956: for (PetscInt g = 0; g < dim; g++) J[d * dim + f] += R[d * dim + g] * J0[g * dim + f];
1957: }
1958: }
1959: PetscCall(PetscLogFlops(18.0));
1960: }
1961: if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
1962: } else if (numCoords == 8) {
1963: const PetscInt dim = 2;
1965: if (v) {
1966: for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);
1967: }
1968: if (J) {
1969: for (d = 0; d < dim; d++) {
1970: J[d * dim + 0] = 0.5 * (PetscRealPart(coords[vorder[1] * dim + d]) - PetscRealPart(coords[vorder[0] * dim + d]));
1971: J[d * dim + 1] = 0.5 * (PetscRealPart(coords[vorder[3] * dim + d]) - PetscRealPart(coords[vorder[0] * dim + d]));
1972: }
1973: PetscCall(PetscLogFlops(8.0));
1974: DMPlex_Det2D_Internal(detJ, J);
1975: }
1976: if (invJ) DMPlex_Invert2D_Internal(invJ, J, *detJ);
1977: } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this quadrilateral is %" PetscInt_FMT " != 8 or 12", numCoords);
1978: } else {
1979: const PetscInt Nv = 4;
1980: const PetscInt dimR = 2;
1981: PetscInt zToPlex[4] = {0, 1, 3, 2};
1982: PetscReal zOrder[12];
1983: PetscReal zCoeff[12];
1984: PetscInt i, j, k, l, dim;
1986: if (isTensor) {
1987: zToPlex[2] = 2;
1988: zToPlex[3] = 3;
1989: }
1990: if (numCoords == 12) {
1991: dim = 3;
1992: } else if (numCoords == 8) {
1993: dim = 2;
1994: } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this quadrilateral is %" PetscInt_FMT " != 8 or 12", numCoords);
1995: for (i = 0; i < Nv; i++) {
1996: PetscInt zi = zToPlex[i];
1998: for (j = 0; j < dim; j++) zOrder[dim * i + j] = PetscRealPart(coords[dim * zi + j]);
1999: }
2000: for (j = 0; j < dim; j++) {
2001: /* Nodal basis for evaluation at the vertices: (1 \mp xi) (1 \mp eta):
2002: \phi^0 = (1 - xi - eta + xi eta) --> 1 = 1/4 ( \phi^0 + \phi^1 + \phi^2 + \phi^3)
2003: \phi^1 = (1 + xi - eta - xi eta) --> xi = 1/4 (-\phi^0 + \phi^1 - \phi^2 + \phi^3)
2004: \phi^2 = (1 - xi + eta - xi eta) --> eta = 1/4 (-\phi^0 - \phi^1 + \phi^2 + \phi^3)
2005: \phi^3 = (1 + xi + eta + xi eta) --> xi eta = 1/4 ( \phi^0 - \phi^1 - \phi^2 + \phi^3)
2006: */
2007: zCoeff[dim * 0 + j] = 0.25 * (zOrder[dim * 0 + j] + zOrder[dim * 1 + j] + zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
2008: zCoeff[dim * 1 + j] = 0.25 * (-zOrder[dim * 0 + j] + zOrder[dim * 1 + j] - zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
2009: zCoeff[dim * 2 + j] = 0.25 * (-zOrder[dim * 0 + j] - zOrder[dim * 1 + j] + zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
2010: zCoeff[dim * 3 + j] = 0.25 * (zOrder[dim * 0 + j] - zOrder[dim * 1 + j] - zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
2011: }
2012: for (i = 0; i < Nq; i++) {
2013: PetscReal xi = points[dimR * i], eta = points[dimR * i + 1];
2015: if (v) {
2016: PetscReal extPoint[4];
2018: extPoint[0] = 1.;
2019: extPoint[1] = xi;
2020: extPoint[2] = eta;
2021: extPoint[3] = xi * eta;
2022: for (j = 0; j < dim; j++) {
2023: PetscReal val = 0.;
2025: for (k = 0; k < Nv; k++) val += extPoint[k] * zCoeff[dim * k + j];
2026: v[i * dim + j] = val;
2027: }
2028: }
2029: if (J) {
2030: PetscReal extJ[8];
2032: extJ[0] = 0.;
2033: extJ[1] = 0.;
2034: extJ[2] = 1.;
2035: extJ[3] = 0.;
2036: extJ[4] = 0.;
2037: extJ[5] = 1.;
2038: extJ[6] = eta;
2039: extJ[7] = xi;
2040: for (j = 0; j < dim; j++) {
2041: for (k = 0; k < dimR; k++) {
2042: PetscReal val = 0.;
2044: for (l = 0; l < Nv; l++) val += zCoeff[dim * l + j] * extJ[dimR * l + k];
2045: J[i * dim * dim + dim * j + k] = val;
2046: }
2047: }
2048: if (dim == 3) { /* put the cross product in the third component of the Jacobian */
2049: PetscReal x, y, z;
2050: PetscReal *iJ = &J[i * dim * dim];
2051: PetscReal norm;
2053: x = iJ[1 * dim + 0] * iJ[2 * dim + 1] - iJ[1 * dim + 1] * iJ[2 * dim + 0];
2054: y = iJ[0 * dim + 1] * iJ[2 * dim + 0] - iJ[0 * dim + 0] * iJ[2 * dim + 1];
2055: z = iJ[0 * dim + 0] * iJ[1 * dim + 1] - iJ[0 * dim + 1] * iJ[1 * dim + 0];
2056: norm = PetscSqrtReal(x * x + y * y + z * z);
2057: iJ[2] = x / norm;
2058: iJ[5] = y / norm;
2059: iJ[8] = z / norm;
2060: DMPlex_Det3D_Internal(&detJ[i], &J[i * dim * dim]);
2061: if (invJ) DMPlex_Invert3D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);
2062: } else {
2063: DMPlex_Det2D_Internal(&detJ[i], &J[i * dim * dim]);
2064: if (invJ) DMPlex_Invert2D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);
2065: }
2066: }
2067: }
2068: }
2069: PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
2070: PetscFunctionReturn(PETSC_SUCCESS);
2071: }
2073: static PetscErrorCode DMPlexComputeTetrahedronGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
2074: {
2075: const PetscScalar *array;
2076: PetscScalar *coords = NULL;
2077: const PetscInt dim = 3;
2078: PetscInt numCoords, d;
2079: PetscBool isDG;
2081: PetscFunctionBegin;
2082: PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
2083: PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
2084: *detJ = 0.0;
2085: if (v0) {
2086: for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
2087: }
2088: if (J) {
2089: for (d = 0; d < dim; d++) {
2090: /* I orient with outward face normals */
2091: J[d * dim + 0] = 0.5 * (PetscRealPart(coords[2 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2092: J[d * dim + 1] = 0.5 * (PetscRealPart(coords[1 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2093: J[d * dim + 2] = 0.5 * (PetscRealPart(coords[3 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2094: }
2095: PetscCall(PetscLogFlops(18.0));
2096: DMPlex_Det3D_Internal(detJ, J);
2097: }
2098: if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
2099: PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
2100: PetscFunctionReturn(PETSC_SUCCESS);
2101: }
2103: static PetscErrorCode DMPlexComputeHexahedronGeometry_Internal(DM dm, PetscInt e, PetscInt Nq, const PetscReal points[], PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
2104: {
2105: const PetscScalar *array;
2106: PetscScalar *coords = NULL;
2107: const PetscInt dim = 3;
2108: PetscInt numCoords, d;
2109: PetscBool isDG;
2111: PetscFunctionBegin;
2112: PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
2113: PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
2114: if (!Nq) {
2115: *detJ = 0.0;
2116: if (v) {
2117: for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);
2118: }
2119: if (J) {
2120: for (d = 0; d < dim; d++) {
2121: J[d * dim + 0] = 0.5 * (PetscRealPart(coords[3 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2122: J[d * dim + 1] = 0.5 * (PetscRealPart(coords[1 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2123: J[d * dim + 2] = 0.5 * (PetscRealPart(coords[4 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2124: }
2125: PetscCall(PetscLogFlops(18.0));
2126: DMPlex_Det3D_Internal(detJ, J);
2127: }
2128: if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
2129: } else {
2130: const PetscInt Nv = 8;
2131: const PetscInt zToPlex[8] = {0, 3, 1, 2, 4, 5, 7, 6};
2132: const PetscInt dim = 3;
2133: const PetscInt dimR = 3;
2134: PetscReal zOrder[24];
2135: PetscReal zCoeff[24];
2136: PetscInt i, j, k, l;
2138: for (i = 0; i < Nv; i++) {
2139: PetscInt zi = zToPlex[i];
2141: for (j = 0; j < dim; j++) zOrder[dim * i + j] = PetscRealPart(coords[dim * zi + j]);
2142: }
2143: for (j = 0; j < dim; j++) {
2144: zCoeff[dim * 0 + j] = 0.125 * (zOrder[dim * 0 + j] + zOrder[dim * 1 + j] + zOrder[dim * 2 + j] + zOrder[dim * 3 + j] + zOrder[dim * 4 + j] + zOrder[dim * 5 + j] + zOrder[dim * 6 + j] + zOrder[dim * 7 + j]);
2145: zCoeff[dim * 1 + j] = 0.125 * (-zOrder[dim * 0 + j] + zOrder[dim * 1 + j] - zOrder[dim * 2 + j] + zOrder[dim * 3 + j] - zOrder[dim * 4 + j] + zOrder[dim * 5 + j] - zOrder[dim * 6 + j] + zOrder[dim * 7 + j]);
2146: zCoeff[dim * 2 + j] = 0.125 * (-zOrder[dim * 0 + j] - zOrder[dim * 1 + j] + zOrder[dim * 2 + j] + zOrder[dim * 3 + j] - zOrder[dim * 4 + j] - zOrder[dim * 5 + j] + zOrder[dim * 6 + j] + zOrder[dim * 7 + j]);
2147: zCoeff[dim * 3 + j] = 0.125 * (zOrder[dim * 0 + j] - zOrder[dim * 1 + j] - zOrder[dim * 2 + j] + zOrder[dim * 3 + j] + zOrder[dim * 4 + j] - zOrder[dim * 5 + j] - zOrder[dim * 6 + j] + zOrder[dim * 7 + j]);
2148: zCoeff[dim * 4 + j] = 0.125 * (-zOrder[dim * 0 + j] - zOrder[dim * 1 + j] - zOrder[dim * 2 + j] - zOrder[dim * 3 + j] + zOrder[dim * 4 + j] + zOrder[dim * 5 + j] + zOrder[dim * 6 + j] + zOrder[dim * 7 + j]);
2149: zCoeff[dim * 5 + j] = 0.125 * (+zOrder[dim * 0 + j] - zOrder[dim * 1 + j] + zOrder[dim * 2 + j] - zOrder[dim * 3 + j] - zOrder[dim * 4 + j] + zOrder[dim * 5 + j] - zOrder[dim * 6 + j] + zOrder[dim * 7 + j]);
2150: zCoeff[dim * 6 + j] = 0.125 * (+zOrder[dim * 0 + j] + zOrder[dim * 1 + j] - zOrder[dim * 2 + j] - zOrder[dim * 3 + j] - zOrder[dim * 4 + j] - zOrder[dim * 5 + j] + zOrder[dim * 6 + j] + zOrder[dim * 7 + j]);
2151: zCoeff[dim * 7 + j] = 0.125 * (-zOrder[dim * 0 + j] + zOrder[dim * 1 + j] + zOrder[dim * 2 + j] - zOrder[dim * 3 + j] + zOrder[dim * 4 + j] - zOrder[dim * 5 + j] - zOrder[dim * 6 + j] + zOrder[dim * 7 + j]);
2152: }
2153: for (i = 0; i < Nq; i++) {
2154: PetscReal xi = points[dimR * i], eta = points[dimR * i + 1], theta = points[dimR * i + 2];
2156: if (v) {
2157: PetscReal extPoint[8];
2159: extPoint[0] = 1.;
2160: extPoint[1] = xi;
2161: extPoint[2] = eta;
2162: extPoint[3] = xi * eta;
2163: extPoint[4] = theta;
2164: extPoint[5] = theta * xi;
2165: extPoint[6] = theta * eta;
2166: extPoint[7] = theta * eta * xi;
2167: for (j = 0; j < dim; j++) {
2168: PetscReal val = 0.;
2170: for (k = 0; k < Nv; k++) val += extPoint[k] * zCoeff[dim * k + j];
2171: v[i * dim + j] = val;
2172: }
2173: }
2174: if (J) {
2175: PetscReal extJ[24];
2177: extJ[0] = 0.;
2178: extJ[1] = 0.;
2179: extJ[2] = 0.;
2180: extJ[3] = 1.;
2181: extJ[4] = 0.;
2182: extJ[5] = 0.;
2183: extJ[6] = 0.;
2184: extJ[7] = 1.;
2185: extJ[8] = 0.;
2186: extJ[9] = eta;
2187: extJ[10] = xi;
2188: extJ[11] = 0.;
2189: extJ[12] = 0.;
2190: extJ[13] = 0.;
2191: extJ[14] = 1.;
2192: extJ[15] = theta;
2193: extJ[16] = 0.;
2194: extJ[17] = xi;
2195: extJ[18] = 0.;
2196: extJ[19] = theta;
2197: extJ[20] = eta;
2198: extJ[21] = theta * eta;
2199: extJ[22] = theta * xi;
2200: extJ[23] = eta * xi;
2202: for (j = 0; j < dim; j++) {
2203: for (k = 0; k < dimR; k++) {
2204: PetscReal val = 0.;
2206: for (l = 0; l < Nv; l++) val += zCoeff[dim * l + j] * extJ[dimR * l + k];
2207: J[i * dim * dim + dim * j + k] = val;
2208: }
2209: }
2210: DMPlex_Det3D_Internal(&detJ[i], &J[i * dim * dim]);
2211: if (invJ) DMPlex_Invert3D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);
2212: }
2213: }
2214: }
2215: PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
2216: PetscFunctionReturn(PETSC_SUCCESS);
2217: }
2219: static PetscErrorCode DMPlexComputeTriangularPrismGeometry_Internal(DM dm, PetscInt e, PetscInt Nq, const PetscReal points[], PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
2220: {
2221: const PetscScalar *array;
2222: PetscScalar *coords = NULL;
2223: const PetscInt dim = 3;
2224: PetscInt numCoords, d;
2225: PetscBool isDG;
2227: PetscFunctionBegin;
2228: PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
2229: PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
2230: if (!Nq) {
2231: /* Assume that the map to the reference is affine */
2232: *detJ = 0.0;
2233: if (v) {
2234: for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);
2235: }
2236: if (J) {
2237: for (d = 0; d < dim; d++) {
2238: J[d * dim + 0] = 0.5 * (PetscRealPart(coords[2 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2239: J[d * dim + 1] = 0.5 * (PetscRealPart(coords[1 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2240: J[d * dim + 2] = 0.5 * (PetscRealPart(coords[4 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2241: }
