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: {
9: PetscInt refct;
10: PetscDTNodeType nodeFamily;
11: PetscReal gaussJacobiExp;
12: PetscInt nComputed;
13: PetscReal **nodesets;
14: PetscBool endpoints;
15: };
17: /* users set node families for PETSCDUALSPACELAGRANGE with just the inputs to this function, but internally we create
18: * an object that can cache the computations across multiple dual spaces */
19: static PetscErrorCode Petsc1DNodeFamilyCreate(PetscDTNodeType family, PetscReal gaussJacobiExp, PetscBool endpoints, Petsc1DNodeFamily *nf)
20: {
21: Petsc1DNodeFamily f;
25: PetscNew(&f);
26: switch (family) {
27: case PETSCDTNODES_GAUSSJACOBI:
28: case PETSCDTNODES_EQUISPACED:
29: f->nodeFamily = family;
30: break;
31: default: SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Unknown 1D node family");
32: }
33: f->endpoints = endpoints;
34: f->gaussJacobiExp = 0.;
35: if (family == PETSCDTNODES_GAUSSJACOBI) {
36: if (gaussJacobiExp <= -1.) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Gauss-Jacobi exponent must be > -1.\n");
37: f->gaussJacobiExp = gaussJacobiExp;
38: }
39: f->refct = 1;
40: *nf = f;
41: return(0);
42: }
44: static PetscErrorCode Petsc1DNodeFamilyReference(Petsc1DNodeFamily nf)
45: {
47: if (nf) nf->refct++;
48: return(0);
49: }
51: static PetscErrorCode Petsc1DNodeFamilyDestroy(Petsc1DNodeFamily *nf)
52: {
53: PetscInt i, nc;
57: if (!(*nf)) return(0);
58: if (--(*nf)->refct > 0) {
59: *nf = NULL;
60: return(0);
61: }
62: nc = (*nf)->nComputed;
63: for (i = 0; i < nc; i++) {
64: PetscFree((*nf)->nodesets[i]);
65: }
66: PetscFree((*nf)->nodesets);
67: PetscFree(*nf);
68: *nf = NULL;
69: return(0);
70: }
72: static PetscErrorCode Petsc1DNodeFamilyGetNodeSets(Petsc1DNodeFamily f, PetscInt degree, PetscReal ***nodesets)
73: {
74: PetscInt nc;
78: nc = f->nComputed;
79: if (degree >= nc) {
80: PetscInt i, j;
81: PetscReal **new_nodesets;
82: PetscReal *w;
84: PetscMalloc1(degree + 1, &new_nodesets);
85: PetscArraycpy(new_nodesets, f->nodesets, nc);
86: PetscFree(f->nodesets);
87: f->nodesets = new_nodesets;
88: PetscMalloc1(degree + 1, &w);
89: for (i = nc; i < degree + 1; i++) {
90: PetscMalloc1(i + 1, &(f->nodesets[i]));
91: if (!i) {
92: f->nodesets[i][0] = 0.5;
93: } else {
94: switch (f->nodeFamily) {
95: case PETSCDTNODES_EQUISPACED:
96: if (f->endpoints) {
97: for (j = 0; j <= i; j++) f->nodesets[i][j] = (PetscReal) j / (PetscReal) i;
98: } else {
99: /* these nodes are at the centroids of the small simplices created by the equispaced nodes that include
100: * the endpoints */
101: for (j = 0; j <= i; j++) f->nodesets[i][j] = ((PetscReal) j + 0.5) / ((PetscReal) i + 1.);
102: }
103: break;
104: case PETSCDTNODES_GAUSSJACOBI:
105: if (f->endpoints) {
106: PetscDTGaussLobattoJacobiQuadrature(i + 1, 0., 1., f->gaussJacobiExp, f->gaussJacobiExp, f->nodesets[i], w);
107: } else {
108: PetscDTGaussJacobiQuadrature(i + 1, 0., 1., f->gaussJacobiExp, f->gaussJacobiExp, f->nodesets[i], w);
109: }
110: break;
111: default: SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Unknown 1D node family");
112: }
113: }
114: }
115: PetscFree(w);
116: f->nComputed = degree + 1;
117: }
118: *nodesets = f->nodesets;
119: return(0);
120: }
122: /* http://arxiv.org/abs/2002.09421 for details */
123: static PetscErrorCode PetscNodeRecursive_Internal(PetscInt dim, PetscInt degree, PetscReal **nodesets, PetscInt tup[], PetscReal node[])
124: {
125: PetscReal w;
126: PetscInt i, j;
130: w = 0.;
131: if (dim == 1) {
132: node[0] = nodesets[degree][tup[0]];
133: node[1] = nodesets[degree][tup[1]];
134: } else {
135: for (i = 0; i < dim + 1; i++) node[i] = 0.;
136: for (i = 0; i < dim + 1; i++) {
137: PetscReal wi = nodesets[degree][degree-tup[i]];
139: for (j = 0; j < dim+1; j++) tup[dim+1+j] = tup[j+(j>=i)];
140: PetscNodeRecursive_Internal(dim-1,degree-tup[i],nodesets,&tup[dim+1],&node[dim+1]);
141: for (j = 0; j < dim+1; j++) node[j+(j>=i)] += wi * node[dim+1+j];
142: w += wi;
143: }
144: for (i = 0; i < dim+1; i++) node[i] /= w;
145: }
146: return(0);
147: }
149: /* compute simplex nodes for the biunit simplex from the 1D node family */
150: static PetscErrorCode Petsc1DNodeFamilyComputeSimplexNodes(Petsc1DNodeFamily f, PetscInt dim, PetscInt degree, PetscReal points[])
151: {
152: PetscInt *tup;
153: PetscInt k;
154: PetscInt npoints;
155: PetscReal **nodesets = NULL;
156: PetscInt worksize;
157: PetscReal *nodework;
158: PetscInt *tupwork;
162: if (dim < 0) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Must have non-negative dimension\n");
163: if (degree < 0) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Must have non-negative degree\n");
164: if (!dim) return(0);
165: PetscCalloc1(dim+2, &tup);
166: k = 0;
167: PetscDTBinomialInt(degree + dim, dim, &npoints);
168: Petsc1DNodeFamilyGetNodeSets(f, degree, &nodesets);
169: worksize = ((dim + 2) * (dim + 3)) / 2;
170: PetscMalloc2(worksize, &nodework, worksize, &tupwork);
171: /* loop over the tuples of length dim with sum at most degree */
172: for (k = 0; k < npoints; k++) {
173: PetscInt i;
175: /* turn thm into tuples of length dim + 1 with sum equal to degree (barycentric indice) */
176: tup[0] = degree;
177: for (i = 0; i < dim; i++) {
178: tup[0] -= tup[i+1];
179: }
180: switch(f->nodeFamily) {
181: case PETSCDTNODES_EQUISPACED:
182: /* compute equispaces nodes on the unit reference triangle */
183: if (f->endpoints) {
184: for (i = 0; i < dim; i++) {
185: points[dim*k + i] = (PetscReal) tup[i+1] / (PetscReal) degree;
186: }
187: } else {
188: for (i = 0; i < dim; i++) {
189: /* these nodes are at the centroids of the small simplices created by the equispaced nodes that include
190: * the endpoints */
191: points[dim*k + i] = ((PetscReal) tup[i+1] + 1./(dim+1.)) / (PetscReal) (degree + 1.);
192: }
193: }
194: break;
195: default:
196: /* compute equispaces nodes on the barycentric reference triangle (the trace on the first dim dimensions are the
197: * unit reference triangle nodes */
198: for (i = 0; i < dim + 1; i++) tupwork[i] = tup[i];
199: PetscNodeRecursive_Internal(dim, degree, nodesets, tupwork, nodework);
200: for (i = 0; i < dim; i++) points[dim*k + i] = nodework[i + 1];
201: break;
202: }
203: PetscDualSpaceLatticePointLexicographic_Internal(dim, degree, &tup[1]);
204: }
205: /* map from unit simplex to biunit simplex */
206: for (k = 0; k < npoints * dim; k++) points[k] = points[k] * 2. - 1.;
207: PetscFree2(nodework, tupwork);
208: PetscFree(tup);
209: return(0);
210: }
212: /* 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
213: * on that mesh point, we have to be careful about getting/adding everything in the right place.
214: *
215: * With nodal dofs like PETSCDUALSPACELAGRANGE makes, the general approach to calculate the value of dofs associate
216: * with a node A is
217: * - transform the node locations x(A) by the map that takes the mesh point to its reorientation, x' = phi(x(A))
218: * - figure out which node was originally at the location of the transformed point, A' = idx(x')
219: * - if the dofs are not scalars, figure out how to represent the transformed dofs in terms of the basis
220: * of dofs at A' (using pushforward/pullback rules)
221: *
222: * The one sticky point with this approach is the "A' = idx(x')" step: trying to go from real valued coordinates
223: * back to indices. I don't want to rely on floating point tolerances. Additionally, PETSCDUALSPACELAGRANGE may
224: * eventually support quasi-Lagrangian dofs, which could involve quadrature at multiple points, so the location "x(A)"
225: * would be ambiguous.
226: *
227: * So each dof gets an integer value coordinate (nodeIdx in the structure below). The choice of integer coordinates
228: * is somewhat arbitrary, as long as all of the relevant symmetries of the mesh point correspond to *permutations* of
229: * the integer coordinates, which do not depend on numerical precision.
230: *
231: * So
232: *
233: * - DMPlexGetTransitiveClosure_Internal() tells me how an orientation turns into a permutation of the vertices of a
234: * mesh point
235: * - The permutation of the vertices, and the nodeIdx values assigned to them, tells what permutation in index space
236: * is associated with the orientation
237: * - I uses that permutation to get xi' = phi(xi(A)), the integer coordinate of the transformed dof
238: * - I can without numerical issues compute A' = idx(xi')
239: *
240: * Here are some examples of how the process works
241: *
242: * - With a triangle:
243: *
244: * The triangle has the following integer coordinates for vertices, taken from the barycentric triangle
245: *
246: * closure order 2
247: * nodeIdx (0,0,1)
248: * \
249: * +
250: * |\
251: * | \
252: * | \
253: * | \ closure order 1
254: * | \ / nodeIdx (0,1,0)
255: * +-----+
256: * \
257: * closure order 0
258: * nodeIdx (1,0,0)
259: *
260: * If I do DMPlexGetTransitiveClosure_Internal() with orientation 1, the vertices would appear
261: * in the order (1, 2, 0)
262: *
263: * If I list the nodeIdx of each vertex in closure order for orientation 0 (0, 1, 2) and orientation 1 (1, 2, 0), I
264: * see
265: *
266: * orientation 0 | orientation 1
267: *
268: * [0] (1,0,0) [1] (0,1,0)
269: * [1] (0,1,0) [2] (0,0,1)
270: * [2] (0,0,1) [0] (1,0,0)
271: * A B
272: *
273: * In other words, B is the result of a row permutation of A. But, there is also
274: * a column permutation that accomplishes the same result, (2,0,1).
275: *
276: * So if a dof has nodeIdx coordinate (a,b,c), after the transformation its nodeIdx coordinate
277: * is (c,a,b), and the transformed degree of freedom will be a linear combination of dofs
278: * that originally had coordinate (c,a,b).
279: *
280: * - With a quadrilateral:
281: *
282: * The quadrilateral has the following integer coordinates for vertices, taken from concatenating barycentric
283: * coordinates for two segments:
284: *
285: * closure order 3 closure order 2
286: * nodeIdx (1,0,0,1) nodeIdx (0,1,0,1)
287: * \ /
288: * +----+
289: * | |
290: * | |
291: * +----+
292: * / \
293: * closure order 0 closure order 1
294: * nodeIdx (1,0,1,0) nodeIdx (0,1,1,0)
295: *
296: * If I do DMPlexGetTransitiveClosure_Internal() with orientation 1, the vertices would appear
297: * in the order (1, 2, 3, 0)
298: *
299: * If I list the nodeIdx of each vertex in closure order for orientation 0 (0, 1, 2, 3) and
300: * orientation 1 (1, 2, 3, 0), I see
301: *
302: * orientation 0 | orientation 1
303: *
304: * [0] (1,0,1,0) [1] (0,1,1,0)
305: * [1] (0,1,1,0) [2] (0,1,0,1)
306: * [2] (0,1,0,1) [3] (1,0,0,1)
307: * [3] (1,0,0,1) [0] (1,0,1,0)
308: * A B
309: *
310: * The column permutation that accomplishes the same result is (3,2,0,1).
311: *
312: * So if a dof has nodeIdx coordinate (a,b,c,d), after the transformation its nodeIdx coordinate
313: * is (d,c,a,b), and the transformed degree of freedom will be a linear combination of dofs
314: * that originally had coordinate (d,c,a,b).
315: *
316: * Previously PETSCDUALSPACELAGRANGE had hardcoded symmetries for the triangle and quadrilateral,
317: * but this approach will work for any polytope, such as the wedge (triangular prism).
318: */
319: struct _n_PetscLagNodeIndices
320: {
321: PetscInt refct;
322: PetscInt nodeIdxDim;
323: PetscInt nodeVecDim;
324: PetscInt nNodes;
325: PetscInt *nodeIdx; /* for each node an index of size nodeIdxDim */
326: PetscReal *nodeVec; /* for each node a vector of size nodeVecDim */
327: PetscInt *perm; /* if these are vertices, perm takes DMPlex point index to closure order;
328: if these are nodes, perm lists nodes in index revlex order */
329: };
331: /* this is just here so I can access the values in tests/ex1.c outside the library */
332: PetscErrorCode PetscLagNodeIndicesGetData_Internal(PetscLagNodeIndices ni, PetscInt *nodeIdxDim, PetscInt *nodeVecDim, PetscInt *nNodes, const PetscInt *nodeIdx[], const PetscReal *nodeVec[])
333: {
335: *nodeIdxDim = ni->nodeIdxDim;
336: *nodeVecDim = ni->nodeVecDim;
337: *nNodes = ni->nNodes;
338: *nodeIdx = ni->nodeIdx;
339: *nodeVec = ni->nodeVec;
340: return(0);
341: }
343: static PetscErrorCode PetscLagNodeIndicesReference(PetscLagNodeIndices ni)
344: {
346: if (ni) ni->refct++;
347: return(0);
348: }
350: static PetscErrorCode PetscLagNodeIndicesDuplicate(PetscLagNodeIndices ni, PetscLagNodeIndices *niNew)
351: {
355: PetscNew(niNew);
356: (*niNew)->refct = 1;
357: (*niNew)->nodeIdxDim = ni->nodeIdxDim;
358: (*niNew)->nodeVecDim = ni->nodeVecDim;
359: (*niNew)->nNodes = ni->nNodes;
360: PetscMalloc1(ni->nNodes * ni->nodeIdxDim, &((*niNew)->nodeIdx));
361: PetscArraycpy((*niNew)->nodeIdx, ni->nodeIdx, ni->nNodes * ni->nodeIdxDim);
362: PetscMalloc1(ni->nNodes * ni->nodeVecDim, &((*niNew)->nodeVec));
363: PetscArraycpy((*niNew)->nodeVec, ni->nodeVec, ni->nNodes * ni->nodeVecDim);
364: (*niNew)->perm = NULL;
365: return(0);
366: }
368: static PetscErrorCode PetscLagNodeIndicesDestroy(PetscLagNodeIndices *ni)
369: {
373: if (!(*ni)) return(0);
374: if (--(*ni)->refct > 0) {
375: *ni = NULL;
376: return(0);
377: }
378: PetscFree((*ni)->nodeIdx);
379: PetscFree((*ni)->nodeVec);
380: PetscFree((*ni)->perm);
381: PetscFree(*ni);
382: *ni = NULL;
383: return(0);
384: }
386: /* The vertices are given nodeIdx coordinates (e.g. the corners of the barycentric triangle). Those coordinates are
387: * in some other order, and to understand the effect of different symmetries, we need them to be in closure order.
388: *
389: * If sortIdx is PETSC_FALSE, the coordinates are already in revlex order, otherwise we must sort them
390: * to that order before we do the real work of this function, which is
391: *
392: * - mark the vertices in closure order
393: * - sort them in revlex order
394: * - use the resulting permutation to list the vertex coordinates in closure order
395: */
396: static PetscErrorCode PetscLagNodeIndicesComputeVertexOrder(DM dm, PetscLagNodeIndices ni, PetscBool sortIdx)
397: {
398: PetscInt v, w, vStart, vEnd, c, d;
399: PetscInt nVerts;
400: PetscInt closureSize = 0;
401: PetscInt *closure = NULL;
402: PetscInt *closureOrder;
403: PetscInt *invClosureOrder;
404: PetscInt *revlexOrder;
405: PetscInt *newNodeIdx;
406: PetscInt dim;
407: Vec coordVec;
408: const PetscScalar *coords;
409: PetscErrorCode ierr;
412: DMGetDimension(dm, &dim);
413: DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);
414: nVerts = vEnd - vStart;
415: PetscMalloc1(nVerts, &closureOrder);
416: PetscMalloc1(nVerts, &invClosureOrder);
417: PetscMalloc1(nVerts, &revlexOrder);
418: if (sortIdx) { /* bubble sort nodeIdx into revlex order */
419: PetscInt nodeIdxDim = ni->nodeIdxDim;
420: PetscInt *idxOrder;
422: PetscMalloc1(nVerts * nodeIdxDim, &newNodeIdx);
423: PetscMalloc1(nVerts, &idxOrder);
424: for (v = 0; v < nVerts; v++) idxOrder[v] = v;
425: for (v = 0; v < nVerts; v++) {
426: for (w = v + 1; w < nVerts; w++) {
427: const PetscInt *iv = &(ni->nodeIdx[idxOrder[v] * nodeIdxDim]);
428: const PetscInt *iw = &(ni->nodeIdx[idxOrder[w] * nodeIdxDim]);
429: PetscInt diff = 0;
431: for (d = nodeIdxDim - 1; d >= 0; d--) if ((diff = (iv[d] - iw[d]))) break;
432: if (diff > 0) {
433: PetscInt swap = idxOrder[v];
435: idxOrder[v] = idxOrder[w];
436: idxOrder[w] = swap;
437: }
438: }
439: }
440: for (v = 0; v < nVerts; v++) {
441: for (d = 0; d < nodeIdxDim; d++) {
442: newNodeIdx[v * ni->nodeIdxDim + d] = ni->nodeIdx[idxOrder[v] * nodeIdxDim + d];
443: }
444: }
445: PetscFree(ni->nodeIdx);
446: ni->nodeIdx = newNodeIdx;
447: newNodeIdx = NULL;
448: PetscFree(idxOrder);
449: }
450: DMPlexGetTransitiveClosure(dm, 0, PETSC_TRUE, &closureSize, &closure);
451: c = closureSize - nVerts;
452: for (v = 0; v < nVerts; v++) closureOrder[v] = closure[2 * (c + v)] - vStart;
453: for (v = 0; v < nVerts; v++) invClosureOrder[closureOrder[v]] = v;
454: DMPlexRestoreTransitiveClosure(dm, 0, PETSC_TRUE, &closureSize, &closure);
455: DMGetCoordinatesLocal(dm, &coordVec);
456: VecGetArrayRead(coordVec, &coords);
457: /* bubble sort closure vertices by coordinates in revlex order */
458: for (v = 0; v < nVerts; v++) revlexOrder[v] = v;
459: for (v = 0; v < nVerts; v++) {
460: for (w = v + 1; w < nVerts; w++) {
461: const PetscScalar *cv = &coords[closureOrder[revlexOrder[v]] * dim];
462: const PetscScalar *cw = &coords[closureOrder[revlexOrder[w]] * dim];
463: PetscReal diff = 0;
465: for (d = dim - 1; d >= 0; d--) if ((diff = PetscRealPart(cv[d] - cw[d])) != 0.) break;
466: if (diff > 0.) {
467: PetscInt swap = revlexOrder[v];
469: revlexOrder[v] = revlexOrder[w];
470: revlexOrder[w] = swap;
471: }
472: }
473: }
474: VecRestoreArrayRead(coordVec, &coords);
475: PetscMalloc1(ni->nodeIdxDim * nVerts, &newNodeIdx);
476: /* reorder nodeIdx to be in closure order */
477: for (v = 0; v < nVerts; v++) {
478: for (d = 0; d < ni->nodeIdxDim; d++) {
479: newNodeIdx[revlexOrder[v] * ni->nodeIdxDim + d] = ni->nodeIdx[v * ni->nodeIdxDim + d];
480: }
481: }
482: PetscFree(ni->nodeIdx);
483: ni->nodeIdx = newNodeIdx;
484: ni->perm = invClosureOrder;
485: PetscFree(revlexOrder);
486: PetscFree(closureOrder);
487: return(0);
488: }
490: /* the coordinates of the simplex vertices are the corners of the barycentric simplex.
