Actual source code: plexgeometry.c
1: #include <petsc/private/dmpleximpl.h>
2: #include <petsc/private/petscfeimpl.h>
3: #include <petscblaslapack.h>
4: #include <petsctime.h>
6: const char *const DMPlexCoordMaps[] = {"none", "shear", "flare", "annulus", "shell", "sinusoid", "unknown", "DMPlexCoordMap", "DM_COORD_MAP_", NULL};
8: /*@
9: DMPlexFindVertices - Try to find DAG points based on their coordinates.
11: Not Collective (provided `DMGetCoordinatesLocalSetUp()` has been already called)
13: Input Parameters:
14: + dm - The `DMPLEX` object
15: . coordinates - The `Vec` of coordinates of the sought points
16: - eps - The tolerance or `PETSC_DEFAULT`
18: Output Parameter:
19: . points - The `IS` of found DAG points or -1
21: Level: intermediate
23: Notes:
24: The length of `Vec` coordinates must be npoints * dim where dim is the spatial dimension returned by `DMGetCoordinateDim()` and npoints is the number of sought points.
26: The output `IS` is living on `PETSC_COMM_SELF` and its length is npoints.
27: Each rank does the search independently.
28: If this rank's local `DMPLEX` portion contains the DAG point corresponding to the i-th tuple of coordinates, the i-th entry of the output `IS` is set to that DAG point, otherwise to -1.
30: The output `IS` must be destroyed by user.
32: The tolerance is interpreted as the maximum Euclidean (L2) distance of the sought point from the specified coordinates.
34: Complexity of this function is currently O(mn) with m number of vertices to find and n number of vertices in the local mesh. This could probably be improved if needed.
36: .seealso: `DMPLEX`, `DMPlexCreate()`, `DMGetCoordinatesLocal()`
37: @*/
38: PetscErrorCode DMPlexFindVertices(DM dm, Vec coordinates, PetscReal eps, IS *points)
39: {
40: PetscInt c, cdim, i, j, o, p, vStart, vEnd;
41: PetscInt npoints;
42: const PetscScalar *coord;
43: Vec allCoordsVec;
44: const PetscScalar *allCoords;
45: PetscInt *dagPoints;
47: PetscFunctionBegin;
48: if (eps < 0) eps = PETSC_SQRT_MACHINE_EPSILON;
49: PetscCall(DMGetCoordinateDim(dm, &cdim));
50: {
51: PetscInt n;
53: PetscCall(VecGetLocalSize(coordinates, &n));
54: PetscCheck(n % cdim == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Given coordinates Vec has local length %" PetscInt_FMT " not divisible by coordinate dimension %" PetscInt_FMT " of given DM", n, cdim);
55: npoints = n / cdim;
56: }
57: PetscCall(DMGetCoordinatesLocal(dm, &allCoordsVec));
58: PetscCall(VecGetArrayRead(allCoordsVec, &allCoords));
59: PetscCall(VecGetArrayRead(coordinates, &coord));
60: PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
61: if (PetscDefined(USE_DEBUG)) {
62: /* check coordinate section is consistent with DM dimension */
63: PetscSection cs;
64: PetscInt ndof;
66: PetscCall(DMGetCoordinateSection(dm, &cs));
67: for (p = vStart; p < vEnd; p++) {
68: PetscCall(PetscSectionGetDof(cs, p, &ndof));
69: PetscCheck(ndof == cdim, PETSC_COMM_SELF, PETSC_ERR_PLIB, "point %" PetscInt_FMT ": ndof = %" PetscInt_FMT " != %" PetscInt_FMT " = cdim", p, ndof, cdim);
70: }
71: }
72: PetscCall(PetscMalloc1(npoints, &dagPoints));
73: if (eps == 0.0) {
74: for (i = 0, j = 0; i < npoints; i++, j += cdim) {
75: dagPoints[i] = -1;
76: for (p = vStart, o = 0; p < vEnd; p++, o += cdim) {
77: for (c = 0; c < cdim; c++) {
78: if (coord[j + c] != allCoords[o + c]) break;
79: }
80: if (c == cdim) {
81: dagPoints[i] = p;
82: break;
83: }
84: }
85: }
86: } else {
87: for (i = 0, j = 0; i < npoints; i++, j += cdim) {
88: PetscReal norm;
90: dagPoints[i] = -1;
91: for (p = vStart, o = 0; p < vEnd; p++, o += cdim) {
92: norm = 0.0;
93: for (c = 0; c < cdim; c++) norm += PetscRealPart(PetscSqr(coord[j + c] - allCoords[o + c]));
94: norm = PetscSqrtReal(norm);
95: if (norm <= eps) {
96: dagPoints[i] = p;
97: break;
98: }
99: }
100: }
101: }
102: PetscCall(VecRestoreArrayRead(allCoordsVec, &allCoords));
103: PetscCall(VecRestoreArrayRead(coordinates, &coord));
104: PetscCall(ISCreateGeneral(PETSC_COMM_SELF, npoints, dagPoints, PETSC_OWN_POINTER, points));
105: PetscFunctionReturn(PETSC_SUCCESS);
106: }
108: #if 0
109: static PetscErrorCode DMPlexGetLineIntersection_2D_Internal(const PetscReal segmentA[], const PetscReal segmentB[], PetscReal intersection[], PetscBool *hasIntersection)
110: {
111: const PetscReal p0_x = segmentA[0 * 2 + 0];
112: const PetscReal p0_y = segmentA[0 * 2 + 1];
113: const PetscReal p1_x = segmentA[1 * 2 + 0];
114: const PetscReal p1_y = segmentA[1 * 2 + 1];
115: const PetscReal p2_x = segmentB[0 * 2 + 0];
116: const PetscReal p2_y = segmentB[0 * 2 + 1];
117: const PetscReal p3_x = segmentB[1 * 2 + 0];
118: const PetscReal p3_y = segmentB[1 * 2 + 1];
119: const PetscReal s1_x = p1_x - p0_x;
120: const PetscReal s1_y = p1_y - p0_y;
121: const PetscReal s2_x = p3_x - p2_x;
122: const PetscReal s2_y = p3_y - p2_y;
123: const PetscReal denom = (-s2_x * s1_y + s1_x * s2_y);
125: PetscFunctionBegin;
126: *hasIntersection = PETSC_FALSE;
127: /* Non-parallel lines */
128: if (denom != 0.0) {
129: const PetscReal s = (-s1_y * (p0_x - p2_x) + s1_x * (p0_y - p2_y)) / denom;
130: const PetscReal t = (s2_x * (p0_y - p2_y) - s2_y * (p0_x - p2_x)) / denom;
132: if (s >= 0 && s <= 1 && t >= 0 && t <= 1) {
133: *hasIntersection = PETSC_TRUE;
134: if (intersection) {
135: intersection[0] = p0_x + (t * s1_x);
136: intersection[1] = p0_y + (t * s1_y);
137: }
138: }
139: }
140: PetscFunctionReturn(PETSC_SUCCESS);
141: }
143: /* The plane is segmentB x segmentC: https://en.wikipedia.org/wiki/Line%E2%80%93plane_intersection */
144: static PetscErrorCode DMPlexGetLinePlaneIntersection_3D_Internal(const PetscReal segmentA[], const PetscReal segmentB[], const PetscReal segmentC[], PetscReal intersection[], PetscBool *hasIntersection)
145: {
146: const PetscReal p0_x = segmentA[0 * 3 + 0];
147: const PetscReal p0_y = segmentA[0 * 3 + 1];
148: const PetscReal p0_z = segmentA[0 * 3 + 2];
149: const PetscReal p1_x = segmentA[1 * 3 + 0];
150: const PetscReal p1_y = segmentA[1 * 3 + 1];
151: const PetscReal p1_z = segmentA[1 * 3 + 2];
152: const PetscReal q0_x = segmentB[0 * 3 + 0];
153: const PetscReal q0_y = segmentB[0 * 3 + 1];
154: const PetscReal q0_z = segmentB[0 * 3 + 2];
155: const PetscReal q1_x = segmentB[1 * 3 + 0];
156: const PetscReal q1_y = segmentB[1 * 3 + 1];
157: const PetscReal q1_z = segmentB[1 * 3 + 2];
158: const PetscReal r0_x = segmentC[0 * 3 + 0];
159: const PetscReal r0_y = segmentC[0 * 3 + 1];
160: const PetscReal r0_z = segmentC[0 * 3 + 2];
161: const PetscReal r1_x = segmentC[1 * 3 + 0];
162: const PetscReal r1_y = segmentC[1 * 3 + 1];
163: const PetscReal r1_z = segmentC[1 * 3 + 2];
164: const PetscReal s0_x = p1_x - p0_x;
165: const PetscReal s0_y = p1_y - p0_y;
166: const PetscReal s0_z = p1_z - p0_z;
167: const PetscReal s1_x = q1_x - q0_x;
168: const PetscReal s1_y = q1_y - q0_y;
169: const PetscReal s1_z = q1_z - q0_z;
170: const PetscReal s2_x = r1_x - r0_x;
171: const PetscReal s2_y = r1_y - r0_y;
172: const PetscReal s2_z = r1_z - r0_z;
173: const PetscReal s3_x = s1_y * s2_z - s1_z * s2_y; /* s1 x s2 */
174: const PetscReal s3_y = s1_z * s2_x - s1_x * s2_z;
175: const PetscReal s3_z = s1_x * s2_y - s1_y * s2_x;
176: const PetscReal s4_x = s0_y * s2_z - s0_z * s2_y; /* s0 x s2 */
177: const PetscReal s4_y = s0_z * s2_x - s0_x * s2_z;
178: const PetscReal s4_z = s0_x * s2_y - s0_y * s2_x;
179: const PetscReal s5_x = s1_y * s0_z - s1_z * s0_y; /* s1 x s0 */
180: const PetscReal s5_y = s1_z * s0_x - s1_x * s0_z;
181: const PetscReal s5_z = s1_x * s0_y - s1_y * s0_x;
182: const PetscReal denom = -(s0_x * s3_x + s0_y * s3_y + s0_z * s3_z); /* -s0 . (s1 x s2) */
184: PetscFunctionBegin;
185: *hasIntersection = PETSC_FALSE;
186: /* Line not parallel to plane */
187: if (denom != 0.0) {
188: const PetscReal t = (s3_x * (p0_x - q0_x) + s3_y * (p0_y - q0_y) + s3_z * (p0_z - q0_z)) / denom;
189: const PetscReal u = (s4_x * (p0_x - q0_x) + s4_y * (p0_y - q0_y) + s4_z * (p0_z - q0_z)) / denom;
190: const PetscReal v = (s5_x * (p0_x - q0_x) + s5_y * (p0_y - q0_y) + s5_z * (p0_z - q0_z)) / denom;
192: if (t >= 0 && t <= 1 && u >= 0 && u <= 1 && v >= 0 && v <= 1) {
193: *hasIntersection = PETSC_TRUE;
194: if (intersection) {
195: intersection[0] = p0_x + (t * s0_x);
196: intersection[1] = p0_y + (t * s0_y);
197: intersection[2] = p0_z + (t * s0_z);
198: }
199: }
200: }
201: PetscFunctionReturn(PETSC_SUCCESS);
202: }
203: #endif
205: static PetscErrorCode DMPlexGetPlaneSimplexIntersection_Coords_Internal(DM dm, PetscInt dim, PetscInt cdim, const PetscScalar coords[], const PetscReal p[], const PetscReal normal[], PetscBool *pos, PetscInt *Nint, PetscReal intPoints[])
206: {
207: PetscReal d[4]; // distance of vertices to the plane
208: PetscReal dp; // distance from origin to the plane
209: PetscInt n = 0;
211: PetscFunctionBegin;
212: if (pos) *pos = PETSC_FALSE;
213: if (Nint) *Nint = 0;
214: if (PetscDefined(USE_DEBUG)) {
215: PetscReal mag = DMPlex_NormD_Internal(cdim, normal);
216: PetscCheck(PetscAbsReal(mag - (PetscReal)1.0) < PETSC_SMALL, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Normal vector is not normalized: %g", (double)mag);
217: }
219: dp = DMPlex_DotRealD_Internal(cdim, normal, p);
220: for (PetscInt v = 0; v < dim + 1; ++v) {
221: // d[v] is positive, zero, or negative if vertex i is above, on, or below the plane
222: #if defined(PETSC_USE_COMPLEX)
223: PetscReal c[4];
224: for (PetscInt i = 0; i < cdim; ++i) c[i] = PetscRealPart(coords[v * cdim + i]);
225: d[v] = DMPlex_DotRealD_Internal(cdim, normal, c);
226: #else
227: d[v] = DMPlex_DotRealD_Internal(cdim, normal, &coords[v * cdim]);
228: #endif
229: d[v] -= dp;
230: }
232: // If all d are positive or negative, no intersection
233: {
234: PetscInt v;
235: for (v = 0; v < dim + 1; ++v)
236: if (d[v] >= 0.) break;
237: if (v == dim + 1) PetscFunctionReturn(PETSC_SUCCESS);
238: for (v = 0; v < dim + 1; ++v)
239: if (d[v] <= 0.) break;
240: if (v == dim + 1) {
241: if (pos) *pos = PETSC_TRUE;
242: PetscFunctionReturn(PETSC_SUCCESS);
243: }
244: }
246: for (PetscInt v = 0; v < dim + 1; ++v) {
247: // Points with zero distance are automatically added to the list.
248: if (PetscAbsReal(d[v]) < PETSC_MACHINE_EPSILON) {
249: for (PetscInt i = 0; i < cdim; ++i) intPoints[n * cdim + i] = PetscRealPart(coords[v * cdim + i]);
250: ++n;
251: } else {
252: // For each point with nonzero distance, seek another point with opposite sign
253: // and higher index, and compute the intersection of the line between those
254: // points and the plane.
255: for (PetscInt w = v + 1; w < dim + 1; ++w) {
256: if (d[v] * d[w] < 0.) {
257: PetscReal inv_dist = 1. / (d[v] - d[w]);
258: for (PetscInt i = 0; i < cdim; ++i) intPoints[n * cdim + i] = (d[v] * PetscRealPart(coords[w * cdim + i]) - d[w] * PetscRealPart(coords[v * cdim + i])) * inv_dist;
259: ++n;
260: }
261: }
262: }
263: }
264: // TODO order output points if there are 4
265: *Nint = n;
266: PetscFunctionReturn(PETSC_SUCCESS);
267: }
269: static PetscErrorCode DMPlexGetPlaneSimplexIntersection_Internal(DM dm, PetscInt dim, PetscInt c, const PetscReal p[], const PetscReal normal[], PetscBool *pos, PetscInt *Nint, PetscReal intPoints[])
270: {
271: const PetscScalar *array;
272: PetscScalar *coords = NULL;
273: PetscInt numCoords;
274: PetscBool isDG;
275: PetscInt cdim;
277: PetscFunctionBegin;
278: PetscCall(DMGetCoordinateDim(dm, &cdim));
279: PetscCheck(cdim == dim, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "DM has coordinates in %" PetscInt_FMT "D instead of %" PetscInt_FMT "D", cdim, dim);
280: PetscCall(DMPlexGetCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
281: PetscCheck(numCoords == dim * (dim + 1), PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Tetrahedron should have %" PetscInt_FMT " coordinates, not %" PetscInt_FMT, dim * (dim + 1), numCoords);
282: PetscCall(PetscArrayzero(intPoints, dim * (dim + 1)));
284: PetscCall(DMPlexGetPlaneSimplexIntersection_Coords_Internal(dm, dim, cdim, coords, p, normal, pos, Nint, intPoints));
286: PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
287: PetscFunctionReturn(PETSC_SUCCESS);
288: }
290: static PetscErrorCode DMPlexGetPlaneQuadIntersection_Internal(DM dm, PetscInt dim, PetscInt c, const PetscReal p[], const PetscReal normal[], PetscBool *pos, PetscInt *Nint, PetscReal intPoints[])
291: {
292: const PetscScalar *array;
293: PetscScalar *coords = NULL;
294: PetscInt numCoords;
295: PetscBool isDG;
296: PetscInt cdim;
297: PetscScalar tcoords[6] = {0., 0., 0., 0., 0., 0.};
298: const PetscInt vertsA[3] = {0, 1, 3};
299: const PetscInt vertsB[3] = {1, 2, 3};
300: PetscInt NintA, NintB;
302: PetscFunctionBegin;
303: PetscCall(DMGetCoordinateDim(dm, &cdim));
304: PetscCheck(cdim == dim, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "DM has coordinates in %" PetscInt_FMT "D instead of %" PetscInt_FMT "D", cdim, dim);
305: PetscCall(DMPlexGetCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
306: PetscCheck(numCoords == dim * 4, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Quadrilateral should have %" PetscInt_FMT " coordinates, not %" PetscInt_FMT, dim * 4, numCoords);
307: PetscCall(PetscArrayzero(intPoints, dim * 4));
309: for (PetscInt v = 0; v < 3; ++v)
310: for (PetscInt d = 0; d < cdim; ++d) tcoords[v * cdim + d] = coords[vertsA[v] * cdim + d];
311: PetscCall(DMPlexGetPlaneSimplexIntersection_Coords_Internal(dm, dim, cdim, tcoords, p, normal, pos, &NintA, intPoints));
312: for (PetscInt v = 0; v < 3; ++v)
313: for (PetscInt d = 0; d < cdim; ++d) tcoords[v * cdim + d] = coords[vertsB[v] * cdim + d];
314: PetscCall(DMPlexGetPlaneSimplexIntersection_Coords_Internal(dm, dim, cdim, tcoords, p, normal, pos, &NintB, &intPoints[NintA * cdim]));
315: *Nint = NintA + NintB;
317: PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
318: PetscFunctionReturn(PETSC_SUCCESS);
319: }
321: static PetscErrorCode DMPlexGetPlaneHexIntersection_Internal(DM dm, PetscInt dim, PetscInt c, const PetscReal p[], const PetscReal normal[], PetscBool *pos, PetscInt *Nint, PetscReal intPoints[])
322: {
323: const PetscScalar *array;
324: PetscScalar *coords = NULL;
325: PetscInt numCoords;
326: PetscBool isDG;
327: PetscInt cdim;
328: PetscScalar tcoords[12] = {0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.};
329: // We split using the (2, 4) main diagonal, so all tets contain those vertices
330: const PetscInt vertsA[4] = {0, 1, 2, 4};
331: const PetscInt vertsB[4] = {0, 2, 3, 4};
332: const PetscInt vertsC[4] = {1, 7, 2, 4};
333: const PetscInt vertsD[4] = {2, 7, 6, 4};
334: const PetscInt vertsE[4] = {3, 5, 4, 2};
335: const PetscInt vertsF[4] = {4, 5, 6, 2};
336: PetscInt NintA, NintB, NintC, NintD, NintE, NintF, Nsum = 0;
338: PetscFunctionBegin;
339: PetscCall(DMGetCoordinateDim(dm, &cdim));
340: PetscCheck(cdim == dim, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "DM has coordinates in %" PetscInt_FMT "D instead of %" PetscInt_FMT "D", cdim, dim);
341: PetscCall(DMPlexGetCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
342: PetscCheck(numCoords == dim * 8, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Hexahedron should have %" PetscInt_FMT " coordinates, not %" PetscInt_FMT, dim * 8, numCoords);
343: PetscCall(PetscArrayzero(intPoints, dim * 18));
345: for (PetscInt v = 0; v < 4; ++v)
346: for (PetscInt d = 0; d < cdim; ++d) tcoords[v * cdim + d] = coords[vertsA[v] * cdim + d];
347: PetscCall(DMPlexGetPlaneSimplexIntersection_Coords_Internal(dm, dim, cdim, tcoords, p, normal, pos, &NintA, &intPoints[Nsum * cdim]));
348: Nsum += NintA;
349: for (PetscInt v = 0; v < 4; ++v)
350: for (PetscInt d = 0; d < cdim; ++d) tcoords[v * cdim + d] = coords[vertsB[v] * cdim + d];
351: PetscCall(DMPlexGetPlaneSimplexIntersection_Coords_Internal(dm, dim, cdim, tcoords, p, normal, pos, &NintB, &intPoints[Nsum * cdim]));
352: Nsum += NintB;
353: for (PetscInt v = 0; v < 4; ++v)
354: for (PetscInt d = 0; d < cdim; ++d) tcoords[v * cdim + d] = coords[vertsC[v] * cdim + d];
355: PetscCall(DMPlexGetPlaneSimplexIntersection_Coords_Internal(dm, dim, cdim, tcoords, p, normal, pos, &NintC, &intPoints[Nsum * cdim]));
356: Nsum += NintC;
357: for (PetscInt v = 0; v < 4; ++v)
358: for (PetscInt d = 0; d < cdim; ++d) tcoords[v * cdim + d] = coords[vertsD[v] * cdim + d];
359: PetscCall(DMPlexGetPlaneSimplexIntersection_Coords_Internal(dm, dim, cdim, tcoords, p, normal, pos, &NintD, &intPoints[Nsum * cdim]));
360: Nsum += NintD;
361: for (PetscInt v = 0; v < 4; ++v)
362: for (PetscInt d = 0; d < cdim; ++d) tcoords[v * cdim + d] = coords[vertsE[v] * cdim + d];
363: PetscCall(DMPlexGetPlaneSimplexIntersection_Coords_Internal(dm, dim, cdim, tcoords, p, normal, pos, &NintE, &intPoints[Nsum * cdim]));
364: Nsum += NintE;
365: for (PetscInt v = 0; v < 4; ++v)
366: for (PetscInt d = 0; d < cdim; ++d) tcoords[v * cdim + d] = coords[vertsF[v] * cdim + d];
367: PetscCall(DMPlexGetPlaneSimplexIntersection_Coords_Internal(dm, dim, cdim, tcoords, p, normal, pos, &NintF, &intPoints[Nsum * cdim]));
368: Nsum += NintF;
369: *Nint = Nsum;
371: PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
372: PetscFunctionReturn(PETSC_SUCCESS);
373: }
375: /*
376: DMPlexGetPlaneCellIntersection_Internal - Finds the intersection of a plane with a cell
378: Not collective
380: Input Parameters:
381: + dm - the DM
382: . c - the mesh point
383: . p - a point on the plane.
384: - normal - a normal vector to the plane, must be normalized
386: Output Parameters:
387: . pos - `PETSC_TRUE` is the cell is on the positive side of the plane, `PETSC_FALSE` on the negative side
388: + Nint - the number of intersection points, in [0, 4]
389: - intPoints - the coordinates of the intersection points, should be length at least 12
391: Note: The `pos` argument is only meaningful if the number of intersections is 0. The algorithmic idea comes from https://github.com/chrisk314/tet-plane-intersection.
