Actual source code: dspacelagrange.c
1: #include <petsc/private/petscfeimpl.h>
2: #include <petscdmplex.h>
3: #include <petscblaslapack.h>
5: PetscErrorCode DMPlexGetTransitiveClosure_Internal(DM, PetscInt, PetscInt, PetscBool, PetscInt *, PetscInt *[]);
7: struct _n_Petsc1DNodeFamily {
8: PetscInt refct;
9: PetscDTNodeType nodeFamily;
10: PetscReal gaussJacobiExp;
11: PetscInt nComputed;
12: PetscReal **nodesets;
13: PetscBool endpoints;
14: };
16: /* users set node families for PETSCDUALSPACELAGRANGE with just the inputs to this function, but internally we create
17: * an object that can cache the computations across multiple dual spaces */
18: static PetscErrorCode Petsc1DNodeFamilyCreate(PetscDTNodeType family, PetscReal gaussJacobiExp, PetscBool endpoints, Petsc1DNodeFamily *nf)
19: {
20: Petsc1DNodeFamily f;
22: PetscFunctionBegin;
23: PetscCall(PetscNew(&f));
24: switch (family) {
25: case PETSCDTNODES_GAUSSJACOBI:
26: case PETSCDTNODES_EQUISPACED:
27: f->nodeFamily = family;
28: break;
29: default:
30: SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Unknown 1D node family");
31: }
32: f->endpoints = endpoints;
33: f->gaussJacobiExp = 0.;
34: if (family == PETSCDTNODES_GAUSSJACOBI) {
35: PetscCheck(gaussJacobiExp > -1., PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Gauss-Jacobi exponent must be > -1.");
36: f->gaussJacobiExp = gaussJacobiExp;
37: }
38: f->refct = 1;
39: *nf = f;
40: PetscFunctionReturn(PETSC_SUCCESS);
41: }
43: static PetscErrorCode Petsc1DNodeFamilyReference(Petsc1DNodeFamily nf)
44: {
45: PetscFunctionBegin;
46: if (nf) nf->refct++;
47: PetscFunctionReturn(PETSC_SUCCESS);
48: }
50: static PetscErrorCode Petsc1DNodeFamilyDestroy(Petsc1DNodeFamily *nf)
51: {
52: PetscInt i, nc;
54: PetscFunctionBegin;
55: if (!*nf) PetscFunctionReturn(PETSC_SUCCESS);
56: if (--(*nf)->refct > 0) {
57: *nf = NULL;
58: PetscFunctionReturn(PETSC_SUCCESS);
59: }
60: nc = (*nf)->nComputed;
61: for (i = 0; i < nc; i++) PetscCall(PetscFree((*nf)->nodesets[i]));
62: PetscCall(PetscFree((*nf)->nodesets));
63: PetscCall(PetscFree(*nf));
64: *nf = NULL;
65: PetscFunctionReturn(PETSC_SUCCESS);
66: }
68: static PetscErrorCode Petsc1DNodeFamilyGetNodeSets(Petsc1DNodeFamily f, PetscInt degree, PetscReal ***nodesets)
69: {
70: PetscInt nc;
72: PetscFunctionBegin;
73: nc = f->nComputed;
74: if (degree >= nc) {
75: PetscInt i, j;
76: PetscReal **new_nodesets;
77: PetscReal *w;
79: PetscCall(PetscMalloc1(degree + 1, &new_nodesets));
80: PetscCall(PetscArraycpy(new_nodesets, f->nodesets, nc));
81: PetscCall(PetscFree(f->nodesets));
82: f->nodesets = new_nodesets;
83: PetscCall(PetscMalloc1(degree + 1, &w));
84: for (i = nc; i < degree + 1; i++) {
85: PetscCall(PetscMalloc1(i + 1, &f->nodesets[i]));
86: if (!i) {
87: f->nodesets[i][0] = 0.5;
88: } else {
89: switch (f->nodeFamily) {
90: case PETSCDTNODES_EQUISPACED:
91: if (f->endpoints) {
92: for (j = 0; j <= i; j++) f->nodesets[i][j] = (PetscReal)j / (PetscReal)i;
93: } else {
94: /* these nodes are at the centroids of the small simplices created by the equispaced nodes that include
95: * the endpoints */
96: for (j = 0; j <= i; j++) f->nodesets[i][j] = ((PetscReal)j + 0.5) / ((PetscReal)i + 1.);
97: }
98: break;
99: case PETSCDTNODES_GAUSSJACOBI:
100: if (f->endpoints) {
101: PetscCall(PetscDTGaussLobattoJacobiQuadrature(i + 1, 0., 1., f->gaussJacobiExp, f->gaussJacobiExp, f->nodesets[i], w));
102: } else {
103: PetscCall(PetscDTGaussJacobiQuadrature(i + 1, 0., 1., f->gaussJacobiExp, f->gaussJacobiExp, f->nodesets[i], w));
104: }
105: break;
106: default:
107: SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Unknown 1D node family");
108: }
109: }
110: }
111: PetscCall(PetscFree(w));
112: f->nComputed = degree + 1;
113: }
114: *nodesets = f->nodesets;
115: PetscFunctionReturn(PETSC_SUCCESS);
116: }
118: /* http://arxiv.org/abs/2002.09421 for details */
119: static PetscErrorCode PetscNodeRecursive_Internal(PetscInt dim, PetscInt degree, PetscReal **nodesets, PetscInt tup[], PetscReal node[])
120: {
121: PetscReal w;
122: PetscInt i, j;
124: PetscFunctionBeginHot;
125: w = 0.;
126: if (dim == 1) {
127: node[0] = nodesets[degree][tup[0]];
128: node[1] = nodesets[degree][tup[1]];
129: } else {
130: for (i = 0; i < dim + 1; i++) node[i] = 0.;
131: for (i = 0; i < dim + 1; i++) {
132: PetscReal wi = nodesets[degree][degree - tup[i]];
134: for (j = 0; j < dim + 1; j++) tup[dim + 1 + j] = tup[j + (j >= i)];
135: PetscCall(PetscNodeRecursive_Internal(dim - 1, degree - tup[i], nodesets, &tup[dim + 1], &node[dim + 1]));
136: for (j = 0; j < dim + 1; j++) node[j + (j >= i)] += wi * node[dim + 1 + j];
137: w += wi;
138: }
139: for (i = 0; i < dim + 1; i++) node[i] /= w;
140: }
141: PetscFunctionReturn(PETSC_SUCCESS);
142: }
144: /* compute simplex nodes for the biunit simplex from the 1D node family */
145: static PetscErrorCode Petsc1DNodeFamilyComputeSimplexNodes(Petsc1DNodeFamily f, PetscInt dim, PetscInt degree, PetscReal points[])
146: {
147: PetscInt *tup;
148: PetscInt k;
149: PetscInt npoints;
150: PetscReal **nodesets = NULL;
151: PetscInt worksize;
152: PetscReal *nodework;
153: PetscInt *tupwork;
155: PetscFunctionBegin;
156: PetscCheck(dim >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Must have non-negative dimension");
157: PetscCheck(degree >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Must have non-negative degree");
158: if (!dim) PetscFunctionReturn(PETSC_SUCCESS);
159: PetscCall(PetscCalloc1(dim + 2, &tup));
160: k = 0;
161: PetscCall(PetscDTBinomialInt(degree + dim, dim, &npoints));
162: PetscCall(Petsc1DNodeFamilyGetNodeSets(f, degree, &nodesets));
163: worksize = ((dim + 2) * (dim + 3)) / 2;
164: PetscCall(PetscCalloc2(worksize, &nodework, worksize, &tupwork));
165: /* loop over the tuples of length dim with sum at most degree */
166: for (k = 0; k < npoints; k++) {
167: PetscInt i;
169: /* turn thm into tuples of length dim + 1 with sum equal to degree (barycentric indice) */
170: tup[0] = degree;
171: for (i = 0; i < dim; i++) tup[0] -= tup[i + 1];
172: switch (f->nodeFamily) {
173: case PETSCDTNODES_EQUISPACED:
174: /* compute equispaces nodes on the unit reference triangle */
175: if (f->endpoints) {
176: PetscCheck(degree > 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Must have positive degree");
177: for (i = 0; i < dim; i++) points[dim * k + i] = (PetscReal)tup[i + 1] / (PetscReal)degree;
178: } else {
179: for (i = 0; i < dim; i++) {
180: /* these nodes are at the centroids of the small simplices created by the equispaced nodes that include
181: * the endpoints */
182: points[dim * k + i] = ((PetscReal)tup[i + 1] + 1. / (dim + 1.)) / (PetscReal)(degree + 1.);
183: }
184: }
185: break;
186: default:
187: /* compute equispaced nodes on the barycentric reference triangle (the trace on the first dim dimensions are the
188: * unit reference triangle nodes */
189: for (i = 0; i < dim + 1; i++) tupwork[i] = tup[i];
190: PetscCall(PetscNodeRecursive_Internal(dim, degree, nodesets, tupwork, nodework));
191: for (i = 0; i < dim; i++) points[dim * k + i] = nodework[i + 1];
192: break;
193: }
194: PetscCall(PetscDualSpaceLatticePointLexicographic_Internal(dim, degree, &tup[1]));
195: }
196: /* map from unit simplex to biunit simplex */
197: for (k = 0; k < npoints * dim; k++) points[k] = points[k] * 2. - 1.;
198: PetscCall(PetscFree2(nodework, tupwork));
199: PetscCall(PetscFree(tup));
200: PetscFunctionReturn(PETSC_SUCCESS);
201: }
203: /* 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
204: * on that mesh point, we have to be careful about getting/adding everything in the right place.
205: *
206: * With nodal dofs like PETSCDUALSPACELAGRANGE makes, the general approach to calculate the value of dofs associate
207: * with a node A is
208: * - transform the node locations x(A) by the map that takes the mesh point to its reorientation, x' = phi(x(A))
209: * - figure out which node was originally at the location of the transformed point, A' = idx(x')
210: * - if the dofs are not scalars, figure out how to represent the transformed dofs in terms of the basis
211: * of dofs at A' (using pushforward/pullback rules)
212: *
213: * The one sticky point with this approach is the "A' = idx(x')" step: trying to go from real valued coordinates
214: * back to indices. I don't want to rely on floating point tolerances. Additionally, PETSCDUALSPACELAGRANGE may
215: * eventually support quasi-Lagrangian dofs, which could involve quadrature at multiple points, so the location "x(A)"
216: * would be ambiguous.
217: *
218: * So each dof gets an integer value coordinate (nodeIdx in the structure below). The choice of integer coordinates
219: * is somewhat arbitrary, as long as all of the relevant symmetries of the mesh point correspond to *permutations* of
220: * the integer coordinates, which do not depend on numerical precision.
221: *
222: * So
223: *
224: * - DMPlexGetTransitiveClosure_Internal() tells me how an orientation turns into a permutation of the vertices of a
225: * mesh point
226: * - The permutation of the vertices, and the nodeIdx values assigned to them, tells what permutation in index space
227: * is associated with the orientation
228: * - I uses that permutation to get xi' = phi(xi(A)), the integer coordinate of the transformed dof
229: * - I can without numerical issues compute A' = idx(xi')
230: *
231: * Here are some examples of how the process works
232: *
233: * - With a triangle:
234: *
235: * The triangle has the following integer coordinates for vertices, taken from the barycentric triangle
236: *
237: * closure order 2
238: * nodeIdx (0,0,1)
239: * \
240: * +
241: * |\
242: * | \
243: * | \
244: * | \ closure order 1
245: * | \ / nodeIdx (0,1,0)
246: * +-----+
247: * \
248: * closure order 0
249: * nodeIdx (1,0,0)
250: *
251: * If I do DMPlexGetTransitiveClosure_Internal() with orientation 1, the vertices would appear
252: * in the order (1, 2, 0)
253: *
254: * If I list the nodeIdx of each vertex in closure order for orientation 0 (0, 1, 2) and orientation 1 (1, 2, 0), I
255: * see
256: *
257: * orientation 0 | orientation 1
258: *
259: * [0] (1,0,0) [1] (0,1,0)
260: * [1] (0,1,0) [2] (0,0,1)
261: * [2] (0,0,1) [0] (1,0,0)
262: * A B
263: *
264: * In other words, B is the result of a row permutation of A. But, there is also
265: * a column permutation that accomplishes the same result, (2,0,1).
266: *
267: * So if a dof has nodeIdx coordinate (a,b,c), after the transformation its nodeIdx coordinate
268: * is (c,a,b), and the transformed degree of freedom will be a linear combination of dofs
269: * that originally had coordinate (c,a,b).
270: *
271: * - With a quadrilateral:
272: *
273: * The quadrilateral has the following integer coordinates for vertices, taken from concatenating barycentric
274: * coordinates for two segments:
275: *
276: * closure order 3 closure order 2
277: * nodeIdx (1,0,0,1) nodeIdx (0,1,0,1)
278: * \ /
279: * +----+
280: * | |
281: * | |
282: * +----+
283: * / \
284: * closure order 0 closure order 1
285: * nodeIdx (1,0,1,0) nodeIdx (0,1,1,0)
286: *
287: * If I do DMPlexGetTransitiveClosure_Internal() with orientation 1, the vertices would appear
288: * in the order (1, 2, 3, 0)
289: *
290: * If I list the nodeIdx of each vertex in closure order for orientation 0 (0, 1, 2, 3) and
291: * orientation 1 (1, 2, 3, 0), I see
292: *
293: * orientation 0 | orientation 1
294: *
295: * [0] (1,0,1,0) [1] (0,1,1,0)
296: * [1] (0,1,1,0) [2] (0,1,0,1)
297: * [2] (0,1,0,1) [3] (1,0,0,1)
298: * [3] (1,0,0,1) [0] (1,0,1,0)
299: * A B
300: *
301: * The column permutation that accomplishes the same result is (3,2,0,1).
302: *
303: * So if a dof has nodeIdx coordinate (a,b,c,d), after the transformation its nodeIdx coordinate
304: * is (d,c,a,b), and the transformed degree of freedom will be a linear combination of dofs
305: * that originally had coordinate (d,c,a,b).
306: *
307: * Previously PETSCDUALSPACELAGRANGE had hardcoded symmetries for the triangle and quadrilateral,
308: * but this approach will work for any polytope, such as the wedge (triangular prism).
309: */
310: struct _n_PetscLagNodeIndices {
311: PetscInt refct;
312: PetscInt nodeIdxDim;
313: PetscInt nodeVecDim;
314: PetscInt nNodes;
315: PetscInt *nodeIdx; /* for each node an index of size nodeIdxDim */
316: PetscReal *nodeVec; /* for each node a vector of size nodeVecDim */
317: PetscInt *perm; /* if these are vertices, perm takes DMPlex point index to closure order;
318: if these are nodes, perm lists nodes in index revlex order */
319: };
321: /* this is just here so I can access the values in tests/ex1.c outside the library */
322: PetscErrorCode PetscLagNodeIndicesGetData_Internal(PetscLagNodeIndices ni, PetscInt *nodeIdxDim, PetscInt *nodeVecDim, PetscInt *nNodes, const PetscInt *nodeIdx[], const PetscReal *nodeVec[])
323: {
324: PetscFunctionBegin;
325: *nodeIdxDim = ni->nodeIdxDim;
326: *nodeVecDim = ni->nodeVecDim;
327: *nNodes = ni->nNodes;
328: *nodeIdx = ni->nodeIdx;
329: *nodeVec = ni->nodeVec;
330: PetscFunctionReturn(PETSC_SUCCESS);
331: }
333: static PetscErrorCode PetscLagNodeIndicesReference(PetscLagNodeIndices ni)
334: {
335: PetscFunctionBegin;
336: if (ni) ni->refct++;
337: PetscFunctionReturn(PETSC_SUCCESS);
338: }
340: static PetscErrorCode PetscLagNodeIndicesDuplicate(PetscLagNodeIndices ni, PetscLagNodeIndices *niNew)
341: {
342: PetscFunctionBegin;
343: PetscCall(PetscNew(niNew));
344: (*niNew)->refct = 1;
345: (*niNew)->nodeIdxDim = ni->nodeIdxDim;
346: (*niNew)->nodeVecDim = ni->nodeVecDim;
347: (*niNew)->nNodes = ni->nNodes;
348: PetscCall(PetscMalloc1(ni->nNodes * ni->nodeIdxDim, &((*niNew)->nodeIdx)));
349: PetscCall(PetscArraycpy((*niNew)->nodeIdx, ni->nodeIdx, ni->nNodes * ni->nodeIdxDim));
350: PetscCall(PetscMalloc1(ni->nNodes * ni->nodeVecDim, &((*niNew)->nodeVec)));
351: PetscCall(PetscArraycpy((*niNew)->nodeVec, ni->nodeVec, ni->nNodes * ni->nodeVecDim));
352: (*niNew)->perm = NULL;
353: PetscFunctionReturn(PETSC_SUCCESS);
354: }
356: static PetscErrorCode PetscLagNodeIndicesDestroy(PetscLagNodeIndices *ni)
357: {
358: PetscFunctionBegin;
359: if (!*ni) PetscFunctionReturn(PETSC_SUCCESS);
360: if (--(*ni)->refct > 0) {
361: *ni = NULL;
362: PetscFunctionReturn(PETSC_SUCCESS);
363: }
364: PetscCall(PetscFree((*ni)->nodeIdx));
365: PetscCall(PetscFree((*ni)->nodeVec));
366: PetscCall(PetscFree((*ni)->perm));
367: PetscCall(PetscFree(*ni));
368: *ni = NULL;
369: PetscFunctionReturn(PETSC_SUCCESS);
370: }
372: /* The vertices are given nodeIdx coordinates (e.g. the corners of the barycentric triangle). Those coordinates are
373: * in some other order, and to understand the effect of different symmetries, we need them to be in closure order.
374: *
375: * If sortIdx is PETSC_FALSE, the coordinates are already in revlex order, otherwise we must sort them
376: * to that order before we do the real work of this function, which is
377: *
378: * - mark the vertices in closure order
379: * - sort them in revlex order
380: * - use the resulting permutation to list the vertex coordinates in closure order
381: */
382: static PetscErrorCode PetscLagNodeIndicesComputeVertexOrder(DM dm, PetscLagNodeIndices ni, PetscBool sortIdx)
383: {
384: PetscInt v, w, vStart, vEnd, c, d;
385: PetscInt nVerts;
386: PetscInt closureSize = 0;
387: PetscInt *closure = NULL;
388: PetscInt *closureOrder;
389: PetscInt *invClosureOrder;
390: PetscInt *revlexOrder;
391: PetscInt *newNodeIdx;
392: PetscInt dim;
393: Vec coordVec;
394: const PetscScalar *coords;
396: PetscFunctionBegin;
397: PetscCall(DMGetDimension(dm, &dim));
398: PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
399: nVerts = vEnd - vStart;
400: PetscCall(PetscMalloc1(nVerts, &closureOrder));
401: PetscCall(PetscMalloc1(nVerts, &invClosureOrder));
402: PetscCall(PetscMalloc1(nVerts, &revlexOrder));
403: if (sortIdx) { /* bubble sort nodeIdx into revlex order */
404: PetscInt nodeIdxDim = ni->nodeIdxDim;
405: PetscInt *idxOrder;
407: PetscCall(PetscMalloc1(nVerts * nodeIdxDim, &newNodeIdx));
408: PetscCall(PetscMalloc1(nVerts, &idxOrder));
409: for (v = 0; v < nVerts; v++) idxOrder[v] = v;
410: for (v = 0; v < nVerts; v++) {
411: for (w = v + 1; w < nVerts; w++) {
412: const PetscInt *iv = &(ni->nodeIdx[idxOrder[v] * nodeIdxDim]);
413: const PetscInt *iw = &(ni->nodeIdx[idxOrder[w] * nodeIdxDim]);
414: PetscInt diff = 0;
416: for (d = nodeIdxDim - 1; d >= 0; d--)
417: if ((diff = (iv[d] - iw[d]))) break;
418: if (diff > 0) {
419: PetscInt swap = idxOrder[v];
421: idxOrder[v] = idxOrder[w];
422: idxOrder[w] = swap;
423: }
424: }
425: }
426: for (v = 0; v < nVerts; v++) {
427: for (d = 0; d < nodeIdxDim; d++) newNodeIdx[v * ni->nodeIdxDim + d] = ni->nodeIdx[idxOrder[v] * nodeIdxDim + d];
428: }
429: PetscCall(PetscFree(ni->nodeIdx));
430: ni->nodeIdx = newNodeIdx;
431: newNodeIdx = NULL;
432: PetscCall(PetscFree(idxOrder));
433: }
434: PetscCall(DMPlexGetTransitiveClosure(dm, 0, PETSC_TRUE, &closureSize, &closure));
435: c = closureSize - nVerts;
436: for (v = 0; v < nVerts; v++) closureOrder[v] = closure[2 * (c + v)] - vStart;
437: for (v = 0; v < nVerts; v++) invClosureOrder[closureOrder[v]] = v;
438: PetscCall(DMPlexRestoreTransitiveClosure(dm, 0, PETSC_TRUE, &closureSize, &closure));
439: PetscCall(DMGetCoordinatesLocal(dm, &coordVec));
440: PetscCall(VecGetArrayRead(coordVec, &coords));
441: /* bubble sort closure vertices by coordinates in revlex order */
442: for (v = 0; v < nVerts; v++) revlexOrder[v] = v;
443: for (v = 0; v < nVerts; v++) {
444: for (w = v + 1; w < nVerts; w++) {
445: const PetscScalar *cv = &coords[closureOrder[revlexOrder[v]] * dim];
446: const PetscScalar *cw = &coords[closureOrder[revlexOrder[w]] * dim];
447: PetscReal diff = 0;
449: for (d = dim - 1; d >= 0; d--)
450: if ((diff = PetscRealPart(cv[d] - cw[d])) != 0.) break;
451: if (diff > 0.) {
452: PetscInt swap = revlexOrder[v];
454: revlexOrder[v] = revlexOrder[w];
455: revlexOrder[w] = swap;
456: }
457: }
458: }
459: PetscCall(VecRestoreArrayRead(coordVec, &coords));
460: PetscCall(PetscMalloc1(ni->nodeIdxDim * nVerts, &newNodeIdx));
461: /* reorder nodeIdx to be in closure order */
462: for (v = 0; v < nVerts; v++) {
463: for (d = 0; d < ni->nodeIdxDim; d++) newNodeIdx[revlexOrder[v] * ni->nodeIdxDim + d] = ni->nodeIdx[v * ni->nodeIdxDim + d];
464: }
465: PetscCall(PetscFree(ni->nodeIdx));
466: ni->nodeIdx = newNodeIdx;
467: ni->perm = invClosureOrder;
468: PetscCall(PetscFree(revlexOrder));
469: PetscCall(PetscFree(closureOrder));
470: PetscFunctionReturn(PETSC_SUCCESS);
471: }
473: /* the coordinates of the simplex vertices are the corners of the barycentric simplex.