491: * When we stack them on top of each other in revlex order, they look like the identity matrix */
492: static PetscErrorCode PetscLagNodeIndicesCreateSimplexVertices(DM dm, PetscLagNodeIndices *nodeIndices)
493: {
494: PetscLagNodeIndices ni;
495: PetscInt dim, d;
500: PetscNew(&ni);
501: DMGetDimension(dm, &dim);
502: ni->nodeIdxDim = dim + 1;
503: ni->nodeVecDim = 0;
504: ni->nNodes = dim + 1;
505: ni->refct = 1;
506: PetscCalloc1((dim + 1)*(dim + 1), &(ni->nodeIdx));
507: for (d = 0; d < dim + 1; d++) ni->nodeIdx[d*(dim + 2)] = 1;
508: PetscLagNodeIndicesComputeVertexOrder(dm, ni, PETSC_FALSE);
509: *nodeIndices = ni;
510: return(0);
511: }
513: /* A polytope that is a tensor product of a facet and a segment.
514: * We take whatever coordinate system was being used for the facet
515: * and we concatenate the barycentric coordinates for the vertices
516: * at the end of the segment, (1,0) and (0,1), to get a coordinate
517: * system for the tensor product element */
518: static PetscErrorCode PetscLagNodeIndicesCreateTensorVertices(DM dm, PetscLagNodeIndices facetni, PetscLagNodeIndices *nodeIndices)
519: {
520: PetscLagNodeIndices ni;
521: PetscInt nodeIdxDim, subNodeIdxDim = facetni->nodeIdxDim;
522: PetscInt nVerts, nSubVerts = facetni->nNodes;
523: PetscInt dim, d, e, f, g;
528: PetscNew(&ni);
529: DMGetDimension(dm, &dim);
530: ni->nodeIdxDim = nodeIdxDim = subNodeIdxDim + 2;
531: ni->nodeVecDim = 0;
532: ni->nNodes = nVerts = 2 * nSubVerts;
533: ni->refct = 1;
534: PetscCalloc1(nodeIdxDim * nVerts, &(ni->nodeIdx));
535: for (f = 0, d = 0; d < 2; d++) {
536: for (e = 0; e < nSubVerts; e++, f++) {
537: for (g = 0; g < subNodeIdxDim; g++) {
538: ni->nodeIdx[f * nodeIdxDim + g] = facetni->nodeIdx[e * subNodeIdxDim + g];
539: }
540: ni->nodeIdx[f * nodeIdxDim + subNodeIdxDim] = (1 - d);
541: ni->nodeIdx[f * nodeIdxDim + subNodeIdxDim + 1] = d;
542: }
543: }
544: PetscLagNodeIndicesComputeVertexOrder(dm, ni, PETSC_TRUE);
545: *nodeIndices = ni;
546: return(0);
547: }
549: /* This helps us compute symmetries, and it also helps us compute coordinates for dofs that are being pushed
550: * forward from a boundary mesh point.
551: *
552: * Input:
553: *
554: * dm - the target reference cell where we want new coordinates and dof directions to be valid
555: * vert - the vertex coordinate system for the target reference cell
556: * p - the point in the target reference cell that the dofs are coming from
557: * vertp - the vertex coordinate system for p's reference cell
558: * ornt - the resulting coordinates and dof vectors will be for p under this orientation
559: * nodep - the node coordinates and dof vectors in p's reference cell
560: * formDegree - the form degree that the dofs transform as
561: *
562: * Output:
563: *
564: * pfNodeIdx - the node coordinates for p's dofs, in the dm reference cell, from the ornt perspective
565: * pfNodeVec - the node dof vectors for p's dofs, in the dm reference cell, from the ornt perspective
566: */
567: static PetscErrorCode PetscLagNodeIndicesPushForward(DM dm, PetscLagNodeIndices vert, PetscInt p, PetscLagNodeIndices vertp, PetscLagNodeIndices nodep, PetscInt ornt, PetscInt formDegree, PetscInt pfNodeIdx[], PetscReal pfNodeVec[])
568: {
569: PetscInt *closureVerts;
570: PetscInt closureSize = 0;
571: PetscInt *closure = NULL;
572: PetscInt dim, pdim, c, i, j, k, n, v, vStart, vEnd;
573: PetscInt nSubVert = vertp->nNodes;
574: PetscInt nodeIdxDim = vert->nodeIdxDim;
575: PetscInt subNodeIdxDim = vertp->nodeIdxDim;
576: PetscInt nNodes = nodep->nNodes;
577: const PetscInt *vertIdx = vert->nodeIdx;
578: const PetscInt *subVertIdx = vertp->nodeIdx;
579: const PetscInt *nodeIdx = nodep->nodeIdx;
580: const PetscReal *nodeVec = nodep->nodeVec;
581: PetscReal *J, *Jstar;
582: PetscReal detJ;
583: PetscInt depth, pdepth, Nk, pNk;
584: Vec coordVec;
585: PetscScalar *newCoords = NULL;
586: const PetscScalar *oldCoords = NULL;
587: PetscErrorCode ierr;
590: DMGetDimension(dm, &dim);
591: DMPlexGetDepth(dm, &depth);
592: DMGetCoordinatesLocal(dm, &coordVec);
593: DMPlexGetPointDepth(dm, p, &pdepth);
594: pdim = pdepth != depth ? pdepth != 0 ? pdepth : 0 : dim;
595: DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);
596: DMGetWorkArray(dm, nSubVert, MPIU_INT, &closureVerts);
597: DMPlexGetTransitiveClosure_Internal(dm, p, ornt, PETSC_TRUE, &closureSize, &closure);
598: c = closureSize - nSubVert;
599: /* we want which cell closure indices the closure of this point corresponds to */
600: for (v = 0; v < nSubVert; v++) closureVerts[v] = vert->perm[closure[2 * (c + v)] - vStart];
601: DMPlexRestoreTransitiveClosure(dm, p, PETSC_TRUE, &closureSize, &closure);
602: /* push forward indices */
603: for (i = 0; i < nodeIdxDim; i++) { /* for every component of the target index space */
604: /* check if this is a component that all vertices around this point have in common */
605: for (j = 1; j < nSubVert; j++) {
606: if (vertIdx[closureVerts[j] * nodeIdxDim + i] != vertIdx[closureVerts[0] * nodeIdxDim + i]) break;
607: }
608: if (j == nSubVert) { /* all vertices have this component in common, directly copy to output */
609: PetscInt val = vertIdx[closureVerts[0] * nodeIdxDim + i];
610: for (n = 0; n < nNodes; n++) pfNodeIdx[n * nodeIdxDim + i] = val;
611: } else {
612: PetscInt subi = -1;
613: /* there must be a component in vertp that looks the same */
614: for (k = 0; k < subNodeIdxDim; k++) {
615: for (j = 0; j < nSubVert; j++) {
616: if (vertIdx[closureVerts[j] * nodeIdxDim + i] != subVertIdx[j * subNodeIdxDim + k]) break;
617: }
618: if (j == nSubVert) {
619: subi = k;
620: break;
621: }
622: }
623: if (subi < 0) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Did not find matching coordinate\n");
624: /* that component in the vertp system becomes component i in the vert system for each dof */
625: for (n = 0; n < nNodes; n++) pfNodeIdx[n * nodeIdxDim + i] = nodeIdx[n * subNodeIdxDim + subi];
626: }
627: }
628: /* push forward vectors */
629: DMGetWorkArray(dm, dim * dim, MPIU_REAL, &J);
630: if (ornt != 0) { /* temporarily change the coordinate vector so
631: DMPlexComputeCellGeometryAffineFEM gives us the Jacobian we want */
632: PetscInt closureSize2 = 0;
633: PetscInt *closure2 = NULL;
635: DMPlexGetTransitiveClosure_Internal(dm, p, 0, PETSC_TRUE, &closureSize2, &closure2);
636: PetscMalloc1(dim * nSubVert, &newCoords);
637: VecGetArrayRead(coordVec, &oldCoords);
638: for (v = 0; v < nSubVert; v++) {
639: PetscInt d;
640: for (d = 0; d < dim; d++) {
641: newCoords[(closure2[2 * (c + v)] - vStart) * dim + d] = oldCoords[closureVerts[v] * dim + d];
642: }
643: }
644: VecRestoreArrayRead(coordVec, &oldCoords);
645: DMPlexRestoreTransitiveClosure(dm, p, PETSC_TRUE, &closureSize2, &closure2);
646: VecPlaceArray(coordVec, newCoords);
647: }
648: DMPlexComputeCellGeometryAffineFEM(dm, p, NULL, J, NULL, &detJ);
649: if (ornt != 0) {
650: VecResetArray(coordVec);
651: PetscFree(newCoords);
652: }
653: DMRestoreWorkArray(dm, nSubVert, MPIU_INT, &closureVerts);
654: /* compactify */
655: for (i = 0; i < dim; i++) for (j = 0; j < pdim; j++) J[i * pdim + j] = J[i * dim + j];
656: /* We have the Jacobian mapping the point's reference cell to this reference cell:
657: * pulling back a function to the point and applying the dof is what we want,
658: * so we get the pullback matrix and multiply the dof by that matrix on the right */
659: PetscDTBinomialInt(dim, PetscAbsInt(formDegree), &Nk);
660: PetscDTBinomialInt(pdim, PetscAbsInt(formDegree), &pNk);
661: DMGetWorkArray(dm, pNk * Nk, MPIU_REAL, &Jstar);
662: PetscDTAltVPullbackMatrix(pdim, dim, J, formDegree, Jstar);
663: for (n = 0; n < nNodes; n++) {
664: for (i = 0; i < Nk; i++) {
665: PetscReal val = 0.;
666: for (j = 0; j < pNk; j++) val += nodeVec[n * pNk + j] * Jstar[j * Nk + i];
667: pfNodeVec[n * Nk + i] = val;
668: }
669: }
670: DMRestoreWorkArray(dm, pNk * Nk, MPIU_REAL, &Jstar);
671: DMRestoreWorkArray(dm, dim * dim, MPIU_REAL, &J);
672: return(0);
673: }
675: /* given to sets of nodes, take the tensor product, where the product of the dof indices is concatenation and the
676: * product of the dof vectors is the wedge product */
677: static PetscErrorCode PetscLagNodeIndicesTensor(PetscLagNodeIndices tracei, PetscInt dimT, PetscInt kT, PetscLagNodeIndices fiberi, PetscInt dimF, PetscInt kF, PetscLagNodeIndices *nodeIndices)
678: {
679: PetscInt dim = dimT + dimF;
680: PetscInt nodeIdxDim, nNodes;
681: PetscInt formDegree = kT + kF;
682: PetscInt Nk, NkT, NkF;
683: PetscInt MkT, MkF;
684: PetscLagNodeIndices ni;
685: PetscInt i, j, l;
686: PetscReal *projF, *projT;
687: PetscReal *projFstar, *projTstar;
688: PetscReal *workF, *workF2, *workT, *workT2, *work, *work2;
689: PetscReal *wedgeMat;
690: PetscReal sign;
694: PetscDTBinomialInt(dim, PetscAbsInt(formDegree), &Nk);
695: PetscDTBinomialInt(dimT, PetscAbsInt(kT), &NkT);
696: PetscDTBinomialInt(dimF, PetscAbsInt(kF), &NkF);
697: PetscDTBinomialInt(dim, PetscAbsInt(kT), &MkT);
698: PetscDTBinomialInt(dim, PetscAbsInt(kF), &MkF);
699: PetscNew(&ni);
700: ni->nodeIdxDim = nodeIdxDim = tracei->nodeIdxDim + fiberi->nodeIdxDim;
701: ni->nodeVecDim = Nk;
702: ni->nNodes = nNodes = tracei->nNodes * fiberi->nNodes;
703: ni->refct = 1;
704: PetscMalloc1(nNodes * nodeIdxDim, &(ni->nodeIdx));
705: /* first concatenate the indices */
706: for (l = 0, j = 0; j < fiberi->nNodes; j++) {
707: for (i = 0; i < tracei->nNodes; i++, l++) {
708: PetscInt m, n = 0;
710: for (m = 0; m < tracei->nodeIdxDim; m++) ni->nodeIdx[l * nodeIdxDim + n++] = tracei->nodeIdx[i * tracei->nodeIdxDim + m];
711: for (m = 0; m < fiberi->nodeIdxDim; m++) ni->nodeIdx[l * nodeIdxDim + n++] = fiberi->nodeIdx[j * fiberi->nodeIdxDim + m];
712: }
713: }
715: /* now wedge together the push-forward vectors */
716: PetscMalloc1(nNodes * Nk, &(ni->nodeVec));
717: PetscCalloc2(dimT*dim, &projT, dimF*dim, &projF);
718: for (i = 0; i < dimT; i++) projT[i * (dim + 1)] = 1.;
719: for (i = 0; i < dimF; i++) projF[i * (dim + dimT + 1) + dimT] = 1.;
720: PetscMalloc2(MkT*NkT, &projTstar, MkF*NkF, &projFstar);
721: PetscDTAltVPullbackMatrix(dim, dimT, projT, kT, projTstar);
722: PetscDTAltVPullbackMatrix(dim, dimF, projF, kF, projFstar);
723: PetscMalloc6(MkT, &workT, MkT, &workT2, MkF, &workF, MkF, &workF2, Nk, &work, Nk, &work2);
724: PetscMalloc1(Nk * MkT, &wedgeMat);
725: sign = (PetscAbsInt(kT * kF) & 1) ? -1. : 1.;
726: for (l = 0, j = 0; j < fiberi->nNodes; j++) {
727: PetscInt d, e;
729: /* push forward fiber k-form */
730: for (d = 0; d < MkF; d++) {
731: PetscReal val = 0.;
732: for (e = 0; e < NkF; e++) val += projFstar[d * NkF + e] * fiberi->nodeVec[j * NkF + e];
733: workF[d] = val;
734: }
735: /* Hodge star to proper form if necessary */
736: if (kF < 0) {
737: for (d = 0; d < MkF; d++) workF2[d] = workF[d];
738: PetscDTAltVStar(dim, PetscAbsInt(kF), 1, workF2, workF);
739: }
740: /* Compute the matrix that wedges this form with one of the trace k-form */
741: PetscDTAltVWedgeMatrix(dim, PetscAbsInt(kF), PetscAbsInt(kT), workF, wedgeMat);
742: for (i = 0; i < tracei->nNodes; i++, l++) {
743: /* push forward trace k-form */
744: for (d = 0; d < MkT; d++) {
745: PetscReal val = 0.;
746: for (e = 0; e < NkT; e++) val += projTstar[d * NkT + e] * tracei->nodeVec[i * NkT + e];
747: workT[d] = val;
748: }
749: /* Hodge star to proper form if necessary */
750: if (kT < 0) {
751: for (d = 0; d < MkT; d++) workT2[d] = workT[d];
752: PetscDTAltVStar(dim, PetscAbsInt(kT), 1, workT2, workT);
753: }
754: /* compute the wedge product of the push-forward trace form and firer forms */
755: for (d = 0; d < Nk; d++) {
756: PetscReal val = 0.;
757: for (e = 0; e < MkT; e++) val += wedgeMat[d * MkT + e] * workT[e];
758: work[d] = val;
759: }
760: /* inverse Hodge star from proper form if necessary */
761: if (formDegree < 0) {
762: for (d = 0; d < Nk; d++) work2[d] = work[d];
763: PetscDTAltVStar(dim, PetscAbsInt(formDegree), -1, work2, work);
764: }
765: /* insert into the array (adjusting for sign) */
766: for (d = 0; d < Nk; d++) ni->nodeVec[l * Nk + d] = sign * work[d];
767: }
768: }
769: PetscFree(wedgeMat);
770: PetscFree6(workT, workT2, workF, workF2, work, work2);
771: PetscFree2(projTstar, projFstar);
772: PetscFree2(projT, projF);
773: *nodeIndices = ni;
774: return(0);
775: }
777: /* simple union of two sets of nodes */
778: static PetscErrorCode PetscLagNodeIndicesMerge(PetscLagNodeIndices niA, PetscLagNodeIndices niB, PetscLagNodeIndices *nodeIndices)
779: {
780: PetscLagNodeIndices ni;
781: PetscInt nodeIdxDim, nodeVecDim, nNodes;
782: PetscErrorCode ierr;
785: PetscNew(&ni);
786: ni->nodeIdxDim = nodeIdxDim = niA->nodeIdxDim;
787: if (niB->nodeIdxDim != nodeIdxDim) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Cannot merge PetscLagNodeIndices with different nodeIdxDim");
788: ni->nodeVecDim = nodeVecDim = niA->nodeVecDim;
789: if (niB->nodeVecDim != nodeVecDim) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Cannot merge PetscLagNodeIndices with different nodeVecDim");
790: ni->nNodes = nNodes = niA->nNodes + niB->nNodes;
791: ni->refct = 1;
792: PetscMalloc1(nNodes * nodeIdxDim, &(ni->nodeIdx));
793: PetscMalloc1(nNodes * nodeVecDim, &(ni->nodeVec));
794: PetscArraycpy(ni->nodeIdx, niA->nodeIdx, niA->nNodes * nodeIdxDim);
795: PetscArraycpy(ni->nodeVec, niA->nodeVec, niA->nNodes * nodeVecDim);
796: PetscArraycpy(&(ni->nodeIdx[niA->nNodes * nodeIdxDim]), niB->nodeIdx, niB->nNodes * nodeIdxDim);
797: PetscArraycpy(&(ni->nodeVec[niA->nNodes * nodeVecDim]), niB->nodeVec, niB->nNodes * nodeVecDim);
798: *nodeIndices = ni;
799: return(0);
800: }
802: #define PETSCTUPINTCOMPREVLEX(N) \
803: static int PetscTupIntCompRevlex_##N(const void *a, const void *b) \
804: { \
805: const PetscInt *A = (const PetscInt *) a; \
806: const PetscInt *B = (const PetscInt *) b; \
807: int i; \
808: PetscInt diff = 0; \
809: for (i = 0; i < N; i++) { \
810: diff = A[N - i] - B[N - i]; \
811: if (diff) break; \
812: } \
813: return (diff <= 0) ? (diff < 0) ? -1 : 0 : 1; \
814: }
816: PETSCTUPINTCOMPREVLEX(3)
817: PETSCTUPINTCOMPREVLEX(4)
818: PETSCTUPINTCOMPREVLEX(5)
819: PETSCTUPINTCOMPREVLEX(6)
820: PETSCTUPINTCOMPREVLEX(7)
822: static int PetscTupIntCompRevlex_N(const void *a, const void *b)
823: {
824: const PetscInt *A = (const PetscInt *) a;
825: const PetscInt *B = (const PetscInt *) b;
826: int i;
827: int N = A[0];
828: PetscInt diff = 0;
829: for (i = 0; i < N; i++) {
830: diff = A[N - i] - B[N - i];
831: if (diff) break;
832: }
833: return (diff <= 0) ? (diff < 0) ? -1 : 0 : 1;
834: }
836: /* The nodes are not necessarily in revlex order wrt nodeIdx: get the permutation
837: * that puts them in that order */
838: static PetscErrorCode PetscLagNodeIndicesGetPermutation(PetscLagNodeIndices ni, PetscInt *perm[])
839: {
843: if (!(ni->perm)) {
844: PetscInt *sorter;
845: PetscInt m = ni->nNodes;
846: PetscInt nodeIdxDim = ni->nodeIdxDim;
847: PetscInt i, j, k, l;
848: PetscInt *prm;
849: int (*comp) (const void *, const void *);
851: PetscMalloc1((nodeIdxDim + 2) * m, &sorter);
852: for (k = 0, l = 0, i = 0; i < m; i++) {
853: sorter[k++] = nodeIdxDim + 1;
854: sorter[k++] = i;
855: for (j = 0; j < nodeIdxDim; j++) sorter[k++] = ni->nodeIdx[l++];
856: }
857: switch (nodeIdxDim) {
858: case 2:
859: comp = PetscTupIntCompRevlex_3;
860: break;
861: case 3:
862: comp = PetscTupIntCompRevlex_4;
863: break;
864: case 4:
865: comp = PetscTupIntCompRevlex_5;
866: break;
867: case 5:
868: comp = PetscTupIntCompRevlex_6;
869: break;
870: case 6:
871: comp = PetscTupIntCompRevlex_7;
872: break;
873: default:
874: comp = PetscTupIntCompRevlex_N;
875: break;
876: }
877: qsort(sorter, m, (nodeIdxDim + 2) * sizeof(PetscInt), comp);
878: PetscMalloc1(m, &prm);
879: for (i = 0; i < m; i++) prm[i] = sorter[(nodeIdxDim + 2) * i + 1];
880: ni->perm = prm;
881: PetscFree(sorter);
882: }
883: *perm = ni->perm;
884: return(0);
885: }
887: static PetscErrorCode PetscDualSpaceDestroy_Lagrange(PetscDualSpace sp)
888: {
889: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *) sp->data;
890: PetscErrorCode ierr;
893: if (lag->symperms) {
894: PetscInt **selfSyms = lag->symperms[0];
896: if (selfSyms) {
897: PetscInt i, **allocated = &selfSyms[-lag->selfSymOff];
899: for (i = 0; i < lag->numSelfSym; i++) {
900: PetscFree(allocated[i]);
901: }
902: PetscFree(allocated);
903: }
904: PetscFree(lag->symperms);
905: }
906: if (lag->symflips) {
907: PetscScalar **selfSyms = lag->symflips[0];
909: if (selfSyms) {
