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: /*@
7: DMPlexFindVertices - Try to find DAG points based on their coordinates.
9: Not Collective (provided `DMGetCoordinatesLocalSetUp()` has been already called)
11: Input Parameters:
12: + dm - The `DMPLEX` object
13: . coordinates - The `Vec` of coordinates of the sought points
14: - eps - The tolerance or `PETSC_DEFAULT`
16: Output Parameter:
17: . points - The `IS` of found DAG points or -1
19: Level: intermediate
21: Notes:
22: 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.
24: The output `IS` is living on `PETSC_COMM_SELF` and its length is npoints.
25: Each rank does the search independently.
26: 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.
28: The output `IS` must be destroyed by user.
30: The tolerance is interpreted as the maximum Euclidean (L2) distance of the sought point from the specified coordinates.
32: 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.
34: .seealso: `DMPLEX`, `DMPlexCreate()`, `DMGetCoordinatesLocal()`
35: @*/
36: PetscErrorCode DMPlexFindVertices(DM dm, Vec coordinates, PetscReal eps, IS *points)
37: {
38: PetscInt c, cdim, i, j, o, p, vStart, vEnd;
39: PetscInt npoints;
40: const PetscScalar *coord;
41: Vec allCoordsVec;
42: const PetscScalar *allCoords;
43: PetscInt *dagPoints;
45: PetscFunctionBegin;
46: if (eps < 0) eps = PETSC_SQRT_MACHINE_EPSILON;
47: PetscCall(DMGetCoordinateDim(dm, &cdim));
48: {
49: PetscInt n;
51: PetscCall(VecGetLocalSize(coordinates, &n));
52: 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);
53: npoints = n / cdim;
54: }
55: PetscCall(DMGetCoordinatesLocal(dm, &allCoordsVec));
56: PetscCall(VecGetArrayRead(allCoordsVec, &allCoords));
57: PetscCall(VecGetArrayRead(coordinates, &coord));
58: PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
59: if (PetscDefined(USE_DEBUG)) {
60: /* check coordinate section is consistent with DM dimension */
61: PetscSection cs;
62: PetscInt ndof;
64: PetscCall(DMGetCoordinateSection(dm, &cs));
65: for (p = vStart; p < vEnd; p++) {
66: PetscCall(PetscSectionGetDof(cs, p, &ndof));
67: PetscCheck(ndof == cdim, PETSC_COMM_SELF, PETSC_ERR_PLIB, "point %" PetscInt_FMT ": ndof = %" PetscInt_FMT " != %" PetscInt_FMT " = cdim", p, ndof, cdim);
68: }
69: }
70: PetscCall(PetscMalloc1(npoints, &dagPoints));
71: if (eps == 0.0) {
72: for (i = 0, j = 0; i < npoints; i++, j += cdim) {
73: dagPoints[i] = -1;
74: for (p = vStart, o = 0; p < vEnd; p++, o += cdim) {
75: for (c = 0; c < cdim; c++) {
76: if (coord[j + c] != allCoords[o + c]) break;
77: }
78: if (c == cdim) {
79: dagPoints[i] = p;
80: break;
81: }
82: }
83: }
84: } else {
85: for (i = 0, j = 0; i < npoints; i++, j += cdim) {
86: PetscReal norm;
88: dagPoints[i] = -1;
89: for (p = vStart, o = 0; p < vEnd; p++, o += cdim) {
90: norm = 0.0;
91: for (c = 0; c < cdim; c++) norm += PetscRealPart(PetscSqr(coord[j + c] - allCoords[o + c]));
92: norm = PetscSqrtReal(norm);
93: if (norm <= eps) {
94: dagPoints[i] = p;
95: break;
96: }
97: }
98: }
99: }
100: PetscCall(VecRestoreArrayRead(allCoordsVec, &allCoords));
101: PetscCall(VecRestoreArrayRead(coordinates, &coord));
102: PetscCall(ISCreateGeneral(PETSC_COMM_SELF, npoints, dagPoints, PETSC_OWN_POINTER, points));
103: PetscFunctionReturn(PETSC_SUCCESS);
104: }
106: static PetscErrorCode DMPlexGetLineIntersection_2D_Internal(const PetscReal segmentA[], const PetscReal segmentB[], PetscReal intersection[], PetscBool *hasIntersection)
107: {
108: const PetscReal p0_x = segmentA[0 * 2 + 0];
109: const PetscReal p0_y = segmentA[0 * 2 + 1];
110: const PetscReal p1_x = segmentA[1 * 2 + 0];
111: const PetscReal p1_y = segmentA[1 * 2 + 1];
112: const PetscReal p2_x = segmentB[0 * 2 + 0];
113: const PetscReal p2_y = segmentB[0 * 2 + 1];
114: const PetscReal p3_x = segmentB[1 * 2 + 0];
115: const PetscReal p3_y = segmentB[1 * 2 + 1];
116: const PetscReal s1_x = p1_x - p0_x;
117: const PetscReal s1_y = p1_y - p0_y;
118: const PetscReal s2_x = p3_x - p2_x;
119: const PetscReal s2_y = p3_y - p2_y;
120: const PetscReal denom = (-s2_x * s1_y + s1_x * s2_y);
122: PetscFunctionBegin;
123: *hasIntersection = PETSC_FALSE;
124: /* Non-parallel lines */
125: if (denom != 0.0) {
126: const PetscReal s = (-s1_y * (p0_x - p2_x) + s1_x * (p0_y - p2_y)) / denom;
127: const PetscReal t = (s2_x * (p0_y - p2_y) - s2_y * (p0_x - p2_x)) / denom;
129: if (s >= 0 && s <= 1 && t >= 0 && t <= 1) {
130: *hasIntersection = PETSC_TRUE;
131: if (intersection) {
132: intersection[0] = p0_x + (t * s1_x);
133: intersection[1] = p0_y + (t * s1_y);
134: }
135: }
136: }
137: PetscFunctionReturn(PETSC_SUCCESS);
138: }
140: /* The plane is segmentB x segmentC: https://en.wikipedia.org/wiki/Line%E2%80%93plane_intersection */
141: static PetscErrorCode DMPlexGetLinePlaneIntersection_3D_Internal(const PetscReal segmentA[], const PetscReal segmentB[], const PetscReal segmentC[], PetscReal intersection[], PetscBool *hasIntersection)
142: {
143: const PetscReal p0_x = segmentA[0 * 3 + 0];
144: const PetscReal p0_y = segmentA[0 * 3 + 1];
145: const PetscReal p0_z = segmentA[0 * 3 + 2];
146: const PetscReal p1_x = segmentA[1 * 3 + 0];
147: const PetscReal p1_y = segmentA[1 * 3 + 1];
148: const PetscReal p1_z = segmentA[1 * 3 + 2];
149: const PetscReal q0_x = segmentB[0 * 3 + 0];
150: const PetscReal q0_y = segmentB[0 * 3 + 1];
151: const PetscReal q0_z = segmentB[0 * 3 + 2];
152: const PetscReal q1_x = segmentB[1 * 3 + 0];
153: const PetscReal q1_y = segmentB[1 * 3 + 1];
154: const PetscReal q1_z = segmentB[1 * 3 + 2];
155: const PetscReal r0_x = segmentC[0 * 3 + 0];
156: const PetscReal r0_y = segmentC[0 * 3 + 1];
157: const PetscReal r0_z = segmentC[0 * 3 + 2];
158: const PetscReal r1_x = segmentC[1 * 3 + 0];
159: const PetscReal r1_y = segmentC[1 * 3 + 1];
160: const PetscReal r1_z = segmentC[1 * 3 + 2];
161: const PetscReal s0_x = p1_x - p0_x;
162: const PetscReal s0_y = p1_y - p0_y;
163: const PetscReal s0_z = p1_z - p0_z;
164: const PetscReal s1_x = q1_x - q0_x;
165: const PetscReal s1_y = q1_y - q0_y;
166: const PetscReal s1_z = q1_z - q0_z;
167: const PetscReal s2_x = r1_x - r0_x;
168: const PetscReal s2_y = r1_y - r0_y;
169: const PetscReal s2_z = r1_z - r0_z;
170: const PetscReal s3_x = s1_y * s2_z - s1_z * s2_y; /* s1 x s2 */
171: const PetscReal s3_y = s1_z * s2_x - s1_x * s2_z;
172: const PetscReal s3_z = s1_x * s2_y - s1_y * s2_x;
173: const PetscReal s4_x = s0_y * s2_z - s0_z * s2_y; /* s0 x s2 */
174: const PetscReal s4_y = s0_z * s2_x - s0_x * s2_z;
175: const PetscReal s4_z = s0_x * s2_y - s0_y * s2_x;
176: const PetscReal s5_x = s1_y * s0_z - s1_z * s0_y; /* s1 x s0 */
177: const PetscReal s5_y = s1_z * s0_x - s1_x * s0_z;
178: const PetscReal s5_z = s1_x * s0_y - s1_y * s0_x;
179: const PetscReal denom = -(s0_x * s3_x + s0_y * s3_y + s0_z * s3_z); /* -s0 . (s1 x s2) */
181: PetscFunctionBegin;
182: *hasIntersection = PETSC_FALSE;
183: /* Line not parallel to plane */
184: if (denom != 0.0) {
185: const PetscReal t = (s3_x * (p0_x - q0_x) + s3_y * (p0_y - q0_y) + s3_z * (p0_z - q0_z)) / denom;
186: const PetscReal u = (s4_x * (p0_x - q0_x) + s4_y * (p0_y - q0_y) + s4_z * (p0_z - q0_z)) / denom;
187: const PetscReal v = (s5_x * (p0_x - q0_x) + s5_y * (p0_y - q0_y) + s5_z * (p0_z - q0_z)) / denom;
189: if (t >= 0 && t <= 1 && u >= 0 && u <= 1 && v >= 0 && v <= 1) {
190: *hasIntersection = PETSC_TRUE;
191: if (intersection) {
192: intersection[0] = p0_x + (t * s0_x);
193: intersection[1] = p0_y + (t * s0_y);
194: intersection[2] = p0_z + (t * s0_z);
195: }
196: }
197: }
198: PetscFunctionReturn(PETSC_SUCCESS);
199: }
201: static PetscErrorCode DMPlexLocatePoint_Simplex_1D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
202: {
203: const PetscReal eps = PETSC_SQRT_MACHINE_EPSILON;
204: const PetscReal x = PetscRealPart(point[0]);
205: PetscReal v0, J, invJ, detJ;
206: PetscReal xi;
208: PetscFunctionBegin;
209: PetscCall(DMPlexComputeCellGeometryFEM(dm, c, NULL, &v0, &J, &invJ, &detJ));
210: xi = invJ * (x - v0);
212: if ((xi >= -eps) && (xi <= 2. + eps)) *cell = c;
213: else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
214: PetscFunctionReturn(PETSC_SUCCESS);
215: }
217: static PetscErrorCode DMPlexLocatePoint_Simplex_2D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
218: {
219: const PetscInt embedDim = 2;
220: const PetscReal eps = PETSC_SQRT_MACHINE_EPSILON;
221: PetscReal x = PetscRealPart(point[0]);
222: PetscReal y = PetscRealPart(point[1]);
223: PetscReal v0[2], J[4], invJ[4], detJ;
224: PetscReal xi, eta;
226: PetscFunctionBegin;
227: PetscCall(DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ));
228: xi = invJ[0 * embedDim + 0] * (x - v0[0]) + invJ[0 * embedDim + 1] * (y - v0[1]);
229: eta = invJ[1 * embedDim + 0] * (x - v0[0]) + invJ[1 * embedDim + 1] * (y - v0[1]);
231: if ((xi >= -eps) && (eta >= -eps) && (xi + eta <= 2.0 + eps)) *cell = c;
232: else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
233: PetscFunctionReturn(PETSC_SUCCESS);
234: }
236: static PetscErrorCode DMPlexClosestPoint_Simplex_2D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscReal cpoint[])
237: {
238: const PetscInt embedDim = 2;
239: PetscReal x = PetscRealPart(point[0]);
240: PetscReal y = PetscRealPart(point[1]);
241: PetscReal v0[2], J[4], invJ[4], detJ;
242: PetscReal xi, eta, r;
244: PetscFunctionBegin;
245: PetscCall(DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ));
246: xi = invJ[0 * embedDim + 0] * (x - v0[0]) + invJ[0 * embedDim + 1] * (y - v0[1]);
247: eta = invJ[1 * embedDim + 0] * (x - v0[0]) + invJ[1 * embedDim + 1] * (y - v0[1]);
249: xi = PetscMax(xi, 0.0);
250: eta = PetscMax(eta, 0.0);
251: if (xi + eta > 2.0) {
252: r = (xi + eta) / 2.0;
253: xi /= r;
254: eta /= r;
255: }
256: cpoint[0] = J[0 * embedDim + 0] * xi + J[0 * embedDim + 1] * eta + v0[0];
257: cpoint[1] = J[1 * embedDim + 0] * xi + J[1 * embedDim + 1] * eta + v0[1];
258: PetscFunctionReturn(PETSC_SUCCESS);
259: }
261: static PetscErrorCode DMPlexLocatePoint_Quad_2D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
262: {
263: const PetscScalar *array;
264: PetscScalar *coords = NULL;
265: const PetscInt faces[8] = {0, 1, 1, 2, 2, 3, 3, 0};
266: PetscReal x = PetscRealPart(point[0]);
267: PetscReal y = PetscRealPart(point[1]);
268: PetscInt crossings = 0, numCoords, f;
269: PetscBool isDG;
271: PetscFunctionBegin;
272: PetscCall(DMPlexGetCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
273: PetscCheck(numCoords == 8, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Quadrilateral should have 8 coordinates, not %" PetscInt_FMT, numCoords);
274: for (f = 0; f < 4; ++f) {
275: PetscReal x_i = PetscRealPart(coords[faces[2 * f + 0] * 2 + 0]);
276: PetscReal y_i = PetscRealPart(coords[faces[2 * f + 0] * 2 + 1]);
277: PetscReal x_j = PetscRealPart(coords[faces[2 * f + 1] * 2 + 0]);
278: PetscReal y_j = PetscRealPart(coords[faces[2 * f + 1] * 2 + 1]);
279: PetscReal slope = (y_j - y_i) / (x_j - x_i);
280: PetscBool cond1 = (x_i <= x) && (x < x_j) ? PETSC_TRUE : PETSC_FALSE;
281: PetscBool cond2 = (x_j <= x) && (x < x_i) ? PETSC_TRUE : PETSC_FALSE;
282: PetscBool above = (y < slope * (x - x_i) + y_i) ? PETSC_TRUE : PETSC_FALSE;
283: if ((cond1 || cond2) && above) ++crossings;
284: }
285: if (crossings % 2) *cell = c;
286: else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
287: PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
288: PetscFunctionReturn(PETSC_SUCCESS);
289: }
291: static PetscErrorCode DMPlexLocatePoint_Simplex_3D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
292: {
293: const PetscInt embedDim = 3;
294: const PetscReal eps = PETSC_SQRT_MACHINE_EPSILON;
295: PetscReal v0[3], J[9], invJ[9], detJ;
296: PetscReal x = PetscRealPart(point[0]);
297: PetscReal y = PetscRealPart(point[1]);
298: PetscReal z = PetscRealPart(point[2]);
299: PetscReal xi, eta, zeta;
301: PetscFunctionBegin;
302: PetscCall(DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, invJ, &detJ));
303: xi = invJ[0 * embedDim + 0] * (x - v0[0]) + invJ[0 * embedDim + 1] * (y - v0[1]) + invJ[0 * embedDim + 2] * (z - v0[2]);
304: eta = invJ[1 * embedDim + 0] * (x - v0[0]) + invJ[1 * embedDim + 1] * (y - v0[1]) + invJ[1 * embedDim + 2] * (z - v0[2]);
305: zeta = invJ[2 * embedDim + 0] * (x - v0[0]) + invJ[2 * embedDim + 1] * (y - v0[1]) + invJ[2 * embedDim + 2] * (z - v0[2]);
307: if ((xi >= -eps) && (eta >= -eps) && (zeta >= -eps) && (xi + eta + zeta <= 2.0 + eps)) *cell = c;
308: else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
309: PetscFunctionReturn(PETSC_SUCCESS);
310: }
312: static PetscErrorCode DMPlexLocatePoint_General_3D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
313: {
314: const PetscScalar *array;
315: PetscScalar *coords = NULL;
316: 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};
317: PetscBool found = PETSC_TRUE;
318: PetscInt numCoords, f;
319: PetscBool isDG;
321: PetscFunctionBegin;
322: PetscCall(DMPlexGetCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
323: PetscCheck(numCoords == 24, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Quadrilateral should have 8 coordinates, not %" PetscInt_FMT, numCoords);
324: for (f = 0; f < 6; ++f) {
325: /* Check the point is under plane */
326: /* Get face normal */
327: PetscReal v_i[3];
328: PetscReal v_j[3];
329: PetscReal normal[3];
330: PetscReal pp[3];
331: PetscReal dot;
333: v_i[0] = PetscRealPart(coords[faces[f * 4 + 3] * 3 + 0] - coords[faces[f * 4 + 0] * 3 + 0]);
334: v_i[1] = PetscRealPart(coords[faces[f * 4 + 3] * 3 + 1] - coords[faces[f * 4 + 0] * 3 + 1]);
335: v_i[2] = PetscRealPart(coords[faces[f * 4 + 3] * 3 + 2] - coords[faces[f * 4 + 0] * 3 + 2]);
336: v_j[0] = PetscRealPart(coords[faces[f * 4 + 1] * 3 + 0] - coords[faces[f * 4 + 0] * 3 + 0]);
337: v_j[1] = PetscRealPart(coords[faces[f * 4 + 1] * 3 + 1] - coords[faces[f * 4 + 0] * 3 + 1]);
338: v_j[2] = PetscRealPart(coords[faces[f * 4 + 1] * 3 + 2] - coords[faces[f * 4 + 0] * 3 + 2]);
339: normal[0] = v_i[1] * v_j[2] - v_i[2] * v_j[1];
340: normal[1] = v_i[2] * v_j[0] - v_i[0] * v_j[2];
341: normal[2] = v_i[0] * v_j[1] - v_i[1] * v_j[0];
342: pp[0] = PetscRealPart(coords[faces[f * 4 + 0] * 3 + 0] - point[0]);
343: pp[1] = PetscRealPart(coords[faces[f * 4 + 0] * 3 + 1] - point[1]);
344: pp[2] = PetscRealPart(coords[faces[f * 4 + 0] * 3 + 2] - point[2]);
345: dot = normal[0] * pp[0] + normal[1] * pp[1] + normal[2] * pp[2];
347: /* Check that projected point is in face (2D location problem) */
348: if (dot < 0.0) {
349: found = PETSC_FALSE;
350: break;
351: }
352: }
353: if (found) *cell = c;
354: else *cell = DMLOCATEPOINT_POINT_NOT_FOUND;
355: PetscCall(DMPlexRestoreCellCoordinates(dm, c, &isDG, &numCoords, &array, &coords));
356: PetscFunctionReturn(PETSC_SUCCESS);
357: }
359: static PetscErrorCode PetscGridHashInitialize_Internal(PetscGridHash box, PetscInt dim, const PetscScalar point[])
360: {
361: PetscInt d;
363: PetscFunctionBegin;
364: box->dim = dim;
365: for (d = 0; d < dim; ++d) box->lower[d] = box->upper[d] = point ? PetscRealPart(point[d]) : 0.;
366: PetscFunctionReturn(PETSC_SUCCESS);
367: }
369: PetscErrorCode PetscGridHashCreate(MPI_Comm comm, PetscInt dim, const PetscScalar point[], PetscGridHash *box)
370: {
371: PetscFunctionBegin;
372: PetscCall(PetscMalloc1(1, box));
373: PetscCall(PetscGridHashInitialize_Internal(*box, dim, point));
374: PetscFunctionReturn(PETSC_SUCCESS);
375: }
377: PetscErrorCode PetscGridHashEnlarge(PetscGridHash box, const PetscScalar point[])
378: {
379: PetscInt d;
381: PetscFunctionBegin;
382: for (d = 0; d < box->dim; ++d) {
383: box->lower[d] = PetscMin(box->lower[d], PetscRealPart(point[d]));
384: box->upper[d] = PetscMax(box->upper[d], PetscRealPart(point[d]));
385: }
386: PetscFunctionReturn(PETSC_SUCCESS);
387: }
389: /*
390: PetscGridHashSetGrid - Divide the grid into boxes
392: Not Collective
394: Input Parameters:
395: + box - The grid hash object
396: . n - The number of boxes in each dimension, or `PETSC_DETERMINE`
397: - h - The box size in each dimension, only used if n[d] == `PETSC_DETERMINE`
399: Level: developer
401: .seealso: `DMPLEX`, `PetscGridHashCreate()`
402: */
403: PetscErrorCode PetscGridHashSetGrid(PetscGridHash box, const PetscInt n[], const PetscReal h[])
404: {
405: PetscInt d;
407: PetscFunctionBegin;
408: for (d = 0; d < box->dim; ++d) {
409: box->extent[d] = box->upper[d] - box->lower[d];
410: if (n[d] == PETSC_DETERMINE) {
411: box->h[d] = h[d];
412: box->n[d] = PetscCeilReal(box->extent[d] / h[d]);
413: } else {
414: box->n[d] = n[d];
415: box->h[d] = box->extent[d] / n[d];
416: }
417: }
418: PetscFunctionReturn(PETSC_SUCCESS);
419: }
421: /*
422: PetscGridHashGetEnclosingBox - Find the grid boxes containing each input point
424: Not Collective
426: Input Parameters:
427: + box - The grid hash object
428: . numPoints - The number of input points
429: - points - The input point coordinates
431: Output Parameters:
432: + dboxes - An array of numPoints*dim integers expressing the enclosing box as (i_0, i_1, ..., i_dim)
433: - boxes - An array of numPoints integers expressing the enclosing box as single number, or NULL
435: Level: developer
437: Note:
438: This only guarantees that a box contains a point, not that a cell does.
440: .seealso: `DMPLEX`, `PetscGridHashCreate()`
441: */
442: PetscErrorCode PetscGridHashGetEnclosingBox(PetscGridHash box, PetscInt numPoints, const PetscScalar points[], PetscInt dboxes[], PetscInt boxes[])
443: {
444: const PetscReal *lower = box->lower;
445: const PetscReal *upper = box->upper;
446: const PetscReal *h = box->h;
447: const PetscInt *n = box->n;
448: const PetscInt dim = box->dim;
449: PetscInt d, p;
451: PetscFunctionBegin;
452: for (p = 0; p < numPoints; ++p) {
453: for (d = 0; d < dim; ++d) {
454: PetscInt dbox = PetscFloorReal((PetscRealPart(points[p * dim + d]) - lower[d]) / h[d]);
456: if (dbox == n[d] && PetscAbsReal(PetscRealPart(points[p * dim + d]) - upper[d]) < 1.0e-9) dbox = n[d] - 1;
457: if (dbox == -1 && PetscAbsReal(PetscRealPart(points[p * dim + d]) - lower[d]) < 1.0e-9) dbox = 0;
458: 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", 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);
459: dboxes[p * dim + d] = dbox;
460: }
461: if (boxes)
462: for (d = dim - 2, boxes[p] = dboxes[p * dim + dim - 1]; d >= 0; --d) boxes[p] = boxes[p] * n[d] + dboxes[p * dim + d];
463: }
464: PetscFunctionReturn(PETSC_SUCCESS);
465: }
467: /*
468: PetscGridHashGetEnclosingBoxQuery - Find the grid boxes containing each input point
470: Not Collective
472: Input Parameters:
473: + box - The grid hash object
474: . cellSection - The PetscSection mapping cells to boxes
475: . numPoints - The number of input points
476: - points - The input point coordinates
478: Output Parameters:
479: + dboxes - An array of `numPoints`*`dim` integers expressing the enclosing box as (i_0, i_1, ..., i_dim)
480: . boxes - An array of `numPoints` integers expressing the enclosing box as single number, or `NULL`
481: - found - Flag indicating if point was located within a box
483: Level: developer
485: Note:
486: 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.