393: Level: developer
395: .seealso:
396: @*/
397: static PetscErrorCode DMPlexGetPlaneCellIntersection_Internal(DM dm, PetscInt c, const PetscReal p[], const PetscReal normal[], PetscBool *pos, PetscInt *Nint, PetscReal intPoints[])
398: {
399: DMPolytopeType ct;
401: PetscFunctionBegin;
402: PetscCall(DMPlexGetCellType(dm, c, &ct));
403: switch (ct) {
404: case DM_POLYTOPE_SEGMENT:
405: case DM_POLYTOPE_TRIANGLE:
406: case DM_POLYTOPE_TETRAHEDRON:
407: PetscCall(DMPlexGetPlaneSimplexIntersection_Internal(dm, DMPolytopeTypeGetDim(ct), c, p, normal, pos, Nint, intPoints));
408: break;
409: case DM_POLYTOPE_QUADRILATERAL:
410: PetscCall(DMPlexGetPlaneQuadIntersection_Internal(dm, DMPolytopeTypeGetDim(ct), c, p, normal, pos, Nint, intPoints));
411: break;
412: case DM_POLYTOPE_HEXAHEDRON:
413: PetscCall(DMPlexGetPlaneHexIntersection_Internal(dm, DMPolytopeTypeGetDim(ct), c, p, normal, pos, Nint, intPoints));
414: break;
415: default:
416: SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No plane intersection for cell %" PetscInt_FMT " with type %s", c, DMPolytopeTypes[ct]);
417: }
418: PetscFunctionReturn(PETSC_SUCCESS);
419: }
421: static PetscErrorCode DMPlexLocatePoint_Simplex_1D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
422: {
423: const PetscReal eps = PETSC_SQRT_MACHINE_EPSILON;
424: const PetscReal x = PetscRealPart(point[0]);
425: PetscReal v0, J, invJ, detJ;
426: PetscReal xi;
428: PetscFunctionBegin;
429: PetscCall(DMPlexComputeCellGeometryFEM(dm, c, NULL, &v0, &J, &invJ, &detJ));
430: xi = invJ * (x - v0);
432: if ((xi >= -eps) && (xi <= 2. + eps)) *cell = c;
433: else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
434: PetscFunctionReturn(PETSC_SUCCESS);
435: }
437: static PetscErrorCode DMPlexLocatePoint_Simplex_2D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
438: {
439: const PetscReal eps = PETSC_SQRT_MACHINE_EPSILON;
440: PetscReal xi[2] = {0., 0.};
441: PetscReal x[3], v0[3], J[9], invJ[9], detJ;
442: PetscInt embedDim;
444: PetscFunctionBegin;
445: PetscCall(DMGetCoordinateDim(dm, &embedDim));
446: PetscCall(DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ));
447: for (PetscInt j = 0; j < embedDim; ++j) x[j] = PetscRealPart(point[j]);
448: for (PetscInt i = 0; i < 2; ++i) {
449: for (PetscInt j = 0; j < embedDim; ++j) xi[i] += invJ[i * embedDim + j] * (x[j] - v0[j]);
450: }
451: if ((xi[0] >= -eps) && (xi[1] >= -eps) && (xi[0] + xi[1] <= 2.0 + eps)) *cell = c;
452: else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
453: PetscFunctionReturn(PETSC_SUCCESS);
454: }
456: static PetscErrorCode DMPlexClosestPoint_Simplex_2D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscReal cpoint[])
457: {
458: const PetscInt embedDim = 2;
459: PetscReal x = PetscRealPart(point[0]);
460: PetscReal y = PetscRealPart(point[1]);
461: PetscReal v0[2], J[4], invJ[4], detJ;
462: PetscReal xi, eta, r;
464: PetscFunctionBegin;
465: PetscCall(DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ));
466: xi = invJ[0 * embedDim + 0] * (x - v0[0]) + invJ[0 * embedDim + 1] * (y - v0[1]);
467: eta = invJ[1 * embedDim + 0] * (x - v0[0]) + invJ[1 * embedDim + 1] * (y - v0[1]);
469: xi = PetscMax(xi, 0.0);
470: eta = PetscMax(eta, 0.0);
471: if (xi + eta > 2.0) {
472: r = (xi + eta) / 2.0;
473: xi /= r;
474: eta /= r;
475: }
476: cpoint[0] = J[0 * embedDim + 0] * xi + J[0 * embedDim + 1] * eta + v0[0];
477: cpoint[1] = J[1 * embedDim + 0] * xi + J[1 * embedDim + 1] * eta + v0[1];
478: PetscFunctionReturn(PETSC_SUCCESS);
479: }
481: // This is the ray-casting, or even-odd algorithm: https://en.wikipedia.org/wiki/Even%E2%80%93odd_rule
482: static PetscErrorCode DMPlexLocatePoint_Quad_2D_Linear_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
483: {
484: const PetscScalar *array;
485: PetscScalar *coords = NULL;
486: const PetscInt faces[8] = {0, 1, 1, 2, 2, 3, 3, 0};
487: PetscReal x = PetscRealPart(point[0]);
488: PetscReal y = PetscRealPart(point[1]);
489: PetscInt crossings = 0, numCoords, embedDim;
490: PetscBool isDG;
492: PetscFunctionBegin;
493: PetscCall(DMPlexGetCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
494: embedDim = numCoords / 4;
495: PetscCheck(!(numCoords % 4), PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Quadrilateral should have 8 coordinates, not %" PetscInt_FMT, numCoords);
496: // Treat linear quads as Monge surfaces, so we just locate on the projection to x-y (could instead project to 2D)
497: for (PetscInt f = 0; f < 4; ++f) {
498: PetscReal x_i = PetscRealPart(coords[faces[2 * f + 0] * embedDim + 0]);
499: PetscReal y_i = PetscRealPart(coords[faces[2 * f + 0] * embedDim + 1]);
500: PetscReal x_j = PetscRealPart(coords[faces[2 * f + 1] * embedDim + 0]);
501: PetscReal y_j = PetscRealPart(coords[faces[2 * f + 1] * embedDim + 1]);
503: if ((x == x_j) && (y == y_j)) {
504: // point is a corner
505: crossings = 1;
506: break;
507: }
508: if ((y_j > y) != (y_i > y)) {
509: PetscReal slope = (x - x_j) * (y_i - y_j) - (x_i - x_j) * (y - y_j);
510: if (slope == 0) {
511: // point is a corner
512: crossings = 1;
513: break;
514: }
515: if ((slope < 0) != (y_i < y_j)) ++crossings;
516: }
517: }
518: if (crossings % 2) *cell = c;
519: else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
520: PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
521: PetscFunctionReturn(PETSC_SUCCESS);
522: }
524: static PetscErrorCode DMPlexLocatePoint_Quad_2D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
525: {
526: DM cdm;
527: PetscInt degree, dimR, dimC;
528: PetscFE fe;
529: PetscClassId id;
530: PetscSpace sp;
531: PetscReal pointR[3], ref[3], error;
532: Vec coords;
533: PetscBool found = PETSC_FALSE;
535: PetscFunctionBegin;
536: PetscCall(DMGetDimension(dm, &dimR));
537: PetscCall(DMGetCoordinateDM(dm, &cdm));
538: PetscCall(DMGetDimension(cdm, &dimC));
539: PetscCall(DMGetField(cdm, 0, NULL, (PetscObject *)&fe));
540: PetscCall(PetscObjectGetClassId((PetscObject)fe, &id));
541: if (id != PETSCFE_CLASSID) degree = 1;
542: else {
543: PetscCall(PetscFEGetBasisSpace(fe, &sp));
544: PetscCall(PetscSpaceGetDegree(sp, °ree, NULL));
545: }
546: if (degree == 1) {
547: /* Use simple location method for linear elements*/
548: PetscCall(DMPlexLocatePoint_Quad_2D_Linear_Internal(dm, point, c, cell));
549: PetscFunctionReturn(PETSC_SUCCESS);
550: }
551: /* Otherwise, we have to solve for the real to reference coordinates */
552: PetscCall(DMGetCoordinatesLocal(dm, &coords));
553: error = PETSC_SQRT_MACHINE_EPSILON;
554: for (PetscInt d = 0; d < dimC; d++) pointR[d] = PetscRealPart(point[d]);
555: PetscCall(DMPlexCoordinatesToReference_FE(cdm, fe, c, 1, pointR, ref, coords, dimC, dimR, 10, &error));
556: if (error < PETSC_SQRT_MACHINE_EPSILON) found = PETSC_TRUE;
557: if ((ref[0] > 1.0 + PETSC_SMALL) || (ref[0] < -1.0 - PETSC_SMALL) || (ref[1] > 1.0 + PETSC_SMALL) || (ref[1] < -1.0 - PETSC_SMALL)) found = PETSC_FALSE;
558: if (PetscDefined(USE_DEBUG) && found) {
559: PetscReal real[3], inverseError = 0, normPoint = DMPlex_NormD_Internal(dimC, pointR);
561: normPoint = normPoint > PETSC_SMALL ? normPoint : 1.0;
562: PetscCall(DMPlexReferenceToCoordinates_FE(cdm, fe, c, 1, ref, real, coords, dimC, dimR));
563: inverseError = DMPlex_DistRealD_Internal(dimC, real, pointR);
564: if (inverseError > PETSC_SQRT_MACHINE_EPSILON * normPoint) found = PETSC_FALSE;
565: if (!found) PetscCall(PetscInfo(dm, "Point (%g, %g, %g) != Mapped Ref Coords (%g, %g, %g) with error %g\n", (double)pointR[0], (double)pointR[1], (double)pointR[2], (double)real[0], (double)real[1], (double)real[2], (double)inverseError));
566: }
567: if (found) *cell = c;
568: else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
569: PetscFunctionReturn(PETSC_SUCCESS);
570: }
572: static PetscErrorCode DMPlexLocatePoint_Simplex_3D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
573: {
574: const PetscInt embedDim = 3;
575: const PetscReal eps = PETSC_SQRT_MACHINE_EPSILON;
576: PetscReal v0[3], J[9], invJ[9], detJ;
577: PetscReal x = PetscRealPart(point[0]);
578: PetscReal y = PetscRealPart(point[1]);
579: PetscReal z = PetscRealPart(point[2]);
580: PetscReal xi, eta, zeta;
582: PetscFunctionBegin;
583: PetscCall(DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ));
584: xi = invJ[0 * embedDim + 0] * (x - v0[0]) + invJ[0 * embedDim + 1] * (y - v0[1]) + invJ[0 * embedDim + 2] * (z - v0[2]);
585: eta = invJ[1 * embedDim + 0] * (x - v0[0]) + invJ[1 * embedDim + 1] * (y - v0[1]) + invJ[1 * embedDim + 2] * (z - v0[2]);
586: zeta = invJ[2 * embedDim + 0] * (x - v0[0]) + invJ[2 * embedDim + 1] * (y - v0[1]) + invJ[2 * embedDim + 2] * (z - v0[2]);
588: if ((xi >= -eps) && (eta >= -eps) && (zeta >= -eps) && (xi + eta + zeta <= 2.0 + eps)) *cell = c;
589: else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
590: PetscFunctionReturn(PETSC_SUCCESS);
591: }
593: static PetscErrorCode DMPlexLocatePoint_Hex_3D_Linear_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
594: {
595: const PetscScalar *array;
596: PetscScalar *coords = NULL;
597: const PetscInt faces[24] = {0, 3, 2, 1, 5, 4, 7, 6, 3, 0, 4, 5, 1, 2, 6, 7, 3, 5, 6, 2, 0, 1, 7, 4};
598: PetscBool found = PETSC_TRUE;
599: PetscInt numCoords, f;
600: PetscBool isDG;
602: PetscFunctionBegin;
603: PetscCall(DMPlexGetCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
604: PetscCheck(numCoords == 24, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Quadrilateral should have 8 coordinates, not %" PetscInt_FMT, numCoords);
605: for (f = 0; f < 6; ++f) {
606: /* Check the point is under plane */
607: /* Get face normal */
608: PetscReal v_i[3];
609: PetscReal v_j[3];
610: PetscReal normal[3];
611: PetscReal pp[3];
612: PetscReal dot;
614: v_i[0] = PetscRealPart(coords[faces[f * 4 + 3] * 3 + 0] - coords[faces[f * 4 + 0] * 3 + 0]);
615: v_i[1] = PetscRealPart(coords[faces[f * 4 + 3] * 3 + 1] - coords[faces[f * 4 + 0] * 3 + 1]);
616: v_i[2] = PetscRealPart(coords[faces[f * 4 + 3] * 3 + 2] - coords[faces[f * 4 + 0] * 3 + 2]);
617: v_j[0] = PetscRealPart(coords[faces[f * 4 + 1] * 3 + 0] - coords[faces[f * 4 + 0] * 3 + 0]);
618: v_j[1] = PetscRealPart(coords[faces[f * 4 + 1] * 3 + 1] - coords[faces[f * 4 + 0] * 3 + 1]);
619: v_j[2] = PetscRealPart(coords[faces[f * 4 + 1] * 3 + 2] - coords[faces[f * 4 + 0] * 3 + 2]);
620: normal[0] = v_i[1] * v_j[2] - v_i[2] * v_j[1];
621: normal[1] = v_i[2] * v_j[0] - v_i[0] * v_j[2];
622: normal[2] = v_i[0] * v_j[1] - v_i[1] * v_j[0];
623: pp[0] = PetscRealPart(coords[faces[f * 4 + 0] * 3 + 0] - point[0]);
624: pp[1] = PetscRealPart(coords[faces[f * 4 + 0] * 3 + 1] - point[1]);
625: pp[2] = PetscRealPart(coords[faces[f * 4 + 0] * 3 + 2] - point[2]);
626: dot = normal[0] * pp[0] + normal[1] * pp[1] + normal[2] * pp[2];
628: /* Check that projected point is in face (2D location problem) */
629: if (dot < 0.0) {
630: found = PETSC_FALSE;
631: break;
632: }
633: }
634: if (found) *cell = c;
635: else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
636: PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
637: PetscFunctionReturn(PETSC_SUCCESS);
638: }
640: static PetscErrorCode DMPlexLocatePoint_Hex_3D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
641: {
642: DM cdm;
643: PetscInt degree, dimR, dimC;
644: PetscFE fe;
645: PetscClassId id;
646: PetscSpace sp;
647: PetscReal pointR[3], ref[3], error;
648: Vec coords;
649: PetscBool found = PETSC_FALSE;
651: PetscFunctionBegin;
652: PetscCall(DMGetDimension(dm, &dimR));
653: PetscCall(DMGetCoordinateDM(dm, &cdm));
654: PetscCall(DMGetDimension(cdm, &dimC));
655: PetscCall(DMGetField(cdm, 0, NULL, (PetscObject *)&fe));
656: PetscCall(PetscObjectGetClassId((PetscObject)fe, &id));
657: if (id != PETSCFE_CLASSID) degree = 1;
658: else {
659: PetscCall(PetscFEGetBasisSpace(fe, &sp));
660: PetscCall(PetscSpaceGetDegree(sp, °ree, NULL));
661: }
662: if (degree == 1) {
663: /* Use simple location method for linear elements*/
664: PetscCall(DMPlexLocatePoint_Hex_3D_Linear_Internal(dm, point, c, cell));
665: PetscFunctionReturn(PETSC_SUCCESS);
666: }
667: /* Otherwise, we have to solve for the real to reference coordinates */
668: PetscCall(DMGetCoordinatesLocal(dm, &coords));
669: error = PETSC_SQRT_MACHINE_EPSILON;
670: for (PetscInt d = 0; d < dimC; d++) pointR[d] = PetscRealPart(point[d]);
671: PetscCall(DMPlexCoordinatesToReference_FE(cdm, fe, c, 1, pointR, ref, coords, dimC, dimR, 10, &error));
672: if (error < PETSC_SQRT_MACHINE_EPSILON) found = PETSC_TRUE;
673: if ((ref[0] > 1.0 + PETSC_SMALL) || (ref[0] < -1.0 - PETSC_SMALL) || (ref[1] > 1.0 + PETSC_SMALL) || (ref[1] < -1.0 - PETSC_SMALL) || (ref[2] > 1.0 + PETSC_SMALL) || (ref[2] < -1.0 - PETSC_SMALL)) found = PETSC_FALSE;
674: if (PetscDefined(USE_DEBUG) && found) {
675: PetscReal real[3], inverseError = 0, normPoint = DMPlex_NormD_Internal(dimC, pointR);
677: normPoint = normPoint > PETSC_SMALL ? normPoint : 1.0;
678: PetscCall(DMPlexReferenceToCoordinates_FE(cdm, fe, c, 1, ref, real, coords, dimC, dimR));
679: inverseError = DMPlex_DistRealD_Internal(dimC, real, pointR);
680: if (inverseError > PETSC_SQRT_MACHINE_EPSILON * normPoint) found = PETSC_FALSE;
681: if (!found) PetscCall(PetscInfo(dm, "Point (%g, %g, %g) != Mapped Ref Coords (%g, %g, %g) with error %g\n", (double)pointR[0], (double)pointR[1], (double)pointR[2], (double)real[0], (double)real[1], (double)real[2], (double)inverseError));
682: }
683: if (found) *cell = c;
684: else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
685: PetscFunctionReturn(PETSC_SUCCESS);
686: }
688: static PetscErrorCode PetscGridHashInitialize_Internal(PetscGridHash box, PetscInt dim, const PetscScalar point[])
689: {
690: PetscInt d;
692: PetscFunctionBegin;
693: box->dim = dim;
694: for (d = 0; d < dim; ++d) box->lower[d] = box->upper[d] = point ? PetscRealPart(point[d]) : 0.;
695: PetscFunctionReturn(PETSC_SUCCESS);
696: }
698: PetscErrorCode PetscGridHashCreate(MPI_Comm comm, PetscInt dim, const PetscScalar point[], PetscGridHash *box)
699: {
700: PetscFunctionBegin;
701: PetscCall(PetscCalloc1(1, box));
702: PetscCall(PetscGridHashInitialize_Internal(*box, dim, point));
703: PetscFunctionReturn(PETSC_SUCCESS);
704: }
706: PetscErrorCode PetscGridHashEnlarge(PetscGridHash box, const PetscScalar point[])
707: {
708: PetscInt d;
710: PetscFunctionBegin;
711: for (d = 0; d < box->dim; ++d) {
712: box->lower[d] = PetscMin(box->lower[d], PetscRealPart(point[d]));
713: box->upper[d] = PetscMax(box->upper[d], PetscRealPart(point[d]));
714: }
715: PetscFunctionReturn(PETSC_SUCCESS);
716: }
718: static PetscErrorCode DMPlexCreateGridHash(DM dm, PetscGridHash *box)
719: {
720: Vec coordinates;
721: const PetscScalar *a;
722: PetscInt cdim, cStart, cEnd;
724: PetscFunctionBegin;
725: PetscCall(DMGetCoordinateDim(dm, &cdim));
726: PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
727: PetscCall(DMGetCoordinatesLocal(dm, &coordinates));
729: PetscCall(VecGetArrayRead(coordinates, &a));
730: PetscCall(PetscGridHashCreate(PetscObjectComm((PetscObject)dm), cdim, a, box));
731: PetscCall(VecRestoreArrayRead(coordinates, &a));
732: for (PetscInt c = cStart; c < cEnd; ++c) {
733: const PetscScalar *array;
734: PetscScalar *coords = NULL;
735: PetscInt numCoords;
736: PetscBool isDG;
738: PetscCall(DMPlexGetCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
739: for (PetscInt i = 0; i < numCoords / cdim; ++i) PetscCall(PetscGridHashEnlarge(*box, &coords[i * cdim]));
740: PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
741: }
742: PetscFunctionReturn(PETSC_SUCCESS);
743: }
745: /*@C
746: PetscGridHashSetGrid - Divide the grid into boxes
748: Not Collective
750: Input Parameters:
751: + box - The grid hash object
752: . n - The number of boxes in each dimension, may use `PETSC_DETERMINE` for the entries
753: - h - The box size in each dimension, only used if n[d] == `PETSC_DETERMINE`, if not needed you can pass in `NULL`
755: Level: developer
757: .seealso: `DMPLEX`, `PetscGridHashCreate()`
758: @*/
759: PetscErrorCode PetscGridHashSetGrid(PetscGridHash box, const PetscInt n[], const PetscReal h[])
760: {
761: PetscInt d;
763: PetscFunctionBegin;
764: PetscAssertPointer(n, 2);
765: if (h) PetscAssertPointer(h, 3);
766: for (d = 0; d < box->dim; ++d) {
767: box->extent[d] = box->upper[d] - box->lower[d];
768: if (n[d] == PETSC_DETERMINE) {
769: PetscCheck(h, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Missing h");
770: box->h[d] = h[d];
771: box->n[d] = PetscCeilReal(box->extent[d] / h[d]);
772: } else {
773: box->n[d] = n[d];
774: box->h[d] = box->extent[d] / n[d];
775: }
776: }
777: PetscFunctionReturn(PETSC_SUCCESS);
778: }
780: /*@C
781: PetscGridHashGetEnclosingBox - Find the grid boxes containing each input point
783: Not Collective
785: Input Parameters:
786: + box - The grid hash object
787: . numPoints - The number of input points
788: - points - The input point coordinates
790: Output Parameters:
791: + dboxes - An array of `numPoints` x `dim` integers expressing the enclosing box as (i_0, i_1, ..., i_dim)
792: - boxes - An array of `numPoints` integers expressing the enclosing box as single number, or `NULL`
794: Level: developer
796: Note:
797: This only guarantees that a box contains a point, not that a cell does.
799: .seealso: `DMPLEX`, `PetscGridHashCreate()`
800: @*/
801: PetscErrorCode PetscGridHashGetEnclosingBox(PetscGridHash box, PetscInt numPoints, const PetscScalar points[], PetscInt dboxes[], PetscInt boxes[])
802: {
803: const PetscReal *lower = box->lower;
804: const PetscReal *upper = box->upper;
805: const PetscReal *h = box->h;
806: const PetscInt *n = box->n;
807: const PetscInt dim = box->dim;
808: PetscInt d, p;
810: PetscFunctionBegin;
811: for (p = 0; p < numPoints; ++p) {
812: for (d = 0; d < dim; ++d) {
813: PetscInt dbox = PetscFloorReal((PetscRealPart(points[p * dim + d]) - lower[d]) / h[d]);
815: if (dbox == n[d] && PetscAbsReal(PetscRealPart(points[p * dim + d]) - upper[d]) < 1.0e-9) dbox = n[d] - 1;
816: if (dbox == -1 && PetscAbsReal(PetscRealPart(points[p * dim + d]) - lower[d]) < 1.0e-9) dbox = 0;
817: PetscCheck(dbox >= 0 && dbox < n[d], PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Input point %" PetscInt_FMT " (%g, %g, %g) is outside of our bounding box (%g, %g, %g) - (%g, %g, %g)", p, (double)PetscRealPart(points[p * dim + 0]), dim > 1 ? (double)PetscRealPart(points[p * dim + 1]) : 0.0, dim > 2 ? (double)PetscRealPart(points[p * dim + 2]) : 0.0, (double)lower[0], (double)lower[1], (double)lower[2], (double)upper[0], (double)upper[1], (double)upper[2]);
818: dboxes[p * dim + d] = dbox;
819: }
820: if (boxes)
821: for (d = dim - 2, boxes[p] = dboxes[p * dim + dim - 1]; d >= 0; --d) boxes[p] = boxes[p] * n[d] + dboxes[p * dim + d];
822: }
823: PetscFunctionReturn(PETSC_SUCCESS);
824: }
826: /*
827: PetscGridHashGetEnclosingBoxQuery - Find the grid boxes containing each input point
829: Not Collective
831: Input Parameters:
832: + box - The grid hash object
833: . cellSection - The PetscSection mapping cells to boxes
834: . numPoints - The number of input points
835: - points - The input point coordinates
837: Output Parameters:
838: + dboxes - An array of `numPoints`*`dim` integers expressing the enclosing box as (i_0, i_1, ..., i_dim)
839: . boxes - An array of `numPoints` integers expressing the enclosing box as single number, or `NULL`
840: - found - Flag indicating if point was located within a box
842: Level: developer
844: Note:
845: This does an additional check that a cell actually contains the point, and found is `PETSC_FALSE` if no cell does. Thus, this function requires that `cellSection` is already constructed.
847: .seealso: `DMPLEX`, `PetscGridHashGetEnclosingBox()`
848: */
849: static PetscErrorCode PetscGridHashGetEnclosingBoxQuery(PetscGridHash box, PetscSection cellSection, PetscInt numPoints, const PetscScalar points[], PetscInt dboxes[], PetscInt boxes[], PetscBool *found)
850: {
851: const PetscReal *lower = box->lower;
852: const PetscReal *upper = box->upper;
853: const PetscReal *h = box->h;
854: const PetscInt *n = box->n;
855: const PetscInt dim = box->dim;
856: PetscInt bStart, bEnd, d, p;
858: PetscFunctionBegin;
860: *found = PETSC_FALSE;
861: PetscCall(PetscSectionGetChart(box->cellSection, &bStart, &bEnd));
862: for (p = 0; p < numPoints; ++p) {
863: for (d = 0; d < dim; ++d) {
864: PetscInt dbox = PetscFloorReal((PetscRealPart(points[p * dim + d]) - lower[d]) / h[d]);
866: if (dbox == n[d] && PetscAbsReal(PetscRealPart(points[p * dim + d]) - upper[d]) < 1.0e-9) dbox = n[d] - 1;
867: if (dbox < 0 || dbox >= n[d]) PetscFunctionReturn(PETSC_SUCCESS);
868: dboxes[p * dim + d] = dbox;
869: }
870: if (boxes)
871: for (d = dim - 2, boxes[p] = dboxes[p * dim + dim - 1]; d >= 0; --d) boxes[p] = boxes[p] * n[d] + dboxes[p * dim + d];
872: // It is possible for a box to overlap no grid cells
873: if (boxes[p] < bStart || boxes[p] >= bEnd) PetscFunctionReturn(PETSC_SUCCESS);
874: }
875: *found = PETSC_TRUE;
876: PetscFunctionReturn(PETSC_SUCCESS);
877: }
879: PetscErrorCode PetscGridHashDestroy(PetscGridHash *box)
880: {
881: PetscFunctionBegin;
882: if (*box) {
883: PetscCall(PetscSectionDestroy(&(*box)->cellSection));
884: PetscCall(ISDestroy(&(*box)->cells));
885: PetscCall(DMLabelDestroy(&(*box)->cellsSparse));
886: }
887: PetscCall(PetscFree(*box));
888: PetscFunctionReturn(PETSC_SUCCESS);
889: }
891: PetscErrorCode DMPlexLocatePoint_Internal(DM dm, PetscInt dim, const PetscScalar point[], PetscInt cellStart, PetscInt *cell)
892: {
893: DMPolytopeType ct;
895: PetscFunctionBegin;
896: PetscCall(DMPlexGetCellType(dm, cellStart, &ct));
897: switch (ct) {
898: case DM_POLYTOPE_SEGMENT:
899: PetscCall(DMPlexLocatePoint_Simplex_1D_Internal(dm, point, cellStart, cell));
900: break;
901: case DM_POLYTOPE_TRIANGLE:
902: PetscCall(DMPlexLocatePoint_Simplex_2D_Internal(dm, point, cellStart, cell));
903: break;
904: case DM_POLYTOPE_QUADRILATERAL:
905: PetscCall(DMPlexLocatePoint_Quad_2D_Internal(dm, point, cellStart, cell));
906: break;
907: case DM_POLYTOPE_TETRAHEDRON:
908: PetscCall(DMPlexLocatePoint_Simplex_3D_Internal(dm, point, cellStart, cell));
909: break;
910: case DM_POLYTOPE_HEXAHEDRON:
911: PetscCall(DMPlexLocatePoint_Hex_3D_Internal(dm, point, cellStart, cell));
912: break;
913: default:
914: SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No point location for cell %" PetscInt_FMT " with type %s", cellStart, DMPolytopeTypes[ct]);
915: }
916: PetscFunctionReturn(PETSC_SUCCESS);
917: }
919: /*
920: DMPlexClosestPoint_Internal - Returns the closest point in the cell to the given point
921: */
922: static PetscErrorCode DMPlexClosestPoint_Internal(DM dm, PetscInt dim, const PetscScalar point[], PetscInt cell, PetscReal cpoint[])
923: {
924: DMPolytopeType ct;
926: PetscFunctionBegin;
927: PetscCall(DMPlexGetCellType(dm, cell, &ct));
928: switch (ct) {
929: case DM_POLYTOPE_TRIANGLE:
930: PetscCall(DMPlexClosestPoint_Simplex_2D_Internal(dm, point, cell, cpoint));
931: break;
932: #if 0
933: case DM_POLYTOPE_QUADRILATERAL:
934: PetscCall(DMPlexClosestPoint_General_2D_Internal(dm, point, cell, cpoint));break;
935: case DM_POLYTOPE_TETRAHEDRON:
936: PetscCall(DMPlexClosestPoint_Simplex_3D_Internal(dm, point, cell, cpoint));break;
937: case DM_POLYTOPE_HEXAHEDRON:
938: PetscCall(DMPlexClosestPoint_General_3D_Internal(dm, point, cell, cpoint));break;
939: #endif
940: default:
941: SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No closest point location for cell %" PetscInt_FMT " with type %s", cell, DMPolytopeTypes[ct]);
942: }
943: PetscFunctionReturn(PETSC_SUCCESS);
944: }
946: /*
947: DMPlexComputeGridHash_Internal - Create a grid hash structure covering the `DMPLEX`
949: Collective
951: Input Parameter:
952: . dm - The `DMPLEX`
954: Output Parameter:
955: . localBox - The grid hash object
957: Level: developer
959: Notes:
960: How do we determine all boxes intersecting a given cell?
962: 1) Get convex body enclosing cell. We will use a box called the box-hull.
964: 2) Get smallest brick of boxes enclosing the box-hull
966: 3) Each box is composed of 6 planes, 3 lower and 3 upper. We loop over dimensions, and
967: for each new plane determine whether the cell is on the negative side, positive side, or intersects it.