474: * When we stack them on top of each other in revlex order, they look like the identity matrix */
475: static PetscErrorCode PetscLagNodeIndicesCreateSimplexVertices(DM dm, PetscLagNodeIndices *nodeIndices)
476: {
477: PetscLagNodeIndices ni;
478: PetscInt dim, d;
480: PetscFunctionBegin;
481: PetscCall(PetscNew(&ni));
482: PetscCall(DMGetDimension(dm, &dim));
483: ni->nodeIdxDim = dim + 1;
484: ni->nodeVecDim = 0;
485: ni->nNodes = dim + 1;
486: ni->refct = 1;
487: PetscCall(PetscCalloc1((dim + 1) * (dim + 1), &ni->nodeIdx));
488: for (d = 0; d < dim + 1; d++) ni->nodeIdx[d * (dim + 2)] = 1;
489: PetscCall(PetscLagNodeIndicesComputeVertexOrder(dm, ni, PETSC_FALSE));
490: *nodeIndices = ni;
491: PetscFunctionReturn(PETSC_SUCCESS);
492: }
494: /* A polytope that is a tensor product of a facet and a segment.
495: * We take whatever coordinate system was being used for the facet
496: * and we concatenate the barycentric coordinates for the vertices
497: * at the end of the segment, (1,0) and (0,1), to get a coordinate
498: * system for the tensor product element */
499: static PetscErrorCode PetscLagNodeIndicesCreateTensorVertices(DM dm, PetscLagNodeIndices facetni, PetscLagNodeIndices *nodeIndices)
500: {
501: PetscLagNodeIndices ni;
502: PetscInt nodeIdxDim, subNodeIdxDim = facetni->nodeIdxDim;
503: PetscInt nVerts, nSubVerts = facetni->nNodes;
504: PetscInt dim, d, e, f, g;
506: PetscFunctionBegin;
507: PetscCall(PetscNew(&ni));
508: PetscCall(DMGetDimension(dm, &dim));
509: ni->nodeIdxDim = nodeIdxDim = subNodeIdxDim + 2;
510: ni->nodeVecDim = 0;
511: ni->nNodes = nVerts = 2 * nSubVerts;
512: ni->refct = 1;
513: PetscCall(PetscCalloc1(nodeIdxDim * nVerts, &ni->nodeIdx));
514: for (f = 0, d = 0; d < 2; d++) {
515: for (e = 0; e < nSubVerts; e++, f++) {
516: for (g = 0; g < subNodeIdxDim; g++) ni->nodeIdx[f * nodeIdxDim + g] = facetni->nodeIdx[e * subNodeIdxDim + g];
517: ni->nodeIdx[f * nodeIdxDim + subNodeIdxDim] = (1 - d);
518: ni->nodeIdx[f * nodeIdxDim + subNodeIdxDim + 1] = d;
519: }
520: }
521: PetscCall(PetscLagNodeIndicesComputeVertexOrder(dm, ni, PETSC_TRUE));
522: *nodeIndices = ni;
523: PetscFunctionReturn(PETSC_SUCCESS);
524: }
526: /* This helps us compute symmetries, and it also helps us compute coordinates for dofs that are being pushed
527: * forward from a boundary mesh point.
528: *
529: * Input:
530: *
531: * dm - the target reference cell where we want new coordinates and dof directions to be valid
532: * vert - the vertex coordinate system for the target reference cell
533: * p - the point in the target reference cell that the dofs are coming from
534: * vertp - the vertex coordinate system for p's reference cell
535: * ornt - the resulting coordinates and dof vectors will be for p under this orientation
536: * nodep - the node coordinates and dof vectors in p's reference cell
537: * formDegree - the form degree that the dofs transform as
538: *
539: * Output:
540: *
541: * pfNodeIdx - the node coordinates for p's dofs, in the dm reference cell, from the ornt perspective
542: * pfNodeVec - the node dof vectors for p's dofs, in the dm reference cell, from the ornt perspective
543: */
544: static PetscErrorCode PetscLagNodeIndicesPushForward(DM dm, PetscLagNodeIndices vert, PetscInt p, PetscLagNodeIndices vertp, PetscLagNodeIndices nodep, PetscInt ornt, PetscInt formDegree, PetscInt pfNodeIdx[], PetscReal pfNodeVec[])
545: {
546: PetscInt *closureVerts;
547: PetscInt closureSize = 0;
548: PetscInt *closure = NULL;
549: PetscInt dim, pdim, c, i, j, k, n, v, vStart, vEnd;
550: PetscInt nSubVert = vertp->nNodes;
551: PetscInt nodeIdxDim = vert->nodeIdxDim;
552: PetscInt subNodeIdxDim = vertp->nodeIdxDim;
553: PetscInt nNodes = nodep->nNodes;
554: const PetscInt *vertIdx = vert->nodeIdx;
555: const PetscInt *subVertIdx = vertp->nodeIdx;
556: const PetscInt *nodeIdx = nodep->nodeIdx;
557: const PetscReal *nodeVec = nodep->nodeVec;
558: PetscReal *J, *Jstar;
559: PetscReal detJ;
560: PetscInt depth, pdepth, Nk, pNk;
561: Vec coordVec;
562: PetscScalar *newCoords = NULL;
563: const PetscScalar *oldCoords = NULL;
565: PetscFunctionBegin;
566: PetscCall(DMGetDimension(dm, &dim));
567: PetscCall(DMPlexGetDepth(dm, &depth));
568: PetscCall(DMGetCoordinatesLocal(dm, &coordVec));
569: PetscCall(DMPlexGetPointDepth(dm, p, &pdepth));
570: pdim = pdepth != depth ? pdepth != 0 ? pdepth : 0 : dim;
571: PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
572: PetscCall(DMGetWorkArray(dm, nSubVert, MPIU_INT, &closureVerts));
573: PetscCall(DMPlexGetTransitiveClosure_Internal(dm, p, ornt, PETSC_TRUE, &closureSize, &closure));
574: c = closureSize - nSubVert;
575: /* we want which cell closure indices the closure of this point corresponds to */
576: for (v = 0; v < nSubVert; v++) closureVerts[v] = vert->perm[closure[2 * (c + v)] - vStart];
577: PetscCall(DMPlexRestoreTransitiveClosure(dm, p, PETSC_TRUE, &closureSize, &closure));
578: /* push forward indices */
579: for (i = 0; i < nodeIdxDim; i++) { /* for every component of the target index space */
580: /* check if this is a component that all vertices around this point have in common */
581: for (j = 1; j < nSubVert; j++) {
582: if (vertIdx[closureVerts[j] * nodeIdxDim + i] != vertIdx[closureVerts[0] * nodeIdxDim + i]) break;
583: }
584: if (j == nSubVert) { /* all vertices have this component in common, directly copy to output */
585: PetscInt val = vertIdx[closureVerts[0] * nodeIdxDim + i];
586: for (n = 0; n < nNodes; n++) pfNodeIdx[n * nodeIdxDim + i] = val;
587: } else {
588: PetscInt subi = -1;
589: /* there must be a component in vertp that looks the same */
590: for (k = 0; k < subNodeIdxDim; k++) {
591: for (j = 0; j < nSubVert; j++) {
592: if (vertIdx[closureVerts[j] * nodeIdxDim + i] != subVertIdx[j * subNodeIdxDim + k]) break;
593: }
594: if (j == nSubVert) {
595: subi = k;
596: break;
597: }
598: }
599: PetscCheck(subi >= 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Did not find matching coordinate");
600: /* that component in the vertp system becomes component i in the vert system for each dof */
601: for (n = 0; n < nNodes; n++) pfNodeIdx[n * nodeIdxDim + i] = nodeIdx[n * subNodeIdxDim + subi];
602: }
603: }
604: /* push forward vectors */
605: PetscCall(DMGetWorkArray(dm, dim * dim, MPIU_REAL, &J));
606: if (ornt != 0) { /* temporarily change the coordinate vector so
607: DMPlexComputeCellGeometryAffineFEM gives us the Jacobian we want */
608: PetscInt closureSize2 = 0;
609: PetscInt *closure2 = NULL;
611: PetscCall(DMPlexGetTransitiveClosure_Internal(dm, p, 0, PETSC_TRUE, &closureSize2, &closure2));
612: PetscCall(PetscMalloc1(dim * nSubVert, &newCoords));
613: PetscCall(VecGetArrayRead(coordVec, &oldCoords));
614: for (v = 0; v < nSubVert; v++) {
615: PetscInt d;
616: for (d = 0; d < dim; d++) newCoords[(closure2[2 * (c + v)] - vStart) * dim + d] = oldCoords[closureVerts[v] * dim + d];
617: }
618: PetscCall(VecRestoreArrayRead(coordVec, &oldCoords));
619: PetscCall(DMPlexRestoreTransitiveClosure(dm, p, PETSC_TRUE, &closureSize2, &closure2));
620: PetscCall(VecPlaceArray(coordVec, newCoords));
621: }
622: PetscCall(DMPlexComputeCellGeometryAffineFEM(dm, p, NULL, J, NULL, &detJ));
623: if (ornt != 0) {
624: PetscCall(VecResetArray(coordVec));
625: PetscCall(PetscFree(newCoords));
626: }
627: PetscCall(DMRestoreWorkArray(dm, nSubVert, MPIU_INT, &closureVerts));
628: /* compactify */
629: for (i = 0; i < dim; i++)
630: for (j = 0; j < pdim; j++) J[i * pdim + j] = J[i * dim + j];
631: /* We have the Jacobian mapping the point's reference cell to this reference cell:
632: * pulling back a function to the point and applying the dof is what we want,
633: * so we get the pullback matrix and multiply the dof by that matrix on the right */
634: PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(formDegree), &Nk));
635: PetscCall(PetscDTBinomialInt(pdim, PetscAbsInt(formDegree), &pNk));
636: PetscCall(DMGetWorkArray(dm, pNk * Nk, MPIU_REAL, &Jstar));
637: PetscCall(PetscDTAltVPullbackMatrix(pdim, dim, J, formDegree, Jstar));
638: for (n = 0; n < nNodes; n++) {
639: for (i = 0; i < Nk; i++) {
640: PetscReal val = 0.;
641: for (j = 0; j < pNk; j++) val += nodeVec[n * pNk + j] * Jstar[j * Nk + i];
642: pfNodeVec[n * Nk + i] = val;
643: }
644: }
645: PetscCall(DMRestoreWorkArray(dm, pNk * Nk, MPIU_REAL, &Jstar));
646: PetscCall(DMRestoreWorkArray(dm, dim * dim, MPIU_REAL, &J));
647: PetscFunctionReturn(PETSC_SUCCESS);
648: }
650: /* given to sets of nodes, take the tensor product, where the product of the dof indices is concatenation and the
651: * product of the dof vectors is the wedge product */
652: static PetscErrorCode PetscLagNodeIndicesTensor(PetscLagNodeIndices tracei, PetscInt dimT, PetscInt kT, PetscLagNodeIndices fiberi, PetscInt dimF, PetscInt kF, PetscLagNodeIndices *nodeIndices)
653: {
654: PetscInt dim = dimT + dimF;
655: PetscInt nodeIdxDim, nNodes;
656: PetscInt formDegree = kT + kF;
657: PetscInt Nk, NkT, NkF;
658: PetscInt MkT, MkF;
659: PetscLagNodeIndices ni;
660: PetscInt i, j, l;
661: PetscReal *projF, *projT;
662: PetscReal *projFstar, *projTstar;
663: PetscReal *workF, *workF2, *workT, *workT2, *work, *work2;
664: PetscReal *wedgeMat;
665: PetscReal sign;
667: PetscFunctionBegin;
668: PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(formDegree), &Nk));
669: PetscCall(PetscDTBinomialInt(dimT, PetscAbsInt(kT), &NkT));
670: PetscCall(PetscDTBinomialInt(dimF, PetscAbsInt(kF), &NkF));
671: PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(kT), &MkT));
672: PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(kF), &MkF));
673: PetscCall(PetscNew(&ni));
674: ni->nodeIdxDim = nodeIdxDim = tracei->nodeIdxDim + fiberi->nodeIdxDim;
675: ni->nodeVecDim = Nk;
676: ni->nNodes = nNodes = tracei->nNodes * fiberi->nNodes;
677: ni->refct = 1;
678: PetscCall(PetscMalloc1(nNodes * nodeIdxDim, &ni->nodeIdx));
679: /* first concatenate the indices */
680: for (l = 0, j = 0; j < fiberi->nNodes; j++) {
681: for (i = 0; i < tracei->nNodes; i++, l++) {
682: PetscInt m, n = 0;
684: for (m = 0; m < tracei->nodeIdxDim; m++) ni->nodeIdx[l * nodeIdxDim + n++] = tracei->nodeIdx[i * tracei->nodeIdxDim + m];
685: for (m = 0; m < fiberi->nodeIdxDim; m++) ni->nodeIdx[l * nodeIdxDim + n++] = fiberi->nodeIdx[j * fiberi->nodeIdxDim + m];
686: }
687: }
689: /* now wedge together the push-forward vectors */
690: PetscCall(PetscMalloc1(nNodes * Nk, &ni->nodeVec));
691: PetscCall(PetscCalloc2(dimT * dim, &projT, dimF * dim, &projF));
692: for (i = 0; i < dimT; i++) projT[i * (dim + 1)] = 1.;
693: for (i = 0; i < dimF; i++) projF[i * (dim + dimT + 1) + dimT] = 1.;
694: PetscCall(PetscMalloc2(MkT * NkT, &projTstar, MkF * NkF, &projFstar));
695: PetscCall(PetscDTAltVPullbackMatrix(dim, dimT, projT, kT, projTstar));
696: PetscCall(PetscDTAltVPullbackMatrix(dim, dimF, projF, kF, projFstar));
697: PetscCall(PetscMalloc6(MkT, &workT, MkT, &workT2, MkF, &workF, MkF, &workF2, Nk, &work, Nk, &work2));
698: PetscCall(PetscMalloc1(Nk * MkT, &wedgeMat));
699: sign = (PetscAbsInt(kT * kF) & 1) ? -1. : 1.;
700: for (l = 0, j = 0; j < fiberi->nNodes; j++) {
701: PetscInt d, e;
703: /* push forward fiber k-form */
704: for (d = 0; d < MkF; d++) {
705: PetscReal val = 0.;
706: for (e = 0; e < NkF; e++) val += projFstar[d * NkF + e] * fiberi->nodeVec[j * NkF + e];
707: workF[d] = val;
708: }
709: /* Hodge star to proper form if necessary */
710: if (kF < 0) {
711: for (d = 0; d < MkF; d++) workF2[d] = workF[d];
712: PetscCall(PetscDTAltVStar(dim, PetscAbsInt(kF), 1, workF2, workF));
713: }
714: /* Compute the matrix that wedges this form with one of the trace k-form */
715: PetscCall(PetscDTAltVWedgeMatrix(dim, PetscAbsInt(kF), PetscAbsInt(kT), workF, wedgeMat));
716: for (i = 0; i < tracei->nNodes; i++, l++) {
717: /* push forward trace k-form */
718: for (d = 0; d < MkT; d++) {
719: PetscReal val = 0.;
720: for (e = 0; e < NkT; e++) val += projTstar[d * NkT + e] * tracei->nodeVec[i * NkT + e];
721: workT[d] = val;
722: }
723: /* Hodge star to proper form if necessary */
724: if (kT < 0) {
725: for (d = 0; d < MkT; d++) workT2[d] = workT[d];
726: PetscCall(PetscDTAltVStar(dim, PetscAbsInt(kT), 1, workT2, workT));
727: }
728: /* compute the wedge product of the push-forward trace form and firer forms */
729: for (d = 0; d < Nk; d++) {
730: PetscReal val = 0.;
731: for (e = 0; e < MkT; e++) val += wedgeMat[d * MkT + e] * workT[e];
732: work[d] = val;
733: }
734: /* inverse Hodge star from proper form if necessary */
735: if (formDegree < 0) {
736: for (d = 0; d < Nk; d++) work2[d] = work[d];
737: PetscCall(PetscDTAltVStar(dim, PetscAbsInt(formDegree), -1, work2, work));
738: }
739: /* insert into the array (adjusting for sign) */
740: for (d = 0; d < Nk; d++) ni->nodeVec[l * Nk + d] = sign * work[d];
741: }
742: }
743: PetscCall(PetscFree(wedgeMat));
744: PetscCall(PetscFree6(workT, workT2, workF, workF2, work, work2));
745: PetscCall(PetscFree2(projTstar, projFstar));
746: PetscCall(PetscFree2(projT, projF));
747: *nodeIndices = ni;
748: PetscFunctionReturn(PETSC_SUCCESS);
749: }
751: /* simple union of two sets of nodes */
752: static PetscErrorCode PetscLagNodeIndicesMerge(PetscLagNodeIndices niA, PetscLagNodeIndices niB, PetscLagNodeIndices *nodeIndices)
753: {
754: PetscLagNodeIndices ni;
755: PetscInt nodeIdxDim, nodeVecDim, nNodes;
757: PetscFunctionBegin;
758: PetscCall(PetscNew(&ni));
759: ni->nodeIdxDim = nodeIdxDim = niA->nodeIdxDim;
760: PetscCheck(niB->nodeIdxDim == nodeIdxDim, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Cannot merge PetscLagNodeIndices with different nodeIdxDim");
761: ni->nodeVecDim = nodeVecDim = niA->nodeVecDim;
762: PetscCheck(niB->nodeVecDim == nodeVecDim, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Cannot merge PetscLagNodeIndices with different nodeVecDim");
763: ni->nNodes = nNodes = niA->nNodes + niB->nNodes;
764: ni->refct = 1;
765: PetscCall(PetscMalloc1(nNodes * nodeIdxDim, &ni->nodeIdx));
766: PetscCall(PetscMalloc1(nNodes * nodeVecDim, &ni->nodeVec));
767: PetscCall(PetscArraycpy(ni->nodeIdx, niA->nodeIdx, niA->nNodes * nodeIdxDim));
768: PetscCall(PetscArraycpy(ni->nodeVec, niA->nodeVec, niA->nNodes * nodeVecDim));
769: PetscCall(PetscArraycpy(&(ni->nodeIdx[niA->nNodes * nodeIdxDim]), niB->nodeIdx, niB->nNodes * nodeIdxDim));
770: PetscCall(PetscArraycpy(&(ni->nodeVec[niA->nNodes * nodeVecDim]), niB->nodeVec, niB->nNodes * nodeVecDim));
771: *nodeIndices = ni;
772: PetscFunctionReturn(PETSC_SUCCESS);
773: }
775: #define PETSCTUPINTCOMPREVLEX(N) \
776: static int PetscConcat_(PetscTupIntCompRevlex_, N)(const void *a, const void *b) \
777: { \
778: const PetscInt *A = (const PetscInt *)a; \
779: const PetscInt *B = (const PetscInt *)b; \
780: int i; \
781: PetscInt diff = 0; \
782: for (i = 0; i < N; i++) { \
783: diff = A[N - i] - B[N - i]; \
784: if (diff) break; \
785: } \
786: return (diff <= 0) ? (diff < 0) ? -1 : 0 : 1; \
787: }
789: PETSCTUPINTCOMPREVLEX(3)
790: PETSCTUPINTCOMPREVLEX(4)
791: PETSCTUPINTCOMPREVLEX(5)
792: PETSCTUPINTCOMPREVLEX(6)
793: PETSCTUPINTCOMPREVLEX(7)
795: static int PetscTupIntCompRevlex_N(const void *a, const void *b)
796: {
797: const PetscInt *A = (const PetscInt *)a;
798: const PetscInt *B = (const PetscInt *)b;
799: int i;
800: int N = A[0];
801: PetscInt diff = 0;
802: for (i = 0; i < N; i++) {
803: diff = A[N - i] - B[N - i];
804: if (diff) break;
805: }
806: return (diff <= 0) ? (diff < 0) ? -1 : 0 : 1;
807: }
809: /* The nodes are not necessarily in revlex order wrt nodeIdx: get the permutation
810: * that puts them in that order */
811: static PetscErrorCode PetscLagNodeIndicesGetPermutation(PetscLagNodeIndices ni, PetscInt *perm[])
812: {
813: PetscFunctionBegin;
814: if (!ni->perm) {
815: PetscInt *sorter;
816: PetscInt m = ni->nNodes;
817: PetscInt nodeIdxDim = ni->nodeIdxDim;
818: PetscInt i, j, k, l;
819: PetscInt *prm;
820: int (*comp)(const void *, const void *);
822: PetscCall(PetscMalloc1((nodeIdxDim + 2) * m, &sorter));
823: for (k = 0, l = 0, i = 0; i < m; i++) {
824: sorter[k++] = nodeIdxDim + 1;
825: sorter[k++] = i;
826: for (j = 0; j < nodeIdxDim; j++) sorter[k++] = ni->nodeIdx[l++];
827: }
828: switch (nodeIdxDim) {
829: case 2:
830: comp = PetscTupIntCompRevlex_3;
831: break;
832: case 3:
833: comp = PetscTupIntCompRevlex_4;
834: break;
835: case 4:
836: comp = PetscTupIntCompRevlex_5;
837: break;
838: case 5:
839: comp = PetscTupIntCompRevlex_6;
840: break;
841: case 6:
842: comp = PetscTupIntCompRevlex_7;
843: break;
844: default:
845: comp = PetscTupIntCompRevlex_N;
846: break;
847: }
848: qsort(sorter, m, (nodeIdxDim + 2) * sizeof(PetscInt), comp);
849: PetscCall(PetscMalloc1(m, &prm));
850: for (i = 0; i < m; i++) prm[i] = sorter[(nodeIdxDim + 2) * i + 1];
851: ni->perm = prm;
852: PetscCall(PetscFree(sorter));
853: }
854: *perm = ni->perm;
855: PetscFunctionReturn(PETSC_SUCCESS);
856: }
858: static PetscErrorCode PetscDualSpaceDestroy_Lagrange(PetscDualSpace sp)
859: {
860: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
862: PetscFunctionBegin;
863: if (lag->symperms) {
864: PetscInt **selfSyms = lag->symperms[0];
866: if (selfSyms) {
867: PetscInt i, **allocated = &selfSyms[-lag->selfSymOff];
869: for (i = 0; i < lag->numSelfSym; i++) PetscCall(PetscFree(allocated[i]));
870: PetscCall(PetscFree(allocated));
871: }
872: PetscCall(PetscFree(lag->symperms));
873: }
874: if (lag->symflips) {
875: PetscScalar **selfSyms = lag->symflips[0];
877: if (selfSyms) {
878: PetscInt i;
879: PetscScalar **allocated = &selfSyms[-lag->selfSymOff];
881: for (i = 0; i < lag->numSelfSym; i++) PetscCall(PetscFree(allocated[i]));
882: PetscCall(PetscFree(allocated));
883: }
884: PetscCall(PetscFree(lag->symflips));
885: }
886: PetscCall(Petsc1DNodeFamilyDestroy(&lag->nodeFamily));
887: PetscCall(PetscLagNodeIndicesDestroy(&lag->vertIndices));
888: PetscCall(PetscLagNodeIndicesDestroy(&lag->intNodeIndices));
889: PetscCall(PetscLagNodeIndicesDestroy(&lag->allNodeIndices));
890: PetscCall(PetscFree(lag));
891: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetContinuity_C", NULL));
892: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetContinuity_C", NULL));
893: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetTensor_C", NULL));
894: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetTensor_C", NULL));
895: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetTrimmed_C", NULL));
896: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetTrimmed_C", NULL));
897: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetNodeType_C", NULL));
898: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetNodeType_C", NULL));
899: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetUseMoments_C", NULL));
900: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetUseMoments_C", NULL));
901: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetMomentOrder_C", NULL));
902: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetMomentOrder_C", NULL));
903: PetscFunctionReturn(PETSC_SUCCESS);
904: }
906: static PetscErrorCode PetscDualSpaceLagrangeView_Ascii(PetscDualSpace sp, PetscViewer viewer)
907: {
908: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
910: PetscFunctionBegin;
911: PetscCall(PetscViewerASCIIPrintf(viewer, "%s %s%sLagrange dual space\n", lag->continuous ? "Continuous" : "Discontinuous", lag->tensorSpace ? "tensor " : "", lag->trimmed ? "trimmed " : ""));
912: PetscFunctionReturn(PETSC_SUCCESS);
913: }
915: static PetscErrorCode PetscDualSpaceView_Lagrange(PetscDualSpace sp, PetscViewer viewer)
916: {
917: PetscBool iascii;
919: PetscFunctionBegin;
922: PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
923: if (iascii) PetscCall(PetscDualSpaceLagrangeView_Ascii(sp, viewer));
924: PetscFunctionReturn(PETSC_SUCCESS);
925: }
927: static PetscErrorCode PetscDualSpaceSetFromOptions_Lagrange(PetscDualSpace sp, PetscOptionItems *PetscOptionsObject)
928: {
929: PetscBool continuous, tensor, trimmed, flg, flg2, flg3;
930: PetscDTNodeType nodeType;
931: PetscReal nodeExponent;
932: PetscInt momentOrder;
933: PetscBool nodeEndpoints, useMoments;
935: PetscFunctionBegin;