910: PetscInt i;
911: PetscScalar **allocated = &selfSyms[-lag->selfSymOff];
913: for (i = 0; i < lag->numSelfSym; i++) {
914: PetscFree(allocated[i]);
915: }
916: PetscFree(allocated);
917: }
918: PetscFree(lag->symflips);
919: }
920: Petsc1DNodeFamilyDestroy(&(lag->nodeFamily));
921: PetscLagNodeIndicesDestroy(&(lag->vertIndices));
922: PetscLagNodeIndicesDestroy(&(lag->intNodeIndices));
923: PetscLagNodeIndicesDestroy(&(lag->allNodeIndices));
924: PetscFree(lag);
925: PetscObjectComposeFunction((PetscObject) sp, "PetscDualSpaceLagrangeGetContinuity_C", NULL);
926: PetscObjectComposeFunction((PetscObject) sp, "PetscDualSpaceLagrangeSetContinuity_C", NULL);
927: PetscObjectComposeFunction((PetscObject) sp, "PetscDualSpaceLagrangeGetTensor_C", NULL);
928: PetscObjectComposeFunction((PetscObject) sp, "PetscDualSpaceLagrangeSetTensor_C", NULL);
929: PetscObjectComposeFunction((PetscObject) sp, "PetscDualSpaceLagrangeGetTrimmed_C", NULL);
930: PetscObjectComposeFunction((PetscObject) sp, "PetscDualSpaceLagrangeSetTrimmed_C", NULL);
931: PetscObjectComposeFunction((PetscObject) sp, "PetscDualSpaceLagrangeGetNodeType_C", NULL);
932: PetscObjectComposeFunction((PetscObject) sp, "PetscDualSpaceLagrangeSetNodeType_C", NULL);
933: PetscObjectComposeFunction((PetscObject) sp, "PetscDualSpaceLagrangeGetUseMoments_C", NULL);
934: PetscObjectComposeFunction((PetscObject) sp, "PetscDualSpaceLagrangeSetUseMoments_C", NULL);
935: PetscObjectComposeFunction((PetscObject) sp, "PetscDualSpaceLagrangeGetMomentOrder_C", NULL);
936: PetscObjectComposeFunction((PetscObject) sp, "PetscDualSpaceLagrangeSetMomentOrder_C", NULL);
937: return(0);
938: }
940: static PetscErrorCode PetscDualSpaceLagrangeView_Ascii(PetscDualSpace sp, PetscViewer viewer)
941: {
942: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *) sp->data;
943: PetscErrorCode ierr;
946: PetscViewerASCIIPrintf(viewer, "%s %s%sLagrange dual space\n", lag->continuous ? "Continuous" : "Discontinuous", lag->tensorSpace ? "tensor " : "", lag->trimmed ? "trimmed " : "");
947: return(0);
948: }
950: static PetscErrorCode PetscDualSpaceView_Lagrange(PetscDualSpace sp, PetscViewer viewer)
951: {
952: PetscBool iascii;
958: PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERASCII, &iascii);
959: if (iascii) {PetscDualSpaceLagrangeView_Ascii(sp, viewer);}
960: return(0);
961: }
963: static PetscErrorCode PetscDualSpaceSetFromOptions_Lagrange(PetscOptionItems *PetscOptionsObject,PetscDualSpace sp)
964: {
965: PetscBool continuous, tensor, trimmed, flg, flg2, flg3;
966: PetscDTNodeType nodeType;
967: PetscReal nodeExponent;
968: PetscInt momentOrder;
969: PetscBool nodeEndpoints, useMoments;
973: PetscDualSpaceLagrangeGetContinuity(sp, &continuous);
974: PetscDualSpaceLagrangeGetTensor(sp, &tensor);
975: PetscDualSpaceLagrangeGetTrimmed(sp, &trimmed);
976: PetscDualSpaceLagrangeGetNodeType(sp, &nodeType, &nodeEndpoints, &nodeExponent);
977: if (nodeType == PETSCDTNODES_DEFAULT) nodeType = PETSCDTNODES_GAUSSJACOBI;
978: PetscDualSpaceLagrangeGetUseMoments(sp, &useMoments);
979: PetscDualSpaceLagrangeGetMomentOrder(sp, &momentOrder);
980: PetscOptionsHead(PetscOptionsObject,"PetscDualSpace Lagrange Options");
981: PetscOptionsBool("-petscdualspace_lagrange_continuity", "Flag for continuous element", "PetscDualSpaceLagrangeSetContinuity", continuous, &continuous, &flg);
982: if (flg) {PetscDualSpaceLagrangeSetContinuity(sp, continuous);}
983: PetscOptionsBool("-petscdualspace_lagrange_tensor", "Flag for tensor dual space", "PetscDualSpaceLagrangeSetTensor", tensor, &tensor, &flg);
984: if (flg) {PetscDualSpaceLagrangeSetTensor(sp, tensor);}
985: PetscOptionsBool("-petscdualspace_lagrange_trimmed", "Flag for trimmed dual space", "PetscDualSpaceLagrangeSetTrimmed", trimmed, &trimmed, &flg);
986: if (flg) {PetscDualSpaceLagrangeSetTrimmed(sp, trimmed);}
987: PetscOptionsEnum("-petscdualspace_lagrange_node_type", "Lagrange node location type", "PetscDualSpaceLagrangeSetNodeType", PetscDTNodeTypes, (PetscEnum)nodeType, (PetscEnum *)&nodeType, &flg);
988: PetscOptionsBool("-petscdualspace_lagrange_node_endpoints", "Flag for nodes that include endpoints", "PetscDualSpaceLagrangeSetNodeType", nodeEndpoints, &nodeEndpoints, &flg2);
989: flg3 = PETSC_FALSE;
990: if (nodeType == PETSCDTNODES_GAUSSJACOBI) {
991: PetscOptionsReal("-petscdualspace_lagrange_node_exponent", "Gauss-Jacobi weight function exponent", "PetscDualSpaceLagrangeSetNodeType", nodeExponent, &nodeExponent, &flg3);
992: }
993: if (flg || flg2 || flg3) {PetscDualSpaceLagrangeSetNodeType(sp, nodeType, nodeEndpoints, nodeExponent);}
994: PetscOptionsBool("-petscdualspace_lagrange_use_moments", "Use moments (where appropriate) for functionals", "PetscDualSpaceLagrangeSetUseMoments", useMoments, &useMoments, &flg);
995: if (flg) {PetscDualSpaceLagrangeSetUseMoments(sp, useMoments);}
996: PetscOptionsInt("-petscdualspace_lagrange_moment_order", "Quadrature order for moment functionals", "PetscDualSpaceLagrangeSetMomentOrder", momentOrder, &momentOrder, &flg);
997: if (flg) {PetscDualSpaceLagrangeSetMomentOrder(sp, momentOrder);}
998: PetscOptionsTail();
999: return(0);
1000: }
1002: static PetscErrorCode PetscDualSpaceDuplicate_Lagrange(PetscDualSpace sp, PetscDualSpace spNew)
1003: {
1004: PetscBool cont, tensor, trimmed, boundary;
1005: PetscDTNodeType nodeType;
1006: PetscReal exponent;
1007: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *) sp->data;
1008: PetscErrorCode ierr;
1011: PetscDualSpaceLagrangeGetContinuity(sp, &cont);
1012: PetscDualSpaceLagrangeSetContinuity(spNew, cont);
1013: PetscDualSpaceLagrangeGetTensor(sp, &tensor);
1014: PetscDualSpaceLagrangeSetTensor(spNew, tensor);
1015: PetscDualSpaceLagrangeGetTrimmed(sp, &trimmed);
1016: PetscDualSpaceLagrangeSetTrimmed(spNew, trimmed);
1017: PetscDualSpaceLagrangeGetNodeType(sp, &nodeType, &boundary, &exponent);
1018: PetscDualSpaceLagrangeSetNodeType(spNew, nodeType, boundary, exponent);
1019: if (lag->nodeFamily) {
1020: PetscDualSpace_Lag *lagnew = (PetscDualSpace_Lag *) spNew->data;
1022: Petsc1DNodeFamilyReference(lag->nodeFamily);
1023: lagnew->nodeFamily = lag->nodeFamily;
1024: }
1025: return(0);
1026: }
1028: /* for making tensor product spaces: take a dual space and product a segment space that has all the same
1029: * specifications (trimmed, continuous, order, node set), except for the form degree */
1030: static PetscErrorCode PetscDualSpaceCreateEdgeSubspace_Lagrange(PetscDualSpace sp, PetscInt order, PetscInt k, PetscInt Nc, PetscBool interiorOnly, PetscDualSpace *bdsp)
1031: {
1032: DM K;
1033: PetscDualSpace_Lag *newlag;
1034: PetscErrorCode ierr;
1037: PetscDualSpaceDuplicate(sp,bdsp);
1038: PetscDualSpaceSetFormDegree(*bdsp, k);
1039: PetscDualSpaceCreateReferenceCell(*bdsp, 1, PETSC_TRUE, &K);
1040: PetscDualSpaceSetDM(*bdsp, K);
1041: DMDestroy(&K);
1042: PetscDualSpaceSetOrder(*bdsp, order);
1043: PetscDualSpaceSetNumComponents(*bdsp, Nc);
1044: newlag = (PetscDualSpace_Lag *) (*bdsp)->data;
1045: newlag->interiorOnly = interiorOnly;
1046: PetscDualSpaceSetUp(*bdsp);
1047: return(0);
1048: }
1050: /* just the points, weights aren't handled */
1051: static PetscErrorCode PetscQuadratureCreateTensor(PetscQuadrature trace, PetscQuadrature fiber, PetscQuadrature *product)
1052: {
1053: PetscInt dimTrace, dimFiber;
1054: PetscInt numPointsTrace, numPointsFiber;
1055: PetscInt dim, numPoints;
1056: const PetscReal *pointsTrace;
1057: const PetscReal *pointsFiber;
1058: PetscReal *points;
1059: PetscInt i, j, k, p;
1060: PetscErrorCode ierr;
1063: PetscQuadratureGetData(trace, &dimTrace, NULL, &numPointsTrace, &pointsTrace, NULL);
1064: PetscQuadratureGetData(fiber, &dimFiber, NULL, &numPointsFiber, &pointsFiber, NULL);
1065: dim = dimTrace + dimFiber;
1066: numPoints = numPointsFiber * numPointsTrace;
1067: PetscMalloc1(numPoints * dim, &points);
1068: for (p = 0, j = 0; j < numPointsFiber; j++) {
1069: for (i = 0; i < numPointsTrace; i++, p++) {
1070: for (k = 0; k < dimTrace; k++) points[p * dim + k] = pointsTrace[i * dimTrace + k];
1071: for (k = 0; k < dimFiber; k++) points[p * dim + dimTrace + k] = pointsFiber[j * dimFiber + k];
1072: }
1073: }
1074: PetscQuadratureCreate(PETSC_COMM_SELF, product);
1075: PetscQuadratureSetData(*product, dim, 0, numPoints, points, NULL);
1076: return(0);
1077: }
1079: /* Kronecker tensor product where matrix is considered a matrix of k-forms, so that
1080: * the entries in the product matrix are wedge products of the entries in the original matrices */
1081: static PetscErrorCode MatTensorAltV(Mat trace, Mat fiber, PetscInt dimTrace, PetscInt kTrace, PetscInt dimFiber, PetscInt kFiber, Mat *product)
1082: {
1083: PetscInt mTrace, nTrace, mFiber, nFiber, m, n, k, i, j, l;
1084: PetscInt dim, NkTrace, NkFiber, Nk;
1085: PetscInt dT, dF;
1086: PetscInt *nnzTrace, *nnzFiber, *nnz;
1087: PetscInt iT, iF, jT, jF, il, jl;
1088: PetscReal *workT, *workT2, *workF, *workF2, *work, *workstar;
1089: PetscReal *projT, *projF;
1090: PetscReal *projTstar, *projFstar;
1091: PetscReal *wedgeMat;
1092: PetscReal sign;
1093: PetscScalar *workS;
1094: Mat prod;
1095: /* this produces dof groups that look like the identity */
1099: MatGetSize(trace, &mTrace, &nTrace);
1100: PetscDTBinomialInt(dimTrace, PetscAbsInt(kTrace), &NkTrace);
1101: if (nTrace % NkTrace) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "point value space of trace matrix is not a multiple of k-form size");
1102: MatGetSize(fiber, &mFiber, &nFiber);
1103: PetscDTBinomialInt(dimFiber, PetscAbsInt(kFiber), &NkFiber);
1104: if (nFiber % NkFiber) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "point value space of fiber matrix is not a multiple of k-form size");
1105: PetscMalloc2(mTrace, &nnzTrace, mFiber, &nnzFiber);
1106: for (i = 0; i < mTrace; i++) {
1107: MatGetRow(trace, i, &(nnzTrace[i]), NULL, NULL);
1108: if (nnzTrace[i] % NkTrace) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "nonzeros in trace matrix are not in k-form size blocks");
1109: }
1110: for (i = 0; i < mFiber; i++) {
1111: MatGetRow(fiber, i, &(nnzFiber[i]), NULL, NULL);
1112: if (nnzFiber[i] % NkFiber) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "nonzeros in fiber matrix are not in k-form size blocks");
1113: }
1114: dim = dimTrace + dimFiber;
1115: k = kFiber + kTrace;
1116: PetscDTBinomialInt(dim, PetscAbsInt(k), &Nk);
1117: m = mTrace * mFiber;
1118: PetscMalloc1(m, &nnz);
1119: for (l = 0, j = 0; j < mFiber; j++) for (i = 0; i < mTrace; i++, l++) nnz[l] = (nnzTrace[i] / NkTrace) * (nnzFiber[j] / NkFiber) * Nk;
1120: n = (nTrace / NkTrace) * (nFiber / NkFiber) * Nk;
1121: MatCreateSeqAIJ(PETSC_COMM_SELF, m, n, 0, nnz, &prod);
1122: PetscFree(nnz);
1123: PetscFree2(nnzTrace,nnzFiber);
1124: /* reasoning about which points each dof needs depends on having zeros computed at points preserved */
1125: MatSetOption(prod, MAT_IGNORE_ZERO_ENTRIES, PETSC_FALSE);
1126: /* compute pullbacks */
1127: PetscDTBinomialInt(dim, PetscAbsInt(kTrace), &dT);
1128: PetscDTBinomialInt(dim, PetscAbsInt(kFiber), &dF);
1129: PetscMalloc4(dimTrace * dim, &projT, dimFiber * dim, &projF, dT * NkTrace, &projTstar, dF * NkFiber, &projFstar);
1130: PetscArrayzero(projT, dimTrace * dim);
1131: for (i = 0; i < dimTrace; i++) projT[i * (dim + 1)] = 1.;
1132: PetscArrayzero(projF, dimFiber * dim);
1133: for (i = 0; i < dimFiber; i++) projF[i * (dim + 1) + dimTrace] = 1.;
1134: PetscDTAltVPullbackMatrix(dim, dimTrace, projT, kTrace, projTstar);
1135: PetscDTAltVPullbackMatrix(dim, dimFiber, projF, kFiber, projFstar);
1136: PetscMalloc5(dT, &workT, dF, &workF, Nk, &work, Nk, &workstar, Nk, &workS);
1137: PetscMalloc2(dT, &workT2, dF, &workF2);
1138: PetscMalloc1(Nk * dT, &wedgeMat);
1139: sign = (PetscAbsInt(kTrace * kFiber) & 1) ? -1. : 1.;
1140: for (i = 0, iF = 0; iF < mFiber; iF++) {
1141: PetscInt ncolsF, nformsF;
1142: const PetscInt *colsF;
1143: const PetscScalar *valsF;
1145: MatGetRow(fiber, iF, &ncolsF, &colsF, &valsF);
1146: nformsF = ncolsF / NkFiber;
1147: for (iT = 0; iT < mTrace; iT++, i++) {
1148: PetscInt ncolsT, nformsT;
1149: const PetscInt *colsT;
1150: const PetscScalar *valsT;
1152: MatGetRow(trace, iT, &ncolsT, &colsT, &valsT);
1153: nformsT = ncolsT / NkTrace;
1154: for (j = 0, jF = 0; jF < nformsF; jF++) {
1155: PetscInt colF = colsF[jF * NkFiber] / NkFiber;
1157: for (il = 0; il < dF; il++) {
1158: PetscReal val = 0.;
1159: for (jl = 0; jl < NkFiber; jl++) val += projFstar[il * NkFiber + jl] * PetscRealPart(valsF[jF * NkFiber + jl]);
1160: workF[il] = val;
1161: }
1162: if (kFiber < 0) {
1163: for (il = 0; il < dF; il++) workF2[il] = workF[il];
1164: PetscDTAltVStar(dim, PetscAbsInt(kFiber), 1, workF2, workF);
1165: }
1166: PetscDTAltVWedgeMatrix(dim, PetscAbsInt(kFiber), PetscAbsInt(kTrace), workF, wedgeMat);
1167: for (jT = 0; jT < nformsT; jT++, j++) {
1168: PetscInt colT = colsT[jT * NkTrace] / NkTrace;
1169: PetscInt col = colF * (nTrace / NkTrace) + colT;
1170: const PetscScalar *vals;
1172: for (il = 0; il < dT; il++) {
1173: PetscReal val = 0.;
1174: for (jl = 0; jl < NkTrace; jl++) val += projTstar[il * NkTrace + jl] * PetscRealPart(valsT[jT * NkTrace + jl]);
1175: workT[il] = val;
1176: }
1177: if (kTrace < 0) {
1178: for (il = 0; il < dT; il++) workT2[il] = workT[il];
1179: PetscDTAltVStar(dim, PetscAbsInt(kTrace), 1, workT2, workT);
1180: }
1182: for (il = 0; il < Nk; il++) {
1183: PetscReal val = 0.;
1184: for (jl = 0; jl < dT; jl++) val += sign * wedgeMat[il * dT + jl] * workT[jl];
1185: work[il] = val;
1186: }
1187: if (k < 0) {
1188: PetscDTAltVStar(dim, PetscAbsInt(k), -1, work, workstar);
1189: #if defined(PETSC_USE_COMPLEX)
1190: for (l = 0; l < Nk; l++) workS[l] = workstar[l];
1191: vals = &workS[0];
1192: #else
1193: vals = &workstar[0];
1194: #endif
1195: } else {
1196: #if defined(PETSC_USE_COMPLEX)
1197: for (l = 0; l < Nk; l++) workS[l] = work[l];
1198: vals = &workS[0];
1199: #else
1200: vals = &work[0];
1201: #endif
1202: }
1203: for (l = 0; l < Nk; l++) {
1204: MatSetValue(prod, i, col * Nk + l, vals[l], INSERT_VALUES);
1205: } /* Nk */
1206: } /* jT */
1207: } /* jF */
1208: MatRestoreRow(trace, iT, &ncolsT, &colsT, &valsT);
1209: } /* iT */
1210: MatRestoreRow(fiber, iF, &ncolsF, &colsF, &valsF);
1211: } /* iF */
1212: PetscFree(wedgeMat);
1213: PetscFree4(projT, projF, projTstar, projFstar);
1214: PetscFree2(workT2, workF2);
1215: PetscFree5(workT, workF, work, workstar, workS);
1216: MatAssemblyBegin(prod, MAT_FINAL_ASSEMBLY);
1217: MatAssemblyEnd(prod, MAT_FINAL_ASSEMBLY);
1218: *product = prod;
1219: return(0);
1220: }
1222: /* Union of quadrature points, with an attempt to identify commont points in the two sets */
1223: static PetscErrorCode PetscQuadraturePointsMerge(PetscQuadrature quadA, PetscQuadrature quadB, PetscQuadrature *quadJoint, PetscInt *aToJoint[], PetscInt *bToJoint[])
1224: {
1225: PetscInt dimA, dimB;
1226: PetscInt nA, nB, nJoint, i, j, d;
1227: const PetscReal *pointsA;
1228: const PetscReal *pointsB;
1229: PetscReal *pointsJoint;
1230: PetscInt *aToJ, *bToJ;
1231: PetscQuadrature qJ;
1232: PetscErrorCode ierr;
1235: PetscQuadratureGetData(quadA, &dimA, NULL, &nA, &pointsA, NULL);
1236: PetscQuadratureGetData(quadB, &dimB, NULL, &nB, &pointsB, NULL);
1237: if (dimA != dimB) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Quadrature points must be in the same dimension");
1238: nJoint = nA;
1239: PetscMalloc1(nA, &aToJ);
1240: for (i = 0; i < nA; i++) aToJ[i] = i;
1241: PetscMalloc1(nB, &bToJ);
1242: for (i = 0; i < nB; i++) {
1243: for (j = 0; j < nA; j++) {
1244: bToJ[i] = -1;
1245: for (d = 0; d < dimA; d++) if (PetscAbsReal(pointsB[i * dimA + d] - pointsA[j * dimA + d]) > PETSC_SMALL) break;
1246: if (d == dimA) {
1247: bToJ[i] = j;
1248: break;
1249: }
1250: }
1251: if (bToJ[i] == -1) {
1252: bToJ[i] = nJoint++;
1253: }
1254: }
1255: *aToJoint = aToJ;
1256: *bToJoint = bToJ;
1257: PetscMalloc1(nJoint * dimA, &pointsJoint);
1258: PetscArraycpy(pointsJoint, pointsA, nA * dimA);
1259: for (i = 0; i < nB; i++) {
1260: if (bToJ[i] >= nA) {
1261: for (d = 0; d < dimA; d++) pointsJoint[bToJ[i] * dimA + d] = pointsB[i * dimA + d];
1262: }
1263: }
1264: PetscQuadratureCreate(PETSC_COMM_SELF, &qJ);
1265: PetscQuadratureSetData(qJ, dimA, 0, nJoint, pointsJoint, NULL);
1266: *quadJoint = qJ;
1267: return(0);
1268: }
1270: /* Matrices matA and matB are both quadrature -> dof matrices: produce a matrix that is joint quadrature -> union of
