Actual source code: plexgeometry.c
1: #include <petsc/private/dmpleximpl.h>
2: #include <petsc/private/petscfeimpl.h>
3: #include <petscblaslapack.h>
4: #include <petsctime.h>
6: const char *const DMPlexCoordMaps[] = {"none", "shear", "flare", "annulus", "shell", "unknown", "DMPlexCoordMap", "DM_COORD_MAP_", NULL};
8: /*@
9: DMPlexFindVertices - Try to find DAG points based on their coordinates.
11: Not Collective (provided `DMGetCoordinatesLocalSetUp()` has been already called)
13: Input Parameters:
14: + dm - The `DMPLEX` object
15: . coordinates - The `Vec` of coordinates of the sought points
16: - eps - The tolerance or `PETSC_DEFAULT`
18: Output Parameter:
19: . points - The `IS` of found DAG points or -1
21: Level: intermediate
23: Notes:
24: The length of `Vec` coordinates must be npoints * dim where dim is the spatial dimension returned by `DMGetCoordinateDim()` and npoints is the number of sought points.
26: The output `IS` is living on `PETSC_COMM_SELF` and its length is npoints.
27: Each rank does the search independently.
28: If this rank's local `DMPLEX` portion contains the DAG point corresponding to the i-th tuple of coordinates, the i-th entry of the output `IS` is set to that DAG point, otherwise to -1.
30: The output `IS` must be destroyed by user.
32: The tolerance is interpreted as the maximum Euclidean (L2) distance of the sought point from the specified coordinates.
34: Complexity of this function is currently O(mn) with m number of vertices to find and n number of vertices in the local mesh. This could probably be improved if needed.
36: .seealso: `DMPLEX`, `DMPlexCreate()`, `DMGetCoordinatesLocal()`
37: @*/
38: PetscErrorCode DMPlexFindVertices(DM dm, Vec coordinates, PetscReal eps, IS *points)
39: {
40: PetscInt c, cdim, i, j, o, p, vStart, vEnd;
41: PetscInt npoints;
42: const PetscScalar *coord;
43: Vec allCoordsVec;
44: const PetscScalar *allCoords;
45: PetscInt *dagPoints;
47: PetscFunctionBegin;
48: if (eps < 0) eps = PETSC_SQRT_MACHINE_EPSILON;
49: PetscCall(DMGetCoordinateDim(dm, &cdim));
50: {
51: PetscInt n;
53: PetscCall(VecGetLocalSize(coordinates, &n));
54: PetscCheck(n % cdim == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Given coordinates Vec has local length %" PetscInt_FMT " not divisible by coordinate dimension %" PetscInt_FMT " of given DM", n, cdim);
55: npoints = n / cdim;
56: }
57: PetscCall(DMGetCoordinatesLocal(dm, &allCoordsVec));
58: PetscCall(VecGetArrayRead(allCoordsVec, &allCoords));
59: PetscCall(VecGetArrayRead(coordinates, &coord));
60: PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
61: if (PetscDefined(USE_DEBUG)) {
62: /* check coordinate section is consistent with DM dimension */
63: PetscSection cs;
64: PetscInt ndof;
66: PetscCall(DMGetCoordinateSection(dm, &cs));
67: for (p = vStart; p < vEnd; p++) {
68: PetscCall(PetscSectionGetDof(cs, p, &ndof));
69: PetscCheck(ndof == cdim, PETSC_COMM_SELF, PETSC_ERR_PLIB, "point %" PetscInt_FMT ": ndof = %" PetscInt_FMT " != %" PetscInt_FMT " = cdim", p, ndof, cdim);
70: }
71: }
72: PetscCall(PetscMalloc1(npoints, &dagPoints));
73: if (eps == 0.0) {
74: for (i = 0, j = 0; i < npoints; i++, j += cdim) {
75: dagPoints[i] = -1;
76: for (p = vStart, o = 0; p < vEnd; p++, o += cdim) {
77: for (c = 0; c < cdim; c++) {
78: if (coord[j + c] != allCoords[o + c]) break;
79: }
80: if (c == cdim) {
81: dagPoints[i] = p;
82: break;
83: }
84: }
85: }
86: } else {
87: for (i = 0, j = 0; i < npoints; i++, j += cdim) {
88: PetscReal norm;
90: dagPoints[i] = -1;
91: for (p = vStart, o = 0; p < vEnd; p++, o += cdim) {
92: norm = 0.0;
93: for (c = 0; c < cdim; c++) norm += PetscRealPart(PetscSqr(coord[j + c] - allCoords[o + c]));
94: norm = PetscSqrtReal(norm);
95: if (norm <= eps) {
96: dagPoints[i] = p;
97: break;
98: }
99: }
100: }
101: }
102: PetscCall(VecRestoreArrayRead(allCoordsVec, &allCoords));
103: PetscCall(VecRestoreArrayRead(coordinates, &coord));
104: PetscCall(ISCreateGeneral(PETSC_COMM_SELF, npoints, dagPoints, PETSC_OWN_POINTER, points));
105: PetscFunctionReturn(PETSC_SUCCESS);
106: }
108: #if 0
109: static PetscErrorCode DMPlexGetLineIntersection_2D_Internal(const PetscReal segmentA[], const PetscReal segmentB[], PetscReal intersection[], PetscBool *hasIntersection)
110: {
111: const PetscReal p0_x = segmentA[0 * 2 + 0];
112: const PetscReal p0_y = segmentA[0 * 2 + 1];
113: const PetscReal p1_x = segmentA[1 * 2 + 0];
114: const PetscReal p1_y = segmentA[1 * 2 + 1];
115: const PetscReal p2_x = segmentB[0 * 2 + 0];
116: const PetscReal p2_y = segmentB[0 * 2 + 1];
117: const PetscReal p3_x = segmentB[1 * 2 + 0];
118: const PetscReal p3_y = segmentB[1 * 2 + 1];
119: const PetscReal s1_x = p1_x - p0_x;
120: const PetscReal s1_y = p1_y - p0_y;
121: const PetscReal s2_x = p3_x - p2_x;
122: const PetscReal s2_y = p3_y - p2_y;
123: const PetscReal denom = (-s2_x * s1_y + s1_x * s2_y);
125: PetscFunctionBegin;
126: *hasIntersection = PETSC_FALSE;
127: /* Non-parallel lines */
128: if (denom != 0.0) {
129: const PetscReal s = (-s1_y * (p0_x - p2_x) + s1_x * (p0_y - p2_y)) / denom;
130: const PetscReal t = (s2_x * (p0_y - p2_y) - s2_y * (p0_x - p2_x)) / denom;
132: if (s >= 0 && s <= 1 && t >= 0 && t <= 1) {
133: *hasIntersection = PETSC_TRUE;
134: if (intersection) {
135: intersection[0] = p0_x + (t * s1_x);
136: intersection[1] = p0_y + (t * s1_y);
137: }
138: }
139: }
140: PetscFunctionReturn(PETSC_SUCCESS);
141: }
143: /* The plane is segmentB x segmentC: https://en.wikipedia.org/wiki/Line%E2%80%93plane_intersection */
144: static PetscErrorCode DMPlexGetLinePlaneIntersection_3D_Internal(const PetscReal segmentA[], const PetscReal segmentB[], const PetscReal segmentC[], PetscReal intersection[], PetscBool *hasIntersection)
145: {
146: const PetscReal p0_x = segmentA[0 * 3 + 0];
147: const PetscReal p0_y = segmentA[0 * 3 + 1];
148: const PetscReal p0_z = segmentA[0 * 3 + 2];
149: const PetscReal p1_x = segmentA[1 * 3 + 0];
150: const PetscReal p1_y = segmentA[1 * 3 + 1];
151: const PetscReal p1_z = segmentA[1 * 3 + 2];
152: const PetscReal q0_x = segmentB[0 * 3 + 0];
153: const PetscReal q0_y = segmentB[0 * 3 + 1];
154: const PetscReal q0_z = segmentB[0 * 3 + 2];
155: const PetscReal q1_x = segmentB[1 * 3 + 0];
156: const PetscReal q1_y = segmentB[1 * 3 + 1];
157: const PetscReal q1_z = segmentB[1 * 3 + 2];
158: const PetscReal r0_x = segmentC[0 * 3 + 0];
159: const PetscReal r0_y = segmentC[0 * 3 + 1];
160: const PetscReal r0_z = segmentC[0 * 3 + 2];
161: const PetscReal r1_x = segmentC[1 * 3 + 0];
162: const PetscReal r1_y = segmentC[1 * 3 + 1];
163: const PetscReal r1_z = segmentC[1 * 3 + 2];
164: const PetscReal s0_x = p1_x - p0_x;
165: const PetscReal s0_y = p1_y - p0_y;
166: const PetscReal s0_z = p1_z - p0_z;
167: const PetscReal s1_x = q1_x - q0_x;
168: const PetscReal s1_y = q1_y - q0_y;
169: const PetscReal s1_z = q1_z - q0_z;
170: const PetscReal s2_x = r1_x - r0_x;
171: const PetscReal s2_y = r1_y - r0_y;
172: const PetscReal s2_z = r1_z - r0_z;
173: const PetscReal s3_x = s1_y * s2_z - s1_z * s2_y; /* s1 x s2 */
174: const PetscReal s3_y = s1_z * s2_x - s1_x * s2_z;
175: const PetscReal s3_z = s1_x * s2_y - s1_y * s2_x;
176: const PetscReal s4_x = s0_y * s2_z - s0_z * s2_y; /* s0 x s2 */
177: const PetscReal s4_y = s0_z * s2_x - s0_x * s2_z;
178: const PetscReal s4_z = s0_x * s2_y - s0_y * s2_x;
179: const PetscReal s5_x = s1_y * s0_z - s1_z * s0_y; /* s1 x s0 */
180: const PetscReal s5_y = s1_z * s0_x - s1_x * s0_z;
181: const PetscReal s5_z = s1_x * s0_y - s1_y * s0_x;
182: const PetscReal denom = -(s0_x * s3_x + s0_y * s3_y + s0_z * s3_z); /* -s0 . (s1 x s2) */
184: PetscFunctionBegin;
185: *hasIntersection = PETSC_FALSE;
186: /* Line not parallel to plane */
187: if (denom != 0.0) {
188: const PetscReal t = (s3_x * (p0_x - q0_x) + s3_y * (p0_y - q0_y) + s3_z * (p0_z - q0_z)) / denom;
189: const PetscReal u = (s4_x * (p0_x - q0_x) + s4_y * (p0_y - q0_y) + s4_z * (p0_z - q0_z)) / denom;
190: const PetscReal v = (s5_x * (p0_x - q0_x) + s5_y * (p0_y - q0_y) + s5_z * (p0_z - q0_z)) / denom;
192: if (t >= 0 && t <= 1 && u >= 0 && u <= 1 && v >= 0 && v <= 1) {
193: *hasIntersection = PETSC_TRUE;
194: if (intersection) {
195: intersection[0] = p0_x + (t * s0_x);
196: intersection[1] = p0_y + (t * s0_y);
197: intersection[2] = p0_z + (t * s0_z);
198: }
199: }
200: }
201: PetscFunctionReturn(PETSC_SUCCESS);
202: }
203: #endif
205: static PetscErrorCode DMPlexGetPlaneSimplexIntersection_Coords_Internal(DM dm, PetscInt dim, PetscInt cdim, const PetscScalar coords[], const PetscReal p[], const PetscReal normal[], PetscBool *pos, PetscInt *Nint, PetscReal intPoints[])
206: {
207: PetscReal d[4]; // distance of vertices to the plane
208: PetscReal dp; // distance from origin to the plane
209: PetscInt n = 0;
211: PetscFunctionBegin;
212: if (pos) *pos = PETSC_FALSE;
213: if (Nint) *Nint = 0;
214: if (PetscDefined(USE_DEBUG)) {
215: PetscReal mag = DMPlex_NormD_Internal(cdim, normal);
216: PetscCheck(PetscAbsReal(mag - (PetscReal)1.0) < PETSC_SMALL, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Normal vector is not normalized: %g", (double)mag);
217: }
219: dp = DMPlex_DotRealD_Internal(cdim, normal, p);
220: for (PetscInt v = 0; v < dim + 1; ++v) {
221: // d[v] is positive, zero, or negative if vertex i is above, on, or below the plane
222: #if defined(PETSC_USE_COMPLEX)
223: PetscReal c[4];
224: for (PetscInt i = 0; i < cdim; ++i) c[i] = PetscRealPart(coords[v * cdim + i]);
225: d[v] = DMPlex_DotRealD_Internal(cdim, normal, c);
226: #else
227: d[v] = DMPlex_DotRealD_Internal(cdim, normal, &coords[v * cdim]);
228: #endif
229: d[v] -= dp;
230: }
232: // If all d are positive or negative, no intersection
233: {
234: PetscInt v;
235: for (v = 0; v < dim + 1; ++v)
236: if (d[v] >= 0.) break;
237: if (v == dim + 1) PetscFunctionReturn(PETSC_SUCCESS);
238: for (v = 0; v < dim + 1; ++v)
239: if (d[v] <= 0.) break;
240: if (v == dim + 1) {
241: if (pos) *pos = PETSC_TRUE;
242: PetscFunctionReturn(PETSC_SUCCESS);
243: }
244: }
246: for (PetscInt v = 0; v < dim + 1; ++v) {
247: // Points with zero distance are automatically added to the list.
248: if (PetscAbsReal(d[v]) < PETSC_MACHINE_EPSILON) {
249: for (PetscInt i = 0; i < cdim; ++i) intPoints[n * cdim + i] = PetscRealPart(coords[v * cdim + i]);
250: ++n;
251: } else {
252: // For each point with nonzero distance, seek another point with opposite sign
253: // and higher index, and compute the intersection of the line between those
254: // points and the plane.
255: for (PetscInt w = v + 1; w < dim + 1; ++w) {
256: if (d[v] * d[w] < 0.) {
257: PetscReal inv_dist = 1. / (d[v] - d[w]);
258: for (PetscInt i = 0; i < cdim; ++i) intPoints[n * cdim + i] = (d[v] * PetscRealPart(coords[w * cdim + i]) - d[w] * PetscRealPart(coords[v * cdim + i])) * inv_dist;
259: ++n;
260: }
261: }
262: }
263: }
264: // TODO order output points if there are 4
265: *Nint = n;
266: PetscFunctionReturn(PETSC_SUCCESS);
267: }
269: static PetscErrorCode DMPlexGetPlaneSimplexIntersection_Internal(DM dm, PetscInt dim, PetscInt c, const PetscReal p[], const PetscReal normal[], PetscBool *pos, PetscInt *Nint, PetscReal intPoints[])
270: {
271: const PetscScalar *array;
272: PetscScalar *coords = NULL;
273: PetscInt numCoords;
274: PetscBool isDG;
275: PetscInt cdim;
277: PetscFunctionBegin;
278: PetscCall(DMGetCoordinateDim(dm, &cdim));
279: PetscCheck(cdim == dim, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "DM has coordinates in %" PetscInt_FMT "D instead of %" PetscInt_FMT "D", cdim, dim);
280: PetscCall(DMPlexGetCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
281: PetscCheck(numCoords == dim * (dim + 1), PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Tetrahedron should have %" PetscInt_FMT " coordinates, not %" PetscInt_FMT, dim * (dim + 1), numCoords);
282: PetscCall(PetscArrayzero(intPoints, dim * (dim + 1)));
284: PetscCall(DMPlexGetPlaneSimplexIntersection_Coords_Internal(dm, dim, cdim, coords, p, normal, pos, Nint, intPoints));
286: PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
287: PetscFunctionReturn(PETSC_SUCCESS);
288: }
290: static PetscErrorCode DMPlexGetPlaneQuadIntersection_Internal(DM dm, PetscInt dim, PetscInt c, const PetscReal p[], const PetscReal normal[], PetscBool *pos, PetscInt *Nint, PetscReal intPoints[])
291: {
292: const PetscScalar *array;
293: PetscScalar *coords = NULL;
294: PetscInt numCoords;
295: PetscBool isDG;
296: PetscInt cdim;
297: PetscScalar tcoords[6] = {0., 0., 0., 0., 0., 0.};
298: const PetscInt vertsA[3] = {0, 1, 3};
299: const PetscInt vertsB[3] = {1, 2, 3};
300: PetscInt NintA, NintB;
302: PetscFunctionBegin;
303: PetscCall(DMGetCoordinateDim(dm, &cdim));
304: PetscCheck(cdim == dim, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "DM has coordinates in %" PetscInt_FMT "D instead of %" PetscInt_FMT "D", cdim, dim);
305: PetscCall(DMPlexGetCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
306: PetscCheck(numCoords == dim * 4, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Quadrilateral should have %" PetscInt_FMT " coordinates, not %" PetscInt_FMT, dim * 4, numCoords);
307: PetscCall(PetscArrayzero(intPoints, dim * 4));
309: for (PetscInt v = 0; v < 3; ++v)
310: for (PetscInt d = 0; d < cdim; ++d) tcoords[v * cdim + d] = coords[vertsA[v] * cdim + d];
311: PetscCall(DMPlexGetPlaneSimplexIntersection_Coords_Internal(dm, dim, cdim, tcoords, p, normal, pos, &NintA, intPoints));
312: for (PetscInt v = 0; v < 3; ++v)
313: for (PetscInt d = 0; d < cdim; ++d) tcoords[v * cdim + d] = coords[vertsB[v] * cdim + d];
314: PetscCall(DMPlexGetPlaneSimplexIntersection_Coords_Internal(dm, dim, cdim, tcoords, p, normal, pos, &NintB, &intPoints[NintA * cdim]));
315: *Nint = NintA + NintB;
317: PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
318: PetscFunctionReturn(PETSC_SUCCESS);
319: }
321: static PetscErrorCode DMPlexGetPlaneHexIntersection_Internal(DM dm, PetscInt dim, PetscInt c, const PetscReal p[], const PetscReal normal[], PetscBool *pos, PetscInt *Nint, PetscReal intPoints[])
322: {
323: const PetscScalar *array;
324: PetscScalar *coords = NULL;
325: PetscInt numCoords;
326: PetscBool isDG;
327: PetscInt cdim;
328: PetscScalar tcoords[12] = {0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.};
329: // We split using the (2, 4) main diagonal, so all tets contain those vertices
330: const PetscInt vertsA[4] = {0, 1, 2, 4};
331: const PetscInt vertsB[4] = {0, 2, 3, 4};
332: const PetscInt vertsC[4] = {1, 7, 2, 4};
333: const PetscInt vertsD[4] = {2, 7, 6, 4};
334: const PetscInt vertsE[4] = {3, 5, 4, 2};
335: const PetscInt vertsF[4] = {4, 5, 6, 2};
336: PetscInt NintA, NintB, NintC, NintD, NintE, NintF, Nsum = 0;
338: PetscFunctionBegin;
339: PetscCall(DMGetCoordinateDim(dm, &cdim));
340: PetscCheck(cdim == dim, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "DM has coordinates in %" PetscInt_FMT "D instead of %" PetscInt_FMT "D", cdim, dim);
341: PetscCall(DMPlexGetCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
342: PetscCheck(numCoords == dim * 8, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Hexahedron should have %" PetscInt_FMT " coordinates, not %" PetscInt_FMT, dim * 8, numCoords);
343: PetscCall(PetscArrayzero(intPoints, dim * 18));
345: for (PetscInt v = 0; v < 4; ++v)
346: for (PetscInt d = 0; d < cdim; ++d) tcoords[v * cdim + d] = coords[vertsA[v] * cdim + d];
347: PetscCall(DMPlexGetPlaneSimplexIntersection_Coords_Internal(dm, dim, cdim, tcoords, p, normal, pos, &NintA, &intPoints[Nsum * cdim]));
348: Nsum += NintA;
349: for (PetscInt v = 0; v < 4; ++v)
350: for (PetscInt d = 0; d < cdim; ++d) tcoords[v * cdim + d] = coords[vertsB[v] * cdim + d];
351: PetscCall(DMPlexGetPlaneSimplexIntersection_Coords_Internal(dm, dim, cdim, tcoords, p, normal, pos, &NintB, &intPoints[Nsum * cdim]));
352: Nsum += NintB;
353: for (PetscInt v = 0; v < 4; ++v)
354: for (PetscInt d = 0; d < cdim; ++d) tcoords[v * cdim + d] = coords[vertsC[v] * cdim + d];
355: PetscCall(DMPlexGetPlaneSimplexIntersection_Coords_Internal(dm, dim, cdim, tcoords, p, normal, pos, &NintC, &intPoints[Nsum * cdim]));
356: Nsum += NintC;
357: for (PetscInt v = 0; v < 4; ++v)
358: for (PetscInt d = 0; d < cdim; ++d) tcoords[v * cdim + d] = coords[vertsD[v] * cdim + d];
359: PetscCall(DMPlexGetPlaneSimplexIntersection_Coords_Internal(dm, dim, cdim, tcoords, p, normal, pos, &NintD, &intPoints[Nsum * cdim]));
360: Nsum += NintD;
361: for (PetscInt v = 0; v < 4; ++v)
362: for (PetscInt d = 0; d < cdim; ++d) tcoords[v * cdim + d] = coords[vertsE[v] * cdim + d];
363: PetscCall(DMPlexGetPlaneSimplexIntersection_Coords_Internal(dm, dim, cdim, tcoords, p, normal, pos, &NintE, &intPoints[Nsum * cdim]));
364: Nsum += NintE;
365: for (PetscInt v = 0; v < 4; ++v)
366: for (PetscInt d = 0; d < cdim; ++d) tcoords[v * cdim + d] = coords[vertsF[v] * cdim + d];
367: PetscCall(DMPlexGetPlaneSimplexIntersection_Coords_Internal(dm, dim, cdim, tcoords, p, normal, pos, &NintF, &intPoints[Nsum * cdim]));
368: Nsum += NintF;
369: *Nint = Nsum;
371: PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
372: PetscFunctionReturn(PETSC_SUCCESS);
373: }
375: /*
376: DMPlexGetPlaneCellIntersection_Internal - Finds the intersection of a plane with a cell
378: Not collective
380: Input Parameters:
381: + dm - the DM
382: . c - the mesh point
383: . p - a point on the plane.
384: - normal - a normal vector to the plane, must be normalized
386: Output Parameters:
387: . pos - `PETSC_TRUE` is the cell is on the positive side of the plane, `PETSC_FALSE` on the negative side
388: + Nint - the number of intersection points, in [0, 4]
389: - intPoints - the coordinates of the intersection points, should be length at least 12
391: Note: The `pos` argument is only meaningful if the number of intersections is 0. The algorithmic idea comes from https://github.com/chrisk314/tet-plane-intersection.
