Actual source code: dspacelagrange.c
1: #include <petsc/private/petscfeimpl.h>
2: #include <petscdmplex.h>
3: #include <petscblaslapack.h>
5: PetscErrorCode DMPlexGetTransitiveClosure_Internal(DM, PetscInt, PetscInt, PetscBool, PetscInt *, PetscInt *[]);
7: struct _n_Petsc1DNodeFamily {
8: PetscInt refct;
9: PetscDTNodeType nodeFamily;
10: PetscReal gaussJacobiExp;
11: PetscInt nComputed;
12: PetscReal **nodesets;
13: PetscBool endpoints;
14: };
16: /* users set node families for PETSCDUALSPACELAGRANGE with just the inputs to this function, but internally we create
17: * an object that can cache the computations across multiple dual spaces */
18: static PetscErrorCode Petsc1DNodeFamilyCreate(PetscDTNodeType family, PetscReal gaussJacobiExp, PetscBool endpoints, Petsc1DNodeFamily *nf)
19: {
20: Petsc1DNodeFamily f;
22: PetscFunctionBegin;
23: PetscCall(PetscNew(&f));
24: switch (family) {
25: case PETSCDTNODES_GAUSSJACOBI:
26: case PETSCDTNODES_EQUISPACED:
27: f->nodeFamily = family;
28: break;
29: default:
30: SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Unknown 1D node family");
31: }
32: f->endpoints = endpoints;
33: f->gaussJacobiExp = 0.;
34: if (family == PETSCDTNODES_GAUSSJACOBI) {
35: PetscCheck(gaussJacobiExp > -1., PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Gauss-Jacobi exponent must be > -1.");
36: f->gaussJacobiExp = gaussJacobiExp;
37: }
38: f->refct = 1;
39: *nf = f;
40: PetscFunctionReturn(PETSC_SUCCESS);
41: }
43: static PetscErrorCode Petsc1DNodeFamilyReference(Petsc1DNodeFamily nf)
44: {
45: PetscFunctionBegin;
46: if (nf) nf->refct++;
47: PetscFunctionReturn(PETSC_SUCCESS);
48: }
50: static PetscErrorCode Petsc1DNodeFamilyDestroy(Petsc1DNodeFamily *nf)
51: {
52: PetscInt i, nc;
54: PetscFunctionBegin;
55: if (!*nf) PetscFunctionReturn(PETSC_SUCCESS);
56: if (--(*nf)->refct > 0) {
57: *nf = NULL;
58: PetscFunctionReturn(PETSC_SUCCESS);
59: }
60: nc = (*nf)->nComputed;
61: for (i = 0; i < nc; i++) PetscCall(PetscFree((*nf)->nodesets[i]));
62: PetscCall(PetscFree((*nf)->nodesets));
63: PetscCall(PetscFree(*nf));
64: *nf = NULL;
65: PetscFunctionReturn(PETSC_SUCCESS);
66: }
68: static PetscErrorCode Petsc1DNodeFamilyGetNodeSets(Petsc1DNodeFamily f, PetscInt degree, PetscReal ***nodesets)
69: {
70: PetscInt nc;
72: PetscFunctionBegin;
73: nc = f->nComputed;
74: if (degree >= nc) {
75: PetscInt i, j;
76: PetscReal **new_nodesets;
77: PetscReal *w;
79: PetscCall(PetscMalloc1(degree + 1, &new_nodesets));
80: PetscCall(PetscArraycpy(new_nodesets, f->nodesets, nc));
81: PetscCall(PetscFree(f->nodesets));
82: f->nodesets = new_nodesets;
83: PetscCall(PetscMalloc1(degree + 1, &w));
84: for (i = nc; i < degree + 1; i++) {
85: PetscCall(PetscMalloc1(i + 1, &f->nodesets[i]));
86: if (!i) {
87: f->nodesets[i][0] = 0.5;
88: } else {
89: switch (f->nodeFamily) {
90: case PETSCDTNODES_EQUISPACED:
91: if (f->endpoints) {
92: for (j = 0; j <= i; j++) f->nodesets[i][j] = (PetscReal)j / (PetscReal)i;
93: } else {
94: /* these nodes are at the centroids of the small simplices created by the equispaced nodes that include
95: * the endpoints */
96: for (j = 0; j <= i; j++) f->nodesets[i][j] = ((PetscReal)j + 0.5) / ((PetscReal)i + 1.);
97: }
98: break;
99: case PETSCDTNODES_GAUSSJACOBI:
100: if (f->endpoints) {
101: PetscCall(PetscDTGaussLobattoJacobiQuadrature(i + 1, 0., 1., f->gaussJacobiExp, f->gaussJacobiExp, f->nodesets[i], w));
102: } else {
103: PetscCall(PetscDTGaussJacobiQuadrature(i + 1, 0., 1., f->gaussJacobiExp, f->gaussJacobiExp, f->nodesets[i], w));
104: }
105: break;
106: default:
107: SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Unknown 1D node family");
108: }
109: }
110: }
111: PetscCall(PetscFree(w));
112: f->nComputed = degree + 1;
113: }
114: *nodesets = f->nodesets;
115: PetscFunctionReturn(PETSC_SUCCESS);
116: }
118: /* http://arxiv.org/abs/2002.09421 for details */
119: static PetscErrorCode PetscNodeRecursive_Internal(PetscInt dim, PetscInt degree, PetscReal **nodesets, PetscInt tup[], PetscReal node[])
120: {
121: PetscReal w;
122: PetscInt i, j;
124: PetscFunctionBeginHot;
125: w = 0.;
126: if (dim == 1) {
127: node[0] = nodesets[degree][tup[0]];
128: node[1] = nodesets[degree][tup[1]];
129: } else {
130: for (i = 0; i < dim + 1; i++) node[i] = 0.;
131: for (i = 0; i < dim + 1; i++) {
132: PetscReal wi = nodesets[degree][degree - tup[i]];
134: for (j = 0; j < dim + 1; j++) tup[dim + 1 + j] = tup[j + (j >= i)];
135: PetscCall(PetscNodeRecursive_Internal(dim - 1, degree - tup[i], nodesets, &tup[dim + 1], &node[dim + 1]));
136: for (j = 0; j < dim + 1; j++) node[j + (j >= i)] += wi * node[dim + 1 + j];
137: w += wi;
138: }
139: for (i = 0; i < dim + 1; i++) node[i] /= w;
140: }
141: PetscFunctionReturn(PETSC_SUCCESS);
142: }
144: /* compute simplex nodes for the biunit simplex from the 1D node family */
145: static PetscErrorCode Petsc1DNodeFamilyComputeSimplexNodes(Petsc1DNodeFamily f, PetscInt dim, PetscInt degree, PetscReal points[])
146: {
147: PetscInt *tup;
148: PetscInt npoints;
149: PetscReal **nodesets = NULL;
150: PetscInt worksize;
151: PetscReal *nodework;
152: PetscInt *tupwork;
154: PetscFunctionBegin;
155: PetscCheck(dim >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Must have non-negative dimension");
156: PetscCheck(degree >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Must have non-negative degree");
157: if (!dim) PetscFunctionReturn(PETSC_SUCCESS);
158: PetscCall(PetscCalloc1(dim + 2, &tup));
159: PetscCall(PetscDTBinomialInt(degree + dim, dim, &npoints));
160: PetscCall(Petsc1DNodeFamilyGetNodeSets(f, degree, &nodesets));
161: worksize = ((dim + 2) * (dim + 3)) / 2;
162: PetscCall(PetscCalloc2(worksize, &nodework, worksize, &tupwork));
163: /* loop over the tuples of length dim with sum at most degree */
164: for (PetscInt k = 0; k < npoints; k++) {
165: PetscInt i;
167: /* turn thm into tuples of length dim + 1 with sum equal to degree (barycentric indice) */
168: tup[0] = degree;
169: for (i = 0; i < dim; i++) tup[0] -= tup[i + 1];
170: switch (f->nodeFamily) {
171: case PETSCDTNODES_EQUISPACED:
172: /* compute equispaces nodes on the unit reference triangle */
173: if (f->endpoints) {
174: PetscCheck(degree > 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Must have positive degree");
175: for (i = 0; i < dim; i++) points[dim * k + i] = (PetscReal)tup[i + 1] / (PetscReal)degree;
176: } else {
177: for (i = 0; i < dim; i++) {
178: /* these nodes are at the centroids of the small simplices created by the equispaced nodes that include
179: * the endpoints */
180: points[dim * k + i] = ((PetscReal)tup[i + 1] + 1. / (dim + 1.)) / (PetscReal)(degree + 1.);
181: }
182: }
183: break;
184: default:
185: /* compute equispaced nodes on the barycentric reference triangle (the trace on the first dim dimensions are the
186: * unit reference triangle nodes */
187: for (i = 0; i < dim + 1; i++) tupwork[i] = tup[i];
188: PetscCall(PetscNodeRecursive_Internal(dim, degree, nodesets, tupwork, nodework));
189: for (i = 0; i < dim; i++) points[dim * k + i] = nodework[i + 1];
190: break;
191: }
192: PetscCall(PetscDualSpaceLatticePointLexicographic_Internal(dim, degree, &tup[1]));
193: }
194: /* map from unit simplex to biunit simplex */
195: for (PetscInt k = 0; k < npoints * dim; k++) points[k] = points[k] * 2. - 1.;
196: PetscCall(PetscFree2(nodework, tupwork));
197: PetscCall(PetscFree(tup));
198: PetscFunctionReturn(PETSC_SUCCESS);
199: }
201: /* If we need to get the dofs from a mesh point, or add values into dofs at a mesh point, and there is more than one dof
202: * on that mesh point, we have to be careful about getting/adding everything in the right place.
203: *
204: * With nodal dofs like PETSCDUALSPACELAGRANGE makes, the general approach to calculate the value of dofs associate
205: * with a node A is
206: * - transform the node locations x(A) by the map that takes the mesh point to its reorientation, x' = phi(x(A))
207: * - figure out which node was originally at the location of the transformed point, A' = idx(x')
208: * - if the dofs are not scalars, figure out how to represent the transformed dofs in terms of the basis
209: * of dofs at A' (using pushforward/pullback rules)
210: *
211: * The one sticky point with this approach is the "A' = idx(x')" step: trying to go from real valued coordinates
212: * back to indices. I don't want to rely on floating point tolerances. Additionally, PETSCDUALSPACELAGRANGE may
213: * eventually support quasi-Lagrangian dofs, which could involve quadrature at multiple points, so the location "x(A)"
214: * would be ambiguous.
215: *
216: * So each dof gets an integer value coordinate (nodeIdx in the structure below). The choice of integer coordinates
217: * is somewhat arbitrary, as long as all of the relevant symmetries of the mesh point correspond to *permutations* of
218: * the integer coordinates, which do not depend on numerical precision.
219: *
220: * So
221: *
222: * - DMPlexGetTransitiveClosure_Internal() tells me how an orientation turns into a permutation of the vertices of a
223: * mesh point
224: * - The permutation of the vertices, and the nodeIdx values assigned to them, tells what permutation in index space
225: * is associated with the orientation
226: * - I uses that permutation to get xi' = phi(xi(A)), the integer coordinate of the transformed dof
227: * - I can without numerical issues compute A' = idx(xi')
228: *
229: * Here are some examples of how the process works
230: *
231: * - With a triangle:
232: *
233: * The triangle has the following integer coordinates for vertices, taken from the barycentric triangle
234: *
235: * closure order 2
236: * nodeIdx (0,0,1)
237: * \
238: * +
239: * |\
240: * | \
241: * | \
242: * | \ closure order 1
243: * | \ / nodeIdx (0,1,0)
244: * +-----+
245: * \
246: * closure order 0
247: * nodeIdx (1,0,0)
248: *
249: * If I do DMPlexGetTransitiveClosure_Internal() with orientation 1, the vertices would appear
250: * in the order (1, 2, 0)
251: *
252: * If I list the nodeIdx of each vertex in closure order for orientation 0 (0, 1, 2) and orientation 1 (1, 2, 0), I
253: * see
254: *
255: * orientation 0 | orientation 1
256: *
257: * [0] (1,0,0) [1] (0,1,0)
258: * [1] (0,1,0) [2] (0,0,1)
259: * [2] (0,0,1) [0] (1,0,0)
260: * A B
261: *
262: * In other words, B is the result of a row permutation of A. But, there is also
263: * a column permutation that accomplishes the same result, (2,0,1).
264: *
265: * So if a dof has nodeIdx coordinate (a,b,c), after the transformation its nodeIdx coordinate
266: * is (c,a,b), and the transformed degree of freedom will be a linear combination of dofs
267: * that originally had coordinate (c,a,b).
268: *
269: * - With a quadrilateral:
270: *
271: * The quadrilateral has the following integer coordinates for vertices, taken from concatenating barycentric
272: * coordinates for two segments:
273: *
274: * closure order 3 closure order 2
275: * nodeIdx (1,0,0,1) nodeIdx (0,1,0,1)
276: * \ /
277: * +----+
278: * | |
279: * | |
280: * +----+
281: * / \
282: * closure order 0 closure order 1
283: * nodeIdx (1,0,1,0) nodeIdx (0,1,1,0)
284: *
285: * If I do DMPlexGetTransitiveClosure_Internal() with orientation 1, the vertices would appear
286: * in the order (1, 2, 3, 0)
287: *
288: * If I list the nodeIdx of each vertex in closure order for orientation 0 (0, 1, 2, 3) and
289: * orientation 1 (1, 2, 3, 0), I see
290: *
291: * orientation 0 | orientation 1
292: *
293: * [0] (1,0,1,0) [1] (0,1,1,0)
294: * [1] (0,1,1,0) [2] (0,1,0,1)
295: * [2] (0,1,0,1) [3] (1,0,0,1)
296: * [3] (1,0,0,1) [0] (1,0,1,0)
297: * A B
298: *
299: * The column permutation that accomplishes the same result is (3,2,0,1).
300: *
301: * So if a dof has nodeIdx coordinate (a,b,c,d), after the transformation its nodeIdx coordinate
302: * is (d,c,a,b), and the transformed degree of freedom will be a linear combination of dofs
303: * that originally had coordinate (d,c,a,b).
304: *
305: * Previously PETSCDUALSPACELAGRANGE had hardcoded symmetries for the triangle and quadrilateral,
306: * but this approach will work for any polytope, such as the wedge (triangular prism).
307: */
308: struct _n_PetscLagNodeIndices {
309: PetscInt refct;
310: PetscInt nodeIdxDim;
311: PetscInt nodeVecDim;
312: PetscInt nNodes;
313: PetscInt *nodeIdx; /* for each node an index of size nodeIdxDim */
314: PetscReal *nodeVec; /* for each node a vector of size nodeVecDim */
315: PetscInt *perm; /* if these are vertices, perm takes DMPlex point index to closure order;
316: if these are nodes, perm lists nodes in index revlex order */
317: };
319: /* this is just here so I can access the values in tests/ex1.c outside the library */
320: PetscErrorCode PetscLagNodeIndicesGetData_Internal(PetscLagNodeIndices ni, PetscInt *nodeIdxDim, PetscInt *nodeVecDim, PetscInt *nNodes, const PetscInt *nodeIdx[], const PetscReal *nodeVec[])
321: {
322: PetscFunctionBegin;
323: *nodeIdxDim = ni->nodeIdxDim;
324: *nodeVecDim = ni->nodeVecDim;
325: *nNodes = ni->nNodes;
326: *nodeIdx = ni->nodeIdx;
327: *nodeVec = ni->nodeVec;
328: PetscFunctionReturn(PETSC_SUCCESS);
329: }
331: static PetscErrorCode PetscLagNodeIndicesReference(PetscLagNodeIndices ni)
332: {
333: PetscFunctionBegin;
334: if (ni) ni->refct++;
335: PetscFunctionReturn(PETSC_SUCCESS);
336: }
338: static PetscErrorCode PetscLagNodeIndicesDuplicate(PetscLagNodeIndices ni, PetscLagNodeIndices *niNew)
339: {
340: PetscFunctionBegin;
341: PetscCall(PetscNew(niNew));
342: (*niNew)->refct = 1;
343: (*niNew)->nodeIdxDim = ni->nodeIdxDim;
344: (*niNew)->nodeVecDim = ni->nodeVecDim;
345: (*niNew)->nNodes = ni->nNodes;
346: PetscCall(PetscMalloc1(ni->nNodes * ni->nodeIdxDim, &((*niNew)->nodeIdx)));
347: PetscCall(PetscArraycpy((*niNew)->nodeIdx, ni->nodeIdx, ni->nNodes * ni->nodeIdxDim));
348: PetscCall(PetscMalloc1(ni->nNodes * ni->nodeVecDim, &((*niNew)->nodeVec)));
349: PetscCall(PetscArraycpy((*niNew)->nodeVec, ni->nodeVec, ni->nNodes * ni->nodeVecDim));
350: (*niNew)->perm = NULL;
351: PetscFunctionReturn(PETSC_SUCCESS);
352: }
354: static PetscErrorCode PetscLagNodeIndicesDestroy(PetscLagNodeIndices *ni)
355: {
356: PetscFunctionBegin;
357: if (!*ni) PetscFunctionReturn(PETSC_SUCCESS);
358: if (--(*ni)->refct > 0) {
359: *ni = NULL;
360: PetscFunctionReturn(PETSC_SUCCESS);
361: }
362: PetscCall(PetscFree((*ni)->nodeIdx));
363: PetscCall(PetscFree((*ni)->nodeVec));
364: PetscCall(PetscFree((*ni)->perm));
365: PetscCall(PetscFree(*ni));
366: *ni = NULL;
367: PetscFunctionReturn(PETSC_SUCCESS);
368: }
370: /* The vertices are given nodeIdx coordinates (e.g. the corners of the barycentric triangle). Those coordinates are
371: * in some other order, and to understand the effect of different symmetries, we need them to be in closure order.