1271: * dofs, where the joint quadrature was produced by PetscQuadraturePointsMerge */
1272: static PetscErrorCode MatricesMerge(Mat matA, Mat matB, PetscInt dim, PetscInt k, PetscInt numMerged, const PetscInt aToMerged[], const PetscInt bToMerged[], Mat *matMerged)
1273: {
1274: PetscInt m, n, mA, nA, mB, nB, Nk, i, j, l;
1275: Mat M;
1276: PetscInt *nnz;
1277: PetscInt maxnnz;
1278: PetscInt *work;
1282: PetscDTBinomialInt(dim, PetscAbsInt(k), &Nk);
1283: MatGetSize(matA, &mA, &nA);
1284: if (nA % Nk) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "matA column space not a multiple of k-form size");
1285: MatGetSize(matB, &mB, &nB);
1286: if (nB % Nk) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "matB column space not a multiple of k-form size");
1287: m = mA + mB;
1288: n = numMerged * Nk;
1289: PetscMalloc1(m, &nnz);
1290: maxnnz = 0;
1291: for (i = 0; i < mA; i++) {
1292: MatGetRow(matA, i, &(nnz[i]), NULL, NULL);
1293: if (nnz[i] % Nk) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "nonzeros in matA are not in k-form size blocks");
1294: maxnnz = PetscMax(maxnnz, nnz[i]);
1295: }
1296: for (i = 0; i < mB; i++) {
1297: MatGetRow(matB, i, &(nnz[i+mA]), NULL, NULL);
1298: if (nnz[i+mA] % Nk) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "nonzeros in matB are not in k-form size blocks");
1299: maxnnz = PetscMax(maxnnz, nnz[i+mA]);
1300: }
1301: MatCreateSeqAIJ(PETSC_COMM_SELF, m, n, 0, nnz, &M);
1302: PetscFree(nnz);
1303: /* reasoning about which points each dof needs depends on having zeros computed at points preserved */
1304: MatSetOption(M, MAT_IGNORE_ZERO_ENTRIES, PETSC_FALSE);
1305: PetscMalloc1(maxnnz, &work);
1306: for (i = 0; i < mA; i++) {
1307: const PetscInt *cols;
1308: const PetscScalar *vals;
1309: PetscInt nCols;
1310: MatGetRow(matA, i, &nCols, &cols, &vals);
1311: for (j = 0; j < nCols / Nk; j++) {
1312: PetscInt newCol = aToMerged[cols[j * Nk] / Nk];
1313: for (l = 0; l < Nk; l++) work[j * Nk + l] = newCol * Nk + l;
1314: }
1315: MatSetValuesBlocked(M, 1, &i, nCols, work, vals, INSERT_VALUES);
1316: MatRestoreRow(matA, i, &nCols, &cols, &vals);
1317: }
1318: for (i = 0; i < mB; i++) {
1319: const PetscInt *cols;
1320: const PetscScalar *vals;
1322: PetscInt row = i + mA;
1323: PetscInt nCols;
1324: MatGetRow(matB, i, &nCols, &cols, &vals);
1325: for (j = 0; j < nCols / Nk; j++) {
1326: PetscInt newCol = bToMerged[cols[j * Nk] / Nk];
1327: for (l = 0; l < Nk; l++) work[j * Nk + l] = newCol * Nk + l;
1328: }
1329: MatSetValuesBlocked(M, 1, &row, nCols, work, vals, INSERT_VALUES);
1330: MatRestoreRow(matB, i, &nCols, &cols, &vals);
1331: }
1332: PetscFree(work);
1333: MatAssemblyBegin(M, MAT_FINAL_ASSEMBLY);
1334: MatAssemblyEnd(M, MAT_FINAL_ASSEMBLY);
1335: *matMerged = M;
1336: return(0);
1337: }
1339: /* Take a dual space and product a segment space that has all the same specifications (trimmed, continuous, order,
1340: * node set), except for the form degree. For computing boundary dofs and for making tensor product spaces */
1341: static PetscErrorCode PetscDualSpaceCreateFacetSubspace_Lagrange(PetscDualSpace sp, DM K, PetscInt f, PetscInt k, PetscInt Ncopies, PetscBool interiorOnly, PetscDualSpace *bdsp)
1342: {
1343: PetscInt Nknew, Ncnew;
1344: PetscInt dim, pointDim = -1;
1345: PetscInt depth;
1346: DM dm;
1347: PetscDualSpace_Lag *newlag;
1348: PetscErrorCode ierr;
1351: PetscDualSpaceGetDM(sp,&dm);
1352: DMGetDimension(dm,&dim);
1353: DMPlexGetDepth(dm,&depth);
1354: PetscDualSpaceDuplicate(sp,bdsp);
1355: PetscDualSpaceSetFormDegree(*bdsp,k);
1356: if (!K) {
1357: PetscBool isSimplex;
1360: if (depth == dim) {
1361: PetscInt coneSize;
1363: pointDim = dim - 1;
1364: DMPlexGetConeSize(dm,f,&coneSize);
1365: isSimplex = (PetscBool) (coneSize == dim);
1366: PetscDualSpaceCreateReferenceCell(*bdsp, dim-1, isSimplex, &K);
1367: } else if (depth == 1) {
1368: pointDim = 0;
1369: PetscDualSpaceCreateReferenceCell(*bdsp, 0, PETSC_TRUE, &K);
1370: } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Unsupported interpolation state of reference element");
1371: } else {
1372: PetscObjectReference((PetscObject)K);
1373: DMGetDimension(K, &pointDim);
1374: }
1375: PetscDualSpaceSetDM(*bdsp, K);
1376: DMDestroy(&K);
1377: PetscDTBinomialInt(pointDim, PetscAbsInt(k), &Nknew);
1378: Ncnew = Nknew * Ncopies;
1379: PetscDualSpaceSetNumComponents(*bdsp, Ncnew);
1380: newlag = (PetscDualSpace_Lag *) (*bdsp)->data;
1381: newlag->interiorOnly = interiorOnly;
1382: PetscDualSpaceSetUp(*bdsp);
1383: return(0);
1384: }
1386: /* Construct simplex nodes from a nodefamily, add Nk dof vectors of length Nk at each node.
1387: * Return the (quadrature, matrix) form of the dofs and the nodeIndices form as well.
1388: *
1389: * Sometimes we want a set of nodes to be contained in the interior of the element,
1390: * even when the node scheme puts nodes on the boundaries. numNodeSkip tells
1391: * the routine how many "layers" of nodes need to be skipped.
1392: * */
1393: static PetscErrorCode PetscDualSpaceLagrangeCreateSimplexNodeMat(Petsc1DNodeFamily nodeFamily, PetscInt dim, PetscInt sum, PetscInt Nk, PetscInt numNodeSkip, PetscQuadrature *iNodes, Mat *iMat, PetscLagNodeIndices *nodeIndices)
1394: {
1395: PetscReal *extraNodeCoords, *nodeCoords;
1396: PetscInt nNodes, nExtraNodes;
1397: PetscInt i, j, k, extraSum = sum + numNodeSkip * (1 + dim);
1398: PetscQuadrature intNodes;
1399: Mat intMat;
1400: PetscLagNodeIndices ni;
1404: PetscDTBinomialInt(dim + sum, dim, &nNodes);
1405: PetscDTBinomialInt(dim + extraSum, dim, &nExtraNodes);
1407: PetscMalloc1(dim * nExtraNodes, &extraNodeCoords);
1408: PetscNew(&ni);
1409: ni->nodeIdxDim = dim + 1;
1410: ni->nodeVecDim = Nk;
1411: ni->nNodes = nNodes * Nk;
1412: ni->refct = 1;
1413: PetscMalloc1(nNodes * Nk * (dim + 1), &(ni->nodeIdx));
1414: PetscMalloc1(nNodes * Nk * Nk, &(ni->nodeVec));
1415: for (i = 0; i < nNodes; i++) for (j = 0; j < Nk; j++) for (k = 0; k < Nk; k++) ni->nodeVec[(i * Nk + j) * Nk + k] = (j == k) ? 1. : 0.;
1416: Petsc1DNodeFamilyComputeSimplexNodes(nodeFamily, dim, extraSum, extraNodeCoords);
1417: if (numNodeSkip) {
1418: PetscInt k;
1419: PetscInt *tup;
1421: PetscMalloc1(dim * nNodes, &nodeCoords);
1422: PetscMalloc1(dim + 1, &tup);
1423: for (k = 0; k < nNodes; k++) {
1424: PetscInt j, c;
1425: PetscInt index;
1427: PetscDTIndexToBary(dim + 1, sum, k, tup);
1428: for (j = 0; j < dim + 1; j++) tup[j] += numNodeSkip;
1429: for (c = 0; c < Nk; c++) {
1430: for (j = 0; j < dim + 1; j++) {
1431: ni->nodeIdx[(k * Nk + c) * (dim + 1) + j] = tup[j] + 1;
1432: }
1433: }
1434: PetscDTBaryToIndex(dim + 1, extraSum, tup, &index);
1435: for (j = 0; j < dim; j++) nodeCoords[k * dim + j] = extraNodeCoords[index * dim + j];
1436: }
1437: PetscFree(tup);
1438: PetscFree(extraNodeCoords);
1439: } else {
1440: PetscInt k;
1441: PetscInt *tup;
1443: nodeCoords = extraNodeCoords;
1444: PetscMalloc1(dim + 1, &tup);
1445: for (k = 0; k < nNodes; k++) {
1446: PetscInt j, c;
1448: PetscDTIndexToBary(dim + 1, sum, k, tup);
1449: for (c = 0; c < Nk; c++) {
1450: for (j = 0; j < dim + 1; j++) {
1451: /* barycentric indices can have zeros, but we don't want to push forward zeros because it makes it harder to
1452: * determine which nodes correspond to which under symmetries, so we increase by 1. This is fine
1453: * because the nodeIdx coordinates don't have any meaning other than helping to identify symmetries */
1454: ni->nodeIdx[(k * Nk + c) * (dim + 1) + j] = tup[j] + 1;
1455: }
1456: }
1457: }
1458: PetscFree(tup);
1459: }
1460: PetscQuadratureCreate(PETSC_COMM_SELF, &intNodes);
1461: PetscQuadratureSetData(intNodes, dim, 0, nNodes, nodeCoords, NULL);
1462: MatCreateSeqAIJ(PETSC_COMM_SELF, nNodes * Nk, nNodes * Nk, Nk, NULL, &intMat);
1463: MatSetOption(intMat,MAT_IGNORE_ZERO_ENTRIES,PETSC_FALSE);
1464: for (j = 0; j < nNodes * Nk; j++) {
1465: PetscInt rem = j % Nk;
1466: PetscInt a, aprev = j - rem;
1467: PetscInt anext = aprev + Nk;
1469: for (a = aprev; a < anext; a++) {
1470: MatSetValue(intMat, j, a, (a == j) ? 1. : 0., INSERT_VALUES);
1471: }
1472: }
1473: MatAssemblyBegin(intMat, MAT_FINAL_ASSEMBLY);
1474: MatAssemblyEnd(intMat, MAT_FINAL_ASSEMBLY);
1475: *iNodes = intNodes;
1476: *iMat = intMat;
1477: *nodeIndices = ni;
1478: return(0);
1479: }
1481: /* once the nodeIndices have been created for the interior of the reference cell, and for all of the boundary cells,
1482: * push forward the boudary dofs and concatenate them into the full node indices for the dual space */
1483: static PetscErrorCode PetscDualSpaceLagrangeCreateAllNodeIdx(PetscDualSpace sp)
1484: {
1485: DM dm;
1486: PetscInt dim, nDofs;
1487: PetscSection section;
1488: PetscInt pStart, pEnd, p;
1489: PetscInt formDegree, Nk;
1490: PetscInt nodeIdxDim, spintdim;
1491: PetscDualSpace_Lag *lag;
1492: PetscLagNodeIndices ni, verti;
1496: lag = (PetscDualSpace_Lag *) sp->data;
1497: verti = lag->vertIndices;
1498: PetscDualSpaceGetDM(sp, &dm);
1499: DMGetDimension(dm, &dim);
1500: PetscDualSpaceGetFormDegree(sp, &formDegree);
1501: PetscDTBinomialInt(dim, PetscAbsInt(formDegree), &Nk);
1502: PetscDualSpaceGetSection(sp, §ion);
1503: PetscSectionGetStorageSize(section, &nDofs);
1504: PetscNew(&ni);
1505: ni->nodeIdxDim = nodeIdxDim = verti->nodeIdxDim;
1506: ni->nodeVecDim = Nk;
1507: ni->nNodes = nDofs;
1508: ni->refct = 1;
1509: PetscMalloc1(nodeIdxDim * nDofs, &(ni->nodeIdx));
1510: PetscMalloc1(Nk * nDofs, &(ni->nodeVec));
1511: DMPlexGetChart(dm, &pStart, &pEnd);
1512: PetscSectionGetDof(section, 0, &spintdim);
1513: if (spintdim) {
1514: PetscArraycpy(ni->nodeIdx, lag->intNodeIndices->nodeIdx, spintdim * nodeIdxDim);
1515: PetscArraycpy(ni->nodeVec, lag->intNodeIndices->nodeVec, spintdim * Nk);
1516: }
1517: for (p = pStart + 1; p < pEnd; p++) {
1518: PetscDualSpace psp = sp->pointSpaces[p];
1519: PetscDualSpace_Lag *plag;
1520: PetscInt dof, off;
1522: PetscSectionGetDof(section, p, &dof);
1523: if (!dof) continue;
1524: plag = (PetscDualSpace_Lag *) psp->data;
1525: PetscSectionGetOffset(section, p, &off);
1526: PetscLagNodeIndicesPushForward(dm, verti, p, plag->vertIndices, plag->intNodeIndices, 0, formDegree, &(ni->nodeIdx[off * nodeIdxDim]), &(ni->nodeVec[off * Nk]));
1527: }
1528: lag->allNodeIndices = ni;
1529: return(0);
1530: }
1532: /* once the (quadrature, Matrix) forms of the dofs have been created for the interior of the
1533: * reference cell and for the boundary cells, jk
1534: * push forward the boundary data and concatenate them into the full (quadrature, matrix) data
1535: * for the dual space */
1536: static PetscErrorCode PetscDualSpaceCreateAllDataFromInteriorData(PetscDualSpace sp)
1537: {
1538: DM dm;
1539: PetscSection section;
1540: PetscInt pStart, pEnd, p, k, Nk, dim, Nc;
1541: PetscInt nNodes;
1542: PetscInt countNodes;
1543: Mat allMat;
1544: PetscQuadrature allNodes;
1545: PetscInt nDofs;
1546: PetscInt maxNzforms, j;
1547: PetscScalar *work;
1548: PetscReal *L, *J, *Jinv, *v0, *pv0;
1549: PetscInt *iwork;
1550: PetscReal *nodes;
1551: PetscErrorCode ierr;
1554: PetscDualSpaceGetDM(sp, &dm);
1555: DMGetDimension(dm, &dim);
1556: PetscDualSpaceGetSection(sp, §ion);
1557: PetscSectionGetStorageSize(section, &nDofs);
1558: DMPlexGetChart(dm, &pStart, &pEnd);
1559: PetscDualSpaceGetFormDegree(sp, &k);
1560: PetscDualSpaceGetNumComponents(sp, &Nc);
1561: PetscDTBinomialInt(dim, PetscAbsInt(k), &Nk);
1562: for (p = pStart, nNodes = 0, maxNzforms = 0; p < pEnd; p++) {
1563: PetscDualSpace psp;
1564: DM pdm;
1565: PetscInt pdim, pNk;
1566: PetscQuadrature intNodes;
1567: Mat intMat;
1569: PetscDualSpaceGetPointSubspace(sp, p, &psp);
1570: if (!psp) continue;
1571: PetscDualSpaceGetDM(psp, &pdm);
1572: DMGetDimension(pdm, &pdim);
1573: if (pdim < PetscAbsInt(k)) continue;
1574: PetscDTBinomialInt(pdim, PetscAbsInt(k), &pNk);
1575: PetscDualSpaceGetInteriorData(psp, &intNodes, &intMat);
1576: if (intNodes) {
1577: PetscInt nNodesp;
1579: PetscQuadratureGetData(intNodes, NULL, NULL, &nNodesp, NULL, NULL);
1580: nNodes += nNodesp;
1581: }
1582: if (intMat) {
1583: PetscInt maxNzsp;
1584: PetscInt maxNzformsp;
1586: MatSeqAIJGetMaxRowNonzeros(intMat, &maxNzsp);
1587: if (maxNzsp % pNk) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "interior matrix is not laid out as blocks of k-forms");
1588: maxNzformsp = maxNzsp / pNk;
1589: maxNzforms = PetscMax(maxNzforms, maxNzformsp);
1590: }
1591: }
1592: MatCreateSeqAIJ(PETSC_COMM_SELF, nDofs, nNodes * Nc, maxNzforms * Nk, NULL, &allMat);
1593: MatSetOption(allMat,MAT_IGNORE_ZERO_ENTRIES,PETSC_FALSE);
1594: PetscMalloc7(dim, &v0, dim, &pv0, dim * dim, &J, dim * dim, &Jinv, Nk * Nk, &L, maxNzforms * Nk, &work, maxNzforms * Nk, &iwork);
1595: for (j = 0; j < dim; j++) pv0[j] = -1.;
1596: PetscMalloc1(dim * nNodes, &nodes);
1597: for (p = pStart, countNodes = 0; p < pEnd; p++) {
1598: PetscDualSpace psp;
1599: PetscQuadrature intNodes;
1600: DM pdm;
1601: PetscInt pdim, pNk;
1602: PetscInt countNodesIn = countNodes;
1603: PetscReal detJ;
1604: Mat intMat;
1606: PetscDualSpaceGetPointSubspace(sp, p, &psp);
1607: if (!psp) continue;
1608: PetscDualSpaceGetDM(psp, &pdm);
1609: DMGetDimension(pdm, &pdim);
1610: if (pdim < PetscAbsInt(k)) continue;
1611: PetscDualSpaceGetInteriorData(psp, &intNodes, &intMat);
1612: if (intNodes == NULL && intMat == NULL) continue;
1613: PetscDTBinomialInt(pdim, PetscAbsInt(k), &pNk);
1614: if (p) {
1615: DMPlexComputeCellGeometryAffineFEM(dm, p, v0, J, Jinv, &detJ);
1616: } else { /* identity */
1617: PetscInt i,j;
1619: for (i = 0; i < dim; i++) for (j = 0; j < dim; j++) J[i * dim + j] = Jinv[i * dim + j] = 0.;
1620: for (i = 0; i < dim; i++) J[i * dim + i] = Jinv[i * dim + i] = 1.;
1621: for (i = 0; i < dim; i++) v0[i] = -1.;
1622: }
1623: if (pdim != dim) { /* compactify Jacobian */
1624: PetscInt i, j;
1626: for (i = 0; i < dim; i++) for (j = 0; j < pdim; j++) J[i * pdim + j] = J[i * dim + j];
1627: }
1628: PetscDTAltVPullbackMatrix(pdim, dim, J, k, L);
1629: if (intNodes) { /* push forward quadrature locations by the affine transformation */
1630: PetscInt nNodesp;
1631: const PetscReal *nodesp;
1632: PetscInt j;
1634: PetscQuadratureGetData(intNodes, NULL, NULL, &nNodesp, &nodesp, NULL);
1635: for (j = 0; j < nNodesp; j++, countNodes++) {
1636: PetscInt d, e;
1638: for (d = 0; d < dim; d++) {
1639: nodes[countNodes * dim + d] = v0[d];
1640: for (e = 0; e < pdim; e++) {
1641: nodes[countNodes * dim + d] += J[d * pdim + e] * (nodesp[j * pdim + e] - pv0[e]);
1642: }
1643: }
1644: }
1645: }
1646: if (intMat) {
1647: PetscInt nrows;
1648: PetscInt off;
1650: PetscSectionGetDof(section, p, &nrows);
1651: PetscSectionGetOffset(section, p, &off);
1652: for (j = 0; j < nrows; j++) {
1653: PetscInt ncols;
1654: const PetscInt *cols;
1655: const PetscScalar *vals;
1656: PetscInt l, d, e;
1657: PetscInt row = j + off;
1659: MatGetRow(intMat, j, &ncols, &cols, &vals);
1660: if (ncols % pNk) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "interior matrix is not laid out as blocks of k-forms");
1661: for (l = 0; l < ncols / pNk; l++) {
1662: PetscInt blockcol;
1664: for (d = 0; d < pNk; d++) {
1665: if ((cols[l * pNk + d] % pNk) != d) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "interior matrix is not laid out as blocks of k-forms");
1666: }
1667: blockcol = cols[l * pNk] / pNk;
1668: for (d = 0; d < Nk; d++) {
1669: iwork[l * Nk + d] = (blockcol + countNodesIn) * Nk + d;
1670: }
1671: for (d = 0; d < Nk; d++) work[l * Nk + d] = 0.;
1672: for (d = 0; d < Nk; d++) {
1673: for (e = 0; e < pNk; e++) {
1674: /* "push forward" dof by pulling back a k-form to be evaluated on the point: multiply on the right by L */
1675: work[l * Nk + d] += vals[l * pNk + e] * L[e * Nk + d];
1676: }
1677: }
1678: }
1679: MatSetValues(allMat, 1, &row, (ncols / pNk) * Nk, iwork, work, INSERT_VALUES);
1680: MatRestoreRow(intMat, j, &ncols, &cols, &vals);
1681: }
1682: }
1683: }
1684: MatAssemblyBegin(allMat, MAT_FINAL_ASSEMBLY);
1685: MatAssemblyEnd(allMat, MAT_FINAL_ASSEMBLY);
1686: PetscQuadratureCreate(PETSC_COMM_SELF, &allNodes);
1687: PetscQuadratureSetData(allNodes, dim, 0, nNodes, nodes, NULL);
1688: PetscFree7(v0, pv0, J, Jinv, L, work, iwork);
1689: MatDestroy(&(sp->allMat));
1690: sp->allMat = allMat;
1691: PetscQuadratureDestroy(&(sp->allNodes));
1692: sp->allNodes = allNodes;
1693: return(0);
1694: }
1696: /* rather than trying to get all data from the functionals, we create
1697: * the functionals from rows of the quadrature -> dof matrix.