393: Level: developer
395: .seealso:
396: @*/
397: static PetscErrorCode DMPlexGetPlaneCellIntersection_Internal(DM dm, PetscInt c, const PetscReal p[], const PetscReal normal[], PetscBool *pos, PetscInt *Nint, PetscReal intPoints[])
398: {
399: DMPolytopeType ct;
401: PetscFunctionBegin;
402: PetscCall(DMPlexGetCellType(dm, c, &ct));
403: switch (ct) {
404: case DM_POLYTOPE_SEGMENT:
405: case DM_POLYTOPE_TRIANGLE:
406: case DM_POLYTOPE_TETRAHEDRON:
407: PetscCall(DMPlexGetPlaneSimplexIntersection_Internal(dm, DMPolytopeTypeGetDim(ct), c, p, normal, pos, Nint, intPoints));
408: break;
409: case DM_POLYTOPE_QUADRILATERAL:
410: PetscCall(DMPlexGetPlaneQuadIntersection_Internal(dm, DMPolytopeTypeGetDim(ct), c, p, normal, pos, Nint, intPoints));
411: break;
412: case DM_POLYTOPE_HEXAHEDRON:
413: PetscCall(DMPlexGetPlaneHexIntersection_Internal(dm, DMPolytopeTypeGetDim(ct), c, p, normal, pos, Nint, intPoints));
414: break;
415: default:
416: SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No plane intersection for cell %" PetscInt_FMT " with type %s", c, DMPolytopeTypes[ct]);
417: }
418: PetscFunctionReturn(PETSC_SUCCESS);
419: }
421: static PetscErrorCode DMPlexLocatePoint_Simplex_1D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
422: {
423: const PetscReal eps = PETSC_SQRT_MACHINE_EPSILON;
424: const PetscReal x = PetscRealPart(point[0]);
425: PetscReal v0, J, invJ, detJ;
426: PetscReal xi;
428: PetscFunctionBegin;
429: PetscCall(DMPlexComputeCellGeometryFEM(dm, c, NULL, &v0, &J, &invJ, &detJ));
430: xi = invJ * (x - v0);
432: if ((xi >= -eps) && (xi <= 2. + eps)) *cell = c;
433: else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
434: PetscFunctionReturn(PETSC_SUCCESS);
435: }
437: static PetscErrorCode DMPlexLocatePoint_Simplex_2D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
438: {
439: const PetscInt embedDim = 2;
440: const PetscReal eps = PETSC_SQRT_MACHINE_EPSILON;
441: PetscReal x = PetscRealPart(point[0]);
442: PetscReal y = PetscRealPart(point[1]);
443: PetscReal v0[2], J[4], invJ[4], detJ;
444: PetscReal xi, eta;
446: PetscFunctionBegin;
447: PetscCall(DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ));
448: xi = invJ[0 * embedDim + 0] * (x - v0[0]) + invJ[0 * embedDim + 1] * (y - v0[1]);
449: eta = invJ[1 * embedDim + 0] * (x - v0[0]) + invJ[1 * embedDim + 1] * (y - v0[1]);
451: if ((xi >= -eps) && (eta >= -eps) && (xi + eta <= 2.0 + eps)) *cell = c;
452: else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
453: PetscFunctionReturn(PETSC_SUCCESS);
454: }
456: static PetscErrorCode DMPlexClosestPoint_Simplex_2D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscReal cpoint[])
457: {
458: const PetscInt embedDim = 2;
459: PetscReal x = PetscRealPart(point[0]);
460: PetscReal y = PetscRealPart(point[1]);
461: PetscReal v0[2], J[4], invJ[4], detJ;
462: PetscReal xi, eta, r;
464: PetscFunctionBegin;
465: PetscCall(DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ));
466: xi = invJ[0 * embedDim + 0] * (x - v0[0]) + invJ[0 * embedDim + 1] * (y - v0[1]);
467: eta = invJ[1 * embedDim + 0] * (x - v0[0]) + invJ[1 * embedDim + 1] * (y - v0[1]);
469: xi = PetscMax(xi, 0.0);
470: eta = PetscMax(eta, 0.0);
471: if (xi + eta > 2.0) {
472: r = (xi + eta) / 2.0;
473: xi /= r;
474: eta /= r;
475: }
476: cpoint[0] = J[0 * embedDim + 0] * xi + J[0 * embedDim + 1] * eta + v0[0];
477: cpoint[1] = J[1 * embedDim + 0] * xi + J[1 * embedDim + 1] * eta + v0[1];
478: PetscFunctionReturn(PETSC_SUCCESS);
479: }
481: // This is the ray-casting, or even-odd algorithm: https://en.wikipedia.org/wiki/Even%E2%80%93odd_rule
482: static PetscErrorCode DMPlexLocatePoint_Quad_2D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
483: {
484: const PetscScalar *array;
485: PetscScalar *coords = NULL;
486: const PetscInt faces[8] = {0, 1, 1, 2, 2, 3, 3, 0};
487: PetscReal x = PetscRealPart(point[0]);
488: PetscReal y = PetscRealPart(point[1]);
489: PetscInt crossings = 0, numCoords, f;
490: PetscBool isDG;
492: PetscFunctionBegin;
493: PetscCall(DMPlexGetCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
494: PetscCheck(numCoords == 8, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Quadrilateral should have 8 coordinates, not %" PetscInt_FMT, numCoords);
495: for (f = 0; f < 4; ++f) {
496: PetscReal x_i = PetscRealPart(coords[faces[2 * f + 0] * 2 + 0]);
497: PetscReal y_i = PetscRealPart(coords[faces[2 * f + 0] * 2 + 1]);
498: PetscReal x_j = PetscRealPart(coords[faces[2 * f + 1] * 2 + 0]);
499: PetscReal y_j = PetscRealPart(coords[faces[2 * f + 1] * 2 + 1]);
501: if ((x == x_j) && (y == y_j)) {
502: // point is a corner
503: crossings = 1;
504: break;
505: }
506: if ((y_j > y) != (y_i > y)) {
507: PetscReal slope = (x - x_j) * (y_i - y_j) - (x_i - x_j) * (y - y_j);
508: if (slope == 0) {
509: // point is a corner
510: crossings = 1;
511: break;
512: }
513: if ((slope < 0) != (y_i < y_j)) ++crossings;
514: }
515: }
516: if (crossings % 2) *cell = c;
517: else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
518: PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
519: PetscFunctionReturn(PETSC_SUCCESS);
520: }
522: static PetscErrorCode DMPlexLocatePoint_Simplex_3D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
523: {
524: const PetscInt embedDim = 3;
525: const PetscReal eps = PETSC_SQRT_MACHINE_EPSILON;
526: PetscReal v0[3], J[9], invJ[9], detJ;
527: PetscReal x = PetscRealPart(point[0]);
528: PetscReal y = PetscRealPart(point[1]);
529: PetscReal z = PetscRealPart(point[2]);
530: PetscReal xi, eta, zeta;
532: PetscFunctionBegin;
533: PetscCall(DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ));
534: xi = invJ[0 * embedDim + 0] * (x - v0[0]) + invJ[0 * embedDim + 1] * (y - v0[1]) + invJ[0 * embedDim + 2] * (z - v0[2]);
535: eta = invJ[1 * embedDim + 0] * (x - v0[0]) + invJ[1 * embedDim + 1] * (y - v0[1]) + invJ[1 * embedDim + 2] * (z - v0[2]);
536: zeta = invJ[2 * embedDim + 0] * (x - v0[0]) + invJ[2 * embedDim + 1] * (y - v0[1]) + invJ[2 * embedDim + 2] * (z - v0[2]);
538: if ((xi >= -eps) && (eta >= -eps) && (zeta >= -eps) && (xi + eta + zeta <= 2.0 + eps)) *cell = c;
539: else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
540: PetscFunctionReturn(PETSC_SUCCESS);
541: }
543: static PetscErrorCode DMPlexLocatePoint_General_3D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
544: {
545: const PetscScalar *array;
546: PetscScalar *coords = NULL;
547: 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};
548: PetscBool found = PETSC_TRUE;
549: PetscInt numCoords, f;
550: PetscBool isDG;
552: PetscFunctionBegin;
553: PetscCall(DMPlexGetCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
554: PetscCheck(numCoords == 24, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Quadrilateral should have 8 coordinates, not %" PetscInt_FMT, numCoords);
555: for (f = 0; f < 6; ++f) {
556: /* Check the point is under plane */
557: /* Get face normal */
558: PetscReal v_i[3];
559: PetscReal v_j[3];
560: PetscReal normal[3];
561: PetscReal pp[3];
562: PetscReal dot;
564: v_i[0] = PetscRealPart(coords[faces[f * 4 + 3] * 3 + 0] - coords[faces[f * 4 + 0] * 3 + 0]);
565: v_i[1] = PetscRealPart(coords[faces[f * 4 + 3] * 3 + 1] - coords[faces[f * 4 + 0] * 3 + 1]);
566: v_i[2] = PetscRealPart(coords[faces[f * 4 + 3] * 3 + 2] - coords[faces[f * 4 + 0] * 3 + 2]);
567: v_j[0] = PetscRealPart(coords[faces[f * 4 + 1] * 3 + 0] - coords[faces[f * 4 + 0] * 3 + 0]);
568: v_j[1] = PetscRealPart(coords[faces[f * 4 + 1] * 3 + 1] - coords[faces[f * 4 + 0] * 3 + 1]);
569: v_j[2] = PetscRealPart(coords[faces[f * 4 + 1] * 3 + 2] - coords[faces[f * 4 + 0] * 3 + 2]);
570: normal[0] = v_i[1] * v_j[2] - v_i[2] * v_j[1];
571: normal[1] = v_i[2] * v_j[0] - v_i[0] * v_j[2];
572: normal[2] = v_i[0] * v_j[1] - v_i[1] * v_j[0];
573: pp[0] = PetscRealPart(coords[faces[f * 4 + 0] * 3 + 0] - point[0]);
574: pp[1] = PetscRealPart(coords[faces[f * 4 + 0] * 3 + 1] - point[1]);
575: pp[2] = PetscRealPart(coords[faces[f * 4 + 0] * 3 + 2] - point[2]);
576: dot = normal[0] * pp[0] + normal[1] * pp[1] + normal[2] * pp[2];
578: /* Check that projected point is in face (2D location problem) */
579: if (dot < 0.0) {
580: found = PETSC_FALSE;
581: break;
582: }
583: }
584: if (found) *cell = c;
585: else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
586: PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
587: PetscFunctionReturn(PETSC_SUCCESS);
588: }
590: static PetscErrorCode PetscGridHashInitialize_Internal(PetscGridHash box, PetscInt dim, const PetscScalar point[])
591: {
592: PetscInt d;
594: PetscFunctionBegin;
595: box->dim = dim;
596: for (d = 0; d < dim; ++d) box->lower[d] = box->upper[d] = point ? PetscRealPart(point[d]) : 0.;
597: PetscFunctionReturn(PETSC_SUCCESS);
598: }
600: PetscErrorCode PetscGridHashCreate(MPI_Comm comm, PetscInt dim, const PetscScalar point[], PetscGridHash *box)
601: {
602: PetscFunctionBegin;
603: PetscCall(PetscCalloc1(1, box));
604: PetscCall(PetscGridHashInitialize_Internal(*box, dim, point));
605: PetscFunctionReturn(PETSC_SUCCESS);
606: }
608: PetscErrorCode PetscGridHashEnlarge(PetscGridHash box, const PetscScalar point[])
609: {
610: PetscInt d;
612: PetscFunctionBegin;
613: for (d = 0; d < box->dim; ++d) {
614: box->lower[d] = PetscMin(box->lower[d], PetscRealPart(point[d]));
615: box->upper[d] = PetscMax(box->upper[d], PetscRealPart(point[d]));
616: }
617: PetscFunctionReturn(PETSC_SUCCESS);
618: }
620: static PetscErrorCode DMPlexCreateGridHash(DM dm, PetscGridHash *box)
621: {
622: Vec coordinates;
623: const PetscScalar *a;
624: PetscInt cdim, cStart, cEnd;
626: PetscFunctionBegin;
627: PetscCall(DMGetCoordinateDim(dm, &cdim));
628: PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
629: PetscCall(DMGetCoordinatesLocal(dm, &coordinates));
631: PetscCall(VecGetArrayRead(coordinates, &a));
632: PetscCall(PetscGridHashCreate(PetscObjectComm((PetscObject)dm), cdim, a, box));
633: PetscCall(VecRestoreArrayRead(coordinates, &a));
634: for (PetscInt c = cStart; c < cEnd; ++c) {
635: const PetscScalar *array;
636: PetscScalar *coords = NULL;
637: PetscInt numCoords;
638: PetscBool isDG;
640: PetscCall(DMPlexGetCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
641: for (PetscInt i = 0; i < numCoords / cdim; ++i) PetscCall(PetscGridHashEnlarge(*box, &coords[i * cdim]));
642: PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
643: }
644: PetscFunctionReturn(PETSC_SUCCESS);
645: }
647: /*@C
648: PetscGridHashSetGrid - Divide the grid into boxes
650: Not Collective
652: Input Parameters:
653: + box - The grid hash object
654: . n - The number of boxes in each dimension, may use `PETSC_DETERMINE` for the entries
655: - h - The box size in each dimension, only used if n[d] == `PETSC_DETERMINE`, if not needed you can pass in `NULL`
657: Level: developer
659: .seealso: `DMPLEX`, `PetscGridHashCreate()`
660: @*/
661: PetscErrorCode PetscGridHashSetGrid(PetscGridHash box, const PetscInt n[], const PetscReal h[])
662: {
663: PetscInt d;
665: PetscFunctionBegin;
666: PetscAssertPointer(n, 2);
667: if (h) PetscAssertPointer(h, 3);
668: for (d = 0; d < box->dim; ++d) {
669: box->extent[d] = box->upper[d] - box->lower[d];
670: if (n[d] == PETSC_DETERMINE) {
671: PetscCheck(h, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Missing h");
672: box->h[d] = h[d];
673: box->n[d] = PetscCeilReal(box->extent[d] / h[d]);
674: } else {
675: box->n[d] = n[d];
676: box->h[d] = box->extent[d] / n[d];
677: }
678: }
679: PetscFunctionReturn(PETSC_SUCCESS);
680: }
682: /*@C
683: PetscGridHashGetEnclosingBox - Find the grid boxes containing each input point
685: Not Collective
687: Input Parameters:
688: + box - The grid hash object
689: . numPoints - The number of input points
690: - points - The input point coordinates
692: Output Parameters:
693: + dboxes - An array of `numPoints` x `dim` integers expressing the enclosing box as (i_0, i_1, ..., i_dim)
694: - boxes - An array of `numPoints` integers expressing the enclosing box as single number, or `NULL`
696: Level: developer
698: Note:
699: This only guarantees that a box contains a point, not that a cell does.
701: .seealso: `DMPLEX`, `PetscGridHashCreate()`
702: @*/
703: PetscErrorCode PetscGridHashGetEnclosingBox(PetscGridHash box, PetscInt numPoints, const PetscScalar points[], PetscInt dboxes[], PetscInt boxes[])
704: {
705: const PetscReal *lower = box->lower;
706: const PetscReal *upper = box->upper;
707: const PetscReal *h = box->h;
708: const PetscInt *n = box->n;
709: const PetscInt dim = box->dim;
710: PetscInt d, p;
712: PetscFunctionBegin;
713: for (p = 0; p < numPoints; ++p) {
714: for (d = 0; d < dim; ++d) {
715: PetscInt dbox = PetscFloorReal((PetscRealPart(points[p * dim + d]) - lower[d]) / h[d]);
717: if (dbox == n[d] && PetscAbsReal(PetscRealPart(points[p * dim + d]) - upper[d]) < 1.0e-9) dbox = n[d] - 1;
718: if (dbox == -1 && PetscAbsReal(PetscRealPart(points[p * dim + d]) - lower[d]) < 1.0e-9) dbox = 0;
719: 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]);
720: dboxes[p * dim + d] = dbox;
721: }
722: if (boxes)
723: for (d = dim - 2, boxes[p] = dboxes[p * dim + dim - 1]; d >= 0; --d) boxes[p] = boxes[p] * n[d] + dboxes[p * dim + d];
724: }
725: PetscFunctionReturn(PETSC_SUCCESS);
726: }
728: /*
729: PetscGridHashGetEnclosingBoxQuery - Find the grid boxes containing each input point
731: Not Collective
733: Input Parameters:
734: + box - The grid hash object
735: . cellSection - The PetscSection mapping cells to boxes
736: . numPoints - The number of input points
737: - points - The input point coordinates
739: Output Parameters:
740: + dboxes - An array of `numPoints`*`dim` integers expressing the enclosing box as (i_0, i_1, ..., i_dim)
741: . boxes - An array of `numPoints` integers expressing the enclosing box as single number, or `NULL`
742: - found - Flag indicating if point was located within a box
744: Level: developer
746: Note:
747: 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.
749: .seealso: `DMPLEX`, `PetscGridHashGetEnclosingBox()`
750: */
751: static PetscErrorCode PetscGridHashGetEnclosingBoxQuery(PetscGridHash box, PetscSection cellSection, PetscInt numPoints, const PetscScalar points[], PetscInt dboxes[], PetscInt boxes[], PetscBool *found)
752: {
753: const PetscReal *lower = box->lower;
754: const PetscReal *upper = box->upper;
755: const PetscReal *h = box->h;
756: const PetscInt *n = box->n;
757: const PetscInt dim = box->dim;
758: PetscInt bStart, bEnd, d, p;
760: PetscFunctionBegin;
762: *found = PETSC_FALSE;
763: PetscCall(PetscSectionGetChart(box->cellSection, &bStart, &bEnd));
764: for (p = 0; p < numPoints; ++p) {
765: for (d = 0; d < dim; ++d) {
766: PetscInt dbox = PetscFloorReal((PetscRealPart(points[p * dim + d]) - lower[d]) / h[d]);
768: if (dbox == n[d] && PetscAbsReal(PetscRealPart(points[p * dim + d]) - upper[d]) < 1.0e-9) dbox = n[d] - 1;
769: if (dbox < 0 || dbox >= n[d]) PetscFunctionReturn(PETSC_SUCCESS);
770: dboxes[p * dim + d] = dbox;
771: }
772: if (boxes)
773: for (d = dim - 2, boxes[p] = dboxes[p * dim + dim - 1]; d >= 0; --d) boxes[p] = boxes[p] * n[d] + dboxes[p * dim + d];
774: // It is possible for a box to overlap no grid cells
775: if (boxes[p] < bStart || boxes[p] >= bEnd) PetscFunctionReturn(PETSC_SUCCESS);
776: }
777: *found = PETSC_TRUE;
778: PetscFunctionReturn(PETSC_SUCCESS);
779: }
781: PetscErrorCode PetscGridHashDestroy(PetscGridHash *box)
782: {
783: PetscFunctionBegin;
784: if (*box) {
785: PetscCall(PetscSectionDestroy(&(*box)->cellSection));
786: PetscCall(ISDestroy(&(*box)->cells));
787: PetscCall(DMLabelDestroy(&(*box)->cellsSparse));
788: }
789: PetscCall(PetscFree(*box));
790: PetscFunctionReturn(PETSC_SUCCESS);
791: }
793: PetscErrorCode DMPlexLocatePoint_Internal(DM dm, PetscInt dim, const PetscScalar point[], PetscInt cellStart, PetscInt *cell)
794: {
795: DMPolytopeType ct;
797: PetscFunctionBegin;
798: PetscCall(DMPlexGetCellType(dm, cellStart, &ct));
799: switch (ct) {
800: case DM_POLYTOPE_SEGMENT:
801: PetscCall(DMPlexLocatePoint_Simplex_1D_Internal(dm, point, cellStart, cell));
802: break;
803: case DM_POLYTOPE_TRIANGLE:
804: PetscCall(DMPlexLocatePoint_Simplex_2D_Internal(dm, point, cellStart, cell));
805: break;
806: case DM_POLYTOPE_QUADRILATERAL:
807: PetscCall(DMPlexLocatePoint_Quad_2D_Internal(dm, point, cellStart, cell));
808: break;
809: case DM_POLYTOPE_TETRAHEDRON:
810: PetscCall(DMPlexLocatePoint_Simplex_3D_Internal(dm, point, cellStart, cell));
811: break;
812: case DM_POLYTOPE_HEXAHEDRON:
813: PetscCall(DMPlexLocatePoint_General_3D_Internal(dm, point, cellStart, cell));
814: break;
815: default:
816: SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No point location for cell %" PetscInt_FMT " with type %s", cellStart, DMPolytopeTypes[ct]);
817: }
818: PetscFunctionReturn(PETSC_SUCCESS);
819: }
821: /*
822: DMPlexClosestPoint_Internal - Returns the closest point in the cell to the given point
823: */
824: static PetscErrorCode DMPlexClosestPoint_Internal(DM dm, PetscInt dim, const PetscScalar point[], PetscInt cell, PetscReal cpoint[])
825: {
826: DMPolytopeType ct;
828: PetscFunctionBegin;
829: PetscCall(DMPlexGetCellType(dm, cell, &ct));
830: switch (ct) {
831: case DM_POLYTOPE_TRIANGLE:
832: PetscCall(DMPlexClosestPoint_Simplex_2D_Internal(dm, point, cell, cpoint));
833: break;
834: #if 0
835: case DM_POLYTOPE_QUADRILATERAL:
836: PetscCall(DMPlexClosestPoint_General_2D_Internal(dm, point, cell, cpoint));break;
837: case DM_POLYTOPE_TETRAHEDRON:
838: PetscCall(DMPlexClosestPoint_Simplex_3D_Internal(dm, point, cell, cpoint));break;
839: case DM_POLYTOPE_HEXAHEDRON:
840: PetscCall(DMPlexClosestPoint_General_3D_Internal(dm, point, cell, cpoint));break;
841: #endif
842: default:
843: SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No closest point location for cell %" PetscInt_FMT " with type %s", cell, DMPolytopeTypes[ct]);
844: }
845: PetscFunctionReturn(PETSC_SUCCESS);
846: }
848: /*
849: DMPlexComputeGridHash_Internal - Create a grid hash structure covering the `DMPLEX`
851: Collective
853: Input Parameter:
854: . dm - The `DMPLEX`
856: Output Parameter:
857: . localBox - The grid hash object
859: Level: developer
861: Notes:
862: How do we determine all boxes intersecting a given cell?
864: 1) Get convex body enclosing cell. We will use a box called the box-hull.
866: 2) Get smallest brick of boxes enclosing the box-hull
868: 3) Each box is composed of 6 planes, 3 lower and 3 upper. We loop over dimensions, and
869: for each new plane determine whether the cell is on the negative side, positive side, or intersects it.
871: a) If the cell is on the negative side of the lower planes, it is not in the box
873: b) If the cell is on the positive side of the upper planes, it is not in the box
875: c) If there is no intersection, it is in the box
877: d) If any intersection point is within the box limits, it is in the box
879: .seealso: `DMPLEX`, `PetscGridHashCreate()`, `PetscGridHashGetEnclosingBox()`
880: */
881: static PetscErrorCode DMPlexComputeGridHash_Internal(DM dm, PetscGridHash *localBox)
882: {
883: PetscInt debug = ((DM_Plex *)dm->data)->printLocate;
884: PetscGridHash lbox;
885: PetscSF sf;
886: const PetscInt *leaves;
887: PetscInt *dboxes, *boxes;
888: PetscInt cdim, cStart, cEnd, Nl = -1;
889: PetscBool flg;
891: PetscFunctionBegin;
892: PetscCall(DMGetCoordinateDim(dm, &cdim));
893: PetscCall(DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd));
894: PetscCall(DMPlexCreateGridHash(dm, &lbox));
895: {
896: PetscInt n[3], d;
898: PetscCall(PetscOptionsGetIntArray(NULL, ((PetscObject)dm)->prefix, "-dm_plex_hash_box_faces", n, &d, &flg));
899: if (flg) {
900: for (PetscInt i = d; i < cdim; ++i) n[i] = n[d - 1];
901: } else {
902: for (PetscInt i = 0; i < cdim; ++i) n[i] = PetscMax(2, PetscFloorReal(PetscPowReal((PetscReal)(cEnd - cStart), 1.0 / cdim) * 0.8));
903: }
904: PetscCall(PetscGridHashSetGrid(lbox, n, NULL));
905: if (debug)
906: 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.,
907: (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.));
908: }
910: PetscCall(DMGetPointSF(dm, &sf));
911: if (sf) PetscCall(PetscSFGetGraph(sf, NULL, &Nl, &leaves, NULL));
912: Nl = PetscMax(Nl, 0);
913: PetscCall(PetscCalloc2(16 * cdim, &dboxes, 16, &boxes));
915: PetscCall(DMLabelCreate(PETSC_COMM_SELF, "cells", &lbox->cellsSparse));
916: PetscCall(DMLabelCreateIndex(lbox->cellsSparse, cStart, cEnd));
917: for (PetscInt c = cStart; c < cEnd; ++c) {
918: PetscReal intPoints[6 * 6 * 6 * 3];
919: const PetscScalar *array;
920: PetscScalar *coords = NULL;
921: const PetscReal *h = lbox->h;
922: PetscReal normal[9] = {1., 0., 0., 0., 1., 0., 0., 0., 1.};
923: PetscReal *lowerIntPoints[3] = {&intPoints[0 * 6 * 6 * 3], &intPoints[1 * 6 * 6 * 3], &intPoints[2 * 6 * 6 * 3]};
924: PetscReal *upperIntPoints[3] = {&intPoints[3 * 6 * 6 * 3], &intPoints[4 * 6 * 6 * 3], &intPoints[5 * 6 * 6 * 3]};
925: PetscReal lp[3], up[3], *tmp;
926: PetscInt numCoords, idx, dlim[6], lowerInt[3], upperInt[3];
927: PetscBool isDG, lower[3], upper[3];
929: PetscCall(PetscFindInt(c, Nl, leaves, &idx));
930: if (idx >= 0) continue;
931: // Get grid of boxes containing the cell
932: PetscCall(DMPlexGetCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
933: PetscCall(PetscGridHashGetEnclosingBox(lbox, numCoords / cdim, coords, dboxes, boxes));
934: PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
935: for (PetscInt d = 0; d < cdim; ++d) dlim[d * 2 + 0] = dlim[d * 2 + 1] = dboxes[d];
936: for (PetscInt d = cdim; d < 3; ++d) dlim[d * 2 + 0] = dlim[d * 2 + 1] = 0;
937: for (PetscInt e = 1; e < numCoords / cdim; ++e) {
938: for (PetscInt d = 0; d < cdim; ++d) {
939: dlim[d * 2 + 0] = PetscMin(dlim[d * 2 + 0], dboxes[e * cdim + d]);
940: dlim[d * 2 + 1] = PetscMax(dlim[d * 2 + 1], dboxes[e * cdim + d]);
941: }
942: }
943: if (debug > 4) {
944: 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]));
945: }
946: // Initialize with lower planes for first box
947: for (PetscInt d = 0; d < cdim; ++d) {
948: lp[d] = lbox->lower[d] + dlim[d * 2 + 0] * h[d];
949: up[d] = lp[d] + h[d];
950: }
951: for (PetscInt d = 0; d < cdim; ++d) {
952: PetscCall(DMPlexGetPlaneCellIntersection_Internal(dm, c, lp, &normal[d * 3], &lower[d], &lowerInt[d], lowerIntPoints[d]));
953: if (debug > 4) {
954: if (!lowerInt[d])
955: 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"));
956: 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]));
957: }
958: }
959: // Loop over grid
960: for (PetscInt k = dlim[2 * 2 + 0]; k <= dlim[2 * 2 + 1]; ++k, lp[2] = up[2], up[2] += h[2]) {
961: if (cdim > 2) PetscCall(DMPlexGetPlaneCellIntersection_Internal(dm, c, up, &normal[3 * 2], &upper[2], &upperInt[2], upperIntPoints[2]));
962: if (cdim > 2 && debug > 4) {
963: 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"));
964: 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]));
965: }
966: for (PetscInt j = dlim[1 * 2 + 0]; j <= dlim[1 * 2 + 1]; ++j, lp[1] = up[1], up[1] += h[1]) {
967: if (cdim > 1) PetscCall(DMPlexGetPlaneCellIntersection_Internal(dm, c, up, &normal[3 * 1], &upper[1], &upperInt[1], upperIntPoints[1]));
968: if (cdim > 1 && debug > 4) {
969: if (!upperInt[1])
970: 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"));
971: 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]));
972: }
973: for (PetscInt i = dlim[0 * 2 + 0]; i <= dlim[0 * 2 + 1]; ++i, lp[0] = up[0], up[0] += h[0]) {
974: const PetscInt box = (k * lbox->n[1] + j) * lbox->n[0] + i;
975: PetscBool excNeg = PETSC_TRUE;
976: PetscBool excPos = PETSC_TRUE;
977: PetscInt NlInt = 0;
978: PetscInt NuInt = 0;
980: PetscCall(DMPlexGetPlaneCellIntersection_Internal(dm, c, up, &normal[3 * 0], &upper[0], &upperInt[0], upperIntPoints[0]));
981: if (debug > 4) {
982: if (!upperInt[0])
983: 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"));
984: 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]));
985: }
986: for (PetscInt d = 0; d < cdim; ++d) {
987: NlInt += lowerInt[d];
988: NuInt += upperInt[d];
989: }
990: // If there is no intersection...