488: .seealso: `DMPLEX`, `PetscGridHashGetEnclosingBox()`
489: */
490: PetscErrorCode PetscGridHashGetEnclosingBoxQuery(PetscGridHash box, PetscSection cellSection, PetscInt numPoints, const PetscScalar points[], PetscInt dboxes[], PetscInt boxes[], PetscBool *found)
491: {
492: const PetscReal *lower = box->lower;
493: const PetscReal *upper = box->upper;
494: const PetscReal *h = box->h;
495: const PetscInt *n = box->n;
496: const PetscInt dim = box->dim;
497: PetscInt bStart, bEnd, d, p;
499: PetscFunctionBegin;
501: *found = PETSC_FALSE;
502: PetscCall(PetscSectionGetChart(box->cellSection, &bStart, &bEnd));
503: for (p = 0; p < numPoints; ++p) {
504: for (d = 0; d < dim; ++d) {
505: PetscInt dbox = PetscFloorReal((PetscRealPart(points[p * dim + d]) - lower[d]) / h[d]);
507: if (dbox == n[d] && PetscAbsReal(PetscRealPart(points[p * dim + d]) - upper[d]) < 1.0e-9) dbox = n[d] - 1;
508: if (dbox < 0 || dbox >= n[d]) PetscFunctionReturn(PETSC_SUCCESS);
509: dboxes[p * dim + d] = dbox;
510: }
511: if (boxes)
512: for (d = dim - 2, boxes[p] = dboxes[p * dim + dim - 1]; d >= 0; --d) boxes[p] = boxes[p] * n[d] + dboxes[p * dim + d];
513: // It is possible for a box to overlap no grid cells
514: if (boxes[p] < bStart || boxes[p] >= bEnd) PetscFunctionReturn(PETSC_SUCCESS);
515: }
516: *found = PETSC_TRUE;
517: PetscFunctionReturn(PETSC_SUCCESS);
518: }
520: PetscErrorCode PetscGridHashDestroy(PetscGridHash *box)
521: {
522: PetscFunctionBegin;
523: if (*box) {
524: PetscCall(PetscSectionDestroy(&(*box)->cellSection));
525: PetscCall(ISDestroy(&(*box)->cells));
526: PetscCall(DMLabelDestroy(&(*box)->cellsSparse));
527: }
528: PetscCall(PetscFree(*box));
529: PetscFunctionReturn(PETSC_SUCCESS);
530: }
532: PetscErrorCode DMPlexLocatePoint_Internal(DM dm, PetscInt dim, const PetscScalar point[], PetscInt cellStart, PetscInt *cell)
533: {
534: DMPolytopeType ct;
536: PetscFunctionBegin;
537: PetscCall(DMPlexGetCellType(dm, cellStart, &ct));
538: switch (ct) {
539: case DM_POLYTOPE_SEGMENT:
540: PetscCall(DMPlexLocatePoint_Simplex_1D_Internal(dm, point, cellStart, cell));
541: break;
542: case DM_POLYTOPE_TRIANGLE:
543: PetscCall(DMPlexLocatePoint_Simplex_2D_Internal(dm, point, cellStart, cell));
544: break;
545: case DM_POLYTOPE_QUADRILATERAL:
546: PetscCall(DMPlexLocatePoint_Quad_2D_Internal(dm, point, cellStart, cell));
547: break;
548: case DM_POLYTOPE_TETRAHEDRON:
549: PetscCall(DMPlexLocatePoint_Simplex_3D_Internal(dm, point, cellStart, cell));
550: break;
551: case DM_POLYTOPE_HEXAHEDRON:
552: PetscCall(DMPlexLocatePoint_General_3D_Internal(dm, point, cellStart, cell));
553: break;
554: default:
555: SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No point location for cell %" PetscInt_FMT " with type %s", cellStart, DMPolytopeTypes[ct]);
556: }
557: PetscFunctionReturn(PETSC_SUCCESS);
558: }
560: /*
561: DMPlexClosestPoint_Internal - Returns the closest point in the cell to the given point
562: */
563: PetscErrorCode DMPlexClosestPoint_Internal(DM dm, PetscInt dim, const PetscScalar point[], PetscInt cell, PetscReal cpoint[])
564: {
565: DMPolytopeType ct;
567: PetscFunctionBegin;
568: PetscCall(DMPlexGetCellType(dm, cell, &ct));
569: switch (ct) {
570: case DM_POLYTOPE_TRIANGLE:
571: PetscCall(DMPlexClosestPoint_Simplex_2D_Internal(dm, point, cell, cpoint));
572: break;
573: #if 0
574: case DM_POLYTOPE_QUADRILATERAL:
575: PetscCall(DMPlexClosestPoint_General_2D_Internal(dm, point, cell, cpoint));break;
576: case DM_POLYTOPE_TETRAHEDRON:
577: PetscCall(DMPlexClosestPoint_Simplex_3D_Internal(dm, point, cell, cpoint));break;
578: case DM_POLYTOPE_HEXAHEDRON:
579: PetscCall(DMPlexClosestPoint_General_3D_Internal(dm, point, cell, cpoint));break;
580: #endif
581: default:
582: SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No closest point location for cell %" PetscInt_FMT " with type %s", cell, DMPolytopeTypes[ct]);
583: }
584: PetscFunctionReturn(PETSC_SUCCESS);
585: }
587: /*
588: DMPlexComputeGridHash_Internal - Create a grid hash structure covering the `DMPLEX`
590: Collective
592: Input Parameter:
593: . dm - The `DMPLEX`
595: Output Parameter:
596: . localBox - The grid hash object
598: Level: developer
600: .seealso: `DMPLEX`, `PetscGridHashCreate()`, `PetscGridHashGetEnclosingBox()`
601: */
602: PetscErrorCode DMPlexComputeGridHash_Internal(DM dm, PetscGridHash *localBox)
603: {
604: PetscInt debug = ((DM_Plex *)dm->data)->printLocate;
605: MPI_Comm comm;
606: PetscGridHash lbox;
607: PetscSF sf;
608: Vec coordinates;
609: PetscSection coordSection;
610: Vec coordsLocal;
611: const PetscScalar *coords;
612: PetscScalar *edgeCoords;
613: PetscInt *dboxes, *boxes;
614: const PetscInt *leaves;
615: PetscInt n[3] = {2, 2, 2};
616: PetscInt dim, N, Nl = 0, maxConeSize, cStart, cEnd, c, eStart, eEnd, i;
617: PetscBool flg;
619: PetscFunctionBegin;
620: PetscCall(PetscObjectGetComm((PetscObject)dm, &comm));
621: PetscCall(DMGetCoordinatesLocal(dm, &coordinates));
622: PetscCall(DMGetCoordinateDim(dm, &dim));
623: PetscCall(DMPlexGetMaxSizes(dm, &maxConeSize, NULL));
624: PetscCall(DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd));
625: PetscCall(VecGetLocalSize(coordinates, &N));
626: PetscCall(VecGetArrayRead(coordinates, &coords));
627: PetscCall(PetscGridHashCreate(comm, dim, coords, &lbox));
628: for (i = 0; i < N; i += dim) PetscCall(PetscGridHashEnlarge(lbox, &coords[i]));
629: PetscCall(VecRestoreArrayRead(coordinates, &coords));
630: c = dim;
631: PetscCall(PetscOptionsGetIntArray(NULL, ((PetscObject)dm)->prefix, "-dm_plex_hash_box_faces", n, &c, &flg));
632: if (flg) {
633: for (i = c; i < dim; ++i) n[i] = n[c - 1];
634: } else {
635: for (i = 0; i < dim; ++i) n[i] = PetscMax(2, PetscFloorReal(PetscPowReal((PetscReal)(cEnd - cStart), 1.0 / dim) * 0.8));
636: }
637: PetscCall(PetscGridHashSetGrid(lbox, n, NULL));
638: if (debug)
639: 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], (double)lbox->lower[2], (double)lbox->upper[0],
640: (double)lbox->upper[1], (double)lbox->upper[2], n[0], n[1], n[2], (double)lbox->h[0], (double)lbox->h[1], (double)lbox->h[2]));
641: #if 0
642: /* Could define a custom reduction to merge these */
643: PetscCall(MPIU_Allreduce(lbox->lower, gbox->lower, 3, MPIU_REAL, MPI_MIN, comm));
644: PetscCall(MPIU_Allreduce(lbox->upper, gbox->upper, 3, MPIU_REAL, MPI_MAX, comm));
645: #endif
646: /* Is there a reason to snap the local bounding box to a division of the global box? */
647: /* Should we compute all overlaps of local boxes? We could do this with a rendevouz scheme partitioning the global box */
648: /* Create label */
649: PetscCall(DMPlexGetDepthStratum(dm, 1, &eStart, &eEnd));
650: if (dim < 2) eStart = eEnd = -1;
651: PetscCall(DMLabelCreate(PETSC_COMM_SELF, "cells", &lbox->cellsSparse));
652: PetscCall(DMLabelCreateIndex(lbox->cellsSparse, cStart, cEnd));
653: /* Compute boxes which overlap each cell: https://stackoverflow.com/questions/13790208/triangle-square-intersection-test-in-2d */
654: PetscCall(DMGetCoordinatesLocal(dm, &coordsLocal));
655: PetscCall(DMGetCoordinateSection(dm, &coordSection));
656: PetscCall(DMGetPointSF(dm, &sf));
657: if (sf) PetscCall(PetscSFGetGraph(sf, NULL, &Nl, &leaves, NULL));
658: Nl = PetscMax(Nl, 0);
659: PetscCall(PetscCalloc3(16 * dim, &dboxes, 16, &boxes, PetscPowInt(maxConeSize, dim) * dim, &edgeCoords));
660: for (c = cStart; c < cEnd; ++c) {
661: const PetscReal *h = lbox->h;
662: PetscScalar *ccoords = NULL;
663: PetscInt csize = 0;
664: PetscInt *closure = NULL;
665: PetscInt Ncl, cl, Ne = 0, idx;
666: PetscScalar point[3];
667: PetscInt dlim[6], d, e, i, j, k;
669: PetscCall(PetscFindInt(c, Nl, leaves, &idx));
670: if (idx >= 0) continue;
671: /* Get all edges in cell */
672: PetscCall(DMPlexGetTransitiveClosure(dm, c, PETSC_TRUE, &Ncl, &closure));
673: for (cl = 0; cl < Ncl * 2; ++cl) {
674: if ((closure[cl] >= eStart) && (closure[cl] < eEnd)) {
675: PetscScalar *ecoords = &edgeCoords[Ne * dim * 2];
676: PetscInt ecsize = dim * 2;
678: PetscCall(DMPlexVecGetClosure(dm, coordSection, coordsLocal, closure[cl], &ecsize, &ecoords));
679: PetscCheck(ecsize == dim * 2, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Got %" PetscInt_FMT " coords for edge, instead of %" PetscInt_FMT, ecsize, dim * 2);
680: ++Ne;
681: }
682: }
683: PetscCall(DMPlexRestoreTransitiveClosure(dm, c, PETSC_TRUE, &Ncl, &closure));
684: /* Find boxes enclosing each vertex */
685: PetscCall(DMPlexVecGetClosure(dm, coordSection, coordsLocal, c, &csize, &ccoords));
686: PetscCall(PetscGridHashGetEnclosingBox(lbox, csize / dim, ccoords, dboxes, boxes));
687: /* Mark cells containing the vertices */
688: for (e = 0; e < csize / dim; ++e) {
689: if (debug)
690: PetscCall(PetscPrintf(PETSC_COMM_SELF, "Cell %" PetscInt_FMT " has vertex (%g, %g, %g) in box %" PetscInt_FMT " (%" PetscInt_FMT ", %" PetscInt_FMT ", %" PetscInt_FMT ")\n", c, (double)PetscRealPart(ccoords[e * dim + 0]), dim > 1 ? (double)PetscRealPart(ccoords[e * dim + 1]) : 0., dim > 2 ? (double)PetscRealPart(ccoords[e * dim + 2]) : 0., boxes[e], dboxes[e * dim + 0], dim > 1 ? dboxes[e * dim + 1] : -1, dim > 2 ? dboxes[e * dim + 2] : -1));
691: PetscCall(DMLabelSetValue(lbox->cellsSparse, c, boxes[e]));
692: }
693: /* Get grid of boxes containing these */
694: for (d = 0; d < dim; ++d) dlim[d * 2 + 0] = dlim[d * 2 + 1] = dboxes[d];
695: for (d = dim; d < 3; ++d) dlim[d * 2 + 0] = dlim[d * 2 + 1] = 0;
696: for (e = 1; e < dim + 1; ++e) {
697: for (d = 0; d < dim; ++d) {
698: dlim[d * 2 + 0] = PetscMin(dlim[d * 2 + 0], dboxes[e * dim + d]);
699: dlim[d * 2 + 1] = PetscMax(dlim[d * 2 + 1], dboxes[e * dim + d]);
700: }
701: }
702: /* Check for intersection of box with cell */
703: for (k = dlim[2 * 2 + 0], point[2] = lbox->lower[2] + k * h[2]; k <= dlim[2 * 2 + 1]; ++k, point[2] += h[2]) {
704: for (j = dlim[1 * 2 + 0], point[1] = lbox->lower[1] + j * h[1]; j <= dlim[1 * 2 + 1]; ++j, point[1] += h[1]) {
705: for (i = dlim[0 * 2 + 0], point[0] = lbox->lower[0] + i * h[0]; i <= dlim[0 * 2 + 1]; ++i, point[0] += h[0]) {
706: const PetscInt box = (k * lbox->n[1] + j) * lbox->n[0] + i;
707: PetscScalar cpoint[3];
708: PetscInt cell, edge, ii, jj, kk;
710: if (debug)
711: PetscCall(PetscPrintf(PETSC_COMM_SELF, "Box %" PetscInt_FMT ": (%.2g, %.2g, %.2g) -- (%.2g, %.2g, %.2g)\n", box, (double)PetscRealPart(point[0]), (double)PetscRealPart(point[1]), (double)PetscRealPart(point[2]), (double)PetscRealPart(point[0] + h[0]), (double)PetscRealPart(point[1] + h[1]), (double)PetscRealPart(point[2] + h[2])));
712: /* Check whether cell contains any vertex of this subbox TODO vectorize this */
713: for (kk = 0, cpoint[2] = point[2]; kk < (dim > 2 ? 2 : 1); ++kk, cpoint[2] += h[2]) {
714: for (jj = 0, cpoint[1] = point[1]; jj < (dim > 1 ? 2 : 1); ++jj, cpoint[1] += h[1]) {
715: for (ii = 0, cpoint[0] = point[0]; ii < 2; ++ii, cpoint[0] += h[0]) {
716: PetscCall(DMPlexLocatePoint_Internal(dm, dim, cpoint, c, &cell));
717: if (cell >= 0) {
718: if (debug)
719: PetscCall(PetscPrintf(PETSC_COMM_SELF, " Cell %" PetscInt_FMT " contains vertex (%.2g, %.2g, %.2g) of box %" PetscInt_FMT "\n", c, (double)PetscRealPart(cpoint[0]), (double)PetscRealPart(cpoint[1]), (double)PetscRealPart(cpoint[2]), box));
720: PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
721: jj = kk = 2;
722: break;
723: }
724: }
725: }
726: }
727: /* Check whether cell edge intersects any face of these subboxes TODO vectorize this */
728: for (edge = 0; edge < Ne; ++edge) {
729: PetscReal segA[6] = {0., 0., 0., 0., 0., 0.};
730: PetscReal segB[6] = {0., 0., 0., 0., 0., 0.};
731: PetscReal segC[6] = {0., 0., 0., 0., 0., 0.};
733: PetscCheck(dim <= 3, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Unexpected dim %" PetscInt_FMT " > 3", dim);
734: for (d = 0; d < dim * 2; ++d) segA[d] = PetscRealPart(edgeCoords[edge * dim * 2 + d]);
735: /* 1D: (x) -- (x+h) 0 -- 1
736: 2D: (x, y) -- (x, y+h) (0, 0) -- (0, 1)
737: (x+h, y) -- (x+h, y+h) (1, 0) -- (1, 1)
738: (x, y) -- (x+h, y) (0, 0) -- (1, 0)
739: (x, y+h) -- (x+h, y+h) (0, 1) -- (1, 1)
740: 3D: (x, y, z) -- (x, y+h, z), (x, y, z) -- (x, y, z+h) (0, 0, 0) -- (0, 1, 0), (0, 0, 0) -- (0, 0, 1)
741: (x+h, y, z) -- (x+h, y+h, z), (x+h, y, z) -- (x+h, y, z+h) (1, 0, 0) -- (1, 1, 0), (1, 0, 0) -- (1, 0, 1)
742: (x, y, z) -- (x+h, y, z), (x, y, z) -- (x, y, z+h) (0, 0, 0) -- (1, 0, 0), (0, 0, 0) -- (0, 0, 1)
743: (x, y+h, z) -- (x+h, y+h, z), (x, y+h, z) -- (x, y+h, z+h) (0, 1, 0) -- (1, 1, 0), (0, 1, 0) -- (0, 1, 1)
744: (x, y, z) -- (x+h, y, z), (x, y, z) -- (x, y+h, z) (0, 0, 0) -- (1, 0, 0), (0, 0, 0) -- (0, 1, 0)
745: (x, y, z+h) -- (x+h, y, z+h), (x, y, z+h) -- (x, y+h, z+h) (0, 0, 1) -- (1, 0, 1), (0, 0, 1) -- (0, 1, 1)
746: */
747: /* Loop over faces with normal in direction d */
748: for (d = 0; d < dim; ++d) {
749: PetscBool intersects = PETSC_FALSE;
750: PetscInt e = (d + 1) % dim;
751: PetscInt f = (d + 2) % dim;
753: /* There are two faces in each dimension */
754: for (ii = 0; ii < 2; ++ii) {
755: segB[d] = PetscRealPart(point[d] + ii * h[d]);
756: segB[dim + d] = PetscRealPart(point[d] + ii * h[d]);
757: segC[d] = PetscRealPart(point[d] + ii * h[d]);
758: segC[dim + d] = PetscRealPart(point[d] + ii * h[d]);
759: if (dim > 1) {
760: segB[e] = PetscRealPart(point[e] + 0 * h[e]);
761: segB[dim + e] = PetscRealPart(point[e] + 1 * h[e]);
762: segC[e] = PetscRealPart(point[e] + 0 * h[e]);
763: segC[dim + e] = PetscRealPart(point[e] + 0 * h[e]);
764: }
765: if (dim > 2) {
766: segB[f] = PetscRealPart(point[f] + 0 * h[f]);
767: segB[dim + f] = PetscRealPart(point[f] + 0 * h[f]);
768: segC[f] = PetscRealPart(point[f] + 0 * h[f]);
769: segC[dim + f] = PetscRealPart(point[f] + 1 * h[f]);
770: }
771: if (dim == 2) {
772: PetscCall(DMPlexGetLineIntersection_2D_Internal(segA, segB, NULL, &intersects));
773: } else if (dim == 3) {
774: PetscCall(DMPlexGetLinePlaneIntersection_3D_Internal(segA, segB, segC, NULL, &intersects));
775: }
776: if (intersects) {
777: if (debug)
778: PetscCall(PetscPrintf(PETSC_COMM_SELF, " Cell %" PetscInt_FMT " edge %" PetscInt_FMT " (%.2g, %.2g, %.2g)--(%.2g, %.2g, %.2g) intersects box %" PetscInt_FMT ", face (%.2g, %.2g, %.2g)--(%.2g, %.2g, %.2g) (%.2g, %.2g, %.2g)--(%.2g, %.2g, %.2g)\n", c, edge, (double)segA[0], (double)segA[1], (double)segA[2], (double)segA[3], (double)segA[4], (double)segA[5], box, (double)segB[0], (double)segB[1], (double)segB[2], (double)segB[3], (double)segB[4], (double)segB[5], (double)segC[0], (double)segC[1], (double)segC[2], (double)segC[3], (double)segC[4], (double)segC[5]));
779: PetscCall(DMLabelSetValue(lbox->cellsSparse, c, box));
780: edge = Ne;
781: break;
782: }
783: }
784: }
785: }
786: }
787: }
788: }
789: PetscCall(DMPlexVecRestoreClosure(dm, coordSection, coordsLocal, c, NULL, &ccoords));
790: }
791: PetscCall(PetscFree3(dboxes, boxes, edgeCoords));
792: if (debug) PetscCall(DMLabelView(lbox->cellsSparse, PETSC_VIEWER_STDOUT_SELF));
793: PetscCall(DMLabelConvertToSection(lbox->cellsSparse, &lbox->cellSection, &lbox->cells));
794: PetscCall(DMLabelDestroy(&lbox->cellsSparse));
795: *localBox = lbox;
796: PetscFunctionReturn(PETSC_SUCCESS);
797: }
799: PetscErrorCode DMLocatePoints_Plex(DM dm, Vec v, DMPointLocationType ltype, PetscSF cellSF)
800: {
801: PetscInt debug = ((DM_Plex *)dm->data)->printLocate;
802: DM_Plex *mesh = (DM_Plex *)dm->data;
803: PetscBool hash = mesh->useHashLocation, reuse = PETSC_FALSE;
804: PetscInt bs, numPoints, p, numFound, *found = NULL;
805: PetscInt dim, Nl = 0, cStart, cEnd, numCells, c, d;
806: PetscSF sf;
807: const PetscInt *leaves;
808: const PetscInt *boxCells;
809: PetscSFNode *cells;
810: PetscScalar *a;
811: PetscMPIInt result;
812: PetscLogDouble t0, t1;
813: PetscReal gmin[3], gmax[3];
814: PetscInt terminating_query_type[] = {0, 0, 0};
816: PetscFunctionBegin;
817: PetscCall(PetscLogEventBegin(DMPLEX_LocatePoints, 0, 0, 0, 0));
818: PetscCall(PetscTime(&t0));
819: 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.");
820: PetscCall(DMGetCoordinateDim(dm, &dim));
821: PetscCall(VecGetBlockSize(v, &bs));
822: PetscCallMPI(MPI_Comm_compare(PetscObjectComm((PetscObject)cellSF), PETSC_COMM_SELF, &result));
823: PetscCheck(result == MPI_IDENT || result == MPI_CONGRUENT, PetscObjectComm((PetscObject)cellSF), PETSC_ERR_SUP, "Trying parallel point location: only local point location supported");
824: 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);
825: PetscCall(DMGetCoordinatesLocalSetUp(dm));
826: PetscCall(DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd));
827: PetscCall(DMGetPointSF(dm, &sf));
828: if (sf) PetscCall(PetscSFGetGraph(sf, NULL, &Nl, &leaves, NULL));
829: Nl = PetscMax(Nl, 0);
830: PetscCall(VecGetLocalSize(v, &numPoints));
831: PetscCall(VecGetArray(v, &a));
832: numPoints /= bs;
833: {
834: const PetscSFNode *sf_cells;
836: PetscCall(PetscSFGetGraph(cellSF, NULL, NULL, NULL, &sf_cells));
837: if (sf_cells) {
838: PetscCall(PetscInfo(dm, "[DMLocatePoints_Plex] Re-using existing StarForest node list\n"));
839: cells = (PetscSFNode *)sf_cells;
840: reuse = PETSC_TRUE;
841: } else {
842: PetscCall(PetscInfo(dm, "[DMLocatePoints_Plex] Creating and initializing new StarForest node list\n"));
843: PetscCall(PetscMalloc1(numPoints, &cells));
844: /* initialize cells if created */
845: for (p = 0; p < numPoints; p++) {
846: cells[p].rank = 0;
847: cells[p].index = DMLOCATEPOINT_POINT_NOT_FOUND;
848: }
849: }
850: }
851: PetscCall(DMGetBoundingBox(dm, gmin, gmax));
852: if (hash) {
853: if (!mesh->lbox) {
854: PetscCall(PetscInfo(dm, "Initializing grid hashing\n"));
855: PetscCall(DMPlexComputeGridHash_Internal(dm, &mesh->lbox));
856: }
857: /* Designate the local box for each point */
858: /* Send points to correct process */
859: /* Search cells that lie in each subbox */
860: /* Should we bin points before doing search? */
861: PetscCall(ISGetIndices(mesh->lbox->cells, &boxCells));
862: }
863: for (p = 0, numFound = 0; p < numPoints; ++p) {
864: const PetscScalar *point = &a[p * bs];
865: PetscInt dbin[3] = {-1, -1, -1}, bin, cell = -1, cellOffset;
866: PetscBool point_outside_domain = PETSC_FALSE;
868: /* check bounding box of domain */
869: for (d = 0; d < dim; d++) {
870: if (PetscRealPart(point[d]) < gmin[d]) {
871: point_outside_domain = PETSC_TRUE;
872: break;
873: }
874: if (PetscRealPart(point[d]) > gmax[d]) {
875: point_outside_domain = PETSC_TRUE;
876: break;
877: }
878: }
879: if (point_outside_domain) {