1698: *
1699: * Ideally most of the uses of PetscDualSpace in PetscFE will switch
1700: * to using intMat and allMat, so that the individual functionals
1701: * don't need to be constructed at all */
1702: static PetscErrorCode PetscDualSpaceComputeFunctionalsFromAllData(PetscDualSpace sp)
1703: {
1704: PetscQuadrature allNodes;
1705: Mat allMat;
1706: PetscInt nDofs;
1707: PetscInt dim, k, Nk, Nc, f;
1708: DM dm;
1709: PetscInt nNodes, spdim;
1710: const PetscReal *nodes = NULL;
1711: PetscSection section;
1712: PetscBool useMoments;
1713: PetscErrorCode ierr;
1716: PetscDualSpaceGetDM(sp, &dm);
1717: DMGetDimension(dm, &dim);
1718: PetscDualSpaceGetNumComponents(sp, &Nc);
1719: PetscDualSpaceGetFormDegree(sp, &k);
1720: PetscDTBinomialInt(dim, PetscAbsInt(k), &Nk);
1721: PetscDualSpaceGetAllData(sp, &allNodes, &allMat);
1722: nNodes = 0;
1723: if (allNodes) {
1724: PetscQuadratureGetData(allNodes, NULL, NULL, &nNodes, &nodes, NULL);
1725: }
1726: MatGetSize(allMat, &nDofs, NULL);
1727: PetscDualSpaceGetSection(sp, §ion);
1728: PetscSectionGetStorageSize(section, &spdim);
1729: if (spdim != nDofs) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "incompatible all matrix size");
1730: PetscMalloc1(nDofs, &(sp->functional));
1731: PetscDualSpaceLagrangeGetUseMoments(sp, &useMoments);
1732: if (useMoments) {
1733: Mat allMat;
1734: PetscInt momentOrder, i;
1735: PetscBool tensor;
1736: const PetscReal *weights;
1737: PetscScalar *array;
1739: if (nDofs != 1) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_SUP, "We do not yet support moments beyond P0, nDofs == %D", nDofs);
1740: PetscDualSpaceLagrangeGetMomentOrder(sp, &momentOrder);
1741: PetscDualSpaceLagrangeGetTensor(sp, &tensor);
1742: if (!tensor) {PetscDTStroudConicalQuadrature(dim, Nc, PetscMax(momentOrder + 1,1), -1.0, 1.0, &(sp->functional[0]));}
1743: else {PetscDTGaussTensorQuadrature(dim, Nc, PetscMax(momentOrder + 1,1), -1.0, 1.0, &(sp->functional[0]));}
1744: /* Need to replace allNodes and allMat */
1745: PetscObjectReference((PetscObject) sp->functional[0]);
1746: PetscQuadratureDestroy(&(sp->allNodes));
1747: sp->allNodes = sp->functional[0];
1748: PetscQuadratureGetData(sp->allNodes, NULL, NULL, &nNodes, NULL, &weights);
1749: MatCreateSeqDense(PETSC_COMM_SELF, nDofs, nNodes * Nc, NULL, &allMat);
1750: MatDenseGetArrayWrite(allMat, &array);
1751: for (i = 0; i < nNodes * Nc; ++i) array[i] = weights[i];
1752: MatDenseRestoreArrayWrite(allMat, &array);
1753: MatAssemblyBegin(allMat, MAT_FINAL_ASSEMBLY);
1754: MatAssemblyEnd(allMat, MAT_FINAL_ASSEMBLY);
1755: MatDestroy(&(sp->allMat));
1756: sp->allMat = allMat;
1757: return(0);
1758: }
1759: for (f = 0; f < nDofs; f++) {
1760: PetscInt ncols, c;
1761: const PetscInt *cols;
1762: const PetscScalar *vals;
1763: PetscReal *nodesf;
1764: PetscReal *weightsf;
1765: PetscInt nNodesf;
1766: PetscInt countNodes;
1768: MatGetRow(allMat, f, &ncols, &cols, &vals);
1769: if (ncols % Nk) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "all matrix is not laid out as blocks of k-forms");
1770: for (c = 1, nNodesf = 1; c < ncols; c++) {
1771: if ((cols[c] / Nc) != (cols[c-1] / Nc)) nNodesf++;
1772: }
1773: PetscMalloc1(dim * nNodesf, &nodesf);
1774: PetscMalloc1(Nc * nNodesf, &weightsf);
1775: for (c = 0, countNodes = 0; c < ncols; c++) {
1776: if (!c || ((cols[c] / Nc) != (cols[c-1] / Nc))) {
1777: PetscInt d;
1779: for (d = 0; d < Nc; d++) {
1780: weightsf[countNodes * Nc + d] = 0.;
1781: }
1782: for (d = 0; d < dim; d++) {
1783: nodesf[countNodes * dim + d] = nodes[(cols[c] / Nc) * dim + d];
1784: }
1785: countNodes++;
1786: }
1787: weightsf[(countNodes - 1) * Nc + (cols[c] % Nc)] = PetscRealPart(vals[c]);
1788: }
1789: PetscQuadratureCreate(PETSC_COMM_SELF, &(sp->functional[f]));
1790: PetscQuadratureSetData(sp->functional[f], dim, Nc, nNodesf, nodesf, weightsf);
1791: MatRestoreRow(allMat, f, &ncols, &cols, &vals);
1792: }
1793: return(0);
1794: }
1796: /* take a matrix meant for k-forms and expand it to one for Ncopies */
1797: static PetscErrorCode PetscDualSpaceLagrangeMatrixCreateCopies(Mat A, PetscInt Nk, PetscInt Ncopies, Mat *Abs)
1798: {
1799: PetscInt m, n, i, j, k;
1800: PetscInt maxnnz, *nnz, *iwork;
1801: Mat Ac;
1805: MatGetSize(A, &m, &n);
1806: if (n % Nk) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Number of columns in A %D is not a multiple of Nk %D", n, Nk);
1807: PetscMalloc1(m * Ncopies, &nnz);
1808: for (i = 0, maxnnz = 0; i < m; i++) {
1809: PetscInt innz;
1810: MatGetRow(A, i, &innz, NULL, NULL);
1811: if (innz % Nk) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_PLIB, "A row %D nnzs is not a multiple of Nk %D", innz, Nk);
1812: for (j = 0; j < Ncopies; j++) nnz[i * Ncopies + j] = innz;
1813: maxnnz = PetscMax(maxnnz, innz);
1814: }
1815: MatCreateSeqAIJ(PETSC_COMM_SELF, m * Ncopies, n * Ncopies, 0, nnz, &Ac);
1816: MatSetOption(Ac, MAT_IGNORE_ZERO_ENTRIES, PETSC_FALSE);
1817: PetscFree(nnz);
1818: PetscMalloc1(maxnnz, &iwork);
1819: for (i = 0; i < m; i++) {
1820: PetscInt innz;
1821: const PetscInt *cols;
1822: const PetscScalar *vals;
1824: MatGetRow(A, i, &innz, &cols, &vals);
1825: for (j = 0; j < innz; j++) iwork[j] = (cols[j] / Nk) * (Nk * Ncopies) + (cols[j] % Nk);
1826: for (j = 0; j < Ncopies; j++) {
1827: PetscInt row = i * Ncopies + j;
1829: MatSetValues(Ac, 1, &row, innz, iwork, vals, INSERT_VALUES);
1830: for (k = 0; k < innz; k++) iwork[k] += Nk;
1831: }
1832: MatRestoreRow(A, i, &innz, &cols, &vals);
1833: }
1834: PetscFree(iwork);
1835: MatAssemblyBegin(Ac, MAT_FINAL_ASSEMBLY);
1836: MatAssemblyEnd(Ac, MAT_FINAL_ASSEMBLY);
1837: *Abs = Ac;
1838: return(0);
1839: }
1841: /* check if a cell is a tensor product of the segment with a facet,
1842: * specifically checking if f and f2 can be the "endpoints" (like the triangles
1843: * at either end of a wedge) */
1844: static PetscErrorCode DMPlexPointIsTensor_Internal_Given(DM dm, PetscInt p, PetscInt f, PetscInt f2, PetscBool *isTensor)
1845: {
1846: PetscInt coneSize, c;
1847: const PetscInt *cone;
1848: const PetscInt *fCone;
1849: const PetscInt *f2Cone;
1850: PetscInt fs[2];
1851: PetscInt meetSize, nmeet;
1852: const PetscInt *meet;
1853: PetscErrorCode ierr;
1856: fs[0] = f;
1857: fs[1] = f2;
1858: DMPlexGetMeet(dm, 2, fs, &meetSize, &meet);
1859: nmeet = meetSize;
1860: DMPlexRestoreMeet(dm, 2, fs, &meetSize, &meet);
1861: /* two points that have a non-empty meet cannot be at opposite ends of a cell */
1862: if (nmeet) {
1863: *isTensor = PETSC_FALSE;
1864: return(0);
1865: }
1866: DMPlexGetConeSize(dm, p, &coneSize);
1867: DMPlexGetCone(dm, p, &cone);
1868: DMPlexGetCone(dm, f, &fCone);
1869: DMPlexGetCone(dm, f2, &f2Cone);
1870: for (c = 0; c < coneSize; c++) {
1871: PetscInt e, ef;
1872: PetscInt d = -1, d2 = -1;
1873: PetscInt dcount, d2count;
1874: PetscInt t = cone[c];
1875: PetscInt tConeSize;
1876: PetscBool tIsTensor;
1877: const PetscInt *tCone;
1879: if (t == f || t == f2) continue;
1880: /* for every other facet in the cone, check that is has
1881: * one ridge in common with each end */
1882: DMPlexGetConeSize(dm, t, &tConeSize);
1883: DMPlexGetCone(dm, t, &tCone);
1885: dcount = 0;
1886: d2count = 0;
1887: for (e = 0; e < tConeSize; e++) {
1888: PetscInt q = tCone[e];
1889: for (ef = 0; ef < coneSize - 2; ef++) {
1890: if (fCone[ef] == q) {
1891: if (dcount) {
1892: *isTensor = PETSC_FALSE;
1893: return(0);
1894: }
1895: d = q;
1896: dcount++;
1897: } else if (f2Cone[ef] == q) {
1898: if (d2count) {
1899: *isTensor = PETSC_FALSE;
1900: return(0);
1901: }
1902: d2 = q;
1903: d2count++;
1904: }
1905: }
1906: }
1907: /* if the whole cell is a tensor with the segment, then this
1908: * facet should be a tensor with the segment */
1909: DMPlexPointIsTensor_Internal_Given(dm, t, d, d2, &tIsTensor);
1910: if (!tIsTensor) {
1911: *isTensor = PETSC_FALSE;
1912: return(0);
1913: }
1914: }
1915: *isTensor = PETSC_TRUE;
1916: return(0);
1917: }
1919: /* determine if a cell is a tensor with a segment by looping over pairs of facets to find a pair
1920: * that could be the opposite ends */
1921: static PetscErrorCode DMPlexPointIsTensor_Internal(DM dm, PetscInt p, PetscBool *isTensor, PetscInt *endA, PetscInt *endB)
1922: {
1923: PetscInt coneSize, c, c2;
1924: const PetscInt *cone;
1925: PetscErrorCode ierr;
1928: DMPlexGetConeSize(dm, p, &coneSize);
1929: if (!coneSize) {
1930: if (isTensor) *isTensor = PETSC_FALSE;
1931: if (endA) *endA = -1;
1932: if (endB) *endB = -1;
1933: }
1934: DMPlexGetCone(dm, p, &cone);
1935: for (c = 0; c < coneSize; c++) {
1936: PetscInt f = cone[c];
1937: PetscInt fConeSize;
1939: DMPlexGetConeSize(dm, f, &fConeSize);
1940: if (fConeSize != coneSize - 2) continue;
1942: for (c2 = c + 1; c2 < coneSize; c2++) {
1943: PetscInt f2 = cone[c2];
1944: PetscBool isTensorff2;
1945: PetscInt f2ConeSize;
1947: DMPlexGetConeSize(dm, f2, &f2ConeSize);
1948: if (f2ConeSize != coneSize - 2) continue;
1950: DMPlexPointIsTensor_Internal_Given(dm, p, f, f2, &isTensorff2);
1951: if (isTensorff2) {
1952: if (isTensor) *isTensor = PETSC_TRUE;
1953: if (endA) *endA = f;
1954: if (endB) *endB = f2;
1955: return(0);
1956: }
1957: }
1958: }
1959: if (isTensor) *isTensor = PETSC_FALSE;
1960: if (endA) *endA = -1;
1961: if (endB) *endB = -1;
1962: return(0);
1963: }
1965: /* determine if a cell is a tensor with a segment by looping over pairs of facets to find a pair
1966: * that could be the opposite ends */
1967: static PetscErrorCode DMPlexPointIsTensor(DM dm, PetscInt p, PetscBool *isTensor, PetscInt *endA, PetscInt *endB)
1968: {
1969: DMPlexInterpolatedFlag interpolated;
1973: DMPlexIsInterpolated(dm, &interpolated);
1974: if (interpolated != DMPLEX_INTERPOLATED_FULL) SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONGSTATE, "Only for interpolated DMPlex's");
1975: DMPlexPointIsTensor_Internal(dm, p, isTensor, endA, endB);
1976: return(0);
1977: }
1979: /* Let k = formDegree and k' = -sign(k) * dim + k. Transform a symmetric frame for k-forms on the biunit simplex into
1980: * a symmetric frame for k'-forms on the biunit simplex.
1981: *
1982: * A frame is "symmetric" if the pullback of every symmetry of the biunit simplex is a permutation of the frame.
1983: *
1984: * forms in the symmetric frame are used as dofs in the untrimmed simplex spaces. This way, symmetries of the
1985: * reference cell result in permutations of dofs grouped by node.
1986: *
1987: * Use T to transform dof matrices for k'-forms into dof matrices for k-forms as a block diagonal transformation on
1988: * the right.
1989: */
1990: static PetscErrorCode BiunitSimplexSymmetricFormTransformation(PetscInt dim, PetscInt formDegree, PetscReal T[])
1991: {
1992: PetscInt k = formDegree;
1993: PetscInt kd = k < 0 ? dim + k : k - dim;
1994: PetscInt Nk;
1995: PetscReal *biToEq, *eqToBi, *biToEqStar, *eqToBiStar;
1996: PetscInt fact;
2000: PetscDTBinomialInt(dim, PetscAbsInt(k), &Nk);
2001: PetscCalloc4(dim * dim, &biToEq, dim * dim, &eqToBi, Nk * Nk, &biToEqStar, Nk * Nk, &eqToBiStar);
2002: /* fill in biToEq: Jacobian of the transformation from the biunit simplex to the equilateral simplex */
2003: fact = 0;
2004: for (PetscInt i = 0; i < dim; i++) {
2005: biToEq[i * dim + i] = PetscSqrtReal(((PetscReal)i + 2.) / (2.*((PetscReal)i+1.)));
2006: fact += 4*(i+1);
2007: for (PetscInt j = i+1; j < dim; j++) {
2008: biToEq[i * dim + j] = PetscSqrtReal(1./(PetscReal)fact);
2009: }
2010: }
2011: /* fill in eqToBi: Jacobian of the transformation from the equilateral simplex to the biunit simplex */
2012: fact = 0;
2013: for (PetscInt j = 0; j < dim; j++) {
2014: eqToBi[j * dim + j] = PetscSqrtReal(2.*((PetscReal)j+1.)/((PetscReal)j+2));
2015: fact += j+1;
2016: for (PetscInt i = 0; i < j; i++) {
2017: eqToBi[i * dim + j] = -PetscSqrtReal(1./(PetscReal)fact);
2018: }
2019: }
2020: PetscDTAltVPullbackMatrix(dim, dim, biToEq, kd, biToEqStar);
2021: PetscDTAltVPullbackMatrix(dim, dim, eqToBi, k, eqToBiStar);
2022: /* product of pullbacks simulates the following steps
2023: *
2024: * 1. start with frame W = [w_1, w_2, ..., w_m] of k forms that is symmetric on the biunit simplex:
2025: if J is the Jacobian of a symmetry of the biunit simplex, then J_k* W = [J_k*w_1, ..., J_k*w_m]
2026: is a permutation of W.
2027: Even though a k' form --- a (dim - k) form represented by its Hodge star --- has the same geometric
2028: content as a k form, W is not a symmetric frame of k' forms on the biunit simplex. That's because,
2029: for general Jacobian J, J_k* != J_k'*.
2030: * 2. pullback W to the equilateral triangle using the k pullback, W_eq = eqToBi_k* W. All symmetries of the
2031: equilateral simplex have orthonormal Jacobians. For an orthonormal Jacobian O, J_k* = J_k'*, so W_eq is
2032: also a symmetric frame for k' forms on the equilateral simplex.
2033: 3. pullback W_eq back to the biunit simplex using the k' pulback, V = biToEq_k'* W_eq = biToEq_k'* eqToBi_k* W.
2034: V is a symmetric frame for k' forms on the biunit simplex.