2242: PetscCall(PetscLogFlops(18.0));
2243: DMPlex_Det3D_Internal(detJ, J);
2244: }
2245: if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
2246: } else {
2247: const PetscInt dim = 3;
2248: const PetscInt dimR = 3;
2249: const PetscInt Nv = 6;
2250: PetscReal verts[18];
2251: PetscReal coeff[18];
2252: PetscInt i, j, k, l;
2254: for (i = 0; i < Nv; ++i)
2255: for (j = 0; j < dim; ++j) verts[dim * i + j] = PetscRealPart(coords[dim * i + j]);
2256: for (j = 0; j < dim; ++j) {
2257: /* Check for triangle,
2258: phi^0 = -1/2 (xi + eta) chi^0 = delta(-1, -1) x(xi) = \sum_k x_k phi^k(xi) = \sum_k chi^k(x) phi^k(xi)
2259: phi^1 = 1/2 (1 + xi) chi^1 = delta( 1, -1) y(xi) = \sum_k y_k phi^k(xi) = \sum_k chi^k(y) phi^k(xi)
2260: phi^2 = 1/2 (1 + eta) chi^2 = delta(-1, 1)
2262: phi^0 + phi^1 + phi^2 = 1 coef_1 = 1/2 ( chi^1 + chi^2)
2263: -phi^0 + phi^1 - phi^2 = xi coef_xi = 1/2 (-chi^0 + chi^1)
2264: -phi^0 - phi^1 + phi^2 = eta coef_eta = 1/2 (-chi^0 + chi^2)
2266: < chi_0 chi_1 chi_2> A / 1 1 1 \ / phi_0 \ <chi> I <phi>^T so we need the inverse transpose
2267: | -1 1 -1 | | phi_1 | =
2268: \ -1 -1 1 / \ phi_2 /
2270: Check phi^0: 1/2 (phi^0 chi^1 + phi^0 chi^2 + phi^0 chi^0 - phi^0 chi^1 + phi^0 chi^0 - phi^0 chi^2) = phi^0 chi^0
2271: */
2272: /* Nodal basis for evaluation at the vertices: {-xi - eta, 1 + xi, 1 + eta} (1 \mp zeta):
2273: \phi^0 = 1/4 ( -xi - eta + xi zeta + eta zeta) --> / 1 1 1 1 1 1 \ 1
2274: \phi^1 = 1/4 (1 + eta - zeta - eta zeta) --> | -1 1 -1 -1 -1 1 | eta
2275: \phi^2 = 1/4 (1 + xi - zeta - xi zeta) --> | -1 -1 1 -1 1 -1 | xi
2276: \phi^3 = 1/4 ( -xi - eta - xi zeta - eta zeta) --> | -1 -1 -1 1 1 1 | zeta
2277: \phi^4 = 1/4 (1 + xi + zeta + xi zeta) --> | 1 1 -1 -1 1 -1 | xi zeta
2278: \phi^5 = 1/4 (1 + eta + zeta + eta zeta) --> \ 1 -1 1 -1 -1 1 / eta zeta
2279: 1/4 / 0 1 1 0 1 1 \
2280: | -1 1 0 -1 0 1 |
2281: | -1 0 1 -1 1 0 |
2282: | 0 -1 -1 0 1 1 |
2283: | 1 0 -1 -1 1 0 |
2284: \ 1 -1 0 -1 0 1 /
2285: */
2286: coeff[dim * 0 + j] = (1. / 4.) * (verts[dim * 1 + j] + verts[dim * 2 + j] + verts[dim * 4 + j] + verts[dim * 5 + j]);
2287: coeff[dim * 1 + j] = (1. / 4.) * (-verts[dim * 0 + j] + verts[dim * 1 + j] - verts[dim * 3 + j] + verts[dim * 5 + j]);
2288: coeff[dim * 2 + j] = (1. / 4.) * (-verts[dim * 0 + j] + verts[dim * 2 + j] - verts[dim * 3 + j] + verts[dim * 4 + j]);
2289: coeff[dim * 3 + j] = (1. / 4.) * (-verts[dim * 1 + j] - verts[dim * 2 + j] + verts[dim * 4 + j] + verts[dim * 5 + j]);
2290: coeff[dim * 4 + j] = (1. / 4.) * (verts[dim * 0 + j] - verts[dim * 2 + j] - verts[dim * 3 + j] + verts[dim * 4 + j]);
2291: coeff[dim * 5 + j] = (1. / 4.) * (verts[dim * 0 + j] - verts[dim * 1 + j] - verts[dim * 3 + j] + verts[dim * 5 + j]);
2292: /* For reference prism:
2293: {0, 0, 0}
2294: {0, 1, 0}
2295: {1, 0, 0}
2296: {0, 0, 1}
2297: {0, 0, 0}
2298: {0, 0, 0}
2299: */
2300: }
2301: for (i = 0; i < Nq; ++i) {
2302: const PetscReal xi = points[dimR * i], eta = points[dimR * i + 1], zeta = points[dimR * i + 2];
2304: if (v) {
2305: PetscReal extPoint[6];
2306: PetscInt c;
2308: extPoint[0] = 1.;
2309: extPoint[1] = eta;
2310: extPoint[2] = xi;
2311: extPoint[3] = zeta;
2312: extPoint[4] = xi * zeta;
2313: extPoint[5] = eta * zeta;
2314: for (c = 0; c < dim; ++c) {
2315: PetscReal val = 0.;
2317: for (k = 0; k < Nv; ++k) val += extPoint[k] * coeff[k * dim + c];
2318: v[i * dim + c] = val;
2319: }
2320: }
2321: if (J) {
2322: PetscReal extJ[18];
2324: extJ[0] = 0.;
2325: extJ[1] = 0.;
2326: extJ[2] = 0.;
2327: extJ[3] = 0.;
2328: extJ[4] = 1.;
2329: extJ[5] = 0.;
2330: extJ[6] = 1.;
2331: extJ[7] = 0.;
2332: extJ[8] = 0.;
2333: extJ[9] = 0.;
2334: extJ[10] = 0.;
2335: extJ[11] = 1.;
2336: extJ[12] = zeta;
2337: extJ[13] = 0.;
2338: extJ[14] = xi;
2339: extJ[15] = 0.;
2340: extJ[16] = zeta;
2341: extJ[17] = eta;
2343: for (j = 0; j < dim; j++) {
2344: for (k = 0; k < dimR; k++) {
2345: PetscReal val = 0.;
2347: for (l = 0; l < Nv; l++) val += coeff[dim * l + j] * extJ[dimR * l + k];
2348: J[i * dim * dim + dim * j + k] = val;
2349: }
2350: }
2351: DMPlex_Det3D_Internal(&detJ[i], &J[i * dim * dim]);
2352: if (invJ) DMPlex_Invert3D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);
2353: }
2354: }
2355: }
2356: PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
2357: PetscFunctionReturn(PETSC_SUCCESS);
2358: }
2360: static PetscErrorCode DMPlexComputeCellGeometryFEM_Implicit(DM dm, PetscInt cell, PetscQuadrature quad, PetscReal *v, PetscReal *J, PetscReal *invJ, PetscReal *detJ)
2361: {
2362: DMPolytopeType ct;
2363: PetscInt depth, dim, coordDim, coneSize, i;
2364: PetscInt Nq = 0;
2365: const PetscReal *points = NULL;
2366: DMLabel depthLabel;
2367: PetscReal xi0[3] = {-1., -1., -1.}, v0[3], J0[9], detJ0;
2368: PetscBool isAffine = PETSC_TRUE;
2370: PetscFunctionBegin;
2371: PetscCall(DMPlexGetDepth(dm, &depth));
2372: PetscCall(DMPlexGetConeSize(dm, cell, &coneSize));
2373: PetscCall(DMPlexGetDepthLabel(dm, &depthLabel));
2374: PetscCall(DMLabelGetValue(depthLabel, cell, &dim));
2375: if (depth == 1 && dim == 1) PetscCall(DMGetDimension(dm, &dim));
2376: PetscCall(DMGetCoordinateDim(dm, &coordDim));
2377: PetscCheck(coordDim <= 3, PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported coordinate dimension %" PetscInt_FMT " > 3", coordDim);
2378: if (quad) PetscCall(PetscQuadratureGetData(quad, NULL, NULL, &Nq, &points, NULL));
2379: PetscCall(DMPlexGetCellType(dm, cell, &ct));
2380: switch (ct) {
2381: case DM_POLYTOPE_POINT:
2382: PetscCall(DMPlexComputePointGeometry_Internal(dm, cell, v, J, invJ, detJ));
2383: isAffine = PETSC_FALSE;
2384: break;
2385: case DM_POLYTOPE_SEGMENT:
2386: case DM_POLYTOPE_POINT_PRISM_TENSOR:
2387: if (Nq) PetscCall(DMPlexComputeLineGeometry_Internal(dm, cell, v0, J0, NULL, &detJ0));
2388: else PetscCall(DMPlexComputeLineGeometry_Internal(dm, cell, v, J, invJ, detJ));
2389: break;
2390: case DM_POLYTOPE_TRIANGLE:
2391: if (Nq) PetscCall(DMPlexComputeTriangleGeometry_Internal(dm, cell, v0, J0, NULL, &detJ0));
2392: else PetscCall(DMPlexComputeTriangleGeometry_Internal(dm, cell, v, J, invJ, detJ));
2393: break;
2394: case DM_POLYTOPE_QUADRILATERAL:
2395: PetscCall(DMPlexComputeRectangleGeometry_Internal(dm, cell, PETSC_FALSE, Nq, points, v, J, invJ, detJ));
2396: isAffine = PETSC_FALSE;
2397: break;
2398: case DM_POLYTOPE_SEG_PRISM_TENSOR:
2399: PetscCall(DMPlexComputeRectangleGeometry_Internal(dm, cell, PETSC_TRUE, Nq, points, v, J, invJ, detJ));
2400: isAffine = PETSC_FALSE;
2401: break;
2402: case DM_POLYTOPE_TETRAHEDRON:
2403: if (Nq) PetscCall(DMPlexComputeTetrahedronGeometry_Internal(dm, cell, v0, J0, NULL, &detJ0));
2404: else PetscCall(DMPlexComputeTetrahedronGeometry_Internal(dm, cell, v, J, invJ, detJ));
2405: break;
2406: case DM_POLYTOPE_HEXAHEDRON:
2407: PetscCall(DMPlexComputeHexahedronGeometry_Internal(dm, cell, Nq, points, v, J, invJ, detJ));
2408: isAffine = PETSC_FALSE;
2409: break;
2410: case DM_POLYTOPE_TRI_PRISM:
2411: PetscCall(DMPlexComputeTriangularPrismGeometry_Internal(dm, cell, Nq, points, v, J, invJ, detJ));
2412: isAffine = PETSC_FALSE;
2413: break;
2414: default:
2415: SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No element geometry for cell %" PetscInt_FMT " with type %s", cell, DMPolytopeTypes[PetscMax(0, PetscMin(ct, DM_NUM_POLYTOPES))]);
2416: }
2417: if (isAffine && Nq) {
2418: if (v) {
2419: for (i = 0; i < Nq; i++) CoordinatesRefToReal(coordDim, dim, xi0, v0, J0, &points[dim * i], &v[coordDim * i]);
2420: }
2421: if (detJ) {
2422: for (i = 0; i < Nq; i++) detJ[i] = detJ0;
2423: }
2424: if (J) {
2425: PetscInt k;
2427: for (i = 0, k = 0; i < Nq; i++) {
2428: PetscInt j;
2430: for (j = 0; j < coordDim * coordDim; j++, k++) J[k] = J0[j];
2431: }
2432: }
2433: if (invJ) {
2434: PetscInt k;
2435: switch (coordDim) {
2436: case 0:
2437: break;
2438: case 1:
2439: invJ[0] = 1. / J0[0];
2440: break;
2441: case 2:
2442: DMPlex_Invert2D_Internal(invJ, J0, detJ0);
2443: break;
2444: case 3:
2445: DMPlex_Invert3D_Internal(invJ, J0, detJ0);
2446: break;
2447: }
2448: for (i = 1, k = coordDim * coordDim; i < Nq; i++) {
2449: PetscInt j;
2451: for (j = 0; j < coordDim * coordDim; j++, k++) invJ[k] = invJ[j];
2452: }
2453: }
2454: }
2455: PetscFunctionReturn(PETSC_SUCCESS);
2456: }
2458: /*@C
2459: DMPlexComputeCellGeometryAffineFEM - Assuming an affine map, compute the Jacobian, inverse Jacobian, and Jacobian determinant for a given cell
2461: Collective
2463: Input Parameters:
2464: + dm - the `DMPLEX`
2465: - cell - the cell
2467: Output Parameters:
2468: + v0 - the translation part of this affine transform, meaning the translation to the origin (not the first vertex of the reference cell)
2469: . J - the Jacobian of the transform from the reference element
2470: . invJ - the inverse of the Jacobian
2471: - detJ - the Jacobian determinant
2473: Level: advanced
2475: .seealso: `DMPLEX`, `DMPlexComputeCellGeometryFEM()`, `DMGetCoordinateSection()`, `DMGetCoordinates()`
2476: @*/
2477: PetscErrorCode DMPlexComputeCellGeometryAffineFEM(DM dm, PetscInt cell, PetscReal *v0, PetscReal *J, PetscReal *invJ, PetscReal *detJ)
2478: {
2479: PetscFunctionBegin;
2480: PetscCall(DMPlexComputeCellGeometryFEM_Implicit(dm, cell, NULL, v0, J, invJ, detJ));
2481: PetscFunctionReturn(PETSC_SUCCESS);
2482: }
2484: static PetscErrorCode DMPlexComputeCellGeometryFEM_FE(DM dm, PetscFE fe, PetscInt point, PetscQuadrature quad, PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
2485: {
2486: const PetscScalar *array;
2487: PetscScalar *coords = NULL;
2488: PetscInt numCoords;
2489: PetscBool isDG;
2490: PetscQuadrature feQuad;
2491: const PetscReal *quadPoints;
2492: PetscTabulation T;
2493: PetscInt dim, cdim, pdim, qdim, Nq, q;
2495: PetscFunctionBegin;
2496: PetscCall(DMGetDimension(dm, &dim));
2497: PetscCall(DMGetCoordinateDim(dm, &cdim));
2498: PetscCall(DMPlexGetCellCoordinates(dm, point, &isDG, &numCoords, &array, &coords));
2499: if (!quad) { /* use the first point of the first functional of the dual space */
2500: PetscDualSpace dsp;
2502: PetscCall(PetscFEGetDualSpace(fe, &dsp));
2503: PetscCall(PetscDualSpaceGetFunctional(dsp, 0, &quad));
2504: PetscCall(PetscQuadratureGetData(quad, &qdim, NULL, &Nq, &quadPoints, NULL));
2505: Nq = 1;
2506: } else {
2507: PetscCall(PetscQuadratureGetData(quad, &qdim, NULL, &Nq, &quadPoints, NULL));
2508: }
2509: PetscCall(PetscFEGetDimension(fe, &pdim));
2510: PetscCall(PetscFEGetQuadrature(fe, &feQuad));
2511: if (feQuad == quad) {
2512: PetscCall(PetscFEGetCellTabulation(fe, J ? 1 : 0, &T));
2513: PetscCheck(numCoords == pdim * cdim, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "There are %" PetscInt_FMT " coordinates for point %" PetscInt_FMT " != %" PetscInt_FMT "*%" PetscInt_FMT, numCoords, point, pdim, cdim);
2514: } else {
2515: PetscCall(PetscFECreateTabulation(fe, 1, Nq, quadPoints, J ? 1 : 0, &T));
2516: }
2517: PetscCheck(qdim == dim, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Point dimension %" PetscInt_FMT " != quadrature dimension %" PetscInt_FMT, dim, qdim);
2518: {
2519: const PetscReal *basis = T->T[0];
2520: const PetscReal *basisDer = T->T[1];
2521: PetscReal detJt;
2523: PetscAssert(Nq == T->Np, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Np %" PetscInt_FMT " != %" PetscInt_FMT, Nq, T->Np);
2524: PetscAssert(pdim == T->Nb, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Nb %" PetscInt_FMT " != %" PetscInt_FMT, pdim, T->Nb);
2525: PetscAssert(dim == T->Nc, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Nc %" PetscInt_FMT " != %" PetscInt_FMT, dim, T->Nc);
2526: PetscAssert(cdim == T->cdim, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "cdim %" PetscInt_FMT " != %" PetscInt_FMT, cdim, T->cdim);
2527: if (v) {