372: *
373: * If sortIdx is PETSC_FALSE, the coordinates are already in revlex order, otherwise we must sort them
374: * to that order before we do the real work of this function, which is
375: *
376: * - mark the vertices in closure order
377: * - sort them in revlex order
378: * - use the resulting permutation to list the vertex coordinates in closure order
379: */
380: static PetscErrorCode PetscLagNodeIndicesComputeVertexOrder(DM dm, PetscLagNodeIndices ni, PetscBool sortIdx)
381: {
382: PetscInt v, w, vStart, vEnd, c, d;
383: PetscInt nVerts;
384: PetscInt closureSize = 0;
385: PetscInt *closure = NULL;
386: PetscInt *closureOrder;
387: PetscInt *invClosureOrder;
388: PetscInt *revlexOrder;
389: PetscInt *newNodeIdx;
390: PetscInt dim;
391: Vec coordVec;
392: const PetscScalar *coords;
394: PetscFunctionBegin;
395: PetscCall(DMGetDimension(dm, &dim));
396: PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
397: nVerts = vEnd - vStart;
398: PetscCall(PetscMalloc1(nVerts, &closureOrder));
399: PetscCall(PetscMalloc1(nVerts, &invClosureOrder));
400: PetscCall(PetscMalloc1(nVerts, &revlexOrder));
401: if (sortIdx) { /* bubble sort nodeIdx into revlex order */
402: PetscInt nodeIdxDim = ni->nodeIdxDim;
403: PetscInt *idxOrder;
405: PetscCall(PetscMalloc1(nVerts * nodeIdxDim, &newNodeIdx));
406: PetscCall(PetscMalloc1(nVerts, &idxOrder));
407: for (v = 0; v < nVerts; v++) idxOrder[v] = v;
408: for (v = 0; v < nVerts; v++) {
409: for (w = v + 1; w < nVerts; w++) {
410: const PetscInt *iv = &(ni->nodeIdx[idxOrder[v] * nodeIdxDim]);
411: const PetscInt *iw = &(ni->nodeIdx[idxOrder[w] * nodeIdxDim]);
412: PetscInt diff = 0;
414: for (d = nodeIdxDim - 1; d >= 0; d--)
415: if ((diff = (iv[d] - iw[d]))) break;
416: if (diff > 0) {
417: PetscInt swap = idxOrder[v];
419: idxOrder[v] = idxOrder[w];
420: idxOrder[w] = swap;
421: }
422: }
423: }
424: for (v = 0; v < nVerts; v++) {
425: for (d = 0; d < nodeIdxDim; d++) newNodeIdx[v * ni->nodeIdxDim + d] = ni->nodeIdx[idxOrder[v] * nodeIdxDim + d];
426: }
427: PetscCall(PetscFree(ni->nodeIdx));
428: ni->nodeIdx = newNodeIdx;
429: newNodeIdx = NULL;
430: PetscCall(PetscFree(idxOrder));
431: }
432: PetscCall(DMPlexGetTransitiveClosure(dm, 0, PETSC_TRUE, &closureSize, &closure));
433: c = closureSize - nVerts;
434: for (v = 0; v < nVerts; v++) closureOrder[v] = closure[2 * (c + v)] - vStart;
435: for (v = 0; v < nVerts; v++) invClosureOrder[closureOrder[v]] = v;
436: PetscCall(DMPlexRestoreTransitiveClosure(dm, 0, PETSC_TRUE, &closureSize, &closure));
437: PetscCall(DMGetCoordinatesLocal(dm, &coordVec));
438: PetscCall(VecGetArrayRead(coordVec, &coords));
439: /* bubble sort closure vertices by coordinates in revlex order */
440: for (v = 0; v < nVerts; v++) revlexOrder[v] = v;
441: for (v = 0; v < nVerts; v++) {
442: for (w = v + 1; w < nVerts; w++) {
443: const PetscScalar *cv = &coords[closureOrder[revlexOrder[v]] * dim];
444: const PetscScalar *cw = &coords[closureOrder[revlexOrder[w]] * dim];
445: PetscReal diff = 0;
447: for (d = dim - 1; d >= 0; d--)
448: if ((diff = PetscRealPart(cv[d] - cw[d])) != 0.) break;
449: if (diff > 0.) {
450: PetscInt swap = revlexOrder[v];
452: revlexOrder[v] = revlexOrder[w];
453: revlexOrder[w] = swap;
454: }
455: }
456: }
457: PetscCall(VecRestoreArrayRead(coordVec, &coords));
458: PetscCall(PetscMalloc1(ni->nodeIdxDim * nVerts, &newNodeIdx));
459: /* reorder nodeIdx to be in closure order */
460: for (v = 0; v < nVerts; v++) {
461: for (d = 0; d < ni->nodeIdxDim; d++) newNodeIdx[revlexOrder[v] * ni->nodeIdxDim + d] = ni->nodeIdx[v * ni->nodeIdxDim + d];
462: }
463: PetscCall(PetscFree(ni->nodeIdx));
464: ni->nodeIdx = newNodeIdx;
465: ni->perm = invClosureOrder;
466: PetscCall(PetscFree(revlexOrder));
467: PetscCall(PetscFree(closureOrder));
468: PetscFunctionReturn(PETSC_SUCCESS);
469: }
471: /* the coordinates of the simplex vertices are the corners of the barycentric simplex.
472: * When we stack them on top of each other in revlex order, they look like the identity matrix */
473: static PetscErrorCode PetscLagNodeIndicesCreateSimplexVertices(DM dm, PetscLagNodeIndices *nodeIndices)
474: {
475: PetscLagNodeIndices ni;
476: PetscInt dim, d;
478: PetscFunctionBegin;
479: PetscCall(PetscNew(&ni));
480: PetscCall(DMGetDimension(dm, &dim));
481: ni->nodeIdxDim = dim + 1;
482: ni->nodeVecDim = 0;
483: ni->nNodes = dim + 1;
484: ni->refct = 1;
485: PetscCall(PetscCalloc1((dim + 1) * (dim + 1), &ni->nodeIdx));
486: for (d = 0; d < dim + 1; d++) ni->nodeIdx[d * (dim + 2)] = 1;
487: PetscCall(PetscLagNodeIndicesComputeVertexOrder(dm, ni, PETSC_FALSE));
488: *nodeIndices = ni;
489: PetscFunctionReturn(PETSC_SUCCESS);
490: }
492: /* A polytope that is a tensor product of a facet and a segment.
493: * We take whatever coordinate system was being used for the facet
494: * and we concatenate the barycentric coordinates for the vertices
495: * at the end of the segment, (1,0) and (0,1), to get a coordinate
496: * system for the tensor product element */
497: static PetscErrorCode PetscLagNodeIndicesCreateTensorVertices(DM dm, PetscLagNodeIndices facetni, PetscLagNodeIndices *nodeIndices)
498: {
499: PetscLagNodeIndices ni;
500: PetscInt nodeIdxDim, subNodeIdxDim = facetni->nodeIdxDim;
501: PetscInt nVerts, nSubVerts = facetni->nNodes;
502: PetscInt dim, d, e, f, g;
504: PetscFunctionBegin;
505: PetscCall(PetscNew(&ni));
506: PetscCall(DMGetDimension(dm, &dim));
507: ni->nodeIdxDim = nodeIdxDim = subNodeIdxDim + 2;
508: ni->nodeVecDim = 0;
509: ni->nNodes = nVerts = 2 * nSubVerts;
510: ni->refct = 1;
511: PetscCall(PetscCalloc1(nodeIdxDim * nVerts, &ni->nodeIdx));
512: for (f = 0, d = 0; d < 2; d++) {
513: for (e = 0; e < nSubVerts; e++, f++) {
514: for (g = 0; g < subNodeIdxDim; g++) ni->nodeIdx[f * nodeIdxDim + g] = facetni->nodeIdx[e * subNodeIdxDim + g];
515: ni->nodeIdx[f * nodeIdxDim + subNodeIdxDim] = (1 - d);
516: ni->nodeIdx[f * nodeIdxDim + subNodeIdxDim + 1] = d;
517: }
518: }
519: PetscCall(PetscLagNodeIndicesComputeVertexOrder(dm, ni, PETSC_TRUE));
520: *nodeIndices = ni;
521: PetscFunctionReturn(PETSC_SUCCESS);
522: }
524: /* This helps us compute symmetries, and it also helps us compute coordinates for dofs that are being pushed
525: * forward from a boundary mesh point.
526: *
527: * Input:
528: *
529: * dm - the target reference cell where we want new coordinates and dof directions to be valid
530: * vert - the vertex coordinate system for the target reference cell
531: * p - the point in the target reference cell that the dofs are coming from
532: * vertp - the vertex coordinate system for p's reference cell
533: * ornt - the resulting coordinates and dof vectors will be for p under this orientation
534: * nodep - the node coordinates and dof vectors in p's reference cell
535: * formDegree - the form degree that the dofs transform as
536: *
537: * Output:
538: *
539: * pfNodeIdx - the node coordinates for p's dofs, in the dm reference cell, from the ornt perspective
540: * pfNodeVec - the node dof vectors for p's dofs, in the dm reference cell, from the ornt perspective
541: */
542: static PetscErrorCode PetscLagNodeIndicesPushForward(DM dm, PetscLagNodeIndices vert, PetscInt p, PetscLagNodeIndices vertp, PetscLagNodeIndices nodep, PetscInt ornt, PetscInt formDegree, PetscInt pfNodeIdx[], PetscReal pfNodeVec[])
543: {
544: PetscInt *closureVerts;
545: PetscInt closureSize = 0;
546: PetscInt *closure = NULL;
547: PetscInt dim, pdim, c, i, j, k, n, v, vStart, vEnd;
548: PetscInt nSubVert = vertp->nNodes;
549: PetscInt nodeIdxDim = vert->nodeIdxDim;
550: PetscInt subNodeIdxDim = vertp->nodeIdxDim;
551: PetscInt nNodes = nodep->nNodes;
552: const PetscInt *vertIdx = vert->nodeIdx;
553: const PetscInt *subVertIdx = vertp->nodeIdx;
554: const PetscInt *nodeIdx = nodep->nodeIdx;
555: const PetscReal *nodeVec = nodep->nodeVec;
556: PetscReal *J, *Jstar;
557: PetscReal detJ;
558: PetscInt depth, pdepth, Nk, pNk;
559: Vec coordVec;
560: PetscScalar *newCoords = NULL;
561: const PetscScalar *oldCoords = NULL;
563: PetscFunctionBegin;
564: PetscCall(DMGetDimension(dm, &dim));
565: PetscCall(DMPlexGetDepth(dm, &depth));
566: PetscCall(DMGetCoordinatesLocal(dm, &coordVec));
567: PetscCall(DMPlexGetPointDepth(dm, p, &pdepth));
568: pdim = pdepth != depth ? pdepth != 0 ? pdepth : 0 : dim;
569: PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
570: PetscCall(DMGetWorkArray(dm, nSubVert, MPIU_INT, &closureVerts));
571: PetscCall(DMPlexGetTransitiveClosure_Internal(dm, p, ornt, PETSC_TRUE, &closureSize, &closure));
572: c = closureSize - nSubVert;
573: /* we want which cell closure indices the closure of this point corresponds to */
574: for (v = 0; v < nSubVert; v++) closureVerts[v] = vert->perm[closure[2 * (c + v)] - vStart];
575: PetscCall(DMPlexRestoreTransitiveClosure(dm, p, PETSC_TRUE, &closureSize, &closure));
576: /* push forward indices */
577: for (i = 0; i < nodeIdxDim; i++) { /* for every component of the target index space */
578: /* check if this is a component that all vertices around this point have in common */
579: for (j = 1; j < nSubVert; j++) {
580: if (vertIdx[closureVerts[j] * nodeIdxDim + i] != vertIdx[closureVerts[0] * nodeIdxDim + i]) break;
581: }
582: if (j == nSubVert) { /* all vertices have this component in common, directly copy to output */
583: PetscInt val = vertIdx[closureVerts[0] * nodeIdxDim + i];
584: for (n = 0; n < nNodes; n++) pfNodeIdx[n * nodeIdxDim + i] = val;
585: } else {
586: PetscInt subi = -1;
587: /* there must be a component in vertp that looks the same */
588: for (k = 0; k < subNodeIdxDim; k++) {
589: for (j = 0; j < nSubVert; j++) {
590: if (vertIdx[closureVerts[j] * nodeIdxDim + i] != subVertIdx[j * subNodeIdxDim + k]) break;
591: }
592: if (j == nSubVert) {
593: subi = k;
594: break;
595: }
596: }
597: PetscCheck(subi >= 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Did not find matching coordinate");
598: /* that component in the vertp system becomes component i in the vert system for each dof */
599: for (n = 0; n < nNodes; n++) pfNodeIdx[n * nodeIdxDim + i] = nodeIdx[n * subNodeIdxDim + subi];
600: }
601: }
602: /* push forward vectors */
603: PetscCall(DMGetWorkArray(dm, dim * dim, MPIU_REAL, &J));
604: if (ornt != 0) { /* temporarily change the coordinate vector so
605: DMPlexComputeCellGeometryAffineFEM gives us the Jacobian we want */
606: PetscInt closureSize2 = 0;
607: PetscInt *closure2 = NULL;
609: PetscCall(DMPlexGetTransitiveClosure_Internal(dm, p, 0, PETSC_TRUE, &closureSize2, &closure2));
610: PetscCall(PetscMalloc1(dim * nSubVert, &newCoords));
611: PetscCall(VecGetArrayRead(coordVec, &oldCoords));
612: for (v = 0; v < nSubVert; v++) {
613: PetscInt d;
614: for (d = 0; d < dim; d++) newCoords[(closure2[2 * (c + v)] - vStart) * dim + d] = oldCoords[closureVerts[v] * dim + d];
615: }
616: PetscCall(VecRestoreArrayRead(coordVec, &oldCoords));
617: PetscCall(DMPlexRestoreTransitiveClosure(dm, p, PETSC_TRUE, &closureSize2, &closure2));
618: PetscCall(VecPlaceArray(coordVec, newCoords));
619: }
620: PetscCall(DMPlexComputeCellGeometryAffineFEM(dm, p, NULL, J, NULL, &detJ));
621: if (ornt != 0) {
622: PetscCall(VecResetArray(coordVec));
623: PetscCall(PetscFree(newCoords));
624: }
625: PetscCall(DMRestoreWorkArray(dm, nSubVert, MPIU_INT, &closureVerts));
626: /* compactify */
627: for (i = 0; i < dim; i++)
628: for (j = 0; j < pdim; j++) J[i * pdim + j] = J[i * dim + j];
629: /* We have the Jacobian mapping the point's reference cell to this reference cell:
630: * pulling back a function to the point and applying the dof is what we want,
631: * so we get the pullback matrix and multiply the dof by that matrix on the right */
632: PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(formDegree), &Nk));
633: PetscCall(PetscDTBinomialInt(pdim, PetscAbsInt(formDegree), &pNk));