2035: */
2036: for (PetscInt i = 0; i < Nk; i++) {
2037: for (PetscInt j = 0; j < Nk; j++) {
2038: PetscReal val = 0.;
2039: for (PetscInt k = 0; k < Nk; k++) val += biToEqStar[i * Nk + k] * eqToBiStar[k * Nk + j];
2040: T[i * Nk + j] = val;
2041: }
2042: }
2043: PetscFree4(biToEq, eqToBi, biToEqStar, eqToBiStar);
2044: return(0);
2045: }
2047: /* permute a quadrature -> dof matrix so that its rows are in revlex order by nodeIdx */
2048: static PetscErrorCode MatPermuteByNodeIdx(Mat A, PetscLagNodeIndices ni, Mat *Aperm)
2049: {
2050: PetscInt m, n, i, j;
2051: PetscInt nodeIdxDim = ni->nodeIdxDim;
2052: PetscInt nodeVecDim = ni->nodeVecDim;
2053: PetscInt *perm;
2054: IS permIS;
2055: IS id;
2056: PetscInt *nIdxPerm;
2057: PetscReal *nVecPerm;
2061: PetscLagNodeIndicesGetPermutation(ni, &perm);
2062: MatGetSize(A, &m, &n);
2063: PetscMalloc1(nodeIdxDim * m, &nIdxPerm);
2064: PetscMalloc1(nodeVecDim * m, &nVecPerm);
2065: for (i = 0; i < m; i++) for (j = 0; j < nodeIdxDim; j++) nIdxPerm[i * nodeIdxDim + j] = ni->nodeIdx[perm[i] * nodeIdxDim + j];
2066: for (i = 0; i < m; i++) for (j = 0; j < nodeVecDim; j++) nVecPerm[i * nodeVecDim + j] = ni->nodeVec[perm[i] * nodeVecDim + j];
2067: ISCreateGeneral(PETSC_COMM_SELF, m, perm, PETSC_USE_POINTER, &permIS);
2068: ISSetPermutation(permIS);
2069: ISCreateStride(PETSC_COMM_SELF, n, 0, 1, &id);
2070: ISSetPermutation(id);
2071: MatPermute(A, permIS, id, Aperm);
2072: ISDestroy(&permIS);
2073: ISDestroy(&id);
2074: for (i = 0; i < m; i++) perm[i] = i;
2075: PetscFree(ni->nodeIdx);
2076: PetscFree(ni->nodeVec);
2077: ni->nodeIdx = nIdxPerm;
2078: ni->nodeVec = nVecPerm;
2079: return(0);
2080: }
2082: static PetscErrorCode PetscDualSpaceSetUp_Lagrange(PetscDualSpace sp)
2083: {
2084: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *) sp->data;
2085: DM dm = sp->dm;
2086: DM dmint = NULL;
2087: PetscInt order;
2088: PetscInt Nc = sp->Nc;
2089: MPI_Comm comm;
2090: PetscBool continuous;
2091: PetscSection section;
2092: PetscInt depth, dim, pStart, pEnd, cStart, cEnd, p, *pStratStart, *pStratEnd, d;
2093: PetscInt formDegree, Nk, Ncopies;
2094: PetscInt tensorf = -1, tensorf2 = -1;
2095: PetscBool tensorCell, tensorSpace;
2096: PetscBool uniform, trimmed;
2097: Petsc1DNodeFamily nodeFamily;
2098: PetscInt numNodeSkip;
2099: DMPlexInterpolatedFlag interpolated;
2100: PetscBool isbdm;
2101: PetscErrorCode ierr;
2104: /* step 1: sanitize input */
2105: PetscObjectGetComm((PetscObject) sp, &comm);
2106: DMGetDimension(dm, &dim);
2107: PetscObjectTypeCompare((PetscObject)sp, PETSCDUALSPACEBDM, &isbdm);
2108: if (isbdm) {
2109: sp->k = -(dim-1); /* form degree of H-div */
2110: PetscObjectChangeTypeName((PetscObject)sp, PETSCDUALSPACELAGRANGE);
2111: }
2112: PetscDualSpaceGetFormDegree(sp, &formDegree);
2113: if (PetscAbsInt(formDegree) > dim) SETERRQ(comm, PETSC_ERR_ARG_OUTOFRANGE, "Form degree must be bounded by dimension");
2114: PetscDTBinomialInt(dim,PetscAbsInt(formDegree),&Nk);
2115: if (sp->Nc <= 0 && lag->numCopies > 0) sp->Nc = Nk * lag->numCopies;
2116: Nc = sp->Nc;
2117: if (Nc % Nk) SETERRQ(comm, PETSC_ERR_ARG_INCOMP, "Number of components is not a multiple of form degree size");
2118: if (lag->numCopies <= 0) lag->numCopies = Nc / Nk;
2119: Ncopies = lag->numCopies;
2120: if (Nc / Nk != Ncopies) SETERRQ(comm, PETSC_ERR_ARG_INCOMP, "Number of copies * (dim choose k) != Nc");
2121: if (!dim) sp->order = 0;
2122: order = sp->order;
2123: uniform = sp->uniform;
2124: if (!uniform) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Variable order not supported yet");
2125: if (lag->trimmed && !formDegree) lag->trimmed = PETSC_FALSE; /* trimmed spaces are the same as full spaces for 0-forms */
2126: if (lag->nodeType == PETSCDTNODES_DEFAULT) {
2127: lag->nodeType = PETSCDTNODES_GAUSSJACOBI;
2128: lag->nodeExponent = 0.;
2129: /* trimmed spaces don't include corner vertices, so don't use end nodes by default */
2130: lag->endNodes = lag->trimmed ? PETSC_FALSE : PETSC_TRUE;
2131: }
2132: /* If a trimmed space and the user did choose nodes with endpoints, skip them by default */
2133: if (lag->numNodeSkip < 0) lag->numNodeSkip = (lag->trimmed && lag->endNodes) ? 1 : 0;
2134: numNodeSkip = lag->numNodeSkip;
2135: if (lag->trimmed && !order) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Cannot have zeroth order trimmed elements");
2136: if (lag->trimmed && PetscAbsInt(formDegree) == dim) { /* convert trimmed n-forms to untrimmed of one polynomial order less */
2137: sp->order--;
2138: order--;
2139: lag->trimmed = PETSC_FALSE;
2140: }
2141: trimmed = lag->trimmed;
2142: if (!order || PetscAbsInt(formDegree) == dim) lag->continuous = PETSC_FALSE;
2143: continuous = lag->continuous;
2144: DMPlexGetDepth(dm, &depth);
2145: DMPlexGetChart(dm, &pStart, &pEnd);
2146: DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);
2147: if (pStart != 0 || cStart != 0) SETERRQ(PetscObjectComm((PetscObject)sp), PETSC_ERR_ARG_WRONGSTATE, "Expect DM with chart starting at zero and cells first");
2148: if (cEnd != 1) SETERRQ(PetscObjectComm((PetscObject)sp), PETSC_ERR_ARG_WRONGSTATE, "Use PETSCDUALSPACEREFINED for multi-cell reference meshes");
2149: DMPlexIsInterpolated(dm, &interpolated);
2150: if (interpolated != DMPLEX_INTERPOLATED_FULL) {
2151: DMPlexInterpolate(dm, &dmint);
2152: } else {
2153: PetscObjectReference((PetscObject)dm);
2154: dmint = dm;
2155: }
2156: tensorCell = PETSC_FALSE;
2157: if (dim > 1) {
2158: DMPlexPointIsTensor(dmint, 0, &tensorCell, &tensorf, &tensorf2);
2159: }
2160: lag->tensorCell = tensorCell;
2161: if (dim < 2 || !lag->tensorCell) lag->tensorSpace = PETSC_FALSE;
2162: tensorSpace = lag->tensorSpace;
2163: if (!lag->nodeFamily) {
2164: Petsc1DNodeFamilyCreate(lag->nodeType, lag->nodeExponent, lag->endNodes, &lag->nodeFamily);
2165: }
2166: nodeFamily = lag->nodeFamily;
2167: if (interpolated != DMPLEX_INTERPOLATED_FULL && continuous && (PetscAbsInt(formDegree) > 0 || order > 1)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Reference element won't support all boundary nodes");
2169: /* step 2: construct the boundary spaces */
2170: PetscMalloc2(depth+1,&pStratStart,depth+1,&pStratEnd);
2171: PetscCalloc1(pEnd,&(sp->pointSpaces));
2172: for (d = 0; d <= depth; ++d) {DMPlexGetDepthStratum(dm, d, &pStratStart[d], &pStratEnd[d]);}
2173: PetscDualSpaceSectionCreate_Internal(sp, §ion);
2174: sp->pointSection = section;
2175: if (continuous && !(lag->interiorOnly)) {
2176: PetscInt h;
2178: for (p = pStratStart[depth - 1]; p < pStratEnd[depth - 1]; p++) { /* calculate the facet dual spaces */
2179: PetscReal v0[3];
2180: DMPolytopeType ptype;
2181: PetscReal J[9], detJ;
2182: PetscInt q;
2184: DMPlexComputeCellGeometryAffineFEM(dm, p, v0, J, NULL, &detJ);
2185: DMPlexGetCellType(dm, p, &ptype);
2187: /* compare to previous facets: if computed, reference that dualspace */
2188: for (q = pStratStart[depth - 1]; q < p; q++) {
2189: DMPolytopeType qtype;
2191: DMPlexGetCellType(dm, q, &qtype);
2192: if (qtype == ptype) break;
2193: }
2194: if (q < p) { /* this facet has the same dual space as that one */
2195: PetscObjectReference((PetscObject)sp->pointSpaces[q]);
2196: sp->pointSpaces[p] = sp->pointSpaces[q];
2197: continue;
2198: }
2199: /* if not, recursively compute this dual space */
2200: PetscDualSpaceCreateFacetSubspace_Lagrange(sp,NULL,p,formDegree,Ncopies,PETSC_FALSE,&sp->pointSpaces[p]);
2201: }
2202: for (h = 2; h <= depth; h++) { /* get the higher subspaces from the facet subspaces */
2203: PetscInt hd = depth - h;
2204: PetscInt hdim = dim - h;
2206: if (hdim < PetscAbsInt(formDegree)) break;
2207: for (p = pStratStart[hd]; p < pStratEnd[hd]; p++) {
2208: PetscInt suppSize, s;
2209: const PetscInt *supp;
2211: DMPlexGetSupportSize(dm, p, &suppSize);
2212: DMPlexGetSupport(dm, p, &supp);
2213: for (s = 0; s < suppSize; s++) {
2214: DM qdm;
2215: PetscDualSpace qsp, psp;
2216: PetscInt c, coneSize, q;
2217: const PetscInt *cone;
2218: const PetscInt *refCone;
2220: q = supp[0];
2221: qsp = sp->pointSpaces[q];
2222: DMPlexGetConeSize(dm, q, &coneSize);
2223: DMPlexGetCone(dm, q, &cone);
2224: for (c = 0; c < coneSize; c++) if (cone[c] == p) break;
2225: if (c == coneSize) SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "cone/support mismatch");
2226: PetscDualSpaceGetDM(qsp, &qdm);
2227: DMPlexGetCone(qdm, 0, &refCone);
2228: /* get the equivalent dual space from the support dual space */
2229: PetscDualSpaceGetPointSubspace(qsp, refCone[c], &psp);
2230: if (!s) {
2231: PetscObjectReference((PetscObject)psp);
2232: sp->pointSpaces[p] = psp;
2233: }
2234: }
2235: }
2236: }
2237: for (p = 1; p < pEnd; p++) {
2238: PetscInt pspdim;
2239: if (!sp->pointSpaces[p]) continue;
2240: PetscDualSpaceGetInteriorDimension(sp->pointSpaces[p], &pspdim);
2241: PetscSectionSetDof(section, p, pspdim);
2242: }
2243: }
2245: if (Ncopies > 1) {
2246: Mat intMatScalar, allMatScalar;
2247: PetscDualSpace scalarsp;
2248: PetscDualSpace_Lag *scalarlag;
2250: PetscDualSpaceDuplicate(sp, &scalarsp);
2251: /* Setting the number of components to Nk is a space with 1 copy of each k-form */
2252: PetscDualSpaceSetNumComponents(scalarsp, Nk);
2253: PetscDualSpaceSetUp(scalarsp);
2254: PetscDualSpaceGetInteriorData(scalarsp, &(sp->intNodes), &intMatScalar);
2255: PetscObjectReference((PetscObject)(sp->intNodes));
2256: if (intMatScalar) {PetscDualSpaceLagrangeMatrixCreateCopies(intMatScalar, Nk, Ncopies, &(sp->intMat));}
2257: PetscDualSpaceGetAllData(scalarsp, &(sp->allNodes), &allMatScalar);
2258: PetscObjectReference((PetscObject)(sp->allNodes));
2259: PetscDualSpaceLagrangeMatrixCreateCopies(allMatScalar, Nk, Ncopies, &(sp->allMat));
2260: sp->spdim = scalarsp->spdim * Ncopies;
2261: sp->spintdim = scalarsp->spintdim * Ncopies;
2262: scalarlag = (PetscDualSpace_Lag *) scalarsp->data;
2263: PetscLagNodeIndicesReference(scalarlag->vertIndices);
2264: lag->vertIndices = scalarlag->vertIndices;
2265: PetscLagNodeIndicesReference(scalarlag->intNodeIndices);
2266: lag->intNodeIndices = scalarlag->intNodeIndices;
2267: PetscLagNodeIndicesReference(scalarlag->allNodeIndices);
2268: lag->allNodeIndices = scalarlag->allNodeIndices;
2269: PetscDualSpaceDestroy(&scalarsp);
2270: PetscSectionSetDof(section, 0, sp->spintdim);
2271: PetscDualSpaceSectionSetUp_Internal(sp, section);
2272: PetscDualSpaceComputeFunctionalsFromAllData(sp);
2273: PetscFree2(pStratStart, pStratEnd);
2274: DMDestroy(&dmint);
2275: return(0);
2276: }
2278: if (trimmed && !continuous) {
2279: /* the dofs of a trimmed space don't have a nice tensor/lattice structure:
2280: * just construct the continuous dual space and copy all of the data over,
2281: * allocating it all to the cell instead of splitting it up between the boundaries */
2282: PetscDualSpace spcont;
2283: PetscInt spdim, f;
2284: PetscQuadrature allNodes;
2285: PetscDualSpace_Lag *lagc;
2286: Mat allMat;
2288: PetscDualSpaceDuplicate(sp, &spcont);
2289: PetscDualSpaceLagrangeSetContinuity(spcont, PETSC_TRUE);
2290: PetscDualSpaceSetUp(spcont);
2291: PetscDualSpaceGetDimension(spcont, &spdim);
2292: sp->spdim = sp->spintdim = spdim;
2293: PetscSectionSetDof(section, 0, spdim);
2294: PetscDualSpaceSectionSetUp_Internal(sp, section);
2295: PetscMalloc1(spdim, &(sp->functional));
2296: for (f = 0; f < spdim; f++) {
2297: PetscQuadrature fn;
2299: PetscDualSpaceGetFunctional(spcont, f, &fn);
2300: PetscObjectReference((PetscObject)fn);
2301: sp->functional[f] = fn;
2302: }
2303: PetscDualSpaceGetAllData(spcont, &allNodes, &allMat);
2304: PetscObjectReference((PetscObject) allNodes);
2305: PetscObjectReference((PetscObject) allNodes);
2306: sp->allNodes = sp->intNodes = allNodes;
2307: PetscObjectReference((PetscObject) allMat);
2308: PetscObjectReference((PetscObject) allMat);
2309: sp->allMat = sp->intMat = allMat;
2310: lagc = (PetscDualSpace_Lag *) spcont->data;
2311: PetscLagNodeIndicesReference(lagc->vertIndices);
2312: lag->vertIndices = lagc->vertIndices;
2313: PetscLagNodeIndicesReference(lagc->allNodeIndices);
2314: PetscLagNodeIndicesReference(lagc->allNodeIndices);
2315: lag->intNodeIndices = lagc->allNodeIndices;
2316: lag->allNodeIndices = lagc->allNodeIndices;
2317: PetscDualSpaceDestroy(&spcont);
2318: PetscFree2(pStratStart, pStratEnd);
2319: DMDestroy(&dmint);
2320: return(0);
2321: }
2323: /* step 3: construct intNodes, and intMat, and combine it with boundray data to make allNodes and allMat */
2324: if (!tensorSpace) {
2325: if (!tensorCell) {PetscLagNodeIndicesCreateSimplexVertices(dm, &(lag->vertIndices));}
2327: if (trimmed) {
2328: /* there is one dof in the interior of the a trimmed element for each full polynomial of with degree at most
2329: * order + k - dim - 1 */
2330: if (order + PetscAbsInt(formDegree) > dim) {
2331: PetscInt sum = order + PetscAbsInt(formDegree) - dim - 1;
2332: PetscInt nDofs;
2334: PetscDualSpaceLagrangeCreateSimplexNodeMat(nodeFamily, dim, sum, Nk, numNodeSkip, &sp->intNodes, &sp->intMat, &(lag->intNodeIndices));
2335: MatGetSize(sp->intMat, &nDofs, NULL);
2336: PetscSectionSetDof(section, 0, nDofs);
2337: }
2338: PetscDualSpaceSectionSetUp_Internal(sp, section);
2339: PetscDualSpaceCreateAllDataFromInteriorData(sp);
2340: PetscDualSpaceLagrangeCreateAllNodeIdx(sp);
2341: } else {
2342: if (!continuous) {
2343: /* if discontinuous just construct one node for each set of dofs (a set of dofs is a basis for the k-form
2344: * space) */
2345: PetscInt sum = order;
2346: PetscInt nDofs;
2348: PetscDualSpaceLagrangeCreateSimplexNodeMat(nodeFamily, dim, sum, Nk, numNodeSkip, &sp->intNodes, &sp->intMat, &(lag->intNodeIndices));
2349: MatGetSize(sp->intMat, &nDofs, NULL);
2350: PetscSectionSetDof(section, 0, nDofs);
2351: PetscDualSpaceSectionSetUp_Internal(sp, section);
2352: PetscObjectReference((PetscObject)(sp->intNodes));
2353: sp->allNodes = sp->intNodes;
2354: PetscObjectReference((PetscObject)(sp->intMat));
2355: sp->allMat = sp->intMat;
2356: PetscLagNodeIndicesReference(lag->intNodeIndices);
2357: lag->allNodeIndices = lag->intNodeIndices;
2358: } else {
2359: /* there is one dof in the interior of the a full element for each trimmed polynomial of with degree at most
2360: * order + k - dim, but with complementary form degree */
2361: if (order + PetscAbsInt(formDegree) > dim) {
2362: PetscDualSpace trimmedsp;
2363: PetscDualSpace_Lag *trimmedlag;
2364: PetscQuadrature intNodes;
2365: PetscInt trFormDegree = formDegree >= 0 ? formDegree - dim : dim - PetscAbsInt(formDegree);
2366: PetscInt nDofs;
2367: Mat intMat;
2369: PetscDualSpaceDuplicate(sp, &trimmedsp);
2370: PetscDualSpaceLagrangeSetTrimmed(trimmedsp, PETSC_TRUE);
2371: PetscDualSpaceSetOrder(trimmedsp, order + PetscAbsInt(formDegree) - dim);
2372: PetscDualSpaceSetFormDegree(trimmedsp, trFormDegree);
2373: trimmedlag = (PetscDualSpace_Lag *) trimmedsp->data;
2374: trimmedlag->numNodeSkip = numNodeSkip + 1;
2375: PetscDualSpaceSetUp(trimmedsp);
2376: PetscDualSpaceGetAllData(trimmedsp, &intNodes, &intMat);
2377: PetscObjectReference((PetscObject)intNodes);
2378: sp->intNodes = intNodes;
2379: PetscLagNodeIndicesReference(trimmedlag->allNodeIndices);
2380: lag->intNodeIndices = trimmedlag->allNodeIndices;
2381: PetscObjectReference((PetscObject)intMat);
2382: if (PetscAbsInt(formDegree) > 0 && PetscAbsInt(formDegree) < dim) {
2383: PetscReal *T;
2384: PetscScalar *work;
2385: PetscInt nCols, nRows;
2386: Mat intMatT;
2388: MatDuplicate(intMat, MAT_COPY_VALUES, &intMatT);
2389: MatGetSize(intMat, &nRows, &nCols);
2390: PetscMalloc2(Nk * Nk, &T, nCols, &work);
2391: BiunitSimplexSymmetricFormTransformation(dim, formDegree, T);
2392: for (PetscInt row = 0; row < nRows; row++) {
2393: PetscInt nrCols;
2394: const PetscInt *rCols;
2395: const PetscScalar *rVals;
2397: MatGetRow(intMat, row, &nrCols, &rCols, &rVals);
2398: if (nrCols % Nk) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "nonzeros in intMat matrix are not in k-form size blocks");
2399: for (PetscInt b = 0; b < nrCols; b += Nk) {
2400: const PetscScalar *v = &rVals[b];
2401: PetscScalar *w = &work[b];
2402: for (PetscInt j = 0; j < Nk; j++) {
2403: w[j] = 0.;
2404: for (PetscInt i = 0; i < Nk; i++) {
2405: w[j] += v[i] * T[i * Nk + j];
2406: }
2407: }
2408: }
2409: MatSetValuesBlocked(intMatT, 1, &row, nrCols, rCols, work, INSERT_VALUES);
2410: MatRestoreRow(intMat, row, &nrCols, &rCols, &rVals);
2411: }
2412: MatAssemblyBegin(intMatT, MAT_FINAL_ASSEMBLY);
2413: MatAssemblyEnd(intMatT, MAT_FINAL_ASSEMBLY);
2414: MatDestroy(&intMat);
2415: intMat = intMatT;
2416: PetscLagNodeIndicesDestroy(&(lag->intNodeIndices));
2417: PetscLagNodeIndicesDuplicate(trimmedlag->allNodeIndices, &(lag->intNodeIndices));
2418: {
2419: PetscInt nNodes = lag->intNodeIndices->nNodes;
2420: PetscReal *newNodeVec = lag->intNodeIndices->nodeVec;
2421: const PetscReal *oldNodeVec = trimmedlag->allNodeIndices->nodeVec;
2423: for (PetscInt n = 0; n < nNodes; n++) {
2424: PetscReal *w = &newNodeVec[n * Nk];
2425: const PetscReal *v = &oldNodeVec[n * Nk];
2427: for (PetscInt j = 0; j < Nk; j++) {
2428: w[j] = 0.;
2429: for (PetscInt i = 0; i < Nk; i++) {
2430: w[j] += v[i] * T[i * Nk + j];
2431: }
2432: }
2433: }
2434: }
2435: PetscFree2(T, work);
2436: }
2437: sp->intMat = intMat;
2438: MatGetSize(sp->intMat, &nDofs, NULL);
2439: PetscDualSpaceDestroy(&trimmedsp);
2440: PetscSectionSetDof(section, 0, nDofs);
2441: }
2442: PetscDualSpaceSectionSetUp_Internal(sp, section);
