Actual source code: dspacelagrange.c
1: #include <petsc/private/petscfeimpl.h>
2: #include <petscdmplex.h>
3: #include <petscblaslapack.h>
5: PetscErrorCode DMPlexGetTransitiveClosure_Internal(DM, PetscInt, PetscInt, PetscBool, PetscInt *, PetscInt *[]);
7: struct _n_Petsc1DNodeFamily {
8: PetscInt refct;
9: PetscDTNodeType nodeFamily;
10: PetscReal gaussJacobiExp;
11: PetscInt nComputed;
12: PetscReal **nodesets;
13: PetscBool endpoints;
14: };
16: /* users set node families for PETSCDUALSPACELAGRANGE with just the inputs to this function, but internally we create
17: * an object that can cache the computations across multiple dual spaces */
18: static PetscErrorCode Petsc1DNodeFamilyCreate(PetscDTNodeType family, PetscReal gaussJacobiExp, PetscBool endpoints, Petsc1DNodeFamily *nf)
19: {
20: Petsc1DNodeFamily f;
22: PetscFunctionBegin;
23: PetscCall(PetscNew(&f));
24: switch (family) {
25: case PETSCDTNODES_GAUSSJACOBI:
26: case PETSCDTNODES_EQUISPACED:
27: f->nodeFamily = family;
28: break;
29: default:
30: SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Unknown 1D node family");
31: }
32: f->endpoints = endpoints;
33: f->gaussJacobiExp = 0.;
34: if (family == PETSCDTNODES_GAUSSJACOBI) {
35: PetscCheck(gaussJacobiExp > -1., PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Gauss-Jacobi exponent must be > -1.");
36: f->gaussJacobiExp = gaussJacobiExp;
37: }
38: f->refct = 1;
39: *nf = f;
40: PetscFunctionReturn(PETSC_SUCCESS);
41: }
43: static PetscErrorCode Petsc1DNodeFamilyReference(Petsc1DNodeFamily nf)
44: {
45: PetscFunctionBegin;
46: if (nf) nf->refct++;
47: PetscFunctionReturn(PETSC_SUCCESS);
48: }
50: static PetscErrorCode Petsc1DNodeFamilyDestroy(Petsc1DNodeFamily *nf)
51: {
52: PetscInt i, nc;
54: PetscFunctionBegin;
55: if (!(*nf)) PetscFunctionReturn(PETSC_SUCCESS);
56: if (--(*nf)->refct > 0) {
57: *nf = NULL;
58: PetscFunctionReturn(PETSC_SUCCESS);
59: }
60: nc = (*nf)->nComputed;
61: for (i = 0; i < nc; i++) PetscCall(PetscFree((*nf)->nodesets[i]));
62: PetscCall(PetscFree((*nf)->nodesets));
63: PetscCall(PetscFree(*nf));
64: *nf = NULL;
65: PetscFunctionReturn(PETSC_SUCCESS);
66: }
68: static PetscErrorCode Petsc1DNodeFamilyGetNodeSets(Petsc1DNodeFamily f, PetscInt degree, PetscReal ***nodesets)
69: {
70: PetscInt nc;
72: PetscFunctionBegin;
73: nc = f->nComputed;
74: if (degree >= nc) {
75: PetscInt i, j;
76: PetscReal **new_nodesets;
77: PetscReal *w;
79: PetscCall(PetscMalloc1(degree + 1, &new_nodesets));
80: PetscCall(PetscArraycpy(new_nodesets, f->nodesets, nc));
81: PetscCall(PetscFree(f->nodesets));
82: f->nodesets = new_nodesets;
83: PetscCall(PetscMalloc1(degree + 1, &w));
84: for (i = nc; i < degree + 1; i++) {
85: PetscCall(PetscMalloc1(i + 1, &(f->nodesets[i])));
86: if (!i) {
87: f->nodesets[i][0] = 0.5;
88: } else {
89: switch (f->nodeFamily) {
90: case PETSCDTNODES_EQUISPACED:
91: if (f->endpoints) {
92: for (j = 0; j <= i; j++) f->nodesets[i][j] = (PetscReal)j / (PetscReal)i;
93: } else {
94: /* these nodes are at the centroids of the small simplices created by the equispaced nodes that include
95: * the endpoints */
96: for (j = 0; j <= i; j++) f->nodesets[i][j] = ((PetscReal)j + 0.5) / ((PetscReal)i + 1.);
97: }
98: break;
99: case PETSCDTNODES_GAUSSJACOBI:
100: if (f->endpoints) {
101: PetscCall(PetscDTGaussLobattoJacobiQuadrature(i + 1, 0., 1., f->gaussJacobiExp, f->gaussJacobiExp, f->nodesets[i], w));
102: } else {
103: PetscCall(PetscDTGaussJacobiQuadrature(i + 1, 0., 1., f->gaussJacobiExp, f->gaussJacobiExp, f->nodesets[i], w));
104: }
105: break;
106: default:
107: SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Unknown 1D node family");
108: }
109: }
110: }
111: PetscCall(PetscFree(w));
112: f->nComputed = degree + 1;
113: }
114: *nodesets = f->nodesets;
115: PetscFunctionReturn(PETSC_SUCCESS);
116: }
118: /* http://arxiv.org/abs/2002.09421 for details */
119: static PetscErrorCode PetscNodeRecursive_Internal(PetscInt dim, PetscInt degree, PetscReal **nodesets, PetscInt tup[], PetscReal node[])
120: {
121: PetscReal w;
122: PetscInt i, j;
124: PetscFunctionBeginHot;
125: w = 0.;
126: if (dim == 1) {
127: node[0] = nodesets[degree][tup[0]];
128: node[1] = nodesets[degree][tup[1]];
129: } else {
130: for (i = 0; i < dim + 1; i++) node[i] = 0.;
131: for (i = 0; i < dim + 1; i++) {
132: PetscReal wi = nodesets[degree][degree - tup[i]];
134: for (j = 0; j < dim + 1; j++) tup[dim + 1 + j] = tup[j + (j >= i)];
135: PetscCall(PetscNodeRecursive_Internal(dim - 1, degree - tup[i], nodesets, &tup[dim + 1], &node[dim + 1]));
136: for (j = 0; j < dim + 1; j++) node[j + (j >= i)] += wi * node[dim + 1 + j];
137: w += wi;
138: }
139: for (i = 0; i < dim + 1; i++) node[i] /= w;
140: }
141: PetscFunctionReturn(PETSC_SUCCESS);
142: }
144: /* compute simplex nodes for the biunit simplex from the 1D node family */
145: static PetscErrorCode Petsc1DNodeFamilyComputeSimplexNodes(Petsc1DNodeFamily f, PetscInt dim, PetscInt degree, PetscReal points[])
146: {
147: PetscInt *tup;
148: PetscInt k;
149: PetscInt npoints;
150: PetscReal **nodesets = NULL;
151: PetscInt worksize;
152: PetscReal *nodework;
153: PetscInt *tupwork;
155: PetscFunctionBegin;
156: PetscCheck(dim >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Must have non-negative dimension");
157: PetscCheck(degree >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Must have non-negative degree");
158: if (!dim) PetscFunctionReturn(PETSC_SUCCESS);
159: PetscCall(PetscCalloc1(dim + 2, &tup));
160: k = 0;
161: PetscCall(PetscDTBinomialInt(degree + dim, dim, &npoints));
162: PetscCall(Petsc1DNodeFamilyGetNodeSets(f, degree, &nodesets));
163: worksize = ((dim + 2) * (dim + 3)) / 2;
164: PetscCall(PetscMalloc2(worksize, &nodework, worksize, &tupwork));
165: /* loop over the tuples of length dim with sum at most degree */
166: for (k = 0; k < npoints; k++) {
167: PetscInt i;
169: /* turn thm into tuples of length dim + 1 with sum equal to degree (barycentric indice) */
170: tup[0] = degree;
171: for (i = 0; i < dim; i++) tup[0] -= tup[i + 1];
172: switch (f->nodeFamily) {
173: case PETSCDTNODES_EQUISPACED:
174: /* compute equispaces nodes on the unit reference triangle */
175: if (f->endpoints) {
176: for (i = 0; i < dim; i++) points[dim * k + i] = (PetscReal)tup[i + 1] / (PetscReal)degree;
177: } else {
178: for (i = 0; i < dim; i++) {
179: /* these nodes are at the centroids of the small simplices created by the equispaced nodes that include
180: * the endpoints */
181: points[dim * k + i] = ((PetscReal)tup[i + 1] + 1. / (dim + 1.)) / (PetscReal)(degree + 1.);
182: }
183: }
184: break;
185: default:
186: /* compute equispaces nodes on the barycentric reference triangle (the trace on the first dim dimensions are the
187: * unit reference triangle nodes */
188: for (i = 0; i < dim + 1; i++) tupwork[i] = tup[i];
189: PetscCall(PetscNodeRecursive_Internal(dim, degree, nodesets, tupwork, nodework));
190: for (i = 0; i < dim; i++) points[dim * k + i] = nodework[i + 1];
191: break;
192: }
193: PetscCall(PetscDualSpaceLatticePointLexicographic_Internal(dim, degree, &tup[1]));
194: }
195: /* map from unit simplex to biunit simplex */
196: for (k = 0; k < npoints * dim; k++) points[k] = points[k] * 2. - 1.;
197: PetscCall(PetscFree2(nodework, tupwork));
198: PetscCall(PetscFree(tup));
199: PetscFunctionReturn(PETSC_SUCCESS);
200: }
202: /* If we need to get the dofs from a mesh point, or add values into dofs at a mesh point, and there is more than one dof
203: * on that mesh point, we have to be careful about getting/adding everything in the right place.
204: *
205: * With nodal dofs like PETSCDUALSPACELAGRANGE makes, the general approach to calculate the value of dofs associate
206: * with a node A is
207: * - transform the node locations x(A) by the map that takes the mesh point to its reorientation, x' = phi(x(A))
208: * - figure out which node was originally at the location of the transformed point, A' = idx(x')
209: * - if the dofs are not scalars, figure out how to represent the transformed dofs in terms of the basis
210: * of dofs at A' (using pushforward/pullback rules)
211: *
212: * The one sticky point with this approach is the "A' = idx(x')" step: trying to go from real valued coordinates
213: * back to indices. I don't want to rely on floating point tolerances. Additionally, PETSCDUALSPACELAGRANGE may
214: * eventually support quasi-Lagrangian dofs, which could involve quadrature at multiple points, so the location "x(A)"
215: * would be ambiguous.
216: *
217: * So each dof gets an integer value coordinate (nodeIdx in the structure below). The choice of integer coordinates
218: * is somewhat arbitrary, as long as all of the relevant symmetries of the mesh point correspond to *permutations* of
219: * the integer coordinates, which do not depend on numerical precision.
220: *
221: * So
222: *
223: * - DMPlexGetTransitiveClosure_Internal() tells me how an orientation turns into a permutation of the vertices of a
224: * mesh point
225: * - The permutation of the vertices, and the nodeIdx values assigned to them, tells what permutation in index space
226: * is associated with the orientation
227: * - I uses that permutation to get xi' = phi(xi(A)), the integer coordinate of the transformed dof
228: * - I can without numerical issues compute A' = idx(xi')
229: *
230: * Here are some examples of how the process works
231: *
232: * - With a triangle:
233: *
234: * The triangle has the following integer coordinates for vertices, taken from the barycentric triangle
235: *
236: * closure order 2
237: * nodeIdx (0,0,1)
238: * \
239: * +
240: * |\
241: * | \
242: * | \
243: * | \ closure order 1
244: * | \ / nodeIdx (0,1,0)
245: * +-----+
246: * \
247: * closure order 0
248: * nodeIdx (1,0,0)
249: *
250: * If I do DMPlexGetTransitiveClosure_Internal() with orientation 1, the vertices would appear
251: * in the order (1, 2, 0)
252: *
253: * If I list the nodeIdx of each vertex in closure order for orientation 0 (0, 1, 2) and orientation 1 (1, 2, 0), I
254: * see
255: *
256: * orientation 0 | orientation 1
257: *
258: * [0] (1,0,0) [1] (0,1,0)
259: * [1] (0,1,0) [2] (0,0,1)
260: * [2] (0,0,1) [0] (1,0,0)
261: * A B
262: *
263: * In other words, B is the result of a row permutation of A. But, there is also
264: * a column permutation that accomplishes the same result, (2,0,1).
265: *
266: * So if a dof has nodeIdx coordinate (a,b,c), after the transformation its nodeIdx coordinate
267: * is (c,a,b), and the transformed degree of freedom will be a linear combination of dofs
268: * that originally had coordinate (c,a,b).
269: *
270: * - With a quadrilateral:
271: *
272: * The quadrilateral has the following integer coordinates for vertices, taken from concatenating barycentric
273: * coordinates for two segments:
274: *
275: * closure order 3 closure order 2
276: * nodeIdx (1,0,0,1) nodeIdx (0,1,0,1)
277: * \ /
278: * +----+
279: * | |
280: * | |
281: * +----+
282: * / \
283: * closure order 0 closure order 1
284: * nodeIdx (1,0,1,0) nodeIdx (0,1,1,0)
285: *
286: * If I do DMPlexGetTransitiveClosure_Internal() with orientation 1, the vertices would appear
287: * in the order (1, 2, 3, 0)
288: *
289: * If I list the nodeIdx of each vertex in closure order for orientation 0 (0, 1, 2, 3) and
290: * orientation 1 (1, 2, 3, 0), I see
291: *
292: * orientation 0 | orientation 1
293: *
294: * [0] (1,0,1,0) [1] (0,1,1,0)
295: * [1] (0,1,1,0) [2] (0,1,0,1)
296: * [2] (0,1,0,1) [3] (1,0,0,1)
297: * [3] (1,0,0,1) [0] (1,0,1,0)
298: * A B
299: *
300: * The column permutation that accomplishes the same result is (3,2,0,1).
301: *
302: * So if a dof has nodeIdx coordinate (a,b,c,d), after the transformation its nodeIdx coordinate
303: * is (d,c,a,b), and the transformed degree of freedom will be a linear combination of dofs
304: * that originally had coordinate (d,c,a,b).
305: *
306: * Previously PETSCDUALSPACELAGRANGE had hardcoded symmetries for the triangle and quadrilateral,
307: * but this approach will work for any polytope, such as the wedge (triangular prism).
308: */
309: struct _n_PetscLagNodeIndices {
310: PetscInt refct;
311: PetscInt nodeIdxDim;
312: PetscInt nodeVecDim;
313: PetscInt nNodes;
314: PetscInt *nodeIdx; /* for each node an index of size nodeIdxDim */
315: PetscReal *nodeVec; /* for each node a vector of size nodeVecDim */
316: PetscInt *perm; /* if these are vertices, perm takes DMPlex point index to closure order;
317: if these are nodes, perm lists nodes in index revlex order */
318: };
320: /* this is just here so I can access the values in tests/ex1.c outside the library */
321: PetscErrorCode PetscLagNodeIndicesGetData_Internal(PetscLagNodeIndices ni, PetscInt *nodeIdxDim, PetscInt *nodeVecDim, PetscInt *nNodes, const PetscInt *nodeIdx[], const PetscReal *nodeVec[])
322: {
323: PetscFunctionBegin;
324: *nodeIdxDim = ni->nodeIdxDim;
325: *nodeVecDim = ni->nodeVecDim;
326: *nNodes = ni->nNodes;
327: *nodeIdx = ni->nodeIdx;
328: *nodeVec = ni->nodeVec;
329: PetscFunctionReturn(PETSC_SUCCESS);
330: }
332: static PetscErrorCode PetscLagNodeIndicesReference(PetscLagNodeIndices ni)
333: {
334: PetscFunctionBegin;
335: if (ni) ni->refct++;
336: PetscFunctionReturn(PETSC_SUCCESS);
337: }
339: static PetscErrorCode PetscLagNodeIndicesDuplicate(PetscLagNodeIndices ni, PetscLagNodeIndices *niNew)
340: {
341: PetscFunctionBegin;
342: PetscCall(PetscNew(niNew));
343: (*niNew)->refct = 1;
344: (*niNew)->nodeIdxDim = ni->nodeIdxDim;
345: (*niNew)->nodeVecDim = ni->nodeVecDim;
346: (*niNew)->nNodes = ni->nNodes;
347: PetscCall(PetscMalloc1(ni->nNodes * ni->nodeIdxDim, &((*niNew)->nodeIdx)));
348: PetscCall(PetscArraycpy((*niNew)->nodeIdx, ni->nodeIdx, ni->nNodes * ni->nodeIdxDim));
349: PetscCall(PetscMalloc1(ni->nNodes * ni->nodeVecDim, &((*niNew)->nodeVec)));
350: PetscCall(PetscArraycpy((*niNew)->nodeVec, ni->nodeVec, ni->nNodes * ni->nodeVecDim));
351: (*niNew)->perm = NULL;
352: PetscFunctionReturn(PETSC_SUCCESS);
353: }
355: static PetscErrorCode PetscLagNodeIndicesDestroy(PetscLagNodeIndices *ni)
356: {
357: PetscFunctionBegin;
358: if (!(*ni)) PetscFunctionReturn(PETSC_SUCCESS);
359: if (--(*ni)->refct > 0) {
360: *ni = NULL;
361: PetscFunctionReturn(PETSC_SUCCESS);
362: }
363: PetscCall(PetscFree((*ni)->nodeIdx));
364: PetscCall(PetscFree((*ni)->nodeVec));
365: PetscCall(PetscFree((*ni)->perm));
366: PetscCall(PetscFree(*ni));
367: *ni = NULL;
368: PetscFunctionReturn(PETSC_SUCCESS);
369: }
371: /* The vertices are given nodeIdx coordinates (e.g. the corners of the barycentric triangle). Those coordinates are
372: * in some other order, and to understand the effect of different symmetries, we need them to be in closure order.
373: *
374: * If sortIdx is PETSC_FALSE, the coordinates are already in revlex order, otherwise we must sort them
375: * to that order before we do the real work of this function, which is
376: *
377: * - mark the vertices in closure order
378: * - sort them in revlex order
379: * - use the resulting permutation to list the vertex coordinates in closure order
380: */
381: static PetscErrorCode PetscLagNodeIndicesComputeVertexOrder(DM dm, PetscLagNodeIndices ni, PetscBool sortIdx)
382: {
383: PetscInt v, w, vStart, vEnd, c, d;
384: PetscInt nVerts;
385: PetscInt closureSize = 0;
386: PetscInt *closure = NULL;
387: PetscInt *closureOrder;
388: PetscInt *invClosureOrder;
389: PetscInt *revlexOrder;
390: PetscInt *newNodeIdx;
391: PetscInt dim;
392: Vec coordVec;
393: const PetscScalar *coords;
395: PetscFunctionBegin;
396: PetscCall(DMGetDimension(dm, &dim));
397: PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
398: nVerts = vEnd - vStart;
399: PetscCall(PetscMalloc1(nVerts, &closureOrder));
400: PetscCall(PetscMalloc1(nVerts, &invClosureOrder));
401: PetscCall(PetscMalloc1(nVerts, &revlexOrder));
402: if (sortIdx) { /* bubble sort nodeIdx into revlex order */
403: PetscInt nodeIdxDim = ni->nodeIdxDim;
404: PetscInt *idxOrder;
406: PetscCall(PetscMalloc1(nVerts * nodeIdxDim, &newNodeIdx));
407: PetscCall(PetscMalloc1(nVerts, &idxOrder));
408: for (v = 0; v < nVerts; v++) idxOrder[v] = v;
409: for (v = 0; v < nVerts; v++) {
410: for (w = v + 1; w < nVerts; w++) {
411: const PetscInt *iv = &(ni->nodeIdx[idxOrder[v] * nodeIdxDim]);
412: const PetscInt *iw = &(ni->nodeIdx[idxOrder[w] * nodeIdxDim]);
413: PetscInt diff = 0;
415: for (d = nodeIdxDim - 1; d >= 0; d--)
416: if ((diff = (iv[d] - iw[d]))) break;
417: if (diff > 0) {
418: PetscInt swap = idxOrder[v];
420: idxOrder[v] = idxOrder[w];
421: idxOrder[w] = swap;
422: }
423: }
424: }
425: for (v = 0; v < nVerts; v++) {
426: for (d = 0; d < nodeIdxDim; d++) newNodeIdx[v * ni->nodeIdxDim + d] = ni->nodeIdx[idxOrder[v] * nodeIdxDim + d];
427: }
428: PetscCall(PetscFree(ni->nodeIdx));
429: ni->nodeIdx = newNodeIdx;
430: newNodeIdx = NULL;
431: PetscCall(PetscFree(idxOrder));
432: }
433: PetscCall(DMPlexGetTransitiveClosure(dm, 0, PETSC_TRUE, &closureSize, &closure));
434: c = closureSize - nVerts;
435: for (v = 0; v < nVerts; v++) closureOrder[v] = closure[2 * (c + v)] - vStart;
436: for (v = 0; v < nVerts; v++) invClosureOrder[closureOrder[v]] = v;
437: PetscCall(DMPlexRestoreTransitiveClosure(dm, 0, PETSC_TRUE, &closureSize, &closure));
438: PetscCall(DMGetCoordinatesLocal(dm, &coordVec));
439: PetscCall(VecGetArrayRead(coordVec, &coords));
440: /* bubble sort closure vertices by coordinates in revlex order */
441: for (v = 0; v < nVerts; v++) revlexOrder[v] = v;
442: for (v = 0; v < nVerts; v++) {
443: for (w = v + 1; w < nVerts; w++) {
444: const PetscScalar *cv = &coords[closureOrder[revlexOrder[v]] * dim];
445: const PetscScalar *cw = &coords[closureOrder[revlexOrder[w]] * dim];
446: PetscReal diff = 0;
448: for (d = dim - 1; d >= 0; d--)
449: if ((diff = PetscRealPart(cv[d] - cw[d])) != 0.) break;
450: if (diff > 0.) {
451: PetscInt swap = revlexOrder[v];
453: revlexOrder[v] = revlexOrder[w];
454: revlexOrder[w] = swap;
455: }
456: }
457: }
458: PetscCall(VecRestoreArrayRead(coordVec, &coords));
459: PetscCall(PetscMalloc1(ni->nodeIdxDim * nVerts, &newNodeIdx));
460: /* reorder nodeIdx to be in closure order */
461: for (v = 0; v < nVerts; v++) {
462: for (d = 0; d < ni->nodeIdxDim; d++) newNodeIdx[revlexOrder[v] * ni->nodeIdxDim + d] = ni->nodeIdx[v * ni->nodeIdxDim + d];
463: }
464: PetscCall(PetscFree(ni->nodeIdx));
465: ni->nodeIdx = newNodeIdx;
466: ni->perm = invClosureOrder;
467: PetscCall(PetscFree(revlexOrder));
468: PetscCall(PetscFree(closureOrder));
469: PetscFunctionReturn(PETSC_SUCCESS);
470: }
472: /* the coordinates of the simplex vertices are the corners of the barycentric simplex.