634: PetscCall(DMGetWorkArray(dm, pNk * Nk, MPIU_REAL, &Jstar));
635: PetscCall(PetscDTAltVPullbackMatrix(pdim, dim, J, formDegree, Jstar));
636: for (n = 0; n < nNodes; n++) {
637: for (i = 0; i < Nk; i++) {
638: PetscReal val = 0.;
639: for (j = 0; j < pNk; j++) val += nodeVec[n * pNk + j] * Jstar[j * Nk + i];
640: pfNodeVec[n * Nk + i] = val;
641: }
642: }
643: PetscCall(DMRestoreWorkArray(dm, pNk * Nk, MPIU_REAL, &Jstar));
644: PetscCall(DMRestoreWorkArray(dm, dim * dim, MPIU_REAL, &J));
645: PetscFunctionReturn(PETSC_SUCCESS);
646: }
648: /* given to sets of nodes, take the tensor product, where the product of the dof indices is concatenation and the
649: * product of the dof vectors is the wedge product */
650: static PetscErrorCode PetscLagNodeIndicesTensor(PetscLagNodeIndices tracei, PetscInt dimT, PetscInt kT, PetscLagNodeIndices fiberi, PetscInt dimF, PetscInt kF, PetscLagNodeIndices *nodeIndices)
651: {
652: PetscInt dim = dimT + dimF;
653: PetscInt nodeIdxDim, nNodes;
654: PetscInt formDegree = kT + kF;
655: PetscInt Nk, NkT, NkF;
656: PetscInt MkT, MkF;
657: PetscLagNodeIndices ni;
658: PetscInt i, j, l;
659: PetscReal *projF, *projT;
660: PetscReal *projFstar, *projTstar;
661: PetscReal *workF, *workF2, *workT, *workT2, *work, *work2;
662: PetscReal *wedgeMat;
663: PetscReal sign;
665: PetscFunctionBegin;
666: PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(formDegree), &Nk));
667: PetscCall(PetscDTBinomialInt(dimT, PetscAbsInt(kT), &NkT));
668: PetscCall(PetscDTBinomialInt(dimF, PetscAbsInt(kF), &NkF));
669: PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(kT), &MkT));
670: PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(kF), &MkF));
671: PetscCall(PetscNew(&ni));
672: ni->nodeIdxDim = nodeIdxDim = tracei->nodeIdxDim + fiberi->nodeIdxDim;
673: ni->nodeVecDim = Nk;
674: ni->nNodes = nNodes = tracei->nNodes * fiberi->nNodes;
675: ni->refct = 1;
676: PetscCall(PetscMalloc1(nNodes * nodeIdxDim, &ni->nodeIdx));
677: /* first concatenate the indices */
678: for (l = 0, j = 0; j < fiberi->nNodes; j++) {
679: for (i = 0; i < tracei->nNodes; i++, l++) {
680: PetscInt m, n = 0;
682: for (m = 0; m < tracei->nodeIdxDim; m++) ni->nodeIdx[l * nodeIdxDim + n++] = tracei->nodeIdx[i * tracei->nodeIdxDim + m];
683: for (m = 0; m < fiberi->nodeIdxDim; m++) ni->nodeIdx[l * nodeIdxDim + n++] = fiberi->nodeIdx[j * fiberi->nodeIdxDim + m];
684: }
685: }
687: /* now wedge together the push-forward vectors */
688: PetscCall(PetscMalloc1(nNodes * Nk, &ni->nodeVec));
689: PetscCall(PetscCalloc2(dimT * dim, &projT, dimF * dim, &projF));
690: for (i = 0; i < dimT; i++) projT[i * (dim + 1)] = 1.;
691: for (i = 0; i < dimF; i++) projF[i * (dim + dimT + 1) + dimT] = 1.;
692: PetscCall(PetscMalloc2(MkT * NkT, &projTstar, MkF * NkF, &projFstar));
693: PetscCall(PetscDTAltVPullbackMatrix(dim, dimT, projT, kT, projTstar));
694: PetscCall(PetscDTAltVPullbackMatrix(dim, dimF, projF, kF, projFstar));
695: PetscCall(PetscMalloc6(MkT, &workT, MkT, &workT2, MkF, &workF, MkF, &workF2, Nk, &work, Nk, &work2));
696: PetscCall(PetscMalloc1(Nk * MkT, &wedgeMat));
697: sign = (PetscAbsInt(kT * kF) & 1) ? -1. : 1.;
698: for (l = 0, j = 0; j < fiberi->nNodes; j++) {
699: PetscInt d, e;
701: /* push forward fiber k-form */
702: for (d = 0; d < MkF; d++) {
703: PetscReal val = 0.;
704: for (e = 0; e < NkF; e++) val += projFstar[d * NkF + e] * fiberi->nodeVec[j * NkF + e];
705: workF[d] = val;
706: }
707: /* Hodge star to proper form if necessary */
708: if (kF < 0) {
709: for (d = 0; d < MkF; d++) workF2[d] = workF[d];
710: PetscCall(PetscDTAltVStar(dim, PetscAbsInt(kF), 1, workF2, workF));
711: }
712: /* Compute the matrix that wedges this form with one of the trace k-form */
713: PetscCall(PetscDTAltVWedgeMatrix(dim, PetscAbsInt(kF), PetscAbsInt(kT), workF, wedgeMat));
714: for (i = 0; i < tracei->nNodes; i++, l++) {
715: /* push forward trace k-form */
716: for (d = 0; d < MkT; d++) {
717: PetscReal val = 0.;
718: for (e = 0; e < NkT; e++) val += projTstar[d * NkT + e] * tracei->nodeVec[i * NkT + e];
719: workT[d] = val;
720: }
721: /* Hodge star to proper form if necessary */
722: if (kT < 0) {
723: for (d = 0; d < MkT; d++) workT2[d] = workT[d];
724: PetscCall(PetscDTAltVStar(dim, PetscAbsInt(kT), 1, workT2, workT));
725: }
726: /* compute the wedge product of the push-forward trace form and firer forms */
727: for (d = 0; d < Nk; d++) {
728: PetscReal val = 0.;
729: for (e = 0; e < MkT; e++) val += wedgeMat[d * MkT + e] * workT[e];
730: work[d] = val;
731: }
732: /* inverse Hodge star from proper form if necessary */
733: if (formDegree < 0) {
734: for (d = 0; d < Nk; d++) work2[d] = work[d];
735: PetscCall(PetscDTAltVStar(dim, PetscAbsInt(formDegree), -1, work2, work));
736: }
737: /* insert into the array (adjusting for sign) */
738: for (d = 0; d < Nk; d++) ni->nodeVec[l * Nk + d] = sign * work[d];
739: }
740: }
741: PetscCall(PetscFree(wedgeMat));
742: PetscCall(PetscFree6(workT, workT2, workF, workF2, work, work2));
743: PetscCall(PetscFree2(projTstar, projFstar));
744: PetscCall(PetscFree2(projT, projF));
745: *nodeIndices = ni;
746: PetscFunctionReturn(PETSC_SUCCESS);
747: }
749: /* simple union of two sets of nodes */
750: static PetscErrorCode PetscLagNodeIndicesMerge(PetscLagNodeIndices niA, PetscLagNodeIndices niB, PetscLagNodeIndices *nodeIndices)
751: {
752: PetscLagNodeIndices ni;
753: PetscInt nodeIdxDim, nodeVecDim, nNodes;
755: PetscFunctionBegin;
756: PetscCall(PetscNew(&ni));
757: ni->nodeIdxDim = nodeIdxDim = niA->nodeIdxDim;
758: PetscCheck(niB->nodeIdxDim == nodeIdxDim, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Cannot merge PetscLagNodeIndices with different nodeIdxDim");
759: ni->nodeVecDim = nodeVecDim = niA->nodeVecDim;
760: PetscCheck(niB->nodeVecDim == nodeVecDim, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Cannot merge PetscLagNodeIndices with different nodeVecDim");
761: ni->nNodes = nNodes = niA->nNodes + niB->nNodes;
762: ni->refct = 1;
763: PetscCall(PetscMalloc1(nNodes * nodeIdxDim, &ni->nodeIdx));
764: PetscCall(PetscMalloc1(nNodes * nodeVecDim, &ni->nodeVec));
765: PetscCall(PetscArraycpy(ni->nodeIdx, niA->nodeIdx, niA->nNodes * nodeIdxDim));
766: PetscCall(PetscArraycpy(ni->nodeVec, niA->nodeVec, niA->nNodes * nodeVecDim));
767: PetscCall(PetscArraycpy(&ni->nodeIdx[niA->nNodes * nodeIdxDim], niB->nodeIdx, niB->nNodes * nodeIdxDim));
768: PetscCall(PetscArraycpy(&ni->nodeVec[niA->nNodes * nodeVecDim], niB->nodeVec, niB->nNodes * nodeVecDim));
769: *nodeIndices = ni;
770: PetscFunctionReturn(PETSC_SUCCESS);
771: }
773: #define PETSCTUPINTCOMPREVLEX(N) \
774: static int PetscConcat_(PetscTupIntCompRevlex_, N)(const void *a, const void *b) \
775: { \
776: const PetscInt *A = (const PetscInt *)a; \
777: const PetscInt *B = (const PetscInt *)b; \
778: int i; \
779: PetscInt diff = 0; \
780: for (i = 0; i < N; i++) { \
781: diff = A[N - i] - B[N - i]; \
782: if (diff) break; \
783: } \
784: return (diff <= 0) ? (diff < 0) ? -1 : 0 : 1; \
785: }
787: PETSCTUPINTCOMPREVLEX(3)
788: PETSCTUPINTCOMPREVLEX(4)
789: PETSCTUPINTCOMPREVLEX(5)
790: PETSCTUPINTCOMPREVLEX(6)
791: PETSCTUPINTCOMPREVLEX(7)
793: static int PetscTupIntCompRevlex_N(const void *a, const void *b)
794: {
795: const PetscInt *A = (const PetscInt *)a;
796: const PetscInt *B = (const PetscInt *)b;
797: PetscInt i;
798: PetscInt N = A[0];
799: PetscInt diff = 0;
800: for (i = 0; i < N; i++) {
801: diff = A[N - i] - B[N - i];
802: if (diff) break;
803: }
804: return (diff <= 0) ? (diff < 0) ? -1 : 0 : 1;
805: }
807: /* The nodes are not necessarily in revlex order wrt nodeIdx: get the permutation
808: * that puts them in that order */
809: static PetscErrorCode PetscLagNodeIndicesGetPermutation(PetscLagNodeIndices ni, PetscInt *perm[])
810: {
811: PetscFunctionBegin;
812: if (!ni->perm) {
813: PetscInt *sorter;
814: PetscInt m = ni->nNodes;
815: PetscInt nodeIdxDim = ni->nodeIdxDim;
816: PetscInt i, j, k, l;
817: PetscInt *prm;
818: int (*comp)(const void *, const void *);
820: PetscCall(PetscMalloc1((nodeIdxDim + 2) * m, &sorter));
821: for (k = 0, l = 0, i = 0; i < m; i++) {
822: sorter[k++] = nodeIdxDim + 1;
823: sorter[k++] = i;
824: for (j = 0; j < nodeIdxDim; j++) sorter[k++] = ni->nodeIdx[l++];
825: }
826: switch (nodeIdxDim) {
827: case 2:
828: comp = PetscTupIntCompRevlex_3;
829: break;
830: case 3:
831: comp = PetscTupIntCompRevlex_4;
832: break;
833: case 4:
834: comp = PetscTupIntCompRevlex_5;
835: break;
836: case 5:
837: comp = PetscTupIntCompRevlex_6;
838: break;
839: case 6:
840: comp = PetscTupIntCompRevlex_7;
841: break;
842: default:
843: comp = PetscTupIntCompRevlex_N;
844: break;
845: }
846: qsort(sorter, m, (nodeIdxDim + 2) * sizeof(PetscInt), comp);
847: PetscCall(PetscMalloc1(m, &prm));
848: for (i = 0; i < m; i++) prm[i] = sorter[(nodeIdxDim + 2) * i + 1];
849: ni->perm = prm;
850: PetscCall(PetscFree(sorter));
851: }
852: *perm = ni->perm;
853: PetscFunctionReturn(PETSC_SUCCESS);
854: }
856: static PetscErrorCode PetscDualSpaceDestroy_Lagrange(PetscDualSpace sp)
857: {
858: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
860: PetscFunctionBegin;
861: if (lag->symperms) {
862: PetscInt **selfSyms = lag->symperms[0];
864: if (selfSyms) {
865: PetscInt i, **allocated = &selfSyms[-lag->selfSymOff];
867: for (i = 0; i < lag->numSelfSym; i++) PetscCall(PetscFree(allocated[i]));
868: PetscCall(PetscFree(allocated));
869: }
870: PetscCall(PetscFree(lag->symperms));
871: }
872: if (lag->symflips) {
873: PetscScalar **selfSyms = lag->symflips[0];
875: if (selfSyms) {
876: PetscInt i;
877: PetscScalar **allocated = &selfSyms[-lag->selfSymOff];
879: for (i = 0; i < lag->numSelfSym; i++) PetscCall(PetscFree(allocated[i]));
880: PetscCall(PetscFree(allocated));
881: }
882: PetscCall(PetscFree(lag->symflips));
883: }
884: PetscCall(Petsc1DNodeFamilyDestroy(&lag->nodeFamily));
885: PetscCall(PetscLagNodeIndicesDestroy(&lag->vertIndices));
886: PetscCall(PetscLagNodeIndicesDestroy(&lag->intNodeIndices));
887: PetscCall(PetscLagNodeIndicesDestroy(&lag->allNodeIndices));
888: PetscCall(PetscFree(lag));
889: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetContinuity_C", NULL));
890: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetContinuity_C", NULL));
891: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetTensor_C", NULL));
892: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetTensor_C", NULL));
893: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetTrimmed_C", NULL));
894: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetTrimmed_C", NULL));
895: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetNodeType_C", NULL));
896: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetNodeType_C", NULL));
897: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetUseMoments_C", NULL));
898: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetUseMoments_C", NULL));
899: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetMomentOrder_C", NULL));
900: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetMomentOrder_C", NULL));
901: PetscFunctionReturn(PETSC_SUCCESS);
902: }
904: static PetscErrorCode PetscDualSpaceLagrangeView_Ascii(PetscDualSpace sp, PetscViewer viewer)
905: {
906: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
908: PetscFunctionBegin;
909: PetscCall(PetscViewerASCIIPrintf(viewer, "%s %s%sLagrange dual space\n", lag->continuous ? "Continuous" : "Discontinuous", lag->tensorSpace ? "tensor " : "", lag->trimmed ? "trimmed " : ""));
910: PetscFunctionReturn(PETSC_SUCCESS);
911: }
913: static PetscErrorCode PetscDualSpaceView_Lagrange(PetscDualSpace sp, PetscViewer viewer)
914: {
915: PetscBool iascii;
917: PetscFunctionBegin;
920: PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
921: if (iascii) PetscCall(PetscDualSpaceLagrangeView_Ascii(sp, viewer));