991: if (!NlInt && !NuInt) {
992: // If the cell is on the negative side of the lower planes, it is not in the box
993: for (PetscInt d = 0; d < cdim; ++d)
994: if (lower[d]) {
995: excNeg = PETSC_FALSE;
996: break;
997: }
998: // If the cell is on the positive side of the upper planes, it is not in the box
999: for (PetscInt d = 0; d < cdim; ++d)
1000: if (!upper[d]) {
1001: excPos = PETSC_FALSE;
1002: break;
1003: }
1004: if (excNeg || excPos) {
1005: if (debug && excNeg) PetscCall(PetscPrintf(PETSC_COMM_SELF, " Cell %" PetscInt_FMT " is on the negative side of the lower plane\n", c));
1006: if (debug && excPos) PetscCall(PetscPrintf(PETSC_COMM_SELF, " Cell %" PetscInt_FMT " is on the positive side of the upper plane\n", c));
1007: continue;
1008: }
1009: // Otherwise it is in the box
1010: if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, " Cell %" PetscInt_FMT " is contained in box %" PetscInt_FMT "\n", c, box));
1011: PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
1012: continue;
1013: }
1014: /*
1015: If any intersection point is within the box limits, it is in the box
1016: We need to have tolerances here since intersection point calculations can introduce errors
1017: Initialize a count to track which planes have intersection outside the box.
1018: if two adjacent planes have intersection points upper and lower all outside the box, look
1019: first at if another plane has intersection points outside the box, if so, it is inside the cell
1020: look next if no intersection points exist on the other planes, and check if the planes are on the
1021: outside of the intersection points but on opposite ends. If so, the box cuts through the cell.
1022: */
1023: PetscInt outsideCount[6] = {0, 0, 0, 0, 0, 0};
1024: for (PetscInt plane = 0; plane < cdim; ++plane) {
1025: for (PetscInt ip = 0; ip < lowerInt[plane]; ++ip) {
1026: PetscInt d;
1028: for (d = 0; d < cdim; ++d) {
1029: if ((lowerIntPoints[plane][ip * cdim + d] < (lp[d] - PETSC_SMALL)) || (lowerIntPoints[plane][ip * cdim + d] > (up[d] + PETSC_SMALL))) {
1030: 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
1031: break;
1032: }
1033: }
1034: if (d == cdim) {
1035: if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, " Cell %" PetscInt_FMT " intersected lower plane %" PetscInt_FMT " of box %" PetscInt_FMT "\n", c, plane, box));
1036: PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
1037: goto end;
1038: }
1039: }
1040: for (PetscInt ip = 0; ip < upperInt[plane]; ++ip) {
1041: PetscInt d;
1043: for (d = 0; d < cdim; ++d) {
1044: if ((upperIntPoints[plane][ip * cdim + d] < (lp[d] - PETSC_SMALL)) || (upperIntPoints[plane][ip * cdim + d] > (up[d] + PETSC_SMALL))) {
1045: 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
1046: break;
1047: }
1048: }
1049: if (d == cdim) {
1050: if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, " Cell %" PetscInt_FMT " intersected upper plane %" PetscInt_FMT " of box %" PetscInt_FMT "\n", c, plane, box));
1051: PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
1052: goto end;
1053: }
1054: }
1055: }
1056: /*
1057: Check the planes with intersections
1058: in 2D, check if the square falls in the middle of a cell
1059: ie all four planes have intersection points outside of the box
1060: You do not want to be doing this, because it means your grid hashing is finer than your grid,
1061: but we should still support it I guess
1062: */
1063: if (cdim == 2) {
1064: PetscInt nIntersects = 0;
1065: for (PetscInt d = 0; d < cdim; ++d) nIntersects += (outsideCount[d] + outsideCount[d + cdim]);
1066: // if the count adds up to 8, that means each plane has 2 external intersections and thus it is in the cell
1067: if (nIntersects == 8) {
1068: PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
1069: goto end;
1070: }
1071: }
1072: /*
1073: In 3 dimensions, if two adjacent planes have at least 3 intersections outside the cell in the appropriate direction,
1074: we then check the 3rd planar dimension. If a plane falls between intersection points, the cell belongs to that box.
1075: If the planes are on opposite sides of the intersection points, the cell belongs to that box and it passes through the cell.
1076: */
1077: if (cdim == 3) {
1078: PetscInt faces[3] = {0, 0, 0}, checkInternalFace = 0;
1079: // Find two adjacent planes with at least 3 intersection points in the upper and lower
1080: // if the third plane has 3 intersection points or more, a pyramid base is formed on that plane and it is in the cell
1081: for (PetscInt d = 0; d < cdim; ++d)
1082: if (outsideCount[d] >= 3 && outsideCount[cdim + d] >= 3) {
1083: faces[d]++;
1084: checkInternalFace++;
1085: }
1086: if (checkInternalFace == 3) {
1087: // All planes have 3 intersection points, add it.
1088: PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
1089: goto end;
1090: }
1091: // Gross, figure out which adjacent faces have at least 3 points
1092: PetscInt nonIntersectingFace = -1;
1093: if (faces[0] == faces[1]) nonIntersectingFace = 2;
1094: if (faces[0] == faces[2]) nonIntersectingFace = 1;
1095: if (faces[1] == faces[2]) nonIntersectingFace = 0;
1096: if (nonIntersectingFace >= 0) {
1097: for (PetscInt plane = 0; plane < cdim; ++plane) {
1098: if (!lowerInt[nonIntersectingFace] && !upperInt[nonIntersectingFace]) continue;
1099: // 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.
1100: for (PetscInt ip = 0; ip < lowerInt[nonIntersectingFace]; ++ip) {
1101: if (lowerIntPoints[plane][ip * cdim + nonIntersectingFace] > lp[nonIntersectingFace] - PETSC_SMALL || lowerIntPoints[plane][ip * cdim + nonIntersectingFace] < up[nonIntersectingFace] + PETSC_SMALL) goto setpoint;
1102: }
1103: for (PetscInt ip = 0; ip < upperInt[nonIntersectingFace]; ++ip) {
1104: if (upperIntPoints[plane][ip * cdim + nonIntersectingFace] > lp[nonIntersectingFace] - PETSC_SMALL || upperIntPoints[plane][ip * cdim + nonIntersectingFace] < up[nonIntersectingFace] + PETSC_SMALL) goto setpoint;
1105: }
1106: goto end;
1107: }
1108: // The points are within the bonds of the non intersecting planes, add it.
1109: setpoint:
1110: PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
1111: goto end;
1112: }
1113: }
1114: end:
1115: lower[0] = upper[0];
1116: lowerInt[0] = upperInt[0];
1117: tmp = lowerIntPoints[0];
1118: lowerIntPoints[0] = upperIntPoints[0];
1119: upperIntPoints[0] = tmp;
1120: }
1121: lp[0] = lbox->lower[0] + dlim[0 * 2 + 0] * h[0];
1122: up[0] = lp[0] + h[0];
1123: lower[1] = upper[1];
1124: lowerInt[1] = upperInt[1];
1125: tmp = lowerIntPoints[1];
1126: lowerIntPoints[1] = upperIntPoints[1];
1127: upperIntPoints[1] = tmp;
1128: }
1129: lp[1] = lbox->lower[1] + dlim[1 * 2 + 0] * h[1];
1130: up[1] = lp[1] + h[1];
1131: lower[2] = upper[2];
1132: lowerInt[2] = upperInt[2];
1133: tmp = lowerIntPoints[2];
1134: lowerIntPoints[2] = upperIntPoints[2];
1135: upperIntPoints[2] = tmp;
1136: }
1137: }
1138: PetscCall(PetscFree2(dboxes, boxes));
1140: if (debug) PetscCall(DMLabelView(lbox->cellsSparse, PETSC_VIEWER_STDOUT_SELF));
1141: PetscCall(DMLabelConvertToSection(lbox->cellsSparse, &lbox->cellSection, &lbox->cells));
1142: PetscCall(DMLabelDestroy(&lbox->cellsSparse));
1143: *localBox = lbox;
1144: PetscFunctionReturn(PETSC_SUCCESS);
1145: }
1147: PetscErrorCode DMLocatePoints_Plex(DM dm, Vec v, DMPointLocationType ltype, PetscSF cellSF)
1148: {
1149: PetscInt debug = ((DM_Plex *)dm->data)->printLocate;
1150: DM_Plex *mesh = (DM_Plex *)dm->data;
1151: PetscBool hash = mesh->useHashLocation, reuse = PETSC_FALSE;
1152: PetscInt bs, numPoints, p, numFound, *found = NULL;
1153: PetscInt dim, Nl = 0, cStart, cEnd, numCells, c, d;
1154: PetscSF sf;
1155: const PetscInt *leaves;
1156: const PetscInt *boxCells;
1157: PetscSFNode *cells;
1158: PetscScalar *a;
1159: PetscMPIInt result;
1160: PetscLogDouble t0, t1;
1161: PetscReal gmin[3], gmax[3];
1162: PetscInt terminating_query_type[] = {0, 0, 0};
1163: PetscMPIInt rank;
1165: PetscFunctionBegin;
1166: PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank));
1167: PetscCall(PetscLogEventBegin(DMPLEX_LocatePoints, 0, 0, 0, 0));
1168: PetscCall(PetscTime(&t0));
1169: 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.");
1170: PetscCall(DMGetCoordinateDim(dm, &dim));
1171: PetscCall(VecGetBlockSize(v, &bs));
1172: PetscCallMPI(MPI_Comm_compare(PetscObjectComm((PetscObject)cellSF), PETSC_COMM_SELF, &result));
1173: PetscCheck(result == MPI_IDENT || result == MPI_CONGRUENT, PetscObjectComm((PetscObject)cellSF), PETSC_ERR_SUP, "Trying parallel point location: only local point location supported");
1174: // We ignore extra coordinates
1175: PetscCheck(bs >= dim, PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Block size for point vector %" PetscInt_FMT " must be the mesh coordinate dimension %" PetscInt_FMT, bs, dim);
1176: PetscCall(DMGetCoordinatesLocalSetUp(dm));
1177: PetscCall(DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd));
1178: PetscCall(DMGetPointSF(dm, &sf));
1179: if (sf) PetscCall(PetscSFGetGraph(sf, NULL, &Nl, &leaves, NULL));
1180: Nl = PetscMax(Nl, 0);
1181: PetscCall(VecGetLocalSize(v, &numPoints));
1182: PetscCall(VecGetArray(v, &a));
1183: numPoints /= bs;
1184: {
1185: const PetscSFNode *sf_cells;
1187: PetscCall(PetscSFGetGraph(cellSF, NULL, NULL, NULL, &sf_cells));
1188: if (sf_cells) {
1189: PetscCall(PetscInfo(dm, "[DMLocatePoints_Plex] Re-using existing StarForest node list\n"));
1190: cells = (PetscSFNode *)sf_cells;
1191: reuse = PETSC_TRUE;
1192: } else {
1193: PetscCall(PetscInfo(dm, "[DMLocatePoints_Plex] Creating and initializing new StarForest node list\n"));
1194: PetscCall(PetscMalloc1(numPoints, &cells));
1195: /* initialize cells if created */
1196: for (p = 0; p < numPoints; p++) {
1197: cells[p].rank = 0;
1198: cells[p].index = DMLOCATEPOINT_POINT_NOT_FOUND;
1199: }
1200: }
1201: }
1202: PetscCall(DMGetBoundingBox(dm, gmin, gmax));
1203: if (hash) {
1204: if (!mesh->lbox) {
1205: PetscCall(PetscInfo(dm, "Initializing grid hashing\n"));
1206: PetscCall(DMPlexComputeGridHash_Internal(dm, &mesh->lbox));
1207: }
1208: /* Designate the local box for each point */
1209: /* Send points to correct process */
1210: /* Search cells that lie in each subbox */
1211: /* Should we bin points before doing search? */
1212: PetscCall(ISGetIndices(mesh->lbox->cells, &boxCells));
1213: }
1214: for (p = 0, numFound = 0; p < numPoints; ++p) {
1215: const PetscScalar *point = &a[p * bs];
1216: PetscInt dbin[3] = {-1, -1, -1}, bin, cell = -1, cellOffset;
1217: PetscBool point_outside_domain = PETSC_FALSE;
1219: /* check bounding box of domain */
1220: for (d = 0; d < dim; d++) {
1221: if (PetscRealPart(point[d]) < gmin[d]) {
1222: point_outside_domain = PETSC_TRUE;
1223: break;
1224: }
1225: if (PetscRealPart(point[d]) > gmax[d]) {
1226: point_outside_domain = PETSC_TRUE;
1227: break;
1228: }
1229: }
1230: if (point_outside_domain) {
1231: cells[p].rank = 0;
1232: cells[p].index = DMLOCATEPOINT_POINT_NOT_FOUND;
1233: terminating_query_type[0]++;
1234: continue;
1235: }
1237: /* check initial values in cells[].index - abort early if found */
1238: if (cells[p].index != DMLOCATEPOINT_POINT_NOT_FOUND) {
1239: c = cells[p].index;
1240: cells[p].index = DMLOCATEPOINT_POINT_NOT_FOUND;
1241: PetscCall(DMPlexLocatePoint_Internal(dm, dim, point, c, &cell));
1242: if (cell >= 0) {
1243: cells[p].rank = 0;
1244: cells[p].index = cell;
1245: numFound++;
1246: }
1247: }
1248: if (cells[p].index != DMLOCATEPOINT_POINT_NOT_FOUND) {
1249: terminating_query_type[1]++;
1250: continue;
1251: }
1253: if (hash) {
1254: PetscBool found_box;
1256: if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, "[%d]Checking point %" PetscInt_FMT " (%.2g, %.2g, %.2g)\n", rank, p, (double)PetscRealPart(point[0]), (double)PetscRealPart(point[1]), dim > 2 ? (double)PetscRealPart(point[2]) : 0.));
1257: /* allow for case that point is outside box - abort early */
1258: PetscCall(PetscGridHashGetEnclosingBoxQuery(mesh->lbox, mesh->lbox->cellSection, 1, point, dbin, &bin, &found_box));
1259: if (found_box) {
1260: if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, "[%d] Found point in box %" PetscInt_FMT " (%" PetscInt_FMT ", %" PetscInt_FMT ", %" PetscInt_FMT ")\n", rank, bin, dbin[0], dbin[1], dim > 2 ? dbin[2] : 0));
1261: /* TODO Lay an interface over this so we can switch between Section (dense) and Label (sparse) */
1262: PetscCall(PetscSectionGetDof(mesh->lbox->cellSection, bin, &numCells));
1263: PetscCall(PetscSectionGetOffset(mesh->lbox->cellSection, bin, &cellOffset));
1264: for (c = cellOffset; c < cellOffset + numCells; ++c) {
1265: if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, "[%d] Checking for point in cell %" PetscInt_FMT "\n", rank, boxCells[c]));
1266: PetscCall(DMPlexLocatePoint_Internal(dm, dim, point, boxCells[c], &cell));
1267: if (cell >= 0) {
1268: if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, "[%d] FOUND in cell %" PetscInt_FMT "\n", rank, cell));
1269: cells[p].rank = 0;
1270: cells[p].index = cell;
1271: numFound++;
1272: terminating_query_type[2]++;
1273: break;
1274: }
1275: }
1276: }
1277: } else {
1278: for (c = cStart; c < cEnd; ++c) {
1279: PetscInt idx;
1281: PetscCall(PetscFindInt(c, Nl, leaves, &idx));
1282: if (idx >= 0) continue;
1283: PetscCall(DMPlexLocatePoint_Internal(dm, dim, point, c, &cell));
1284: if (cell >= 0) {
1285: cells[p].rank = 0;
1286: cells[p].index = cell;
1287: numFound++;
1288: terminating_query_type[2]++;
1289: break;
1290: }
1291: }
1292: }
1293: }
1294: if (hash) PetscCall(ISRestoreIndices(mesh->lbox->cells, &boxCells));
1295: if (ltype == DM_POINTLOCATION_NEAREST && hash && numFound < numPoints) {
1296: for (p = 0; p < numPoints; p++) {
1297: const PetscScalar *point = &a[p * bs];
1298: PetscReal cpoint[3] = {0, 0, 0}, diff[3], best[3] = {PETSC_MAX_REAL, PETSC_MAX_REAL, PETSC_MAX_REAL}, dist, distMax = PETSC_MAX_REAL;
1299: PetscInt dbin[3] = {-1, -1, -1}, bin, cellOffset, d, bestc = -1;
1301: if (cells[p].index < 0) {
1302: PetscCall(PetscGridHashGetEnclosingBox(mesh->lbox, 1, point, dbin, &bin));
1303: PetscCall(PetscSectionGetDof(mesh->lbox->cellSection, bin, &numCells));
1304: PetscCall(PetscSectionGetOffset(mesh->lbox->cellSection, bin, &cellOffset));
1305: for (c = cellOffset; c < cellOffset + numCells; ++c) {
1306: PetscCall(DMPlexClosestPoint_Internal(dm, dim, point, boxCells[c], cpoint));
1307: for (d = 0; d < dim; ++d) diff[d] = cpoint[d] - PetscRealPart(point[d]);
1308: dist = DMPlex_NormD_Internal(dim, diff);
1309: if (dist < distMax) {
1310: for (d = 0; d < dim; ++d) best[d] = cpoint[d];
1311: bestc = boxCells[c];
1312: distMax = dist;
1313: }
1314: }
1315: if (distMax < PETSC_MAX_REAL) {
1316: ++numFound;
1317: cells[p].rank = 0;
1318: cells[p].index = bestc;
1319: for (d = 0; d < dim; ++d) a[p * bs + d] = best[d];
1320: }
1321: }
1322: }
1323: }
1324: /* This code is only be relevant when interfaced to parallel point location */
1325: /* Check for highest numbered proc that claims a point (do we care?) */
1326: if (ltype == DM_POINTLOCATION_REMOVE && numFound < numPoints) {
1327: PetscCall(PetscMalloc1(numFound, &found));
1328: for (p = 0, numFound = 0; p < numPoints; p++) {
1329: if (cells[p].rank >= 0 && cells[p].index >= 0) {
1330: if (numFound < p) cells[numFound] = cells[p];
1331: found[numFound++] = p;
1332: }
1333: }
1334: }
1335: PetscCall(VecRestoreArray(v, &a));
1336: if (!reuse) PetscCall(PetscSFSetGraph(cellSF, cEnd - cStart, numFound, found, PETSC_OWN_POINTER, cells, PETSC_OWN_POINTER));
1337: PetscCall(PetscTime(&t1));
1338: if (hash) {
1339: 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]));
1340: } else {
1341: 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]));
1342: }
1343: PetscCall(PetscInfo(dm, "[DMLocatePoints_Plex] npoints %" PetscInt_FMT " : time(rank0) %1.2e (sec): points/sec %1.4e\n", numPoints, t1 - t0, numPoints / (t1 - t0)));
1344: PetscCall(PetscLogEventEnd(DMPLEX_LocatePoints, 0, 0, 0, 0));
1345: PetscFunctionReturn(PETSC_SUCCESS);
1346: }
1348: /*@
1349: DMPlexComputeProjection2Dto1D - Rewrite coordinates to be the 1D projection of the 2D coordinates
1351: Not Collective
1353: Input/Output Parameter:
1354: . 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
1356: Output Parameter:
1357: . R - The rotation which accomplishes the projection, array of size 4
1359: Level: developer
1361: .seealso: `DMPLEX`, `DMPlexComputeProjection3Dto1D()`, `DMPlexComputeProjection3Dto2D()`
1362: @*/
1363: PetscErrorCode DMPlexComputeProjection2Dto1D(PetscScalar coords[], PetscReal R[])
1364: {
1365: const PetscReal x = PetscRealPart(coords[2] - coords[0]);
1366: const PetscReal y = PetscRealPart(coords[3] - coords[1]);
1367: const PetscReal r = PetscSqrtReal(x * x + y * y), c = x / r, s = y / r;
1369: PetscFunctionBegin;
1370: R[0] = c;
1371: R[1] = -s;
1372: R[2] = s;
1373: R[3] = c;
1374: coords[0] = 0.0;
1375: coords[1] = r;
1376: PetscFunctionReturn(PETSC_SUCCESS);
1377: }
1379: /*@
1380: DMPlexComputeProjection3Dto1D - Rewrite coordinates to be the 1D projection of the 3D coordinates
1382: Not Collective
1384: Input/Output Parameter:
1385: . 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
1387: Output Parameter:
1388: . R - The rotation which accomplishes the projection, an array of size 9
1390: Level: developer
1392: Note:
1393: This uses the basis completion described by Frisvad {cite}`frisvad2012building`
1395: .seealso: `DMPLEX`, `DMPlexComputeProjection2Dto1D()`, `DMPlexComputeProjection3Dto2D()`
1396: @*/
1397: PetscErrorCode DMPlexComputeProjection3Dto1D(PetscScalar coords[], PetscReal R[])
1398: {
1399: PetscReal x = PetscRealPart(coords[3] - coords[0]);
1400: PetscReal y = PetscRealPart(coords[4] - coords[1]);
1401: PetscReal z = PetscRealPart(coords[5] - coords[2]);
1402: PetscReal r = PetscSqrtReal(x * x + y * y + z * z);
1403: PetscReal rinv = 1. / r;
1405: PetscFunctionBegin;
1406: x *= rinv;
1407: y *= rinv;
1408: z *= rinv;
1409: if (x > 0.) {
1410: PetscReal inv1pX = 1. / (1. + x);
1412: R[0] = x;
1413: R[1] = -y;
1414: R[2] = -z;
1415: R[3] = y;
1416: R[4] = 1. - y * y * inv1pX;
1417: R[5] = -y * z * inv1pX;
1418: R[6] = z;
1419: R[7] = -y * z * inv1pX;
1420: R[8] = 1. - z * z * inv1pX;
1421: } else {
1422: PetscReal inv1mX = 1. / (1. - x);
1424: R[0] = x;
1425: R[1] = z;
1426: R[2] = y;
1427: R[3] = y;
1428: R[4] = -y * z * inv1mX;
1429: R[5] = 1. - y * y * inv1mX;
1430: R[6] = z;
1431: R[7] = 1. - z * z * inv1mX;
1432: R[8] = -y * z * inv1mX;
1433: }
1434: coords[0] = 0.0;
1435: coords[1] = r;
1436: coords[2] = 0.0;
1437: PetscFunctionReturn(PETSC_SUCCESS);
1438: }
1440: /*@
1441: DMPlexComputeProjection3Dto2D - Rewrite coordinates of 3 or more coplanar 3D points to a common 2D basis for the
1442: plane. The normal is defined by positive orientation of the first 3 points.
1444: Not Collective
1446: Input Parameter:
1447: . coordSize - Length of coordinate array (3x number of points); must be at least 9 (3 points)
1449: Input/Output Parameter:
1450: . coords - The interlaced coordinates of each coplanar 3D point; on output the first
1451: 2*coordSize/3 entries contain interlaced 2D points, with the rest undefined
1453: Output Parameter:
1454: . 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.
