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 npoints;
149: PetscReal **nodesets = NULL;
150: PetscInt worksize;
151: PetscReal *nodework;
152: PetscInt *tupwork;
154: PetscFunctionBegin;
155: PetscCheck(dim >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Must have non-negative dimension");
156: PetscCheck(degree >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Must have non-negative degree");
157: if (!dim) PetscFunctionReturn(PETSC_SUCCESS);
158: PetscCall(PetscCalloc1(dim + 2, &tup));
159: PetscCall(PetscDTBinomialInt(degree + dim, dim, &npoints));
160: PetscCall(Petsc1DNodeFamilyGetNodeSets(f, degree, &nodesets));
161: worksize = ((dim + 2) * (dim + 3)) / 2;
162: PetscCall(PetscCalloc2(worksize, &nodework, worksize, &tupwork));
163: /* loop over the tuples of length dim with sum at most degree */
164: for (PetscInt k = 0; k < npoints; k++) {
165: PetscInt i;
167: /* turn thm into tuples of length dim + 1 with sum equal to degree (barycentric indice) */
168: tup[0] = degree;
169: for (i = 0; i < dim; i++) tup[0] -= tup[i + 1];
170: switch (f->nodeFamily) {
171: case PETSCDTNODES_EQUISPACED:
172: /* compute equispaces nodes on the unit reference triangle */
173: if (f->endpoints) {
174: PetscCheck(degree > 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Must have positive degree");
175: for (i = 0; i < dim; i++) points[dim * k + i] = (PetscReal)tup[i + 1] / (PetscReal)degree;
176: } else {
177: for (i = 0; i < dim; i++) {
178: /* these nodes are at the centroids of the small simplices created by the equispaced nodes that include
179: * the endpoints */
180: points[dim * k + i] = ((PetscReal)tup[i + 1] + 1. / (dim + 1.)) / (PetscReal)(degree + 1.);
181: }
182: }
183: break;
184: default:
185: /* compute equispaced nodes on the barycentric reference triangle (the trace on the first dim dimensions are the
186: * unit reference triangle nodes */
187: for (i = 0; i < dim + 1; i++) tupwork[i] = tup[i];
188: PetscCall(PetscNodeRecursive_Internal(dim, degree, nodesets, tupwork, nodework));
189: for (i = 0; i < dim; i++) points[dim * k + i] = nodework[i + 1];
190: break;
191: }
192: PetscCall(PetscDualSpaceLatticePointLexicographic_Internal(dim, degree, &tup[1]));
193: }
194: /* map from unit simplex to biunit simplex */
195: for (PetscInt k = 0; k < npoints * dim; k++) points[k] = points[k] * 2. - 1.;
196: PetscCall(PetscFree2(nodework, tupwork));
197: PetscCall(PetscFree(tup));
198: PetscFunctionReturn(PETSC_SUCCESS);
199: }
201: /* 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
202: * on that mesh point, we have to be careful about getting/adding everything in the right place.
203: *
204: * With nodal dofs like PETSCDUALSPACELAGRANGE makes, the general approach to calculate the value of dofs associate
205: * with a node A is
206: * - transform the node locations x(A) by the map that takes the mesh point to its reorientation, x' = phi(x(A))
207: * - figure out which node was originally at the location of the transformed point, A' = idx(x')
208: * - if the dofs are not scalars, figure out how to represent the transformed dofs in terms of the basis
209: * of dofs at A' (using pushforward/pullback rules)
210: *
211: * The one sticky point with this approach is the "A' = idx(x')" step: trying to go from real valued coordinates
212: * back to indices. I don't want to rely on floating point tolerances. Additionally, PETSCDUALSPACELAGRANGE may
213: * eventually support quasi-Lagrangian dofs, which could involve quadrature at multiple points, so the location "x(A)"
214: * would be ambiguous.
215: *
216: * So each dof gets an integer value coordinate (nodeIdx in the structure below). The choice of integer coordinates
217: * is somewhat arbitrary, as long as all of the relevant symmetries of the mesh point correspond to *permutations* of
218: * the integer coordinates, which do not depend on numerical precision.
219: *
220: * So
221: *
222: * - DMPlexGetTransitiveClosure_Internal() tells me how an orientation turns into a permutation of the vertices of a
223: * mesh point
224: * - The permutation of the vertices, and the nodeIdx values assigned to them, tells what permutation in index space
225: * is associated with the orientation
226: * - I uses that permutation to get xi' = phi(xi(A)), the integer coordinate of the transformed dof
227: * - I can without numerical issues compute A' = idx(xi')
228: *
229: * Here are some examples of how the process works
230: *
231: * - With a triangle:
232: *
233: * The triangle has the following integer coordinates for vertices, taken from the barycentric triangle
234: *
235: * closure order 2
236: * nodeIdx (0,0,1)
237: * \
238: * +
239: * |\
240: * | \
241: * | \
242: * | \ closure order 1
243: * | \ / nodeIdx (0,1,0)
244: * +-----+
245: * \
246: * closure order 0
247: * nodeIdx (1,0,0)
248: *
249: * If I do DMPlexGetTransitiveClosure_Internal() with orientation 1, the vertices would appear
250: * in the order (1, 2, 0)
251: *
252: * If I list the nodeIdx of each vertex in closure order for orientation 0 (0, 1, 2) and orientation 1 (1, 2, 0), I
253: * see
254: *
255: * orientation 0 | orientation 1
256: *
257: * [0] (1,0,0) [1] (0,1,0)
258: * [1] (0,1,0) [2] (0,0,1)
259: * [2] (0,0,1) [0] (1,0,0)
260: * A B
261: *
262: * In other words, B is the result of a row permutation of A. But, there is also
263: * a column permutation that accomplishes the same result, (2,0,1).
264: *
265: * So if a dof has nodeIdx coordinate (a,b,c), after the transformation its nodeIdx coordinate
266: * is (c,a,b), and the transformed degree of freedom will be a linear combination of dofs
267: * that originally had coordinate (c,a,b).
268: *
269: * - With a quadrilateral:
270: *
271: * The quadrilateral has the following integer coordinates for vertices, taken from concatenating barycentric
272: * coordinates for two segments:
273: *
274: * closure order 3 closure order 2
275: * nodeIdx (1,0,0,1) nodeIdx (0,1,0,1)
276: * \ /
277: * +----+
278: * | |
279: * | |
280: * +----+
281: * / \
282: * closure order 0 closure order 1
283: * nodeIdx (1,0,1,0) nodeIdx (0,1,1,0)
284: *
285: * If I do DMPlexGetTransitiveClosure_Internal() with orientation 1, the vertices would appear
286: * in the order (1, 2, 3, 0)
287: *
288: * If I list the nodeIdx of each vertex in closure order for orientation 0 (0, 1, 2, 3) and
289: * orientation 1 (1, 2, 3, 0), I see
290: *
291: * orientation 0 | orientation 1
292: *
293: * [0] (1,0,1,0) [1] (0,1,1,0)
294: * [1] (0,1,1,0) [2] (0,1,0,1)
295: * [2] (0,1,0,1) [3] (1,0,0,1)
296: * [3] (1,0,0,1) [0] (1,0,1,0)
297: * A B
298: *
299: * The column permutation that accomplishes the same result is (3,2,0,1).
300: *
301: * So if a dof has nodeIdx coordinate (a,b,c,d), after the transformation its nodeIdx coordinate
302: * is (d,c,a,b), and the transformed degree of freedom will be a linear combination of dofs
303: * that originally had coordinate (d,c,a,b).
304: *
305: * Previously PETSCDUALSPACELAGRANGE had hardcoded symmetries for the triangle and quadrilateral,
306: * but this approach will work for any polytope, such as the wedge (triangular prism).
307: */
308: struct _n_PetscLagNodeIndices {
309: PetscInt refct;
310: PetscInt nodeIdxDim;
311: PetscInt nodeVecDim;
312: PetscInt nNodes;
313: PetscInt *nodeIdx; /* for each node an index of size nodeIdxDim */
314: PetscReal *nodeVec; /* for each node a vector of size nodeVecDim */
315: PetscInt *perm; /* if these are vertices, perm takes DMPlex point index to closure order;
316: if these are nodes, perm lists nodes in index revlex order */
317: };
319: /* this is just here so I can access the values in tests/ex1.c outside the library */
320: PetscErrorCode PetscLagNodeIndicesGetData_Internal(PetscLagNodeIndices ni, PetscInt *nodeIdxDim, PetscInt *nodeVecDim, PetscInt *nNodes, const PetscInt *nodeIdx[], const PetscReal *nodeVec[])
321: {
322: PetscFunctionBegin;
323: *nodeIdxDim = ni->nodeIdxDim;
324: *nodeVecDim = ni->nodeVecDim;
325: *nNodes = ni->nNodes;
326: *nodeIdx = ni->nodeIdx;
327: *nodeVec = ni->nodeVec;
328: PetscFunctionReturn(PETSC_SUCCESS);
329: }
331: static PetscErrorCode PetscLagNodeIndicesReference(PetscLagNodeIndices ni)
332: {
333: PetscFunctionBegin;
334: if (ni) ni->refct++;
335: PetscFunctionReturn(PETSC_SUCCESS);
336: }
338: static PetscErrorCode PetscLagNodeIndicesDuplicate(PetscLagNodeIndices ni, PetscLagNodeIndices *niNew)
339: {
340: PetscFunctionBegin;
341: PetscCall(PetscNew(niNew));
342: (*niNew)->refct = 1;
343: (*niNew)->nodeIdxDim = ni->nodeIdxDim;
344: (*niNew)->nodeVecDim = ni->nodeVecDim;
345: (*niNew)->nNodes = ni->nNodes;
346: PetscCall(PetscMalloc1(ni->nNodes * ni->nodeIdxDim, &((*niNew)->nodeIdx)));
347: PetscCall(PetscArraycpy((*niNew)->nodeIdx, ni->nodeIdx, ni->nNodes * ni->nodeIdxDim));
348: PetscCall(PetscMalloc1(ni->nNodes * ni->nodeVecDim, &((*niNew)->nodeVec)));
349: PetscCall(PetscArraycpy((*niNew)->nodeVec, ni->nodeVec, ni->nNodes * ni->nodeVecDim));
350: (*niNew)->perm = NULL;
351: PetscFunctionReturn(PETSC_SUCCESS);
352: }
354: static PetscErrorCode PetscLagNodeIndicesDestroy(PetscLagNodeIndices *ni)
355: {
356: PetscFunctionBegin;
357: if (!*ni) PetscFunctionReturn(PETSC_SUCCESS);
358: if (--(*ni)->refct > 0) {
359: *ni = NULL;
360: PetscFunctionReturn(PETSC_SUCCESS);
361: }
362: PetscCall(PetscFree((*ni)->nodeIdx));
363: PetscCall(PetscFree((*ni)->nodeVec));
364: PetscCall(PetscFree((*ni)->perm));
365: PetscCall(PetscFree(*ni));
366: *ni = NULL;
367: PetscFunctionReturn(PETSC_SUCCESS);
368: }
370: /* The vertices are given nodeIdx coordinates (e.g. the corners of the barycentric triangle). Those coordinates are
371: * in some other order, and to understand the effect of different symmetries, we need them to be in closure order.
372: *
373: * If sortIdx is PETSC_FALSE, the coordinates are already in revlex order, otherwise we must sort them
374: * to that order before we do the real work of this function, which is
375: *
376: * - mark the vertices in closure order
377: * - sort them in revlex order
378: * - use the resulting permutation to list the vertex coordinates in closure order
379: */
380: static PetscErrorCode PetscLagNodeIndicesComputeVertexOrder(DM dm, PetscLagNodeIndices ni, PetscBool sortIdx)
381: {
382: PetscInt v, w, vStart, vEnd, c, d;
383: PetscInt nVerts;
384: PetscInt closureSize = 0;
385: PetscInt *closure = NULL;
386: PetscInt *closureOrder;
387: PetscInt *invClosureOrder;
388: PetscInt *revlexOrder;
389: PetscInt *newNodeIdx;
390: PetscInt dim;
391: Vec coordVec;
392: const PetscScalar *coords;
394: PetscFunctionBegin;
395: PetscCall(DMGetDimension(dm, &dim));
396: PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
397: nVerts = vEnd - vStart;
398: PetscCall(PetscMalloc1(nVerts, &closureOrder));
399: PetscCall(PetscMalloc1(nVerts, &invClosureOrder));
400: PetscCall(PetscMalloc1(nVerts, &revlexOrder));
401: if (sortIdx) { /* bubble sort nodeIdx into revlex order */
402: PetscInt nodeIdxDim = ni->nodeIdxDim;
403: PetscInt *idxOrder;
405: PetscCall(PetscMalloc1(nVerts * nodeIdxDim, &newNodeIdx));
406: PetscCall(PetscMalloc1(nVerts, &idxOrder));
407: for (v = 0; v < nVerts; v++) idxOrder[v] = v;
408: for (v = 0; v < nVerts; v++) {
409: for (w = v + 1; w < nVerts; w++) {
410: const PetscInt *iv = &(ni->nodeIdx[idxOrder[v] * nodeIdxDim]);
411: const PetscInt *iw = &(ni->nodeIdx[idxOrder[w] * nodeIdxDim]);
412: PetscInt diff = 0;
414: for (d = nodeIdxDim - 1; d >= 0; d--)
415: if ((diff = (iv[d] - iw[d]))) break;
416: if (diff > 0) {
417: PetscInt swap = idxOrder[v];
419: idxOrder[v] = idxOrder[w];
420: idxOrder[w] = swap;
421: }
422: }
423: }
424: for (v = 0; v < nVerts; v++) {
425: for (d = 0; d < nodeIdxDim; d++) newNodeIdx[v * ni->nodeIdxDim + d] = ni->nodeIdx[idxOrder[v] * nodeIdxDim + d];
426: }
427: PetscCall(PetscFree(ni->nodeIdx));
428: ni->nodeIdx = newNodeIdx;
429: newNodeIdx = NULL;
430: PetscCall(PetscFree(idxOrder));
431: }
432: PetscCall(DMPlexGetTransitiveClosure(dm, 0, PETSC_TRUE, &closureSize, &closure));
433: c = closureSize - nVerts;
434: for (v = 0; v < nVerts; v++) closureOrder[v] = closure[2 * (c + v)] - vStart;
435: for (v = 0; v < nVerts; v++) invClosureOrder[closureOrder[v]] = v;
436: PetscCall(DMPlexRestoreTransitiveClosure(dm, 0, PETSC_TRUE, &closureSize, &closure));
437: PetscCall(DMGetCoordinatesLocal(dm, &coordVec));
438: PetscCall(VecGetArrayRead(coordVec, &coords));
439: /* bubble sort closure vertices by coordinates in revlex order */
440: for (v = 0; v < nVerts; v++) revlexOrder[v] = v;
441: for (v = 0; v < nVerts; v++) {
442: for (w = v + 1; w < nVerts; w++) {
443: const PetscScalar *cv = &coords[closureOrder[revlexOrder[v]] * dim];
444: const PetscScalar *cw = &coords[closureOrder[revlexOrder[w]] * dim];
445: PetscReal diff = 0;
447: for (d = dim - 1; d >= 0; d--)
448: if ((diff = PetscRealPart(cv[d] - cw[d])) != 0.) break;
449: if (diff > 0.) {
450: PetscInt swap = revlexOrder[v];
452: revlexOrder[v] = revlexOrder[w];
453: revlexOrder[w] = swap;
454: }
455: }
456: }
457: PetscCall(VecRestoreArrayRead(coordVec, &coords));
458: PetscCall(PetscMalloc1(ni->nodeIdxDim * nVerts, &newNodeIdx));
459: /* reorder nodeIdx to be in closure order */
460: for (v = 0; v < nVerts; v++) {
461: for (d = 0; d < ni->nodeIdxDim; d++) newNodeIdx[revlexOrder[v] * ni->nodeIdxDim + d] = ni->nodeIdx[v * ni->nodeIdxDim + d];
462: }
463: PetscCall(PetscFree(ni->nodeIdx));
464: ni->nodeIdx = newNodeIdx;
465: ni->perm = invClosureOrder;
466: PetscCall(PetscFree(revlexOrder));
467: PetscCall(PetscFree(closureOrder));
468: PetscFunctionReturn(PETSC_SUCCESS);
469: }
471: /* the coordinates of the simplex vertices are the corners of the barycentric simplex.
472: * When we stack them on top of each other in revlex order, they look like the identity matrix */
473: static PetscErrorCode PetscLagNodeIndicesCreateSimplexVertices(DM dm, PetscLagNodeIndices *nodeIndices)
474: {
475: PetscLagNodeIndices ni;
476: PetscInt dim, d;
478: PetscFunctionBegin;
479: PetscCall(PetscNew(&ni));
480: PetscCall(DMGetDimension(dm, &dim));
481: ni->nodeIdxDim = dim + 1;
482: ni->nodeVecDim = 0;
483: ni->nNodes = dim + 1;
484: ni->refct = 1;
485: PetscCall(PetscCalloc1((dim + 1) * (dim + 1), &ni->nodeIdx));
486: for (d = 0; d < dim + 1; d++) ni->nodeIdx[d * (dim + 2)] = 1;
487: PetscCall(PetscLagNodeIndicesComputeVertexOrder(dm, ni, PETSC_FALSE));
488: *nodeIndices = ni;
489: PetscFunctionReturn(PETSC_SUCCESS);
490: }
492: /* A polytope that is a tensor product of a facet and a segment.
493: * We take whatever coordinate system was being used for the facet
494: * and we concatenate the barycentric coordinates for the vertices
495: * at the end of the segment, (1,0) and (0,1), to get a coordinate
496: * system for the tensor product element */
497: static PetscErrorCode PetscLagNodeIndicesCreateTensorVertices(DM dm, PetscLagNodeIndices facetni, PetscLagNodeIndices *nodeIndices)
498: {
499: PetscLagNodeIndices ni;
500: PetscInt nodeIdxDim, subNodeIdxDim = facetni->nodeIdxDim;
501: PetscInt nVerts, nSubVerts = facetni->nNodes;
502: PetscInt dim, d, e, f, g;
504: PetscFunctionBegin;
505: PetscCall(PetscNew(&ni));
506: PetscCall(DMGetDimension(dm, &dim));
507: ni->nodeIdxDim = nodeIdxDim = subNodeIdxDim + 2;
508: ni->nodeVecDim = 0;
509: ni->nNodes = nVerts = 2 * nSubVerts;
510: ni->refct = 1;
511: PetscCall(PetscCalloc1(nodeIdxDim * nVerts, &ni->nodeIdx));
512: for (f = 0, d = 0; d < 2; d++) {
513: for (e = 0; e < nSubVerts; e++, f++) {
514: for (g = 0; g < subNodeIdxDim; g++) ni->nodeIdx[f * nodeIdxDim + g] = facetni->nodeIdx[e * subNodeIdxDim + g];
515: ni->nodeIdx[f * nodeIdxDim + subNodeIdxDim] = (1 - d);
516: ni->nodeIdx[f * nodeIdxDim + subNodeIdxDim + 1] = d;
517: }
518: }
519: PetscCall(PetscLagNodeIndicesComputeVertexOrder(dm, ni, PETSC_TRUE));
520: *nodeIndices = ni;
521: PetscFunctionReturn(PETSC_SUCCESS);
522: }
524: /* This helps us compute symmetries, and it also helps us compute coordinates for dofs that are being pushed
525: * forward from a boundary mesh point.