936: PetscCall(PetscDualSpaceLagrangeGetContinuity(sp, &continuous));
937: PetscCall(PetscDualSpaceLagrangeGetTensor(sp, &tensor));
938: PetscCall(PetscDualSpaceLagrangeGetTrimmed(sp, &trimmed));
939: PetscCall(PetscDualSpaceLagrangeGetNodeType(sp, &nodeType, &nodeEndpoints, &nodeExponent));
940: if (nodeType == PETSCDTNODES_DEFAULT) nodeType = PETSCDTNODES_GAUSSJACOBI;
941: PetscCall(PetscDualSpaceLagrangeGetUseMoments(sp, &useMoments));
942: PetscCall(PetscDualSpaceLagrangeGetMomentOrder(sp, &momentOrder));
943: PetscOptionsHeadBegin(PetscOptionsObject, "PetscDualSpace Lagrange Options");
944: PetscCall(PetscOptionsBool("-petscdualspace_lagrange_continuity", "Flag for continuous element", "PetscDualSpaceLagrangeSetContinuity", continuous, &continuous, &flg));
945: if (flg) PetscCall(PetscDualSpaceLagrangeSetContinuity(sp, continuous));
946: PetscCall(PetscOptionsBool("-petscdualspace_lagrange_tensor", "Flag for tensor dual space", "PetscDualSpaceLagrangeSetTensor", tensor, &tensor, &flg));
947: if (flg) PetscCall(PetscDualSpaceLagrangeSetTensor(sp, tensor));
948: PetscCall(PetscOptionsBool("-petscdualspace_lagrange_trimmed", "Flag for trimmed dual space", "PetscDualSpaceLagrangeSetTrimmed", trimmed, &trimmed, &flg));
949: if (flg) PetscCall(PetscDualSpaceLagrangeSetTrimmed(sp, trimmed));
950: PetscCall(PetscOptionsEnum("-petscdualspace_lagrange_node_type", "Lagrange node location type", "PetscDualSpaceLagrangeSetNodeType", PetscDTNodeTypes, (PetscEnum)nodeType, (PetscEnum *)&nodeType, &flg));
951: PetscCall(PetscOptionsBool("-petscdualspace_lagrange_node_endpoints", "Flag for nodes that include endpoints", "PetscDualSpaceLagrangeSetNodeType", nodeEndpoints, &nodeEndpoints, &flg2));
952: flg3 = PETSC_FALSE;
953: if (nodeType == PETSCDTNODES_GAUSSJACOBI) PetscCall(PetscOptionsReal("-petscdualspace_lagrange_node_exponent", "Gauss-Jacobi weight function exponent", "PetscDualSpaceLagrangeSetNodeType", nodeExponent, &nodeExponent, &flg3));
954: if (flg || flg2 || flg3) PetscCall(PetscDualSpaceLagrangeSetNodeType(sp, nodeType, nodeEndpoints, nodeExponent));
955: PetscCall(PetscOptionsBool("-petscdualspace_lagrange_use_moments", "Use moments (where appropriate) for functionals", "PetscDualSpaceLagrangeSetUseMoments", useMoments, &useMoments, &flg));
956: if (flg) PetscCall(PetscDualSpaceLagrangeSetUseMoments(sp, useMoments));
957: PetscCall(PetscOptionsInt("-petscdualspace_lagrange_moment_order", "Quadrature order for moment functionals", "PetscDualSpaceLagrangeSetMomentOrder", momentOrder, &momentOrder, &flg));
958: if (flg) PetscCall(PetscDualSpaceLagrangeSetMomentOrder(sp, momentOrder));
959: PetscOptionsHeadEnd();
960: PetscFunctionReturn(PETSC_SUCCESS);
961: }
963: static PetscErrorCode PetscDualSpaceDuplicate_Lagrange(PetscDualSpace sp, PetscDualSpace spNew)
964: {
965: PetscBool cont, tensor, trimmed, boundary;
966: PetscDTNodeType nodeType;
967: PetscReal exponent;
968: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
970: PetscFunctionBegin;
971: PetscCall(PetscDualSpaceLagrangeGetContinuity(sp, &cont));
972: PetscCall(PetscDualSpaceLagrangeSetContinuity(spNew, cont));
973: PetscCall(PetscDualSpaceLagrangeGetTensor(sp, &tensor));
974: PetscCall(PetscDualSpaceLagrangeSetTensor(spNew, tensor));
975: PetscCall(PetscDualSpaceLagrangeGetTrimmed(sp, &trimmed));
976: PetscCall(PetscDualSpaceLagrangeSetTrimmed(spNew, trimmed));
977: PetscCall(PetscDualSpaceLagrangeGetNodeType(sp, &nodeType, &boundary, &exponent));
978: PetscCall(PetscDualSpaceLagrangeSetNodeType(spNew, nodeType, boundary, exponent));
979: if (lag->nodeFamily) {
980: PetscDualSpace_Lag *lagnew = (PetscDualSpace_Lag *)spNew->data;
982: PetscCall(Petsc1DNodeFamilyReference(lag->nodeFamily));
983: lagnew->nodeFamily = lag->nodeFamily;
984: }
985: PetscFunctionReturn(PETSC_SUCCESS);
986: }
988: /* for making tensor product spaces: take a dual space and product a segment space that has all the same
989: * specifications (trimmed, continuous, order, node set), except for the form degree */
990: static PetscErrorCode PetscDualSpaceCreateEdgeSubspace_Lagrange(PetscDualSpace sp, PetscInt order, PetscInt k, PetscInt Nc, PetscBool interiorOnly, PetscDualSpace *bdsp)
991: {
992: DM K;
993: PetscDualSpace_Lag *newlag;
995: PetscFunctionBegin;
996: PetscCall(PetscDualSpaceDuplicate(sp, bdsp));
997: PetscCall(PetscDualSpaceSetFormDegree(*bdsp, k));
998: PetscCall(DMPlexCreateReferenceCell(PETSC_COMM_SELF, DMPolytopeTypeSimpleShape(1, PETSC_TRUE), &K));
999: PetscCall(PetscDualSpaceSetDM(*bdsp, K));
1000: PetscCall(DMDestroy(&K));
1001: PetscCall(PetscDualSpaceSetOrder(*bdsp, order));
1002: PetscCall(PetscDualSpaceSetNumComponents(*bdsp, Nc));
1003: newlag = (PetscDualSpace_Lag *)(*bdsp)->data;
1004: newlag->interiorOnly = interiorOnly;
1005: PetscCall(PetscDualSpaceSetUp(*bdsp));
1006: PetscFunctionReturn(PETSC_SUCCESS);
1007: }
1009: /* just the points, weights aren't handled */
1010: static PetscErrorCode PetscQuadratureCreateTensor(PetscQuadrature trace, PetscQuadrature fiber, PetscQuadrature *product)
1011: {
1012: PetscInt dimTrace, dimFiber;
1013: PetscInt numPointsTrace, numPointsFiber;
1014: PetscInt dim, numPoints;
1015: const PetscReal *pointsTrace;
1016: const PetscReal *pointsFiber;
1017: PetscReal *points;
1018: PetscInt i, j, k, p;
1020: PetscFunctionBegin;
1021: PetscCall(PetscQuadratureGetData(trace, &dimTrace, NULL, &numPointsTrace, &pointsTrace, NULL));
1022: PetscCall(PetscQuadratureGetData(fiber, &dimFiber, NULL, &numPointsFiber, &pointsFiber, NULL));
1023: dim = dimTrace + dimFiber;
1024: numPoints = numPointsFiber * numPointsTrace;
1025: PetscCall(PetscMalloc1(numPoints * dim, &points));
1026: for (p = 0, j = 0; j < numPointsFiber; j++) {
1027: for (i = 0; i < numPointsTrace; i++, p++) {
1028: for (k = 0; k < dimTrace; k++) points[p * dim + k] = pointsTrace[i * dimTrace + k];
1029: for (k = 0; k < dimFiber; k++) points[p * dim + dimTrace + k] = pointsFiber[j * dimFiber + k];
1030: }
1031: }
1032: PetscCall(PetscQuadratureCreate(PETSC_COMM_SELF, product));
1033: PetscCall(PetscQuadratureSetData(*product, dim, 0, numPoints, points, NULL));
1034: PetscFunctionReturn(PETSC_SUCCESS);
1035: }
1037: /* Kronecker tensor product where matrix is considered a matrix of k-forms, so that
1038: * the entries in the product matrix are wedge products of the entries in the original matrices */
1039: static PetscErrorCode MatTensorAltV(Mat trace, Mat fiber, PetscInt dimTrace, PetscInt kTrace, PetscInt dimFiber, PetscInt kFiber, Mat *product)
1040: {
1041: PetscInt mTrace, nTrace, mFiber, nFiber, m, n, k, i, j, l;
1042: PetscInt dim, NkTrace, NkFiber, Nk;
1043: PetscInt dT, dF;
1044: PetscInt *nnzTrace, *nnzFiber, *nnz;
1045: PetscInt iT, iF, jT, jF, il, jl;
1046: PetscReal *workT, *workT2, *workF, *workF2, *work, *workstar;
1047: PetscReal *projT, *projF;
1048: PetscReal *projTstar, *projFstar;
1049: PetscReal *wedgeMat;
1050: PetscReal sign;
1051: PetscScalar *workS;
1052: Mat prod;
1053: /* this produces dof groups that look like the identity */
1055: PetscFunctionBegin;
1056: PetscCall(MatGetSize(trace, &mTrace, &nTrace));
1057: PetscCall(PetscDTBinomialInt(dimTrace, PetscAbsInt(kTrace), &NkTrace));
1058: PetscCheck(nTrace % NkTrace == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "point value space of trace matrix is not a multiple of k-form size");
1059: PetscCall(MatGetSize(fiber, &mFiber, &nFiber));
1060: PetscCall(PetscDTBinomialInt(dimFiber, PetscAbsInt(kFiber), &NkFiber));
1061: PetscCheck(nFiber % NkFiber == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "point value space of fiber matrix is not a multiple of k-form size");
1062: PetscCall(PetscMalloc2(mTrace, &nnzTrace, mFiber, &nnzFiber));
1063: for (i = 0; i < mTrace; i++) {
1064: PetscCall(MatGetRow(trace, i, &nnzTrace[i], NULL, NULL));
1065: PetscCheck(nnzTrace[i] % NkTrace == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "nonzeros in trace matrix are not in k-form size blocks");
1066: }
1067: for (i = 0; i < mFiber; i++) {
1068: PetscCall(MatGetRow(fiber, i, &nnzFiber[i], NULL, NULL));
1069: PetscCheck(nnzFiber[i] % NkFiber == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "nonzeros in fiber matrix are not in k-form size blocks");
1070: }
1071: dim = dimTrace + dimFiber;
1072: k = kFiber + kTrace;
1073: PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(k), &Nk));
1074: m = mTrace * mFiber;
1075: PetscCall(PetscMalloc1(m, &nnz));
1076: for (l = 0, j = 0; j < mFiber; j++)
1077: for (i = 0; i < mTrace; i++, l++) nnz[l] = (nnzTrace[i] / NkTrace) * (nnzFiber[j] / NkFiber) * Nk;
1078: n = (nTrace / NkTrace) * (nFiber / NkFiber) * Nk;
1079: PetscCall(MatCreateSeqAIJ(PETSC_COMM_SELF, m, n, 0, nnz, &prod));
1080: PetscCall(PetscObjectSetOptionsPrefix((PetscObject)prod, "altv_"));
1081: PetscCall(PetscFree(nnz));
1082: PetscCall(PetscFree2(nnzTrace, nnzFiber));
1083: /* reasoning about which points each dof needs depends on having zeros computed at points preserved */
1084: PetscCall(MatSetOption(prod, MAT_IGNORE_ZERO_ENTRIES, PETSC_FALSE));
1085: /* compute pullbacks */
1086: PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(kTrace), &dT));
1087: PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(kFiber), &dF));
1088: PetscCall(PetscMalloc4(dimTrace * dim, &projT, dimFiber * dim, &projF, dT * NkTrace, &projTstar, dF * NkFiber, &projFstar));
1089: PetscCall(PetscArrayzero(projT, dimTrace * dim));
1090: for (i = 0; i < dimTrace; i++) projT[i * (dim + 1)] = 1.;
1091: PetscCall(PetscArrayzero(projF, dimFiber * dim));
1092: for (i = 0; i < dimFiber; i++) projF[i * (dim + 1) + dimTrace] = 1.;
1093: PetscCall(PetscDTAltVPullbackMatrix(dim, dimTrace, projT, kTrace, projTstar));
1094: PetscCall(PetscDTAltVPullbackMatrix(dim, dimFiber, projF, kFiber, projFstar));
1095: PetscCall(PetscMalloc5(dT, &workT, dF, &workF, Nk, &work, Nk, &workstar, Nk, &workS));
1096: PetscCall(PetscMalloc2(dT, &workT2, dF, &workF2));
1097: PetscCall(PetscMalloc1(Nk * dT, &wedgeMat));
1098: sign = (PetscAbsInt(kTrace * kFiber) & 1) ? -1. : 1.;
1099: for (i = 0, iF = 0; iF < mFiber; iF++) {
1100: PetscInt ncolsF, nformsF;
1101: const PetscInt *colsF;
1102: const PetscScalar *valsF;
1104: PetscCall(MatGetRow(fiber, iF, &ncolsF, &colsF, &valsF));
1105: nformsF = ncolsF / NkFiber;
1106: for (iT = 0; iT < mTrace; iT++, i++) {
1107: PetscInt ncolsT, nformsT;
1108: const PetscInt *colsT;
1109: const PetscScalar *valsT;
1111: PetscCall(MatGetRow(trace, iT, &ncolsT, &colsT, &valsT));
1112: nformsT = ncolsT / NkTrace;
1113: for (j = 0, jF = 0; jF < nformsF; jF++) {
1114: PetscInt colF = colsF[jF * NkFiber] / NkFiber;
1116: for (il = 0; il < dF; il++) {
1117: PetscReal val = 0.;
1118: for (jl = 0; jl < NkFiber; jl++) val += projFstar[il * NkFiber + jl] * PetscRealPart(valsF[jF * NkFiber + jl]);
1119: workF[il] = val;
1120: }
1121: if (kFiber < 0) {
1122: for (il = 0; il < dF; il++) workF2[il] = workF[il];
1123: PetscCall(PetscDTAltVStar(dim, PetscAbsInt(kFiber), 1, workF2, workF));
1124: }
1125: PetscCall(PetscDTAltVWedgeMatrix(dim, PetscAbsInt(kFiber), PetscAbsInt(kTrace), workF, wedgeMat));
1126: for (jT = 0; jT < nformsT; jT++, j++) {
1127: PetscInt colT = colsT[jT * NkTrace] / NkTrace;
1128: PetscInt col = colF * (nTrace / NkTrace) + colT;
1129: const PetscScalar *vals;
1131: for (il = 0; il < dT; il++) {
1132: PetscReal val = 0.;
1133: for (jl = 0; jl < NkTrace; jl++) val += projTstar[il * NkTrace + jl] * PetscRealPart(valsT[jT * NkTrace + jl]);
1134: workT[il] = val;
1135: }
1136: if (kTrace < 0) {
1137: for (il = 0; il < dT; il++) workT2[il] = workT[il];
1138: PetscCall(PetscDTAltVStar(dim, PetscAbsInt(kTrace), 1, workT2, workT));
1139: }
1141: for (il = 0; il < Nk; il++) {
1142: PetscReal val = 0.;
1143: for (jl = 0; jl < dT; jl++) val += sign * wedgeMat[il * dT + jl] * workT[jl];
1144: work[il] = val;
1145: }
1146: if (k < 0) {
1147: PetscCall(PetscDTAltVStar(dim, PetscAbsInt(k), -1, work, workstar));
1148: #if defined(PETSC_USE_COMPLEX)
1149: for (l = 0; l < Nk; l++) workS[l] = workstar[l];
1150: vals = &workS[0];
1151: #else
1152: vals = &workstar[0];
1153: #endif
1154: } else {
1155: #if defined(PETSC_USE_COMPLEX)
1156: for (l = 0; l < Nk; l++) workS[l] = work[l];
1157: vals = &workS[0];
1158: #else
1159: vals = &work[0];
1160: #endif
1161: }
1162: for (l = 0; l < Nk; l++) PetscCall(MatSetValue(prod, i, col * Nk + l, vals[l], INSERT_VALUES)); /* Nk */
1163: } /* jT */
1164: } /* jF */
1165: PetscCall(MatRestoreRow(trace, iT, &ncolsT, &colsT, &valsT));
1166: } /* iT */
1167: PetscCall(MatRestoreRow(fiber, iF, &ncolsF, &colsF, &valsF));
1168: } /* iF */
1169: PetscCall(PetscFree(wedgeMat));
1170: PetscCall(PetscFree4(projT, projF, projTstar, projFstar));
1171: PetscCall(PetscFree2(workT2, workF2));
1172: PetscCall(PetscFree5(workT, workF, work, workstar, workS));
1173: PetscCall(MatAssemblyBegin(prod, MAT_FINAL_ASSEMBLY));
1174: PetscCall(MatAssemblyEnd(prod, MAT_FINAL_ASSEMBLY));
1175: *product = prod;
1176: PetscFunctionReturn(PETSC_SUCCESS);
1177: }
1179: /* Union of quadrature points, with an attempt to identify common points in the two sets */
1180: static PetscErrorCode PetscQuadraturePointsMerge(PetscQuadrature quadA, PetscQuadrature quadB, PetscQuadrature *quadJoint, PetscInt *aToJoint[], PetscInt *bToJoint[])
1181: {
1182: PetscInt dimA, dimB;
1183: PetscInt nA, nB, nJoint, i, j, d;
1184: const PetscReal *pointsA;
1185: const PetscReal *pointsB;
1186: PetscReal *pointsJoint;
1187: PetscInt *aToJ, *bToJ;
1188: PetscQuadrature qJ;
1190: PetscFunctionBegin;
1191: PetscCall(PetscQuadratureGetData(quadA, &dimA, NULL, &nA, &pointsA, NULL));
1192: PetscCall(PetscQuadratureGetData(quadB, &dimB, NULL, &nB, &pointsB, NULL));
1193: PetscCheck(dimA == dimB, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Quadrature points must be in the same dimension");
1194: nJoint = nA;
1195: PetscCall(PetscMalloc1(nA, &aToJ));
1196: for (i = 0; i < nA; i++) aToJ[i] = i;
1197: PetscCall(PetscMalloc1(nB, &bToJ));
1198: for (i = 0; i < nB; i++) {
1199: for (j = 0; j < nA; j++) {
1200: bToJ[i] = -1;
1201: for (d = 0; d < dimA; d++)
1202: if (PetscAbsReal(pointsB[i * dimA + d] - pointsA[j * dimA + d]) > PETSC_SMALL) break;
1203: if (d == dimA) {
1204: bToJ[i] = j;
1205: break;
1206: }
1207: }
1208: if (bToJ[i] == -1) bToJ[i] = nJoint++;
1209: }
1210: *aToJoint = aToJ;
1211: *bToJoint = bToJ;
1212: PetscCall(PetscMalloc1(nJoint * dimA, &pointsJoint));
1213: PetscCall(PetscArraycpy(pointsJoint, pointsA, nA * dimA));
1214: for (i = 0; i < nB; i++) {
1215: if (bToJ[i] >= nA) {
1216: for (d = 0; d < dimA; d++) pointsJoint[bToJ[i] * dimA + d] = pointsB[i * dimA + d];
1217: }
1218: }
1219: PetscCall(PetscQuadratureCreate(PETSC_COMM_SELF, &qJ));
1220: PetscCall(PetscQuadratureSetData(qJ, dimA, 0, nJoint, pointsJoint, NULL));
1221: *quadJoint = qJ;
1222: PetscFunctionReturn(PETSC_SUCCESS);
1223: }
1225: /* Matrices matA and matB are both quadrature -> dof matrices: produce a matrix that is joint quadrature -> union of
1226: * dofs, where the joint quadrature was produced by PetscQuadraturePointsMerge */
1227: static PetscErrorCode MatricesMerge(Mat matA, Mat matB, PetscInt dim, PetscInt k, PetscInt numMerged, const PetscInt aToMerged[], const PetscInt bToMerged[], Mat *matMerged)
1228: {
1229: PetscInt m, n, mA, nA, mB, nB, Nk, i, j, l;
1230: Mat M;
1231: PetscInt *nnz;
1232: PetscInt maxnnz;
1233: PetscInt *work;
1235: PetscFunctionBegin;
1236: PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(k), &Nk));
1237: PetscCall(MatGetSize(matA, &mA, &nA));
1238: PetscCheck(nA % Nk == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "matA column space not a multiple of k-form size");
1239: PetscCall(MatGetSize(matB, &mB, &nB));
1240: PetscCheck(nB % Nk == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "matB column space not a multiple of k-form size");
1241: m = mA + mB;
1242: n = numMerged * Nk;
1243: PetscCall(PetscMalloc1(m, &nnz));
1244: maxnnz = 0;
1245: for (i = 0; i < mA; i++) {
1246: PetscCall(MatGetRow(matA, i, &nnz[i], NULL, NULL));
1247: PetscCheck(nnz[i] % Nk == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "nonzeros in matA are not in k-form size blocks");
1248: maxnnz = PetscMax(maxnnz, nnz[i]);
1249: }
1250: for (i = 0; i < mB; i++) {
1251: PetscCall(MatGetRow(matB, i, &nnz[i + mA], NULL, NULL));
1252: PetscCheck(nnz[i + mA] % Nk == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "nonzeros in matB are not in k-form size blocks");
1253: maxnnz = PetscMax(maxnnz, nnz[i + mA]);
1254: }
1255: PetscCall(MatCreateSeqAIJ(PETSC_COMM_SELF, m, n, 0, nnz, &M));
1256: PetscCall(PetscObjectSetOptionsPrefix((PetscObject)M, "altv_"));
1257: PetscCall(PetscFree(nnz));
1258: /* reasoning about which points each dof needs depends on having zeros computed at points preserved */
1259: PetscCall(MatSetOption(M, MAT_IGNORE_ZERO_ENTRIES, PETSC_FALSE));
1260: PetscCall(PetscMalloc1(maxnnz, &work));
1261: for (i = 0; i < mA; i++) {
1262: const PetscInt *cols;
1263: const PetscScalar *vals;
1264: PetscInt nCols;
1265: PetscCall(MatGetRow(matA, i, &nCols, &cols, &vals));
1266: for (j = 0; j < nCols / Nk; j++) {
1267: PetscInt newCol = aToMerged[cols[j * Nk] / Nk];
1268: for (l = 0; l < Nk; l++) work[j * Nk + l] = newCol * Nk + l;
1269: }
1270: PetscCall(MatSetValuesBlocked(M, 1, &i, nCols, work, vals, INSERT_VALUES));
1271: PetscCall(MatRestoreRow(matA, i, &nCols, &cols, &vals));
1272: }
1273: for (i = 0; i < mB; i++) {
1274: const PetscInt *cols;
1275: const PetscScalar *vals;
1277: PetscInt row = i + mA;
1278: PetscInt nCols;
1279: PetscCall(MatGetRow(matB, i, &nCols, &cols, &vals));
1280: for (j = 0; j < nCols / Nk; j++) {
1281: PetscInt newCol = bToMerged[cols[j * Nk] / Nk];
1282: for (l = 0; l < Nk; l++) work[j * Nk + l] = newCol * Nk + l;
1283: }
1284: PetscCall(MatSetValuesBlocked(M, 1, &row, nCols, work, vals, INSERT_VALUES));
1285: PetscCall(MatRestoreRow(matB, i, &nCols, &cols, &vals));
1286: }
1287: PetscCall(PetscFree(work));
1288: PetscCall(MatAssemblyBegin(M, MAT_FINAL_ASSEMBLY));
1289: PetscCall(MatAssemblyEnd(M, MAT_FINAL_ASSEMBLY));
1290: *matMerged = M;
1291: PetscFunctionReturn(PETSC_SUCCESS);
1292: }
1294: /* Take a dual space and product a segment space that has all the same specifications (trimmed, continuous, order,
1295: * node set), except for the form degree. For computing boundary dofs and for making tensor product spaces */
1296: static PetscErrorCode PetscDualSpaceCreateFacetSubspace_Lagrange(PetscDualSpace sp, DM K, PetscInt f, PetscInt k, PetscInt Ncopies, PetscBool interiorOnly, PetscDualSpace *bdsp)
1297: {
1298: PetscInt Nknew, Ncnew;
1299: PetscInt dim, pointDim = -1;
1300: PetscInt depth;
1301: DM dm;
1302: PetscDualSpace_Lag *newlag;
1304: PetscFunctionBegin;
1305: PetscCall(PetscDualSpaceGetDM(sp, &dm));
1306: PetscCall(DMGetDimension(dm, &dim));
1307: PetscCall(DMPlexGetDepth(dm, &depth));
1308: PetscCall(PetscDualSpaceDuplicate(sp, bdsp));
1309: PetscCall(PetscDualSpaceSetFormDegree(*bdsp, k));
1310: if (!K) {
1311: if (depth == dim) {
1312: DMPolytopeType ct;
1314: pointDim = dim - 1;
1315: PetscCall(DMPlexGetCellType(dm, f, &ct));
1316: PetscCall(DMPlexCreateReferenceCell(PETSC_COMM_SELF, ct, &K));
1317: } else if (depth == 1) {
1318: pointDim = 0;
1319: PetscCall(DMPlexCreateReferenceCell(PETSC_COMM_SELF, DM_POLYTOPE_POINT, &K));
1320: } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Unsupported interpolation state of reference element");
1321: } else {
1322: PetscCall(PetscObjectReference((PetscObject)K));
1323: PetscCall(DMGetDimension(K, &pointDim));
1324: }
1325: PetscCall(PetscDualSpaceSetDM(*bdsp, K));
1326: PetscCall(DMDestroy(&K));
1327: PetscCall(PetscDTBinomialInt(pointDim, PetscAbsInt(k), &Nknew));
1328: Ncnew = Nknew * Ncopies;
1329: PetscCall(PetscDualSpaceSetNumComponents(*bdsp, Ncnew));
1330: newlag = (PetscDualSpace_Lag *)(*bdsp)->data;
1331: newlag->interiorOnly = interiorOnly;
1332: PetscCall(PetscDualSpaceSetUp(*bdsp));
1333: PetscFunctionReturn(PETSC_SUCCESS);
1334: }
1336: /* Construct simplex nodes from a nodefamily, add Nk dof vectors of length Nk at each node.