2528: PetscCall(PetscArrayzero(v, Nq * cdim));
2529: for (q = 0; q < Nq; ++q) {
2530: PetscInt i, k;
2532: for (k = 0; k < pdim; ++k) {
2533: const PetscInt vertex = k / cdim;
2534: for (i = 0; i < cdim; ++i) v[q * cdim + i] += basis[(q * pdim + k) * cdim + i] * PetscRealPart(coords[vertex * cdim + i]);
2535: }
2536: PetscCall(PetscLogFlops(2.0 * pdim * cdim));
2537: }
2538: }
2539: if (J) {
2540: PetscCall(PetscArrayzero(J, Nq * cdim * cdim));
2541: for (q = 0; q < Nq; ++q) {
2542: PetscInt i, j, k, c, r;
2544: /* J = dx_i/d\xi_j = sum[k=0,n-1] dN_k/d\xi_j * x_i(k) */
2545: for (k = 0; k < pdim; ++k) {
2546: const PetscInt vertex = k / cdim;
2547: for (j = 0; j < dim; ++j) {
2548: for (i = 0; i < cdim; ++i) J[(q * cdim + i) * cdim + j] += basisDer[((q * pdim + k) * cdim + i) * dim + j] * PetscRealPart(coords[vertex * cdim + i]);
2549: }
2550: }
2551: PetscCall(PetscLogFlops(2.0 * pdim * dim * cdim));
2552: if (cdim > dim) {
2553: for (c = dim; c < cdim; ++c)
2554: for (r = 0; r < cdim; ++r) J[r * cdim + c] = r == c ? 1.0 : 0.0;
2555: }
2556: if (!detJ && !invJ) continue;
2557: detJt = 0.;
2558: switch (cdim) {
2559: case 3:
2560: DMPlex_Det3D_Internal(&detJt, &J[q * cdim * dim]);
2561: if (invJ) DMPlex_Invert3D_Internal(&invJ[q * cdim * dim], &J[q * cdim * dim], detJt);
2562: break;
2563: case 2:
2564: DMPlex_Det2D_Internal(&detJt, &J[q * cdim * dim]);
2565: if (invJ) DMPlex_Invert2D_Internal(&invJ[q * cdim * dim], &J[q * cdim * dim], detJt);
2566: break;
2567: case 1:
2568: detJt = J[q * cdim * dim];
2569: if (invJ) invJ[q * cdim * dim] = 1.0 / detJt;
2570: }
2571: if (detJ) detJ[q] = detJt;
2572: }
2573: } else PetscCheck(!detJ && !invJ, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Need J to compute invJ or detJ");
2574: }
2575: if (feQuad != quad) PetscCall(PetscTabulationDestroy(&T));
2576: PetscCall(DMPlexRestoreCellCoordinates(dm, point, &isDG, &numCoords, &array, &coords));
2577: PetscFunctionReturn(PETSC_SUCCESS);
2578: }
2580: /*@C
2581: DMPlexComputeCellGeometryFEM - Compute the Jacobian, inverse Jacobian, and Jacobian determinant at each quadrature point in the given cell
2583: Collective
2585: Input Parameters:
2586: + dm - the `DMPLEX`
2587: . cell - the cell
2588: - quad - the quadrature containing the points in the reference element where the geometry will be evaluated. If `quad` is `NULL`, geometry will be
2589: evaluated at the first vertex of the reference element
2591: Output Parameters:
2592: + v - the image of the transformed quadrature points, otherwise the image of the first vertex in the closure of the reference element
2593: . J - the Jacobian of the transform from the reference element at each quadrature point
2594: . invJ - the inverse of the Jacobian at each quadrature point
2595: - detJ - the Jacobian determinant at each quadrature point
2597: Level: advanced
2599: .seealso: `DMPLEX`, `DMGetCoordinateSection()`, `DMGetCoordinates()`
2600: @*/
2601: PetscErrorCode DMPlexComputeCellGeometryFEM(DM dm, PetscInt cell, PetscQuadrature quad, PetscReal *v, PetscReal *J, PetscReal *invJ, PetscReal *detJ)
2602: {
2603: DM cdm;
2604: PetscFE fe = NULL;
2606: PetscFunctionBegin;
2607: PetscAssertPointer(detJ, 7);
2608: PetscCall(DMGetCoordinateDM(dm, &cdm));
2609: if (cdm) {
2610: PetscClassId id;
2611: PetscInt numFields;
2612: PetscDS prob;
2613: PetscObject disc;
2615: PetscCall(DMGetNumFields(cdm, &numFields));
2616: if (numFields) {
2617: PetscCall(DMGetDS(cdm, &prob));
2618: PetscCall(PetscDSGetDiscretization(prob, 0, &disc));
2619: PetscCall(PetscObjectGetClassId(disc, &id));
2620: if (id == PETSCFE_CLASSID) fe = (PetscFE)disc;
2621: }
2622: }
2623: if (!fe) PetscCall(DMPlexComputeCellGeometryFEM_Implicit(dm, cell, quad, v, J, invJ, detJ));
2624: else PetscCall(DMPlexComputeCellGeometryFEM_FE(dm, fe, cell, quad, v, J, invJ, detJ));
2625: PetscFunctionReturn(PETSC_SUCCESS);
2626: }
2628: static PetscErrorCode DMPlexComputeGeometryFVM_0D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
2629: {
2630: PetscSection coordSection;
2631: Vec coordinates;
2632: const PetscScalar *coords = NULL;
2633: PetscInt d, dof, off;
2635: PetscFunctionBegin;
2636: PetscCall(DMGetCoordinatesLocal(dm, &coordinates));
2637: PetscCall(DMGetCoordinateSection(dm, &coordSection));
2638: PetscCall(VecGetArrayRead(coordinates, &coords));
2640: /* for a point the centroid is just the coord */
2641: if (centroid) {
2642: PetscCall(PetscSectionGetDof(coordSection, cell, &dof));
2643: PetscCall(PetscSectionGetOffset(coordSection, cell, &off));
2644: for (d = 0; d < dof; d++) centroid[d] = PetscRealPart(coords[off + d]);
2645: }
2646: if (normal) {
2647: const PetscInt *support, *cones;
2648: PetscInt supportSize;
2649: PetscReal norm, sign;
2651: /* compute the norm based upon the support centroids */
2652: PetscCall(DMPlexGetSupportSize(dm, cell, &supportSize));
2653: PetscCall(DMPlexGetSupport(dm, cell, &support));
2654: PetscCall(DMPlexComputeCellGeometryFVM(dm, support[0], NULL, normal, NULL));
2656: /* Take the normal from the centroid of the support to the vertex*/
2657: PetscCall(PetscSectionGetDof(coordSection, cell, &dof));
2658: PetscCall(PetscSectionGetOffset(coordSection, cell, &off));
2659: for (d = 0; d < dof; d++) normal[d] -= PetscRealPart(coords[off + d]);
2661: /* Determine the sign of the normal based upon its location in the support */
2662: PetscCall(DMPlexGetCone(dm, support[0], &cones));
2663: sign = cones[0] == cell ? 1.0 : -1.0;
2665: norm = DMPlex_NormD_Internal(dim, normal);
2666: for (d = 0; d < dim; ++d) normal[d] /= (norm * sign);
2667: }
2668: if (vol) *vol = 1.0;
2669: PetscCall(VecRestoreArrayRead(coordinates, &coords));
2670: PetscFunctionReturn(PETSC_SUCCESS);
2671: }
2673: static PetscErrorCode DMPlexComputeGeometryFVM_1D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
2674: {
2675: const PetscScalar *array;
2676: PetscScalar *coords = NULL;
2677: PetscInt cdim, coordSize, d;
2678: PetscBool isDG;
2680: PetscFunctionBegin;
2681: PetscCall(DMGetCoordinateDim(dm, &cdim));
2682: PetscCall(DMPlexGetCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
2683: PetscCheck(coordSize == cdim * 2, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Edge has %" PetscInt_FMT " coordinates != %" PetscInt_FMT, coordSize, cdim * 2);
2684: if (centroid) {
2685: for (d = 0; d < cdim; ++d) centroid[d] = 0.5 * PetscRealPart(coords[d] + coords[cdim + d]);
2686: }
2687: if (normal) {
2688: PetscReal norm;
2690: switch (cdim) {
2691: case 3:
2692: normal[2] = 0.; /* fall through */
2693: case 2:
2694: normal[0] = -PetscRealPart(coords[1] - coords[cdim + 1]);
2695: normal[1] = PetscRealPart(coords[0] - coords[cdim + 0]);
2696: break;
2697: case 1:
2698: normal[0] = 1.0;
2699: break;
2700: default:
2701: SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Dimension %" PetscInt_FMT " not supported", cdim);
2702: }
2703: norm = DMPlex_NormD_Internal(cdim, normal);
2704: for (d = 0; d < cdim; ++d) normal[d] /= norm;
2705: }
2706: if (vol) {
2707: *vol = 0.0;
2708: for (d = 0; d < cdim; ++d) *vol += PetscSqr(PetscRealPart(coords[d] - coords[cdim + d]));
2709: *vol = PetscSqrtReal(*vol);
2710: }
2711: PetscCall(DMPlexRestoreCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
2712: PetscFunctionReturn(PETSC_SUCCESS);
2713: }
2715: /* Centroid_i = (\sum_n A_n Cn_i) / A */
2716: static PetscErrorCode DMPlexComputeGeometryFVM_2D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
2717: {
2718: DMPolytopeType ct;
2719: const PetscScalar *array;
2720: PetscScalar *coords = NULL;
2721: PetscInt coordSize;
2722: PetscBool isDG;
2723: PetscInt fv[4] = {0, 1, 2, 3};
2724: PetscInt cdim, numCorners, p, d;
2726: PetscFunctionBegin;
2727: /* Must check for hybrid cells because prisms have a different orientation scheme */
2728: PetscCall(DMPlexGetCellType(dm, cell, &ct));
2729: switch (ct) {
2730: case DM_POLYTOPE_SEG_PRISM_TENSOR:
2731: fv[2] = 3;
2732: fv[3] = 2;
2733: break;
2734: default:
2735: break;
2736: }
2737: PetscCall(DMGetCoordinateDim(dm, &cdim));
2738: PetscCall(DMPlexGetConeSize(dm, cell, &numCorners));
2739: PetscCall(DMPlexGetCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
2740: {
2741: PetscReal c[3] = {0., 0., 0.}, n[3] = {0., 0., 0.}, origin[3] = {0., 0., 0.}, norm;
2743: for (d = 0; d < cdim; d++) origin[d] = PetscRealPart(coords[d]);
2744: for (p = 0; p < numCorners - 2; ++p) {
2745: PetscReal e0[3] = {0., 0., 0.}, e1[3] = {0., 0., 0.};
2746: for (d = 0; d < cdim; d++) {
2747: e0[d] = PetscRealPart(coords[cdim * fv[p + 1] + d]) - origin[d];
2748: e1[d] = PetscRealPart(coords[cdim * fv[p + 2] + d]) - origin[d];
2749: }
2750: const PetscReal dx = e0[1] * e1[2] - e0[2] * e1[1];
2751: const PetscReal dy = e0[2] * e1[0] - e0[0] * e1[2];
2752: const PetscReal dz = e0[0] * e1[1] - e0[1] * e1[0];
2753: const PetscReal a = PetscSqrtReal(dx * dx + dy * dy + dz * dz);
2755: n[0] += dx;
2756: n[1] += dy;
2757: n[2] += dz;
2758: for (d = 0; d < cdim; d++) c[d] += a * PetscRealPart(origin[d] + coords[cdim * fv[p + 1] + d] + coords[cdim * fv[p + 2] + d]) / 3.;
2759: }
2760: norm = PetscSqrtReal(n[0] * n[0] + n[1] * n[1] + n[2] * n[2]);
2761: // Allow zero volume cells
2762: if (norm != 0) {
2763: n[0] /= norm;
2764: n[1] /= norm;
2765: n[2] /= norm;
2766: c[0] /= norm;
2767: c[1] /= norm;
2768: c[2] /= norm;
2769: }
2770: if (vol) *vol = 0.5 * norm;
2771: if (centroid)
2772: for (d = 0; d < cdim; ++d) centroid[d] = c[d];
2773: if (normal)
2774: for (d = 0; d < cdim; ++d) normal[d] = n[d];
2775: }
2776: PetscCall(DMPlexRestoreCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
2777: PetscFunctionReturn(PETSC_SUCCESS);
2778: }
2780: /* Centroid_i = (\sum_n V_n Cn_i) / V */
2781: static PetscErrorCode DMPlexComputeGeometryFVM_3D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
2782: {
2783: DMPolytopeType ct;
2784: const PetscScalar *array;
2785: PetscScalar *coords = NULL;
2786: PetscInt coordSize;
2787: PetscBool isDG;
2788: PetscReal vsum = 0.0, vtmp, coordsTmp[3 * 3], origin[3];
2789: const PetscInt order[16] = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15};
2790: const PetscInt *cone, *faceSizes, *faces;
2791: const DMPolytopeType *faceTypes;
2792: PetscBool isHybrid = PETSC_FALSE;
2793: PetscInt numFaces, f, fOff = 0, p, d;
2795: PetscFunctionBegin;
2796: PetscCheck(dim <= 3, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "No support for dim %" PetscInt_FMT " > 3", dim);
2797: /* Must check for hybrid cells because prisms have a different orientation scheme */
2798: PetscCall(DMPlexGetCellType(dm, cell, &ct));
2799: switch (ct) {
2800: case DM_POLYTOPE_POINT_PRISM_TENSOR:
2801: case DM_POLYTOPE_SEG_PRISM_TENSOR:
2802: case DM_POLYTOPE_TRI_PRISM_TENSOR:
2803: case DM_POLYTOPE_QUAD_PRISM_TENSOR:
2804: isHybrid = PETSC_TRUE;
2805: default:
2806: break;
2807: }
2809: if (centroid)
2810: for (d = 0; d < dim; ++d) centroid[d] = 0.0;
2811: PetscCall(DMPlexGetCone(dm, cell, &cone));
2813: // Using the closure of faces for coordinates does not work in periodic geometries, so we index into the cell coordinates
2814: PetscCall(DMPlexGetRawFaces_Internal(dm, ct, order, &numFaces, &faceTypes, &faceSizes, &faces));
2815: PetscCall(DMPlexGetCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
2816: for (f = 0; f < numFaces; ++f) {
2817: PetscBool flip = isHybrid && f == 0 ? PETSC_TRUE : PETSC_FALSE; /* The first hybrid face is reversed */
2819: // If using zero as the origin vertex for each tetrahedron, an element far from the origin will have positive and
2820: // negative volumes that nearly cancel, thus incurring rounding error. Here we define origin[] as the first vertex
2821: // so that all tetrahedra have positive volume.