969: a) If the cell is on the negative side of the lower planes, it is not in the box
971: b) If the cell is on the positive side of the upper planes, it is not in the box
973: c) If there is no intersection, it is in the box
975: d) If any intersection point is within the box limits, it is in the box
977: .seealso: `DMPLEX`, `PetscGridHashCreate()`, `PetscGridHashGetEnclosingBox()`
978: */
979: static PetscErrorCode DMPlexComputeGridHash_Internal(DM dm, PetscGridHash *localBox)
980: {
981: PetscInt debug = ((DM_Plex *)dm->data)->printLocate;
982: PetscGridHash lbox;
983: PetscSF sf;
984: const PetscInt *leaves;
985: PetscInt *dboxes, *boxes;
986: PetscInt cdim, cStart, cEnd, Nl = -1;
987: PetscBool flg;
989: PetscFunctionBegin;
990: PetscCall(DMGetCoordinateDim(dm, &cdim));
991: PetscCall(DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd));
992: PetscCall(DMPlexCreateGridHash(dm, &lbox));
993: {
994: PetscInt n[3], d;
996: PetscCall(PetscOptionsGetIntArray(NULL, ((PetscObject)dm)->prefix, "-dm_plex_hash_box_faces", n, &d, &flg));
997: if (flg) {
998: for (PetscInt i = d; i < cdim; ++i) n[i] = n[d - 1];
999: } else {
1000: for (PetscInt i = 0; i < cdim; ++i) n[i] = PetscMax(2, PetscFloorReal(PetscPowReal((PetscReal)(cEnd - cStart), 1.0 / cdim) * 0.8));
1001: }
1002: PetscCall(PetscGridHashSetGrid(lbox, n, NULL));
1003: if (debug)
1004: PetscCall(PetscPrintf(PETSC_COMM_SELF, "GridHash:\n (%g, %g, %g) -- (%g, %g, %g)\n n %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT "\n h %g %g %g\n", (double)lbox->lower[0], (double)lbox->lower[1], cdim > 2 ? (double)lbox->lower[2] : 0.,
1005: (double)lbox->upper[0], (double)lbox->upper[1], cdim > 2 ? (double)lbox->upper[2] : 0, n[0], n[1], cdim > 2 ? n[2] : 0, (double)lbox->h[0], (double)lbox->h[1], cdim > 2 ? (double)lbox->h[2] : 0.));
1006: }
1008: PetscCall(DMGetPointSF(dm, &sf));
1009: if (sf) PetscCall(PetscSFGetGraph(sf, NULL, &Nl, &leaves, NULL));
1010: Nl = PetscMax(Nl, 0);
1011: PetscCall(PetscCalloc2(16 * cdim, &dboxes, 16, &boxes));
1013: PetscCall(DMLabelCreate(PETSC_COMM_SELF, "cells", &lbox->cellsSparse));
1014: PetscCall(DMLabelCreateIndex(lbox->cellsSparse, cStart, cEnd));
1015: for (PetscInt c = cStart; c < cEnd; ++c) {
1016: PetscReal intPoints[6 * 6 * 6 * 3];
1017: const PetscScalar *array;
1018: PetscScalar *coords = NULL;
1019: const PetscReal *h = lbox->h;
1020: PetscReal normal[9] = {1., 0., 0., 0., 1., 0., 0., 0., 1.};
1021: PetscReal *lowerIntPoints[3] = {&intPoints[0 * 6 * 6 * 3], &intPoints[1 * 6 * 6 * 3], &intPoints[2 * 6 * 6 * 3]};
1022: PetscReal *upperIntPoints[3] = {&intPoints[3 * 6 * 6 * 3], &intPoints[4 * 6 * 6 * 3], &intPoints[5 * 6 * 6 * 3]};
1023: PetscReal lp[3], up[3], *tmp;
1024: PetscInt numCoords, idx, dlim[6], lowerInt[3], upperInt[3];
1025: PetscBool isDG, lower[3], upper[3];
1027: PetscCall(PetscFindInt(c, Nl, leaves, &idx));
1028: if (idx >= 0) continue;
1029: // Get grid of boxes containing the cell
1030: PetscCall(DMPlexGetCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
1031: PetscCall(PetscGridHashGetEnclosingBox(lbox, numCoords / cdim, coords, dboxes, boxes));
1032: PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
1033: for (PetscInt d = 0; d < cdim; ++d) dlim[d * 2 + 0] = dlim[d * 2 + 1] = dboxes[d];
1034: for (PetscInt d = cdim; d < 3; ++d) dlim[d * 2 + 0] = dlim[d * 2 + 1] = 0;
1035: for (PetscInt e = 1; e < numCoords / cdim; ++e) {
1036: for (PetscInt d = 0; d < cdim; ++d) {
1037: dlim[d * 2 + 0] = PetscMin(dlim[d * 2 + 0], dboxes[e * cdim + d]);
1038: dlim[d * 2 + 1] = PetscMax(dlim[d * 2 + 1], dboxes[e * cdim + d]);
1039: }
1040: }
1041: if (debug > 4) {
1042: for (PetscInt d = 0; d < cdim; ++d) PetscCall(PetscPrintf(PETSC_COMM_SELF, " Cell %" PetscInt_FMT " direction %" PetscInt_FMT " box limits %" PetscInt_FMT "--%" PetscInt_FMT "\n", c, d, dlim[d * 2 + 0], dlim[d * 2 + 1]));
1043: }
1044: // Initialize with lower planes for first box
1045: for (PetscInt d = 0; d < cdim; ++d) {
1046: lp[d] = lbox->lower[d] + dlim[d * 2 + 0] * h[d];
1047: up[d] = lp[d] + h[d];
1048: }
1049: for (PetscInt d = 0; d < cdim; ++d) {
1050: PetscCall(DMPlexGetPlaneCellIntersection_Internal(dm, c, lp, &normal[d * 3], &lower[d], &lowerInt[d], lowerIntPoints[d]));
1051: if (debug > 4) {
1052: if (!lowerInt[d])
1053: PetscCall(PetscPrintf(PETSC_COMM_SELF, " Cell %" PetscInt_FMT " lower direction %" PetscInt_FMT " (%g, %g, %g) does not intersect %s\n", c, d, (double)lp[0], (double)lp[1], cdim > 2 ? (double)lp[2] : 0., lower[d] ? "positive" : "negative"));
1054: else PetscCall(PetscPrintf(PETSC_COMM_SELF, " Cell %" PetscInt_FMT " lower direction %" PetscInt_FMT " (%g, %g, %g) intersects %" PetscInt_FMT " times\n", c, d, (double)lp[0], (double)lp[1], cdim > 2 ? (double)lp[2] : 0., lowerInt[d]));
1055: }
1056: }
1057: // Loop over grid
1058: for (PetscInt k = dlim[2 * 2 + 0]; k <= dlim[2 * 2 + 1]; ++k, lp[2] = up[2], up[2] += h[2]) {
1059: if (cdim > 2) PetscCall(DMPlexGetPlaneCellIntersection_Internal(dm, c, up, &normal[3 * 2], &upper[2], &upperInt[2], upperIntPoints[2]));
1060: if (cdim > 2 && debug > 4) {
1061: if (!upperInt[2]) PetscCall(PetscPrintf(PETSC_COMM_SELF, " Cell %" PetscInt_FMT " upper direction 2 (%g, %g, %g) does not intersect %s\n", c, (double)up[0], (double)up[1], cdim > 2 ? (double)up[2] : 0., upper[2] ? "positive" : "negative"));
1062: else PetscCall(PetscPrintf(PETSC_COMM_SELF, " Cell %" PetscInt_FMT " upper direction 2 (%g, %g, %g) intersects %" PetscInt_FMT " times\n", c, (double)up[0], (double)up[1], cdim > 2 ? (double)up[2] : 0., upperInt[2]));
1063: }
1064: for (PetscInt j = dlim[1 * 2 + 0]; j <= dlim[1 * 2 + 1]; ++j, lp[1] = up[1], up[1] += h[1]) {
1065: if (cdim > 1) PetscCall(DMPlexGetPlaneCellIntersection_Internal(dm, c, up, &normal[3 * 1], &upper[1], &upperInt[1], upperIntPoints[1]));
1066: if (cdim > 1 && debug > 4) {
1067: if (!upperInt[1])
1068: PetscCall(PetscPrintf(PETSC_COMM_SELF, " Cell %" PetscInt_FMT " upper direction 1 (%g, %g, %g) does not intersect %s\n", c, (double)up[0], (double)up[1], cdim > 2 ? (double)up[2] : 0., upper[1] ? "positive" : "negative"));
1069: else PetscCall(PetscPrintf(PETSC_COMM_SELF, " Cell %" PetscInt_FMT " upper direction 1 (%g, %g, %g) intersects %" PetscInt_FMT " times\n", c, (double)up[0], (double)up[1], cdim > 2 ? (double)up[2] : 0., upperInt[1]));
1070: }
1071: for (PetscInt i = dlim[0 * 2 + 0]; i <= dlim[0 * 2 + 1]; ++i, lp[0] = up[0], up[0] += h[0]) {
1072: const PetscInt box = (k * lbox->n[1] + j) * lbox->n[0] + i;
1073: PetscBool excNeg = PETSC_TRUE;
1074: PetscBool excPos = PETSC_TRUE;
1075: PetscInt NlInt = 0;
1076: PetscInt NuInt = 0;
1078: PetscCall(DMPlexGetPlaneCellIntersection_Internal(dm, c, up, &normal[3 * 0], &upper[0], &upperInt[0], upperIntPoints[0]));
1079: if (debug > 4) {
1080: if (!upperInt[0])
1081: PetscCall(PetscPrintf(PETSC_COMM_SELF, " Cell %" PetscInt_FMT " upper direction 0 (%g, %g, %g) does not intersect %s\n", c, (double)up[0], (double)up[1], cdim > 2 ? (double)up[2] : 0., upper[0] ? "positive" : "negative"));
1082: else PetscCall(PetscPrintf(PETSC_COMM_SELF, " Cell %" PetscInt_FMT " upper direction 0 (%g, %g, %g) intersects %" PetscInt_FMT " times\n", c, (double)up[0], (double)up[1], cdim > 2 ? (double)up[2] : 0., upperInt[0]));
1083: }
1084: for (PetscInt d = 0; d < cdim; ++d) {
1085: NlInt += lowerInt[d];
1086: NuInt += upperInt[d];
1087: }
1088: // If there is no intersection...
1089: if (!NlInt && !NuInt) {
1090: // If the cell is on the negative side of the lower planes, it is not in the box
1091: for (PetscInt d = 0; d < cdim; ++d)
1092: if (lower[d]) {
1093: excNeg = PETSC_FALSE;
1094: break;
1095: }
1096: // If the cell is on the positive side of the upper planes, it is not in the box
1097: for (PetscInt d = 0; d < cdim; ++d)
1098: if (!upper[d]) {
1099: excPos = PETSC_FALSE;
1100: break;
1101: }
1102: if (excNeg || excPos) {
1103: if (debug && excNeg) PetscCall(PetscPrintf(PETSC_COMM_SELF, " Cell %" PetscInt_FMT " is on the negative side of the lower plane\n", c));
1104: if (debug && excPos) PetscCall(PetscPrintf(PETSC_COMM_SELF, " Cell %" PetscInt_FMT " is on the positive side of the upper plane\n", c));
1105: continue;
1106: }
1107: // Otherwise it is in the box
1108: if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, " Cell %" PetscInt_FMT " is contained in box %" PetscInt_FMT "\n", c, box));
1109: PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
1110: continue;
1111: }
1112: /*
1113: If any intersection point is within the box limits, it is in the box
1114: We need to have tolerances here since intersection point calculations can introduce errors
1115: Initialize a count to track which planes have intersection outside the box.
1116: if two adjacent planes have intersection points upper and lower all outside the box, look
1117: first at if another plane has intersection points outside the box, if so, it is inside the cell
1118: look next if no intersection points exist on the other planes, and check if the planes are on the
1119: outside of the intersection points but on opposite ends. If so, the box cuts through the cell.
1120: */
1121: PetscInt outsideCount[6] = {0, 0, 0, 0, 0, 0};
1122: for (PetscInt plane = 0; plane < cdim; ++plane) {
1123: for (PetscInt ip = 0; ip < lowerInt[plane]; ++ip) {
1124: PetscInt d;
1126: for (d = 0; d < cdim; ++d) {
1127: if ((lowerIntPoints[plane][ip * cdim + d] < (lp[d] - PETSC_SMALL)) || (lowerIntPoints[plane][ip * cdim + d] > (up[d] + PETSC_SMALL))) {
1128: if (lowerIntPoints[plane][ip * cdim + d] < (lp[d] - PETSC_SMALL)) outsideCount[d]++; // The lower point is to the left of this box, and we count it
1129: break;
1130: }
1131: }
1132: if (d == cdim) {
1133: if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, " Cell %" PetscInt_FMT " intersected lower plane %" PetscInt_FMT " of box %" PetscInt_FMT "\n", c, plane, box));
1134: PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
1135: goto end;
1136: }
1137: }
1138: for (PetscInt ip = 0; ip < upperInt[plane]; ++ip) {
1139: PetscInt d;
1141: for (d = 0; d < cdim; ++d) {
1142: if ((upperIntPoints[plane][ip * cdim + d] < (lp[d] - PETSC_SMALL)) || (upperIntPoints[plane][ip * cdim + d] > (up[d] + PETSC_SMALL))) {
1143: if (upperIntPoints[plane][ip * cdim + d] > (up[d] + PETSC_SMALL)) outsideCount[cdim + d]++; // The upper point is to the right of this box, and we count it
1144: break;
1145: }
1146: }
1147: if (d == cdim) {
1148: if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, " Cell %" PetscInt_FMT " intersected upper plane %" PetscInt_FMT " of box %" PetscInt_FMT "\n", c, plane, box));
1149: PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
1150: goto end;
1151: }
1152: }
1153: }
1154: /*
1155: Check the planes with intersections
1156: in 2D, check if the square falls in the middle of a cell
1157: ie all four planes have intersection points outside of the box
1158: You do not want to be doing this, because it means your grid hashing is finer than your grid,
1159: but we should still support it I guess
1160: */
1161: if (cdim == 2) {
1162: PetscInt nIntersects = 0;
1163: for (PetscInt d = 0; d < cdim; ++d) nIntersects += (outsideCount[d] + outsideCount[d + cdim]);
1164: // if the count adds up to 8, that means each plane has 2 external intersections and thus it is in the cell
1165: if (nIntersects == 8) {
1166: PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
1167: goto end;
1168: }
1169: }
1170: /*
1171: In 3 dimensions, if two adjacent planes have at least 3 intersections outside the cell in the appropriate direction,
1172: we then check the 3rd planar dimension. If a plane falls between intersection points, the cell belongs to that box.
1173: If the planes are on opposite sides of the intersection points, the cell belongs to that box and it passes through the cell.
1174: */
1175: if (cdim == 3) {
1176: PetscInt faces[3] = {0, 0, 0}, checkInternalFace = 0;
1177: // Find two adjacent planes with at least 3 intersection points in the upper and lower
1178: // if the third plane has 3 intersection points or more, a pyramid base is formed on that plane and it is in the cell
1179: for (PetscInt d = 0; d < cdim; ++d)
1180: if (outsideCount[d] >= 3 && outsideCount[cdim + d] >= 3) {
1181: faces[d]++;
1182: checkInternalFace++;
1183: }
1184: if (checkInternalFace == 3) {
1185: // All planes have 3 intersection points, add it.
1186: PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
1187: goto end;
1188: }
1189: // Gross, figure out which adjacent faces have at least 3 points
1190: PetscInt nonIntersectingFace = -1;
1191: if (faces[0] == faces[1]) nonIntersectingFace = 2;
1192: if (faces[0] == faces[2]) nonIntersectingFace = 1;
1193: if (faces[1] == faces[2]) nonIntersectingFace = 0;
1194: if (nonIntersectingFace >= 0) {
1195: for (PetscInt plane = 0; plane < cdim; ++plane) {
1196: if (!lowerInt[nonIntersectingFace] && !upperInt[nonIntersectingFace]) continue;
1197: // If we have 2 adjacent sides with pyramids of intersection outside of them, and there is a point between the end caps at all, it must be between the two non intersecting ends, and the box is inside the cell.
1198: for (PetscInt ip = 0; ip < lowerInt[nonIntersectingFace]; ++ip) {
1199: if (lowerIntPoints[plane][ip * cdim + nonIntersectingFace] > lp[nonIntersectingFace] - PETSC_SMALL || lowerIntPoints[plane][ip * cdim + nonIntersectingFace] < up[nonIntersectingFace] + PETSC_SMALL) goto setpoint;
1200: }
1201: for (PetscInt ip = 0; ip < upperInt[nonIntersectingFace]; ++ip) {
1202: if (upperIntPoints[plane][ip * cdim + nonIntersectingFace] > lp[nonIntersectingFace] - PETSC_SMALL || upperIntPoints[plane][ip * cdim + nonIntersectingFace] < up[nonIntersectingFace] + PETSC_SMALL) goto setpoint;
1203: }
1204: goto end;
1205: }
1206: // The points are within the bonds of the non intersecting planes, add it.
1207: setpoint:
1208: PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
1209: goto end;
1210: }
1211: }
1212: end:
1213: lower[0] = upper[0];
1214: lowerInt[0] = upperInt[0];
1215: tmp = lowerIntPoints[0];
1216: lowerIntPoints[0] = upperIntPoints[0];
1217: upperIntPoints[0] = tmp;
1218: }
1219: lp[0] = lbox->lower[0] + dlim[0 * 2 + 0] * h[0];
1220: up[0] = lp[0] + h[0];
1221: lower[1] = upper[1];
1222: lowerInt[1] = upperInt[1];
1223: tmp = lowerIntPoints[1];
1224: lowerIntPoints[1] = upperIntPoints[1];
1225: upperIntPoints[1] = tmp;
1226: }
1227: lp[1] = lbox->lower[1] + dlim[1 * 2 + 0] * h[1];
1228: up[1] = lp[1] + h[1];
1229: lower[2] = upper[2];
1230: lowerInt[2] = upperInt[2];
1231: tmp = lowerIntPoints[2];
1232: lowerIntPoints[2] = upperIntPoints[2];
1233: upperIntPoints[2] = tmp;
1234: }
1235: }
1236: PetscCall(PetscFree2(dboxes, boxes));
1238: if (debug) PetscCall(DMLabelView(lbox->cellsSparse, PETSC_VIEWER_STDOUT_SELF));
1239: PetscCall(DMLabelConvertToSection(lbox->cellsSparse, &lbox->cellSection, &lbox->cells));
1240: PetscCall(DMLabelDestroy(&lbox->cellsSparse));
1241: *localBox = lbox;
1242: PetscFunctionReturn(PETSC_SUCCESS);
1243: }
1245: PetscErrorCode DMLocatePoints_Plex(DM dm, Vec v, DMPointLocationType ltype, PetscSF cellSF)
1246: {
1247: PetscInt debug = ((DM_Plex *)dm->data)->printLocate;
1248: DM_Plex *mesh = (DM_Plex *)dm->data;
1249: PetscBool hash = mesh->useHashLocation, reuse = PETSC_FALSE;
1250: PetscInt bs, numPoints, numFound, *found = NULL;
1251: PetscInt cdim, Nl = 0, cStart, cEnd, numCells;
1252: PetscSF sf;
1253: const PetscInt *leaves;
1254: const PetscInt *boxCells;
1255: PetscSFNode *cells;
1256: PetscScalar *a;
1257: PetscMPIInt result;
1258: PetscLogDouble t0, t1;
1259: PetscReal gmin[3], gmax[3];
1260: PetscInt terminating_query_type[] = {0, 0, 0};
1261: PetscMPIInt rank;
1263: PetscFunctionBegin;
1264: PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank));
1265: PetscCall(PetscLogEventBegin(DMPLEX_LocatePoints, 0, 0, 0, 0));
1266: PetscCall(PetscTime(&t0));
1267: PetscCheck(ltype != DM_POINTLOCATION_NEAREST || hash, PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Nearest point location only supported with grid hashing. Use -dm_plex_hash_location to enable it.");
1268: PetscCall(DMGetCoordinateDim(dm, &cdim));
1269: PetscCall(VecGetBlockSize(v, &bs));
1270: PetscCallMPI(MPI_Comm_compare(PetscObjectComm((PetscObject)cellSF), PETSC_COMM_SELF, &result));
1271: PetscCheck(result == MPI_IDENT || result == MPI_CONGRUENT, PetscObjectComm((PetscObject)cellSF), PETSC_ERR_SUP, "Trying parallel point location: only local point location supported");
1272: // We ignore extra coordinates
1273: PetscCheck(bs >= cdim, PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Block size for point vector %" PetscInt_FMT " must be the mesh coordinate dimension %" PetscInt_FMT, bs, cdim);
1274: PetscCall(DMGetCoordinatesLocalSetUp(dm));
1275: PetscCall(DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd));
1276: PetscCall(DMGetPointSF(dm, &sf));
1277: if (sf) PetscCall(PetscSFGetGraph(sf, NULL, &Nl, &leaves, NULL));
1278: Nl = PetscMax(Nl, 0);
1279: PetscCall(VecGetLocalSize(v, &numPoints));
1280: PetscCall(VecGetArray(v, &a));
1281: numPoints /= bs;
1282: {
1283: const PetscSFNode *sf_cells;
1285: PetscCall(PetscSFGetGraph(cellSF, NULL, NULL, NULL, &sf_cells));
1286: if (sf_cells) {
1287: PetscCall(PetscInfo(dm, "[DMLocatePoints_Plex] Re-using existing StarForest node list\n"));
1288: cells = (PetscSFNode *)sf_cells;
1289: reuse = PETSC_TRUE;
1290: } else {
1291: PetscCall(PetscInfo(dm, "[DMLocatePoints_Plex] Creating and initializing new StarForest node list\n"));
1292: PetscCall(PetscMalloc1(numPoints, &cells));
1293: /* initialize cells if created */
1294: for (PetscInt p = 0; p < numPoints; p++) {
1295: cells[p].rank = 0;
1296: cells[p].index = DMLOCATEPOINT_POINT_NOT_FOUND;
1297: }
1298: }
1299: }
1300: PetscCall(DMGetBoundingBox(dm, gmin, gmax));
1301: if (hash) {
1302: if (!mesh->lbox) {
1303: PetscCall(PetscInfo(dm, "Initializing grid hashing\n"));
1304: PetscCall(DMPlexComputeGridHash_Internal(dm, &mesh->lbox));
1305: }
1306: /* Designate the local box for each point */
1307: /* Send points to correct process */
1308: /* Search cells that lie in each subbox */
1309: /* Should we bin points before doing search? */
1310: PetscCall(ISGetIndices(mesh->lbox->cells, &boxCells));
1311: }
1312: numFound = 0;
1313: for (PetscInt p = 0; p < numPoints; ++p) {
1314: const PetscScalar *point = &a[p * bs];
1315: PetscInt dbin[3] = {-1, -1, -1}, bin, cell = -1, cellOffset;
1316: PetscBool point_outside_domain = PETSC_FALSE;
1318: /* check bounding box of domain */
1319: for (PetscInt d = 0; d < cdim; d++) {
1320: if (PetscRealPart(point[d]) < gmin[d]) {
1321: point_outside_domain = PETSC_TRUE;
1322: break;
1323: }
1324: if (PetscRealPart(point[d]) > gmax[d]) {
1325: point_outside_domain = PETSC_TRUE;
1326: break;
1327: }
1328: }
1329: if (point_outside_domain) {
1330: cells[p].rank = 0;
1331: cells[p].index = DMLOCATEPOINT_POINT_NOT_FOUND;
1332: terminating_query_type[0]++;
1333: continue;
1334: }
1336: /* check initial values in cells[].index - abort early if found */
1337: if (cells[p].index != DMLOCATEPOINT_POINT_NOT_FOUND) {
1338: PetscInt c = cells[p].index;
1340: cells[p].index = DMLOCATEPOINT_POINT_NOT_FOUND;
1341: PetscCall(DMPlexLocatePoint_Internal(dm, cdim, point, c, &cell));
1342: if (cell >= 0) {
1343: cells[p].rank = 0;
1344: cells[p].index = cell;
1345: numFound++;
1346: }
1347: }
1348: if (cells[p].index != DMLOCATEPOINT_POINT_NOT_FOUND) {
1349: terminating_query_type[1]++;
1350: continue;
1351: }
1353: if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, "[%d]Checking point %" PetscInt_FMT " (%.2g, %.2g, %.2g)\n", rank, p, (double)PetscRealPart(point[0]), (double)PetscRealPart(point[1]), cdim > 2 ? (double)PetscRealPart(point[2]) : 0.));
1354: if (hash) {
1355: PetscBool found_box;
1357: /* allow for case that point is outside box - abort early */
1358: PetscCall(PetscGridHashGetEnclosingBoxQuery(mesh->lbox, mesh->lbox->cellSection, 1, point, dbin, &bin, &found_box));
1359: if (found_box) {
1360: if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, "[%d] Found point in box %" PetscInt_FMT " (%" PetscInt_FMT ", %" PetscInt_FMT ", %" PetscInt_FMT ")\n", rank, bin, dbin[0], dbin[1], cdim > 2 ? dbin[2] : 0));
1361: /* TODO Lay an interface over this so we can switch between Section (dense) and Label (sparse) */
1362: PetscCall(PetscSectionGetDof(mesh->lbox->cellSection, bin, &numCells));
1363: PetscCall(PetscSectionGetOffset(mesh->lbox->cellSection, bin, &cellOffset));
1364: for (PetscInt c = cellOffset; c < cellOffset + numCells; ++c) {
1365: if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, "[%d] Checking for point in cell %" PetscInt_FMT "\n", rank, boxCells[c]));
1366: PetscCall(DMPlexLocatePoint_Internal(dm, cdim, point, boxCells[c], &cell));
1367: if (cell >= 0) {
1368: if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, "[%d] FOUND in cell %" PetscInt_FMT "\n", rank, cell));
1369: cells[p].rank = 0;
1370: cells[p].index = cell;
1371: numFound++;
1372: terminating_query_type[2]++;
1373: break;
1374: }
1375: }
1376: }
1377: } else {
1378: PetscBool found = PETSC_FALSE;
1379: for (PetscInt c = cStart; c < cEnd; ++c) {
1380: PetscInt idx;
1382: PetscCall(PetscFindInt(c, Nl, leaves, &idx));
1383: if (idx >= 0) continue;
1384: PetscCall(DMPlexLocatePoint_Internal(dm, cdim, point, c, &cell));
1385: if (cell >= 0) {
1386: cells[p].rank = 0;
1387: cells[p].index = cell;
1388: numFound++;
1389: terminating_query_type[2]++;
1390: found = PETSC_TRUE;
1391: break;
1392: }
1393: }
1394: if (!found) terminating_query_type[0]++;
1395: }
1396: }
1397: if (hash) PetscCall(ISRestoreIndices(mesh->lbox->cells, &boxCells));
1398: if (ltype == DM_POINTLOCATION_NEAREST && hash && numFound < numPoints) {
1399: for (PetscInt p = 0; p < numPoints; p++) {
1400: const PetscScalar *point = &a[p * bs];
1401: PetscReal cpoint[3] = {0, 0, 0}, diff[3], best[3] = {PETSC_MAX_REAL, PETSC_MAX_REAL, PETSC_MAX_REAL}, dist, distMax = PETSC_MAX_REAL;
1402: PetscInt dbin[3] = {-1, -1, -1}, bin, cellOffset, bestc = -1;
1404: if (cells[p].index < 0) {
1405: PetscCall(PetscGridHashGetEnclosingBox(mesh->lbox, 1, point, dbin, &bin));
1406: PetscCall(PetscSectionGetDof(mesh->lbox->cellSection, bin, &numCells));
1407: PetscCall(PetscSectionGetOffset(mesh->lbox->cellSection, bin, &cellOffset));
1408: for (PetscInt c = cellOffset; c < cellOffset + numCells; ++c) {
1409: PetscCall(DMPlexClosestPoint_Internal(dm, cdim, point, boxCells[c], cpoint));
1410: for (PetscInt d = 0; d < cdim; ++d) diff[d] = cpoint[d] - PetscRealPart(point[d]);
1411: dist = DMPlex_NormD_Internal(cdim, diff);
1412: if (dist < distMax) {
1413: for (PetscInt d = 0; d < cdim; ++d) best[d] = cpoint[d];
1414: bestc = boxCells[c];
1415: distMax = dist;
1416: }
1417: }
1418: if (distMax < PETSC_MAX_REAL) {
1419: ++numFound;
1420: cells[p].rank = 0;
1421: cells[p].index = bestc;
1422: for (PetscInt d = 0; d < cdim; ++d) a[p * bs + d] = best[d];
1423: }
1424: }
1425: }
1426: }
1427: /* This code is only be relevant when interfaced to parallel point location */
1428: /* Check for highest numbered proc that claims a point (do we care?) */
1429: if (ltype == DM_POINTLOCATION_REMOVE && numFound < numPoints) {
1430: PetscCall(PetscMalloc1(numFound, &found));
1431: numFound = 0;
1432: for (PetscInt p = 0; p < numPoints; p++) {
1433: if (cells[p].rank >= 0 && cells[p].index >= 0) {
1434: if (numFound < p) cells[numFound] = cells[p];
1435: found[numFound++] = p;
1436: }
1437: }
1438: }
1439: PetscCall(VecRestoreArray(v, &a));
1440: if (!reuse) PetscCall(PetscSFSetGraph(cellSF, cEnd - cStart, numFound, found, PETSC_OWN_POINTER, cells, PETSC_OWN_POINTER));
1441: PetscCall(PetscTime(&t1));
1442: if (hash) {
1443: PetscCall(PetscInfo(dm, "[DMLocatePoints_Plex] terminating_query_type : %" PetscInt_FMT " [outside domain] : %" PetscInt_FMT " [inside initial cell] : %" PetscInt_FMT " [hash]\n", terminating_query_type[0], terminating_query_type[1], terminating_query_type[2]));
1444: } else {
1445: PetscCall(PetscInfo(dm, "[DMLocatePoints_Plex] terminating_query_type : %" PetscInt_FMT " [outside domain] : %" PetscInt_FMT " [inside initial cell] : %" PetscInt_FMT " [brute-force]\n", terminating_query_type[0], terminating_query_type[1], terminating_query_type[2]));
1446: }
1447: PetscCall(PetscInfo(dm, "[DMLocatePoints_Plex] npoints %" PetscInt_FMT " : time(rank0) %1.2e (sec): points/sec %1.4e\n", numPoints, t1 - t0, numPoints / (t1 - t0)));
1448: PetscCall(PetscLogEventEnd(DMPLEX_LocatePoints, 0, 0, 0, 0));
1449: PetscFunctionReturn(PETSC_SUCCESS);
1450: }
1452: /*@
1453: DMPlexComputeProjection2Dto1D - Rewrite coordinates to be the 1D projection of the 2D coordinates
1455: Not Collective
1457: Input/Output Parameter:
1458: . coords - The coordinates of a segment, on output the new y-coordinate, and 0 for x, an array of size 4, last two entries are unchanged
1460: Output Parameter:
1461: . R - The rotation which accomplishes the projection, array of size 4
1463: Level: developer
1465: .seealso: `DMPLEX`, `DMPlexComputeProjection3Dto1D()`, `DMPlexComputeProjection3Dto2D()`
1466: @*/
1467: PetscErrorCode DMPlexComputeProjection2Dto1D(PetscScalar coords[], PetscReal R[])
1468: {
1469: const PetscReal x = PetscRealPart(coords[2] - coords[0]);
1470: const PetscReal y = PetscRealPart(coords[3] - coords[1]);
1471: const PetscReal r = PetscSqrtReal(x * x + y * y), c = x / r, s = y / r;
1473: PetscFunctionBegin;
1474: R[0] = c;
1475: R[1] = -s;
1476: R[2] = s;
1477: R[3] = c;
1478: coords[0] = 0.0;
1479: coords[1] = r;
1480: PetscFunctionReturn(PETSC_SUCCESS);
1481: }
1483: /*@
1484: DMPlexComputeProjection3Dto1D - Rewrite coordinates to be the 1D projection of the 3D coordinates
1486: Not Collective
1488: Input/Output Parameter:
1489: . coords - The coordinates of a segment; on output, the new y-coordinate, and 0 for x and z, an array of size 6, the other entries are unchanged
1491: Output Parameter:
1492: . R - The rotation which accomplishes the projection, an array of size 9
1494: Level: developer
1496: Note:
1497: This uses the basis completion described by Frisvad {cite}`frisvad2012building`
1499: .seealso: `DMPLEX`, `DMPlexComputeProjection2Dto1D()`, `DMPlexComputeProjection3Dto2D()`
1500: @*/
1501: PetscErrorCode DMPlexComputeProjection3Dto1D(PetscScalar coords[], PetscReal R[])
1502: {
1503: PetscReal x = PetscRealPart(coords[3] - coords[0]);
1504: PetscReal y = PetscRealPart(coords[4] - coords[1]);
1505: PetscReal z = PetscRealPart(coords[5] - coords[2]);
1506: PetscReal r = PetscSqrtReal(x * x + y * y + z * z);
1507: PetscReal rinv = 1. / r;
1509: PetscFunctionBegin;
1510: x *= rinv;
1511: y *= rinv;
1512: z *= rinv;
1513: if (x > 0.) {
1514: PetscReal inv1pX = 1. / (1. + x);
1516: R[0] = x;
1517: R[1] = -y;
1518: R[2] = -z;
1519: R[3] = y;
1520: R[4] = 1. - y * y * inv1pX;
1521: R[5] = -y * z * inv1pX;
1522: R[6] = z;
1523: R[7] = -y * z * inv1pX;
1524: R[8] = 1. - z * z * inv1pX;
1525: } else {
1526: PetscReal inv1mX = 1. / (1. - x);
1528: R[0] = x;
1529: R[1] = z;
1530: R[2] = y;
1531: R[3] = y;
1532: R[4] = -y * z * inv1mX;
1533: R[5] = 1. - y * y * inv1mX;
1534: R[6] = z;
1535: R[7] = 1. - z * z * inv1mX;
1536: R[8] = -y * z * inv1mX;
1537: }
1538: coords[0] = 0.0;
1539: coords[1] = r;
1540: coords[2] = 0.0;
1541: PetscFunctionReturn(PETSC_SUCCESS);
1542: }
1544: /*@
1545: DMPlexComputeProjection3Dto2D - Rewrite coordinates of 3 or more coplanar 3D points to a common 2D basis for the
1546: plane. The normal is defined by positive orientation of the first 3 points.