1337: * Return the (quadrature, matrix) form of the dofs and the nodeIndices form as well.
1338: *
1339: * Sometimes we want a set of nodes to be contained in the interior of the element,
1340: * even when the node scheme puts nodes on the boundaries. numNodeSkip tells
1341: * the routine how many "layers" of nodes need to be skipped.
1342: * */
1343: static PetscErrorCode PetscDualSpaceLagrangeCreateSimplexNodeMat(Petsc1DNodeFamily nodeFamily, PetscInt dim, PetscInt sum, PetscInt Nk, PetscInt numNodeSkip, PetscQuadrature *iNodes, Mat *iMat, PetscLagNodeIndices *nodeIndices)
1344: {
1345: PetscReal *extraNodeCoords, *nodeCoords;
1346: PetscInt nNodes, nExtraNodes;
1347: PetscInt i, j, k, extraSum = sum + numNodeSkip * (1 + dim);
1348: PetscQuadrature intNodes;
1349: Mat intMat;
1350: PetscLagNodeIndices ni;
1352: PetscFunctionBegin;
1353: PetscCall(PetscDTBinomialInt(dim + sum, dim, &nNodes));
1354: PetscCall(PetscDTBinomialInt(dim + extraSum, dim, &nExtraNodes));
1356: PetscCall(PetscMalloc1(dim * nExtraNodes, &extraNodeCoords));
1357: PetscCall(PetscNew(&ni));
1358: ni->nodeIdxDim = dim + 1;
1359: ni->nodeVecDim = Nk;
1360: ni->nNodes = nNodes * Nk;
1361: ni->refct = 1;
1362: PetscCall(PetscMalloc1(nNodes * Nk * (dim + 1), &ni->nodeIdx));
1363: PetscCall(PetscMalloc1(nNodes * Nk * Nk, &ni->nodeVec));
1364: for (i = 0; i < nNodes; i++)
1365: for (j = 0; j < Nk; j++)
1366: for (k = 0; k < Nk; k++) ni->nodeVec[(i * Nk + j) * Nk + k] = (j == k) ? 1. : 0.;
1367: PetscCall(Petsc1DNodeFamilyComputeSimplexNodes(nodeFamily, dim, extraSum, extraNodeCoords));
1368: if (numNodeSkip) {
1369: PetscInt k;
1370: PetscInt *tup;
1372: PetscCall(PetscMalloc1(dim * nNodes, &nodeCoords));
1373: PetscCall(PetscMalloc1(dim + 1, &tup));
1374: for (k = 0; k < nNodes; k++) {
1375: PetscInt j, c;
1376: PetscInt index;
1378: PetscCall(PetscDTIndexToBary(dim + 1, sum, k, tup));
1379: for (j = 0; j < dim + 1; j++) tup[j] += numNodeSkip;
1380: for (c = 0; c < Nk; c++) {
1381: for (j = 0; j < dim + 1; j++) ni->nodeIdx[(k * Nk + c) * (dim + 1) + j] = tup[j] + 1;
1382: }
1383: PetscCall(PetscDTBaryToIndex(dim + 1, extraSum, tup, &index));
1384: for (j = 0; j < dim; j++) nodeCoords[k * dim + j] = extraNodeCoords[index * dim + j];
1385: }
1386: PetscCall(PetscFree(tup));
1387: PetscCall(PetscFree(extraNodeCoords));
1388: } else {
1389: PetscInt k;
1390: PetscInt *tup;
1392: nodeCoords = extraNodeCoords;
1393: PetscCall(PetscMalloc1(dim + 1, &tup));
1394: for (k = 0; k < nNodes; k++) {
1395: PetscInt j, c;
1397: PetscCall(PetscDTIndexToBary(dim + 1, sum, k, tup));
1398: for (c = 0; c < Nk; c++) {
1399: for (j = 0; j < dim + 1; j++) {
1400: /* barycentric indices can have zeros, but we don't want to push forward zeros because it makes it harder to
1401: * determine which nodes correspond to which under symmetries, so we increase by 1. This is fine
1402: * because the nodeIdx coordinates don't have any meaning other than helping to identify symmetries */
1403: ni->nodeIdx[(k * Nk + c) * (dim + 1) + j] = tup[j] + 1;
1404: }
1405: }
1406: }
1407: PetscCall(PetscFree(tup));
1408: }
1409: PetscCall(PetscQuadratureCreate(PETSC_COMM_SELF, &intNodes));
1410: PetscCall(PetscQuadratureSetData(intNodes, dim, 0, nNodes, nodeCoords, NULL));
1411: PetscCall(MatCreateSeqAIJ(PETSC_COMM_SELF, nNodes * Nk, nNodes * Nk, Nk, NULL, &intMat));
1412: PetscCall(PetscObjectSetOptionsPrefix((PetscObject)intMat, "lag_"));
1413: PetscCall(MatSetOption(intMat, MAT_IGNORE_ZERO_ENTRIES, PETSC_FALSE));
1414: for (j = 0; j < nNodes * Nk; j++) {
1415: PetscInt rem = j % Nk;
1416: PetscInt a, aprev = j - rem;
1417: PetscInt anext = aprev + Nk;
1419: for (a = aprev; a < anext; a++) PetscCall(MatSetValue(intMat, j, a, (a == j) ? 1. : 0., INSERT_VALUES));
1420: }
1421: PetscCall(MatAssemblyBegin(intMat, MAT_FINAL_ASSEMBLY));
1422: PetscCall(MatAssemblyEnd(intMat, MAT_FINAL_ASSEMBLY));
1423: *iNodes = intNodes;
1424: *iMat = intMat;
1425: *nodeIndices = ni;
1426: PetscFunctionReturn(PETSC_SUCCESS);
1427: }
1429: /* once the nodeIndices have been created for the interior of the reference cell, and for all of the boundary cells,
1430: * push forward the boundary dofs and concatenate them into the full node indices for the dual space */
1431: static PetscErrorCode PetscDualSpaceLagrangeCreateAllNodeIdx(PetscDualSpace sp)
1432: {
1433: DM dm;
1434: PetscInt dim, nDofs;
1435: PetscSection section;
1436: PetscInt pStart, pEnd, p;
1437: PetscInt formDegree, Nk;
1438: PetscInt nodeIdxDim, spintdim;
1439: PetscDualSpace_Lag *lag;
1440: PetscLagNodeIndices ni, verti;
1442: PetscFunctionBegin;
1443: lag = (PetscDualSpace_Lag *)sp->data;
1444: verti = lag->vertIndices;
1445: PetscCall(PetscDualSpaceGetDM(sp, &dm));
1446: PetscCall(DMGetDimension(dm, &dim));
1447: PetscCall(PetscDualSpaceGetFormDegree(sp, &formDegree));
1448: PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(formDegree), &Nk));
1449: PetscCall(PetscDualSpaceGetSection(sp, §ion));
1450: PetscCall(PetscSectionGetStorageSize(section, &nDofs));
1451: PetscCall(PetscNew(&ni));
1452: ni->nodeIdxDim = nodeIdxDim = verti->nodeIdxDim;
1453: ni->nodeVecDim = Nk;
1454: ni->nNodes = nDofs;
1455: ni->refct = 1;
1456: PetscCall(PetscMalloc1(nodeIdxDim * nDofs, &ni->nodeIdx));
1457: PetscCall(PetscMalloc1(Nk * nDofs, &ni->nodeVec));
1458: PetscCall(DMPlexGetChart(dm, &pStart, &pEnd));
1459: PetscCall(PetscSectionGetDof(section, 0, &spintdim));
1460: if (spintdim) {
1461: PetscCall(PetscArraycpy(ni->nodeIdx, lag->intNodeIndices->nodeIdx, spintdim * nodeIdxDim));
1462: PetscCall(PetscArraycpy(ni->nodeVec, lag->intNodeIndices->nodeVec, spintdim * Nk));
1463: }
1464: for (p = pStart + 1; p < pEnd; p++) {
1465: PetscDualSpace psp = sp->pointSpaces[p];
1466: PetscDualSpace_Lag *plag;
1467: PetscInt dof, off;
1469: PetscCall(PetscSectionGetDof(section, p, &dof));
1470: if (!dof) continue;
1471: plag = (PetscDualSpace_Lag *)psp->data;
1472: PetscCall(PetscSectionGetOffset(section, p, &off));
1473: PetscCall(PetscLagNodeIndicesPushForward(dm, verti, p, plag->vertIndices, plag->intNodeIndices, 0, formDegree, &ni->nodeIdx[off * nodeIdxDim], &ni->nodeVec[off * Nk]));
1474: }
1475: lag->allNodeIndices = ni;
1476: PetscFunctionReturn(PETSC_SUCCESS);
1477: }
1479: /* once the (quadrature, Matrix) forms of the dofs have been created for the interior of the
1480: * reference cell and for the boundary cells, jk
1481: * push forward the boundary data and concatenate them into the full (quadrature, matrix) data
1482: * for the dual space */
1483: static PetscErrorCode PetscDualSpaceCreateAllDataFromInteriorData(PetscDualSpace sp)
1484: {
1485: DM dm;
1486: PetscSection section;
1487: PetscInt pStart, pEnd, p, k, Nk, dim, Nc;
1488: PetscInt nNodes;
1489: PetscInt countNodes;
1490: Mat allMat;
1491: PetscQuadrature allNodes;
1492: PetscInt nDofs;
1493: PetscInt maxNzforms, j;
1494: PetscScalar *work;
1495: PetscReal *L, *J, *Jinv, *v0, *pv0;
1496: PetscInt *iwork;
1497: PetscReal *nodes;
1499: PetscFunctionBegin;
1500: PetscCall(PetscDualSpaceGetDM(sp, &dm));
1501: PetscCall(DMGetDimension(dm, &dim));
1502: PetscCall(PetscDualSpaceGetSection(sp, §ion));
1503: PetscCall(PetscSectionGetStorageSize(section, &nDofs));
1504: PetscCall(DMPlexGetChart(dm, &pStart, &pEnd));
1505: PetscCall(PetscDualSpaceGetFormDegree(sp, &k));
1506: PetscCall(PetscDualSpaceGetNumComponents(sp, &Nc));
1507: PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(k), &Nk));
1508: for (p = pStart, nNodes = 0, maxNzforms = 0; p < pEnd; p++) {
1509: PetscDualSpace psp;
1510: DM pdm;
1511: PetscInt pdim, pNk;
1512: PetscQuadrature intNodes;
1513: Mat intMat;
1515: PetscCall(PetscDualSpaceGetPointSubspace(sp, p, &psp));
1516: if (!psp) continue;
1517: PetscCall(PetscDualSpaceGetDM(psp, &pdm));
1518: PetscCall(DMGetDimension(pdm, &pdim));
1519: if (pdim < PetscAbsInt(k)) continue;
1520: PetscCall(PetscDTBinomialInt(pdim, PetscAbsInt(k), &pNk));
1521: PetscCall(PetscDualSpaceGetInteriorData(psp, &intNodes, &intMat));
1522: if (intNodes) {
1523: PetscInt nNodesp;
1525: PetscCall(PetscQuadratureGetData(intNodes, NULL, NULL, &nNodesp, NULL, NULL));
1526: nNodes += nNodesp;
1527: }
1528: if (intMat) {
1529: PetscInt maxNzsp;
1530: PetscInt maxNzformsp;
1532: PetscCall(MatSeqAIJGetMaxRowNonzeros(intMat, &maxNzsp));
1533: PetscCheck(maxNzsp % pNk == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "interior matrix is not laid out as blocks of k-forms");
1534: maxNzformsp = maxNzsp / pNk;
1535: maxNzforms = PetscMax(maxNzforms, maxNzformsp);
1536: }
1537: }
1538: PetscCall(MatCreateSeqAIJ(PETSC_COMM_SELF, nDofs, nNodes * Nc, maxNzforms * Nk, NULL, &allMat));
1539: PetscCall(PetscObjectSetOptionsPrefix((PetscObject)allMat, "ds_"));
1540: PetscCall(MatSetOption(allMat, MAT_IGNORE_ZERO_ENTRIES, PETSC_FALSE));
1541: PetscCall(PetscMalloc7(dim, &v0, dim, &pv0, dim * dim, &J, dim * dim, &Jinv, Nk * Nk, &L, maxNzforms * Nk, &work, maxNzforms * Nk, &iwork));
1542: for (j = 0; j < dim; j++) pv0[j] = -1.;
1543: PetscCall(PetscMalloc1(dim * nNodes, &nodes));
1544: for (p = pStart, countNodes = 0; p < pEnd; p++) {
1545: PetscDualSpace psp;
1546: PetscQuadrature intNodes;
1547: DM pdm;
1548: PetscInt pdim, pNk;
1549: PetscInt countNodesIn = countNodes;
1550: PetscReal detJ;
1551: Mat intMat;
1553: PetscCall(PetscDualSpaceGetPointSubspace(sp, p, &psp));
1554: if (!psp) continue;
1555: PetscCall(PetscDualSpaceGetDM(psp, &pdm));
1556: PetscCall(DMGetDimension(pdm, &pdim));
1557: if (pdim < PetscAbsInt(k)) continue;
1558: PetscCall(PetscDualSpaceGetInteriorData(psp, &intNodes, &intMat));
1559: if (intNodes == NULL && intMat == NULL) continue;
1560: PetscCall(PetscDTBinomialInt(pdim, PetscAbsInt(k), &pNk));
1561: if (p) {
1562: PetscCall(DMPlexComputeCellGeometryAffineFEM(dm, p, v0, J, Jinv, &detJ));
1563: } else { /* identity */
1564: PetscInt i, j;
1566: for (i = 0; i < dim; i++)
1567: for (j = 0; j < dim; j++) J[i * dim + j] = Jinv[i * dim + j] = 0.;
1568: for (i = 0; i < dim; i++) J[i * dim + i] = Jinv[i * dim + i] = 1.;
1569: for (i = 0; i < dim; i++) v0[i] = -1.;
1570: }
1571: if (pdim != dim) { /* compactify Jacobian */
1572: PetscInt i, j;
1574: for (i = 0; i < dim; i++)
1575: for (j = 0; j < pdim; j++) J[i * pdim + j] = J[i * dim + j];
1576: }
1577: PetscCall(PetscDTAltVPullbackMatrix(pdim, dim, J, k, L));
1578: if (intNodes) { /* push forward quadrature locations by the affine transformation */
1579: PetscInt nNodesp;
1580: const PetscReal *nodesp;
1581: PetscInt j;
1583: PetscCall(PetscQuadratureGetData(intNodes, NULL, NULL, &nNodesp, &nodesp, NULL));
1584: for (j = 0; j < nNodesp; j++, countNodes++) {
1585: PetscInt d, e;
1587: for (d = 0; d < dim; d++) {
1588: nodes[countNodes * dim + d] = v0[d];
1589: for (e = 0; e < pdim; e++) nodes[countNodes * dim + d] += J[d * pdim + e] * (nodesp[j * pdim + e] - pv0[e]);
1590: }
1591: }
1592: }
1593: if (intMat) {
1594: PetscInt nrows;
1595: PetscInt off;
1597: PetscCall(PetscSectionGetDof(section, p, &nrows));
1598: PetscCall(PetscSectionGetOffset(section, p, &off));
1599: for (j = 0; j < nrows; j++) {
1600: PetscInt ncols;
1601: const PetscInt *cols;
1602: const PetscScalar *vals;
1603: PetscInt l, d, e;
1604: PetscInt row = j + off;
1606: PetscCall(MatGetRow(intMat, j, &ncols, &cols, &vals));
1607: PetscCheck(ncols % pNk == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "interior matrix is not laid out as blocks of k-forms");
1608: for (l = 0; l < ncols / pNk; l++) {
1609: PetscInt blockcol;
1611: for (d = 0; d < pNk; d++) PetscCheck((cols[l * pNk + d] % pNk) == d, PETSC_COMM_SELF, PETSC_ERR_PLIB, "interior matrix is not laid out as blocks of k-forms");
1612: blockcol = cols[l * pNk] / pNk;
1613: for (d = 0; d < Nk; d++) iwork[l * Nk + d] = (blockcol + countNodesIn) * Nk + d;
1614: for (d = 0; d < Nk; d++) work[l * Nk + d] = 0.;
1615: for (d = 0; d < Nk; d++) {
1616: for (e = 0; e < pNk; e++) {
1617: /* "push forward" dof by pulling back a k-form to be evaluated on the point: multiply on the right by L */
1618: work[l * Nk + d] += vals[l * pNk + e] * L[e * Nk + d];
1619: }
1620: }
1621: }
1622: PetscCall(MatSetValues(allMat, 1, &row, (ncols / pNk) * Nk, iwork, work, INSERT_VALUES));
1623: PetscCall(MatRestoreRow(intMat, j, &ncols, &cols, &vals));
1624: }
1625: }
1626: }
1627: PetscCall(MatAssemblyBegin(allMat, MAT_FINAL_ASSEMBLY));
1628: PetscCall(MatAssemblyEnd(allMat, MAT_FINAL_ASSEMBLY));
1629: PetscCall(PetscQuadratureCreate(PETSC_COMM_SELF, &allNodes));
1630: PetscCall(PetscQuadratureSetData(allNodes, dim, 0, nNodes, nodes, NULL));
1631: PetscCall(PetscFree7(v0, pv0, J, Jinv, L, work, iwork));
1632: PetscCall(MatDestroy(&sp->allMat));
1633: sp->allMat = allMat;
1634: PetscCall(PetscQuadratureDestroy(&sp->allNodes));
1635: sp->allNodes = allNodes;
1636: PetscFunctionReturn(PETSC_SUCCESS);
1637: }
1639: static PetscErrorCode PetscDualSpaceComputeFunctionalsFromAllData_Moments(PetscDualSpace sp)
1640: {
1641: Mat allMat;
1642: PetscInt momentOrder, i;
1643: PetscBool tensor = PETSC_FALSE;
1644: const PetscReal *weights;
1645: PetscScalar *array;
1646: PetscInt nDofs;
1647: PetscInt dim, Nc;
1648: DM dm;
1649: PetscQuadrature allNodes;
1650: PetscInt nNodes;
1652: PetscFunctionBegin;
1653: PetscCall(PetscDualSpaceGetDM(sp, &dm));
1654: PetscCall(DMGetDimension(dm, &dim));
1655: PetscCall(PetscDualSpaceGetNumComponents(sp, &Nc));
1656: PetscCall(PetscDualSpaceGetAllData(sp, &allNodes, &allMat));
1657: PetscCall(MatGetSize(allMat, &nDofs, NULL));
1658: PetscCheck(nDofs == 1, PETSC_COMM_SELF, PETSC_ERR_SUP, "We do not yet support moments beyond P0, nDofs == %" PetscInt_FMT, nDofs);
1659: PetscCall(PetscMalloc1(nDofs, &sp->functional));
1660: PetscCall(PetscDualSpaceLagrangeGetMomentOrder(sp, &momentOrder));
1661: PetscCall(PetscDualSpaceLagrangeGetTensor(sp, &tensor));
1662: if (!tensor) PetscCall(PetscDTStroudConicalQuadrature(dim, Nc, PetscMax(momentOrder + 1, 1), -1.0, 1.0, &sp->functional[0]));
1663: else PetscCall(PetscDTGaussTensorQuadrature(dim, Nc, PetscMax(momentOrder + 1, 1), -1.0, 1.0, &sp->functional[0]));
1664: /* Need to replace allNodes and allMat */
1665: PetscCall(PetscObjectReference((PetscObject)sp->functional[0]));
1666: PetscCall(PetscQuadratureDestroy(&sp->allNodes));
1667: sp->allNodes = sp->functional[0];
1668: PetscCall(PetscQuadratureGetData(sp->allNodes, NULL, NULL, &nNodes, NULL, &weights));
1669: PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, nDofs, nNodes * Nc, NULL, &allMat));
1670: PetscCall(PetscObjectSetOptionsPrefix((PetscObject)allMat, "ds_"));
1671: PetscCall(MatDenseGetArrayWrite(allMat, &array));
1672: for (i = 0; i < nNodes * Nc; ++i) array[i] = weights[i];
1673: PetscCall(MatDenseRestoreArrayWrite(allMat, &array));
1674: PetscCall(MatAssemblyBegin(allMat, MAT_FINAL_ASSEMBLY));
1675: PetscCall(MatAssemblyEnd(allMat, MAT_FINAL_ASSEMBLY));
1676: PetscCall(MatDestroy(&sp->allMat));
1677: sp->allMat = allMat;
1678: PetscFunctionReturn(PETSC_SUCCESS);
1679: }
1681: /* rather than trying to get all data from the functionals, we create
1682: * the functionals from rows of the quadrature -> dof matrix.