1456: Level: developer
1458: .seealso: `DMPLEX`, `DMPlexComputeProjection2Dto1D()`, `DMPlexComputeProjection3Dto1D()`
1459: @*/
1460: PetscErrorCode DMPlexComputeProjection3Dto2D(PetscInt coordSize, PetscScalar coords[], PetscReal R[])
1461: {
1462: PetscReal x1[3], x2[3], n[3], c[3], norm;
1463: const PetscInt dim = 3;
1464: PetscInt d, p;
1466: PetscFunctionBegin;
1467: /* 0) Calculate normal vector */
1468: for (d = 0; d < dim; ++d) {
1469: x1[d] = PetscRealPart(coords[1 * dim + d] - coords[0 * dim + d]);
1470: x2[d] = PetscRealPart(coords[2 * dim + d] - coords[0 * dim + d]);
1471: }
1472: // n = x1 \otimes x2
1473: n[0] = x1[1] * x2[2] - x1[2] * x2[1];
1474: n[1] = x1[2] * x2[0] - x1[0] * x2[2];
1475: n[2] = x1[0] * x2[1] - x1[1] * x2[0];
1476: norm = PetscSqrtReal(n[0] * n[0] + n[1] * n[1] + n[2] * n[2]);
1477: for (d = 0; d < dim; d++) n[d] /= norm;
1478: norm = PetscSqrtReal(x1[0] * x1[0] + x1[1] * x1[1] + x1[2] * x1[2]);
1479: for (d = 0; d < dim; d++) x1[d] /= norm;
1480: // x2 = n \otimes x1
1481: x2[0] = n[1] * x1[2] - n[2] * x1[1];
1482: x2[1] = n[2] * x1[0] - n[0] * x1[2];
1483: x2[2] = n[0] * x1[1] - n[1] * x1[0];
1484: for (d = 0; d < dim; d++) {
1485: R[d * dim + 0] = x1[d];
1486: R[d * dim + 1] = x2[d];
1487: R[d * dim + 2] = n[d];
1488: c[d] = PetscRealPart(coords[0 * dim + d]);
1489: }
1490: for (p = 0; p < coordSize / dim; p++) {
1491: PetscReal y[3];
1492: for (d = 0; d < dim; d++) y[d] = PetscRealPart(coords[p * dim + d]) - c[d];
1493: 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];
1494: }
1495: PetscFunctionReturn(PETSC_SUCCESS);
1496: }
1498: PETSC_UNUSED static inline void Volume_Triangle_Internal(PetscReal *vol, PetscReal coords[])
1499: {
1500: /* Signed volume is 1/2 the determinant
1502: | 1 1 1 |
1503: | x0 x1 x2 |
1504: | y0 y1 y2 |
1506: but if x0,y0 is the origin, we have
1508: | x1 x2 |
1509: | y1 y2 |
1510: */
1511: const PetscReal x1 = coords[2] - coords[0], y1 = coords[3] - coords[1];
1512: const PetscReal x2 = coords[4] - coords[0], y2 = coords[5] - coords[1];
1513: PetscReal M[4], detM;
1514: M[0] = x1;
1515: M[1] = x2;
1516: M[2] = y1;
1517: M[3] = y2;
1518: DMPlex_Det2D_Internal(&detM, M);
1519: *vol = 0.5 * detM;
1520: (void)PetscLogFlops(5.0);
1521: }
1523: PETSC_UNUSED static inline void Volume_Tetrahedron_Internal(PetscReal *vol, PetscReal coords[])
1524: {
1525: /* Signed volume is 1/6th of the determinant
1527: | 1 1 1 1 |
1528: | x0 x1 x2 x3 |
1529: | y0 y1 y2 y3 |
1530: | z0 z1 z2 z3 |
1532: but if x0,y0,z0 is the origin, we have
1534: | x1 x2 x3 |
1535: | y1 y2 y3 |
1536: | z1 z2 z3 |
1537: */
1538: const PetscReal x1 = coords[3] - coords[0], y1 = coords[4] - coords[1], z1 = coords[5] - coords[2];
1539: const PetscReal x2 = coords[6] - coords[0], y2 = coords[7] - coords[1], z2 = coords[8] - coords[2];
1540: const PetscReal x3 = coords[9] - coords[0], y3 = coords[10] - coords[1], z3 = coords[11] - coords[2];
1541: const PetscReal onesixth = ((PetscReal)1. / (PetscReal)6.);
1542: PetscReal M[9], detM;
1543: M[0] = x1;
1544: M[1] = x2;
1545: M[2] = x3;
1546: M[3] = y1;
1547: M[4] = y2;
1548: M[5] = y3;
1549: M[6] = z1;
1550: M[7] = z2;
1551: M[8] = z3;
1552: DMPlex_Det3D_Internal(&detM, M);
1553: *vol = -onesixth * detM;
1554: (void)PetscLogFlops(10.0);
1555: }
1557: static inline void Volume_Tetrahedron_Origin_Internal(PetscReal *vol, PetscReal coords[])
1558: {
1559: const PetscReal onesixth = ((PetscReal)1. / (PetscReal)6.);
1560: DMPlex_Det3D_Internal(vol, coords);
1561: *vol *= -onesixth;
1562: }
1564: static PetscErrorCode DMPlexComputePointGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1565: {
1566: PetscSection coordSection;
1567: Vec coordinates;
1568: const PetscScalar *coords;
1569: PetscInt dim, d, off;
1571: PetscFunctionBegin;
1572: PetscCall(DMGetCoordinatesLocal(dm, &coordinates));
1573: PetscCall(DMGetCoordinateSection(dm, &coordSection));
1574: PetscCall(PetscSectionGetDof(coordSection, e, &dim));
1575: if (!dim) PetscFunctionReturn(PETSC_SUCCESS);
1576: PetscCall(PetscSectionGetOffset(coordSection, e, &off));
1577: PetscCall(VecGetArrayRead(coordinates, &coords));
1578: if (v0) {
1579: for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[off + d]);
1580: }
1581: PetscCall(VecRestoreArrayRead(coordinates, &coords));
1582: *detJ = 1.;
1583: if (J) {
1584: for (d = 0; d < dim * dim; d++) J[d] = 0.;
1585: for (d = 0; d < dim; d++) J[d * dim + d] = 1.;
1586: if (invJ) {
1587: for (d = 0; d < dim * dim; d++) invJ[d] = 0.;
1588: for (d = 0; d < dim; d++) invJ[d * dim + d] = 1.;
1589: }
1590: }
1591: PetscFunctionReturn(PETSC_SUCCESS);
1592: }
1594: /*@C
1595: DMPlexGetCellCoordinates - Get coordinates for a cell, taking into account periodicity
1597: Not Collective
1599: Input Parameters:
1600: + dm - The `DMPLEX`
1601: - cell - The cell number
1603: Output Parameters:
1604: + isDG - Using cellwise coordinates
1605: . Nc - The number of coordinates
1606: . array - The coordinate array
1607: - coords - The cell coordinates
1609: Level: developer
1611: .seealso: `DMPLEX`, `DMPlexRestoreCellCoordinates()`, `DMGetCoordinatesLocal()`, `DMGetCellCoordinatesLocal()`
1612: @*/
1613: PetscErrorCode DMPlexGetCellCoordinates(DM dm, PetscInt cell, PetscBool *isDG, PetscInt *Nc, const PetscScalar *array[], PetscScalar *coords[])
1614: {
1615: DM cdm;
1616: Vec coordinates;
1617: PetscSection cs;
1618: const PetscScalar *ccoords;
1619: PetscInt pStart, pEnd;
1621: PetscFunctionBeginHot;
1622: *isDG = PETSC_FALSE;
1623: *Nc = 0;
1624: *array = NULL;
1625: *coords = NULL;
1626: /* Check for cellwise coordinates */
1627: PetscCall(DMGetCellCoordinateSection(dm, &cs));
1628: if (!cs) goto cg;
1629: /* Check that the cell exists in the cellwise section */
1630: PetscCall(PetscSectionGetChart(cs, &pStart, &pEnd));
1631: if (cell < pStart || cell >= pEnd) goto cg;
1632: /* Check for cellwise coordinates for this cell */
1633: PetscCall(PetscSectionGetDof(cs, cell, Nc));
1634: if (!*Nc) goto cg;
1635: /* Check for cellwise coordinates */
1636: PetscCall(DMGetCellCoordinatesLocalNoncollective(dm, &coordinates));
1637: if (!coordinates) goto cg;
1638: /* Get cellwise coordinates */
1639: PetscCall(DMGetCellCoordinateDM(dm, &cdm));
1640: PetscCall(VecGetArrayRead(coordinates, array));
1641: PetscCall(DMPlexPointLocalRead(cdm, cell, *array, &ccoords));
1642: PetscCall(DMGetWorkArray(cdm, *Nc, MPIU_SCALAR, coords));
1643: PetscCall(PetscArraycpy(*coords, ccoords, *Nc));
1644: PetscCall(VecRestoreArrayRead(coordinates, array));
1645: *isDG = PETSC_TRUE;
1646: PetscFunctionReturn(PETSC_SUCCESS);
1647: cg:
1648: /* Use continuous coordinates */
1649: PetscCall(DMGetCoordinateDM(dm, &cdm));
1650: PetscCall(DMGetCoordinateSection(dm, &cs));
1651: PetscCall(DMGetCoordinatesLocalNoncollective(dm, &coordinates));
1652: PetscCall(DMPlexVecGetOrientedClosure_Internal(cdm, cs, PETSC_FALSE, coordinates, cell, 0, Nc, coords));
1653: PetscFunctionReturn(PETSC_SUCCESS);
1654: }
1656: /*@C
1657: DMPlexRestoreCellCoordinates - Get coordinates for a cell, taking into account periodicity
1659: Not Collective
1661: Input Parameters:
1662: + dm - The `DMPLEX`
1663: - cell - The cell number
1665: Output Parameters:
1666: + isDG - Using cellwise coordinates
1667: . Nc - The number of coordinates
1668: . array - The coordinate array
1669: - coords - The cell coordinates
1671: Level: developer
1673: .seealso: `DMPLEX`, `DMPlexGetCellCoordinates()`, `DMGetCoordinatesLocal()`, `DMGetCellCoordinatesLocal()`
1674: @*/
1675: PetscErrorCode DMPlexRestoreCellCoordinates(DM dm, PetscInt cell, PetscBool *isDG, PetscInt *Nc, const PetscScalar *array[], PetscScalar *coords[])
1676: {
1677: DM cdm;
1678: PetscSection cs;
1679: Vec coordinates;
1681: PetscFunctionBeginHot;
1682: if (*isDG) {
1683: PetscCall(DMGetCellCoordinateDM(dm, &cdm));
1684: PetscCall(DMRestoreWorkArray(cdm, *Nc, MPIU_SCALAR, coords));
1685: } else {
1686: PetscCall(DMGetCoordinateDM(dm, &cdm));
1687: PetscCall(DMGetCoordinateSection(dm, &cs));
1688: PetscCall(DMGetCoordinatesLocalNoncollective(dm, &coordinates));
1689: PetscCall(DMPlexVecRestoreClosure(cdm, cs, coordinates, cell, Nc, coords));
1690: }
1691: PetscFunctionReturn(PETSC_SUCCESS);
1692: }
1694: static PetscErrorCode DMPlexComputeLineGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1695: {
1696: const PetscScalar *array;
1697: PetscScalar *coords = NULL;
1698: PetscInt numCoords, d;
1699: PetscBool isDG;
1701: PetscFunctionBegin;
1702: PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
1703: PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
1704: *detJ = 0.0;
1705: if (numCoords == 6) {
1706: const PetscInt dim = 3;
1707: PetscReal R[9], J0;
1709: if (v0) {
1710: for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
1711: }
1712: PetscCall(DMPlexComputeProjection3Dto1D(coords, R));
1713: if (J) {
1714: J0 = 0.5 * PetscRealPart(coords[1]);
1715: J[0] = R[0] * J0;
1716: J[1] = R[1];
1717: J[2] = R[2];
1718: J[3] = R[3] * J0;
1719: J[4] = R[4];
1720: J[5] = R[5];
1721: J[6] = R[6] * J0;
1722: J[7] = R[7];
1723: J[8] = R[8];
1724: DMPlex_Det3D_Internal(detJ, J);
1725: if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
1726: }
1727: } else if (numCoords == 4) {
1728: const PetscInt dim = 2;
1729: PetscReal R[4], J0;
1731: if (v0) {
1732: for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
1733: }
1734: PetscCall(DMPlexComputeProjection2Dto1D(coords, R));
1735: if (J) {
1736: J0 = 0.5 * PetscRealPart(coords[1]);
1737: J[0] = R[0] * J0;
1738: J[1] = R[1];
1739: J[2] = R[2] * J0;
1740: J[3] = R[3];
1741: DMPlex_Det2D_Internal(detJ, J);
1742: if (invJ) DMPlex_Invert2D_Internal(invJ, J, *detJ);
1743: }
1744: } else if (numCoords == 2) {
1745: const PetscInt dim = 1;
1747: if (v0) {
1748: for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
1749: }
1750: if (J) {
1751: J[0] = 0.5 * (PetscRealPart(coords[1]) - PetscRealPart(coords[0]));
1752: *detJ = J[0];
1753: PetscCall(PetscLogFlops(2.0));
1754: if (invJ) {
1755: invJ[0] = 1.0 / J[0];
1756: PetscCall(PetscLogFlops(1.0));
1757: }
1758: }
1759: } 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);
1760: PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
1761: PetscFunctionReturn(PETSC_SUCCESS);
1762: }
1764: static PetscErrorCode DMPlexComputeTriangleGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1765: {
1766: const PetscScalar *array;
1767: PetscScalar *coords = NULL;
1768: PetscInt numCoords, d;
1769: PetscBool isDG;
1771: PetscFunctionBegin;
1772: PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
1773: PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
1774: *detJ = 0.0;
1775: if (numCoords == 9) {
1776: const PetscInt dim = 3;
1777: PetscReal R[9], J0[9] = {1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0};
1779: if (v0) {
1780: for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
1781: }
1782: PetscCall(DMPlexComputeProjection3Dto2D(numCoords, coords, R));
1783: if (J) {
1784: const PetscInt pdim = 2;
1786: for (d = 0; d < pdim; d++) {
1787: for (PetscInt f = 0; f < pdim; f++) J0[d * dim + f] = 0.5 * (PetscRealPart(coords[(f + 1) * pdim + d]) - PetscRealPart(coords[0 * pdim + d]));
1788: }
1789: PetscCall(PetscLogFlops(8.0));
1790: DMPlex_Det3D_Internal(detJ, J0);
1791: for (d = 0; d < dim; d++) {
1792: for (PetscInt f = 0; f < dim; f++) {
1793: J[d * dim + f] = 0.0;
1794: for (PetscInt g = 0; g < dim; g++) J[d * dim + f] += R[d * dim + g] * J0[g * dim + f];
1795: }
1796: }
1797: PetscCall(PetscLogFlops(18.0));
1798: }
1799: if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
1800: } else if (numCoords == 6) {
1801: const PetscInt dim = 2;
1803: if (v0) {
1804: for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
1805: }
1806: if (J) {
1807: for (d = 0; d < dim; d++) {
1808: for (PetscInt f = 0; f < dim; f++) J[d * dim + f] = 0.5 * (PetscRealPart(coords[(f + 1) * dim + d]) - PetscRealPart(coords[0 * dim + d]));
1809: }
1810: PetscCall(PetscLogFlops(8.0));
1811: DMPlex_Det2D_Internal(detJ, J);
1812: }
1813: if (invJ) DMPlex_Invert2D_Internal(invJ, J, *detJ);
1814: } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this triangle is %" PetscInt_FMT " != 6 or 9", numCoords);
1815: PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
1816: PetscFunctionReturn(PETSC_SUCCESS);
1817: }
1819: static PetscErrorCode DMPlexComputeRectangleGeometry_Internal(DM dm, PetscInt e, PetscBool isTensor, PetscInt Nq, const PetscReal points[], PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1820: {
1821: const PetscScalar *array;
1822: PetscScalar *coords = NULL;
1823: PetscInt numCoords, d;
1824: PetscBool isDG;
1826: PetscFunctionBegin;
1827: PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
1828: PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
1829: if (!Nq) {
1830: PetscInt vorder[4] = {0, 1, 2, 3};
1832: if (isTensor) {
1833: vorder[2] = 3;
1834: vorder[3] = 2;
1835: }
1836: *detJ = 0.0;
1837: if (numCoords == 12) {
1838: const PetscInt dim = 3;
1839: PetscReal R[9], J0[9] = {1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0};
1841: if (v) {
1842: for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);
1843: }
1844: PetscCall(DMPlexComputeProjection3Dto2D(numCoords, coords, R));
1845: if (J) {
1846: const PetscInt pdim = 2;
1848: for (d = 0; d < pdim; d++) {
1849: J0[d * dim + 0] = 0.5 * (PetscRealPart(coords[vorder[1] * pdim + d]) - PetscRealPart(coords[vorder[0] * pdim + d]));
1850: J0[d * dim + 1] = 0.5 * (PetscRealPart(coords[vorder[2] * pdim + d]) - PetscRealPart(coords[vorder[1] * pdim + d]));
1851: }
1852: PetscCall(PetscLogFlops(8.0));
1853: DMPlex_Det3D_Internal(detJ, J0);
1854: for (d = 0; d < dim; d++) {
1855: for (PetscInt f = 0; f < dim; f++) {
1856: J[d * dim + f] = 0.0;
1857: for (PetscInt g = 0; g < dim; g++) J[d * dim + f] += R[d * dim + g] * J0[g * dim + f];
1858: }
1859: }
1860: PetscCall(PetscLogFlops(18.0));
1861: }
1862: if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
1863: } else if (numCoords == 8) {
1864: const PetscInt dim = 2;
1866: if (v) {
1867: for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);
1868: }
1869: if (J) {
1870: for (d = 0; d < dim; d++) {
1871: J[d * dim + 0] = 0.5 * (PetscRealPart(coords[vorder[1] * dim + d]) - PetscRealPart(coords[vorder[0] * dim + d]));
1872: J[d * dim + 1] = 0.5 * (PetscRealPart(coords[vorder[3] * dim + d]) - PetscRealPart(coords[vorder[0] * dim + d]));
1873: }
1874: PetscCall(PetscLogFlops(8.0));
1875: DMPlex_Det2D_Internal(detJ, J);
1876: }
1877: if (invJ) DMPlex_Invert2D_Internal(invJ, J, *detJ);
1878: } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this quadrilateral is %" PetscInt_FMT " != 8 or 12", numCoords);
1879: } else {
1880: const PetscInt Nv = 4;
1881: const PetscInt dimR = 2;
1882: PetscInt zToPlex[4] = {0, 1, 3, 2};
1883: PetscReal zOrder[12];
1884: PetscReal zCoeff[12];
1885: PetscInt i, j, k, l, dim;
1887: if (isTensor) {
1888: zToPlex[2] = 2;
1889: zToPlex[3] = 3;
1890: }
1891: if (numCoords == 12) {
1892: dim = 3;
1893: } else if (numCoords == 8) {
1894: dim = 2;
1895: } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this quadrilateral is %" PetscInt_FMT " != 8 or 12", numCoords);
1896: for (i = 0; i < Nv; i++) {
1897: PetscInt zi = zToPlex[i];
1899: for (j = 0; j < dim; j++) zOrder[dim * i + j] = PetscRealPart(coords[dim * zi + j]);
1900: }
1901: for (j = 0; j < dim; j++) {
1902: /* Nodal basis for evaluation at the vertices: (1 \mp xi) (1 \mp eta):
1903: \phi^0 = (1 - xi - eta + xi eta) --> 1 = 1/4 ( \phi^0 + \phi^1 + \phi^2 + \phi^3)
1904: \phi^1 = (1 + xi - eta - xi eta) --> xi = 1/4 (-\phi^0 + \phi^1 - \phi^2 + \phi^3)
1905: \phi^2 = (1 - xi + eta - xi eta) --> eta = 1/4 (-\phi^0 - \phi^1 + \phi^2 + \phi^3)
1906: \phi^3 = (1 + xi + eta + xi eta) --> xi eta = 1/4 ( \phi^0 - \phi^1 - \phi^2 + \phi^3)
1907: */
1908: zCoeff[dim * 0 + j] = 0.25 * (zOrder[dim * 0 + j] + zOrder[dim * 1 + j] + zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
1909: zCoeff[dim * 1 + j] = 0.25 * (-zOrder[dim * 0 + j] + zOrder[dim * 1 + j] - zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
1910: zCoeff[dim * 2 + j] = 0.25 * (-zOrder[dim * 0 + j] - zOrder[dim * 1 + j] + zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
1911: zCoeff[dim * 3 + j] = 0.25 * (zOrder[dim * 0 + j] - zOrder[dim * 1 + j] - zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
1912: }
1913: for (i = 0; i < Nq; i++) {
1914: PetscReal xi = points[dimR * i], eta = points[dimR * i + 1];
1916: if (v) {
1917: PetscReal extPoint[4];
1919: extPoint[0] = 1.;
1920: extPoint[1] = xi;
1921: extPoint[2] = eta;
1922: extPoint[3] = xi * eta;
1923: for (j = 0; j < dim; j++) {
1924: PetscReal val = 0.;
1926: for (k = 0; k < Nv; k++) val += extPoint[k] * zCoeff[dim * k + j];
1927: v[i * dim + j] = val;
1928: }
1929: }
1930: if (J) {
1931: PetscReal extJ[8];
1933: extJ[0] = 0.;
1934: extJ[1] = 0.;
1935: extJ[2] = 1.;
1936: extJ[3] = 0.;
1937: extJ[4] = 0.;
1938: extJ[5] = 1.;
1939: extJ[6] = eta;
1940: extJ[7] = xi;
1941: for (j = 0; j < dim; j++) {
1942: for (k = 0; k < dimR; k++) {
1943: PetscReal val = 0.;
1945: for (l = 0; l < Nv; l++) val += zCoeff[dim * l + j] * extJ[dimR * l + k];
1946: J[i * dim * dim + dim * j + k] = val;
1947: }
1948: }
1949: if (dim == 3) { /* put the cross product in the third component of the Jacobian */
1950: PetscReal x, y, z;
1951: PetscReal *iJ = &J[i * dim * dim];
1952: PetscReal norm;
1954: x = iJ[1 * dim + 0] * iJ[2 * dim + 1] - iJ[1 * dim + 1] * iJ[2 * dim + 0];
1955: y = iJ[0 * dim + 1] * iJ[2 * dim + 0] - iJ[0 * dim + 0] * iJ[2 * dim + 1];
1956: z = iJ[0 * dim + 0] * iJ[1 * dim + 1] - iJ[0 * dim + 1] * iJ[1 * dim + 0];
1957: norm = PetscSqrtReal(x * x + y * y + z * z);
1958: iJ[2] = x / norm;
1959: iJ[5] = y / norm;
1960: iJ[8] = z / norm;
1961: DMPlex_Det3D_Internal(&detJ[i], &J[i * dim * dim]);
1962: if (invJ) DMPlex_Invert3D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);
1963: } else {
1964: DMPlex_Det2D_Internal(&detJ[i], &J[i * dim * dim]);
1965: if (invJ) DMPlex_Invert2D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);
1966: }
1967: }
1968: }
1969: }
1970: PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
1971: PetscFunctionReturn(PETSC_SUCCESS);
1972: }
1974: static PetscErrorCode DMPlexComputeTetrahedronGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1975: {
1976: const PetscScalar *array;
1977: PetscScalar *coords = NULL;
1978: const PetscInt dim = 3;
1979: PetscInt numCoords, d;
1980: PetscBool isDG;
1982: PetscFunctionBegin;
1983: PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
1984: PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
1985: *detJ = 0.0;
1986: if (v0) {
1987: for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
1988: }
1989: if (J) {
1990: for (d = 0; d < dim; d++) {
1991: /* I orient with outward face normals */
1992: J[d * dim + 0] = 0.5 * (PetscRealPart(coords[2 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
1993: J[d * dim + 1] = 0.5 * (PetscRealPart(coords[1 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
1994: J[d * dim + 2] = 0.5 * (PetscRealPart(coords[3 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
1995: }
1996: PetscCall(PetscLogFlops(18.0));
1997: DMPlex_Det3D_Internal(detJ, J);
1998: }
1999: if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
2000: PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
2001: PetscFunctionReturn(PETSC_SUCCESS);
2002: }
2004: static PetscErrorCode DMPlexComputeHexahedronGeometry_Internal(DM dm, PetscInt e, PetscInt Nq, const PetscReal points[], PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
2005: {
2006: const PetscScalar *array;
2007: PetscScalar *coords = NULL;
2008: const PetscInt dim = 3;
2009: PetscInt numCoords, d;
2010: PetscBool isDG;
2012: PetscFunctionBegin;
2013: PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
2014: PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
2015: if (!Nq) {
2016: *detJ = 0.0;
2017: if (v) {
2018: for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);
2019: }
2020: if (J) {
2021: for (d = 0; d < dim; d++) {
2022: J[d * dim + 0] = 0.5 * (PetscRealPart(coords[3 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2023: J[d * dim + 1] = 0.5 * (PetscRealPart(coords[1 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2024: J[d * dim + 2] = 0.5 * (PetscRealPart(coords[4 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2025: }
2026: PetscCall(PetscLogFlops(18.0));
2027: DMPlex_Det3D_Internal(detJ, J);
2028: }
2029: if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
2030: } else {
2031: const PetscInt Nv = 8;
2032: const PetscInt zToPlex[8] = {0, 3, 1, 2, 4, 5, 7, 6};
2033: const PetscInt dim = 3;
2034: const PetscInt dimR = 3;
2035: PetscReal zOrder[24];
2036: PetscReal zCoeff[24];
2037: PetscInt i, j, k, l;
2039: for (i = 0; i < Nv; i++) {
2040: PetscInt zi = zToPlex[i];
2042: for (j = 0; j < dim; j++) zOrder[dim * i + j] = PetscRealPart(coords[dim * zi + j]);
2043: }
2044: for (j = 0; j < dim; j++) {
2045: 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]);
2046: 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]);
2047: 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]);
2048: 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]);
2049: 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]);
2050: 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]);
2051: 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]);
2052: 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]);
2053: }
2054: for (i = 0; i < Nq; i++) {
2055: PetscReal xi = points[dimR * i], eta = points[dimR * i + 1], theta = points[dimR * i + 2];
2057: if (v) {
2058: PetscReal extPoint[8];
2060: extPoint[0] = 1.;
2061: extPoint[1] = xi;
2062: extPoint[2] = eta;
2063: extPoint[3] = xi * eta;
2064: extPoint[4] = theta;
2065: extPoint[5] = theta * xi;
2066: extPoint[6] = theta * eta;
2067: extPoint[7] = theta * eta * xi;
2068: for (j = 0; j < dim; j++) {
2069: PetscReal val = 0.;
2071: for (k = 0; k < Nv; k++) val += extPoint[k] * zCoeff[dim * k + j];
2072: v[i * dim + j] = val;
2073: }
2074: }
2075: if (J) {
2076: PetscReal extJ[24];
2078: extJ[0] = 0.;
2079: extJ[1] = 0.;
2080: extJ[2] = 0.;
2081: extJ[3] = 1.;
2082: extJ[4] = 0.;
2083: extJ[5] = 0.;
2084: extJ[6] = 0.;
2085: extJ[7] = 1.;
2086: extJ[8] = 0.;
2087: extJ[9] = eta;
2088: extJ[10] = xi;
2089: extJ[11] = 0.;
2090: extJ[12] = 0.;
2091: extJ[13] = 0.;
2092: extJ[14] = 1.;
2093: extJ[15] = theta;
2094: extJ[16] = 0.;
2095: extJ[17] = xi;
2096: extJ[18] = 0.;
2097: extJ[19] = theta;
2098: extJ[20] = eta;
2099: extJ[21] = theta * eta;
2100: extJ[22] = theta * xi;
2101: extJ[23] = eta * xi;
2103: for (j = 0; j < dim; j++) {
2104: for (k = 0; k < dimR; k++) {
2105: PetscReal val = 0.;
2107: for (l = 0; l < Nv; l++) val += zCoeff[dim * l + j] * extJ[dimR * l + k];
2108: J[i * dim * dim + dim * j + k] = val;
2109: }
2110: }
2111: DMPlex_Det3D_Internal(&detJ[i], &J[i * dim * dim]);
2112: if (invJ) DMPlex_Invert3D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);
2113: }
2114: }
2115: }
2116: PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
2117: PetscFunctionReturn(PETSC_SUCCESS);
2118: }
2120: static PetscErrorCode DMPlexComputeTriangularPrismGeometry_Internal(DM dm, PetscInt e, PetscInt Nq, const PetscReal points[], PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
2121: {
2122: const PetscScalar *array;
2123: PetscScalar *coords = NULL;
2124: const PetscInt dim = 3;
2125: PetscInt numCoords, d;
2126: PetscBool isDG;