1548: Not Collective
1550: Input Parameter:
1551: . coordSize - Length of coordinate array (3x number of points); must be at least 9 (3 points)
1553: Input/Output Parameter:
1554: . coords - The interlaced coordinates of each coplanar 3D point; on output the first
1555: 2*coordSize/3 entries contain interlaced 2D points, with the rest undefined
1557: Output Parameter:
1558: . R - 3x3 row-major rotation matrix whose columns are the tangent basis [t1, t2, n]. Multiplying by R^T transforms from original frame to tangent frame.
1560: Level: developer
1562: .seealso: `DMPLEX`, `DMPlexComputeProjection2Dto1D()`, `DMPlexComputeProjection3Dto1D()`
1563: @*/
1564: PetscErrorCode DMPlexComputeProjection3Dto2D(PetscInt coordSize, PetscScalar coords[], PetscReal R[])
1565: {
1566: PetscReal x1[3], x2[3], n[3], c[3], norm;
1567: const PetscInt dim = 3;
1568: PetscInt d, p;
1570: PetscFunctionBegin;
1571: /* 0) Calculate normal vector */
1572: for (d = 0; d < dim; ++d) {
1573: x1[d] = PetscRealPart(coords[1 * dim + d] - coords[0 * dim + d]);
1574: x2[d] = PetscRealPart(coords[2 * dim + d] - coords[0 * dim + d]);
1575: }
1576: // n = x1 \otimes x2
1577: n[0] = x1[1] * x2[2] - x1[2] * x2[1];
1578: n[1] = x1[2] * x2[0] - x1[0] * x2[2];
1579: n[2] = x1[0] * x2[1] - x1[1] * x2[0];
1580: norm = PetscSqrtReal(n[0] * n[0] + n[1] * n[1] + n[2] * n[2]);
1581: for (d = 0; d < dim; d++) n[d] /= norm;
1582: norm = PetscSqrtReal(x1[0] * x1[0] + x1[1] * x1[1] + x1[2] * x1[2]);
1583: for (d = 0; d < dim; d++) x1[d] /= norm;
1584: // x2 = n \otimes x1
1585: x2[0] = n[1] * x1[2] - n[2] * x1[1];
1586: x2[1] = n[2] * x1[0] - n[0] * x1[2];
1587: x2[2] = n[0] * x1[1] - n[1] * x1[0];
1588: for (d = 0; d < dim; d++) {
1589: R[d * dim + 0] = x1[d];
1590: R[d * dim + 1] = x2[d];
1591: R[d * dim + 2] = n[d];
1592: c[d] = PetscRealPart(coords[0 * dim + d]);
1593: }
1594: for (p = 0; p < coordSize / dim; p++) {
1595: PetscReal y[3];
1596: for (d = 0; d < dim; d++) y[d] = PetscRealPart(coords[p * dim + d]) - c[d];
1597: for (d = 0; d < 2; d++) coords[p * 2 + d] = R[0 * dim + d] * y[0] + R[1 * dim + d] * y[1] + R[2 * dim + d] * y[2];
1598: }
1599: PetscFunctionReturn(PETSC_SUCCESS);
1600: }
1602: PETSC_UNUSED static inline void Volume_Triangle_Internal(PetscReal *vol, PetscReal coords[])
1603: {
1604: /* Signed volume is 1/2 the determinant
1606: | 1 1 1 |
1607: | x0 x1 x2 |
1608: | y0 y1 y2 |
1610: but if x0,y0 is the origin, we have
1612: | x1 x2 |
1613: | y1 y2 |
1614: */
1615: const PetscReal x1 = coords[2] - coords[0], y1 = coords[3] - coords[1];
1616: const PetscReal x2 = coords[4] - coords[0], y2 = coords[5] - coords[1];
1617: PetscReal M[4], detM;
1618: M[0] = x1;
1619: M[1] = x2;
1620: M[2] = y1;
1621: M[3] = y2;
1622: DMPlex_Det2D_Internal(&detM, M);
1623: *vol = 0.5 * detM;
1624: (void)PetscLogFlops(5.0);
1625: }
1627: PETSC_UNUSED static inline void Volume_Tetrahedron_Internal(PetscReal *vol, PetscReal coords[])
1628: {
1629: /* Signed volume is 1/6th of the determinant
1631: | 1 1 1 1 |
1632: | x0 x1 x2 x3 |
1633: | y0 y1 y2 y3 |
1634: | z0 z1 z2 z3 |
1636: but if x0,y0,z0 is the origin, we have
1638: | x1 x2 x3 |
1639: | y1 y2 y3 |
1640: | z1 z2 z3 |
1641: */
1642: const PetscReal x1 = coords[3] - coords[0], y1 = coords[4] - coords[1], z1 = coords[5] - coords[2];
1643: const PetscReal x2 = coords[6] - coords[0], y2 = coords[7] - coords[1], z2 = coords[8] - coords[2];
1644: const PetscReal x3 = coords[9] - coords[0], y3 = coords[10] - coords[1], z3 = coords[11] - coords[2];
1645: const PetscReal onesixth = ((PetscReal)1. / (PetscReal)6.);
1646: PetscReal M[9], detM;
1647: M[0] = x1;
1648: M[1] = x2;
1649: M[2] = x3;
1650: M[3] = y1;
1651: M[4] = y2;
1652: M[5] = y3;
1653: M[6] = z1;
1654: M[7] = z2;
1655: M[8] = z3;
1656: DMPlex_Det3D_Internal(&detM, M);
1657: *vol = -onesixth * detM;
1658: (void)PetscLogFlops(10.0);
1659: }
1661: static inline void Volume_Tetrahedron_Origin_Internal(PetscReal *vol, PetscReal coords[])
1662: {
1663: const PetscReal onesixth = ((PetscReal)1. / (PetscReal)6.);
1664: DMPlex_Det3D_Internal(vol, coords);
1665: *vol *= -onesixth;
1666: }
1668: static PetscErrorCode DMPlexComputePointGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1669: {
1670: PetscSection coordSection;
1671: Vec coordinates;
1672: const PetscScalar *coords;
1673: PetscInt dim, d, off;
1675: PetscFunctionBegin;
1676: PetscCall(DMGetCoordinatesLocal(dm, &coordinates));
1677: PetscCall(DMGetCoordinateSection(dm, &coordSection));
1678: PetscCall(PetscSectionGetDof(coordSection, e, &dim));
1679: if (!dim) PetscFunctionReturn(PETSC_SUCCESS);
1680: PetscCall(PetscSectionGetOffset(coordSection, e, &off));
1681: PetscCall(VecGetArrayRead(coordinates, &coords));
1682: if (v0) {
1683: for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[off + d]);
1684: }
1685: PetscCall(VecRestoreArrayRead(coordinates, &coords));
1686: *detJ = 1.;
1687: if (J) {
1688: for (d = 0; d < dim * dim; d++) J[d] = 0.;
1689: for (d = 0; d < dim; d++) J[d * dim + d] = 1.;
1690: if (invJ) {
1691: for (d = 0; d < dim * dim; d++) invJ[d] = 0.;
1692: for (d = 0; d < dim; d++) invJ[d * dim + d] = 1.;
1693: }
1694: }
1695: PetscFunctionReturn(PETSC_SUCCESS);
1696: }
1698: /*@C
1699: DMPlexGetCellCoordinates - Get coordinates for a cell, taking into account periodicity
1701: Not Collective
1703: Input Parameters:
1704: + dm - The `DMPLEX`
1705: - cell - The cell number
1707: Output Parameters:
1708: + isDG - Using cellwise coordinates
1709: . Nc - The number of coordinates
1710: . array - The coordinate array
1711: - coords - The cell coordinates
1713: Level: developer
1715: .seealso: `DMPLEX`, `DMPlexRestoreCellCoordinates()`, `DMGetCoordinatesLocal()`, `DMGetCellCoordinatesLocal()`
1716: @*/
1717: PetscErrorCode DMPlexGetCellCoordinates(DM dm, PetscInt cell, PetscBool *isDG, PetscInt *Nc, const PetscScalar *array[], PetscScalar *coords[])
1718: {
1719: DM cdm;
1720: Vec coordinates;
1721: PetscSection cs;
1722: const PetscScalar *ccoords;
1723: PetscInt pStart, pEnd;
1725: PetscFunctionBeginHot;
1726: *isDG = PETSC_FALSE;
1727: *Nc = 0;
1728: *array = NULL;
1729: *coords = NULL;
1730: /* Check for cellwise coordinates */
1731: PetscCall(DMGetCellCoordinateSection(dm, &cs));
1732: if (!cs) goto cg;
1733: /* Check that the cell exists in the cellwise section */
1734: PetscCall(PetscSectionGetChart(cs, &pStart, &pEnd));
1735: if (cell < pStart || cell >= pEnd) goto cg;
1736: /* Check for cellwise coordinates for this cell */
1737: PetscCall(PetscSectionGetDof(cs, cell, Nc));
1738: if (!*Nc) goto cg;
1739: /* Check for cellwise coordinates */
1740: PetscCall(DMGetCellCoordinatesLocalNoncollective(dm, &coordinates));
1741: if (!coordinates) goto cg;
1742: /* Get cellwise coordinates */
1743: PetscCall(DMGetCellCoordinateDM(dm, &cdm));
1744: PetscCall(VecGetArrayRead(coordinates, array));
1745: PetscCall(DMPlexPointLocalRead(cdm, cell, *array, &ccoords));
1746: PetscCall(DMGetWorkArray(cdm, *Nc, MPIU_SCALAR, coords));
1747: PetscCall(PetscArraycpy(*coords, ccoords, *Nc));
1748: PetscCall(VecRestoreArrayRead(coordinates, array));
1749: *isDG = PETSC_TRUE;
1750: PetscFunctionReturn(PETSC_SUCCESS);
1751: cg:
1752: /* Use continuous coordinates */
1753: PetscCall(DMGetCoordinateDM(dm, &cdm));
1754: PetscCall(DMGetCoordinateSection(dm, &cs));
1755: PetscCall(DMGetCoordinatesLocalNoncollective(dm, &coordinates));
1756: PetscCall(DMPlexVecGetOrientedClosure_Internal(cdm, cs, PETSC_FALSE, coordinates, cell, 0, Nc, coords));
1757: PetscFunctionReturn(PETSC_SUCCESS);
1758: }
1760: /*@C
1761: DMPlexRestoreCellCoordinates - Get coordinates for a cell, taking into account periodicity
1763: Not Collective
1765: Input Parameters:
1766: + dm - The `DMPLEX`
1767: - cell - The cell number
1769: Output Parameters:
1770: + isDG - Using cellwise coordinates
1771: . Nc - The number of coordinates
1772: . array - The coordinate array
1773: - coords - The cell coordinates
1775: Level: developer
1777: .seealso: `DMPLEX`, `DMPlexGetCellCoordinates()`, `DMGetCoordinatesLocal()`, `DMGetCellCoordinatesLocal()`
1778: @*/
1779: PetscErrorCode DMPlexRestoreCellCoordinates(DM dm, PetscInt cell, PetscBool *isDG, PetscInt *Nc, const PetscScalar *array[], PetscScalar *coords[])
1780: {
1781: DM cdm;
1782: PetscSection cs;
1783: Vec coordinates;
1785: PetscFunctionBeginHot;
1786: if (*isDG) {
1787: PetscCall(DMGetCellCoordinateDM(dm, &cdm));
1788: PetscCall(DMRestoreWorkArray(cdm, *Nc, MPIU_SCALAR, coords));
1789: } else {
1790: PetscCall(DMGetCoordinateDM(dm, &cdm));
1791: PetscCall(DMGetCoordinateSection(dm, &cs));
1792: PetscCall(DMGetCoordinatesLocalNoncollective(dm, &coordinates));
1793: PetscCall(DMPlexVecRestoreClosure(cdm, cs, coordinates, cell, Nc, coords));
1794: }
1795: PetscFunctionReturn(PETSC_SUCCESS);
1796: }
1798: static PetscErrorCode DMPlexComputeLineGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1799: {
1800: const PetscScalar *array;
1801: PetscScalar *coords = NULL;
1802: PetscInt numCoords, d;
1803: PetscBool isDG;
1805: PetscFunctionBegin;
1806: PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
1807: PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
1808: *detJ = 0.0;
1809: if (numCoords == 6) {
1810: const PetscInt dim = 3;
1811: PetscReal R[9], J0;
1813: if (v0) {
1814: for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
1815: }
1816: PetscCall(DMPlexComputeProjection3Dto1D(coords, R));
1817: if (J) {
1818: J0 = 0.5 * PetscRealPart(coords[1]);
1819: J[0] = R[0] * J0;
1820: J[1] = R[1];
1821: J[2] = R[2];
1822: J[3] = R[3] * J0;
1823: J[4] = R[4];
1824: J[5] = R[5];
1825: J[6] = R[6] * J0;
1826: J[7] = R[7];
1827: J[8] = R[8];
1828: DMPlex_Det3D_Internal(detJ, J);
1829: if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
1830: }
1831: } else if (numCoords == 4) {
1832: const PetscInt dim = 2;
1833: PetscReal R[4], J0;
1835: if (v0) {
1836: for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
1837: }
1838: PetscCall(DMPlexComputeProjection2Dto1D(coords, R));
1839: if (J) {
1840: J0 = 0.5 * PetscRealPart(coords[1]);
1841: J[0] = R[0] * J0;
1842: J[1] = R[1];
1843: J[2] = R[2] * J0;
1844: J[3] = R[3];
1845: DMPlex_Det2D_Internal(detJ, J);
1846: if (invJ) DMPlex_Invert2D_Internal(invJ, J, *detJ);
1847: }
1848: } else if (numCoords == 2) {
1849: const PetscInt dim = 1;
1851: if (v0) {
1852: for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
1853: }
1854: if (J) {
1855: J[0] = 0.5 * (PetscRealPart(coords[1]) - PetscRealPart(coords[0]));
1856: *detJ = J[0];
1857: PetscCall(PetscLogFlops(2.0));
1858: if (invJ) {
1859: invJ[0] = 1.0 / J[0];
1860: PetscCall(PetscLogFlops(1.0));
1861: }
1862: }
1863: } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for segment %" PetscInt_FMT " is %" PetscInt_FMT " != 2 or 4 or 6", e, numCoords);
1864: PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
1865: PetscFunctionReturn(PETSC_SUCCESS);
1866: }
1868: static PetscErrorCode DMPlexComputeTriangleGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1869: {
1870: const PetscScalar *array;
1871: PetscScalar *coords = NULL;
1872: PetscInt numCoords, d;
1873: PetscBool isDG;
1875: PetscFunctionBegin;
1876: PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
1877: PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
1878: *detJ = 0.0;
1879: if (numCoords == 9) {
1880: const PetscInt dim = 3;
1881: PetscReal R[9], J0[9] = {1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0};
1883: if (v0) {
1884: for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
1885: }
1886: PetscCall(DMPlexComputeProjection3Dto2D(numCoords, coords, R));
1887: if (J) {
1888: const PetscInt pdim = 2;
1890: for (d = 0; d < pdim; d++) {
1891: for (PetscInt f = 0; f < pdim; f++) J0[d * dim + f] = 0.5 * (PetscRealPart(coords[(f + 1) * pdim + d]) - PetscRealPart(coords[0 * pdim + d]));
1892: }
1893: PetscCall(PetscLogFlops(8.0));
1894: DMPlex_Det3D_Internal(detJ, J0);
1895: for (d = 0; d < dim; d++) {
1896: for (PetscInt f = 0; f < dim; f++) {
1897: J[d * dim + f] = 0.0;
1898: for (PetscInt g = 0; g < dim; g++) J[d * dim + f] += R[d * dim + g] * J0[g * dim + f];
1899: }
1900: }
1901: PetscCall(PetscLogFlops(18.0));
1902: }
1903: if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
1904: } else if (numCoords == 6) {
1905: const PetscInt dim = 2;
1907: if (v0) {
1908: for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
1909: }
1910: if (J) {
1911: for (d = 0; d < dim; d++) {
1912: for (PetscInt f = 0; f < dim; f++) J[d * dim + f] = 0.5 * (PetscRealPart(coords[(f + 1) * dim + d]) - PetscRealPart(coords[0 * dim + d]));
1913: }
1914: PetscCall(PetscLogFlops(8.0));
1915: DMPlex_Det2D_Internal(detJ, J);
1916: }
1917: if (invJ) DMPlex_Invert2D_Internal(invJ, J, *detJ);
1918: } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this triangle is %" PetscInt_FMT " != 6 or 9", numCoords);
1919: PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
1920: PetscFunctionReturn(PETSC_SUCCESS);
1921: }
1923: static PetscErrorCode DMPlexComputeRectangleGeometry_Internal(DM dm, PetscInt e, PetscBool isTensor, PetscInt Nq, const PetscReal points[], PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1924: {
1925: const PetscScalar *array;
1926: PetscScalar *coords = NULL;
1927: PetscInt numCoords, d;
1928: PetscBool isDG;
1930: PetscFunctionBegin;
1931: PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
1932: PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
1933: if (!Nq) {
1934: PetscInt vorder[4] = {0, 1, 2, 3};
1936: if (isTensor) {
1937: vorder[2] = 3;
1938: vorder[3] = 2;
1939: }
1940: *detJ = 0.0;
1941: if (numCoords == 12) {
1942: const PetscInt dim = 3;
1943: PetscReal R[9], J0[9] = {1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0};
1945: if (v) {
1946: for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);
1947: }
1948: PetscCall(DMPlexComputeProjection3Dto2D(numCoords, coords, R));
1949: if (J) {
1950: const PetscInt pdim = 2;
1952: for (d = 0; d < pdim; d++) {
1953: J0[d * dim + 0] = 0.5 * (PetscRealPart(coords[vorder[1] * pdim + d]) - PetscRealPart(coords[vorder[0] * pdim + d]));
1954: J0[d * dim + 1] = 0.5 * (PetscRealPart(coords[vorder[2] * pdim + d]) - PetscRealPart(coords[vorder[1] * pdim + d]));
1955: }
1956: PetscCall(PetscLogFlops(8.0));
1957: DMPlex_Det3D_Internal(detJ, J0);
1958: for (d = 0; d < dim; d++) {
1959: for (PetscInt f = 0; f < dim; f++) {
1960: J[d * dim + f] = 0.0;
1961: for (PetscInt g = 0; g < dim; g++) J[d * dim + f] += R[d * dim + g] * J0[g * dim + f];
1962: }
1963: }
1964: PetscCall(PetscLogFlops(18.0));
1965: }
1966: if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
1967: } else if (numCoords == 8) {
1968: const PetscInt dim = 2;
1970: if (v) {
1971: for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);
1972: }
1973: if (J) {
1974: for (d = 0; d < dim; d++) {
1975: J[d * dim + 0] = 0.5 * (PetscRealPart(coords[vorder[1] * dim + d]) - PetscRealPart(coords[vorder[0] * dim + d]));
1976: J[d * dim + 1] = 0.5 * (PetscRealPart(coords[vorder[3] * dim + d]) - PetscRealPart(coords[vorder[0] * dim + d]));
1977: }
1978: PetscCall(PetscLogFlops(8.0));
1979: DMPlex_Det2D_Internal(detJ, J);
1980: }
1981: if (invJ) DMPlex_Invert2D_Internal(invJ, J, *detJ);
1982: } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this quadrilateral is %" PetscInt_FMT " != 8 or 12", numCoords);
1983: } else {
1984: const PetscInt Nv = 4;
1985: const PetscInt dimR = 2;
1986: PetscInt zToPlex[4] = {0, 1, 3, 2};
1987: PetscReal zOrder[12];
1988: PetscReal zCoeff[12];
1989: PetscInt i, j, k, l, dim;
1991: if (isTensor) {
1992: zToPlex[2] = 2;
1993: zToPlex[3] = 3;
1994: }
1995: if (numCoords == 12) {
1996: dim = 3;
1997: } else if (numCoords == 8) {
1998: dim = 2;
1999: } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this quadrilateral is %" PetscInt_FMT " != 8 or 12", numCoords);
2000: for (i = 0; i < Nv; i++) {
2001: PetscInt zi = zToPlex[i];
2003: for (j = 0; j < dim; j++) zOrder[dim * i + j] = PetscRealPart(coords[dim * zi + j]);
2004: }
2005: for (j = 0; j < dim; j++) {
2006: /* Nodal basis for evaluation at the vertices: (1 \mp xi) (1 \mp eta):
2007: \phi^0 = (1 - xi - eta + xi eta) --> 1 = 1/4 ( \phi^0 + \phi^1 + \phi^2 + \phi^3)
2008: \phi^1 = (1 + xi - eta - xi eta) --> xi = 1/4 (-\phi^0 + \phi^1 - \phi^2 + \phi^3)
2009: \phi^2 = (1 - xi + eta - xi eta) --> eta = 1/4 (-\phi^0 - \phi^1 + \phi^2 + \phi^3)
2010: \phi^3 = (1 + xi + eta + xi eta) --> xi eta = 1/4 ( \phi^0 - \phi^1 - \phi^2 + \phi^3)
2011: */
2012: zCoeff[dim * 0 + j] = 0.25 * (zOrder[dim * 0 + j] + zOrder[dim * 1 + j] + zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
2013: zCoeff[dim * 1 + j] = 0.25 * (-zOrder[dim * 0 + j] + zOrder[dim * 1 + j] - zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
2014: zCoeff[dim * 2 + j] = 0.25 * (-zOrder[dim * 0 + j] - zOrder[dim * 1 + j] + zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
2015: zCoeff[dim * 3 + j] = 0.25 * (zOrder[dim * 0 + j] - zOrder[dim * 1 + j] - zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
2016: }
2017: for (i = 0; i < Nq; i++) {
2018: PetscReal xi = points[dimR * i], eta = points[dimR * i + 1];
2020: if (v) {
2021: PetscReal extPoint[4];
2023: extPoint[0] = 1.;
2024: extPoint[1] = xi;
2025: extPoint[2] = eta;
2026: extPoint[3] = xi * eta;
2027: for (j = 0; j < dim; j++) {
2028: PetscReal val = 0.;
2030: for (k = 0; k < Nv; k++) val += extPoint[k] * zCoeff[dim * k + j];
2031: v[i * dim + j] = val;
2032: }
2033: }
2034: if (J) {
2035: PetscReal extJ[8];
2037: extJ[0] = 0.;
2038: extJ[1] = 0.;
2039: extJ[2] = 1.;
2040: extJ[3] = 0.;
2041: extJ[4] = 0.;
2042: extJ[5] = 1.;
2043: extJ[6] = eta;
2044: extJ[7] = xi;
2045: for (j = 0; j < dim; j++) {
2046: for (k = 0; k < dimR; k++) {
2047: PetscReal val = 0.;
2049: for (l = 0; l < Nv; l++) val += zCoeff[dim * l + j] * extJ[dimR * l + k];
2050: J[i * dim * dim + dim * j + k] = val;
2051: }
2052: }
2053: if (dim == 3) { /* put the cross product in the third component of the Jacobian */
2054: PetscReal x, y, z;
2055: PetscReal *iJ = &J[i * dim * dim];
2056: PetscReal norm;
2058: x = iJ[1 * dim + 0] * iJ[2 * dim + 1] - iJ[1 * dim + 1] * iJ[2 * dim + 0];
2059: y = iJ[0 * dim + 1] * iJ[2 * dim + 0] - iJ[0 * dim + 0] * iJ[2 * dim + 1];
2060: z = iJ[0 * dim + 0] * iJ[1 * dim + 1] - iJ[0 * dim + 1] * iJ[1 * dim + 0];
2061: norm = PetscSqrtReal(x * x + y * y + z * z);
2062: iJ[2] = x / norm;
2063: iJ[5] = y / norm;
2064: iJ[8] = z / norm;
2065: DMPlex_Det3D_Internal(&detJ[i], &J[i * dim * dim]);
2066: if (invJ) DMPlex_Invert3D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);
2067: } else {
2068: DMPlex_Det2D_Internal(&detJ[i], &J[i * dim * dim]);
2069: if (invJ) DMPlex_Invert2D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);
2070: }
2071: }
2072: }
2073: }
2074: PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
2075: PetscFunctionReturn(PETSC_SUCCESS);
2076: }
2078: static PetscErrorCode DMPlexComputeTetrahedronGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
2079: {
2080: const PetscScalar *array;
2081: PetscScalar *coords = NULL;
2082: const PetscInt dim = 3;
2083: PetscInt numCoords, d;
2084: PetscBool isDG;
2086: PetscFunctionBegin;
2087: PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
2088: PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
2089: *detJ = 0.0;
2090: if (v0) {
2091: for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
2092: }
2093: if (J) {
2094: for (d = 0; d < dim; d++) {
2095: /* I orient with outward face normals */
2096: J[d * dim + 0] = 0.5 * (PetscRealPart(coords[2 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2097: J[d * dim + 1] = 0.5 * (PetscRealPart(coords[1 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2098: J[d * dim + 2] = 0.5 * (PetscRealPart(coords[3 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2099: }
2100: PetscCall(PetscLogFlops(18.0));
2101: DMPlex_Det3D_Internal(detJ, J);
2102: }
2103: if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
2104: PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
2105: PetscFunctionReturn(PETSC_SUCCESS);
2106: }
2108: static PetscErrorCode DMPlexComputeHexahedronGeometry_Internal(DM dm, PetscInt e, PetscInt Nq, const PetscReal points[], PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
2109: {
2110: const PetscScalar *array;
2111: PetscScalar *coords = NULL;
2112: const PetscInt dim = 3;
2113: PetscInt numCoords, d;
2114: PetscBool isDG;