473: * When we stack them on top of each other in revlex order, they look like the identity matrix */
474: static PetscErrorCode PetscLagNodeIndicesCreateSimplexVertices(DM dm, PetscLagNodeIndices *nodeIndices)
475: {
476: PetscLagNodeIndices ni;
477: PetscInt dim, d;
479: PetscFunctionBegin;
480: PetscCall(PetscNew(&ni));
481: PetscCall(DMGetDimension(dm, &dim));
482: ni->nodeIdxDim = dim + 1;
483: ni->nodeVecDim = 0;
484: ni->nNodes = dim + 1;
485: ni->refct = 1;
486: PetscCall(PetscCalloc1((dim + 1) * (dim + 1), &(ni->nodeIdx)));
487: for (d = 0; d < dim + 1; d++) ni->nodeIdx[d * (dim + 2)] = 1;
488: PetscCall(PetscLagNodeIndicesComputeVertexOrder(dm, ni, PETSC_FALSE));
489: *nodeIndices = ni;
490: PetscFunctionReturn(PETSC_SUCCESS);
491: }
493: /* A polytope that is a tensor product of a facet and a segment.
494: * We take whatever coordinate system was being used for the facet
495: * and we concatenate the barycentric coordinates for the vertices
496: * at the end of the segment, (1,0) and (0,1), to get a coordinate
497: * system for the tensor product element */
498: static PetscErrorCode PetscLagNodeIndicesCreateTensorVertices(DM dm, PetscLagNodeIndices facetni, PetscLagNodeIndices *nodeIndices)
499: {
500: PetscLagNodeIndices ni;
501: PetscInt nodeIdxDim, subNodeIdxDim = facetni->nodeIdxDim;
502: PetscInt nVerts, nSubVerts = facetni->nNodes;
503: PetscInt dim, d, e, f, g;
505: PetscFunctionBegin;
506: PetscCall(PetscNew(&ni));
507: PetscCall(DMGetDimension(dm, &dim));
508: ni->nodeIdxDim = nodeIdxDim = subNodeIdxDim + 2;
509: ni->nodeVecDim = 0;
510: ni->nNodes = nVerts = 2 * nSubVerts;
511: ni->refct = 1;
512: PetscCall(PetscCalloc1(nodeIdxDim * nVerts, &(ni->nodeIdx)));
513: for (f = 0, d = 0; d < 2; d++) {
514: for (e = 0; e < nSubVerts; e++, f++) {
515: for (g = 0; g < subNodeIdxDim; g++) ni->nodeIdx[f * nodeIdxDim + g] = facetni->nodeIdx[e * subNodeIdxDim + g];
516: ni->nodeIdx[f * nodeIdxDim + subNodeIdxDim] = (1 - d);
517: ni->nodeIdx[f * nodeIdxDim + subNodeIdxDim + 1] = d;
518: }
519: }
520: PetscCall(PetscLagNodeIndicesComputeVertexOrder(dm, ni, PETSC_TRUE));
521: *nodeIndices = ni;
522: PetscFunctionReturn(PETSC_SUCCESS);
523: }
525: /* This helps us compute symmetries, and it also helps us compute coordinates for dofs that are being pushed
526: * forward from a boundary mesh point.
527: *
528: * Input:
529: *
530: * dm - the target reference cell where we want new coordinates and dof directions to be valid
531: * vert - the vertex coordinate system for the target reference cell
532: * p - the point in the target reference cell that the dofs are coming from
533: * vertp - the vertex coordinate system for p's reference cell
534: * ornt - the resulting coordinates and dof vectors will be for p under this orientation
535: * nodep - the node coordinates and dof vectors in p's reference cell
536: * formDegree - the form degree that the dofs transform as
537: *
538: * Output:
539: *
540: * pfNodeIdx - the node coordinates for p's dofs, in the dm reference cell, from the ornt perspective
541: * pfNodeVec - the node dof vectors for p's dofs, in the dm reference cell, from the ornt perspective
542: */
543: static PetscErrorCode PetscLagNodeIndicesPushForward(DM dm, PetscLagNodeIndices vert, PetscInt p, PetscLagNodeIndices vertp, PetscLagNodeIndices nodep, PetscInt ornt, PetscInt formDegree, PetscInt pfNodeIdx[], PetscReal pfNodeVec[])
544: {
545: PetscInt *closureVerts;
546: PetscInt closureSize = 0;
547: PetscInt *closure = NULL;
548: PetscInt dim, pdim, c, i, j, k, n, v, vStart, vEnd;
549: PetscInt nSubVert = vertp->nNodes;
550: PetscInt nodeIdxDim = vert->nodeIdxDim;
551: PetscInt subNodeIdxDim = vertp->nodeIdxDim;
552: PetscInt nNodes = nodep->nNodes;
553: const PetscInt *vertIdx = vert->nodeIdx;
554: const PetscInt *subVertIdx = vertp->nodeIdx;
555: const PetscInt *nodeIdx = nodep->nodeIdx;
556: const PetscReal *nodeVec = nodep->nodeVec;
557: PetscReal *J, *Jstar;
558: PetscReal detJ;
559: PetscInt depth, pdepth, Nk, pNk;
560: Vec coordVec;
561: PetscScalar *newCoords = NULL;
562: const PetscScalar *oldCoords = NULL;
564: PetscFunctionBegin;
565: PetscCall(DMGetDimension(dm, &dim));
566: PetscCall(DMPlexGetDepth(dm, &depth));
567: PetscCall(DMGetCoordinatesLocal(dm, &coordVec));
568: PetscCall(DMPlexGetPointDepth(dm, p, &pdepth));
569: pdim = pdepth != depth ? pdepth != 0 ? pdepth : 0 : dim;
570: PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
571: PetscCall(DMGetWorkArray(dm, nSubVert, MPIU_INT, &closureVerts));
572: PetscCall(DMPlexGetTransitiveClosure_Internal(dm, p, ornt, PETSC_TRUE, &closureSize, &closure));
573: c = closureSize - nSubVert;
574: /* we want which cell closure indices the closure of this point corresponds to */
575: for (v = 0; v < nSubVert; v++) closureVerts[v] = vert->perm[closure[2 * (c + v)] - vStart];
576: PetscCall(DMPlexRestoreTransitiveClosure(dm, p, PETSC_TRUE, &closureSize, &closure));
577: /* push forward indices */
578: for (i = 0; i < nodeIdxDim; i++) { /* for every component of the target index space */
579: /* check if this is a component that all vertices around this point have in common */
580: for (j = 1; j < nSubVert; j++) {
581: if (vertIdx[closureVerts[j] * nodeIdxDim + i] != vertIdx[closureVerts[0] * nodeIdxDim + i]) break;
582: }
583: if (j == nSubVert) { /* all vertices have this component in common, directly copy to output */
584: PetscInt val = vertIdx[closureVerts[0] * nodeIdxDim + i];
585: for (n = 0; n < nNodes; n++) pfNodeIdx[n * nodeIdxDim + i] = val;
586: } else {
587: PetscInt subi = -1;
588: /* there must be a component in vertp that looks the same */
589: for (k = 0; k < subNodeIdxDim; k++) {
590: for (j = 0; j < nSubVert; j++) {
591: if (vertIdx[closureVerts[j] * nodeIdxDim + i] != subVertIdx[j * subNodeIdxDim + k]) break;
592: }
593: if (j == nSubVert) {
594: subi = k;
595: break;
596: }
597: }
598: PetscCheck(subi >= 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Did not find matching coordinate");
599: /* that component in the vertp system becomes component i in the vert system for each dof */
600: for (n = 0; n < nNodes; n++) pfNodeIdx[n * nodeIdxDim + i] = nodeIdx[n * subNodeIdxDim + subi];
601: }
602: }
603: /* push forward vectors */
604: PetscCall(DMGetWorkArray(dm, dim * dim, MPIU_REAL, &J));
605: if (ornt != 0) { /* temporarily change the coordinate vector so
606: DMPlexComputeCellGeometryAffineFEM gives us the Jacobian we want */
607: PetscInt closureSize2 = 0;
608: PetscInt *closure2 = NULL;
610: PetscCall(DMPlexGetTransitiveClosure_Internal(dm, p, 0, PETSC_TRUE, &closureSize2, &closure2));
611: PetscCall(PetscMalloc1(dim * nSubVert, &newCoords));
612: PetscCall(VecGetArrayRead(coordVec, &oldCoords));
613: for (v = 0; v < nSubVert; v++) {
614: PetscInt d;
615: for (d = 0; d < dim; d++) newCoords[(closure2[2 * (c + v)] - vStart) * dim + d] = oldCoords[closureVerts[v] * dim + d];
616: }
617: PetscCall(VecRestoreArrayRead(coordVec, &oldCoords));
618: PetscCall(DMPlexRestoreTransitiveClosure(dm, p, PETSC_TRUE, &closureSize2, &closure2));
619: PetscCall(VecPlaceArray(coordVec, newCoords));
620: }
621: PetscCall(DMPlexComputeCellGeometryAffineFEM(dm, p, NULL, J, NULL, &detJ));
622: if (ornt != 0) {
623: PetscCall(VecResetArray(coordVec));
624: PetscCall(PetscFree(newCoords));
625: }
626: PetscCall(DMRestoreWorkArray(dm, nSubVert, MPIU_INT, &closureVerts));
627: /* compactify */
628: for (i = 0; i < dim; i++)
629: for (j = 0; j < pdim; j++) J[i * pdim + j] = J[i * dim + j];
630: /* We have the Jacobian mapping the point's reference cell to this reference cell:
631: * pulling back a function to the point and applying the dof is what we want,
632: * so we get the pullback matrix and multiply the dof by that matrix on the right */
633: PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(formDegree), &Nk));
634: PetscCall(PetscDTBinomialInt(pdim, PetscAbsInt(formDegree), &pNk));
635: PetscCall(DMGetWorkArray(dm, pNk * Nk, MPIU_REAL, &Jstar));
636: PetscCall(PetscDTAltVPullbackMatrix(pdim, dim, J, formDegree, Jstar));
637: for (n = 0; n < nNodes; n++) {
638: for (i = 0; i < Nk; i++) {
639: PetscReal val = 0.;
640: for (j = 0; j < pNk; j++) val += nodeVec[n * pNk + j] * Jstar[j * Nk + i];
641: pfNodeVec[n * Nk + i] = val;
642: }
643: }
644: PetscCall(DMRestoreWorkArray(dm, pNk * Nk, MPIU_REAL, &Jstar));
645: PetscCall(DMRestoreWorkArray(dm, dim * dim, MPIU_REAL, &J));
646: PetscFunctionReturn(PETSC_SUCCESS);
647: }
649: /* given to sets of nodes, take the tensor product, where the product of the dof indices is concatenation and the
650: * product of the dof vectors is the wedge product */
651: static PetscErrorCode PetscLagNodeIndicesTensor(PetscLagNodeIndices tracei, PetscInt dimT, PetscInt kT, PetscLagNodeIndices fiberi, PetscInt dimF, PetscInt kF, PetscLagNodeIndices *nodeIndices)
652: {
653: PetscInt dim = dimT + dimF;
654: PetscInt nodeIdxDim, nNodes;
655: PetscInt formDegree = kT + kF;
656: PetscInt Nk, NkT, NkF;
657: PetscInt MkT, MkF;
658: PetscLagNodeIndices ni;
659: PetscInt i, j, l;
660: PetscReal *projF, *projT;
661: PetscReal *projFstar, *projTstar;
662: PetscReal *workF, *workF2, *workT, *workT2, *work, *work2;
663: PetscReal *wedgeMat;
664: PetscReal sign;
666: PetscFunctionBegin;
667: PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(formDegree), &Nk));
668: PetscCall(PetscDTBinomialInt(dimT, PetscAbsInt(kT), &NkT));
669: PetscCall(PetscDTBinomialInt(dimF, PetscAbsInt(kF), &NkF));
670: PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(kT), &MkT));
671: PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(kF), &MkF));
672: PetscCall(PetscNew(&ni));
673: ni->nodeIdxDim = nodeIdxDim = tracei->nodeIdxDim + fiberi->nodeIdxDim;
674: ni->nodeVecDim = Nk;
675: ni->nNodes = nNodes = tracei->nNodes * fiberi->nNodes;
676: ni->refct = 1;
677: PetscCall(PetscMalloc1(nNodes * nodeIdxDim, &(ni->nodeIdx)));
678: /* first concatenate the indices */
679: for (l = 0, j = 0; j < fiberi->nNodes; j++) {
680: for (i = 0; i < tracei->nNodes; i++, l++) {
681: PetscInt m, n = 0;
683: for (m = 0; m < tracei->nodeIdxDim; m++) ni->nodeIdx[l * nodeIdxDim + n++] = tracei->nodeIdx[i * tracei->nodeIdxDim + m];
684: for (m = 0; m < fiberi->nodeIdxDim; m++) ni->nodeIdx[l * nodeIdxDim + n++] = fiberi->nodeIdx[j * fiberi->nodeIdxDim + m];
685: }
686: }
688: /* now wedge together the push-forward vectors */
689: PetscCall(PetscMalloc1(nNodes * Nk, &(ni->nodeVec)));
690: PetscCall(PetscCalloc2(dimT * dim, &projT, dimF * dim, &projF));
691: for (i = 0; i < dimT; i++) projT[i * (dim + 1)] = 1.;
692: for (i = 0; i < dimF; i++) projF[i * (dim + dimT + 1) + dimT] = 1.;
693: PetscCall(PetscMalloc2(MkT * NkT, &projTstar, MkF * NkF, &projFstar));
694: PetscCall(PetscDTAltVPullbackMatrix(dim, dimT, projT, kT, projTstar));
695: PetscCall(PetscDTAltVPullbackMatrix(dim, dimF, projF, kF, projFstar));
696: PetscCall(PetscMalloc6(MkT, &workT, MkT, &workT2, MkF, &workF, MkF, &workF2, Nk, &work, Nk, &work2));
697: PetscCall(PetscMalloc1(Nk * MkT, &wedgeMat));
698: sign = (PetscAbsInt(kT * kF) & 1) ? -1. : 1.;
699: for (l = 0, j = 0; j < fiberi->nNodes; j++) {
700: PetscInt d, e;
702: /* push forward fiber k-form */
703: for (d = 0; d < MkF; d++) {
704: PetscReal val = 0.;
705: for (e = 0; e < NkF; e++) val += projFstar[d * NkF + e] * fiberi->nodeVec[j * NkF + e];
706: workF[d] = val;
707: }
708: /* Hodge star to proper form if necessary */
709: if (kF < 0) {
710: for (d = 0; d < MkF; d++) workF2[d] = workF[d];
711: PetscCall(PetscDTAltVStar(dim, PetscAbsInt(kF), 1, workF2, workF));
712: }
713: /* Compute the matrix that wedges this form with one of the trace k-form */
714: PetscCall(PetscDTAltVWedgeMatrix(dim, PetscAbsInt(kF), PetscAbsInt(kT), workF, wedgeMat));
715: for (i = 0; i < tracei->nNodes; i++, l++) {
716: /* push forward trace k-form */
717: for (d = 0; d < MkT; d++) {
718: PetscReal val = 0.;
719: for (e = 0; e < NkT; e++) val += projTstar[d * NkT + e] * tracei->nodeVec[i * NkT + e];
720: workT[d] = val;
721: }
722: /* Hodge star to proper form if necessary */
723: if (kT < 0) {
724: for (d = 0; d < MkT; d++) workT2[d] = workT[d];
725: PetscCall(PetscDTAltVStar(dim, PetscAbsInt(kT), 1, workT2, workT));
726: }
727: /* compute the wedge product of the push-forward trace form and firer forms */
728: for (d = 0; d < Nk; d++) {
729: PetscReal val = 0.;
730: for (e = 0; e < MkT; e++) val += wedgeMat[d * MkT + e] * workT[e];
731: work[d] = val;
732: }
733: /* inverse Hodge star from proper form if necessary */
734: if (formDegree < 0) {
735: for (d = 0; d < Nk; d++) work2[d] = work[d];
736: PetscCall(PetscDTAltVStar(dim, PetscAbsInt(formDegree), -1, work2, work));
737: }
738: /* insert into the array (adjusting for sign) */
739: for (d = 0; d < Nk; d++) ni->nodeVec[l * Nk + d] = sign * work[d];
740: }
741: }
742: PetscCall(PetscFree(wedgeMat));
743: PetscCall(PetscFree6(workT, workT2, workF, workF2, work, work2));
744: PetscCall(PetscFree2(projTstar, projFstar));
745: PetscCall(PetscFree2(projT, projF));
746: *nodeIndices = ni;
747: PetscFunctionReturn(PETSC_SUCCESS);
748: }
750: /* simple union of two sets of nodes */
751: static PetscErrorCode PetscLagNodeIndicesMerge(PetscLagNodeIndices niA, PetscLagNodeIndices niB, PetscLagNodeIndices *nodeIndices)
752: {
753: PetscLagNodeIndices ni;
754: PetscInt nodeIdxDim, nodeVecDim, nNodes;
756: PetscFunctionBegin;
757: PetscCall(PetscNew(&ni));
758: ni->nodeIdxDim = nodeIdxDim = niA->nodeIdxDim;
759: PetscCheck(niB->nodeIdxDim == nodeIdxDim, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Cannot merge PetscLagNodeIndices with different nodeIdxDim");
760: ni->nodeVecDim = nodeVecDim = niA->nodeVecDim;
761: PetscCheck(niB->nodeVecDim == nodeVecDim, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Cannot merge PetscLagNodeIndices with different nodeVecDim");
762: ni->nNodes = nNodes = niA->nNodes + niB->nNodes;
763: ni->refct = 1;
764: PetscCall(PetscMalloc1(nNodes * nodeIdxDim, &(ni->nodeIdx)));
765: PetscCall(PetscMalloc1(nNodes * nodeVecDim, &(ni->nodeVec)));
766: PetscCall(PetscArraycpy(ni->nodeIdx, niA->nodeIdx, niA->nNodes * nodeIdxDim));
767: PetscCall(PetscArraycpy(ni->nodeVec, niA->nodeVec, niA->nNodes * nodeVecDim));
768: PetscCall(PetscArraycpy(&(ni->nodeIdx[niA->nNodes * nodeIdxDim]), niB->nodeIdx, niB->nNodes * nodeIdxDim));
769: PetscCall(PetscArraycpy(&(ni->nodeVec[niA->nNodes * nodeVecDim]), niB->nodeVec, niB->nNodes * nodeVecDim));
770: *nodeIndices = ni;
771: PetscFunctionReturn(PETSC_SUCCESS);
772: }
774: #define PETSCTUPINTCOMPREVLEX(N) \
775: static int PetscConcat_(PetscTupIntCompRevlex_, N)(const void *a, const void *b) \
776: { \
777: const PetscInt *A = (const PetscInt *)a; \
778: const PetscInt *B = (const PetscInt *)b; \
779: int i; \
780: PetscInt diff = 0; \
781: for (i = 0; i < N; i++) { \
782: diff = A[N - i] - B[N - i]; \
783: if (diff) break; \
784: } \
785: return (diff <= 0) ? (diff < 0) ? -1 : 0 : 1; \
786: }
788: PETSCTUPINTCOMPREVLEX(3)
789: PETSCTUPINTCOMPREVLEX(4)
790: PETSCTUPINTCOMPREVLEX(5)
791: PETSCTUPINTCOMPREVLEX(6)
792: PETSCTUPINTCOMPREVLEX(7)
794: static int PetscTupIntCompRevlex_N(const void *a, const void *b)
795: {
796: const PetscInt *A = (const PetscInt *)a;
797: const PetscInt *B = (const PetscInt *)b;
798: int i;
799: int N = A[0];
800: PetscInt diff = 0;
801: for (i = 0; i < N; i++) {
802: diff = A[N - i] - B[N - i];
803: if (diff) break;
804: }
805: return (diff <= 0) ? (diff < 0) ? -1 : 0 : 1;
806: }
808: /* The nodes are not necessarily in revlex order wrt nodeIdx: get the permutation
809: * that puts them in that order */
810: static PetscErrorCode PetscLagNodeIndicesGetPermutation(PetscLagNodeIndices ni, PetscInt *perm[])
811: {
812: PetscFunctionBegin;
813: if (!(ni->perm)) {
814: PetscInt *sorter;
815: PetscInt m = ni->nNodes;
816: PetscInt nodeIdxDim = ni->nodeIdxDim;
817: PetscInt i, j, k, l;
818: PetscInt *prm;
819: int (*comp)(const void *, const void *);
821: PetscCall(PetscMalloc1((nodeIdxDim + 2) * m, &sorter));
822: for (k = 0, l = 0, i = 0; i < m; i++) {
823: sorter[k++] = nodeIdxDim + 1;
824: sorter[k++] = i;
825: for (j = 0; j < nodeIdxDim; j++) sorter[k++] = ni->nodeIdx[l++];
826: }
827: switch (nodeIdxDim) {
828: case 2:
829: comp = PetscTupIntCompRevlex_3;
830: break;
831: case 3:
832: comp = PetscTupIntCompRevlex_4;
833: break;
834: case 4:
835: comp = PetscTupIntCompRevlex_5;
836: break;
837: case 5:
838: comp = PetscTupIntCompRevlex_6;
839: break;
840: case 6:
841: comp = PetscTupIntCompRevlex_7;
842: break;
843: default:
844: comp = PetscTupIntCompRevlex_N;
845: break;
846: }
847: qsort(sorter, m, (nodeIdxDim + 2) * sizeof(PetscInt), comp);
848: PetscCall(PetscMalloc1(m, &prm));
849: for (i = 0; i < m; i++) prm[i] = sorter[(nodeIdxDim + 2) * i + 1];
850: ni->perm = prm;
851: PetscCall(PetscFree(sorter));
852: }
853: *perm = ni->perm;
854: PetscFunctionReturn(PETSC_SUCCESS);
855: }
857: static PetscErrorCode PetscDualSpaceDestroy_Lagrange(PetscDualSpace sp)
858: {
859: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
861: PetscFunctionBegin;
862: if (lag->symperms) {
863: PetscInt **selfSyms = lag->symperms[0];
865: if (selfSyms) {
866: PetscInt i, **allocated = &selfSyms[-lag->selfSymOff];
868: for (i = 0; i < lag->numSelfSym; i++) PetscCall(PetscFree(allocated[i]));
869: PetscCall(PetscFree(allocated));
870: }
871: PetscCall(PetscFree(lag->symperms));
872: }
873: if (lag->symflips) {
874: PetscScalar **selfSyms = lag->symflips[0];
876: if (selfSyms) {
877: PetscInt i;
878: PetscScalar **allocated = &selfSyms[-lag->selfSymOff];
880: for (i = 0; i < lag->numSelfSym; i++) PetscCall(PetscFree(allocated[i]));
881: PetscCall(PetscFree(allocated));
882: }
883: PetscCall(PetscFree(lag->symflips));
884: }
885: PetscCall(Petsc1DNodeFamilyDestroy(&(lag->nodeFamily)));
886: PetscCall(PetscLagNodeIndicesDestroy(&(lag->vertIndices)));
887: PetscCall(PetscLagNodeIndicesDestroy(&(lag->intNodeIndices)));
888: PetscCall(PetscLagNodeIndicesDestroy(&(lag->allNodeIndices)));
889: PetscCall(PetscFree(lag));
890: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetContinuity_C", NULL));
891: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetContinuity_C", NULL));
892: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetTensor_C", NULL));
893: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetTensor_C", NULL));
894: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetTrimmed_C", NULL));
895: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetTrimmed_C", NULL));
896: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetNodeType_C", NULL));
897: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetNodeType_C", NULL));
898: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetUseMoments_C", NULL));
899: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetUseMoments_C", NULL));
900: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetMomentOrder_C", NULL));
901: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetMomentOrder_C", NULL));
902: PetscFunctionReturn(PETSC_SUCCESS);
903: }
905: static PetscErrorCode PetscDualSpaceLagrangeView_Ascii(PetscDualSpace sp, PetscViewer viewer)
906: {
907: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
909: PetscFunctionBegin;
910: PetscCall(PetscViewerASCIIPrintf(viewer, "%s %s%sLagrange dual space\n", lag->continuous ? "Continuous" : "Discontinuous", lag->tensorSpace ? "tensor " : "", lag->trimmed ? "trimmed " : ""));
911: PetscFunctionReturn(PETSC_SUCCESS);
912: }
914: static PetscErrorCode PetscDualSpaceView_Lagrange(PetscDualSpace sp, PetscViewer viewer)
915: {
916: PetscBool iascii;
918: PetscFunctionBegin;
921: PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
922: if (iascii) PetscCall(PetscDualSpaceLagrangeView_Ascii(sp, viewer));
923: PetscFunctionReturn(PETSC_SUCCESS);
924: }
926: static PetscErrorCode PetscDualSpaceSetFromOptions_Lagrange(PetscDualSpace sp, PetscOptionItems *PetscOptionsObject)
927: {
928: PetscBool continuous, tensor, trimmed, flg, flg2, flg3;
929: PetscDTNodeType nodeType;
930: PetscReal nodeExponent;