526: *
527: * Input:
528: *
529: * dm - the target reference cell where we want new coordinates and dof directions to be valid
530: * vert - the vertex coordinate system for the target reference cell
531: * p - the point in the target reference cell that the dofs are coming from
532: * vertp - the vertex coordinate system for p's reference cell
533: * ornt - the resulting coordinates and dof vectors will be for p under this orientation
534: * nodep - the node coordinates and dof vectors in p's reference cell
535: * formDegree - the form degree that the dofs transform as
536: *
537: * Output:
538: *
539: * pfNodeIdx - the node coordinates for p's dofs, in the dm reference cell, from the ornt perspective
540: * pfNodeVec - the node dof vectors for p's dofs, in the dm reference cell, from the ornt perspective
541: */
542: static PetscErrorCode PetscLagNodeIndicesPushForward(DM dm, PetscLagNodeIndices vert, PetscInt p, PetscLagNodeIndices vertp, PetscLagNodeIndices nodep, PetscInt ornt, PetscInt formDegree, PetscInt pfNodeIdx[], PetscReal pfNodeVec[])
543: {
544: PetscInt *closureVerts;
545: PetscInt closureSize = 0;
546: PetscInt *closure = NULL;
547: PetscInt dim, pdim, c, i, j, k, n, v, vStart, vEnd;
548: PetscInt nSubVert = vertp->nNodes;
549: PetscInt nodeIdxDim = vert->nodeIdxDim;
550: PetscInt subNodeIdxDim = vertp->nodeIdxDim;
551: PetscInt nNodes = nodep->nNodes;
552: const PetscInt *vertIdx = vert->nodeIdx;
553: const PetscInt *subVertIdx = vertp->nodeIdx;
554: const PetscInt *nodeIdx = nodep->nodeIdx;
555: const PetscReal *nodeVec = nodep->nodeVec;
556: PetscReal *J, *Jstar;
557: PetscReal detJ;
558: PetscInt depth, pdepth, Nk, pNk;
559: Vec coordVec;
560: PetscScalar *newCoords = NULL;
561: const PetscScalar *oldCoords = NULL;
563: PetscFunctionBegin;
564: PetscCall(DMGetDimension(dm, &dim));
565: PetscCall(DMPlexGetDepth(dm, &depth));
566: PetscCall(DMGetCoordinatesLocal(dm, &coordVec));
567: PetscCall(DMPlexGetPointDepth(dm, p, &pdepth));
568: pdim = pdepth != depth ? pdepth != 0 ? pdepth : 0 : dim;
569: PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
570: PetscCall(DMGetWorkArray(dm, nSubVert, MPIU_INT, &closureVerts));
571: PetscCall(DMPlexGetTransitiveClosure_Internal(dm, p, ornt, PETSC_TRUE, &closureSize, &closure));
572: c = closureSize - nSubVert;
573: /* we want which cell closure indices the closure of this point corresponds to */
574: for (v = 0; v < nSubVert; v++) closureVerts[v] = vert->perm[closure[2 * (c + v)] - vStart];
575: PetscCall(DMPlexRestoreTransitiveClosure(dm, p, PETSC_TRUE, &closureSize, &closure));
576: /* push forward indices */
577: for (i = 0; i < nodeIdxDim; i++) { /* for every component of the target index space */
578: /* check if this is a component that all vertices around this point have in common */
579: for (j = 1; j < nSubVert; j++) {
580: if (vertIdx[closureVerts[j] * nodeIdxDim + i] != vertIdx[closureVerts[0] * nodeIdxDim + i]) break;
581: }
582: if (j == nSubVert) { /* all vertices have this component in common, directly copy to output */
583: PetscInt val = vertIdx[closureVerts[0] * nodeIdxDim + i];
584: for (n = 0; n < nNodes; n++) pfNodeIdx[n * nodeIdxDim + i] = val;
585: } else {
586: PetscInt subi = -1;
587: /* there must be a component in vertp that looks the same */
588: for (k = 0; k < subNodeIdxDim; k++) {
589: for (j = 0; j < nSubVert; j++) {
590: if (vertIdx[closureVerts[j] * nodeIdxDim + i] != subVertIdx[j * subNodeIdxDim + k]) break;
591: }
592: if (j == nSubVert) {
593: subi = k;
594: break;
595: }
596: }
597: PetscCheck(subi >= 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Did not find matching coordinate");
598: /* that component in the vertp system becomes component i in the vert system for each dof */
599: for (n = 0; n < nNodes; n++) pfNodeIdx[n * nodeIdxDim + i] = nodeIdx[n * subNodeIdxDim + subi];
600: }
601: }
602: /* push forward vectors */
603: PetscCall(DMGetWorkArray(dm, dim * dim, MPIU_REAL, &J));
604: if (ornt != 0) { /* temporarily change the coordinate vector so
605: DMPlexComputeCellGeometryAffineFEM gives us the Jacobian we want */
606: PetscInt closureSize2 = 0;
607: PetscInt *closure2 = NULL;
609: PetscCall(DMPlexGetTransitiveClosure_Internal(dm, p, 0, PETSC_TRUE, &closureSize2, &closure2));
610: PetscCall(PetscMalloc1(dim * nSubVert, &newCoords));
611: PetscCall(VecGetArrayRead(coordVec, &oldCoords));
612: for (v = 0; v < nSubVert; v++) {
613: PetscInt d;
614: for (d = 0; d < dim; d++) newCoords[(closure2[2 * (c + v)] - vStart) * dim + d] = oldCoords[closureVerts[v] * dim + d];
615: }
616: PetscCall(VecRestoreArrayRead(coordVec, &oldCoords));
617: PetscCall(DMPlexRestoreTransitiveClosure(dm, p, PETSC_TRUE, &closureSize2, &closure2));
618: PetscCall(VecPlaceArray(coordVec, newCoords));
619: }
620: PetscCall(DMPlexComputeCellGeometryAffineFEM(dm, p, NULL, J, NULL, &detJ));
621: if (ornt != 0) {
622: PetscCall(VecResetArray(coordVec));
623: PetscCall(PetscFree(newCoords));
624: }
625: PetscCall(DMRestoreWorkArray(dm, nSubVert, MPIU_INT, &closureVerts));
626: /* compactify */
627: for (i = 0; i < dim; i++)
628: for (j = 0; j < pdim; j++) J[i * pdim + j] = J[i * dim + j];
629: /* We have the Jacobian mapping the point's reference cell to this reference cell:
630: * pulling back a function to the point and applying the dof is what we want,
631: * so we get the pullback matrix and multiply the dof by that matrix on the right */
632: PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(formDegree), &Nk));
633: PetscCall(PetscDTBinomialInt(pdim, PetscAbsInt(formDegree), &pNk));
634: PetscCall(DMGetWorkArray(dm, pNk * Nk, MPIU_REAL, &Jstar));
635: PetscCall(PetscDTAltVPullbackMatrix(pdim, dim, J, formDegree, Jstar));
636: for (n = 0; n < nNodes; n++) {
637: for (i = 0; i < Nk; i++) {
638: PetscReal val = 0.;
639: for (j = 0; j < pNk; j++) val += nodeVec[n * pNk + j] * Jstar[j * Nk + i];
640: pfNodeVec[n * Nk + i] = val;
641: }
642: }
643: PetscCall(DMRestoreWorkArray(dm, pNk * Nk, MPIU_REAL, &Jstar));
644: PetscCall(DMRestoreWorkArray(dm, dim * dim, MPIU_REAL, &J));
645: PetscFunctionReturn(PETSC_SUCCESS);
646: }
648: /* given to sets of nodes, take the tensor product, where the product of the dof indices is concatenation and the
649: * product of the dof vectors is the wedge product */
650: static PetscErrorCode PetscLagNodeIndicesTensor(PetscLagNodeIndices tracei, PetscInt dimT, PetscInt kT, PetscLagNodeIndices fiberi, PetscInt dimF, PetscInt kF, PetscLagNodeIndices *nodeIndices)
651: {
652: PetscInt dim = dimT + dimF;
653: PetscInt nodeIdxDim, nNodes;
654: PetscInt formDegree = kT + kF;
655: PetscInt Nk, NkT, NkF;
656: PetscInt MkT, MkF;
657: PetscLagNodeIndices ni;
658: PetscInt i, j, l;
659: PetscReal *projF, *projT;
660: PetscReal *projFstar, *projTstar;
661: PetscReal *workF, *workF2, *workT, *workT2, *work, *work2;
662: PetscReal *wedgeMat;
663: PetscReal sign;
665: PetscFunctionBegin;
666: PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(formDegree), &Nk));
667: PetscCall(PetscDTBinomialInt(dimT, PetscAbsInt(kT), &NkT));
668: PetscCall(PetscDTBinomialInt(dimF, PetscAbsInt(kF), &NkF));
669: PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(kT), &MkT));
670: PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(kF), &MkF));
671: PetscCall(PetscNew(&ni));
672: ni->nodeIdxDim = nodeIdxDim = tracei->nodeIdxDim + fiberi->nodeIdxDim;
673: ni->nodeVecDim = Nk;
674: ni->nNodes = nNodes = tracei->nNodes * fiberi->nNodes;
675: ni->refct = 1;
676: PetscCall(PetscMalloc1(nNodes * nodeIdxDim, &ni->nodeIdx));
677: /* first concatenate the indices */
678: for (l = 0, j = 0; j < fiberi->nNodes; j++) {
679: for (i = 0; i < tracei->nNodes; i++, l++) {
680: PetscInt m, n = 0;
682: for (m = 0; m < tracei->nodeIdxDim; m++) ni->nodeIdx[l * nodeIdxDim + n++] = tracei->nodeIdx[i * tracei->nodeIdxDim + m];
683: for (m = 0; m < fiberi->nodeIdxDim; m++) ni->nodeIdx[l * nodeIdxDim + n++] = fiberi->nodeIdx[j * fiberi->nodeIdxDim + m];
684: }
685: }
687: /* now wedge together the push-forward vectors */
688: PetscCall(PetscMalloc1(nNodes * Nk, &ni->nodeVec));
689: PetscCall(PetscCalloc2(dimT * dim, &projT, dimF * dim, &projF));
690: for (i = 0; i < dimT; i++) projT[i * (dim + 1)] = 1.;
691: for (i = 0; i < dimF; i++) projF[i * (dim + dimT + 1) + dimT] = 1.;
692: PetscCall(PetscMalloc2(MkT * NkT, &projTstar, MkF * NkF, &projFstar));
693: PetscCall(PetscDTAltVPullbackMatrix(dim, dimT, projT, kT, projTstar));
694: PetscCall(PetscDTAltVPullbackMatrix(dim, dimF, projF, kF, projFstar));
695: PetscCall(PetscMalloc6(MkT, &workT, MkT, &workT2, MkF, &workF, MkF, &workF2, Nk, &work, Nk, &work2));
696: PetscCall(PetscMalloc1(Nk * MkT, &wedgeMat));
697: sign = (PetscAbsInt(kT * kF) & 1) ? -1. : 1.;
698: for (l = 0, j = 0; j < fiberi->nNodes; j++) {
699: PetscInt d, e;
701: /* push forward fiber k-form */
702: for (d = 0; d < MkF; d++) {
703: PetscReal val = 0.;
704: for (e = 0; e < NkF; e++) val += projFstar[d * NkF + e] * fiberi->nodeVec[j * NkF + e];
705: workF[d] = val;
706: }
707: /* Hodge star to proper form if necessary */
708: if (kF < 0) {
709: for (d = 0; d < MkF; d++) workF2[d] = workF[d];
710: PetscCall(PetscDTAltVStar(dim, PetscAbsInt(kF), 1, workF2, workF));
711: }
712: /* Compute the matrix that wedges this form with one of the trace k-form */
713: PetscCall(PetscDTAltVWedgeMatrix(dim, PetscAbsInt(kF), PetscAbsInt(kT), workF, wedgeMat));
714: for (i = 0; i < tracei->nNodes; i++, l++) {
715: /* push forward trace k-form */
716: for (d = 0; d < MkT; d++) {
717: PetscReal val = 0.;
718: for (e = 0; e < NkT; e++) val += projTstar[d * NkT + e] * tracei->nodeVec[i * NkT + e];
719: workT[d] = val;
720: }
721: /* Hodge star to proper form if necessary */
722: if (kT < 0) {
723: for (d = 0; d < MkT; d++) workT2[d] = workT[d];
724: PetscCall(PetscDTAltVStar(dim, PetscAbsInt(kT), 1, workT2, workT));
725: }
726: /* compute the wedge product of the push-forward trace form and firer forms */
727: for (d = 0; d < Nk; d++) {
728: PetscReal val = 0.;
729: for (e = 0; e < MkT; e++) val += wedgeMat[d * MkT + e] * workT[e];
730: work[d] = val;
731: }
732: /* inverse Hodge star from proper form if necessary */
733: if (formDegree < 0) {
734: for (d = 0; d < Nk; d++) work2[d] = work[d];
735: PetscCall(PetscDTAltVStar(dim, PetscAbsInt(formDegree), -1, work2, work));
736: }
737: /* insert into the array (adjusting for sign) */
738: for (d = 0; d < Nk; d++) ni->nodeVec[l * Nk + d] = sign * work[d];
739: }
740: }
741: PetscCall(PetscFree(wedgeMat));
742: PetscCall(PetscFree6(workT, workT2, workF, workF2, work, work2));
743: PetscCall(PetscFree2(projTstar, projFstar));
744: PetscCall(PetscFree2(projT, projF));
745: *nodeIndices = ni;
746: PetscFunctionReturn(PETSC_SUCCESS);
747: }
749: /* simple union of two sets of nodes */
750: static PetscErrorCode PetscLagNodeIndicesMerge(PetscLagNodeIndices niA, PetscLagNodeIndices niB, PetscLagNodeIndices *nodeIndices)
751: {
752: PetscLagNodeIndices ni;
753: PetscInt nodeIdxDim, nodeVecDim, nNodes;
755: PetscFunctionBegin;
756: PetscCall(PetscNew(&ni));
757: ni->nodeIdxDim = nodeIdxDim = niA->nodeIdxDim;
758: PetscCheck(niB->nodeIdxDim == nodeIdxDim, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Cannot merge PetscLagNodeIndices with different nodeIdxDim");
759: ni->nodeVecDim = nodeVecDim = niA->nodeVecDim;
760: PetscCheck(niB->nodeVecDim == nodeVecDim, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Cannot merge PetscLagNodeIndices with different nodeVecDim");
761: ni->nNodes = nNodes = niA->nNodes + niB->nNodes;
762: ni->refct = 1;
763: PetscCall(PetscMalloc1(nNodes * nodeIdxDim, &ni->nodeIdx));
764: PetscCall(PetscMalloc1(nNodes * nodeVecDim, &ni->nodeVec));
765: PetscCall(PetscArraycpy(ni->nodeIdx, niA->nodeIdx, niA->nNodes * nodeIdxDim));
766: PetscCall(PetscArraycpy(ni->nodeVec, niA->nodeVec, niA->nNodes * nodeVecDim));
767: PetscCall(PetscArraycpy(&ni->nodeIdx[niA->nNodes * nodeIdxDim], niB->nodeIdx, niB->nNodes * nodeIdxDim));
768: PetscCall(PetscArraycpy(&ni->nodeVec[niA->nNodes * nodeVecDim], niB->nodeVec, niB->nNodes * nodeVecDim));
769: *nodeIndices = ni;
770: PetscFunctionReturn(PETSC_SUCCESS);
771: }
773: #define PETSCTUPINTCOMPREVLEX(N) \
774: static int PetscConcat_(PetscTupIntCompRevlex_, N)(const void *a, const void *b) \
775: { \
776: const PetscInt *A = (const PetscInt *)a; \
777: const PetscInt *B = (const PetscInt *)b; \
778: int i; \
779: PetscInt diff = 0; \
780: for (i = 0; i < N; i++) { \
781: diff = A[N - i] - B[N - i]; \
782: if (diff) break; \
783: } \
784: return (diff <= 0) ? (diff < 0) ? -1 : 0 : 1; \
785: }
787: PETSCTUPINTCOMPREVLEX(3)
788: PETSCTUPINTCOMPREVLEX(4)
789: PETSCTUPINTCOMPREVLEX(5)
790: PETSCTUPINTCOMPREVLEX(6)
791: PETSCTUPINTCOMPREVLEX(7)
793: static int PetscTupIntCompRevlex_N(const void *a, const void *b)
794: {
795: const PetscInt *A = (const PetscInt *)a;
796: const PetscInt *B = (const PetscInt *)b;
797: PetscInt i;
798: PetscInt N = A[0];
799: PetscInt diff = 0;
800: for (i = 0; i < N; i++) {
801: diff = A[N - i] - B[N - i];
802: if (diff) break;
803: }
804: return (diff <= 0) ? (diff < 0) ? -1 : 0 : 1;
805: }
807: /* The nodes are not necessarily in revlex order wrt nodeIdx: get the permutation
808: * that puts them in that order */
809: static PetscErrorCode PetscLagNodeIndicesGetPermutation(PetscLagNodeIndices ni, PetscInt *perm[])
810: {
811: PetscFunctionBegin;
812: if (!ni->perm) {
813: PetscInt *sorter;
814: PetscInt m = ni->nNodes;
815: PetscInt nodeIdxDim = ni->nodeIdxDim;
816: PetscInt i, j, k, l;
817: PetscInt *prm;
818: int (*comp)(const void *, const void *);
820: PetscCall(PetscMalloc1((nodeIdxDim + 2) * m, &sorter));
821: for (k = 0, l = 0, i = 0; i < m; i++) {
822: sorter[k++] = nodeIdxDim + 1;
823: sorter[k++] = i;
824: for (j = 0; j < nodeIdxDim; j++) sorter[k++] = ni->nodeIdx[l++];
825: }
826: switch (nodeIdxDim) {
827: case 2:
828: comp = PetscTupIntCompRevlex_3;
829: break;
830: case 3:
831: comp = PetscTupIntCompRevlex_4;
832: break;
833: case 4:
834: comp = PetscTupIntCompRevlex_5;
835: break;
836: case 5:
837: comp = PetscTupIntCompRevlex_6;
838: break;
839: case 6:
840: comp = PetscTupIntCompRevlex_7;
841: break;
842: default:
843: comp = PetscTupIntCompRevlex_N;
844: break;
845: }
846: qsort(sorter, m, (nodeIdxDim + 2) * sizeof(PetscInt), comp);
847: PetscCall(PetscMalloc1(m, &prm));
848: for (i = 0; i < m; i++) prm[i] = sorter[(nodeIdxDim + 2) * i + 1];
849: ni->perm = prm;
850: PetscCall(PetscFree(sorter));
851: }
852: *perm = ni->perm;
853: PetscFunctionReturn(PETSC_SUCCESS);
854: }
856: static PetscErrorCode PetscDualSpaceDestroy_Lagrange(PetscDualSpace sp)
857: {
858: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
860: PetscFunctionBegin;
861: if (lag->symperms) {
862: PetscInt **selfSyms = lag->symperms[0];
864: if (selfSyms) {
865: PetscInt i, **allocated = &selfSyms[-lag->selfSymOff];
867: for (i = 0; i < lag->numSelfSym; i++) PetscCall(PetscFree(allocated[i]));
868: PetscCall(PetscFree(allocated));
869: }
870: PetscCall(PetscFree(lag->symperms));
871: }
872: if (lag->symflips) {
873: PetscScalar **selfSyms = lag->symflips[0];
875: if (selfSyms) {
876: PetscInt i;
877: PetscScalar **allocated = &selfSyms[-lag->selfSymOff];
879: for (i = 0; i < lag->numSelfSym; i++) PetscCall(PetscFree(allocated[i]));
880: PetscCall(PetscFree(allocated));
881: }
882: PetscCall(PetscFree(lag->symflips));
883: }
884: PetscCall(Petsc1DNodeFamilyDestroy(&lag->nodeFamily));
885: PetscCall(PetscLagNodeIndicesDestroy(&lag->vertIndices));
886: PetscCall(PetscLagNodeIndicesDestroy(&lag->intNodeIndices));
887: PetscCall(PetscLagNodeIndicesDestroy(&lag->allNodeIndices));
888: PetscCall(PetscFree(lag));
889: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetContinuity_C", NULL));
890: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetContinuity_C", NULL));
891: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetTensor_C", NULL));
892: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetTensor_C", NULL));
893: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetTrimmed_C", NULL));
894: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetTrimmed_C", NULL));
895: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetNodeType_C", NULL));
896: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetNodeType_C", NULL));
897: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetUseMoments_C", NULL));
898: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetUseMoments_C", NULL));
899: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetMomentOrder_C", NULL));
900: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetMomentOrder_C", NULL));
901: PetscFunctionReturn(PETSC_SUCCESS);
902: }
904: static PetscErrorCode PetscDualSpaceLagrangeView_Ascii(PetscDualSpace sp, PetscViewer viewer)
905: {
906: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
908: PetscFunctionBegin;
909: PetscCall(PetscViewerASCIIPrintf(viewer, "%s %s%sLagrange dual space\n", lag->continuous ? "Continuous" : "Discontinuous", lag->tensorSpace ? "tensor " : "", lag->trimmed ? "trimmed " : ""));
910: PetscFunctionReturn(PETSC_SUCCESS);
911: }
913: static PetscErrorCode PetscDualSpaceView_Lagrange(PetscDualSpace sp, PetscViewer viewer)
914: {
915: PetscBool iascii;
917: PetscFunctionBegin;
920: PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
921: if (iascii) PetscCall(PetscDualSpaceLagrangeView_Ascii(sp, viewer));
922: PetscFunctionReturn(PETSC_SUCCESS);
923: }
925: static PetscErrorCode PetscDualSpaceSetFromOptions_Lagrange(PetscDualSpace sp, PetscOptionItems PetscOptionsObject)
926: {
927: PetscBool continuous, tensor, trimmed, flg, flg2, flg3;
928: PetscDTNodeType nodeType;
929: PetscReal nodeExponent;
930: PetscInt momentOrder;
931: PetscBool nodeEndpoints, useMoments;
933: PetscFunctionBegin;
934: PetscCall(PetscDualSpaceLagrangeGetContinuity(sp, &continuous));
935: PetscCall(PetscDualSpaceLagrangeGetTensor(sp, &tensor));
936: PetscCall(PetscDualSpaceLagrangeGetTrimmed(sp, &trimmed));
937: PetscCall(PetscDualSpaceLagrangeGetNodeType(sp, &nodeType, &nodeEndpoints, &nodeExponent));
938: if (nodeType == PETSCDTNODES_DEFAULT) nodeType = PETSCDTNODES_GAUSSJACOBI;
939: PetscCall(PetscDualSpaceLagrangeGetUseMoments(sp, &useMoments));
940: PetscCall(PetscDualSpaceLagrangeGetMomentOrder(sp, &momentOrder));
941: PetscOptionsHeadBegin(PetscOptionsObject, "PetscDualSpace Lagrange Options");
942: PetscCall(PetscOptionsBool("-petscdualspace_lagrange_continuity", "Flag for continuous element", "PetscDualSpaceLagrangeSetContinuity", continuous, &continuous, &flg));
943: if (flg) PetscCall(PetscDualSpaceLagrangeSetContinuity(sp, continuous));