880: cells[p].rank = 0;
881: cells[p].index = DMLOCATEPOINT_POINT_NOT_FOUND;
882: terminating_query_type[0]++;
883: continue;
884: }
886: /* check initial values in cells[].index - abort early if found */
887: if (cells[p].index != DMLOCATEPOINT_POINT_NOT_FOUND) {
888: c = cells[p].index;
889: cells[p].index = DMLOCATEPOINT_POINT_NOT_FOUND;
890: PetscCall(DMPlexLocatePoint_Internal(dm, dim, point, c, &cell));
891: if (cell >= 0) {
892: cells[p].rank = 0;
893: cells[p].index = cell;
894: numFound++;
895: }
896: }
897: if (cells[p].index != DMLOCATEPOINT_POINT_NOT_FOUND) {
898: terminating_query_type[1]++;
899: continue;
900: }
902: if (hash) {
903: PetscBool found_box;
905: if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, "Checking point %" PetscInt_FMT " (%.2g, %.2g, %.2g)\n", p, (double)PetscRealPart(point[0]), (double)PetscRealPart(point[1]), (double)PetscRealPart(point[2])));
906: /* allow for case that point is outside box - abort early */
907: PetscCall(PetscGridHashGetEnclosingBoxQuery(mesh->lbox, mesh->lbox->cellSection, 1, point, dbin, &bin, &found_box));
908: if (found_box) {
909: if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, " Found point in box %" PetscInt_FMT " (%" PetscInt_FMT ", %" PetscInt_FMT ", %" PetscInt_FMT ")\n", bin, dbin[0], dbin[1], dbin[2]));
910: /* TODO Lay an interface over this so we can switch between Section (dense) and Label (sparse) */
911: PetscCall(PetscSectionGetDof(mesh->lbox->cellSection, bin, &numCells));
912: PetscCall(PetscSectionGetOffset(mesh->lbox->cellSection, bin, &cellOffset));
913: for (c = cellOffset; c < cellOffset + numCells; ++c) {
914: if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, " Checking for point in cell %" PetscInt_FMT "\n", boxCells[c]));
915: PetscCall(DMPlexLocatePoint_Internal(dm, dim, point, boxCells[c], &cell));
916: if (cell >= 0) {
917: if (debug) PetscCall(PetscPrintf(PETSC_COMM_SELF, " FOUND in cell %" PetscInt_FMT "\n", cell));
918: cells[p].rank = 0;
919: cells[p].index = cell;
920: numFound++;
921: terminating_query_type[2]++;
922: break;
923: }
924: }
925: }
926: } else {
927: for (c = cStart; c < cEnd; ++c) {
928: PetscInt idx;
930: PetscCall(PetscFindInt(c, Nl, leaves, &idx));
931: if (idx >= 0) continue;
932: PetscCall(DMPlexLocatePoint_Internal(dm, dim, point, c, &cell));
933: if (cell >= 0) {
934: cells[p].rank = 0;
935: cells[p].index = cell;
936: numFound++;
937: terminating_query_type[2]++;
938: break;
939: }
940: }
941: }
942: }
943: if (hash) PetscCall(ISRestoreIndices(mesh->lbox->cells, &boxCells));
944: if (ltype == DM_POINTLOCATION_NEAREST && hash && numFound < numPoints) {
945: for (p = 0; p < numPoints; p++) {
946: const PetscScalar *point = &a[p * bs];
947: PetscReal cpoint[3], diff[3], best[3] = {PETSC_MAX_REAL, PETSC_MAX_REAL, PETSC_MAX_REAL}, dist, distMax = PETSC_MAX_REAL;
948: PetscInt dbin[3] = {-1, -1, -1}, bin, cellOffset, d, bestc = -1;
950: if (cells[p].index < 0) {
951: PetscCall(PetscGridHashGetEnclosingBox(mesh->lbox, 1, point, dbin, &bin));
952: PetscCall(PetscSectionGetDof(mesh->lbox->cellSection, bin, &numCells));
953: PetscCall(PetscSectionGetOffset(mesh->lbox->cellSection, bin, &cellOffset));
954: for (c = cellOffset; c < cellOffset + numCells; ++c) {
955: PetscCall(DMPlexClosestPoint_Internal(dm, dim, point, boxCells[c], cpoint));
956: for (d = 0; d < dim; ++d) diff[d] = cpoint[d] - PetscRealPart(point[d]);
957: dist = DMPlex_NormD_Internal(dim, diff);
958: if (dist < distMax) {
959: for (d = 0; d < dim; ++d) best[d] = cpoint[d];
960: bestc = boxCells[c];
961: distMax = dist;
962: }
963: }
964: if (distMax < PETSC_MAX_REAL) {
965: ++numFound;
966: cells[p].rank = 0;
967: cells[p].index = bestc;
968: for (d = 0; d < dim; ++d) a[p * bs + d] = best[d];
969: }
970: }
971: }
972: }
973: /* This code is only be relevant when interfaced to parallel point location */
974: /* Check for highest numbered proc that claims a point (do we care?) */
975: if (ltype == DM_POINTLOCATION_REMOVE && numFound < numPoints) {
976: PetscCall(PetscMalloc1(numFound, &found));
977: for (p = 0, numFound = 0; p < numPoints; p++) {
978: if (cells[p].rank >= 0 && cells[p].index >= 0) {
979: if (numFound < p) cells[numFound] = cells[p];
980: found[numFound++] = p;
981: }
982: }
983: }
984: PetscCall(VecRestoreArray(v, &a));
985: if (!reuse) PetscCall(PetscSFSetGraph(cellSF, cEnd - cStart, numFound, found, PETSC_OWN_POINTER, cells, PETSC_OWN_POINTER));
986: PetscCall(PetscTime(&t1));
987: if (hash) {
988: 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]));
989: } else {
990: 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]));
991: }
992: PetscCall(PetscInfo(dm, "[DMLocatePoints_Plex] npoints %" PetscInt_FMT " : time(rank0) %1.2e (sec): points/sec %1.4e\n", numPoints, t1 - t0, (double)((double)numPoints / (t1 - t0))));
993: PetscCall(PetscLogEventEnd(DMPLEX_LocatePoints, 0, 0, 0, 0));
994: PetscFunctionReturn(PETSC_SUCCESS);
995: }
997: /*@C
998: DMPlexComputeProjection2Dto1D - Rewrite coordinates to be the 1D projection of the 2D coordinates
1000: Not Collective
1002: Input/Output Parameter:
1003: . coords - The coordinates of a segment, on output the new y-coordinate, and 0 for x
1005: Output Parameter:
1006: . R - The rotation which accomplishes the projection
1008: Level: developer
1010: .seealso: `DMPLEX`, `DMPlexComputeProjection3Dto1D()`, `DMPlexComputeProjection3Dto2D()`
1011: @*/
1012: PetscErrorCode DMPlexComputeProjection2Dto1D(PetscScalar coords[], PetscReal R[])
1013: {
1014: const PetscReal x = PetscRealPart(coords[2] - coords[0]);
1015: const PetscReal y = PetscRealPart(coords[3] - coords[1]);
1016: const PetscReal r = PetscSqrtReal(x * x + y * y), c = x / r, s = y / r;
1018: PetscFunctionBegin;
1019: R[0] = c;
1020: R[1] = -s;
1021: R[2] = s;
1022: R[3] = c;
1023: coords[0] = 0.0;
1024: coords[1] = r;
1025: PetscFunctionReturn(PETSC_SUCCESS);
1026: }
1028: /*@C
1029: DMPlexComputeProjection3Dto1D - Rewrite coordinates to be the 1D projection of the 3D coordinates
1031: Not Collective
1033: Input/Output Parameter:
1034: . coords - The coordinates of a segment; on output, the new y-coordinate, and 0 for x and z
1036: Output Parameter:
1037: . R - The rotation which accomplishes the projection
1039: Note:
1040: This uses the basis completion described by Frisvad in http://www.imm.dtu.dk/~jerf/papers/abstracts/onb.html, DOI:10.1080/2165347X.2012.689606
1042: Level: developer
1044: .seealso: `DMPLEX`, `DMPlexComputeProjection2Dto1D()`, `DMPlexComputeProjection3Dto2D()`
1045: @*/
1046: PetscErrorCode DMPlexComputeProjection3Dto1D(PetscScalar coords[], PetscReal R[])
1047: {
1048: PetscReal x = PetscRealPart(coords[3] - coords[0]);
1049: PetscReal y = PetscRealPart(coords[4] - coords[1]);
1050: PetscReal z = PetscRealPart(coords[5] - coords[2]);
1051: PetscReal r = PetscSqrtReal(x * x + y * y + z * z);
1052: PetscReal rinv = 1. / r;
1053: PetscFunctionBegin;
1055: x *= rinv;
1056: y *= rinv;
1057: z *= rinv;
1058: if (x > 0.) {
1059: PetscReal inv1pX = 1. / (1. + x);
1061: R[0] = x;
1062: R[1] = -y;
1063: R[2] = -z;
1064: R[3] = y;
1065: R[4] = 1. - y * y * inv1pX;
1066: R[5] = -y * z * inv1pX;
1067: R[6] = z;
1068: R[7] = -y * z * inv1pX;
1069: R[8] = 1. - z * z * inv1pX;
1070: } else {
1071: PetscReal inv1mX = 1. / (1. - x);
1073: R[0] = x;
1074: R[1] = z;
1075: R[2] = y;
1076: R[3] = y;
1077: R[4] = -y * z * inv1mX;
1078: R[5] = 1. - y * y * inv1mX;
1079: R[6] = z;
1080: R[7] = 1. - z * z * inv1mX;
1081: R[8] = -y * z * inv1mX;
1082: }
1083: coords[0] = 0.0;
1084: coords[1] = r;
1085: PetscFunctionReturn(PETSC_SUCCESS);
1086: }
1088: /*@
1089: DMPlexComputeProjection3Dto2D - Rewrite coordinates of 3 or more coplanar 3D points to a common 2D basis for the
1090: plane. The normal is defined by positive orientation of the first 3 points.
1092: Not Collective
1094: Input Parameter:
1095: . coordSize - Length of coordinate array (3x number of points); must be at least 9 (3 points)
1097: Input/Output Parameter:
1098: . coords - The interlaced coordinates of each coplanar 3D point; on output the first
1099: 2*coordSize/3 entries contain interlaced 2D points, with the rest undefined
1101: Output Parameter:
1102: . 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.
1104: Level: developer
1106: .seealso: `DMPLEX`, `DMPlexComputeProjection2Dto1D()`, `DMPlexComputeProjection3Dto1D()`
1107: @*/
1108: PetscErrorCode DMPlexComputeProjection3Dto2D(PetscInt coordSize, PetscScalar coords[], PetscReal R[])
1109: {
1110: PetscReal x1[3], x2[3], n[3], c[3], norm;
1111: const PetscInt dim = 3;
1112: PetscInt d, p;
1114: PetscFunctionBegin;
1115: /* 0) Calculate normal vector */
1116: for (d = 0; d < dim; ++d) {
1117: x1[d] = PetscRealPart(coords[1 * dim + d] - coords[0 * dim + d]);
1118: x2[d] = PetscRealPart(coords[2 * dim + d] - coords[0 * dim + d]);
1119: }
1120: // n = x1 \otimes x2
1121: n[0] = x1[1] * x2[2] - x1[2] * x2[1];
1122: n[1] = x1[2] * x2[0] - x1[0] * x2[2];
1123: n[2] = x1[0] * x2[1] - x1[1] * x2[0];
1124: norm = PetscSqrtReal(n[0] * n[0] + n[1] * n[1] + n[2] * n[2]);
1125: for (d = 0; d < dim; d++) n[d] /= norm;
1126: norm = PetscSqrtReal(x1[0] * x1[0] + x1[1] * x1[1] + x1[2] * x1[2]);
1127: for (d = 0; d < dim; d++) x1[d] /= norm;
1128: // x2 = n \otimes x1
1129: x2[0] = n[1] * x1[2] - n[2] * x1[1];
1130: x2[1] = n[2] * x1[0] - n[0] * x1[2];
1131: x2[2] = n[0] * x1[1] - n[1] * x1[0];
1132: for (d = 0; d < dim; d++) {
1133: R[d * dim + 0] = x1[d];
1134: R[d * dim + 1] = x2[d];
1135: R[d * dim + 2] = n[d];
1136: c[d] = PetscRealPart(coords[0 * dim + d]);
1137: }
1138: for (p = 0; p < coordSize / dim; p++) {
1139: PetscReal y[3];
1140: for (d = 0; d < dim; d++) y[d] = PetscRealPart(coords[p * dim + d]) - c[d];
1141: 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];
1142: }
1143: PetscFunctionReturn(PETSC_SUCCESS);
1144: }
1146: PETSC_UNUSED static inline void Volume_Triangle_Internal(PetscReal *vol, PetscReal coords[])
1147: {
1148: /* Signed volume is 1/2 the determinant
1150: | 1 1 1 |
1151: | x0 x1 x2 |
1152: | y0 y1 y2 |
1154: but if x0,y0 is the origin, we have
1156: | x1 x2 |
1157: | y1 y2 |
1158: */
1159: const PetscReal x1 = coords[2] - coords[0], y1 = coords[3] - coords[1];
1160: const PetscReal x2 = coords[4] - coords[0], y2 = coords[5] - coords[1];
1161: PetscReal M[4], detM;
1162: M[0] = x1;
1163: M[1] = x2;
1164: M[2] = y1;
1165: M[3] = y2;
1166: DMPlex_Det2D_Internal(&detM, M);
1167: *vol = 0.5 * detM;
1168: (void)PetscLogFlops(5.0);
1169: }
1171: PETSC_UNUSED static inline void Volume_Tetrahedron_Internal(PetscReal *vol, PetscReal coords[])
1172: {
1173: /* Signed volume is 1/6th of the determinant
1175: | 1 1 1 1 |
1176: | x0 x1 x2 x3 |
1177: | y0 y1 y2 y3 |
1178: | z0 z1 z2 z3 |
1180: but if x0,y0,z0 is the origin, we have
1182: | x1 x2 x3 |
1183: | y1 y2 y3 |
1184: | z1 z2 z3 |
1185: */
1186: const PetscReal x1 = coords[3] - coords[0], y1 = coords[4] - coords[1], z1 = coords[5] - coords[2];
1187: const PetscReal x2 = coords[6] - coords[0], y2 = coords[7] - coords[1], z2 = coords[8] - coords[2];
1188: const PetscReal x3 = coords[9] - coords[0], y3 = coords[10] - coords[1], z3 = coords[11] - coords[2];
1189: const PetscReal onesixth = ((PetscReal)1. / (PetscReal)6.);
1190: PetscReal M[9], detM;
1191: M[0] = x1;
1192: M[1] = x2;
1193: M[2] = x3;
1194: M[3] = y1;
1195: M[4] = y2;
1196: M[5] = y3;
1197: M[6] = z1;
1198: M[7] = z2;
1199: M[8] = z3;
1200: DMPlex_Det3D_Internal(&detM, M);
1201: *vol = -onesixth * detM;
1202: (void)PetscLogFlops(10.0);
1203: }
1205: static inline void Volume_Tetrahedron_Origin_Internal(PetscReal *vol, PetscReal coords[])
1206: {
1207: const PetscReal onesixth = ((PetscReal)1. / (PetscReal)6.);
1208: DMPlex_Det3D_Internal(vol, coords);
1209: *vol *= -onesixth;
1210: }
1212: static PetscErrorCode DMPlexComputePointGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1213: {
1214: PetscSection coordSection;
1215: Vec coordinates;
1216: const PetscScalar *coords;
1217: PetscInt dim, d, off;
1219: PetscFunctionBegin;
1220: PetscCall(DMGetCoordinatesLocal(dm, &coordinates));
1221: PetscCall(DMGetCoordinateSection(dm, &coordSection));
1222: PetscCall(PetscSectionGetDof(coordSection, e, &dim));
1223: if (!dim) PetscFunctionReturn(PETSC_SUCCESS);
1224: PetscCall(PetscSectionGetOffset(coordSection, e, &off));
1225: PetscCall(VecGetArrayRead(coordinates, &coords));
1226: if (v0) {
1227: for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[off + d]);
1228: }
1229: PetscCall(VecRestoreArrayRead(coordinates, &coords));
1230: *detJ = 1.;
1231: if (J) {
1232: for (d = 0; d < dim * dim; d++) J[d] = 0.;
1233: for (d = 0; d < dim; d++) J[d * dim + d] = 1.;
1234: if (invJ) {
1235: for (d = 0; d < dim * dim; d++) invJ[d] = 0.;
1236: for (d = 0; d < dim; d++) invJ[d * dim + d] = 1.;
1237: }
1238: }
1239: PetscFunctionReturn(PETSC_SUCCESS);
1240: }
1242: /*@C
1243: DMPlexGetCellCoordinates - Get coordinates for a cell, taking into account periodicity
1245: Not Collective
1247: Input Parameters:
1248: + dm - The `DMPLEX`
1249: - cell - The cell number
1251: Output Parameters:
1252: + isDG - Using cellwise coordinates
1253: . Nc - The number of coordinates
1254: . array - The coordinate array
1255: - coords - The cell coordinates
1257: Level: developer
1259: .seealso: `DMPLEX`, `DMPlexRestoreCellCoordinates()`, `DMGetCoordinatesLocal()`, `DMGetCellCoordinatesLocal()`
1260: @*/
1261: PetscErrorCode DMPlexGetCellCoordinates(DM dm, PetscInt cell, PetscBool *isDG, PetscInt *Nc, const PetscScalar *array[], PetscScalar *coords[])
1262: {
1263: DM cdm;
1264: Vec coordinates;
1265: PetscSection cs;
1266: const PetscScalar *ccoords;
1267: PetscInt pStart, pEnd;
1269: PetscFunctionBeginHot;
1270: *isDG = PETSC_FALSE;
1271: *Nc = 0;
1272: *array = NULL;
1273: *coords = NULL;
1274: /* Check for cellwise coordinates */
1275: PetscCall(DMGetCellCoordinateSection(dm, &cs));
1276: if (!cs) goto cg;
1277: /* Check that the cell exists in the cellwise section */
1278: PetscCall(PetscSectionGetChart(cs, &pStart, &pEnd));
1279: if (cell < pStart || cell >= pEnd) goto cg;
1280: /* Check for cellwise coordinates for this cell */
1281: PetscCall(PetscSectionGetDof(cs, cell, Nc));
1282: if (!*Nc) goto cg;
1283: /* Check for cellwise coordinates */
1284: PetscCall(DMGetCellCoordinatesLocalNoncollective(dm, &coordinates));
1285: if (!coordinates) goto cg;
1286: /* Get cellwise coordinates */
1287: PetscCall(DMGetCellCoordinateDM(dm, &cdm));
1288: PetscCall(VecGetArrayRead(coordinates, array));
1289: PetscCall(DMPlexPointLocalRead(cdm, cell, *array, &ccoords));
1290: PetscCall(DMGetWorkArray(cdm, *Nc, MPIU_SCALAR, coords));
1291: PetscCall(PetscArraycpy(*coords, ccoords, *Nc));
1292: PetscCall(VecRestoreArrayRead(coordinates, array));
1293: *isDG = PETSC_TRUE;
1294: PetscFunctionReturn(PETSC_SUCCESS);
1295: cg:
1296: /* Use continuous coordinates */
1297: PetscCall(DMGetCoordinateDM(dm, &cdm));
1298: PetscCall(DMGetCoordinateSection(dm, &cs));
1299: PetscCall(DMGetCoordinatesLocalNoncollective(dm, &coordinates));
1300: PetscCall(DMPlexVecGetClosure(cdm, cs, coordinates, cell, Nc, coords));
1301: PetscFunctionReturn(PETSC_SUCCESS);
1302: }
1304: /*@C
1305: DMPlexRestoreCellCoordinates - Get coordinates for a cell, taking into account periodicity
1307: Not Collective
1309: Input Parameters:
1310: + dm - The `DMPLEX`
1311: - cell - The cell number
1313: Output Parameters:
1314: + isDG - Using cellwise coordinates
1315: . Nc - The number of coordinates
1316: . array - The coordinate array
1317: - coords - The cell coordinates
1319: Level: developer
1321: .seealso: `DMPLEX`, `DMPlexGetCellCoordinates()`, `DMGetCoordinatesLocal()`, `DMGetCellCoordinatesLocal()`
1322: @*/
1323: PetscErrorCode DMPlexRestoreCellCoordinates(DM dm, PetscInt cell, PetscBool *isDG, PetscInt *Nc, const PetscScalar *array[], PetscScalar *coords[])
1324: {
1325: DM cdm;
1326: PetscSection cs;
1327: Vec coordinates;
1329: PetscFunctionBeginHot;
1330: if (*isDG) {
1331: PetscCall(DMGetCellCoordinateDM(dm, &cdm));
1332: PetscCall(DMRestoreWorkArray(cdm, *Nc, MPIU_SCALAR, coords));
1333: } else {
1334: PetscCall(DMGetCoordinateDM(dm, &cdm));
1335: PetscCall(DMGetCoordinateSection(dm, &cs));
1336: PetscCall(DMGetCoordinatesLocalNoncollective(dm, &coordinates));
1337: PetscCall(DMPlexVecRestoreClosure(cdm, cs, coordinates, cell, Nc, (PetscScalar **)coords));
1338: }
1339: PetscFunctionReturn(PETSC_SUCCESS);
1340: }
1342: static PetscErrorCode DMPlexComputeLineGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1343: {
1344: const PetscScalar *array;
1345: PetscScalar *coords = NULL;
1346: PetscInt numCoords, d;
1347: PetscBool isDG;
1349: PetscFunctionBegin;
1350: PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
1351: PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
1352: *detJ = 0.0;
1353: if (numCoords == 6) {
1354: const PetscInt dim = 3;
1355: PetscReal R[9], J0;
1357: if (v0) {
1358: for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
1359: }
1360: PetscCall(DMPlexComputeProjection3Dto1D(coords, R));
1361: if (J) {
1362: J0 = 0.5 * PetscRealPart(coords[1]);
1363: J[0] = R[0] * J0;
1364: J[1] = R[1];
1365: J[2] = R[2];
1366: J[3] = R[3] * J0;
1367: J[4] = R[4];
1368: J[5] = R[5];
1369: J[6] = R[6] * J0;
1370: J[7] = R[7];
1371: J[8] = R[8];
1372: DMPlex_Det3D_Internal(detJ, J);
1373: if (invJ) DMPlex_Invert2D_Internal(invJ, J, *detJ);
1374: }
1375: } else if (numCoords == 4) {
1376: const PetscInt dim = 2;
1377: PetscReal R[4], J0;
1379: if (v0) {
1380: for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
1381: }
1382: PetscCall(DMPlexComputeProjection2Dto1D(coords, R));
1383: if (J) {
1384: J0 = 0.5 * PetscRealPart(coords[1]);
1385: J[0] = R[0] * J0;
1386: J[1] = R[1];
1387: J[2] = R[2] * J0;
1388: J[3] = R[3];
1389: DMPlex_Det2D_Internal(detJ, J);
1390: if (invJ) DMPlex_Invert2D_Internal(invJ, J, *detJ);
1391: }
1392: } else if (numCoords == 2) {
1393: const PetscInt dim = 1;
1395: if (v0) {
1396: for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
1397: }
1398: if (J) {
1399: J[0] = 0.5 * (PetscRealPart(coords[1]) - PetscRealPart(coords[0]));
1400: *detJ = J[0];
1401: PetscCall(PetscLogFlops(2.0));
1402: if (invJ) {
1403: invJ[0] = 1.0 / J[0];
1404: PetscCall(PetscLogFlops(1.0));
1405: }
1406: }
1407: } 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);
1408: PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
1409: PetscFunctionReturn(PETSC_SUCCESS);