931: PetscInt momentOrder;
932: PetscBool nodeEndpoints, useMoments;
934: PetscFunctionBegin;
935: PetscCall(PetscDualSpaceLagrangeGetContinuity(sp, &continuous));
936: PetscCall(PetscDualSpaceLagrangeGetTensor(sp, &tensor));
937: PetscCall(PetscDualSpaceLagrangeGetTrimmed(sp, &trimmed));
938: PetscCall(PetscDualSpaceLagrangeGetNodeType(sp, &nodeType, &nodeEndpoints, &nodeExponent));
939: if (nodeType == PETSCDTNODES_DEFAULT) nodeType = PETSCDTNODES_GAUSSJACOBI;
940: PetscCall(PetscDualSpaceLagrangeGetUseMoments(sp, &useMoments));
941: PetscCall(PetscDualSpaceLagrangeGetMomentOrder(sp, &momentOrder));
942: PetscOptionsHeadBegin(PetscOptionsObject, "PetscDualSpace Lagrange Options");
943: PetscCall(PetscOptionsBool("-petscdualspace_lagrange_continuity", "Flag for continuous element", "PetscDualSpaceLagrangeSetContinuity", continuous, &continuous, &flg));
944: if (flg) PetscCall(PetscDualSpaceLagrangeSetContinuity(sp, continuous));
945: PetscCall(PetscOptionsBool("-petscdualspace_lagrange_tensor", "Flag for tensor dual space", "PetscDualSpaceLagrangeSetTensor", tensor, &tensor, &flg));
946: if (flg) PetscCall(PetscDualSpaceLagrangeSetTensor(sp, tensor));
947: PetscCall(PetscOptionsBool("-petscdualspace_lagrange_trimmed", "Flag for trimmed dual space", "PetscDualSpaceLagrangeSetTrimmed", trimmed, &trimmed, &flg));
948: if (flg) PetscCall(PetscDualSpaceLagrangeSetTrimmed(sp, trimmed));
949: PetscCall(PetscOptionsEnum("-petscdualspace_lagrange_node_type", "Lagrange node location type", "PetscDualSpaceLagrangeSetNodeType", PetscDTNodeTypes, (PetscEnum)nodeType, (PetscEnum *)&nodeType, &flg));
950: PetscCall(PetscOptionsBool("-petscdualspace_lagrange_node_endpoints", "Flag for nodes that include endpoints", "PetscDualSpaceLagrangeSetNodeType", nodeEndpoints, &nodeEndpoints, &flg2));
951: flg3 = PETSC_FALSE;
952: if (nodeType == PETSCDTNODES_GAUSSJACOBI) PetscCall(PetscOptionsReal("-petscdualspace_lagrange_node_exponent", "Gauss-Jacobi weight function exponent", "PetscDualSpaceLagrangeSetNodeType", nodeExponent, &nodeExponent, &flg3));
953: if (flg || flg2 || flg3) PetscCall(PetscDualSpaceLagrangeSetNodeType(sp, nodeType, nodeEndpoints, nodeExponent));
954: PetscCall(PetscOptionsBool("-petscdualspace_lagrange_use_moments", "Use moments (where appropriate) for functionals", "PetscDualSpaceLagrangeSetUseMoments", useMoments, &useMoments, &flg));
955: if (flg) PetscCall(PetscDualSpaceLagrangeSetUseMoments(sp, useMoments));
956: PetscCall(PetscOptionsInt("-petscdualspace_lagrange_moment_order", "Quadrature order for moment functionals", "PetscDualSpaceLagrangeSetMomentOrder", momentOrder, &momentOrder, &flg));
957: if (flg) PetscCall(PetscDualSpaceLagrangeSetMomentOrder(sp, momentOrder));
958: PetscOptionsHeadEnd();
959: PetscFunctionReturn(PETSC_SUCCESS);
960: }
962: static PetscErrorCode PetscDualSpaceDuplicate_Lagrange(PetscDualSpace sp, PetscDualSpace spNew)
963: {
964: PetscBool cont, tensor, trimmed, boundary;
965: PetscDTNodeType nodeType;
966: PetscReal exponent;
967: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
969: PetscFunctionBegin;
970: PetscCall(PetscDualSpaceLagrangeGetContinuity(sp, &cont));
971: PetscCall(PetscDualSpaceLagrangeSetContinuity(spNew, cont));
972: PetscCall(PetscDualSpaceLagrangeGetTensor(sp, &tensor));
973: PetscCall(PetscDualSpaceLagrangeSetTensor(spNew, tensor));
974: PetscCall(PetscDualSpaceLagrangeGetTrimmed(sp, &trimmed));
975: PetscCall(PetscDualSpaceLagrangeSetTrimmed(spNew, trimmed));
976: PetscCall(PetscDualSpaceLagrangeGetNodeType(sp, &nodeType, &boundary, &exponent));
977: PetscCall(PetscDualSpaceLagrangeSetNodeType(spNew, nodeType, boundary, exponent));
978: if (lag->nodeFamily) {
979: PetscDualSpace_Lag *lagnew = (PetscDualSpace_Lag *)spNew->data;
981: PetscCall(Petsc1DNodeFamilyReference(lag->nodeFamily));
982: lagnew->nodeFamily = lag->nodeFamily;
983: }
984: PetscFunctionReturn(PETSC_SUCCESS);
985: }
987: /* for making tensor product spaces: take a dual space and product a segment space that has all the same
988: * specifications (trimmed, continuous, order, node set), except for the form degree */
989: static PetscErrorCode PetscDualSpaceCreateEdgeSubspace_Lagrange(PetscDualSpace sp, PetscInt order, PetscInt k, PetscInt Nc, PetscBool interiorOnly, PetscDualSpace *bdsp)
990: {
991: DM K;
992: PetscDualSpace_Lag *newlag;
994: PetscFunctionBegin;
995: PetscCall(PetscDualSpaceDuplicate(sp, bdsp));
996: PetscCall(PetscDualSpaceSetFormDegree(*bdsp, k));
997: PetscCall(DMPlexCreateReferenceCell(PETSC_COMM_SELF, DMPolytopeTypeSimpleShape(1, PETSC_TRUE), &K));
998: PetscCall(PetscDualSpaceSetDM(*bdsp, K));
999: PetscCall(DMDestroy(&K));
1000: PetscCall(PetscDualSpaceSetOrder(*bdsp, order));
1001: PetscCall(PetscDualSpaceSetNumComponents(*bdsp, Nc));
1002: newlag = (PetscDualSpace_Lag *)(*bdsp)->data;
1003: newlag->interiorOnly = interiorOnly;
1004: PetscCall(PetscDualSpaceSetUp(*bdsp));
1005: PetscFunctionReturn(PETSC_SUCCESS);
1006: }
1008: /* just the points, weights aren't handled */
1009: static PetscErrorCode PetscQuadratureCreateTensor(PetscQuadrature trace, PetscQuadrature fiber, PetscQuadrature *product)
1010: {
1011: PetscInt dimTrace, dimFiber;
1012: PetscInt numPointsTrace, numPointsFiber;
1013: PetscInt dim, numPoints;
1014: const PetscReal *pointsTrace;
1015: const PetscReal *pointsFiber;
1016: PetscReal *points;
1017: PetscInt i, j, k, p;
1019: PetscFunctionBegin;
1020: PetscCall(PetscQuadratureGetData(trace, &dimTrace, NULL, &numPointsTrace, &pointsTrace, NULL));
1021: PetscCall(PetscQuadratureGetData(fiber, &dimFiber, NULL, &numPointsFiber, &pointsFiber, NULL));
1022: dim = dimTrace + dimFiber;
1023: numPoints = numPointsFiber * numPointsTrace;
1024: PetscCall(PetscMalloc1(numPoints * dim, &points));
1025: for (p = 0, j = 0; j < numPointsFiber; j++) {
1026: for (i = 0; i < numPointsTrace; i++, p++) {
1027: for (k = 0; k < dimTrace; k++) points[p * dim + k] = pointsTrace[i * dimTrace + k];
1028: for (k = 0; k < dimFiber; k++) points[p * dim + dimTrace + k] = pointsFiber[j * dimFiber + k];
1029: }
1030: }
1031: PetscCall(PetscQuadratureCreate(PETSC_COMM_SELF, product));
1032: PetscCall(PetscQuadratureSetData(*product, dim, 0, numPoints, points, NULL));
1033: PetscFunctionReturn(PETSC_SUCCESS);
1034: }
1036: /* Kronecker tensor product where matrix is considered a matrix of k-forms, so that
1037: * the entries in the product matrix are wedge products of the entries in the original matrices */
1038: static PetscErrorCode MatTensorAltV(Mat trace, Mat fiber, PetscInt dimTrace, PetscInt kTrace, PetscInt dimFiber, PetscInt kFiber, Mat *product)
1039: {
1040: PetscInt mTrace, nTrace, mFiber, nFiber, m, n, k, i, j, l;
1041: PetscInt dim, NkTrace, NkFiber, Nk;
1042: PetscInt dT, dF;
1043: PetscInt *nnzTrace, *nnzFiber, *nnz;
1044: PetscInt iT, iF, jT, jF, il, jl;
1045: PetscReal *workT, *workT2, *workF, *workF2, *work, *workstar;
1046: PetscReal *projT, *projF;
1047: PetscReal *projTstar, *projFstar;
1048: PetscReal *wedgeMat;
1049: PetscReal sign;
1050: PetscScalar *workS;
1051: Mat prod;
1052: /* this produces dof groups that look like the identity */
1054: PetscFunctionBegin;
1055: PetscCall(MatGetSize(trace, &mTrace, &nTrace));
1056: PetscCall(PetscDTBinomialInt(dimTrace, PetscAbsInt(kTrace), &NkTrace));
1057: PetscCheck(nTrace % NkTrace == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "point value space of trace matrix is not a multiple of k-form size");
1058: PetscCall(MatGetSize(fiber, &mFiber, &nFiber));
1059: PetscCall(PetscDTBinomialInt(dimFiber, PetscAbsInt(kFiber), &NkFiber));
1060: PetscCheck(nFiber % NkFiber == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "point value space of fiber matrix is not a multiple of k-form size");
1061: PetscCall(PetscMalloc2(mTrace, &nnzTrace, mFiber, &nnzFiber));
1062: for (i = 0; i < mTrace; i++) {
1063: PetscCall(MatGetRow(trace, i, &(nnzTrace[i]), NULL, NULL));
1064: PetscCheck(nnzTrace[i] % NkTrace == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "nonzeros in trace matrix are not in k-form size blocks");
1065: }
1066: for (i = 0; i < mFiber; i++) {
1067: PetscCall(MatGetRow(fiber, i, &(nnzFiber[i]), NULL, NULL));
1068: PetscCheck(nnzFiber[i] % NkFiber == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "nonzeros in fiber matrix are not in k-form size blocks");
1069: }
1070: dim = dimTrace + dimFiber;
1071: k = kFiber + kTrace;
1072: PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(k), &Nk));
1073: m = mTrace * mFiber;
1074: PetscCall(PetscMalloc1(m, &nnz));
1075: for (l = 0, j = 0; j < mFiber; j++)
1076: for (i = 0; i < mTrace; i++, l++) nnz[l] = (nnzTrace[i] / NkTrace) * (nnzFiber[j] / NkFiber) * Nk;
1077: n = (nTrace / NkTrace) * (nFiber / NkFiber) * Nk;
1078: PetscCall(MatCreateSeqAIJ(PETSC_COMM_SELF, m, n, 0, nnz, &prod));
1079: PetscCall(PetscFree(nnz));
1080: PetscCall(PetscFree2(nnzTrace, nnzFiber));
1081: /* reasoning about which points each dof needs depends on having zeros computed at points preserved */
1082: PetscCall(MatSetOption(prod, MAT_IGNORE_ZERO_ENTRIES, PETSC_FALSE));
1083: /* compute pullbacks */
1084: PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(kTrace), &dT));
1085: PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(kFiber), &dF));
1086: PetscCall(PetscMalloc4(dimTrace * dim, &projT, dimFiber * dim, &projF, dT * NkTrace, &projTstar, dF * NkFiber, &projFstar));
1087: PetscCall(PetscArrayzero(projT, dimTrace * dim));
1088: for (i = 0; i < dimTrace; i++) projT[i * (dim + 1)] = 1.;
1089: PetscCall(PetscArrayzero(projF, dimFiber * dim));
1090: for (i = 0; i < dimFiber; i++) projF[i * (dim + 1) + dimTrace] = 1.;
1091: PetscCall(PetscDTAltVPullbackMatrix(dim, dimTrace, projT, kTrace, projTstar));
1092: PetscCall(PetscDTAltVPullbackMatrix(dim, dimFiber, projF, kFiber, projFstar));
1093: PetscCall(PetscMalloc5(dT, &workT, dF, &workF, Nk, &work, Nk, &workstar, Nk, &workS));
1094: PetscCall(PetscMalloc2(dT, &workT2, dF, &workF2));
1095: PetscCall(PetscMalloc1(Nk * dT, &wedgeMat));
1096: sign = (PetscAbsInt(kTrace * kFiber) & 1) ? -1. : 1.;
1097: for (i = 0, iF = 0; iF < mFiber; iF++) {
1098: PetscInt ncolsF, nformsF;
1099: const PetscInt *colsF;
1100: const PetscScalar *valsF;
1102: PetscCall(MatGetRow(fiber, iF, &ncolsF, &colsF, &valsF));
1103: nformsF = ncolsF / NkFiber;
1104: for (iT = 0; iT < mTrace; iT++, i++) {
1105: PetscInt ncolsT, nformsT;
1106: const PetscInt *colsT;
1107: const PetscScalar *valsT;
1109: PetscCall(MatGetRow(trace, iT, &ncolsT, &colsT, &valsT));
1110: nformsT = ncolsT / NkTrace;
1111: for (j = 0, jF = 0; jF < nformsF; jF++) {
1112: PetscInt colF = colsF[jF * NkFiber] / NkFiber;
1114: for (il = 0; il < dF; il++) {
1115: PetscReal val = 0.;
1116: for (jl = 0; jl < NkFiber; jl++) val += projFstar[il * NkFiber + jl] * PetscRealPart(valsF[jF * NkFiber + jl]);
1117: workF[il] = val;
1118: }
1119: if (kFiber < 0) {
1120: for (il = 0; il < dF; il++) workF2[il] = workF[il];
1121: PetscCall(PetscDTAltVStar(dim, PetscAbsInt(kFiber), 1, workF2, workF));
1122: }
1123: PetscCall(PetscDTAltVWedgeMatrix(dim, PetscAbsInt(kFiber), PetscAbsInt(kTrace), workF, wedgeMat));
1124: for (jT = 0; jT < nformsT; jT++, j++) {
1125: PetscInt colT = colsT[jT * NkTrace] / NkTrace;
1126: PetscInt col = colF * (nTrace / NkTrace) + colT;
1127: const PetscScalar *vals;
1129: for (il = 0; il < dT; il++) {
1130: PetscReal val = 0.;
1131: for (jl = 0; jl < NkTrace; jl++) val += projTstar[il * NkTrace + jl] * PetscRealPart(valsT[jT * NkTrace + jl]);
1132: workT[il] = val;
1133: }
1134: if (kTrace < 0) {
1135: for (il = 0; il < dT; il++) workT2[il] = workT[il];
1136: PetscCall(PetscDTAltVStar(dim, PetscAbsInt(kTrace), 1, workT2, workT));
1137: }
1139: for (il = 0; il < Nk; il++) {
1140: PetscReal val = 0.;
1141: for (jl = 0; jl < dT; jl++) val += sign * wedgeMat[il * dT + jl] * workT[jl];
1142: work[il] = val;
1143: }
1144: if (k < 0) {
1145: PetscCall(PetscDTAltVStar(dim, PetscAbsInt(k), -1, work, workstar));
1146: #if defined(PETSC_USE_COMPLEX)
1147: for (l = 0; l < Nk; l++) workS[l] = workstar[l];
1148: vals = &workS[0];
1149: #else
1150: vals = &workstar[0];
1151: #endif
1152: } else {
1153: #if defined(PETSC_USE_COMPLEX)
1154: for (l = 0; l < Nk; l++) workS[l] = work[l];
1155: vals = &workS[0];
1156: #else
1157: vals = &work[0];
1158: #endif
1159: }
1160: for (l = 0; l < Nk; l++) PetscCall(MatSetValue(prod, i, col * Nk + l, vals[l], INSERT_VALUES)); /* Nk */
1161: } /* jT */
1162: } /* jF */
1163: PetscCall(MatRestoreRow(trace, iT, &ncolsT, &colsT, &valsT));
1164: } /* iT */
1165: PetscCall(MatRestoreRow(fiber, iF, &ncolsF, &colsF, &valsF));
1166: } /* iF */
1167: PetscCall(PetscFree(wedgeMat));
1168: PetscCall(PetscFree4(projT, projF, projTstar, projFstar));
1169: PetscCall(PetscFree2(workT2, workF2));
1170: PetscCall(PetscFree5(workT, workF, work, workstar, workS));
1171: PetscCall(MatAssemblyBegin(prod, MAT_FINAL_ASSEMBLY));
1172: PetscCall(MatAssemblyEnd(prod, MAT_FINAL_ASSEMBLY));
1173: *product = prod;
1174: PetscFunctionReturn(PETSC_SUCCESS);
1175: }
1177: /* Union of quadrature points, with an attempt to identify commont points in the two sets */
1178: static PetscErrorCode PetscQuadraturePointsMerge(PetscQuadrature quadA, PetscQuadrature quadB, PetscQuadrature *quadJoint, PetscInt *aToJoint[], PetscInt *bToJoint[])
1179: {
1180: PetscInt dimA, dimB;
1181: PetscInt nA, nB, nJoint, i, j, d;
1182: const PetscReal *pointsA;
1183: const PetscReal *pointsB;
1184: PetscReal *pointsJoint;
1185: PetscInt *aToJ, *bToJ;
1186: PetscQuadrature qJ;
1188: PetscFunctionBegin;
1189: PetscCall(PetscQuadratureGetData(quadA, &dimA, NULL, &nA, &pointsA, NULL));
1190: PetscCall(PetscQuadratureGetData(quadB, &dimB, NULL, &nB, &pointsB, NULL));
1191: PetscCheck(dimA == dimB, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Quadrature points must be in the same dimension");
1192: nJoint = nA;
1193: PetscCall(PetscMalloc1(nA, &aToJ));
1194: for (i = 0; i < nA; i++) aToJ[i] = i;
1195: PetscCall(PetscMalloc1(nB, &bToJ));
1196: for (i = 0; i < nB; i++) {
1197: for (j = 0; j < nA; j++) {
1198: bToJ[i] = -1;
1199: for (d = 0; d < dimA; d++)
1200: if (PetscAbsReal(pointsB[i * dimA + d] - pointsA[j * dimA + d]) > PETSC_SMALL) break;
1201: if (d == dimA) {
1202: bToJ[i] = j;
1203: break;
1204: }
1205: }
1206: if (bToJ[i] == -1) bToJ[i] = nJoint++;
1207: }
1208: *aToJoint = aToJ;
1209: *bToJoint = bToJ;
1210: PetscCall(PetscMalloc1(nJoint * dimA, &pointsJoint));
1211: PetscCall(PetscArraycpy(pointsJoint, pointsA, nA * dimA));
1212: for (i = 0; i < nB; i++) {
1213: if (bToJ[i] >= nA) {
1214: for (d = 0; d < dimA; d++) pointsJoint[bToJ[i] * dimA + d] = pointsB[i * dimA + d];
1215: }
1216: }
1217: PetscCall(PetscQuadratureCreate(PETSC_COMM_SELF, &qJ));
1218: PetscCall(PetscQuadratureSetData(qJ, dimA, 0, nJoint, pointsJoint, NULL));
1219: *quadJoint = qJ;
1220: PetscFunctionReturn(PETSC_SUCCESS);
1221: }
1223: /* Matrices matA and matB are both quadrature -> dof matrices: produce a matrix that is joint quadrature -> union of
1224: * dofs, where the joint quadrature was produced by PetscQuadraturePointsMerge */
1225: static PetscErrorCode MatricesMerge(Mat matA, Mat matB, PetscInt dim, PetscInt k, PetscInt numMerged, const PetscInt aToMerged[], const PetscInt bToMerged[], Mat *matMerged)
1226: {
1227: PetscInt m, n, mA, nA, mB, nB, Nk, i, j, l;
1228: Mat M;
1229: PetscInt *nnz;
1230: PetscInt maxnnz;
1231: PetscInt *work;
1233: PetscFunctionBegin;
1234: PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(k), &Nk));
1235: PetscCall(MatGetSize(matA, &mA, &nA));
1236: PetscCheck(nA % Nk == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "matA column space not a multiple of k-form size");
1237: PetscCall(MatGetSize(matB, &mB, &nB));
1238: PetscCheck(nB % Nk == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "matB column space not a multiple of k-form size");
1239: m = mA + mB;
1240: n = numMerged * Nk;
1241: PetscCall(PetscMalloc1(m, &nnz));
1242: maxnnz = 0;
1243: for (i = 0; i < mA; i++) {
1244: PetscCall(MatGetRow(matA, i, &(nnz[i]), NULL, NULL));
1245: PetscCheck(nnz[i] % Nk == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "nonzeros in matA are not in k-form size blocks");
1246: maxnnz = PetscMax(maxnnz, nnz[i]);
1247: }
1248: for (i = 0; i < mB; i++) {
1249: PetscCall(MatGetRow(matB, i, &(nnz[i + mA]), NULL, NULL));
1250: PetscCheck(nnz[i + mA] % Nk == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "nonzeros in matB are not in k-form size blocks");
1251: maxnnz = PetscMax(maxnnz, nnz[i + mA]);
1252: }
1253: PetscCall(MatCreateSeqAIJ(PETSC_COMM_SELF, m, n, 0, nnz, &M));
1254: PetscCall(PetscFree(nnz));
1255: /* reasoning about which points each dof needs depends on having zeros computed at points preserved */
1256: PetscCall(MatSetOption(M, MAT_IGNORE_ZERO_ENTRIES, PETSC_FALSE));
1257: PetscCall(PetscMalloc1(maxnnz, &work));
1258: for (i = 0; i < mA; i++) {
1259: const PetscInt *cols;
1260: const PetscScalar *vals;
1261: PetscInt nCols;
1262: PetscCall(MatGetRow(matA, i, &nCols, &cols, &vals));
1263: for (j = 0; j < nCols / Nk; j++) {
1264: PetscInt newCol = aToMerged[cols[j * Nk] / Nk];
1265: for (l = 0; l < Nk; l++) work[j * Nk + l] = newCol * Nk + l;
1266: }
1267: PetscCall(MatSetValuesBlocked(M, 1, &i, nCols, work, vals, INSERT_VALUES));
1268: PetscCall(MatRestoreRow(matA, i, &nCols, &cols, &vals));
1269: }
1270: for (i = 0; i < mB; i++) {
1271: const PetscInt *cols;
1272: const PetscScalar *vals;
1274: PetscInt row = i + mA;
1275: PetscInt nCols;
1276: PetscCall(MatGetRow(matB, i, &nCols, &cols, &vals));
1277: for (j = 0; j < nCols / Nk; j++) {
1278: PetscInt newCol = bToMerged[cols[j * Nk] / Nk];
1279: for (l = 0; l < Nk; l++) work[j * Nk + l] = newCol * Nk + l;
1280: }
1281: PetscCall(MatSetValuesBlocked(M, 1, &row, nCols, work, vals, INSERT_VALUES));
1282: PetscCall(MatRestoreRow(matB, i, &nCols, &cols, &vals));
1283: }
1284: PetscCall(PetscFree(work));
1285: PetscCall(MatAssemblyBegin(M, MAT_FINAL_ASSEMBLY));
1286: PetscCall(MatAssemblyEnd(M, MAT_FINAL_ASSEMBLY));
1287: *matMerged = M;
1288: PetscFunctionReturn(PETSC_SUCCESS);
1289: }
1291: /* Take a dual space and product a segment space that has all the same specifications (trimmed, continuous, order,
1292: * node set), except for the form degree. For computing boundary dofs and for making tensor product spaces */
1293: static PetscErrorCode PetscDualSpaceCreateFacetSubspace_Lagrange(PetscDualSpace sp, DM K, PetscInt f, PetscInt k, PetscInt Ncopies, PetscBool interiorOnly, PetscDualSpace *bdsp)
1294: {
1295: PetscInt Nknew, Ncnew;
1296: PetscInt dim, pointDim = -1;
1297: PetscInt depth;
1298: DM dm;
1299: PetscDualSpace_Lag *newlag;
1301: PetscFunctionBegin;
1302: PetscCall(PetscDualSpaceGetDM(sp, &dm));
1303: PetscCall(DMGetDimension(dm, &dim));
1304: PetscCall(DMPlexGetDepth(dm, &depth));
1305: PetscCall(PetscDualSpaceDuplicate(sp, bdsp));
1306: PetscCall(PetscDualSpaceSetFormDegree(*bdsp, k));
1307: if (!K) {
1308: if (depth == dim) {
1309: DMPolytopeType ct;
1311: pointDim = dim - 1;
1312: PetscCall(DMPlexGetCellType(dm, f, &ct));
1313: PetscCall(DMPlexCreateReferenceCell(PETSC_COMM_SELF, ct, &K));
1314: } else if (depth == 1) {
1315: pointDim = 0;
1316: PetscCall(DMPlexCreateReferenceCell(PETSC_COMM_SELF, DM_POLYTOPE_POINT, &K));
1317: } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Unsupported interpolation state of reference element");
1318: } else {
1319: PetscCall(PetscObjectReference((PetscObject)K));
1320: PetscCall(DMGetDimension(K, &pointDim));
1321: }
1322: PetscCall(PetscDualSpaceSetDM(*bdsp, K));
1323: PetscCall(DMDestroy(&K));
1324: PetscCall(PetscDTBinomialInt(pointDim, PetscAbsInt(k), &Nknew));
1325: Ncnew = Nknew * Ncopies;
1326: PetscCall(PetscDualSpaceSetNumComponents(*bdsp, Ncnew));
1327: newlag = (PetscDualSpace_Lag *)(*bdsp)->data;
1328: newlag->interiorOnly = interiorOnly;
1329: PetscCall(PetscDualSpaceSetUp(*bdsp));
1330: PetscFunctionReturn(PETSC_SUCCESS);
1331: }
1333: /* Construct simplex nodes from a nodefamily, add Nk dof vectors of length Nk at each node.