944: PetscCall(PetscOptionsBool("-petscdualspace_lagrange_tensor", "Flag for tensor dual space", "PetscDualSpaceLagrangeSetTensor", tensor, &tensor, &flg));
945: if (flg) PetscCall(PetscDualSpaceLagrangeSetTensor(sp, tensor));
946: PetscCall(PetscOptionsBool("-petscdualspace_lagrange_trimmed", "Flag for trimmed dual space", "PetscDualSpaceLagrangeSetTrimmed", trimmed, &trimmed, &flg));
947: if (flg) PetscCall(PetscDualSpaceLagrangeSetTrimmed(sp, trimmed));
948: PetscCall(PetscOptionsEnum("-petscdualspace_lagrange_node_type", "Lagrange node location type", "PetscDualSpaceLagrangeSetNodeType", PetscDTNodeTypes, (PetscEnum)nodeType, (PetscEnum *)&nodeType, &flg));
949: PetscCall(PetscOptionsBool("-petscdualspace_lagrange_node_endpoints", "Flag for nodes that include endpoints", "PetscDualSpaceLagrangeSetNodeType", nodeEndpoints, &nodeEndpoints, &flg2));
950: flg3 = PETSC_FALSE;
951: if (nodeType == PETSCDTNODES_GAUSSJACOBI) PetscCall(PetscOptionsReal("-petscdualspace_lagrange_node_exponent", "Gauss-Jacobi weight function exponent", "PetscDualSpaceLagrangeSetNodeType", nodeExponent, &nodeExponent, &flg3));
952: if (flg || flg2 || flg3) PetscCall(PetscDualSpaceLagrangeSetNodeType(sp, nodeType, nodeEndpoints, nodeExponent));
953: PetscCall(PetscOptionsBool("-petscdualspace_lagrange_use_moments", "Use moments (where appropriate) for functionals", "PetscDualSpaceLagrangeSetUseMoments", useMoments, &useMoments, &flg));
954: if (flg) PetscCall(PetscDualSpaceLagrangeSetUseMoments(sp, useMoments));
955: PetscCall(PetscOptionsInt("-petscdualspace_lagrange_moment_order", "Quadrature order for moment functionals", "PetscDualSpaceLagrangeSetMomentOrder", momentOrder, &momentOrder, &flg));
956: if (flg) PetscCall(PetscDualSpaceLagrangeSetMomentOrder(sp, momentOrder));
957: PetscOptionsHeadEnd();
958: PetscFunctionReturn(PETSC_SUCCESS);
959: }
961: static PetscErrorCode PetscDualSpaceDuplicate_Lagrange(PetscDualSpace sp, PetscDualSpace spNew)
962: {
963: PetscBool cont, tensor, trimmed, boundary, mom;
964: PetscDTNodeType nodeType;
965: PetscReal exponent;
966: PetscInt n;
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: PetscCall(PetscDualSpaceLagrangeGetUseMoments(sp, &mom));
985: PetscCall(PetscDualSpaceLagrangeSetUseMoments(spNew, mom));
986: PetscCall(PetscDualSpaceLagrangeGetMomentOrder(sp, &n));
987: PetscCall(PetscDualSpaceLagrangeSetMomentOrder(spNew, n));
988: PetscFunctionReturn(PETSC_SUCCESS);
989: }
991: /* for making tensor product spaces: take a dual space and product a segment space that has all the same
992: * specifications (trimmed, continuous, order, node set), except for the form degree */
993: static PetscErrorCode PetscDualSpaceCreateEdgeSubspace_Lagrange(PetscDualSpace sp, PetscInt order, PetscInt k, PetscInt Nc, PetscBool interiorOnly, PetscDualSpace *bdsp)
994: {
995: DM K;
996: PetscDualSpace_Lag *newlag;
998: PetscFunctionBegin;
999: PetscCall(PetscDualSpaceDuplicate(sp, bdsp));
1000: PetscCall(PetscDualSpaceSetFormDegree(*bdsp, k));
1001: PetscCall(DMPlexCreateReferenceCell(PETSC_COMM_SELF, DMPolytopeTypeSimpleShape(1, PETSC_TRUE), &K));
1002: PetscCall(PetscDualSpaceSetDM(*bdsp, K));
1003: PetscCall(DMDestroy(&K));
1004: PetscCall(PetscDualSpaceSetOrder(*bdsp, order));
1005: PetscCall(PetscDualSpaceSetNumComponents(*bdsp, Nc));
1006: newlag = (PetscDualSpace_Lag *)(*bdsp)->data;
1007: newlag->interiorOnly = interiorOnly;
1008: PetscCall(PetscDualSpaceSetUp(*bdsp));
1009: PetscFunctionReturn(PETSC_SUCCESS);
1010: }
1012: /* just the points, weights aren't handled */
1013: static PetscErrorCode PetscQuadratureCreateTensor(PetscQuadrature trace, PetscQuadrature fiber, PetscQuadrature *product)
1014: {
1015: PetscInt dimTrace, dimFiber;
1016: PetscInt numPointsTrace, numPointsFiber;
1017: PetscInt dim, numPoints;
1018: const PetscReal *pointsTrace;
1019: const PetscReal *pointsFiber;
1020: PetscReal *points;
1021: PetscInt i, j, k, p;
1023: PetscFunctionBegin;
1024: PetscCall(PetscQuadratureGetData(trace, &dimTrace, NULL, &numPointsTrace, &pointsTrace, NULL));
1025: PetscCall(PetscQuadratureGetData(fiber, &dimFiber, NULL, &numPointsFiber, &pointsFiber, NULL));
1026: dim = dimTrace + dimFiber;
1027: numPoints = numPointsFiber * numPointsTrace;
1028: PetscCall(PetscMalloc1(numPoints * dim, &points));
1029: for (p = 0, j = 0; j < numPointsFiber; j++) {
1030: for (i = 0; i < numPointsTrace; i++, p++) {
1031: for (k = 0; k < dimTrace; k++) points[p * dim + k] = pointsTrace[i * dimTrace + k];
1032: for (k = 0; k < dimFiber; k++) points[p * dim + dimTrace + k] = pointsFiber[j * dimFiber + k];
1033: }
1034: }
1035: PetscCall(PetscQuadratureCreate(PETSC_COMM_SELF, product));
1036: PetscCall(PetscQuadratureSetData(*product, dim, 0, numPoints, points, NULL));
1037: PetscFunctionReturn(PETSC_SUCCESS);
1038: }
1040: /* Kronecker tensor product where matrix is considered a matrix of k-forms, so that
1041: * the entries in the product matrix are wedge products of the entries in the original matrices */
1042: static PetscErrorCode MatTensorAltV(Mat trace, Mat fiber, PetscInt dimTrace, PetscInt kTrace, PetscInt dimFiber, PetscInt kFiber, Mat *product)
1043: {
1044: PetscInt mTrace, nTrace, mFiber, nFiber, m, n, k, i, j, l;
1045: PetscInt dim, NkTrace, NkFiber, Nk;
1046: PetscInt dT, dF;
1047: PetscInt *nnzTrace, *nnzFiber, *nnz;
1048: PetscInt iT, iF, jT, jF, il, jl;
1049: PetscReal *workT, *workT2, *workF, *workF2, *work, *workstar;
1050: PetscReal *projT, *projF;
1051: PetscReal *projTstar, *projFstar;
1052: PetscReal *wedgeMat;
1053: PetscReal sign;
1054: PetscScalar *workS;
1055: Mat prod;
1056: /* this produces dof groups that look like the identity */
1058: PetscFunctionBegin;
1059: PetscCall(MatGetSize(trace, &mTrace, &nTrace));
1060: PetscCall(PetscDTBinomialInt(dimTrace, PetscAbsInt(kTrace), &NkTrace));
1061: PetscCheck(nTrace % NkTrace == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "point value space of trace matrix is not a multiple of k-form size");
1062: PetscCall(MatGetSize(fiber, &mFiber, &nFiber));
1063: PetscCall(PetscDTBinomialInt(dimFiber, PetscAbsInt(kFiber), &NkFiber));
1064: PetscCheck(nFiber % NkFiber == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "point value space of fiber matrix is not a multiple of k-form size");
1065: PetscCall(PetscMalloc2(mTrace, &nnzTrace, mFiber, &nnzFiber));
1066: for (i = 0; i < mTrace; i++) {
1067: PetscCall(MatGetRow(trace, i, &nnzTrace[i], NULL, NULL));
1068: PetscCheck(nnzTrace[i] % NkTrace == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "nonzeros in trace matrix are not in k-form size blocks");
1069: }
1070: for (i = 0; i < mFiber; i++) {
1071: PetscCall(MatGetRow(fiber, i, &nnzFiber[i], NULL, NULL));
1072: PetscCheck(nnzFiber[i] % NkFiber == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "nonzeros in fiber matrix are not in k-form size blocks");
1073: }
1074: dim = dimTrace + dimFiber;
1075: k = kFiber + kTrace;
1076: PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(k), &Nk));
1077: m = mTrace * mFiber;
1078: PetscCall(PetscMalloc1(m, &nnz));
1079: for (l = 0, j = 0; j < mFiber; j++)
1080: for (i = 0; i < mTrace; i++, l++) nnz[l] = (nnzTrace[i] / NkTrace) * (nnzFiber[j] / NkFiber) * Nk;
1081: n = (nTrace / NkTrace) * (nFiber / NkFiber) * Nk;
1082: PetscCall(MatCreateSeqAIJ(PETSC_COMM_SELF, m, n, 0, nnz, &prod));
1083: PetscCall(PetscObjectSetOptionsPrefix((PetscObject)prod, "altv_"));
1084: PetscCall(PetscFree(nnz));
1085: PetscCall(PetscFree2(nnzTrace, nnzFiber));
1086: /* reasoning about which points each dof needs depends on having zeros computed at points preserved */
1087: PetscCall(MatSetOption(prod, MAT_IGNORE_ZERO_ENTRIES, PETSC_FALSE));
1088: /* compute pullbacks */
1089: PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(kTrace), &dT));
1090: PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(kFiber), &dF));
1091: PetscCall(PetscMalloc4(dimTrace * dim, &projT, dimFiber * dim, &projF, dT * NkTrace, &projTstar, dF * NkFiber, &projFstar));
1092: PetscCall(PetscArrayzero(projT, dimTrace * dim));
1093: for (i = 0; i < dimTrace; i++) projT[i * (dim + 1)] = 1.;
1094: PetscCall(PetscArrayzero(projF, dimFiber * dim));
1095: for (i = 0; i < dimFiber; i++) projF[i * (dim + 1) + dimTrace] = 1.;
1096: PetscCall(PetscDTAltVPullbackMatrix(dim, dimTrace, projT, kTrace, projTstar));
1097: PetscCall(PetscDTAltVPullbackMatrix(dim, dimFiber, projF, kFiber, projFstar));
1098: PetscCall(PetscMalloc5(dT, &workT, dF, &workF, Nk, &work, Nk, &workstar, Nk, &workS));
1099: PetscCall(PetscMalloc2(dT, &workT2, dF, &workF2));
1100: PetscCall(PetscMalloc1(Nk * dT, &wedgeMat));
1101: sign = (PetscAbsInt(kTrace * kFiber) & 1) ? -1. : 1.;
1102: for (i = 0, iF = 0; iF < mFiber; iF++) {
1103: PetscInt ncolsF, nformsF;
1104: const PetscInt *colsF;
1105: const PetscScalar *valsF;
1107: PetscCall(MatGetRow(fiber, iF, &ncolsF, &colsF, &valsF));
1108: nformsF = ncolsF / NkFiber;
1109: for (iT = 0; iT < mTrace; iT++, i++) {
1110: PetscInt ncolsT, nformsT;
1111: const PetscInt *colsT;
1112: const PetscScalar *valsT;
1114: PetscCall(MatGetRow(trace, iT, &ncolsT, &colsT, &valsT));
1115: nformsT = ncolsT / NkTrace;
1116: for (j = 0, jF = 0; jF < nformsF; jF++) {
1117: PetscInt colF = colsF[jF * NkFiber] / NkFiber;
1119: for (il = 0; il < dF; il++) {
1120: PetscReal val = 0.;
1121: for (jl = 0; jl < NkFiber; jl++) val += projFstar[il * NkFiber + jl] * PetscRealPart(valsF[jF * NkFiber + jl]);
1122: workF[il] = val;
1123: }
1124: if (kFiber < 0) {
1125: for (il = 0; il < dF; il++) workF2[il] = workF[il];
1126: PetscCall(PetscDTAltVStar(dim, PetscAbsInt(kFiber), 1, workF2, workF));
1127: }
1128: PetscCall(PetscDTAltVWedgeMatrix(dim, PetscAbsInt(kFiber), PetscAbsInt(kTrace), workF, wedgeMat));
1129: for (jT = 0; jT < nformsT; jT++, j++) {
1130: PetscInt colT = colsT[jT * NkTrace] / NkTrace;
1131: PetscInt col = colF * (nTrace / NkTrace) + colT;
1132: const PetscScalar *vals;
1134: for (il = 0; il < dT; il++) {
1135: PetscReal val = 0.;
1136: for (jl = 0; jl < NkTrace; jl++) val += projTstar[il * NkTrace + jl] * PetscRealPart(valsT[jT * NkTrace + jl]);
1137: workT[il] = val;
1138: }
1139: if (kTrace < 0) {
1140: for (il = 0; il < dT; il++) workT2[il] = workT[il];
1141: PetscCall(PetscDTAltVStar(dim, PetscAbsInt(kTrace), 1, workT2, workT));
1142: }
1144: for (il = 0; il < Nk; il++) {
1145: PetscReal val = 0.;
1146: for (jl = 0; jl < dT; jl++) val += sign * wedgeMat[il * dT + jl] * workT[jl];
1147: work[il] = val;
1148: }
1149: if (k < 0) {
1150: PetscCall(PetscDTAltVStar(dim, PetscAbsInt(k), -1, work, workstar));
1151: #if defined(PETSC_USE_COMPLEX)
1152: for (l = 0; l < Nk; l++) workS[l] = workstar[l];
1153: vals = &workS[0];
1154: #else
1155: vals = &workstar[0];
1156: #endif
1157: } else {
1158: #if defined(PETSC_USE_COMPLEX)
1159: for (l = 0; l < Nk; l++) workS[l] = work[l];
1160: vals = &workS[0];
1161: #else
1162: vals = &work[0];
1163: #endif
1164: }
1165: for (l = 0; l < Nk; l++) PetscCall(MatSetValue(prod, i, col * Nk + l, vals[l], INSERT_VALUES)); /* Nk */
1166: } /* jT */
1167: } /* jF */
1168: PetscCall(MatRestoreRow(trace, iT, &ncolsT, &colsT, &valsT));
1169: } /* iT */
1170: PetscCall(MatRestoreRow(fiber, iF, &ncolsF, &colsF, &valsF));
1171: } /* iF */
1172: PetscCall(PetscFree(wedgeMat));
1173: PetscCall(PetscFree4(projT, projF, projTstar, projFstar));
1174: PetscCall(PetscFree2(workT2, workF2));
1175: PetscCall(PetscFree5(workT, workF, work, workstar, workS));
1176: PetscCall(MatAssemblyBegin(prod, MAT_FINAL_ASSEMBLY));
1177: PetscCall(MatAssemblyEnd(prod, MAT_FINAL_ASSEMBLY));
1178: *product = prod;
1179: PetscFunctionReturn(PETSC_SUCCESS);
1180: }
1182: /* Union of quadrature points, with an attempt to identify common points in the two sets */
1183: static PetscErrorCode PetscQuadraturePointsMerge(PetscQuadrature quadA, PetscQuadrature quadB, PetscQuadrature *quadJoint, PetscInt *aToJoint[], PetscInt *bToJoint[])
1184: {
1185: PetscInt dimA, dimB;
1186: PetscInt nA, nB, nJoint, i, j, d;
1187: const PetscReal *pointsA;
1188: const PetscReal *pointsB;
1189: PetscReal *pointsJoint;
1190: PetscInt *aToJ, *bToJ;
1191: PetscQuadrature qJ;
1193: PetscFunctionBegin;
1194: PetscCall(PetscQuadratureGetData(quadA, &dimA, NULL, &nA, &pointsA, NULL));
1195: PetscCall(PetscQuadratureGetData(quadB, &dimB, NULL, &nB, &pointsB, NULL));
1196: PetscCheck(dimA == dimB, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Quadrature points must be in the same dimension");
1197: nJoint = nA;
1198: PetscCall(PetscMalloc1(nA, &aToJ));
1199: for (i = 0; i < nA; i++) aToJ[i] = i;
1200: PetscCall(PetscMalloc1(nB, &bToJ));
1201: for (i = 0; i < nB; i++) {
1202: for (j = 0; j < nA; j++) {
1203: bToJ[i] = -1;
1204: for (d = 0; d < dimA; d++)
1205: if (PetscAbsReal(pointsB[i * dimA + d] - pointsA[j * dimA + d]) > PETSC_SMALL) break;
1206: if (d == dimA) {
1207: bToJ[i] = j;
1208: break;
1209: }
1210: }
1211: if (bToJ[i] == -1) bToJ[i] = nJoint++;
1212: }
1213: *aToJoint = aToJ;
1214: *bToJoint = bToJ;
1215: PetscCall(PetscMalloc1(nJoint * dimA, &pointsJoint));
1216: PetscCall(PetscArraycpy(pointsJoint, pointsA, nA * dimA));
1217: for (i = 0; i < nB; i++) {
1218: if (bToJ[i] >= nA) {
1219: for (d = 0; d < dimA; d++) pointsJoint[bToJ[i] * dimA + d] = pointsB[i * dimA + d];
1220: }
1221: }
1222: PetscCall(PetscQuadratureCreate(PETSC_COMM_SELF, &qJ));
1223: PetscCall(PetscQuadratureSetData(qJ, dimA, 0, nJoint, pointsJoint, NULL));
1224: *quadJoint = qJ;
1225: PetscFunctionReturn(PETSC_SUCCESS);
1226: }
1228: /* Matrices matA and matB are both quadrature -> dof matrices: produce a matrix that is joint quadrature -> union of
1229: * dofs, where the joint quadrature was produced by PetscQuadraturePointsMerge */
1230: static PetscErrorCode MatricesMerge(Mat matA, Mat matB, PetscInt dim, PetscInt k, PetscInt numMerged, const PetscInt aToMerged[], const PetscInt bToMerged[], Mat *matMerged)
1231: {
1232: PetscInt m, n, mA, nA, mB, nB, Nk, i, j, l;
1233: Mat M;
1234: PetscInt *nnz;
1235: PetscInt maxnnz;
1236: PetscInt *work;
1238: PetscFunctionBegin;
1239: PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(k), &Nk));
1240: PetscCall(MatGetSize(matA, &mA, &nA));
1241: PetscCheck(nA % Nk == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "matA column space not a multiple of k-form size");
1242: PetscCall(MatGetSize(matB, &mB, &nB));
1243: PetscCheck(nB % Nk == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "matB column space not a multiple of k-form size");
1244: m = mA + mB;
1245: n = numMerged * Nk;
1246: PetscCall(PetscMalloc1(m, &nnz));
1247: maxnnz = 0;
1248: for (i = 0; i < mA; i++) {
1249: PetscCall(MatGetRow(matA, i, &nnz[i], NULL, NULL));
1250: PetscCheck(nnz[i] % Nk == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "nonzeros in matA are not in k-form size blocks");
1251: maxnnz = PetscMax(maxnnz, nnz[i]);
1252: }
1253: for (i = 0; i < mB; i++) {
1254: PetscCall(MatGetRow(matB, i, &nnz[i + mA], NULL, NULL));
1255: PetscCheck(nnz[i + mA] % Nk == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "nonzeros in matB are not in k-form size blocks");
1256: maxnnz = PetscMax(maxnnz, nnz[i + mA]);
1257: }
1258: PetscCall(MatCreateSeqAIJ(PETSC_COMM_SELF, m, n, 0, nnz, &M));
1259: PetscCall(PetscObjectSetOptionsPrefix((PetscObject)M, "altv_"));
1260: PetscCall(PetscFree(nnz));
1261: /* reasoning about which points each dof needs depends on having zeros computed at points preserved */
1262: PetscCall(MatSetOption(M, MAT_IGNORE_ZERO_ENTRIES, PETSC_FALSE));
1263: PetscCall(PetscMalloc1(maxnnz, &work));
1264: for (i = 0; i < mA; i++) {
1265: const PetscInt *cols;
1266: const PetscScalar *vals;
1267: PetscInt nCols;
1268: PetscCall(MatGetRow(matA, i, &nCols, &cols, &vals));
1269: for (j = 0; j < nCols / Nk; j++) {
1270: PetscInt newCol = aToMerged[cols[j * Nk] / Nk];
1271: for (l = 0; l < Nk; l++) work[j * Nk + l] = newCol * Nk + l;
1272: }
1273: PetscCall(MatSetValuesBlocked(M, 1, &i, nCols, work, vals, INSERT_VALUES));
1274: PetscCall(MatRestoreRow(matA, i, &nCols, &cols, &vals));
1275: }
1276: for (i = 0; i < mB; i++) {
1277: const PetscInt *cols;
1278: const PetscScalar *vals;
1280: PetscInt row = i + mA;
1281: PetscInt nCols;
1282: PetscCall(MatGetRow(matB, i, &nCols, &cols, &vals));
1283: for (j = 0; j < nCols / Nk; j++) {
1284: PetscInt newCol = bToMerged[cols[j * Nk] / Nk];
1285: for (l = 0; l < Nk; l++) work[j * Nk + l] = newCol * Nk + l;
1286: }
1287: PetscCall(MatSetValuesBlocked(M, 1, &row, nCols, work, vals, INSERT_VALUES));
1288: PetscCall(MatRestoreRow(matB, i, &nCols, &cols, &vals));
1289: }
1290: PetscCall(PetscFree(work));
1291: PetscCall(MatAssemblyBegin(M, MAT_FINAL_ASSEMBLY));
1292: PetscCall(MatAssemblyEnd(M, MAT_FINAL_ASSEMBLY));
1293: *matMerged = M;
1294: PetscFunctionReturn(PETSC_SUCCESS);
1295: }
1297: /* Take a dual space and product a segment space that has all the same specifications (trimmed, continuous, order,
1298: * node set), except for the form degree. For computing boundary dofs and for making tensor product spaces */
1299: static PetscErrorCode PetscDualSpaceCreateFacetSubspace_Lagrange(PetscDualSpace sp, DM K, PetscInt f, PetscInt k, PetscInt Ncopies, PetscBool interiorOnly, PetscDualSpace *bdsp)
1300: {
1301: PetscInt Nknew, Ncnew;
1302: PetscInt dim, pointDim = -1;
1303: PetscInt depth;
1304: DM dm;
1305: PetscDualSpace_Lag *newlag;
1307: PetscFunctionBegin;
1308: PetscCall(PetscDualSpaceGetDM(sp, &dm));
1309: PetscCall(DMGetDimension(dm, &dim));
1310: PetscCall(DMPlexGetDepth(dm, &depth));
1311: PetscCall(PetscDualSpaceDuplicate(sp, bdsp));
1312: PetscCall(PetscDualSpaceSetFormDegree(*bdsp, k));
1313: if (!K) {
1314: if (depth == dim) {
1315: DMPolytopeType ct;
1317: pointDim = dim - 1;
1318: PetscCall(DMPlexGetCellType(dm, f, &ct));
1319: PetscCall(DMPlexCreateReferenceCell(PETSC_COMM_SELF, ct, &K));
1320: } else if (depth == 1) {
1321: pointDim = 0;
1322: PetscCall(DMPlexCreateReferenceCell(PETSC_COMM_SELF, DM_POLYTOPE_POINT, &K));
1323: } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Unsupported interpolation state of reference element");
1324: } else {
1325: PetscCall(PetscObjectReference((PetscObject)K));
1326: PetscCall(DMGetDimension(K, &pointDim));
1327: }
1328: PetscCall(PetscDualSpaceSetDM(*bdsp, K));
1329: PetscCall(DMDestroy(&K));
1330: PetscCall(PetscDTBinomialInt(pointDim, PetscAbsInt(k), &Nknew));
1331: Ncnew = Nknew * Ncopies;
1332: PetscCall(PetscDualSpaceSetNumComponents(*bdsp, Ncnew));
1333: newlag = (PetscDualSpace_Lag *)(*bdsp)->data;
1334: newlag->interiorOnly = interiorOnly;
1335: PetscCall(PetscDualSpaceSetUp(*bdsp));
1336: PetscFunctionReturn(PETSC_SUCCESS);
1337: }
1339: /* Construct simplex nodes from a nodefamily, add Nk dof vectors of length Nk at each node.