1410: }
1412: static PetscErrorCode DMPlexComputeTriangleGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1413: {
1414: const PetscScalar *array;
1415: PetscScalar *coords = NULL;
1416: PetscInt numCoords, d;
1417: PetscBool isDG;
1419: PetscFunctionBegin;
1420: PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
1421: PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
1422: *detJ = 0.0;
1423: if (numCoords == 9) {
1424: const PetscInt dim = 3;
1425: PetscReal R[9], J0[9] = {1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0};
1427: if (v0) {
1428: for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
1429: }
1430: PetscCall(DMPlexComputeProjection3Dto2D(numCoords, coords, R));
1431: if (J) {
1432: const PetscInt pdim = 2;
1434: for (d = 0; d < pdim; d++) {
1435: for (PetscInt f = 0; f < pdim; f++) J0[d * dim + f] = 0.5 * (PetscRealPart(coords[(f + 1) * pdim + d]) - PetscRealPart(coords[0 * pdim + d]));
1436: }
1437: PetscCall(PetscLogFlops(8.0));
1438: DMPlex_Det3D_Internal(detJ, J0);
1439: for (d = 0; d < dim; d++) {
1440: for (PetscInt f = 0; f < dim; f++) {
1441: J[d * dim + f] = 0.0;
1442: for (PetscInt g = 0; g < dim; g++) J[d * dim + f] += R[d * dim + g] * J0[g * dim + f];
1443: }
1444: }
1445: PetscCall(PetscLogFlops(18.0));
1446: }
1447: if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
1448: } else if (numCoords == 6) {
1449: const PetscInt dim = 2;
1451: if (v0) {
1452: for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
1453: }
1454: if (J) {
1455: for (d = 0; d < dim; d++) {
1456: for (PetscInt f = 0; f < dim; f++) J[d * dim + f] = 0.5 * (PetscRealPart(coords[(f + 1) * dim + d]) - PetscRealPart(coords[0 * dim + d]));
1457: }
1458: PetscCall(PetscLogFlops(8.0));
1459: DMPlex_Det2D_Internal(detJ, J);
1460: }
1461: if (invJ) DMPlex_Invert2D_Internal(invJ, J, *detJ);
1462: } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this triangle is %" PetscInt_FMT " != 6 or 9", numCoords);
1463: PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
1464: PetscFunctionReturn(PETSC_SUCCESS);
1465: }
1467: static PetscErrorCode DMPlexComputeRectangleGeometry_Internal(DM dm, PetscInt e, PetscBool isTensor, PetscInt Nq, const PetscReal points[], PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1468: {
1469: const PetscScalar *array;
1470: PetscScalar *coords = NULL;
1471: PetscInt numCoords, d;
1472: PetscBool isDG;
1474: PetscFunctionBegin;
1475: PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
1476: PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
1477: if (!Nq) {
1478: PetscInt vorder[4] = {0, 1, 2, 3};
1480: if (isTensor) {
1481: vorder[2] = 3;
1482: vorder[3] = 2;
1483: }
1484: *detJ = 0.0;
1485: if (numCoords == 12) {
1486: const PetscInt dim = 3;
1487: PetscReal R[9], J0[9] = {1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0};
1489: if (v) {
1490: for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);
1491: }
1492: PetscCall(DMPlexComputeProjection3Dto2D(numCoords, coords, R));
1493: if (J) {
1494: const PetscInt pdim = 2;
1496: for (d = 0; d < pdim; d++) {
1497: J0[d * dim + 0] = 0.5 * (PetscRealPart(coords[vorder[1] * pdim + d]) - PetscRealPart(coords[vorder[0] * pdim + d]));
1498: J0[d * dim + 1] = 0.5 * (PetscRealPart(coords[vorder[2] * pdim + d]) - PetscRealPart(coords[vorder[1] * pdim + d]));
1499: }
1500: PetscCall(PetscLogFlops(8.0));
1501: DMPlex_Det3D_Internal(detJ, J0);
1502: for (d = 0; d < dim; d++) {
1503: for (PetscInt f = 0; f < dim; f++) {
1504: J[d * dim + f] = 0.0;
1505: for (PetscInt g = 0; g < dim; g++) J[d * dim + f] += R[d * dim + g] * J0[g * dim + f];
1506: }
1507: }
1508: PetscCall(PetscLogFlops(18.0));
1509: }
1510: if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
1511: } else if (numCoords == 8) {
1512: const PetscInt dim = 2;
1514: if (v) {
1515: for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);
1516: }
1517: if (J) {
1518: for (d = 0; d < dim; d++) {
1519: J[d * dim + 0] = 0.5 * (PetscRealPart(coords[vorder[1] * dim + d]) - PetscRealPart(coords[vorder[0] * dim + d]));
1520: J[d * dim + 1] = 0.5 * (PetscRealPart(coords[vorder[3] * dim + d]) - PetscRealPart(coords[vorder[0] * dim + d]));
1521: }
1522: PetscCall(PetscLogFlops(8.0));
1523: DMPlex_Det2D_Internal(detJ, J);
1524: }
1525: if (invJ) DMPlex_Invert2D_Internal(invJ, J, *detJ);
1526: } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this quadrilateral is %" PetscInt_FMT " != 8 or 12", numCoords);
1527: } else {
1528: const PetscInt Nv = 4;
1529: const PetscInt dimR = 2;
1530: PetscInt zToPlex[4] = {0, 1, 3, 2};
1531: PetscReal zOrder[12];
1532: PetscReal zCoeff[12];
1533: PetscInt i, j, k, l, dim;
1535: if (isTensor) {
1536: zToPlex[2] = 2;
1537: zToPlex[3] = 3;
1538: }
1539: if (numCoords == 12) {
1540: dim = 3;
1541: } else if (numCoords == 8) {
1542: dim = 2;
1543: } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this quadrilateral is %" PetscInt_FMT " != 8 or 12", numCoords);
1544: for (i = 0; i < Nv; i++) {
1545: PetscInt zi = zToPlex[i];
1547: for (j = 0; j < dim; j++) zOrder[dim * i + j] = PetscRealPart(coords[dim * zi + j]);
1548: }
1549: for (j = 0; j < dim; j++) {
1550: /* Nodal basis for evaluation at the vertices: (1 \mp xi) (1 \mp eta):
1551: \phi^0 = (1 - xi - eta + xi eta) --> 1 = 1/4 ( \phi^0 + \phi^1 + \phi^2 + \phi^3)
1552: \phi^1 = (1 + xi - eta - xi eta) --> xi = 1/4 (-\phi^0 + \phi^1 - \phi^2 + \phi^3)
1553: \phi^2 = (1 - xi + eta - xi eta) --> eta = 1/4 (-\phi^0 - \phi^1 + \phi^2 + \phi^3)
1554: \phi^3 = (1 + xi + eta + xi eta) --> xi eta = 1/4 ( \phi^0 - \phi^1 - \phi^2 + \phi^3)
1555: */
1556: zCoeff[dim * 0 + j] = 0.25 * (zOrder[dim * 0 + j] + zOrder[dim * 1 + j] + zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
1557: zCoeff[dim * 1 + j] = 0.25 * (-zOrder[dim * 0 + j] + zOrder[dim * 1 + j] - zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
1558: zCoeff[dim * 2 + j] = 0.25 * (-zOrder[dim * 0 + j] - zOrder[dim * 1 + j] + zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
1559: zCoeff[dim * 3 + j] = 0.25 * (zOrder[dim * 0 + j] - zOrder[dim * 1 + j] - zOrder[dim * 2 + j] + zOrder[dim * 3 + j]);
1560: }
1561: for (i = 0; i < Nq; i++) {
1562: PetscReal xi = points[dimR * i], eta = points[dimR * i + 1];
1564: if (v) {
1565: PetscReal extPoint[4];
1567: extPoint[0] = 1.;
1568: extPoint[1] = xi;
1569: extPoint[2] = eta;
1570: extPoint[3] = xi * eta;
1571: for (j = 0; j < dim; j++) {
1572: PetscReal val = 0.;
1574: for (k = 0; k < Nv; k++) val += extPoint[k] * zCoeff[dim * k + j];
1575: v[i * dim + j] = val;
1576: }
1577: }
1578: if (J) {
1579: PetscReal extJ[8];
1581: extJ[0] = 0.;
1582: extJ[1] = 0.;
1583: extJ[2] = 1.;
1584: extJ[3] = 0.;
1585: extJ[4] = 0.;
1586: extJ[5] = 1.;
1587: extJ[6] = eta;
1588: extJ[7] = xi;
1589: for (j = 0; j < dim; j++) {
1590: for (k = 0; k < dimR; k++) {
1591: PetscReal val = 0.;
1593: for (l = 0; l < Nv; l++) val += zCoeff[dim * l + j] * extJ[dimR * l + k];
1594: J[i * dim * dim + dim * j + k] = val;
1595: }
1596: }
1597: if (dim == 3) { /* put the cross product in the third component of the Jacobian */
1598: PetscReal x, y, z;
1599: PetscReal *iJ = &J[i * dim * dim];
1600: PetscReal norm;
1602: x = iJ[1 * dim + 0] * iJ[2 * dim + 1] - iJ[1 * dim + 1] * iJ[2 * dim + 0];
1603: y = iJ[0 * dim + 1] * iJ[2 * dim + 0] - iJ[0 * dim + 0] * iJ[2 * dim + 1];
1604: z = iJ[0 * dim + 0] * iJ[1 * dim + 1] - iJ[0 * dim + 1] * iJ[1 * dim + 0];
1605: norm = PetscSqrtReal(x * x + y * y + z * z);
1606: iJ[2] = x / norm;
1607: iJ[5] = y / norm;
1608: iJ[8] = z / norm;
1609: DMPlex_Det3D_Internal(&detJ[i], &J[i * dim * dim]);
1610: if (invJ) DMPlex_Invert3D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);
1611: } else {
1612: DMPlex_Det2D_Internal(&detJ[i], &J[i * dim * dim]);
1613: if (invJ) DMPlex_Invert2D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);
1614: }
1615: }
1616: }
1617: }
1618: PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
1619: PetscFunctionReturn(PETSC_SUCCESS);
1620: }
1622: static PetscErrorCode DMPlexComputeTetrahedronGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1623: {
1624: const PetscScalar *array;
1625: PetscScalar *coords = NULL;
1626: const PetscInt dim = 3;
1627: PetscInt numCoords, d;
1628: PetscBool isDG;
1630: PetscFunctionBegin;
1631: PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
1632: PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
1633: *detJ = 0.0;
1634: if (v0) {
1635: for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);
1636: }
1637: if (J) {
1638: for (d = 0; d < dim; d++) {
1639: /* I orient with outward face normals */
1640: J[d * dim + 0] = 0.5 * (PetscRealPart(coords[2 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
1641: J[d * dim + 1] = 0.5 * (PetscRealPart(coords[1 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
1642: J[d * dim + 2] = 0.5 * (PetscRealPart(coords[3 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
1643: }
1644: PetscCall(PetscLogFlops(18.0));
1645: DMPlex_Det3D_Internal(detJ, J);
1646: }
1647: if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
1648: PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
1649: PetscFunctionReturn(PETSC_SUCCESS);
1650: }
1652: static PetscErrorCode DMPlexComputeHexahedronGeometry_Internal(DM dm, PetscInt e, PetscInt Nq, const PetscReal points[], PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1653: {
1654: const PetscScalar *array;
1655: PetscScalar *coords = NULL;
1656: const PetscInt dim = 3;
1657: PetscInt numCoords, d;
1658: PetscBool isDG;
1660: PetscFunctionBegin;
1661: PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
1662: PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
1663: if (!Nq) {
1664: *detJ = 0.0;
1665: if (v) {
1666: for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);
1667: }
1668: if (J) {
1669: for (d = 0; d < dim; d++) {
1670: J[d * dim + 0] = 0.5 * (PetscRealPart(coords[3 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
1671: J[d * dim + 1] = 0.5 * (PetscRealPart(coords[1 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
1672: J[d * dim + 2] = 0.5 * (PetscRealPart(coords[4 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
1673: }
1674: PetscCall(PetscLogFlops(18.0));
1675: DMPlex_Det3D_Internal(detJ, J);
1676: }
1677: if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
1678: } else {
1679: const PetscInt Nv = 8;
1680: const PetscInt zToPlex[8] = {0, 3, 1, 2, 4, 5, 7, 6};
1681: const PetscInt dim = 3;
1682: const PetscInt dimR = 3;
1683: PetscReal zOrder[24];
1684: PetscReal zCoeff[24];
1685: PetscInt i, j, k, l;
1687: for (i = 0; i < Nv; i++) {
1688: PetscInt zi = zToPlex[i];
1690: for (j = 0; j < dim; j++) zOrder[dim * i + j] = PetscRealPart(coords[dim * zi + j]);
1691: }
1692: for (j = 0; j < dim; j++) {
1693: 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]);
1694: 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]);
1695: 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]);
1696: 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]);
1697: 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]);
1698: 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]);
1699: 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]);
1700: 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]);
1701: }
1702: for (i = 0; i < Nq; i++) {
1703: PetscReal xi = points[dimR * i], eta = points[dimR * i + 1], theta = points[dimR * i + 2];
1705: if (v) {
1706: PetscReal extPoint[8];
1708: extPoint[0] = 1.;
1709: extPoint[1] = xi;
1710: extPoint[2] = eta;
1711: extPoint[3] = xi * eta;
1712: extPoint[4] = theta;
1713: extPoint[5] = theta * xi;
1714: extPoint[6] = theta * eta;
1715: extPoint[7] = theta * eta * xi;
1716: for (j = 0; j < dim; j++) {
1717: PetscReal val = 0.;
1719: for (k = 0; k < Nv; k++) val += extPoint[k] * zCoeff[dim * k + j];
1720: v[i * dim + j] = val;
1721: }
1722: }
1723: if (J) {
1724: PetscReal extJ[24];
1726: extJ[0] = 0.;
1727: extJ[1] = 0.;
1728: extJ[2] = 0.;
1729: extJ[3] = 1.;
1730: extJ[4] = 0.;
1731: extJ[5] = 0.;
1732: extJ[6] = 0.;
1733: extJ[7] = 1.;
1734: extJ[8] = 0.;
1735: extJ[9] = eta;
1736: extJ[10] = xi;
1737: extJ[11] = 0.;
1738: extJ[12] = 0.;
1739: extJ[13] = 0.;
1740: extJ[14] = 1.;
1741: extJ[15] = theta;
1742: extJ[16] = 0.;
1743: extJ[17] = xi;
1744: extJ[18] = 0.;
1745: extJ[19] = theta;
1746: extJ[20] = eta;
1747: extJ[21] = theta * eta;
1748: extJ[22] = theta * xi;
1749: extJ[23] = eta * xi;
1751: for (j = 0; j < dim; j++) {
1752: for (k = 0; k < dimR; k++) {
1753: PetscReal val = 0.;
1755: for (l = 0; l < Nv; l++) val += zCoeff[dim * l + j] * extJ[dimR * l + k];
1756: J[i * dim * dim + dim * j + k] = val;
1757: }
1758: }
1759: DMPlex_Det3D_Internal(&detJ[i], &J[i * dim * dim]);
1760: if (invJ) DMPlex_Invert3D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);
1761: }
1762: }
1763: }
1764: PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
1765: PetscFunctionReturn(PETSC_SUCCESS);
1766: }
1768: static PetscErrorCode DMPlexComputeTriangularPrismGeometry_Internal(DM dm, PetscInt e, PetscInt Nq, const PetscReal points[], PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
1769: {
1770: const PetscScalar *array;
1771: PetscScalar *coords = NULL;
1772: const PetscInt dim = 3;
1773: PetscInt numCoords, d;
1774: PetscBool isDG;
1776: PetscFunctionBegin;
1777: PetscCall(DMPlexGetCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
1778: PetscCheck(!invJ || J, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "In order to compute invJ, J must not be NULL");
1779: if (!Nq) {
1780: /* Assume that the map to the reference is affine */
1781: *detJ = 0.0;
1782: if (v) {
1783: for (d = 0; d < dim; d++) v[d] = PetscRealPart(coords[d]);
1784: }
1785: if (J) {
1786: for (d = 0; d < dim; d++) {
1787: J[d * dim + 0] = 0.5 * (PetscRealPart(coords[2 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
1788: J[d * dim + 1] = 0.5 * (PetscRealPart(coords[1 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
1789: J[d * dim + 2] = 0.5 * (PetscRealPart(coords[4 * dim + d]) - PetscRealPart(coords[0 * dim + d]));
1790: }
1791: PetscCall(PetscLogFlops(18.0));
1792: DMPlex_Det3D_Internal(detJ, J);
1793: }
1794: if (invJ) DMPlex_Invert3D_Internal(invJ, J, *detJ);
1795: } else {
1796: const PetscInt dim = 3;
1797: const PetscInt dimR = 3;
1798: const PetscInt Nv = 6;
1799: PetscReal verts[18];
1800: PetscReal coeff[18];
1801: PetscInt i, j, k, l;
1803: for (i = 0; i < Nv; ++i)
1804: for (j = 0; j < dim; ++j) verts[dim * i + j] = PetscRealPart(coords[dim * i + j]);
1805: for (j = 0; j < dim; ++j) {
1806: /* Check for triangle,
1807: 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)
1808: 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)
1809: phi^2 = 1/2 (1 + eta) chi^2 = delta(-1, 1)
1811: phi^0 + phi^1 + phi^2 = 1 coef_1 = 1/2 ( chi^1 + chi^2)
1812: -phi^0 + phi^1 - phi^2 = xi coef_xi = 1/2 (-chi^0 + chi^1)
1813: -phi^0 - phi^1 + phi^2 = eta coef_eta = 1/2 (-chi^0 + chi^2)
1815: < chi_0 chi_1 chi_2> A / 1 1 1 \ / phi_0 \ <chi> I <phi>^T so we need the inverse transpose
1816: | -1 1 -1 | | phi_1 | =
1817: \ -1 -1 1 / \ phi_2 /
1819: 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
1820: */
1821: /* Nodal basis for evaluation at the vertices: {-xi - eta, 1 + xi, 1 + eta} (1 \mp zeta):
1822: \phi^0 = 1/4 ( -xi - eta + xi zeta + eta zeta) --> / 1 1 1 1 1 1 \ 1
1823: \phi^1 = 1/4 (1 + eta - zeta - eta zeta) --> | -1 1 -1 -1 -1 1 | eta
1824: \phi^2 = 1/4 (1 + xi - zeta - xi zeta) --> | -1 -1 1 -1 1 -1 | xi
1825: \phi^3 = 1/4 ( -xi - eta - xi zeta - eta zeta) --> | -1 -1 -1 1 1 1 | zeta
1826: \phi^4 = 1/4 (1 + xi + zeta + xi zeta) --> | 1 1 -1 -1 1 -1 | xi zeta
1827: \phi^5 = 1/4 (1 + eta + zeta + eta zeta) --> \ 1 -1 1 -1 -1 1 / eta zeta
1828: 1/4 / 0 1 1 0 1 1 \
1829: | -1 1 0 -1 0 1 |
1830: | -1 0 1 -1 1 0 |
1831: | 0 -1 -1 0 1 1 |
1832: | 1 0 -1 -1 1 0 |
1833: \ 1 -1 0 -1 0 1 /
1834: */
1835: coeff[dim * 0 + j] = (1. / 4.) * (verts[dim * 1 + j] + verts[dim * 2 + j] + verts[dim * 4 + j] + verts[dim * 5 + j]);
1836: coeff[dim * 1 + j] = (1. / 4.) * (-verts[dim * 0 + j] + verts[dim * 1 + j] - verts[dim * 3 + j] + verts[dim * 5 + j]);
1837: coeff[dim * 2 + j] = (1. / 4.) * (-verts[dim * 0 + j] + verts[dim * 2 + j] - verts[dim * 3 + j] + verts[dim * 4 + j]);
1838: coeff[dim * 3 + j] = (1. / 4.) * (-verts[dim * 1 + j] - verts[dim * 2 + j] + verts[dim * 4 + j] + verts[dim * 5 + j]);
1839: coeff[dim * 4 + j] = (1. / 4.) * (verts[dim * 0 + j] - verts[dim * 2 + j] - verts[dim * 3 + j] + verts[dim * 4 + j]);
1840: coeff[dim * 5 + j] = (1. / 4.) * (verts[dim * 0 + j] - verts[dim * 1 + j] - verts[dim * 3 + j] + verts[dim * 5 + j]);
1841: /* For reference prism:
1842: {0, 0, 0}
1843: {0, 1, 0}
1844: {1, 0, 0}
1845: {0, 0, 1}
1846: {0, 0, 0}
1847: {0, 0, 0}
1848: */
1849: }
1850: for (i = 0; i < Nq; ++i) {
1851: const PetscReal xi = points[dimR * i], eta = points[dimR * i + 1], zeta = points[dimR * i + 2];
1853: if (v) {
1854: PetscReal extPoint[6];
1855: PetscInt c;
1857: extPoint[0] = 1.;
1858: extPoint[1] = eta;
1859: extPoint[2] = xi;
1860: extPoint[3] = zeta;
1861: extPoint[4] = xi * zeta;
1862: extPoint[5] = eta * zeta;
1863: for (c = 0; c < dim; ++c) {
1864: PetscReal val = 0.;
1866: for (k = 0; k < Nv; ++k) val += extPoint[k] * coeff[k * dim + c];
1867: v[i * dim + c] = val;
1868: }
1869: }
1870: if (J) {
1871: PetscReal extJ[18];
1873: extJ[0] = 0.;
1874: extJ[1] = 0.;
1875: extJ[2] = 0.;
1876: extJ[3] = 0.;
1877: extJ[4] = 1.;
1878: extJ[5] = 0.;
1879: extJ[6] = 1.;
1880: extJ[7] = 0.;
1881: extJ[8] = 0.;
1882: extJ[9] = 0.;
1883: extJ[10] = 0.;
1884: extJ[11] = 1.;
1885: extJ[12] = zeta;
1886: extJ[13] = 0.;
1887: extJ[14] = xi;
1888: extJ[15] = 0.;
1889: extJ[16] = zeta;
1890: extJ[17] = eta;
1892: for (j = 0; j < dim; j++) {
1893: for (k = 0; k < dimR; k++) {
1894: PetscReal val = 0.;
1896: for (l = 0; l < Nv; l++) val += coeff[dim * l + j] * extJ[dimR * l + k];
1897: J[i * dim * dim + dim * j + k] = val;
1898: }
1899: }
1900: DMPlex_Det3D_Internal(&detJ[i], &J[i * dim * dim]);
1901: if (invJ) DMPlex_Invert3D_Internal(&invJ[i * dim * dim], &J[i * dim * dim], detJ[i]);
1902: }
1903: }
1904: }
1905: PetscCall(DMPlexRestoreCellCoordinates(dm, e, &isDG, &numCoords, &array, &coords));
1906: PetscFunctionReturn(PETSC_SUCCESS);
1907: }
1909: static PetscErrorCode DMPlexComputeCellGeometryFEM_Implicit(DM dm, PetscInt cell, PetscQuadrature quad, PetscReal *v, PetscReal *J, PetscReal *invJ, PetscReal *detJ)