2128: PetscFunctionBegin;
2129: PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
2130: PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
2131: if (!Nq) {
2132: /* Assume that the map to the reference is affine */
2133: *detJ = 0.0;
2134: if (v) {
2135: for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);
2136: }
2137: if (J) {
2138: for (d = 0; d < dim; d++) {
2139: J[d * dim + 0] = 0.5 * (PetscRealPart(coords[2 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2140: J[d * dim + 1] = 0.5 * (PetscRealPart(coords[1 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2141: J[d * dim + 2] = 0.5 * (PetscRealPart(coords[4 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
2142: }
2143: PetscCall(PetscLogFlops(18.0));
2144: DMPlex_Det3D_Internal(detJ, J);
2145: }
2146: if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
2147: } else {
2148: const PetscInt dim = 3;
2149: const PetscInt dimR = 3;
2150: const PetscInt Nv = 6;
2151: PetscReal verts[18];
2152: PetscReal coeff[18];
2153: PetscInt i, j, k, l;
2155: for (i = 0; i < Nv; ++i)
2156: for (j = 0; j < dim; ++j) verts[dim * i + j] = PetscRealPart(coords[dim * i + j]);
2157: for (j = 0; j < dim; ++j) {
2158: /* Check for triangle,
2159: 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)
2160: 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)
2161: phi^2 = 1/2 (1 + eta) chi^2 = delta(-1, 1)
2163: phi^0 + phi^1 + phi^2 = 1 coef_1 = 1/2 ( chi^1 + chi^2)
2164: -phi^0 + phi^1 - phi^2 = xi coef_xi = 1/2 (-chi^0 + chi^1)
2165: -phi^0 - phi^1 + phi^2 = eta coef_eta = 1/2 (-chi^0 + chi^2)
2167: < chi_0 chi_1 chi_2> A / 1 1 1 \ / phi_0 \ <chi> I <phi>^T so we need the inverse transpose
2168: | -1 1 -1 | | phi_1 | =
2169: \ -1 -1 1 / \ phi_2 /
2171: 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
2172: */
2173: /* Nodal basis for evaluation at the vertices: {-xi - eta, 1 + xi, 1 + eta} (1 \mp zeta):
2174: \phi^0 = 1/4 ( -xi - eta + xi zeta + eta zeta) --> / 1 1 1 1 1 1 \ 1
2175: \phi^1 = 1/4 (1 + eta - zeta - eta zeta) --> | -1 1 -1 -1 -1 1 | eta
2176: \phi^2 = 1/4 (1 + xi - zeta - xi zeta) --> | -1 -1 1 -1 1 -1 | xi
2177: \phi^3 = 1/4 ( -xi - eta - xi zeta - eta zeta) --> | -1 -1 -1 1 1 1 | zeta
2178: \phi^4 = 1/4 (1 + xi + zeta + xi zeta) --> | 1 1 -1 -1 1 -1 | xi zeta
2179: \phi^5 = 1/4 (1 + eta + zeta + eta zeta) --> \ 1 -1 1 -1 -1 1 / eta zeta
2180: 1/4 / 0 1 1 0 1 1 \
2181: | -1 1 0 -1 0 1 |
2182: | -1 0 1 -1 1 0 |
2183: | 0 -1 -1 0 1 1 |
2184: | 1 0 -1 -1 1 0 |
2185: \ 1 -1 0 -1 0 1 /
2186: */
2187: coeff[dim * 0 + j] = (1. / 4.) * (verts[dim * 1 + j] + verts[dim * 2 + j] + verts[dim * 4 + j] + verts[dim * 5 + j]);
2188: coeff[dim * 1 + j] = (1. / 4.) * (-verts[dim * 0 + j] + verts[dim * 1 + j] - verts[dim * 3 + j] + verts[dim * 5 + j]);
2189: coeff[dim * 2 + j] = (1. / 4.) * (-verts[dim * 0 + j] + verts[dim * 2 + j] - verts[dim * 3 + j] + verts[dim * 4 + j]);
2190: coeff[dim * 3 + j] = (1. / 4.) * (-verts[dim * 1 + j] - verts[dim * 2 + j] + verts[dim * 4 + j] + verts[dim * 5 + j]);
2191: coeff[dim * 4 + j] = (1. / 4.) * (verts[dim * 0 + j] - verts[dim * 2 + j] - verts[dim * 3 + j] + verts[dim * 4 + j]);
2192: coeff[dim * 5 + j] = (1. / 4.) * (verts[dim * 0 + j] - verts[dim * 1 + j] - verts[dim * 3 + j] + verts[dim * 5 + j]);
2193: /* For reference prism:
2194: {0, 0, 0}
2195: {0, 1, 0}
2196: {1, 0, 0}
2197: {0, 0, 1}
2198: {0, 0, 0}
2199: {0, 0, 0}
2200: */
2201: }
2202: for (i = 0; i < Nq; ++i) {
2203: const PetscReal xi = points[dimR * i], eta = points[dimR * i + 1], zeta = points[dimR * i + 2];
2205: if (v) {
2206: PetscReal extPoint[6];
2207: PetscInt c;
2209: extPoint[0] = 1.;
2210: extPoint[1] = eta;
2211: extPoint[2] = xi;
2212: extPoint[3] = zeta;
2213: extPoint[4] = xi * zeta;
2214: extPoint[5] = eta * zeta;
2215: for (c = 0; c < dim; ++c) {
2216: PetscReal val = 0.;
2218: for (k = 0; k < Nv; ++k) val += extPoint[k] * coeff[k * dim + c];
2219: v[i * dim + c] = val;
2220: }
2221: }
2222: if (J) {
2223: PetscReal extJ[18];
2225: extJ[0] = 0.;
2226: extJ[1] = 0.;
2227: extJ[2] = 0.;
2228: extJ[3] = 0.;
2229: extJ[4] = 1.;
2230: extJ[5] = 0.;
2231: extJ[6] = 1.;
2232: extJ[7] = 0.;
2233: extJ[8] = 0.;
2234: extJ[9] = 0.;
2235: extJ[10] = 0.;
2236: extJ[11] = 1.;
2237: extJ[12] = zeta;
2238: extJ[13] = 0.;
2239: extJ[14] = xi;
2240: extJ[15] = 0.;
2241: extJ[16] = zeta;
2242: extJ[17] = eta;
2244: for (j = 0; j < dim; j++) {
2245: for (k = 0; k < dimR; k++) {
2246: PetscReal val = 0.;
2248: for (l = 0; l < Nv; l++) val += coeff[dim * l + j] * extJ[dimR * l + k];
2249: J[i * dim * dim + dim * j + k] = val;
2250: }
2251: }
2252: DMPlex_Det3D_Internal(&detJ[i], &J[i * dim * dim]);
2253: if (invJ) DMPlex_Invert3D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);
2254: }
2255: }
2256: }
2257: PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
2258: PetscFunctionReturn(PETSC_SUCCESS);
2259: }
2261: static PetscErrorCode DMPlexComputeCellGeometryFEM_Implicit(DM dm, PetscInt cell, PetscQuadrature quad, PetscReal *v, PetscReal *J, PetscReal *invJ, PetscReal *detJ)
2262: {
2263: DMPolytopeType ct;
2264: PetscInt depth, dim, coordDim, coneSize, i;
2265: PetscInt Nq = 0;
2266: const PetscReal *points = NULL;
2267: DMLabel depthLabel;
2268: PetscReal xi0[3] = {-1., -1., -1.}, v0[3], J0[9], detJ0;
2269: PetscBool isAffine = PETSC_TRUE;
2271: PetscFunctionBegin;
2272: PetscCall(DMPlexGetDepth(dm, &depth));
2273: PetscCall(DMPlexGetConeSize(dm, cell, &coneSize));
2274: PetscCall(DMPlexGetDepthLabel(dm, &depthLabel));
2275: PetscCall(DMLabelGetValue(depthLabel, cell, &dim));
2276: if (depth == 1 && dim == 1) PetscCall(DMGetDimension(dm, &dim));
2277: PetscCall(DMGetCoordinateDim(dm, &coordDim));
2278: PetscCheck(coordDim <= 3, PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported coordinate dimension %" PetscInt_FMT " > 3", coordDim);
2279: if (quad) PetscCall(PetscQuadratureGetData(quad, NULL, NULL, &Nq, &points, NULL));
2280: PetscCall(DMPlexGetCellType(dm, cell, &ct));
2281: switch (ct) {
2282: case DM_POLYTOPE_POINT:
2283: PetscCall(DMPlexComputePointGeometry_Internal(dm, cell, v, J, invJ, detJ));
2284: isAffine = PETSC_FALSE;
2285: break;
2286: case DM_POLYTOPE_SEGMENT:
2287: case DM_POLYTOPE_POINT_PRISM_TENSOR:
2288: if (Nq) PetscCall(DMPlexComputeLineGeometry_Internal(dm, cell, v0, J0, NULL, &detJ0));
2289: else PetscCall(DMPlexComputeLineGeometry_Internal(dm, cell, v, J, invJ, detJ));
2290: break;
2291: case DM_POLYTOPE_TRIANGLE:
2292: if (Nq) PetscCall(DMPlexComputeTriangleGeometry_Internal(dm, cell, v0, J0, NULL, &detJ0));
2293: else PetscCall(DMPlexComputeTriangleGeometry_Internal(dm, cell, v, J, invJ, detJ));
2294: break;
2295: case DM_POLYTOPE_QUADRILATERAL:
2296: PetscCall(DMPlexComputeRectangleGeometry_Internal(dm, cell, PETSC_FALSE, Nq, points, v, J, invJ, detJ));
2297: isAffine = PETSC_FALSE;
2298: break;
2299: case DM_POLYTOPE_SEG_PRISM_TENSOR:
2300: PetscCall(DMPlexComputeRectangleGeometry_Internal(dm, cell, PETSC_TRUE, Nq, points, v, J, invJ, detJ));
2301: isAffine = PETSC_FALSE;
2302: break;
2303: case DM_POLYTOPE_TETRAHEDRON:
2304: if (Nq) PetscCall(DMPlexComputeTetrahedronGeometry_Internal(dm, cell, v0, J0, NULL, &detJ0));
2305: else PetscCall(DMPlexComputeTetrahedronGeometry_Internal(dm, cell, v, J, invJ, detJ));
2306: break;
2307: case DM_POLYTOPE_HEXAHEDRON:
2308: PetscCall(DMPlexComputeHexahedronGeometry_Internal(dm, cell, Nq, points, v, J, invJ, detJ));
2309: isAffine = PETSC_FALSE;
2310: break;
2311: case DM_POLYTOPE_TRI_PRISM:
2312: PetscCall(DMPlexComputeTriangularPrismGeometry_Internal(dm, cell, Nq, points, v, J, invJ, detJ));
2313: isAffine = PETSC_FALSE;
2314: break;
2315: default:
2316: 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))]);
2317: }
2318: if (isAffine && Nq) {
2319: if (v) {
2320: for (i = 0; i < Nq; i++) CoordinatesRefToReal(coordDim, dim, xi0, v0, J0, &points[dim * i], &v[coordDim * i]);
2321: }
2322: if (detJ) {
2323: for (i = 0; i < Nq; i++) detJ[i] = detJ0;
2324: }
2325: if (J) {
2326: PetscInt k;
2328: for (i = 0, k = 0; i < Nq; i++) {
2329: PetscInt j;
2331: for (j = 0; j < coordDim * coordDim; j++, k++) J[k] = J0[j];
2332: }
2333: }
2334: if (invJ) {
2335: PetscInt k;
2336: switch (coordDim) {
2337: case 0:
2338: break;
2339: case 1:
2340: invJ[0] = 1. / J0[0];
2341: break;
2342: case 2:
2343: DMPlex_Invert2D_Internal(invJ, J0, detJ0);
2344: break;
2345: case 3:
2346: DMPlex_Invert3D_Internal(invJ, J0, detJ0);
2347: break;
2348: }
2349: for (i = 1, k = coordDim * coordDim; i < Nq; i++) {
2350: PetscInt j;
2352: for (j = 0; j < coordDim * coordDim; j++, k++) invJ[k] = invJ[j];
2353: }
2354: }
2355: }
2356: PetscFunctionReturn(PETSC_SUCCESS);
2357: }
2359: /*@C
2360: DMPlexComputeCellGeometryAffineFEM - Assuming an affine map, compute the Jacobian, inverse Jacobian, and Jacobian determinant for a given cell
2362: Collective
2364: Input Parameters:
2365: + dm - the `DMPLEX`
2366: - cell - the cell
2368: Output Parameters:
2369: + v0 - the translation part of this affine transform, meaning the translation to the origin (not the first vertex of the reference cell)
2370: . J - the Jacobian of the transform from the reference element
2371: . invJ - the inverse of the Jacobian
2372: - detJ - the Jacobian determinant
2374: Level: advanced
2376: .seealso: `DMPLEX`, `DMPlexComputeCellGeometryFEM()`, `DMGetCoordinateSection()`, `DMGetCoordinates()`
2377: @*/
2378: PetscErrorCode DMPlexComputeCellGeometryAffineFEM(DM dm, PetscInt cell, PetscReal *v0, PetscReal *J, PetscReal *invJ, PetscReal *detJ)
2379: {
2380: PetscFunctionBegin;
2381: PetscCall(DMPlexComputeCellGeometryFEM_Implicit(dm, cell, NULL, v0, J, invJ, detJ));
2382: PetscFunctionReturn(PETSC_SUCCESS);
2383: }
2385: static PetscErrorCode DMPlexComputeCellGeometryFEM_FE(DM dm, PetscFE fe, PetscInt point, PetscQuadrature quad, PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
2386: {
2387: const PetscScalar *array;
2388: PetscScalar *coords = NULL;
2389: PetscInt numCoords;
2390: PetscBool isDG;
2391: PetscQuadrature feQuad;
2392: const PetscReal *quadPoints;
2393: PetscTabulation T;
2394: PetscInt dim, cdim, pdim, qdim, Nq, q;
2396: PetscFunctionBegin;
2397: PetscCall(DMGetDimension(dm, &dim));
2398: PetscCall(DMGetCoordinateDim(dm, &cdim));
2399: PetscCall(DMPlexGetCellCoordinates(dm, point, &isDG, &numCoords, &array, &coords));
2400: if (!quad) { /* use the first point of the first functional of the dual space */
2401: PetscDualSpace dsp;
2403: PetscCall(PetscFEGetDualSpace(fe, &dsp));
2404: PetscCall(PetscDualSpaceGetFunctional(dsp, 0, &quad));
2405: PetscCall(PetscQuadratureGetData(quad, &qdim, NULL, &Nq, &quadPoints, NULL));
2406: Nq = 1;
2407: } else {
2408: PetscCall(PetscQuadratureGetData(quad, &qdim, NULL, &Nq, &quadPoints, NULL));
2409: }
2410: PetscCall(PetscFEGetDimension(fe, &pdim));
2411: PetscCall(PetscFEGetQuadrature(fe, &feQuad));
2412: if (feQuad == quad) {
2413: PetscCall(PetscFEGetCellTabulation(fe, J ? 1 : 0, &T));
2414: 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);
2415: } else {
2416: PetscCall(PetscFECreateTabulation(fe, 1, Nq, quadPoints, J ? 1 : 0, &T));
2417: }
2418: PetscCheck(qdim == dim, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Point dimension %" PetscInt_FMT " != quadrature dimension %" PetscInt_FMT, dim, qdim);
2419: {
2420: const PetscReal *basis = T->T[0];
2421: const PetscReal *basisDer = T->T[1];
2422: PetscReal detJt;
2424: PetscAssert(Nq == T->Np, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Np %" PetscInt_FMT " != %" PetscInt_FMT, Nq, T->Np);
2425: PetscAssert(pdim == T->Nb, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Nb %" PetscInt_FMT " != %" PetscInt_FMT, pdim, T->Nb);
2426: PetscAssert(dim == T->Nc, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Nc %" PetscInt_FMT " != %" PetscInt_FMT, dim, T->Nc);
2427: PetscAssert(cdim == T->cdim, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "cdim %" PetscInt_FMT " != %" PetscInt_FMT, cdim, T->cdim);
2428: if (v) {
2429: PetscCall(PetscArrayzero(v, Nq * cdim));
2430: for (q = 0; q < Nq; ++q) {
2431: PetscInt i, k;
2433: for (k = 0; k < pdim; ++k) {
2434: const PetscInt vertex = k / cdim;
2435: for (i = 0; i < cdim; ++i) v[q * cdim + i] += basis[(q * pdim + k) * cdim + i] * PetscRealPart(coords[vertex * cdim + i]);
2436: }
2437: PetscCall(PetscLogFlops(2.0 * pdim * cdim));
2438: }
2439: }
2440: if (J) {
2441: PetscCall(PetscArrayzero(J, Nq * cdim * cdim));
2442: for (q = 0; q < Nq; ++q) {
2443: PetscInt i, j, k, c, r;
2445: /* J = dx_i/d\xi_j = sum[k=0,n-1] dN_k/d\xi_j * x_i(k) */
2446: for (k = 0; k < pdim; ++k) {
2447: const PetscInt vertex = k / cdim;
2448: for (j = 0; j < dim; ++j) {
2449: 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]);
2450: }
2451: }
2452: PetscCall(PetscLogFlops(2.0 * pdim * dim * cdim));
2453: if (cdim > dim) {
2454: for (c = dim; c < cdim; ++c)
2455: for (r = 0; r < cdim; ++r) J[r * cdim + c] = r == c ? 1.0 : 0.0;
2456: }
2457: if (!detJ && !invJ) continue;
2458: detJt = 0.;
2459: switch (cdim) {
2460: case 3:
2461: DMPlex_Det3D_Internal(&detJt, &J[q * cdim * dim]);
2462: if (invJ) DMPlex_Invert3D_Internal(&invJ[q * cdim * dim], &J[q * cdim * dim], detJt);
2463: break;
2464: case 2:
2465: DMPlex_Det2D_Internal(&detJt, &J[q * cdim * dim]);
2466: if (invJ) DMPlex_Invert2D_Internal(&invJ[q * cdim * dim], &J[q * cdim * dim], detJt);
2467: break;
2468: case 1:
2469: detJt = J[q * cdim * dim];
2470: if (invJ) invJ[q * cdim * dim] = 1.0 / detJt;
2471: }
2472: if (detJ) detJ[q] = detJt;
2473: }
2474: } else PetscCheck(!detJ && !invJ, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Need J to compute invJ or detJ");
2475: }
2476: if (feQuad != quad) PetscCall(PetscTabulationDestroy(&T));
2477: PetscCall(DMPlexRestoreCellCoordinates(dm, point, &isDG, &numCoords, &array, &coords));
2478: PetscFunctionReturn(PETSC_SUCCESS);
2479: }
2481: /*@C
2482: DMPlexComputeCellGeometryFEM - Compute the Jacobian, inverse Jacobian, and Jacobian determinant at each quadrature point in the given cell
2484: Collective
2486: Input Parameters:
2487: + dm - the `DMPLEX`
2488: . cell - the cell
2489: - quad - the quadrature containing the points in the reference element where the geometry will be evaluated. If `quad` is `NULL`, geometry will be
2490: evaluated at the first vertex of the reference element
2492: Output Parameters:
2493: + v - the image of the transformed quadrature points, otherwise the image of the first vertex in the closure of the reference element
2494: . J - the Jacobian of the transform from the reference element at each quadrature point
2495: . invJ - the inverse of the Jacobian at each quadrature point
2496: - detJ - the Jacobian determinant at each quadrature point
2498: Level: advanced
2500: .seealso: `DMPLEX`, `DMGetCoordinateSection()`, `DMGetCoordinates()`
2501: @*/
2502: PetscErrorCode DMPlexComputeCellGeometryFEM(DM dm, PetscInt cell, PetscQuadrature quad, PetscReal *v, PetscReal *J, PetscReal *invJ, PetscReal *detJ)
2503: {
2504: DM cdm;
2505: PetscFE fe = NULL;
2507: PetscFunctionBegin;
2508: PetscAssertPointer(detJ, 7);
2509: PetscCall(DMGetCoordinateDM(dm, &cdm));
2510: if (cdm) {
2511: PetscClassId id;
2512: PetscInt numFields;
2513: PetscDS prob;
2514: PetscObject disc;
2516: PetscCall(DMGetNumFields(cdm, &numFields));
2517: if (numFields) {
2518: PetscCall(DMGetDS(cdm, &prob));
2519: PetscCall(PetscDSGetDiscretization(prob, 0, &disc));
2520: PetscCall(PetscObjectGetClassId(disc, &id));
2521: if (id == PETSCFE_CLASSID) fe = (PetscFE)disc;
2522: }
2523: }
2524: if (!fe) PetscCall(DMPlexComputeCellGeometryFEM_Implicit(dm, cell, quad, v, J, invJ, detJ));
2525: else PetscCall(DMPlexComputeCellGeometryFEM_FE(dm, fe, cell, quad, v, J, invJ, detJ));
2526: PetscFunctionReturn(PETSC_SUCCESS);
2527: }
2529: static PetscErrorCode DMPlexComputeGeometryFVM_0D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
2530: {
2531: PetscSection coordSection;
2532: Vec coordinates;
2533: const PetscScalar *coords = NULL;
2534: PetscInt d, dof, off;
2536: PetscFunctionBegin;
2537: PetscCall(DMGetCoordinatesLocal(dm, &coordinates));
2538: PetscCall(DMGetCoordinateSection(dm, &coordSection));
2539: PetscCall(VecGetArrayRead(coordinates, &coords));
2541: /* for a point the centroid is just the coord */
2542: if (centroid) {
2543: PetscCall(PetscSectionGetDof(coordSection, cell, &dof));
2544: PetscCall(PetscSectionGetOffset(coordSection, cell, &off));
2545: for (d = 0; d < dof; d++) centroid[d] = PetscRealPart(coords[off + d]);
2546: }
2547: if (normal) {
2548: const PetscInt *support, *cones;
2549: PetscInt supportSize;
2550: PetscReal norm, sign;
2552: /* compute the norm based upon the support centroids */
2553: PetscCall(DMPlexGetSupportSize(dm, cell, &supportSize));
2554: PetscCall(DMPlexGetSupport(dm, cell, &support));
2555: PetscCall(DMPlexComputeCellGeometryFVM(dm, support[0], NULL, normal, NULL));
2557: /* Take the normal from the centroid of the support to the vertex*/
2558: PetscCall(PetscSectionGetDof(coordSection, cell, &dof));
2559: PetscCall(PetscSectionGetOffset(coordSection, cell, &off));
2560: for (d = 0; d < dof; d++) normal[d] -= PetscRealPart(coords[off + d]);
2562: /* Determine the sign of the normal based upon its location in the support */
2563: PetscCall(DMPlexGetCone(dm, support[0], &cones));
2564: sign = cones[0] == cell ? 1.0 : -1.0;
2566: norm = DMPlex_NormD_Internal(dim, normal);
2567: for (d = 0; d < dim; ++d) normal[d] /= (norm * sign);
2568: }
2569: if (vol) *vol = 1.0;
2570: PetscCall(VecRestoreArrayRead(coordinates, &coords));
2571: PetscFunctionReturn(PETSC_SUCCESS);
2572: }
2574: static PetscErrorCode DMPlexComputeGeometryFVM_1D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
2575: {
2576: const PetscScalar *array;
2577: PetscScalar *coords = NULL;
2578: PetscInt cdim, coordSize, d;
2579: PetscBool isDG;
2581: PetscFunctionBegin;
2582: PetscCall(DMGetCoordinateDim(dm, &cdim));
2583: PetscCall(DMPlexGetCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
2584: PetscCheck(coordSize == cdim * 2, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Edge has %" PetscInt_FMT " coordinates != %" PetscInt_FMT, coordSize, cdim * 2);
2585: if (centroid) {
2586: for (d = 0; d < cdim; ++d) centroid[d] = 0.5 * PetscRealPart(coords[d] + coords[cdim + d]);
2587: }
2588: if (normal) {
2589: PetscReal norm;
2591: switch (cdim) {
2592: case 3:
2593: normal[2] = 0.; /* fall through */
2594: case 2:
2595: normal[0] = -PetscRealPart(coords[1] - coords[cdim + 1]);
2596: normal[1] = PetscRealPart(coords[0] - coords[cdim + 0]);
2597: break;
2598: case 1:
2599: normal[0] = 1.0;
2600: break;
2601: default:
2602: SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Dimension %" PetscInt_FMT " not supported", cdim);
2603: }
2604: norm = DMPlex_NormD_Internal(cdim, normal);
2605: for (d = 0; d < cdim; ++d) normal[d] /= norm;
2606: }
2607: if (vol) {
2608: *vol = 0.0;
2609: for (d = 0; d < cdim; ++d) *vol += PetscSqr(PetscRealPart(coords[d] - coords[cdim + d]));
2610: *vol = PetscSqrtReal(*vol);
2611: }
2612: PetscCall(DMPlexRestoreCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
2613: PetscFunctionReturn(PETSC_SUCCESS);
2614: }
2616: /* Centroid_i = (\sum_n A_n Cn_i) / A */
2617: static PetscErrorCode DMPlexComputeGeometryFVM_2D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
2618: {
2619: DMPolytopeType ct;
2620: const PetscScalar *array;
2621: PetscScalar *coords = NULL;
2622: PetscInt coordSize;
2623: PetscBool isDG;
2624: PetscInt fv[4] = {0, 1, 2, 3};
2625: PetscInt cdim, numCorners, p, d;
2627: PetscFunctionBegin;
2628: /* Must check for hybrid cells because prisms have a different orientation scheme */
2629: PetscCall(DMPlexGetCellType(dm, cell, &ct));
2630: switch (ct) {
2631: case DM_POLYTOPE_SEG_PRISM_TENSOR:
2632: fv[2] = 3;
2633: fv[3] = 2;
2634: break;
2635: default:
2636: break;
2637: }
2638: PetscCall(DMGetCoordinateDim(dm, &cdim));
2639: PetscCall(DMPlexGetConeSize(dm, cell, &numCorners));
2640: PetscCall(DMPlexGetCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
2641: {
2642: PetscReal c[3] = {0., 0., 0.}, n[3] = {0., 0., 0.}, origin[3] = {0., 0., 0.}, norm;
2644: for (d = 0; d < cdim; d++) origin[d] = PetscRealPart(coords[d]);
2645: for (p = 0; p < numCorners - 2; ++p) {
2646: PetscReal e0[3] = {0., 0., 0.}, e1[3] = {0., 0., 0.};
2647: for (d = 0; d < cdim; d++) {
2648: e0[d] = PetscRealPart(coords[cdim * fv[p + 1] + d]) - origin[d];
2649: e1[d] = PetscRealPart(coords[cdim * fv[p + 2] + d]) - origin[d];
2650: }
2651: const PetscReal dx = e0[1] * e1[2] - e0[2] * e1[1];
2652: const PetscReal dy = e0[2] * e1[0] - e0[0] * e1[2];
2653: const PetscReal dz = e0[0] * e1[1] - e0[1] * e1[0];
2654: const PetscReal a = PetscSqrtReal(dx * dx + dy * dy + dz * dz);
2656: n[0] += dx;
2657: n[1] += dy;
2658: n[2] += dz;
2659: 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.;
2660: }
2661: norm = PetscSqrtReal(n[0] * n[0] + n[1] * n[1] + n[2] * n[2]);
2662: // Allow zero volume cells
2663: if (norm != 0) {
2664: n[0] /= norm;
2665: n[1] /= norm;
2666: n[2] /= norm;
2667: c[0] /= norm;
2668: c[1] /= norm;
2669: c[2] /= norm;
2670: }
2671: if (vol) *vol = 0.5 * norm;
2672: if (centroid)
2673: for (d = 0; d < cdim; ++d) centroid[d] = c[d];
2674: if (normal)
2675: for (d = 0; d < cdim; ++d) normal[d] = n[d];
2676: }
2677: PetscCall(DMPlexRestoreCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
2678: PetscFunctionReturn(PETSC_SUCCESS);
2679: }
2681: /* Centroid_i = (\sum_n V_n Cn_i) / V */
2682: static PetscErrorCode DMPlexComputeGeometryFVM_3D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
2683: {
2684: DMPolytopeType ct;
2685: const PetscScalar *array;
2686: PetscScalar *coords = NULL;
2687: PetscInt coordSize;
2688: PetscBool isDG;
2689: PetscReal vsum = 0.0, vtmp, coordsTmp[3 * 3], origin[3];
2690: const PetscInt order[16] = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15};
2691: const PetscInt *cone, *faceSizes, *faces;
2692: const DMPolytopeType *faceTypes;
2693: PetscBool isHybrid = PETSC_FALSE;
2694: PetscInt numFaces, f, fOff = 0, p, d;
2696: PetscFunctionBegin;
2697: PetscCheck(dim <= 3, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "No support for dim %" PetscInt_FMT " > 3", dim);
2698: /* Must check for hybrid cells because prisms have a different orientation scheme */
2699: PetscCall(DMPlexGetCellType(dm, cell, &ct));
2700: switch (ct) {
2701: case DM_POLYTOPE_POINT_PRISM_TENSOR:
2702: case DM_POLYTOPE_SEG_PRISM_TENSOR:
2703: case DM_POLYTOPE_TRI_PRISM_TENSOR:
2704: case DM_POLYTOPE_QUAD_PRISM_TENSOR:
2705: isHybrid = PETSC_TRUE;
2706: default:
2707: break;
2708: }
2710: if (centroid)
2711: for (d = 0; d < dim; ++d) centroid[d] = 0.0;
2712: PetscCall(DMPlexGetCone(dm, cell, &cone));
2714: // Using the closure of faces for coordinates does not work in periodic geometries, so we index into the cell coordinates
2715: PetscCall(DMPlexGetRawFaces_Internal(dm, ct, order, &numFaces, &faceTypes, &faceSizes, &faces));
2716: PetscCall(DMPlexGetCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
2717: for (f = 0; f < numFaces; ++f) {
2718: PetscBool flip = isHybrid && f == 0 ? PETSC_TRUE : PETSC_FALSE; /* The first hybrid face is reversed */
2720: // If using zero as the origin vertex for each tetrahedron, an element far from the origin will have positive and
2721: // negative volumes that nearly cancel, thus incurring rounding error. Here we define origin[] as the first vertex
2722: // so that all tetrahedra have positive volume.