1683: *
1684: * Ideally most of the uses of PetscDualSpace in PetscFE will switch
1685: * to using intMat and allMat, so that the individual functionals
1686: * don't need to be constructed at all */
1687: PETSC_INTERN PetscErrorCode PetscDualSpaceComputeFunctionalsFromAllData(PetscDualSpace sp)
1688: {
1689: PetscQuadrature allNodes;
1690: Mat allMat;
1691: PetscInt nDofs;
1692: PetscInt dim, Nc, f;
1693: DM dm;
1694: PetscInt nNodes, spdim;
1695: const PetscReal *nodes = NULL;
1696: PetscSection section;
1697: PetscBool useMoments;
1699: PetscFunctionBegin;
1700: PetscCall(PetscDualSpaceGetDM(sp, &dm));
1701: PetscCall(DMGetDimension(dm, &dim));
1702: PetscCall(PetscDualSpaceGetNumComponents(sp, &Nc));
1703: PetscCall(PetscDualSpaceGetAllData(sp, &allNodes, &allMat));
1704: nNodes = 0;
1705: if (allNodes) PetscCall(PetscQuadratureGetData(allNodes, NULL, NULL, &nNodes, &nodes, NULL));
1706: PetscCall(MatGetSize(allMat, &nDofs, NULL));
1707: PetscCall(PetscDualSpaceGetSection(sp, §ion));
1708: PetscCall(PetscSectionGetStorageSize(section, &spdim));
1709: PetscCheck(spdim == nDofs, PETSC_COMM_SELF, PETSC_ERR_PLIB, "incompatible all matrix size");
1710: PetscCall(PetscMalloc1(nDofs, &sp->functional));
1711: PetscCall(PetscDualSpaceLagrangeGetUseMoments(sp, &useMoments));
1712: for (f = 0; f < nDofs; f++) {
1713: PetscInt ncols, c;
1714: const PetscInt *cols;
1715: const PetscScalar *vals;
1716: PetscReal *nodesf;
1717: PetscReal *weightsf;
1718: PetscInt nNodesf;
1719: PetscInt countNodes;
1721: PetscCall(MatGetRow(allMat, f, &ncols, &cols, &vals));
1722: for (c = 1, nNodesf = 1; c < ncols; c++) {
1723: if ((cols[c] / Nc) != (cols[c - 1] / Nc)) nNodesf++;
1724: }
1725: PetscCall(PetscMalloc1(dim * nNodesf, &nodesf));
1726: PetscCall(PetscMalloc1(Nc * nNodesf, &weightsf));
1727: for (c = 0, countNodes = 0; c < ncols; c++) {
1728: if (!c || ((cols[c] / Nc) != (cols[c - 1] / Nc))) {
1729: PetscInt d;
1731: for (d = 0; d < Nc; d++) weightsf[countNodes * Nc + d] = 0.;
1732: for (d = 0; d < dim; d++) nodesf[countNodes * dim + d] = nodes[(cols[c] / Nc) * dim + d];
1733: countNodes++;
1734: }
1735: weightsf[(countNodes - 1) * Nc + (cols[c] % Nc)] = PetscRealPart(vals[c]);
1736: }
1737: PetscCall(PetscQuadratureCreate(PETSC_COMM_SELF, &sp->functional[f]));
1738: PetscCall(PetscQuadratureSetData(sp->functional[f], dim, Nc, nNodesf, nodesf, weightsf));
1739: PetscCall(MatRestoreRow(allMat, f, &ncols, &cols, &vals));
1740: }
1741: PetscFunctionReturn(PETSC_SUCCESS);
1742: }
1744: /* check if a cell is a tensor product of the segment with a facet,
1745: * specifically checking if f and f2 can be the "endpoints" (like the triangles
1746: * at either end of a wedge) */
1747: static PetscErrorCode DMPlexPointIsTensor_Internal_Given(DM dm, PetscInt p, PetscInt f, PetscInt f2, PetscBool *isTensor)
1748: {
1749: PetscInt coneSize, c;
1750: const PetscInt *cone;
1751: const PetscInt *fCone;
1752: const PetscInt *f2Cone;
1753: PetscInt fs[2];
1754: PetscInt meetSize, nmeet;
1755: const PetscInt *meet;
1757: PetscFunctionBegin;
1758: fs[0] = f;
1759: fs[1] = f2;
1760: PetscCall(DMPlexGetMeet(dm, 2, fs, &meetSize, &meet));
1761: nmeet = meetSize;
1762: PetscCall(DMPlexRestoreMeet(dm, 2, fs, &meetSize, &meet));
1763: /* two points that have a non-empty meet cannot be at opposite ends of a cell */
1764: if (nmeet) {
1765: *isTensor = PETSC_FALSE;
1766: PetscFunctionReturn(PETSC_SUCCESS);
1767: }
1768: PetscCall(DMPlexGetConeSize(dm, p, &coneSize));
1769: PetscCall(DMPlexGetCone(dm, p, &cone));
1770: PetscCall(DMPlexGetCone(dm, f, &fCone));
1771: PetscCall(DMPlexGetCone(dm, f2, &f2Cone));
1772: for (c = 0; c < coneSize; c++) {
1773: PetscInt e, ef;
1774: PetscInt d = -1, d2 = -1;
1775: PetscInt dcount, d2count;
1776: PetscInt t = cone[c];
1777: PetscInt tConeSize;
1778: PetscBool tIsTensor;
1779: const PetscInt *tCone;
1781: if (t == f || t == f2) continue;
1782: /* for every other facet in the cone, check that is has
1783: * one ridge in common with each end */
1784: PetscCall(DMPlexGetConeSize(dm, t, &tConeSize));
1785: PetscCall(DMPlexGetCone(dm, t, &tCone));
1787: dcount = 0;
1788: d2count = 0;
1789: for (e = 0; e < tConeSize; e++) {
1790: PetscInt q = tCone[e];
1791: for (ef = 0; ef < coneSize - 2; ef++) {
1792: if (fCone[ef] == q) {
1793: if (dcount) {
1794: *isTensor = PETSC_FALSE;
1795: PetscFunctionReturn(PETSC_SUCCESS);
1796: }
1797: d = q;
1798: dcount++;
1799: } else if (f2Cone[ef] == q) {
1800: if (d2count) {
1801: *isTensor = PETSC_FALSE;
1802: PetscFunctionReturn(PETSC_SUCCESS);
1803: }
1804: d2 = q;
1805: d2count++;
1806: }
1807: }
1808: }
1809: /* if the whole cell is a tensor with the segment, then this
1810: * facet should be a tensor with the segment */
1811: PetscCall(DMPlexPointIsTensor_Internal_Given(dm, t, d, d2, &tIsTensor));
1812: if (!tIsTensor) {
1813: *isTensor = PETSC_FALSE;
1814: PetscFunctionReturn(PETSC_SUCCESS);
1815: }
1816: }
1817: *isTensor = PETSC_TRUE;
1818: PetscFunctionReturn(PETSC_SUCCESS);
1819: }
1821: /* determine if a cell is a tensor with a segment by looping over pairs of facets to find a pair
1822: * that could be the opposite ends */
1823: static PetscErrorCode DMPlexPointIsTensor_Internal(DM dm, PetscInt p, PetscBool *isTensor, PetscInt *endA, PetscInt *endB)
1824: {
1825: PetscInt coneSize, c, c2;
1826: const PetscInt *cone;
1828: PetscFunctionBegin;
1829: PetscCall(DMPlexGetConeSize(dm, p, &coneSize));
1830: if (!coneSize) {
1831: if (isTensor) *isTensor = PETSC_FALSE;
1832: if (endA) *endA = -1;
1833: if (endB) *endB = -1;
1834: }
1835: PetscCall(DMPlexGetCone(dm, p, &cone));
1836: for (c = 0; c < coneSize; c++) {
1837: PetscInt f = cone[c];
1838: PetscInt fConeSize;
1840: PetscCall(DMPlexGetConeSize(dm, f, &fConeSize));
1841: if (fConeSize != coneSize - 2) continue;
1843: for (c2 = c + 1; c2 < coneSize; c2++) {
1844: PetscInt f2 = cone[c2];
1845: PetscBool isTensorff2;
1846: PetscInt f2ConeSize;
1848: PetscCall(DMPlexGetConeSize(dm, f2, &f2ConeSize));
1849: if (f2ConeSize != coneSize - 2) continue;
1851: PetscCall(DMPlexPointIsTensor_Internal_Given(dm, p, f, f2, &isTensorff2));
1852: if (isTensorff2) {
1853: if (isTensor) *isTensor = PETSC_TRUE;
1854: if (endA) *endA = f;
1855: if (endB) *endB = f2;
1856: PetscFunctionReturn(PETSC_SUCCESS);
1857: }
1858: }
1859: }
1860: if (isTensor) *isTensor = PETSC_FALSE;
1861: if (endA) *endA = -1;
1862: if (endB) *endB = -1;
1863: PetscFunctionReturn(PETSC_SUCCESS);
1864: }
1866: /* determine if a cell is a tensor with a segment by looping over pairs of facets to find a pair
1867: * that could be the opposite ends */
1868: static PetscErrorCode DMPlexPointIsTensor(DM dm, PetscInt p, PetscBool *isTensor, PetscInt *endA, PetscInt *endB)
1869: {
1870: DMPlexInterpolatedFlag interpolated;
1872: PetscFunctionBegin;
1873: PetscCall(DMPlexIsInterpolated(dm, &interpolated));
1874: PetscCheck(interpolated == DMPLEX_INTERPOLATED_FULL, PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONGSTATE, "Only for interpolated DMPlex's");
1875: PetscCall(DMPlexPointIsTensor_Internal(dm, p, isTensor, endA, endB));
1876: PetscFunctionReturn(PETSC_SUCCESS);
1877: }
1879: /* Let k = formDegree and k' = -sign(k) * dim + k. Transform a symmetric frame for k-forms on the biunit simplex into
1880: * a symmetric frame for k'-forms on the biunit simplex.
1881: *
1882: * A frame is "symmetric" if the pullback of every symmetry of the biunit simplex is a permutation of the frame.
1883: *
1884: * forms in the symmetric frame are used as dofs in the untrimmed simplex spaces. This way, symmetries of the
1885: * reference cell result in permutations of dofs grouped by node.
1886: *
1887: * Use T to transform dof matrices for k'-forms into dof matrices for k-forms as a block diagonal transformation on
1888: * the right.
1889: */
1890: static PetscErrorCode BiunitSimplexSymmetricFormTransformation(PetscInt dim, PetscInt formDegree, PetscReal T[])
1891: {
1892: PetscInt k = formDegree;
1893: PetscInt kd = k < 0 ? dim + k : k - dim;
1894: PetscInt Nk;
1895: PetscReal *biToEq, *eqToBi, *biToEqStar, *eqToBiStar;
1896: PetscInt fact;
1898: PetscFunctionBegin;
1899: PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(k), &Nk));
1900: PetscCall(PetscCalloc4(dim * dim, &biToEq, dim * dim, &eqToBi, Nk * Nk, &biToEqStar, Nk * Nk, &eqToBiStar));
1901: /* fill in biToEq: Jacobian of the transformation from the biunit simplex to the equilateral simplex */
1902: fact = 0;
1903: for (PetscInt i = 0; i < dim; i++) {
1904: biToEq[i * dim + i] = PetscSqrtReal(((PetscReal)i + 2.) / (2. * ((PetscReal)i + 1.)));
1905: fact += 4 * (i + 1);
1906: for (PetscInt j = i + 1; j < dim; j++) biToEq[i * dim + j] = PetscSqrtReal(1. / (PetscReal)fact);
1907: }
1908: /* fill in eqToBi: Jacobian of the transformation from the equilateral simplex to the biunit simplex */
1909: fact = 0;
1910: for (PetscInt j = 0; j < dim; j++) {
1911: eqToBi[j * dim + j] = PetscSqrtReal(2. * ((PetscReal)j + 1.) / ((PetscReal)j + 2));
1912: fact += j + 1;
1913: for (PetscInt i = 0; i < j; i++) eqToBi[i * dim + j] = -PetscSqrtReal(1. / (PetscReal)fact);
1914: }
1915: PetscCall(PetscDTAltVPullbackMatrix(dim, dim, biToEq, kd, biToEqStar));
1916: PetscCall(PetscDTAltVPullbackMatrix(dim, dim, eqToBi, k, eqToBiStar));
1917: /* product of pullbacks simulates the following steps
1918: *
1919: * 1. start with frame W = [w_1, w_2, ..., w_m] of k forms that is symmetric on the biunit simplex:
1920: if J is the Jacobian of a symmetry of the biunit simplex, then J_k* W = [J_k*w_1, ..., J_k*w_m]
1921: is a permutation of W.
1922: Even though a k' form --- a (dim - k) form represented by its Hodge star --- has the same geometric
1923: content as a k form, W is not a symmetric frame of k' forms on the biunit simplex. That's because,
1924: for general Jacobian J, J_k* != J_k'*.
1925: * 2. pullback W to the equilateral triangle using the k pullback, W_eq = eqToBi_k* W. All symmetries of the
1926: equilateral simplex have orthonormal Jacobians. For an orthonormal Jacobian O, J_k* = J_k'*, so W_eq is
1927: also a symmetric frame for k' forms on the equilateral simplex.
1928: 3. pullback W_eq back to the biunit simplex using the k' pulback, V = biToEq_k'* W_eq = biToEq_k'* eqToBi_k* W.
1929: V is a symmetric frame for k' forms on the biunit simplex.