1334: * Return the (quadrature, matrix) form of the dofs and the nodeIndices form as well.
1335: *
1336: * Sometimes we want a set of nodes to be contained in the interior of the element,
1337: * even when the node scheme puts nodes on the boundaries. numNodeSkip tells
1338: * the routine how many "layers" of nodes need to be skipped.
1339: * */
1340: static PetscErrorCode PetscDualSpaceLagrangeCreateSimplexNodeMat(Petsc1DNodeFamily nodeFamily, PetscInt dim, PetscInt sum, PetscInt Nk, PetscInt numNodeSkip, PetscQuadrature *iNodes, Mat *iMat, PetscLagNodeIndices *nodeIndices)
1341: {
1342: PetscReal *extraNodeCoords, *nodeCoords;
1343: PetscInt nNodes, nExtraNodes;
1344: PetscInt i, j, k, extraSum = sum + numNodeSkip * (1 + dim);
1345: PetscQuadrature intNodes;
1346: Mat intMat;
1347: PetscLagNodeIndices ni;
1349: PetscFunctionBegin;
1350: PetscCall(PetscDTBinomialInt(dim + sum, dim, &nNodes));
1351: PetscCall(PetscDTBinomialInt(dim + extraSum, dim, &nExtraNodes));
1353: PetscCall(PetscMalloc1(dim * nExtraNodes, &extraNodeCoords));
1354: PetscCall(PetscNew(&ni));
1355: ni->nodeIdxDim = dim + 1;
1356: ni->nodeVecDim = Nk;
1357: ni->nNodes = nNodes * Nk;
1358: ni->refct = 1;
1359: PetscCall(PetscMalloc1(nNodes * Nk * (dim + 1), &(ni->nodeIdx)));
1360: PetscCall(PetscMalloc1(nNodes * Nk * Nk, &(ni->nodeVec)));
1361: for (i = 0; i < nNodes; i++)
1362: for (j = 0; j < Nk; j++)
1363: for (k = 0; k < Nk; k++) ni->nodeVec[(i * Nk + j) * Nk + k] = (j == k) ? 1. : 0.;
1364: PetscCall(Petsc1DNodeFamilyComputeSimplexNodes(nodeFamily, dim, extraSum, extraNodeCoords));
1365: if (numNodeSkip) {
1366: PetscInt k;
1367: PetscInt *tup;
1369: PetscCall(PetscMalloc1(dim * nNodes, &nodeCoords));
1370: PetscCall(PetscMalloc1(dim + 1, &tup));
1371: for (k = 0; k < nNodes; k++) {
1372: PetscInt j, c;
1373: PetscInt index;
1375: PetscCall(PetscDTIndexToBary(dim + 1, sum, k, tup));
1376: for (j = 0; j < dim + 1; j++) tup[j] += numNodeSkip;
1377: for (c = 0; c < Nk; c++) {
1378: for (j = 0; j < dim + 1; j++) ni->nodeIdx[(k * Nk + c) * (dim + 1) + j] = tup[j] + 1;
1379: }
1380: PetscCall(PetscDTBaryToIndex(dim + 1, extraSum, tup, &index));
1381: for (j = 0; j < dim; j++) nodeCoords[k * dim + j] = extraNodeCoords[index * dim + j];
1382: }
1383: PetscCall(PetscFree(tup));
1384: PetscCall(PetscFree(extraNodeCoords));
1385: } else {
1386: PetscInt k;
1387: PetscInt *tup;
1389: nodeCoords = extraNodeCoords;
1390: PetscCall(PetscMalloc1(dim + 1, &tup));
1391: for (k = 0; k < nNodes; k++) {
1392: PetscInt j, c;
1394: PetscCall(PetscDTIndexToBary(dim + 1, sum, k, tup));
1395: for (c = 0; c < Nk; c++) {
1396: for (j = 0; j < dim + 1; j++) {
1397: /* barycentric indices can have zeros, but we don't want to push forward zeros because it makes it harder to
1398: * determine which nodes correspond to which under symmetries, so we increase by 1. This is fine
1399: * because the nodeIdx coordinates don't have any meaning other than helping to identify symmetries */
1400: ni->nodeIdx[(k * Nk + c) * (dim + 1) + j] = tup[j] + 1;
1401: }
1402: }
1403: }
1404: PetscCall(PetscFree(tup));
1405: }
1406: PetscCall(PetscQuadratureCreate(PETSC_COMM_SELF, &intNodes));
1407: PetscCall(PetscQuadratureSetData(intNodes, dim, 0, nNodes, nodeCoords, NULL));
1408: PetscCall(MatCreateSeqAIJ(PETSC_COMM_SELF, nNodes * Nk, nNodes * Nk, Nk, NULL, &intMat));
1409: PetscCall(MatSetOption(intMat, MAT_IGNORE_ZERO_ENTRIES, PETSC_FALSE));
1410: for (j = 0; j < nNodes * Nk; j++) {
1411: PetscInt rem = j % Nk;
1412: PetscInt a, aprev = j - rem;
1413: PetscInt anext = aprev + Nk;
1415: for (a = aprev; a < anext; a++) PetscCall(MatSetValue(intMat, j, a, (a == j) ? 1. : 0., INSERT_VALUES));
1416: }
1417: PetscCall(MatAssemblyBegin(intMat, MAT_FINAL_ASSEMBLY));
1418: PetscCall(MatAssemblyEnd(intMat, MAT_FINAL_ASSEMBLY));
1419: *iNodes = intNodes;
1420: *iMat = intMat;
1421: *nodeIndices = ni;
1422: PetscFunctionReturn(PETSC_SUCCESS);
1423: }
1425: /* once the nodeIndices have been created for the interior of the reference cell, and for all of the boundary cells,
1426: * push forward the boundary dofs and concatenate them into the full node indices for the dual space */
1427: static PetscErrorCode PetscDualSpaceLagrangeCreateAllNodeIdx(PetscDualSpace sp)
1428: {
1429: DM dm;
1430: PetscInt dim, nDofs;
1431: PetscSection section;
1432: PetscInt pStart, pEnd, p;
1433: PetscInt formDegree, Nk;
1434: PetscInt nodeIdxDim, spintdim;
1435: PetscDualSpace_Lag *lag;
1436: PetscLagNodeIndices ni, verti;
1438: PetscFunctionBegin;
1439: lag = (PetscDualSpace_Lag *)sp->data;
1440: verti = lag->vertIndices;
1441: PetscCall(PetscDualSpaceGetDM(sp, &dm));
1442: PetscCall(DMGetDimension(dm, &dim));
1443: PetscCall(PetscDualSpaceGetFormDegree(sp, &formDegree));
1444: PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(formDegree), &Nk));
1445: PetscCall(PetscDualSpaceGetSection(sp, §ion));
1446: PetscCall(PetscSectionGetStorageSize(section, &nDofs));
1447: PetscCall(PetscNew(&ni));
1448: ni->nodeIdxDim = nodeIdxDim = verti->nodeIdxDim;
1449: ni->nodeVecDim = Nk;
1450: ni->nNodes = nDofs;
1451: ni->refct = 1;
1452: PetscCall(PetscMalloc1(nodeIdxDim * nDofs, &(ni->nodeIdx)));
1453: PetscCall(PetscMalloc1(Nk * nDofs, &(ni->nodeVec)));
1454: PetscCall(DMPlexGetChart(dm, &pStart, &pEnd));
1455: PetscCall(PetscSectionGetDof(section, 0, &spintdim));
1456: if (spintdim) {
1457: PetscCall(PetscArraycpy(ni->nodeIdx, lag->intNodeIndices->nodeIdx, spintdim * nodeIdxDim));
1458: PetscCall(PetscArraycpy(ni->nodeVec, lag->intNodeIndices->nodeVec, spintdim * Nk));
1459: }
1460: for (p = pStart + 1; p < pEnd; p++) {
1461: PetscDualSpace psp = sp->pointSpaces[p];
1462: PetscDualSpace_Lag *plag;
1463: PetscInt dof, off;
1465: PetscCall(PetscSectionGetDof(section, p, &dof));
1466: if (!dof) continue;
1467: plag = (PetscDualSpace_Lag *)psp->data;
1468: PetscCall(PetscSectionGetOffset(section, p, &off));
1469: PetscCall(PetscLagNodeIndicesPushForward(dm, verti, p, plag->vertIndices, plag->intNodeIndices, 0, formDegree, &(ni->nodeIdx[off * nodeIdxDim]), &(ni->nodeVec[off * Nk])));
1470: }
1471: lag->allNodeIndices = ni;
1472: PetscFunctionReturn(PETSC_SUCCESS);
1473: }
1475: /* once the (quadrature, Matrix) forms of the dofs have been created for the interior of the
1476: * reference cell and for the boundary cells, jk
1477: * push forward the boundary data and concatenate them into the full (quadrature, matrix) data
1478: * for the dual space */
1479: static PetscErrorCode PetscDualSpaceCreateAllDataFromInteriorData(PetscDualSpace sp)
1480: {
1481: DM dm;
1482: PetscSection section;
1483: PetscInt pStart, pEnd, p, k, Nk, dim, Nc;
1484: PetscInt nNodes;
1485: PetscInt countNodes;
1486: Mat allMat;
1487: PetscQuadrature allNodes;
1488: PetscInt nDofs;
1489: PetscInt maxNzforms, j;
1490: PetscScalar *work;
1491: PetscReal *L, *J, *Jinv, *v0, *pv0;
1492: PetscInt *iwork;
1493: PetscReal *nodes;
1495: PetscFunctionBegin;
1496: PetscCall(PetscDualSpaceGetDM(sp, &dm));
1497: PetscCall(DMGetDimension(dm, &dim));
1498: PetscCall(PetscDualSpaceGetSection(sp, §ion));
1499: PetscCall(PetscSectionGetStorageSize(section, &nDofs));
1500: PetscCall(DMPlexGetChart(dm, &pStart, &pEnd));
1501: PetscCall(PetscDualSpaceGetFormDegree(sp, &k));
1502: PetscCall(PetscDualSpaceGetNumComponents(sp, &Nc));
1503: PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(k), &Nk));
1504: for (p = pStart, nNodes = 0, maxNzforms = 0; p < pEnd; p++) {
1505: PetscDualSpace psp;
1506: DM pdm;
1507: PetscInt pdim, pNk;
1508: PetscQuadrature intNodes;
1509: Mat intMat;
1511: PetscCall(PetscDualSpaceGetPointSubspace(sp, p, &psp));
1512: if (!psp) continue;
1513: PetscCall(PetscDualSpaceGetDM(psp, &pdm));
1514: PetscCall(DMGetDimension(pdm, &pdim));
1515: if (pdim < PetscAbsInt(k)) continue;
1516: PetscCall(PetscDTBinomialInt(pdim, PetscAbsInt(k), &pNk));
1517: PetscCall(PetscDualSpaceGetInteriorData(psp, &intNodes, &intMat));
1518: if (intNodes) {
1519: PetscInt nNodesp;
1521: PetscCall(PetscQuadratureGetData(intNodes, NULL, NULL, &nNodesp, NULL, NULL));
1522: nNodes += nNodesp;
1523: }
1524: if (intMat) {
1525: PetscInt maxNzsp;
1526: PetscInt maxNzformsp;
1528: PetscCall(MatSeqAIJGetMaxRowNonzeros(intMat, &maxNzsp));
1529: PetscCheck(maxNzsp % pNk == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "interior matrix is not laid out as blocks of k-forms");
1530: maxNzformsp = maxNzsp / pNk;
1531: maxNzforms = PetscMax(maxNzforms, maxNzformsp);
1532: }
1533: }
1534: PetscCall(MatCreateSeqAIJ(PETSC_COMM_SELF, nDofs, nNodes * Nc, maxNzforms * Nk, NULL, &allMat));
1535: PetscCall(MatSetOption(allMat, MAT_IGNORE_ZERO_ENTRIES, PETSC_FALSE));
1536: PetscCall(PetscMalloc7(dim, &v0, dim, &pv0, dim * dim, &J, dim * dim, &Jinv, Nk * Nk, &L, maxNzforms * Nk, &work, maxNzforms * Nk, &iwork));
1537: for (j = 0; j < dim; j++) pv0[j] = -1.;
1538: PetscCall(PetscMalloc1(dim * nNodes, &nodes));
1539: for (p = pStart, countNodes = 0; p < pEnd; p++) {
1540: PetscDualSpace psp;
1541: PetscQuadrature intNodes;
1542: DM pdm;
1543: PetscInt pdim, pNk;
1544: PetscInt countNodesIn = countNodes;
1545: PetscReal detJ;
1546: Mat intMat;
1548: PetscCall(PetscDualSpaceGetPointSubspace(sp, p, &psp));
1549: if (!psp) continue;
1550: PetscCall(PetscDualSpaceGetDM(psp, &pdm));
1551: PetscCall(DMGetDimension(pdm, &pdim));
1552: if (pdim < PetscAbsInt(k)) continue;
1553: PetscCall(PetscDualSpaceGetInteriorData(psp, &intNodes, &intMat));
1554: if (intNodes == NULL && intMat == NULL) continue;
1555: PetscCall(PetscDTBinomialInt(pdim, PetscAbsInt(k), &pNk));
1556: if (p) {
1557: PetscCall(DMPlexComputeCellGeometryAffineFEM(dm, p, v0, J, Jinv, &detJ));
1558: } else { /* identity */
1559: PetscInt i, j;
1561: for (i = 0; i < dim; i++)
1562: for (j = 0; j < dim; j++) J[i * dim + j] = Jinv[i * dim + j] = 0.;
1563: for (i = 0; i < dim; i++) J[i * dim + i] = Jinv[i * dim + i] = 1.;
1564: for (i = 0; i < dim; i++) v0[i] = -1.;
1565: }
1566: if (pdim != dim) { /* compactify Jacobian */
1567: PetscInt i, j;
1569: for (i = 0; i < dim; i++)
1570: for (j = 0; j < pdim; j++) J[i * pdim + j] = J[i * dim + j];
1571: }
1572: PetscCall(PetscDTAltVPullbackMatrix(pdim, dim, J, k, L));
1573: if (intNodes) { /* push forward quadrature locations by the affine transformation */
1574: PetscInt nNodesp;
1575: const PetscReal *nodesp;
1576: PetscInt j;
1578: PetscCall(PetscQuadratureGetData(intNodes, NULL, NULL, &nNodesp, &nodesp, NULL));
1579: for (j = 0; j < nNodesp; j++, countNodes++) {
1580: PetscInt d, e;
1582: for (d = 0; d < dim; d++) {
1583: nodes[countNodes * dim + d] = v0[d];
1584: for (e = 0; e < pdim; e++) nodes[countNodes * dim + d] += J[d * pdim + e] * (nodesp[j * pdim + e] - pv0[e]);
1585: }
1586: }
1587: }
1588: if (intMat) {
1589: PetscInt nrows;
1590: PetscInt off;
1592: PetscCall(PetscSectionGetDof(section, p, &nrows));
1593: PetscCall(PetscSectionGetOffset(section, p, &off));
1594: for (j = 0; j < nrows; j++) {
1595: PetscInt ncols;
1596: const PetscInt *cols;
1597: const PetscScalar *vals;
1598: PetscInt l, d, e;
1599: PetscInt row = j + off;
1601: PetscCall(MatGetRow(intMat, j, &ncols, &cols, &vals));
1602: PetscCheck(ncols % pNk == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "interior matrix is not laid out as blocks of k-forms");
1603: for (l = 0; l < ncols / pNk; l++) {
1604: PetscInt blockcol;
1606: for (d = 0; d < pNk; d++) PetscCheck((cols[l * pNk + d] % pNk) == d, PETSC_COMM_SELF, PETSC_ERR_PLIB, "interior matrix is not laid out as blocks of k-forms");
1607: blockcol = cols[l * pNk] / pNk;
1608: for (d = 0; d < Nk; d++) iwork[l * Nk + d] = (blockcol + countNodesIn) * Nk + d;
1609: for (d = 0; d < Nk; d++) work[l * Nk + d] = 0.;
1610: for (d = 0; d < Nk; d++) {
1611: for (e = 0; e < pNk; e++) {
1612: /* "push forward" dof by pulling back a k-form to be evaluated on the point: multiply on the right by L */
1613: work[l * Nk + d] += vals[l * pNk + e] * L[e * Nk + d];
1614: }
1615: }
1616: }
1617: PetscCall(MatSetValues(allMat, 1, &row, (ncols / pNk) * Nk, iwork, work, INSERT_VALUES));
1618: PetscCall(MatRestoreRow(intMat, j, &ncols, &cols, &vals));
1619: }
1620: }
1621: }
1622: PetscCall(MatAssemblyBegin(allMat, MAT_FINAL_ASSEMBLY));
1623: PetscCall(MatAssemblyEnd(allMat, MAT_FINAL_ASSEMBLY));
1624: PetscCall(PetscQuadratureCreate(PETSC_COMM_SELF, &allNodes));
1625: PetscCall(PetscQuadratureSetData(allNodes, dim, 0, nNodes, nodes, NULL));
1626: PetscCall(PetscFree7(v0, pv0, J, Jinv, L, work, iwork));
1627: PetscCall(MatDestroy(&(sp->allMat)));
1628: sp->allMat = allMat;
1629: PetscCall(PetscQuadratureDestroy(&(sp->allNodes)));
1630: sp->allNodes = allNodes;
1631: PetscFunctionReturn(PETSC_SUCCESS);
1632: }
1634: /* rather than trying to get all data from the functionals, we create
1635: * the functionals from rows of the quadrature -> dof matrix.