1340: * Return the (quadrature, matrix) form of the dofs and the nodeIndices form as well.
1341: *
1342: * Sometimes we want a set of nodes to be contained in the interior of the element,
1343: * even when the node scheme puts nodes on the boundaries. numNodeSkip tells
1344: * the routine how many "layers" of nodes need to be skipped.
1345: * */
1346: static PetscErrorCode PetscDualSpaceLagrangeCreateSimplexNodeMat(Petsc1DNodeFamily nodeFamily, PetscInt dim, PetscInt sum, PetscInt Nk, PetscInt numNodeSkip, PetscQuadrature *iNodes, Mat *iMat, PetscLagNodeIndices *nodeIndices)
1347: {
1348: PetscReal *extraNodeCoords, *nodeCoords;
1349: PetscInt nNodes, nExtraNodes;
1350: PetscInt i, j, k, extraSum = sum + numNodeSkip * (1 + dim);
1351: PetscQuadrature intNodes;
1352: Mat intMat;
1353: PetscLagNodeIndices ni;
1355: PetscFunctionBegin;
1356: PetscCall(PetscDTBinomialInt(dim + sum, dim, &nNodes));
1357: PetscCall(PetscDTBinomialInt(dim + extraSum, dim, &nExtraNodes));
1359: PetscCall(PetscMalloc1(dim * nExtraNodes, &extraNodeCoords));
1360: PetscCall(PetscNew(&ni));
1361: ni->nodeIdxDim = dim + 1;
1362: ni->nodeVecDim = Nk;
1363: ni->nNodes = nNodes * Nk;
1364: ni->refct = 1;
1365: PetscCall(PetscMalloc1(nNodes * Nk * (dim + 1), &ni->nodeIdx));
1366: PetscCall(PetscMalloc1(nNodes * Nk * Nk, &ni->nodeVec));
1367: for (i = 0; i < nNodes; i++)
1368: for (j = 0; j < Nk; j++)
1369: for (k = 0; k < Nk; k++) ni->nodeVec[(i * Nk + j) * Nk + k] = (j == k) ? 1. : 0.;
1370: PetscCall(Petsc1DNodeFamilyComputeSimplexNodes(nodeFamily, dim, extraSum, extraNodeCoords));
1371: if (numNodeSkip) {
1372: PetscInt k;
1373: PetscInt *tup;
1375: PetscCall(PetscMalloc1(dim * nNodes, &nodeCoords));
1376: PetscCall(PetscMalloc1(dim + 1, &tup));
1377: for (k = 0; k < nNodes; k++) {
1378: PetscInt j, c;
1379: PetscInt index;
1381: PetscCall(PetscDTIndexToBary(dim + 1, sum, k, tup));
1382: for (j = 0; j < dim + 1; j++) tup[j] += numNodeSkip;
1383: for (c = 0; c < Nk; c++) {
1384: for (j = 0; j < dim + 1; j++) ni->nodeIdx[(k * Nk + c) * (dim + 1) + j] = tup[j] + 1;
1385: }
1386: PetscCall(PetscDTBaryToIndex(dim + 1, extraSum, tup, &index));
1387: for (j = 0; j < dim; j++) nodeCoords[k * dim + j] = extraNodeCoords[index * dim + j];
1388: }
1389: PetscCall(PetscFree(tup));
1390: PetscCall(PetscFree(extraNodeCoords));
1391: } else {
1392: PetscInt k;
1393: PetscInt *tup;
1395: nodeCoords = extraNodeCoords;
1396: PetscCall(PetscMalloc1(dim + 1, &tup));
1397: for (k = 0; k < nNodes; k++) {
1398: PetscInt j, c;
1400: PetscCall(PetscDTIndexToBary(dim + 1, sum, k, tup));
1401: for (c = 0; c < Nk; c++) {
1402: for (j = 0; j < dim + 1; j++) {
1403: /* barycentric indices can have zeros, but we don't want to push forward zeros because it makes it harder to
1404: * determine which nodes correspond to which under symmetries, so we increase by 1. This is fine
1405: * because the nodeIdx coordinates don't have any meaning other than helping to identify symmetries */
1406: ni->nodeIdx[(k * Nk + c) * (dim + 1) + j] = tup[j] + 1;
1407: }
1408: }
1409: }
1410: PetscCall(PetscFree(tup));
1411: }
1412: PetscCall(PetscQuadratureCreate(PETSC_COMM_SELF, &intNodes));
1413: PetscCall(PetscQuadratureSetData(intNodes, dim, 0, nNodes, nodeCoords, NULL));
1414: PetscCall(MatCreateSeqAIJ(PETSC_COMM_SELF, nNodes * Nk, nNodes * Nk, Nk, NULL, &intMat));
1415: PetscCall(PetscObjectSetOptionsPrefix((PetscObject)intMat, "lag_"));
1416: PetscCall(MatSetOption(intMat, MAT_IGNORE_ZERO_ENTRIES, PETSC_FALSE));
1417: for (j = 0; j < nNodes * Nk; j++) {
1418: PetscInt rem = j % Nk;
1419: PetscInt a, aprev = j - rem;
1420: PetscInt anext = aprev + Nk;
1422: for (a = aprev; a < anext; a++) PetscCall(MatSetValue(intMat, j, a, (a == j) ? 1. : 0., INSERT_VALUES));
1423: }
1424: PetscCall(MatAssemblyBegin(intMat, MAT_FINAL_ASSEMBLY));
1425: PetscCall(MatAssemblyEnd(intMat, MAT_FINAL_ASSEMBLY));
1426: *iNodes = intNodes;
1427: *iMat = intMat;
1428: *nodeIndices = ni;
1429: PetscFunctionReturn(PETSC_SUCCESS);
1430: }
1432: /* once the nodeIndices have been created for the interior of the reference cell, and for all of the boundary cells,
1433: * push forward the boundary dofs and concatenate them into the full node indices for the dual space */
1434: static PetscErrorCode PetscDualSpaceLagrangeCreateAllNodeIdx(PetscDualSpace sp)
1435: {
1436: DM dm;
1437: PetscInt dim, nDofs;
1438: PetscSection section;
1439: PetscInt pStart, pEnd, p;
1440: PetscInt formDegree, Nk;
1441: PetscInt nodeIdxDim, spintdim;
1442: PetscDualSpace_Lag *lag;
1443: PetscLagNodeIndices ni, verti;
1445: PetscFunctionBegin;
1446: lag = (PetscDualSpace_Lag *)sp->data;
1447: verti = lag->vertIndices;
1448: PetscCall(PetscDualSpaceGetDM(sp, &dm));
1449: PetscCall(DMGetDimension(dm, &dim));
1450: PetscCall(PetscDualSpaceGetFormDegree(sp, &formDegree));
1451: PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(formDegree), &Nk));
1452: PetscCall(PetscDualSpaceGetSection(sp, §ion));
1453: PetscCall(PetscSectionGetStorageSize(section, &nDofs));
1454: PetscCall(PetscNew(&ni));
1455: ni->nodeIdxDim = nodeIdxDim = verti->nodeIdxDim;
1456: ni->nodeVecDim = Nk;
1457: ni->nNodes = nDofs;
1458: ni->refct = 1;
1459: PetscCall(PetscMalloc1(nodeIdxDim * nDofs, &ni->nodeIdx));
1460: PetscCall(PetscMalloc1(Nk * nDofs, &ni->nodeVec));
1461: PetscCall(DMPlexGetChart(dm, &pStart, &pEnd));
1462: PetscCall(PetscSectionGetDof(section, 0, &spintdim));
1463: if (spintdim) {
1464: PetscCall(PetscArraycpy(ni->nodeIdx, lag->intNodeIndices->nodeIdx, spintdim * nodeIdxDim));
1465: PetscCall(PetscArraycpy(ni->nodeVec, lag->intNodeIndices->nodeVec, spintdim * Nk));
1466: }
1467: for (p = pStart + 1; p < pEnd; p++) {
1468: PetscDualSpace psp = sp->pointSpaces[p];
1469: PetscDualSpace_Lag *plag;
1470: PetscInt dof, off;
1472: PetscCall(PetscSectionGetDof(section, p, &dof));
1473: if (!dof) continue;
1474: plag = (PetscDualSpace_Lag *)psp->data;
1475: PetscCall(PetscSectionGetOffset(section, p, &off));
1476: PetscCall(PetscLagNodeIndicesPushForward(dm, verti, p, plag->vertIndices, plag->intNodeIndices, 0, formDegree, &ni->nodeIdx[off * nodeIdxDim], &ni->nodeVec[off * Nk]));
1477: }
1478: lag->allNodeIndices = ni;
1479: PetscFunctionReturn(PETSC_SUCCESS);
1480: }
1482: /* once the (quadrature, Matrix) forms of the dofs have been created for the interior of the
1483: * reference cell and for the boundary cells, jk
1484: * push forward the boundary data and concatenate them into the full (quadrature, matrix) data
1485: * for the dual space */
1486: static PetscErrorCode PetscDualSpaceCreateAllDataFromInteriorData(PetscDualSpace sp)
1487: {
1488: DM dm;
1489: PetscSection section;
1490: PetscInt pStart, pEnd, p, k, Nk, dim, Nc;
1491: PetscInt nNodes;
1492: PetscInt countNodes;
1493: Mat allMat;
1494: PetscQuadrature allNodes;
1495: PetscInt nDofs;
1496: PetscInt maxNzforms, j;
1497: PetscScalar *work;
1498: PetscReal *L, *J, *Jinv, *v0, *pv0;
1499: PetscInt *iwork;
1500: PetscReal *nodes;
1502: PetscFunctionBegin;
1503: PetscCall(PetscDualSpaceGetDM(sp, &dm));
1504: PetscCall(DMGetDimension(dm, &dim));
1505: PetscCall(PetscDualSpaceGetSection(sp, §ion));
1506: PetscCall(PetscSectionGetStorageSize(section, &nDofs));
1507: PetscCall(DMPlexGetChart(dm, &pStart, &pEnd));
1508: PetscCall(PetscDualSpaceGetFormDegree(sp, &k));
1509: PetscCall(PetscDualSpaceGetNumComponents(sp, &Nc));
1510: PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(k), &Nk));
1511: for (p = pStart, nNodes = 0, maxNzforms = 0; p < pEnd; p++) {
1512: PetscDualSpace psp;
1513: DM pdm;
1514: PetscInt pdim, pNk;
1515: PetscQuadrature intNodes;
1516: Mat intMat;
1518: PetscCall(PetscDualSpaceGetPointSubspace(sp, p, &psp));
1519: if (!psp) continue;
1520: PetscCall(PetscDualSpaceGetDM(psp, &pdm));
1521: PetscCall(DMGetDimension(pdm, &pdim));
1522: if (pdim < PetscAbsInt(k)) continue;
1523: PetscCall(PetscDTBinomialInt(pdim, PetscAbsInt(k), &pNk));
1524: PetscCall(PetscDualSpaceGetInteriorData(psp, &intNodes, &intMat));
1525: if (intNodes) {
1526: PetscInt nNodesp;
1528: PetscCall(PetscQuadratureGetData(intNodes, NULL, NULL, &nNodesp, NULL, NULL));
1529: nNodes += nNodesp;
1530: }
1531: if (intMat) {
1532: PetscInt maxNzsp;
1533: PetscInt maxNzformsp;
1535: PetscCall(MatSeqAIJGetMaxRowNonzeros(intMat, &maxNzsp));
1536: PetscCheck(maxNzsp % pNk == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "interior matrix is not laid out as blocks of k-forms");
1537: maxNzformsp = maxNzsp / pNk;
1538: maxNzforms = PetscMax(maxNzforms, maxNzformsp);
1539: }
1540: }
1541: PetscCall(MatCreateSeqAIJ(PETSC_COMM_SELF, nDofs, nNodes * Nc, maxNzforms * Nk, NULL, &allMat));
1542: PetscCall(PetscObjectSetOptionsPrefix((PetscObject)allMat, "ds_"));
1543: PetscCall(MatSetOption(allMat, MAT_IGNORE_ZERO_ENTRIES, PETSC_FALSE));
1544: PetscCall(PetscMalloc7(dim, &v0, dim, &pv0, dim * dim, &J, dim * dim, &Jinv, Nk * Nk, &L, maxNzforms * Nk, &work, maxNzforms * Nk, &iwork));
1545: for (j = 0; j < dim; j++) pv0[j] = -1.;
1546: PetscCall(PetscMalloc1(dim * nNodes, &nodes));
1547: for (p = pStart, countNodes = 0; p < pEnd; p++) {
1548: PetscDualSpace psp;
1549: PetscQuadrature intNodes;
1550: DM pdm;
1551: PetscInt pdim, pNk;
1552: PetscInt countNodesIn = countNodes;
1553: PetscReal detJ;
1554: Mat intMat;
1556: PetscCall(PetscDualSpaceGetPointSubspace(sp, p, &psp));
1557: if (!psp) continue;
1558: PetscCall(PetscDualSpaceGetDM(psp, &pdm));
1559: PetscCall(DMGetDimension(pdm, &pdim));
1560: if (pdim < PetscAbsInt(k)) continue;
1561: PetscCall(PetscDualSpaceGetInteriorData(psp, &intNodes, &intMat));
1562: if (intNodes == NULL && intMat == NULL) continue;
1563: PetscCall(PetscDTBinomialInt(pdim, PetscAbsInt(k), &pNk));
1564: if (p) {
1565: PetscCall(DMPlexComputeCellGeometryAffineFEM(dm, p, v0, J, Jinv, &detJ));
1566: } else { /* identity */
1567: PetscInt i, j;
1569: for (i = 0; i < dim; i++)
1570: for (j = 0; j < dim; j++) J[i * dim + j] = Jinv[i * dim + j] = 0.;
1571: for (i = 0; i < dim; i++) J[i * dim + i] = Jinv[i * dim + i] = 1.;
1572: for (i = 0; i < dim; i++) v0[i] = -1.;
1573: }
1574: if (pdim != dim) { /* compactify Jacobian */
1575: PetscInt i, j;
1577: for (i = 0; i < dim; i++)
1578: for (j = 0; j < pdim; j++) J[i * pdim + j] = J[i * dim + j];
1579: }
1580: PetscCall(PetscDTAltVPullbackMatrix(pdim, dim, J, k, L));
1581: if (intNodes) { /* push forward quadrature locations by the affine transformation */
1582: PetscInt nNodesp;
1583: const PetscReal *nodesp;
1584: PetscInt j;
1586: PetscCall(PetscQuadratureGetData(intNodes, NULL, NULL, &nNodesp, &nodesp, NULL));
1587: for (j = 0; j < nNodesp; j++, countNodes++) {
1588: PetscInt d, e;
1590: for (d = 0; d < dim; d++) {
1591: nodes[countNodes * dim + d] = v0[d];
1592: for (e = 0; e < pdim; e++) nodes[countNodes * dim + d] += J[d * pdim + e] * (nodesp[j * pdim + e] - pv0[e]);
1593: }
1594: }
1595: }
1596: if (intMat) {
1597: PetscInt nrows;
1598: PetscInt off;
1600: PetscCall(PetscSectionGetDof(section, p, &nrows));
1601: PetscCall(PetscSectionGetOffset(section, p, &off));
1602: for (j = 0; j < nrows; j++) {
1603: PetscInt ncols;
1604: const PetscInt *cols;
1605: const PetscScalar *vals;
1606: PetscInt l, d, e;
1607: PetscInt row = j + off;
1609: PetscCall(MatGetRow(intMat, j, &ncols, &cols, &vals));
1610: PetscCheck(ncols % pNk == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "interior matrix is not laid out as blocks of k-forms");
1611: for (l = 0; l < ncols / pNk; l++) {
1612: PetscInt blockcol;
1614: 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");
1615: blockcol = cols[l * pNk] / pNk;
1616: for (d = 0; d < Nk; d++) iwork[l * Nk + d] = (blockcol + countNodesIn) * Nk + d;
1617: for (d = 0; d < Nk; d++) work[l * Nk + d] = 0.;
1618: for (d = 0; d < Nk; d++) {
1619: for (e = 0; e < pNk; e++) {
1620: /* "push forward" dof by pulling back a k-form to be evaluated on the point: multiply on the right by L */
1621: work[l * Nk + d] += vals[l * pNk + e] * L[e * Nk + d];
1622: }
1623: }
1624: }
1625: PetscCall(MatSetValues(allMat, 1, &row, (ncols / pNk) * Nk, iwork, work, INSERT_VALUES));
1626: PetscCall(MatRestoreRow(intMat, j, &ncols, &cols, &vals));
1627: }
1628: }
1629: }
1630: PetscCall(MatAssemblyBegin(allMat, MAT_FINAL_ASSEMBLY));
1631: PetscCall(MatAssemblyEnd(allMat, MAT_FINAL_ASSEMBLY));
1632: PetscCall(PetscQuadratureCreate(PETSC_COMM_SELF, &allNodes));
1633: PetscCall(PetscQuadratureSetData(allNodes, dim, 0, nNodes, nodes, NULL));
1634: PetscCall(PetscFree7(v0, pv0, J, Jinv, L, work, iwork));
1635: PetscCall(MatDestroy(&sp->allMat));
1636: sp->allMat = allMat;
1637: PetscCall(PetscQuadratureDestroy(&sp->allNodes));
1638: sp->allNodes = allNodes;
1639: PetscFunctionReturn(PETSC_SUCCESS);
1640: }
1642: static PetscErrorCode PetscDualSpaceComputeFunctionalsFromAllData_Moments(PetscDualSpace sp)
1643: {
1644: Mat allMat;
1645: PetscInt momentOrder, i;
1646: PetscBool tensor = PETSC_FALSE;
1647: const PetscReal *weights;
1648: PetscScalar *array;
1649: PetscInt nDofs;
1650: PetscInt dim, Nc;
1651: DM dm;
1652: PetscQuadrature allNodes;
1653: PetscInt nNodes;
1655: PetscFunctionBegin;
1656: PetscCall(PetscDualSpaceGetDM(sp, &dm));
1657: PetscCall(DMGetDimension(dm, &dim));
1658: PetscCall(PetscDualSpaceGetNumComponents(sp, &Nc));
1659: PetscCall(PetscDualSpaceGetAllData(sp, &allNodes, &allMat));
1660: PetscCall(MatGetSize(allMat, &nDofs, NULL));
1661: PetscCheck(nDofs == 1, PETSC_COMM_SELF, PETSC_ERR_SUP, "We do not yet support moments beyond P0, nDofs == %" PetscInt_FMT, nDofs);
1662: PetscCall(PetscMalloc1(nDofs, &sp->functional));
1663: PetscCall(PetscDualSpaceLagrangeGetMomentOrder(sp, &momentOrder));
1664: PetscCall(PetscDualSpaceLagrangeGetTensor(sp, &tensor));
1665: if (!tensor) PetscCall(PetscDTStroudConicalQuadrature(dim, Nc, PetscMax(momentOrder + 1, 1), -1.0, 1.0, &sp->functional[0]));
1666: else PetscCall(PetscDTGaussTensorQuadrature(dim, Nc, PetscMax(momentOrder + 1, 1), -1.0, 1.0, &sp->functional[0]));
1667: /* Need to replace allNodes and allMat */
1668: PetscCall(PetscObjectReference((PetscObject)sp->functional[0]));
1669: PetscCall(PetscQuadratureDestroy(&sp->allNodes));
1670: sp->allNodes = sp->functional[0];
1671: PetscCall(PetscQuadratureGetData(sp->allNodes, NULL, NULL, &nNodes, NULL, &weights));
1672: PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, nDofs, nNodes * Nc, NULL, &allMat));
1673: PetscCall(PetscObjectSetOptionsPrefix((PetscObject)allMat, "ds_"));
1674: PetscCall(MatDenseGetArrayWrite(allMat, &array));
1675: for (i = 0; i < nNodes * Nc; ++i) array[i] = weights[i];
1676: PetscCall(MatDenseRestoreArrayWrite(allMat, &array));
1677: PetscCall(MatAssemblyBegin(allMat, MAT_FINAL_ASSEMBLY));
1678: PetscCall(MatAssemblyEnd(allMat, MAT_FINAL_ASSEMBLY));
1679: PetscCall(MatDestroy(&sp->allMat));
1680: sp->allMat = allMat;
1681: PetscFunctionReturn(PETSC_SUCCESS);
1682: }
1684: /* rather than trying to get all data from the functionals, we create
1685: * the functionals from rows of the quadrature -> dof matrix.