1910: {
1911: DMPolytopeType ct;
1912: PetscInt depth, dim, coordDim, coneSize, i;
1913: PetscInt Nq = 0;
1914: const PetscReal *points = NULL;
1915: DMLabel depthLabel;
1916: PetscReal xi0[3] = {-1., -1., -1.}, v0[3], J0[9], detJ0;
1917: PetscBool isAffine = PETSC_TRUE;
1919: PetscFunctionBegin;
1920: PetscCall(DMPlexGetDepth(dm, &depth));
1921: PetscCall(DMPlexGetConeSize(dm, cell, &coneSize));
1922: PetscCall(DMPlexGetDepthLabel(dm, &depthLabel));
1923: PetscCall(DMLabelGetValue(depthLabel, cell, &dim));
1924: if (depth == 1 && dim == 1) PetscCall(DMGetDimension(dm, &dim));
1925: PetscCall(DMGetCoordinateDim(dm, &coordDim));
1926: PetscCheck(coordDim <= 3, PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported coordinate dimension %" PetscInt_FMT " > 3", coordDim);
1927: if (quad) PetscCall(PetscQuadratureGetData(quad, NULL, NULL, &Nq, &points, NULL));
1928: PetscCall(DMPlexGetCellType(dm, cell, &ct));
1929: switch (ct) {
1930: case DM_POLYTOPE_POINT:
1931: PetscCall(DMPlexComputePointGeometry_Internal(dm, cell, v, J, invJ, detJ));
1932: isAffine = PETSC_FALSE;
1933: break;
1934: case DM_POLYTOPE_SEGMENT:
1935: case DM_POLYTOPE_POINT_PRISM_TENSOR:
1936: if (Nq) PetscCall(DMPlexComputeLineGeometry_Internal(dm, cell, v0, J0, NULL, &detJ0));
1937: else PetscCall(DMPlexComputeLineGeometry_Internal(dm, cell, v, J, invJ, detJ));
1938: break;
1939: case DM_POLYTOPE_TRIANGLE:
1940: if (Nq) PetscCall(DMPlexComputeTriangleGeometry_Internal(dm, cell, v0, J0, NULL, &detJ0));
1941: else PetscCall(DMPlexComputeTriangleGeometry_Internal(dm, cell, v, J, invJ, detJ));
1942: break;
1943: case DM_POLYTOPE_QUADRILATERAL:
1944: PetscCall(DMPlexComputeRectangleGeometry_Internal(dm, cell, PETSC_FALSE, Nq, points, v, J, invJ, detJ));
1945: isAffine = PETSC_FALSE;
1946: break;
1947: case DM_POLYTOPE_SEG_PRISM_TENSOR:
1948: PetscCall(DMPlexComputeRectangleGeometry_Internal(dm, cell, PETSC_TRUE, Nq, points, v, J, invJ, detJ));
1949: isAffine = PETSC_FALSE;
1950: break;
1951: case DM_POLYTOPE_TETRAHEDRON:
1952: if (Nq) PetscCall(DMPlexComputeTetrahedronGeometry_Internal(dm, cell, v0, J0, NULL, &detJ0));
1953: else PetscCall(DMPlexComputeTetrahedronGeometry_Internal(dm, cell, v, J, invJ, detJ));
1954: break;
1955: case DM_POLYTOPE_HEXAHEDRON:
1956: PetscCall(DMPlexComputeHexahedronGeometry_Internal(dm, cell, Nq, points, v, J, invJ, detJ));
1957: isAffine = PETSC_FALSE;
1958: break;
1959: case DM_POLYTOPE_TRI_PRISM:
1960: PetscCall(DMPlexComputeTriangularPrismGeometry_Internal(dm, cell, Nq, points, v, J, invJ, detJ));
1961: isAffine = PETSC_FALSE;
1962: break;
1963: default:
1964: 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))]);
1965: }
1966: if (isAffine && Nq) {
1967: if (v) {
1968: for (i = 0; i < Nq; i++) CoordinatesRefToReal(coordDim, dim, xi0, v0, J0, &points[dim * i], &v[coordDim * i]);
1969: }
1970: if (detJ) {
1971: for (i = 0; i < Nq; i++) detJ[i] = detJ0;
1972: }
1973: if (J) {
1974: PetscInt k;
1976: for (i = 0, k = 0; i < Nq; i++) {
1977: PetscInt j;
1979: for (j = 0; j < coordDim * coordDim; j++, k++) J[k] = J0[j];
1980: }
1981: }
1982: if (invJ) {
1983: PetscInt k;
1984: switch (coordDim) {
1985: case 0:
1986: break;
1987: case 1:
1988: invJ[0] = 1. / J0[0];
1989: break;
1990: case 2:
1991: DMPlex_Invert2D_Internal(invJ, J0, detJ0);
1992: break;
1993: case 3:
1994: DMPlex_Invert3D_Internal(invJ, J0, detJ0);
1995: break;
1996: }
1997: for (i = 1, k = coordDim * coordDim; i < Nq; i++) {
1998: PetscInt j;
2000: for (j = 0; j < coordDim * coordDim; j++, k++) invJ[k] = invJ[j];
2001: }
2002: }
2003: }
2004: PetscFunctionReturn(PETSC_SUCCESS);
2005: }
2007: /*@C
2008: DMPlexComputeCellGeometryAffineFEM - Assuming an affine map, compute the Jacobian, inverse Jacobian, and Jacobian determinant for a given cell
2010: Collective
2012: Input Parameters:
2013: + dm - the `DMPLEX`
2014: - cell - the cell
2016: Output Parameters:
2017: + v0 - the translation part of this affine transform, meaning the translation to the origin (not the first vertex of the reference cell)
2018: . J - the Jacobian of the transform from the reference element
2019: . invJ - the inverse of the Jacobian
2020: - detJ - the Jacobian determinant
2022: Level: advanced
2024: .seealso: `DMPLEX`, `DMPlexComputeCellGeometryFEM()`, `DMGetCoordinateSection()`, `DMGetCoordinates()`
2025: @*/
2026: PetscErrorCode DMPlexComputeCellGeometryAffineFEM(DM dm, PetscInt cell, PetscReal *v0, PetscReal *J, PetscReal *invJ, PetscReal *detJ)
2027: {
2028: PetscFunctionBegin;
2029: PetscCall(DMPlexComputeCellGeometryFEM_Implicit(dm, cell, NULL, v0, J, invJ, detJ));
2030: PetscFunctionReturn(PETSC_SUCCESS);
2031: }
2033: static PetscErrorCode DMPlexComputeCellGeometryFEM_FE(DM dm, PetscFE fe, PetscInt point, PetscQuadrature quad, PetscReal v[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
2034: {
2035: const PetscScalar *array;
2036: PetscScalar *coords = NULL;
2037: PetscInt numCoords;
2038: PetscBool isDG;
2039: PetscQuadrature feQuad;
2040: const PetscReal *quadPoints;
2041: PetscTabulation T;
2042: PetscInt dim, cdim, pdim, qdim, Nq, q;
2044: PetscFunctionBegin;
2045: PetscCall(DMGetDimension(dm, &dim));
2046: PetscCall(DMGetCoordinateDim(dm, &cdim));
2047: PetscCall(DMPlexGetCellCoordinates(dm, point, &isDG, &numCoords, &array, &coords));
2048: if (!quad) { /* use the first point of the first functional of the dual space */
2049: PetscDualSpace dsp;
2051: PetscCall(PetscFEGetDualSpace(fe, &dsp));
2052: PetscCall(PetscDualSpaceGetFunctional(dsp, 0, &quad));
2053: PetscCall(PetscQuadratureGetData(quad, &qdim, NULL, &Nq, &quadPoints, NULL));
2054: Nq = 1;
2055: } else {
2056: PetscCall(PetscQuadratureGetData(quad, &qdim, NULL, &Nq, &quadPoints, NULL));
2057: }
2058: PetscCall(PetscFEGetDimension(fe, &pdim));
2059: PetscCall(PetscFEGetQuadrature(fe, &feQuad));
2060: if (feQuad == quad) {
2061: PetscCall(PetscFEGetCellTabulation(fe, J ? 1 : 0, &T));
2062: 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);
2063: } else {
2064: PetscCall(PetscFECreateTabulation(fe, 1, Nq, quadPoints, J ? 1 : 0, &T));
2065: }
2066: PetscCheck(qdim == dim, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Point dimension %" PetscInt_FMT " != quadrature dimension %" PetscInt_FMT, dim, qdim);
2067: {
2068: const PetscReal *basis = T->T[0];
2069: const PetscReal *basisDer = T->T[1];
2070: PetscReal detJt;
2072: #if defined(PETSC_USE_DEBUG)
2073: PetscCheck(Nq == T->Np, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Np %" PetscInt_FMT " != %" PetscInt_FMT, Nq, T->Np);
2074: PetscCheck(pdim == T->Nb, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Nb %" PetscInt_FMT " != %" PetscInt_FMT, pdim, T->Nb);
2075: PetscCheck(dim == T->Nc, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Nc %" PetscInt_FMT " != %" PetscInt_FMT, dim, T->Nc);
2076: PetscCheck(cdim == T->cdim, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "cdim %" PetscInt_FMT " != %" PetscInt_FMT, cdim, T->cdim);
2077: #endif
2078: if (v) {
2079: PetscCall(PetscArrayzero(v, Nq * cdim));
2080: for (q = 0; q < Nq; ++q) {
2081: PetscInt i, k;
2083: for (k = 0; k < pdim; ++k) {
2084: const PetscInt vertex = k / cdim;
2085: for (i = 0; i < cdim; ++i) v[q * cdim + i] += basis[(q * pdim + k) * cdim + i] * PetscRealPart(coords[vertex * cdim + i]);
2086: }
2087: PetscCall(PetscLogFlops(2.0 * pdim * cdim));
2088: }
2089: }
2090: if (J) {
2091: PetscCall(PetscArrayzero(J, Nq * cdim * cdim));
2092: for (q = 0; q < Nq; ++q) {
2093: PetscInt i, j, k, c, r;
2095: /* J = dx_i/d\xi_j = sum[k=0,n-1] dN_k/d\xi_j * x_i(k) */
2096: for (k = 0; k < pdim; ++k) {
2097: const PetscInt vertex = k / cdim;
2098: for (j = 0; j < dim; ++j) {
2099: 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]);
2100: }
2101: }
2102: PetscCall(PetscLogFlops(2.0 * pdim * dim * cdim));
2103: if (cdim > dim) {
2104: for (c = dim; c < cdim; ++c)
2105: for (r = 0; r < cdim; ++r) J[r * cdim + c] = r == c ? 1.0 : 0.0;
2106: }
2107: if (!detJ && !invJ) continue;
2108: detJt = 0.;
2109: switch (cdim) {
2110: case 3:
2111: DMPlex_Det3D_Internal(&detJt, &J[q * cdim * dim]);
2112: if (invJ) DMPlex_Invert3D_Internal(&invJ[q * cdim * dim], &J[q * cdim * dim], detJt);
2113: break;
2114: case 2:
2115: DMPlex_Det2D_Internal(&detJt, &J[q * cdim * dim]);
2116: if (invJ) DMPlex_Invert2D_Internal(&invJ[q * cdim * dim], &J[q * cdim * dim], detJt);
2117: break;
2118: case 1:
2119: detJt = J[q * cdim * dim];
2120: if (invJ) invJ[q * cdim * dim] = 1.0 / detJt;
2121: }
2122: if (detJ) detJ[q] = detJt;
2123: }
2124: } else PetscCheck(!detJ && !invJ, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Need J to compute invJ or detJ");
2125: }
2126: if (feQuad != quad) PetscCall(PetscTabulationDestroy(&T));
2127: PetscCall(DMPlexRestoreCellCoordinates(dm, point, &isDG, &numCoords, &array, &coords));
2128: PetscFunctionReturn(PETSC_SUCCESS);
2129: }
2131: /*@C
2132: DMPlexComputeCellGeometryFEM - Compute the Jacobian, inverse Jacobian, and Jacobian determinant at each quadrature point in the given cell
2134: Collective
2136: Input Parameters:
2137: + dm - the `DMPLEX`
2138: . cell - the cell
2139: - quad - the quadrature containing the points in the reference element where the geometry will be evaluated. If `quad` is `NULL`, geometry will be
2140: evaluated at the first vertex of the reference element
2142: Output Parameters:
2143: + v - the image of the transformed quadrature points, otherwise the image of the first vertex in the closure of the reference element
2144: . J - the Jacobian of the transform from the reference element at each quadrature point
2145: . invJ - the inverse of the Jacobian at each quadrature point
2146: - detJ - the Jacobian determinant at each quadrature point
2148: Level: advanced
2150: .seealso: `DMPLEX`, `DMGetCoordinateSection()`, `DMGetCoordinates()`
2151: @*/
2152: PetscErrorCode DMPlexComputeCellGeometryFEM(DM dm, PetscInt cell, PetscQuadrature quad, PetscReal *v, PetscReal *J, PetscReal *invJ, PetscReal *detJ)
2153: {
2154: DM cdm;
2155: PetscFE fe = NULL;
2157: PetscFunctionBegin;
2159: PetscCall(DMGetCoordinateDM(dm, &cdm));
2160: if (cdm) {
2161: PetscClassId id;
2162: PetscInt numFields;
2163: PetscDS prob;
2164: PetscObject disc;
2166: PetscCall(DMGetNumFields(cdm, &numFields));
2167: if (numFields) {
2168: PetscCall(DMGetDS(cdm, &prob));
2169: PetscCall(PetscDSGetDiscretization(prob, 0, &disc));
2170: PetscCall(PetscObjectGetClassId(disc, &id));
2171: if (id == PETSCFE_CLASSID) fe = (PetscFE)disc;
2172: }
2173: }
2174: if (!fe) PetscCall(DMPlexComputeCellGeometryFEM_Implicit(dm, cell, quad, v, J, invJ, detJ));
2175: else PetscCall(DMPlexComputeCellGeometryFEM_FE(dm, fe, cell, quad, v, J, invJ, detJ));
2176: PetscFunctionReturn(PETSC_SUCCESS);
2177: }
2179: static PetscErrorCode DMPlexComputeGeometryFVM_0D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
2180: {
2181: PetscSection coordSection;
2182: Vec coordinates;
2183: const PetscScalar *coords = NULL;
2184: PetscInt d, dof, off;
2186: PetscFunctionBegin;
2187: PetscCall(DMGetCoordinatesLocal(dm, &coordinates));
2188: PetscCall(DMGetCoordinateSection(dm, &coordSection));
2189: PetscCall(VecGetArrayRead(coordinates, &coords));
2191: /* for a point the centroid is just the coord */
2192: if (centroid) {
2193: PetscCall(PetscSectionGetDof(coordSection, cell, &dof));
2194: PetscCall(PetscSectionGetOffset(coordSection, cell, &off));
2195: for (d = 0; d < dof; d++) centroid[d] = PetscRealPart(coords[off + d]);
2196: }
2197: if (normal) {
2198: const PetscInt *support, *cones;
2199: PetscInt supportSize;
2200: PetscReal norm, sign;
2202: /* compute the norm based upon the support centroids */
2203: PetscCall(DMPlexGetSupportSize(dm, cell, &supportSize));
2204: PetscCall(DMPlexGetSupport(dm, cell, &support));
2205: PetscCall(DMPlexComputeCellGeometryFVM(dm, support[0], NULL, normal, NULL));
2207: /* Take the normal from the centroid of the support to the vertex*/
2208: PetscCall(PetscSectionGetDof(coordSection, cell, &dof));
2209: PetscCall(PetscSectionGetOffset(coordSection, cell, &off));
2210: for (d = 0; d < dof; d++) normal[d] -= PetscRealPart(coords[off + d]);
2212: /* Determine the sign of the normal based upon its location in the support */
2213: PetscCall(DMPlexGetCone(dm, support[0], &cones));
2214: sign = cones[0] == cell ? 1.0 : -1.0;
2216: norm = DMPlex_NormD_Internal(dim, normal);
2217: for (d = 0; d < dim; ++d) normal[d] /= (norm * sign);
2218: }
2219: if (vol) *vol = 1.0;
2220: PetscCall(VecRestoreArrayRead(coordinates, &coords));
2221: PetscFunctionReturn(PETSC_SUCCESS);
2222: }
2224: static PetscErrorCode DMPlexComputeGeometryFVM_1D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
2225: {
2226: const PetscScalar *array;
2227: PetscScalar *coords = NULL;
2228: PetscInt cdim, coordSize, d;
2229: PetscBool isDG;
2231: PetscFunctionBegin;
2232: PetscCall(DMGetCoordinateDim(dm, &cdim));
2233: PetscCall(DMPlexGetCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
2234: PetscCheck(coordSize == cdim * 2, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Edge has %" PetscInt_FMT " coordinates != %" PetscInt_FMT, coordSize, cdim * 2);
2235: if (centroid) {
2236: for (d = 0; d < cdim; ++d) centroid[d] = 0.5 * PetscRealPart(coords[d] + coords[cdim + d]);
2237: }
2238: if (normal) {
2239: PetscReal norm;
2241: switch (cdim) {
2242: case 3:
2243: normal[2] = 0.; /* fall through */
2244: case 2:
2245: normal[0] = -PetscRealPart(coords[1] - coords[cdim + 1]);
2246: normal[1] = PetscRealPart(coords[0] - coords[cdim + 0]);
2247: break;
2248: case 1:
2249: normal[0] = 1.0;
2250: break;
2251: default:
2252: SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Dimension %" PetscInt_FMT " not supported", cdim);
2253: }
2254: norm = DMPlex_NormD_Internal(cdim, normal);
2255: for (d = 0; d < cdim; ++d) normal[d] /= norm;
2256: }
2257: if (vol) {
2258: *vol = 0.0;
2259: for (d = 0; d < cdim; ++d) *vol += PetscSqr(PetscRealPart(coords[d] - coords[cdim + d]));
2260: *vol = PetscSqrtReal(*vol);
2261: }
2262: PetscCall(DMPlexRestoreCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
2263: PetscFunctionReturn(PETSC_SUCCESS);
2264: }
2266: /* Centroid_i = (\sum_n A_n Cn_i) / A */
2267: static PetscErrorCode DMPlexComputeGeometryFVM_2D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
2268: {
2269: DMPolytopeType ct;
2270: const PetscScalar *array;
2271: PetscScalar *coords = NULL;
2272: PetscInt coordSize;
2273: PetscBool isDG;
2274: PetscInt fv[4] = {0, 1, 2, 3};
2275: PetscInt cdim, numCorners, p, d;
2277: PetscFunctionBegin;
2278: /* Must check for hybrid cells because prisms have a different orientation scheme */
2279: PetscCall(DMPlexGetCellType(dm, cell, &ct));
2280: switch (ct) {
2281: case DM_POLYTOPE_SEG_PRISM_TENSOR:
2282: fv[2] = 3;
2283: fv[3] = 2;
2284: break;
2285: default:
2286: break;
2287: }
2288: PetscCall(DMGetCoordinateDim(dm, &cdim));
2289: PetscCall(DMPlexGetConeSize(dm, cell, &numCorners));
2290: PetscCall(DMPlexGetCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
2291: {
2292: PetscReal c[3] = {0., 0., 0.}, n[3] = {0., 0., 0.}, origin[3] = {0., 0., 0.}, norm;
2294: for (d = 0; d < cdim; d++) origin[d] = PetscRealPart(coords[d]);
2295: for (p = 0; p < numCorners - 2; ++p) {
2296: PetscReal e0[3] = {0., 0., 0.}, e1[3] = {0., 0., 0.};
2297: for (d = 0; d < cdim; d++) {
2298: e0[d] = PetscRealPart(coords[cdim * fv[p + 1] + d]) - origin[d];
2299: e1[d] = PetscRealPart(coords[cdim * fv[p + 2] + d]) - origin[d];
2300: }
2301: const PetscReal dx = e0[1] * e1[2] - e0[2] * e1[1];
2302: const PetscReal dy = e0[2] * e1[0] - e0[0] * e1[2];
2303: const PetscReal dz = e0[0] * e1[1] - e0[1] * e1[0];
2304: const PetscReal a = PetscSqrtReal(dx * dx + dy * dy + dz * dz);
2306: n[0] += dx;
2307: n[1] += dy;
2308: n[2] += dz;
2309: 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.;
2310: }
2311: norm = PetscSqrtReal(n[0] * n[0] + n[1] * n[1] + n[2] * n[2]);
2312: n[0] /= norm;
2313: n[1] /= norm;
2314: n[2] /= norm;
2315: c[0] /= norm;
2316: c[1] /= norm;
2317: c[2] /= norm;
2318: if (vol) *vol = 0.5 * norm;
2319: if (centroid)
2320: for (d = 0; d < cdim; ++d) centroid[d] = c[d];
2321: if (normal)
2322: for (d = 0; d < cdim; ++d) normal[d] = n[d];
2323: }
2324: PetscCall(DMPlexRestoreCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
2325: PetscFunctionReturn(PETSC_SUCCESS);
2326: }
2328: /* Centroid_i = (\sum_n V_n Cn_i) / V */
2329: static PetscErrorCode DMPlexComputeGeometryFVM_3D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
2330: {
2331: DMPolytopeType ct;
2332: const PetscScalar *array;
2333: PetscScalar *coords = NULL;
2334: PetscInt coordSize;
2335: PetscBool isDG;
2336: PetscReal vsum = 0.0, vtmp, coordsTmp[3 * 3], origin[3];
2337: const PetscInt order[16] = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15};
2338: const PetscInt *cone, *faceSizes, *faces;
2339: const DMPolytopeType *faceTypes;
2340: PetscBool isHybrid = PETSC_FALSE;
2341: PetscInt numFaces, f, fOff = 0, p, d;
2343: PetscFunctionBegin;
2344: PetscCheck(dim <= 3, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "No support for dim %" PetscInt_FMT " > 3", dim);
2345: /* Must check for hybrid cells because prisms have a different orientation scheme */
2346: PetscCall(DMPlexGetCellType(dm, cell, &ct));
2347: switch (ct) {
2348: case DM_POLYTOPE_POINT_PRISM_TENSOR:
2349: case DM_POLYTOPE_SEG_PRISM_TENSOR:
2350: case DM_POLYTOPE_TRI_PRISM_TENSOR:
2351: case DM_POLYTOPE_QUAD_PRISM_TENSOR:
2352: isHybrid = PETSC_TRUE;
2353: default:
2354: break;
2355: }
2357: if (centroid)
2358: for (d = 0; d < dim; ++d) centroid[d] = 0.0;
2359: PetscCall(DMPlexGetCone(dm, cell, &cone));
2361: // Using the closure of faces for coordinates does not work in periodic geometries, so we index into the cell coordinates
2362: PetscCall(DMPlexGetRawFaces_Internal(dm, ct, order, &numFaces, &faceTypes, &faceSizes, &faces));
2363: PetscCall(DMPlexGetCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
2364: for (f = 0; f < numFaces; ++f) {
2365: PetscBool flip = isHybrid && f == 0 ? PETSC_TRUE : PETSC_FALSE; /* The first hybrid face is reversed */
2367: // If using zero as the origin vertex for each tetrahedron, an element far from the origin will have positive and
2368: // negative volumes that nearly cancel, thus incurring rounding error. Here we define origin[] as the first vertex
2369: // so that all tetrahedra have positive volume.