1636: *
1637: * Ideally most of the uses of PetscDualSpace in PetscFE will switch
1638: * to using intMat and allMat, so that the individual functionals
1639: * don't need to be constructed at all */
1640: static PetscErrorCode PetscDualSpaceComputeFunctionalsFromAllData(PetscDualSpace sp)
1641: {
1642: PetscQuadrature allNodes;
1643: Mat allMat;
1644: PetscInt nDofs;
1645: PetscInt dim, k, Nk, Nc, f;
1646: DM dm;
1647: PetscInt nNodes, spdim;
1648: const PetscReal *nodes = NULL;
1649: PetscSection section;
1650: PetscBool useMoments;
1652: PetscFunctionBegin;
1653: PetscCall(PetscDualSpaceGetDM(sp, &dm));
1654: PetscCall(DMGetDimension(dm, &dim));
1655: PetscCall(PetscDualSpaceGetNumComponents(sp, &Nc));
1656: PetscCall(PetscDualSpaceGetFormDegree(sp, &k));
1657: PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(k), &Nk));
1658: PetscCall(PetscDualSpaceGetAllData(sp, &allNodes, &allMat));
1659: nNodes = 0;
1660: if (allNodes) PetscCall(PetscQuadratureGetData(allNodes, NULL, NULL, &nNodes, &nodes, NULL));
1661: PetscCall(MatGetSize(allMat, &nDofs, NULL));
1662: PetscCall(PetscDualSpaceGetSection(sp, §ion));
1663: PetscCall(PetscSectionGetStorageSize(section, &spdim));
1664: PetscCheck(spdim == nDofs, PETSC_COMM_SELF, PETSC_ERR_PLIB, "incompatible all matrix size");
1665: PetscCall(PetscMalloc1(nDofs, &(sp->functional)));
1666: PetscCall(PetscDualSpaceLagrangeGetUseMoments(sp, &useMoments));
1667: if (useMoments) {
1668: Mat allMat;
1669: PetscInt momentOrder, i;
1670: PetscBool tensor = PETSC_FALSE;
1671: const PetscReal *weights;
1672: PetscScalar *array;
1674: PetscCheck(nDofs == 1, PETSC_COMM_SELF, PETSC_ERR_SUP, "We do not yet support moments beyond P0, nDofs == %" PetscInt_FMT, nDofs);
1675: PetscCall(PetscDualSpaceLagrangeGetMomentOrder(sp, &momentOrder));
1676: PetscCall(PetscDualSpaceLagrangeGetTensor(sp, &tensor));
1677: if (!tensor) PetscCall(PetscDTStroudConicalQuadrature(dim, Nc, PetscMax(momentOrder + 1, 1), -1.0, 1.0, &(sp->functional[0])));
1678: else PetscCall(PetscDTGaussTensorQuadrature(dim, Nc, PetscMax(momentOrder + 1, 1), -1.0, 1.0, &(sp->functional[0])));
1679: /* Need to replace allNodes and allMat */
1680: PetscCall(PetscObjectReference((PetscObject)sp->functional[0]));
1681: PetscCall(PetscQuadratureDestroy(&(sp->allNodes)));
1682: sp->allNodes = sp->functional[0];
1683: PetscCall(PetscQuadratureGetData(sp->allNodes, NULL, NULL, &nNodes, NULL, &weights));
1684: PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, nDofs, nNodes * Nc, NULL, &allMat));
1685: PetscCall(MatDenseGetArrayWrite(allMat, &array));
1686: for (i = 0; i < nNodes * Nc; ++i) array[i] = weights[i];
1687: PetscCall(MatDenseRestoreArrayWrite(allMat, &array));
1688: PetscCall(MatAssemblyBegin(allMat, MAT_FINAL_ASSEMBLY));
1689: PetscCall(MatAssemblyEnd(allMat, MAT_FINAL_ASSEMBLY));
1690: PetscCall(MatDestroy(&(sp->allMat)));
1691: sp->allMat = allMat;
1692: PetscFunctionReturn(PETSC_SUCCESS);
1693: }
1694: for (f = 0; f < nDofs; f++) {
1695: PetscInt ncols, c;
1696: const PetscInt *cols;
1697: const PetscScalar *vals;
1698: PetscReal *nodesf;
1699: PetscReal *weightsf;
1700: PetscInt nNodesf;
1701: PetscInt countNodes;
1703: PetscCall(MatGetRow(allMat, f, &ncols, &cols, &vals));
1704: PetscCheck(ncols % Nk == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "all matrix is not laid out as blocks of k-forms");
1705: for (c = 1, nNodesf = 1; c < ncols; c++) {
1706: if ((cols[c] / Nc) != (cols[c - 1] / Nc)) nNodesf++;
1707: }
1708: PetscCall(PetscMalloc1(dim * nNodesf, &nodesf));
1709: PetscCall(PetscMalloc1(Nc * nNodesf, &weightsf));
1710: for (c = 0, countNodes = 0; c < ncols; c++) {
1711: if (!c || ((cols[c] / Nc) != (cols[c - 1] / Nc))) {
1712: PetscInt d;
1714: for (d = 0; d < Nc; d++) weightsf[countNodes * Nc + d] = 0.;
1715: for (d = 0; d < dim; d++) nodesf[countNodes * dim + d] = nodes[(cols[c] / Nc) * dim + d];
1716: countNodes++;
1717: }
1718: weightsf[(countNodes - 1) * Nc + (cols[c] % Nc)] = PetscRealPart(vals[c]);
1719: }
1720: PetscCall(PetscQuadratureCreate(PETSC_COMM_SELF, &(sp->functional[f])));
1721: PetscCall(PetscQuadratureSetData(sp->functional[f], dim, Nc, nNodesf, nodesf, weightsf));
1722: PetscCall(MatRestoreRow(allMat, f, &ncols, &cols, &vals));
1723: }
1724: PetscFunctionReturn(PETSC_SUCCESS);
1725: }
1727: /* take a matrix meant for k-forms and expand it to one for Ncopies */
1728: static PetscErrorCode PetscDualSpaceLagrangeMatrixCreateCopies(Mat A, PetscInt Nk, PetscInt Ncopies, Mat *Abs)
1729: {
1730: PetscInt m, n, i, j, k;
1731: PetscInt maxnnz, *nnz, *iwork;
1732: Mat Ac;
1734: PetscFunctionBegin;
1735: PetscCall(MatGetSize(A, &m, &n));
1736: PetscCheck(n % Nk == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Number of columns in A %" PetscInt_FMT " is not a multiple of Nk %" PetscInt_FMT, n, Nk);
1737: PetscCall(PetscMalloc1(m * Ncopies, &nnz));
1738: for (i = 0, maxnnz = 0; i < m; i++) {
1739: PetscInt innz;
1740: PetscCall(MatGetRow(A, i, &innz, NULL, NULL));
1741: PetscCheck(innz % Nk == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "A row %" PetscInt_FMT " nnzs is not a multiple of Nk %" PetscInt_FMT, innz, Nk);
1742: for (j = 0; j < Ncopies; j++) nnz[i * Ncopies + j] = innz;
1743: maxnnz = PetscMax(maxnnz, innz);
1744: }
1745: PetscCall(MatCreateSeqAIJ(PETSC_COMM_SELF, m * Ncopies, n * Ncopies, 0, nnz, &Ac));
1746: PetscCall(MatSetOption(Ac, MAT_IGNORE_ZERO_ENTRIES, PETSC_FALSE));
1747: PetscCall(PetscFree(nnz));
1748: PetscCall(PetscMalloc1(maxnnz, &iwork));
1749: for (i = 0; i < m; i++) {
1750: PetscInt innz;
1751: const PetscInt *cols;
1752: const PetscScalar *vals;
1754: PetscCall(MatGetRow(A, i, &innz, &cols, &vals));
1755: for (j = 0; j < innz; j++) iwork[j] = (cols[j] / Nk) * (Nk * Ncopies) + (cols[j] % Nk);
1756: for (j = 0; j < Ncopies; j++) {
1757: PetscInt row = i * Ncopies + j;
1759: PetscCall(MatSetValues(Ac, 1, &row, innz, iwork, vals, INSERT_VALUES));
1760: for (k = 0; k < innz; k++) iwork[k] += Nk;
1761: }
1762: PetscCall(MatRestoreRow(A, i, &innz, &cols, &vals));
1763: }
1764: PetscCall(PetscFree(iwork));
1765: PetscCall(MatAssemblyBegin(Ac, MAT_FINAL_ASSEMBLY));
1766: PetscCall(MatAssemblyEnd(Ac, MAT_FINAL_ASSEMBLY));
1767: *Abs = Ac;
1768: PetscFunctionReturn(PETSC_SUCCESS);
1769: }
1771: /* check if a cell is a tensor product of the segment with a facet,
1772: * specifically checking if f and f2 can be the "endpoints" (like the triangles
1773: * at either end of a wedge) */
1774: static PetscErrorCode DMPlexPointIsTensor_Internal_Given(DM dm, PetscInt p, PetscInt f, PetscInt f2, PetscBool *isTensor)
1775: {
1776: PetscInt coneSize, c;
1777: const PetscInt *cone;
1778: const PetscInt *fCone;
1779: const PetscInt *f2Cone;
1780: PetscInt fs[2];
1781: PetscInt meetSize, nmeet;
1782: const PetscInt *meet;
1784: PetscFunctionBegin;
1785: fs[0] = f;
1786: fs[1] = f2;
1787: PetscCall(DMPlexGetMeet(dm, 2, fs, &meetSize, &meet));
1788: nmeet = meetSize;
1789: PetscCall(DMPlexRestoreMeet(dm, 2, fs, &meetSize, &meet));
1790: /* two points that have a non-empty meet cannot be at opposite ends of a cell */
1791: if (nmeet) {
1792: *isTensor = PETSC_FALSE;
1793: PetscFunctionReturn(PETSC_SUCCESS);
1794: }
1795: PetscCall(DMPlexGetConeSize(dm, p, &coneSize));
1796: PetscCall(DMPlexGetCone(dm, p, &cone));
1797: PetscCall(DMPlexGetCone(dm, f, &fCone));
1798: PetscCall(DMPlexGetCone(dm, f2, &f2Cone));
1799: for (c = 0; c < coneSize; c++) {
1800: PetscInt e, ef;
1801: PetscInt d = -1, d2 = -1;
1802: PetscInt dcount, d2count;
1803: PetscInt t = cone[c];
1804: PetscInt tConeSize;
1805: PetscBool tIsTensor;
1806: const PetscInt *tCone;
1808: if (t == f || t == f2) continue;
1809: /* for every other facet in the cone, check that is has
1810: * one ridge in common with each end */
1811: PetscCall(DMPlexGetConeSize(dm, t, &tConeSize));
1812: PetscCall(DMPlexGetCone(dm, t, &tCone));
1814: dcount = 0;
1815: d2count = 0;
1816: for (e = 0; e < tConeSize; e++) {
1817: PetscInt q = tCone[e];
1818: for (ef = 0; ef < coneSize - 2; ef++) {
1819: if (fCone[ef] == q) {
1820: if (dcount) {
1821: *isTensor = PETSC_FALSE;
1822: PetscFunctionReturn(PETSC_SUCCESS);
1823: }
1824: d = q;
1825: dcount++;
1826: } else if (f2Cone[ef] == q) {
1827: if (d2count) {
1828: *isTensor = PETSC_FALSE;
1829: PetscFunctionReturn(PETSC_SUCCESS);
1830: }
1831: d2 = q;
1832: d2count++;
1833: }
1834: }
1835: }
1836: /* if the whole cell is a tensor with the segment, then this
1837: * facet should be a tensor with the segment */
1838: PetscCall(DMPlexPointIsTensor_Internal_Given(dm, t, d, d2, &tIsTensor));
1839: if (!tIsTensor) {
1840: *isTensor = PETSC_FALSE;
1841: PetscFunctionReturn(PETSC_SUCCESS);
1842: }
1843: }
1844: *isTensor = PETSC_TRUE;
1845: PetscFunctionReturn(PETSC_SUCCESS);
1846: }
1848: /* determine if a cell is a tensor with a segment by looping over pairs of facets to find a pair
1849: * that could be the opposite ends */
1850: static PetscErrorCode DMPlexPointIsTensor_Internal(DM dm, PetscInt p, PetscBool *isTensor, PetscInt *endA, PetscInt *endB)
1851: {
1852: PetscInt coneSize, c, c2;
1853: const PetscInt *cone;
1855: PetscFunctionBegin;
1856: PetscCall(DMPlexGetConeSize(dm, p, &coneSize));
1857: if (!coneSize) {
1858: if (isTensor) *isTensor = PETSC_FALSE;
1859: if (endA) *endA = -1;
1860: if (endB) *endB = -1;
1861: }
1862: PetscCall(DMPlexGetCone(dm, p, &cone));
1863: for (c = 0; c < coneSize; c++) {
1864: PetscInt f = cone[c];
1865: PetscInt fConeSize;
1867: PetscCall(DMPlexGetConeSize(dm, f, &fConeSize));
1868: if (fConeSize != coneSize - 2) continue;
1870: for (c2 = c + 1; c2 < coneSize; c2++) {
1871: PetscInt f2 = cone[c2];
1872: PetscBool isTensorff2;
1873: PetscInt f2ConeSize;
1875: PetscCall(DMPlexGetConeSize(dm, f2, &f2ConeSize));
1876: if (f2ConeSize != coneSize - 2) continue;
1878: PetscCall(DMPlexPointIsTensor_Internal_Given(dm, p, f, f2, &isTensorff2));
1879: if (isTensorff2) {
1880: if (isTensor) *isTensor = PETSC_TRUE;
1881: if (endA) *endA = f;
1882: if (endB) *endB = f2;
1883: PetscFunctionReturn(PETSC_SUCCESS);
1884: }
1885: }
1886: }
1887: if (isTensor) *isTensor = PETSC_FALSE;
1888: if (endA) *endA = -1;
1889: if (endB) *endB = -1;
1890: PetscFunctionReturn(PETSC_SUCCESS);
1891: }
1893: /* determine if a cell is a tensor with a segment by looping over pairs of facets to find a pair
1894: * that could be the opposite ends */
1895: static PetscErrorCode DMPlexPointIsTensor(DM dm, PetscInt p, PetscBool *isTensor, PetscInt *endA, PetscInt *endB)
1896: {
1897: DMPlexInterpolatedFlag interpolated;
1899: PetscFunctionBegin;
1900: PetscCall(DMPlexIsInterpolated(dm, &interpolated));
1901: PetscCheck(interpolated == DMPLEX_INTERPOLATED_FULL, PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONGSTATE, "Only for interpolated DMPlex's");
1902: PetscCall(DMPlexPointIsTensor_Internal(dm, p, isTensor, endA, endB));
1903: PetscFunctionReturn(PETSC_SUCCESS);
1904: }
1906: /* Let k = formDegree and k' = -sign(k) * dim + k. Transform a symmetric frame for k-forms on the biunit simplex into
1907: * a symmetric frame for k'-forms on the biunit simplex.
1908: *
1909: * A frame is "symmetric" if the pullback of every symmetry of the biunit simplex is a permutation of the frame.
1910: *
1911: * forms in the symmetric frame are used as dofs in the untrimmed simplex spaces. This way, symmetries of the
1912: * reference cell result in permutations of dofs grouped by node.
1913: *
1914: * Use T to transform dof matrices for k'-forms into dof matrices for k-forms as a block diagonal transformation on
1915: * the right.
1916: */
1917: static PetscErrorCode BiunitSimplexSymmetricFormTransformation(PetscInt dim, PetscInt formDegree, PetscReal T[])
1918: {
1919: PetscInt k = formDegree;
1920: PetscInt kd = k < 0 ? dim + k : k - dim;
1921: PetscInt Nk;
1922: PetscReal *biToEq, *eqToBi, *biToEqStar, *eqToBiStar;
1923: PetscInt fact;
1925: PetscFunctionBegin;
1926: PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(k), &Nk));
1927: PetscCall(PetscCalloc4(dim * dim, &biToEq, dim * dim, &eqToBi, Nk * Nk, &biToEqStar, Nk * Nk, &eqToBiStar));
1928: /* fill in biToEq: Jacobian of the transformation from the biunit simplex to the equilateral simplex */
1929: fact = 0;
1930: for (PetscInt i = 0; i < dim; i++) {
1931: biToEq[i * dim + i] = PetscSqrtReal(((PetscReal)i + 2.) / (2. * ((PetscReal)i + 1.)));
1932: fact += 4 * (i + 1);
1933: for (PetscInt j = i + 1; j < dim; j++) biToEq[i * dim + j] = PetscSqrtReal(1. / (PetscReal)fact);
1934: }
1935: /* fill in eqToBi: Jacobian of the transformation from the equilateral simplex to the biunit simplex */
1936: fact = 0;
1937: for (PetscInt j = 0; j < dim; j++) {
1938: eqToBi[j * dim + j] = PetscSqrtReal(2. * ((PetscReal)j + 1.) / ((PetscReal)j + 2));
1939: fact += j + 1;
1940: for (PetscInt i = 0; i < j; i++) eqToBi[i * dim + j] = -PetscSqrtReal(1. / (PetscReal)fact);
1941: }
1942: PetscCall(PetscDTAltVPullbackMatrix(dim, dim, biToEq, kd, biToEqStar));
1943: PetscCall(PetscDTAltVPullbackMatrix(dim, dim, eqToBi, k, eqToBiStar));
1944: /* product of pullbacks simulates the following steps
1945: *
1946: * 1. start with frame W = [w_1, w_2, ..., w_m] of k forms that is symmetric on the biunit simplex:
1947: if J is the Jacobian of a symmetry of the biunit simplex, then J_k* W = [J_k*w_1, ..., J_k*w_m]
1948: is a permutation of W.
1949: Even though a k' form --- a (dim - k) form represented by its Hodge star --- has the same geometric
1950: content as a k form, W is not a symmetric frame of k' forms on the biunit simplex. That's because,
1951: for general Jacobian J, J_k* != J_k'*.
1952: * 2. pullback W to the equilateral triangle using the k pullback, W_eq = eqToBi_k* W. All symmetries of the
1953: equilateral simplex have orthonormal Jacobians. For an orthonormal Jacobian O, J_k* = J_k'*, so W_eq is
1954: also a symmetric frame for k' forms on the equilateral simplex.
1955: 3. pullback W_eq back to the biunit simplex using the k' pulback, V = biToEq_k'* W_eq = biToEq_k'* eqToBi_k* W.
1956: V is a symmetric frame for k' forms on the biunit simplex.