1686: *
1687: * Ideally most of the uses of PetscDualSpace in PetscFE will switch
1688: * to using intMat and allMat, so that the individual functionals
1689: * don't need to be constructed at all */
1690: PETSC_INTERN PetscErrorCode PetscDualSpaceComputeFunctionalsFromAllData(PetscDualSpace sp)
1691: {
1692: PetscQuadrature allNodes;
1693: Mat allMat;
1694: PetscInt nDofs;
1695: PetscInt dim, Nc, f;
1696: DM dm;
1697: PetscInt nNodes, spdim;
1698: const PetscReal *nodes = NULL;
1699: PetscSection section;
1701: PetscFunctionBegin;
1702: PetscCall(PetscDualSpaceGetDM(sp, &dm));
1703: PetscCall(DMGetDimension(dm, &dim));
1704: PetscCall(PetscDualSpaceGetNumComponents(sp, &Nc));
1705: PetscCall(PetscDualSpaceGetAllData(sp, &allNodes, &allMat));
1706: nNodes = 0;
1707: if (allNodes) PetscCall(PetscQuadratureGetData(allNodes, NULL, NULL, &nNodes, &nodes, NULL));
1708: PetscCall(MatGetSize(allMat, &nDofs, NULL));
1709: PetscCall(PetscDualSpaceGetSection(sp, §ion));
1710: PetscCall(PetscSectionGetStorageSize(section, &spdim));
1711: PetscCheck(spdim == nDofs, PETSC_COMM_SELF, PETSC_ERR_PLIB, "incompatible all matrix size");
1712: PetscCall(PetscMalloc1(nDofs, &sp->functional));
1713: for (f = 0; f < nDofs; f++) {
1714: PetscInt ncols, c;
1715: const PetscInt *cols;
1716: const PetscScalar *vals;
1717: PetscReal *nodesf;
1718: PetscReal *weightsf;
1719: PetscInt nNodesf;
1720: PetscInt countNodes;
1722: PetscCall(MatGetRow(allMat, f, &ncols, &cols, &vals));
1723: for (c = 1, nNodesf = 1; c < ncols; c++) {
1724: if ((cols[c] / Nc) != (cols[c - 1] / Nc)) nNodesf++;
1725: }
1726: PetscCall(PetscMalloc1(dim * nNodesf, &nodesf));
1727: PetscCall(PetscMalloc1(Nc * nNodesf, &weightsf));
1728: for (c = 0, countNodes = 0; c < ncols; c++) {
1729: if (!c || ((cols[c] / Nc) != (cols[c - 1] / Nc))) {
1730: PetscInt d;
1732: for (d = 0; d < Nc; d++) weightsf[countNodes * Nc + d] = 0.;
1733: for (d = 0; d < dim; d++) nodesf[countNodes * dim + d] = nodes[(cols[c] / Nc) * dim + d];
1734: countNodes++;
1735: }
1736: weightsf[(countNodes - 1) * Nc + (cols[c] % Nc)] = PetscRealPart(vals[c]);
1737: }
1738: PetscCall(PetscQuadratureCreate(PETSC_COMM_SELF, &sp->functional[f]));
1739: PetscCall(PetscQuadratureSetData(sp->functional[f], dim, Nc, nNodesf, nodesf, weightsf));
1740: PetscCall(MatRestoreRow(allMat, f, &ncols, &cols, &vals));
1741: }
1742: PetscFunctionReturn(PETSC_SUCCESS);
1743: }
1745: /* check if a cell is a tensor product of the segment with a facet,
1746: * specifically checking if f and f2 can be the "endpoints" (like the triangles
1747: * at either end of a wedge) */
1748: static PetscErrorCode DMPlexPointIsTensor_Internal_Given(DM dm, PetscInt p, PetscInt f, PetscInt f2, PetscBool *isTensor)
1749: {
1750: PetscInt coneSize, c;
1751: const PetscInt *cone;
1752: const PetscInt *fCone;
1753: const PetscInt *f2Cone;
1754: PetscInt fs[2];
1755: PetscInt meetSize, nmeet;
1756: const PetscInt *meet;
1758: PetscFunctionBegin;
1759: fs[0] = f;
1760: fs[1] = f2;
1761: PetscCall(DMPlexGetMeet(dm, 2, fs, &meetSize, &meet));
1762: nmeet = meetSize;
1763: PetscCall(DMPlexRestoreMeet(dm, 2, fs, &meetSize, &meet));
1764: /* two points that have a non-empty meet cannot be at opposite ends of a cell */
1765: if (nmeet) {
1766: *isTensor = PETSC_FALSE;
1767: PetscFunctionReturn(PETSC_SUCCESS);
1768: }
1769: PetscCall(DMPlexGetConeSize(dm, p, &coneSize));
1770: PetscCall(DMPlexGetCone(dm, p, &cone));
1771: PetscCall(DMPlexGetCone(dm, f, &fCone));
1772: PetscCall(DMPlexGetCone(dm, f2, &f2Cone));
1773: for (c = 0; c < coneSize; c++) {
1774: PetscInt e, ef;
1775: PetscInt d = -1, d2 = -1;
1776: PetscInt dcount, d2count;
1777: PetscInt t = cone[c];
1778: PetscInt tConeSize;
1779: PetscBool tIsTensor;
1780: const PetscInt *tCone;
1782: if (t == f || t == f2) continue;
1783: /* for every other facet in the cone, check that is has
1784: * one ridge in common with each end */
1785: PetscCall(DMPlexGetConeSize(dm, t, &tConeSize));
1786: PetscCall(DMPlexGetCone(dm, t, &tCone));
1788: dcount = 0;
1789: d2count = 0;
1790: for (e = 0; e < tConeSize; e++) {
1791: PetscInt q = tCone[e];
1792: for (ef = 0; ef < coneSize - 2; ef++) {
1793: if (fCone[ef] == q) {
1794: if (dcount) {
1795: *isTensor = PETSC_FALSE;
1796: PetscFunctionReturn(PETSC_SUCCESS);
1797: }
1798: d = q;
1799: dcount++;
1800: } else if (f2Cone[ef] == q) {
1801: if (d2count) {
1802: *isTensor = PETSC_FALSE;
1803: PetscFunctionReturn(PETSC_SUCCESS);
1804: }
1805: d2 = q;
1806: d2count++;
1807: }
1808: }
1809: }
1810: /* if the whole cell is a tensor with the segment, then this
1811: * facet should be a tensor with the segment */
1812: PetscCall(DMPlexPointIsTensor_Internal_Given(dm, t, d, d2, &tIsTensor));
1813: if (!tIsTensor) {
1814: *isTensor = PETSC_FALSE;
1815: PetscFunctionReturn(PETSC_SUCCESS);
1816: }
1817: }
1818: *isTensor = PETSC_TRUE;
1819: PetscFunctionReturn(PETSC_SUCCESS);
1820: }
1822: /* determine if a cell is a tensor with a segment by looping over pairs of facets to find a pair
1823: * that could be the opposite ends */
1824: static PetscErrorCode DMPlexPointIsTensor_Internal(DM dm, PetscInt p, PetscBool *isTensor, PetscInt *endA, PetscInt *endB)
1825: {
1826: PetscInt coneSize, c, c2;
1827: const PetscInt *cone;
1829: PetscFunctionBegin;
1830: PetscCall(DMPlexGetConeSize(dm, p, &coneSize));
1831: if (!coneSize) {
1832: if (isTensor) *isTensor = PETSC_FALSE;
1833: if (endA) *endA = -1;
1834: if (endB) *endB = -1;
1835: }
1836: PetscCall(DMPlexGetCone(dm, p, &cone));
1837: for (c = 0; c < coneSize; c++) {
1838: PetscInt f = cone[c];
1839: PetscInt fConeSize;
1841: PetscCall(DMPlexGetConeSize(dm, f, &fConeSize));
1842: if (fConeSize != coneSize - 2) continue;
1844: for (c2 = c + 1; c2 < coneSize; c2++) {
1845: PetscInt f2 = cone[c2];
1846: PetscBool isTensorff2;
1847: PetscInt f2ConeSize;
1849: PetscCall(DMPlexGetConeSize(dm, f2, &f2ConeSize));
1850: if (f2ConeSize != coneSize - 2) continue;
1852: PetscCall(DMPlexPointIsTensor_Internal_Given(dm, p, f, f2, &isTensorff2));
1853: if (isTensorff2) {
1854: if (isTensor) *isTensor = PETSC_TRUE;
1855: if (endA) *endA = f;
1856: if (endB) *endB = f2;
1857: PetscFunctionReturn(PETSC_SUCCESS);
1858: }
1859: }
1860: }
1861: if (isTensor) *isTensor = PETSC_FALSE;
1862: if (endA) *endA = -1;
1863: if (endB) *endB = -1;
1864: PetscFunctionReturn(PETSC_SUCCESS);
1865: }
1867: /* determine if a cell is a tensor with a segment by looping over pairs of facets to find a pair
1868: * that could be the opposite ends */
1869: static PetscErrorCode DMPlexPointIsTensor(DM dm, PetscInt p, PetscBool *isTensor, PetscInt *endA, PetscInt *endB)
1870: {
1871: DMPlexInterpolatedFlag interpolated;
1873: PetscFunctionBegin;
1874: PetscCall(DMPlexIsInterpolated(dm, &interpolated));
1875: PetscCheck(interpolated == DMPLEX_INTERPOLATED_FULL, PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONGSTATE, "Only for interpolated DMPlex's");
1876: PetscCall(DMPlexPointIsTensor_Internal(dm, p, isTensor, endA, endB));
1877: PetscFunctionReturn(PETSC_SUCCESS);
1878: }
1880: /* Let k = formDegree and k' = -sign(k) * dim + k. Transform a symmetric frame for k-forms on the biunit simplex into
1881: * a symmetric frame for k'-forms on the biunit simplex.
1882: *
1883: * A frame is "symmetric" if the pullback of every symmetry of the biunit simplex is a permutation of the frame.
1884: *
1885: * forms in the symmetric frame are used as dofs in the untrimmed simplex spaces. This way, symmetries of the
1886: * reference cell result in permutations of dofs grouped by node.
1887: *
1888: * Use T to transform dof matrices for k'-forms into dof matrices for k-forms as a block diagonal transformation on
1889: * the right.
1890: */
1891: static PetscErrorCode BiunitSimplexSymmetricFormTransformation(PetscInt dim, PetscInt formDegree, PetscReal T[])
1892: {
1893: PetscInt k = formDegree;
1894: PetscInt kd = k < 0 ? dim + k : k - dim;
1895: PetscInt Nk;
1896: PetscReal *biToEq, *eqToBi, *biToEqStar, *eqToBiStar;
1897: PetscInt fact;
1899: PetscFunctionBegin;
1900: PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(k), &Nk));
1901: PetscCall(PetscCalloc4(dim * dim, &biToEq, dim * dim, &eqToBi, Nk * Nk, &biToEqStar, Nk * Nk, &eqToBiStar));
1902: /* fill in biToEq: Jacobian of the transformation from the biunit simplex to the equilateral simplex */
1903: fact = 0;
1904: for (PetscInt i = 0; i < dim; i++) {
1905: biToEq[i * dim + i] = PetscSqrtReal(((PetscReal)i + 2.) / (2. * ((PetscReal)i + 1.)));
1906: fact += 4 * (i + 1);
1907: for (PetscInt j = i + 1; j < dim; j++) biToEq[i * dim + j] = PetscSqrtReal(1. / (PetscReal)fact);
1908: }
1909: /* fill in eqToBi: Jacobian of the transformation from the equilateral simplex to the biunit simplex */
1910: fact = 0;
1911: for (PetscInt j = 0; j < dim; j++) {
1912: eqToBi[j * dim + j] = PetscSqrtReal(2. * ((PetscReal)j + 1.) / ((PetscReal)j + 2));
1913: fact += j + 1;
1914: for (PetscInt i = 0; i < j; i++) eqToBi[i * dim + j] = -PetscSqrtReal(1. / (PetscReal)fact);
1915: }
1916: PetscCall(PetscDTAltVPullbackMatrix(dim, dim, biToEq, kd, biToEqStar));
1917: PetscCall(PetscDTAltVPullbackMatrix(dim, dim, eqToBi, k, eqToBiStar));
1918: /* product of pullbacks simulates the following steps
1919: *
1920: * 1. start with frame W = [w_1, w_2, ..., w_m] of k forms that is symmetric on the biunit simplex:
1921: if J is the Jacobian of a symmetry of the biunit simplex, then J_k* W = [J_k*w_1, ..., J_k*w_m]
1922: is a permutation of W.
1923: Even though a k' form --- a (dim - k) form represented by its Hodge star --- has the same geometric
1924: content as a k form, W is not a symmetric frame of k' forms on the biunit simplex. That's because,
1925: for general Jacobian J, J_k* != J_k'*.
1926: * 2. pullback W to the equilateral triangle using the k pullback, W_eq = eqToBi_k* W. All symmetries of the
1927: equilateral simplex have orthonormal Jacobians. For an orthonormal Jacobian O, J_k* = J_k'*, so W_eq is
1928: also a symmetric frame for k' forms on the equilateral simplex.
1929: 3. pullback W_eq back to the biunit simplex using the k' pulback, V = biToEq_k'* W_eq = biToEq_k'* eqToBi_k* W.
1930: V is a symmetric frame for k' forms on the biunit simplex.
1931: */
1932: for (PetscInt i = 0; i < Nk; i++) {
1933: for (PetscInt j = 0; j < Nk; j++) {
1934: PetscReal val = 0.;
1935: for (PetscInt k = 0; k < Nk; k++) val += biToEqStar[i * Nk + k] * eqToBiStar[k * Nk + j];
1936: T[i * Nk + j] = val;
1937: }
1938: }
1939: PetscCall(PetscFree4(biToEq, eqToBi, biToEqStar, eqToBiStar));
1940: PetscFunctionReturn(PETSC_SUCCESS);
1941: }
1943: /* permute a quadrature -> dof matrix so that its rows are in revlex order by nodeIdx */
1944: static PetscErrorCode MatPermuteByNodeIdx(Mat A, PetscLagNodeIndices ni, Mat *Aperm)
1945: {
1946: PetscInt m, n, i, j;
1947: PetscInt nodeIdxDim = ni->nodeIdxDim;
1948: PetscInt nodeVecDim = ni->nodeVecDim;
1949: PetscInt *perm;
1950: IS permIS;
1951: IS id;
1952: PetscInt *nIdxPerm;
1953: PetscReal *nVecPerm;
1955: PetscFunctionBegin;
1956: PetscCall(PetscLagNodeIndicesGetPermutation(ni, &perm));
1957: PetscCall(MatGetSize(A, &m, &n));
1958: PetscCall(PetscMalloc1(nodeIdxDim * m, &nIdxPerm));
1959: PetscCall(PetscMalloc1(nodeVecDim * m, &nVecPerm));
1960: for (i = 0; i < m; i++)
1961: for (j = 0; j < nodeIdxDim; j++) nIdxPerm[i * nodeIdxDim + j] = ni->nodeIdx[perm[i] * nodeIdxDim + j];
1962: for (i = 0; i < m; i++)
1963: for (j = 0; j < nodeVecDim; j++) nVecPerm[i * nodeVecDim + j] = ni->nodeVec[perm[i] * nodeVecDim + j];
1964: PetscCall(ISCreateGeneral(PETSC_COMM_SELF, m, perm, PETSC_USE_POINTER, &permIS));
1965: PetscCall(ISSetPermutation(permIS));
1966: PetscCall(ISCreateStride(PETSC_COMM_SELF, n, 0, 1, &id));
1967: PetscCall(ISSetPermutation(id));
1968: PetscCall(MatPermute(A, permIS, id, Aperm));
1969: PetscCall(ISDestroy(&permIS));
1970: PetscCall(ISDestroy(&id));
1971: for (i = 0; i < m; i++) perm[i] = i;
1972: PetscCall(PetscFree(ni->nodeIdx));
1973: PetscCall(PetscFree(ni->nodeVec));
1974: ni->nodeIdx = nIdxPerm;
1975: ni->nodeVec = nVecPerm;
1976: PetscFunctionReturn(PETSC_SUCCESS);
1977: }
1979: static PetscErrorCode PetscDualSpaceSetUp_Lagrange(PetscDualSpace sp)
1980: {
1981: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
1982: DM dm = sp->dm;
1983: DM dmint = NULL;
1984: PetscInt order;
1985: PetscInt Nc;
1986: MPI_Comm comm;
1987: PetscBool continuous;
1988: PetscSection section;
1989: PetscInt depth, dim, pStart, pEnd, cStart, cEnd, p, *pStratStart, *pStratEnd, d;
1990: PetscInt formDegree, Nk, Ncopies;
1991: PetscInt tensorf = -1, tensorf2 = -1;
1992: PetscBool tensorCell, tensorSpace;
1993: PetscBool uniform, trimmed;
1994: Petsc1DNodeFamily nodeFamily;
1995: PetscInt numNodeSkip;
1996: DMPlexInterpolatedFlag interpolated;
1997: PetscBool isbdm;
1999: PetscFunctionBegin;
2000: /* step 1: sanitize input */
2001: PetscCall(PetscObjectGetComm((PetscObject)sp, &comm));
2002: PetscCall(DMGetDimension(dm, &dim));
2003: PetscCall(PetscObjectTypeCompare((PetscObject)sp, PETSCDUALSPACEBDM, &isbdm));
2004: if (isbdm) {
2005: sp->k = -(dim - 1); /* form degree of H-div */
2006: PetscCall(PetscObjectChangeTypeName((PetscObject)sp, PETSCDUALSPACELAGRANGE));
2007: }
2008: PetscCall(PetscDualSpaceGetFormDegree(sp, &formDegree));
2009: PetscCheck(PetscAbsInt(formDegree) <= dim, comm, PETSC_ERR_ARG_OUTOFRANGE, "Form degree must be bounded by dimension");
2010: PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(formDegree), &Nk));
2011: if (sp->Nc <= 0 && lag->numCopies > 0) sp->Nc = Nk * lag->numCopies;
2012: Nc = sp->Nc;
2013: PetscCheck(Nc % Nk == 0, comm, PETSC_ERR_ARG_INCOMP, "Number of components is not a multiple of form degree size");
2014: if (lag->numCopies <= 0) lag->numCopies = Nc / Nk;
2015: Ncopies = lag->numCopies;
2016: PetscCheck(Nc / Nk == Ncopies, comm, PETSC_ERR_ARG_INCOMP, "Number of copies * (dim choose k) != Nc");
2017: if (!dim) sp->order = 0;
2018: order = sp->order;
2019: uniform = sp->uniform;
2020: PetscCheck(uniform, PETSC_COMM_SELF, PETSC_ERR_SUP, "Variable order not supported yet");
2021: if (lag->trimmed && !formDegree) lag->trimmed = PETSC_FALSE; /* trimmed spaces are the same as full spaces for 0-forms */
2022: if (lag->nodeType == PETSCDTNODES_DEFAULT) {
2023: lag->nodeType = PETSCDTNODES_GAUSSJACOBI;
2024: lag->nodeExponent = 0.;
2025: /* trimmed spaces don't include corner vertices, so don't use end nodes by default */
2026: lag->endNodes = lag->trimmed ? PETSC_FALSE : PETSC_TRUE;
2027: }
2028: /* If a trimmed space and the user did choose nodes with endpoints, skip them by default */
2029: if (lag->numNodeSkip < 0) lag->numNodeSkip = (lag->trimmed && lag->endNodes) ? 1 : 0;
2030: numNodeSkip = lag->numNodeSkip;
2031: PetscCheck(!lag->trimmed || order, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Cannot have zeroth order trimmed elements");
2032: if (lag->trimmed && PetscAbsInt(formDegree) == dim) { /* convert trimmed n-forms to untrimmed of one polynomial order less */
2033: sp->order--;
2034: order--;
2035: lag->trimmed = PETSC_FALSE;
2036: }
2037: trimmed = lag->trimmed;
2038: if (!order || PetscAbsInt(formDegree) == dim) lag->continuous = PETSC_FALSE;
2039: continuous = lag->continuous;
2040: PetscCall(DMPlexGetDepth(dm, &depth));
2041: PetscCall(DMPlexGetChart(dm, &pStart, &pEnd));
2042: PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
2043: PetscCheck(pStart == 0 && cStart == 0, PetscObjectComm((PetscObject)sp), PETSC_ERR_ARG_WRONGSTATE, "Expect DM with chart starting at zero and cells first");
2044: PetscCheck(cEnd == 1, PetscObjectComm((PetscObject)sp), PETSC_ERR_ARG_WRONGSTATE, "Use PETSCDUALSPACEREFINED for multi-cell reference meshes");
2045: PetscCall(DMPlexIsInterpolated(dm, &interpolated));
2046: if (interpolated != DMPLEX_INTERPOLATED_FULL) {
2047: PetscCall(DMPlexInterpolate(dm, &dmint));
2048: } else {
2049: PetscCall(PetscObjectReference((PetscObject)dm));
2050: dmint = dm;
2051: }
2052: tensorCell = PETSC_FALSE;
2053: if (dim > 1) PetscCall(DMPlexPointIsTensor(dmint, 0, &tensorCell, &tensorf, &tensorf2));
2054: lag->tensorCell = tensorCell;
2055: if (dim < 2 || !lag->tensorCell) lag->tensorSpace = PETSC_FALSE;
2056: tensorSpace = lag->tensorSpace;
2057: if (!lag->nodeFamily) PetscCall(Petsc1DNodeFamilyCreate(lag->nodeType, lag->nodeExponent, lag->endNodes, &lag->nodeFamily));
2058: nodeFamily = lag->nodeFamily;
2059: 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");
2061: if (Ncopies > 1) {
2062: PetscDualSpace scalarsp;
2064: PetscCall(PetscDualSpaceDuplicate(sp, &scalarsp));
2065: /* Setting the number of components to Nk is a space with 1 copy of each k-form */
2066: sp->setupcalled = PETSC_FALSE;
2067: PetscCall(PetscDualSpaceSetNumComponents(scalarsp, Nk));
2068: PetscCall(PetscDualSpaceSetUp(scalarsp));