2370: if (f == 0)
2371: for (d = 0; d < dim; d++) origin[d] = PetscRealPart(coords[d]);
2372: switch (faceTypes[f]) {
2373: case DM_POLYTOPE_TRIANGLE:
2374: for (d = 0; d < dim; ++d) {
2375: coordsTmp[0 * dim + d] = PetscRealPart(coords[faces[fOff + 0] * dim + d]) - origin[d];
2376: coordsTmp[1 * dim + d] = PetscRealPart(coords[faces[fOff + 1] * dim + d]) - origin[d];
2377: coordsTmp[2 * dim + d] = PetscRealPart(coords[faces[fOff + 2] * dim + d]) - origin[d];
2378: }
2379: Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
2380: if (flip) vtmp = -vtmp;
2381: vsum += vtmp;
2382: if (centroid) { /* Centroid of OABC = (a+b+c)/4 */
2383: for (d = 0; d < dim; ++d) {
2384: for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p * dim + d] * vtmp;
2385: }
2386: }
2387: break;
2388: case DM_POLYTOPE_QUADRILATERAL:
2389: case DM_POLYTOPE_SEG_PRISM_TENSOR: {
2390: PetscInt fv[4] = {0, 1, 2, 3};
2392: /* Side faces for hybrid cells are are stored as tensor products */
2393: if (isHybrid && f > 1) {
2394: fv[2] = 3;
2395: fv[3] = 2;
2396: }
2397: /* DO FOR PYRAMID */
2398: /* First tet */
2399: for (d = 0; d < dim; ++d) {
2400: coordsTmp[0 * dim + d] = PetscRealPart(coords[faces[fOff + fv[0]] * dim + d]) - origin[d];
2401: coordsTmp[1 * dim + d] = PetscRealPart(coords[faces[fOff + fv[1]] * dim + d]) - origin[d];
2402: coordsTmp[2 * dim + d] = PetscRealPart(coords[faces[fOff + fv[3]] * dim + d]) - origin[d];
2403: }
2404: Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
2405: if (flip) vtmp = -vtmp;
2406: vsum += vtmp;
2407: if (centroid) {
2408: for (d = 0; d < dim; ++d) {
2409: for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p * dim + d] * vtmp;
2410: }
2411: }
2412: /* Second tet */
2413: for (d = 0; d < dim; ++d) {
2414: coordsTmp[0 * dim + d] = PetscRealPart(coords[faces[fOff + fv[1]] * dim + d]) - origin[d];
2415: coordsTmp[1 * dim + d] = PetscRealPart(coords[faces[fOff + fv[2]] * dim + d]) - origin[d];
2416: coordsTmp[2 * dim + d] = PetscRealPart(coords[faces[fOff + fv[3]] * dim + d]) - origin[d];
2417: }
2418: Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
2419: if (flip) vtmp = -vtmp;
2420: vsum += vtmp;
2421: if (centroid) {
2422: for (d = 0; d < dim; ++d) {
2423: for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p * dim + d] * vtmp;
2424: }
2425: }
2426: break;
2427: }
2428: default:
2429: SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Cannot handle face %" PetscInt_FMT " of type %s", cone[f], DMPolytopeTypes[ct]);
2430: }
2431: fOff += faceSizes[f];
2432: }
2433: PetscCall(DMPlexRestoreRawFaces_Internal(dm, ct, order, &numFaces, &faceTypes, &faceSizes, &faces));
2434: PetscCall(DMPlexRestoreCellCoordinates(dm, cell, &isDG, &coordSize, &array, &coords));
2435: if (vol) *vol = PetscAbsReal(vsum);
2436: if (normal)
2437: for (d = 0; d < dim; ++d) normal[d] = 0.0;
2438: if (centroid)
2439: for (d = 0; d < dim; ++d) centroid[d] = centroid[d] / (vsum * 4) + origin[d];
2440: PetscFunctionReturn(PETSC_SUCCESS);
2441: }
2443: /*@C
2444: DMPlexComputeCellGeometryFVM - Compute the volume for a given cell
2446: Collective
2448: Input Parameters:
2449: + dm - the `DMPLEX`
2450: - cell - the cell
2452: Output Parameters:
2453: + volume - the cell volume
2454: . centroid - the cell centroid
2455: - normal - the cell normal, if appropriate
2457: Level: advanced
2459: .seealso: `DMPLEX`, `DMGetCoordinateSection()`, `DMGetCoordinates()`
2460: @*/
2461: PetscErrorCode DMPlexComputeCellGeometryFVM(DM dm, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
2462: {
2463: PetscInt depth, dim;
2465: PetscFunctionBegin;
2466: PetscCall(DMPlexGetDepth(dm, &depth));
2467: PetscCall(DMGetDimension(dm, &dim));
2468: PetscCheck(depth == dim, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Mesh must be interpolated");
2469: PetscCall(DMPlexGetPointDepth(dm, cell, &depth));
2470: switch (depth) {
2471: case 0:
2472: PetscCall(DMPlexComputeGeometryFVM_0D_Internal(dm, dim, cell, vol, centroid, normal));
2473: break;
2474: case 1:
2475: PetscCall(DMPlexComputeGeometryFVM_1D_Internal(dm, dim, cell, vol, centroid, normal));
2476: break;
2477: case 2:
2478: PetscCall(DMPlexComputeGeometryFVM_2D_Internal(dm, dim, cell, vol, centroid, normal));
2479: break;
2480: case 3:
2481: PetscCall(DMPlexComputeGeometryFVM_3D_Internal(dm, dim, cell, vol, centroid, normal));
2482: break;
2483: default:
2484: SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported dimension %" PetscInt_FMT " (depth %" PetscInt_FMT ") for element geometry computation", dim, depth);
2485: }
2486: PetscFunctionReturn(PETSC_SUCCESS);
2487: }
2489: /*@
2490: DMPlexComputeGeometryFVM - Computes the cell and face geometry for a finite volume method
2492: Input Parameter:
2493: . dm - The `DMPLEX`
2495: Output Parameters:
2496: + cellgeom - A `Vec` of `PetscFVCellGeom` data
2497: - facegeom - A `Vec` of `PetscFVFaceGeom` data
2499: Level: developer
2501: .seealso: `DMPLEX`, `PetscFVFaceGeom`, `PetscFVCellGeom`
2502: @*/
2503: PetscErrorCode DMPlexComputeGeometryFVM(DM dm, Vec *cellgeom, Vec *facegeom)
2504: {
2505: DM dmFace, dmCell;
2506: DMLabel ghostLabel;
2507: PetscSection sectionFace, sectionCell;
2508: PetscSection coordSection;
2509: Vec coordinates;
2510: PetscScalar *fgeom, *cgeom;
2511: PetscReal minradius, gminradius;
2512: PetscInt dim, cStart, cEnd, cEndInterior, c, fStart, fEnd, f;
2514: PetscFunctionBegin;
2515: PetscCall(DMGetDimension(dm, &dim));
2516: PetscCall(DMGetCoordinateSection(dm, &coordSection));
2517: PetscCall(DMGetCoordinatesLocal(dm, &coordinates));
2518: /* Make cell centroids and volumes */
2519: PetscCall(DMClone(dm, &dmCell));
2520: PetscCall(DMSetCoordinateSection(dmCell, PETSC_DETERMINE, coordSection));
2521: PetscCall(DMSetCoordinatesLocal(dmCell, coordinates));
2522: PetscCall(PetscSectionCreate(PetscObjectComm((PetscObject)dm), §ionCell));
2523: PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
2524: PetscCall(DMPlexGetGhostCellStratum(dm, &cEndInterior, NULL));
2525: PetscCall(PetscSectionSetChart(sectionCell, cStart, cEnd));
2526: for (c = cStart; c < cEnd; ++c) PetscCall(PetscSectionSetDof(sectionCell, c, (PetscInt)PetscCeilReal(((PetscReal)sizeof(PetscFVCellGeom)) / sizeof(PetscScalar))));
2527: PetscCall(PetscSectionSetUp(sectionCell));
2528: PetscCall(DMSetLocalSection(dmCell, sectionCell));
2529: PetscCall(PetscSectionDestroy(§ionCell));
2530: PetscCall(DMCreateLocalVector(dmCell, cellgeom));
2531: if (cEndInterior < 0) cEndInterior = cEnd;
2532: PetscCall(VecGetArray(*cellgeom, &cgeom));
2533: for (c = cStart; c < cEndInterior; ++c) {
2534: PetscFVCellGeom *cg;
2536: PetscCall(DMPlexPointLocalRef(dmCell, c, cgeom, &cg));
2537: PetscCall(PetscArrayzero(cg, 1));
2538: PetscCall(DMPlexComputeCellGeometryFVM(dmCell, c, &cg->volume, cg->centroid, NULL));
2539: }
2540: /* Compute face normals and minimum cell radius */
2541: PetscCall(DMClone(dm, &dmFace));
2542: PetscCall(PetscSectionCreate(PetscObjectComm((PetscObject)dm), §ionFace));
2543: PetscCall(DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd));
2544: PetscCall(PetscSectionSetChart(sectionFace, fStart, fEnd));
2545: for (f = fStart; f < fEnd; ++f) PetscCall(PetscSectionSetDof(sectionFace, f, (PetscInt)PetscCeilReal(((PetscReal)sizeof(PetscFVFaceGeom)) / sizeof(PetscScalar))));
2546: PetscCall(PetscSectionSetUp(sectionFace));
2547: PetscCall(DMSetLocalSection(dmFace, sectionFace));
2548: PetscCall(PetscSectionDestroy(§ionFace));
2549: PetscCall(DMCreateLocalVector(dmFace, facegeom));
2550: PetscCall(VecGetArray(*facegeom, &fgeom));
2551: PetscCall(DMGetLabel(dm, "ghost", &ghostLabel));
2552: minradius = PETSC_MAX_REAL;
2553: for (f = fStart; f < fEnd; ++f) {
2554: PetscFVFaceGeom *fg;
2555: PetscReal area;
2556: const PetscInt *cells;
2557: PetscInt ncells, ghost = -1, d, numChildren;
2559: if (ghostLabel) PetscCall(DMLabelGetValue(ghostLabel, f, &ghost));
2560: PetscCall(DMPlexGetTreeChildren(dm, f, &numChildren, NULL));
2561: PetscCall(DMPlexGetSupport(dm, f, &cells));
2562: PetscCall(DMPlexGetSupportSize(dm, f, &ncells));
2563: /* It is possible to get a face with no support when using partition overlap */
2564: if (!ncells || ghost >= 0 || numChildren) continue;
2565: PetscCall(DMPlexPointLocalRef(dmFace, f, fgeom, &fg));
2566: PetscCall(DMPlexComputeCellGeometryFVM(dm, f, &area, fg->centroid, fg->normal));
2567: for (d = 0; d < dim; ++d) fg->normal[d] *= area;
2568: /* Flip face orientation if necessary to match ordering in support, and Update minimum radius */
2569: {
2570: PetscFVCellGeom *cL, *cR;
2571: PetscReal *lcentroid, *rcentroid;
2572: PetscReal l[3], r[3], v[3];
2574: PetscCall(DMPlexPointLocalRead(dmCell, cells[0], cgeom, &cL));
2575: lcentroid = cells[0] >= cEndInterior ? fg->centroid : cL->centroid;
2576: if (ncells > 1) {
2577: PetscCall(DMPlexPointLocalRead(dmCell, cells[1], cgeom, &cR));
2578: rcentroid = cells[1] >= cEndInterior ? fg->centroid : cR->centroid;
2579: } else {
2580: rcentroid = fg->centroid;
2581: }
2582: PetscCall(DMLocalizeCoordinateReal_Internal(dm, dim, fg->centroid, lcentroid, l));
2583: PetscCall(DMLocalizeCoordinateReal_Internal(dm, dim, fg->centroid, rcentroid, r));
2584: DMPlex_WaxpyD_Internal(dim, -1, l, r, v);
2585: if (DMPlex_DotRealD_Internal(dim, fg->normal, v) < 0) {
2586: for (d = 0; d < dim; ++d) fg->normal[d] = -fg->normal[d];
2587: }
2588: if (DMPlex_DotRealD_Internal(dim, fg->normal, v) <= 0) {
2589: 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]);
2590: 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]);
2591: SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Direction for face %" PetscInt_FMT " could not be fixed", f);
2592: }
2593: if (cells[0] < cEndInterior) {
2594: DMPlex_WaxpyD_Internal(dim, -1, fg->centroid, cL->centroid, v);
2595: minradius = PetscMin(minradius, DMPlex_NormD_Internal(dim, v));
2596: }
2597: if (ncells > 1 && cells[1] < cEndInterior) {
2598: DMPlex_WaxpyD_Internal(dim, -1, fg->centroid, cR->centroid, v);
2599: minradius = PetscMin(minradius, DMPlex_NormD_Internal(dim, v));
2600: }
2601: }
2602: }
2603: PetscCall(MPIU_Allreduce(&minradius, &gminradius, 1, MPIU_REAL, MPIU_MIN, PetscObjectComm((PetscObject)dm)));
2604: PetscCall(DMPlexSetMinRadius(dm, gminradius));
2605: /* Compute centroids of ghost cells */
2606: for (c = cEndInterior; c < cEnd; ++c) {
2607: PetscFVFaceGeom *fg;
2608: const PetscInt *cone, *support;
2609: PetscInt coneSize, supportSize, s;
2611: PetscCall(DMPlexGetConeSize(dmCell, c, &coneSize));
2612: PetscCheck(coneSize == 1, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Ghost cell %" PetscInt_FMT " has cone size %" PetscInt_FMT " != 1", c, coneSize);
2613: PetscCall(DMPlexGetCone(dmCell, c, &cone));
2614: PetscCall(DMPlexGetSupportSize(dmCell, cone[0], &supportSize));
2615: PetscCheck(supportSize == 2, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Face %" PetscInt_FMT " has support size %" PetscInt_FMT " != 2", cone[0], supportSize);
2616: PetscCall(DMPlexGetSupport(dmCell, cone[0], &support));
2617: PetscCall(DMPlexPointLocalRef(dmFace, cone[0], fgeom, &fg));
2618: for (s = 0; s < 2; ++s) {
2619: /* Reflect ghost centroid across plane of face */
2620: if (support[s] == c) {
2621: PetscFVCellGeom *ci;
2622: PetscFVCellGeom *cg;
2623: PetscReal c2f[3], a;
2625: PetscCall(DMPlexPointLocalRead(dmCell, support[(s + 1) % 2], cgeom, &ci));
2626: DMPlex_WaxpyD_Internal(dim, -1, ci->centroid, fg->centroid, c2f); /* cell to face centroid */
2627: a = DMPlex_DotRealD_Internal(dim, c2f, fg->normal) / DMPlex_DotRealD_Internal(dim, fg->normal, fg->normal);
2628: PetscCall(DMPlexPointLocalRef(dmCell, support[s], cgeom, &cg));
2629: DMPlex_WaxpyD_Internal(dim, 2 * a, fg->normal, ci->centroid, cg->centroid);
2630: cg->volume = ci->volume;
2631: }
2632: }
2633: }
2634: PetscCall(VecRestoreArray(*facegeom, &fgeom));
2635: PetscCall(VecRestoreArray(*cellgeom, &cgeom));
2636: PetscCall(DMDestroy(&dmCell));
2637: PetscCall(DMDestroy(&dmFace));
2638: PetscFunctionReturn(PETSC_SUCCESS);
2639: }
2641: /*@C
2642: DMPlexGetMinRadius - Returns the minimum distance from any cell centroid to a face
2644: Not Collective
2646: Input Parameter:
2647: . dm - the `DMPLEX`
2649: Output Parameter:
2650: . minradius - the minimum cell radius
2652: Level: developer
2654: .seealso: `DMPLEX`, `DMGetCoordinates()`
2655: @*/
2656: PetscErrorCode DMPlexGetMinRadius(DM dm, PetscReal *minradius)
2657: {
2658: PetscFunctionBegin;
2661: *minradius = ((DM_Plex *)dm->data)->minradius;
2662: PetscFunctionReturn(PETSC_SUCCESS);
2663: }
2665: /*@C
2666: DMPlexSetMinRadius - Sets the minimum distance from the cell centroid to a face
2668: Logically Collective
2670: Input Parameters:
2671: + dm - the `DMPLEX`
2672: - minradius - the minimum cell radius
2674: Level: developer
2676: .seealso: `DMPLEX`, `DMSetCoordinates()`
2677: @*/
2678: PetscErrorCode DMPlexSetMinRadius(DM dm, PetscReal minradius)
2679: {
2680: PetscFunctionBegin;
2682: ((DM_Plex *)dm->data)->minradius = minradius;
2683: PetscFunctionReturn(PETSC_SUCCESS);
2684: }
2686: static PetscErrorCode BuildGradientReconstruction_Internal(DM dm, PetscFV fvm, DM dmFace, PetscScalar *fgeom, DM dmCell, PetscScalar *cgeom)
2687: {
2688: DMLabel ghostLabel;
2689: PetscScalar *dx, *grad, **gref;
2690: PetscInt dim, cStart, cEnd, c, cEndInterior, maxNumFaces;
2692: PetscFunctionBegin;
2693: PetscCall(DMGetDimension(dm, &dim));
2694: PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
2695: PetscCall(DMPlexGetGhostCellStratum(dm, &cEndInterior, NULL));
2696: cEndInterior = cEndInterior < 0 ? cEnd : cEndInterior;
2697: PetscCall(DMPlexGetMaxSizes(dm, &maxNumFaces, NULL));
2698: PetscCall(PetscFVLeastSquaresSetMaxFaces(fvm, maxNumFaces));
2699: PetscCall(DMGetLabel(dm, "ghost", &ghostLabel));
2700: PetscCall(PetscMalloc3(maxNumFaces * dim, &dx, maxNumFaces * dim, &grad, maxNumFaces, &gref));
2701: for (c = cStart; c < cEndInterior; c++) {
2702: const PetscInt *faces;
2703: PetscInt numFaces, usedFaces, f, d;
2704: PetscFVCellGeom *cg;
2705: PetscBool boundary;
2706: PetscInt ghost;
2708: // do not attempt to compute a gradient reconstruction stencil in a ghost cell. It will never be used
2709: PetscCall(DMLabelGetValue(ghostLabel, c, &ghost));
2710: if (ghost >= 0) continue;
2712: PetscCall(DMPlexPointLocalRead(dmCell, c, cgeom, &cg));
2713: PetscCall(DMPlexGetConeSize(dm, c, &numFaces));
2714: PetscCall(DMPlexGetCone(dm, c, &faces));
2715: 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);
2716: for (f = 0, usedFaces = 0; f < numFaces; ++f) {
2717: PetscFVCellGeom *cg1;
2718: PetscFVFaceGeom *fg;
2719: const PetscInt *fcells;
2720: PetscInt ncell, side;
2722: PetscCall(DMLabelGetValue(ghostLabel, faces[f], &ghost));
2723: PetscCall(DMIsBoundaryPoint(dm, faces[f], &boundary));
2724: if ((ghost >= 0) || boundary) continue;
2725: PetscCall(DMPlexGetSupport(dm, faces[f], &fcells));
2726: side = (c != fcells[0]); /* c is on left=0 or right=1 of face */
2727: ncell = fcells[!side]; /* the neighbor */
2728: PetscCall(DMPlexPointLocalRef(dmFace, faces[f], fgeom, &fg));
2729: PetscCall(DMPlexPointLocalRead(dmCell, ncell, cgeom, &cg1));
2730: for (d = 0; d < dim; ++d) dx[usedFaces * dim + d] = cg1->centroid[d] - cg->centroid[d];
2731: gref[usedFaces++] = fg->grad[side]; /* Gradient reconstruction term will go here */
2732: }
2733: PetscCheck(usedFaces, PETSC_COMM_SELF, PETSC_ERR_USER, "Mesh contains isolated cell (no neighbors). Is it intentional?");
2734: PetscCall(PetscFVComputeGradient(fvm, usedFaces, dx, grad));
2735: for (f = 0, usedFaces = 0; f < numFaces; ++f) {
2736: PetscCall(DMLabelGetValue(ghostLabel, faces[f], &ghost));
2737: PetscCall(DMIsBoundaryPoint(dm, faces[f], &boundary));
2738: if ((ghost >= 0) || boundary) continue;
2739: for (d = 0; d < dim; ++d) gref[usedFaces][d] = grad[usedFaces * dim + d];
2740: ++usedFaces;
2741: }
2742: }
2743: PetscCall(PetscFree3(dx, grad, gref));
2744: PetscFunctionReturn(PETSC_SUCCESS);
2745: }
2747: static PetscErrorCode BuildGradientReconstruction_Internal_Tree(DM dm, PetscFV fvm, DM dmFace, PetscScalar *fgeom, DM dmCell, PetscScalar *cgeom)
2748: {
2749: DMLabel ghostLabel;
2750: PetscScalar *dx, *grad, **gref;
2751: PetscInt dim, cStart, cEnd, c, cEndInterior, fStart, fEnd, f, nStart, nEnd, maxNumFaces = 0;
2752: PetscSection neighSec;
2753: PetscInt(*neighbors)[2];
2754: PetscInt *counter;
2756: PetscFunctionBegin;
2757: PetscCall(DMGetDimension(dm, &dim));
2758: PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
2759: PetscCall(DMPlexGetGhostCellStratum(dm, &cEndInterior, NULL));
2760: if (cEndInterior < 0) cEndInterior = cEnd;
2761: PetscCall(PetscSectionCreate(PetscObjectComm((PetscObject)dm), &neighSec));
2762: PetscCall(PetscSectionSetChart(neighSec, cStart, cEndInterior));
2763: PetscCall(DMPlexGetHeightStratum(dm, 1, &fStart, &fEnd));
2764: PetscCall(DMGetLabel(dm, "ghost", &ghostLabel));
2765: for (f = fStart; f < fEnd; f++) {
2766: const PetscInt *fcells;
2767: PetscBool boundary;
2768: PetscInt ghost = -1;
2769: PetscInt numChildren, numCells, c;