2822: if (f == 0)
2823: for (d = 0; d < dim; d++) origin[d] = PetscRealPart(coords[d]);
2824: switch (faceTypes[f]) {
2825: case DM_POLYTOPE_TRIANGLE:
2826: for (d = 0; d < dim; ++d) {
2827: coordsTmp[0 * dim + d] = PetscRealPart(coords[faces[fOff + 0] * dim + d]) - origin[d];
2828: coordsTmp[1 * dim + d] = PetscRealPart(coords[faces[fOff + 1] * dim + d]) - origin[d];
2829: coordsTmp[2 * dim + d] = PetscRealPart(coords[faces[fOff + 2] * dim + d]) - origin[d];
2830: }
2831: Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
2832: if (flip) vtmp = -vtmp;
2833: vsum += vtmp;
2834: if (centroid) { /* Centroid of OABC = (a+b+c)/4 */
2835: for (d = 0; d < dim; ++d) {
2836: for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p * dim + d] * vtmp;
2837: }
2838: }
2839: break;
2840: case DM_POLYTOPE_QUADRILATERAL:
2841: case DM_POLYTOPE_SEG_PRISM_TENSOR: {
2842: PetscInt fv[4] = {0, 1, 2, 3};
2844: /* Side faces for hybrid cells are stored as tensor products */
2845: if (isHybrid && f > 1) {
2846: fv[2] = 3;
2847: fv[3] = 2;
2848: }
2849: /* DO FOR PYRAMID */
2850: /* First tet */
2851: for (d = 0; d < dim; ++d) {
2852: coordsTmp[0 * dim + d] = PetscRealPart(coords[faces[fOff + fv[0]] * dim + d]) - origin[d];
2853: coordsTmp[1 * dim + d] = PetscRealPart(coords[faces[fOff + fv[1]] * dim + d]) - origin[d];
2854: coordsTmp[2 * dim + d] = PetscRealPart(coords[faces[fOff + fv[3]] * dim + d]) - origin[d];
2855: }
2856: Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
2857: if (flip) vtmp = -vtmp;
2858: vsum += vtmp;
2859: if (centroid) {
2860: for (d = 0; d < dim; ++d) {
2861: for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p * dim + d] * vtmp;
2862: }
2863: }
2864: /* Second tet */
2865: for (d = 0; d < dim; ++d) {
2866: coordsTmp[0 * dim + d] = PetscRealPart(coords[faces[fOff + fv[1]] * dim + d]) - origin[d];
2867: coordsTmp[1 * dim + d] = PetscRealPart(coords[faces[fOff + fv[2]] * dim + d]) - origin[d];
2868: coordsTmp[2 * dim + d] = PetscRealPart(coords[faces[fOff + fv[3]] * dim + d]) - origin[d];
2869: }
2870: Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
2871: if (flip) vtmp = -vtmp;
2872: vsum += vtmp;
2873: if (centroid) {
2874: for (d = 0; d < dim; ++d) {
2875: for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p * dim + d] * vtmp;
2876: }
2877: }
2878: break;
2879: }
2880: default:
2881: SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Cannot handle face %" PetscInt_FMT " of type %s", cone[f], DMPolytopeTypes[ct]);
2882: }
2883: fOff += faceSizes[f];
2884: }
2885: PetscCall(DMPlexRestoreRawFaces_Internal(dm, ct, order, &numFaces, &faceTypes, &faceSizes, &faces));
2886: PetscCall(DMPlexRestoreCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
2887: if (vol) *vol = PetscAbsReal(vsum);
2888: if (normal)
2889: for (d = 0; d < dim; ++d) normal[d] = 0.0;
2890: if (centroid)
2891: for (d = 0; d < dim; ++d) centroid[d] = centroid[d] / (vsum * 4) + origin[d];
2892: PetscFunctionReturn(PETSC_SUCCESS);
2893: }
2895: /*@C
2896: DMPlexComputeCellGeometryFVM - Compute the volume for a given cell
2898: Collective
2900: Input Parameters:
2901: + dm - the `DMPLEX`
2902: - cell - the cell
2904: Output Parameters:
2905: + vol - the cell volume
2906: . centroid - the cell centroid
2907: - normal - the cell normal, if appropriate
2909: Level: advanced
2911: .seealso: `DMPLEX`, `DMGetCoordinateSection()`, `DMGetCoordinates()`
2912: @*/
2913: PetscErrorCode DMPlexComputeCellGeometryFVM(DM dm, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
2914: {
2915: PetscInt depth, dim;
2917: PetscFunctionBegin;
2918: PetscCall(DMPlexGetDepth(dm, &depth));
2919: PetscCall(DMGetDimension(dm, &dim));
2920: PetscCheck(depth == dim, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Mesh must be interpolated");
2921: PetscCall(DMPlexGetPointDepth(dm, cell, &depth));
2922: switch (depth) {
2923: case 0:
2924: PetscCall(DMPlexComputeGeometryFVM_0D_Internal(dm, dim, cell, vol, centroid, normal));
2925: break;
2926: case 1:
2927: PetscCall(DMPlexComputeGeometryFVM_1D_Internal(dm, dim, cell, vol, centroid, normal));
2928: break;
2929: case 2:
2930: PetscCall(DMPlexComputeGeometryFVM_2D_Internal(dm, dim, cell, vol, centroid, normal));
2931: break;
2932: case 3:
2933: PetscCall(DMPlexComputeGeometryFVM_3D_Internal(dm, dim, cell, vol, centroid, normal));
2934: break;
2935: default:
2936: SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported dimension %" PetscInt_FMT " (depth %" PetscInt_FMT ") for element geometry computation", dim, depth);
2937: }
2938: PetscFunctionReturn(PETSC_SUCCESS);
2939: }
2941: /*@
2942: DMPlexComputeGeometryFVM - Computes the cell and face geometry for a finite volume method
2944: Input Parameter:
2945: . dm - The `DMPLEX`
2947: Output Parameters:
2948: + cellgeom - A `Vec` of `PetscFVCellGeom` data
2949: - facegeom - A `Vec` of `PetscFVFaceGeom` data
2951: Level: developer
2953: .seealso: `DMPLEX`, `PetscFVFaceGeom`, `PetscFVCellGeom`
2954: @*/
2955: PetscErrorCode DMPlexComputeGeometryFVM(DM dm, Vec *cellgeom, Vec *facegeom)
2956: {
2957: DM dmFace, dmCell;
2958: DMLabel ghostLabel;
2959: PetscSection sectionFace, sectionCell;
2960: PetscSection coordSection;
2961: Vec coordinates;
2962: PetscScalar *fgeom, *cgeom;
2963: PetscReal minradius, gminradius;
2964: PetscInt dim, cStart, cEnd, cEndInterior, c, fStart, fEnd, f;
2966: PetscFunctionBegin;
2967: PetscCall(DMGetDimension(dm, &dim));
2968: PetscCall(DMGetCoordinateSection(dm, &coordSection));
2969: PetscCall(DMGetCoordinatesLocal(dm, &coordinates));
2970: /* Make cell centroids and volumes */
2971: PetscCall(DMClone(dm, &dmCell));
2972: PetscCall(DMSetCoordinateSection(dmCell, PETSC_DETERMINE, coordSection));
2973: PetscCall(DMSetCoordinatesLocal(dmCell, coordinates));
2974: PetscCall(PetscSectionCreate(PetscObjectComm((PetscObject)dm), §ionCell));
2975: PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
2976: PetscCall(DMPlexGetCellTypeStratum(dm, DM_POLYTOPE_FV_GHOST, &cEndInterior, NULL));
2977: PetscCall(PetscSectionSetChart(sectionCell, cStart, cEnd));
2978: for (c = cStart; c < cEnd; ++c) PetscCall(PetscSectionSetDof(sectionCell, c, (PetscInt)PetscCeilReal(((PetscReal)sizeof(PetscFVCellGeom)) / sizeof(PetscScalar))));
2979: PetscCall(PetscSectionSetUp(sectionCell));
2980: PetscCall(DMSetLocalSection(dmCell, sectionCell));
2981: PetscCall(PetscSectionDestroy(§ionCell));
2982: PetscCall(DMCreateLocalVector(dmCell, cellgeom));
2983: if (cEndInterior < 0) cEndInterior = cEnd;
2984: PetscCall(VecGetArray(*cellgeom, &cgeom));
2985: for (c = cStart; c < cEndInterior; ++c) {
2986: PetscFVCellGeom *cg;
2988: PetscCall(DMPlexPointLocalRef(dmCell, c, cgeom, &cg));
2989: PetscCall(PetscArrayzero(cg, 1));
2990: PetscCall(DMPlexComputeCellGeometryFVM(dmCell, c, &cg->volume, cg->centroid, NULL));
2991: }
2992: /* Compute face normals and minimum cell radius */
2993: PetscCall(DMClone(dm, &dmFace));
2994: PetscCall(PetscSectionCreate(PetscObjectComm((PetscObject)dm), §ionFace));
2995: PetscCall(DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd));
2996: PetscCall(PetscSectionSetChart(sectionFace, fStart, fEnd));
2997: for (f = fStart; f < fEnd; ++f) PetscCall(PetscSectionSetDof(sectionFace, f, (PetscInt)PetscCeilReal(((PetscReal)sizeof(PetscFVFaceGeom)) / sizeof(PetscScalar))));
2998: PetscCall(PetscSectionSetUp(sectionFace));
2999: PetscCall(DMSetLocalSection(dmFace, sectionFace));
3000: PetscCall(PetscSectionDestroy(§ionFace));
3001: PetscCall(DMCreateLocalVector(dmFace, facegeom));
3002: PetscCall(VecGetArray(*facegeom, &fgeom));
3003: PetscCall(DMGetLabel(dm, "ghost", &ghostLabel));
3004: minradius = PETSC_MAX_REAL;
3005: for (f = fStart; f < fEnd; ++f) {
3006: PetscFVFaceGeom *fg;
3007: PetscReal area;
3008: const PetscInt *cells;
3009: PetscInt ncells, ghost = -1, d, numChildren;
3011: if (ghostLabel) PetscCall(DMLabelGetValue(ghostLabel, f, &ghost));
3012: PetscCall(DMPlexGetTreeChildren(dm, f, &numChildren, NULL));
3013: PetscCall(DMPlexGetSupport(dm, f, &cells));
3014: PetscCall(DMPlexGetSupportSize(dm, f, &ncells));
3015: /* It is possible to get a face with no support when using partition overlap */
3016: if (!ncells || ghost >= 0 || numChildren) continue;
3017: PetscCall(DMPlexPointLocalRef(dmFace, f, fgeom, &fg));
3018: PetscCall(DMPlexComputeCellGeometryFVM(dm, f, &area, fg->centroid, fg->normal));
3019: for (d = 0; d < dim; ++d) fg->normal[d] *= area;
3020: /* Flip face orientation if necessary to match ordering in support, and Update minimum radius */
3021: {
3022: PetscFVCellGeom *cL, *cR;
3023: PetscReal *lcentroid, *rcentroid;
3024: PetscReal l[3], r[3], v[3];
3026: PetscCall(DMPlexPointLocalRead(dmCell, cells[0], cgeom, &cL));
3027: lcentroid = cells[0] >= cEndInterior ? fg->centroid : cL->centroid;
3028: if (ncells > 1) {
3029: PetscCall(DMPlexPointLocalRead(dmCell, cells[1], cgeom, &cR));
3030: rcentroid = cells[1] >= cEndInterior ? fg->centroid : cR->centroid;
3031: } else {
3032: rcentroid = fg->centroid;
3033: }
3034: PetscCall(DMLocalizeCoordinateReal_Internal(dm, dim, fg->centroid, lcentroid, l));
3035: PetscCall(DMLocalizeCoordinateReal_Internal(dm, dim, fg->centroid, rcentroid, r));
3036: DMPlex_WaxpyD_Internal(dim, -1, l, r, v);
3037: if (DMPlex_DotRealD_Internal(dim, fg->normal, v) < 0) {
3038: for (d = 0; d < dim; ++d) fg->normal[d] = -fg->normal[d];
3039: }
3040: if (DMPlex_DotRealD_Internal(dim, fg->normal, v) <= 0) {
3041: PetscCheck(dim != 2, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Direction for face %" PetscInt_FMT " could not be fixed, normal (%g,%g) v (%g,%g)", f, (double)fg->normal[0], (double)fg->normal[1], (double)v[0], (double)v[1]);
3042: PetscCheck(dim != 3, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Direction for face %" PetscInt_FMT " could not be fixed, normal (%g,%g,%g) v (%g,%g,%g)", f, (double)fg->normal[0], (double)fg->normal[1], (double)fg->normal[2], (double)v[0], (double)v[1], (double)v[2]);
3043: SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Direction for face %" PetscInt_FMT " could not be fixed", f);
3044: }
3045: if (cells[0] < cEndInterior) {
3046: DMPlex_WaxpyD_Internal(dim, -1, fg->centroid, cL->centroid, v);
3047: minradius = PetscMin(minradius, DMPlex_NormD_Internal(dim, v));
3048: }
3049: if (ncells > 1 && cells[1] < cEndInterior) {
3050: DMPlex_WaxpyD_Internal(dim, -1, fg->centroid, cR->centroid, v);
3051: minradius = PetscMin(minradius, DMPlex_NormD_Internal(dim, v));
3052: }
3053: }
3054: }
3055: PetscCallMPI(MPIU_Allreduce(&minradius, &gminradius, 1, MPIU_REAL, MPIU_MIN, PetscObjectComm((PetscObject)dm)));
3056: PetscCall(DMPlexSetMinRadius(dm, gminradius));
3057: /* Compute centroids of ghost cells */
3058: for (c = cEndInterior; c < cEnd; ++c) {
3059: PetscFVFaceGeom *fg;
3060: const PetscInt *cone, *support;
3061: PetscInt coneSize, supportSize, s;
3063: PetscCall(DMPlexGetConeSize(dmCell, c, &coneSize));
3064: PetscCheck(coneSize == 1, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Ghost cell %" PetscInt_FMT " has cone size %" PetscInt_FMT " != 1", c, coneSize);
3065: PetscCall(DMPlexGetCone(dmCell, c, &cone));