2723: if (f == 0)
2724: for (d = 0; d < dim; d++) origin[d] = PetscRealPart(coords[d]);
2725: switch (faceTypes[f]) {
2726: case DM_POLYTOPE_TRIANGLE:
2727: for (d = 0; d < dim; ++d) {
2728: coordsTmp[0 * dim + d] = PetscRealPart(coords[faces[fOff + 0] * dim + d]) - origin[d];
2729: coordsTmp[1 * dim + d] = PetscRealPart(coords[faces[fOff + 1] * dim + d]) - origin[d];
2730: coordsTmp[2 * dim + d] = PetscRealPart(coords[faces[fOff + 2] * dim + d]) - origin[d];
2731: }
2732: Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
2733: if (flip) vtmp = -vtmp;
2734: vsum += vtmp;
2735: if (centroid) { /* Centroid of OABC = (a+b+c)/4 */
2736: for (d = 0; d < dim; ++d) {
2737: for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p * dim + d] * vtmp;
2738: }
2739: }
2740: break;
2741: case DM_POLYTOPE_QUADRILATERAL:
2742: case DM_POLYTOPE_SEG_PRISM_TENSOR: {
2743: PetscInt fv[4] = {0, 1, 2, 3};
2745: /* Side faces for hybrid cells are stored as tensor products */
2746: if (isHybrid && f > 1) {
2747: fv[2] = 3;
2748: fv[3] = 2;
2749: }
2750: /* DO FOR PYRAMID */
2751: /* First tet */
2752: for (d = 0; d < dim; ++d) {
2753: coordsTmp[0 * dim + d] = PetscRealPart(coords[faces[fOff + fv[0]] * dim + d]) - origin[d];
2754: coordsTmp[1 * dim + d] = PetscRealPart(coords[faces[fOff + fv[1]] * dim + d]) - origin[d];
2755: coordsTmp[2 * dim + d] = PetscRealPart(coords[faces[fOff + fv[3]] * dim + d]) - origin[d];
2756: }
2757: Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
2758: if (flip) vtmp = -vtmp;
2759: vsum += vtmp;
2760: if (centroid) {
2761: for (d = 0; d < dim; ++d) {
2762: for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p * dim + d] * vtmp;
2763: }
2764: }
2765: /* Second tet */
2766: for (d = 0; d < dim; ++d) {
2767: coordsTmp[0 * dim + d] = PetscRealPart(coords[faces[fOff + fv[1]] * dim + d]) - origin[d];
2768: coordsTmp[1 * dim + d] = PetscRealPart(coords[faces[fOff + fv[2]] * dim + d]) - origin[d];
2769: coordsTmp[2 * dim + d] = PetscRealPart(coords[faces[fOff + fv[3]] * dim + d]) - origin[d];
2770: }
2771: Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
2772: if (flip) vtmp = -vtmp;
2773: vsum += vtmp;
2774: if (centroid) {
2775: for (d = 0; d < dim; ++d) {
2776: for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p * dim + d] * vtmp;
2777: }
2778: }
2779: break;
2780: }
2781: default:
2782: SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Cannot handle face %" PetscInt_FMT " of type %s", cone[f], DMPolytopeTypes[ct]);
2783: }
2784: fOff += faceSizes[f];
2785: }
2786: PetscCall(DMPlexRestoreRawFaces_Internal(dm, ct, order, &numFaces, &faceTypes, &faceSizes, &faces));
2787: PetscCall(DMPlexRestoreCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
2788: if (vol) *vol = PetscAbsReal(vsum);
2789: if (normal)
2790: for (d = 0; d < dim; ++d) normal[d] = 0.0;
2791: if (centroid)
2792: for (d = 0; d < dim; ++d) centroid[d] = centroid[d] / (vsum * 4) + origin[d];
2793: PetscFunctionReturn(PETSC_SUCCESS);
2794: }
2796: /*@C
2797: DMPlexComputeCellGeometryFVM - Compute the volume for a given cell
2799: Collective
2801: Input Parameters:
2802: + dm - the `DMPLEX`
2803: - cell - the cell
2805: Output Parameters:
2806: + vol - the cell volume
2807: . centroid - the cell centroid
2808: - normal - the cell normal, if appropriate
2810: Level: advanced
2812: .seealso: `DMPLEX`, `DMGetCoordinateSection()`, `DMGetCoordinates()`
2813: @*/
2814: PetscErrorCode DMPlexComputeCellGeometryFVM(DM dm, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
2815: {
2816: PetscInt depth, dim;
2818: PetscFunctionBegin;
2819: PetscCall(DMPlexGetDepth(dm, &depth));
2820: PetscCall(DMGetDimension(dm, &dim));
2821: PetscCheck(depth == dim, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Mesh must be interpolated");
2822: PetscCall(DMPlexGetPointDepth(dm, cell, &depth));
2823: switch (depth) {
2824: case 0:
2825: PetscCall(DMPlexComputeGeometryFVM_0D_Internal(dm, dim, cell, vol, centroid, normal));
2826: break;
2827: case 1:
2828: PetscCall(DMPlexComputeGeometryFVM_1D_Internal(dm, dim, cell, vol, centroid, normal));
2829: break;
2830: case 2:
2831: PetscCall(DMPlexComputeGeometryFVM_2D_Internal(dm, dim, cell, vol, centroid, normal));
2832: break;
2833: case 3:
2834: PetscCall(DMPlexComputeGeometryFVM_3D_Internal(dm, dim, cell, vol, centroid, normal));
2835: break;
2836: default:
2837: SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported dimension %" PetscInt_FMT " (depth %" PetscInt_FMT ") for element geometry computation", dim, depth);
2838: }
2839: PetscFunctionReturn(PETSC_SUCCESS);
2840: }
2842: /*@
2843: DMPlexComputeGeometryFVM - Computes the cell and face geometry for a finite volume method
2845: Input Parameter:
2846: . dm - The `DMPLEX`
2848: Output Parameters:
2849: + cellgeom - A `Vec` of `PetscFVCellGeom` data
2850: - facegeom - A `Vec` of `PetscFVFaceGeom` data
2852: Level: developer
2854: .seealso: `DMPLEX`, `PetscFVFaceGeom`, `PetscFVCellGeom`
2855: @*/
2856: PetscErrorCode DMPlexComputeGeometryFVM(DM dm, Vec *cellgeom, Vec *facegeom)
2857: {
2858: DM dmFace, dmCell;
2859: DMLabel ghostLabel;
2860: PetscSection sectionFace, sectionCell;
2861: PetscSection coordSection;
2862: Vec coordinates;
2863: PetscScalar *fgeom, *cgeom;
2864: PetscReal minradius, gminradius;
2865: PetscInt dim, cStart, cEnd, cEndInterior, c, fStart, fEnd, f;
2867: PetscFunctionBegin;
2868: PetscCall(DMGetDimension(dm, &dim));
2869: PetscCall(DMGetCoordinateSection(dm, &coordSection));
2870: PetscCall(DMGetCoordinatesLocal(dm, &coordinates));
2871: /* Make cell centroids and volumes */
2872: PetscCall(DMClone(dm, &dmCell));
2873: PetscCall(DMSetCoordinateSection(dmCell, PETSC_DETERMINE, coordSection));
2874: PetscCall(DMSetCoordinatesLocal(dmCell, coordinates));
2875: PetscCall(PetscSectionCreate(PetscObjectComm((PetscObject)dm), §ionCell));
2876: PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
2877: PetscCall(DMPlexGetCellTypeStratum(dm, DM_POLYTOPE_FV_GHOST, &cEndInterior, NULL));
2878: PetscCall(PetscSectionSetChart(sectionCell, cStart, cEnd));
2879: for (c = cStart; c < cEnd; ++c) PetscCall(PetscSectionSetDof(sectionCell, c, (PetscInt)PetscCeilReal(((PetscReal)sizeof(PetscFVCellGeom)) / sizeof(PetscScalar))));
2880: PetscCall(PetscSectionSetUp(sectionCell));
2881: PetscCall(DMSetLocalSection(dmCell, sectionCell));
2882: PetscCall(PetscSectionDestroy(§ionCell));
2883: PetscCall(DMCreateLocalVector(dmCell, cellgeom));
2884: if (cEndInterior < 0) cEndInterior = cEnd;
2885: PetscCall(VecGetArray(*cellgeom, &cgeom));
2886: for (c = cStart; c < cEndInterior; ++c) {
2887: PetscFVCellGeom *cg;
2889: PetscCall(DMPlexPointLocalRef(dmCell, c, cgeom, &cg));
2890: PetscCall(PetscArrayzero(cg, 1));
2891: PetscCall(DMPlexComputeCellGeometryFVM(dmCell, c, &cg->volume, cg->centroid, NULL));
2892: }
2893: /* Compute face normals and minimum cell radius */
2894: PetscCall(DMClone(dm, &dmFace));
2895: PetscCall(PetscSectionCreate(PetscObjectComm((PetscObject)dm), §ionFace));
2896: PetscCall(DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd));
2897: PetscCall(PetscSectionSetChart(sectionFace, fStart, fEnd));
2898: for (f = fStart; f < fEnd; ++f) PetscCall(PetscSectionSetDof(sectionFace, f, (PetscInt)PetscCeilReal(((PetscReal)sizeof(PetscFVFaceGeom)) / sizeof(PetscScalar))));
2899: PetscCall(PetscSectionSetUp(sectionFace));
2900: PetscCall(DMSetLocalSection(dmFace, sectionFace));
2901: PetscCall(PetscSectionDestroy(§ionFace));
2902: PetscCall(DMCreateLocalVector(dmFace, facegeom));
2903: PetscCall(VecGetArray(*facegeom, &fgeom));
2904: PetscCall(DMGetLabel(dm, "ghost", &ghostLabel));
2905: minradius = PETSC_MAX_REAL;
2906: for (f = fStart; f < fEnd; ++f) {
2907: PetscFVFaceGeom *fg;
2908: PetscReal area;
2909: const PetscInt *cells;
2910: PetscInt ncells, ghost = -1, d, numChildren;
2912: if (ghostLabel) PetscCall(DMLabelGetValue(ghostLabel, f, &ghost));
2913: PetscCall(DMPlexGetTreeChildren(dm, f, &numChildren, NULL));
2914: PetscCall(DMPlexGetSupport(dm, f, &cells));
2915: PetscCall(DMPlexGetSupportSize(dm, f, &ncells));
2916: /* It is possible to get a face with no support when using partition overlap */
2917: if (!ncells || ghost >= 0 || numChildren) continue;
2918: PetscCall(DMPlexPointLocalRef(dmFace, f, fgeom, &fg));
2919: PetscCall(DMPlexComputeCellGeometryFVM(dm, f, &area, fg->centroid, fg->normal));
2920: for (d = 0; d < dim; ++d) fg->normal[d] *= area;
2921: /* Flip face orientation if necessary to match ordering in support, and Update minimum radius */
2922: {
2923: PetscFVCellGeom *cL, *cR;
2924: PetscReal *lcentroid, *rcentroid;
2925: PetscReal l[3], r[3], v[3];
2927: PetscCall(DMPlexPointLocalRead(dmCell, cells[0], cgeom, &cL));
2928: lcentroid = cells[0] >= cEndInterior ? fg->centroid : cL->centroid;
2929: if (ncells > 1) {
2930: PetscCall(DMPlexPointLocalRead(dmCell, cells[1], cgeom, &cR));
2931: rcentroid = cells[1] >= cEndInterior ? fg->centroid : cR->centroid;
2932: } else {
2933: rcentroid = fg->centroid;
2934: }
2935: PetscCall(DMLocalizeCoordinateReal_Internal(dm, dim, fg->centroid, lcentroid, l));
2936: PetscCall(DMLocalizeCoordinateReal_Internal(dm, dim, fg->centroid, rcentroid, r));
2937: DMPlex_WaxpyD_Internal(dim, -1, l, r, v);
2938: if (DMPlex_DotRealD_Internal(dim, fg->normal, v) < 0) {
2939: for (d = 0; d < dim; ++d) fg->normal[d] = -fg->normal[d];
2940: }
2941: if (DMPlex_DotRealD_Internal(dim, fg->normal, v) <= 0) {
2942: 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]);
2943: 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]);
2944: SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Direction for face %" PetscInt_FMT " could not be fixed", f);
2945: }
2946: if (cells[0] < cEndInterior) {
2947: DMPlex_WaxpyD_Internal(dim, -1, fg->centroid, cL->centroid, v);
2948: minradius = PetscMin(minradius, DMPlex_NormD_Internal(dim, v));
2949: }
2950: if (ncells > 1 && cells[1] < cEndInterior) {
2951: DMPlex_WaxpyD_Internal(dim, -1, fg->centroid, cR->centroid, v);
2952: minradius = PetscMin(minradius, DMPlex_NormD_Internal(dim, v));
2953: }
2954: }
2955: }
2956: PetscCallMPI(MPIU_Allreduce(&minradius, &gminradius, 1, MPIU_REAL, MPIU_MIN, PetscObjectComm((PetscObject)dm)));
2957: PetscCall(DMPlexSetMinRadius(dm, gminradius));
2958: /* Compute centroids of ghost cells */
2959: for (c = cEndInterior; c < cEnd; ++c) {
2960: PetscFVFaceGeom *fg;
2961: const PetscInt *cone, *support;
2962: PetscInt coneSize, supportSize, s;
2964: PetscCall(DMPlexGetConeSize(dmCell, c, &coneSize));
2965: PetscCheck(coneSize == 1, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Ghost cell %" PetscInt_FMT " has cone size %" PetscInt_FMT " != 1", c, coneSize);
2966: PetscCall(DMPlexGetCone(dmCell, c, &cone));
2967: PetscCall(DMPlexGetSupportSize(dmCell, cone[0], &supportSize));
2968: PetscCheck(supportSize == 2, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Face %" PetscInt_FMT " has support size %" PetscInt_FMT " != 2", cone[0], supportSize);
2969: PetscCall(DMPlexGetSupport(dmCell, cone[0], &support));
2970: PetscCall(DMPlexPointLocalRef(dmFace, cone[0], fgeom, &fg));
2971: for (s = 0; s < 2; ++s) {
2972: /* Reflect ghost centroid across plane of face */
2973: if (support[s] == c) {
2974: PetscFVCellGeom *ci;
2975: PetscFVCellGeom *cg;
2976: PetscReal c2f[3], a;
2978: PetscCall(DMPlexPointLocalRead(dmCell, support[(s + 1) % 2], cgeom, &ci));
2979: DMPlex_WaxpyD_Internal(dim, -1, ci->centroid, fg->centroid, c2f); /* cell to face centroid */
2980: a = DMPlex_DotRealD_Internal(dim, c2f, fg->normal) / DMPlex_DotRealD_Internal(dim, fg->normal, fg->normal);
2981: PetscCall(DMPlexPointLocalRef(dmCell, support[s], cgeom, &cg));
2982: DMPlex_WaxpyD_Internal(dim, 2 * a, fg->normal, ci->centroid, cg->centroid);
2983: cg->volume = ci->volume;
2984: }
2985: }
2986: }
2987: PetscCall(VecRestoreArray(*facegeom, &fgeom));
2988: PetscCall(VecRestoreArray(*cellgeom, &cgeom));
2989: PetscCall(DMDestroy(&dmCell));
2990: PetscCall(DMDestroy(&dmFace));
2991: PetscFunctionReturn(PETSC_SUCCESS);
2992: }
2994: /*@
2995: DMPlexGetMinRadius - Returns the minimum distance from any cell centroid to a face
2997: Not Collective
2999: Input Parameter:
3000: . dm - the `DMPLEX`
3002: Output Parameter:
3003: . minradius - the minimum cell radius
3005: Level: developer
3007: .seealso: `DMPLEX`, `DMGetCoordinates()`
3008: @*/
3009: PetscErrorCode DMPlexGetMinRadius(DM dm, PetscReal *minradius)
3010: {
3011: PetscFunctionBegin;
3013: PetscAssertPointer(minradius, 2);
3014: *minradius = ((DM_Plex *)dm->data)->minradius;
3015: PetscFunctionReturn(PETSC_SUCCESS);
3016: }
3018: /*@
3019: DMPlexSetMinRadius - Sets the minimum distance from the cell centroid to a face
3021: Logically Collective
3023: Input Parameters:
3024: + dm - the `DMPLEX`
3025: - minradius - the minimum cell radius
3027: Level: developer
3029: .seealso: `DMPLEX`, `DMSetCoordinates()`
3030: @*/
3031: PetscErrorCode DMPlexSetMinRadius(DM dm, PetscReal minradius)
3032: {
3033: PetscFunctionBegin;
3035: ((DM_Plex *)dm->data)->minradius = minradius;
3036: PetscFunctionReturn(PETSC_SUCCESS);
3037: }
3039: static PetscErrorCode BuildGradientReconstruction_Internal(DM dm, PetscFV fvm, DM dmFace, PetscScalar *fgeom, DM dmCell, PetscScalar *cgeom)
3040: {
3041: DMLabel ghostLabel;
3042: PetscScalar *dx, *grad, **gref;
3043: PetscInt dim, cStart, cEnd, c, cEndInterior, maxNumFaces;
3045: PetscFunctionBegin;
3046: PetscCall(DMGetDimension(dm, &dim));
3047: PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
3048: PetscCall(DMPlexGetCellTypeStratum(dm, DM_POLYTOPE_FV_GHOST, &cEndInterior, NULL));
3049: cEndInterior = cEndInterior < 0 ? cEnd : cEndInterior;
3050: PetscCall(DMPlexGetMaxSizes(dm, &maxNumFaces, NULL));
3051: PetscCall(PetscFVLeastSquaresSetMaxFaces(fvm, maxNumFaces));
3052: PetscCall(DMGetLabel(dm, "ghost", &ghostLabel));
3053: PetscCall(PetscMalloc3(maxNumFaces * dim, &dx, maxNumFaces * dim, &grad, maxNumFaces, &gref));
3054: for (c = cStart; c < cEndInterior; c++) {
3055: const PetscInt *faces;
3056: PetscInt numFaces, usedFaces, f, d;
3057: PetscFVCellGeom *cg;
3058: PetscBool boundary;
3059: PetscInt ghost;
3061: // do not attempt to compute a gradient reconstruction stencil in a ghost cell. It will never be used
3062: PetscCall(DMLabelGetValue(ghostLabel, c, &ghost));
3063: if (ghost >= 0) continue;
3065: PetscCall(DMPlexPointLocalRead(dmCell, c, cgeom, &cg));
3066: PetscCall(DMPlexGetConeSize(dm, c, &numFaces));
3067: PetscCall(DMPlexGetCone(dm, c, &faces));
3068: 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);
3069: for (f = 0, usedFaces = 0; f < numFaces; ++f) {
3070: PetscFVCellGeom *cg1;
3071: PetscFVFaceGeom *fg;
3072: const PetscInt *fcells;
3073: PetscInt ncell, side;
3075: PetscCall(DMLabelGetValue(ghostLabel, faces[f], &ghost));
3076: PetscCall(DMIsBoundaryPoint(dm, faces[f], &boundary));
3077: if ((ghost >= 0) || boundary) continue;
3078: PetscCall(DMPlexGetSupport(dm, faces[f], &fcells));
3079: side = (c != fcells[0]); /* c is on left=0 or right=1 of face */
3080: ncell = fcells[!side]; /* the neighbor */
3081: PetscCall(DMPlexPointLocalRef(dmFace, faces[f], fgeom, &fg));
3082: PetscCall(DMPlexPointLocalRead(dmCell, ncell, cgeom, &cg1));
3083: for (d = 0; d < dim; ++d) dx[usedFaces * dim + d] = cg1->centroid[d] - cg->centroid[d];
3084: gref[usedFaces++] = fg->grad[side]; /* Gradient reconstruction term will go here */
3085: }
3086: PetscCheck(usedFaces, PETSC_COMM_SELF, PETSC_ERR_USER, "Mesh contains isolated cell (no neighbors). Is it intentional?");
3087: PetscCall(PetscFVComputeGradient(fvm, usedFaces, dx, grad));
3088: for (f = 0, usedFaces = 0; f < numFaces; ++f) {
3089: PetscCall(DMLabelGetValue(ghostLabel, faces[f], &ghost));
3090: PetscCall(DMIsBoundaryPoint(dm, faces[f], &boundary));
3091: if ((ghost >= 0) || boundary) continue;
3092: for (d = 0; d < dim; ++d) gref[usedFaces][d] = grad[usedFaces * dim + d];
3093: ++usedFaces;
3094: }
3095: }
3096: PetscCall(PetscFree3(dx, grad, gref));
3097: PetscFunctionReturn(PETSC_SUCCESS);
3098: }
3100: static PetscErrorCode BuildGradientReconstruction_Internal_Tree(DM dm, PetscFV fvm, DM dmFace, PetscScalar *fgeom, DM dmCell, PetscScalar *cgeom)
3101: {
3102: DMLabel ghostLabel;
3103: PetscScalar *dx, *grad, **gref;
3104: PetscInt dim, cStart, cEnd, c, cEndInterior, fStart, fEnd, f, nStart, nEnd, maxNumFaces = 0;
3105: PetscSection neighSec;
3106: PetscInt(*neighbors)[2];
3107: PetscInt *counter;
3109: PetscFunctionBegin;
3110: PetscCall(DMGetDimension(dm, &dim));
3111: PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
3112: PetscCall(DMPlexGetCellTypeStratum(dm, DM_POLYTOPE_FV_GHOST, &cEndInterior, NULL));
3113: if (cEndInterior < 0) cEndInterior = cEnd;
3114: PetscCall(PetscSectionCreate(PetscObjectComm((PetscObject)dm), &neighSec));
3115: PetscCall(PetscSectionSetChart(neighSec, cStart, cEndInterior));
3116: PetscCall(DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd));
3117: PetscCall(DMGetLabel(dm, "ghost", &ghostLabel));
3118: for (f = fStart; f < fEnd; f++) {
3119: const PetscInt *fcells;
3120: PetscBool boundary;
3121: PetscInt ghost = -1;
3122: PetscInt numChildren, numCells, c;
3124: if (ghostLabel) PetscCall(DMLabelGetValue(ghostLabel, f, &ghost));
3125: PetscCall(DMIsBoundaryPoint(dm, f, &boundary));
3126: PetscCall(DMPlexGetTreeChildren(dm, f, &numChildren, NULL));
3127: if ((ghost >= 0) || boundary || numChildren) continue;
3128: PetscCall(DMPlexGetSupportSize(dm, f, &numCells));
3129: if (numCells == 2) {
3130: PetscCall(DMPlexGetSupport(dm, f, &fcells));
3131: for (c = 0; c < 2; c++) {
3132: PetscInt cell = fcells[c];
3134: if (cell >= cStart && cell < cEndInterior) PetscCall(PetscSectionAddDof(neighSec, cell, 1));
3135: }
3136: }
3137: }
3138: PetscCall(PetscSectionSetUp(neighSec));
3139: PetscCall(PetscSectionGetMaxDof(neighSec, &maxNumFaces));
3140: PetscCall(PetscFVLeastSquaresSetMaxFaces(fvm, maxNumFaces));
3141: nStart = 0;