2116: PetscFunctionBegin;
2117: PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
2118: PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
2119: if (!Nq) {
2120: *detJ = 0.0;
2121: if (v) {
2122: for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);
2123: }
2124: if (J) {
2125: for (d = 0; d < dim; d++) {
2126: J[d * dim + 0] = 0.5 * (PetscRealPart(coords[3 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2127: J[d * dim + 1] = 0.5 * (PetscRealPart(coords[1 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2128: J[d * dim + 2] = 0.5 * (PetscRealPart(coords[4 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2129: }
2130: PetscCall(PetscLogFlops(18.0));
2131: DMPlex_Det3D_Internal(detJ, J);
2132: }
2133: if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
2134: } else {
2135: const PetscInt Nv = 8;
2136: const PetscInt zToPlex[8] = {0, 3, 1, 2, 4, 5, 7, 6};
2137: const PetscInt dim = 3;
2138: const PetscInt dimR = 3;
2139: PetscReal zOrder[24];
2140: PetscReal zCoeff[24];
2141: PetscInt i, j, k, l;
2143: for (i = 0; i < Nv; i++) {
2144: PetscInt zi = zToPlex[i];
2146: for (j = 0; j < dim; j++) zOrder[dim * i + j] = PetscRealPart(coords[dim * zi + j]);
2147: }
2148: for (j = 0; j < dim; j++) {
2149: zCoeff[dim * 0 + j] = 0.125 * (zOrder[dim * 0 + j] + zOrder[dim * 1 + j] + zOrder[dim * 2 + j] + zOrder[dim * 3 + j] + zOrder[dim * 4 + j] + zOrder[dim * 5 + j] + zOrder[dim * 6 + j] + zOrder[dim * 7 + j]);
2150: zCoeff[dim * 1 + j] = 0.125 * (-zOrder[dim * 0 + j] + zOrder[dim * 1 + j] - zOrder[dim * 2 + j] + zOrder[dim * 3 + j] - zOrder[dim * 4 + j] + zOrder[dim * 5 + j] - zOrder[dim * 6 + j] + zOrder[dim * 7 + j]);
2151: zCoeff[dim * 2 + j] = 0.125 * (-zOrder[dim * 0 + j] - zOrder[dim * 1 + j] + zOrder[dim * 2 + j] + zOrder[dim * 3 + j] - zOrder[dim * 4 + j] - zOrder[dim * 5 + j] + zOrder[dim * 6 + j] + zOrder[dim * 7 + j]);
2152: zCoeff[dim * 3 + j] = 0.125 * (zOrder[dim * 0 + j] - zOrder[dim * 1 + j] - zOrder[dim * 2 + j] + zOrder[dim * 3 + j] + zOrder[dim * 4 + j] - zOrder[dim * 5 + j] - zOrder[dim * 6 + j] + zOrder[dim * 7 + j]);
2153: zCoeff[dim * 4 + j] = 0.125 * (-zOrder[dim * 0 + j] - zOrder[dim * 1 + j] - zOrder[dim * 2 + j] - zOrder[dim * 3 + j] + zOrder[dim * 4 + j] + zOrder[dim * 5 + j] + zOrder[dim * 6 + j] + zOrder[dim * 7 + j]);
2154: zCoeff[dim * 5 + j] = 0.125 * (+zOrder[dim * 0 + j] - zOrder[dim * 1 + j] + zOrder[dim * 2 + j] - zOrder[dim * 3 + j] - zOrder[dim * 4 + j] + zOrder[dim * 5 + j] - zOrder[dim * 6 + j] + zOrder[dim * 7 + j]);
2155: zCoeff[dim * 6 + j] = 0.125 * (+zOrder[dim * 0 + j] + zOrder[dim * 1 + j] - zOrder[dim * 2 + j] - zOrder[dim * 3 + j] - zOrder[dim * 4 + j] - zOrder[dim * 5 + j] + zOrder[dim * 6 + j] + zOrder[dim * 7 + j]);
2156: zCoeff[dim * 7 + j] = 0.125 * (-zOrder[dim * 0 + j] + zOrder[dim * 1 + j] + zOrder[dim * 2 + j] - zOrder[dim * 3 + j] + zOrder[dim * 4 + j] - zOrder[dim * 5 + j] - zOrder[dim * 6 + j] + zOrder[dim * 7 + j]);
2157: }
2158: for (i = 0; i < Nq; i++) {
2159: PetscReal xi = points[dimR * i], eta = points[dimR * i + 1], theta = points[dimR * i + 2];
2161: if (v) {
2162: PetscReal extPoint[8];
2164: extPoint[0] = 1.;
2165: extPoint[1] = xi;
2166: extPoint[2] = eta;
2167: extPoint[3] = xi * eta;
2168: extPoint[4] = theta;
2169: extPoint[5] = theta * xi;
2170: extPoint[6] = theta * eta;
2171: extPoint[7] = theta * eta * xi;
2172: for (j = 0; j < dim; j++) {
2173: PetscReal val = 0.;
2175: for (k = 0; k < Nv; k++) val += extPoint[k] * zCoeff[dim * k + j];
2176: v[i * dim + j] = val;
2177: }
2178: }
2179: if (J) {
2180: PetscReal extJ[24];
2182: extJ[0] = 0.;
2183: extJ[1] = 0.;
2184: extJ[2] = 0.;
2185: extJ[3] = 1.;
2186: extJ[4] = 0.;
2187: extJ[5] = 0.;
2188: extJ[6] = 0.;
2189: extJ[7] = 1.;
2190: extJ[8] = 0.;
2191: extJ[9] = eta;
2192: extJ[10] = xi;
2193: extJ[11] = 0.;
2194: extJ[12] = 0.;
2195: extJ[13] = 0.;
2196: extJ[14] = 1.;
2197: extJ[15] = theta;
2198: extJ[16] = 0.;
2199: extJ[17] = xi;
2200: extJ[18] = 0.;
2201: extJ[19] = theta;
2202: extJ[20] = eta;
2203: extJ[21] = theta * eta;
2204: extJ[22] = theta * xi;
2205: extJ[23] = eta * xi;
2207: for (j = 0; j < dim; j++) {
2208: for (k = 0; k < dimR; k++) {
2209: PetscReal val = 0.;
2211: for (l = 0; l < Nv; l++) val += zCoeff[dim * l + j] * extJ[dimR * l + k];
2212: J[i * dim * dim + dim * j + k] = val;
2213: }
2214: }
2215: DMPlex_Det3D_Internal(&detJ[i], &J[i * dim * dim]);
2216: if (invJ) DMPlex_Invert3D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);
2217: }
2218: }
2219: }
2220: PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
2221: PetscFunctionReturn(PETSC_SUCCESS);
2222: }
2224: static PetscErrorCode DMPlexComputeTriangularPrismGeometry_Internal(DM dm, PetscInt e, PetscInt Nq, const PetscReal points[], PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
2225: {
2226: const PetscScalar *array;
2227: PetscScalar *coords = NULL;
2228: const PetscInt dim = 3;
2229: PetscInt numCoords, d;
2230: PetscBool isDG;
2232: PetscFunctionBegin;
2233: PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
2234: PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
2235: if (!Nq) {
2236: /* Assume that the map to the reference is affine */
2237: *detJ = 0.0;
2238: if (v) {
2239: for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);
2240: }
2241: if (J) {
2242: for (d = 0; d < dim; d++) {
2243: J[d * dim + 0] = 0.5 * (PetscRealPart(coords[2 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2244: J[d * dim + 1] = 0.5 * (PetscRealPart(coords[1 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2245: J[d * dim + 2] = 0.5 * (PetscRealPart(coords[4 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2246: }
2247: PetscCall(PetscLogFlops(18.0));
2248: DMPlex_Det3D_Internal(detJ, J);
2249: }
2250: if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
2251: } else {
2252: const PetscInt dim = 3;
2253: const PetscInt dimR = 3;
2254: const PetscInt Nv = 6;
2255: PetscReal verts[18];
2256: PetscReal coeff[18];
2257: PetscInt i, j, k, l;
2259: for (i = 0; i < Nv; ++i)
2260: for (j = 0; j < dim; ++j) verts[dim * i + j] = PetscRealPart(coords[dim * i + j]);
2261: for (j = 0; j < dim; ++j) {
2262: /* Check for triangle,
2263: phi^0 = -1/2 (xi + eta) chi^0 = delta(-1, -1) x(xi) = \sum_k x_k phi^k(xi) = \sum_k chi^k(x) phi^k(xi)
2264: phi^1 = 1/2 (1 + xi) chi^1 = delta( 1, -1) y(xi) = \sum_k y_k phi^k(xi) = \sum_k chi^k(y) phi^k(xi)
2265: phi^2 = 1/2 (1 + eta) chi^2 = delta(-1, 1)
2267: phi^0 + phi^1 + phi^2 = 1 coef_1 = 1/2 ( chi^1 + chi^2)
2268: -phi^0 + phi^1 - phi^2 = xi coef_xi = 1/2 (-chi^0 + chi^1)
2269: -phi^0 - phi^1 + phi^2 = eta coef_eta = 1/2 (-chi^0 + chi^2)
2271: < chi_0 chi_1 chi_2> A / 1 1 1 \ / phi_0 \ <chi> I <phi>^T so we need the inverse transpose
2272: | -1 1 -1 | | phi_1 | =
2273: \ -1 -1 1 / \ phi_2 /
2275: Check phi^0: 1/2 (phi^0 chi^1 + phi^0 chi^2 + phi^0 chi^0 - phi^0 chi^1 + phi^0 chi^0 - phi^0 chi^2) = phi^0 chi^0
2276: */
2277: /* Nodal basis for evaluation at the vertices: {-xi - eta, 1 + xi, 1 + eta} (1 \mp zeta):
2278: \phi^0 = 1/4 ( -xi - eta + xi zeta + eta zeta) --> / 1 1 1 1 1 1 \ 1
2279: \phi^1 = 1/4 (1 + eta - zeta - eta zeta) --> | -1 1 -1 -1 -1 1 | eta
2280: \phi^2 = 1/4 (1 + xi - zeta - xi zeta) --> | -1 -1 1 -1 1 -1 | xi
2281: \phi^3 = 1/4 ( -xi - eta - xi zeta - eta zeta) --> | -1 -1 -1 1 1 1 | zeta
2282: \phi^4 = 1/4 (1 + xi + zeta + xi zeta) --> | 1 1 -1 -1 1 -1 | xi zeta
2283: \phi^5 = 1/4 (1 + eta + zeta + eta zeta) --> \ 1 -1 1 -1 -1 1 / eta zeta
2284: 1/4 / 0 1 1 0 1 1 \
2285: | -1 1 0 -1 0 1 |
2286: | -1 0 1 -1 1 0 |
2287: | 0 -1 -1 0 1 1 |
2288: | 1 0 -1 -1 1 0 |
2289: \ 1 -1 0 -1 0 1 /
2290: */
2291: coeff[dim * 0 + j] = (1. / 4.) * (verts[dim * 1 + j] + verts[dim * 2 + j] + verts[dim * 4 + j] + verts[dim * 5 + j]);
2292: coeff[dim * 1 + j] = (1. / 4.) * (-verts[dim * 0 + j] + verts[dim * 1 + j] - verts[dim * 3 + j] + verts[dim * 5 + j]);
2293: coeff[dim * 2 + j] = (1. / 4.) * (-verts[dim * 0 + j] + verts[dim * 2 + j] - verts[dim * 3 + j] + verts[dim * 4 + j]);
2294: coeff[dim * 3 + j] = (1. / 4.) * (-verts[dim * 1 + j] - verts[dim * 2 + j] + verts[dim * 4 + j] + verts[dim * 5 + j]);
2295: coeff[dim * 4 + j] = (1. / 4.) * (verts[dim * 0 + j] - verts[dim * 2 + j] - verts[dim * 3 + j] + verts[dim * 4 + j]);
2296: coeff[dim * 5 + j] = (1. / 4.) * (verts[dim * 0 + j] - verts[dim * 1 + j] - verts[dim * 3 + j] + verts[dim * 5 + j]);
2297: /* For reference prism:
2298: {0, 0, 0}
2299: {0, 1, 0}
2300: {1, 0, 0}
2301: {0, 0, 1}
2302: {0, 0, 0}
2303: {0, 0, 0}
2304: */
2305: }
2306: for (i = 0; i < Nq; ++i) {
2307: const PetscReal xi = points[dimR * i], eta = points[dimR * i + 1], zeta = points[dimR * i + 2];
2309: if (v) {
2310: PetscReal extPoint[6];
2311: PetscInt c;
2313: extPoint[0] = 1.;
2314: extPoint[1] = eta;
2315: extPoint[2] = xi;
2316: extPoint[3] = zeta;
2317: extPoint[4] = xi * zeta;
2318: extPoint[5] = eta * zeta;
2319: for (c = 0; c < dim; ++c) {
2320: PetscReal val = 0.;
2322: for (k = 0; k < Nv; ++k) val += extPoint[k] * coeff[k * dim + c];
2323: v[i * dim + c] = val;
2324: }
2325: }
2326: if (J) {
2327: PetscReal extJ[18];
2329: extJ[0] = 0.;
2330: extJ[1] = 0.;
2331: extJ[2] = 0.;
2332: extJ[3] = 0.;
2333: extJ[4] = 1.;
2334: extJ[5] = 0.;
2335: extJ[6] = 1.;
2336: extJ[7] = 0.;
2337: extJ[8] = 0.;
2338: extJ[9] = 0.;
2339: extJ[10] = 0.;
2340: extJ[11] = 1.;
2341: extJ[12] = zeta;
2342: extJ[13] = 0.;
2343: extJ[14] = xi;
2344: extJ[15] = 0.;
2345: extJ[16] = zeta;
2346: extJ[17] = eta;
2348: for (j = 0; j < dim; j++) {
2349: for (k = 0; k < dimR; k++) {
2350: PetscReal val = 0.;
2352: for (l = 0; l < Nv; l++) val += coeff[dim * l + j] * extJ[dimR * l + k];
2353: J[i * dim * dim + dim * j + k] = val;
2354: }
2355: }
2356: DMPlex_Det3D_Internal(&detJ[i], &J[i * dim * dim]);
2357: if (invJ) DMPlex_Invert3D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);
2358: }
2359: }
2360: }
2361: PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
2362: PetscFunctionReturn(PETSC_SUCCESS);
2363: }
2365: static PetscErrorCode DMPlexComputeCellGeometryFEM_Implicit(DM dm, PetscInt cell, PetscQuadrature quad, PetscReal *v, PetscReal *J, PetscReal *invJ, PetscReal *detJ)
2366: {
2367: DMPolytopeType ct;
2368: PetscInt depth, dim, coordDim, coneSize, i;
2369: PetscInt Nq = 0;
2370: const PetscReal *points = NULL;
2371: DMLabel depthLabel;
2372: PetscReal xi0[3] = {-1., -1., -1.}, v0[3], J0[9], detJ0;
2373: PetscBool isAffine = PETSC_TRUE;
2375: PetscFunctionBegin;
2376: PetscCall(DMPlexGetDepth(dm, &depth));
2377: PetscCall(DMPlexGetConeSize(dm, cell, &coneSize));
2378: PetscCall(DMPlexGetDepthLabel(dm, &depthLabel));
2379: PetscCall(DMLabelGetValue(depthLabel, cell, &dim));
2380: if (depth == 1 && dim == 1) PetscCall(DMGetDimension(dm, &dim));
2381: PetscCall(DMGetCoordinateDim(dm, &coordDim));
2382: PetscCheck(coordDim <= 3, PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported coordinate dimension %" PetscInt_FMT " > 3", coordDim);
2383: if (quad) PetscCall(PetscQuadratureGetData(quad, NULL, NULL, &Nq, &points, NULL));
2384: PetscCall(DMPlexGetCellType(dm, cell, &ct));
2385: switch (ct) {
2386: case DM_POLYTOPE_POINT:
2387: PetscCall(DMPlexComputePointGeometry_Internal(dm, cell, v, J, invJ, detJ));
2388: isAffine = PETSC_FALSE;
2389: break;
2390: case DM_POLYTOPE_SEGMENT:
2391: case DM_POLYTOPE_POINT_PRISM_TENSOR:
2392: if (Nq) PetscCall(DMPlexComputeLineGeometry_Internal(dm, cell, v0, J0, NULL, &detJ0));
2393: else PetscCall(DMPlexComputeLineGeometry_Internal(dm, cell, v, J, invJ, detJ));
2394: break;
2395: case DM_POLYTOPE_TRIANGLE:
2396: if (Nq) PetscCall(DMPlexComputeTriangleGeometry_Internal(dm, cell, v0, J0, NULL, &detJ0));
2397: else PetscCall(DMPlexComputeTriangleGeometry_Internal(dm, cell, v, J, invJ, detJ));
2398: break;
2399: case DM_POLYTOPE_QUADRILATERAL:
2400: PetscCall(DMPlexComputeRectangleGeometry_Internal(dm, cell, PETSC_FALSE, Nq, points, v, J, invJ, detJ));
2401: isAffine = PETSC_FALSE;
2402: break;
2403: case DM_POLYTOPE_SEG_PRISM_TENSOR:
2404: PetscCall(DMPlexComputeRectangleGeometry_Internal(dm, cell, PETSC_TRUE, Nq, points, v, J, invJ, detJ));
2405: isAffine = PETSC_FALSE;
2406: break;
2407: case DM_POLYTOPE_TETRAHEDRON:
2408: if (Nq) PetscCall(DMPlexComputeTetrahedronGeometry_Internal(dm, cell, v0, J0, NULL, &detJ0));
2409: else PetscCall(DMPlexComputeTetrahedronGeometry_Internal(dm, cell, v, J, invJ, detJ));
2410: break;
2411: case DM_POLYTOPE_HEXAHEDRON:
2412: PetscCall(DMPlexComputeHexahedronGeometry_Internal(dm, cell, Nq, points, v, J, invJ, detJ));
2413: isAffine = PETSC_FALSE;
2414: break;
2415: case DM_POLYTOPE_TRI_PRISM:
2416: PetscCall(DMPlexComputeTriangularPrismGeometry_Internal(dm, cell, Nq, points, v, J, invJ, detJ));
2417: isAffine = PETSC_FALSE;
2418: break;
2419: default:
2420: SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No element geometry for cell %" PetscInt_FMT " with type %s", cell, DMPolytopeTypes[PetscMax(0, PetscMin(ct, DM_NUM_POLYTOPES))]);
2421: }
2422: if (isAffine && Nq) {
2423: if (v) {
2424: for (i = 0; i < Nq; i++) CoordinatesRefToReal(coordDim, dim, xi0, v0, J0, &points[dim * i], &v[coordDim * i]);
2425: }
2426: if (detJ) {
2427: for (i = 0; i < Nq; i++) detJ[i] = detJ0;
2428: }
2429: if (J) {
2430: PetscInt k;
2432: for (i = 0, k = 0; i < Nq; i++) {
2433: PetscInt j;
2435: for (j = 0; j < coordDim * coordDim; j++, k++) J[k] = J0[j];
2436: }
2437: }
2438: if (invJ) {
2439: PetscInt k;
2440: switch (coordDim) {
2441: case 0:
2442: break;
2443: case 1:
2444: invJ[0] = 1. / J0[0];
2445: break;
2446: case 2:
2447: DMPlex_Invert2D_Internal(invJ, J0, detJ0);
2448: break;
2449: case 3:
2450: DMPlex_Invert3D_Internal(invJ, J0, detJ0);
2451: break;
2452: }
2453: for (i = 1, k = coordDim * coordDim; i < Nq; i++) {
2454: PetscInt j;
2456: for (j = 0; j < coordDim * coordDim; j++, k++) invJ[k] = invJ[j];
2457: }
2458: }
2459: }
2460: PetscFunctionReturn(PETSC_SUCCESS);
2461: }
2463: /*@C
2464: DMPlexComputeCellGeometryAffineFEM - Assuming an affine map, compute the Jacobian, inverse Jacobian, and Jacobian determinant for a given cell
2466: Collective
2468: Input Parameters:
2469: + dm - the `DMPLEX`
2470: - cell - the cell
2472: Output Parameters:
2473: + v0 - the translation part of this affine transform, meaning the translation to the origin (not the first vertex of the reference cell)
2474: . J - the Jacobian of the transform from the reference element
2475: . invJ - the inverse of the Jacobian
2476: - detJ - the Jacobian determinant
2478: Level: advanced
2480: .seealso: `DMPLEX`, `DMPlexComputeCellGeometryFEM()`, `DMGetCoordinateSection()`, `DMGetCoordinates()`
2481: @*/
2482: PetscErrorCode DMPlexComputeCellGeometryAffineFEM(DM dm, PetscInt cell, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
2483: {
2484: PetscFunctionBegin;
2485: PetscCall(DMPlexComputeCellGeometryFEM_Implicit(dm, cell, NULL, v0, J, invJ, detJ));
2486: PetscFunctionReturn(PETSC_SUCCESS);
2487: }
2489: static PetscErrorCode DMPlexComputeCellGeometryFEM_FE(DM dm, PetscFE fe, PetscInt point, PetscQuadrature quad, PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
2490: {
2491: const PetscScalar *array;
2492: PetscScalar *coords = NULL;
2493: PetscInt numCoords;
2494: PetscBool isDG;
2495: PetscQuadrature feQuad;
2496: const PetscReal *quadPoints;
2497: PetscTabulation T;
2498: PetscInt dim, cdim, pdim, qdim, Nq, q;
2500: PetscFunctionBegin;
2501: PetscCall(DMGetDimension(dm, &dim));
2502: PetscCall(DMGetCoordinateDim(dm, &cdim));
2503: PetscCall(DMPlexGetCellCoordinates(dm, point, &isDG, &numCoords, &array, &coords));
2504: if (!quad) { /* use the first point of the first functional of the dual space */
2505: PetscDualSpace dsp;
2507: PetscCall(PetscFEGetDualSpace(fe, &dsp));
2508: PetscCall(PetscDualSpaceGetFunctional(dsp, 0, &quad));
2509: PetscCall(PetscQuadratureGetData(quad, &qdim, NULL, &Nq, &quadPoints, NULL));
2510: Nq = 1;
2511: } else {
2512: PetscCall(PetscQuadratureGetData(quad, &qdim, NULL, &Nq, &quadPoints, NULL));
2513: }
2514: PetscCall(PetscFEGetDimension(fe, &pdim));
2515: PetscCall(PetscFEGetQuadrature(fe, &feQuad));
2516: if (feQuad == quad) {
2517: PetscCall(PetscFEGetCellTabulation(fe, J ? 1 : 0, &T));
2518: PetscCheck(numCoords == pdim * cdim, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "There are %" PetscInt_FMT " coordinates for point %" PetscInt_FMT " != %" PetscInt_FMT "*%" PetscInt_FMT, numCoords, point, pdim, cdim);
2519: } else {
2520: PetscCall(PetscFECreateTabulation(fe, 1, Nq, quadPoints, J ? 1 : 0, &T));
2521: }
2522: PetscCheck(qdim == dim, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Point dimension %" PetscInt_FMT " != quadrature dimension %" PetscInt_FMT, dim, qdim);
2523: {
2524: const PetscReal *basis = T->T[0];
2525: const PetscReal *basisDer = T->T[1];
2526: PetscReal detJt;
2528: PetscAssert(Nq == T->Np, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Np %" PetscInt_FMT " != %" PetscInt_FMT, Nq, T->Np);
2529: PetscAssert(pdim == T->Nb, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Nb %" PetscInt_FMT " != %" PetscInt_FMT, pdim, T->Nb);
2530: PetscAssert(cdim == T->Nc, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Nc %" PetscInt_FMT " != %" PetscInt_FMT, cdim, T->Nc);
2531: PetscAssert(dim == T->cdim, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "cdim %" PetscInt_FMT " != %" PetscInt_FMT, dim, T->cdim);
2532: if (v) {
2533: PetscCall(PetscArrayzero(v, Nq * cdim));
2534: for (q = 0; q < Nq; ++q) {
2535: PetscInt i, k;
2537: for (k = 0; k < pdim; ++k) {
2538: const PetscInt vertex = k / cdim;
2539: for (i = 0; i < cdim; ++i) v[q * cdim + i] += basis[(q * pdim + k) * cdim + i] * PetscRealPart(coords[vertex * cdim + i]);
2540: }
2541: PetscCall(PetscLogFlops(2.0 * pdim * cdim));
2542: }
2543: }
2544: if (J) {
2545: PetscCall(PetscArrayzero(J, Nq * cdim * cdim));
2546: for (q = 0; q < Nq; ++q) {
2547: PetscInt i, j, k, c, r;
2549: /* J = dx_i/d\xi_j = sum[k=0,n-1] dN_k/d\xi_j * x_i(k) */
2550: for (k = 0; k < pdim; ++k) {
2551: const PetscInt vertex = k / cdim;
2552: for (j = 0; j < dim; ++j) {
2553: for (i = 0; i < cdim; ++i) J[(q * cdim + i) * cdim + j] += basisDer[((q * pdim + k) * cdim + i) * dim + j] * PetscRealPart(coords[vertex * cdim + i]);
2554: }
2555: }
2556: PetscCall(PetscLogFlops(2.0 * pdim * dim * cdim));
2557: if (cdim > dim) {
2558: for (c = dim; c < cdim; ++c)
2559: for (r = 0; r < cdim; ++r) J[r * cdim + c] = r == c ? 1.0 : 0.0;
2560: }
2561: if (!detJ && !invJ) continue;
2562: detJt = 0.;
2563: switch (cdim) {
2564: case 3:
2565: DMPlex_Det3D_Internal(&detJt, &J[q * cdim * dim]);
2566: if (invJ) DMPlex_Invert3D_Internal(&invJ[q * cdim * dim], &J[q * cdim * dim], detJt);
2567: break;
2568: case 2:
2569: DMPlex_Det2D_Internal(&detJt, &J[q * cdim * dim]);
2570: if (invJ) DMPlex_Invert2D_Internal(&invJ[q * cdim * dim], &J[q * cdim * dim], detJt);
2571: break;
2572: case 1:
2573: detJt = J[q * cdim * dim];
2574: if (invJ) invJ[q * cdim * dim] = 1.0 / detJt;
2575: }
2576: if (detJ) detJ[q] = detJt;
2577: }
2578: } else PetscCheck(!detJ && !invJ, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Need J to compute invJ or detJ");
2579: }
2580: if (feQuad != quad) PetscCall(PetscTabulationDestroy(&T));
2581: PetscCall(DMPlexRestoreCellCoordinates(dm, point, &isDG, &numCoords, &array, &coords));
2582: PetscFunctionReturn(PETSC_SUCCESS);
2583: }
2585: /*@C
2586: DMPlexComputeCellGeometryFEM - Compute the Jacobian, inverse Jacobian, and Jacobian determinant at each quadrature point in the given cell
2588: Collective
2590: Input Parameters:
2591: + dm - the `DMPLEX`
2592: . cell - the cell
2593: - quad - the quadrature containing the points in the reference element where the geometry will be evaluated. If `quad` is `NULL`, geometry will be
2594: evaluated at the first vertex of the reference element
2596: Output Parameters:
2597: + v - the image of the transformed quadrature points, otherwise the image of the first vertex in the closure of the reference element
2598: . J - the Jacobian of the transform from the reference element at each quadrature point
2599: . invJ - the inverse of the Jacobian at each quadrature point
2600: - detJ - the Jacobian determinant at each quadrature point
2602: Level: advanced
2604: Note:
2605: Implicit cell geometry must be used when the topological mesh dimension is not equal to the coordinate dimension, for instance for embedded manifolds.