922: PetscFunctionReturn(PETSC_SUCCESS);
923: }
925: static PetscErrorCode PetscDualSpaceSetFromOptions_Lagrange(PetscDualSpace sp, PetscOptionItems *PetscOptionsObject)
926: {
927: PetscBool continuous, tensor, trimmed, flg, flg2, flg3;
928: PetscDTNodeType nodeType;
929: PetscReal nodeExponent;
930: PetscInt momentOrder;
931: PetscBool nodeEndpoints, useMoments;
933: PetscFunctionBegin;
934: PetscCall(PetscDualSpaceLagrangeGetContinuity(sp, &continuous));
935: PetscCall(PetscDualSpaceLagrangeGetTensor(sp, &tensor));
936: PetscCall(PetscDualSpaceLagrangeGetTrimmed(sp, &trimmed));
937: PetscCall(PetscDualSpaceLagrangeGetNodeType(sp, &nodeType, &nodeEndpoints, &nodeExponent));
938: if (nodeType == PETSCDTNODES_DEFAULT) nodeType = PETSCDTNODES_GAUSSJACOBI;
939: PetscCall(PetscDualSpaceLagrangeGetUseMoments(sp, &useMoments));
940: PetscCall(PetscDualSpaceLagrangeGetMomentOrder(sp, &momentOrder));
941: PetscOptionsHeadBegin(PetscOptionsObject, "PetscDualSpace Lagrange Options");
942: PetscCall(PetscOptionsBool("-petscdualspace_lagrange_continuity", "Flag for continuous element", "PetscDualSpaceLagrangeSetContinuity", continuous, &continuous, &flg));
943: if (flg) PetscCall(PetscDualSpaceLagrangeSetContinuity(sp, continuous));
944: PetscCall(PetscOptionsBool("-petscdualspace_lagrange_tensor", "Flag for tensor dual space", "PetscDualSpaceLagrangeSetTensor", tensor, &tensor, &flg));
945: if (flg) PetscCall(PetscDualSpaceLagrangeSetTensor(sp, tensor));
946: PetscCall(PetscOptionsBool("-petscdualspace_lagrange_trimmed", "Flag for trimmed dual space", "PetscDualSpaceLagrangeSetTrimmed", trimmed, &trimmed, &flg));
947: if (flg) PetscCall(PetscDualSpaceLagrangeSetTrimmed(sp, trimmed));
948: PetscCall(PetscOptionsEnum("-petscdualspace_lagrange_node_type", "Lagrange node location type", "PetscDualSpaceLagrangeSetNodeType", PetscDTNodeTypes, (PetscEnum)nodeType, (PetscEnum *)&nodeType, &flg));
949: PetscCall(PetscOptionsBool("-petscdualspace_lagrange_node_endpoints", "Flag for nodes that include endpoints", "PetscDualSpaceLagrangeSetNodeType", nodeEndpoints, &nodeEndpoints, &flg2));
950: flg3 = PETSC_FALSE;
951: if (nodeType == PETSCDTNODES_GAUSSJACOBI) PetscCall(PetscOptionsReal("-petscdualspace_lagrange_node_exponent", "Gauss-Jacobi weight function exponent", "PetscDualSpaceLagrangeSetNodeType", nodeExponent, &nodeExponent, &flg3));
952: if (flg || flg2 || flg3) PetscCall(PetscDualSpaceLagrangeSetNodeType(sp, nodeType, nodeEndpoints, nodeExponent));
953: PetscCall(PetscOptionsBool("-petscdualspace_lagrange_use_moments", "Use moments (where appropriate) for functionals", "PetscDualSpaceLagrangeSetUseMoments", useMoments, &useMoments, &flg));
954: if (flg) PetscCall(PetscDualSpaceLagrangeSetUseMoments(sp, useMoments));
955: PetscCall(PetscOptionsInt("-petscdualspace_lagrange_moment_order", "Quadrature order for moment functionals", "PetscDualSpaceLagrangeSetMomentOrder", momentOrder, &momentOrder, &flg));
956: if (flg) PetscCall(PetscDualSpaceLagrangeSetMomentOrder(sp, momentOrder));
957: PetscOptionsHeadEnd();
958: PetscFunctionReturn(PETSC_SUCCESS);
959: }
961: static PetscErrorCode PetscDualSpaceDuplicate_Lagrange(PetscDualSpace sp, PetscDualSpace spNew)
962: {
963: PetscBool cont, tensor, trimmed, boundary;
964: PetscDTNodeType nodeType;
965: PetscReal exponent;
966: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
968: PetscFunctionBegin;
969: PetscCall(PetscDualSpaceLagrangeGetContinuity(sp, &cont));
970: PetscCall(PetscDualSpaceLagrangeSetContinuity(spNew, cont));
971: PetscCall(PetscDualSpaceLagrangeGetTensor(sp, &tensor));
972: PetscCall(PetscDualSpaceLagrangeSetTensor(spNew, tensor));
973: PetscCall(PetscDualSpaceLagrangeGetTrimmed(sp, &trimmed));
974: PetscCall(PetscDualSpaceLagrangeSetTrimmed(spNew, trimmed));
975: PetscCall(PetscDualSpaceLagrangeGetNodeType(sp, &nodeType, &boundary, &exponent));
976: PetscCall(PetscDualSpaceLagrangeSetNodeType(spNew, nodeType, boundary, exponent));
977: if (lag->nodeFamily) {
978: PetscDualSpace_Lag *lagnew = (PetscDualSpace_Lag *)spNew->data;
980: PetscCall(Petsc1DNodeFamilyReference(lag->nodeFamily));
981: lagnew->nodeFamily = lag->nodeFamily;
982: }
983: PetscFunctionReturn(PETSC_SUCCESS);
984: }
986: /* for making tensor product spaces: take a dual space and product a segment space that has all the same
987: * specifications (trimmed, continuous, order, node set), except for the form degree */
988: static PetscErrorCode PetscDualSpaceCreateEdgeSubspace_Lagrange(PetscDualSpace sp, PetscInt order, PetscInt k, PetscInt Nc, PetscBool interiorOnly, PetscDualSpace *bdsp)
989: {
990: DM K;
991: PetscDualSpace_Lag *newlag;
993: PetscFunctionBegin;
994: PetscCall(PetscDualSpaceDuplicate(sp, bdsp));
995: PetscCall(PetscDualSpaceSetFormDegree(*bdsp, k));
996: PetscCall(DMPlexCreateReferenceCell(PETSC_COMM_SELF, DMPolytopeTypeSimpleShape(1, PETSC_TRUE), &K));
997: PetscCall(PetscDualSpaceSetDM(*bdsp, K));
998: PetscCall(DMDestroy(&K));
999: PetscCall(PetscDualSpaceSetOrder(*bdsp, order));
1000: PetscCall(PetscDualSpaceSetNumComponents(*bdsp, Nc));
1001: newlag = (PetscDualSpace_Lag *)(*bdsp)->data;
1002: newlag->interiorOnly = interiorOnly;
1003: PetscCall(PetscDualSpaceSetUp(*bdsp));
1004: PetscFunctionReturn(PETSC_SUCCESS);
1005: }
1007: /* just the points, weights aren't handled */
1008: static PetscErrorCode PetscQuadratureCreateTensor(PetscQuadrature trace, PetscQuadrature fiber, PetscQuadrature *product)
1009: {
1010: PetscInt dimTrace, dimFiber;
1011: PetscInt numPointsTrace, numPointsFiber;
1012: PetscInt dim, numPoints;
1013: const PetscReal *pointsTrace;
1014: const PetscReal *pointsFiber;
1015: PetscReal *points;
1016: PetscInt i, j, k, p;
1018: PetscFunctionBegin;
1019: PetscCall(PetscQuadratureGetData(trace, &dimTrace, NULL, &numPointsTrace, &pointsTrace, NULL));
1020: PetscCall(PetscQuadratureGetData(fiber, &dimFiber, NULL, &numPointsFiber, &pointsFiber, NULL));
1021: dim = dimTrace + dimFiber;
1022: numPoints = numPointsFiber * numPointsTrace;
1023: PetscCall(PetscMalloc1(numPoints * dim, &points));
1024: for (p = 0, j = 0; j < numPointsFiber; j++) {
1025: for (i = 0; i < numPointsTrace; i++, p++) {
1026: for (k = 0; k < dimTrace; k++) points[p * dim + k] = pointsTrace[i * dimTrace + k];
1027: for (k = 0; k < dimFiber; k++) points[p * dim + dimTrace + k] = pointsFiber[j * dimFiber + k];
1028: }
1029: }
1030: PetscCall(PetscQuadratureCreate(PETSC_COMM_SELF, product));
1031: PetscCall(PetscQuadratureSetData(*product, dim, 0, numPoints, points, NULL));
1032: PetscFunctionReturn(PETSC_SUCCESS);
1033: }
1035: /* Kronecker tensor product where matrix is considered a matrix of k-forms, so that
1036: * the entries in the product matrix are wedge products of the entries in the original matrices */
1037: static PetscErrorCode MatTensorAltV(Mat trace, Mat fiber, PetscInt dimTrace, PetscInt kTrace, PetscInt dimFiber, PetscInt kFiber, Mat *product)
1038: {
1039: PetscInt mTrace, nTrace, mFiber, nFiber, m, n, k, i, j, l;
1040: PetscInt dim, NkTrace, NkFiber, Nk;
1041: PetscInt dT, dF;
1042: PetscInt *nnzTrace, *nnzFiber, *nnz;
1043: PetscInt iT, iF, jT, jF, il, jl;
1044: PetscReal *workT, *workT2, *workF, *workF2, *work, *workstar;
1045: PetscReal *projT, *projF;
1046: PetscReal *projTstar, *projFstar;
1047: PetscReal *wedgeMat;
1048: PetscReal sign;
1049: PetscScalar *workS;
1050: Mat prod;
1051: /* this produces dof groups that look like the identity */
1053: PetscFunctionBegin;
1054: PetscCall(MatGetSize(trace, &mTrace, &nTrace));
1055: PetscCall(PetscDTBinomialInt(dimTrace, PetscAbsInt(kTrace), &NkTrace));
1056: PetscCheck(nTrace % NkTrace == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "point value space of trace matrix is not a multiple of k-form size");
1057: PetscCall(MatGetSize(fiber, &mFiber, &nFiber));
1058: PetscCall(PetscDTBinomialInt(dimFiber, PetscAbsInt(kFiber), &NkFiber));
1059: PetscCheck(nFiber % NkFiber == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "point value space of fiber matrix is not a multiple of k-form size");
1060: PetscCall(PetscMalloc2(mTrace, &nnzTrace, mFiber, &nnzFiber));
1061: for (i = 0; i < mTrace; i++) {
1062: PetscCall(MatGetRow(trace, i, &nnzTrace[i], NULL, NULL));
1063: PetscCheck(nnzTrace[i] % NkTrace == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "nonzeros in trace matrix are not in k-form size blocks");
1064: }
1065: for (i = 0; i < mFiber; i++) {
1066: PetscCall(MatGetRow(fiber, i, &nnzFiber[i], NULL, NULL));
1067: PetscCheck(nnzFiber[i] % NkFiber == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "nonzeros in fiber matrix are not in k-form size blocks");
1068: }
1069: dim = dimTrace + dimFiber;
1070: k = kFiber + kTrace;
1071: PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(k), &Nk));
1072: m = mTrace * mFiber;
1073: PetscCall(PetscMalloc1(m, &nnz));
1074: for (l = 0, j = 0; j < mFiber; j++)
1075: for (i = 0; i < mTrace; i++, l++) nnz[l] = (nnzTrace[i] / NkTrace) * (nnzFiber[j] / NkFiber) * Nk;
1076: n = (nTrace / NkTrace) * (nFiber / NkFiber) * Nk;
1077: PetscCall(MatCreateSeqAIJ(PETSC_COMM_SELF, m, n, 0, nnz, &prod));
1078: PetscCall(PetscObjectSetOptionsPrefix((PetscObject)prod, "altv_"));
1079: PetscCall(PetscFree(nnz));
1080: PetscCall(PetscFree2(nnzTrace, nnzFiber));
1081: /* reasoning about which points each dof needs depends on having zeros computed at points preserved */
1082: PetscCall(MatSetOption(prod, MAT_IGNORE_ZERO_ENTRIES, PETSC_FALSE));
1083: /* compute pullbacks */
1084: PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(kTrace), &dT));
1085: PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(kFiber), &dF));
1086: PetscCall(PetscMalloc4(dimTrace * dim, &projT, dimFiber * dim, &projF, dT * NkTrace, &projTstar, dF * NkFiber, &projFstar));
1087: PetscCall(PetscArrayzero(projT, dimTrace * dim));
1088: for (i = 0; i < dimTrace; i++) projT[i * (dim + 1)] = 1.;
1089: PetscCall(PetscArrayzero(projF, dimFiber * dim));
1090: for (i = 0; i < dimFiber; i++) projF[i * (dim + 1) + dimTrace] = 1.;
1091: PetscCall(PetscDTAltVPullbackMatrix(dim, dimTrace, projT, kTrace, projTstar));
1092: PetscCall(PetscDTAltVPullbackMatrix(dim, dimFiber, projF, kFiber, projFstar));
1093: PetscCall(PetscMalloc5(dT, &workT, dF, &workF, Nk, &work, Nk, &workstar, Nk, &workS));
1094: PetscCall(PetscMalloc2(dT, &workT2, dF, &workF2));
1095: PetscCall(PetscMalloc1(Nk * dT, &wedgeMat));
1096: sign = (PetscAbsInt(kTrace * kFiber) & 1) ? -1. : 1.;
1097: for (i = 0, iF = 0; iF < mFiber; iF++) {
1098: PetscInt ncolsF, nformsF;
1099: const PetscInt *colsF;
1100: const PetscScalar *valsF;
1102: PetscCall(MatGetRow(fiber, iF, &ncolsF, &colsF, &valsF));
1103: nformsF = ncolsF / NkFiber;
1104: for (iT = 0; iT < mTrace; iT++, i++) {
1105: PetscInt ncolsT, nformsT;
1106: const PetscInt *colsT;
1107: const PetscScalar *valsT;
1109: PetscCall(MatGetRow(trace, iT, &ncolsT, &colsT, &valsT));
1110: nformsT = ncolsT / NkTrace;
1111: for (j = 0, jF = 0; jF < nformsF; jF++) {
1112: PetscInt colF = colsF[jF * NkFiber] / NkFiber;
1114: for (il = 0; il < dF; il++) {
1115: PetscReal val = 0.;
1116: for (jl = 0; jl < NkFiber; jl++) val += projFstar[il * NkFiber + jl] * PetscRealPart(valsF[jF * NkFiber + jl]);
1117: workF[il] = val;
1118: }
1119: if (kFiber < 0) {
1120: for (il = 0; il < dF; il++) workF2[il] = workF[il];
1121: PetscCall(PetscDTAltVStar(dim, PetscAbsInt(kFiber), 1, workF2, workF));
1122: }
1123: PetscCall(PetscDTAltVWedgeMatrix(dim, PetscAbsInt(kFiber), PetscAbsInt(kTrace), workF, wedgeMat));
1124: for (jT = 0; jT < nformsT; jT++, j++) {
1125: PetscInt colT = colsT[jT * NkTrace] / NkTrace;
1126: PetscInt col = colF * (nTrace / NkTrace) + colT;
1127: const PetscScalar *vals;
1129: for (il = 0; il < dT; il++) {
1130: PetscReal val = 0.;
1131: for (jl = 0; jl < NkTrace; jl++) val += projTstar[il * NkTrace + jl] * PetscRealPart(valsT[jT * NkTrace + jl]);