1957: */
1958: for (PetscInt i = 0; i < Nk; i++) {
1959: for (PetscInt j = 0; j < Nk; j++) {
1960: PetscReal val = 0.;
1961: for (PetscInt k = 0; k < Nk; k++) val += biToEqStar[i * Nk + k] * eqToBiStar[k * Nk + j];
1962: T[i * Nk + j] = val;
1963: }
1964: }
1965: PetscCall(PetscFree4(biToEq, eqToBi, biToEqStar, eqToBiStar));
1966: PetscFunctionReturn(PETSC_SUCCESS);
1967: }
1969: /* permute a quadrature -> dof matrix so that its rows are in revlex order by nodeIdx */
1970: static PetscErrorCode MatPermuteByNodeIdx(Mat A, PetscLagNodeIndices ni, Mat *Aperm)
1971: {
1972: PetscInt m, n, i, j;
1973: PetscInt nodeIdxDim = ni->nodeIdxDim;
1974: PetscInt nodeVecDim = ni->nodeVecDim;
1975: PetscInt *perm;
1976: IS permIS;
1977: IS id;
1978: PetscInt *nIdxPerm;
1979: PetscReal *nVecPerm;
1981: PetscFunctionBegin;
1982: PetscCall(PetscLagNodeIndicesGetPermutation(ni, &perm));
1983: PetscCall(MatGetSize(A, &m, &n));
1984: PetscCall(PetscMalloc1(nodeIdxDim * m, &nIdxPerm));
1985: PetscCall(PetscMalloc1(nodeVecDim * m, &nVecPerm));
1986: for (i = 0; i < m; i++)
1987: for (j = 0; j < nodeIdxDim; j++) nIdxPerm[i * nodeIdxDim + j] = ni->nodeIdx[perm[i] * nodeIdxDim + j];
1988: for (i = 0; i < m; i++)
1989: for (j = 0; j < nodeVecDim; j++) nVecPerm[i * nodeVecDim + j] = ni->nodeVec[perm[i] * nodeVecDim + j];
1990: PetscCall(ISCreateGeneral(PETSC_COMM_SELF, m, perm, PETSC_USE_POINTER, &permIS));
1991: PetscCall(ISSetPermutation(permIS));
1992: PetscCall(ISCreateStride(PETSC_COMM_SELF, n, 0, 1, &id));
1993: PetscCall(ISSetPermutation(id));
1994: PetscCall(MatPermute(A, permIS, id, Aperm));
1995: PetscCall(ISDestroy(&permIS));
1996: PetscCall(ISDestroy(&id));
1997: for (i = 0; i < m; i++) perm[i] = i;
1998: PetscCall(PetscFree(ni->nodeIdx));
1999: PetscCall(PetscFree(ni->nodeVec));
2000: ni->nodeIdx = nIdxPerm;
2001: ni->nodeVec = nVecPerm;
2002: PetscFunctionReturn(PETSC_SUCCESS);
2003: }
2005: static PetscErrorCode PetscDualSpaceSetUp_Lagrange(PetscDualSpace sp)
2006: {
2007: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2008: DM dm = sp->dm;
2009: DM dmint = NULL;
2010: PetscInt order;
2011: PetscInt Nc = sp->Nc;
2012: MPI_Comm comm;
2013: PetscBool continuous;
2014: PetscSection section;
2015: PetscInt depth, dim, pStart, pEnd, cStart, cEnd, p, *pStratStart, *pStratEnd, d;
2016: PetscInt formDegree, Nk, Ncopies;
2017: PetscInt tensorf = -1, tensorf2 = -1;
2018: PetscBool tensorCell, tensorSpace;
2019: PetscBool uniform, trimmed;
2020: Petsc1DNodeFamily nodeFamily;
2021: PetscInt numNodeSkip;
2022: DMPlexInterpolatedFlag interpolated;
2023: PetscBool isbdm;
2025: PetscFunctionBegin;
2026: /* step 1: sanitize input */
2027: PetscCall(PetscObjectGetComm((PetscObject)sp, &comm));
2028: PetscCall(DMGetDimension(dm, &dim));
2029: PetscCall(PetscObjectTypeCompare((PetscObject)sp, PETSCDUALSPACEBDM, &isbdm));
2030: if (isbdm) {
2031: sp->k = -(dim - 1); /* form degree of H-div */
2032: PetscCall(PetscObjectChangeTypeName((PetscObject)sp, PETSCDUALSPACELAGRANGE));
2033: }
2034: PetscCall(PetscDualSpaceGetFormDegree(sp, &formDegree));
2035: PetscCheck(PetscAbsInt(formDegree) <= dim, comm, PETSC_ERR_ARG_OUTOFRANGE, "Form degree must be bounded by dimension");
2036: PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(formDegree), &Nk));
2037: if (sp->Nc <= 0 && lag->numCopies > 0) sp->Nc = Nk * lag->numCopies;
2038: Nc = sp->Nc;
2039: PetscCheck(Nc % Nk == 0, comm, PETSC_ERR_ARG_INCOMP, "Number of components is not a multiple of form degree size");
2040: if (lag->numCopies <= 0) lag->numCopies = Nc / Nk;
2041: Ncopies = lag->numCopies;
2042: PetscCheck(Nc / Nk == Ncopies, comm, PETSC_ERR_ARG_INCOMP, "Number of copies * (dim choose k) != Nc");
2043: if (!dim) sp->order = 0;
2044: order = sp->order;
2045: uniform = sp->uniform;
2046: PetscCheck(uniform, PETSC_COMM_SELF, PETSC_ERR_SUP, "Variable order not supported yet");
2047: if (lag->trimmed && !formDegree) lag->trimmed = PETSC_FALSE; /* trimmed spaces are the same as full spaces for 0-forms */
2048: if (lag->nodeType == PETSCDTNODES_DEFAULT) {
2049: lag->nodeType = PETSCDTNODES_GAUSSJACOBI;
2050: lag->nodeExponent = 0.;
2051: /* trimmed spaces don't include corner vertices, so don't use end nodes by default */
2052: lag->endNodes = lag->trimmed ? PETSC_FALSE : PETSC_TRUE;
2053: }
2054: /* If a trimmed space and the user did choose nodes with endpoints, skip them by default */
2055: if (lag->numNodeSkip < 0) lag->numNodeSkip = (lag->trimmed && lag->endNodes) ? 1 : 0;
2056: numNodeSkip = lag->numNodeSkip;
2057: PetscCheck(!lag->trimmed || order, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Cannot have zeroth order trimmed elements");
2058: if (lag->trimmed && PetscAbsInt(formDegree) == dim) { /* convert trimmed n-forms to untrimmed of one polynomial order less */
2059: sp->order--;
2060: order--;
2061: lag->trimmed = PETSC_FALSE;
2062: }
2063: trimmed = lag->trimmed;
2064: if (!order || PetscAbsInt(formDegree) == dim) lag->continuous = PETSC_FALSE;
2065: continuous = lag->continuous;
2066: PetscCall(DMPlexGetDepth(dm, &depth));
2067: PetscCall(DMPlexGetChart(dm, &pStart, &pEnd));
2068: PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
2069: PetscCheck(pStart == 0 && cStart == 0, PetscObjectComm((PetscObject)sp), PETSC_ERR_ARG_WRONGSTATE, "Expect DM with chart starting at zero and cells first");
2070: PetscCheck(cEnd == 1, PetscObjectComm((PetscObject)sp), PETSC_ERR_ARG_WRONGSTATE, "Use PETSCDUALSPACEREFINED for multi-cell reference meshes");
2071: PetscCall(DMPlexIsInterpolated(dm, &interpolated));
2072: if (interpolated != DMPLEX_INTERPOLATED_FULL) {
2073: PetscCall(DMPlexInterpolate(dm, &dmint));
2074: } else {
2075: PetscCall(PetscObjectReference((PetscObject)dm));
2076: dmint = dm;
2077: }
2078: tensorCell = PETSC_FALSE;
2079: if (dim > 1) PetscCall(DMPlexPointIsTensor(dmint, 0, &tensorCell, &tensorf, &tensorf2));
2080: lag->tensorCell = tensorCell;
2081: if (dim < 2 || !lag->tensorCell) lag->tensorSpace = PETSC_FALSE;
2082: tensorSpace = lag->tensorSpace;
2083: if (!lag->nodeFamily) PetscCall(Petsc1DNodeFamilyCreate(lag->nodeType, lag->nodeExponent, lag->endNodes, &lag->nodeFamily));
2084: nodeFamily = lag->nodeFamily;
2085: PetscCheck(interpolated == DMPLEX_INTERPOLATED_FULL || !continuous || (PetscAbsInt(formDegree) <= 0 && order <= 1), PETSC_COMM_SELF, PETSC_ERR_PLIB, "Reference element won't support all boundary nodes");
2087: /* step 2: construct the boundary spaces */
2088: PetscCall(PetscMalloc2(depth + 1, &pStratStart, depth + 1, &pStratEnd));
2089: PetscCall(PetscCalloc1(pEnd, &(sp->pointSpaces)));
2090: for (d = 0; d <= depth; ++d) PetscCall(DMPlexGetDepthStratum(dm, d, &pStratStart[d], &pStratEnd[d]));
2091: PetscCall(PetscDualSpaceSectionCreate_Internal(sp, §ion));
2092: sp->pointSection = section;
2093: if (continuous && !(lag->interiorOnly)) {
2094: PetscInt h;
2096: for (p = pStratStart[depth - 1]; p < pStratEnd[depth - 1]; p++) { /* calculate the facet dual spaces */
2097: PetscReal v0[3];
2098: DMPolytopeType ptype;
2099: PetscReal J[9], detJ;
2100: PetscInt q;
2102: PetscCall(DMPlexComputeCellGeometryAffineFEM(dm, p, v0, J, NULL, &detJ));
2103: PetscCall(DMPlexGetCellType(dm, p, &ptype));
2105: /* compare to previous facets: if computed, reference that dualspace */
2106: for (q = pStratStart[depth - 1]; q < p; q++) {
2107: DMPolytopeType qtype;
2109: PetscCall(DMPlexGetCellType(dm, q, &qtype));
2110: if (qtype == ptype) break;
2111: }
2112: if (q < p) { /* this facet has the same dual space as that one */
2113: PetscCall(PetscObjectReference((PetscObject)sp->pointSpaces[q]));
2114: sp->pointSpaces[p] = sp->pointSpaces[q];
2115: continue;
2116: }
2117: /* if not, recursively compute this dual space */
2118: PetscCall(PetscDualSpaceCreateFacetSubspace_Lagrange(sp, NULL, p, formDegree, Ncopies, PETSC_FALSE, &sp->pointSpaces[p]));
2119: }
2120: for (h = 2; h <= depth; h++) { /* get the higher subspaces from the facet subspaces */
2121: PetscInt hd = depth - h;
2122: PetscInt hdim = dim - h;
2124: if (hdim < PetscAbsInt(formDegree)) break;
2125: for (p = pStratStart[hd]; p < pStratEnd[hd]; p++) {
2126: PetscInt suppSize, s;
2127: const PetscInt *supp;
2129: PetscCall(DMPlexGetSupportSize(dm, p, &suppSize));
2130: PetscCall(DMPlexGetSupport(dm, p, &supp));
2131: for (s = 0; s < suppSize; s++) {
2132: DM qdm;
2133: PetscDualSpace qsp, psp;
2134: PetscInt c, coneSize, q;
2135: const PetscInt *cone;
2136: const PetscInt *refCone;
2138: q = supp[0];
2139: qsp = sp->pointSpaces[q];
2140: PetscCall(DMPlexGetConeSize(dm, q, &coneSize));
2141: PetscCall(DMPlexGetCone(dm, q, &cone));
2142: for (c = 0; c < coneSize; c++)
2143: if (cone[c] == p) break;
2144: PetscCheck(c != coneSize, PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "cone/support mismatch");
2145: PetscCall(PetscDualSpaceGetDM(qsp, &qdm));
2146: PetscCall(DMPlexGetCone(qdm, 0, &refCone));
2147: /* get the equivalent dual space from the support dual space */
2148: PetscCall(PetscDualSpaceGetPointSubspace(qsp, refCone[c], &psp));
2149: if (!s) {
2150: PetscCall(PetscObjectReference((PetscObject)psp));
2151: sp->pointSpaces[p] = psp;
2152: }
2153: }
2154: }
2155: }
2156: for (p = 1; p < pEnd; p++) {
2157: PetscInt pspdim;
2158: if (!sp->pointSpaces[p]) continue;
2159: PetscCall(PetscDualSpaceGetInteriorDimension(sp->pointSpaces[p], &pspdim));
2160: PetscCall(PetscSectionSetDof(section, p, pspdim));
2161: }
2162: }
2164: if (Ncopies > 1) {
2165: Mat intMatScalar, allMatScalar;
2166: PetscDualSpace scalarsp;
2167: PetscDualSpace_Lag *scalarlag;
2169: PetscCall(PetscDualSpaceDuplicate(sp, &scalarsp));
2170: /* Setting the number of components to Nk is a space with 1 copy of each k-form */
2171: PetscCall(PetscDualSpaceSetNumComponents(scalarsp, Nk));
2172: PetscCall(PetscDualSpaceSetUp(scalarsp));
2173: PetscCall(PetscDualSpaceGetInteriorData(scalarsp, &(sp->intNodes), &intMatScalar));
2174: PetscCall(PetscObjectReference((PetscObject)(sp->intNodes)));
2175: if (intMatScalar) PetscCall(PetscDualSpaceLagrangeMatrixCreateCopies(intMatScalar, Nk, Ncopies, &(sp->intMat)));
2176: PetscCall(PetscDualSpaceGetAllData(scalarsp, &(sp->allNodes), &allMatScalar));
2177: PetscCall(PetscObjectReference((PetscObject)(sp->allNodes)));
2178: PetscCall(PetscDualSpaceLagrangeMatrixCreateCopies(allMatScalar, Nk, Ncopies, &(sp->allMat)));
2179: sp->spdim = scalarsp->spdim * Ncopies;
2180: sp->spintdim = scalarsp->spintdim * Ncopies;
2181: scalarlag = (PetscDualSpace_Lag *)scalarsp->data;
2182: PetscCall(PetscLagNodeIndicesReference(scalarlag->vertIndices));
2183: lag->vertIndices = scalarlag->vertIndices;
2184: PetscCall(PetscLagNodeIndicesReference(scalarlag->intNodeIndices));
2185: lag->intNodeIndices = scalarlag->intNodeIndices;
2186: PetscCall(PetscLagNodeIndicesReference(scalarlag->allNodeIndices));
2187: lag->allNodeIndices = scalarlag->allNodeIndices;
2188: PetscCall(PetscDualSpaceDestroy(&scalarsp));
2189: PetscCall(PetscSectionSetDof(section, 0, sp->spintdim));
2190: PetscCall(PetscDualSpaceSectionSetUp_Internal(sp, section));
2191: PetscCall(PetscDualSpaceComputeFunctionalsFromAllData(sp));
2192: PetscCall(PetscFree2(pStratStart, pStratEnd));
2193: PetscCall(DMDestroy(&dmint));
2194: PetscFunctionReturn(PETSC_SUCCESS);
2195: }
2197: if (trimmed && !continuous) {
2198: /* the dofs of a trimmed space don't have a nice tensor/lattice structure:
2199: * just construct the continuous dual space and copy all of the data over,
2200: * allocating it all to the cell instead of splitting it up between the boundaries */
2201: PetscDualSpace spcont;
2202: PetscInt spdim, f;
2203: PetscQuadrature allNodes;
2204: PetscDualSpace_Lag *lagc;
2205: Mat allMat;
2207: PetscCall(PetscDualSpaceDuplicate(sp, &spcont));
2208: PetscCall(PetscDualSpaceLagrangeSetContinuity(spcont, PETSC_TRUE));
2209: PetscCall(PetscDualSpaceSetUp(spcont));
2210: PetscCall(PetscDualSpaceGetDimension(spcont, &spdim));
2211: sp->spdim = sp->spintdim = spdim;
2212: PetscCall(PetscSectionSetDof(section, 0, spdim));
2213: PetscCall(PetscDualSpaceSectionSetUp_Internal(sp, section));
2214: PetscCall(PetscMalloc1(spdim, &(sp->functional)));
2215: for (f = 0; f < spdim; f++) {
2216: PetscQuadrature fn;
2218: PetscCall(PetscDualSpaceGetFunctional(spcont, f, &fn));
2219: PetscCall(PetscObjectReference((PetscObject)fn));
2220: sp->functional[f] = fn;
2221: }
2222: PetscCall(PetscDualSpaceGetAllData(spcont, &allNodes, &allMat));
2223: PetscCall(PetscObjectReference((PetscObject)allNodes));
2224: PetscCall(PetscObjectReference((PetscObject)allNodes));
2225: sp->allNodes = sp->intNodes = allNodes;
2226: PetscCall(PetscObjectReference((PetscObject)allMat));
2227: PetscCall(PetscObjectReference((PetscObject)allMat));
2228: sp->allMat = sp->intMat = allMat;
2229: lagc = (PetscDualSpace_Lag *)spcont->data;
2230: PetscCall(PetscLagNodeIndicesReference(lagc->vertIndices));
2231: lag->vertIndices = lagc->vertIndices;
2232: PetscCall(PetscLagNodeIndicesReference(lagc->allNodeIndices));
2233: PetscCall(PetscLagNodeIndicesReference(lagc->allNodeIndices));
2234: lag->intNodeIndices = lagc->allNodeIndices;
2235: lag->allNodeIndices = lagc->allNodeIndices;
2236: PetscCall(PetscDualSpaceDestroy(&spcont));
2237: PetscCall(PetscFree2(pStratStart, pStratEnd));
2238: PetscCall(DMDestroy(&dmint));
2239: PetscFunctionReturn(PETSC_SUCCESS);
2240: }
2242: /* step 3: construct intNodes, and intMat, and combine it with boundray data to make allNodes and allMat */
2243: if (!tensorSpace) {
2244: if (!tensorCell) PetscCall(PetscLagNodeIndicesCreateSimplexVertices(dm, &(lag->vertIndices)));
2246: if (trimmed) {
2247: /* there is one dof in the interior of the a trimmed element for each full polynomial of with degree at most
2248: * order + k - dim - 1 */
2249: if (order + PetscAbsInt(formDegree) > dim) {
2250: PetscInt sum = order + PetscAbsInt(formDegree) - dim - 1;
2251: PetscInt nDofs;
2253: PetscCall(PetscDualSpaceLagrangeCreateSimplexNodeMat(nodeFamily, dim, sum, Nk, numNodeSkip, &sp->intNodes, &sp->intMat, &(lag->intNodeIndices)));
2254: PetscCall(MatGetSize(sp->intMat, &nDofs, NULL));
2255: PetscCall(PetscSectionSetDof(section, 0, nDofs));
2256: }
2257: PetscCall(PetscDualSpaceSectionSetUp_Internal(sp, section));
2258: PetscCall(PetscDualSpaceCreateAllDataFromInteriorData(sp));
2259: PetscCall(PetscDualSpaceLagrangeCreateAllNodeIdx(sp));
2260: } else {
2261: if (!continuous) {
2262: /* if discontinuous just construct one node for each set of dofs (a set of dofs is a basis for the k-form
2263: * space) */
2264: PetscInt sum = order;
2265: PetscInt nDofs;
2267: PetscCall(PetscDualSpaceLagrangeCreateSimplexNodeMat(nodeFamily, dim, sum, Nk, numNodeSkip, &sp->intNodes, &sp->intMat, &(lag->intNodeIndices)));
2268: PetscCall(MatGetSize(sp->intMat, &nDofs, NULL));
2269: PetscCall(PetscSectionSetDof(section, 0, nDofs));
2270: PetscCall(PetscDualSpaceSectionSetUp_Internal(sp, section));
2271: PetscCall(PetscObjectReference((PetscObject)(sp->intNodes)));
2272: sp->allNodes = sp->intNodes;
2273: PetscCall(PetscObjectReference((PetscObject)(sp->intMat)));
2274: sp->allMat = sp->intMat;
2275: PetscCall(PetscLagNodeIndicesReference(lag->intNodeIndices));
2276: lag->allNodeIndices = lag->intNodeIndices;
2277: } else {
2278: /* there is one dof in the interior of the a full element for each trimmed polynomial of with degree at most
2279: * order + k - dim, but with complementary form degree */
2280: if (order + PetscAbsInt(formDegree) > dim) {
2281: PetscDualSpace trimmedsp;
2282: PetscDualSpace_Lag *trimmedlag;
2283: PetscQuadrature intNodes;
2284: PetscInt trFormDegree = formDegree >= 0 ? formDegree - dim : dim - PetscAbsInt(formDegree);
2285: PetscInt nDofs;
2286: Mat intMat;
2288: PetscCall(PetscDualSpaceDuplicate(sp, &trimmedsp));
2289: PetscCall(PetscDualSpaceLagrangeSetTrimmed(trimmedsp, PETSC_TRUE));
2290: PetscCall(PetscDualSpaceSetOrder(trimmedsp, order + PetscAbsInt(formDegree) - dim));
2291: PetscCall(PetscDualSpaceSetFormDegree(trimmedsp, trFormDegree));
2292: trimmedlag = (PetscDualSpace_Lag *)trimmedsp->data;
2293: trimmedlag->numNodeSkip = numNodeSkip + 1;
2294: PetscCall(PetscDualSpaceSetUp(trimmedsp));
2295: PetscCall(PetscDualSpaceGetAllData(trimmedsp, &intNodes, &intMat));
2296: PetscCall(PetscObjectReference((PetscObject)intNodes));
2297: sp->intNodes = intNodes;
2298: PetscCall(PetscLagNodeIndicesReference(trimmedlag->allNodeIndices));
2299: lag->intNodeIndices = trimmedlag->allNodeIndices;
2300: PetscCall(PetscObjectReference((PetscObject)intMat));
2301: if (PetscAbsInt(formDegree) > 0 && PetscAbsInt(formDegree) < dim) {
2302: PetscReal *T;
2303: PetscScalar *work;
2304: PetscInt nCols, nRows;
2305: Mat intMatT;
2307: PetscCall(MatDuplicate(intMat, MAT_COPY_VALUES, &intMatT));
2308: PetscCall(MatGetSize(intMat, &nRows, &nCols));
2309: PetscCall(PetscMalloc2(Nk * Nk, &T, nCols, &work));
2310: PetscCall(BiunitSimplexSymmetricFormTransformation(dim, formDegree, T));
2311: for (PetscInt row = 0; row < nRows; row++) {
2312: PetscInt nrCols;
2313: const PetscInt *rCols;
2314: const PetscScalar *rVals;
2316: PetscCall(MatGetRow(intMat, row, &nrCols, &rCols, &rVals));
2317: PetscCheck(nrCols % Nk == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "nonzeros in intMat matrix are not in k-form size blocks");
2318: for (PetscInt b = 0; b < nrCols; b += Nk) {
2319: const PetscScalar *v = &rVals[b];
2320: PetscScalar *w = &work[b];
2321: for (PetscInt j = 0; j < Nk; j++) {
2322: w[j] = 0.;
2323: for (PetscInt i = 0; i < Nk; i++) w[j] += v[i] * T[i * Nk + j];
2324: }
2325: }
2326: PetscCall(MatSetValuesBlocked(intMatT, 1, &row, nrCols, rCols, work, INSERT_VALUES));
2327: PetscCall(MatRestoreRow(intMat, row, &nrCols, &rCols, &rVals));
2328: }
2329: PetscCall(MatAssemblyBegin(intMatT, MAT_FINAL_ASSEMBLY));
2330: PetscCall(MatAssemblyEnd(intMatT, MAT_FINAL_ASSEMBLY));
2331: PetscCall(MatDestroy(&intMat));
2332: intMat = intMatT;
2333: PetscCall(PetscLagNodeIndicesDestroy(&(lag->intNodeIndices)));
2334: PetscCall(PetscLagNodeIndicesDuplicate(trimmedlag->allNodeIndices, &(lag->intNodeIndices)));
2335: {
2336: PetscInt nNodes = lag->intNodeIndices->nNodes;
2337: PetscReal *newNodeVec = lag->intNodeIndices->nodeVec;
2338: const PetscReal *oldNodeVec = trimmedlag->allNodeIndices->nodeVec;
2340: for (PetscInt n = 0; n < nNodes; n++) {
2341: PetscReal *w = &newNodeVec[n * Nk];
2342: const PetscReal *v = &oldNodeVec[n * Nk];
2344: for (PetscInt j = 0; j < Nk; j++) {
2345: w[j] = 0.;
2346: for (PetscInt i = 0; i < Nk; i++) w[j] += v[i] * T[i * Nk + j];
2347: }
2348: }
2349: }
2350: PetscCall(PetscFree2(T, work));
2351: }
2352: sp->intMat = intMat;
2353: PetscCall(MatGetSize(sp->intMat, &nDofs, NULL));
2354: PetscCall(PetscDualSpaceDestroy(&trimmedsp));
2355: PetscCall(PetscSectionSetDof(section, 0, nDofs));
2356: }
2357: PetscCall(PetscDualSpaceSectionSetUp_Internal(sp, section));
2358: PetscCall(PetscDualSpaceCreateAllDataFromInteriorData(sp));
2359: PetscCall(PetscDualSpaceLagrangeCreateAllNodeIdx(sp));