2771: if (ghostLabel) PetscCall(DMLabelGetValue(ghostLabel, f, &ghost));
2772: PetscCall(DMIsBoundaryPoint(dm, f, &boundary));
2773: PetscCall(DMPlexGetTreeChildren(dm, f, &numChildren, NULL));
2774: if ((ghost >= 0) || boundary || numChildren) continue;
2775: PetscCall(DMPlexGetSupportSize(dm, f, &numCells));
2776: if (numCells == 2) {
2777: PetscCall(DMPlexGetSupport(dm, f, &fcells));
2778: for (c = 0; c < 2; c++) {
2779: PetscInt cell = fcells[c];
2781: if (cell >= cStart && cell < cEndInterior) PetscCall(PetscSectionAddDof(neighSec, cell, 1));
2782: }
2783: }
2784: }
2785: PetscCall(PetscSectionSetUp(neighSec));
2786: PetscCall(PetscSectionGetMaxDof(neighSec, &maxNumFaces));
2787: PetscCall(PetscFVLeastSquaresSetMaxFaces(fvm, maxNumFaces));
2788: nStart = 0;
2789: PetscCall(PetscSectionGetStorageSize(neighSec, &nEnd));
2790: PetscCall(PetscMalloc1((nEnd - nStart), &neighbors));
2791: PetscCall(PetscCalloc1((cEndInterior - cStart), &counter));
2792: for (f = fStart; f < fEnd; f++) {
2793: const PetscInt *fcells;
2794: PetscBool boundary;
2795: PetscInt ghost = -1;
2796: PetscInt numChildren, numCells, c;
2798: if (ghostLabel) PetscCall(DMLabelGetValue(ghostLabel, f, &ghost));
2799: PetscCall(DMIsBoundaryPoint(dm, f, &boundary));
2800: PetscCall(DMPlexGetTreeChildren(dm, f, &numChildren, NULL));
2801: if ((ghost >= 0) || boundary || numChildren) continue;
2802: PetscCall(DMPlexGetSupportSize(dm, f, &numCells));
2803: if (numCells == 2) {
2804: PetscCall(DMPlexGetSupport(dm, f, &fcells));
2805: for (c = 0; c < 2; c++) {
2806: PetscInt cell = fcells[c], off;
2808: if (cell >= cStart && cell < cEndInterior) {
2809: PetscCall(PetscSectionGetOffset(neighSec, cell, &off));
2810: off += counter[cell - cStart]++;
2811: neighbors[off][0] = f;
2812: neighbors[off][1] = fcells[1 - c];
2813: }
2814: }
2815: }
2816: }
2817: PetscCall(PetscFree(counter));
2818: PetscCall(PetscMalloc3(maxNumFaces * dim, &dx, maxNumFaces * dim, &grad, maxNumFaces, &gref));
2819: for (c = cStart; c < cEndInterior; c++) {
2820: PetscInt numFaces, f, d, off, ghost = -1;
2821: PetscFVCellGeom *cg;
2823: PetscCall(DMPlexPointLocalRead(dmCell, c, cgeom, &cg));
2824: PetscCall(PetscSectionGetDof(neighSec, c, &numFaces));
2825: PetscCall(PetscSectionGetOffset(neighSec, c, &off));
2827: // do not attempt to compute a gradient reconstruction stencil in a ghost cell. It will never be used
2828: if (ghostLabel) PetscCall(DMLabelGetValue(ghostLabel, c, &ghost));
2829: if (ghost >= 0) continue;
2831: 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);
2832: for (f = 0; f < numFaces; ++f) {
2833: PetscFVCellGeom *cg1;
2834: PetscFVFaceGeom *fg;
2835: const PetscInt *fcells;
2836: PetscInt ncell, side, nface;
2838: nface = neighbors[off + f][0];
2839: ncell = neighbors[off + f][1];
2840: PetscCall(DMPlexGetSupport(dm, nface, &fcells));
2841: side = (c != fcells[0]);
2842: PetscCall(DMPlexPointLocalRef(dmFace, nface, fgeom, &fg));
2843: PetscCall(DMPlexPointLocalRead(dmCell, ncell, cgeom, &cg1));
2844: for (d = 0; d < dim; ++d) dx[f * dim + d] = cg1->centroid[d] - cg->centroid[d];
2845: gref[f] = fg->grad[side]; /* Gradient reconstruction term will go here */
2846: }
2847: PetscCall(PetscFVComputeGradient(fvm, numFaces, dx, grad));
2848: for (f = 0; f < numFaces; ++f) {
2849: for (d = 0; d < dim; ++d) gref[f][d] = grad[f * dim + d];
2850: }
2851: }
2852: PetscCall(PetscFree3(dx, grad, gref));
2853: PetscCall(PetscSectionDestroy(&neighSec));
2854: PetscCall(PetscFree(neighbors));
2855: PetscFunctionReturn(PETSC_SUCCESS);
2856: }
2858: /*@
2859: DMPlexComputeGradientFVM - Compute geometric factors for gradient reconstruction, which are stored in the geometry data, and compute layout for gradient data
2861: Collective
2863: Input Parameters:
2864: + dm - The `DMPLEX`
2865: . fvm - The `PetscFV`
2866: - cellGeometry - The face geometry from `DMPlexComputeCellGeometryFVM()`
2868: Input/Output Parameter:
2869: . faceGeometry - The face geometry from `DMPlexComputeFaceGeometryFVM()`; on output
2870: the geometric factors for gradient calculation are inserted
2872: Output Parameter:
2873: . dmGrad - The `DM` describing the layout of gradient data
2875: Level: developer
2877: .seealso: `DMPLEX`, `DMPlexGetFaceGeometryFVM()`, `DMPlexGetCellGeometryFVM()`
2878: @*/
2879: PetscErrorCode DMPlexComputeGradientFVM(DM dm, PetscFV fvm, Vec faceGeometry, Vec cellGeometry, DM *dmGrad)
2880: {
2881: DM dmFace, dmCell;
2882: PetscScalar *fgeom, *cgeom;
2883: PetscSection sectionGrad, parentSection;
2884: PetscInt dim, pdim, cStart, cEnd, cEndInterior, c;
2886: PetscFunctionBegin;
2887: PetscCall(DMGetDimension(dm, &dim));
2888: PetscCall(PetscFVGetNumComponents(fvm, &pdim));
2889: PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
2890: PetscCall(DMPlexGetGhostCellStratum(dm, &cEndInterior, NULL));
2891: /* Construct the interpolant corresponding to each face from the least-square solution over the cell neighborhood */
2892: PetscCall(VecGetDM(faceGeometry, &dmFace));
2893: PetscCall(VecGetDM(cellGeometry, &dmCell));
2894: PetscCall(VecGetArray(faceGeometry, &fgeom));
2895: PetscCall(VecGetArray(cellGeometry, &cgeom));
2896: PetscCall(DMPlexGetTree(dm, &parentSection, NULL, NULL, NULL, NULL));
2897: if (!parentSection) {
2898: PetscCall(BuildGradientReconstruction_Internal(dm, fvm, dmFace, fgeom, dmCell, cgeom));
2899: } else {
2900: PetscCall(BuildGradientReconstruction_Internal_Tree(dm, fvm, dmFace, fgeom, dmCell, cgeom));
2901: }
2902: PetscCall(VecRestoreArray(faceGeometry, &fgeom));
2903: PetscCall(VecRestoreArray(cellGeometry, &cgeom));
2904: /* Create storage for gradients */
2905: PetscCall(DMClone(dm, dmGrad));
2906: PetscCall(PetscSectionCreate(PetscObjectComm((PetscObject)dm), §ionGrad));
2907: PetscCall(PetscSectionSetChart(sectionGrad, cStart, cEnd));
2908: for (c = cStart; c < cEnd; ++c) PetscCall(PetscSectionSetDof(sectionGrad, c, pdim * dim));
2909: PetscCall(PetscSectionSetUp(sectionGrad));
2910: PetscCall(DMSetLocalSection(*dmGrad, sectionGrad));
2911: PetscCall(PetscSectionDestroy(§ionGrad));
2912: PetscFunctionReturn(PETSC_SUCCESS);
2913: }
2915: /*@
2916: DMPlexGetDataFVM - Retrieve precomputed cell geometry
2918: Collective
2920: Input Parameters:
2921: + dm - The `DM`
2922: - fv - The `PetscFV`
2924: Output Parameters:
2925: + cellGeometry - The cell geometry
2926: . faceGeometry - The face geometry
2927: - gradDM - The gradient matrices
2929: Level: developer
2931: .seealso: `DMPLEX`, `DMPlexComputeGeometryFVM()`
2932: @*/
2933: PetscErrorCode DMPlexGetDataFVM(DM dm, PetscFV fv, Vec *cellgeom, Vec *facegeom, DM *gradDM)
2934: {
2935: PetscObject cellgeomobj, facegeomobj;
2937: PetscFunctionBegin;
2938: PetscCall(PetscObjectQuery((PetscObject)dm, "DMPlex_cellgeom_fvm", &cellgeomobj));
2939: if (!cellgeomobj) {
2940: Vec cellgeomInt, facegeomInt;
2942: PetscCall(DMPlexComputeGeometryFVM(dm, &cellgeomInt, &facegeomInt));
2943: PetscCall(PetscObjectCompose((PetscObject)dm, "DMPlex_cellgeom_fvm", (PetscObject)cellgeomInt));
2944: PetscCall(PetscObjectCompose((PetscObject)dm, "DMPlex_facegeom_fvm", (PetscObject)facegeomInt));
2945: PetscCall(VecDestroy(&cellgeomInt));
2946: PetscCall(VecDestroy(&facegeomInt));
2947: PetscCall(PetscObjectQuery((PetscObject)dm, "DMPlex_cellgeom_fvm", &cellgeomobj));
2948: }
2949: PetscCall(PetscObjectQuery((PetscObject)dm, "DMPlex_facegeom_fvm", &facegeomobj));
2950: if (cellgeom) *cellgeom = (Vec)cellgeomobj;
2951: if (facegeom) *facegeom = (Vec)facegeomobj;
2952: if (gradDM) {
2953: PetscObject gradobj;
2954: PetscBool computeGradients;
2956: PetscCall(PetscFVGetComputeGradients(fv, &computeGradients));
2957: if (!computeGradients) {
2958: *gradDM = NULL;
2959: PetscFunctionReturn(PETSC_SUCCESS);
2960: }
2961: PetscCall(PetscObjectQuery((PetscObject)dm, "DMPlex_dmgrad_fvm", &gradobj));
2962: if (!gradobj) {
2963: DM dmGradInt;
2965: PetscCall(DMPlexComputeGradientFVM(dm, fv, (Vec)facegeomobj, (Vec)cellgeomobj, &dmGradInt));
2966: PetscCall(PetscObjectCompose((PetscObject)dm, "DMPlex_dmgrad_fvm", (PetscObject)dmGradInt));
2967: PetscCall(DMDestroy(&dmGradInt));
2968: PetscCall(PetscObjectQuery((PetscObject)dm, "DMPlex_dmgrad_fvm", &gradobj));
2969: }
2970: *gradDM = (DM)gradobj;
2971: }
2972: PetscFunctionReturn(PETSC_SUCCESS);
2973: }
2975: static PetscErrorCode DMPlexCoordinatesToReference_NewtonUpdate(PetscInt dimC, PetscInt dimR, PetscScalar *J, PetscScalar *invJ, PetscScalar *work, PetscReal *resNeg, PetscReal *guess)
2976: {
2977: PetscInt l, m;
2979: PetscFunctionBeginHot;
2980: if (dimC == dimR && dimR <= 3) {
2981: /* invert Jacobian, multiply */
2982: PetscScalar det, idet;
2984: switch (dimR) {
2985: case 1:
2986: invJ[0] = 1. / J[0];
2987: break;
2988: case 2:
2989: det = J[0] * J[3] - J[1] * J[2];
2990: idet = 1. / det;
2991: invJ[0] = J[3] * idet;
2992: invJ[1] = -J[1] * idet;
2993: invJ[2] = -J[2] * idet;
2994: invJ[3] = J[0] * idet;
2995: break;
2996: case 3: {
2997: invJ[0] = J[4] * J[8] - J[5] * J[7];
2998: invJ[1] = J[2] * J[7] - J[1] * J[8];
2999: invJ[2] = J[1] * J[5] - J[2] * J[4];
3000: det = invJ[0] * J[0] + invJ[1] * J[3] + invJ[2] * J[6];
3001: idet = 1. / det;
3002: invJ[0] *= idet;
3003: invJ[1] *= idet;
3004: invJ[2] *= idet;
3005: invJ[3] = idet * (J[5] * J[6] - J[3] * J[8]);
3006: invJ[4] = idet * (J[0] * J[8] - J[2] * J[6]);
3007: invJ[5] = idet * (J[2] * J[3] - J[0] * J[5]);
3008: invJ[6] = idet * (J[3] * J[7] - J[4] * J[6]);
3009: invJ[7] = idet * (J[1] * J[6] - J[0] * J[7]);
3010: invJ[8] = idet * (J[0] * J[4] - J[1] * J[3]);
3011: } break;
3012: }
3013: for (l = 0; l < dimR; l++) {
3014: for (m = 0; m < dimC; m++) guess[l] += PetscRealPart(invJ[l * dimC + m]) * resNeg[m];
3015: }
3016: } else {
3017: #if defined(PETSC_USE_COMPLEX)
3018: char transpose = 'C';
3019: #else
3020: char transpose = 'T';
3021: #endif
3022: PetscBLASInt m = dimR;
3023: PetscBLASInt n = dimC;
3024: PetscBLASInt one = 1;
3025: PetscBLASInt worksize = dimR * dimC, info;
3027: for (l = 0; l < dimC; l++) invJ[l] = resNeg[l];
3029: PetscCallBLAS("LAPACKgels", LAPACKgels_(&transpose, &m, &n, &one, J, &m, invJ, &n, work, &worksize, &info));
3030: PetscCheck(info == 0, PETSC_COMM_SELF, PETSC_ERR_LIB, "Bad argument to GELS");
3032: for (l = 0; l < dimR; l++) guess[l] += PetscRealPart(invJ[l]);
3033: }
3034: PetscFunctionReturn(PETSC_SUCCESS);
3035: }
3037: static PetscErrorCode DMPlexCoordinatesToReference_Tensor(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal realCoords[], PetscReal refCoords[], Vec coords, PetscInt dimC, PetscInt dimR)
3038: {
3039: PetscInt coordSize, i, j, k, l, m, maxIts = 7, numV = (1 << dimR);
3040: PetscScalar *coordsScalar = NULL;
3041: PetscReal *cellData, *cellCoords, *cellCoeffs, *extJ, *resNeg;
3042: PetscScalar *J, *invJ, *work;
3044: PetscFunctionBegin;
3046: PetscCall(DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar));
3047: PetscCheck(coordSize >= dimC * numV, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Expecting at least %" PetscInt_FMT " coordinates, got %" PetscInt_FMT, dimC * (1 << dimR), coordSize);
3048: PetscCall(DMGetWorkArray(dm, 2 * coordSize + dimR + dimC, MPIU_REAL, &cellData));
3049: PetscCall(DMGetWorkArray(dm, 3 * dimR * dimC, MPIU_SCALAR, &J));
3050: cellCoords = &cellData[0];
3051: cellCoeffs = &cellData[coordSize];
3052: extJ = &cellData[2 * coordSize];
3053: resNeg = &cellData[2 * coordSize + dimR];
3054: invJ = &J[dimR * dimC];
3055: work = &J[2 * dimR * dimC];
3056: if (dimR == 2) {
3057: const PetscInt zToPlex[4] = {0, 1, 3, 2};
3059: for (i = 0; i < 4; i++) {
3060: PetscInt plexI = zToPlex[i];
3062: for (j = 0; j < dimC; j++) cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
3063: }
3064: } else if (dimR == 3) {
3065: const PetscInt zToPlex[8] = {0, 3, 1, 2, 4, 5, 7, 6};
3067: for (i = 0; i < 8; i++) {
3068: PetscInt plexI = zToPlex[i];
3070: for (j = 0; j < dimC; j++) cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
3071: }
3072: } else {
3073: for (i = 0; i < coordSize; i++) cellCoords[i] = PetscRealPart(coordsScalar[i]);
3074: }
3075: /* Perform the shuffling transform that converts values at the corners of [-1,1]^d to coefficients */
3076: for (i = 0; i < dimR; i++) {
3077: PetscReal *swap;
3079: for (j = 0; j < (numV / 2); j++) {
3080: for (k = 0; k < dimC; k++) {
3081: cellCoeffs[dimC * j + k] = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] + cellCoords[dimC * 2 * j + k]);
3082: cellCoeffs[dimC * (j + (numV / 2)) + k] = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] - cellCoords[dimC * 2 * j + k]);
3083: }
3084: }
3086: if (i < dimR - 1) {
3087: swap = cellCoeffs;
3088: cellCoeffs = cellCoords;
3089: cellCoords = swap;
3090: }
3091: }
3092: PetscCall(PetscArrayzero(refCoords, numPoints * dimR));
3093: for (j = 0; j < numPoints; j++) {
3094: for (i = 0; i < maxIts; i++) {
3095: PetscReal *guess = &refCoords[dimR * j];
3097: /* compute -residual and Jacobian */
3098: for (k = 0; k < dimC; k++) resNeg[k] = realCoords[dimC * j + k];
3099: for (k = 0; k < dimC * dimR; k++) J[k] = 0.;
3100: for (k = 0; k < numV; k++) {
3101: PetscReal extCoord = 1.;
3102: for (l = 0; l < dimR; l++) {
3103: PetscReal coord = guess[l];
3104: PetscInt dep = (k & (1 << l)) >> l;
3106: extCoord *= dep * coord + !dep;
3107: extJ[l] = dep;
3109: for (m = 0; m < dimR; m++) {
3110: PetscReal coord = guess[m];
3111: PetscInt dep = ((k & (1 << m)) >> m) && (m != l);
3112: PetscReal mult = dep * coord + !dep;
3114: extJ[l] *= mult;
3115: }
3116: }
3117: for (l = 0; l < dimC; l++) {
3118: PetscReal coeff = cellCoeffs[dimC * k + l];
3120: resNeg[l] -= coeff * extCoord;
3121: for (m = 0; m < dimR; m++) J[dimR * l + m] += coeff * extJ[m];
3122: }
3123: }
3124: if (0 && PetscDefined(USE_DEBUG)) {
3125: PetscReal maxAbs = 0.;
3127: for (l = 0; l < dimC; l++) maxAbs = PetscMax(maxAbs, PetscAbsReal(resNeg[l]));
3128: PetscCall(PetscInfo(dm, "cell %" PetscInt_FMT ", point %" PetscInt_FMT ", iter %" PetscInt_FMT ": res %g\n", cell, j, i, (double)maxAbs));
3129: }
3131: PetscCall(DMPlexCoordinatesToReference_NewtonUpdate(dimC, dimR, J, invJ, work, resNeg, guess));
3132: }
3133: }
3134: PetscCall(DMRestoreWorkArray(dm, 3 * dimR * dimC, MPIU_SCALAR, &J));
3135: PetscCall(DMRestoreWorkArray(dm, 2 * coordSize + dimR + dimC, MPIU_REAL, &cellData));
3136: PetscCall(DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar));
3137: PetscFunctionReturn(PETSC_SUCCESS);
3138: }
3140: static PetscErrorCode DMPlexReferenceToCoordinates_Tensor(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal refCoords[], PetscReal realCoords[], Vec coords, PetscInt dimC, PetscInt dimR)
3141: {
3142: PetscInt coordSize, i, j, k, l, numV = (1 << dimR);
3143: PetscScalar *coordsScalar = NULL;
3144: PetscReal *cellData, *cellCoords, *cellCoeffs;
3146: PetscFunctionBegin;
3148: PetscCall(DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar));
3149: PetscCheck(coordSize >= dimC * numV, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Expecting at least %" PetscInt_FMT " coordinates, got %" PetscInt_FMT, dimC * (1 << dimR), coordSize);
3150: PetscCall(DMGetWorkArray(dm, 2 * coordSize, MPIU_REAL, &cellData));
3151: cellCoords = &cellData[0];
3152: cellCoeffs = &cellData[coordSize];
3153: if (dimR == 2) {
3154: const PetscInt zToPlex[4] = {0, 1, 3, 2};
3156: for (i = 0; i < 4; i++) {
3157: PetscInt plexI = zToPlex[i];
3159: for (j = 0; j < dimC; j++) cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
3160: }
3161: } else if (dimR == 3) {
3162: const PetscInt zToPlex[8] = {0, 3, 1, 2, 4, 5, 7, 6};
3164: for (i = 0; i < 8; i++) {
3165: PetscInt plexI = zToPlex[i];
3167: for (j = 0; j < dimC; j++) cellCoords[dimC * i + j] = PetscRealPart(coordsScalar[dimC * plexI + j]);
3168: }
3169: } else {
3170: for (i = 0; i < coordSize; i++) cellCoords[i] = PetscRealPart(coordsScalar[i]);
3171: }
3172: /* Perform the shuffling transform that converts values at the corners of [-1,1]^d to coefficients */
3173: for (i = 0; i < dimR; i++) {
3174: PetscReal *swap;
3176: for (j = 0; j < (numV / 2); j++) {
3177: for (k = 0; k < dimC; k++) {
3178: cellCoeffs[dimC * j + k] = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] + cellCoords[dimC * 2 * j + k]);
3179: cellCoeffs[dimC * (j + (numV / 2)) + k] = 0.5 * (cellCoords[dimC * (2 * j + 1) + k] - cellCoords[dimC * 2 * j + k]);
3180: }
3181: }
3183: if (i < dimR - 1) {
3184: swap = cellCoeffs;
3185: cellCoeffs = cellCoords;
3186: cellCoords = swap;
3187: }
3188: }
3189: PetscCall(PetscArrayzero(realCoords, numPoints * dimC));
3190: for (j = 0; j < numPoints; j++) {
3191: const PetscReal *guess = &refCoords[dimR * j];
3192: PetscReal *mapped = &realCoords[dimC * j];
3194: for (k = 0; k < numV; k++) {
3195: PetscReal extCoord = 1.;
3196: for (l = 0; l < dimR; l++) {
3197: PetscReal coord = guess[l];
3198: PetscInt dep = (k & (1 << l)) >> l;
3200: extCoord *= dep * coord + !dep;
3201: }
3202: for (l = 0; l < dimC; l++) {
3203: PetscReal coeff = cellCoeffs[dimC * k + l];
3205: mapped[l] += coeff * extCoord;
3206: }
3207: }
3208: }