1132: workT[il] = val;
1133: }
1134: if (kTrace < 0) {
1135: for (il = 0; il < dT; il++) workT2[il] = workT[il];
1136: PetscCall(PetscDTAltVStar(dim, PetscAbsInt(kTrace), 1, workT2, workT));
1137: }
1139: for (il = 0; il < Nk; il++) {
1140: PetscReal val = 0.;
1141: for (jl = 0; jl < dT; jl++) val += sign * wedgeMat[il * dT + jl] * workT[jl];
1142: work[il] = val;
1143: }
1144: if (k < 0) {
1145: PetscCall(PetscDTAltVStar(dim, PetscAbsInt(k), -1, work, workstar));
1146: #if defined(PETSC_USE_COMPLEX)
1147: for (l = 0; l < Nk; l++) workS[l] = workstar[l];
1148: vals = &workS[0];
1149: #else
1150: vals = &workstar[0];
1151: #endif
1152: } else {
1153: #if defined(PETSC_USE_COMPLEX)
1154: for (l = 0; l < Nk; l++) workS[l] = work[l];
1155: vals = &workS[0];
1156: #else
1157: vals = &work[0];
1158: #endif
1159: }
1160: for (l = 0; l < Nk; l++) PetscCall(MatSetValue(prod, i, col * Nk + l, vals[l], INSERT_VALUES)); /* Nk */
1161: } /* jT */
1162: } /* jF */
1163: PetscCall(MatRestoreRow(trace, iT, &ncolsT, &colsT, &valsT));
1164: } /* iT */
1165: PetscCall(MatRestoreRow(fiber, iF, &ncolsF, &colsF, &valsF));
1166: } /* iF */
1167: PetscCall(PetscFree(wedgeMat));
1168: PetscCall(PetscFree4(projT, projF, projTstar, projFstar));
1169: PetscCall(PetscFree2(workT2, workF2));
1170: PetscCall(PetscFree5(workT, workF, work, workstar, workS));
1171: PetscCall(MatAssemblyBegin(prod, MAT_FINAL_ASSEMBLY));
1172: PetscCall(MatAssemblyEnd(prod, MAT_FINAL_ASSEMBLY));
1173: *product = prod;
1174: PetscFunctionReturn(PETSC_SUCCESS);
1175: }
1177: /* Union of quadrature points, with an attempt to identify common points in the two sets */
1178: static PetscErrorCode PetscQuadraturePointsMerge(PetscQuadrature quadA, PetscQuadrature quadB, PetscQuadrature *quadJoint, PetscInt *aToJoint[], PetscInt *bToJoint[])
1179: {
1180: PetscInt dimA, dimB;
1181: PetscInt nA, nB, nJoint, i, j, d;
1182: const PetscReal *pointsA;
1183: const PetscReal *pointsB;
1184: PetscReal *pointsJoint;
1185: PetscInt *aToJ, *bToJ;
1186: PetscQuadrature qJ;
1188: PetscFunctionBegin;
1189: PetscCall(PetscQuadratureGetData(quadA, &dimA, NULL, &nA, &pointsA, NULL));
1190: PetscCall(PetscQuadratureGetData(quadB, &dimB, NULL, &nB, &pointsB, NULL));
1191: PetscCheck(dimA == dimB, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Quadrature points must be in the same dimension");
1192: nJoint = nA;
1193: PetscCall(PetscMalloc1(nA, &aToJ));
1194: for (i = 0; i < nA; i++) aToJ[i] = i;
1195: PetscCall(PetscMalloc1(nB, &bToJ));
1196: for (i = 0; i < nB; i++) {
1197: for (j = 0; j < nA; j++) {
1198: bToJ[i] = -1;
1199: for (d = 0; d < dimA; d++)
1200: if (PetscAbsReal(pointsB[i * dimA + d] - pointsA[j * dimA + d]) > PETSC_SMALL) break;
1201: if (d == dimA) {
1202: bToJ[i] = j;
1203: break;
1204: }
1205: }
1206: if (bToJ[i] == -1) bToJ[i] = nJoint++;
1207: }
1208: *aToJoint = aToJ;
1209: *bToJoint = bToJ;
1210: PetscCall(PetscMalloc1(nJoint * dimA, &pointsJoint));
1211: PetscCall(PetscArraycpy(pointsJoint, pointsA, nA * dimA));
1212: for (i = 0; i < nB; i++) {
1213: if (bToJ[i] >= nA) {
1214: for (d = 0; d < dimA; d++) pointsJoint[bToJ[i] * dimA + d] = pointsB[i * dimA + d];
1215: }
1216: }
1217: PetscCall(PetscQuadratureCreate(PETSC_COMM_SELF, &qJ));
1218: PetscCall(PetscQuadratureSetData(qJ, dimA, 0, nJoint, pointsJoint, NULL));
1219: *quadJoint = qJ;
1220: PetscFunctionReturn(PETSC_SUCCESS);
1221: }
1223: /* Matrices matA and matB are both quadrature -> dof matrices: produce a matrix that is joint quadrature -> union of
1224: * dofs, where the joint quadrature was produced by PetscQuadraturePointsMerge */
1225: static PetscErrorCode MatricesMerge(Mat matA, Mat matB, PetscInt dim, PetscInt k, PetscInt numMerged, const PetscInt aToMerged[], const PetscInt bToMerged[], Mat *matMerged)
1226: {
1227: PetscInt m, n, mA, nA, mB, nB, Nk, i, j, l;
1228: Mat M;
1229: PetscInt *nnz;
1230: PetscInt maxnnz;
1231: PetscInt *work;
1233: PetscFunctionBegin;
1234: PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(k), &Nk));
1235: PetscCall(MatGetSize(matA, &mA, &nA));
1236: PetscCheck(nA % Nk == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "matA column space not a multiple of k-form size");
1237: PetscCall(MatGetSize(matB, &mB, &nB));
1238: PetscCheck(nB % Nk == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "matB column space not a multiple of k-form size");
1239: m = mA + mB;
1240: n = numMerged * Nk;
1241: PetscCall(PetscMalloc1(m, &nnz));
1242: maxnnz = 0;
1243: for (i = 0; i < mA; i++) {
1244: PetscCall(MatGetRow(matA, i, &nnz[i], NULL, NULL));
1245: PetscCheck(nnz[i] % Nk == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "nonzeros in matA are not in k-form size blocks");
1246: maxnnz = PetscMax(maxnnz, nnz[i]);
1247: }
1248: for (i = 0; i < mB; i++) {
1249: PetscCall(MatGetRow(matB, i, &nnz[i + mA], NULL, NULL));
1250: PetscCheck(nnz[i + mA] % Nk == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "nonzeros in matB are not in k-form size blocks");
1251: maxnnz = PetscMax(maxnnz, nnz[i + mA]);
1252: }
1253: PetscCall(MatCreateSeqAIJ(PETSC_COMM_SELF, m, n, 0, nnz, &M));
1254: PetscCall(PetscObjectSetOptionsPrefix((PetscObject)M, "altv_"));
1255: PetscCall(PetscFree(nnz));
1256: /* reasoning about which points each dof needs depends on having zeros computed at points preserved */
1257: PetscCall(MatSetOption(M, MAT_IGNORE_ZERO_ENTRIES, PETSC_FALSE));
1258: PetscCall(PetscMalloc1(maxnnz, &work));
1259: for (i = 0; i < mA; i++) {
1260: const PetscInt *cols;
1261: const PetscScalar *vals;
1262: PetscInt nCols;
1263: PetscCall(MatGetRow(matA, i, &nCols, &cols, &vals));
1264: for (j = 0; j < nCols / Nk; j++) {
1265: PetscInt newCol = aToMerged[cols[j * Nk] / Nk];
1266: for (l = 0; l < Nk; l++) work[j * Nk + l] = newCol * Nk + l;
1267: }
1268: PetscCall(MatSetValuesBlocked(M, 1, &i, nCols, work, vals, INSERT_VALUES));
1269: PetscCall(MatRestoreRow(matA, i, &nCols, &cols, &vals));
1270: }
1271: for (i = 0; i < mB; i++) {
1272: const PetscInt *cols;
1273: const PetscScalar *vals;
1275: PetscInt row = i + mA;
1276: PetscInt nCols;
1277: PetscCall(MatGetRow(matB, i, &nCols, &cols, &vals));
1278: for (j = 0; j < nCols / Nk; j++) {
1279: PetscInt newCol = bToMerged[cols[j * Nk] / Nk];
1280: for (l = 0; l < Nk; l++) work[j * Nk + l] = newCol * Nk + l;
1281: }
1282: PetscCall(MatSetValuesBlocked(M, 1, &row, nCols, work, vals, INSERT_VALUES));
1283: PetscCall(MatRestoreRow(matB, i, &nCols, &cols, &vals));
1284: }
1285: PetscCall(PetscFree(work));
1286: PetscCall(MatAssemblyBegin(M, MAT_FINAL_ASSEMBLY));
1287: PetscCall(MatAssemblyEnd(M, MAT_FINAL_ASSEMBLY));
1288: *matMerged = M;
1289: PetscFunctionReturn(PETSC_SUCCESS);
1290: }
1292: /* Take a dual space and product a segment space that has all the same specifications (trimmed, continuous, order,
1293: * node set), except for the form degree. For computing boundary dofs and for making tensor product spaces */
1294: static PetscErrorCode PetscDualSpaceCreateFacetSubspace_Lagrange(PetscDualSpace sp, DM K, PetscInt f, PetscInt k, PetscInt Ncopies, PetscBool interiorOnly, PetscDualSpace *bdsp)
1295: {
1296: PetscInt Nknew, Ncnew;
1297: PetscInt dim, pointDim = -1;
1298: PetscInt depth;
1299: DM dm;
1300: PetscDualSpace_Lag *newlag;
1302: PetscFunctionBegin;
1303: PetscCall(PetscDualSpaceGetDM(sp, &dm));
1304: PetscCall(DMGetDimension(dm, &dim));
1305: PetscCall(DMPlexGetDepth(dm, &depth));
1306: PetscCall(PetscDualSpaceDuplicate(sp, bdsp));
1307: PetscCall(PetscDualSpaceSetFormDegree(*bdsp, k));
1308: if (!K) {
1309: if (depth == dim) {
1310: DMPolytopeType ct;
1312: pointDim = dim - 1;
1313: PetscCall(DMPlexGetCellType(dm, f, &ct));
1314: PetscCall(DMPlexCreateReferenceCell(PETSC_COMM_SELF, ct, &K));
1315: } else if (depth == 1) {
1316: pointDim = 0;
1317: PetscCall(DMPlexCreateReferenceCell(PETSC_COMM_SELF, DM_POLYTOPE_POINT, &K));
1318: } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Unsupported interpolation state of reference element");
1319: } else {
1320: PetscCall(PetscObjectReference((PetscObject)K));
1321: PetscCall(DMGetDimension(K, &pointDim));
1322: }
1323: PetscCall(PetscDualSpaceSetDM(*bdsp, K));
1324: PetscCall(DMDestroy(&K));
1325: PetscCall(PetscDTBinomialInt(pointDim, PetscAbsInt(k), &Nknew));
1326: Ncnew = Nknew * Ncopies;
1327: PetscCall(PetscDualSpaceSetNumComponents(*bdsp, Ncnew));
1328: newlag = (PetscDualSpace_Lag *)(*bdsp)->data;
1329: newlag->interiorOnly = interiorOnly;
1330: PetscCall(PetscDualSpaceSetUp(*bdsp));
1331: PetscFunctionReturn(PETSC_SUCCESS);
1332: }
1334: /* Construct simplex nodes from a nodefamily, add Nk dof vectors of length Nk at each node.
1335: * Return the (quadrature, matrix) form of the dofs and the nodeIndices form as well.
1336: *
1337: * Sometimes we want a set of nodes to be contained in the interior of the element,
1338: * even when the node scheme puts nodes on the boundaries. numNodeSkip tells
1339: * the routine how many "layers" of nodes need to be skipped.
1340: * */
1341: static PetscErrorCode PetscDualSpaceLagrangeCreateSimplexNodeMat(Petsc1DNodeFamily nodeFamily, PetscInt dim, PetscInt sum, PetscInt Nk, PetscInt numNodeSkip, PetscQuadrature *iNodes, Mat *iMat, PetscLagNodeIndices *nodeIndices)
1342: {
1343: PetscReal *extraNodeCoords, *nodeCoords;
1344: PetscInt nNodes, nExtraNodes;
1345: PetscInt i, j, k, extraSum = sum + numNodeSkip * (1 + dim);
1346: PetscQuadrature intNodes;
1347: Mat intMat;
1348: PetscLagNodeIndices ni;
1350: PetscFunctionBegin;
1351: PetscCall(PetscDTBinomialInt(dim + sum, dim, &nNodes));
1352: PetscCall(PetscDTBinomialInt(dim + extraSum, dim, &nExtraNodes));
1354: PetscCall(PetscMalloc1(dim * nExtraNodes, &extraNodeCoords));
1355: PetscCall(PetscNew(&ni));
1356: ni->nodeIdxDim = dim + 1;
1357: ni->nodeVecDim = Nk;
1358: ni->nNodes = nNodes * Nk;
1359: ni->refct = 1;
1360: PetscCall(PetscMalloc1(nNodes * Nk * (dim + 1), &ni->nodeIdx));
1361: PetscCall(PetscMalloc1(nNodes * Nk * Nk, &ni->nodeVec));
1362: for (i = 0; i < nNodes; i++)
1363: for (j = 0; j < Nk; j++)
1364: for (k = 0; k < Nk; k++) ni->nodeVec[(i * Nk + j) * Nk + k] = (j == k) ? 1. : 0.;
1365: PetscCall(Petsc1DNodeFamilyComputeSimplexNodes(nodeFamily, dim, extraSum, extraNodeCoords));
1366: if (numNodeSkip) {
1367: PetscInt k;
1368: PetscInt *tup;
1370: PetscCall(PetscMalloc1(dim * nNodes, &nodeCoords));
1371: PetscCall(PetscMalloc1(dim + 1, &tup));
1372: for (k = 0; k < nNodes; k++) {
1373: PetscInt j, c;
1374: PetscInt index;
1376: PetscCall(PetscDTIndexToBary(dim + 1, sum, k, tup));
1377: for (j = 0; j < dim + 1; j++) tup[j] += numNodeSkip;
1378: for (c = 0; c < Nk; c++) {
1379: for (j = 0; j < dim + 1; j++) ni->nodeIdx[(k * Nk + c) * (dim + 1) + j] = tup[j] + 1;
1380: }
1381: PetscCall(PetscDTBaryToIndex(dim + 1, extraSum, tup, &index));
1382: for (j = 0; j < dim; j++) nodeCoords[k * dim + j] = extraNodeCoords[index * dim + j];
1383: }
1384: PetscCall(PetscFree(tup));
1385: PetscCall(PetscFree(extraNodeCoords));
1386: } else {
1387: PetscInt k;
1388: PetscInt *tup;
1390: nodeCoords = extraNodeCoords;
1391: PetscCall(PetscMalloc1(dim + 1, &tup));
1392: for (k = 0; k < nNodes; k++) {
1393: PetscInt j, c;
1395: PetscCall(PetscDTIndexToBary(dim + 1, sum, k, tup));
1396: for (c = 0; c < Nk; c++) {
1397: for (j = 0; j < dim + 1; j++) {
1398: /* barycentric indices can have zeros, but we don't want to push forward zeros because it makes it harder to
1399: * determine which nodes correspond to which under symmetries, so we increase by 1. This is fine
1400: * because the nodeIdx coordinates don't have any meaning other than helping to identify symmetries */
1401: ni->nodeIdx[(k * Nk + c) * (dim + 1) + j] = tup[j] + 1;
1402: }
1403: }
1404: }
1405: PetscCall(PetscFree(tup));
1406: }
1407: PetscCall(PetscQuadratureCreate(PETSC_COMM_SELF, &intNodes));