1930: */
1931: for (PetscInt i = 0; i < Nk; i++) {
1932: for (PetscInt j = 0; j < Nk; j++) {
1933: PetscReal val = 0.;
1934: for (PetscInt k = 0; k < Nk; k++) val += biToEqStar[i * Nk + k] * eqToBiStar[k * Nk + j];
1935: T[i * Nk + j] = val;
1936: }
1937: }
1938: PetscCall(PetscFree4(biToEq, eqToBi, biToEqStar, eqToBiStar));
1939: PetscFunctionReturn(PETSC_SUCCESS);
1940: }
1942: /* permute a quadrature -> dof matrix so that its rows are in revlex order by nodeIdx */
1943: static PetscErrorCode MatPermuteByNodeIdx(Mat A, PetscLagNodeIndices ni, Mat *Aperm)
1944: {
1945: PetscInt m, n, i, j;
1946: PetscInt nodeIdxDim = ni->nodeIdxDim;
1947: PetscInt nodeVecDim = ni->nodeVecDim;
1948: PetscInt *perm;
1949: IS permIS;
1950: IS id;
1951: PetscInt *nIdxPerm;
1952: PetscReal *nVecPerm;
1954: PetscFunctionBegin;
1955: PetscCall(PetscLagNodeIndicesGetPermutation(ni, &perm));
1956: PetscCall(MatGetSize(A, &m, &n));
1957: PetscCall(PetscMalloc1(nodeIdxDim * m, &nIdxPerm));
1958: PetscCall(PetscMalloc1(nodeVecDim * m, &nVecPerm));
1959: for (i = 0; i < m; i++)
1960: for (j = 0; j < nodeIdxDim; j++) nIdxPerm[i * nodeIdxDim + j] = ni->nodeIdx[perm[i] * nodeIdxDim + j];
1961: for (i = 0; i < m; i++)
1962: for (j = 0; j < nodeVecDim; j++) nVecPerm[i * nodeVecDim + j] = ni->nodeVec[perm[i] * nodeVecDim + j];
1963: PetscCall(ISCreateGeneral(PETSC_COMM_SELF, m, perm, PETSC_USE_POINTER, &permIS));
1964: PetscCall(ISSetPermutation(permIS));
1965: PetscCall(ISCreateStride(PETSC_COMM_SELF, n, 0, 1, &id));
1966: PetscCall(ISSetPermutation(id));
1967: PetscCall(MatPermute(A, permIS, id, Aperm));
1968: PetscCall(ISDestroy(&permIS));
1969: PetscCall(ISDestroy(&id));
1970: for (i = 0; i < m; i++) perm[i] = i;
1971: PetscCall(PetscFree(ni->nodeIdx));
1972: PetscCall(PetscFree(ni->nodeVec));
1973: ni->nodeIdx = nIdxPerm;
1974: ni->nodeVec = nVecPerm;
1975: PetscFunctionReturn(PETSC_SUCCESS);
1976: }
1978: static PetscErrorCode PetscDualSpaceSetUp_Lagrange(PetscDualSpace sp)
1979: {
1980: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
1981: DM dm = sp->dm;
1982: DM dmint = NULL;
1983: PetscInt order;
1984: PetscInt Nc = sp->Nc;
1985: MPI_Comm comm;
1986: PetscBool continuous;
1987: PetscSection section;
1988: PetscInt depth, dim, pStart, pEnd, cStart, cEnd, p, *pStratStart, *pStratEnd, d;
1989: PetscInt formDegree, Nk, Ncopies;
1990: PetscInt tensorf = -1, tensorf2 = -1;
1991: PetscBool tensorCell, tensorSpace;
1992: PetscBool uniform, trimmed;
1993: Petsc1DNodeFamily nodeFamily;
1994: PetscInt numNodeSkip;
1995: DMPlexInterpolatedFlag interpolated;
1996: PetscBool isbdm;
1998: PetscFunctionBegin;
1999: /* step 1: sanitize input */
2000: PetscCall(PetscObjectGetComm((PetscObject)sp, &comm));
2001: PetscCall(DMGetDimension(dm, &dim));
2002: PetscCall(PetscObjectTypeCompare((PetscObject)sp, PETSCDUALSPACEBDM, &isbdm));
2003: if (isbdm) {
2004: sp->k = -(dim - 1); /* form degree of H-div */
2005: PetscCall(PetscObjectChangeTypeName((PetscObject)sp, PETSCDUALSPACELAGRANGE));
2006: }
2007: PetscCall(PetscDualSpaceGetFormDegree(sp, &formDegree));
2008: PetscCheck(PetscAbsInt(formDegree) <= dim, comm, PETSC_ERR_ARG_OUTOFRANGE, "Form degree must be bounded by dimension");
2009: PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(formDegree), &Nk));
2010: if (sp->Nc <= 0 && lag->numCopies > 0) sp->Nc = Nk * lag->numCopies;
2011: Nc = sp->Nc;
2012: PetscCheck(Nc % Nk == 0, comm, PETSC_ERR_ARG_INCOMP, "Number of components is not a multiple of form degree size");
2013: if (lag->numCopies <= 0) lag->numCopies = Nc / Nk;
2014: Ncopies = lag->numCopies;
2015: PetscCheck(Nc / Nk == Ncopies, comm, PETSC_ERR_ARG_INCOMP, "Number of copies * (dim choose k) != Nc");
2016: if (!dim) sp->order = 0;
2017: order = sp->order;
2018: uniform = sp->uniform;
2019: PetscCheck(uniform, PETSC_COMM_SELF, PETSC_ERR_SUP, "Variable order not supported yet");
2020: if (lag->trimmed && !formDegree) lag->trimmed = PETSC_FALSE; /* trimmed spaces are the same as full spaces for 0-forms */
2021: if (lag->nodeType == PETSCDTNODES_DEFAULT) {
2022: lag->nodeType = PETSCDTNODES_GAUSSJACOBI;
2023: lag->nodeExponent = 0.;
2024: /* trimmed spaces don't include corner vertices, so don't use end nodes by default */
2025: lag->endNodes = lag->trimmed ? PETSC_FALSE : PETSC_TRUE;
2026: }
2027: /* If a trimmed space and the user did choose nodes with endpoints, skip them by default */
2028: if (lag->numNodeSkip < 0) lag->numNodeSkip = (lag->trimmed && lag->endNodes) ? 1 : 0;
2029: numNodeSkip = lag->numNodeSkip;
2030: PetscCheck(!lag->trimmed || order, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Cannot have zeroth order trimmed elements");
2031: if (lag->trimmed && PetscAbsInt(formDegree) == dim) { /* convert trimmed n-forms to untrimmed of one polynomial order less */
2032: sp->order--;
2033: order--;
2034: lag->trimmed = PETSC_FALSE;
2035: }
2036: trimmed = lag->trimmed;
2037: if (!order || PetscAbsInt(formDegree) == dim) lag->continuous = PETSC_FALSE;
2038: continuous = lag->continuous;
2039: PetscCall(DMPlexGetDepth(dm, &depth));
2040: PetscCall(DMPlexGetChart(dm, &pStart, &pEnd));
2041: PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
2042: PetscCheck(pStart == 0 && cStart == 0, PetscObjectComm((PetscObject)sp), PETSC_ERR_ARG_WRONGSTATE, "Expect DM with chart starting at zero and cells first");
2043: PetscCheck(cEnd == 1, PetscObjectComm((PetscObject)sp), PETSC_ERR_ARG_WRONGSTATE, "Use PETSCDUALSPACEREFINED for multi-cell reference meshes");
2044: PetscCall(DMPlexIsInterpolated(dm, &interpolated));
2045: if (interpolated != DMPLEX_INTERPOLATED_FULL) {
2046: PetscCall(DMPlexInterpolate(dm, &dmint));
2047: } else {
2048: PetscCall(PetscObjectReference((PetscObject)dm));
2049: dmint = dm;
2050: }
2051: tensorCell = PETSC_FALSE;
2052: if (dim > 1) PetscCall(DMPlexPointIsTensor(dmint, 0, &tensorCell, &tensorf, &tensorf2));
2053: lag->tensorCell = tensorCell;
2054: if (dim < 2 || !lag->tensorCell) lag->tensorSpace = PETSC_FALSE;
2055: tensorSpace = lag->tensorSpace;
2056: if (!lag->nodeFamily) PetscCall(Petsc1DNodeFamilyCreate(lag->nodeType, lag->nodeExponent, lag->endNodes, &lag->nodeFamily));
2057: nodeFamily = lag->nodeFamily;
2058: PetscCheck(interpolated == DMPLEX_INTERPOLATED_FULL || !continuous || (PetscAbsInt(formDegree) <= 0 && order <= 1), PETSC_COMM_SELF, PETSC_ERR_PLIB, "Reference element won't support all boundary nodes");
2060: if (Ncopies > 1) {
2061: PetscDualSpace scalarsp;
2063: PetscCall(PetscDualSpaceDuplicate(sp, &scalarsp));
2064: /* Setting the number of components to Nk is a space with 1 copy of each k-form */
2065: sp->setupcalled = PETSC_FALSE;
2066: PetscCall(PetscDualSpaceSetNumComponents(scalarsp, Nk));
2067: PetscCall(PetscDualSpaceSetUp(scalarsp));
2068: PetscCall(PetscDualSpaceSetType(sp, PETSCDUALSPACESUM));
2069: PetscCall(PetscDualSpaceSumSetNumSubspaces(sp, Ncopies));
2070: PetscCall(PetscDualSpaceSumSetConcatenate(sp, PETSC_TRUE));
2071: PetscCall(PetscDualSpaceSumSetInterleave(sp, PETSC_TRUE, PETSC_FALSE));
2072: for (PetscInt i = 0; i < Ncopies; i++) PetscCall(PetscDualSpaceSumSetSubspace(sp, i, scalarsp));
2073: PetscCall(PetscDualSpaceSetUp(sp));
2074: PetscCall(PetscDualSpaceDestroy(&scalarsp));
2075: PetscCall(DMDestroy(&dmint));
2076: PetscFunctionReturn(PETSC_SUCCESS);
2077: }
2079: /* step 2: construct the boundary spaces */
2080: PetscCall(PetscMalloc2(depth + 1, &pStratStart, depth + 1, &pStratEnd));
2081: PetscCall(PetscCalloc1(pEnd, &sp->pointSpaces));
2082: for (d = 0; d <= depth; ++d) PetscCall(DMPlexGetDepthStratum(dm, d, &pStratStart[d], &pStratEnd[d]));
2083: PetscCall(PetscDualSpaceSectionCreate_Internal(sp, §ion));
2084: sp->pointSection = section;
2085: if (continuous && !lag->interiorOnly) {
2086: PetscInt h;
2088: for (p = pStratStart[depth - 1]; p < pStratEnd[depth - 1]; p++) { /* calculate the facet dual spaces */
2089: PetscReal v0[3];
2090: DMPolytopeType ptype;
2091: PetscReal J[9], detJ;
2092: PetscInt q;
2094: PetscCall(DMPlexComputeCellGeometryAffineFEM(dm, p, v0, J, NULL, &detJ));
2095: PetscCall(DMPlexGetCellType(dm, p, &ptype));
2097: /* compare to previous facets: if computed, reference that dualspace */
2098: for (q = pStratStart[depth - 1]; q < p; q++) {
2099: DMPolytopeType qtype;
2101: PetscCall(DMPlexGetCellType(dm, q, &qtype));
2102: if (qtype == ptype) break;
2103: }
2104: if (q < p) { /* this facet has the same dual space as that one */
2105: PetscCall(PetscObjectReference((PetscObject)sp->pointSpaces[q]));
2106: sp->pointSpaces[p] = sp->pointSpaces[q];
2107: continue;
2108: }
2109: /* if not, recursively compute this dual space */
2110: PetscCall(PetscDualSpaceCreateFacetSubspace_Lagrange(sp, NULL, p, formDegree, Ncopies, PETSC_FALSE, &sp->pointSpaces[p]));
2111: }
2112: for (h = 2; h <= depth; h++) { /* get the higher subspaces from the facet subspaces */
2113: PetscInt hd = depth - h;
2114: PetscInt hdim = dim - h;
2116: if (hdim < PetscAbsInt(formDegree)) break;
2117: for (p = pStratStart[hd]; p < pStratEnd[hd]; p++) {
2118: PetscInt suppSize, s;
2119: const PetscInt *supp;
2121: PetscCall(DMPlexGetSupportSize(dm, p, &suppSize));
2122: PetscCall(DMPlexGetSupport(dm, p, &supp));
2123: for (s = 0; s < suppSize; s++) {
2124: DM qdm;
2125: PetscDualSpace qsp, psp;
2126: PetscInt c, coneSize, q;
2127: const PetscInt *cone;
2128: const PetscInt *refCone;
2130: q = supp[s];
2131: qsp = sp->pointSpaces[q];
2132: PetscCall(DMPlexGetConeSize(dm, q, &coneSize));
2133: PetscCall(DMPlexGetCone(dm, q, &cone));
2134: for (c = 0; c < coneSize; c++)
2135: if (cone[c] == p) break;
2136: PetscCheck(c != coneSize, PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "cone/support mismatch");
2137: PetscCall(PetscDualSpaceGetDM(qsp, &qdm));
2138: PetscCall(DMPlexGetCone(qdm, 0, &refCone));
2139: /* get the equivalent dual space from the support dual space */
2140: PetscCall(PetscDualSpaceGetPointSubspace(qsp, refCone[c], &psp));
2141: if (!s) {
2142: PetscCall(PetscObjectReference((PetscObject)psp));
2143: sp->pointSpaces[p] = psp;
2144: }
2145: }
2146: }
2147: }
2148: for (p = 1; p < pEnd; p++) {
2149: PetscInt pspdim;
2150: if (!sp->pointSpaces[p]) continue;
2151: PetscCall(PetscDualSpaceGetInteriorDimension(sp->pointSpaces[p], &pspdim));
2152: PetscCall(PetscSectionSetDof(section, p, pspdim));
2153: }
2154: }
2156: if (trimmed && !continuous) {
2157: /* the dofs of a trimmed space don't have a nice tensor/lattice structure:
2158: * just construct the continuous dual space and copy all of the data over,
2159: * allocating it all to the cell instead of splitting it up between the boundaries */
2160: PetscDualSpace spcont;
2161: PetscInt spdim, f;
2162: PetscQuadrature allNodes;
2163: PetscDualSpace_Lag *lagc;
2164: Mat allMat;
2166: PetscCall(PetscDualSpaceDuplicate(sp, &spcont));
2167: PetscCall(PetscDualSpaceLagrangeSetContinuity(spcont, PETSC_TRUE));
2168: PetscCall(PetscDualSpaceSetUp(spcont));
2169: PetscCall(PetscDualSpaceGetDimension(spcont, &spdim));
2170: sp->spdim = sp->spintdim = spdim;
2171: PetscCall(PetscSectionSetDof(section, 0, spdim));
2172: PetscCall(PetscDualSpaceSectionSetUp_Internal(sp, section));
2173: PetscCall(PetscMalloc1(spdim, &sp->functional));
2174: for (f = 0; f < spdim; f++) {
2175: PetscQuadrature fn;
2177: PetscCall(PetscDualSpaceGetFunctional(spcont, f, &fn));
2178: PetscCall(PetscObjectReference((PetscObject)fn));
2179: sp->functional[f] = fn;
2180: }
2181: PetscCall(PetscDualSpaceGetAllData(spcont, &allNodes, &allMat));
2182: PetscCall(PetscObjectReference((PetscObject)allNodes));
2183: PetscCall(PetscObjectReference((PetscObject)allNodes));
2184: sp->allNodes = sp->intNodes = allNodes;
2185: PetscCall(PetscObjectReference((PetscObject)allMat));
2186: PetscCall(PetscObjectReference((PetscObject)allMat));
2187: sp->allMat = sp->intMat = allMat;
2188: lagc = (PetscDualSpace_Lag *)spcont->data;
2189: PetscCall(PetscLagNodeIndicesReference(lagc->vertIndices));
2190: lag->vertIndices = lagc->vertIndices;
2191: PetscCall(PetscLagNodeIndicesReference(lagc->allNodeIndices));
2192: PetscCall(PetscLagNodeIndicesReference(lagc->allNodeIndices));
2193: lag->intNodeIndices = lagc->allNodeIndices;
2194: lag->allNodeIndices = lagc->allNodeIndices;
2195: PetscCall(PetscDualSpaceDestroy(&spcont));
2196: PetscCall(PetscFree2(pStratStart, pStratEnd));
2197: PetscCall(DMDestroy(&dmint));
2198: PetscFunctionReturn(PETSC_SUCCESS);
2199: }
2201: /* step 3: construct intNodes, and intMat, and combine it with boundray data to make allNodes and allMat */
2202: if (!tensorSpace) {
2203: if (!tensorCell) PetscCall(PetscLagNodeIndicesCreateSimplexVertices(dm, &lag->vertIndices));
2205: if (trimmed) {
2206: /* there is one dof in the interior of the a trimmed element for each full polynomial of with degree at most
2207: * order + k - dim - 1 */
2208: if (order + PetscAbsInt(formDegree) > dim) {
2209: PetscInt sum = order + PetscAbsInt(formDegree) - dim - 1;
2210: PetscInt nDofs;
2212: PetscCall(PetscDualSpaceLagrangeCreateSimplexNodeMat(nodeFamily, dim, sum, Nk, numNodeSkip, &sp->intNodes, &sp->intMat, &lag->intNodeIndices));
2213: PetscCall(MatGetSize(sp->intMat, &nDofs, NULL));
2214: PetscCall(PetscSectionSetDof(section, 0, nDofs));
2215: }
2216: PetscCall(PetscDualSpaceSectionSetUp_Internal(sp, section));
2217: PetscCall(PetscDualSpaceCreateAllDataFromInteriorData(sp));
2218: PetscCall(PetscDualSpaceLagrangeCreateAllNodeIdx(sp));
2219: } else {
2220: if (!continuous) {
2221: /* if discontinuous just construct one node for each set of dofs (a set of dofs is a basis for the k-form
2222: * space) */
2223: PetscInt sum = order;
2224: PetscInt nDofs;
2226: PetscCall(PetscDualSpaceLagrangeCreateSimplexNodeMat(nodeFamily, dim, sum, Nk, numNodeSkip, &sp->intNodes, &sp->intMat, &lag->intNodeIndices));
2227: PetscCall(MatGetSize(sp->intMat, &nDofs, NULL));
2228: PetscCall(PetscSectionSetDof(section, 0, nDofs));
2229: PetscCall(PetscDualSpaceSectionSetUp_Internal(sp, section));
2230: PetscCall(PetscObjectReference((PetscObject)sp->intNodes));
2231: sp->allNodes = sp->intNodes;
2232: PetscCall(PetscObjectReference((PetscObject)sp->intMat));
2233: sp->allMat = sp->intMat;
2234: PetscCall(PetscLagNodeIndicesReference(lag->intNodeIndices));
2235: lag->allNodeIndices = lag->intNodeIndices;
2236: } else {
2237: /* there is one dof in the interior of the a full element for each trimmed polynomial of with degree at most
2238: * order + k - dim, but with complementary form degree */
2239: if (order + PetscAbsInt(formDegree) > dim) {
2240: PetscDualSpace trimmedsp;
2241: PetscDualSpace_Lag *trimmedlag;
2242: PetscQuadrature intNodes;
2243: PetscInt trFormDegree = formDegree >= 0 ? formDegree - dim : dim - PetscAbsInt(formDegree);
2244: PetscInt nDofs;
2245: Mat intMat;
2247: PetscCall(PetscDualSpaceDuplicate(sp, &trimmedsp));
2248: PetscCall(PetscDualSpaceLagrangeSetTrimmed(trimmedsp, PETSC_TRUE));
2249: PetscCall(PetscDualSpaceSetOrder(trimmedsp, order + PetscAbsInt(formDegree) - dim));
2250: PetscCall(PetscDualSpaceSetFormDegree(trimmedsp, trFormDegree));
2251: trimmedlag = (PetscDualSpace_Lag *)trimmedsp->data;
2252: trimmedlag->numNodeSkip = numNodeSkip + 1;
2253: PetscCall(PetscDualSpaceSetUp(trimmedsp));
2254: PetscCall(PetscDualSpaceGetAllData(trimmedsp, &intNodes, &intMat));
2255: PetscCall(PetscObjectReference((PetscObject)intNodes));
2256: sp->intNodes = intNodes;
2257: PetscCall(PetscLagNodeIndicesReference(trimmedlag->allNodeIndices));
2258: lag->intNodeIndices = trimmedlag->allNodeIndices;
2259: PetscCall(PetscObjectReference((PetscObject)intMat));
2260: if (PetscAbsInt(formDegree) > 0 && PetscAbsInt(formDegree) < dim) {
2261: PetscReal *T;
2262: PetscScalar *work;
2263: PetscInt nCols, nRows;
2264: Mat intMatT;
2266: PetscCall(MatDuplicate(intMat, MAT_COPY_VALUES, &intMatT));
2267: PetscCall(MatGetSize(intMat, &nRows, &nCols));
2268: PetscCall(PetscMalloc2(Nk * Nk, &T, nCols, &work));
2269: PetscCall(BiunitSimplexSymmetricFormTransformation(dim, formDegree, T));
2270: for (PetscInt row = 0; row < nRows; row++) {
2271: PetscInt nrCols;
2272: const PetscInt *rCols;
2273: const PetscScalar *rVals;
2275: PetscCall(MatGetRow(intMat, row, &nrCols, &rCols, &rVals));
2276: PetscCheck(nrCols % Nk == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "nonzeros in intMat matrix are not in k-form size blocks");
2277: for (PetscInt b = 0; b < nrCols; b += Nk) {
2278: const PetscScalar *v = &rVals[b];
2279: PetscScalar *w = &work[b];
2280: for (PetscInt j = 0; j < Nk; j++) {
2281: w[j] = 0.;
2282: for (PetscInt i = 0; i < Nk; i++) w[j] += v[i] * T[i * Nk + j];
2283: }
2284: }
2285: PetscCall(MatSetValuesBlocked(intMatT, 1, &row, nrCols, rCols, work, INSERT_VALUES));
2286: PetscCall(MatRestoreRow(intMat, row, &nrCols, &rCols, &rVals));
2287: }
2288: PetscCall(MatAssemblyBegin(intMatT, MAT_FINAL_ASSEMBLY));
2289: PetscCall(MatAssemblyEnd(intMatT, MAT_FINAL_ASSEMBLY));
2290: PetscCall(MatDestroy(&intMat));
2291: intMat = intMatT;
2292: PetscCall(PetscLagNodeIndicesDestroy(&lag->intNodeIndices));
2293: PetscCall(PetscLagNodeIndicesDuplicate(trimmedlag->allNodeIndices, &lag->intNodeIndices));
2294: {
2295: PetscInt nNodes = lag->intNodeIndices->nNodes;
2296: PetscReal *newNodeVec = lag->intNodeIndices->nodeVec;
2297: const PetscReal *oldNodeVec = trimmedlag->allNodeIndices->nodeVec;
2299: for (PetscInt n = 0; n < nNodes; n++) {
2300: PetscReal *w = &newNodeVec[n * Nk];
2301: const PetscReal *v = &oldNodeVec[n * Nk];
2303: for (PetscInt j = 0; j < Nk; j++) {
2304: w[j] = 0.;
2305: for (PetscInt i = 0; i < Nk; i++) w[j] += v[i] * T[i * Nk + j];
2306: }
2307: }
2308: }
2309: PetscCall(PetscFree2(T, work));
2310: }
2311: sp->intMat = intMat;
2312: PetscCall(MatGetSize(sp->intMat, &nDofs, NULL));
2313: PetscCall(PetscDualSpaceDestroy(&trimmedsp));
2314: PetscCall(PetscSectionSetDof(section, 0, nDofs));
2315: }
2316: PetscCall(PetscDualSpaceSectionSetUp_Internal(sp, section));
2317: PetscCall(PetscDualSpaceCreateAllDataFromInteriorData(sp));
2318: PetscCall(PetscDualSpaceLagrangeCreateAllNodeIdx(sp));
2319: }
2320: }
2321: } else {
2322: PetscQuadrature intNodesTrace = NULL;
2323: PetscQuadrature intNodesFiber = NULL;
2324: PetscQuadrature intNodes = NULL;
2325: PetscLagNodeIndices intNodeIndices = NULL;
2326: Mat intMat = NULL;
2328: if (PetscAbsInt(formDegree) < dim) { /* get the trace k-forms on the first facet, and the 0-forms on the edge,
2329: and wedge them together to create some of the k-form dofs */
2330: PetscDualSpace trace, fiber;
2331: PetscDualSpace_Lag *tracel, *fiberl;
2332: Mat intMatTrace, intMatFiber;
2334: if (sp->pointSpaces[tensorf]) {
2335: PetscCall(PetscObjectReference((PetscObject)sp->pointSpaces[tensorf]));
2336: trace = sp->pointSpaces[tensorf];
2337: } else {
2338: PetscCall(PetscDualSpaceCreateFacetSubspace_Lagrange(sp, NULL, tensorf, formDegree, Ncopies, PETSC_TRUE, &trace));
2339: }
2340: PetscCall(PetscDualSpaceCreateEdgeSubspace_Lagrange(sp, order, 0, 1, PETSC_TRUE, &fiber));
2341: tracel = (PetscDualSpace_Lag *)trace->data;
2342: fiberl = (PetscDualSpace_Lag *)fiber->data;
2343: PetscCall(PetscLagNodeIndicesCreateTensorVertices(dm, tracel->vertIndices, &lag->vertIndices));
2344: PetscCall(PetscDualSpaceGetInteriorData(trace, &intNodesTrace, &intMatTrace));