2069: PetscCall(PetscDualSpaceSetType(sp, PETSCDUALSPACESUM));
2070: PetscCall(PetscDualSpaceSumSetNumSubspaces(sp, Ncopies));
2071: PetscCall(PetscDualSpaceSumSetConcatenate(sp, PETSC_TRUE));
2072: PetscCall(PetscDualSpaceSumSetInterleave(sp, PETSC_TRUE, PETSC_FALSE));
2073: for (PetscInt i = 0; i < Ncopies; i++) PetscCall(PetscDualSpaceSumSetSubspace(sp, i, scalarsp));
2074: PetscCall(PetscDualSpaceSetUp(sp));
2075: PetscCall(PetscDualSpaceDestroy(&scalarsp));
2076: PetscCall(DMDestroy(&dmint));
2077: PetscFunctionReturn(PETSC_SUCCESS);
2078: }
2080: /* step 2: construct the boundary spaces */
2081: PetscCall(PetscMalloc2(depth + 1, &pStratStart, depth + 1, &pStratEnd));
2082: PetscCall(PetscCalloc1(pEnd, &sp->pointSpaces));
2083: for (d = 0; d <= depth; ++d) PetscCall(DMPlexGetDepthStratum(dm, d, &pStratStart[d], &pStratEnd[d]));
2084: PetscCall(PetscDualSpaceSectionCreate_Internal(sp, §ion));
2085: sp->pointSection = section;
2086: if (continuous && !lag->interiorOnly) {
2087: PetscInt h;
2089: for (p = pStratStart[depth - 1]; p < pStratEnd[depth - 1]; p++) { /* calculate the facet dual spaces */
2090: PetscReal v0[3];
2091: DMPolytopeType ptype;
2092: PetscReal J[9], detJ;
2093: PetscInt q;
2095: PetscCall(DMPlexComputeCellGeometryAffineFEM(dm, p, v0, J, NULL, &detJ));
2096: PetscCall(DMPlexGetCellType(dm, p, &ptype));
2098: /* compare to previous facets: if computed, reference that dualspace */
2099: for (q = pStratStart[depth - 1]; q < p; q++) {
2100: DMPolytopeType qtype;
2102: PetscCall(DMPlexGetCellType(dm, q, &qtype));
2103: if (qtype == ptype) break;
2104: }
2105: if (q < p) { /* this facet has the same dual space as that one */
2106: PetscCall(PetscObjectReference((PetscObject)sp->pointSpaces[q]));
2107: sp->pointSpaces[p] = sp->pointSpaces[q];
2108: continue;
2109: }
2110: /* if not, recursively compute this dual space */
2111: PetscCall(PetscDualSpaceCreateFacetSubspace_Lagrange(sp, NULL, p, formDegree, Ncopies, PETSC_FALSE, &sp->pointSpaces[p]));
2112: }
2113: for (h = 2; h <= depth; h++) { /* get the higher subspaces from the facet subspaces */
2114: PetscInt hd = depth - h;
2115: PetscInt hdim = dim - h;
2117: if (hdim < PetscAbsInt(formDegree)) break;
2118: for (p = pStratStart[hd]; p < pStratEnd[hd]; p++) {
2119: PetscInt suppSize, s;
2120: const PetscInt *supp;
2122: PetscCall(DMPlexGetSupportSize(dm, p, &suppSize));
2123: PetscCall(DMPlexGetSupport(dm, p, &supp));
2124: for (s = 0; s < suppSize; s++) {
2125: DM qdm;
2126: PetscDualSpace qsp, psp;
2127: PetscInt c, coneSize, q;
2128: const PetscInt *cone;
2129: const PetscInt *refCone;
2131: q = supp[s];
2132: qsp = sp->pointSpaces[q];
2133: PetscCall(DMPlexGetConeSize(dm, q, &coneSize));
2134: PetscCall(DMPlexGetCone(dm, q, &cone));
2135: for (c = 0; c < coneSize; c++)
2136: if (cone[c] == p) break;
2137: PetscCheck(c != coneSize, PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "cone/support mismatch");
2138: PetscCall(PetscDualSpaceGetDM(qsp, &qdm));
2139: PetscCall(DMPlexGetCone(qdm, 0, &refCone));
2140: /* get the equivalent dual space from the support dual space */
2141: PetscCall(PetscDualSpaceGetPointSubspace(qsp, refCone[c], &psp));
2142: if (!s) {
2143: PetscCall(PetscObjectReference((PetscObject)psp));
2144: sp->pointSpaces[p] = psp;
2145: }
2146: }
2147: }
2148: }
2149: for (p = 1; p < pEnd; p++) {
2150: PetscInt pspdim;
2151: if (!sp->pointSpaces[p]) continue;
2152: PetscCall(PetscDualSpaceGetInteriorDimension(sp->pointSpaces[p], &pspdim));
2153: PetscCall(PetscSectionSetDof(section, p, pspdim));
2154: }
2155: }
2157: if (trimmed && !continuous) {
2158: /* the dofs of a trimmed space don't have a nice tensor/lattice structure:
2159: * just construct the continuous dual space and copy all of the data over,
2160: * allocating it all to the cell instead of splitting it up between the boundaries */
2161: PetscDualSpace spcont;
2162: PetscInt spdim, f;
2163: PetscQuadrature allNodes;
2164: PetscDualSpace_Lag *lagc;
2165: Mat allMat;
2167: PetscCall(PetscDualSpaceDuplicate(sp, &spcont));
2168: PetscCall(PetscDualSpaceLagrangeSetContinuity(spcont, PETSC_TRUE));
2169: PetscCall(PetscDualSpaceSetUp(spcont));
2170: PetscCall(PetscDualSpaceGetDimension(spcont, &spdim));
2171: sp->spdim = sp->spintdim = spdim;
2172: PetscCall(PetscSectionSetDof(section, 0, spdim));
2173: PetscCall(PetscDualSpaceSectionSetUp_Internal(sp, section));
2174: PetscCall(PetscMalloc1(spdim, &sp->functional));
2175: for (f = 0; f < spdim; f++) {
2176: PetscQuadrature fn;
2178: PetscCall(PetscDualSpaceGetFunctional(spcont, f, &fn));
2179: PetscCall(PetscObjectReference((PetscObject)fn));
2180: sp->functional[f] = fn;
2181: }
2182: PetscCall(PetscDualSpaceGetAllData(spcont, &allNodes, &allMat));
2183: PetscCall(PetscObjectReference((PetscObject)allNodes));
2184: PetscCall(PetscObjectReference((PetscObject)allNodes));
2185: sp->allNodes = sp->intNodes = allNodes;
2186: PetscCall(PetscObjectReference((PetscObject)allMat));
2187: PetscCall(PetscObjectReference((PetscObject)allMat));
2188: sp->allMat = sp->intMat = allMat;
2189: lagc = (PetscDualSpace_Lag *)spcont->data;
2190: PetscCall(PetscLagNodeIndicesReference(lagc->vertIndices));
2191: lag->vertIndices = lagc->vertIndices;
2192: PetscCall(PetscLagNodeIndicesReference(lagc->allNodeIndices));
2193: PetscCall(PetscLagNodeIndicesReference(lagc->allNodeIndices));
2194: lag->intNodeIndices = lagc->allNodeIndices;
2195: lag->allNodeIndices = lagc->allNodeIndices;
2196: PetscCall(PetscDualSpaceDestroy(&spcont));
2197: PetscCall(PetscFree2(pStratStart, pStratEnd));
2198: PetscCall(DMDestroy(&dmint));
2199: PetscFunctionReturn(PETSC_SUCCESS);
2200: }
2202: /* step 3: construct intNodes, and intMat, and combine it with boundray data to make allNodes and allMat */
2203: if (!tensorSpace) {
2204: if (!tensorCell) PetscCall(PetscLagNodeIndicesCreateSimplexVertices(dm, &lag->vertIndices));
2206: if (trimmed) {
2207: /* there is one dof in the interior of the a trimmed element for each full polynomial of with degree at most
2208: * order + k - dim - 1 */
2209: if (order + PetscAbsInt(formDegree) > dim) {
2210: PetscInt sum = order + PetscAbsInt(formDegree) - dim - 1;
2211: PetscInt nDofs;
2213: PetscCall(PetscDualSpaceLagrangeCreateSimplexNodeMat(nodeFamily, dim, sum, Nk, numNodeSkip, &sp->intNodes, &sp->intMat, &lag->intNodeIndices));
2214: PetscCall(MatGetSize(sp->intMat, &nDofs, NULL));
2215: PetscCall(PetscSectionSetDof(section, 0, nDofs));
2216: }
2217: PetscCall(PetscDualSpaceSectionSetUp_Internal(sp, section));
2218: PetscCall(PetscDualSpaceCreateAllDataFromInteriorData(sp));
2219: PetscCall(PetscDualSpaceLagrangeCreateAllNodeIdx(sp));
2220: } else {
2221: if (!continuous) {
2222: /* if discontinuous just construct one node for each set of dofs (a set of dofs is a basis for the k-form
2223: * space) */
2224: PetscInt sum = order;
2225: PetscInt nDofs;
2227: PetscCall(PetscDualSpaceLagrangeCreateSimplexNodeMat(nodeFamily, dim, sum, Nk, numNodeSkip, &sp->intNodes, &sp->intMat, &lag->intNodeIndices));
2228: PetscCall(MatGetSize(sp->intMat, &nDofs, NULL));
2229: PetscCall(PetscSectionSetDof(section, 0, nDofs));
2230: PetscCall(PetscDualSpaceSectionSetUp_Internal(sp, section));
2231: PetscCall(PetscObjectReference((PetscObject)sp->intNodes));
2232: sp->allNodes = sp->intNodes;
2233: PetscCall(PetscObjectReference((PetscObject)sp->intMat));
2234: sp->allMat = sp->intMat;
2235: PetscCall(PetscLagNodeIndicesReference(lag->intNodeIndices));
2236: lag->allNodeIndices = lag->intNodeIndices;
2237: } else {
2238: /* there is one dof in the interior of the a full element for each trimmed polynomial of with degree at most
2239: * order + k - dim, but with complementary form degree */
2240: if (order + PetscAbsInt(formDegree) > dim) {
2241: PetscDualSpace trimmedsp;
2242: PetscDualSpace_Lag *trimmedlag;
2243: PetscQuadrature intNodes;
2244: PetscInt trFormDegree = formDegree >= 0 ? formDegree - dim : dim - PetscAbsInt(formDegree);
2245: PetscInt nDofs;
2246: Mat intMat;
2248: PetscCall(PetscDualSpaceDuplicate(sp, &trimmedsp));
2249: PetscCall(PetscDualSpaceLagrangeSetTrimmed(trimmedsp, PETSC_TRUE));
2250: PetscCall(PetscDualSpaceSetOrder(trimmedsp, order + PetscAbsInt(formDegree) - dim));
2251: PetscCall(PetscDualSpaceSetFormDegree(trimmedsp, trFormDegree));
2252: trimmedlag = (PetscDualSpace_Lag *)trimmedsp->data;
2253: trimmedlag->numNodeSkip = numNodeSkip + 1;
2254: PetscCall(PetscDualSpaceSetUp(trimmedsp));
2255: PetscCall(PetscDualSpaceGetAllData(trimmedsp, &intNodes, &intMat));
2256: PetscCall(PetscObjectReference((PetscObject)intNodes));
2257: sp->intNodes = intNodes;
2258: PetscCall(PetscLagNodeIndicesReference(trimmedlag->allNodeIndices));
2259: lag->intNodeIndices = trimmedlag->allNodeIndices;
2260: PetscCall(PetscObjectReference((PetscObject)intMat));
2261: if (PetscAbsInt(formDegree) > 0 && PetscAbsInt(formDegree) < dim) {
2262: PetscReal *T;
2263: PetscScalar *work;
2264: PetscInt nCols, nRows;
2265: Mat intMatT;
2267: PetscCall(MatDuplicate(intMat, MAT_COPY_VALUES, &intMatT));
2268: PetscCall(MatGetSize(intMat, &nRows, &nCols));
2269: PetscCall(PetscMalloc2(Nk * Nk, &T, nCols, &work));
2270: PetscCall(BiunitSimplexSymmetricFormTransformation(dim, formDegree, T));
2271: for (PetscInt row = 0; row < nRows; row++) {
2272: PetscInt nrCols;
2273: const PetscInt *rCols;
2274: const PetscScalar *rVals;
2276: PetscCall(MatGetRow(intMat, row, &nrCols, &rCols, &rVals));
2277: PetscCheck(nrCols % Nk == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "nonzeros in intMat matrix are not in k-form size blocks");
2278: for (PetscInt b = 0; b < nrCols; b += Nk) {
2279: const PetscScalar *v = &rVals[b];
2280: PetscScalar *w = &work[b];
2281: for (PetscInt j = 0; j < Nk; j++) {
2282: w[j] = 0.;
2283: for (PetscInt i = 0; i < Nk; i++) w[j] += v[i] * T[i * Nk + j];
2284: }
2285: }
2286: PetscCall(MatSetValuesBlocked(intMatT, 1, &row, nrCols, rCols, work, INSERT_VALUES));
2287: PetscCall(MatRestoreRow(intMat, row, &nrCols, &rCols, &rVals));
2288: }
2289: PetscCall(MatAssemblyBegin(intMatT, MAT_FINAL_ASSEMBLY));
2290: PetscCall(MatAssemblyEnd(intMatT, MAT_FINAL_ASSEMBLY));
2291: PetscCall(MatDestroy(&intMat));
2292: intMat = intMatT;
2293: PetscCall(PetscLagNodeIndicesDestroy(&lag->intNodeIndices));
2294: PetscCall(PetscLagNodeIndicesDuplicate(trimmedlag->allNodeIndices, &lag->intNodeIndices));
2295: {
2296: PetscInt nNodes = lag->intNodeIndices->nNodes;
2297: PetscReal *newNodeVec = lag->intNodeIndices->nodeVec;
2298: const PetscReal *oldNodeVec = trimmedlag->allNodeIndices->nodeVec;
2300: for (PetscInt n = 0; n < nNodes; n++) {
2301: PetscReal *w = &newNodeVec[n * Nk];
2302: const PetscReal *v = &oldNodeVec[n * Nk];
2304: for (PetscInt j = 0; j < Nk; j++) {
2305: w[j] = 0.;
2306: for (PetscInt i = 0; i < Nk; i++) w[j] += v[i] * T[i * Nk + j];
2307: }
2308: }
2309: }
2310: PetscCall(PetscFree2(T, work));
2311: }
2312: sp->intMat = intMat;
2313: PetscCall(MatGetSize(sp->intMat, &nDofs, NULL));
2314: PetscCall(PetscDualSpaceDestroy(&trimmedsp));
2315: PetscCall(PetscSectionSetDof(section, 0, nDofs));
2316: }
2317: PetscCall(PetscDualSpaceSectionSetUp_Internal(sp, section));
2318: PetscCall(PetscDualSpaceCreateAllDataFromInteriorData(sp));
2319: PetscCall(PetscDualSpaceLagrangeCreateAllNodeIdx(sp));
2320: }
2321: }
2322: } else {
2323: PetscQuadrature intNodesTrace = NULL;
2324: PetscQuadrature intNodesFiber = NULL;
2325: PetscQuadrature intNodes = NULL;
2326: PetscLagNodeIndices intNodeIndices = NULL;
2327: Mat intMat = NULL;
2329: if (PetscAbsInt(formDegree) < dim) { /* get the trace k-forms on the first facet, and the 0-forms on the edge,
2330: and wedge them together to create some of the k-form dofs */
2331: PetscDualSpace trace, fiber;
2332: PetscDualSpace_Lag *tracel, *fiberl;
2333: Mat intMatTrace, intMatFiber;
2335: if (sp->pointSpaces[tensorf]) {
2336: PetscCall(PetscObjectReference((PetscObject)sp->pointSpaces[tensorf]));
2337: trace = sp->pointSpaces[tensorf];
2338: } else {
2339: PetscCall(PetscDualSpaceCreateFacetSubspace_Lagrange(sp, NULL, tensorf, formDegree, Ncopies, PETSC_TRUE, &trace));
2340: }
2341: PetscCall(PetscDualSpaceCreateEdgeSubspace_Lagrange(sp, order, 0, 1, PETSC_TRUE, &fiber));
2342: tracel = (PetscDualSpace_Lag *)trace->data;
2343: fiberl = (PetscDualSpace_Lag *)fiber->data;
2344: PetscCall(PetscLagNodeIndicesCreateTensorVertices(dm, tracel->vertIndices, &lag->vertIndices));
2345: PetscCall(PetscDualSpaceGetInteriorData(trace, &intNodesTrace, &intMatTrace));
2346: PetscCall(PetscDualSpaceGetInteriorData(fiber, &intNodesFiber, &intMatFiber));
2347: if (intNodesTrace && intNodesFiber) {
2348: PetscCall(PetscQuadratureCreateTensor(intNodesTrace, intNodesFiber, &intNodes));
2349: PetscCall(MatTensorAltV(intMatTrace, intMatFiber, dim - 1, formDegree, 1, 0, &intMat));
2350: PetscCall(PetscLagNodeIndicesTensor(tracel->intNodeIndices, dim - 1, formDegree, fiberl->intNodeIndices, 1, 0, &intNodeIndices));
2351: }
2352: PetscCall(PetscObjectReference((PetscObject)intNodesTrace));
2353: PetscCall(PetscObjectReference((PetscObject)intNodesFiber));
2354: PetscCall(PetscDualSpaceDestroy(&fiber));
2355: PetscCall(PetscDualSpaceDestroy(&trace));
2356: }
2357: if (PetscAbsInt(formDegree) > 0) { /* get the trace (k-1)-forms on the first facet, and the 1-forms on the edge,
2358: and wedge them together to create the remaining k-form dofs */
2359: PetscDualSpace trace, fiber;
2360: PetscDualSpace_Lag *tracel, *fiberl;
2361: PetscQuadrature intNodesTrace2, intNodesFiber2, intNodes2;
2362: PetscLagNodeIndices intNodeIndices2;
2363: Mat intMatTrace, intMatFiber, intMat2;
2364: PetscInt traceDegree = formDegree > 0 ? formDegree - 1 : formDegree + 1;
2365: PetscInt fiberDegree = formDegree > 0 ? 1 : -1;
2367: PetscCall(PetscDualSpaceCreateFacetSubspace_Lagrange(sp, NULL, tensorf, traceDegree, Ncopies, PETSC_TRUE, &trace));
2368: PetscCall(PetscDualSpaceCreateEdgeSubspace_Lagrange(sp, order, fiberDegree, 1, PETSC_TRUE, &fiber));
2369: tracel = (PetscDualSpace_Lag *)trace->data;
2370: fiberl = (PetscDualSpace_Lag *)fiber->data;
2371: if (!lag->vertIndices) PetscCall(PetscLagNodeIndicesCreateTensorVertices(dm, tracel->vertIndices, &lag->vertIndices));
2372: PetscCall(PetscDualSpaceGetInteriorData(trace, &intNodesTrace2, &intMatTrace));
2373: PetscCall(PetscDualSpaceGetInteriorData(fiber, &intNodesFiber2, &intMatFiber));
2374: if (intNodesTrace2 && intNodesFiber2) {
2375: PetscCall(PetscQuadratureCreateTensor(intNodesTrace2, intNodesFiber2, &intNodes2));
2376: PetscCall(MatTensorAltV(intMatTrace, intMatFiber, dim - 1, traceDegree, 1, fiberDegree, &intMat2));
2377: PetscCall(PetscLagNodeIndicesTensor(tracel->intNodeIndices, dim - 1, traceDegree, fiberl->intNodeIndices, 1, fiberDegree, &intNodeIndices2));
2378: if (!intMat) {
2379: intMat = intMat2;
2380: intNodes = intNodes2;
2381: intNodeIndices = intNodeIndices2;
2382: } else {
2383: /* merge the matrices, quadrature points, and nodes */
2384: PetscInt nM;
2385: PetscInt nDof, nDof2;
2386: PetscInt *toMerged = NULL, *toMerged2 = NULL;
2387: PetscQuadrature merged = NULL;
2388: PetscLagNodeIndices intNodeIndicesMerged = NULL;
2389: Mat matMerged = NULL;
2391: PetscCall(MatGetSize(intMat, &nDof, NULL));
2392: PetscCall(MatGetSize(intMat2, &nDof2, NULL));
2393: PetscCall(PetscQuadraturePointsMerge(intNodes, intNodes2, &merged, &toMerged, &toMerged2));
2394: PetscCall(PetscQuadratureGetData(merged, NULL, NULL, &nM, NULL, NULL));
2395: PetscCall(MatricesMerge(intMat, intMat2, dim, formDegree, nM, toMerged, toMerged2, &matMerged));
2396: PetscCall(PetscLagNodeIndicesMerge(intNodeIndices, intNodeIndices2, &intNodeIndicesMerged));
2397: PetscCall(PetscFree(toMerged));
2398: PetscCall(PetscFree(toMerged2));
2399: PetscCall(MatDestroy(&intMat));
2400: PetscCall(MatDestroy(&intMat2));
2401: PetscCall(PetscQuadratureDestroy(&intNodes));
2402: PetscCall(PetscQuadratureDestroy(&intNodes2));
2403: PetscCall(PetscLagNodeIndicesDestroy(&intNodeIndices));
2404: PetscCall(PetscLagNodeIndicesDestroy(&intNodeIndices2));
2405: intNodes = merged;
2406: intMat = matMerged;
2407: intNodeIndices = intNodeIndicesMerged;
2408: if (!trimmed) {
2409: /* I think users expect that, when a node has a full basis for the k-forms,
2410: * they should be consecutive dofs. That isn't the case for trimmed spaces,
2411: * but is for some of the nodes in untrimmed spaces, so in that case we
2412: * sort them to group them by node */
2413: Mat intMatPerm;
2415: PetscCall(MatPermuteByNodeIdx(intMat, intNodeIndices, &intMatPerm));
2416: PetscCall(MatDestroy(&intMat));
2417: intMat = intMatPerm;
2418: }
2419: }
2420: }
2421: PetscCall(PetscDualSpaceDestroy(&fiber));
2422: PetscCall(PetscDualSpaceDestroy(&trace));
2423: }
2424: PetscCall(PetscQuadratureDestroy(&intNodesTrace));
2425: PetscCall(PetscQuadratureDestroy(&intNodesFiber));
2426: sp->intNodes = intNodes;