1408: PetscCall(PetscQuadratureSetData(intNodes, dim, 0, nNodes, nodeCoords, NULL));
1409: PetscCall(MatCreateSeqAIJ(PETSC_COMM_SELF, nNodes * Nk, nNodes * Nk, Nk, NULL, &intMat));
1410: PetscCall(PetscObjectSetOptionsPrefix((PetscObject)intMat, "lag_"));
1411: PetscCall(MatSetOption(intMat, MAT_IGNORE_ZERO_ENTRIES, PETSC_FALSE));
1412: for (j = 0; j < nNodes * Nk; j++) {
1413: PetscInt rem = j % Nk;
1414: PetscInt a, aprev = j - rem;
1415: PetscInt anext = aprev + Nk;
1417: for (a = aprev; a < anext; a++) PetscCall(MatSetValue(intMat, j, a, (a == j) ? 1. : 0., INSERT_VALUES));
1418: }
1419: PetscCall(MatAssemblyBegin(intMat, MAT_FINAL_ASSEMBLY));
1420: PetscCall(MatAssemblyEnd(intMat, MAT_FINAL_ASSEMBLY));
1421: *iNodes = intNodes;
1422: *iMat = intMat;
1423: *nodeIndices = ni;
1424: PetscFunctionReturn(PETSC_SUCCESS);
1425: }
1427: /* once the nodeIndices have been created for the interior of the reference cell, and for all of the boundary cells,
1428: * push forward the boundary dofs and concatenate them into the full node indices for the dual space */
1429: static PetscErrorCode PetscDualSpaceLagrangeCreateAllNodeIdx(PetscDualSpace sp)
1430: {
1431: DM dm;
1432: PetscInt dim, nDofs;
1433: PetscSection section;
1434: PetscInt pStart, pEnd, p;
1435: PetscInt formDegree, Nk;
1436: PetscInt nodeIdxDim, spintdim;
1437: PetscDualSpace_Lag *lag;
1438: PetscLagNodeIndices ni, verti;
1440: PetscFunctionBegin;
1441: lag = (PetscDualSpace_Lag *)sp->data;
1442: verti = lag->vertIndices;
1443: PetscCall(PetscDualSpaceGetDM(sp, &dm));
1444: PetscCall(DMGetDimension(dm, &dim));
1445: PetscCall(PetscDualSpaceGetFormDegree(sp, &formDegree));
1446: PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(formDegree), &Nk));
1447: PetscCall(PetscDualSpaceGetSection(sp, §ion));
1448: PetscCall(PetscSectionGetStorageSize(section, &nDofs));
1449: PetscCall(PetscNew(&ni));
1450: ni->nodeIdxDim = nodeIdxDim = verti->nodeIdxDim;
1451: ni->nodeVecDim = Nk;
1452: ni->nNodes = nDofs;
1453: ni->refct = 1;
1454: PetscCall(PetscMalloc1(nodeIdxDim * nDofs, &ni->nodeIdx));
1455: PetscCall(PetscMalloc1(Nk * nDofs, &ni->nodeVec));
1456: PetscCall(DMPlexGetChart(dm, &pStart, &pEnd));
1457: PetscCall(PetscSectionGetDof(section, 0, &spintdim));
1458: if (spintdim) {
1459: PetscCall(PetscArraycpy(ni->nodeIdx, lag->intNodeIndices->nodeIdx, spintdim * nodeIdxDim));
1460: PetscCall(PetscArraycpy(ni->nodeVec, lag->intNodeIndices->nodeVec, spintdim * Nk));
1461: }
1462: for (p = pStart + 1; p < pEnd; p++) {
1463: PetscDualSpace psp = sp->pointSpaces[p];
1464: PetscDualSpace_Lag *plag;
1465: PetscInt dof, off;
1467: PetscCall(PetscSectionGetDof(section, p, &dof));
1468: if (!dof) continue;
1469: plag = (PetscDualSpace_Lag *)psp->data;
1470: PetscCall(PetscSectionGetOffset(section, p, &off));
1471: PetscCall(PetscLagNodeIndicesPushForward(dm, verti, p, plag->vertIndices, plag->intNodeIndices, 0, formDegree, &ni->nodeIdx[off * nodeIdxDim], &ni->nodeVec[off * Nk]));
1472: }
1473: lag->allNodeIndices = ni;
1474: PetscFunctionReturn(PETSC_SUCCESS);
1475: }
1477: /* once the (quadrature, Matrix) forms of the dofs have been created for the interior of the
1478: * reference cell and for the boundary cells, jk
1479: * push forward the boundary data and concatenate them into the full (quadrature, matrix) data
1480: * for the dual space */
1481: static PetscErrorCode PetscDualSpaceCreateAllDataFromInteriorData(PetscDualSpace sp)
1482: {
1483: DM dm;
1484: PetscSection section;
1485: PetscInt pStart, pEnd, p, k, Nk, dim, Nc;
1486: PetscInt nNodes;
1487: PetscInt countNodes;
1488: Mat allMat;
1489: PetscQuadrature allNodes;
1490: PetscInt nDofs;
1491: PetscInt maxNzforms, j;
1492: PetscScalar *work;
1493: PetscReal *L, *J, *Jinv, *v0, *pv0;
1494: PetscInt *iwork;
1495: PetscReal *nodes;
1497: PetscFunctionBegin;
1498: PetscCall(PetscDualSpaceGetDM(sp, &dm));
1499: PetscCall(DMGetDimension(dm, &dim));
1500: PetscCall(PetscDualSpaceGetSection(sp, §ion));
1501: PetscCall(PetscSectionGetStorageSize(section, &nDofs));
1502: PetscCall(DMPlexGetChart(dm, &pStart, &pEnd));
1503: PetscCall(PetscDualSpaceGetFormDegree(sp, &k));
1504: PetscCall(PetscDualSpaceGetNumComponents(sp, &Nc));
1505: PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(k), &Nk));
1506: for (p = pStart, nNodes = 0, maxNzforms = 0; p < pEnd; p++) {
1507: PetscDualSpace psp;
1508: DM pdm;
1509: PetscInt pdim, pNk;
1510: PetscQuadrature intNodes;
1511: Mat intMat;
1513: PetscCall(PetscDualSpaceGetPointSubspace(sp, p, &psp));
1514: if (!psp) continue;
1515: PetscCall(PetscDualSpaceGetDM(psp, &pdm));
1516: PetscCall(DMGetDimension(pdm, &pdim));
1517: if (pdim < PetscAbsInt(k)) continue;
1518: PetscCall(PetscDTBinomialInt(pdim, PetscAbsInt(k), &pNk));
1519: PetscCall(PetscDualSpaceGetInteriorData(psp, &intNodes, &intMat));
1520: if (intNodes) {
1521: PetscInt nNodesp;
1523: PetscCall(PetscQuadratureGetData(intNodes, NULL, NULL, &nNodesp, NULL, NULL));
1524: nNodes += nNodesp;
1525: }
1526: if (intMat) {
1527: PetscInt maxNzsp;
1528: PetscInt maxNzformsp;
1530: PetscCall(MatSeqAIJGetMaxRowNonzeros(intMat, &maxNzsp));
1531: PetscCheck(maxNzsp % pNk == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "interior matrix is not laid out as blocks of k-forms");
1532: maxNzformsp = maxNzsp / pNk;
1533: maxNzforms = PetscMax(maxNzforms, maxNzformsp);
1534: }
1535: }
1536: PetscCall(MatCreateSeqAIJ(PETSC_COMM_SELF, nDofs, nNodes * Nc, maxNzforms * Nk, NULL, &allMat));
1537: PetscCall(PetscObjectSetOptionsPrefix((PetscObject)allMat, "ds_"));
1538: PetscCall(MatSetOption(allMat, MAT_IGNORE_ZERO_ENTRIES, PETSC_FALSE));
1539: PetscCall(PetscMalloc7(dim, &v0, dim, &pv0, dim * dim, &J, dim * dim, &Jinv, Nk * Nk, &L, maxNzforms * Nk, &work, maxNzforms * Nk, &iwork));
1540: for (j = 0; j < dim; j++) pv0[j] = -1.;
1541: PetscCall(PetscMalloc1(dim * nNodes, &nodes));
1542: for (p = pStart, countNodes = 0; p < pEnd; p++) {
1543: PetscDualSpace psp;
1544: PetscQuadrature intNodes;
1545: DM pdm;
1546: PetscInt pdim, pNk;
1547: PetscInt countNodesIn = countNodes;
1548: PetscReal detJ;
1549: Mat intMat;
1551: PetscCall(PetscDualSpaceGetPointSubspace(sp, p, &psp));
1552: if (!psp) continue;
1553: PetscCall(PetscDualSpaceGetDM(psp, &pdm));
1554: PetscCall(DMGetDimension(pdm, &pdim));
1555: if (pdim < PetscAbsInt(k)) continue;
1556: PetscCall(PetscDualSpaceGetInteriorData(psp, &intNodes, &intMat));
1557: if (intNodes == NULL && intMat == NULL) continue;
1558: PetscCall(PetscDTBinomialInt(pdim, PetscAbsInt(k), &pNk));
1559: if (p) {
1560: PetscCall(DMPlexComputeCellGeometryAffineFEM(dm, p, v0, J, Jinv, &detJ));
1561: } else { /* identity */
1562: PetscInt i, j;
1564: for (i = 0; i < dim; i++)
1565: for (j = 0; j < dim; j++) J[i * dim + j] = Jinv[i * dim + j] = 0.;
1566: for (i = 0; i < dim; i++) J[i * dim + i] = Jinv[i * dim + i] = 1.;
1567: for (i = 0; i < dim; i++) v0[i] = -1.;
1568: }
1569: if (pdim != dim) { /* compactify Jacobian */
1570: PetscInt i, j;
1572: for (i = 0; i < dim; i++)
1573: for (j = 0; j < pdim; j++) J[i * pdim + j] = J[i * dim + j];
1574: }
1575: PetscCall(PetscDTAltVPullbackMatrix(pdim, dim, J, k, L));
1576: if (intNodes) { /* push forward quadrature locations by the affine transformation */
1577: PetscInt nNodesp;
1578: const PetscReal *nodesp;
1579: PetscInt j;
1581: PetscCall(PetscQuadratureGetData(intNodes, NULL, NULL, &nNodesp, &nodesp, NULL));
1582: for (j = 0; j < nNodesp; j++, countNodes++) {
1583: PetscInt d, e;
1585: for (d = 0; d < dim; d++) {
1586: nodes[countNodes * dim + d] = v0[d];
1587: for (e = 0; e < pdim; e++) nodes[countNodes * dim + d] += J[d * pdim + e] * (nodesp[j * pdim + e] - pv0[e]);
1588: }
1589: }
1590: }
1591: if (intMat) {
1592: PetscInt nrows;
1593: PetscInt off;
1595: PetscCall(PetscSectionGetDof(section, p, &nrows));
1596: PetscCall(PetscSectionGetOffset(section, p, &off));
1597: for (j = 0; j < nrows; j++) {
1598: PetscInt ncols;
1599: const PetscInt *cols;
1600: const PetscScalar *vals;
1601: PetscInt l, d, e;
1602: PetscInt row = j + off;
1604: PetscCall(MatGetRow(intMat, j, &ncols, &cols, &vals));
1605: PetscCheck(ncols % pNk == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "interior matrix is not laid out as blocks of k-forms");
1606: for (l = 0; l < ncols / pNk; l++) {
1607: PetscInt blockcol;
1609: 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");
1610: blockcol = cols[l * pNk] / pNk;
1611: for (d = 0; d < Nk; d++) iwork[l * Nk + d] = (blockcol + countNodesIn) * Nk + d;
1612: for (d = 0; d < Nk; d++) work[l * Nk + d] = 0.;
1613: for (d = 0; d < Nk; d++) {
1614: for (e = 0; e < pNk; e++) {
1615: /* "push forward" dof by pulling back a k-form to be evaluated on the point: multiply on the right by L */
1616: work[l * Nk + d] += vals[l * pNk + e] * L[e * Nk + d];
1617: }
1618: }
1619: }
1620: PetscCall(MatSetValues(allMat, 1, &row, (ncols / pNk) * Nk, iwork, work, INSERT_VALUES));
1621: PetscCall(MatRestoreRow(intMat, j, &ncols, &cols, &vals));
1622: }
1623: }
1624: }
1625: PetscCall(MatAssemblyBegin(allMat, MAT_FINAL_ASSEMBLY));
1626: PetscCall(MatAssemblyEnd(allMat, MAT_FINAL_ASSEMBLY));
1627: PetscCall(PetscQuadratureCreate(PETSC_COMM_SELF, &allNodes));
1628: PetscCall(PetscQuadratureSetData(allNodes, dim, 0, nNodes, nodes, NULL));
1629: PetscCall(PetscFree7(v0, pv0, J, Jinv, L, work, iwork));
1630: PetscCall(MatDestroy(&sp->allMat));
1631: sp->allMat = allMat;
1632: PetscCall(PetscQuadratureDestroy(&sp->allNodes));
1633: sp->allNodes = allNodes;
1634: PetscFunctionReturn(PETSC_SUCCESS);
1635: }
1637: static PetscErrorCode PetscDualSpaceComputeFunctionalsFromAllData_Moments(PetscDualSpace sp)
1638: {
1639: Mat allMat;
1640: PetscInt momentOrder, i;
1641: PetscBool tensor = PETSC_FALSE;
1642: const PetscReal *weights;
1643: PetscScalar *array;
1644: PetscInt nDofs;
1645: PetscInt dim, Nc;
1646: DM dm;
1647: PetscQuadrature allNodes;
1648: PetscInt nNodes;
1650: PetscFunctionBegin;
1651: PetscCall(PetscDualSpaceGetDM(sp, &dm));
1652: PetscCall(DMGetDimension(dm, &dim));
1653: PetscCall(PetscDualSpaceGetNumComponents(sp, &Nc));
1654: PetscCall(PetscDualSpaceGetAllData(sp, &allNodes, &allMat));
1655: PetscCall(MatGetSize(allMat, &nDofs, NULL));
1656: PetscCheck(nDofs == 1, PETSC_COMM_SELF, PETSC_ERR_SUP, "We do not yet support moments beyond P0, nDofs == %" PetscInt_FMT, nDofs);
1657: PetscCall(PetscMalloc1(nDofs, &sp->functional));
1658: PetscCall(PetscDualSpaceLagrangeGetMomentOrder(sp, &momentOrder));
1659: PetscCall(PetscDualSpaceLagrangeGetTensor(sp, &tensor));
1660: if (!tensor) PetscCall(PetscDTStroudConicalQuadrature(dim, Nc, PetscMax(momentOrder + 1, 1), -1.0, 1.0, &sp->functional[0]));
1661: else PetscCall(PetscDTGaussTensorQuadrature(dim, Nc, PetscMax(momentOrder + 1, 1), -1.0, 1.0, &sp->functional[0]));
1662: /* Need to replace allNodes and allMat */
1663: PetscCall(PetscObjectReference((PetscObject)sp->functional[0]));
1664: PetscCall(PetscQuadratureDestroy(&sp->allNodes));
1665: sp->allNodes = sp->functional[0];
1666: PetscCall(PetscQuadratureGetData(sp->allNodes, NULL, NULL, &nNodes, NULL, &weights));
1667: PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, nDofs, nNodes * Nc, NULL, &allMat));
1668: PetscCall(PetscObjectSetOptionsPrefix((PetscObject)allMat, "ds_"));
1669: PetscCall(MatDenseGetArrayWrite(allMat, &array));
1670: for (i = 0; i < nNodes * Nc; ++i) array[i] = weights[i];
1671: PetscCall(MatDenseRestoreArrayWrite(allMat, &array));
1672: PetscCall(MatAssemblyBegin(allMat, MAT_FINAL_ASSEMBLY));
1673: PetscCall(MatAssemblyEnd(allMat, MAT_FINAL_ASSEMBLY));
1674: PetscCall(MatDestroy(&sp->allMat));
1675: sp->allMat = allMat;
1676: PetscFunctionReturn(PETSC_SUCCESS);
1677: }
1679: /* rather than trying to get all data from the functionals, we create
1680: * the functionals from rows of the quadrature -> dof matrix.