3066: PetscCall(DMPlexGetSupportSize(dmCell, cone[0], &supportSize));
3067: PetscCheck(supportSize == 2, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Face %" PetscInt_FMT " has support size %" PetscInt_FMT " != 2", cone[0], supportSize);
3068: PetscCall(DMPlexGetSupport(dmCell, cone[0], &support));
3069: PetscCall(DMPlexPointLocalRef(dmFace, cone[0], fgeom, &fg));
3070: for (s = 0; s < 2; ++s) {
3071: /* Reflect ghost centroid across plane of face */
3072: if (support[s] == c) {
3073: PetscFVCellGeom *ci;
3074: PetscFVCellGeom *cg;
3075: PetscReal c2f[3], a;
3077: PetscCall(DMPlexPointLocalRead(dmCell, support[(s + 1) % 2], cgeom, &ci));
3078: DMPlex_WaxpyD_Internal(dim, -1, ci->centroid, fg->centroid, c2f); /* cell to face centroid */
3079: a = DMPlex_DotRealD_Internal(dim, c2f, fg->normal) / DMPlex_DotRealD_Internal(dim, fg->normal, fg->normal);
3080: PetscCall(DMPlexPointLocalRef(dmCell, support[s], cgeom, &cg));
3081: DMPlex_WaxpyD_Internal(dim, 2 * a, fg->normal, ci->centroid, cg->centroid);
3082: cg->volume = ci->volume;
3083: }
3084: }
3085: }
3086: PetscCall(VecRestoreArray(*facegeom, &fgeom));
3087: PetscCall(VecRestoreArray(*cellgeom, &cgeom));
3088: PetscCall(DMDestroy(&dmCell));
3089: PetscCall(DMDestroy(&dmFace));
3090: PetscFunctionReturn(PETSC_SUCCESS);
3091: }
3093: /*@
3094: DMPlexGetMinRadius - Returns the minimum distance from any cell centroid to a face
3096: Not Collective
3098: Input Parameter:
3099: . dm - the `DMPLEX`
3101: Output Parameter:
3102: . minradius - the minimum cell radius
3104: Level: developer
3106: .seealso: `DMPLEX`, `DMGetCoordinates()`
3107: @*/
3108: PetscErrorCode DMPlexGetMinRadius(DM dm, PetscReal *minradius)
3109: {
3110: PetscFunctionBegin;
3112: PetscAssertPointer(minradius, 2);
3113: *minradius = ((DM_Plex *)dm->data)->minradius;
3114: PetscFunctionReturn(PETSC_SUCCESS);
3115: }
3117: /*@
3118: DMPlexSetMinRadius - Sets the minimum distance from the cell centroid to a face
3120: Logically Collective
3122: Input Parameters:
3123: + dm - the `DMPLEX`
3124: - minradius - the minimum cell radius
3126: Level: developer
3128: .seealso: `DMPLEX`, `DMSetCoordinates()`
3129: @*/
3130: PetscErrorCode DMPlexSetMinRadius(DM dm, PetscReal minradius)
3131: {
3132: PetscFunctionBegin;
3134: ((DM_Plex *)dm->data)->minradius = minradius;
3135: PetscFunctionReturn(PETSC_SUCCESS);
3136: }
3138: static PetscErrorCode BuildGradientReconstruction_Internal(DM dm, PetscFV fvm, DM dmFace, PetscScalar *fgeom, DM dmCell, PetscScalar *cgeom)
3139: {
3140: DMLabel ghostLabel;
3141: PetscScalar *dx, *grad, **gref;
3142: PetscInt dim, cStart, cEnd, c, cEndInterior, maxNumFaces;
3144: PetscFunctionBegin;
3145: PetscCall(DMGetDimension(dm, &dim));
3146: PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
3147: PetscCall(DMPlexGetCellTypeStratum(dm, DM_POLYTOPE_FV_GHOST, &cEndInterior, NULL));
3148: cEndInterior = cEndInterior < 0 ? cEnd : cEndInterior;
3149: PetscCall(DMPlexGetMaxSizes(dm, &maxNumFaces, NULL));
3150: PetscCall(PetscFVLeastSquaresSetMaxFaces(fvm, maxNumFaces));
3151: PetscCall(DMGetLabel(dm, "ghost", &ghostLabel));
3152: PetscCall(PetscMalloc3(maxNumFaces * dim, &dx, maxNumFaces * dim, &grad, maxNumFaces, &gref));
3153: for (c = cStart; c < cEndInterior; c++) {
3154: const PetscInt *faces;
3155: PetscInt numFaces, usedFaces, f, d;
3156: PetscFVCellGeom *cg;
3157: PetscBool boundary;
3158: PetscInt ghost;
3160: // do not attempt to compute a gradient reconstruction stencil in a ghost cell. It will never be used
3161: PetscCall(DMLabelGetValue(ghostLabel, c, &ghost));
3162: if (ghost >= 0) continue;
3164: PetscCall(DMPlexPointLocalRead(dmCell, c, cgeom, &cg));
3165: PetscCall(DMPlexGetConeSize(dm, c, &numFaces));
3166: PetscCall(DMPlexGetCone(dm, c, &faces));
3167: PetscCheck(numFaces >= dim, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Cell %" PetscInt_FMT " has only %" PetscInt_FMT " faces, not enough for gradient reconstruction", c, numFaces);
3168: for (f = 0, usedFaces = 0; f < numFaces; ++f) {
3169: PetscFVCellGeom *cg1;
3170: PetscFVFaceGeom *fg;
3171: const PetscInt *fcells;
3172: PetscInt ncell, side;
3174: PetscCall(DMLabelGetValue(ghostLabel, faces[f], &ghost));
3175: PetscCall(DMIsBoundaryPoint(dm, faces[f], &boundary));
3176: if ((ghost >= 0) || boundary) continue;
3177: PetscCall(DMPlexGetSupport(dm, faces[f], &fcells));
3178: side = (c != fcells[0]); /* c is on left=0 or right=1 of face */
3179: ncell = fcells[!side]; /* the neighbor */
3180: PetscCall(DMPlexPointLocalRef(dmFace, faces[f], fgeom, &fg));
3181: PetscCall(DMPlexPointLocalRead(dmCell, ncell, cgeom, &cg1));
3182: for (d = 0; d < dim; ++d) dx[usedFaces * dim + d] = cg1->centroid[d] - cg->centroid[d];
3183: gref[usedFaces++] = fg->grad[side]; /* Gradient reconstruction term will go here */
3184: }
3185: PetscCheck(usedFaces, PETSC_COMM_SELF, PETSC_ERR_USER, "Mesh contains isolated cell (no neighbors). Is it intentional?");
3186: PetscCall(PetscFVComputeGradient(fvm, usedFaces, dx, grad));
3187: for (f = 0, usedFaces = 0; f < numFaces; ++f) {
3188: PetscCall(DMLabelGetValue(ghostLabel, faces[f], &ghost));
3189: PetscCall(DMIsBoundaryPoint(dm, faces[f], &boundary));
3190: if ((ghost >= 0) || boundary) continue;
3191: for (d = 0; d < dim; ++d) gref[usedFaces][d] = grad[usedFaces * dim + d];
3192: ++usedFaces;
3193: }
3194: }
3195: PetscCall(PetscFree3(dx, grad, gref));
3196: PetscFunctionReturn(PETSC_SUCCESS);
3197: }
3199: static PetscErrorCode BuildGradientReconstruction_Internal_Tree(DM dm, PetscFV fvm, DM dmFace, PetscScalar *fgeom, DM dmCell, PetscScalar *cgeom)
3200: {
3201: DMLabel ghostLabel;
3202: PetscScalar *dx, *grad, **gref;
3203: PetscInt dim, cStart, cEnd, c, cEndInterior, fStart, fEnd, f, nStart, nEnd, maxNumFaces = 0;
3204: PetscSection neighSec;
3205: PetscInt(*neighbors)[2];
3206: PetscInt *counter;
3208: PetscFunctionBegin;
3209: PetscCall(DMGetDimension(dm, &dim));
3210: PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
3211: PetscCall(DMPlexGetCellTypeStratum(dm, DM_POLYTOPE_FV_GHOST, &cEndInterior, NULL));
3212: if (cEndInterior < 0) cEndInterior = cEnd;
3213: PetscCall(PetscSectionCreate(PetscObjectComm((PetscObject)dm), &neighSec));
3214: PetscCall(PetscSectionSetChart(neighSec, cStart, cEndInterior));
3215: PetscCall(DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd));
3216: PetscCall(DMGetLabel(dm, "ghost", &ghostLabel));
3217: for (f = fStart; f < fEnd; f++) {
3218: const PetscInt *fcells;
3219: PetscBool boundary;
3220: PetscInt ghost = -1;
3221: PetscInt numChildren, numCells, c;
3223: if (ghostLabel) PetscCall(DMLabelGetValue(ghostLabel, f, &ghost));
3224: PetscCall(DMIsBoundaryPoint(dm, f, &boundary));
3225: PetscCall(DMPlexGetTreeChildren(dm, f, &numChildren, NULL));
3226: if ((ghost >= 0) || boundary || numChildren) continue;
3227: PetscCall(DMPlexGetSupportSize(dm, f, &numCells));
3228: if (numCells == 2) {
3229: PetscCall(DMPlexGetSupport(dm, f, &fcells));
3230: for (c = 0; c < 2; c++) {
3231: PetscInt cell = fcells[c];
3233: if (cell >= cStart && cell < cEndInterior) PetscCall(PetscSectionAddDof(neighSec, cell, 1));
3234: }
3235: }
3236: }
3237: PetscCall(PetscSectionSetUp(neighSec));
3238: PetscCall(PetscSectionGetMaxDof(neighSec, &maxNumFaces));
3239: PetscCall(PetscFVLeastSquaresSetMaxFaces(fvm, maxNumFaces));
3240: nStart = 0;
3241: PetscCall(PetscSectionGetStorageSize(neighSec, &nEnd));
3242: PetscCall(PetscMalloc1(nEnd - nStart, &neighbors));
3243: PetscCall(PetscCalloc1(cEndInterior - cStart, &counter));
3244: for (f = fStart; f < fEnd; f++) {
3245: const PetscInt *fcells;
3246: PetscBool boundary;
3247: PetscInt ghost = -1;
3248: PetscInt numChildren, numCells, c;
3250: if (ghostLabel) PetscCall(DMLabelGetValue(ghostLabel, f, &ghost));
3251: PetscCall(DMIsBoundaryPoint(dm, f, &boundary));
3252: PetscCall(DMPlexGetTreeChildren(dm, f, &numChildren, NULL));
3253: if ((ghost >= 0) || boundary || numChildren) continue;
3254: PetscCall(DMPlexGetSupportSize(dm, f, &numCells));
3255: if (numCells == 2) {
3256: PetscCall(DMPlexGetSupport(dm, f, &fcells));
3257: for (c = 0; c < 2; c++) {
3258: PetscInt cell = fcells[c], off;
3260: if (cell >= cStart && cell < cEndInterior) {
3261: PetscCall(PetscSectionGetOffset(neighSec, cell, &off));
3262: off += counter[cell - cStart]++;
3263: neighbors[off][0] = f;
3264: neighbors[off][1] = fcells[1 - c];
3265: }
3266: }
3267: }
3268: }
3269: PetscCall(PetscFree(counter));
3270: PetscCall(PetscMalloc3(maxNumFaces * dim, &dx, maxNumFaces * dim, &grad, maxNumFaces, &gref));
3271: for (c = cStart; c < cEndInterior; c++) {
3272: PetscInt numFaces, f, d, off, ghost = -1;
3273: PetscFVCellGeom *cg;
3275: PetscCall(DMPlexPointLocalRead(dmCell, c, cgeom, &cg));
3276: PetscCall(PetscSectionGetDof(neighSec, c, &numFaces));
3277: PetscCall(PetscSectionGetOffset(neighSec, c, &off));
3279: // do not attempt to compute a gradient reconstruction stencil in a ghost cell. It will never be used
3280: if (ghostLabel) PetscCall(DMLabelGetValue(ghostLabel, c, &ghost));
3281: if (ghost >= 0) continue;
3283: PetscCheck(numFaces >= dim, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Cell %" PetscInt_FMT " has only %" PetscInt_FMT " faces, not enough for gradient reconstruction", c, numFaces);
3284: for (f = 0; f < numFaces; ++f) {
3285: PetscFVCellGeom *cg1;
3286: PetscFVFaceGeom *fg;
3287: const PetscInt *fcells;
3288: PetscInt ncell, side, nface;
3290: nface = neighbors[off + f][0];
3291: ncell = neighbors[off + f][1];
3292: PetscCall(DMPlexGetSupport(dm, nface, &fcells));
3293: side = (c != fcells[0]);
3294: PetscCall(DMPlexPointLocalRef(dmFace, nface, fgeom, &fg));
3295: PetscCall(DMPlexPointLocalRead(dmCell, ncell, cgeom, &cg1));
3296: for (d = 0; d < dim; ++d) dx[f * dim + d] = cg1->centroid[d] - cg->centroid[d];
3297: gref[f] = fg->grad[side]; /* Gradient reconstruction term will go here */
3298: }
3299: PetscCall(PetscFVComputeGradient(fvm, numFaces, dx, grad));
3300: for (f = 0; f < numFaces; ++f) {
3301: for (d = 0; d < dim; ++d) gref[f][d] = grad[f * dim + d];
3302: }
3303: }
3304: PetscCall(PetscFree3(dx, grad, gref));
3305: PetscCall(PetscSectionDestroy(&neighSec));
3306: PetscCall(PetscFree(neighbors));
3307: PetscFunctionReturn(PETSC_SUCCESS);
3308: }
3310: /*@
3311: DMPlexComputeGradientFVM - Compute geometric factors for gradient reconstruction, which are stored in the geometry data, and compute layout for gradient data
3313: Collective
3315: Input Parameters:
3316: + dm - The `DMPLEX`
3317: . fvm - The `PetscFV`
3318: - cellGeometry - The face geometry from `DMPlexComputeCellGeometryFVM()`
3320: Input/Output Parameter:
3321: . faceGeometry - The face geometry from `DMPlexComputeFaceGeometryFVM()`; on output
3322: the geometric factors for gradient calculation are inserted
3324: Output Parameter:
3325: . dmGrad - The `DM` describing the layout of gradient data
3327: Level: developer
3329: .seealso: `DMPLEX`, `DMPlexGetFaceGeometryFVM()`, `DMPlexGetCellGeometryFVM()`
3330: @*/
3331: PetscErrorCode DMPlexComputeGradientFVM(DM dm, PetscFV fvm, Vec faceGeometry, Vec cellGeometry, DM *dmGrad)