2427: sp->intMat = intMat;
2428: lag->intNodeIndices = intNodeIndices;
2429: {
2430: PetscInt nDofs = 0;
2432: if (intMat) PetscCall(MatGetSize(intMat, &nDofs, NULL));
2433: PetscCall(PetscSectionSetDof(section, 0, nDofs));
2434: }
2435: PetscCall(PetscDualSpaceSectionSetUp_Internal(sp, section));
2436: if (continuous) {
2437: PetscCall(PetscDualSpaceCreateAllDataFromInteriorData(sp));
2438: PetscCall(PetscDualSpaceLagrangeCreateAllNodeIdx(sp));
2439: } else {
2440: PetscCall(PetscObjectReference((PetscObject)intNodes));
2441: sp->allNodes = intNodes;
2442: PetscCall(PetscObjectReference((PetscObject)intMat));
2443: sp->allMat = intMat;
2444: PetscCall(PetscLagNodeIndicesReference(intNodeIndices));
2445: lag->allNodeIndices = intNodeIndices;
2446: }
2447: }
2448: PetscCall(PetscSectionGetStorageSize(section, &sp->spdim));
2449: PetscCall(PetscSectionGetConstrainedStorageSize(section, &sp->spintdim));
2450: // TODO: fix this, computing functionals from moments should be no different for nodal vs modal
2451: if (lag->useMoments) {
2452: PetscCall(PetscDualSpaceComputeFunctionalsFromAllData_Moments(sp));
2453: } else {
2454: PetscCall(PetscDualSpaceComputeFunctionalsFromAllData(sp));
2455: }
2456: PetscCall(PetscFree2(pStratStart, pStratEnd));
2457: PetscCall(DMDestroy(&dmint));
2458: PetscFunctionReturn(PETSC_SUCCESS);
2459: }
2461: /* Create a matrix that represents the transformation that DMPlexVecGetClosure() would need
2462: * to get the representation of the dofs for a mesh point if the mesh point had this orientation
2463: * relative to the cell */
2464: PetscErrorCode PetscDualSpaceCreateInteriorSymmetryMatrix_Lagrange(PetscDualSpace sp, PetscInt ornt, Mat *symMat)
2465: {
2466: PetscDualSpace_Lag *lag;
2467: DM dm;
2468: PetscLagNodeIndices vertIndices, intNodeIndices;
2469: PetscLagNodeIndices ni;
2470: PetscInt nodeIdxDim, nodeVecDim, nNodes;
2471: PetscInt formDegree;
2472: PetscInt *perm, *permOrnt;
2473: PetscInt *nnz;
2474: PetscInt n;
2475: PetscInt maxGroupSize;
2476: PetscScalar *V, *W, *work;
2477: Mat A;
2479: PetscFunctionBegin;
2480: if (!sp->spintdim) {
2481: *symMat = NULL;
2482: PetscFunctionReturn(PETSC_SUCCESS);
2483: }
2484: lag = (PetscDualSpace_Lag *)sp->data;
2485: vertIndices = lag->vertIndices;
2486: intNodeIndices = lag->intNodeIndices;
2487: PetscCall(PetscDualSpaceGetDM(sp, &dm));
2488: PetscCall(PetscDualSpaceGetFormDegree(sp, &formDegree));
2489: PetscCall(PetscNew(&ni));
2490: ni->refct = 1;
2491: ni->nodeIdxDim = nodeIdxDim = intNodeIndices->nodeIdxDim;
2492: ni->nodeVecDim = nodeVecDim = intNodeIndices->nodeVecDim;
2493: ni->nNodes = nNodes = intNodeIndices->nNodes;
2494: PetscCall(PetscMalloc1(nNodes * nodeIdxDim, &ni->nodeIdx));
2495: PetscCall(PetscMalloc1(nNodes * nodeVecDim, &ni->nodeVec));
2496: /* push forward the dofs by the symmetry of the reference element induced by ornt */
2497: PetscCall(PetscLagNodeIndicesPushForward(dm, vertIndices, 0, vertIndices, intNodeIndices, ornt, formDegree, ni->nodeIdx, ni->nodeVec));
2498: /* get the revlex order for both the original and transformed dofs */
2499: PetscCall(PetscLagNodeIndicesGetPermutation(intNodeIndices, &perm));
2500: PetscCall(PetscLagNodeIndicesGetPermutation(ni, &permOrnt));
2501: PetscCall(PetscMalloc1(nNodes, &nnz));
2502: for (n = 0, maxGroupSize = 0; n < nNodes;) { /* incremented in the loop */
2503: PetscInt *nind = &(ni->nodeIdx[permOrnt[n] * nodeIdxDim]);
2504: PetscInt m, nEnd;
2505: PetscInt groupSize;
2506: /* for each group of dofs that have the same nodeIdx coordinate */
2507: for (nEnd = n + 1; nEnd < nNodes; nEnd++) {
2508: PetscInt *mind = &(ni->nodeIdx[permOrnt[nEnd] * nodeIdxDim]);
2509: PetscInt d;
2511: /* compare the oriented permutation indices */
2512: for (d = 0; d < nodeIdxDim; d++)
2513: if (mind[d] != nind[d]) break;
2514: if (d < nodeIdxDim) break;
2515: }
2516: /* permOrnt[[n, nEnd)] is a group of dofs that, under the symmetry are at the same location */
2518: /* the symmetry had better map the group of dofs with the same permuted nodeIdx
2519: * to a group of dofs with the same size, otherwise we messed up */
2520: if (PetscDefined(USE_DEBUG)) {
2521: PetscInt m;
2522: PetscInt *nind = &(intNodeIndices->nodeIdx[perm[n] * nodeIdxDim]);
2524: for (m = n + 1; m < nEnd; m++) {
2525: PetscInt *mind = &(intNodeIndices->nodeIdx[perm[m] * nodeIdxDim]);
2526: PetscInt d;
2528: /* compare the oriented permutation indices */
2529: for (d = 0; d < nodeIdxDim; d++)
2530: if (mind[d] != nind[d]) break;
2531: if (d < nodeIdxDim) break;
2532: }
2533: PetscCheck(m >= nEnd, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Dofs with same index after symmetry not same block size");
2534: }
2535: groupSize = nEnd - n;
2536: /* each pushforward dof vector will be expressed in a basis of the unpermuted dofs */
2537: for (m = n; m < nEnd; m++) nnz[permOrnt[m]] = groupSize;
2539: maxGroupSize = PetscMax(maxGroupSize, nEnd - n);
2540: n = nEnd;
2541: }
2542: PetscCheck(maxGroupSize <= nodeVecDim, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Dofs are not in blocks that can be solved");
2543: PetscCall(MatCreateSeqAIJ(PETSC_COMM_SELF, nNodes, nNodes, 0, nnz, &A));
2544: PetscCall(PetscObjectSetOptionsPrefix((PetscObject)A, "lag_"));
2545: PetscCall(PetscFree(nnz));
2546: PetscCall(PetscMalloc3(maxGroupSize * nodeVecDim, &V, maxGroupSize * nodeVecDim, &W, nodeVecDim * 2, &work));
2547: for (n = 0; n < nNodes;) { /* incremented in the loop */
2548: PetscInt *nind = &(ni->nodeIdx[permOrnt[n] * nodeIdxDim]);
2549: PetscInt nEnd;
2550: PetscInt m;
2551: PetscInt groupSize;
2552: for (nEnd = n + 1; nEnd < nNodes; nEnd++) {
2553: PetscInt *mind = &(ni->nodeIdx[permOrnt[nEnd] * nodeIdxDim]);
2554: PetscInt d;
2556: /* compare the oriented permutation indices */
2557: for (d = 0; d < nodeIdxDim; d++)
2558: if (mind[d] != nind[d]) break;
2559: if (d < nodeIdxDim) break;
2560: }
2561: groupSize = nEnd - n;
2562: /* get all of the vectors from the original and all of the pushforward vectors */
2563: for (m = n; m < nEnd; m++) {
2564: PetscInt d;
2566: for (d = 0; d < nodeVecDim; d++) {
2567: V[(m - n) * nodeVecDim + d] = intNodeIndices->nodeVec[perm[m] * nodeVecDim + d];
2568: W[(m - n) * nodeVecDim + d] = ni->nodeVec[permOrnt[m] * nodeVecDim + d];
2569: }
2570: }
2571: /* now we have to solve for W in terms of V: the systems isn't always square, but the span
2572: * of V and W should always be the same, so the solution of the normal equations works */
2573: {
2574: char transpose = 'N';
2575: PetscBLASInt bm, bn, bnrhs, blda, bldb, blwork, info;
2577: PetscCall(PetscBLASIntCast(nodeVecDim, &bm));
2578: PetscCall(PetscBLASIntCast(groupSize, &bn));
2579: PetscCall(PetscBLASIntCast(groupSize, &bnrhs));
2580: PetscCall(PetscBLASIntCast(bm, &blda));
2581: PetscCall(PetscBLASIntCast(bm, &bldb));
2582: PetscCall(PetscBLASIntCast(2 * nodeVecDim, &blwork));
2583: PetscCallBLAS("LAPACKgels", LAPACKgels_(&transpose, &bm, &bn, &bnrhs, V, &blda, W, &bldb, work, &blwork, &info));
2584: PetscCheck(info == 0, PETSC_COMM_SELF, PETSC_ERR_LIB, "Bad argument to GELS");
2585: /* repack */
2586: {
2587: PetscInt i, j;
2589: for (i = 0; i < groupSize; i++) {
2590: for (j = 0; j < groupSize; j++) {
2591: /* notice the different leading dimension */
2592: V[i * groupSize + j] = W[i * nodeVecDim + j];
2593: }
2594: }
2595: }
2596: if (PetscDefined(USE_DEBUG)) {
2597: PetscReal res;
2599: /* check that the normal error is 0 */
2600: for (m = n; m < nEnd; m++) {
2601: PetscInt d;
2603: for (d = 0; d < nodeVecDim; d++) W[(m - n) * nodeVecDim + d] = ni->nodeVec[permOrnt[m] * nodeVecDim + d];
2604: }
2605: res = 0.;
2606: for (PetscInt i = 0; i < groupSize; i++) {
2607: for (PetscInt j = 0; j < nodeVecDim; j++) {
2608: for (PetscInt k = 0; k < groupSize; k++) W[i * nodeVecDim + j] -= V[i * groupSize + k] * intNodeIndices->nodeVec[perm[n + k] * nodeVecDim + j];
2609: res += PetscAbsScalar(W[i * nodeVecDim + j]);
2610: }
2611: }
2612: PetscCheck(res <= PETSC_SMALL, PETSC_COMM_SELF, PETSC_ERR_LIB, "Dof block did not solve");
2613: }
2614: }
2615: PetscCall(MatSetValues(A, groupSize, &permOrnt[n], groupSize, &perm[n], V, INSERT_VALUES));
2616: n = nEnd;
2617: }
2618: PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
2619: PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
2620: *symMat = A;
2621: PetscCall(PetscFree3(V, W, work));
2622: PetscCall(PetscLagNodeIndicesDestroy(&ni));
2623: PetscFunctionReturn(PETSC_SUCCESS);
2624: }
2626: // get the symmetries of closure points
2627: PETSC_INTERN PetscErrorCode PetscDualSpaceGetBoundarySymmetries_Internal(PetscDualSpace sp, PetscInt ***symperms, PetscScalar ***symflips)
2628: {
2629: PetscInt closureSize = 0;
2630: PetscInt *closure = NULL;
2631: PetscInt r;
2633: PetscFunctionBegin;
2634: PetscCall(DMPlexGetTransitiveClosure(sp->dm, 0, PETSC_TRUE, &closureSize, &closure));
2635: for (r = 0; r < closureSize; r++) {
2636: PetscDualSpace psp;
2637: PetscInt point = closure[2 * r];
2638: PetscInt pspintdim;
2639: const PetscInt ***psymperms = NULL;
2640: const PetscScalar ***psymflips = NULL;
2642: if (!point) continue;
2643: PetscCall(PetscDualSpaceGetPointSubspace(sp, point, &psp));
2644: if (!psp) continue;
2645: PetscCall(PetscDualSpaceGetInteriorDimension(psp, &pspintdim));
2646: if (!pspintdim) continue;
2647: PetscCall(PetscDualSpaceGetSymmetries(psp, &psymperms, &psymflips));
2648: symperms[r] = (PetscInt **)(psymperms ? psymperms[0] : NULL);
2649: symflips[r] = (PetscScalar **)(psymflips ? psymflips[0] : NULL);
2650: }
2651: PetscCall(DMPlexRestoreTransitiveClosure(sp->dm, 0, PETSC_TRUE, &closureSize, &closure));
2652: PetscFunctionReturn(PETSC_SUCCESS);
2653: }
2655: #define BaryIndex(perEdge, a, b, c) (((b) * (2 * perEdge + 1 - (b))) / 2) + (c)
2657: #define CartIndex(perEdge, a, b) (perEdge * (a) + b)
2659: /* the existing interface for symmetries is insufficient for all cases:
2660: * - it should be sufficient for form degrees that are scalar (0 and n)
2661: * - it should be sufficient for hypercube dofs
2662: * - it isn't sufficient for simplex cells with non-scalar form degrees if
2663: * there are any dofs in the interior
2664: *
2665: * We compute the general transformation matrices, and if they fit, we return them,
2666: * otherwise we error (but we should probably change the interface to allow for
2667: * these symmetries)
2668: */
2669: static PetscErrorCode PetscDualSpaceGetSymmetries_Lagrange(PetscDualSpace sp, const PetscInt ****perms, const PetscScalar ****flips)
2670: {
2671: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2672: PetscInt dim, order, Nc;
2674: PetscFunctionBegin;
2675: PetscCall(PetscDualSpaceGetOrder(sp, &order));
2676: PetscCall(PetscDualSpaceGetNumComponents(sp, &Nc));
2677: PetscCall(DMGetDimension(sp->dm, &dim));
2678: if (!lag->symComputed) { /* store symmetries */
2679: PetscInt pStart, pEnd, p;
2680: PetscInt numPoints;
2681: PetscInt numFaces;
2682: PetscInt spintdim;
2683: PetscInt ***symperms;
2684: PetscScalar ***symflips;
2686: PetscCall(DMPlexGetChart(sp->dm, &pStart, &pEnd));
2687: numPoints = pEnd - pStart;
2688: {
2689: DMPolytopeType ct;
2690: /* The number of arrangements is no longer based on the number of faces */
2691: PetscCall(DMPlexGetCellType(sp->dm, 0, &ct));
2692: numFaces = DMPolytopeTypeGetNumArrangements(ct) / 2;
2693: }
2694: PetscCall(PetscCalloc1(numPoints, &symperms));
2695: PetscCall(PetscCalloc1(numPoints, &symflips));
2696: spintdim = sp->spintdim;
2697: /* The nodal symmetry behavior is not present when tensorSpace != tensorCell: someone might want this for the "S"
2698: * family of FEEC spaces. Most used in particular are discontinuous polynomial L2 spaces in tensor cells, where
2699: * the symmetries are not necessary for FE assembly. So for now we assume this is the case and don't return
2700: * symmetries if tensorSpace != tensorCell */
2701: if (spintdim && 0 < dim && dim < 3 && (lag->tensorSpace == lag->tensorCell)) { /* compute self symmetries */
2702: PetscInt **cellSymperms;
2703: PetscScalar **cellSymflips;
2704: PetscInt ornt;
2705: PetscInt nCopies = Nc / lag->intNodeIndices->nodeVecDim;
2706: PetscInt nNodes = lag->intNodeIndices->nNodes;
2708: lag->numSelfSym = 2 * numFaces;
2709: lag->selfSymOff = numFaces;
2710: PetscCall(PetscCalloc1(2 * numFaces, &cellSymperms));
2711: PetscCall(PetscCalloc1(2 * numFaces, &cellSymflips));
2712: /* we want to be able to index symmetries directly with the orientations, which range from [-numFaces,numFaces) */
2713: symperms[0] = &cellSymperms[numFaces];
2714: symflips[0] = &cellSymflips[numFaces];
2715: PetscCheck(lag->intNodeIndices->nodeVecDim * nCopies == Nc, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Node indices incompatible with dofs");
2716: PetscCheck(nNodes * nCopies == spintdim, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Node indices incompatible with dofs");
2717: 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 */
2718: Mat symMat;
2719: PetscInt *perm;
2720: PetscScalar *flips;
2721: PetscInt i;
2723: if (!ornt) continue;
2724: PetscCall(PetscMalloc1(spintdim, &perm));
2725: PetscCall(PetscCalloc1(spintdim, &flips));
2726: for (i = 0; i < spintdim; i++) perm[i] = -1;
2727: PetscCall(PetscDualSpaceCreateInteriorSymmetryMatrix_Lagrange(sp, ornt, &symMat));
2728: for (i = 0; i < nNodes; i++) {
2729: PetscInt ncols;
2730: PetscInt j, k;
2731: const PetscInt *cols;
2732: const PetscScalar *vals;
2733: PetscBool nz_seen = PETSC_FALSE;
2735: PetscCall(MatGetRow(symMat, i, &ncols, &cols, &vals));
2736: for (j = 0; j < ncols; j++) {
2737: if (PetscAbsScalar(vals[j]) > PETSC_SMALL) {
2738: 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");
2739: nz_seen = PETSC_TRUE;
2740: 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");
2741: 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");
2742: 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");
2743: for (k = 0; k < nCopies; k++) perm[cols[j] * nCopies + k] = i * nCopies + k;
2744: if (PetscRealPart(vals[j]) < 0.) {
2745: for (k = 0; k < nCopies; k++) flips[i * nCopies + k] = -1.;
2746: } else {
2747: for (k = 0; k < nCopies; k++) flips[i * nCopies + k] = 1.;
2748: }
2749: }
2750: }
2751: PetscCall(MatRestoreRow(symMat, i, &ncols, &cols, &vals));
2752: }
2753: PetscCall(MatDestroy(&symMat));
2754: /* if there were no sign flips, keep NULL */
2755: for (i = 0; i < spintdim; i++)
2756: if (flips[i] != 1.) break;
2757: if (i == spintdim) {
2758: PetscCall(PetscFree(flips));
2759: flips = NULL;
2760: }
2761: /* if the permutation is identity, keep NULL */
2762: for (i = 0; i < spintdim; i++)
2763: if (perm[i] != i) break;
2764: if (i == spintdim) {
2765: PetscCall(PetscFree(perm));
2766: perm = NULL;
2767: }
2768: symperms[0][ornt] = perm;
2769: symflips[0][ornt] = flips;
2770: }
2771: /* if no orientations produced non-identity permutations, keep NULL */
2772: for (ornt = -numFaces; ornt < numFaces; ornt++)
2773: if (symperms[0][ornt]) break;
2774: if (ornt == numFaces) {
2775: PetscCall(PetscFree(cellSymperms));
2776: symperms[0] = NULL;
2777: }
2778: /* if no orientations produced sign flips, keep NULL */
2779: for (ornt = -numFaces; ornt < numFaces; ornt++)
2780: if (symflips[0][ornt]) break;
2781: if (ornt == numFaces) {
2782: PetscCall(PetscFree(cellSymflips));
2783: symflips[0] = NULL;
2784: }
2785: }
2786: PetscCall(PetscDualSpaceGetBoundarySymmetries_Internal(sp, symperms, symflips));
2787: for (p = 0; p < pEnd; p++)
2788: if (symperms[p]) break;
2789: if (p == pEnd) {
2790: PetscCall(PetscFree(symperms));
2791: symperms = NULL;
2792: }
2793: for (p = 0; p < pEnd; p++)
2794: if (symflips[p]) break;
2795: if (p == pEnd) {
2796: PetscCall(PetscFree(symflips));
2797: symflips = NULL;
2798: }
2799: lag->symperms = symperms;
2800: lag->symflips = symflips;
2801: lag->symComputed = PETSC_TRUE;
2802: }
2803: if (perms) *perms = (const PetscInt ***)lag->symperms;
2804: if (flips) *flips = (const PetscScalar ***)lag->symflips;
2805: PetscFunctionReturn(PETSC_SUCCESS);
2806: }
2808: static PetscErrorCode PetscDualSpaceLagrangeGetContinuity_Lagrange(PetscDualSpace sp, PetscBool *continuous)
2809: {
2810: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2812: PetscFunctionBegin;
2814: PetscAssertPointer(continuous, 2);
2815: *continuous = lag->continuous;
2816: PetscFunctionReturn(PETSC_SUCCESS);
2817: }
2819: static PetscErrorCode PetscDualSpaceLagrangeSetContinuity_Lagrange(PetscDualSpace sp, PetscBool continuous)
2820: {
2821: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2823: PetscFunctionBegin;
2825: lag->continuous = continuous;
2826: PetscFunctionReturn(PETSC_SUCCESS);
2827: }
2829: /*@
2830: PetscDualSpaceLagrangeGetContinuity - Retrieves the flag for element continuity
2832: Not Collective
2834: Input Parameter:
2835: . sp - the `PetscDualSpace`