2360: }
2361: }
2362: } else {
2363: PetscQuadrature intNodesTrace = NULL;
2364: PetscQuadrature intNodesFiber = NULL;
2365: PetscQuadrature intNodes = NULL;
2366: PetscLagNodeIndices intNodeIndices = NULL;
2367: Mat intMat = NULL;
2369: if (PetscAbsInt(formDegree) < dim) { /* get the trace k-forms on the first facet, and the 0-forms on the edge,
2370: and wedge them together to create some of the k-form dofs */
2371: PetscDualSpace trace, fiber;
2372: PetscDualSpace_Lag *tracel, *fiberl;
2373: Mat intMatTrace, intMatFiber;
2375: if (sp->pointSpaces[tensorf]) {
2376: PetscCall(PetscObjectReference((PetscObject)(sp->pointSpaces[tensorf])));
2377: trace = sp->pointSpaces[tensorf];
2378: } else {
2379: PetscCall(PetscDualSpaceCreateFacetSubspace_Lagrange(sp, NULL, tensorf, formDegree, Ncopies, PETSC_TRUE, &trace));
2380: }
2381: PetscCall(PetscDualSpaceCreateEdgeSubspace_Lagrange(sp, order, 0, 1, PETSC_TRUE, &fiber));
2382: tracel = (PetscDualSpace_Lag *)trace->data;
2383: fiberl = (PetscDualSpace_Lag *)fiber->data;
2384: PetscCall(PetscLagNodeIndicesCreateTensorVertices(dm, tracel->vertIndices, &(lag->vertIndices)));
2385: PetscCall(PetscDualSpaceGetInteriorData(trace, &intNodesTrace, &intMatTrace));
2386: PetscCall(PetscDualSpaceGetInteriorData(fiber, &intNodesFiber, &intMatFiber));
2387: if (intNodesTrace && intNodesFiber) {
2388: PetscCall(PetscQuadratureCreateTensor(intNodesTrace, intNodesFiber, &intNodes));
2389: PetscCall(MatTensorAltV(intMatTrace, intMatFiber, dim - 1, formDegree, 1, 0, &intMat));
2390: PetscCall(PetscLagNodeIndicesTensor(tracel->intNodeIndices, dim - 1, formDegree, fiberl->intNodeIndices, 1, 0, &intNodeIndices));
2391: }
2392: PetscCall(PetscObjectReference((PetscObject)intNodesTrace));
2393: PetscCall(PetscObjectReference((PetscObject)intNodesFiber));
2394: PetscCall(PetscDualSpaceDestroy(&fiber));
2395: PetscCall(PetscDualSpaceDestroy(&trace));
2396: }
2397: if (PetscAbsInt(formDegree) > 0) { /* get the trace (k-1)-forms on the first facet, and the 1-forms on the edge,
2398: and wedge them together to create the remaining k-form dofs */
2399: PetscDualSpace trace, fiber;
2400: PetscDualSpace_Lag *tracel, *fiberl;
2401: PetscQuadrature intNodesTrace2, intNodesFiber2, intNodes2;
2402: PetscLagNodeIndices intNodeIndices2;
2403: Mat intMatTrace, intMatFiber, intMat2;
2404: PetscInt traceDegree = formDegree > 0 ? formDegree - 1 : formDegree + 1;
2405: PetscInt fiberDegree = formDegree > 0 ? 1 : -1;
2407: PetscCall(PetscDualSpaceCreateFacetSubspace_Lagrange(sp, NULL, tensorf, traceDegree, Ncopies, PETSC_TRUE, &trace));
2408: PetscCall(PetscDualSpaceCreateEdgeSubspace_Lagrange(sp, order, fiberDegree, 1, PETSC_TRUE, &fiber));
2409: tracel = (PetscDualSpace_Lag *)trace->data;
2410: fiberl = (PetscDualSpace_Lag *)fiber->data;
2411: if (!lag->vertIndices) PetscCall(PetscLagNodeIndicesCreateTensorVertices(dm, tracel->vertIndices, &(lag->vertIndices)));
2412: PetscCall(PetscDualSpaceGetInteriorData(trace, &intNodesTrace2, &intMatTrace));
2413: PetscCall(PetscDualSpaceGetInteriorData(fiber, &intNodesFiber2, &intMatFiber));
2414: if (intNodesTrace2 && intNodesFiber2) {
2415: PetscCall(PetscQuadratureCreateTensor(intNodesTrace2, intNodesFiber2, &intNodes2));
2416: PetscCall(MatTensorAltV(intMatTrace, intMatFiber, dim - 1, traceDegree, 1, fiberDegree, &intMat2));
2417: PetscCall(PetscLagNodeIndicesTensor(tracel->intNodeIndices, dim - 1, traceDegree, fiberl->intNodeIndices, 1, fiberDegree, &intNodeIndices2));
2418: if (!intMat) {
2419: intMat = intMat2;
2420: intNodes = intNodes2;
2421: intNodeIndices = intNodeIndices2;
2422: } else {
2423: /* merge the matrices, quadrature points, and nodes */
2424: PetscInt nM;
2425: PetscInt nDof, nDof2;
2426: PetscInt *toMerged = NULL, *toMerged2 = NULL;
2427: PetscQuadrature merged = NULL;
2428: PetscLagNodeIndices intNodeIndicesMerged = NULL;
2429: Mat matMerged = NULL;
2431: PetscCall(MatGetSize(intMat, &nDof, NULL));
2432: PetscCall(MatGetSize(intMat2, &nDof2, NULL));
2433: PetscCall(PetscQuadraturePointsMerge(intNodes, intNodes2, &merged, &toMerged, &toMerged2));
2434: PetscCall(PetscQuadratureGetData(merged, NULL, NULL, &nM, NULL, NULL));
2435: PetscCall(MatricesMerge(intMat, intMat2, dim, formDegree, nM, toMerged, toMerged2, &matMerged));
2436: PetscCall(PetscLagNodeIndicesMerge(intNodeIndices, intNodeIndices2, &intNodeIndicesMerged));
2437: PetscCall(PetscFree(toMerged));
2438: PetscCall(PetscFree(toMerged2));
2439: PetscCall(MatDestroy(&intMat));
2440: PetscCall(MatDestroy(&intMat2));
2441: PetscCall(PetscQuadratureDestroy(&intNodes));
2442: PetscCall(PetscQuadratureDestroy(&intNodes2));
2443: PetscCall(PetscLagNodeIndicesDestroy(&intNodeIndices));
2444: PetscCall(PetscLagNodeIndicesDestroy(&intNodeIndices2));
2445: intNodes = merged;
2446: intMat = matMerged;
2447: intNodeIndices = intNodeIndicesMerged;
2448: if (!trimmed) {
2449: /* I think users expect that, when a node has a full basis for the k-forms,
2450: * they should be consecutive dofs. That isn't the case for trimmed spaces,
2451: * but is for some of the nodes in untrimmed spaces, so in that case we
2452: * sort them to group them by node */
2453: Mat intMatPerm;
2455: PetscCall(MatPermuteByNodeIdx(intMat, intNodeIndices, &intMatPerm));
2456: PetscCall(MatDestroy(&intMat));
2457: intMat = intMatPerm;
2458: }
2459: }
2460: }
2461: PetscCall(PetscDualSpaceDestroy(&fiber));
2462: PetscCall(PetscDualSpaceDestroy(&trace));
2463: }
2464: PetscCall(PetscQuadratureDestroy(&intNodesTrace));
2465: PetscCall(PetscQuadratureDestroy(&intNodesFiber));
2466: sp->intNodes = intNodes;
2467: sp->intMat = intMat;
2468: lag->intNodeIndices = intNodeIndices;
2469: {
2470: PetscInt nDofs = 0;
2472: if (intMat) PetscCall(MatGetSize(intMat, &nDofs, NULL));
2473: PetscCall(PetscSectionSetDof(section, 0, nDofs));
2474: }
2475: PetscCall(PetscDualSpaceSectionSetUp_Internal(sp, section));
2476: if (continuous) {
2477: PetscCall(PetscDualSpaceCreateAllDataFromInteriorData(sp));
2478: PetscCall(PetscDualSpaceLagrangeCreateAllNodeIdx(sp));
2479: } else {
2480: PetscCall(PetscObjectReference((PetscObject)intNodes));
2481: sp->allNodes = intNodes;
2482: PetscCall(PetscObjectReference((PetscObject)intMat));
2483: sp->allMat = intMat;
2484: PetscCall(PetscLagNodeIndicesReference(intNodeIndices));
2485: lag->allNodeIndices = intNodeIndices;
2486: }
2487: }
2488: PetscCall(PetscSectionGetStorageSize(section, &sp->spdim));
2489: PetscCall(PetscSectionGetConstrainedStorageSize(section, &sp->spintdim));
2490: PetscCall(PetscDualSpaceComputeFunctionalsFromAllData(sp));
2491: PetscCall(PetscFree2(pStratStart, pStratEnd));
2492: PetscCall(DMDestroy(&dmint));
2493: PetscFunctionReturn(PETSC_SUCCESS);
2494: }
2496: /* Create a matrix that represents the transformation that DMPlexVecGetClosure() would need
2497: * to get the representation of the dofs for a mesh point if the mesh point had this orientation
2498: * relative to the cell */
2499: PetscErrorCode PetscDualSpaceCreateInteriorSymmetryMatrix_Lagrange(PetscDualSpace sp, PetscInt ornt, Mat *symMat)
2500: {
2501: PetscDualSpace_Lag *lag;
2502: DM dm;
2503: PetscLagNodeIndices vertIndices, intNodeIndices;
2504: PetscLagNodeIndices ni;
2505: PetscInt nodeIdxDim, nodeVecDim, nNodes;
2506: PetscInt formDegree;
2507: PetscInt *perm, *permOrnt;
2508: PetscInt *nnz;
2509: PetscInt n;
2510: PetscInt maxGroupSize;
2511: PetscScalar *V, *W, *work;
2512: Mat A;
2514: PetscFunctionBegin;
2515: if (!sp->spintdim) {
2516: *symMat = NULL;
2517: PetscFunctionReturn(PETSC_SUCCESS);
2518: }
2519: lag = (PetscDualSpace_Lag *)sp->data;
2520: vertIndices = lag->vertIndices;
2521: intNodeIndices = lag->intNodeIndices;
2522: PetscCall(PetscDualSpaceGetDM(sp, &dm));
2523: PetscCall(PetscDualSpaceGetFormDegree(sp, &formDegree));
2524: PetscCall(PetscNew(&ni));
2525: ni->refct = 1;
2526: ni->nodeIdxDim = nodeIdxDim = intNodeIndices->nodeIdxDim;
2527: ni->nodeVecDim = nodeVecDim = intNodeIndices->nodeVecDim;
2528: ni->nNodes = nNodes = intNodeIndices->nNodes;
2529: PetscCall(PetscMalloc1(nNodes * nodeIdxDim, &(ni->nodeIdx)));
2530: PetscCall(PetscMalloc1(nNodes * nodeVecDim, &(ni->nodeVec)));
2531: /* push forward the dofs by the symmetry of the reference element induced by ornt */
2532: PetscCall(PetscLagNodeIndicesPushForward(dm, vertIndices, 0, vertIndices, intNodeIndices, ornt, formDegree, ni->nodeIdx, ni->nodeVec));
2533: /* get the revlex order for both the original and transformed dofs */
2534: PetscCall(PetscLagNodeIndicesGetPermutation(intNodeIndices, &perm));
2535: PetscCall(PetscLagNodeIndicesGetPermutation(ni, &permOrnt));
2536: PetscCall(PetscMalloc1(nNodes, &nnz));
2537: for (n = 0, maxGroupSize = 0; n < nNodes;) { /* incremented in the loop */
2538: PetscInt *nind = &(ni->nodeIdx[permOrnt[n] * nodeIdxDim]);
2539: PetscInt m, nEnd;
2540: PetscInt groupSize;
2541: /* for each group of dofs that have the same nodeIdx coordinate */
2542: for (nEnd = n + 1; nEnd < nNodes; nEnd++) {
2543: PetscInt *mind = &(ni->nodeIdx[permOrnt[nEnd] * nodeIdxDim]);
2544: PetscInt d;
2546: /* compare the oriented permutation indices */
2547: for (d = 0; d < nodeIdxDim; d++)
2548: if (mind[d] != nind[d]) break;
2549: if (d < nodeIdxDim) break;
2550: }
2551: /* permOrnt[[n, nEnd)] is a group of dofs that, under the symmetry are at the same location */
2553: /* the symmetry had better map the group of dofs with the same permuted nodeIdx
2554: * to a group of dofs with the same size, otherwise we messed up */
2555: if (PetscDefined(USE_DEBUG)) {
2556: PetscInt m;
2557: PetscInt *nind = &(intNodeIndices->nodeIdx[perm[n] * nodeIdxDim]);
2559: for (m = n + 1; m < nEnd; m++) {
2560: PetscInt *mind = &(intNodeIndices->nodeIdx[perm[m] * nodeIdxDim]);
2561: PetscInt d;
2563: /* compare the oriented permutation indices */
2564: for (d = 0; d < nodeIdxDim; d++)
2565: if (mind[d] != nind[d]) break;
2566: if (d < nodeIdxDim) break;
2567: }
2568: PetscCheck(m >= nEnd, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Dofs with same index after symmetry not same block size");
2569: }
2570: groupSize = nEnd - n;
2571: /* each pushforward dof vector will be expressed in a basis of the unpermuted dofs */
2572: for (m = n; m < nEnd; m++) nnz[permOrnt[m]] = groupSize;
2574: maxGroupSize = PetscMax(maxGroupSize, nEnd - n);
2575: n = nEnd;
2576: }
2577: PetscCheck(maxGroupSize <= nodeVecDim, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Dofs are not in blocks that can be solved");
2578: PetscCall(MatCreateSeqAIJ(PETSC_COMM_SELF, nNodes, nNodes, 0, nnz, &A));
2579: PetscCall(PetscFree(nnz));
2580: PetscCall(PetscMalloc3(maxGroupSize * nodeVecDim, &V, maxGroupSize * nodeVecDim, &W, nodeVecDim * 2, &work));
2581: for (n = 0; n < nNodes;) { /* incremented in the loop */
2582: PetscInt *nind = &(ni->nodeIdx[permOrnt[n] * nodeIdxDim]);
2583: PetscInt nEnd;
2584: PetscInt m;
2585: PetscInt groupSize;
2586: for (nEnd = n + 1; nEnd < nNodes; nEnd++) {
2587: PetscInt *mind = &(ni->nodeIdx[permOrnt[nEnd] * nodeIdxDim]);
2588: PetscInt d;
2590: /* compare the oriented permutation indices */
2591: for (d = 0; d < nodeIdxDim; d++)
2592: if (mind[d] != nind[d]) break;
2593: if (d < nodeIdxDim) break;
2594: }
2595: groupSize = nEnd - n;
2596: /* get all of the vectors from the original and all of the pushforward vectors */
2597: for (m = n; m < nEnd; m++) {
2598: PetscInt d;
2600: for (d = 0; d < nodeVecDim; d++) {
2601: V[(m - n) * nodeVecDim + d] = intNodeIndices->nodeVec[perm[m] * nodeVecDim + d];
2602: W[(m - n) * nodeVecDim + d] = ni->nodeVec[permOrnt[m] * nodeVecDim + d];
2603: }
2604: }
2605: /* now we have to solve for W in terms of V: the systems isn't always square, but the span
2606: * of V and W should always be the same, so the solution of the normal equations works */
2607: {
2608: char transpose = 'N';
2609: PetscBLASInt bm = nodeVecDim;
2610: PetscBLASInt bn = groupSize;
2611: PetscBLASInt bnrhs = groupSize;
2612: PetscBLASInt blda = bm;
2613: PetscBLASInt bldb = bm;
2614: PetscBLASInt blwork = 2 * nodeVecDim;
2615: PetscBLASInt info;
2617: PetscCallBLAS("LAPACKgels", LAPACKgels_(&transpose, &bm, &bn, &bnrhs, V, &blda, W, &bldb, work, &blwork, &info));
2618: PetscCheck(info == 0, PETSC_COMM_SELF, PETSC_ERR_LIB, "Bad argument to GELS");
2619: /* repack */
2620: {
2621: PetscInt i, j;
2623: for (i = 0; i < groupSize; i++) {
2624: for (j = 0; j < groupSize; j++) {
2625: /* notice the different leading dimension */
2626: V[i * groupSize + j] = W[i * nodeVecDim + j];
2627: }
2628: }
2629: }
2630: if (PetscDefined(USE_DEBUG)) {
2631: PetscReal res;
2633: /* check that the normal error is 0 */
2634: for (m = n; m < nEnd; m++) {
2635: PetscInt d;
2637: for (d = 0; d < nodeVecDim; d++) W[(m - n) * nodeVecDim + d] = ni->nodeVec[permOrnt[m] * nodeVecDim + d];
2638: }
2639: res = 0.;
2640: for (PetscInt i = 0; i < groupSize; i++) {
2641: for (PetscInt j = 0; j < nodeVecDim; j++) {
2642: for (PetscInt k = 0; k < groupSize; k++) W[i * nodeVecDim + j] -= V[i * groupSize + k] * intNodeIndices->nodeVec[perm[n + k] * nodeVecDim + j];
2643: res += PetscAbsScalar(W[i * nodeVecDim + j]);
2644: }
2645: }
2646: PetscCheck(res <= PETSC_SMALL, PETSC_COMM_SELF, PETSC_ERR_LIB, "Dof block did not solve");
2647: }
2648: }
2649: PetscCall(MatSetValues(A, groupSize, &permOrnt[n], groupSize, &perm[n], V, INSERT_VALUES));
2650: n = nEnd;
2651: }
2652: PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
2653: PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
2654: *symMat = A;
2655: PetscCall(PetscFree3(V, W, work));
2656: PetscCall(PetscLagNodeIndicesDestroy(&ni));
2657: PetscFunctionReturn(PETSC_SUCCESS);
2658: }
2660: #define BaryIndex(perEdge, a, b, c) (((b) * (2 * perEdge + 1 - (b))) / 2) + (c)
2662: #define CartIndex(perEdge, a, b) (perEdge * (a) + b)
2664: /* the existing interface for symmetries is insufficient for all cases:
2665: * - it should be sufficient for form degrees that are scalar (0 and n)
2666: * - it should be sufficient for hypercube dofs
2667: * - it isn't sufficient for simplex cells with non-scalar form degrees if
2668: * there are any dofs in the interior
2669: *
2670: * We compute the general transformation matrices, and if they fit, we return them,
2671: * otherwise we error (but we should probably change the interface to allow for
2672: * these symmetries)
2673: */
2674: static PetscErrorCode PetscDualSpaceGetSymmetries_Lagrange(PetscDualSpace sp, const PetscInt ****perms, const PetscScalar ****flips)
2675: {
2676: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2677: PetscInt dim, order, Nc;
2679: PetscFunctionBegin;
2680: PetscCall(PetscDualSpaceGetOrder(sp, &order));
2681: PetscCall(PetscDualSpaceGetNumComponents(sp, &Nc));
2682: PetscCall(DMGetDimension(sp->dm, &dim));
2683: if (!lag->symComputed) { /* store symmetries */
2684: PetscInt pStart, pEnd, p;
2685: PetscInt numPoints;
2686: PetscInt numFaces;
2687: PetscInt spintdim;
2688: PetscInt ***symperms;
2689: PetscScalar ***symflips;
2691: PetscCall(DMPlexGetChart(sp->dm, &pStart, &pEnd));
2692: numPoints = pEnd - pStart;
2693: {
2694: DMPolytopeType ct;
2695: /* The number of arrangements is no longer based on the number of faces */
2696: PetscCall(DMPlexGetCellType(sp->dm, 0, &ct));
2697: numFaces = DMPolytopeTypeGetNumArrangments(ct) / 2;
2698: }
2699: PetscCall(PetscCalloc1(numPoints, &symperms));
2700: PetscCall(PetscCalloc1(numPoints, &symflips));
2701: spintdim = sp->spintdim;
2702: /* The nodal symmetry behavior is not present when tensorSpace != tensorCell: someone might want this for the "S"
2703: * family of FEEC spaces. Most used in particular are discontinuous polynomial L2 spaces in tensor cells, where
2704: * the symmetries are not necessary for FE assembly. So for now we assume this is the case and don't return
2705: * symmetries if tensorSpace != tensorCell */
2706: if (spintdim && 0 < dim && dim < 3 && (lag->tensorSpace == lag->tensorCell)) { /* compute self symmetries */
2707: PetscInt **cellSymperms;
2708: PetscScalar **cellSymflips;
2709: PetscInt ornt;
2710: PetscInt nCopies = Nc / lag->intNodeIndices->nodeVecDim;
2711: PetscInt nNodes = lag->intNodeIndices->nNodes;
2713: lag->numSelfSym = 2 * numFaces;
2714: lag->selfSymOff = numFaces;
2715: PetscCall(PetscCalloc1(2 * numFaces, &cellSymperms));
2716: PetscCall(PetscCalloc1(2 * numFaces, &cellSymflips));
2717: /* we want to be able to index symmetries directly with the orientations, which range from [-numFaces,numFaces) */
2718: symperms[0] = &cellSymperms[numFaces];
2719: symflips[0] = &cellSymflips[numFaces];
2720: PetscCheck(lag->intNodeIndices->nodeVecDim * nCopies == Nc, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Node indices incompatible with dofs");
2721: PetscCheck(nNodes * nCopies == spintdim, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Node indices incompatible with dofs");
2722: for (ornt = -numFaces; ornt < numFaces; ornt++) { /* for every symmetry, compute the symmetry matrix, and extract rows to see if it fits in the perm + flip framework */
2723: Mat symMat;
2724: PetscInt *perm;
2725: PetscScalar *flips;
2726: PetscInt i;
2728: if (!ornt) continue;
2729: PetscCall(PetscMalloc1(spintdim, &perm));
2730: PetscCall(PetscCalloc1(spintdim, &flips));
2731: for (i = 0; i < spintdim; i++) perm[i] = -1;
2732: PetscCall(PetscDualSpaceCreateInteriorSymmetryMatrix_Lagrange(sp, ornt, &symMat));
2733: for (i = 0; i < nNodes; i++) {
2734: PetscInt ncols;
2735: PetscInt j, k;
2736: const PetscInt *cols;
2737: const PetscScalar *vals;
2738: PetscBool nz_seen = PETSC_FALSE;
2740: PetscCall(MatGetRow(symMat, i, &ncols, &cols, &vals));
2741: for (j = 0; j < ncols; j++) {
2742: if (PetscAbsScalar(vals[j]) > PETSC_SMALL) {
2743: PetscCheck(!nz_seen, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "This dual space has symmetries that can't be described as a permutation + sign flips");
2744: nz_seen = PETSC_TRUE;
2745: PetscCheck(PetscAbsReal(PetscAbsScalar(vals[j]) - PetscRealConstant(1.)) <= PETSC_SMALL, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "This dual space has symmetries that can't be described as a permutation + sign flips");
2746: PetscCheck(PetscAbsReal(PetscImaginaryPart(vals[j])) <= PETSC_SMALL, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "This dual space has symmetries that can't be described as a permutation + sign flips");
2747: PetscCheck(perm[cols[j] * nCopies] < 0, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "This dual space has symmetries that can't be described as a permutation + sign flips");
2748: for (k = 0; k < nCopies; k++) perm[cols[j] * nCopies + k] = i * nCopies + k;
2749: if (PetscRealPart(vals[j]) < 0.) {
2750: for (k = 0; k < nCopies; k++) flips[i * nCopies + k] = -1.;
2751: } else {
2752: for (k = 0; k < nCopies; k++) flips[i * nCopies + k] = 1.;
2753: }
2754: }
2755: }
2756: PetscCall(MatRestoreRow(symMat, i, &ncols, &cols, &vals));
2757: }
2758: PetscCall(MatDestroy(&symMat));
2759: /* if there were no sign flips, keep NULL */