3142: PetscCall(PetscSectionGetStorageSize(neighSec, &nEnd));
3143: PetscCall(PetscMalloc1(nEnd - nStart, &neighbors));
3144: PetscCall(PetscCalloc1(cEndInterior - cStart, &counter));
3145: for (f = fStart; f < fEnd; f++) {
3146: const PetscInt *fcells;
3147: PetscBool boundary;
3148: PetscInt ghost = -1;
3149: PetscInt numChildren, numCells, c;
3151: if (ghostLabel) PetscCall(DMLabelGetValue(ghostLabel, f, &ghost));
3152: PetscCall(DMIsBoundaryPoint(dm, f, &boundary));
3153: PetscCall(DMPlexGetTreeChildren(dm, f, &numChildren, NULL));
3154: if ((ghost >= 0) || boundary || numChildren) continue;
3155: PetscCall(DMPlexGetSupportSize(dm, f, &numCells));
3156: if (numCells == 2) {
3157: PetscCall(DMPlexGetSupport(dm, f, &fcells));
3158: for (c = 0; c < 2; c++) {
3159: PetscInt cell = fcells[c], off;
3161: if (cell >= cStart && cell < cEndInterior) {
3162: PetscCall(PetscSectionGetOffset(neighSec, cell, &off));
3163: off += counter[cell - cStart]++;
3164: neighbors[off][0] = f;
3165: neighbors[off][1] = fcells[1 - c];
3166: }
3167: }
3168: }
3169: }
3170: PetscCall(PetscFree(counter));
3171: PetscCall(PetscMalloc3(maxNumFaces * dim, &dx, maxNumFaces * dim, &grad, maxNumFaces, &gref));
3172: for (c = cStart; c < cEndInterior; c++) {
3173: PetscInt numFaces, f, d, off, ghost = -1;
3174: PetscFVCellGeom *cg;
3176: PetscCall(DMPlexPointLocalRead(dmCell, c, cgeom, &cg));
3177: PetscCall(PetscSectionGetDof(neighSec, c, &numFaces));
3178: PetscCall(PetscSectionGetOffset(neighSec, c, &off));
3180: // do not attempt to compute a gradient reconstruction stencil in a ghost cell. It will never be used
3181: if (ghostLabel) PetscCall(DMLabelGetValue(ghostLabel, c, &ghost));
3182: if (ghost >= 0) continue;
3184: 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);
3185: for (f = 0; f < numFaces; ++f) {
3186: PetscFVCellGeom *cg1;
3187: PetscFVFaceGeom *fg;
3188: const PetscInt *fcells;
3189: PetscInt ncell, side, nface;
3191: nface = neighbors[off + f][0];
3192: ncell = neighbors[off + f][1];
3193: PetscCall(DMPlexGetSupport(dm, nface, &fcells));
3194: side = (c != fcells[0]);
3195: PetscCall(DMPlexPointLocalRef(dmFace, nface, fgeom, &fg));
3196: PetscCall(DMPlexPointLocalRead(dmCell, ncell, cgeom, &cg1));
3197: for (d = 0; d < dim; ++d) dx[f * dim + d] = cg1->centroid[d] - cg->centroid[d];
3198: gref[f] = fg->grad[side]; /* Gradient reconstruction term will go here */
3199: }
3200: PetscCall(PetscFVComputeGradient(fvm, numFaces, dx, grad));
3201: for (f = 0; f < numFaces; ++f) {
3202: for (d = 0; d < dim; ++d) gref[f][d] = grad[f * dim + d];
3203: }
3204: }
3205: PetscCall(PetscFree3(dx, grad, gref));
3206: PetscCall(PetscSectionDestroy(&neighSec));
3207: PetscCall(PetscFree(neighbors));
3208: PetscFunctionReturn(PETSC_SUCCESS);
3209: }
3211: /*@
3212: DMPlexComputeGradientFVM - Compute geometric factors for gradient reconstruction, which are stored in the geometry data, and compute layout for gradient data
3214: Collective
3216: Input Parameters:
3217: + dm - The `DMPLEX`
3218: . fvm - The `PetscFV`
3219: - cellGeometry - The face geometry from `DMPlexComputeCellGeometryFVM()`
3221: Input/Output Parameter:
3222: . faceGeometry - The face geometry from `DMPlexComputeFaceGeometryFVM()`; on output
3223: the geometric factors for gradient calculation are inserted
3225: Output Parameter:
3226: . dmGrad - The `DM` describing the layout of gradient data
3228: Level: developer
3230: .seealso: `DMPLEX`, `DMPlexGetFaceGeometryFVM()`, `DMPlexGetCellGeometryFVM()`
3231: @*/
3232: PetscErrorCode DMPlexComputeGradientFVM(DM dm, PetscFV fvm, Vec faceGeometry, Vec cellGeometry, DM *dmGrad)
3233: {
3234: DM dmFace, dmCell;
3235: PetscScalar *fgeom, *cgeom;
3236: PetscSection sectionGrad, parentSection;
3237: PetscInt dim, pdim, cStart, cEnd, cEndInterior, c;
3239: PetscFunctionBegin;
3240: PetscCall(DMGetDimension(dm, &dim));
3241: PetscCall(PetscFVGetNumComponents(fvm, &pdim));
3242: PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
3243: PetscCall(DMPlexGetCellTypeStratum(dm, DM_POLYTOPE_FV_GHOST, &cEndInterior, NULL));
3244: /* Construct the interpolant corresponding to each face from the least-square solution over the cell neighborhood */
3245: PetscCall(VecGetDM(faceGeometry, &dmFace));
3246: PetscCall(VecGetDM(cellGeometry, &dmCell));
3247: PetscCall(VecGetArray(faceGeometry, &fgeom));
3248: PetscCall(VecGetArray(cellGeometry, &cgeom));
3249: PetscCall(DMPlexGetTree(dm, &parentSection, NULL, NULL, NULL, NULL));
3250: if (!parentSection) {
3251: PetscCall(BuildGradientReconstruction_Internal(dm, fvm, dmFace, fgeom, dmCell, cgeom));
3252: } else {
3253: PetscCall(BuildGradientReconstruction_Internal_Tree(dm, fvm, dmFace, fgeom, dmCell, cgeom));
3254: }
3255: PetscCall(VecRestoreArray(faceGeometry, &fgeom));
3256: PetscCall(VecRestoreArray(cellGeometry, &cgeom));
3257: /* Create storage for gradients */
3258: PetscCall(DMClone(dm, dmGrad));
3259: PetscCall(PetscSectionCreate(PetscObjectComm((PetscObject)dm), §ionGrad));
3260: PetscCall(PetscSectionSetChart(sectionGrad, cStart, cEnd));
3261: for (c = cStart; c < cEnd; ++c) PetscCall(PetscSectionSetDof(sectionGrad, c, pdim * dim));
3262: PetscCall(PetscSectionSetUp(sectionGrad));
3263: PetscCall(DMSetLocalSection(*dmGrad, sectionGrad));
3264: PetscCall(PetscSectionDestroy(§ionGrad));
3265: PetscFunctionReturn(PETSC_SUCCESS);
3266: }
3268: /*@
3269: DMPlexGetDataFVM - Retrieve precomputed cell geometry
3271: Collective
3273: Input Parameters:
3274: + dm - The `DM`
3275: - fv - The `PetscFV`
3277: Output Parameters:
3278: + cellgeom - The cell geometry
3279: . facegeom - The face geometry
3280: - gradDM - The gradient matrices
3282: Level: developer
3284: .seealso: `DMPLEX`, `DMPlexComputeGeometryFVM()`
3285: @*/
3286: PetscErrorCode DMPlexGetDataFVM(DM dm, PetscFV fv, Vec *cellgeom, Vec *facegeom, DM *gradDM)
3287: {
3288: PetscObject cellgeomobj, facegeomobj;
3290: PetscFunctionBegin;
3291: PetscCall(PetscObjectQuery((PetscObject)dm, "DMPlex_cellgeom_fvm", &cellgeomobj));
3292: if (!cellgeomobj) {
3293: Vec cellgeomInt, facegeomInt;
3295: PetscCall(DMPlexComputeGeometryFVM(dm, &cellgeomInt, &facegeomInt));
3296: PetscCall(PetscObjectCompose((PetscObject)dm, "DMPlex_cellgeom_fvm", (PetscObject)cellgeomInt));
3297: PetscCall(PetscObjectCompose((PetscObject)dm, "DMPlex_facegeom_fvm", (PetscObject)facegeomInt));
3298: PetscCall(VecDestroy(&cellgeomInt));
3299: PetscCall(VecDestroy(&facegeomInt));
3300: PetscCall(PetscObjectQuery((PetscObject)dm, "DMPlex_cellgeom_fvm", &cellgeomobj));
3301: }
3302: PetscCall(PetscObjectQuery((PetscObject)dm, "DMPlex_facegeom_fvm", &facegeomobj));
3303: if (cellgeom) *cellgeom = (Vec)cellgeomobj;
3304: if (facegeom) *facegeom = (Vec)facegeomobj;
3305: if (gradDM) {
3306: PetscObject gradobj;
3307: PetscBool computeGradients;
3309: PetscCall(PetscFVGetComputeGradients(fv, &computeGradients));
3310: if (!computeGradients) {
3311: *gradDM = NULL;
3312: PetscFunctionReturn(PETSC_SUCCESS);
3313: }
3314: PetscCall(PetscObjectQuery((PetscObject)dm, "DMPlex_dmgrad_fvm", &gradobj));
3315: if (!gradobj) {
3316: DM dmGradInt;
3318: PetscCall(DMPlexComputeGradientFVM(dm, fv, (Vec)facegeomobj, (Vec)cellgeomobj, &dmGradInt));
3319: PetscCall(PetscObjectCompose((PetscObject)dm, "DMPlex_dmgrad_fvm", (PetscObject)dmGradInt));
3320: PetscCall(DMDestroy(&dmGradInt));
3321: PetscCall(PetscObjectQuery((PetscObject)dm, "DMPlex_dmgrad_fvm", &gradobj));
3322: }
3323: *gradDM = (DM)gradobj;
3324: }
3325: PetscFunctionReturn(PETSC_SUCCESS);
3326: }
3328: static PetscErrorCode DMPlexCoordinatesToReference_NewtonUpdate(PetscInt dimC, PetscInt dimR, PetscScalar *J, PetscScalar *invJ, PetscScalar *work, PetscReal *resNeg, PetscReal *guess)
3329: {
3330: PetscInt l, m;
3332: PetscFunctionBeginHot;
3333: if (dimC == dimR && dimR <= 3) {
3334: /* invert Jacobian, multiply */
3335: PetscScalar det, idet;
3337: switch (dimR) {
3338: case 1:
3339: invJ[0] = 1. / J[0];
3340: break;
3341: case 2:
3342: det = J[0] * J[3] - J[1] * J[2];
3343: idet = 1. / det;
3344: invJ[0] = J[3] * idet;
3345: invJ[1] = -J[1] * idet;
3346: invJ[2] = -J[2] * idet;
3347: invJ[3] = J[0] * idet;
3348: break;
3349: case 3: {
3350: invJ[0] = J[4] * J[8] - J[5] * J[7];
3351: invJ[1] = J[2] * J[7] - J[1] * J[8];
3352: invJ[2] = J[1] * J[5] - J[2] * J[4];
3353: det = invJ[0] * J[0] + invJ[1] * J[3] + invJ[2] * J[6];
3354: idet = 1. / det;
3355: invJ[0] *= idet;
3356: invJ[1] *= idet;
3357: invJ[2] *= idet;
3358: invJ[3] = idet * (J[5] * J[6] - J[3] * J[8]);
3359: invJ[4] = idet * (J[0] * J[8] - J[2] * J[6]);
3360: invJ[5] = idet * (J[2] * J[3] - J[0] * J[5]);
3361: invJ[6] = idet * (J[3] * J[7] - J[4] * J[6]);
3362: invJ[7] = idet * (J[1] * J[6] - J[0] * J[7]);
3363: invJ[8] = idet * (J[0] * J[4] - J[1] * J[3]);
3364: } break;
3365: }
3366: for (l = 0; l < dimR; l++) {
3367: for (m = 0; m < dimC; m++) guess[l] += PetscRealPart(invJ[l * dimC + m]) * resNeg[m];
3368: }
3369: } else {
3370: #if defined(PETSC_USE_COMPLEX)
3371: char transpose = 'C';
3372: #else
3373: char transpose = 'T';
3374: #endif
3375: PetscBLASInt m, n, one = 1, worksize, info;
3377: PetscCall(PetscBLASIntCast(dimR, &m));
3378: PetscCall(PetscBLASIntCast(dimC, &n));
3379: PetscCall(PetscBLASIntCast(dimC * dimC, &worksize));
3380: for (l = 0; l < dimC; l++) invJ[l] = resNeg[l];
3382: PetscCallBLAS("LAPACKgels", LAPACKgels_(&transpose, &m, &n, &one, J, &m, invJ, &n, work, &worksize, &info));
3383: PetscCheck(info == 0, PETSC_COMM_SELF, PETSC_ERR_LIB, "Bad argument to GELS %" PetscBLASInt_FMT, info);
3385: for (l = 0; l < dimR; l++) guess[l] += PetscRealPart(invJ[l]);
3386: }
3387: PetscFunctionReturn(PETSC_SUCCESS);
3388: }
3390: static PetscErrorCode DMPlexCoordinatesToReference_Tensor(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal realCoords[], PetscReal refCoords[], Vec coords, PetscInt dimC, PetscInt dimR)
3391: {
3392: PetscInt coordSize, i, j, k, l, m, maxIts = 7, numV = (1 << dimR);
3393: PetscScalar *coordsScalar = NULL;
3394: PetscReal *cellData, *cellCoords, *cellCoeffs, *extJ, *resNeg;
3395: PetscScalar *J, *invJ, *work;
3397: PetscFunctionBegin;
3399: PetscCall(DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar));
3400: PetscCheck(coordSize >= dimC * numV, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Expecting at least %" PetscInt_FMT " coordinates, got %" PetscInt_FMT, dimC * (1 << dimR), coordSize);
3401: PetscCall(DMGetWorkArray(dm, 2 * coordSize + dimR + dimC, MPIU_REAL, &cellData));
3402: PetscCall(DMGetWorkArray(dm, 3 * dimR * dimC, MPIU_SCALAR, &J));
3403: cellCoords = &cellData[0];
3404: cellCoeffs = &cellData[coordSize];
3405: extJ = &cellData[2 * coordSize];
3406: resNeg = &cellData[2 * coordSize + dimR];
3407: invJ = &J[dimR * dimC];
3408: work = &J[2 * dimR * dimC];
3409: if (dimR == 2) {
3410: const PetscInt zToPlex[4] = {0, 1, 3, 2};
3412: for (i = 0; i < 4; i++) {
3413: PetscInt plexI = zToPlex[i];
3415: for (j = 0; j < dimC; j++) cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
3416: }
3417: } else if (dimR == 3) {
3418: const PetscInt zToPlex[8] = {0, 3, 1, 2, 4, 5, 7, 6};
3420: for (i = 0; i < 8; i++) {
3421: PetscInt plexI = zToPlex[i];
3423: for (j = 0; j < dimC; j++) cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
3424: }
3425: } else {
3426: for (i = 0; i < coordSize; i++) cellCoords[i] = PetscRealPart(coordsScalar[i]);
3427: }
3428: /* Perform the shuffling transform that converts values at the corners of [-1,1]^d to coefficients */
3429: for (i = 0; i < dimR; i++) {
3430: PetscReal *swap;
3432: for (j = 0; j < (numV / 2); j++) {
3433: for (k = 0; k < dimC; k++) {
3434: cellCoeffs[dimC * j + k] = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] + cellCoords[dimC * 2 * j + k]);
3435: cellCoeffs[dimC * (j + (numV / 2)) + k] = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] - cellCoords[dimC * 2 * j + k]);
3436: }
3437: }
3439: if (i < dimR - 1) {
3440: swap = cellCoeffs;
3441: cellCoeffs = cellCoords;
3442: cellCoords = swap;
3443: }
3444: }
3445: PetscCall(PetscArrayzero(refCoords, numPoints * dimR));
3446: for (j = 0; j < numPoints; j++) {
3447: for (i = 0; i < maxIts; i++) {
3448: PetscReal *guess = &refCoords[dimR * j];
3450: /* compute -residual and Jacobian */
3451: for (k = 0; k < dimC; k++) resNeg[k] = realCoords[dimC * j + k];
3452: for (k = 0; k < dimC * dimR; k++) J[k] = 0.;
3453: for (k = 0; k < numV; k++) {
3454: PetscReal extCoord = 1.;
3455: for (l = 0; l < dimR; l++) {
3456: PetscReal coord = guess[l];
3457: PetscInt dep = (k & (1 << l)) >> l;
3459: extCoord *= dep * coord + !dep;
3460: extJ[l] = dep;
3462: for (m = 0; m < dimR; m++) {
3463: PetscReal coord = guess[m];
3464: PetscInt dep = ((k & (1 << m)) >> m) && (m != l);
3465: PetscReal mult = dep * coord + !dep;
3467: extJ[l] *= mult;
3468: }
3469: }
3470: for (l = 0; l < dimC; l++) {
3471: PetscReal coeff = cellCoeffs[dimC * k + l];
3473: resNeg[l] -= coeff * extCoord;
3474: for (m = 0; m < dimR; m++) J[dimR * l + m] += coeff * extJ[m];
3475: }
3476: }
3477: if (0 && PetscDefined(USE_DEBUG)) {
3478: PetscReal maxAbs = 0.;
3480: for (l = 0; l < dimC; l++) maxAbs = PetscMax(maxAbs, PetscAbsReal(resNeg[l]));
3481: PetscCall(PetscInfo(dm, "cell %" PetscInt_FMT ", point %" PetscInt_FMT ", iter %" PetscInt_FMT ": res %g\n", cell, j, i, (double)maxAbs));
3482: }
3484: PetscCall(DMPlexCoordinatesToReference_NewtonUpdate(dimC, dimR, J, invJ, work, resNeg, guess));
3485: }
3486: }
3487: PetscCall(DMRestoreWorkArray(dm, 3 * dimR * dimC, MPIU_SCALAR, &J));
3488: PetscCall(DMRestoreWorkArray(dm, 2 * coordSize + dimR + dimC, MPIU_REAL, &cellData));
3489: PetscCall(DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar));
3490: PetscFunctionReturn(PETSC_SUCCESS);
3491: }
3493: static PetscErrorCode DMPlexReferenceToCoordinates_Tensor(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal refCoords[], PetscReal realCoords[], Vec coords, PetscInt dimC, PetscInt dimR)
3494: {
3495: PetscInt coordSize, i, j, k, l, numV = (1 << dimR);
3496: PetscScalar *coordsScalar = NULL;
3497: PetscReal *cellData, *cellCoords, *cellCoeffs;
3499: PetscFunctionBegin;
3501: PetscCall(DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar));
3502: PetscCheck(coordSize >= dimC * numV, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Expecting at least %" PetscInt_FMT " coordinates, got %" PetscInt_FMT, dimC * (1 << dimR), coordSize);
3503: PetscCall(DMGetWorkArray(dm, 2 * coordSize, MPIU_REAL, &cellData));
3504: cellCoords = &cellData[0];
3505: cellCoeffs = &cellData[coordSize];
3506: if (dimR == 2) {
3507: const PetscInt zToPlex[4] = {0, 1, 3, 2};
3509: for (i = 0; i < 4; i++) {
3510: PetscInt plexI = zToPlex[i];
3512: for (j = 0; j < dimC; j++) cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
3513: }
3514: } else if (dimR == 3) {
3515: const PetscInt zToPlex[8] = {0, 3, 1, 2, 4, 5, 7, 6};
3517: for (i = 0; i < 8; i++) {
3518: PetscInt plexI = zToPlex[i];
3520: for (j = 0; j < dimC; j++) cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
3521: }
3522: } else {
3523: for (i = 0; i < coordSize; i++) cellCoords[i] = PetscRealPart(coordsScalar[i]);
3524: }
3525: /* Perform the shuffling transform that converts values at the corners of [-1,1]^d to coefficients */
3526: for (i = 0; i < dimR; i++) {
3527: PetscReal *swap;
3529: for (j = 0; j < (numV / 2); j++) {
3530: for (k = 0; k < dimC; k++) {
3531: cellCoeffs[dimC * j + k] = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] + cellCoords[dimC * 2 * j + k]);
3532: cellCoeffs[dimC * (j + (numV / 2)) + k] = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] - cellCoords[dimC * 2 * j + k]);
3533: }
3534: }
3536: if (i < dimR - 1) {
3537: swap = cellCoeffs;
3538: cellCoeffs = cellCoords;
3539: cellCoords = swap;
3540: }
3541: }
3542: PetscCall(PetscArrayzero(realCoords, numPoints * dimC));
3543: for (j = 0; j < numPoints; j++) {
3544: const PetscReal *guess = &refCoords[dimR * j];
3545: PetscReal *mapped = &realCoords[dimC * j];
3547: for (k = 0; k < numV; k++) {
3548: PetscReal extCoord = 1.;
3549: for (l = 0; l < dimR; l++) {
3550: PetscReal coord = guess[l];
3551: PetscInt dep = (k & (1 << l)) >> l;
3553: extCoord *= dep * coord + !dep;
3554: }
3555: for (l = 0; l < dimC; l++) {
3556: PetscReal coeff = cellCoeffs[dimC * k + l];
3558: mapped[l] += coeff * extCoord;
3559: }
3560: }
3561: }
3562: PetscCall(DMRestoreWorkArray(dm, 2 * coordSize, MPIU_REAL, &cellData));
3563: PetscCall(DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar));
3564: PetscFunctionReturn(PETSC_SUCCESS);
3565: }
3567: /* TODO: TOBY please fix this for Nc > 1 */
3568: static PetscErrorCode DMPlexCoordinatesToReference_FE(DM dm, PetscFE fe, PetscInt cell, PetscInt numPoints, const PetscReal realCoords[], PetscReal refCoords[], Vec coords, PetscInt Nc, PetscInt dimR)
3569: {
3570: PetscInt numComp, pdim, i, j, k, l, m, maxIter = 7, coordSize;
3571: PetscScalar *nodes = NULL;
3572: PetscReal *invV, *modes;
3573: PetscReal *B, *D, *resNeg;
3574: PetscScalar *J, *invJ, *work;
3576: PetscFunctionBegin;
3577: PetscCall(PetscFEGetDimension(fe, &pdim));
3578: PetscCall(PetscFEGetNumComponents(fe, &numComp));
3579: 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);
3580: PetscCall(DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &nodes));
3581: /* convert nodes to values in the stable evaluation basis */
3582: PetscCall(DMGetWorkArray(dm, pdim, MPIU_REAL, &modes));
3583: invV = fe->invV;
3584: for (i = 0; i < pdim; ++i) {
3585: modes[i] = 0.;
3586: for (j = 0; j < pdim; ++j) modes[i] += invV[i * pdim + j] * PetscRealPart(nodes[j]);
3587: }
3588: PetscCall(DMGetWorkArray(dm, pdim * Nc + pdim * Nc * dimR + Nc, MPIU_REAL, &B));
3589: D = &B[pdim * Nc];
3590: resNeg = &D[pdim * Nc * dimR];
3591: PetscCall(DMGetWorkArray(dm, 3 * Nc * dimR, MPIU_SCALAR, &J));
3592: invJ = &J[Nc * dimR];
3593: work = &invJ[Nc * dimR];
3594: for (i = 0; i < numPoints * dimR; i++) refCoords[i] = 0.;