2837: Output Parameter:
2838: . continuous - flag for element continuity
2840: Level: intermediate
2842: .seealso: `PETSCDUALSPACELAGRANGE`, `PetscDualSpace`, `PetscDualSpaceLagrangeSetContinuity()`
2843: @*/
2844: PetscErrorCode PetscDualSpaceLagrangeGetContinuity(PetscDualSpace sp, PetscBool *continuous)
2845: {
2846: PetscFunctionBegin;
2848: PetscAssertPointer(continuous, 2);
2849: PetscTryMethod(sp, "PetscDualSpaceLagrangeGetContinuity_C", (PetscDualSpace, PetscBool *), (sp, continuous));
2850: PetscFunctionReturn(PETSC_SUCCESS);
2851: }
2853: /*@
2854: PetscDualSpaceLagrangeSetContinuity - Indicate whether the element is continuous
2856: Logically Collective
2858: Input Parameters:
2859: + sp - the `PetscDualSpace`
2860: - continuous - flag for element continuity
2862: Options Database Key:
2863: . -petscdualspace_lagrange_continuity <bool> - use a continuous element
2865: Level: intermediate
2867: .seealso: `PETSCDUALSPACELAGRANGE`, `PetscDualSpace`, `PetscDualSpaceLagrangeGetContinuity()`
2868: @*/
2869: PetscErrorCode PetscDualSpaceLagrangeSetContinuity(PetscDualSpace sp, PetscBool continuous)
2870: {
2871: PetscFunctionBegin;
2874: PetscTryMethod(sp, "PetscDualSpaceLagrangeSetContinuity_C", (PetscDualSpace, PetscBool), (sp, continuous));
2875: PetscFunctionReturn(PETSC_SUCCESS);
2876: }
2878: static PetscErrorCode PetscDualSpaceLagrangeGetTensor_Lagrange(PetscDualSpace sp, PetscBool *tensor)
2879: {
2880: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2882: PetscFunctionBegin;
2883: *tensor = lag->tensorSpace;
2884: PetscFunctionReturn(PETSC_SUCCESS);
2885: }
2887: static PetscErrorCode PetscDualSpaceLagrangeSetTensor_Lagrange(PetscDualSpace sp, PetscBool tensor)
2888: {
2889: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2891: PetscFunctionBegin;
2892: lag->tensorSpace = tensor;
2893: PetscFunctionReturn(PETSC_SUCCESS);
2894: }
2896: static PetscErrorCode PetscDualSpaceLagrangeGetTrimmed_Lagrange(PetscDualSpace sp, PetscBool *trimmed)
2897: {
2898: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2900: PetscFunctionBegin;
2901: *trimmed = lag->trimmed;
2902: PetscFunctionReturn(PETSC_SUCCESS);
2903: }
2905: static PetscErrorCode PetscDualSpaceLagrangeSetTrimmed_Lagrange(PetscDualSpace sp, PetscBool trimmed)
2906: {
2907: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2909: PetscFunctionBegin;
2910: lag->trimmed = trimmed;
2911: PetscFunctionReturn(PETSC_SUCCESS);
2912: }
2914: static PetscErrorCode PetscDualSpaceLagrangeGetNodeType_Lagrange(PetscDualSpace sp, PetscDTNodeType *nodeType, PetscBool *boundary, PetscReal *exponent)
2915: {
2916: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2918: PetscFunctionBegin;
2919: if (nodeType) *nodeType = lag->nodeType;
2920: if (boundary) *boundary = lag->endNodes;
2921: if (exponent) *exponent = lag->nodeExponent;
2922: PetscFunctionReturn(PETSC_SUCCESS);
2923: }
2925: static PetscErrorCode PetscDualSpaceLagrangeSetNodeType_Lagrange(PetscDualSpace sp, PetscDTNodeType nodeType, PetscBool boundary, PetscReal exponent)
2926: {
2927: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2929: PetscFunctionBegin;
2930: PetscCheck(nodeType != PETSCDTNODES_GAUSSJACOBI || exponent > -1., PetscObjectComm((PetscObject)sp), PETSC_ERR_ARG_OUTOFRANGE, "Exponent must be > -1");
2931: lag->nodeType = nodeType;
2932: lag->endNodes = boundary;
2933: lag->nodeExponent = exponent;
2934: PetscFunctionReturn(PETSC_SUCCESS);
2935: }
2937: static PetscErrorCode PetscDualSpaceLagrangeGetUseMoments_Lagrange(PetscDualSpace sp, PetscBool *useMoments)
2938: {
2939: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2941: PetscFunctionBegin;
2942: *useMoments = lag->useMoments;
2943: PetscFunctionReturn(PETSC_SUCCESS);
2944: }
2946: static PetscErrorCode PetscDualSpaceLagrangeSetUseMoments_Lagrange(PetscDualSpace sp, PetscBool useMoments)
2947: {
2948: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2950: PetscFunctionBegin;
2951: lag->useMoments = useMoments;
2952: PetscFunctionReturn(PETSC_SUCCESS);
2953: }
2955: static PetscErrorCode PetscDualSpaceLagrangeGetMomentOrder_Lagrange(PetscDualSpace sp, PetscInt *momentOrder)
2956: {
2957: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2959: PetscFunctionBegin;
2960: *momentOrder = lag->momentOrder;
2961: PetscFunctionReturn(PETSC_SUCCESS);
2962: }
2964: static PetscErrorCode PetscDualSpaceLagrangeSetMomentOrder_Lagrange(PetscDualSpace sp, PetscInt momentOrder)
2965: {
2966: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2968: PetscFunctionBegin;
2969: lag->momentOrder = momentOrder;
2970: PetscFunctionReturn(PETSC_SUCCESS);
2971: }
2973: /*@
2974: PetscDualSpaceLagrangeGetTensor - Get the tensor nature of the dual space
2976: Not Collective
2978: Input Parameter:
2979: . sp - The `PetscDualSpace`
2981: Output Parameter:
2982: . tensor - Whether the dual space has tensor layout (vs. simplicial)
2984: Level: intermediate
2986: .seealso: `PETSCDUALSPACELAGRANGE`, `PetscDualSpace`, `PetscDualSpaceLagrangeSetTensor()`, `PetscDualSpaceCreate()`
2987: @*/
2988: PetscErrorCode PetscDualSpaceLagrangeGetTensor(PetscDualSpace sp, PetscBool *tensor)
2989: {
2990: PetscFunctionBegin;
2992: PetscAssertPointer(tensor, 2);
2993: PetscTryMethod(sp, "PetscDualSpaceLagrangeGetTensor_C", (PetscDualSpace, PetscBool *), (sp, tensor));
2994: PetscFunctionReturn(PETSC_SUCCESS);
2995: }
2997: /*@
2998: PetscDualSpaceLagrangeSetTensor - Set the tensor nature of the dual space
3000: Not Collective
3002: Input Parameters:
3003: + sp - The `PetscDualSpace`
3004: - tensor - Whether the dual space has tensor layout (vs. simplicial)
3006: Level: intermediate
3008: .seealso: `PETSCDUALSPACELAGRANGE`, `PetscDualSpace`, `PetscDualSpaceLagrangeGetTensor()`, `PetscDualSpaceCreate()`
3009: @*/
3010: PetscErrorCode PetscDualSpaceLagrangeSetTensor(PetscDualSpace sp, PetscBool tensor)
3011: {
3012: PetscFunctionBegin;
3014: PetscTryMethod(sp, "PetscDualSpaceLagrangeSetTensor_C", (PetscDualSpace, PetscBool), (sp, tensor));
3015: PetscFunctionReturn(PETSC_SUCCESS);
3016: }
3018: /*@
3019: PetscDualSpaceLagrangeGetTrimmed - Get the trimmed nature of the dual space
3021: Not Collective
3023: Input Parameter:
3024: . sp - The `PetscDualSpace`
3026: Output Parameter:
3027: . 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)
3029: Level: intermediate
3031: .seealso: `PETSCDUALSPACELAGRANGE`, `PetscDualSpace`, `PetscDualSpaceLagrangeSetTrimmed()`, `PetscDualSpaceCreate()`
3032: @*/
3033: PetscErrorCode PetscDualSpaceLagrangeGetTrimmed(PetscDualSpace sp, PetscBool *trimmed)
3034: {
3035: PetscFunctionBegin;
3037: PetscAssertPointer(trimmed, 2);
3038: PetscTryMethod(sp, "PetscDualSpaceLagrangeGetTrimmed_C", (PetscDualSpace, PetscBool *), (sp, trimmed));
3039: PetscFunctionReturn(PETSC_SUCCESS);
3040: }
3042: /*@
3043: PetscDualSpaceLagrangeSetTrimmed - Set the trimmed nature of the dual space
3045: Not Collective
3047: Input Parameters:
3048: + sp - The `PetscDualSpace`
3049: - 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)
3051: Level: intermediate
3053: .seealso: `PETSCDUALSPACELAGRANGE`, `PetscDualSpace`, `PetscDualSpaceLagrangeGetTrimmed()`, `PetscDualSpaceCreate()`
3054: @*/
3055: PetscErrorCode PetscDualSpaceLagrangeSetTrimmed(PetscDualSpace sp, PetscBool trimmed)
3056: {
3057: PetscFunctionBegin;
3059: PetscTryMethod(sp, "PetscDualSpaceLagrangeSetTrimmed_C", (PetscDualSpace, PetscBool), (sp, trimmed));
3060: PetscFunctionReturn(PETSC_SUCCESS);
3061: }
3063: /*@
3064: PetscDualSpaceLagrangeGetNodeType - Get a description of how nodes are laid out for Lagrange polynomials in this
3065: dual space
3067: Not Collective
3069: Input Parameter:
3070: . sp - The `PetscDualSpace`
3072: Output Parameters:
3073: + nodeType - The type of nodes
3074: . boundary - Whether the node type is one that includes endpoints (if nodeType is `PETSCDTNODES_GAUSSJACOBI`, nodes that
3075: include the boundary are Gauss-Lobatto-Jacobi nodes)
3076: - exponent - If nodeType is `PETSCDTNODES_GAUSSJACOBI`, indicates the exponent used for both ends of the 1D Jacobi weight function
3077: '0' is Gauss-Legendre, '-0.5' is Gauss-Chebyshev of the first type, '0.5' is Gauss-Chebyshev of the second type
3079: Level: advanced
3081: .seealso: `PETSCDUALSPACELAGRANGE`, `PetscDualSpace`, `PetscDTNodeType`, `PetscDualSpaceLagrangeSetNodeType()`
3082: @*/
3083: PetscErrorCode PetscDualSpaceLagrangeGetNodeType(PetscDualSpace sp, PeOp PetscDTNodeType *nodeType, PeOp PetscBool *boundary, PeOp PetscReal *exponent)
3084: {
3085: PetscFunctionBegin;
3087: if (nodeType) PetscAssertPointer(nodeType, 2);
3088: if (boundary) PetscAssertPointer(boundary, 3);
3089: if (exponent) PetscAssertPointer(exponent, 4);
3090: PetscTryMethod(sp, "PetscDualSpaceLagrangeGetNodeType_C", (PetscDualSpace, PetscDTNodeType *, PetscBool *, PetscReal *), (sp, nodeType, boundary, exponent));
3091: PetscFunctionReturn(PETSC_SUCCESS);
3092: }
3094: /*@
3095: PetscDualSpaceLagrangeSetNodeType - Set a description of how nodes are laid out for Lagrange polynomials in this
3096: dual space
3098: Logically Collective
3100: Input Parameters:
3101: + sp - The `PetscDualSpace`
3102: . nodeType - The type of nodes
3103: . boundary - Whether the node type is one that includes endpoints (if nodeType is `PETSCDTNODES_GAUSSJACOBI`, nodes that
3104: include the boundary are Gauss-Lobatto-Jacobi nodes)
3105: - exponent - If nodeType is `PETSCDTNODES_GAUSSJACOBI`, indicates the exponent used for both ends of the 1D Jacobi weight function
3106: '0' is Gauss-Legendre, '-0.5' is Gauss-Chebyshev of the first type, '0.5' is Gauss-Chebyshev of the second type
3108: Level: advanced
3110: .seealso: `PETSCDUALSPACELAGRANGE`, `PetscDualSpace`, `PetscDTNodeType`, `PetscDualSpaceLagrangeGetNodeType()`
3111: @*/
3112: PetscErrorCode PetscDualSpaceLagrangeSetNodeType(PetscDualSpace sp, PetscDTNodeType nodeType, PetscBool boundary, PetscReal exponent)
3113: {
3114: PetscFunctionBegin;
3116: PetscTryMethod(sp, "PetscDualSpaceLagrangeSetNodeType_C", (PetscDualSpace, PetscDTNodeType, PetscBool, PetscReal), (sp, nodeType, boundary, exponent));
3117: PetscFunctionReturn(PETSC_SUCCESS);
3118: }
3120: /*@
3121: PetscDualSpaceLagrangeGetUseMoments - Get the flag for using moment functionals
3123: Not Collective
3125: Input Parameter:
3126: . sp - The `PetscDualSpace`
3128: Output Parameter:
3129: . useMoments - Moment flag
3131: Level: advanced
3133: .seealso: `PETSCDUALSPACELAGRANGE`, `PetscDualSpace`, `PetscDualSpaceLagrangeSetUseMoments()`
3134: @*/
3135: PetscErrorCode PetscDualSpaceLagrangeGetUseMoments(PetscDualSpace sp, PetscBool *useMoments)
3136: {
3137: PetscFunctionBegin;
3139: PetscAssertPointer(useMoments, 2);
3140: PetscUseMethod(sp, "PetscDualSpaceLagrangeGetUseMoments_C", (PetscDualSpace, PetscBool *), (sp, useMoments));
3141: PetscFunctionReturn(PETSC_SUCCESS);
3142: }
3144: /*@
3145: PetscDualSpaceLagrangeSetUseMoments - Set the flag for moment functionals
3147: Logically Collective
3149: Input Parameters:
3150: + sp - The `PetscDualSpace`
3151: - useMoments - The flag for moment functionals
3153: Level: advanced
3155: .seealso: `PETSCDUALSPACELAGRANGE`, `PetscDualSpace`, `PetscDualSpaceLagrangeGetUseMoments()`
3156: @*/
3157: PetscErrorCode PetscDualSpaceLagrangeSetUseMoments(PetscDualSpace sp, PetscBool useMoments)
3158: {
3159: PetscFunctionBegin;
3161: PetscTryMethod(sp, "PetscDualSpaceLagrangeSetUseMoments_C", (PetscDualSpace, PetscBool), (sp, useMoments));
3162: PetscFunctionReturn(PETSC_SUCCESS);
3163: }
3165: /*@
3166: PetscDualSpaceLagrangeGetMomentOrder - Get the order for moment integration
3168: Not Collective
3170: Input Parameter:
3171: . sp - The `PetscDualSpace`
3173: Output Parameter:
3174: . order - Moment integration order
3176: Level: advanced
3178: .seealso: `PETSCDUALSPACELAGRANGE`, `PetscDualSpace`, `PetscDualSpaceLagrangeSetMomentOrder()`
3179: @*/
3180: PetscErrorCode PetscDualSpaceLagrangeGetMomentOrder(PetscDualSpace sp, PetscInt *order)
3181: {
3182: PetscFunctionBegin;
3184: PetscAssertPointer(order, 2);
3185: PetscUseMethod(sp, "PetscDualSpaceLagrangeGetMomentOrder_C", (PetscDualSpace, PetscInt *), (sp, order));
3186: PetscFunctionReturn(PETSC_SUCCESS);
3187: }
3189: /*@
3190: PetscDualSpaceLagrangeSetMomentOrder - Set the order for moment integration
3192: Logically Collective
3194: Input Parameters:
3195: + sp - The `PetscDualSpace`
3196: - order - The order for moment integration
3198: Level: advanced
3200: .seealso: `PETSCDUALSPACELAGRANGE`, `PetscDualSpace`, `PetscDualSpaceLagrangeGetMomentOrder()`
3201: @*/
3202: PetscErrorCode PetscDualSpaceLagrangeSetMomentOrder(PetscDualSpace sp, PetscInt order)
3203: {
3204: PetscFunctionBegin;
3206: PetscTryMethod(sp, "PetscDualSpaceLagrangeSetMomentOrder_C", (PetscDualSpace, PetscInt), (sp, order));
3207: PetscFunctionReturn(PETSC_SUCCESS);
3208: }
3210: static PetscErrorCode PetscDualSpaceInitialize_Lagrange(PetscDualSpace sp)
3211: {
3212: PetscFunctionBegin;
3213: sp->ops->destroy = PetscDualSpaceDestroy_Lagrange;
3214: sp->ops->view = PetscDualSpaceView_Lagrange;
3215: sp->ops->setfromoptions = PetscDualSpaceSetFromOptions_Lagrange;
3216: sp->ops->duplicate = PetscDualSpaceDuplicate_Lagrange;
3217: sp->ops->setup = PetscDualSpaceSetUp_Lagrange;
3218: sp->ops->createheightsubspace = NULL;
3219: sp->ops->createpointsubspace = NULL;
3220: sp->ops->getsymmetries = PetscDualSpaceGetSymmetries_Lagrange;
3221: sp->ops->apply = PetscDualSpaceApplyDefault;
3222: sp->ops->applyall = PetscDualSpaceApplyAllDefault;
3223: sp->ops->applyint = PetscDualSpaceApplyInteriorDefault;
3224: sp->ops->createalldata = PetscDualSpaceCreateAllDataDefault;
3225: sp->ops->createintdata = PetscDualSpaceCreateInteriorDataDefault;
3226: PetscFunctionReturn(PETSC_SUCCESS);
3227: }
3229: /*MC
3230: PETSCDUALSPACELAGRANGE = "lagrange" - A `PetscDualSpaceType` that encapsulates a dual space of pointwise evaluation functionals
3232: Level: intermediate
3234: Developer Note:
3235: This `PetscDualSpace` seems to manage directly trimmed and untrimmed polynomials as well as tensor and non-tensor polynomials while for `PetscSpace` there seems to
3236: be different `PetscSpaceType` for them.
3238: .seealso: `PetscDualSpace`, `PetscDualSpaceType`, `PetscDualSpaceCreate()`, `PetscDualSpaceSetType()`,
3239: `PetscDualSpaceLagrangeSetMomentOrder()`, `PetscDualSpaceLagrangeGetMomentOrder()`, `PetscDualSpaceLagrangeSetUseMoments()`, `PetscDualSpaceLagrangeGetUseMoments()`,
3240: `PetscDualSpaceLagrangeSetNodeType, PetscDualSpaceLagrangeGetNodeType, PetscDualSpaceLagrangeGetContinuity, PetscDualSpaceLagrangeSetContinuity,
3241: `PetscDualSpaceLagrangeGetTensor()`, `PetscDualSpaceLagrangeSetTensor()`, `PetscDualSpaceLagrangeGetTrimmed()`, `PetscDualSpaceLagrangeSetTrimmed()`
3242: M*/
3243: PETSC_EXTERN PetscErrorCode PetscDualSpaceCreate_Lagrange(PetscDualSpace sp)
3244: {
3245: PetscDualSpace_Lag *lag;
3247: PetscFunctionBegin;
3249: PetscCall(PetscNew(&lag));
3250: sp->data = lag;
3252: lag->tensorCell = PETSC_FALSE;
3253: lag->tensorSpace = PETSC_FALSE;
3254: lag->continuous = PETSC_TRUE;
3255: lag->numCopies = PETSC_DEFAULT;
3256: lag->numNodeSkip = PETSC_DEFAULT;
3257: lag->nodeType = PETSCDTNODES_DEFAULT;
3258: lag->useMoments = PETSC_FALSE;
3259: lag->momentOrder = 0;
3261: PetscCall(PetscDualSpaceInitialize_Lagrange(sp));
3262: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetContinuity_C", PetscDualSpaceLagrangeGetContinuity_Lagrange));
3263: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetContinuity_C", PetscDualSpaceLagrangeSetContinuity_Lagrange));
3264: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetTensor_C", PetscDualSpaceLagrangeGetTensor_Lagrange));
3265: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetTensor_C", PetscDualSpaceLagrangeSetTensor_Lagrange));
3266: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetTrimmed_C", PetscDualSpaceLagrangeGetTrimmed_Lagrange));
3267: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetTrimmed_C", PetscDualSpaceLagrangeSetTrimmed_Lagrange));
3268: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetNodeType_C", PetscDualSpaceLagrangeGetNodeType_Lagrange));
3269: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetNodeType_C", PetscDualSpaceLagrangeSetNodeType_Lagrange));
3270: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetUseMoments_C", PetscDualSpaceLagrangeGetUseMoments_Lagrange));
3271: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetUseMoments_C", PetscDualSpaceLagrangeSetUseMoments_Lagrange));
3272: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetMomentOrder_C", PetscDualSpaceLagrangeGetMomentOrder_Lagrange));
3273: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetMomentOrder_C", PetscDualSpaceLagrangeSetMomentOrder_Lagrange));
3274: PetscFunctionReturn(PETSC_SUCCESS);
3275: }