2443: PetscDualSpaceCreateAllDataFromInteriorData(sp);
2444: PetscDualSpaceLagrangeCreateAllNodeIdx(sp);
2445: }
2446: }
2447: } else {
2448: PetscQuadrature intNodesTrace = NULL;
2449: PetscQuadrature intNodesFiber = NULL;
2450: PetscQuadrature intNodes = NULL;
2451: PetscLagNodeIndices intNodeIndices = NULL;
2452: Mat intMat = NULL;
2454: if (PetscAbsInt(formDegree) < dim) { /* get the trace k-forms on the first facet, and the 0-forms on the edge,
2455: and wedge them together to create some of the k-form dofs */
2456: PetscDualSpace trace, fiber;
2457: PetscDualSpace_Lag *tracel, *fiberl;
2458: Mat intMatTrace, intMatFiber;
2460: if (sp->pointSpaces[tensorf]) {
2461: PetscObjectReference((PetscObject)(sp->pointSpaces[tensorf]));
2462: trace = sp->pointSpaces[tensorf];
2463: } else {
2464: PetscDualSpaceCreateFacetSubspace_Lagrange(sp,NULL,tensorf,formDegree,Ncopies,PETSC_TRUE,&trace);
2465: }
2466: PetscDualSpaceCreateEdgeSubspace_Lagrange(sp,order,0,1,PETSC_TRUE,&fiber);
2467: tracel = (PetscDualSpace_Lag *) trace->data;
2468: fiberl = (PetscDualSpace_Lag *) fiber->data;
2469: PetscLagNodeIndicesCreateTensorVertices(dm, tracel->vertIndices, &(lag->vertIndices));
2470: PetscDualSpaceGetInteriorData(trace, &intNodesTrace, &intMatTrace);
2471: PetscDualSpaceGetInteriorData(fiber, &intNodesFiber, &intMatFiber);
2472: if (intNodesTrace && intNodesFiber) {
2473: PetscQuadratureCreateTensor(intNodesTrace, intNodesFiber, &intNodes);
2474: MatTensorAltV(intMatTrace, intMatFiber, dim-1, formDegree, 1, 0, &intMat);
2475: PetscLagNodeIndicesTensor(tracel->intNodeIndices, dim - 1, formDegree, fiberl->intNodeIndices, 1, 0, &intNodeIndices);
2476: }
2477: PetscObjectReference((PetscObject) intNodesTrace);
2478: PetscObjectReference((PetscObject) intNodesFiber);
2479: PetscDualSpaceDestroy(&fiber);
2480: PetscDualSpaceDestroy(&trace);
2481: }
2482: if (PetscAbsInt(formDegree) > 0) { /* get the trace (k-1)-forms on the first facet, and the 1-forms on the edge,
2483: and wedge them together to create the remaining k-form dofs */
2484: PetscDualSpace trace, fiber;
2485: PetscDualSpace_Lag *tracel, *fiberl;
2486: PetscQuadrature intNodesTrace2, intNodesFiber2, intNodes2;
2487: PetscLagNodeIndices intNodeIndices2;
2488: Mat intMatTrace, intMatFiber, intMat2;
2489: PetscInt traceDegree = formDegree > 0 ? formDegree - 1 : formDegree + 1;
2490: PetscInt fiberDegree = formDegree > 0 ? 1 : -1;
2492: PetscDualSpaceCreateFacetSubspace_Lagrange(sp,NULL,tensorf,traceDegree,Ncopies,PETSC_TRUE,&trace);
2493: PetscDualSpaceCreateEdgeSubspace_Lagrange(sp,order,fiberDegree,1,PETSC_TRUE,&fiber);
2494: tracel = (PetscDualSpace_Lag *) trace->data;
2495: fiberl = (PetscDualSpace_Lag *) fiber->data;
2496: if (!lag->vertIndices) {
2497: PetscLagNodeIndicesCreateTensorVertices(dm, tracel->vertIndices, &(lag->vertIndices));
2498: }
2499: PetscDualSpaceGetInteriorData(trace, &intNodesTrace2, &intMatTrace);
2500: PetscDualSpaceGetInteriorData(fiber, &intNodesFiber2, &intMatFiber);
2501: if (intNodesTrace2 && intNodesFiber2) {
2502: PetscQuadratureCreateTensor(intNodesTrace2, intNodesFiber2, &intNodes2);
2503: MatTensorAltV(intMatTrace, intMatFiber, dim-1, traceDegree, 1, fiberDegree, &intMat2);
2504: PetscLagNodeIndicesTensor(tracel->intNodeIndices, dim - 1, traceDegree, fiberl->intNodeIndices, 1, fiberDegree, &intNodeIndices2);
2505: if (!intMat) {
2506: intMat = intMat2;
2507: intNodes = intNodes2;
2508: intNodeIndices = intNodeIndices2;
2509: } else {
2510: /* merge the matrices, quadrature points, and nodes */
2511: PetscInt nM;
2512: PetscInt nDof, nDof2;
2513: PetscInt *toMerged = NULL, *toMerged2 = NULL;
2514: PetscQuadrature merged = NULL;
2515: PetscLagNodeIndices intNodeIndicesMerged = NULL;
2516: Mat matMerged = NULL;
2518: MatGetSize(intMat, &nDof, NULL);
2519: MatGetSize(intMat2, &nDof2, NULL);
2520: PetscQuadraturePointsMerge(intNodes, intNodes2, &merged, &toMerged, &toMerged2);
2521: PetscQuadratureGetData(merged, NULL, NULL, &nM, NULL, NULL);
2522: MatricesMerge(intMat, intMat2, dim, formDegree, nM, toMerged, toMerged2, &matMerged);
2523: PetscLagNodeIndicesMerge(intNodeIndices, intNodeIndices2, &intNodeIndicesMerged);
2524: PetscFree(toMerged);
2525: PetscFree(toMerged2);
2526: MatDestroy(&intMat);
2527: MatDestroy(&intMat2);
2528: PetscQuadratureDestroy(&intNodes);
2529: PetscQuadratureDestroy(&intNodes2);
2530: PetscLagNodeIndicesDestroy(&intNodeIndices);
2531: PetscLagNodeIndicesDestroy(&intNodeIndices2);
2532: intNodes = merged;
2533: intMat = matMerged;
2534: intNodeIndices = intNodeIndicesMerged;
2535: if (!trimmed) {
2536: /* I think users expect that, when a node has a full basis for the k-forms,
2537: * they should be consecutive dofs. That isn't the case for trimmed spaces,
2538: * but is for some of the nodes in untrimmed spaces, so in that case we
2539: * sort them to group them by node */
2540: Mat intMatPerm;
2542: MatPermuteByNodeIdx(intMat, intNodeIndices, &intMatPerm);
2543: MatDestroy(&intMat);
2544: intMat = intMatPerm;
2545: }
2546: }
2547: }
2548: PetscDualSpaceDestroy(&fiber);
2549: PetscDualSpaceDestroy(&trace);
2550: }
2551: PetscQuadratureDestroy(&intNodesTrace);
2552: PetscQuadratureDestroy(&intNodesFiber);
2553: sp->intNodes = intNodes;
2554: sp->intMat = intMat;
2555: lag->intNodeIndices = intNodeIndices;
2556: {
2557: PetscInt nDofs = 0;
2559: if (intMat) {
2560: MatGetSize(intMat, &nDofs, NULL);
2561: }
2562: PetscSectionSetDof(section, 0, nDofs);
2563: }
2564: PetscDualSpaceSectionSetUp_Internal(sp, section);
2565: if (continuous) {
2566: PetscDualSpaceCreateAllDataFromInteriorData(sp);
2567: PetscDualSpaceLagrangeCreateAllNodeIdx(sp);
2568: } else {
2569: PetscObjectReference((PetscObject) intNodes);
2570: sp->allNodes = intNodes;
2571: PetscObjectReference((PetscObject) intMat);
2572: sp->allMat = intMat;
2573: PetscLagNodeIndicesReference(intNodeIndices);
2574: lag->allNodeIndices = intNodeIndices;
2575: }
2576: }
2577: PetscSectionGetStorageSize(section, &sp->spdim);
2578: PetscSectionGetConstrainedStorageSize(section, &sp->spintdim);
2579: PetscDualSpaceComputeFunctionalsFromAllData(sp);
2580: PetscFree2(pStratStart, pStratEnd);
2581: DMDestroy(&dmint);
2582: return(0);
2583: }
2585: /* Create a matrix that represents the transformation that DMPlexVecGetClosure() would need
2586: * to get the representation of the dofs for a mesh point if the mesh point had this orientation
2587: * relative to the cell */
2588: PetscErrorCode PetscDualSpaceCreateInteriorSymmetryMatrix_Lagrange(PetscDualSpace sp, PetscInt ornt, Mat *symMat)
2589: {
2590: PetscDualSpace_Lag *lag;
2591: DM dm;
2592: PetscLagNodeIndices vertIndices, intNodeIndices;
2593: PetscLagNodeIndices ni;
2594: PetscInt nodeIdxDim, nodeVecDim, nNodes;
2595: PetscInt formDegree;
2596: PetscInt *perm, *permOrnt;
2597: PetscInt *nnz;
2598: PetscInt n;
2599: PetscInt maxGroupSize;
2600: PetscScalar *V, *W, *work;
2601: Mat A;
2605: if (!sp->spintdim) {
2606: *symMat = NULL;
2607: return(0);
2608: }
2609: lag = (PetscDualSpace_Lag *) sp->data;
2610: vertIndices = lag->vertIndices;
2611: intNodeIndices = lag->intNodeIndices;
2612: PetscDualSpaceGetDM(sp, &dm);
2613: PetscDualSpaceGetFormDegree(sp, &formDegree);
2614: PetscNew(&ni);
2615: ni->refct = 1;
2616: ni->nodeIdxDim = nodeIdxDim = intNodeIndices->nodeIdxDim;
2617: ni->nodeVecDim = nodeVecDim = intNodeIndices->nodeVecDim;
2618: ni->nNodes = nNodes = intNodeIndices->nNodes;
2619: PetscMalloc1(nNodes * nodeIdxDim, &(ni->nodeIdx));
2620: PetscMalloc1(nNodes * nodeVecDim, &(ni->nodeVec));
2621: /* push forward the dofs by the symmetry of the reference element induced by ornt */
2622: PetscLagNodeIndicesPushForward(dm, vertIndices, 0, vertIndices, intNodeIndices, ornt, formDegree, ni->nodeIdx, ni->nodeVec);
2623: /* get the revlex order for both the original and transformed dofs */
2624: PetscLagNodeIndicesGetPermutation(intNodeIndices, &perm);
2625: PetscLagNodeIndicesGetPermutation(ni, &permOrnt);
2626: PetscMalloc1(nNodes, &nnz);
2627: for (n = 0, maxGroupSize = 0; n < nNodes;) { /* incremented in the loop */
2628: PetscInt *nind = &(ni->nodeIdx[permOrnt[n] * nodeIdxDim]);
2629: PetscInt m, nEnd;
2630: PetscInt groupSize;
2631: /* for each group of dofs that have the same nodeIdx coordinate */
2632: for (nEnd = n + 1; nEnd < nNodes; nEnd++) {
2633: PetscInt *mind = &(ni->nodeIdx[permOrnt[nEnd] * nodeIdxDim]);
2634: PetscInt d;
2636: /* compare the oriented permutation indices */
2637: for (d = 0; d < nodeIdxDim; d++) if (mind[d] != nind[d]) break;
2638: if (d < nodeIdxDim) break;
2639: }
2640: /* permOrnt[[n, nEnd)] is a group of dofs that, under the symmetry are at the same location */
2642: /* the symmetry had better map the group of dofs with the same permuted nodeIdx
2643: * to a group of dofs with the same size, otherwise we messed up */
2644: if (PetscDefined(USE_DEBUG)) {
2645: PetscInt m;
2646: PetscInt *nind = &(intNodeIndices->nodeIdx[perm[n] * nodeIdxDim]);
2648: for (m = n + 1; m < nEnd; m++) {
2649: PetscInt *mind = &(intNodeIndices->nodeIdx[perm[m] * nodeIdxDim]);
2650: PetscInt d;
2652: /* compare the oriented permutation indices */
2653: for (d = 0; d < nodeIdxDim; d++) if (mind[d] != nind[d]) break;
2654: if (d < nodeIdxDim) break;
2655: }
2656: if (m < nEnd) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Dofs with same index after symmetry not same block size");
2657: }
2658: groupSize = nEnd - n;
2659: /* each pushforward dof vector will be expressed in a basis of the unpermuted dofs */
2660: for (m = n; m < nEnd; m++) nnz[permOrnt[m]] = groupSize;
2662: maxGroupSize = PetscMax(maxGroupSize, nEnd - n);
2663: n = nEnd;
2664: }
2665: if (maxGroupSize > nodeVecDim) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Dofs are not in blocks that can be solved");
2666: MatCreateSeqAIJ(PETSC_COMM_SELF, nNodes, nNodes, 0, nnz, &A);
2667: PetscFree(nnz);
2668: PetscMalloc3(maxGroupSize * nodeVecDim, &V, maxGroupSize * nodeVecDim, &W, nodeVecDim * 2, &work);
2669: for (n = 0; n < nNodes;) { /* incremented in the loop */
2670: PetscInt *nind = &(ni->nodeIdx[permOrnt[n] * nodeIdxDim]);
2671: PetscInt nEnd;
2672: PetscInt m;
2673: PetscInt groupSize;
2674: for (nEnd = n + 1; nEnd < nNodes; nEnd++) {
2675: PetscInt *mind = &(ni->nodeIdx[permOrnt[nEnd] * nodeIdxDim]);
2676: PetscInt d;
2678: /* compare the oriented permutation indices */
2679: for (d = 0; d < nodeIdxDim; d++) if (mind[d] != nind[d]) break;
2680: if (d < nodeIdxDim) break;
2681: }
2682: groupSize = nEnd - n;
2683: /* get all of the vectors from the original and all of the pushforward vectors */
2684: for (m = n; m < nEnd; m++) {
2685: PetscInt d;
2687: for (d = 0; d < nodeVecDim; d++) {
2688: V[(m - n) * nodeVecDim + d] = intNodeIndices->nodeVec[perm[m] * nodeVecDim + d];
2689: W[(m - n) * nodeVecDim + d] = ni->nodeVec[permOrnt[m] * nodeVecDim + d];
2690: }
2691: }
2692: /* now we have to solve for W in terms of V: the systems isn't always square, but the span
2693: * of V and W should always be the same, so the solution of the normal equations works */
2694: {
2695: char transpose = 'N';
2696: PetscBLASInt bm = nodeVecDim;
2697: PetscBLASInt bn = groupSize;
2698: PetscBLASInt bnrhs = groupSize;
2699: PetscBLASInt blda = bm;
2700: PetscBLASInt bldb = bm;
2701: PetscBLASInt blwork = 2 * nodeVecDim;
2702: PetscBLASInt info;
2704: PetscStackCallBLAS("LAPACKgels",LAPACKgels_(&transpose,&bm,&bn,&bnrhs,V,&blda,W,&bldb,work,&blwork, &info));
2705: if (info != 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"Bad argument to GELS");
2706: /* repack */
2707: {
2708: PetscInt i, j;
2710: for (i = 0; i < groupSize; i++) {
2711: for (j = 0; j < groupSize; j++) {
2712: /* notice the different leading dimension */
2713: V[i * groupSize + j] = W[i * nodeVecDim + j];
2714: }
2715: }
2716: }
2717: if (PetscDefined(USE_DEBUG)) {
2718: PetscReal res;
2720: /* check that the normal error is 0 */
2721: for (m = n; m < nEnd; m++) {
2722: PetscInt d;
2724: for (d = 0; d < nodeVecDim; d++) {
2725: W[(m - n) * nodeVecDim + d] = ni->nodeVec[permOrnt[m] * nodeVecDim + d];
2726: }
2727: }
2728: res = 0.;
2729: for (PetscInt i = 0; i < groupSize; i++) {
2730: for (PetscInt j = 0; j < nodeVecDim; j++) {
2731: for (PetscInt k = 0; k < groupSize; k++) {
2732: W[i * nodeVecDim + j] -= V[i * groupSize + k] * intNodeIndices->nodeVec[perm[n+k] * nodeVecDim + j];
2733: }
2734: res += PetscAbsScalar(W[i * nodeVecDim + j]);
2735: }
2736: }
2737: if (res > PETSC_SMALL) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"Dof block did not solve");
2738: }
2739: }
2740: MatSetValues(A, groupSize, &permOrnt[n], groupSize, &perm[n], V, INSERT_VALUES);
2741: n = nEnd;
2742: }
2743: MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY);
2744: MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY);
2745: *symMat = A;
2746: PetscFree3(V,W,work);
2747: PetscLagNodeIndicesDestroy(&ni);
2748: return(0);
2749: }
2751: #define BaryIndex(perEdge,a,b,c) (((b)*(2*perEdge+1-(b)))/2)+(c)
2753: #define CartIndex(perEdge,a,b) (perEdge*(a)+b)
2755: /* the existing interface for symmetries is insufficient for all cases:
2756: * - it should be sufficient for form degrees that are scalar (0 and n)
2757: * - it should be sufficient for hypercube dofs
2758: * - it isn't sufficient for simplex cells with non-scalar form degrees if
2759: * there are any dofs in the interior
2760: *
2761: * We compute the general transformation matrices, and if they fit, we return them,
2762: * otherwise we error (but we should probably change the interface to allow for
2763: * these symmetries)
2764: */
2765: static PetscErrorCode PetscDualSpaceGetSymmetries_Lagrange(PetscDualSpace sp, const PetscInt ****perms, const PetscScalar ****flips)
2766: {
2767: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *) sp->data;
2768: PetscInt dim, order, Nc;
2769: PetscErrorCode ierr;
2772: PetscDualSpaceGetOrder(sp,&order);
2773: PetscDualSpaceGetNumComponents(sp,&Nc);
2774: DMGetDimension(sp->dm,&dim);
2775: if (!lag->symComputed) { /* store symmetries */
2776: PetscInt pStart, pEnd, p;
2777: PetscInt numPoints;
2778: PetscInt numFaces;
2779: PetscInt spintdim;
2780: PetscInt ***symperms;
2781: PetscScalar ***symflips;
2783: DMPlexGetChart(sp->dm, &pStart, &pEnd);
2784: numPoints = pEnd - pStart;
2785: DMPlexGetConeSize(sp->dm, 0, &numFaces);
2786: PetscCalloc1(numPoints,&symperms);
2787: PetscCalloc1(numPoints,&symflips);
2788: spintdim = sp->spintdim;
2789: /* The nodal symmetry behavior is not present when tensorSpace != tensorCell: someone might want this for the "S"
2790: * family of FEEC spaces. Most used in particular are discontinuous polynomial L2 spaces in tensor cells, where
2791: * the symmetries are not necessary for FE assembly. So for now we assume this is the case and don't return
2792: * symmetries if tensorSpace != tensorCell */
2793: if (spintdim && 0 < dim && dim < 3 && (lag->tensorSpace == lag->tensorCell)) { /* compute self symmetries */
2794: PetscInt **cellSymperms;
2795: PetscScalar **cellSymflips;
2796: PetscInt ornt;
2797: PetscInt nCopies = Nc / lag->intNodeIndices->nodeVecDim;
2798: PetscInt nNodes = lag->intNodeIndices->nNodes;
2800: lag->numSelfSym = 2 * numFaces;
2801: lag->selfSymOff = numFaces;
2802: PetscCalloc1(2*numFaces,&cellSymperms);
2803: PetscCalloc1(2*numFaces,&cellSymflips);
2804: /* we want to be able to index symmetries directly with the orientations, which range from [-numFaces,numFaces) */
2805: symperms[0] = &cellSymperms[numFaces];
2806: symflips[0] = &cellSymflips[numFaces];
2807: if (lag->intNodeIndices->nodeVecDim * nCopies != Nc) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Node indices incompatible with dofs");
2808: if (nNodes * nCopies != spintdim) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Node indices incompatible with dofs");
2809: 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 */
2810: Mat symMat;
2811: PetscInt *perm;
2812: PetscScalar *flips;
2813: PetscInt i;
2815: if (!ornt) continue;
2816: PetscMalloc1(spintdim, &perm);
2817: PetscCalloc1(spintdim, &flips);
2818: for (i = 0; i < spintdim; i++) perm[i] = -1;
2819: PetscDualSpaceCreateInteriorSymmetryMatrix_Lagrange(sp, ornt, &symMat);
2820: for (i = 0; i < nNodes; i++) {
2821: PetscInt ncols;
2822: PetscInt j, k;
2823: const PetscInt *cols;
2824: const PetscScalar *vals;
2825: PetscBool nz_seen = PETSC_FALSE;
2827: MatGetRow(symMat, i, &ncols, &cols, &vals);
2828: for (j = 0; j < ncols; j++) {
2829: if (PetscAbsScalar(vals[j]) > PETSC_SMALL) {
2830: if (nz_seen) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "This dual space has symmetries that can't be described as a permutation + sign flips");
2831: nz_seen = PETSC_TRUE;
2832: if (PetscAbsReal(PetscAbsScalar(vals[j]) - PetscRealConstant(1.)) > PETSC_SMALL) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "This dual space has symmetries that can't be described as a permutation + sign flips");
2833: if (PetscAbsReal(PetscImaginaryPart(vals[j])) > PETSC_SMALL) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "This dual space has symmetries that can't be described as a permutation + sign flips");
2834: if (perm[cols[j] * nCopies] >= 0) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "This dual space has symmetries that can't be described as a permutation + sign flips");
2835: for (k = 0; k < nCopies; k++) {
2836: perm[cols[j] * nCopies + k] = i * nCopies + k;
2837: }
2838: if (PetscRealPart(vals[j]) < 0.) {