2760: for (i = 0; i < spintdim; i++)
2761: if (flips[i] != 1.) break;
2762: if (i == spintdim) {
2763: PetscCall(PetscFree(flips));
2764: flips = NULL;
2765: }
2766: /* if the permutation is identity, keep NULL */
2767: for (i = 0; i < spintdim; i++)
2768: if (perm[i] != i) break;
2769: if (i == spintdim) {
2770: PetscCall(PetscFree(perm));
2771: perm = NULL;
2772: }
2773: symperms[0][ornt] = perm;
2774: symflips[0][ornt] = flips;
2775: }
2776: /* if no orientations produced non-identity permutations, keep NULL */
2777: for (ornt = -numFaces; ornt < numFaces; ornt++)
2778: if (symperms[0][ornt]) break;
2779: if (ornt == numFaces) {
2780: PetscCall(PetscFree(cellSymperms));
2781: symperms[0] = NULL;
2782: }
2783: /* if no orientations produced sign flips, keep NULL */
2784: for (ornt = -numFaces; ornt < numFaces; ornt++)
2785: if (symflips[0][ornt]) break;
2786: if (ornt == numFaces) {
2787: PetscCall(PetscFree(cellSymflips));
2788: symflips[0] = NULL;
2789: }
2790: }
2791: { /* get the symmetries of closure points */
2792: PetscInt closureSize = 0;
2793: PetscInt *closure = NULL;
2794: PetscInt r;
2796: PetscCall(DMPlexGetTransitiveClosure(sp->dm, 0, PETSC_TRUE, &closureSize, &closure));
2797: for (r = 0; r < closureSize; r++) {
2798: PetscDualSpace psp;
2799: PetscInt point = closure[2 * r];
2800: PetscInt pspintdim;
2801: const PetscInt ***psymperms = NULL;
2802: const PetscScalar ***psymflips = NULL;
2804: if (!point) continue;
2805: PetscCall(PetscDualSpaceGetPointSubspace(sp, point, &psp));
2806: if (!psp) continue;
2807: PetscCall(PetscDualSpaceGetInteriorDimension(psp, &pspintdim));
2808: if (!pspintdim) continue;
2809: PetscCall(PetscDualSpaceGetSymmetries(psp, &psymperms, &psymflips));
2810: symperms[r] = (PetscInt **)(psymperms ? psymperms[0] : NULL);
2811: symflips[r] = (PetscScalar **)(psymflips ? psymflips[0] : NULL);
2812: }
2813: PetscCall(DMPlexRestoreTransitiveClosure(sp->dm, 0, PETSC_TRUE, &closureSize, &closure));
2814: }
2815: for (p = 0; p < pEnd; p++)
2816: if (symperms[p]) break;
2817: if (p == pEnd) {
2818: PetscCall(PetscFree(symperms));
2819: symperms = NULL;
2820: }
2821: for (p = 0; p < pEnd; p++)
2822: if (symflips[p]) break;
2823: if (p == pEnd) {
2824: PetscCall(PetscFree(symflips));
2825: symflips = NULL;
2826: }
2827: lag->symperms = symperms;
2828: lag->symflips = symflips;
2829: lag->symComputed = PETSC_TRUE;
2830: }
2831: if (perms) *perms = (const PetscInt ***)lag->symperms;
2832: if (flips) *flips = (const PetscScalar ***)lag->symflips;
2833: PetscFunctionReturn(PETSC_SUCCESS);
2834: }
2836: static PetscErrorCode PetscDualSpaceLagrangeGetContinuity_Lagrange(PetscDualSpace sp, PetscBool *continuous)
2837: {
2838: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2840: PetscFunctionBegin;
2843: *continuous = lag->continuous;
2844: PetscFunctionReturn(PETSC_SUCCESS);
2845: }
2847: static PetscErrorCode PetscDualSpaceLagrangeSetContinuity_Lagrange(PetscDualSpace sp, PetscBool continuous)
2848: {
2849: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2851: PetscFunctionBegin;
2853: lag->continuous = continuous;
2854: PetscFunctionReturn(PETSC_SUCCESS);
2855: }
2857: /*@
2858: PetscDualSpaceLagrangeGetContinuity - Retrieves the flag for element continuity
2860: Not Collective
2862: Input Parameter:
2863: . sp - the `PetscDualSpace`
2865: Output Parameter:
2866: . continuous - flag for element continuity
2868: Level: intermediate
2870: .seealso: `PetscDualSpace`, `PetscDualSpaceLagrangeSetContinuity()`
2871: @*/
2872: PetscErrorCode PetscDualSpaceLagrangeGetContinuity(PetscDualSpace sp, PetscBool *continuous)
2873: {
2874: PetscFunctionBegin;
2877: PetscTryMethod(sp, "PetscDualSpaceLagrangeGetContinuity_C", (PetscDualSpace, PetscBool *), (sp, continuous));
2878: PetscFunctionReturn(PETSC_SUCCESS);
2879: }
2881: /*@
2882: PetscDualSpaceLagrangeSetContinuity - Indicate whether the element is continuous
2884: Logically Collective
2886: Input Parameters:
2887: + sp - the `PetscDualSpace`
2888: - continuous - flag for element continuity
2890: Options Database Key:
2891: . -petscdualspace_lagrange_continuity <bool> - use a continuous element
2893: Level: intermediate
2895: .seealso: `PetscDualSpace`, `PetscDualSpaceLagrangeGetContinuity()`
2896: @*/
2897: PetscErrorCode PetscDualSpaceLagrangeSetContinuity(PetscDualSpace sp, PetscBool continuous)
2898: {
2899: PetscFunctionBegin;
2902: PetscTryMethod(sp, "PetscDualSpaceLagrangeSetContinuity_C", (PetscDualSpace, PetscBool), (sp, continuous));
2903: PetscFunctionReturn(PETSC_SUCCESS);
2904: }
2906: static PetscErrorCode PetscDualSpaceLagrangeGetTensor_Lagrange(PetscDualSpace sp, PetscBool *tensor)
2907: {
2908: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2910: PetscFunctionBegin;
2911: *tensor = lag->tensorSpace;
2912: PetscFunctionReturn(PETSC_SUCCESS);
2913: }
2915: static PetscErrorCode PetscDualSpaceLagrangeSetTensor_Lagrange(PetscDualSpace sp, PetscBool tensor)
2916: {
2917: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2919: PetscFunctionBegin;
2920: lag->tensorSpace = tensor;
2921: PetscFunctionReturn(PETSC_SUCCESS);
2922: }
2924: static PetscErrorCode PetscDualSpaceLagrangeGetTrimmed_Lagrange(PetscDualSpace sp, PetscBool *trimmed)
2925: {
2926: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2928: PetscFunctionBegin;
2929: *trimmed = lag->trimmed;
2930: PetscFunctionReturn(PETSC_SUCCESS);
2931: }
2933: static PetscErrorCode PetscDualSpaceLagrangeSetTrimmed_Lagrange(PetscDualSpace sp, PetscBool trimmed)
2934: {
2935: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2937: PetscFunctionBegin;
2938: lag->trimmed = trimmed;
2939: PetscFunctionReturn(PETSC_SUCCESS);
2940: }
2942: static PetscErrorCode PetscDualSpaceLagrangeGetNodeType_Lagrange(PetscDualSpace sp, PetscDTNodeType *nodeType, PetscBool *boundary, PetscReal *exponent)
2943: {
2944: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2946: PetscFunctionBegin;
2947: if (nodeType) *nodeType = lag->nodeType;
2948: if (boundary) *boundary = lag->endNodes;
2949: if (exponent) *exponent = lag->nodeExponent;
2950: PetscFunctionReturn(PETSC_SUCCESS);
2951: }
2953: static PetscErrorCode PetscDualSpaceLagrangeSetNodeType_Lagrange(PetscDualSpace sp, PetscDTNodeType nodeType, PetscBool boundary, PetscReal exponent)
2954: {
2955: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2957: PetscFunctionBegin;
2958: PetscCheck(nodeType != PETSCDTNODES_GAUSSJACOBI || exponent > -1., PetscObjectComm((PetscObject)sp), PETSC_ERR_ARG_OUTOFRANGE, "Exponent must be > -1");
2959: lag->nodeType = nodeType;
2960: lag->endNodes = boundary;
2961: lag->nodeExponent = exponent;
2962: PetscFunctionReturn(PETSC_SUCCESS);
2963: }
2965: static PetscErrorCode PetscDualSpaceLagrangeGetUseMoments_Lagrange(PetscDualSpace sp, PetscBool *useMoments)
2966: {
2967: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2969: PetscFunctionBegin;
2970: *useMoments = lag->useMoments;
2971: PetscFunctionReturn(PETSC_SUCCESS);
2972: }
2974: static PetscErrorCode PetscDualSpaceLagrangeSetUseMoments_Lagrange(PetscDualSpace sp, PetscBool useMoments)
2975: {
2976: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2978: PetscFunctionBegin;
2979: lag->useMoments = useMoments;
2980: PetscFunctionReturn(PETSC_SUCCESS);
2981: }
2983: static PetscErrorCode PetscDualSpaceLagrangeGetMomentOrder_Lagrange(PetscDualSpace sp, PetscInt *momentOrder)
2984: {
2985: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2987: PetscFunctionBegin;
2988: *momentOrder = lag->momentOrder;
2989: PetscFunctionReturn(PETSC_SUCCESS);
2990: }
2992: static PetscErrorCode PetscDualSpaceLagrangeSetMomentOrder_Lagrange(PetscDualSpace sp, PetscInt momentOrder)
2993: {
2994: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2996: PetscFunctionBegin;
2997: lag->momentOrder = momentOrder;
2998: PetscFunctionReturn(PETSC_SUCCESS);
2999: }
3001: /*@
3002: PetscDualSpaceLagrangeGetTensor - Get the tensor nature of the dual space
3004: Not Collective
3006: Input Parameter:
3007: . sp - The `PetscDualSpace`
3009: Output Parameter:
3010: . tensor - Whether the dual space has tensor layout (vs. simplicial)
3012: Level: intermediate
3014: .seealso: `PetscDualSpace`, `PetscDualSpaceLagrangeSetTensor()`, `PetscDualSpaceCreate()`
3015: @*/
3016: PetscErrorCode PetscDualSpaceLagrangeGetTensor(PetscDualSpace sp, PetscBool *tensor)
3017: {
3018: PetscFunctionBegin;
3021: PetscTryMethod(sp, "PetscDualSpaceLagrangeGetTensor_C", (PetscDualSpace, PetscBool *), (sp, tensor));
3022: PetscFunctionReturn(PETSC_SUCCESS);
3023: }
3025: /*@
3026: PetscDualSpaceLagrangeSetTensor - Set the tensor nature of the dual space
3028: Not Collective
3030: Input Parameters:
3031: + sp - The `PetscDualSpace`
3032: - tensor - Whether the dual space has tensor layout (vs. simplicial)
3034: Level: intermediate
3036: .seealso: `PetscDualSpace`, `PetscDualSpaceLagrangeGetTensor()`, `PetscDualSpaceCreate()`
3037: @*/
3038: PetscErrorCode PetscDualSpaceLagrangeSetTensor(PetscDualSpace sp, PetscBool tensor)
3039: {
3040: PetscFunctionBegin;
3042: PetscTryMethod(sp, "PetscDualSpaceLagrangeSetTensor_C", (PetscDualSpace, PetscBool), (sp, tensor));
3043: PetscFunctionReturn(PETSC_SUCCESS);
3044: }
3046: /*@
3047: PetscDualSpaceLagrangeGetTrimmed - Get the trimmed nature of the dual space
3049: Not Collective
3051: Input Parameter:
3052: . sp - The `PetscDualSpace`
3054: Output Parameter:
3055: . trimmed - Whether the dual space represents to dual basis of a trimmed polynomial space (e.g. Raviart-Thomas and higher order / other form degree variants)
3057: Level: intermediate
3059: .seealso: `PetscDualSpace`, `PetscDualSpaceLagrangeSetTrimmed()`, `PetscDualSpaceCreate()`
3060: @*/
3061: PetscErrorCode PetscDualSpaceLagrangeGetTrimmed(PetscDualSpace sp, PetscBool *trimmed)
3062: {
3063: PetscFunctionBegin;
3066: PetscTryMethod(sp, "PetscDualSpaceLagrangeGetTrimmed_C", (PetscDualSpace, PetscBool *), (sp, trimmed));
3067: PetscFunctionReturn(PETSC_SUCCESS);
3068: }
3070: /*@
3071: PetscDualSpaceLagrangeSetTrimmed - Set the trimmed nature of the dual space
3073: Not Collective
3075: Input Parameters:
3076: + sp - The `PetscDualSpace`
3077: - trimmed - Whether the dual space represents to dual basis of a trimmed polynomial space (e.g. Raviart-Thomas and higher order / other form degree variants)
3079: Level: intermediate
3081: .seealso: `PetscDualSpace`, `PetscDualSpaceLagrangeGetTrimmed()`, `PetscDualSpaceCreate()`
3082: @*/
3083: PetscErrorCode PetscDualSpaceLagrangeSetTrimmed(PetscDualSpace sp, PetscBool trimmed)
3084: {
3085: PetscFunctionBegin;
3087: PetscTryMethod(sp, "PetscDualSpaceLagrangeSetTrimmed_C", (PetscDualSpace, PetscBool), (sp, trimmed));
3088: PetscFunctionReturn(PETSC_SUCCESS);
3089: }
3091: /*@
3092: PetscDualSpaceLagrangeGetNodeType - Get a description of how nodes are laid out for Lagrange polynomials in this
3093: dual space
3095: Not Collective
3097: Input Parameter:
3098: . sp - The `PetscDualSpace`
3100: Output Parameters:
3101: + nodeType - The type of nodes
3102: . boundary - Whether the node type is one that includes endpoints (if nodeType is `PETSCDTNODES_GAUSSJACOBI`, nodes that
3103: include the boundary are Gauss-Lobatto-Jacobi nodes)
3104: - exponent - If nodeType is `PETSCDTNODES_GAUSJACOBI`, indicates the exponent used for both ends of the 1D Jacobi weight function
3105: '0' is Gauss-Legendre, '-0.5' is Gauss-Chebyshev of the first type, '0.5' is Gauss-Chebyshev of the second type
3107: Level: advanced
3109: .seealso: `PetscDualSpace`, `PetscDTNodeType`, `PetscDualSpaceLagrangeSetNodeType()`
3110: @*/
3111: PetscErrorCode PetscDualSpaceLagrangeGetNodeType(PetscDualSpace sp, PetscDTNodeType *nodeType, PetscBool *boundary, PetscReal *exponent)
3112: {
3113: PetscFunctionBegin;
3118: PetscTryMethod(sp, "PetscDualSpaceLagrangeGetNodeType_C", (PetscDualSpace, PetscDTNodeType *, PetscBool *, PetscReal *), (sp, nodeType, boundary, exponent));
3119: PetscFunctionReturn(PETSC_SUCCESS);
3120: }
3122: /*@
3123: PetscDualSpaceLagrangeSetNodeType - Set a description of how nodes are laid out for Lagrange polynomials in this
3124: dual space
3126: Logically Collective
3128: Input Parameters:
3129: + sp - The `PetscDualSpace`
3130: . nodeType - The type of nodes
3131: . boundary - Whether the node type is one that includes endpoints (if nodeType is `PETSCDTNODES_GAUSSJACOBI`, nodes that
3132: include the boundary are Gauss-Lobatto-Jacobi nodes)
3133: - exponent - If nodeType is `PETSCDTNODES_GAUSJACOBI`, indicates the exponent used for both ends of the 1D Jacobi weight function
3134: '0' is Gauss-Legendre, '-0.5' is Gauss-Chebyshev of the first type, '0.5' is Gauss-Chebyshev of the second type
3136: Level: advanced
3138: .seealso: `PetscDualSpace`, `PetscDTNodeType`, `PetscDualSpaceLagrangeGetNodeType()`
3139: @*/
3140: PetscErrorCode PetscDualSpaceLagrangeSetNodeType(PetscDualSpace sp, PetscDTNodeType nodeType, PetscBool boundary, PetscReal exponent)
3141: {
3142: PetscFunctionBegin;
3144: PetscTryMethod(sp, "PetscDualSpaceLagrangeSetNodeType_C", (PetscDualSpace, PetscDTNodeType, PetscBool, PetscReal), (sp, nodeType, boundary, exponent));
3145: PetscFunctionReturn(PETSC_SUCCESS);
3146: }
3148: /*@
3149: PetscDualSpaceLagrangeGetUseMoments - Get the flag for using moment functionals
3151: Not Collective
3153: Input Parameter:
3154: . sp - The `PetscDualSpace`
3156: Output Parameter:
3157: . useMoments - Moment flag
3159: Level: advanced
3161: .seealso: `PetscDualSpace`, `PetscDualSpaceLagrangeSetUseMoments()`
3162: @*/
3163: PetscErrorCode PetscDualSpaceLagrangeGetUseMoments(PetscDualSpace sp, PetscBool *useMoments)
3164: {
3165: PetscFunctionBegin;
3168: PetscUseMethod(sp, "PetscDualSpaceLagrangeGetUseMoments_C", (PetscDualSpace, PetscBool *), (sp, useMoments));
3169: PetscFunctionReturn(PETSC_SUCCESS);
3170: }
3172: /*@
3173: PetscDualSpaceLagrangeSetUseMoments - Set the flag for moment functionals
3175: Logically Collective
3177: Input Parameters:
3178: + sp - The `PetscDualSpace`
3179: - useMoments - The flag for moment functionals
3181: Level: advanced
3183: .seealso: `PetscDualSpace`, `PetscDualSpaceLagrangeGetUseMoments()`
3184: @*/
3185: PetscErrorCode PetscDualSpaceLagrangeSetUseMoments(PetscDualSpace sp, PetscBool useMoments)
3186: {
3187: PetscFunctionBegin;
3189: PetscTryMethod(sp, "PetscDualSpaceLagrangeSetUseMoments_C", (PetscDualSpace, PetscBool), (sp, useMoments));
3190: PetscFunctionReturn(PETSC_SUCCESS);
3191: }
3193: /*@
3194: PetscDualSpaceLagrangeGetMomentOrder - Get the order for moment integration
3196: Not Collective
3198: Input Parameter:
3199: . sp - The `PetscDualSpace`
3201: Output Parameter:
3202: . order - Moment integration order
3204: Level: advanced
3206: .seealso: `PetscDualSpace`, `PetscDualSpaceLagrangeSetMomentOrder()`
3207: @*/
3208: PetscErrorCode PetscDualSpaceLagrangeGetMomentOrder(PetscDualSpace sp, PetscInt *order)
3209: {
3210: PetscFunctionBegin;
3213: PetscUseMethod(sp, "PetscDualSpaceLagrangeGetMomentOrder_C", (PetscDualSpace, PetscInt *), (sp, order));
3214: PetscFunctionReturn(PETSC_SUCCESS);
3215: }
3217: /*@
3218: PetscDualSpaceLagrangeSetMomentOrder - Set the order for moment integration
3220: Logically Collective
3222: Input Parameters:
3223: + sp - The `PetscDualSpace`
3224: - order - The order for moment integration
3226: Level: advanced
3228: .seealso: `PetscDualSpace`, `PetscDualSpaceLagrangeGetMomentOrder()`
3229: @*/
3230: PetscErrorCode PetscDualSpaceLagrangeSetMomentOrder(PetscDualSpace sp, PetscInt order)
3231: {
3232: PetscFunctionBegin;
3234: PetscTryMethod(sp, "PetscDualSpaceLagrangeSetMomentOrder_C", (PetscDualSpace, PetscInt), (sp, order));
3235: PetscFunctionReturn(PETSC_SUCCESS);
3236: }
3238: static PetscErrorCode PetscDualSpaceInitialize_Lagrange(PetscDualSpace sp)
3239: {
3240: PetscFunctionBegin;
3241: sp->ops->destroy = PetscDualSpaceDestroy_Lagrange;
3242: sp->ops->view = PetscDualSpaceView_Lagrange;
3243: sp->ops->setfromoptions = PetscDualSpaceSetFromOptions_Lagrange;
3244: sp->ops->duplicate = PetscDualSpaceDuplicate_Lagrange;
3245: sp->ops->setup = PetscDualSpaceSetUp_Lagrange;
3246: sp->ops->createheightsubspace = NULL;
3247: sp->ops->createpointsubspace = NULL;
3248: sp->ops->getsymmetries = PetscDualSpaceGetSymmetries_Lagrange;
3249: sp->ops->apply = PetscDualSpaceApplyDefault;
3250: sp->ops->applyall = PetscDualSpaceApplyAllDefault;
3251: sp->ops->applyint = PetscDualSpaceApplyInteriorDefault;
3252: sp->ops->createalldata = PetscDualSpaceCreateAllDataDefault;
3253: sp->ops->createintdata = PetscDualSpaceCreateInteriorDataDefault;
3254: PetscFunctionReturn(PETSC_SUCCESS);
3255: }
3257: /*MC
3258: PETSCDUALSPACELAGRANGE = "lagrange" - A `PetscDualSpaceType` that encapsulates a dual space of pointwise evaluation functionals
3260: Level: intermediate
3262: .seealso: `PetscDualSpace`, `PetscDualSpaceType`, `PetscDualSpaceCreate()`, `PetscDualSpaceSetType()`
3263: M*/
3264: PETSC_EXTERN PetscErrorCode PetscDualSpaceCreate_Lagrange(PetscDualSpace sp)
3265: {
3266: PetscDualSpace_Lag *lag;
3268: PetscFunctionBegin;
3270: PetscCall(PetscNew(&lag));
3271: sp->data = lag;
3273: lag->tensorCell = PETSC_FALSE;
3274: lag->tensorSpace = PETSC_FALSE;
3275: lag->continuous = PETSC_TRUE;
3276: lag->numCopies = PETSC_DEFAULT;
3277: lag->numNodeSkip = PETSC_DEFAULT;
3278: lag->nodeType = PETSCDTNODES_DEFAULT;
3279: lag->useMoments = PETSC_FALSE;
3280: lag->momentOrder = 0;
3282: PetscCall(PetscDualSpaceInitialize_Lagrange(sp));
3283: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetContinuity_C", PetscDualSpaceLagrangeGetContinuity_Lagrange));
3284: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetContinuity_C", PetscDualSpaceLagrangeSetContinuity_Lagrange));
3285: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetTensor_C", PetscDualSpaceLagrangeGetTensor_Lagrange));
3286: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetTensor_C", PetscDualSpaceLagrangeSetTensor_Lagrange));
3287: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetTrimmed_C", PetscDualSpaceLagrangeGetTrimmed_Lagrange));
3288: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetTrimmed_C", PetscDualSpaceLagrangeSetTrimmed_Lagrange));
3289: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetNodeType_C", PetscDualSpaceLagrangeGetNodeType_Lagrange));
3290: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetNodeType_C", PetscDualSpaceLagrangeSetNodeType_Lagrange));
3291: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetUseMoments_C", PetscDualSpaceLagrangeGetUseMoments_Lagrange));
3292: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetUseMoments_C", PetscDualSpaceLagrangeSetUseMoments_Lagrange));
3293: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetMomentOrder_C", PetscDualSpaceLagrangeGetMomentOrder_Lagrange));
3294: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetMomentOrder_C", PetscDualSpaceLagrangeSetMomentOrder_Lagrange));
3295: PetscFunctionReturn(PETSC_SUCCESS);
3296: }