3332: {
3333: DM dmFace, dmCell;
3334: PetscScalar *fgeom, *cgeom;
3335: PetscSection sectionGrad, parentSection;
3336: PetscInt dim, pdim, cStart, cEnd, cEndInterior, c;
3338: PetscFunctionBegin;
3339: PetscCall(DMGetDimension(dm, &dim));
3340: PetscCall(PetscFVGetNumComponents(fvm, &pdim));
3341: PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
3342: PetscCall(DMPlexGetCellTypeStratum(dm, DM_POLYTOPE_FV_GHOST, &cEndInterior, NULL));
3343: /* Construct the interpolant corresponding to each face from the least-square solution over the cell neighborhood */
3344: PetscCall(VecGetDM(faceGeometry, &dmFace));
3345: PetscCall(VecGetDM(cellGeometry, &dmCell));
3346: PetscCall(VecGetArray(faceGeometry, &fgeom));
3347: PetscCall(VecGetArray(cellGeometry, &cgeom));
3348: PetscCall(DMPlexGetTree(dm, &parentSection, NULL, NULL, NULL, NULL));
3349: if (!parentSection) {
3350: PetscCall(BuildGradientReconstruction_Internal(dm, fvm, dmFace, fgeom, dmCell, cgeom));
3351: } else {
3352: PetscCall(BuildGradientReconstruction_Internal_Tree(dm, fvm, dmFace, fgeom, dmCell, cgeom));
3353: }
3354: PetscCall(VecRestoreArray(faceGeometry, &fgeom));
3355: PetscCall(VecRestoreArray(cellGeometry, &cgeom));
3356: /* Create storage for gradients */
3357: PetscCall(DMClone(dm, dmGrad));
3358: PetscCall(PetscSectionCreate(PetscObjectComm((PetscObject)dm), §ionGrad));
3359: PetscCall(PetscSectionSetChart(sectionGrad, cStart, cEnd));
3360: for (c = cStart; c < cEnd; ++c) PetscCall(PetscSectionSetDof(sectionGrad, c, pdim * dim));
3361: PetscCall(PetscSectionSetUp(sectionGrad));
3362: PetscCall(DMSetLocalSection(*dmGrad, sectionGrad));
3363: PetscCall(PetscSectionDestroy(§ionGrad));
3364: PetscFunctionReturn(PETSC_SUCCESS);
3365: }
3367: /*@
3368: DMPlexGetDataFVM - Retrieve precomputed cell geometry
3370: Collective
3372: Input Parameters:
3373: + dm - The `DM`
3374: - fv - The `PetscFV`
3376: Output Parameters:
3377: + cellgeom - The cell geometry
3378: . facegeom - The face geometry
3379: - gradDM - The gradient matrices
3381: Level: developer
3383: .seealso: `DMPLEX`, `DMPlexComputeGeometryFVM()`
3384: @*/
3385: PetscErrorCode DMPlexGetDataFVM(DM dm, PetscFV fv, Vec *cellgeom, Vec *facegeom, DM *gradDM)
3386: {
3387: PetscObject cellgeomobj, facegeomobj;
3389: PetscFunctionBegin;
3390: PetscCall(PetscObjectQuery((PetscObject)dm, "DMPlex_cellgeom_fvm", &cellgeomobj));
3391: if (!cellgeomobj) {
3392: Vec cellgeomInt, facegeomInt;
3394: PetscCall(DMPlexComputeGeometryFVM(dm, &cellgeomInt, &facegeomInt));
3395: PetscCall(PetscObjectCompose((PetscObject)dm, "DMPlex_cellgeom_fvm", (PetscObject)cellgeomInt));
3396: PetscCall(PetscObjectCompose((PetscObject)dm, "DMPlex_facegeom_fvm", (PetscObject)facegeomInt));
3397: PetscCall(VecDestroy(&cellgeomInt));
3398: PetscCall(VecDestroy(&facegeomInt));
3399: PetscCall(PetscObjectQuery((PetscObject)dm, "DMPlex_cellgeom_fvm", &cellgeomobj));
3400: }
3401: PetscCall(PetscObjectQuery((PetscObject)dm, "DMPlex_facegeom_fvm", &facegeomobj));
3402: if (cellgeom) *cellgeom = (Vec)cellgeomobj;
3403: if (facegeom) *facegeom = (Vec)facegeomobj;
3404: if (gradDM) {
3405: PetscObject gradobj;
3406: PetscBool computeGradients;
3408: PetscCall(PetscFVGetComputeGradients(fv, &computeGradients));
3409: if (!computeGradients) {
3410: *gradDM = NULL;
3411: PetscFunctionReturn(PETSC_SUCCESS);
3412: }
3413: PetscCall(PetscObjectQuery((PetscObject)dm, "DMPlex_dmgrad_fvm", &gradobj));
3414: if (!gradobj) {
3415: DM dmGradInt;
3417: PetscCall(DMPlexComputeGradientFVM(dm, fv, (Vec)facegeomobj, (Vec)cellgeomobj, &dmGradInt));
3418: PetscCall(PetscObjectCompose((PetscObject)dm, "DMPlex_dmgrad_fvm", (PetscObject)dmGradInt));
3419: PetscCall(DMDestroy(&dmGradInt));
3420: PetscCall(PetscObjectQuery((PetscObject)dm, "DMPlex_dmgrad_fvm", &gradobj));
3421: }
3422: *gradDM = (DM)gradobj;
3423: }
3424: PetscFunctionReturn(PETSC_SUCCESS);
3425: }
3427: static PetscErrorCode DMPlexCoordinatesToReference_NewtonUpdate(PetscInt dimC, PetscInt dimR, PetscScalar *J, PetscScalar *invJ, PetscScalar *work, PetscReal *resNeg, PetscReal *guess)
3428: {
3429: PetscInt l, m;
3431: PetscFunctionBeginHot;
3432: if (dimC == dimR && dimR <= 3) {
3433: /* invert Jacobian, multiply */
3434: PetscScalar det, idet;
3436: switch (dimR) {
3437: case 1:
3438: invJ[0] = 1. / J[0];
3439: break;
3440: case 2:
3441: det = J[0] * J[3] - J[1] * J[2];
3442: idet = 1. / det;
3443: invJ[0] = J[3] * idet;
3444: invJ[1] = -J[1] * idet;
3445: invJ[2] = -J[2] * idet;
3446: invJ[3] = J[0] * idet;
3447: break;
3448: case 3: {
3449: invJ[0] = J[4] * J[8] - J[5] * J[7];
3450: invJ[1] = J[2] * J[7] - J[1] * J[8];
3451: invJ[2] = J[1] * J[5] - J[2] * J[4];
3452: det = invJ[0] * J[0] + invJ[1] * J[3] + invJ[2] * J[6];
3453: idet = 1. / det;
3454: invJ[0] *= idet;
3455: invJ[1] *= idet;
3456: invJ[2] *= idet;
3457: invJ[3] = idet * (J[5] * J[6] - J[3] * J[8]);
3458: invJ[4] = idet * (J[0] * J[8] - J[2] * J[6]);
3459: invJ[5] = idet * (J[2] * J[3] - J[0] * J[5]);
3460: invJ[6] = idet * (J[3] * J[7] - J[4] * J[6]);
3461: invJ[7] = idet * (J[1] * J[6] - J[0] * J[7]);
3462: invJ[8] = idet * (J[0] * J[4] - J[1] * J[3]);
3463: } break;
3464: }
3465: for (l = 0; l < dimR; l++) {
3466: for (m = 0; m < dimC; m++) guess[l] += PetscRealPart(invJ[l * dimC + m]) * resNeg[m];
3467: }
3468: } else {
3469: #if defined(PETSC_USE_COMPLEX)
3470: char transpose = 'C';
3471: #else
3472: char transpose = 'T';
3473: #endif
3474: PetscBLASInt m, n, one = 1, worksize, info;
3476: PetscCall(PetscBLASIntCast(dimR, &m));
3477: PetscCall(PetscBLASIntCast(dimC, &n));
3478: PetscCall(PetscBLASIntCast(dimC * dimC, &worksize));
3479: for (l = 0; l < dimC; l++) invJ[l] = resNeg[l];
3481: PetscCallBLAS("LAPACKgels", LAPACKgels_(&transpose, &m, &n, &one, J, &m, invJ, &n, work, &worksize, &info));
3482: PetscCheck(info == 0, PETSC_COMM_SELF, PETSC_ERR_LIB, "Bad argument to GELS %" PetscBLASInt_FMT, info);
3484: for (l = 0; l < dimR; l++) guess[l] += PetscRealPart(invJ[l]);
3485: }
3486: PetscFunctionReturn(PETSC_SUCCESS);
3487: }
3489: static PetscErrorCode DMPlexCoordinatesToReference_Tensor(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal realCoords[], PetscReal refCoords[], Vec coords, PetscInt dimC, PetscInt dimR)
3490: {
3491: PetscInt coordSize, i, j, k, l, m, maxIts = 7, numV = (1 << dimR);
3492: PetscScalar *coordsScalar = NULL;
3493: PetscReal *cellData, *cellCoords, *cellCoeffs, *extJ, *resNeg;
3494: PetscScalar *J, *invJ, *work;
3496: PetscFunctionBegin;
3498: PetscCall(DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar));
3499: PetscCheck(coordSize >= dimC * numV, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Expecting at least %" PetscInt_FMT " coordinates, got %" PetscInt_FMT, dimC * (1 << dimR), coordSize);
3500: PetscCall(DMGetWorkArray(dm, 2 * coordSize + dimR + dimC, MPIU_REAL, &cellData));
3501: PetscCall(DMGetWorkArray(dm, 3 * dimR * dimC, MPIU_SCALAR, &J));
3502: cellCoords = &cellData[0];
3503: cellCoeffs = &cellData[coordSize];
3504: extJ = &cellData[2 * coordSize];
3505: resNeg = &cellData[2 * coordSize + dimR];
3506: invJ = &J[dimR * dimC];
3507: work = &J[2 * dimR * dimC];
3508: if (dimR == 2) {
3509: const PetscInt zToPlex[4] = {0, 1, 3, 2};
3511: for (i = 0; i < 4; i++) {
3512: PetscInt plexI = zToPlex[i];
3514: for (j = 0; j < dimC; j++) cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
3515: }
3516: } else if (dimR == 3) {
3517: const PetscInt zToPlex[8] = {0, 3, 1, 2, 4, 5, 7, 6};
3519: for (i = 0; i < 8; i++) {
3520: PetscInt plexI = zToPlex[i];
3522: for (j = 0; j < dimC; j++) cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
3523: }
3524: } else {
3525: for (i = 0; i < coordSize; i++) cellCoords[i] = PetscRealPart(coordsScalar[i]);
3526: }
3527: /* Perform the shuffling transform that converts values at the corners of [-1,1]^d to coefficients */
3528: for (i = 0; i < dimR; i++) {
3529: PetscReal *swap;
3531: for (j = 0; j < (numV / 2); j++) {
3532: for (k = 0; k < dimC; k++) {
3533: cellCoeffs[dimC * j + k] = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] + cellCoords[dimC * 2 * j + k]);
3534: cellCoeffs[dimC * (j + (numV / 2)) + k] = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] - cellCoords[dimC * 2 * j + k]);
3535: }
3536: }
3538: if (i < dimR - 1) {
3539: swap = cellCoeffs;
3540: cellCoeffs = cellCoords;
3541: cellCoords = swap;
3542: }
3543: }
3544: PetscCall(PetscArrayzero(refCoords, numPoints * dimR));
3545: for (j = 0; j < numPoints; j++) {
3546: for (i = 0; i < maxIts; i++) {
3547: PetscReal *guess = &refCoords[dimR * j];
3549: /* compute -residual and Jacobian */
3550: for (k = 0; k < dimC; k++) resNeg[k] = realCoords[dimC * j + k];
3551: for (k = 0; k < dimC * dimR; k++) J[k] = 0.;
3552: for (k = 0; k < numV; k++) {
3553: PetscReal extCoord = 1.;
3554: for (l = 0; l < dimR; l++) {
3555: PetscReal coord = guess[l];
3556: PetscInt dep = (k & (1 << l)) >> l;
3558: extCoord *= dep * coord + !dep;
3559: extJ[l] = dep;
3561: for (m = 0; m < dimR; m++) {
3562: PetscReal coord = guess[m];
3563: PetscInt dep = ((k & (1 << m)) >> m) && (m != l);
3564: PetscReal mult = dep * coord + !dep;
3566: extJ[l] *= mult;
3567: }
3568: }
3569: for (l = 0; l < dimC; l++) {
3570: PetscReal coeff = cellCoeffs[dimC * k + l];
3572: resNeg[l] -= coeff * extCoord;
3573: for (m = 0; m < dimR; m++) J[dimR * l + m] += coeff * extJ[m];
3574: }
3575: }
3576: if (0 && PetscDefined(USE_DEBUG)) {
3577: PetscReal maxAbs = 0.;
3579: for (l = 0; l < dimC; l++) maxAbs = PetscMax(maxAbs, PetscAbsReal(resNeg[l]));
3580: PetscCall(PetscInfo(dm, "cell %" PetscInt_FMT ", point %" PetscInt_FMT ", iter %" PetscInt_FMT ": res %g\n", cell, j, i, (double)maxAbs));
3581: }
3583: PetscCall(DMPlexCoordinatesToReference_NewtonUpdate(dimC, dimR, J, invJ, work, resNeg, guess));
3584: }
3585: }
3586: PetscCall(DMRestoreWorkArray(dm, 3 * dimR * dimC, MPIU_SCALAR, &J));
3587: PetscCall(DMRestoreWorkArray(dm, 2 * coordSize + dimR + dimC, MPIU_REAL, &cellData));
3588: PetscCall(DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar));
3589: PetscFunctionReturn(PETSC_SUCCESS);
3590: }
3592: static PetscErrorCode DMPlexReferenceToCoordinates_Tensor(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal refCoords[], PetscReal realCoords[], Vec coords, PetscInt dimC, PetscInt dimR)
3593: {
3594: PetscInt coordSize, i, j, k, l, numV = (1 << dimR);
3595: PetscScalar *coordsScalar = NULL;
3596: PetscReal *cellData, *cellCoords, *cellCoeffs;
3598: PetscFunctionBegin;
3600: PetscCall(DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar));
3601: PetscCheck(coordSize >= dimC * numV, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Expecting at least %" PetscInt_FMT " coordinates, got %" PetscInt_FMT, dimC * (1 << dimR), coordSize);
3602: PetscCall(DMGetWorkArray(dm, 2 * coordSize, MPIU_REAL, &cellData));
3603: cellCoords = &cellData[0];
3604: cellCoeffs = &cellData[coordSize];
3605: if (dimR == 2) {
3606: const PetscInt zToPlex[4] = {0, 1, 3, 2};
3608: for (i = 0; i < 4; i++) {
3609: PetscInt plexI = zToPlex[i];
3611: for (j = 0; j < dimC; j++) cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