1681: *
1682: * Ideally most of the uses of PetscDualSpace in PetscFE will switch
1683: * to using intMat and allMat, so that the individual functionals
1684: * don't need to be constructed at all */
1685: PETSC_INTERN PetscErrorCode PetscDualSpaceComputeFunctionalsFromAllData(PetscDualSpace sp)
1686: {
1687: PetscQuadrature allNodes;
1688: Mat allMat;
1689: PetscInt nDofs;
1690: PetscInt dim, Nc, f;
1691: DM dm;
1692: PetscInt nNodes, spdim;
1693: const PetscReal *nodes = NULL;
1694: PetscSection section;
1695: PetscBool useMoments;
1697: PetscFunctionBegin;
1698: PetscCall(PetscDualSpaceGetDM(sp, &dm));
1699: PetscCall(DMGetDimension(dm, &dim));
1700: PetscCall(PetscDualSpaceGetNumComponents(sp, &Nc));
1701: PetscCall(PetscDualSpaceGetAllData(sp, &allNodes, &allMat));
1702: nNodes = 0;
1703: if (allNodes) PetscCall(PetscQuadratureGetData(allNodes, NULL, NULL, &nNodes, &nodes, NULL));
1704: PetscCall(MatGetSize(allMat, &nDofs, NULL));
1705: PetscCall(PetscDualSpaceGetSection(sp, §ion));
1706: PetscCall(PetscSectionGetStorageSize(section, &spdim));
1707: PetscCheck(spdim == nDofs, PETSC_COMM_SELF, PETSC_ERR_PLIB, "incompatible all matrix size");
1708: PetscCall(PetscMalloc1(nDofs, &sp->functional));
1709: PetscCall(PetscDualSpaceLagrangeGetUseMoments(sp, &useMoments));
1710: for (f = 0; f < nDofs; f++) {
1711: PetscInt ncols, c;
1712: const PetscInt *cols;
1713: const PetscScalar *vals;
1714: PetscReal *nodesf;
1715: PetscReal *weightsf;
1716: PetscInt nNodesf;
1717: PetscInt countNodes;
1719: PetscCall(MatGetRow(allMat, f, &ncols, &cols, &vals));
1720: for (c = 1, nNodesf = 1; c < ncols; c++) {
1721: if ((cols[c] / Nc) != (cols[c - 1] / Nc)) nNodesf++;
1722: }
1723: PetscCall(PetscMalloc1(dim * nNodesf, &nodesf));
1724: PetscCall(PetscMalloc1(Nc * nNodesf, &weightsf));
1725: for (c = 0, countNodes = 0; c < ncols; c++) {
1726: if (!c || ((cols[c] / Nc) != (cols[c - 1] / Nc))) {
1727: PetscInt d;
1729: for (d = 0; d < Nc; d++) weightsf[countNodes * Nc + d] = 0.;
1730: for (d = 0; d < dim; d++) nodesf[countNodes * dim + d] = nodes[(cols[c] / Nc) * dim + d];
1731: countNodes++;
1732: }
1733: weightsf[(countNodes - 1) * Nc + (cols[c] % Nc)] = PetscRealPart(vals[c]);
1734: }
1735: PetscCall(PetscQuadratureCreate(PETSC_COMM_SELF, &sp->functional[f]));
1736: PetscCall(PetscQuadratureSetData(sp->functional[f], dim, Nc, nNodesf, nodesf, weightsf));
1737: PetscCall(MatRestoreRow(allMat, f, &ncols, &cols, &vals));
1738: }
1739: PetscFunctionReturn(PETSC_SUCCESS);
1740: }
1742: /* check if a cell is a tensor product of the segment with a facet,
1743: * specifically checking if f and f2 can be the "endpoints" (like the triangles
1744: * at either end of a wedge) */
1745: static PetscErrorCode DMPlexPointIsTensor_Internal_Given(DM dm, PetscInt p, PetscInt f, PetscInt f2, PetscBool *isTensor)
1746: {
1747: PetscInt coneSize, c;
1748: const PetscInt *cone;
1749: const PetscInt *fCone;
1750: const PetscInt *f2Cone;
1751: PetscInt fs[2];
1752: PetscInt meetSize, nmeet;
1753: const PetscInt *meet;
1755: PetscFunctionBegin;
1756: fs[0] = f;
1757: fs[1] = f2;
1758: PetscCall(DMPlexGetMeet(dm, 2, fs, &meetSize, &meet));
1759: nmeet = meetSize;
1760: PetscCall(DMPlexRestoreMeet(dm, 2, fs, &meetSize, &meet));
1761: /* two points that have a non-empty meet cannot be at opposite ends of a cell */
1762: if (nmeet) {
1763: *isTensor = PETSC_FALSE;
1764: PetscFunctionReturn(PETSC_SUCCESS);
1765: }
1766: PetscCall(DMPlexGetConeSize(dm, p, &coneSize));
1767: PetscCall(DMPlexGetCone(dm, p, &cone));
1768: PetscCall(DMPlexGetCone(dm, f, &fCone));
1769: PetscCall(DMPlexGetCone(dm, f2, &f2Cone));
1770: for (c = 0; c < coneSize; c++) {
1771: PetscInt e, ef;
1772: PetscInt d = -1, d2 = -1;
1773: PetscInt dcount, d2count;
1774: PetscInt t = cone[c];
1775: PetscInt tConeSize;
1776: PetscBool tIsTensor;
1777: const PetscInt *tCone;
1779: if (t == f || t == f2) continue;
1780: /* for every other facet in the cone, check that is has
1781: * one ridge in common with each end */
1782: PetscCall(DMPlexGetConeSize(dm, t, &tConeSize));
1783: PetscCall(DMPlexGetCone(dm, t, &tCone));
1785: dcount = 0;
1786: d2count = 0;
1787: for (e = 0; e < tConeSize; e++) {
1788: PetscInt q = tCone[e];
1789: for (ef = 0; ef < coneSize - 2; ef++) {
1790: if (fCone[ef] == q) {
1791: if (dcount) {
1792: *isTensor = PETSC_FALSE;
1793: PetscFunctionReturn(PETSC_SUCCESS);
1794: }
1795: d = q;
1796: dcount++;
1797: } else if (f2Cone[ef] == q) {
1798: if (d2count) {
1799: *isTensor = PETSC_FALSE;
1800: PetscFunctionReturn(PETSC_SUCCESS);
1801: }
1802: d2 = q;
1803: d2count++;
1804: }
1805: }
1806: }
1807: /* if the whole cell is a tensor with the segment, then this
1808: * facet should be a tensor with the segment */
1809: PetscCall(DMPlexPointIsTensor_Internal_Given(dm, t, d, d2, &tIsTensor));
1810: if (!tIsTensor) {
1811: *isTensor = PETSC_FALSE;
1812: PetscFunctionReturn(PETSC_SUCCESS);
1813: }
1814: }
1815: *isTensor = PETSC_TRUE;
1816: PetscFunctionReturn(PETSC_SUCCESS);
1817: }
1819: /* determine if a cell is a tensor with a segment by looping over pairs of facets to find a pair
1820: * that could be the opposite ends */
1821: static PetscErrorCode DMPlexPointIsTensor_Internal(DM dm, PetscInt p, PetscBool *isTensor, PetscInt *endA, PetscInt *endB)
1822: {
1823: PetscInt coneSize, c, c2;
1824: const PetscInt *cone;
1826: PetscFunctionBegin;
1827: PetscCall(DMPlexGetConeSize(dm, p, &coneSize));
1828: if (!coneSize) {
1829: if (isTensor) *isTensor = PETSC_FALSE;
1830: if (endA) *endA = -1;
1831: if (endB) *endB = -1;
1832: }
1833: PetscCall(DMPlexGetCone(dm, p, &cone));
1834: for (c = 0; c < coneSize; c++) {
1835: PetscInt f = cone[c];
1836: PetscInt fConeSize;
1838: PetscCall(DMPlexGetConeSize(dm, f, &fConeSize));
1839: if (fConeSize != coneSize - 2) continue;
1841: for (c2 = c + 1; c2 < coneSize; c2++) {
1842: PetscInt f2 = cone[c2];
1843: PetscBool isTensorff2;
1844: PetscInt f2ConeSize;
1846: PetscCall(DMPlexGetConeSize(dm, f2, &f2ConeSize));
1847: if (f2ConeSize != coneSize - 2) continue;
1849: PetscCall(DMPlexPointIsTensor_Internal_Given(dm, p, f, f2, &isTensorff2));
1850: if (isTensorff2) {
1851: if (isTensor) *isTensor = PETSC_TRUE;
1852: if (endA) *endA = f;
1853: if (endB) *endB = f2;
1854: PetscFunctionReturn(PETSC_SUCCESS);
1855: }
1856: }
1857: }
1858: if (isTensor) *isTensor = PETSC_FALSE;
1859: if (endA) *endA = -1;
1860: if (endB) *endB = -1;
1861: PetscFunctionReturn(PETSC_SUCCESS);
1862: }
1864: /* determine if a cell is a tensor with a segment by looping over pairs of facets to find a pair
1865: * that could be the opposite ends */
1866: static PetscErrorCode DMPlexPointIsTensor(DM dm, PetscInt p, PetscBool *isTensor, PetscInt *endA, PetscInt *endB)
1867: {
1868: DMPlexInterpolatedFlag interpolated;
1870: PetscFunctionBegin;
1871: PetscCall(DMPlexIsInterpolated(dm, &interpolated));
1872: PetscCheck(interpolated == DMPLEX_INTERPOLATED_FULL, PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONGSTATE, "Only for interpolated DMPlex's");
1873: PetscCall(DMPlexPointIsTensor_Internal(dm, p, isTensor, endA, endB));
1874: PetscFunctionReturn(PETSC_SUCCESS);
1875: }
1877: /* Let k = formDegree and k' = -sign(k) * dim + k. Transform a symmetric frame for k-forms on the biunit simplex into
1878: * a symmetric frame for k'-forms on the biunit simplex.
1879: *
1880: * A frame is "symmetric" if the pullback of every symmetry of the biunit simplex is a permutation of the frame.
1881: *
1882: * forms in the symmetric frame are used as dofs in the untrimmed simplex spaces. This way, symmetries of the
1883: * reference cell result in permutations of dofs grouped by node.
1884: *
1885: * Use T to transform dof matrices for k'-forms into dof matrices for k-forms as a block diagonal transformation on
1886: * the right.
1887: */
1888: static PetscErrorCode BiunitSimplexSymmetricFormTransformation(PetscInt dim, PetscInt formDegree, PetscReal T[])
1889: {
1890: PetscInt k = formDegree;
1891: PetscInt kd = k < 0 ? dim + k : k - dim;
1892: PetscInt Nk;
1893: PetscReal *biToEq, *eqToBi, *biToEqStar, *eqToBiStar;
1894: PetscInt fact;
1896: PetscFunctionBegin;
1897: PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(k), &Nk));
1898: PetscCall(PetscCalloc4(dim * dim, &biToEq, dim * dim, &eqToBi, Nk * Nk, &biToEqStar, Nk * Nk, &eqToBiStar));
1899: /* fill in biToEq: Jacobian of the transformation from the biunit simplex to the equilateral simplex */
1900: fact = 0;
1901: for (PetscInt i = 0; i < dim; i++) {
1902: biToEq[i * dim + i] = PetscSqrtReal(((PetscReal)i + 2.) / (2. * ((PetscReal)i + 1.)));
1903: fact += 4 * (i + 1);
1904: for (PetscInt j = i + 1; j < dim; j++) biToEq[i * dim + j] = PetscSqrtReal(1. / (PetscReal)fact);
1905: }
1906: /* fill in eqToBi: Jacobian of the transformation from the equilateral simplex to the biunit simplex */
1907: fact = 0;
1908: for (PetscInt j = 0; j < dim; j++) {
1909: eqToBi[j * dim + j] = PetscSqrtReal(2. * ((PetscReal)j + 1.) / ((PetscReal)j + 2));
1910: fact += j + 1;
1911: for (PetscInt i = 0; i < j; i++) eqToBi[i * dim + j] = -PetscSqrtReal(1. / (PetscReal)fact);
1912: }
1913: PetscCall(PetscDTAltVPullbackMatrix(dim, dim, biToEq, kd, biToEqStar));
1914: PetscCall(PetscDTAltVPullbackMatrix(dim, dim, eqToBi, k, eqToBiStar));
1915: /* product of pullbacks simulates the following steps
1916: *
1917: * 1. start with frame W = [w_1, w_2, ..., w_m] of k forms that is symmetric on the biunit simplex:
1918: if J is the Jacobian of a symmetry of the biunit simplex, then J_k* W = [J_k*w_1, ..., J_k*w_m]
1919: is a permutation of W.
1920: Even though a k' form --- a (dim - k) form represented by its Hodge star --- has the same geometric
1921: content as a k form, W is not a symmetric frame of k' forms on the biunit simplex. That's because,
1922: for general Jacobian J, J_k* != J_k'*.
1923: * 2. pullback W to the equilateral triangle using the k pullback, W_eq = eqToBi_k* W. All symmetries of the
1924: equilateral simplex have orthonormal Jacobians. For an orthonormal Jacobian O, J_k* = J_k'*, so W_eq is
1925: also a symmetric frame for k' forms on the equilateral simplex.
1926: 3. pullback W_eq back to the biunit simplex using the k' pulback, V = biToEq_k'* W_eq = biToEq_k'* eqToBi_k* W.
1927: V is a symmetric frame for k' forms on the biunit simplex.
1928: */
1929: for (PetscInt i = 0; i < Nk; i++) {
1930: for (PetscInt j = 0; j < Nk; j++) {
1931: PetscReal val = 0.;
1932: for (PetscInt k = 0; k < Nk; k++) val += biToEqStar[i * Nk + k] * eqToBiStar[k * Nk + j];
1933: T[i * Nk + j] = val;
1934: }
1935: }
1936: PetscCall(PetscFree4(biToEq, eqToBi, biToEqStar, eqToBiStar));
1937: PetscFunctionReturn(PETSC_SUCCESS);
1938: }
1940: /* permute a quadrature -> dof matrix so that its rows are in revlex order by nodeIdx */
1941: static PetscErrorCode MatPermuteByNodeIdx(Mat A, PetscLagNodeIndices ni, Mat *Aperm)
1942: {
1943: PetscInt m, n, i, j;
1944: PetscInt nodeIdxDim = ni->nodeIdxDim;
1945: PetscInt nodeVecDim = ni->nodeVecDim;
1946: PetscInt *perm;
1947: IS permIS;
1948: IS id;
1949: PetscInt *nIdxPerm;
1950: PetscReal *nVecPerm;
1952: PetscFunctionBegin;
1953: PetscCall(PetscLagNodeIndicesGetPermutation(ni, &perm));
1954: PetscCall(MatGetSize(A, &m, &n));
1955: PetscCall(PetscMalloc1(nodeIdxDim * m, &nIdxPerm));
1956: PetscCall(PetscMalloc1(nodeVecDim * m, &nVecPerm));
1957: for (i = 0; i < m; i++)
1958: for (j = 0; j < nodeIdxDim; j++) nIdxPerm[i * nodeIdxDim + j] = ni->nodeIdx[perm[i] * nodeIdxDim + j];
1959: for (i = 0; i < m; i++)
1960: for (j = 0; j < nodeVecDim; j++) nVecPerm[i * nodeVecDim + j] = ni->nodeVec[perm[i] * nodeVecDim + j];
1961: PetscCall(ISCreateGeneral(PETSC_COMM_SELF, m, perm, PETSC_USE_POINTER, &permIS));
1962: PetscCall(ISSetPermutation(permIS));
1963: PetscCall(ISCreateStride(PETSC_COMM_SELF, n, 0, 1, &id));
1964: PetscCall(ISSetPermutation(id));
1965: PetscCall(MatPermute(A, permIS, id, Aperm));
1966: PetscCall(ISDestroy(&permIS));
1967: PetscCall(ISDestroy(&id));
1968: for (i = 0; i < m; i++) perm[i] = i;
1969: PetscCall(PetscFree(ni->nodeIdx));
1970: PetscCall(PetscFree(ni->nodeVec));
1971: ni->nodeIdx = nIdxPerm;
1972: ni->nodeVec = nVecPerm;
1973: PetscFunctionReturn(PETSC_SUCCESS);
1974: }
1976: static PetscErrorCode PetscDualSpaceSetUp_Lagrange(PetscDualSpace sp)
1977: {
1978: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
1979: DM dm = sp->dm;
1980: DM dmint = NULL;
1981: PetscInt order;
1982: PetscInt Nc;
1983: MPI_Comm comm;
1984: PetscBool continuous;
1985: PetscSection section;
1986: PetscInt depth, dim, pStart, pEnd, cStart, cEnd, p, *pStratStart, *pStratEnd, d;
1987: PetscInt formDegree, Nk, Ncopies;
1988: PetscInt tensorf = -1, tensorf2 = -1;
1989: PetscBool tensorCell, tensorSpace;
1990: PetscBool uniform, trimmed;
1991: Petsc1DNodeFamily nodeFamily;
1992: PetscInt numNodeSkip;
1993: DMPlexInterpolatedFlag interpolated;
1994: PetscBool isbdm;
1996: PetscFunctionBegin;
1997: /* step 1: sanitize input */
1998: PetscCall(PetscObjectGetComm((PetscObject)sp, &comm));
1999: PetscCall(DMGetDimension(dm, &dim));
2000: PetscCall(PetscObjectTypeCompare((PetscObject)sp, PETSCDUALSPACEBDM, &isbdm));
2001: if (isbdm) {
2002: sp->k = -(dim - 1); /* form degree of H-div */
2003: PetscCall(PetscObjectChangeTypeName((PetscObject)sp, PETSCDUALSPACELAGRANGE));
2004: }
2005: PetscCall(PetscDualSpaceGetFormDegree(sp, &formDegree));
2006: PetscCheck(PetscAbsInt(formDegree) <= dim, comm, PETSC_ERR_ARG_OUTOFRANGE, "Form degree must be bounded by dimension");
2007: PetscCall(PetscDTBinomialInt(dim, PetscAbsInt(formDegree), &Nk));
2008: if (sp->Nc <= 0 && lag->numCopies > 0) sp->Nc = Nk * lag->numCopies;