2839: for (k = 0; k < nCopies; k++) {
2840: flips[i * nCopies + k] = -1.;
2841: }
2842: } else {
2843: for (k = 0; k < nCopies; k++) {
2844: flips[i * nCopies + k] = 1.;
2845: }
2846: }
2847: }
2848: }
2849: MatRestoreRow(symMat, i, &ncols, &cols, &vals);
2850: }
2851: MatDestroy(&symMat);
2852: /* if there were no sign flips, keep NULL */
2853: for (i = 0; i < spintdim; i++) if (flips[i] != 1.) break;
2854: if (i == spintdim) {
2855: PetscFree(flips);
2856: flips = NULL;
2857: }
2858: /* if the permutation is identity, keep NULL */
2859: for (i = 0; i < spintdim; i++) if (perm[i] != i) break;
2860: if (i == spintdim) {
2861: PetscFree(perm);
2862: perm = NULL;
2863: }
2864: symperms[0][ornt] = perm;
2865: symflips[0][ornt] = flips;
2866: }
2867: /* if no orientations produced non-identity permutations, keep NULL */
2868: for (ornt = -numFaces; ornt < numFaces; ornt++) if (symperms[0][ornt]) break;
2869: if (ornt == numFaces) {
2870: PetscFree(cellSymperms);
2871: symperms[0] = NULL;
2872: }
2873: /* if no orientations produced sign flips, keep NULL */
2874: for (ornt = -numFaces; ornt < numFaces; ornt++) if (symflips[0][ornt]) break;
2875: if (ornt == numFaces) {
2876: PetscFree(cellSymflips);
2877: symflips[0] = NULL;
2878: }
2879: }
2880: { /* get the symmetries of closure points */
2881: PetscInt closureSize = 0;
2882: PetscInt *closure = NULL;
2883: PetscInt r;
2885: DMPlexGetTransitiveClosure(sp->dm,0,PETSC_TRUE,&closureSize,&closure);
2886: for (r = 0; r < closureSize; r++) {
2887: PetscDualSpace psp;
2888: PetscInt point = closure[2 * r];
2889: PetscInt pspintdim;
2890: const PetscInt ***psymperms = NULL;
2891: const PetscScalar ***psymflips = NULL;
2893: if (!point) continue;
2894: PetscDualSpaceGetPointSubspace(sp, point, &psp);
2895: if (!psp) continue;
2896: PetscDualSpaceGetInteriorDimension(psp, &pspintdim);
2897: if (!pspintdim) continue;
2898: PetscDualSpaceGetSymmetries(psp,&psymperms,&psymflips);
2899: symperms[r] = (PetscInt **) (psymperms ? psymperms[0] : NULL);
2900: symflips[r] = (PetscScalar **) (psymflips ? psymflips[0] : NULL);
2901: }
2902: DMPlexRestoreTransitiveClosure(sp->dm,0,PETSC_TRUE,&closureSize,&closure);
2903: }
2904: for (p = 0; p < pEnd; p++) if (symperms[p]) break;
2905: if (p == pEnd) {
2906: PetscFree(symperms);
2907: symperms = NULL;
2908: }
2909: for (p = 0; p < pEnd; p++) if (symflips[p]) break;
2910: if (p == pEnd) {
2911: PetscFree(symflips);
2912: symflips = NULL;
2913: }
2914: lag->symperms = symperms;
2915: lag->symflips = symflips;
2916: lag->symComputed = PETSC_TRUE;
2917: }
2918: if (perms) *perms = (const PetscInt ***) lag->symperms;
2919: if (flips) *flips = (const PetscScalar ***) lag->symflips;
2920: return(0);
2921: }
2923: static PetscErrorCode PetscDualSpaceLagrangeGetContinuity_Lagrange(PetscDualSpace sp, PetscBool *continuous)
2924: {
2925: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *) sp->data;
2930: *continuous = lag->continuous;
2931: return(0);
2932: }
2934: static PetscErrorCode PetscDualSpaceLagrangeSetContinuity_Lagrange(PetscDualSpace sp, PetscBool continuous)
2935: {
2936: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *) sp->data;
2940: lag->continuous = continuous;
2941: return(0);
2942: }
2944: /*@
2945: PetscDualSpaceLagrangeGetContinuity - Retrieves the flag for element continuity
2947: Not Collective
2949: Input Parameter:
2950: . sp - the PetscDualSpace
2952: Output Parameter:
2953: . continuous - flag for element continuity
2955: Level: intermediate
2957: .seealso: PetscDualSpaceLagrangeSetContinuity()
2958: @*/
2959: PetscErrorCode PetscDualSpaceLagrangeGetContinuity(PetscDualSpace sp, PetscBool *continuous)
2960: {
2966: PetscTryMethod(sp, "PetscDualSpaceLagrangeGetContinuity_C", (PetscDualSpace,PetscBool*),(sp,continuous));
2967: return(0);
2968: }
2970: /*@
2971: PetscDualSpaceLagrangeSetContinuity - Indicate whether the element is continuous
2973: Logically Collective on sp
2975: Input Parameters:
2976: + sp - the PetscDualSpace
2977: - continuous - flag for element continuity
2979: Options Database:
2980: . -petscdualspace_lagrange_continuity <bool>
2982: Level: intermediate
2984: .seealso: PetscDualSpaceLagrangeGetContinuity()
2985: @*/
2986: PetscErrorCode PetscDualSpaceLagrangeSetContinuity(PetscDualSpace sp, PetscBool continuous)
2987: {
2993: PetscTryMethod(sp, "PetscDualSpaceLagrangeSetContinuity_C", (PetscDualSpace,PetscBool),(sp,continuous));
2994: return(0);
2995: }
2997: static PetscErrorCode PetscDualSpaceLagrangeGetTensor_Lagrange(PetscDualSpace sp, PetscBool *tensor)
2998: {
2999: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
3002: *tensor = lag->tensorSpace;
3003: return(0);
3004: }
3006: static PetscErrorCode PetscDualSpaceLagrangeSetTensor_Lagrange(PetscDualSpace sp, PetscBool tensor)
3007: {
3008: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
3011: lag->tensorSpace = tensor;
3012: return(0);
3013: }
3015: static PetscErrorCode PetscDualSpaceLagrangeGetTrimmed_Lagrange(PetscDualSpace sp, PetscBool *trimmed)
3016: {
3017: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
3020: *trimmed = lag->trimmed;
3021: return(0);
3022: }
3024: static PetscErrorCode PetscDualSpaceLagrangeSetTrimmed_Lagrange(PetscDualSpace sp, PetscBool trimmed)
3025: {
3026: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
3029: lag->trimmed = trimmed;
3030: return(0);
3031: }
3033: static PetscErrorCode PetscDualSpaceLagrangeGetNodeType_Lagrange(PetscDualSpace sp, PetscDTNodeType *nodeType, PetscBool *boundary, PetscReal *exponent)
3034: {
3035: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
3038: if (nodeType) *nodeType = lag->nodeType;
3039: if (boundary) *boundary = lag->endNodes;
3040: if (exponent) *exponent = lag->nodeExponent;
3041: return(0);
3042: }
3044: static PetscErrorCode PetscDualSpaceLagrangeSetNodeType_Lagrange(PetscDualSpace sp, PetscDTNodeType nodeType, PetscBool boundary, PetscReal exponent)
3045: {
3046: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
3049: if (nodeType == PETSCDTNODES_GAUSSJACOBI && exponent <= -1.) SETERRQ(PetscObjectComm((PetscObject) sp), PETSC_ERR_ARG_OUTOFRANGE, "Exponent must be > -1");
3050: lag->nodeType = nodeType;
3051: lag->endNodes = boundary;
3052: lag->nodeExponent = exponent;
3053: return(0);
3054: }
3056: static PetscErrorCode PetscDualSpaceLagrangeGetUseMoments_Lagrange(PetscDualSpace sp, PetscBool *useMoments)
3057: {
3058: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
3061: *useMoments = lag->useMoments;
3062: return(0);
3063: }
3065: static PetscErrorCode PetscDualSpaceLagrangeSetUseMoments_Lagrange(PetscDualSpace sp, PetscBool useMoments)
3066: {
3067: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
3070: lag->useMoments = useMoments;
3071: return(0);
3072: }
3074: static PetscErrorCode PetscDualSpaceLagrangeGetMomentOrder_Lagrange(PetscDualSpace sp, PetscInt *momentOrder)
3075: {
3076: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
3079: *momentOrder = lag->momentOrder;
3080: return(0);
3081: }
3083: static PetscErrorCode PetscDualSpaceLagrangeSetMomentOrder_Lagrange(PetscDualSpace sp, PetscInt momentOrder)
3084: {
3085: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
3088: lag->momentOrder = momentOrder;
3089: return(0);
3090: }
3092: /*@
3093: PetscDualSpaceLagrangeGetTensor - Get the tensor nature of the dual space
3095: Not collective
3097: Input Parameter:
3098: . sp - The PetscDualSpace
3100: Output Parameter:
3101: . tensor - Whether the dual space has tensor layout (vs. simplicial)
3103: Level: intermediate
3105: .seealso: PetscDualSpaceLagrangeSetTensor(), PetscDualSpaceCreate()
3106: @*/
3107: PetscErrorCode PetscDualSpaceLagrangeGetTensor(PetscDualSpace sp, PetscBool *tensor)
3108: {
3114: PetscTryMethod(sp,"PetscDualSpaceLagrangeGetTensor_C",(PetscDualSpace,PetscBool *),(sp,tensor));
3115: return(0);
3116: }
3118: /*@
3119: PetscDualSpaceLagrangeSetTensor - Set the tensor nature of the dual space
3121: Not collective
3123: Input Parameters:
3124: + sp - The PetscDualSpace
3125: - tensor - Whether the dual space has tensor layout (vs. simplicial)
3127: Level: intermediate
3129: .seealso: PetscDualSpaceLagrangeGetTensor(), PetscDualSpaceCreate()
3130: @*/
3131: PetscErrorCode PetscDualSpaceLagrangeSetTensor(PetscDualSpace sp, PetscBool tensor)
3132: {
3137: PetscTryMethod(sp,"PetscDualSpaceLagrangeSetTensor_C",(PetscDualSpace,PetscBool),(sp,tensor));
3138: return(0);
3139: }
3141: /*@
3142: PetscDualSpaceLagrangeGetTrimmed - Get the trimmed nature of the dual space
3144: Not collective
3146: Input Parameter:
3147: . sp - The PetscDualSpace
3149: Output Parameter:
3150: . 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)
3152: Level: intermediate
3154: .seealso: PetscDualSpaceLagrangeSetTrimmed(), PetscDualSpaceCreate()
3155: @*/
3156: PetscErrorCode PetscDualSpaceLagrangeGetTrimmed(PetscDualSpace sp, PetscBool *trimmed)
3157: {
3163: PetscTryMethod(sp,"PetscDualSpaceLagrangeGetTrimmed_C",(PetscDualSpace,PetscBool *),(sp,trimmed));
3164: return(0);
3165: }
3167: /*@
3168: PetscDualSpaceLagrangeSetTrimmed - Set the trimmed nature of the dual space
3170: Not collective
3172: Input Parameters:
3173: + sp - The PetscDualSpace
3174: - 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)
3176: Level: intermediate
3178: .seealso: PetscDualSpaceLagrangeGetTrimmed(), PetscDualSpaceCreate()
3179: @*/
3180: PetscErrorCode PetscDualSpaceLagrangeSetTrimmed(PetscDualSpace sp, PetscBool trimmed)
3181: {
3186: PetscTryMethod(sp,"PetscDualSpaceLagrangeSetTrimmed_C",(PetscDualSpace,PetscBool),(sp,trimmed));
3187: return(0);
3188: }
3190: /*@
3191: PetscDualSpaceLagrangeGetNodeType - Get a description of how nodes are laid out for Lagrange polynomials in this
3192: dual space
3194: Not collective
3196: Input Parameter:
3197: . sp - The PetscDualSpace
3199: Output Parameters:
3200: + nodeType - The type of nodes
3201: . boundary - Whether the node type is one that includes endpoints (if nodeType is PETSCDTNODES_GAUSSJACOBI, nodes that
3202: include the boundary are Gauss-Lobatto-Jacobi nodes)
3203: - exponent - If nodeType is PETSCDTNODES_GAUSJACOBI, indicates the exponent used for both ends of the 1D Jacobi weight function
3204: '0' is Gauss-Legendre, '-0.5' is Gauss-Chebyshev of the first type, '0.5' is Gauss-Chebyshev of the second type
3206: Level: advanced
3208: .seealso: PetscDTNodeType, PetscDualSpaceLagrangeSetNodeType()
3209: @*/
3210: PetscErrorCode PetscDualSpaceLagrangeGetNodeType(PetscDualSpace sp, PetscDTNodeType *nodeType, PetscBool *boundary, PetscReal *exponent)
3211: {
3219: PetscTryMethod(sp,"PetscDualSpaceLagrangeGetNodeType_C",(PetscDualSpace,PetscDTNodeType *,PetscBool *,PetscReal *),(sp,nodeType,boundary,exponent));
3220: return(0);
3221: }
3223: /*@
3224: PetscDualSpaceLagrangeSetNodeType - Set a description of how nodes are laid out for Lagrange polynomials in this
3225: dual space
3227: Logically collective
3229: Input Parameters:
3230: + sp - The PetscDualSpace
3231: . nodeType - The type of nodes
3232: . boundary - Whether the node type is one that includes endpoints (if nodeType is PETSCDTNODES_GAUSSJACOBI, nodes that
3233: include the boundary are Gauss-Lobatto-Jacobi nodes)
3234: - exponent - If nodeType is PETSCDTNODES_GAUSJACOBI, indicates the exponent used for both ends of the 1D Jacobi weight function
3235: '0' is Gauss-Legendre, '-0.5' is Gauss-Chebyshev of the first type, '0.5' is Gauss-Chebyshev of the second type
3237: Level: advanced
3239: .seealso: PetscDTNodeType, PetscDualSpaceLagrangeGetNodeType()
3240: @*/
3241: PetscErrorCode PetscDualSpaceLagrangeSetNodeType(PetscDualSpace sp, PetscDTNodeType nodeType, PetscBool boundary, PetscReal exponent)
3242: {
3247: PetscTryMethod(sp,"PetscDualSpaceLagrangeSetNodeType_C",(PetscDualSpace,PetscDTNodeType,PetscBool,PetscReal),(sp,nodeType,boundary,exponent));
3248: return(0);
3249: }
3251: /*@
3252: PetscDualSpaceLagrangeGetUseMoments - Get the flag for using moment functionals
3254: Not collective
3256: Input Parameter:
3257: . sp - The PetscDualSpace
3259: Output Parameter:
3260: . useMoments - Moment flag
3262: Level: advanced
3264: .seealso: PetscDualSpaceLagrangeSetUseMoments()
3265: @*/
3266: PetscErrorCode PetscDualSpaceLagrangeGetUseMoments(PetscDualSpace sp, PetscBool *useMoments)
3267: {
3273: PetscUseMethod(sp,"PetscDualSpaceLagrangeGetUseMoments_C",(PetscDualSpace,PetscBool *),(sp,useMoments));
3274: return(0);
3275: }
3277: /*@
3278: PetscDualSpaceLagrangeSetUseMoments - Set the flag for moment functionals
3280: Logically collective
3282: Input Parameters:
3283: + sp - The PetscDualSpace
3284: - useMoments - The flag for moment functionals
3286: Level: advanced
3288: .seealso: PetscDualSpaceLagrangeGetUseMoments()
3289: @*/
3290: PetscErrorCode PetscDualSpaceLagrangeSetUseMoments(PetscDualSpace sp, PetscBool useMoments)
3291: {
3296: PetscTryMethod(sp,"PetscDualSpaceLagrangeSetUseMoments_C",(PetscDualSpace,PetscBool),(sp,useMoments));
3297: return(0);
3298: }
3300: /*@
3301: PetscDualSpaceLagrangeGetMomentOrder - Get the order for moment integration
3303: Not collective
3305: Input Parameter:
3306: . sp - The PetscDualSpace
3308: Output Parameter:
3309: . order - Moment integration order
3311: Level: advanced
3313: .seealso: PetscDualSpaceLagrangeSetMomentOrder()
3314: @*/
3315: PetscErrorCode PetscDualSpaceLagrangeGetMomentOrder(PetscDualSpace sp, PetscInt *order)
3316: {
3322: PetscUseMethod(sp,"PetscDualSpaceLagrangeGetMomentOrder_C",(PetscDualSpace,PetscInt *),(sp,order));
3323: return(0);
3324: }
3326: /*@
3327: PetscDualSpaceLagrangeSetMomentOrder - Set the order for moment integration
3329: Logically collective
3331: Input Parameters:
3332: + sp - The PetscDualSpace
3333: - order - The order for moment integration
3335: Level: advanced
3337: .seealso: PetscDualSpaceLagrangeGetMomentOrder()
3338: @*/
3339: PetscErrorCode PetscDualSpaceLagrangeSetMomentOrder(PetscDualSpace sp, PetscInt order)
3340: {
3345: PetscTryMethod(sp,"PetscDualSpaceLagrangeSetMomentOrder_C",(PetscDualSpace,PetscInt),(sp,order));
3346: return(0);
3347: }
3349: static PetscErrorCode PetscDualSpaceInitialize_Lagrange(PetscDualSpace sp)
3350: {
3352: sp->ops->destroy = PetscDualSpaceDestroy_Lagrange;
3353: sp->ops->view = PetscDualSpaceView_Lagrange;
3354: sp->ops->setfromoptions = PetscDualSpaceSetFromOptions_Lagrange;
3355: sp->ops->duplicate = PetscDualSpaceDuplicate_Lagrange;
3356: sp->ops->setup = PetscDualSpaceSetUp_Lagrange;
3357: sp->ops->createheightsubspace = NULL;
3358: sp->ops->createpointsubspace = NULL;
3359: sp->ops->getsymmetries = PetscDualSpaceGetSymmetries_Lagrange;
3360: sp->ops->apply = PetscDualSpaceApplyDefault;
3361: sp->ops->applyall = PetscDualSpaceApplyAllDefault;
3362: sp->ops->applyint = PetscDualSpaceApplyInteriorDefault;
3363: sp->ops->createalldata = PetscDualSpaceCreateAllDataDefault;
3364: sp->ops->createintdata = PetscDualSpaceCreateInteriorDataDefault;
3365: return(0);
3366: }
3368: /*MC
3369: PETSCDUALSPACELAGRANGE = "lagrange" - A PetscDualSpace object that encapsulates a dual space of pointwise evaluation functionals
3371: Level: intermediate
3373: .seealso: PetscDualSpaceType, PetscDualSpaceCreate(), PetscDualSpaceSetType()
3374: M*/
3375: PETSC_EXTERN PetscErrorCode PetscDualSpaceCreate_Lagrange(PetscDualSpace sp)
3376: {
3377: PetscDualSpace_Lag *lag;
3378: PetscErrorCode ierr;
3382: PetscNewLog(sp,&lag);
3383: sp->data = lag;
3385: lag->tensorCell = PETSC_FALSE;
3386: lag->tensorSpace = PETSC_FALSE;
3387: lag->continuous = PETSC_TRUE;
3388: lag->numCopies = PETSC_DEFAULT;
3389: lag->numNodeSkip = PETSC_DEFAULT;
3390: lag->nodeType = PETSCDTNODES_DEFAULT;
3391: lag->useMoments = PETSC_FALSE;
3392: lag->momentOrder = 0;
3394: PetscDualSpaceInitialize_Lagrange(sp);
3395: PetscObjectComposeFunction((PetscObject) sp, "PetscDualSpaceLagrangeGetContinuity_C", PetscDualSpaceLagrangeGetContinuity_Lagrange);
3396: PetscObjectComposeFunction((PetscObject) sp, "PetscDualSpaceLagrangeSetContinuity_C", PetscDualSpaceLagrangeSetContinuity_Lagrange);
3397: PetscObjectComposeFunction((PetscObject) sp, "PetscDualSpaceLagrangeGetTensor_C", PetscDualSpaceLagrangeGetTensor_Lagrange);
3398: PetscObjectComposeFunction((PetscObject) sp, "PetscDualSpaceLagrangeSetTensor_C", PetscDualSpaceLagrangeSetTensor_Lagrange);
3399: PetscObjectComposeFunction((PetscObject) sp, "PetscDualSpaceLagrangeGetTrimmed_C", PetscDualSpaceLagrangeGetTrimmed_Lagrange);
3400: PetscObjectComposeFunction((PetscObject) sp, "PetscDualSpaceLagrangeSetTrimmed_C", PetscDualSpaceLagrangeSetTrimmed_Lagrange);
3401: PetscObjectComposeFunction((PetscObject) sp, "PetscDualSpaceLagrangeGetNodeType_C", PetscDualSpaceLagrangeGetNodeType_Lagrange);
3402: PetscObjectComposeFunction((PetscObject) sp, "PetscDualSpaceLagrangeSetNodeType_C", PetscDualSpaceLagrangeSetNodeType_Lagrange);
3403: PetscObjectComposeFunction((PetscObject) sp, "PetscDualSpaceLagrangeGetUseMoments_C", PetscDualSpaceLagrangeGetUseMoments_Lagrange);
3404: PetscObjectComposeFunction((PetscObject) sp, "PetscDualSpaceLagrangeSetUseMoments_C", PetscDualSpaceLagrangeSetUseMoments_Lagrange);
3405: PetscObjectComposeFunction((PetscObject) sp, "PetscDualSpaceLagrangeGetMomentOrder_C", PetscDualSpaceLagrangeGetMomentOrder_Lagrange);
3406: PetscObjectComposeFunction((PetscObject) sp, "PetscDualSpaceLagrangeSetMomentOrder_C", PetscDualSpaceLagrangeSetMomentOrder_Lagrange);
3407: return(0);
3408: }