3612: }
3613: } else if (dimR == 3) {
3614: const PetscInt zToPlex[8] = {0, 3, 1, 2, 4, 5, 7, 6};
3616: for (i = 0; i < 8; i++) {
3617: PetscInt plexI = zToPlex[i];
3619: for (j = 0; j < dimC; j++) cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
3620: }
3621: } else {
3622: for (i = 0; i < coordSize; i++) cellCoords[i] = PetscRealPart(coordsScalar[i]);
3623: }
3624: /* Perform the shuffling transform that converts values at the corners of [-1,1]^d to coefficients */
3625: for (i = 0; i < dimR; i++) {
3626: PetscReal *swap;
3628: for (j = 0; j < (numV / 2); j++) {
3629: for (k = 0; k < dimC; k++) {
3630: cellCoeffs[dimC * j + k] = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] + cellCoords[dimC * 2 * j + k]);
3631: cellCoeffs[dimC * (j + (numV / 2)) + k] = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] - cellCoords[dimC * 2 * j + k]);
3632: }
3633: }
3635: if (i < dimR - 1) {
3636: swap = cellCoeffs;
3637: cellCoeffs = cellCoords;
3638: cellCoords = swap;
3639: }
3640: }
3641: PetscCall(PetscArrayzero(realCoords, numPoints * dimC));
3642: for (j = 0; j < numPoints; j++) {
3643: const PetscReal *guess = &refCoords[dimR * j];
3644: PetscReal *mapped = &realCoords[dimC * j];
3646: for (k = 0; k < numV; k++) {
3647: PetscReal extCoord = 1.;
3648: for (l = 0; l < dimR; l++) {
3649: PetscReal coord = guess[l];
3650: PetscInt dep = (k & (1 << l)) >> l;
3652: extCoord *= dep * coord + !dep;
3653: }
3654: for (l = 0; l < dimC; l++) {
3655: PetscReal coeff = cellCoeffs[dimC * k + l];
3657: mapped[l] += coeff * extCoord;
3658: }
3659: }
3660: }
3661: PetscCall(DMRestoreWorkArray(dm, 2 * coordSize, MPIU_REAL, &cellData));
3662: PetscCall(DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar));
3663: PetscFunctionReturn(PETSC_SUCCESS);
3664: }
3666: PetscErrorCode DMPlexCoordinatesToReference_FE(DM dm, PetscFE fe, PetscInt cell, PetscInt numPoints, const PetscReal realCoords[], PetscReal refCoords[], Vec coords, PetscInt Nc, PetscInt dimR, PetscInt maxIter, PetscReal *tol)
3667: {
3668: PetscInt numComp, pdim, i, j, k, l, m, coordSize;
3669: PetscScalar *nodes = NULL;
3670: PetscReal *invV, *modes;
3671: PetscReal *B, *D, *resNeg;
3672: PetscScalar *J, *invJ, *work;
3673: PetscReal tolerance = tol == NULL ? 0.0 : *tol;
3675: PetscFunctionBegin;
3676: PetscCall(PetscFEGetDimension(fe, &pdim));
3677: PetscCall(PetscFEGetNumComponents(fe, &numComp));
3678: PetscCheck(numComp == Nc, PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "coordinate discretization must have as many components (%" PetscInt_FMT ") as embedding dimension (!= %" PetscInt_FMT ")", numComp, Nc);
3679: /* we shouldn't apply inverse closure permutation, if one exists */
3680: PetscCall(DMPlexVecGetOrientedClosure_Internal(dm, NULL, PETSC_FALSE, coords, cell, 0, &coordSize, &nodes));
3681: /* convert nodes to values in the stable evaluation basis */
3682: PetscCall(DMGetWorkArray(dm, pdim, MPIU_REAL, &modes));
3683: invV = fe->invV;
3684: for (i = 0; i < pdim; ++i) {
3685: modes[i] = 0.;
3686: for (j = 0; j < pdim; ++j) modes[i] += invV[i * pdim + j] * PetscRealPart(nodes[j]);
3687: }
3688: PetscCall(DMGetWorkArray(dm, pdim * Nc + pdim * Nc * dimR + Nc, MPIU_REAL, &B));
3689: D = &B[pdim * Nc];
3690: resNeg = &D[pdim * Nc * dimR];
3691: PetscCall(DMGetWorkArray(dm, 3 * Nc * dimR, MPIU_SCALAR, &J));
3692: invJ = &J[Nc * dimR];
3693: work = &invJ[Nc * dimR];
3694: for (i = 0; i < numPoints * dimR; i++) refCoords[i] = 0.;
3695: for (j = 0; j < numPoints; j++) {
3696: PetscReal normPoint = DMPlex_NormD_Internal(Nc, &realCoords[j * Nc]);
3697: normPoint = normPoint > PETSC_SMALL ? normPoint : 1.0;
3698: for (i = 0; i < maxIter; i++) { /* we could batch this so that we're not making big B and D arrays all the time */
3699: PetscReal *guess = &refCoords[j * dimR], error = 0;
3700: PetscCall(PetscSpaceEvaluate(fe->basisSpace, 1, guess, B, D, NULL));
3701: for (k = 0; k < Nc; k++) resNeg[k] = realCoords[j * Nc + k];
3702: for (k = 0; k < Nc * dimR; k++) J[k] = 0.;
3703: for (k = 0; k < pdim; k++) {
3704: for (l = 0; l < Nc; l++) {
3705: resNeg[l] -= modes[k] * B[k * Nc + l];
3706: for (m = 0; m < dimR; m++) J[l * dimR + m] += modes[k] * D[(k * Nc + l) * dimR + m];
3707: }
3708: }
3709: if (0 && PetscDefined(USE_DEBUG)) {
3710: PetscReal maxAbs = 0.;
3712: for (l = 0; l < Nc; l++) maxAbs = PetscMax(maxAbs, PetscAbsReal(resNeg[l]));
3713: PetscCall(PetscInfo(dm, "cell %" PetscInt_FMT ", point %" PetscInt_FMT ", iter %" PetscInt_FMT ": res %g\n", cell, j, i, (double)maxAbs));
3714: }
3715: error = DMPlex_NormD_Internal(Nc, resNeg);
3716: if (error < tolerance * normPoint) {
3717: if (tol) *tol = error / normPoint;
3718: break;
3719: }
3720: PetscCall(DMPlexCoordinatesToReference_NewtonUpdate(Nc, dimR, J, invJ, work, resNeg, guess));
3721: }
3722: }
3723: PetscCall(DMRestoreWorkArray(dm, 3 * Nc * dimR, MPIU_SCALAR, &J));
3724: PetscCall(DMRestoreWorkArray(dm, pdim * Nc + pdim * Nc * dimR + Nc, MPIU_REAL, &B));
3725: PetscCall(DMRestoreWorkArray(dm, pdim, MPIU_REAL, &modes));
3726: PetscCall(DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &nodes));
3727: PetscFunctionReturn(PETSC_SUCCESS);
3728: }
3730: /* TODO: TOBY please fix this for Nc > 1 */
3731: PetscErrorCode DMPlexReferenceToCoordinates_FE(DM dm, PetscFE fe, PetscInt cell, PetscInt numPoints, const PetscReal refCoords[], PetscReal realCoords[], Vec coords, PetscInt Nc, PetscInt dimR)
3732: {
3733: PetscInt numComp, pdim, i, j, k, l, coordSize;
3734: PetscScalar *nodes = NULL;
3735: PetscReal *invV, *modes;
3736: PetscReal *B;
3738: PetscFunctionBegin;
3739: PetscCall(PetscFEGetDimension(fe, &pdim));
3740: PetscCall(PetscFEGetNumComponents(fe, &numComp));
3741: PetscCheck(numComp == Nc, PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "coordinate discretization must have as many components (%" PetscInt_FMT ") as embedding dimension (!= %" PetscInt_FMT ")", numComp, Nc);
3742: /* we shouldn't apply inverse closure permutation, if one exists */
3743: PetscCall(DMPlexVecGetOrientedClosure_Internal(dm, NULL, PETSC_FALSE, coords, cell, 0, &coordSize, &nodes));
3744: /* convert nodes to values in the stable evaluation basis */
3745: PetscCall(DMGetWorkArray(dm, pdim, MPIU_REAL, &modes));
3746: invV = fe->invV;
3747: for (i = 0; i < pdim; ++i) {
3748: modes[i] = 0.;
3749: for (j = 0; j < pdim; ++j) modes[i] += invV[i * pdim + j] * PetscRealPart(nodes[j]);
3750: }
3751: PetscCall(DMGetWorkArray(dm, numPoints * pdim * Nc, MPIU_REAL, &B));
3752: PetscCall(PetscSpaceEvaluate(fe->basisSpace, numPoints, refCoords, B, NULL, NULL));
3753: for (i = 0; i < numPoints * Nc; i++) realCoords[i] = 0.;
3754: for (j = 0; j < numPoints; j++) {
3755: PetscReal *mapped = &realCoords[j * Nc];
3757: for (k = 0; k < pdim; k++) {
3758: for (l = 0; l < Nc; l++) mapped[l] += modes[k] * B[(j * pdim + k) * Nc + l];
3759: }
3760: }
3761: PetscCall(DMRestoreWorkArray(dm, numPoints * pdim * Nc, MPIU_REAL, &B));
3762: PetscCall(DMRestoreWorkArray(dm, pdim, MPIU_REAL, &modes));
3763: PetscCall(DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &nodes));
3764: PetscFunctionReturn(PETSC_SUCCESS);
3765: }
3767: /*@
3768: DMPlexCoordinatesToReference - Pull coordinates back from the mesh to the reference element
3769: using a single element map.
3771: Not Collective
3773: Input Parameters:
3774: + dm - The mesh, with coordinate maps defined either by a `PetscDS` for the coordinate `DM` (see `DMGetCoordinateDM()`) or
3775: implicitly by the coordinates of the corner vertices of the cell: as an affine map for simplicial elements, or
3776: as a multilinear map for tensor-product elements
3777: . cell - the cell whose map is used.
3778: . numPoints - the number of points to locate
3779: - realCoords - (numPoints x coordinate dimension) array of coordinates (see `DMGetCoordinateDim()`)
3781: Output Parameter:
3782: . refCoords - (`numPoints` x `dimension`) array of reference coordinates (see `DMGetDimension()`)
3784: Level: intermediate
3786: Notes:
3787: This inversion will be accurate inside the reference element, but may be inaccurate for
3788: mappings that do not extend uniquely outside the reference cell (e.g, most non-affine maps)
3790: .seealso: `DMPLEX`, `DMPlexReferenceToCoordinates()`
3791: @*/
3792: PetscErrorCode DMPlexCoordinatesToReference(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal realCoords[], PetscReal refCoords[])
3793: {
3794: PetscInt dimC, dimR, depth, cStart, cEnd, i;
3795: DM coordDM = NULL;
3796: Vec coords;
3797: PetscFE fe = NULL;
3799: PetscFunctionBegin;
3801: PetscCall(DMGetDimension(dm, &dimR));
3802: PetscCall(DMGetCoordinateDim(dm, &dimC));
3803: if (dimR <= 0 || dimC <= 0 || numPoints <= 0) PetscFunctionReturn(PETSC_SUCCESS);
3804: PetscCall(DMPlexGetDepth(dm, &depth));
3805: PetscCall(DMGetCoordinatesLocal(dm, &coords));
3806: PetscCall(DMGetCoordinateDM(dm, &coordDM));
3807: if (coordDM) {
3808: PetscInt coordFields;
3810: PetscCall(DMGetNumFields(coordDM, &coordFields));
3811: if (coordFields) {
3812: PetscClassId id;
3813: PetscObject disc;
3815: PetscCall(DMGetField(coordDM, 0, NULL, &disc));
3816: PetscCall(PetscObjectGetClassId(disc, &id));
3817: if (id == PETSCFE_CLASSID) fe = (PetscFE)disc;
3818: }
3819: }
3820: PetscCall(DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd));
3821: PetscCheck(cell >= cStart && cell < cEnd, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "point %" PetscInt_FMT " not in cell range [%" PetscInt_FMT ",%" PetscInt_FMT ")", cell, cStart, cEnd);
3822: if (!fe) { /* implicit discretization: affine or multilinear */
3823: PetscInt coneSize;
3824: PetscBool isSimplex, isTensor;
3826: PetscCall(DMPlexGetConeSize(dm, cell, &coneSize));
3827: isSimplex = (coneSize == (dimR + 1)) ? PETSC_TRUE : PETSC_FALSE;
3828: isTensor = (coneSize == ((depth == 1) ? (1 << dimR) : (2 * dimR))) ? PETSC_TRUE : PETSC_FALSE;
3829: if (isSimplex) {
3830: PetscReal detJ, *v0, *J, *invJ;
3832: PetscCall(DMGetWorkArray(dm, dimC + 2 * dimC * dimC, MPIU_REAL, &v0));
3833: J = &v0[dimC];
3834: invJ = &J[dimC * dimC];
3835: PetscCall(DMPlexComputeCellGeometryAffineFEM(dm, cell, v0, J, invJ, &detJ));
3836: for (i = 0; i < numPoints; i++) { /* Apply the inverse affine transformation for each point */
3837: const PetscReal x0[3] = {-1., -1., -1.};
3839: CoordinatesRealToRef(dimC, dimR, x0, v0, invJ, &realCoords[dimC * i], &refCoords[dimR * i]);
3840: }
3841: PetscCall(DMRestoreWorkArray(dm, dimC + 2 * dimC * dimC, MPIU_REAL, &v0));
3842: } else if (isTensor) {
3843: PetscCall(DMPlexCoordinatesToReference_Tensor(coordDM, cell, numPoints, realCoords, refCoords, coords, dimC, dimR));
3844: } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Unrecognized cone size %" PetscInt_FMT, coneSize);
3845: } else {
3846: PetscCall(DMPlexCoordinatesToReference_FE(coordDM, fe, cell, numPoints, realCoords, refCoords, coords, dimC, dimR, 7, NULL));
3847: }
3848: PetscFunctionReturn(PETSC_SUCCESS);
3849: }
3851: /*@
3852: DMPlexReferenceToCoordinates - Map references coordinates to coordinates in the mesh for a single element map.