2607: .seealso: `DMPLEX`, `DMGetCoordinateSection()`, `DMGetCoordinates()`
2608: @*/
2609: PetscErrorCode DMPlexComputeCellGeometryFEM(DM dm, PetscInt cell, PetscQuadrature quad, PetscReal *v, PetscReal J[], PetscReal invJ[], PetscReal *detJ)
2610: {
2611: DM cdm;
2612: PetscFE fe = NULL;
2613: PetscInt dim, cdim;
2615: PetscFunctionBegin;
2616: PetscAssertPointer(detJ, 7);
2617: PetscCall(DMGetDimension(dm, &dim));
2618: PetscCall(DMGetCoordinateDim(dm, &cdim));
2619: PetscCall(DMGetCoordinateDM(dm, &cdm));
2620: if (cdm) {
2621: PetscClassId id;
2622: PetscInt numFields;
2623: PetscDS prob;
2624: PetscObject disc;
2626: PetscCall(DMGetNumFields(cdm, &numFields));
2627: if (numFields) {
2628: PetscCall(DMGetDS(cdm, &prob));
2629: PetscCall(PetscDSGetDiscretization(prob, 0, &disc));
2630: PetscCall(PetscObjectGetClassId(disc, &id));
2631: if (id == PETSCFE_CLASSID) fe = (PetscFE)disc;
2632: }
2633: }
2634: if (!fe || (dim != cdim)) PetscCall(DMPlexComputeCellGeometryFEM_Implicit(dm, cell, quad, v, J, invJ, detJ));
2635: else PetscCall(DMPlexComputeCellGeometryFEM_FE(dm, fe, cell, quad, v, J, invJ, detJ));
2636: PetscFunctionReturn(PETSC_SUCCESS);
2637: }
2639: static PetscErrorCode DMPlexComputeGeometryFVM_0D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
2640: {
2641: PetscSection coordSection;
2642: Vec coordinates;
2643: const PetscScalar *coords = NULL;
2644: PetscInt d, dof, off;
2646: PetscFunctionBegin;
2647: PetscCall(DMGetCoordinatesLocal(dm, &coordinates));
2648: PetscCall(DMGetCoordinateSection(dm, &coordSection));
2649: PetscCall(VecGetArrayRead(coordinates, &coords));
2651: /* for a point the centroid is just the coord */
2652: if (centroid) {
2653: PetscCall(PetscSectionGetDof(coordSection, cell, &dof));
2654: PetscCall(PetscSectionGetOffset(coordSection, cell, &off));
2655: for (d = 0; d < dof; d++) centroid[d] = PetscRealPart(coords[off + d]);
2656: }
2657: if (normal) {
2658: const PetscInt *support, *cones;
2659: PetscInt supportSize;
2660: PetscReal norm, sign;
2662: /* compute the norm based upon the support centroids */
2663: PetscCall(DMPlexGetSupportSize(dm, cell, &supportSize));
2664: PetscCall(DMPlexGetSupport(dm, cell, &support));
2665: PetscCall(DMPlexComputeCellGeometryFVM(dm, support[0], NULL, normal, NULL));
2667: /* Take the normal from the centroid of the support to the vertex*/
2668: PetscCall(PetscSectionGetDof(coordSection, cell, &dof));
2669: PetscCall(PetscSectionGetOffset(coordSection, cell, &off));
2670: for (d = 0; d < dof; d++) normal[d] -= PetscRealPart(coords[off + d]);
2672: /* Determine the sign of the normal based upon its location in the support */
2673: PetscCall(DMPlexGetCone(dm, support[0], &cones));
2674: sign = cones[0] == cell ? 1.0 : -1.0;
2676: norm = DMPlex_NormD_Internal(dim, normal);
2677: for (d = 0; d < dim; ++d) normal[d] /= (norm * sign);
2678: }
2679: if (vol) *vol = 1.0;
2680: PetscCall(VecRestoreArrayRead(coordinates, &coords));
2681: PetscFunctionReturn(PETSC_SUCCESS);
2682: }
2684: static PetscErrorCode DMPlexComputeGeometryFVM_1D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
2685: {
2686: const PetscScalar *array;
2687: PetscScalar *coords = NULL;
2688: PetscInt cdim, coordSize, d;
2689: PetscBool isDG;
2691: PetscFunctionBegin;
2692: PetscCall(DMGetCoordinateDim(dm, &cdim));
2693: PetscCall(DMPlexGetCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
2694: PetscCheck(coordSize == cdim * 2, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Edge has %" PetscInt_FMT " coordinates != %" PetscInt_FMT, coordSize, cdim * 2);
2695: if (centroid) {
2696: for (d = 0; d < cdim; ++d) centroid[d] = 0.5 * PetscRealPart(coords[d] + coords[cdim + d]);
2697: }
2698: if (normal) {
2699: PetscReal norm;
2701: switch (cdim) {
2702: case 3:
2703: normal[2] = 0.; /* fall through */
2704: case 2:
2705: normal[0] = -PetscRealPart(coords[1] - coords[cdim + 1]);
2706: normal[1] = PetscRealPart(coords[0] - coords[cdim + 0]);
2707: break;
2708: case 1:
2709: normal[0] = 1.0;
2710: break;
2711: default:
2712: SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Dimension %" PetscInt_FMT " not supported", cdim);
2713: }
2714: norm = DMPlex_NormD_Internal(cdim, normal);
2715: for (d = 0; d < cdim; ++d) normal[d] /= norm;
2716: }
2717: if (vol) {
2718: *vol = 0.0;
2719: for (d = 0; d < cdim; ++d) *vol += PetscSqr(PetscRealPart(coords[d] - coords[cdim + d]));
2720: *vol = PetscSqrtReal(*vol);
2721: }
2722: PetscCall(DMPlexRestoreCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
2723: PetscFunctionReturn(PETSC_SUCCESS);
2724: }
2726: /* Centroid_i = (\sum_n A_n Cn_i) / A */
2727: static PetscErrorCode DMPlexComputeGeometryFVM_2D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
2728: {
2729: DMPolytopeType ct;
2730: const PetscScalar *array;
2731: PetscScalar *coords = NULL;
2732: PetscInt coordSize;
2733: PetscBool isDG;
2734: PetscInt fv[4] = {0, 1, 2, 3};
2735: PetscInt cdim, numCorners, p, d;
2737: PetscFunctionBegin;
2738: /* Must check for hybrid cells because prisms have a different orientation scheme */
2739: PetscCall(DMPlexGetCellType(dm, cell, &ct));
2740: switch (ct) {
2741: case DM_POLYTOPE_SEG_PRISM_TENSOR:
2742: fv[2] = 3;
2743: fv[3] = 2;
2744: break;
2745: default:
2746: break;
2747: }
2748: PetscCall(DMGetCoordinateDim(dm, &cdim));
2749: PetscCall(DMPlexGetConeSize(dm, cell, &numCorners));
2750: PetscCall(DMPlexGetCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
2751: {
2752: PetscReal c[3] = {0., 0., 0.}, n[3] = {0., 0., 0.}, origin[3] = {0., 0., 0.}, norm;
2754: for (d = 0; d < cdim; d++) origin[d] = PetscRealPart(coords[d]);
2755: for (p = 0; p < numCorners - 2; ++p) {
2756: PetscReal e0[3] = {0., 0., 0.}, e1[3] = {0., 0., 0.};
2757: for (d = 0; d < cdim; d++) {
2758: e0[d] = PetscRealPart(coords[cdim * fv[p + 1] + d]) - origin[d];
2759: e1[d] = PetscRealPart(coords[cdim * fv[p + 2] + d]) - origin[d];
2760: }
2761: const PetscReal dx = e0[1] * e1[2] - e0[2] * e1[1];
2762: const PetscReal dy = e0[2] * e1[0] - e0[0] * e1[2];
2763: const PetscReal dz = e0[0] * e1[1] - e0[1] * e1[0];
2764: const PetscReal a = PetscSqrtReal(dx * dx + dy * dy + dz * dz);
2766: n[0] += dx;
2767: n[1] += dy;
2768: n[2] += dz;
2769: for (d = 0; d < cdim; d++) c[d] += a * PetscRealPart(origin[d] + coords[cdim * fv[p + 1] + d] + coords[cdim * fv[p + 2] + d]) / 3.;
2770: }
2771: norm = PetscSqrtReal(n[0] * n[0] + n[1] * n[1] + n[2] * n[2]);
2772: // Allow zero volume cells
2773: if (norm != 0) {
2774: n[0] /= norm;
2775: n[1] /= norm;
2776: n[2] /= norm;
2777: c[0] /= norm;
2778: c[1] /= norm;
2779: c[2] /= norm;
2780: }
2781: if (vol) *vol = 0.5 * norm;
2782: if (centroid)
2783: for (d = 0; d < cdim; ++d) centroid[d] = c[d];
2784: if (normal)
2785: for (d = 0; d < cdim; ++d) normal[d] = n[d];
2786: }
2787: PetscCall(DMPlexRestoreCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
2788: PetscFunctionReturn(PETSC_SUCCESS);
2789: }
2791: /* Centroid_i = (\sum_n V_n Cn_i) / V */
2792: static PetscErrorCode DMPlexComputeGeometryFVM_3D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
2793: {
2794: DMPolytopeType ct;
2795: const PetscScalar *array;
2796: PetscScalar *coords = NULL;
2797: PetscInt coordSize;
2798: PetscBool isDG;
2799: PetscReal vsum = 0.0, vtmp, coordsTmp[3 * 3], origin[3];
2800: const PetscInt order[16] = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15};
2801: const PetscInt *cone, *faceSizes, *faces;
2802: const DMPolytopeType *faceTypes;
2803: PetscBool isHybrid = PETSC_FALSE;
2804: PetscInt numFaces, f, fOff = 0, p, d;
2806: PetscFunctionBegin;
2807: PetscCheck(dim <= 3, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "No support for dim %" PetscInt_FMT " > 3", dim);
2808: /* Must check for hybrid cells because prisms have a different orientation scheme */
2809: PetscCall(DMPlexGetCellType(dm, cell, &ct));
2810: switch (ct) {
2811: case DM_POLYTOPE_POINT_PRISM_TENSOR:
2812: case DM_POLYTOPE_SEG_PRISM_TENSOR:
2813: case DM_POLYTOPE_TRI_PRISM_TENSOR:
2814: case DM_POLYTOPE_QUAD_PRISM_TENSOR:
2815: isHybrid = PETSC_TRUE;
2816: default:
2817: break;
2818: }
2820: if (centroid)
2821: for (d = 0; d < dim; ++d) centroid[d] = 0.0;
2822: PetscCall(DMPlexGetCone(dm, cell, &cone));
2824: // Using the closure of faces for coordinates does not work in periodic geometries, so we index into the cell coordinates
2825: PetscCall(DMPlexGetRawFaces_Internal(dm, ct, order, &numFaces, &faceTypes, &faceSizes, &faces));
2826: PetscCall(DMPlexGetCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
2827: for (f = 0; f < numFaces; ++f) {
2828: PetscBool flip = isHybrid && f == 0 ? PETSC_TRUE : PETSC_FALSE; /* The first hybrid face is reversed */
2830: // If using zero as the origin vertex for each tetrahedron, an element far from the origin will have positive and
2831: // negative volumes that nearly cancel, thus incurring rounding error. Here we define origin[] as the first vertex
2832: // so that all tetrahedra have positive volume.
2833: if (f == 0)
2834: for (d = 0; d < dim; d++) origin[d] = PetscRealPart(coords[d]);
2835: switch (faceTypes[f]) {
2836: case DM_POLYTOPE_TRIANGLE:
2837: for (d = 0; d < dim; ++d) {
2838: coordsTmp[0 * dim + d] = PetscRealPart(coords[faces[fOff + 0] * dim + d]) - origin[d];
2839: coordsTmp[1 * dim + d] = PetscRealPart(coords[faces[fOff + 1] * dim + d]) - origin[d];
2840: coordsTmp[2 * dim + d] = PetscRealPart(coords[faces[fOff + 2] * dim + d]) - origin[d];
2841: }
2842: Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
2843: if (flip) vtmp = -vtmp;
2844: vsum += vtmp;
2845: if (centroid) { /* Centroid of OABC = (a+b+c)/4 */
2846: for (d = 0; d < dim; ++d) {
2847: for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p * dim + d] * vtmp;
2848: }
2849: }
2850: break;
2851: case DM_POLYTOPE_QUADRILATERAL:
2852: case DM_POLYTOPE_SEG_PRISM_TENSOR: {
2853: PetscInt fv[4] = {0, 1, 2, 3};
2855: /* Side faces for hybrid cells are stored as tensor products */
2856: if (isHybrid && f > 1) {
2857: fv[2] = 3;
2858: fv[3] = 2;
2859: }
2860: /* DO FOR PYRAMID */
2861: /* First tet */
2862: for (d = 0; d < dim; ++d) {
2863: coordsTmp[0 * dim + d] = PetscRealPart(coords[faces[fOff + fv[0]] * dim + d]) - origin[d];
2864: coordsTmp[1 * dim + d] = PetscRealPart(coords[faces[fOff + fv[1]] * dim + d]) - origin[d];
2865: coordsTmp[2 * dim + d] = PetscRealPart(coords[faces[fOff + fv[3]] * dim + d]) - origin[d];
2866: }
2867: Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
2868: if (flip) vtmp = -vtmp;
2869: vsum += vtmp;
2870: if (centroid) {
2871: for (d = 0; d < dim; ++d) {
2872: for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p * dim + d] * vtmp;
2873: }
2874: }
2875: /* Second tet */
2876: for (d = 0; d < dim; ++d) {
2877: coordsTmp[0 * dim + d] = PetscRealPart(coords[faces[fOff + fv[1]] * dim + d]) - origin[d];
2878: coordsTmp[1 * dim + d] = PetscRealPart(coords[faces[fOff + fv[2]] * dim + d]) - origin[d];
2879: coordsTmp[2 * dim + d] = PetscRealPart(coords[faces[fOff + fv[3]] * dim + d]) - origin[d];
2880: }
2881: Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
2882: if (flip) vtmp = -vtmp;
2883: vsum += vtmp;
2884: if (centroid) {
2885: for (d = 0; d < dim; ++d) {
2886: for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p * dim + d] * vtmp;
2887: }
2888: }
2889: break;
2890: }
2891: default:
2892: SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Cannot handle face %" PetscInt_FMT " of type %s", cone[f], DMPolytopeTypes[ct]);
2893: }
2894: fOff += faceSizes[f];
2895: }
2896: PetscCall(DMPlexRestoreRawFaces_Internal(dm, ct, order, &numFaces, &faceTypes, &faceSizes, &faces));
2897: PetscCall(DMPlexRestoreCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
2898: if (vol) *vol = PetscAbsReal(vsum);
2899: if (normal)
2900: for (d = 0; d < dim; ++d) normal[d] = 0.0;
2901: if (centroid)
2902: for (d = 0; d < dim; ++d) centroid[d] = centroid[d] / (vsum * 4) + origin[d];
2903: PetscFunctionReturn(PETSC_SUCCESS);
2904: }
2906: /*@C
2907: DMPlexComputeCellGeometryFVM - Compute the volume for a given cell
2909: Collective
2911: Input Parameters:
2912: + dm - the `DMPLEX`
2913: - cell - the cell
2915: Output Parameters:
2916: + vol - the cell volume
2917: . centroid - the cell centroid
2918: - normal - the cell normal, if appropriate
2920: Level: advanced
2922: .seealso: `DMPLEX`, `DMGetCoordinateSection()`, `DMGetCoordinates()`
2923: @*/
2924: PetscErrorCode DMPlexComputeCellGeometryFVM(DM dm, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
2925: {
2926: PetscInt depth, dim;
2928: PetscFunctionBegin;
2929: PetscCall(DMPlexGetDepth(dm, &depth));
2930: PetscCall(DMGetDimension(dm, &dim));
2931: PetscCheck(depth == dim, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Mesh must be interpolated");
2932: PetscCall(DMPlexGetPointDepth(dm, cell, &depth));
2933: switch (depth) {
2934: case 0:
2935: PetscCall(DMPlexComputeGeometryFVM_0D_Internal(dm, dim, cell, vol, centroid, normal));
2936: break;
2937: case 1:
2938: PetscCall(DMPlexComputeGeometryFVM_1D_Internal(dm, dim, cell, vol, centroid, normal));
2939: break;
2940: case 2:
2941: PetscCall(DMPlexComputeGeometryFVM_2D_Internal(dm, dim, cell, vol, centroid, normal));
2942: break;
2943: case 3:
2944: PetscCall(DMPlexComputeGeometryFVM_3D_Internal(dm, dim, cell, vol, centroid, normal));
2945: break;
2946: default:
2947: SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported dimension %" PetscInt_FMT " (depth %" PetscInt_FMT ") for element geometry computation", dim, depth);
2948: }
2949: PetscFunctionReturn(PETSC_SUCCESS);
2950: }
2952: /*@
2953: DMPlexComputeGeometryFVM - Computes the cell and face geometry for a finite volume method
2955: Input Parameter:
2956: . dm - The `DMPLEX`
2958: Output Parameters:
2959: + cellgeom - A `Vec` of `PetscFVCellGeom` data
2960: - facegeom - A `Vec` of `PetscFVFaceGeom` data
2962: Level: developer
2964: .seealso: `DMPLEX`, `PetscFVFaceGeom`, `PetscFVCellGeom`
2965: @*/
2966: PetscErrorCode DMPlexComputeGeometryFVM(DM dm, Vec *cellgeom, Vec *facegeom)
2967: {
2968: DM dmFace, dmCell;
2969: DMLabel ghostLabel;
2970: PetscSection sectionFace, sectionCell;
2971: PetscSection coordSection;
2972: Vec coordinates;
2973: PetscScalar *fgeom, *cgeom;
2974: PetscReal minradius, gminradius;
2975: PetscInt dim, cStart, cEnd, cEndInterior, c, fStart, fEnd, f;
2977: PetscFunctionBegin;
2978: PetscCall(DMGetDimension(dm, &dim));
2979: PetscCall(DMGetCoordinateSection(dm, &coordSection));
2980: PetscCall(DMGetCoordinatesLocal(dm, &coordinates));
2981: /* Make cell centroids and volumes */
2982: PetscCall(DMClone(dm, &dmCell));
2983: PetscCall(DMSetCoordinateSection(dmCell, PETSC_DETERMINE, coordSection));
2984: PetscCall(DMSetCoordinatesLocal(dmCell, coordinates));
2985: PetscCall(PetscSectionCreate(PetscObjectComm((PetscObject)dm), §ionCell));
2986: PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
2987: PetscCall(DMPlexGetCellTypeStratum(dm, DM_POLYTOPE_FV_GHOST, &cEndInterior, NULL));
2988: PetscCall(PetscSectionSetChart(sectionCell, cStart, cEnd));
2989: for (c = cStart; c < cEnd; ++c) PetscCall(PetscSectionSetDof(sectionCell, c, (PetscInt)PetscCeilReal(((PetscReal)sizeof(PetscFVCellGeom)) / sizeof(PetscScalar))));
2990: PetscCall(PetscSectionSetUp(sectionCell));
2991: PetscCall(DMSetLocalSection(dmCell, sectionCell));
2992: PetscCall(PetscSectionDestroy(§ionCell));
2993: PetscCall(DMCreateLocalVector(dmCell, cellgeom));
2994: if (cEndInterior < 0) cEndInterior = cEnd;
2995: PetscCall(VecGetArray(*cellgeom, &cgeom));
2996: for (c = cStart; c < cEndInterior; ++c) {
2997: PetscFVCellGeom *cg;
2999: PetscCall(DMPlexPointLocalRef(dmCell, c, cgeom, &cg));
3000: PetscCall(PetscArrayzero(cg, 1));
3001: PetscCall(DMPlexComputeCellGeometryFVM(dmCell, c, &cg->volume, cg->centroid, NULL));
3002: }
3003: /* Compute face normals and minimum cell radius */
3004: PetscCall(DMClone(dm, &dmFace));
3005: PetscCall(PetscSectionCreate(PetscObjectComm((PetscObject)dm), §ionFace));
3006: PetscCall(DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd));
3007: PetscCall(PetscSectionSetChart(sectionFace, fStart, fEnd));
3008: for (f = fStart; f < fEnd; ++f) PetscCall(PetscSectionSetDof(sectionFace, f, (PetscInt)PetscCeilReal(((PetscReal)sizeof(PetscFVFaceGeom)) / sizeof(PetscScalar))));
3009: PetscCall(PetscSectionSetUp(sectionFace));
3010: PetscCall(DMSetLocalSection(dmFace, sectionFace));
3011: PetscCall(PetscSectionDestroy(§ionFace));
3012: PetscCall(DMCreateLocalVector(dmFace, facegeom));
3013: PetscCall(VecGetArray(*facegeom, &fgeom));
3014: PetscCall(DMGetLabel(dm, "ghost", &ghostLabel));
3015: minradius = PETSC_MAX_REAL;
3016: for (f = fStart; f < fEnd; ++f) {
3017: PetscFVFaceGeom *fg;
3018: PetscReal area;
3019: const PetscInt *cells;
3020: PetscInt ncells, ghost = -1, d, numChildren;
3022: if (ghostLabel) PetscCall(DMLabelGetValue(ghostLabel, f, &ghost));
3023: PetscCall(DMPlexGetTreeChildren(dm, f, &numChildren, NULL));
3024: PetscCall(DMPlexGetSupport(dm, f, &cells));
3025: PetscCall(DMPlexGetSupportSize(dm, f, &ncells));
3026: /* It is possible to get a face with no support when using partition overlap */
3027: if (!ncells || ghost >= 0 || numChildren) continue;
3028: PetscCall(DMPlexPointLocalRef(dmFace, f, fgeom, &fg));
3029: PetscCall(DMPlexComputeCellGeometryFVM(dm, f, &area, fg->centroid, fg->normal));
3030: for (d = 0; d < dim; ++d) fg->normal[d] *= area;
3031: /* Flip face orientation if necessary to match ordering in support, and Update minimum radius */
3032: {
3033: PetscFVCellGeom *cL, *cR;
3034: PetscReal *lcentroid, *rcentroid;
3035: PetscReal l[3], r[3], v[3];
3037: PetscCall(DMPlexPointLocalRead(dmCell, cells[0], cgeom, &cL));
3038: lcentroid = cells[0] >= cEndInterior ? fg->centroid : cL->centroid;
3039: if (ncells > 1) {
3040: PetscCall(DMPlexPointLocalRead(dmCell, cells[1], cgeom, &cR));
3041: rcentroid = cells[1] >= cEndInterior ? fg->centroid : cR->centroid;
3042: } else {
3043: rcentroid = fg->centroid;
3044: }
3045: PetscCall(DMLocalizeCoordinateReal_Internal(dm, dim, fg->centroid, lcentroid, l));
3046: PetscCall(DMLocalizeCoordinateReal_Internal(dm, dim, fg->centroid, rcentroid, r));
3047: DMPlex_WaxpyD_Internal(dim, -1, l, r, v);
3048: if (DMPlex_DotRealD_Internal(dim, fg->normal, v) < 0) {
3049: for (d = 0; d < dim; ++d) fg->normal[d] = -fg->normal[d];
3050: }
3051: if (DMPlex_DotRealD_Internal(dim, fg->normal, v) <= 0) {
3052: PetscCheck(dim != 2, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Direction for face %" PetscInt_FMT " could not be fixed, normal (%g,%g) v (%g,%g)", f, (double)fg->normal[0], (double)fg->normal[1], (double)v[0], (double)v[1]);
3053: PetscCheck(dim != 3, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Direction for face %" PetscInt_FMT " could not be fixed, normal (%g,%g,%g) v (%g,%g,%g)", f, (double)fg->normal[0], (double)fg->normal[1], (double)fg->normal[2], (double)v[0], (double)v[1], (double)v[2]);
3054: SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Direction for face %" PetscInt_FMT " could not be fixed", f);
3055: }
3056: if (cells[0] < cEndInterior) {
3057: DMPlex_WaxpyD_Internal(dim, -1, fg->centroid, cL->centroid, v);
3058: minradius = PetscMin(minradius, DMPlex_NormD_Internal(dim, v));
3059: }
3060: if (ncells > 1 && cells[1] < cEndInterior) {
3061: DMPlex_WaxpyD_Internal(dim, -1, fg->centroid, cR->centroid, v);
3062: minradius = PetscMin(minradius, DMPlex_NormD_Internal(dim, v));
3063: }
3064: }
3065: }
3066: PetscCallMPI(MPIU_Allreduce(&minradius, &gminradius, 1, MPIU_REAL, MPIU_MIN, PetscObjectComm((PetscObject)dm)));
3067: PetscCall(DMPlexSetMinRadius(dm, gminradius));
3068: /* Compute centroids of ghost cells */
3069: for (c = cEndInterior; c < cEnd; ++c) {
3070: PetscFVFaceGeom *fg;
3071: const PetscInt *cone, *support;
3072: PetscInt coneSize, supportSize, s;
3074: PetscCall(DMPlexGetConeSize(dmCell, c, &coneSize));
3075: PetscCheck(coneSize == 1, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Ghost cell %" PetscInt_FMT " has cone size %" PetscInt_FMT " != 1", c, coneSize);
3076: PetscCall(DMPlexGetCone(dmCell, c, &cone));
3077: PetscCall(DMPlexGetSupportSize(dmCell, cone[0], &supportSize));
3078: PetscCheck(supportSize == 2, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Face %" PetscInt_FMT " has support size %" PetscInt_FMT " != 2", cone[0], supportSize);
3079: PetscCall(DMPlexGetSupport(dmCell, cone[0], &support));
3080: PetscCall(DMPlexPointLocalRef(dmFace, cone[0], fgeom, &fg));
3081: for (s = 0; s < 2; ++s) {
3082: /* Reflect ghost centroid across plane of face */
3083: if (support[s] == c) {
3084: PetscFVCellGeom *ci;
3085: PetscFVCellGeom *cg;
3086: PetscReal c2f[3], a;
3088: PetscCall(DMPlexPointLocalRead(dmCell, support[(s + 1) % 2], cgeom, &ci));
3089: DMPlex_WaxpyD_Internal(dim, -1, ci->centroid, fg->centroid, c2f); /* cell to face centroid */
3090: a = DMPlex_DotRealD_Internal(dim, c2f, fg->normal) / DMPlex_DotRealD_Internal(dim, fg->normal, fg->normal);
3091: PetscCall(DMPlexPointLocalRef(dmCell, support[s], cgeom, &cg));
3092: DMPlex_WaxpyD_Internal(dim, 2 * a, fg->normal, ci->centroid, cg->centroid);
3093: cg->volume = ci->volume;
3094: }
3095: }
3096: }
3097: PetscCall(VecRestoreArray(*facegeom, &fgeom));
3098: PetscCall(VecRestoreArray(*cellgeom, &cgeom));
3099: PetscCall(DMDestroy(&dmCell));
3100: PetscCall(DMDestroy(&dmFace));
3101: PetscFunctionReturn(PETSC_SUCCESS);
3102: }
3104: /*@
3105: DMPlexGetMinRadius - Returns the minimum distance from any cell centroid to a face
3107: Not Collective
3109: Input Parameter:
3110: . dm - the `DMPLEX`
3112: Output Parameter:
3113: . minradius - the minimum cell radius
3115: Level: developer
3117: .seealso: `DMPLEX`, `DMGetCoordinates()`
3118: @*/
3119: PetscErrorCode DMPlexGetMinRadius(DM dm, PetscReal *minradius)
3120: {
3121: PetscFunctionBegin;
3123: PetscAssertPointer(minradius, 2);
3124: *minradius = ((DM_Plex *)dm->data)->minradius;
3125: PetscFunctionReturn(PETSC_SUCCESS);
3126: }
3128: /*@
3129: DMPlexSetMinRadius - Sets the minimum distance from the cell centroid to a face
3131: Logically Collective
3133: Input Parameters:
3134: + dm - the `DMPLEX`
3135: - minradius - the minimum cell radius
3137: Level: developer
3139: .seealso: `DMPLEX`, `DMSetCoordinates()`
3140: @*/
3141: PetscErrorCode DMPlexSetMinRadius(DM dm, PetscReal minradius)
3142: {
3143: PetscFunctionBegin;
3145: ((DM_Plex *)dm->data)->minradius = minradius;