3209: PetscCall(DMRestoreWorkArray(dm, 2 * coordSize, MPIU_REAL, &cellData));
3210: PetscCall(DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &coordsScalar));
3211: PetscFunctionReturn(PETSC_SUCCESS);
3212: }
3214: /* TODO: TOBY please fix this for Nc > 1 */
3215: static PetscErrorCode DMPlexCoordinatesToReference_FE(DM dm, PetscFE fe, PetscInt cell, PetscInt numPoints, const PetscReal realCoords[], PetscReal refCoords[], Vec coords, PetscInt Nc, PetscInt dimR)
3216: {
3217: PetscInt numComp, pdim, i, j, k, l, m, maxIter = 7, coordSize;
3218: PetscScalar *nodes = NULL;
3219: PetscReal *invV, *modes;
3220: PetscReal *B, *D, *resNeg;
3221: PetscScalar *J, *invJ, *work;
3223: PetscFunctionBegin;
3224: PetscCall(PetscFEGetDimension(fe, &pdim));
3225: PetscCall(PetscFEGetNumComponents(fe, &numComp));
3226: 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);
3227: PetscCall(DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &nodes));
3228: /* convert nodes to values in the stable evaluation basis */
3229: PetscCall(DMGetWorkArray(dm, pdim, MPIU_REAL, &modes));
3230: invV = fe->invV;
3231: for (i = 0; i < pdim; ++i) {
3232: modes[i] = 0.;
3233: for (j = 0; j < pdim; ++j) modes[i] += invV[i * pdim + j] * PetscRealPart(nodes[j]);
3234: }
3235: PetscCall(DMGetWorkArray(dm, pdim * Nc + pdim * Nc * dimR + Nc, MPIU_REAL, &B));
3236: D = &B[pdim * Nc];
3237: resNeg = &D[pdim * Nc * dimR];
3238: PetscCall(DMGetWorkArray(dm, 3 * Nc * dimR, MPIU_SCALAR, &J));
3239: invJ = &J[Nc * dimR];
3240: work = &invJ[Nc * dimR];
3241: for (i = 0; i < numPoints * dimR; i++) refCoords[i] = 0.;
3242: for (j = 0; j < numPoints; j++) {
3243: for (i = 0; i < maxIter; i++) { /* we could batch this so that we're not making big B and D arrays all the time */
3244: PetscReal *guess = &refCoords[j * dimR];
3245: PetscCall(PetscSpaceEvaluate(fe->basisSpace, 1, guess, B, D, NULL));
3246: for (k = 0; k < Nc; k++) resNeg[k] = realCoords[j * Nc + k];
3247: for (k = 0; k < Nc * dimR; k++) J[k] = 0.;
3248: for (k = 0; k < pdim; k++) {
3249: for (l = 0; l < Nc; l++) {
3250: resNeg[l] -= modes[k] * B[k * Nc + l];
3251: for (m = 0; m < dimR; m++) J[l * dimR + m] += modes[k] * D[(k * Nc + l) * dimR + m];
3252: }
3253: }
3254: if (0 && PetscDefined(USE_DEBUG)) {
3255: PetscReal maxAbs = 0.;
3257: for (l = 0; l < Nc; l++) maxAbs = PetscMax(maxAbs, PetscAbsReal(resNeg[l]));
3258: PetscCall(PetscInfo(dm, "cell %" PetscInt_FMT ", point %" PetscInt_FMT ", iter %" PetscInt_FMT ": res %g\n", cell, j, i, (double)maxAbs));
3259: }
3260: PetscCall(DMPlexCoordinatesToReference_NewtonUpdate(Nc, dimR, J, invJ, work, resNeg, guess));
3261: }
3262: }
3263: PetscCall(DMRestoreWorkArray(dm, 3 * Nc * dimR, MPIU_SCALAR, &J));
3264: PetscCall(DMRestoreWorkArray(dm, pdim * Nc + pdim * Nc * dimR + Nc, MPIU_REAL, &B));
3265: PetscCall(DMRestoreWorkArray(dm, pdim, MPIU_REAL, &modes));
3266: PetscCall(DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &nodes));
3267: PetscFunctionReturn(PETSC_SUCCESS);
3268: }
3270: /* TODO: TOBY please fix this for Nc > 1 */
3271: static PetscErrorCode DMPlexReferenceToCoordinates_FE(DM dm, PetscFE fe, PetscInt cell, PetscInt numPoints, const PetscReal refCoords[], PetscReal realCoords[], Vec coords, PetscInt Nc, PetscInt dimR)
3272: {
3273: PetscInt numComp, pdim, i, j, k, l, coordSize;
3274: PetscScalar *nodes = NULL;
3275: PetscReal *invV, *modes;
3276: PetscReal *B;
3278: PetscFunctionBegin;
3279: PetscCall(PetscFEGetDimension(fe, &pdim));
3280: PetscCall(PetscFEGetNumComponents(fe, &numComp));
3281: 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);
3282: PetscCall(DMPlexVecGetClosure(dm, NULL, coords, cell, &coordSize, &nodes));
3283: /* convert nodes to values in the stable evaluation basis */
3284: PetscCall(DMGetWorkArray(dm, pdim, MPIU_REAL, &modes));
3285: invV = fe->invV;
3286: for (i = 0; i < pdim; ++i) {
3287: modes[i] = 0.;
3288: for (j = 0; j < pdim; ++j) modes[i] += invV[i * pdim + j] * PetscRealPart(nodes[j]);
3289: }
3290: PetscCall(DMGetWorkArray(dm, numPoints * pdim * Nc, MPIU_REAL, &B));
3291: PetscCall(PetscSpaceEvaluate(fe->basisSpace, numPoints, refCoords, B, NULL, NULL));
3292: for (i = 0; i < numPoints * Nc; i++) realCoords[i] = 0.;
3293: for (j = 0; j < numPoints; j++) {
3294: PetscReal *mapped = &realCoords[j * Nc];
3296: for (k = 0; k < pdim; k++) {
3297: for (l = 0; l < Nc; l++) mapped[l] += modes[k] * B[(j * pdim + k) * Nc + l];
3298: }
3299: }
3300: PetscCall(DMRestoreWorkArray(dm, numPoints * pdim * Nc, MPIU_REAL, &B));
3301: PetscCall(DMRestoreWorkArray(dm, pdim, MPIU_REAL, &modes));
3302: PetscCall(DMPlexVecRestoreClosure(dm, NULL, coords, cell, &coordSize, &nodes));
3303: PetscFunctionReturn(PETSC_SUCCESS);
3304: }
3306: /*@
3307: DMPlexCoordinatesToReference - Pull coordinates back from the mesh to the reference element using a single element
3308: map. This inversion will be accurate inside the reference element, but may be inaccurate for mappings that do not
3309: extend uniquely outside the reference cell (e.g, most non-affine maps)
3311: Not Collective
3313: Input Parameters:
3314: + dm - The mesh, with coordinate maps defined either by a `PetscDS` for the coordinate `DM` (see `DMGetCoordinateDM()`) or
3315: implicitly by the coordinates of the corner vertices of the cell: as an affine map for simplicial elements, or
3316: as a multilinear map for tensor-product elements
3317: . cell - the cell whose map is used.
3318: . numPoints - the number of points to locate
3319: - realCoords - (numPoints x coordinate dimension) array of coordinates (see `DMGetCoordinateDim()`)
3321: Output Parameter:
3322: . refCoords - (`numPoints` x `dimension`) array of reference coordinates (see `DMGetDimension()`)
3324: Level: intermediate
3326: .seealso: `DMPLEX`, `DMPlexReferenceToCoordinates()`
3327: @*/
3328: PetscErrorCode DMPlexCoordinatesToReference(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal realCoords[], PetscReal refCoords[])
3329: {
3330: PetscInt dimC, dimR, depth, cStart, cEnd, i;
3331: DM coordDM = NULL;
3332: Vec coords;
3333: PetscFE fe = NULL;
3335: PetscFunctionBegin;
3337: PetscCall(DMGetDimension(dm, &dimR));
3338: PetscCall(DMGetCoordinateDim(dm, &dimC));
3339: if (dimR <= 0 || dimC <= 0 || numPoints <= 0) PetscFunctionReturn(PETSC_SUCCESS);
3340: PetscCall(DMPlexGetDepth(dm, &depth));
3341: PetscCall(DMGetCoordinatesLocal(dm, &coords));
3342: PetscCall(DMGetCoordinateDM(dm, &coordDM));
3343: if (coordDM) {
3344: PetscInt coordFields;
3346: PetscCall(DMGetNumFields(coordDM, &coordFields));
3347: if (coordFields) {
3348: PetscClassId id;
3349: PetscObject disc;
3351: PetscCall(DMGetField(coordDM, 0, NULL, &disc));
3352: PetscCall(PetscObjectGetClassId(disc, &id));
3353: if (id == PETSCFE_CLASSID) fe = (PetscFE)disc;
3354: }
3355: }
3356: PetscCall(DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd));
3357: 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);
3358: if (!fe) { /* implicit discretization: affine or multilinear */
3359: PetscInt coneSize;
3360: PetscBool isSimplex, isTensor;
3362: PetscCall(DMPlexGetConeSize(dm, cell, &coneSize));
3363: isSimplex = (coneSize == (dimR + 1)) ? PETSC_TRUE : PETSC_FALSE;
3364: isTensor = (coneSize == ((depth == 1) ? (1 << dimR) : (2 * dimR))) ? PETSC_TRUE : PETSC_FALSE;
3365: if (isSimplex) {
3366: PetscReal detJ, *v0, *J, *invJ;
3368: PetscCall(DMGetWorkArray(dm, dimC + 2 * dimC * dimC, MPIU_REAL, &v0));
3369: J = &v0[dimC];
3370: invJ = &J[dimC * dimC];
3371: PetscCall(DMPlexComputeCellGeometryAffineFEM(dm, cell, v0, J, invJ, &detJ));
3372: for (i = 0; i < numPoints; i++) { /* Apply the inverse affine transformation for each point */
3373: const PetscReal x0[3] = {-1., -1., -1.};
3375: CoordinatesRealToRef(dimC, dimR, x0, v0, invJ, &realCoords[dimC * i], &refCoords[dimR * i]);
3376: }
3377: PetscCall(DMRestoreWorkArray(dm, dimC + 2 * dimC * dimC, MPIU_REAL, &v0));
3378: } else if (isTensor) {
3379: PetscCall(DMPlexCoordinatesToReference_Tensor(coordDM, cell, numPoints, realCoords, refCoords, coords, dimC, dimR));
3380: } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Unrecognized cone size %" PetscInt_FMT, coneSize);
3381: } else {
3382: PetscCall(DMPlexCoordinatesToReference_FE(coordDM, fe, cell, numPoints, realCoords, refCoords, coords, dimC, dimR));
3383: }
3384: PetscFunctionReturn(PETSC_SUCCESS);
3385: }
3387: /*@
3388: DMPlexReferenceToCoordinates - Map references coordinates to coordinates in the the mesh for a single element map.
3390: Not Collective
3392: Input Parameters:
3393: + dm - The mesh, with coordinate maps defined either by a PetscDS for the coordinate `DM` (see `DMGetCoordinateDM()`) or
3394: implicitly by the coordinates of the corner vertices of the cell: as an affine map for simplicial elements, or
3395: as a multilinear map for tensor-product elements
3396: . cell - the cell whose map is used.
3397: . numPoints - the number of points to locate
3398: - refCoords - (numPoints x dimension) array of reference coordinates (see `DMGetDimension()`)
3400: Output Parameter:
3401: . realCoords - (numPoints x coordinate dimension) array of coordinates (see `DMGetCoordinateDim()`)
3403: Level: intermediate
3405: .seealso: `DMPLEX`, `DMPlexCoordinatesToReference()`
3406: @*/
3407: PetscErrorCode DMPlexReferenceToCoordinates(DM dm, PetscInt cell, PetscInt numPoints, const PetscReal refCoords[], PetscReal realCoords[])
3408: {
3409: PetscInt dimC, dimR, depth, cStart, cEnd, i;
3410: DM coordDM = NULL;
3411: Vec coords;
3412: PetscFE fe = NULL;
3414: PetscFunctionBegin;
3416: PetscCall(DMGetDimension(dm, &dimR));
3417: PetscCall(DMGetCoordinateDim(dm, &dimC));
3418: if (dimR <= 0 || dimC <= 0 || numPoints <= 0) PetscFunctionReturn(PETSC_SUCCESS);
3419: PetscCall(DMPlexGetDepth(dm, &depth));
3420: PetscCall(DMGetCoordinatesLocal(dm, &coords));
3421: PetscCall(DMGetCoordinateDM(dm, &coordDM));
3422: if (coordDM) {
3423: PetscInt coordFields;
3425: PetscCall(DMGetNumFields(coordDM, &coordFields));
3426: if (coordFields) {
3427: PetscClassId id;
3428: PetscObject disc;
3430: PetscCall(DMGetField(coordDM, 0, NULL, &disc));
3431: PetscCall(PetscObjectGetClassId(disc, &id));
3432: if (id == PETSCFE_CLASSID) fe = (PetscFE)disc;
3433: }
3434: }
3435: PetscCall(DMPlexGetSimplexOrBoxCells(dm, 0, &cStart, &cEnd));
3436: 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);
3437: if (!fe) { /* implicit discretization: affine or multilinear */
3438: PetscInt coneSize;
3439: PetscBool isSimplex, isTensor;
3441: PetscCall(DMPlexGetConeSize(dm, cell, &coneSize));
3442: isSimplex = (coneSize == (dimR + 1)) ? PETSC_TRUE : PETSC_FALSE;
3443: isTensor = (coneSize == ((depth == 1) ? (1 << dimR) : (2 * dimR))) ? PETSC_TRUE : PETSC_FALSE;
3444: if (isSimplex) {
3445: PetscReal detJ, *v0, *J;
3447: PetscCall(DMGetWorkArray(dm, dimC + 2 * dimC * dimC, MPIU_REAL, &v0));
3448: J = &v0[dimC];
3449: PetscCall(DMPlexComputeCellGeometryAffineFEM(dm, cell, v0, J, NULL, &detJ));
3450: for (i = 0; i < numPoints; i++) { /* Apply the affine transformation for each point */
3451: const PetscReal xi0[3] = {-1., -1., -1.};
3453: CoordinatesRefToReal(dimC, dimR, xi0, v0, J, &refCoords[dimR * i], &realCoords[dimC * i]);
3454: }
3455: PetscCall(DMRestoreWorkArray(dm, dimC + 2 * dimC * dimC, MPIU_REAL, &v0));
3456: } else if (isTensor) {
3457: PetscCall(DMPlexReferenceToCoordinates_Tensor(coordDM, cell, numPoints, refCoords, realCoords, coords, dimC, dimR));
3458: } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Unrecognized cone size %" PetscInt_FMT, coneSize);
3459: } else {
3460: PetscCall(DMPlexReferenceToCoordinates_FE(coordDM, fe, cell, numPoints, refCoords, realCoords, coords, dimC, dimR));
3461: }
3462: PetscFunctionReturn(PETSC_SUCCESS);
3463: }
3465: /*@C
3466: DMPlexRemapGeometry - This function maps the original `DM` coordinates to new coordinates.
3468: Not Collective
3470: Input Parameters:
3471: + dm - The `DM`
3472: . time - The time
3473: - func - The function transforming current coordinates to new coordaintes
3475: Calling sequence of `func`:
3476: .vb
3477: void func(PetscInt dim, PetscInt Nf, PetscInt NfAux,
3478: const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
3479: const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
3480: PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f[]);
3481: .ve
3482: + dim - The spatial dimension
3483: . Nf - The number of input fields (here 1)
3484: . NfAux - The number of input auxiliary fields
3485: . uOff - The offset of the coordinates in u[] (here 0)
3486: . uOff_x - The offset of the coordinates in u_x[] (here 0)
3487: . u - The coordinate values at this point in space
3488: . u_t - The coordinate time derivative at this point in space (here `NULL`)
3489: . u_x - The coordinate derivatives at this point in space
3490: . aOff - The offset of each auxiliary field in u[]
3491: . aOff_x - The offset of each auxiliary field in u_x[]
3492: . a - The auxiliary field values at this point in space
3493: . a_t - The auxiliary field time derivative at this point in space (or `NULL`)
3494: . a_x - The auxiliary field derivatives at this point in space
3495: . t - The current time
3496: . x - The coordinates of this point (here not used)
3497: . numConstants - The number of constants
3498: . constants - The value of each constant
3499: - f - The new coordinates at this point in space
3501: Level: intermediate
3503: .seealso: `DMPLEX`, `DMGetCoordinates()`, `DMGetCoordinatesLocal()`, `DMGetCoordinateDM()`, `DMProjectFieldLocal()`, `DMProjectFieldLabelLocal()`
3504: @*/
3505: PetscErrorCode DMPlexRemapGeometry(DM dm, PetscReal time, void (*func)(PetscInt, PetscInt, PetscInt, const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[], PetscReal, const PetscReal[], PetscInt, const PetscScalar[], PetscScalar[]))
3506: {
3507: DM cdm;
3508: DMField cf;
3509: Vec lCoords, tmpCoords;
3511: PetscFunctionBegin;
3512: PetscCall(DMGetCoordinateDM(dm, &cdm));
3513: PetscCall(DMGetCoordinatesLocal(dm, &lCoords));
3514: PetscCall(DMGetLocalVector(cdm, &tmpCoords));
3515: PetscCall(VecCopy(lCoords, tmpCoords));
3516: /* We have to do the coordinate field manually right now since the coordinate DM will not have its own */
3517: PetscCall(DMGetCoordinateField(dm, &cf));
3518: cdm->coordinates[0].field = cf;
3519: PetscCall(DMProjectFieldLocal(cdm, time, tmpCoords, &func, INSERT_VALUES, lCoords));
3520: cdm->coordinates[0].field = NULL;
3521: PetscCall(DMRestoreLocalVector(cdm, &tmpCoords));
3522: PetscCall(DMSetCoordinatesLocal(dm, lCoords));
3523: PetscFunctionReturn(PETSC_SUCCESS);
3524: }
3526: /* Shear applies the transformation, assuming we fix z,
3527: / 1 0 m_0 \
3528: | 0 1 m_1 |
3529: \ 0 0 1 /
3530: */
3531: static void f0_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[])
3532: {
3533: const PetscInt Nc = uOff[1] - uOff[0];
3534: const PetscInt ax = (PetscInt)PetscRealPart(constants[0]);
3535: PetscInt c;
3537: for (c = 0; c < Nc; ++c) coords[c] = u[c] + constants[c + 1] * u[ax];
3538: }
3540: /*@C
3541: DMPlexShearGeometry - This shears the domain, meaning adds a multiple of the shear coordinate to all other coordinates.
3543: Not Collective
3545: Input Parameters:
3546: + dm - The `DMPLEX`
3547: . direction - The shear coordinate direction, e.g. 0 is the x-axis
3548: - multipliers - The multiplier m for each direction which is not the shear direction
3550: Level: intermediate
3552: .seealso: `DMPLEX`, `DMPlexRemapGeometry()`
3553: @*/
3554: PetscErrorCode DMPlexShearGeometry(DM dm, DMDirection direction, PetscReal multipliers[])
3555: {
3556: DM cdm;
3557: PetscDS cds;
3558: PetscObject obj;
3559: PetscClassId id;
3560: PetscScalar *moduli;
3561: const PetscInt dir = (PetscInt)direction;
3562: PetscInt dE, d, e;
3564: PetscFunctionBegin;
3565: PetscCall(DMGetCoordinateDM(dm, &cdm));
3566: PetscCall(DMGetCoordinateDim(dm, &dE));
3567: PetscCall(PetscMalloc1(dE + 1, &moduli));
3568: moduli[0] = dir;
3569: for (d = 0, e = 0; d < dE; ++d) moduli[d + 1] = d == dir ? 0.0 : (multipliers ? multipliers[e++] : 1.0);
3570: PetscCall(DMGetDS(cdm, &cds));
3571: PetscCall(PetscDSGetDiscretization(cds, 0, &obj));
3572: PetscCall(PetscObjectGetClassId(obj, &id));
3573: if (id != PETSCFE_CLASSID) {
3574: Vec lCoords;
3575: PetscSection cSection;
3576: PetscScalar *coords;
3577: PetscInt vStart, vEnd, v;
3579: PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
3580: PetscCall(DMGetCoordinateSection(dm, &cSection));
3581: PetscCall(DMGetCoordinatesLocal(dm, &lCoords));
3582: PetscCall(VecGetArray(lCoords, &coords));
3583: for (v = vStart; v < vEnd; ++v) {
3584: PetscReal ds;
3585: PetscInt off, c;
3587: PetscCall(PetscSectionGetOffset(cSection, v, &off));
3588: ds = PetscRealPart(coords[off + dir]);
3589: for (c = 0; c < dE; ++c) coords[off + c] += moduli[c] * ds;
3590: }
3591: PetscCall(VecRestoreArray(lCoords, &coords));
3592: } else {
3593: PetscCall(PetscDSSetConstants(cds, dE + 1, moduli));
3594: PetscCall(DMPlexRemapGeometry(dm, 0.0, f0_shear));
3595: }
3596: PetscCall(PetscFree(moduli));
3597: PetscFunctionReturn(PETSC_SUCCESS);
3598: }