3854: Not Collective
3856: Input Parameters:
3857: + dm - The mesh, with coordinate maps defined either by a PetscDS for the coordinate `DM` (see `DMGetCoordinateDM()`) or
3858: implicitly by the coordinates of the corner vertices of the cell: as an affine map for simplicial elements, or
3859: as a multilinear map for tensor-product elements
3860: . cell - the cell whose map is used.
3861: . numPoints - the number of points to locate
3862: - refCoords - (numPoints x dimension) array of reference coordinates (see `DMGetDimension()`)
3864: Output Parameter:
3865: . realCoords - (numPoints x coordinate dimension) array of coordinates (see `DMGetCoordinateDim()`)
3867: Level: intermediate
3869: .seealso: `DMPLEX`, `DMPlexCoordinatesToReference()`
3870: @*/
3871: PetscErrorCode DMPlexReferenceToCoordinates(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal refCoords[], PetscReal realCoords[])
3872: {
3873: PetscInt dimC, dimR, depth, cStart, cEnd, i;
3874: DM coordDM = NULL;
3875: Vec coords;
3876: PetscFE fe = NULL;
3878: PetscFunctionBegin;
3880: PetscCall(DMGetDimension(dm, &dimR));
3881: PetscCall(DMGetCoordinateDim(dm, &dimC));
3882: if (dimR <= 0 || dimC <= 0 || numPoints <= 0) PetscFunctionReturn(PETSC_SUCCESS);
3883: PetscCall(DMPlexGetDepth(dm, &depth));
3884: PetscCall(DMGetCoordinatesLocal(dm, &coords));
3885: PetscCall(DMGetCoordinateDM(dm, &coordDM));
3886: if (coordDM) {
3887: PetscInt coordFields;
3889: PetscCall(DMGetNumFields(coordDM, &coordFields));
3890: if (coordFields) {
3891: PetscClassId id;
3892: PetscObject disc;
3894: PetscCall(DMGetField(coordDM, 0, NULL, &disc));
3895: PetscCall(PetscObjectGetClassId(disc, &id));
3896: if (id == PETSCFE_CLASSID) fe = (PetscFE)disc;
3897: }
3898: }
3899: PetscCall(DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd));
3900: PetscCheck(cell >= cStart && cell < cEnd, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "point %" PetscInt_FMT " not in cell range [%" PetscInt_FMT ",%" PetscInt_FMT ")", cell, cStart, cEnd);
3901: if (!fe) { /* implicit discretization: affine or multilinear */
3902: PetscInt coneSize;
3903: PetscBool isSimplex, isTensor;
3905: PetscCall(DMPlexGetConeSize(dm, cell, &coneSize));
3906: isSimplex = (coneSize == (dimR + 1)) ? PETSC_TRUE : PETSC_FALSE;
3907: isTensor = (coneSize == ((depth == 1) ? (1 << dimR) : (2 * dimR))) ? PETSC_TRUE : PETSC_FALSE;
3908: if (isSimplex) {
3909: PetscReal detJ, *v0, *J;
3911: PetscCall(DMGetWorkArray(dm, dimC + 2 * dimC * dimC, MPIU_REAL, &v0));
3912: J = &v0[dimC];
3913: PetscCall(DMPlexComputeCellGeometryAffineFEM(dm, cell, v0, J, NULL, &detJ));
3914: for (i = 0; i < numPoints; i++) { /* Apply the affine transformation for each point */
3915: const PetscReal xi0[3] = {-1., -1., -1.};
3917: CoordinatesRefToReal(dimC, dimR, xi0, v0, J, &refCoords[dimR * i], &realCoords[dimC * i]);
3918: }
3919: PetscCall(DMRestoreWorkArray(dm, dimC + 2 * dimC * dimC, MPIU_REAL, &v0));
3920: } else if (isTensor) {
3921: PetscCall(DMPlexReferenceToCoordinates_Tensor(coordDM, cell, numPoints, refCoords, realCoords, coords, dimC, dimR));
3922: } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Unrecognized cone size %" PetscInt_FMT, coneSize);
3923: } else {
3924: PetscCall(DMPlexReferenceToCoordinates_FE(coordDM, fe, cell, numPoints, refCoords, realCoords, coords, dimC, dimR));
3925: }
3926: PetscFunctionReturn(PETSC_SUCCESS);
3927: }
3929: void coordMap_identity(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
3930: {
3931: const PetscInt Nc = uOff[1] - uOff[0];
3932: PetscInt c;
3934: for (c = 0; c < Nc; ++c) f0[c] = u[c];
3935: }
3937: /* Shear applies the transformation, assuming we fix z,
3938: / 1 0 m_0 \
3939: | 0 1 m_1 |
3940: \ 0 0 1 /
3941: */
3942: void coordMap_shear(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar coords[])
3943: {
3944: const PetscInt Nc = uOff[1] - uOff[0];
3945: const PetscInt ax = (PetscInt)PetscRealPart(constants[0]);
3946: PetscInt c;
3948: for (c = 0; c < Nc; ++c) coords[c] = u[c] + constants[c + 1] * u[ax];
3949: }
3951: /* Flare applies the transformation, assuming we fix x_f,
3953: x_i = x_i * alpha_i x_f
3954: */
3955: void coordMap_flare(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar coords[])
3956: {
3957: const PetscInt Nc = uOff[1] - uOff[0];
3958: const PetscInt cf = (PetscInt)PetscRealPart(constants[0]);
3959: PetscInt c;
3961: for (c = 0; c < Nc; ++c) coords[c] = u[c] * (c == cf ? 1.0 : constants[c + 1] * u[cf]);
3962: }
3964: /*
3965: We would like to map the unit square to a quarter of the annulus between circles of radius 1 and 2. We start by mapping the straight sections, which
3966: will correspond to the top and bottom of our square. So
3968: (0,0)--(1,0) ==> (1,0)--(2,0) Just a shift of (1,0)
3969: (0,1)--(1,1) ==> (0,1)--(0,2) Switch x and y
3971: So it looks like we want to map each layer in y to a ray, so x is the radius and y is the angle:
3973: (x, y) ==> (x+1, \pi/2 y) in (r', \theta') space
3974: ==> ((x+1) cos(\pi/2 y), (x+1) sin(\pi/2 y)) in (x', y') space
3975: */
3976: void coordMap_annulus(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar xp[])
3977: {
3978: const PetscReal ri = PetscRealPart(constants[0]);
3979: const PetscReal ro = PetscRealPart(constants[1]);
3981: xp[0] = (x[0] * (ro - ri) + ri) * PetscCosReal(0.5 * PETSC_PI * x[1]);
3982: xp[1] = (x[0] * (ro - ri) + ri) * PetscSinReal(0.5 * PETSC_PI * x[1]);
3983: }
3985: /*
3986: We would like to map the unit cube to a hemisphere of the spherical shell between balls of radius 1 and 2. We want to map the bottom surface onto the
3987: lower hemisphere and the upper surface onto the top, letting z be the radius.
3989: (x, y) ==> ((z+3)/2, \pi/2 (|x| or |y|), arctan y/x) in (r', \theta', \phi') space
3990: ==> ((z+3)/2 \cos(\theta') cos(\phi'), (z+3)/2 \cos(\theta') sin(\phi'), (z+3)/2 sin(\theta')) in (x', y', z') space
3991: */
3992: void coordMap_shell(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar xp[])
3993: {
3994: const PetscReal pi4 = PETSC_PI / 4.0;
3995: const PetscReal ri = PetscRealPart(constants[0]);
3996: const PetscReal ro = PetscRealPart(constants[1]);
3997: const PetscReal rp = (x[2] + 1) * 0.5 * (ro - ri) + ri;
3998: const PetscReal phip = PetscAtan2Real(x[1], x[0]);
3999: const PetscReal thetap = 0.5 * PETSC_PI * (1.0 - ((((phip <= pi4) && (phip >= -pi4)) || ((phip >= 3.0 * pi4) || (phip <= -3.0 * pi4))) ? PetscAbsReal(x[0]) : PetscAbsReal(x[1])));
4001: xp[0] = rp * PetscCosReal(thetap) * PetscCosReal(phip);
4002: xp[1] = rp * PetscCosReal(thetap) * PetscSinReal(phip);
4003: xp[2] = rp * PetscSinReal(thetap);
4004: }
4006: /*@C
4007: DMPlexRemapGeometry - This function maps the original `DM` coordinates to new coordinates.
4009: Not Collective
4011: Input Parameters:
4012: + dm - The `DM`
4013: . time - The time
4014: - func - The function transforming current coordinates to new coordinates
4016: Calling sequence of `func`:
4017: + dim - The spatial dimension
4018: . Nf - The number of input fields (here 1)
4019: . NfAux - The number of input auxiliary fields
4020: . uOff - The offset of the coordinates in u[] (here 0)
4021: . uOff_x - The offset of the coordinates in u_x[] (here 0)
4022: . u - The coordinate values at this point in space
4023: . u_t - The coordinate time derivative at this point in space (here `NULL`)
4024: . u_x - The coordinate derivatives at this point in space
4025: . aOff - The offset of each auxiliary field in u[]
4026: . aOff_x - The offset of each auxiliary field in u_x[]
4027: . a - The auxiliary field values at this point in space
4028: . a_t - The auxiliary field time derivative at this point in space (or `NULL`)
4029: . a_x - The auxiliary field derivatives at this point in space
4030: . t - The current time
4031: . x - The coordinates of this point (here not used)
4032: . numConstants - The number of constants
4033: . constants - The value of each constant
4034: - f - The new coordinates at this point in space
4036: Level: intermediate
4038: .seealso: `DMPLEX`, `DMGetCoordinates()`, `DMGetCoordinatesLocal()`, `DMGetCoordinateDM()`, `DMProjectFieldLocal()`, `DMProjectFieldLabelLocal()`
4039: @*/
4040: PetscErrorCode DMPlexRemapGeometry(DM dm, PetscReal time, void (*func)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f[]))
4041: {
4042: DM cdm;
4043: PetscDS cds;
4044: DMField cf;
4045: PetscObject obj;
4046: PetscClassId id;
4047: Vec lCoords, tmpCoords;
4049: PetscFunctionBegin;
4050: PetscCall(DMGetCoordinateDM(dm, &cdm));
4051: PetscCall(DMGetCoordinatesLocal(dm, &lCoords));
4052: PetscCall(DMGetDS(cdm, &cds));
4053: PetscCall(PetscDSGetDiscretization(cds, 0, &obj));
4054: PetscCall(PetscObjectGetClassId(obj, &id));
4055: if (id != PETSCFE_CLASSID) {
4056: PetscSection cSection;
4057: const PetscScalar *constants;
4058: PetscScalar *coords, f[16];
4059: PetscInt dim, cdim, Nc, vStart, vEnd;
4061: PetscCall(DMGetDimension(dm, &dim));
4062: PetscCall(DMGetCoordinateDim(dm, &cdim));
4063: PetscCheck(cdim <= 16, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Affine version of DMPlexRemapGeometry is currently limited to dimensions <= 16, not %" PetscInt_FMT, cdim);
4064: PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
4065: PetscCall(DMGetCoordinateSection(dm, &cSection));
4066: PetscCall(PetscDSGetConstants(cds, &Nc, &constants));
4067: PetscCall(VecGetArrayWrite(lCoords, &coords));
4068: for (PetscInt v = vStart; v < vEnd; ++v) {
4069: PetscInt uOff[2] = {0, cdim};
4070: PetscInt off, c;
4072: PetscCall(PetscSectionGetOffset(cSection, v, &off));
4073: (*func)(dim, 1, 0, uOff, NULL, &coords[off], NULL, NULL, NULL, NULL, NULL, NULL, NULL, 0.0, NULL, Nc, constants, f);
4074: for (c = 0; c < cdim; ++c) coords[off + c] = f[c];
4075: }
4076: PetscCall(VecRestoreArrayWrite(lCoords, &coords));
4077: } else {
4078: PetscCall(DMGetLocalVector(cdm, &tmpCoords));
4079: PetscCall(VecCopy(lCoords, tmpCoords));
4080: /* We have to do the coordinate field manually right now since the coordinate DM will not have its own */
4081: PetscCall(DMGetCoordinateField(dm, &cf));
4082: cdm->coordinates[0].field = cf;
4083: PetscCall(DMProjectFieldLocal(cdm, time, tmpCoords, &func, INSERT_VALUES, lCoords));
4084: cdm->coordinates[0].field = NULL;
4085: PetscCall(DMRestoreLocalVector(cdm, &tmpCoords));
4086: PetscCall(DMSetCoordinatesLocal(dm, lCoords));
4087: }
4088: PetscFunctionReturn(PETSC_SUCCESS);
4089: }
4091: /*@
4092: DMPlexShearGeometry - This shears the domain, meaning adds a multiple of the shear coordinate to all other coordinates.
4094: Not Collective
4096: Input Parameters:
4097: + dm - The `DMPLEX`
4098: . direction - The shear coordinate direction, e.g. `DM_X` is the x-axis
4099: - multipliers - The multiplier m for each direction which is not the shear direction
4101: Level: intermediate
4103: .seealso: `DMPLEX`, `DMPlexRemapGeometry()`, `DMDirection`, `DM_X`, `DM_Y`, `DM_Z`
4104: @*/
4105: PetscErrorCode DMPlexShearGeometry(DM dm, DMDirection direction, PetscReal multipliers[])
4106: {
4107: DM cdm;
4108: PetscDS cds;
4109: PetscScalar *moduli;
4110: const PetscInt dir = (PetscInt)direction;
4111: PetscInt dE, d, e;
4113: PetscFunctionBegin;
4114: PetscCall(DMGetCoordinateDM(dm, &cdm));
4115: PetscCall(DMGetCoordinateDim(dm, &dE));
4116: PetscCall(PetscMalloc1(dE + 1, &moduli));
4117: moduli[0] = dir;
4118: for (d = 0, e = 0; d < dE; ++d) moduli[d + 1] = d == dir ? 0.0 : (multipliers ? multipliers[e++] : 1.0);
4119: PetscCall(DMGetDS(cdm, &cds));
4120: PetscCall(PetscDSSetConstants(cds, dE + 1, moduli));
4121: PetscCall(DMPlexRemapGeometry(dm, 0.0, coordMap_shear));
4122: PetscCall(PetscFree(moduli));
4123: PetscFunctionReturn(PETSC_SUCCESS);
4124: }