3146: PetscFunctionReturn(PETSC_SUCCESS);
3147: }
3149: /*@C
3150: DMPlexGetCoordinateMap - Returns the function used to map coordinates of newly generated mesh points
3152: Not Collective
3154: Input Parameter:
3155: . dm - the `DMPLEX`
3157: Output Parameter:
3158: . coordFunc - the mapping function
3160: Level: developer
3162: Note:
3163: This function maps from the gnerated coordinate for the new point to the actual coordinate. Thus it is only practical for manifolds with a nice analytical definition that you can get to from any starting point, like a sphere,
3165: .seealso: `DMPLEX`, `DMGetCoordinates()`, `DMPlexSetCoordinateMap()`
3166: @*/
3167: PetscErrorCode DMPlexGetCoordinateMap(DM dm, PetscPointFunc *coordFunc)
3168: {
3169: PetscFunctionBegin;
3171: PetscAssertPointer(coordFunc, 2);
3172: *coordFunc = ((DM_Plex *)dm->data)->coordFunc;
3173: PetscFunctionReturn(PETSC_SUCCESS);
3174: }
3176: /*@C
3177: DMPlexSetCoordinateMap - Sets the function used to map coordinates of newly generated mesh points
3179: Logically Collective
3181: Input Parameters:
3182: + dm - the `DMPLEX`
3183: - coordFunc - the mapping function
3185: Level: developer
3187: Note:
3188: This function maps from the gnerated coordinate for the new point to the actual coordinate. Thus it is only practical for manifolds with a nice analytical definition that you can get to from any starting point, like a sphere,
3190: .seealso: `DMPLEX`, `DMSetCoordinates()`, `DMPlexGetCoordinateMap()`
3191: @*/
3192: PetscErrorCode DMPlexSetCoordinateMap(DM dm, PetscPointFunc coordFunc)
3193: {
3194: PetscFunctionBegin;
3196: ((DM_Plex *)dm->data)->coordFunc = coordFunc;
3197: PetscFunctionReturn(PETSC_SUCCESS);
3198: }
3200: static PetscErrorCode BuildGradientReconstruction_Internal(DM dm, PetscFV fvm, DM dmFace, PetscScalar *fgeom, DM dmCell, PetscScalar *cgeom)
3201: {
3202: DMLabel ghostLabel;
3203: PetscScalar *dx, *grad, **gref;
3204: PetscInt dim, cStart, cEnd, c, cEndInterior, maxNumFaces;
3206: PetscFunctionBegin;
3207: PetscCall(DMGetDimension(dm, &dim));
3208: PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
3209: PetscCall(DMPlexGetCellTypeStratum(dm, DM_POLYTOPE_FV_GHOST, &cEndInterior, NULL));
3210: cEndInterior = cEndInterior < 0 ? cEnd : cEndInterior;
3211: PetscCall(DMPlexGetMaxSizes(dm, &maxNumFaces, NULL));
3212: PetscCall(PetscFVLeastSquaresSetMaxFaces(fvm, maxNumFaces));
3213: PetscCall(DMGetLabel(dm, "ghost", &ghostLabel));
3214: PetscCall(PetscMalloc3(maxNumFaces * dim, &dx, maxNumFaces * dim, &grad, maxNumFaces, &gref));
3215: for (c = cStart; c < cEndInterior; c++) {
3216: const PetscInt *faces;
3217: PetscInt numFaces, usedFaces, f, d;
3218: PetscFVCellGeom *cg;
3219: PetscBool boundary;
3220: PetscInt ghost;
3222: // do not attempt to compute a gradient reconstruction stencil in a ghost cell. It will never be used
3223: PetscCall(DMLabelGetValue(ghostLabel, c, &ghost));
3224: if (ghost >= 0) continue;
3226: PetscCall(DMPlexPointLocalRead(dmCell, c, cgeom, &cg));
3227: PetscCall(DMPlexGetConeSize(dm, c, &numFaces));
3228: PetscCall(DMPlexGetCone(dm, c, &faces));
3229: PetscCheck(numFaces >= dim, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Cell %" PetscInt_FMT " has only %" PetscInt_FMT " faces, not enough for gradient reconstruction", c, numFaces);
3230: for (f = 0, usedFaces = 0; f < numFaces; ++f) {
3231: PetscFVCellGeom *cg1;
3232: PetscFVFaceGeom *fg;
3233: const PetscInt *fcells;
3234: PetscInt ncell, side;
3236: PetscCall(DMLabelGetValue(ghostLabel, faces[f], &ghost));
3237: PetscCall(DMIsBoundaryPoint(dm, faces[f], &boundary));
3238: if ((ghost >= 0) || boundary) continue;
3239: PetscCall(DMPlexGetSupport(dm, faces[f], &fcells));
3240: side = (c != fcells[0]); /* c is on left=0 or right=1 of face */
3241: ncell = fcells[!side]; /* the neighbor */
3242: PetscCall(DMPlexPointLocalRef(dmFace, faces[f], fgeom, &fg));
3243: PetscCall(DMPlexPointLocalRead(dmCell, ncell, cgeom, &cg1));
3244: for (d = 0; d < dim; ++d) dx[usedFaces * dim + d] = cg1->centroid[d] - cg->centroid[d];
3245: gref[usedFaces++] = fg->grad[side]; /* Gradient reconstruction term will go here */
3246: }
3247: PetscCheck(usedFaces, PETSC_COMM_SELF, PETSC_ERR_USER, "Mesh contains isolated cell (no neighbors). Is it intentional?");
3248: PetscCall(PetscFVComputeGradient(fvm, usedFaces, dx, grad));
3249: for (f = 0, usedFaces = 0; f < numFaces; ++f) {
3250: PetscCall(DMLabelGetValue(ghostLabel, faces[f], &ghost));
3251: PetscCall(DMIsBoundaryPoint(dm, faces[f], &boundary));
3252: if ((ghost >= 0) || boundary) continue;
3253: for (d = 0; d < dim; ++d) gref[usedFaces][d] = grad[usedFaces * dim + d];
3254: ++usedFaces;
3255: }
3256: }
3257: PetscCall(PetscFree3(dx, grad, gref));
3258: PetscFunctionReturn(PETSC_SUCCESS);
3259: }
3261: static PetscErrorCode BuildGradientReconstruction_Internal_Tree(DM dm, PetscFV fvm, DM dmFace, PetscScalar *fgeom, DM dmCell, PetscScalar *cgeom)
3262: {
3263: DMLabel ghostLabel;
3264: PetscScalar *dx, *grad, **gref;
3265: PetscInt dim, cStart, cEnd, c, cEndInterior, fStart, fEnd, f, nStart, nEnd, maxNumFaces = 0;
3266: PetscSection neighSec;
3267: PetscInt (*neighbors)[2];
3268: PetscInt *counter;
3270: PetscFunctionBegin;
3271: PetscCall(DMGetDimension(dm, &dim));
3272: PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
3273: PetscCall(DMPlexGetCellTypeStratum(dm, DM_POLYTOPE_FV_GHOST, &cEndInterior, NULL));
3274: if (cEndInterior < 0) cEndInterior = cEnd;
3275: PetscCall(PetscSectionCreate(PetscObjectComm((PetscObject)dm), &neighSec));
3276: PetscCall(PetscSectionSetChart(neighSec, cStart, cEndInterior));
3277: PetscCall(DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd));
3278: PetscCall(DMGetLabel(dm, "ghost", &ghostLabel));
3279: for (f = fStart; f < fEnd; f++) {
3280: const PetscInt *fcells;
3281: PetscBool boundary;
3282: PetscInt ghost = -1;
3283: PetscInt numChildren, numCells, c;
3285: if (ghostLabel) PetscCall(DMLabelGetValue(ghostLabel, f, &ghost));
3286: PetscCall(DMIsBoundaryPoint(dm, f, &boundary));
3287: PetscCall(DMPlexGetTreeChildren(dm, f, &numChildren, NULL));
3288: if ((ghost >= 0) || boundary || numChildren) continue;
3289: PetscCall(DMPlexGetSupportSize(dm, f, &numCells));
3290: if (numCells == 2) {
3291: PetscCall(DMPlexGetSupport(dm, f, &fcells));
3292: for (c = 0; c < 2; c++) {
3293: PetscInt cell = fcells[c];
3295: if (cell >= cStart && cell < cEndInterior) PetscCall(PetscSectionAddDof(neighSec, cell, 1));
3296: }
3297: }
3298: }
3299: PetscCall(PetscSectionSetUp(neighSec));
3300: PetscCall(PetscSectionGetMaxDof(neighSec, &maxNumFaces));
3301: PetscCall(PetscFVLeastSquaresSetMaxFaces(fvm, maxNumFaces));
3302: nStart = 0;
3303: PetscCall(PetscSectionGetStorageSize(neighSec, &nEnd));
3304: PetscCall(PetscMalloc1(nEnd - nStart, &neighbors));
3305: PetscCall(PetscCalloc1(cEndInterior - cStart, &counter));
3306: for (f = fStart; f < fEnd; f++) {
3307: const PetscInt *fcells;
3308: PetscBool boundary;
3309: PetscInt ghost = -1;
3310: PetscInt numChildren, numCells, c;
3312: if (ghostLabel) PetscCall(DMLabelGetValue(ghostLabel, f, &ghost));
3313: PetscCall(DMIsBoundaryPoint(dm, f, &boundary));
3314: PetscCall(DMPlexGetTreeChildren(dm, f, &numChildren, NULL));
3315: if ((ghost >= 0) || boundary || numChildren) continue;
3316: PetscCall(DMPlexGetSupportSize(dm, f, &numCells));
3317: if (numCells == 2) {
3318: PetscCall(DMPlexGetSupport(dm, f, &fcells));
3319: for (c = 0; c < 2; c++) {
3320: PetscInt cell = fcells[c], off;
3322: if (cell >= cStart && cell < cEndInterior) {
3323: PetscCall(PetscSectionGetOffset(neighSec, cell, &off));
3324: off += counter[cell - cStart]++;
3325: neighbors[off][0] = f;
3326: neighbors[off][1] = fcells[1 - c];
3327: }
3328: }
3329: }
3330: }
3331: PetscCall(PetscFree(counter));
3332: PetscCall(PetscMalloc3(maxNumFaces * dim, &dx, maxNumFaces * dim, &grad, maxNumFaces, &gref));
3333: for (c = cStart; c < cEndInterior; c++) {
3334: PetscInt numFaces, f, d, off, ghost = -1;
3335: PetscFVCellGeom *cg;
3337: PetscCall(DMPlexPointLocalRead(dmCell, c, cgeom, &cg));
3338: PetscCall(PetscSectionGetDof(neighSec, c, &numFaces));
3339: PetscCall(PetscSectionGetOffset(neighSec, c, &off));
3341: // do not attempt to compute a gradient reconstruction stencil in a ghost cell. It will never be used
3342: if (ghostLabel) PetscCall(DMLabelGetValue(ghostLabel, c, &ghost));
3343: if (ghost >= 0) continue;
3345: PetscCheck(numFaces >= dim, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Cell %" PetscInt_FMT " has only %" PetscInt_FMT " faces, not enough for gradient reconstruction", c, numFaces);
3346: for (f = 0; f < numFaces; ++f) {
3347: PetscFVCellGeom *cg1;
3348: PetscFVFaceGeom *fg;
3349: const PetscInt *fcells;
3350: PetscInt ncell, side, nface;
3352: nface = neighbors[off + f][0];
3353: ncell = neighbors[off + f][1];
3354: PetscCall(DMPlexGetSupport(dm, nface, &fcells));
3355: side = (c != fcells[0]);
3356: PetscCall(DMPlexPointLocalRef(dmFace, nface, fgeom, &fg));
3357: PetscCall(DMPlexPointLocalRead(dmCell, ncell, cgeom, &cg1));
3358: for (d = 0; d < dim; ++d) dx[f * dim + d] = cg1->centroid[d] - cg->centroid[d];
3359: gref[f] = fg->grad[side]; /* Gradient reconstruction term will go here */
3360: }
3361: PetscCall(PetscFVComputeGradient(fvm, numFaces, dx, grad));
3362: for (f = 0; f < numFaces; ++f) {
3363: for (d = 0; d < dim; ++d) gref[f][d] = grad[f * dim + d];
3364: }
3365: }
3366: PetscCall(PetscFree3(dx, grad, gref));
3367: PetscCall(PetscSectionDestroy(&neighSec));
3368: PetscCall(PetscFree(neighbors));
3369: PetscFunctionReturn(PETSC_SUCCESS);
3370: }
3372: /*@
3373: DMPlexComputeGradientFVM - Compute geometric factors for gradient reconstruction, which are stored in the geometry data, and compute layout for gradient data
3375: Collective
3377: Input Parameters:
3378: + dm - The `DMPLEX`
3379: . fvm - The `PetscFV`
3380: - cellGeometry - The face geometry from `DMPlexComputeCellGeometryFVM()`
3382: Input/Output Parameter:
3383: . faceGeometry - The face geometry from `DMPlexComputeFaceGeometryFVM()`; on output
3384: the geometric factors for gradient calculation are inserted
3386: Output Parameter:
3387: . dmGrad - The `DM` describing the layout of gradient data
3389: Level: developer
3391: .seealso: `DMPLEX`, `DMPlexGetFaceGeometryFVM()`, `DMPlexGetCellGeometryFVM()`
3392: @*/
3393: PetscErrorCode DMPlexComputeGradientFVM(DM dm, PetscFV fvm, Vec faceGeometry, Vec cellGeometry, DM *dmGrad)
3394: {
3395: DM dmFace, dmCell;
3396: PetscScalar *fgeom, *cgeom;
3397: PetscSection sectionGrad, parentSection;
3398: PetscInt dim, pdim, cStart, cEnd, cEndInterior, c;
3400: PetscFunctionBegin;
3401: PetscCall(DMGetDimension(dm, &dim));
3402: PetscCall(PetscFVGetNumComponents(fvm, &pdim));
3403: PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
3404: PetscCall(DMPlexGetCellTypeStratum(dm, DM_POLYTOPE_FV_GHOST, &cEndInterior, NULL));
3405: /* Construct the interpolant corresponding to each face from the least-square solution over the cell neighborhood */
3406: PetscCall(VecGetDM(faceGeometry, &dmFace));
3407: PetscCall(VecGetDM(cellGeometry, &dmCell));
3408: PetscCall(VecGetArray(faceGeometry, &fgeom));
3409: PetscCall(VecGetArray(cellGeometry, &cgeom));
3410: PetscCall(DMPlexGetTree(dm, &parentSection, NULL, NULL, NULL, NULL));
3411: if (!parentSection) {
3412: PetscCall(BuildGradientReconstruction_Internal(dm, fvm, dmFace, fgeom, dmCell, cgeom));
3413: } else {
3414: PetscCall(BuildGradientReconstruction_Internal_Tree(dm, fvm, dmFace, fgeom, dmCell, cgeom));
3415: }
3416: PetscCall(VecRestoreArray(faceGeometry, &fgeom));
3417: PetscCall(VecRestoreArray(cellGeometry, &cgeom));
3418: /* Create storage for gradients */
3419: PetscCall(DMClone(dm, dmGrad));
3420: PetscCall(PetscSectionCreate(PetscObjectComm((PetscObject)dm), §ionGrad));
3421: PetscCall(PetscSectionSetChart(sectionGrad, cStart, cEnd));
3422: for (c = cStart; c < cEnd; ++c) PetscCall(PetscSectionSetDof(sectionGrad, c, pdim * dim));
3423: PetscCall(PetscSectionSetUp(sectionGrad));
3424: PetscCall(DMSetLocalSection(*dmGrad, sectionGrad));
3425: PetscCall(PetscSectionDestroy(§ionGrad));
3426: PetscFunctionReturn(PETSC_SUCCESS);
3427: }
3429: /*@
3430: DMPlexGetDataFVM - Retrieve precomputed cell geometry
3432: Collective
3434: Input Parameters:
3435: + dm - The `DM`
3436: - fv - The `PetscFV`
3438: Output Parameters:
3439: + cellgeom - The cell geometry
3440: . facegeom - The face geometry
3441: - gradDM - The gradient matrices
3443: Level: developer
3445: .seealso: `DMPLEX`, `DMPlexComputeGeometryFVM()`
3446: @*/
3447: PetscErrorCode DMPlexGetDataFVM(DM dm, PetscFV fv, Vec *cellgeom, Vec *facegeom, DM *gradDM)
3448: {
3449: PetscObject cellgeomobj, facegeomobj;
3451: PetscFunctionBegin;
3452: PetscCall(PetscObjectQuery((PetscObject)dm, "DMPlex_cellgeom_fvm", &cellgeomobj));
3453: if (!cellgeomobj) {
3454: Vec cellgeomInt, facegeomInt;
3456: PetscCall(DMPlexComputeGeometryFVM(dm, &cellgeomInt, &facegeomInt));
3457: PetscCall(PetscObjectCompose((PetscObject)dm, "DMPlex_cellgeom_fvm", (PetscObject)cellgeomInt));
3458: PetscCall(PetscObjectCompose((PetscObject)dm, "DMPlex_facegeom_fvm", (PetscObject)facegeomInt));
3459: PetscCall(VecDestroy(&cellgeomInt));
3460: PetscCall(VecDestroy(&facegeomInt));
3461: PetscCall(PetscObjectQuery((PetscObject)dm, "DMPlex_cellgeom_fvm", &cellgeomobj));
3462: }
3463: PetscCall(PetscObjectQuery((PetscObject)dm, "DMPlex_facegeom_fvm", &facegeomobj));
3464: if (cellgeom) *cellgeom = (Vec)cellgeomobj;
3465: if (facegeom) *facegeom = (Vec)facegeomobj;
3466: if (gradDM) {
3467: PetscObject gradobj;
3468: PetscBool computeGradients;
3470: PetscCall(PetscFVGetComputeGradients(fv, &computeGradients));
3471: if (!computeGradients) {
3472: *gradDM = NULL;
3473: PetscFunctionReturn(PETSC_SUCCESS);
3474: }
3475: PetscCall(PetscObjectQuery((PetscObject)dm, "DMPlex_dmgrad_fvm", &gradobj));
3476: if (!gradobj) {
3477: DM dmGradInt;
3479: PetscCall(DMPlexComputeGradientFVM(dm, fv, (Vec)facegeomobj, (Vec)cellgeomobj, &dmGradInt));
3480: PetscCall(PetscObjectCompose((PetscObject)dm, "DMPlex_dmgrad_fvm", (PetscObject)dmGradInt));
3481: PetscCall(DMDestroy(&dmGradInt));
3482: PetscCall(PetscObjectQuery((PetscObject)dm, "DMPlex_dmgrad_fvm", &gradobj));
3483: }
3484: *gradDM = (DM)gradobj;
3485: }
3486: PetscFunctionReturn(PETSC_SUCCESS);
3487: }
3489: static PetscErrorCode DMPlexCoordinatesToReference_NewtonUpdate(PetscInt dimC, PetscInt dimR, PetscScalar *J, PetscScalar *invJ, PetscScalar *work, PetscReal *resNeg, PetscReal *guess)
3490: {
3491: PetscInt l, m;
3493: PetscFunctionBeginHot;
3494: if (dimC == dimR && dimR <= 3) {
3495: /* invert Jacobian, multiply */
3496: PetscScalar det, idet;
3498: switch (dimR) {
3499: case 1:
3500: invJ[0] = 1. / J[0];
3501: break;
3502: case 2:
3503: det = J[0] * J[3] - J[1] * J[2];
3504: idet = 1. / det;
3505: invJ[0] = J[3] * idet;
3506: invJ[1] = -J[1] * idet;
3507: invJ[2] = -J[2] * idet;
3508: invJ[3] = J[0] * idet;
3509: break;
3510: case 3: {
3511: invJ[0] = J[4] * J[8] - J[5] * J[7];
3512: invJ[1] = J[2] * J[7] - J[1] * J[8];
3513: invJ[2] = J[1] * J[5] - J[2] * J[4];
3514: det = invJ[0] * J[0] + invJ[1] * J[3] + invJ[2] * J[6];
3515: idet = 1. / det;
3516: invJ[0] *= idet;
3517: invJ[1] *= idet;
3518: invJ[2] *= idet;
3519: invJ[3] = idet * (J[5] * J[6] - J[3] * J[8]);
3520: invJ[4] = idet * (J[0] * J[8] - J[2] * J[6]);
3521: invJ[5] = idet * (J[2] * J[3] - J[0] * J[5]);
3522: invJ[6] = idet * (J[3] * J[7] - J[4] * J[6]);
3523: invJ[7] = idet * (J[1] * J[6] - J[0] * J[7]);
3524: invJ[8] = idet * (J[0] * J[4] - J[1] * J[3]);
3525: } break;
3526: }
3527: for (l = 0; l < dimR; l++) {
3528: for (m = 0; m < dimC; m++) guess[l] += PetscRealPart(invJ[l * dimC + m]) * resNeg[m];
3529: }
3530: } else {
3531: #if defined(PETSC_USE_COMPLEX)
3532: char transpose = 'C';
3533: #else
3534: char transpose = 'T';
3535: #endif
3536: PetscBLASInt m, n, one = 1, worksize, info;
3538: PetscCall(PetscBLASIntCast(dimR, &m));
3539: PetscCall(PetscBLASIntCast(dimC, &n));
3540: PetscCall(PetscBLASIntCast(dimC * dimC, &worksize));
3541: for (l = 0; l < dimC; l++) invJ[l] = resNeg[l];
3543: PetscCallBLAS("LAPACKgels", LAPACKgels_(&transpose, &m, &n, &one, J, &m, invJ, &n, work, &worksize, &info));
3544: PetscCheck(info == 0, PETSC_COMM_SELF, PETSC_ERR_LIB, "Bad argument to GELS %" PetscBLASInt_FMT, info);
3546: for (l = 0; l < dimR; l++) guess[l] += PetscRealPart(invJ[l]);
3547: }
3548: PetscFunctionReturn(PETSC_SUCCESS);
3549: }
3551: static PetscErrorCode DMPlexCoordinatesToReference_Tensor(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal realCoords[], PetscReal refCoords[], Vec coords, PetscInt dimC, PetscInt dimR)
3552: {
3553: PetscInt coordSize, i, j, k, l, m, maxIts = 7, numV = (1 << dimR);
3554: PetscScalar *coordsScalar = NULL;
3555: PetscReal *cellData, *cellCoords, *cellCoeffs, *extJ, *resNeg;
3556: PetscScalar *J, *invJ, *work;
3558: PetscFunctionBegin;
3560: PetscCall(DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar));
3561: PetscCheck(coordSize >= dimC * numV, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Expecting at least %" PetscInt_FMT " coordinates, got %" PetscInt_FMT, dimC * (1 << dimR), coordSize);
3562: PetscCall(DMGetWorkArray(dm, 2 * coordSize + dimR + dimC, MPIU_REAL, &cellData));
3563: PetscCall(DMGetWorkArray(dm, 3 * dimR * dimC, MPIU_SCALAR, &J));
3564: cellCoords = &cellData[0];
3565: cellCoeffs = &cellData[coordSize];
3566: extJ = &cellData[2 * coordSize];
3567: resNeg = &cellData[2 * coordSize + dimR];
3568: invJ = &J[dimR * dimC];
3569: work = &J[2 * dimR * dimC];
3570: if (dimR == 2) {
3571: const PetscInt zToPlex[4] = {0, 1, 3, 2};
3573: for (i = 0; i < 4; i++) {
3574: PetscInt plexI = zToPlex[i];
3576: for (j = 0; j < dimC; j++) cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
3577: }
3578: } else if (dimR == 3) {
3579: const PetscInt zToPlex[8] = {0, 3, 1, 2, 4, 5, 7, 6};
3581: for (i = 0; i < 8; i++) {
3582: PetscInt plexI = zToPlex[i];
3584: for (j = 0; j < dimC; j++) cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
3585: }
3586: } else {
3587: for (i = 0; i < coordSize; i++) cellCoords[i] = PetscRealPart(coordsScalar[i]);
3588: }
3589: /* Perform the shuffling transform that converts values at the corners of [-1,1]^d to coefficients */
3590: for (i = 0; i < dimR; i++) {
3591: PetscReal *swap;
3593: for (j = 0; j < (numV / 2); j++) {
3594: for (k = 0; k < dimC; k++) {
3595: cellCoeffs[dimC * j + k] = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] + cellCoords[dimC * 2 * j + k]);
3596: cellCoeffs[dimC * (j + (numV / 2)) + k] = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] - cellCoords[dimC * 2 * j + k]);
3597: }
3598: }
3600: if (i < dimR - 1) {
3601: swap = cellCoeffs;
3602: cellCoeffs = cellCoords;
3603: cellCoords = swap;
3604: }
3605: }
3606: PetscCall(PetscArrayzero(refCoords, numPoints * dimR));
3607: for (j = 0; j < numPoints; j++) {
3608: for (i = 0; i < maxIts; i++) {
3609: PetscReal *guess = &refCoords[dimR * j];
3611: /* compute -residual and Jacobian */
3612: for (k = 0; k < dimC; k++) resNeg[k] = realCoords[dimC * j + k];
3613: for (k = 0; k < dimC * dimR; k++) J[k] = 0.;
3614: for (k = 0; k < numV; k++) {
3615: PetscReal extCoord = 1.;
3616: for (l = 0; l < dimR; l++) {
3617: PetscReal coord = guess[l];
3618: PetscInt dep = (k & (1 << l)) >> l;
3620: extCoord *= dep * coord + !dep;
3621: extJ[l] = dep;
3623: for (m = 0; m < dimR; m++) {
3624: PetscReal coord = guess[m];
3625: PetscInt dep = ((k & (1 << m)) >> m) && (m != l);
3626: PetscReal mult = dep * coord + !dep;
3628: extJ[l] *= mult;
3629: }
3630: }
3631: for (l = 0; l < dimC; l++) {
3632: PetscReal coeff = cellCoeffs[dimC * k + l];
3634: resNeg[l] -= coeff * extCoord;
3635: for (m = 0; m < dimR; m++) J[dimR * l + m] += coeff * extJ[m];
3636: }
3637: }
3638: if (0 && PetscDefined(USE_DEBUG)) {
3639: PetscReal maxAbs = 0.;
3641: for (l = 0; l < dimC; l++) maxAbs = PetscMax(maxAbs, PetscAbsReal(resNeg[l]));
3642: PetscCall(PetscInfo(dm, "cell %" PetscInt_FMT ", point %" PetscInt_FMT ", iter %" PetscInt_FMT ": res %g\n", cell, j, i, (double)maxAbs));
3643: }
3645: PetscCall(DMPlexCoordinatesToReference_NewtonUpdate(dimC, dimR, J, invJ, work, resNeg, guess));
3646: }
3647: }
3648: PetscCall(DMRestoreWorkArray(dm, 3 * dimR * dimC, MPIU_SCALAR, &J));
3649: PetscCall(DMRestoreWorkArray(dm, 2 * coordSize + dimR + dimC, MPIU_REAL, &cellData));
3650: PetscCall(DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar));
3651: PetscFunctionReturn(PETSC_SUCCESS);
3652: }
3654: static PetscErrorCode DMPlexReferenceToCoordinates_Tensor(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal refCoords[], PetscReal realCoords[], Vec coords, PetscInt dimC, PetscInt dimR)
3655: {
3656: PetscInt coordSize, i, j, k, l, numV = (1 << dimR);
3657: PetscScalar *coordsScalar = NULL;
3658: PetscReal *cellData, *cellCoords, *cellCoeffs;
3660: PetscFunctionBegin;
3662: PetscCall(DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar));
3663: PetscCheck(coordSize >= dimC * numV, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Expecting at least %" PetscInt_FMT " coordinates, got %" PetscInt_FMT, dimC * (1 << dimR), coordSize);
3664: PetscCall(DMGetWorkArray(dm, 2 * coordSize, MPIU_REAL, &cellData));
3665: cellCoords = &cellData[0];
3666: cellCoeffs = &cellData[coordSize];
3667: if (dimR == 2) {
3668: const PetscInt zToPlex[4] = {0, 1, 3, 2};
3670: for (i = 0; i < 4; i++) {
3671: PetscInt plexI = zToPlex[i];
3673: for (j = 0; j < dimC; j++) cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
3674: }
3675: } else if (dimR == 3) {
3676: const PetscInt zToPlex[8] = {0, 3, 1, 2, 4, 5, 7, 6};
3678: for (i = 0; i < 8; i++) {
3679: PetscInt plexI = zToPlex[i];
3681: for (j = 0; j < dimC; j++) cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
3682: }
3683: } else {
3684: for (i = 0; i < coordSize; i++) cellCoords[i] = PetscRealPart(coordsScalar[i]);
3685: }
3686: /* Perform the shuffling transform that converts values at the corners of [-1,1]^d to coefficients */
3687: for (i = 0; i < dimR; i++) {
3688: PetscReal *swap;
3690: for (j = 0; j < (numV / 2); j++) {
3691: for (k = 0; k < dimC; k++) {
3692: cellCoeffs[dimC * j + k] = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] + cellCoords[dimC * 2 * j + k]);
3693: cellCoeffs[dimC * (j + (numV / 2)) + k] = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] - cellCoords[dimC * 2 * j + k]);