3595: for (j = 0; j < numPoints; j++) {
3596: for (i = 0; i < maxIter; i++) { /* we could batch this so that we're not making big B and D arrays all the time */
3597: PetscReal *guess = &refCoords[j * dimR];
3598: PetscCall(PetscSpaceEvaluate(fe->basisSpace, 1, guess, B, D, NULL));
3599: for (k = 0; k < Nc; k++) resNeg[k] = realCoords[j * Nc + k];
3600: for (k = 0; k < Nc * dimR; k++) J[k] = 0.;
3601: for (k = 0; k < pdim; k++) {
3602: for (l = 0; l < Nc; l++) {
3603: resNeg[l] -= modes[k] * B[k * Nc + l];
3604: for (m = 0; m < dimR; m++) J[l * dimR + m] += modes[k] * D[(k * Nc + l) * dimR + m];
3605: }
3606: }
3607: if (0 && PetscDefined(USE_DEBUG)) {
3608: PetscReal maxAbs = 0.;
3610: for (l = 0; l < Nc; l++) maxAbs = PetscMax(maxAbs, PetscAbsReal(resNeg[l]));
3611: PetscCall(PetscInfo(dm, "cell %" PetscInt_FMT ", point %" PetscInt_FMT ", iter %" PetscInt_FMT ": res %g\n", cell, j, i, (double)maxAbs));
3612: }
3613: PetscCall(DMPlexCoordinatesToReference_NewtonUpdate(Nc, dimR, J, invJ, work, resNeg, guess));
3614: }
3615: }
3616: PetscCall(DMRestoreWorkArray(dm, 3 * Nc * dimR, MPIU_SCALAR, &J));
3617: PetscCall(DMRestoreWorkArray(dm, pdim * Nc + pdim * Nc * dimR + Nc, MPIU_REAL, &B));
3618: PetscCall(DMRestoreWorkArray(dm, pdim, MPIU_REAL, &modes));
3619: PetscCall(DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &nodes));
3620: PetscFunctionReturn(PETSC_SUCCESS);
3621: }
3623: /* TODO: TOBY please fix this for Nc > 1 */
3624: static PetscErrorCode DMPlexReferenceToCoordinates_FE(DM dm, PetscFE fe, PetscInt cell, PetscInt numPoints, const PetscReal refCoords[], PetscReal realCoords[], Vec coords, PetscInt Nc, PetscInt dimR)
3625: {
3626: PetscInt numComp, pdim, i, j, k, l, coordSize;
3627: PetscScalar *nodes = NULL;
3628: PetscReal *invV, *modes;
3629: PetscReal *B;
3631: PetscFunctionBegin;
3632: PetscCall(PetscFEGetDimension(fe, &pdim));
3633: PetscCall(PetscFEGetNumComponents(fe, &numComp));
3634: 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);
3635: PetscCall(DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &nodes));
3636: /* convert nodes to values in the stable evaluation basis */
3637: PetscCall(DMGetWorkArray(dm, pdim, MPIU_REAL, &modes));
3638: invV = fe->invV;
3639: for (i = 0; i < pdim; ++i) {
3640: modes[i] = 0.;
3641: for (j = 0; j < pdim; ++j) modes[i] += invV[i * pdim + j] * PetscRealPart(nodes[j]);
3642: }
3643: PetscCall(DMGetWorkArray(dm, numPoints * pdim * Nc, MPIU_REAL, &B));
3644: PetscCall(PetscSpaceEvaluate(fe->basisSpace, numPoints, refCoords, B, NULL, NULL));
3645: for (i = 0; i < numPoints * Nc; i++) realCoords[i] = 0.;
3646: for (j = 0; j < numPoints; j++) {
3647: PetscReal *mapped = &realCoords[j * Nc];
3649: for (k = 0; k < pdim; k++) {
3650: for (l = 0; l < Nc; l++) mapped[l] += modes[k] * B[(j * pdim + k) * Nc + l];
3651: }
3652: }
3653: PetscCall(DMRestoreWorkArray(dm, numPoints * pdim * Nc, MPIU_REAL, &B));
3654: PetscCall(DMRestoreWorkArray(dm, pdim, MPIU_REAL, &modes));
3655: PetscCall(DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &nodes));
3656: PetscFunctionReturn(PETSC_SUCCESS);
3657: }
3659: /*@
3660: DMPlexCoordinatesToReference - Pull coordinates back from the mesh to the reference element
3661: using a single element map.
3663: Not Collective
3665: Input Parameters:
3666: + dm - The mesh, with coordinate maps defined either by a `PetscDS` for the coordinate `DM` (see `DMGetCoordinateDM()`) or
3667: implicitly by the coordinates of the corner vertices of the cell: as an affine map for simplicial elements, or
3668: as a multilinear map for tensor-product elements
3669: . cell - the cell whose map is used.
3670: . numPoints - the number of points to locate
3671: - realCoords - (numPoints x coordinate dimension) array of coordinates (see `DMGetCoordinateDim()`)
3673: Output Parameter:
3674: . refCoords - (`numPoints` x `dimension`) array of reference coordinates (see `DMGetDimension()`)
3676: Level: intermediate
3678: Notes:
3679: This inversion will be accurate inside the reference element, but may be inaccurate for
3680: mappings that do not extend uniquely outside the reference cell (e.g, most non-affine maps)
3682: .seealso: `DMPLEX`, `DMPlexReferenceToCoordinates()`
3683: @*/
3684: PetscErrorCode DMPlexCoordinatesToReference(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal realCoords[], PetscReal refCoords[])
3685: {
3686: PetscInt dimC, dimR, depth, cStart, cEnd, i;
3687: DM coordDM = NULL;
3688: Vec coords;
3689: PetscFE fe = NULL;
3691: PetscFunctionBegin;
3693: PetscCall(DMGetDimension(dm, &dimR));
3694: PetscCall(DMGetCoordinateDim(dm, &dimC));
3695: if (dimR <= 0 || dimC <= 0 || numPoints <= 0) PetscFunctionReturn(PETSC_SUCCESS);
3696: PetscCall(DMPlexGetDepth(dm, &depth));
3697: PetscCall(DMGetCoordinatesLocal(dm, &coords));
3698: PetscCall(DMGetCoordinateDM(dm, &coordDM));
3699: if (coordDM) {
3700: PetscInt coordFields;
3702: PetscCall(DMGetNumFields(coordDM, &coordFields));
3703: if (coordFields) {
3704: PetscClassId id;
3705: PetscObject disc;
3707: PetscCall(DMGetField(coordDM, 0, NULL, &disc));
3708: PetscCall(PetscObjectGetClassId(disc, &id));
3709: if (id == PETSCFE_CLASSID) fe = (PetscFE)disc;
3710: }
3711: }
3712: PetscCall(DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd));
3713: 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);
3714: if (!fe) { /* implicit discretization: affine or multilinear */
3715: PetscInt coneSize;
3716: PetscBool isSimplex, isTensor;
3718: PetscCall(DMPlexGetConeSize(dm, cell, &coneSize));
3719: isSimplex = (coneSize == (dimR + 1)) ? PETSC_TRUE : PETSC_FALSE;
3720: isTensor = (coneSize == ((depth == 1) ? (1 << dimR) : (2 * dimR))) ? PETSC_TRUE : PETSC_FALSE;
3721: if (isSimplex) {
3722: PetscReal detJ, *v0, *J, *invJ;
3724: PetscCall(DMGetWorkArray(dm, dimC + 2 * dimC * dimC, MPIU_REAL, &v0));
3725: J = &v0[dimC];
3726: invJ = &J[dimC * dimC];
3727: PetscCall(DMPlexComputeCellGeometryAffineFEM(dm, cell, v0, J, invJ, &detJ));
3728: for (i = 0; i < numPoints; i++) { /* Apply the inverse affine transformation for each point */
3729: const PetscReal x0[3] = {-1., -1., -1.};
3731: CoordinatesRealToRef(dimC, dimR, x0, v0, invJ, &realCoords[dimC * i], &refCoords[dimR * i]);
3732: }
3733: PetscCall(DMRestoreWorkArray(dm, dimC + 2 * dimC * dimC, MPIU_REAL, &v0));
3734: } else if (isTensor) {
3735: PetscCall(DMPlexCoordinatesToReference_Tensor(coordDM, cell, numPoints, realCoords, refCoords, coords, dimC, dimR));
3736: } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Unrecognized cone size %" PetscInt_FMT, coneSize);
3737: } else {
3738: PetscCall(DMPlexCoordinatesToReference_FE(coordDM, fe, cell, numPoints, realCoords, refCoords, coords, dimC, dimR));
3739: }
3740: PetscFunctionReturn(PETSC_SUCCESS);
3741: }
3743: /*@
3744: DMPlexReferenceToCoordinates - Map references coordinates to coordinates in the mesh for a single element map.
3746: Not Collective
3748: Input Parameters:
3749: + dm - The mesh, with coordinate maps defined either by a PetscDS for the coordinate `DM` (see `DMGetCoordinateDM()`) or
3750: implicitly by the coordinates of the corner vertices of the cell: as an affine map for simplicial elements, or
3751: as a multilinear map for tensor-product elements
3752: . cell - the cell whose map is used.
3753: . numPoints - the number of points to locate
3754: - refCoords - (numPoints x dimension) array of reference coordinates (see `DMGetDimension()`)
3756: Output Parameter:
3757: . realCoords - (numPoints x coordinate dimension) array of coordinates (see `DMGetCoordinateDim()`)
3759: Level: intermediate
3761: .seealso: `DMPLEX`, `DMPlexCoordinatesToReference()`
3762: @*/
3763: PetscErrorCode DMPlexReferenceToCoordinates(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal refCoords[], PetscReal realCoords[])
3764: {
3765: PetscInt dimC, dimR, depth, cStart, cEnd, i;
3766: DM coordDM = NULL;
3767: Vec coords;
3768: PetscFE fe = NULL;
3770: PetscFunctionBegin;
3772: PetscCall(DMGetDimension(dm, &dimR));
3773: PetscCall(DMGetCoordinateDim(dm, &dimC));
3774: if (dimR <= 0 || dimC <= 0 || numPoints <= 0) PetscFunctionReturn(PETSC_SUCCESS);
3775: PetscCall(DMPlexGetDepth(dm, &depth));
3776: PetscCall(DMGetCoordinatesLocal(dm, &coords));
3777: PetscCall(DMGetCoordinateDM(dm, &coordDM));
3778: if (coordDM) {
3779: PetscInt coordFields;
3781: PetscCall(DMGetNumFields(coordDM, &coordFields));
3782: if (coordFields) {
3783: PetscClassId id;
3784: PetscObject disc;
3786: PetscCall(DMGetField(coordDM, 0, NULL, &disc));
3787: PetscCall(PetscObjectGetClassId(disc, &id));
3788: if (id == PETSCFE_CLASSID) fe = (PetscFE)disc;
3789: }
3790: }
3791: PetscCall(DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd));
3792: 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);
3793: if (!fe) { /* implicit discretization: affine or multilinear */
3794: PetscInt coneSize;
3795: PetscBool isSimplex, isTensor;
3797: PetscCall(DMPlexGetConeSize(dm, cell, &coneSize));
3798: isSimplex = (coneSize == (dimR + 1)) ? PETSC_TRUE : PETSC_FALSE;
3799: isTensor = (coneSize == ((depth == 1) ? (1 << dimR) : (2 * dimR))) ? PETSC_TRUE : PETSC_FALSE;
3800: if (isSimplex) {
3801: PetscReal detJ, *v0, *J;
3803: PetscCall(DMGetWorkArray(dm, dimC + 2 * dimC * dimC, MPIU_REAL, &v0));
3804: J = &v0[dimC];
3805: PetscCall(DMPlexComputeCellGeometryAffineFEM(dm, cell, v0, J, NULL, &detJ));
3806: for (i = 0; i < numPoints; i++) { /* Apply the affine transformation for each point */
3807: const PetscReal xi0[3] = {-1., -1., -1.};
3809: CoordinatesRefToReal(dimC, dimR, xi0, v0, J, &refCoords[dimR * i], &realCoords[dimC * i]);
3810: }
3811: PetscCall(DMRestoreWorkArray(dm, dimC + 2 * dimC * dimC, MPIU_REAL, &v0));
3812: } else if (isTensor) {
3813: PetscCall(DMPlexReferenceToCoordinates_Tensor(coordDM, cell, numPoints, refCoords, realCoords, coords, dimC, dimR));
3814: } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Unrecognized cone size %" PetscInt_FMT, coneSize);
3815: } else {
3816: PetscCall(DMPlexReferenceToCoordinates_FE(coordDM, fe, cell, numPoints, refCoords, realCoords, coords, dimC, dimR));
3817: }
3818: PetscFunctionReturn(PETSC_SUCCESS);
3819: }
3821: 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[])
3822: {
3823: const PetscInt Nc = uOff[1] - uOff[0];
3824: PetscInt c;
3826: for (c = 0; c < Nc; ++c) f0[c] = u[c];
3827: }
3829: /* Shear applies the transformation, assuming we fix z,
3830: / 1 0 m_0 \
3831: | 0 1 m_1 |
3832: \ 0 0 1 /
3833: */
3834: 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[])
3835: {
3836: const PetscInt Nc = uOff[1] - uOff[0];
3837: const PetscInt ax = (PetscInt)PetscRealPart(constants[0]);
3838: PetscInt c;
3840: for (c = 0; c < Nc; ++c) coords[c] = u[c] + constants[c + 1] * u[ax];
3841: }
3843: /* Flare applies the transformation, assuming we fix x_f,
3845: x_i = x_i * alpha_i x_f
3846: */
3847: 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[])
3848: {
3849: const PetscInt Nc = uOff[1] - uOff[0];
3850: const PetscInt cf = (PetscInt)PetscRealPart(constants[0]);
3851: PetscInt c;
3853: for (c = 0; c < Nc; ++c) coords[c] = u[c] * (c == cf ? 1.0 : constants[c + 1] * u[cf]);
3854: }
3856: /*
3857: 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
3858: will correspond to the top and bottom of our square. So
3860: (0,0)--(1,0) ==> (1,0)--(2,0) Just a shift of (1,0)
3861: (0,1)--(1,1) ==> (0,1)--(0,2) Switch x and y
3863: 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:
3865: (x, y) ==> (x+1, \pi/2 y) in (r', \theta') space
3866: ==> ((x+1) cos(\pi/2 y), (x+1) sin(\pi/2 y)) in (x', y') space
3867: */
3868: 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[])
3869: {
3870: const PetscReal ri = PetscRealPart(constants[0]);
3871: const PetscReal ro = PetscRealPart(constants[1]);
3873: xp[0] = (x[0] * (ro - ri) + ri) * PetscCosReal(0.5 * PETSC_PI * x[1]);
3874: xp[1] = (x[0] * (ro - ri) + ri) * PetscSinReal(0.5 * PETSC_PI * x[1]);
3875: }
3877: /*
3878: 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
3879: lower hemisphere and the upper surface onto the top, letting z be the radius.
3881: (x, y) ==> ((z+3)/2, \pi/2 (|x| or |y|), arctan y/x) in (r', \theta', \phi') space
3882: ==> ((z+3)/2 \cos(\theta') cos(\phi'), (z+3)/2 \cos(\theta') sin(\phi'), (z+3)/2 sin(\theta')) in (x', y', z') space
3883: */
3884: 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[])
3885: {
3886: const PetscReal pi4 = PETSC_PI / 4.0;
3887: const PetscReal ri = PetscRealPart(constants[0]);
3888: const PetscReal ro = PetscRealPart(constants[1]);
3889: const PetscReal rp = (x[2] + 1) * 0.5 * (ro - ri) + ri;
3890: const PetscReal phip = PetscAtan2Real(x[1], x[0]);
3891: 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])));
3893: xp[0] = rp * PetscCosReal(thetap) * PetscCosReal(phip);
3894: xp[1] = rp * PetscCosReal(thetap) * PetscSinReal(phip);
3895: xp[2] = rp * PetscSinReal(thetap);
3896: }
3898: /*@C
3899: DMPlexRemapGeometry - This function maps the original `DM` coordinates to new coordinates.
3901: Not Collective
3903: Input Parameters:
3904: + dm - The `DM`
3905: . time - The time
3906: - func - The function transforming current coordinates to new coordinates
3908: Calling sequence of `func`:
3909: + dim - The spatial dimension
3910: . Nf - The number of input fields (here 1)
3911: . NfAux - The number of input auxiliary fields
3912: . uOff - The offset of the coordinates in u[] (here 0)
3913: . uOff_x - The offset of the coordinates in u_x[] (here 0)
3914: . u - The coordinate values at this point in space
3915: . u_t - The coordinate time derivative at this point in space (here `NULL`)
3916: . u_x - The coordinate derivatives at this point in space
3917: . aOff - The offset of each auxiliary field in u[]
3918: . aOff_x - The offset of each auxiliary field in u_x[]
3919: . a - The auxiliary field values at this point in space
3920: . a_t - The auxiliary field time derivative at this point in space (or `NULL`)
3921: . a_x - The auxiliary field derivatives at this point in space
3922: . t - The current time
3923: . x - The coordinates of this point (here not used)
3924: . numConstants - The number of constants
3925: . constants - The value of each constant
3926: - f - The new coordinates at this point in space
3928: Level: intermediate
3930: .seealso: `DMPLEX`, `DMGetCoordinates()`, `DMGetCoordinatesLocal()`, `DMGetCoordinateDM()`, `DMProjectFieldLocal()`, `DMProjectFieldLabelLocal()`
3931: @*/
3932: 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[]))
3933: {
3934: DM cdm;
3935: PetscDS cds;
3936: DMField cf;
3937: PetscObject obj;
3938: PetscClassId id;
3939: Vec lCoords, tmpCoords;
3941: PetscFunctionBegin;
3942: PetscCall(DMGetCoordinateDM(dm, &cdm));
3943: PetscCall(DMGetCoordinatesLocal(dm, &lCoords));
3944: PetscCall(DMGetDS(cdm, &cds));
3945: PetscCall(PetscDSGetDiscretization(cds, 0, &obj));
3946: PetscCall(PetscObjectGetClassId(obj, &id));
3947: if (id != PETSCFE_CLASSID) {
3948: PetscSection cSection;
3949: const PetscScalar *constants;
3950: PetscScalar *coords, f[16];
3951: PetscInt dim, cdim, Nc, vStart, vEnd;
3953: PetscCall(DMGetDimension(dm, &dim));
3954: PetscCall(DMGetCoordinateDim(dm, &cdim));
3955: PetscCheck(cdim <= 16, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Affine version of DMPlexRemapGeometry is currently limited to dimensions <= 16, not %" PetscInt_FMT, cdim);
3956: PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
3957: PetscCall(DMGetCoordinateSection(dm, &cSection));
3958: PetscCall(PetscDSGetConstants(cds, &Nc, &constants));
3959: PetscCall(VecGetArrayWrite(lCoords, &coords));
3960: for (PetscInt v = vStart; v < vEnd; ++v) {
3961: PetscInt uOff[2] = {0, cdim};
3962: PetscInt off, c;
3964: PetscCall(PetscSectionGetOffset(cSection, v, &off));
3965: (*func)(dim, 1, 0, uOff, NULL, &coords[off], NULL, NULL, NULL, NULL, NULL, NULL, NULL, 0.0, NULL, Nc, constants, f);
3966: for (c = 0; c < cdim; ++c) coords[off + c] = f[c];
3967: }
3968: PetscCall(VecRestoreArrayWrite(lCoords, &coords));
3969: } else {
3970: PetscCall(DMGetLocalVector(cdm, &tmpCoords));
3971: PetscCall(VecCopy(lCoords, tmpCoords));
3972: /* We have to do the coordinate field manually right now since the coordinate DM will not have its own */
3973: PetscCall(DMGetCoordinateField(dm, &cf));
3974: cdm->coordinates[0].field = cf;
3975: PetscCall(DMProjectFieldLocal(cdm, time, tmpCoords, &func, INSERT_VALUES, lCoords));
3976: cdm->coordinates[0].field = NULL;
3977: PetscCall(DMRestoreLocalVector(cdm, &tmpCoords));
3978: PetscCall(DMSetCoordinatesLocal(dm, lCoords));
3979: }
3980: PetscFunctionReturn(PETSC_SUCCESS);
3981: }
3983: /*@
3984: DMPlexShearGeometry - This shears the domain, meaning adds a multiple of the shear coordinate to all other coordinates.
3986: Not Collective
3988: Input Parameters:
3989: + dm - The `DMPLEX`
3990: . direction - The shear coordinate direction, e.g. `DM_X` is the x-axis
3991: - multipliers - The multiplier m for each direction which is not the shear direction
3993: Level: intermediate
3995: .seealso: `DMPLEX`, `DMPlexRemapGeometry()`, `DMDirection`, `DM_X`, `DM_Y`, `DM_Z`
3996: @*/
3997: PetscErrorCode DMPlexShearGeometry(DM dm, DMDirection direction, PetscReal multipliers[])
3998: {
3999: DM cdm;
4000: PetscDS cds;
4001: PetscScalar *moduli;
4002: const PetscInt dir = (PetscInt)direction;
4003: PetscInt dE, d, e;
4005: PetscFunctionBegin;
4006: PetscCall(DMGetCoordinateDM(dm, &cdm));
4007: PetscCall(DMGetCoordinateDim(dm, &dE));
4008: PetscCall(PetscMalloc1(dE + 1, &moduli));
4009: moduli[0] = dir;
4010: for (d = 0, e = 0; d < dE; ++d) moduli[d + 1] = d == dir ? 0.0 : (multipliers ? multipliers[e++] : 1.0);
4011: PetscCall(DMGetDS(cdm, &cds));
4012: PetscCall(PetscDSSetConstants(cds, dE + 1, moduli));
4013: PetscCall(DMPlexRemapGeometry(dm, 0.0, coordMap_shear));
4014: PetscCall(PetscFree(moduli));
4015: PetscFunctionReturn(PETSC_SUCCESS);
4016: }