2345: PetscCall(PetscDualSpaceGetInteriorData(fiber, &intNodesFiber, &intMatFiber));
2346: if (intNodesTrace && intNodesFiber) {
2347: PetscCall(PetscQuadratureCreateTensor(intNodesTrace, intNodesFiber, &intNodes));
2348: PetscCall(MatTensorAltV(intMatTrace, intMatFiber, dim - 1, formDegree, 1, 0, &intMat));
2349: PetscCall(PetscLagNodeIndicesTensor(tracel->intNodeIndices, dim - 1, formDegree, fiberl->intNodeIndices, 1, 0, &intNodeIndices));
2350: }
2351: PetscCall(PetscObjectReference((PetscObject)intNodesTrace));
2352: PetscCall(PetscObjectReference((PetscObject)intNodesFiber));
2353: PetscCall(PetscDualSpaceDestroy(&fiber));
2354: PetscCall(PetscDualSpaceDestroy(&trace));
2355: }
2356: if (PetscAbsInt(formDegree) > 0) { /* get the trace (k-1)-forms on the first facet, and the 1-forms on the edge,
2357: and wedge them together to create the remaining k-form dofs */
2358: PetscDualSpace trace, fiber;
2359: PetscDualSpace_Lag *tracel, *fiberl;
2360: PetscQuadrature intNodesTrace2, intNodesFiber2, intNodes2;
2361: PetscLagNodeIndices intNodeIndices2;
2362: Mat intMatTrace, intMatFiber, intMat2;
2363: PetscInt traceDegree = formDegree > 0 ? formDegree - 1 : formDegree + 1;
2364: PetscInt fiberDegree = formDegree > 0 ? 1 : -1;
2366: PetscCall(PetscDualSpaceCreateFacetSubspace_Lagrange(sp, NULL, tensorf, traceDegree, Ncopies, PETSC_TRUE, &trace));
2367: PetscCall(PetscDualSpaceCreateEdgeSubspace_Lagrange(sp, order, fiberDegree, 1, PETSC_TRUE, &fiber));
2368: tracel = (PetscDualSpace_Lag *)trace->data;
2369: fiberl = (PetscDualSpace_Lag *)fiber->data;
2370: if (!lag->vertIndices) PetscCall(PetscLagNodeIndicesCreateTensorVertices(dm, tracel->vertIndices, &lag->vertIndices));
2371: PetscCall(PetscDualSpaceGetInteriorData(trace, &intNodesTrace2, &intMatTrace));
2372: PetscCall(PetscDualSpaceGetInteriorData(fiber, &intNodesFiber2, &intMatFiber));
2373: if (intNodesTrace2 && intNodesFiber2) {
2374: PetscCall(PetscQuadratureCreateTensor(intNodesTrace2, intNodesFiber2, &intNodes2));
2375: PetscCall(MatTensorAltV(intMatTrace, intMatFiber, dim - 1, traceDegree, 1, fiberDegree, &intMat2));
2376: PetscCall(PetscLagNodeIndicesTensor(tracel->intNodeIndices, dim - 1, traceDegree, fiberl->intNodeIndices, 1, fiberDegree, &intNodeIndices2));
2377: if (!intMat) {
2378: intMat = intMat2;
2379: intNodes = intNodes2;
2380: intNodeIndices = intNodeIndices2;
2381: } else {
2382: /* merge the matrices, quadrature points, and nodes */
2383: PetscInt nM;
2384: PetscInt nDof, nDof2;
2385: PetscInt *toMerged = NULL, *toMerged2 = NULL;
2386: PetscQuadrature merged = NULL;
2387: PetscLagNodeIndices intNodeIndicesMerged = NULL;
2388: Mat matMerged = NULL;
2390: PetscCall(MatGetSize(intMat, &nDof, NULL));
2391: PetscCall(MatGetSize(intMat2, &nDof2, NULL));
2392: PetscCall(PetscQuadraturePointsMerge(intNodes, intNodes2, &merged, &toMerged, &toMerged2));
2393: PetscCall(PetscQuadratureGetData(merged, NULL, NULL, &nM, NULL, NULL));
2394: PetscCall(MatricesMerge(intMat, intMat2, dim, formDegree, nM, toMerged, toMerged2, &matMerged));
2395: PetscCall(PetscLagNodeIndicesMerge(intNodeIndices, intNodeIndices2, &intNodeIndicesMerged));
2396: PetscCall(PetscFree(toMerged));
2397: PetscCall(PetscFree(toMerged2));
2398: PetscCall(MatDestroy(&intMat));
2399: PetscCall(MatDestroy(&intMat2));
2400: PetscCall(PetscQuadratureDestroy(&intNodes));
2401: PetscCall(PetscQuadratureDestroy(&intNodes2));
2402: PetscCall(PetscLagNodeIndicesDestroy(&intNodeIndices));
2403: PetscCall(PetscLagNodeIndicesDestroy(&intNodeIndices2));
2404: intNodes = merged;
2405: intMat = matMerged;
2406: intNodeIndices = intNodeIndicesMerged;
2407: if (!trimmed) {
2408: /* I think users expect that, when a node has a full basis for the k-forms,
2409: * they should be consecutive dofs. That isn't the case for trimmed spaces,
2410: * but is for some of the nodes in untrimmed spaces, so in that case we
2411: * sort them to group them by node */
2412: Mat intMatPerm;
2414: PetscCall(MatPermuteByNodeIdx(intMat, intNodeIndices, &intMatPerm));
2415: PetscCall(MatDestroy(&intMat));
2416: intMat = intMatPerm;
2417: }
2418: }
2419: }
2420: PetscCall(PetscDualSpaceDestroy(&fiber));
2421: PetscCall(PetscDualSpaceDestroy(&trace));
2422: }
2423: PetscCall(PetscQuadratureDestroy(&intNodesTrace));
2424: PetscCall(PetscQuadratureDestroy(&intNodesFiber));
2425: sp->intNodes = intNodes;
2426: sp->intMat = intMat;
2427: lag->intNodeIndices = intNodeIndices;
2428: {
2429: PetscInt nDofs = 0;
2431: if (intMat) PetscCall(MatGetSize(intMat, &nDofs, NULL));
2432: PetscCall(PetscSectionSetDof(section, 0, nDofs));
2433: }
2434: PetscCall(PetscDualSpaceSectionSetUp_Internal(sp, section));
2435: if (continuous) {
2436: PetscCall(PetscDualSpaceCreateAllDataFromInteriorData(sp));
2437: PetscCall(PetscDualSpaceLagrangeCreateAllNodeIdx(sp));
2438: } else {
2439: PetscCall(PetscObjectReference((PetscObject)intNodes));
2440: sp->allNodes = intNodes;
2441: PetscCall(PetscObjectReference((PetscObject)intMat));
2442: sp->allMat = intMat;
2443: PetscCall(PetscLagNodeIndicesReference(intNodeIndices));
2444: lag->allNodeIndices = intNodeIndices;
2445: }
2446: }
2447: PetscCall(PetscSectionGetStorageSize(section, &sp->spdim));
2448: PetscCall(PetscSectionGetConstrainedStorageSize(section, &sp->spintdim));
2449: // TODO: fix this, computing functionals from moments should be no different for nodal vs modal
2450: if (lag->useMoments) {
2451: PetscCall(PetscDualSpaceComputeFunctionalsFromAllData_Moments(sp));
2452: } else {
2453: PetscCall(PetscDualSpaceComputeFunctionalsFromAllData(sp));
2454: }
2455: PetscCall(PetscFree2(pStratStart, pStratEnd));
2456: PetscCall(DMDestroy(&dmint));
2457: PetscFunctionReturn(PETSC_SUCCESS);
2458: }
2460: /* Create a matrix that represents the transformation that DMPlexVecGetClosure() would need
2461: * to get the representation of the dofs for a mesh point if the mesh point had this orientation
2462: * relative to the cell */
2463: PetscErrorCode PetscDualSpaceCreateInteriorSymmetryMatrix_Lagrange(PetscDualSpace sp, PetscInt ornt, Mat *symMat)
2464: {
2465: PetscDualSpace_Lag *lag;
2466: DM dm;
2467: PetscLagNodeIndices vertIndices, intNodeIndices;
2468: PetscLagNodeIndices ni;
2469: PetscInt nodeIdxDim, nodeVecDim, nNodes;
2470: PetscInt formDegree;
2471: PetscInt *perm, *permOrnt;
2472: PetscInt *nnz;
2473: PetscInt n;
2474: PetscInt maxGroupSize;
2475: PetscScalar *V, *W, *work;
2476: Mat A;
2478: PetscFunctionBegin;
2479: if (!sp->spintdim) {
2480: *symMat = NULL;
2481: PetscFunctionReturn(PETSC_SUCCESS);
2482: }
2483: lag = (PetscDualSpace_Lag *)sp->data;
2484: vertIndices = lag->vertIndices;
2485: intNodeIndices = lag->intNodeIndices;
2486: PetscCall(PetscDualSpaceGetDM(sp, &dm));
2487: PetscCall(PetscDualSpaceGetFormDegree(sp, &formDegree));
2488: PetscCall(PetscNew(&ni));
2489: ni->refct = 1;
2490: ni->nodeIdxDim = nodeIdxDim = intNodeIndices->nodeIdxDim;
2491: ni->nodeVecDim = nodeVecDim = intNodeIndices->nodeVecDim;
2492: ni->nNodes = nNodes = intNodeIndices->nNodes;
2493: PetscCall(PetscMalloc1(nNodes * nodeIdxDim, &ni->nodeIdx));
2494: PetscCall(PetscMalloc1(nNodes * nodeVecDim, &ni->nodeVec));
2495: /* push forward the dofs by the symmetry of the reference element induced by ornt */
2496: PetscCall(PetscLagNodeIndicesPushForward(dm, vertIndices, 0, vertIndices, intNodeIndices, ornt, formDegree, ni->nodeIdx, ni->nodeVec));
2497: /* get the revlex order for both the original and transformed dofs */
2498: PetscCall(PetscLagNodeIndicesGetPermutation(intNodeIndices, &perm));
2499: PetscCall(PetscLagNodeIndicesGetPermutation(ni, &permOrnt));
2500: PetscCall(PetscMalloc1(nNodes, &nnz));
2501: for (n = 0, maxGroupSize = 0; n < nNodes;) { /* incremented in the loop */
2502: PetscInt *nind = &(ni->nodeIdx[permOrnt[n] * nodeIdxDim]);
2503: PetscInt m, nEnd;
2504: PetscInt groupSize;
2505: /* for each group of dofs that have the same nodeIdx coordinate */
2506: for (nEnd = n + 1; nEnd < nNodes; nEnd++) {
2507: PetscInt *mind = &(ni->nodeIdx[permOrnt[nEnd] * nodeIdxDim]);
2508: PetscInt d;
2510: /* compare the oriented permutation indices */
2511: for (d = 0; d < nodeIdxDim; d++)
2512: if (mind[d] != nind[d]) break;
2513: if (d < nodeIdxDim) break;
2514: }
2515: /* permOrnt[[n, nEnd)] is a group of dofs that, under the symmetry are at the same location */
2517: /* the symmetry had better map the group of dofs with the same permuted nodeIdx
2518: * to a group of dofs with the same size, otherwise we messed up */
2519: if (PetscDefined(USE_DEBUG)) {
2520: PetscInt m;
2521: PetscInt *nind = &(intNodeIndices->nodeIdx[perm[n] * nodeIdxDim]);
2523: for (m = n + 1; m < nEnd; m++) {
2524: PetscInt *mind = &(intNodeIndices->nodeIdx[perm[m] * nodeIdxDim]);
2525: PetscInt d;
2527: /* compare the oriented permutation indices */
2528: for (d = 0; d < nodeIdxDim; d++)
2529: if (mind[d] != nind[d]) break;
2530: if (d < nodeIdxDim) break;
2531: }
2532: PetscCheck(m >= nEnd, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Dofs with same index after symmetry not same block size");
2533: }
2534: groupSize = nEnd - n;
2535: /* each pushforward dof vector will be expressed in a basis of the unpermuted dofs */
2536: for (m = n; m < nEnd; m++) nnz[permOrnt[m]] = groupSize;
2538: maxGroupSize = PetscMax(maxGroupSize, nEnd - n);
2539: n = nEnd;
2540: }
2541: PetscCheck(maxGroupSize <= nodeVecDim, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Dofs are not in blocks that can be solved");
2542: PetscCall(MatCreateSeqAIJ(PETSC_COMM_SELF, nNodes, nNodes, 0, nnz, &A));
2543: PetscCall(PetscObjectSetOptionsPrefix((PetscObject)A, "lag_"));
2544: PetscCall(PetscFree(nnz));
2545: PetscCall(PetscMalloc3(maxGroupSize * nodeVecDim, &V, maxGroupSize * nodeVecDim, &W, nodeVecDim * 2, &work));
2546: for (n = 0; n < nNodes;) { /* incremented in the loop */
2547: PetscInt *nind = &(ni->nodeIdx[permOrnt[n] * nodeIdxDim]);
2548: PetscInt nEnd;
2549: PetscInt m;
2550: PetscInt groupSize;
2551: for (nEnd = n + 1; nEnd < nNodes; nEnd++) {
2552: PetscInt *mind = &(ni->nodeIdx[permOrnt[nEnd] * nodeIdxDim]);
2553: PetscInt d;
2555: /* compare the oriented permutation indices */
2556: for (d = 0; d < nodeIdxDim; d++)
2557: if (mind[d] != nind[d]) break;
2558: if (d < nodeIdxDim) break;
2559: }
2560: groupSize = nEnd - n;
2561: /* get all of the vectors from the original and all of the pushforward vectors */
2562: for (m = n; m < nEnd; m++) {
2563: PetscInt d;
2565: for (d = 0; d < nodeVecDim; d++) {
2566: V[(m - n) * nodeVecDim + d] = intNodeIndices->nodeVec[perm[m] * nodeVecDim + d];
2567: W[(m - n) * nodeVecDim + d] = ni->nodeVec[permOrnt[m] * nodeVecDim + d];
2568: }
2569: }
2570: /* now we have to solve for W in terms of V: the systems isn't always square, but the span
2571: * of V and W should always be the same, so the solution of the normal equations works */
2572: {
2573: char transpose = 'N';
2574: PetscBLASInt bm = nodeVecDim;
2575: PetscBLASInt bn = groupSize;
2576: PetscBLASInt bnrhs = groupSize;
2577: PetscBLASInt blda = bm;
2578: PetscBLASInt bldb = bm;
2579: PetscBLASInt blwork = 2 * nodeVecDim;
2580: PetscBLASInt info;
2582: PetscCallBLAS("LAPACKgels", LAPACKgels_(&transpose, &bm, &bn, &bnrhs, V, &blda, W, &bldb, work, &blwork, &info));
2583: PetscCheck(info == 0, PETSC_COMM_SELF, PETSC_ERR_LIB, "Bad argument to GELS");
2584: /* repack */
2585: {
2586: PetscInt i, j;
2588: for (i = 0; i < groupSize; i++) {
2589: for (j = 0; j < groupSize; j++) {
2590: /* notice the different leading dimension */
2591: V[i * groupSize + j] = W[i * nodeVecDim + j];
2592: }
2593: }
2594: }
2595: if (PetscDefined(USE_DEBUG)) {
2596: PetscReal res;
2598: /* check that the normal error is 0 */
2599: for (m = n; m < nEnd; m++) {
2600: PetscInt d;
2602: for (d = 0; d < nodeVecDim; d++) W[(m - n) * nodeVecDim + d] = ni->nodeVec[permOrnt[m] * nodeVecDim + d];
2603: }
2604: res = 0.;
2605: for (PetscInt i = 0; i < groupSize; i++) {
2606: for (PetscInt j = 0; j < nodeVecDim; j++) {
2607: for (PetscInt k = 0; k < groupSize; k++) W[i * nodeVecDim + j] -= V[i * groupSize + k] * intNodeIndices->nodeVec[perm[n + k] * nodeVecDim + j];
2608: res += PetscAbsScalar(W[i * nodeVecDim + j]);
2609: }
2610: }
2611: PetscCheck(res <= PETSC_SMALL, PETSC_COMM_SELF, PETSC_ERR_LIB, "Dof block did not solve");
2612: }
2613: }
2614: PetscCall(MatSetValues(A, groupSize, &permOrnt[n], groupSize, &perm[n], V, INSERT_VALUES));
2615: n = nEnd;
2616: }
2617: PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
2618: PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
2619: *symMat = A;
2620: PetscCall(PetscFree3(V, W, work));
2621: PetscCall(PetscLagNodeIndicesDestroy(&ni));
2622: PetscFunctionReturn(PETSC_SUCCESS);
2623: }
2625: // get the symmetries of closure points
2626: PETSC_INTERN PetscErrorCode PetscDualSpaceGetBoundarySymmetries_Internal(PetscDualSpace sp, PetscInt ***symperms, PetscScalar ***symflips)
2627: {
2628: PetscInt closureSize = 0;
2629: PetscInt *closure = NULL;
2630: PetscInt r;
2632: PetscFunctionBegin;
2633: PetscCall(DMPlexGetTransitiveClosure(sp->dm, 0, PETSC_TRUE, &closureSize, &closure));
2634: for (r = 0; r < closureSize; r++) {
2635: PetscDualSpace psp;
2636: PetscInt point = closure[2 * r];
2637: PetscInt pspintdim;
2638: const PetscInt ***psymperms = NULL;
2639: const PetscScalar ***psymflips = NULL;
2641: if (!point) continue;
2642: PetscCall(PetscDualSpaceGetPointSubspace(sp, point, &psp));
2643: if (!psp) continue;
2644: PetscCall(PetscDualSpaceGetInteriorDimension(psp, &pspintdim));
2645: if (!pspintdim) continue;
2646: PetscCall(PetscDualSpaceGetSymmetries(psp, &psymperms, &psymflips));
2647: symperms[r] = (PetscInt **)(psymperms ? psymperms[0] : NULL);
2648: symflips[r] = (PetscScalar **)(psymflips ? psymflips[0] : NULL);
2649: }
2650: PetscCall(DMPlexRestoreTransitiveClosure(sp->dm, 0, PETSC_TRUE, &closureSize, &closure));
2651: PetscFunctionReturn(PETSC_SUCCESS);
2652: }
2654: #define BaryIndex(perEdge, a, b, c) (((b) * (2 * perEdge + 1 - (b))) / 2) + (c)
2656: #define CartIndex(perEdge, a, b) (perEdge * (a) + b)
2658: /* the existing interface for symmetries is insufficient for all cases:
2659: * - it should be sufficient for form degrees that are scalar (0 and n)
2660: * - it should be sufficient for hypercube dofs
2661: * - it isn't sufficient for simplex cells with non-scalar form degrees if
2662: * there are any dofs in the interior
2663: *
2664: * We compute the general transformation matrices, and if they fit, we return them,
2665: * otherwise we error (but we should probably change the interface to allow for
2666: * these symmetries)
2667: */
2668: static PetscErrorCode PetscDualSpaceGetSymmetries_Lagrange(PetscDualSpace sp, const PetscInt ****perms, const PetscScalar ****flips)
2669: {
2670: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2671: PetscInt dim, order, Nc;
2673: PetscFunctionBegin;
2674: PetscCall(PetscDualSpaceGetOrder(sp, &order));
2675: PetscCall(PetscDualSpaceGetNumComponents(sp, &Nc));
2676: PetscCall(DMGetDimension(sp->dm, &dim));
2677: if (!lag->symComputed) { /* store symmetries */
2678: PetscInt pStart, pEnd, p;
2679: PetscInt numPoints;
2680: PetscInt numFaces;
2681: PetscInt spintdim;
2682: PetscInt ***symperms;
2683: PetscScalar ***symflips;
2685: PetscCall(DMPlexGetChart(sp->dm, &pStart, &pEnd));
2686: numPoints = pEnd - pStart;
2687: {
2688: DMPolytopeType ct;
2689: /* The number of arrangements is no longer based on the number of faces */
2690: PetscCall(DMPlexGetCellType(sp->dm, 0, &ct));
2691: numFaces = DMPolytopeTypeGetNumArrangements(ct) / 2;
2692: }
2693: PetscCall(PetscCalloc1(numPoints, &symperms));
2694: PetscCall(PetscCalloc1(numPoints, &symflips));
2695: spintdim = sp->spintdim;
2696: /* The nodal symmetry behavior is not present when tensorSpace != tensorCell: someone might want this for the "S"
2697: * family of FEEC spaces. Most used in particular are discontinuous polynomial L2 spaces in tensor cells, where
2698: * the symmetries are not necessary for FE assembly. So for now we assume this is the case and don't return
2699: * symmetries if tensorSpace != tensorCell */
2700: if (spintdim && 0 < dim && dim < 3 && (lag->tensorSpace == lag->tensorCell)) { /* compute self symmetries */
2701: PetscInt **cellSymperms;
2702: PetscScalar **cellSymflips;
2703: PetscInt ornt;
2704: PetscInt nCopies = Nc / lag->intNodeIndices->nodeVecDim;
2705: PetscInt nNodes = lag->intNodeIndices->nNodes;
2707: lag->numSelfSym = 2 * numFaces;
2708: lag->selfSymOff = numFaces;
2709: PetscCall(PetscCalloc1(2 * numFaces, &cellSymperms));
2710: PetscCall(PetscCalloc1(2 * numFaces, &cellSymflips));
2711: /* we want to be able to index symmetries directly with the orientations, which range from [-numFaces,numFaces) */
2712: symperms[0] = &cellSymperms[numFaces];
2713: symflips[0] = &cellSymflips[numFaces];
2714: PetscCheck(lag->intNodeIndices->nodeVecDim * nCopies == Nc, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Node indices incompatible with dofs");
2715: PetscCheck(nNodes * nCopies == spintdim, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Node indices incompatible with dofs");
2716: 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 */
2717: Mat symMat;
2718: PetscInt *perm;
2719: PetscScalar *flips;
2720: PetscInt i;
2722: if (!ornt) continue;
2723: PetscCall(PetscMalloc1(spintdim, &perm));
2724: PetscCall(PetscCalloc1(spintdim, &flips));
2725: for (i = 0; i < spintdim; i++) perm[i] = -1;
2726: PetscCall(PetscDualSpaceCreateInteriorSymmetryMatrix_Lagrange(sp, ornt, &symMat));
2727: for (i = 0; i < nNodes; i++) {
2728: PetscInt ncols;
2729: PetscInt j, k;
2730: const PetscInt *cols;
2731: const PetscScalar *vals;
2732: PetscBool nz_seen = PETSC_FALSE;
2734: PetscCall(MatGetRow(symMat, i, &ncols, &cols, &vals));
2735: for (j = 0; j < ncols; j++) {
2736: if (PetscAbsScalar(vals[j]) > PETSC_SMALL) {
2737: PetscCheck(!nz_seen, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "This dual space has symmetries that can't be described as a permutation + sign flips");
2738: nz_seen = PETSC_TRUE;
2739: PetscCheck(PetscAbsReal(PetscAbsScalar(vals[j]) - PetscRealConstant(1.)) <= PETSC_SMALL, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "This dual space has symmetries that can't be described as a permutation + sign flips");
2740: PetscCheck(PetscAbsReal(PetscImaginaryPart(vals[j])) <= PETSC_SMALL, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "This dual space has symmetries that can't be described as a permutation + sign flips");
2741: PetscCheck(perm[cols[j] * nCopies] < 0, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "This dual space has symmetries that can't be described as a permutation + sign flips");
2742: for (k = 0; k < nCopies; k++) perm[cols[j] * nCopies + k] = i * nCopies + k;
2743: if (PetscRealPart(vals[j]) < 0.) {
2744: for (k = 0; k < nCopies; k++) flips[i * nCopies + k] = -1.;
2745: } else {
2746: for (k = 0; k < nCopies; k++) flips[i * nCopies + k] = 1.;
2747: }
2748: }
2749: }
2750: PetscCall(MatRestoreRow(symMat, i, &ncols, &cols, &vals));
2751: }
2752: PetscCall(MatDestroy(&symMat));
2753: /* if there were no sign flips, keep NULL */
2754: for (i = 0; i < spintdim; i++)