3694: }
3695: }
3697: if (i < dimR - 1) {
3698: swap = cellCoeffs;
3699: cellCoeffs = cellCoords;
3700: cellCoords = swap;
3701: }
3702: }
3703: PetscCall(PetscArrayzero(realCoords, numPoints * dimC));
3704: for (j = 0; j < numPoints; j++) {
3705: const PetscReal *guess = &refCoords[dimR * j];
3706: PetscReal *mapped = &realCoords[dimC * j];
3708: for (k = 0; k < numV; k++) {
3709: PetscReal extCoord = 1.;
3710: for (l = 0; l < dimR; l++) {
3711: PetscReal coord = guess[l];
3712: PetscInt dep = (k & (1 << l)) >> l;
3714: extCoord *= dep * coord + !dep;
3715: }
3716: for (l = 0; l < dimC; l++) {
3717: PetscReal coeff = cellCoeffs[dimC * k + l];
3719: mapped[l] += coeff * extCoord;
3720: }
3721: }
3722: }
3723: PetscCall(DMRestoreWorkArray(dm, 2 * coordSize, MPIU_REAL, &cellData));
3724: PetscCall(DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar));
3725: PetscFunctionReturn(PETSC_SUCCESS);
3726: }
3728: PetscErrorCode DMPlexCoordinatesToReference_FE(DM dm, PetscFE fe, PetscInt cell, PetscInt numPoints, const PetscReal realCoords[], PetscReal refCoords[], Vec coords, PetscInt Nc, PetscInt dimR, PetscInt maxIter, PetscReal *tol)
3729: {
3730: PetscInt numComp, pdim, i, j, k, l, m, coordSize;
3731: PetscScalar *nodes = NULL;
3732: PetscReal *invV, *modes;
3733: PetscReal *B, *D, *resNeg;
3734: PetscScalar *J, *invJ, *work;
3735: PetscReal tolerance = tol == NULL ? 0.0 : *tol;
3737: PetscFunctionBegin;
3738: PetscCall(PetscFEGetDimension(fe, &pdim));
3739: PetscCall(PetscFEGetNumComponents(fe, &numComp));
3740: PetscCheck(numComp == Nc, PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "coordinate discretization must have as many components (%" PetscInt_FMT ") as embedding dimension (!= %" PetscInt_FMT ")", numComp, Nc);
3741: /* we shouldn't apply inverse closure permutation, if one exists */
3742: PetscCall(DMPlexVecGetOrientedClosure_Internal(dm, NULL, PETSC_FALSE, coords, cell, 0, &coordSize, &nodes));
3743: /* convert nodes to values in the stable evaluation basis */
3744: PetscCall(DMGetWorkArray(dm, pdim, MPIU_REAL, &modes));
3745: invV = fe->invV;
3746: for (i = 0; i < pdim; ++i) {
3747: modes[i] = 0.;
3748: for (j = 0; j < pdim; ++j) modes[i] += invV[i * pdim + j] * PetscRealPart(nodes[j]);
3749: }
3750: PetscCall(DMGetWorkArray(dm, pdim * Nc + pdim * Nc * dimR + Nc, MPIU_REAL, &B));
3751: D = &B[pdim * Nc];
3752: resNeg = &D[pdim * Nc * dimR];
3753: PetscCall(DMGetWorkArray(dm, 3 * Nc * dimR, MPIU_SCALAR, &J));
3754: invJ = &J[Nc * dimR];
3755: work = &invJ[Nc * dimR];
3756: for (i = 0; i < numPoints * dimR; i++) refCoords[i] = 0.;
3757: for (j = 0; j < numPoints; j++) {
3758: PetscReal normPoint = DMPlex_NormD_Internal(Nc, &realCoords[j * Nc]);
3759: normPoint = normPoint > PETSC_SMALL ? normPoint : 1.0;
3760: for (i = 0; i < maxIter; i++) { /* we could batch this so that we're not making big B and D arrays all the time */
3761: PetscReal *guess = &refCoords[j * dimR], error = 0;
3762: PetscCall(PetscSpaceEvaluate(fe->basisSpace, 1, guess, B, D, NULL));
3763: for (k = 0; k < Nc; k++) resNeg[k] = realCoords[j * Nc + k];
3764: for (k = 0; k < Nc * dimR; k++) J[k] = 0.;
3765: for (k = 0; k < pdim; k++) {
3766: for (l = 0; l < Nc; l++) {
3767: resNeg[l] -= modes[k] * B[k * Nc + l];
3768: for (m = 0; m < dimR; m++) J[l * dimR + m] += modes[k] * D[(k * Nc + l) * dimR + m];
3769: }
3770: }
3771: if (0 && PetscDefined(USE_DEBUG)) {
3772: PetscReal maxAbs = 0.;
3774: for (l = 0; l < Nc; l++) maxAbs = PetscMax(maxAbs, PetscAbsReal(resNeg[l]));
3775: PetscCall(PetscInfo(dm, "cell %" PetscInt_FMT ", point %" PetscInt_FMT ", iter %" PetscInt_FMT ": res %g\n", cell, j, i, (double)maxAbs));
3776: }
3777: error = DMPlex_NormD_Internal(Nc, resNeg);
3778: if (error < tolerance * normPoint) {
3779: if (tol) *tol = error / normPoint;
3780: break;
3781: }
3782: PetscCall(DMPlexCoordinatesToReference_NewtonUpdate(Nc, dimR, J, invJ, work, resNeg, guess));
3783: }
3784: }
3785: PetscCall(DMRestoreWorkArray(dm, 3 * Nc * dimR, MPIU_SCALAR, &J));
3786: PetscCall(DMRestoreWorkArray(dm, pdim * Nc + pdim * Nc * dimR + Nc, MPIU_REAL, &B));
3787: PetscCall(DMRestoreWorkArray(dm, pdim, MPIU_REAL, &modes));
3788: PetscCall(DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &nodes));
3789: PetscFunctionReturn(PETSC_SUCCESS);
3790: }
3792: /* TODO: TOBY please fix this for Nc > 1 */
3793: PetscErrorCode DMPlexReferenceToCoordinates_FE(DM dm, PetscFE fe, PetscInt cell, PetscInt numPoints, const PetscReal refCoords[], PetscReal realCoords[], Vec coords, PetscInt Nc, PetscInt dimR)
3794: {
3795: PetscInt numComp, pdim, i, j, k, l, coordSize;
3796: PetscScalar *nodes = NULL;
3797: PetscReal *invV, *modes;
3798: PetscReal *B;
3800: PetscFunctionBegin;
3801: PetscCall(PetscFEGetDimension(fe, &pdim));
3802: PetscCall(PetscFEGetNumComponents(fe, &numComp));
3803: PetscCheck(numComp == Nc, PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "coordinate discretization must have as many components (%" PetscInt_FMT ") as embedding dimension (!= %" PetscInt_FMT ")", numComp, Nc);
3804: /* we shouldn't apply inverse closure permutation, if one exists */
3805: PetscCall(DMPlexVecGetOrientedClosure_Internal(dm, NULL, PETSC_FALSE, coords, cell, 0, &coordSize, &nodes));
3806: /* convert nodes to values in the stable evaluation basis */
3807: PetscCall(DMGetWorkArray(dm, pdim, MPIU_REAL, &modes));
3808: invV = fe->invV;
3809: for (i = 0; i < pdim; ++i) {
3810: modes[i] = 0.;
3811: for (j = 0; j < pdim; ++j) modes[i] += invV[i * pdim + j] * PetscRealPart(nodes[j]);
3812: }
3813: PetscCall(DMGetWorkArray(dm, numPoints * pdim * Nc, MPIU_REAL, &B));
3814: PetscCall(PetscSpaceEvaluate(fe->basisSpace, numPoints, refCoords, B, NULL, NULL));
3815: for (i = 0; i < numPoints * Nc; i++) realCoords[i] = 0.;
3816: for (j = 0; j < numPoints; j++) {
3817: PetscReal *mapped = &realCoords[j * Nc];
3819: for (k = 0; k < pdim; k++) {
3820: for (l = 0; l < Nc; l++) mapped[l] += modes[k] * B[(j * pdim + k) * Nc + l];
3821: }
3822: }
3823: PetscCall(DMRestoreWorkArray(dm, numPoints * pdim * Nc, MPIU_REAL, &B));
3824: PetscCall(DMRestoreWorkArray(dm, pdim, MPIU_REAL, &modes));
3825: PetscCall(DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &nodes));
3826: PetscFunctionReturn(PETSC_SUCCESS);
3827: }
3829: /*@
3830: DMPlexCoordinatesToReference - Pull coordinates back from the mesh to the reference element
3831: using a single element map.
3833: Not Collective
3835: Input Parameters:
3836: + dm - The mesh, with coordinate maps defined either by a `PetscDS` for the coordinate `DM` (see `DMGetCoordinateDM()`) or
3837: implicitly by the coordinates of the corner vertices of the cell: as an affine map for simplicial elements, or
3838: as a multilinear map for tensor-product elements
3839: . cell - the cell whose map is used.
3840: . numPoints - the number of points to locate
3841: - realCoords - (numPoints x coordinate dimension) array of coordinates (see `DMGetCoordinateDim()`)
3843: Output Parameter:
3844: . refCoords - (`numPoints` x `dimension`) array of reference coordinates (see `DMGetDimension()`)
3846: Level: intermediate
3848: Notes:
3849: This inversion will be accurate inside the reference element, but may be inaccurate for
3850: mappings that do not extend uniquely outside the reference cell (e.g, most non-affine maps)
3852: .seealso: `DMPLEX`, `DMPlexReferenceToCoordinates()`
3853: @*/
3854: PetscErrorCode DMPlexCoordinatesToReference(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal realCoords[], PetscReal refCoords[])
3855: {
3856: PetscInt dimC, dimR, depth, cStart, cEnd, i;
3857: DM coordDM = NULL;
3858: Vec coords;
3859: PetscFE fe = NULL;
3861: PetscFunctionBegin;
3863: PetscCall(DMGetDimension(dm, &dimR));
3864: PetscCall(DMGetCoordinateDim(dm, &dimC));
3865: if (dimR <= 0 || dimC <= 0 || numPoints <= 0) PetscFunctionReturn(PETSC_SUCCESS);
3866: PetscCall(DMPlexGetDepth(dm, &depth));
3867: PetscCall(DMGetCoordinatesLocal(dm, &coords));
3868: PetscCall(DMGetCoordinateDM(dm, &coordDM));
3869: if (coordDM) {
3870: PetscInt coordFields;
3872: PetscCall(DMGetNumFields(coordDM, &coordFields));
3873: if (coordFields) {
3874: PetscClassId id;
3875: PetscObject disc;
3877: PetscCall(DMGetField(coordDM, 0, NULL, &disc));
3878: PetscCall(PetscObjectGetClassId(disc, &id));
3879: if (id == PETSCFE_CLASSID) fe = (PetscFE)disc;
3880: }
3881: }
3882: PetscCall(DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd));
3883: PetscCheck(cell >= cStart && cell < cEnd, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "point %" PetscInt_FMT " not in cell range [%" PetscInt_FMT ",%" PetscInt_FMT ")", cell, cStart, cEnd);
3884: if (!fe) { /* implicit discretization: affine or multilinear */
3885: PetscInt coneSize;
3886: PetscBool isSimplex, isTensor;
3888: PetscCall(DMPlexGetConeSize(dm, cell, &coneSize));
3889: isSimplex = (coneSize == (dimR + 1)) ? PETSC_TRUE : PETSC_FALSE;
3890: isTensor = (coneSize == ((depth == 1) ? (1 << dimR) : (2 * dimR))) ? PETSC_TRUE : PETSC_FALSE;
3891: if (isSimplex) {
3892: PetscReal detJ, *v0, *J, *invJ;
3894: PetscCall(DMGetWorkArray(dm, dimC + 2 * dimC * dimC, MPIU_REAL, &v0));
3895: J = &v0[dimC];
3896: invJ = &J[dimC * dimC];
3897: PetscCall(DMPlexComputeCellGeometryAffineFEM(dm, cell, v0, J, invJ, &detJ));
3898: for (i = 0; i < numPoints; i++) { /* Apply the inverse affine transformation for each point */
3899: const PetscReal x0[3] = {-1., -1., -1.};
3901: CoordinatesRealToRef(dimC, dimR, x0, v0, invJ, &realCoords[dimC * i], &refCoords[dimR * i]);
3902: }
3903: PetscCall(DMRestoreWorkArray(dm, dimC + 2 * dimC * dimC, MPIU_REAL, &v0));
3904: } else if (isTensor) {
3905: PetscCall(DMPlexCoordinatesToReference_Tensor(coordDM, cell, numPoints, realCoords, refCoords, coords, dimC, dimR));
3906: } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Unrecognized cone size %" PetscInt_FMT, coneSize);
3907: } else {
3908: PetscCall(DMPlexCoordinatesToReference_FE(coordDM, fe, cell, numPoints, realCoords, refCoords, coords, dimC, dimR, 7, NULL));
3909: }
3910: PetscFunctionReturn(PETSC_SUCCESS);
3911: }
3913: /*@
3914: DMPlexReferenceToCoordinates - Map references coordinates to coordinates in the mesh for a single element map.
3916: Not Collective
3918: Input Parameters:
3919: + dm - The mesh, with coordinate maps defined either by a PetscDS for the coordinate `DM` (see `DMGetCoordinateDM()`) or
3920: implicitly by the coordinates of the corner vertices of the cell: as an affine map for simplicial elements, or
3921: as a multilinear map for tensor-product elements
3922: . cell - the cell whose map is used.
3923: . numPoints - the number of points to locate
3924: - refCoords - (numPoints x dimension) array of reference coordinates (see `DMGetDimension()`)
3926: Output Parameter:
3927: . realCoords - (numPoints x coordinate dimension) array of coordinates (see `DMGetCoordinateDim()`)
3929: Level: intermediate
3931: .seealso: `DMPLEX`, `DMPlexCoordinatesToReference()`
3932: @*/
3933: PetscErrorCode DMPlexReferenceToCoordinates(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal refCoords[], PetscReal realCoords[])
3934: {
3935: PetscInt dimC, dimR, depth, cStart, cEnd, i;
3936: DM coordDM = NULL;
3937: Vec coords;
3938: PetscFE fe = NULL;
3940: PetscFunctionBegin;
3942: PetscCall(DMGetDimension(dm, &dimR));
3943: PetscCall(DMGetCoordinateDim(dm, &dimC));
3944: if (dimR <= 0 || dimC <= 0 || numPoints <= 0) PetscFunctionReturn(PETSC_SUCCESS);
3945: PetscCall(DMPlexGetDepth(dm, &depth));
3946: PetscCall(DMGetCoordinatesLocal(dm, &coords));
3947: PetscCall(DMGetCoordinateDM(dm, &coordDM));
3948: if (coordDM) {
3949: PetscInt coordFields;
3951: PetscCall(DMGetNumFields(coordDM, &coordFields));
3952: if (coordFields) {
3953: PetscClassId id;
3954: PetscObject disc;
3956: PetscCall(DMGetField(coordDM, 0, NULL, &disc));
3957: PetscCall(PetscObjectGetClassId(disc, &id));
3958: if (id == PETSCFE_CLASSID) fe = (PetscFE)disc;
3959: }
3960: }
3961: PetscCall(DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd));
3962: PetscCheck(cell >= cStart && cell < cEnd, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "point %" PetscInt_FMT " not in cell range [%" PetscInt_FMT ",%" PetscInt_FMT ")", cell, cStart, cEnd);
3963: if (!fe) { /* implicit discretization: affine or multilinear */
3964: PetscInt coneSize;
3965: PetscBool isSimplex, isTensor;
3967: PetscCall(DMPlexGetConeSize(dm, cell, &coneSize));
3968: isSimplex = (coneSize == (dimR + 1)) ? PETSC_TRUE : PETSC_FALSE;
3969: isTensor = (coneSize == ((depth == 1) ? (1 << dimR) : (2 * dimR))) ? PETSC_TRUE : PETSC_FALSE;
3970: if (isSimplex) {
3971: PetscReal detJ, *v0, *J;
3973: PetscCall(DMGetWorkArray(dm, dimC + 2 * dimC * dimC, MPIU_REAL, &v0));
3974: J = &v0[dimC];
3975: PetscCall(DMPlexComputeCellGeometryAffineFEM(dm, cell, v0, J, NULL, &detJ));
3976: for (i = 0; i < numPoints; i++) { /* Apply the affine transformation for each point */
3977: const PetscReal xi0[3] = {-1., -1., -1.};
3979: CoordinatesRefToReal(dimC, dimR, xi0, v0, J, &refCoords[dimR * i], &realCoords[dimC * i]);
3980: }
3981: PetscCall(DMRestoreWorkArray(dm, dimC + 2 * dimC * dimC, MPIU_REAL, &v0));
3982: } else if (isTensor) {
3983: PetscCall(DMPlexReferenceToCoordinates_Tensor(coordDM, cell, numPoints, refCoords, realCoords, coords, dimC, dimR));
3984: } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Unrecognized cone size %" PetscInt_FMT, coneSize);
3985: } else {
3986: PetscCall(DMPlexReferenceToCoordinates_FE(coordDM, fe, cell, numPoints, refCoords, realCoords, coords, dimC, dimR));
3987: }
3988: PetscFunctionReturn(PETSC_SUCCESS);
3989: }
3991: void coordMap_identity(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
3992: {
3993: const PetscInt Nc = uOff[1] - uOff[0];
3994: PetscInt c;
3996: for (c = 0; c < Nc; ++c) f0[c] = u[c];
3997: }
3999: /* Shear applies the transformation, assuming we fix z,
4000: / 1 0 m_0 \
4001: | 0 1 m_1 |
4002: \ 0 0 1 /
4003: */
4004: void coordMap_shear(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar coords[])
4005: {
4006: const PetscInt Nc = uOff[1] - uOff[0];
4007: const PetscInt ax = (PetscInt)PetscRealPart(constants[0]);
4008: PetscInt c;
4010: for (c = 0; c < Nc; ++c) coords[c] = u[c] + constants[c + 1] * u[ax];
4011: }
4013: /* Flare applies the transformation, assuming we fix x_f,
4015: x_i = x_i * alpha_i x_f
4016: */
4017: void coordMap_flare(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar coords[])
4018: {
4019: const PetscInt Nc = uOff[1] - uOff[0];
4020: const PetscInt cf = (PetscInt)PetscRealPart(constants[0]);
4021: PetscInt c;
4023: for (c = 0; c < Nc; ++c) coords[c] = u[c] * (c == cf ? 1.0 : constants[c + 1] * u[cf]);
4024: }
4026: /*
4027: We would like to map the unit square to a quarter of the annulus between circles of radius 1 and 2. We start by mapping the straight sections, which
4028: will correspond to the top and bottom of our square. So
4030: (0,0)--(1,0) ==> (1,0)--(2,0) Just a shift of (1,0)
4031: (0,1)--(1,1) ==> (0,1)--(0,2) Switch x and y
4033: So it looks like we want to map each layer in y to a ray, so x is the radius and y is the angle:
4035: (x, y) ==> (x+1, \pi/2 y) in (r', \theta') space
4036: ==> ((x+1) cos(\pi/2 y), (x+1) sin(\pi/2 y)) in (x', y') space
4037: */
4038: void coordMap_annulus(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar xp[])
4039: {
4040: const PetscReal ri = PetscRealPart(constants[0]);
4041: const PetscReal ro = PetscRealPart(constants[1]);
4043: xp[0] = (x[0] * (ro - ri) + ri) * PetscCosReal(0.5 * PETSC_PI * x[1]);
4044: xp[1] = (x[0] * (ro - ri) + ri) * PetscSinReal(0.5 * PETSC_PI * x[1]);
4045: }
4047: /*
4048: We would like to map the unit cube to a hemisphere of the spherical shell between balls of radius 1 and 2. We want to map the bottom surface onto the
4049: lower hemisphere and the upper surface onto the top, letting z be the radius.
4051: (x, y) ==> ((z+3)/2, \pi/2 (|x| or |y|), arctan y/x) in (r', \theta', \phi') space
4052: ==> ((z+3)/2 \cos(\theta') cos(\phi'), (z+3)/2 \cos(\theta') sin(\phi'), (z+3)/2 sin(\theta')) in (x', y', z') space
4053: */
4054: void coordMap_shell(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar xp[])
4055: {
4056: const PetscReal pi4 = PETSC_PI / 4.0;
4057: const PetscReal ri = PetscRealPart(constants[0]);
4058: const PetscReal ro = PetscRealPart(constants[1]);
4059: const PetscReal rp = (x[2] + 1) * 0.5 * (ro - ri) + ri;
4060: const PetscReal phip = PetscAtan2Real(x[1], x[0]);
4061: const PetscReal thetap = 0.5 * PETSC_PI * (1.0 - ((((phip <= pi4) && (phip >= -pi4)) || ((phip >= 3.0 * pi4) || (phip <= -3.0 * pi4))) ? PetscAbsReal(x[0]) : PetscAbsReal(x[1])));
4063: xp[0] = rp * PetscCosReal(thetap) * PetscCosReal(phip);
4064: xp[1] = rp * PetscCosReal(thetap) * PetscSinReal(phip);
4065: xp[2] = rp * PetscSinReal(thetap);
4066: }
4068: void coordMap_sinusoid(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar xp[])
4069: {
4070: const PetscReal c = PetscRealPart(constants[0]);
4071: const PetscReal m = PetscRealPart(constants[1]);
4072: const PetscReal n = PetscRealPart(constants[2]);
4074: xp[0] = x[0];
4075: xp[1] = x[1];
4076: if (dim > 2) xp[2] = c * PetscCosReal(2. * m * PETSC_PI * x[0]) * PetscCosReal(2. * n * PETSC_PI * x[1]);
4077: }
4079: /*@C
4080: DMPlexRemapGeometry - This function maps the original `DM` coordinates to new coordinates.
4082: Not Collective
4084: Input Parameters:
4085: + dm - The `DM`
4086: . time - The time
4087: - func - The function transforming current coordinates to new coordinates
4089: Calling sequence of `func`:
4090: + dim - The spatial dimension
4091: . Nf - The number of input fields (here 1)
4092: . NfAux - The number of input auxiliary fields
4093: . uOff - The offset of the coordinates in u[] (here 0)
4094: . uOff_x - The offset of the coordinates in u_x[] (here 0)
4095: . u - The coordinate values at this point in space
4096: . u_t - The coordinate time derivative at this point in space (here `NULL`)
4097: . u_x - The coordinate derivatives at this point in space
4098: . aOff - The offset of each auxiliary field in u[]
4099: . aOff_x - The offset of each auxiliary field in u_x[]
4100: . a - The auxiliary field values at this point in space
4101: . a_t - The auxiliary field time derivative at this point in space (or `NULL`)
4102: . a_x - The auxiliary field derivatives at this point in space
4103: . t - The current time
4104: . x - The coordinates of this point (here not used)
4105: . numConstants - The number of constants
4106: . constants - The value of each constant
4107: - f - The new coordinates at this point in space
4109: Level: intermediate
4111: .seealso: `DMPLEX`, `DMGetCoordinates()`, `DMGetCoordinatesLocal()`, `DMGetCoordinateDM()`, `DMProjectFieldLocal()`, `DMProjectFieldLabelLocal()`
4112: @*/
4113: PetscErrorCode DMPlexRemapGeometry(DM dm, PetscReal time, void (*func)(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f[]))
4114: {
4115: DM cdm;
4116: PetscDS cds;
4117: DMField cf;
4118: PetscObject obj;
4119: PetscClassId id;
4120: Vec lCoords, tmpCoords;
4122: PetscFunctionBegin;
4123: if (!func) PetscCall(DMPlexGetCoordinateMap(dm, &func));
4124: PetscCall(DMGetCoordinateDM(dm, &cdm));
4125: PetscCall(DMGetCoordinatesLocal(dm, &lCoords));
4126: PetscCall(DMGetDS(cdm, &cds));
4127: PetscCall(PetscDSGetDiscretization(cds, 0, &obj));
4128: PetscCall(PetscObjectGetClassId(obj, &id));
4129: if (id != PETSCFE_CLASSID) {
4130: PetscSection cSection;
4131: const PetscScalar *constants;
4132: PetscScalar *coords, f[16];
4133: PetscInt dim, cdim, Nc, vStart, vEnd;
4135: PetscCall(DMGetDimension(dm, &dim));
4136: PetscCall(DMGetCoordinateDim(dm, &cdim));
4137: PetscCheck(cdim <= 16, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Affine version of DMPlexRemapGeometry is currently limited to dimensions <= 16, not %" PetscInt_FMT, cdim);
4138: PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
4139: PetscCall(DMGetCoordinateSection(dm, &cSection));
4140: PetscCall(PetscDSGetConstants(cds, &Nc, &constants));
4141: PetscCall(VecGetArrayWrite(lCoords, &coords));
4142: for (PetscInt v = vStart; v < vEnd; ++v) {
4143: PetscInt uOff[2] = {0, cdim};
4144: PetscInt off, c;
4146: PetscCall(PetscSectionGetOffset(cSection, v, &off));
4147: (*func)(dim, 1, 0, uOff, NULL, &coords[off], NULL, NULL, NULL, NULL, NULL, NULL, NULL, 0.0, NULL, Nc, constants, f);
4148: for (c = 0; c < cdim; ++c) coords[off + c] = f[c];
4149: }
4150: PetscCall(VecRestoreArrayWrite(lCoords, &coords));
4151: } else {
4152: PetscCall(DMGetLocalVector(cdm, &tmpCoords));
4153: PetscCall(VecCopy(lCoords, tmpCoords));
4154: /* We have to do the coordinate field manually right now since the coordinate DM will not have its own */
4155: PetscCall(DMGetCoordinateField(dm, &cf));
4156: cdm->coordinates[0].field = cf;
4157: PetscCall(DMProjectFieldLocal(cdm, time, tmpCoords, &func, INSERT_VALUES, lCoords));
4158: cdm->coordinates[0].field = NULL;
4159: PetscCall(DMRestoreLocalVector(cdm, &tmpCoords));
4160: PetscCall(DMSetCoordinatesLocal(dm, lCoords));
4161: }
4162: PetscFunctionReturn(PETSC_SUCCESS);
4163: }
4165: /*@
4166: DMPlexShearGeometry - This shears the domain, meaning adds a multiple of the shear coordinate to all other coordinates.
4168: Not Collective
4170: Input Parameters:
4171: + dm - The `DMPLEX`
4172: . direction - The shear coordinate direction, e.g. `DM_X` is the x-axis
4173: - multipliers - The multiplier m for each direction which is not the shear direction
4175: Level: intermediate
4177: .seealso: `DMPLEX`, `DMPlexRemapGeometry()`, `DMDirection`, `DM_X`, `DM_Y`, `DM_Z`
4178: @*/
4179: PetscErrorCode DMPlexShearGeometry(DM dm, DMDirection direction, PetscReal multipliers[])
4180: {
4181: DM cdm;
4182: PetscDS cds;
4183: PetscScalar *moduli;
4184: const PetscInt dir = (PetscInt)direction;
4185: PetscInt dE, d, e;
4187: PetscFunctionBegin;
4188: PetscCall(DMGetCoordinateDM(dm, &cdm));
4189: PetscCall(DMGetCoordinateDim(dm, &dE));
4190: PetscCall(PetscMalloc1(dE + 1, &moduli));
4191: moduli[0] = dir;
4192: for (d = 0, e = 0; d < dE; ++d) moduli[d + 1] = d == dir ? 0.0 : (multipliers ? multipliers[e++] : 1.0);
4193: PetscCall(DMGetDS(cdm, &cds));
4194: PetscCall(PetscDSSetConstants(cds, dE + 1, moduli));
4195: PetscCall(DMPlexRemapGeometry(dm, 0.0, coordMap_shear));
4196: PetscCall(PetscFree(moduli));
4197: PetscFunctionReturn(PETSC_SUCCESS);
4198: }