2755: if (flips[i] != 1.) break;
2756: if (i == spintdim) {
2757: PetscCall(PetscFree(flips));
2758: flips = NULL;
2759: }
2760: /* if the permutation is identity, keep NULL */
2761: for (i = 0; i < spintdim; i++)
2762: if (perm[i] != i) break;
2763: if (i == spintdim) {
2764: PetscCall(PetscFree(perm));
2765: perm = NULL;
2766: }
2767: symperms[0][ornt] = perm;
2768: symflips[0][ornt] = flips;
2769: }
2770: /* if no orientations produced non-identity permutations, keep NULL */
2771: for (ornt = -numFaces; ornt < numFaces; ornt++)
2772: if (symperms[0][ornt]) break;
2773: if (ornt == numFaces) {
2774: PetscCall(PetscFree(cellSymperms));
2775: symperms[0] = NULL;
2776: }
2777: /* if no orientations produced sign flips, keep NULL */
2778: for (ornt = -numFaces; ornt < numFaces; ornt++)
2779: if (symflips[0][ornt]) break;
2780: if (ornt == numFaces) {
2781: PetscCall(PetscFree(cellSymflips));
2782: symflips[0] = NULL;
2783: }
2784: }
2785: PetscCall(PetscDualSpaceGetBoundarySymmetries_Internal(sp, symperms, symflips));
2786: for (p = 0; p < pEnd; p++)
2787: if (symperms[p]) break;
2788: if (p == pEnd) {
2789: PetscCall(PetscFree(symperms));
2790: symperms = NULL;
2791: }
2792: for (p = 0; p < pEnd; p++)
2793: if (symflips[p]) break;
2794: if (p == pEnd) {
2795: PetscCall(PetscFree(symflips));
2796: symflips = NULL;
2797: }
2798: lag->symperms = symperms;
2799: lag->symflips = symflips;
2800: lag->symComputed = PETSC_TRUE;
2801: }
2802: if (perms) *perms = (const PetscInt ***)lag->symperms;
2803: if (flips) *flips = (const PetscScalar ***)lag->symflips;
2804: PetscFunctionReturn(PETSC_SUCCESS);
2805: }
2807: static PetscErrorCode PetscDualSpaceLagrangeGetContinuity_Lagrange(PetscDualSpace sp, PetscBool *continuous)
2808: {
2809: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2811: PetscFunctionBegin;
2813: PetscAssertPointer(continuous, 2);
2814: *continuous = lag->continuous;
2815: PetscFunctionReturn(PETSC_SUCCESS);
2816: }
2818: static PetscErrorCode PetscDualSpaceLagrangeSetContinuity_Lagrange(PetscDualSpace sp, PetscBool continuous)
2819: {
2820: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2822: PetscFunctionBegin;
2824: lag->continuous = continuous;
2825: PetscFunctionReturn(PETSC_SUCCESS);
2826: }
2828: /*@
2829: PetscDualSpaceLagrangeGetContinuity - Retrieves the flag for element continuity
2831: Not Collective
2833: Input Parameter:
2834: . sp - the `PetscDualSpace`
2836: Output Parameter:
2837: . continuous - flag for element continuity
2839: Level: intermediate
2841: .seealso: `PETSCDUALSPACELAGRANGE`, `PetscDualSpace`, `PetscDualSpaceLagrangeSetContinuity()`
2842: @*/
2843: PetscErrorCode PetscDualSpaceLagrangeGetContinuity(PetscDualSpace sp, PetscBool *continuous)
2844: {
2845: PetscFunctionBegin;
2847: PetscAssertPointer(continuous, 2);
2848: PetscTryMethod(sp, "PetscDualSpaceLagrangeGetContinuity_C", (PetscDualSpace, PetscBool *), (sp, continuous));
2849: PetscFunctionReturn(PETSC_SUCCESS);
2850: }
2852: /*@
2853: PetscDualSpaceLagrangeSetContinuity - Indicate whether the element is continuous
2855: Logically Collective
2857: Input Parameters:
2858: + sp - the `PetscDualSpace`
2859: - continuous - flag for element continuity
2861: Options Database Key:
2862: . -petscdualspace_lagrange_continuity <bool> - use a continuous element
2864: Level: intermediate
2866: .seealso: `PETSCDUALSPACELAGRANGE`, `PetscDualSpace`, `PetscDualSpaceLagrangeGetContinuity()`
2867: @*/
2868: PetscErrorCode PetscDualSpaceLagrangeSetContinuity(PetscDualSpace sp, PetscBool continuous)
2869: {
2870: PetscFunctionBegin;
2873: PetscTryMethod(sp, "PetscDualSpaceLagrangeSetContinuity_C", (PetscDualSpace, PetscBool), (sp, continuous));
2874: PetscFunctionReturn(PETSC_SUCCESS);
2875: }
2877: static PetscErrorCode PetscDualSpaceLagrangeGetTensor_Lagrange(PetscDualSpace sp, PetscBool *tensor)
2878: {
2879: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2881: PetscFunctionBegin;
2882: *tensor = lag->tensorSpace;
2883: PetscFunctionReturn(PETSC_SUCCESS);
2884: }
2886: static PetscErrorCode PetscDualSpaceLagrangeSetTensor_Lagrange(PetscDualSpace sp, PetscBool tensor)
2887: {
2888: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2890: PetscFunctionBegin;
2891: lag->tensorSpace = tensor;
2892: PetscFunctionReturn(PETSC_SUCCESS);
2893: }
2895: static PetscErrorCode PetscDualSpaceLagrangeGetTrimmed_Lagrange(PetscDualSpace sp, PetscBool *trimmed)
2896: {
2897: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2899: PetscFunctionBegin;
2900: *trimmed = lag->trimmed;
2901: PetscFunctionReturn(PETSC_SUCCESS);
2902: }
2904: static PetscErrorCode PetscDualSpaceLagrangeSetTrimmed_Lagrange(PetscDualSpace sp, PetscBool trimmed)
2905: {
2906: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2908: PetscFunctionBegin;
2909: lag->trimmed = trimmed;
2910: PetscFunctionReturn(PETSC_SUCCESS);
2911: }
2913: static PetscErrorCode PetscDualSpaceLagrangeGetNodeType_Lagrange(PetscDualSpace sp, PetscDTNodeType *nodeType, PetscBool *boundary, PetscReal *exponent)
2914: {
2915: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2917: PetscFunctionBegin;
2918: if (nodeType) *nodeType = lag->nodeType;
2919: if (boundary) *boundary = lag->endNodes;
2920: if (exponent) *exponent = lag->nodeExponent;
2921: PetscFunctionReturn(PETSC_SUCCESS);
2922: }
2924: static PetscErrorCode PetscDualSpaceLagrangeSetNodeType_Lagrange(PetscDualSpace sp, PetscDTNodeType nodeType, PetscBool boundary, PetscReal exponent)
2925: {
2926: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2928: PetscFunctionBegin;
2929: PetscCheck(nodeType != PETSCDTNODES_GAUSSJACOBI || exponent > -1., PetscObjectComm((PetscObject)sp), PETSC_ERR_ARG_OUTOFRANGE, "Exponent must be > -1");
2930: lag->nodeType = nodeType;
2931: lag->endNodes = boundary;
2932: lag->nodeExponent = exponent;
2933: PetscFunctionReturn(PETSC_SUCCESS);
2934: }
2936: static PetscErrorCode PetscDualSpaceLagrangeGetUseMoments_Lagrange(PetscDualSpace sp, PetscBool *useMoments)
2937: {
2938: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2940: PetscFunctionBegin;
2941: *useMoments = lag->useMoments;
2942: PetscFunctionReturn(PETSC_SUCCESS);
2943: }
2945: static PetscErrorCode PetscDualSpaceLagrangeSetUseMoments_Lagrange(PetscDualSpace sp, PetscBool useMoments)
2946: {
2947: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2949: PetscFunctionBegin;
2950: lag->useMoments = useMoments;
2951: PetscFunctionReturn(PETSC_SUCCESS);
2952: }
2954: static PetscErrorCode PetscDualSpaceLagrangeGetMomentOrder_Lagrange(PetscDualSpace sp, PetscInt *momentOrder)
2955: {
2956: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2958: PetscFunctionBegin;
2959: *momentOrder = lag->momentOrder;
2960: PetscFunctionReturn(PETSC_SUCCESS);
2961: }
2963: static PetscErrorCode PetscDualSpaceLagrangeSetMomentOrder_Lagrange(PetscDualSpace sp, PetscInt momentOrder)
2964: {
2965: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2967: PetscFunctionBegin;
2968: lag->momentOrder = momentOrder;
2969: PetscFunctionReturn(PETSC_SUCCESS);
2970: }
2972: /*@
2973: PetscDualSpaceLagrangeGetTensor - Get the tensor nature of the dual space
2975: Not Collective
2977: Input Parameter:
2978: . sp - The `PetscDualSpace`
2980: Output Parameter:
2981: . tensor - Whether the dual space has tensor layout (vs. simplicial)
2983: Level: intermediate
2985: .seealso: `PETSCDUALSPACELAGRANGE`, `PetscDualSpace`, `PetscDualSpaceLagrangeSetTensor()`, `PetscDualSpaceCreate()`
2986: @*/
2987: PetscErrorCode PetscDualSpaceLagrangeGetTensor(PetscDualSpace sp, PetscBool *tensor)
2988: {
2989: PetscFunctionBegin;
2991: PetscAssertPointer(tensor, 2);
2992: PetscTryMethod(sp, "PetscDualSpaceLagrangeGetTensor_C", (PetscDualSpace, PetscBool *), (sp, tensor));
2993: PetscFunctionReturn(PETSC_SUCCESS);
2994: }
2996: /*@
2997: PetscDualSpaceLagrangeSetTensor - Set the tensor nature of the dual space
2999: Not Collective
3001: Input Parameters:
3002: + sp - The `PetscDualSpace`
3003: - tensor - Whether the dual space has tensor layout (vs. simplicial)
3005: Level: intermediate
3007: .seealso: `PETSCDUALSPACELAGRANGE`, `PetscDualSpace`, `PetscDualSpaceLagrangeGetTensor()`, `PetscDualSpaceCreate()`
3008: @*/
3009: PetscErrorCode PetscDualSpaceLagrangeSetTensor(PetscDualSpace sp, PetscBool tensor)
3010: {
3011: PetscFunctionBegin;
3013: PetscTryMethod(sp, "PetscDualSpaceLagrangeSetTensor_C", (PetscDualSpace, PetscBool), (sp, tensor));
3014: PetscFunctionReturn(PETSC_SUCCESS);
3015: }
3017: /*@
3018: PetscDualSpaceLagrangeGetTrimmed - Get the trimmed nature of the dual space
3020: Not Collective
3022: Input Parameter:
3023: . sp - The `PetscDualSpace`
3025: Output Parameter:
3026: . 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)
3028: Level: intermediate
3030: .seealso: `PETSCDUALSPACELAGRANGE`, `PetscDualSpace`, `PetscDualSpaceLagrangeSetTrimmed()`, `PetscDualSpaceCreate()`
3031: @*/
3032: PetscErrorCode PetscDualSpaceLagrangeGetTrimmed(PetscDualSpace sp, PetscBool *trimmed)
3033: {
3034: PetscFunctionBegin;
3036: PetscAssertPointer(trimmed, 2);
3037: PetscTryMethod(sp, "PetscDualSpaceLagrangeGetTrimmed_C", (PetscDualSpace, PetscBool *), (sp, trimmed));
3038: PetscFunctionReturn(PETSC_SUCCESS);
3039: }
3041: /*@
3042: PetscDualSpaceLagrangeSetTrimmed - Set the trimmed nature of the dual space
3044: Not Collective
3046: Input Parameters:
3047: + sp - The `PetscDualSpace`
3048: - 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)
3050: Level: intermediate
3052: .seealso: `PETSCDUALSPACELAGRANGE`, `PetscDualSpace`, `PetscDualSpaceLagrangeGetTrimmed()`, `PetscDualSpaceCreate()`
3053: @*/
3054: PetscErrorCode PetscDualSpaceLagrangeSetTrimmed(PetscDualSpace sp, PetscBool trimmed)
3055: {
3056: PetscFunctionBegin;
3058: PetscTryMethod(sp, "PetscDualSpaceLagrangeSetTrimmed_C", (PetscDualSpace, PetscBool), (sp, trimmed));
3059: PetscFunctionReturn(PETSC_SUCCESS);
3060: }
3062: /*@
3063: PetscDualSpaceLagrangeGetNodeType - Get a description of how nodes are laid out for Lagrange polynomials in this
3064: dual space
3066: Not Collective
3068: Input Parameter:
3069: . sp - The `PetscDualSpace`
3071: Output Parameters:
3072: + nodeType - The type of nodes
3073: . boundary - Whether the node type is one that includes endpoints (if nodeType is `PETSCDTNODES_GAUSSJACOBI`, nodes that
3074: include the boundary are Gauss-Lobatto-Jacobi nodes)
3075: - exponent - If nodeType is `PETSCDTNODES_GAUSJACOBI`, indicates the exponent used for both ends of the 1D Jacobi weight function
3076: '0' is Gauss-Legendre, '-0.5' is Gauss-Chebyshev of the first type, '0.5' is Gauss-Chebyshev of the second type
3078: Level: advanced
3080: .seealso: `PETSCDUALSPACELAGRANGE`, `PetscDualSpace`, `PetscDTNodeType`, `PetscDualSpaceLagrangeSetNodeType()`
3081: @*/
3082: PetscErrorCode PetscDualSpaceLagrangeGetNodeType(PetscDualSpace sp, PetscDTNodeType *nodeType, PetscBool *boundary, PetscReal *exponent)
3083: {
3084: PetscFunctionBegin;
3086: if (nodeType) PetscAssertPointer(nodeType, 2);
3087: if (boundary) PetscAssertPointer(boundary, 3);
3088: if (exponent) PetscAssertPointer(exponent, 4);
3089: PetscTryMethod(sp, "PetscDualSpaceLagrangeGetNodeType_C", (PetscDualSpace, PetscDTNodeType *, PetscBool *, PetscReal *), (sp, nodeType, boundary, exponent));
3090: PetscFunctionReturn(PETSC_SUCCESS);
3091: }
3093: /*@
3094: PetscDualSpaceLagrangeSetNodeType - Set a description of how nodes are laid out for Lagrange polynomials in this
3095: dual space
3097: Logically Collective
3099: Input Parameters:
3100: + sp - The `PetscDualSpace`
3101: . nodeType - The type of nodes
3102: . boundary - Whether the node type is one that includes endpoints (if nodeType is `PETSCDTNODES_GAUSSJACOBI`, nodes that
3103: include the boundary are Gauss-Lobatto-Jacobi nodes)
3104: - exponent - If nodeType is `PETSCDTNODES_GAUSJACOBI`, indicates the exponent used for both ends of the 1D Jacobi weight function
3105: '0' is Gauss-Legendre, '-0.5' is Gauss-Chebyshev of the first type, '0.5' is Gauss-Chebyshev of the second type
3107: Level: advanced
3109: .seealso: `PETSCDUALSPACELAGRANGE`, `PetscDualSpace`, `PetscDTNodeType`, `PetscDualSpaceLagrangeGetNodeType()`
3110: @*/
3111: PetscErrorCode PetscDualSpaceLagrangeSetNodeType(PetscDualSpace sp, PetscDTNodeType nodeType, PetscBool boundary, PetscReal exponent)
3112: {
3113: PetscFunctionBegin;
3115: PetscTryMethod(sp, "PetscDualSpaceLagrangeSetNodeType_C", (PetscDualSpace, PetscDTNodeType, PetscBool, PetscReal), (sp, nodeType, boundary, exponent));
3116: PetscFunctionReturn(PETSC_SUCCESS);
3117: }
3119: /*@
3120: PetscDualSpaceLagrangeGetUseMoments - Get the flag for using moment functionals
3122: Not Collective
3124: Input Parameter:
3125: . sp - The `PetscDualSpace`
3127: Output Parameter:
3128: . useMoments - Moment flag
3130: Level: advanced
3132: .seealso: `PETSCDUALSPACELAGRANGE`, `PetscDualSpace`, `PetscDualSpaceLagrangeSetUseMoments()`
3133: @*/
3134: PetscErrorCode PetscDualSpaceLagrangeGetUseMoments(PetscDualSpace sp, PetscBool *useMoments)
3135: {
3136: PetscFunctionBegin;
3138: PetscAssertPointer(useMoments, 2);
3139: PetscUseMethod(sp, "PetscDualSpaceLagrangeGetUseMoments_C", (PetscDualSpace, PetscBool *), (sp, useMoments));
3140: PetscFunctionReturn(PETSC_SUCCESS);
3141: }
3143: /*@
3144: PetscDualSpaceLagrangeSetUseMoments - Set the flag for moment functionals
3146: Logically Collective
3148: Input Parameters:
3149: + sp - The `PetscDualSpace`
3150: - useMoments - The flag for moment functionals
3152: Level: advanced
3154: .seealso: `PETSCDUALSPACELAGRANGE`, `PetscDualSpace`, `PetscDualSpaceLagrangeGetUseMoments()`
3155: @*/
3156: PetscErrorCode PetscDualSpaceLagrangeSetUseMoments(PetscDualSpace sp, PetscBool useMoments)
3157: {
3158: PetscFunctionBegin;
3160: PetscTryMethod(sp, "PetscDualSpaceLagrangeSetUseMoments_C", (PetscDualSpace, PetscBool), (sp, useMoments));
3161: PetscFunctionReturn(PETSC_SUCCESS);
3162: }
3164: /*@
3165: PetscDualSpaceLagrangeGetMomentOrder - Get the order for moment integration
3167: Not Collective
3169: Input Parameter:
3170: . sp - The `PetscDualSpace`
3172: Output Parameter:
3173: . order - Moment integration order
3175: Level: advanced
3177: .seealso: `PETSCDUALSPACELAGRANGE`, `PetscDualSpace`, `PetscDualSpaceLagrangeSetMomentOrder()`
3178: @*/
3179: PetscErrorCode PetscDualSpaceLagrangeGetMomentOrder(PetscDualSpace sp, PetscInt *order)
3180: {
3181: PetscFunctionBegin;
3183: PetscAssertPointer(order, 2);
3184: PetscUseMethod(sp, "PetscDualSpaceLagrangeGetMomentOrder_C", (PetscDualSpace, PetscInt *), (sp, order));
3185: PetscFunctionReturn(PETSC_SUCCESS);
3186: }
3188: /*@
3189: PetscDualSpaceLagrangeSetMomentOrder - Set the order for moment integration
3191: Logically Collective
3193: Input Parameters:
3194: + sp - The `PetscDualSpace`
3195: - order - The order for moment integration
3197: Level: advanced
3199: .seealso: `PETSCDUALSPACELAGRANGE`, `PetscDualSpace`, `PetscDualSpaceLagrangeGetMomentOrder()`
3200: @*/
3201: PetscErrorCode PetscDualSpaceLagrangeSetMomentOrder(PetscDualSpace sp, PetscInt order)
3202: {
3203: PetscFunctionBegin;
3205: PetscTryMethod(sp, "PetscDualSpaceLagrangeSetMomentOrder_C", (PetscDualSpace, PetscInt), (sp, order));
3206: PetscFunctionReturn(PETSC_SUCCESS);
3207: }
3209: static PetscErrorCode PetscDualSpaceInitialize_Lagrange(PetscDualSpace sp)
3210: {
3211: PetscFunctionBegin;
3212: sp->ops->destroy = PetscDualSpaceDestroy_Lagrange;
3213: sp->ops->view = PetscDualSpaceView_Lagrange;
3214: sp->ops->setfromoptions = PetscDualSpaceSetFromOptions_Lagrange;
3215: sp->ops->duplicate = PetscDualSpaceDuplicate_Lagrange;
3216: sp->ops->setup = PetscDualSpaceSetUp_Lagrange;
3217: sp->ops->createheightsubspace = NULL;
3218: sp->ops->createpointsubspace = NULL;
3219: sp->ops->getsymmetries = PetscDualSpaceGetSymmetries_Lagrange;
3220: sp->ops->apply = PetscDualSpaceApplyDefault;
3221: sp->ops->applyall = PetscDualSpaceApplyAllDefault;
3222: sp->ops->applyint = PetscDualSpaceApplyInteriorDefault;
3223: sp->ops->createalldata = PetscDualSpaceCreateAllDataDefault;
3224: sp->ops->createintdata = PetscDualSpaceCreateInteriorDataDefault;
3225: PetscFunctionReturn(PETSC_SUCCESS);
3226: }
3228: /*MC
3229: PETSCDUALSPACELAGRANGE = "lagrange" - A `PetscDualSpaceType` that encapsulates a dual space of pointwise evaluation functionals
3231: Level: intermediate
3233: Developer Note:
3234: This `PetscDualSpace` seems to manage directly trimmed and untrimmed polynomials as well as tensor and non-tensor polynomials while for `PetscSpace` there seems to
3235: be different `PetscSpaceType` for them.
3237: .seealso: `PetscDualSpace`, `PetscDualSpaceType`, `PetscDualSpaceCreate()`, `PetscDualSpaceSetType()`,
3238: `PetscDualSpaceLagrangeSetMomentOrder()`, `PetscDualSpaceLagrangeGetMomentOrder()`, `PetscDualSpaceLagrangeSetUseMoments()`, `PetscDualSpaceLagrangeGetUseMoments()`,
3239: `PetscDualSpaceLagrangeSetNodeType, PetscDualSpaceLagrangeGetNodeType, PetscDualSpaceLagrangeGetContinuity, PetscDualSpaceLagrangeSetContinuity,
3240: `PetscDualSpaceLagrangeGetTensor()`, `PetscDualSpaceLagrangeSetTensor()`, `PetscDualSpaceLagrangeGetTrimmed()`, `PetscDualSpaceLagrangeSetTrimmed()`
3241: M*/
3242: PETSC_EXTERN PetscErrorCode PetscDualSpaceCreate_Lagrange(PetscDualSpace sp)
3243: {
3244: PetscDualSpace_Lag *lag;
3246: PetscFunctionBegin;
3248: PetscCall(PetscNew(&lag));
3249: sp->data = lag;
3251: lag->tensorCell = PETSC_FALSE;
3252: lag->tensorSpace = PETSC_FALSE;
3253: lag->continuous = PETSC_TRUE;
3254: lag->numCopies = PETSC_DEFAULT;
3255: lag->numNodeSkip = PETSC_DEFAULT;
3256: lag->nodeType = PETSCDTNODES_DEFAULT;
3257: lag->useMoments = PETSC_FALSE;
3258: lag->momentOrder = 0;
3260: PetscCall(PetscDualSpaceInitialize_Lagrange(sp));
3261: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetContinuity_C", PetscDualSpaceLagrangeGetContinuity_Lagrange));
3262: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetContinuity_C", PetscDualSpaceLagrangeSetContinuity_Lagrange));
3263: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetTensor_C", PetscDualSpaceLagrangeGetTensor_Lagrange));
3264: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetTensor_C", PetscDualSpaceLagrangeSetTensor_Lagrange));
3265: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetTrimmed_C", PetscDualSpaceLagrangeGetTrimmed_Lagrange));
3266: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetTrimmed_C", PetscDualSpaceLagrangeSetTrimmed_Lagrange));
3267: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetNodeType_C", PetscDualSpaceLagrangeGetNodeType_Lagrange));
3268: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetNodeType_C", PetscDualSpaceLagrangeSetNodeType_Lagrange));
3269: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetUseMoments_C", PetscDualSpaceLagrangeGetUseMoments_Lagrange));
3270: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetUseMoments_C", PetscDualSpaceLagrangeSetUseMoments_Lagrange));
3271: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetMomentOrder_C", PetscDualSpaceLagrangeGetMomentOrder_Lagrange));
3272: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetMomentOrder_C", PetscDualSpaceLagrangeSetMomentOrder_Lagrange));
3273: PetscFunctionReturn(PETSC_SUCCESS);
3274: }