2009: Nc = sp->Nc;
2010: PetscCheck(Nc % Nk == 0, comm, PETSC_ERR_ARG_INCOMP, "Number of components is not a multiple of form degree size");
2011: if (lag->numCopies <= 0) lag->numCopies = Nc / Nk;
2012: Ncopies = lag->numCopies;
2013: PetscCheck(Nc / Nk == Ncopies, comm, PETSC_ERR_ARG_INCOMP, "Number of copies * (dim choose k) != Nc");
2014: if (!dim) sp->order = 0;
2015: order = sp->order;
2016: uniform = sp->uniform;
2017: PetscCheck(uniform, PETSC_COMM_SELF, PETSC_ERR_SUP, "Variable order not supported yet");
2018: if (lag->trimmed && !formDegree) lag->trimmed = PETSC_FALSE; /* trimmed spaces are the same as full spaces for 0-forms */
2019: if (lag->nodeType == PETSCDTNODES_DEFAULT) {
2020: lag->nodeType = PETSCDTNODES_GAUSSJACOBI;
2021: lag->nodeExponent = 0.;
2022: /* trimmed spaces don't include corner vertices, so don't use end nodes by default */
2023: lag->endNodes = lag->trimmed ? PETSC_FALSE : PETSC_TRUE;
2024: }
2025: /* If a trimmed space and the user did choose nodes with endpoints, skip them by default */
2026: if (lag->numNodeSkip < 0) lag->numNodeSkip = (lag->trimmed && lag->endNodes) ? 1 : 0;
2027: numNodeSkip = lag->numNodeSkip;
2028: PetscCheck(!lag->trimmed || order, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Cannot have zeroth order trimmed elements");
2029: if (lag->trimmed && PetscAbsInt(formDegree) == dim) { /* convert trimmed n-forms to untrimmed of one polynomial order less */
2030: sp->order--;
2031: order--;
2032: lag->trimmed = PETSC_FALSE;
2033: }
2034: trimmed = lag->trimmed;
2035: if (!order || PetscAbsInt(formDegree) == dim) lag->continuous = PETSC_FALSE;
2036: continuous = lag->continuous;
2037: PetscCall(DMPlexGetDepth(dm, &depth));
2038: PetscCall(DMPlexGetChart(dm, &pStart, &pEnd));
2039: PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
2040: PetscCheck(pStart == 0 && cStart == 0, PetscObjectComm((PetscObject)sp), PETSC_ERR_ARG_WRONGSTATE, "Expect DM with chart starting at zero and cells first");
2041: PetscCheck(cEnd == 1, PetscObjectComm((PetscObject)sp), PETSC_ERR_ARG_WRONGSTATE, "Use PETSCDUALSPACEREFINED for multi-cell reference meshes");
2042: PetscCall(DMPlexIsInterpolated(dm, &interpolated));
2043: if (interpolated != DMPLEX_INTERPOLATED_FULL) {
2044: PetscCall(DMPlexInterpolate(dm, &dmint));
2045: } else {
2046: PetscCall(PetscObjectReference((PetscObject)dm));
2047: dmint = dm;
2048: }
2049: tensorCell = PETSC_FALSE;
2050: if (dim > 1) PetscCall(DMPlexPointIsTensor(dmint, 0, &tensorCell, &tensorf, &tensorf2));
2051: lag->tensorCell = tensorCell;
2052: if (dim < 2 || !lag->tensorCell) lag->tensorSpace = PETSC_FALSE;
2053: tensorSpace = lag->tensorSpace;
2054: if (!lag->nodeFamily) PetscCall(Petsc1DNodeFamilyCreate(lag->nodeType, lag->nodeExponent, lag->endNodes, &lag->nodeFamily));
2055: nodeFamily = lag->nodeFamily;
2056: 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");
2058: if (Ncopies > 1) {
2059: PetscDualSpace scalarsp;
2061: PetscCall(PetscDualSpaceDuplicate(sp, &scalarsp));
2062: /* Setting the number of components to Nk is a space with 1 copy of each k-form */
2063: sp->setupcalled = PETSC_FALSE;
2064: PetscCall(PetscDualSpaceSetNumComponents(scalarsp, Nk));
2065: PetscCall(PetscDualSpaceSetUp(scalarsp));
2066: PetscCall(PetscDualSpaceSetType(sp, PETSCDUALSPACESUM));
2067: PetscCall(PetscDualSpaceSumSetNumSubspaces(sp, Ncopies));
2068: PetscCall(PetscDualSpaceSumSetConcatenate(sp, PETSC_TRUE));
2069: PetscCall(PetscDualSpaceSumSetInterleave(sp, PETSC_TRUE, PETSC_FALSE));
2070: for (PetscInt i = 0; i < Ncopies; i++) PetscCall(PetscDualSpaceSumSetSubspace(sp, i, scalarsp));
2071: PetscCall(PetscDualSpaceSetUp(sp));
2072: PetscCall(PetscDualSpaceDestroy(&scalarsp));
2073: PetscCall(DMDestroy(&dmint));
2074: PetscFunctionReturn(PETSC_SUCCESS);
2075: }
2077: /* step 2: construct the boundary spaces */
2078: PetscCall(PetscMalloc2(depth + 1, &pStratStart, depth + 1, &pStratEnd));
2079: PetscCall(PetscCalloc1(pEnd, &sp->pointSpaces));
2080: for (d = 0; d <= depth; ++d) PetscCall(DMPlexGetDepthStratum(dm, d, &pStratStart[d], &pStratEnd[d]));
2081: PetscCall(PetscDualSpaceSectionCreate_Internal(sp, §ion));
2082: sp->pointSection = section;
2083: if (continuous && !lag->interiorOnly) {
2084: PetscInt h;
2086: for (p = pStratStart[depth - 1]; p < pStratEnd[depth - 1]; p++) { /* calculate the facet dual spaces */
2087: PetscReal v0[3];
2088: DMPolytopeType ptype;
2089: PetscReal J[9], detJ;
2090: PetscInt q;
2092: PetscCall(DMPlexComputeCellGeometryAffineFEM(dm, p, v0, J, NULL, &detJ));
2093: PetscCall(DMPlexGetCellType(dm, p, &ptype));
2095: /* compare to previous facets: if computed, reference that dualspace */
2096: for (q = pStratStart[depth - 1]; q < p; q++) {
2097: DMPolytopeType qtype;
2099: PetscCall(DMPlexGetCellType(dm, q, &qtype));
2100: if (qtype == ptype) break;
2101: }
2102: if (q < p) { /* this facet has the same dual space as that one */
2103: PetscCall(PetscObjectReference((PetscObject)sp->pointSpaces[q]));
2104: sp->pointSpaces[p] = sp->pointSpaces[q];
2105: continue;
2106: }
2107: /* if not, recursively compute this dual space */
2108: PetscCall(PetscDualSpaceCreateFacetSubspace_Lagrange(sp, NULL, p, formDegree, Ncopies, PETSC_FALSE, &sp->pointSpaces[p]));
2109: }
2110: for (h = 2; h <= depth; h++) { /* get the higher subspaces from the facet subspaces */
2111: PetscInt hd = depth - h;
2112: PetscInt hdim = dim - h;
2114: if (hdim < PetscAbsInt(formDegree)) break;
2115: for (p = pStratStart[hd]; p < pStratEnd[hd]; p++) {
2116: PetscInt suppSize, s;
2117: const PetscInt *supp;
2119: PetscCall(DMPlexGetSupportSize(dm, p, &suppSize));
2120: PetscCall(DMPlexGetSupport(dm, p, &supp));
2121: for (s = 0; s < suppSize; s++) {
2122: DM qdm;
2123: PetscDualSpace qsp, psp;
2124: PetscInt c, coneSize, q;
2125: const PetscInt *cone;
2126: const PetscInt *refCone;
2128: q = supp[s];
2129: qsp = sp->pointSpaces[q];
2130: PetscCall(DMPlexGetConeSize(dm, q, &coneSize));
2131: PetscCall(DMPlexGetCone(dm, q, &cone));
2132: for (c = 0; c < coneSize; c++)
2133: if (cone[c] == p) break;
2134: PetscCheck(c != coneSize, PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "cone/support mismatch");
2135: PetscCall(PetscDualSpaceGetDM(qsp, &qdm));
2136: PetscCall(DMPlexGetCone(qdm, 0, &refCone));
2137: /* get the equivalent dual space from the support dual space */
2138: PetscCall(PetscDualSpaceGetPointSubspace(qsp, refCone[c], &psp));
2139: if (!s) {
2140: PetscCall(PetscObjectReference((PetscObject)psp));
2141: sp->pointSpaces[p] = psp;
2142: }
2143: }
2144: }
2145: }
2146: for (p = 1; p < pEnd; p++) {
2147: PetscInt pspdim;
2148: if (!sp->pointSpaces[p]) continue;
2149: PetscCall(PetscDualSpaceGetInteriorDimension(sp->pointSpaces[p], &pspdim));
2150: PetscCall(PetscSectionSetDof(section, p, pspdim));
2151: }
2152: }
2154: if (trimmed && !continuous) {
2155: /* the dofs of a trimmed space don't have a nice tensor/lattice structure:
2156: * just construct the continuous dual space and copy all of the data over,
2157: * allocating it all to the cell instead of splitting it up between the boundaries */
2158: PetscDualSpace spcont;
2159: PetscInt spdim, f;
2160: PetscQuadrature allNodes;
2161: PetscDualSpace_Lag *lagc;
2162: Mat allMat;
2164: PetscCall(PetscDualSpaceDuplicate(sp, &spcont));
2165: PetscCall(PetscDualSpaceLagrangeSetContinuity(spcont, PETSC_TRUE));
2166: PetscCall(PetscDualSpaceSetUp(spcont));
2167: PetscCall(PetscDualSpaceGetDimension(spcont, &spdim));
2168: sp->spdim = sp->spintdim = spdim;
2169: PetscCall(PetscSectionSetDof(section, 0, spdim));
2170: PetscCall(PetscDualSpaceSectionSetUp_Internal(sp, section));
2171: PetscCall(PetscMalloc1(spdim, &sp->functional));
2172: for (f = 0; f < spdim; f++) {
2173: PetscQuadrature fn;
2175: PetscCall(PetscDualSpaceGetFunctional(spcont, f, &fn));
2176: PetscCall(PetscObjectReference((PetscObject)fn));
2177: sp->functional[f] = fn;
2178: }
2179: PetscCall(PetscDualSpaceGetAllData(spcont, &allNodes, &allMat));
2180: PetscCall(PetscObjectReference((PetscObject)allNodes));
2181: PetscCall(PetscObjectReference((PetscObject)allNodes));
2182: sp->allNodes = sp->intNodes = allNodes;
2183: PetscCall(PetscObjectReference((PetscObject)allMat));
2184: PetscCall(PetscObjectReference((PetscObject)allMat));
2185: sp->allMat = sp->intMat = allMat;
2186: lagc = (PetscDualSpace_Lag *)spcont->data;
2187: PetscCall(PetscLagNodeIndicesReference(lagc->vertIndices));
2188: lag->vertIndices = lagc->vertIndices;
2189: PetscCall(PetscLagNodeIndicesReference(lagc->allNodeIndices));
2190: PetscCall(PetscLagNodeIndicesReference(lagc->allNodeIndices));
2191: lag->intNodeIndices = lagc->allNodeIndices;
2192: lag->allNodeIndices = lagc->allNodeIndices;
2193: PetscCall(PetscDualSpaceDestroy(&spcont));
2194: PetscCall(PetscFree2(pStratStart, pStratEnd));
2195: PetscCall(DMDestroy(&dmint));
2196: PetscFunctionReturn(PETSC_SUCCESS);
2197: }
2199: /* step 3: construct intNodes, and intMat, and combine it with boundray data to make allNodes and allMat */
2200: if (!tensorSpace) {
2201: if (!tensorCell) PetscCall(PetscLagNodeIndicesCreateSimplexVertices(dm, &lag->vertIndices));
2203: if (trimmed) {
2204: /* there is one dof in the interior of the a trimmed element for each full polynomial of with degree at most
2205: * order + k - dim - 1 */
2206: if (order + PetscAbsInt(formDegree) > dim) {
2207: PetscInt sum = order + PetscAbsInt(formDegree) - dim - 1;
2208: PetscInt nDofs;
2210: PetscCall(PetscDualSpaceLagrangeCreateSimplexNodeMat(nodeFamily, dim, sum, Nk, numNodeSkip, &sp->intNodes, &sp->intMat, &lag->intNodeIndices));
2211: PetscCall(MatGetSize(sp->intMat, &nDofs, NULL));
2212: PetscCall(PetscSectionSetDof(section, 0, nDofs));
2213: }
2214: PetscCall(PetscDualSpaceSectionSetUp_Internal(sp, section));
2215: PetscCall(PetscDualSpaceCreateAllDataFromInteriorData(sp));
2216: PetscCall(PetscDualSpaceLagrangeCreateAllNodeIdx(sp));
2217: } else {
2218: if (!continuous) {
2219: /* if discontinuous just construct one node for each set of dofs (a set of dofs is a basis for the k-form
2220: * space) */
2221: PetscInt sum = order;
2222: PetscInt nDofs;
2224: PetscCall(PetscDualSpaceLagrangeCreateSimplexNodeMat(nodeFamily, dim, sum, Nk, numNodeSkip, &sp->intNodes, &sp->intMat, &lag->intNodeIndices));
2225: PetscCall(MatGetSize(sp->intMat, &nDofs, NULL));
2226: PetscCall(PetscSectionSetDof(section, 0, nDofs));
2227: PetscCall(PetscDualSpaceSectionSetUp_Internal(sp, section));
2228: PetscCall(PetscObjectReference((PetscObject)sp->intNodes));
2229: sp->allNodes = sp->intNodes;
2230: PetscCall(PetscObjectReference((PetscObject)sp->intMat));
2231: sp->allMat = sp->intMat;
2232: PetscCall(PetscLagNodeIndicesReference(lag->intNodeIndices));
2233: lag->allNodeIndices = lag->intNodeIndices;
2234: } else {
2235: /* there is one dof in the interior of the a full element for each trimmed polynomial of with degree at most
2236: * order + k - dim, but with complementary form degree */
2237: if (order + PetscAbsInt(formDegree) > dim) {
2238: PetscDualSpace trimmedsp;
2239: PetscDualSpace_Lag *trimmedlag;
2240: PetscQuadrature intNodes;
2241: PetscInt trFormDegree = formDegree >= 0 ? formDegree - dim : dim - PetscAbsInt(formDegree);
2242: PetscInt nDofs;
2243: Mat intMat;
2245: PetscCall(PetscDualSpaceDuplicate(sp, &trimmedsp));
2246: PetscCall(PetscDualSpaceLagrangeSetTrimmed(trimmedsp, PETSC_TRUE));
2247: PetscCall(PetscDualSpaceSetOrder(trimmedsp, order + PetscAbsInt(formDegree) - dim));
2248: PetscCall(PetscDualSpaceSetFormDegree(trimmedsp, trFormDegree));
2249: trimmedlag = (PetscDualSpace_Lag *)trimmedsp->data;
2250: trimmedlag->numNodeSkip = numNodeSkip + 1;
2251: PetscCall(PetscDualSpaceSetUp(trimmedsp));
2252: PetscCall(PetscDualSpaceGetAllData(trimmedsp, &intNodes, &intMat));
2253: PetscCall(PetscObjectReference((PetscObject)intNodes));
2254: sp->intNodes = intNodes;
2255: PetscCall(PetscLagNodeIndicesReference(trimmedlag->allNodeIndices));
2256: lag->intNodeIndices = trimmedlag->allNodeIndices;
2257: PetscCall(PetscObjectReference((PetscObject)intMat));
2258: if (PetscAbsInt(formDegree) > 0 && PetscAbsInt(formDegree) < dim) {
2259: PetscReal *T;
2260: PetscScalar *work;
2261: PetscInt nCols, nRows;
2262: Mat intMatT;
2264: PetscCall(MatDuplicate(intMat, MAT_COPY_VALUES, &intMatT));
2265: PetscCall(MatGetSize(intMat, &nRows, &nCols));
2266: PetscCall(PetscMalloc2(Nk * Nk, &T, nCols, &work));
2267: PetscCall(BiunitSimplexSymmetricFormTransformation(dim, formDegree, T));
2268: for (PetscInt row = 0; row < nRows; row++) {
2269: PetscInt nrCols;
2270: const PetscInt *rCols;
2271: const PetscScalar *rVals;
2273: PetscCall(MatGetRow(intMat, row, &nrCols, &rCols, &rVals));
2274: PetscCheck(nrCols % Nk == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "nonzeros in intMat matrix are not in k-form size blocks");
2275: for (PetscInt b = 0; b < nrCols; b += Nk) {
2276: const PetscScalar *v = &rVals[b];
2277: PetscScalar *w = &work[b];
2278: for (PetscInt j = 0; j < Nk; j++) {
2279: w[j] = 0.;
2280: for (PetscInt i = 0; i < Nk; i++) w[j] += v[i] * T[i * Nk + j];
2281: }
2282: }
2283: PetscCall(MatSetValuesBlocked(intMatT, 1, &row, nrCols, rCols, work, INSERT_VALUES));
2284: PetscCall(MatRestoreRow(intMat, row, &nrCols, &rCols, &rVals));
2285: }
2286: PetscCall(MatAssemblyBegin(intMatT, MAT_FINAL_ASSEMBLY));
2287: PetscCall(MatAssemblyEnd(intMatT, MAT_FINAL_ASSEMBLY));
2288: PetscCall(MatDestroy(&intMat));
2289: intMat = intMatT;
2290: PetscCall(PetscLagNodeIndicesDestroy(&lag->intNodeIndices));
2291: PetscCall(PetscLagNodeIndicesDuplicate(trimmedlag->allNodeIndices, &lag->intNodeIndices));
2292: {
2293: PetscInt nNodes = lag->intNodeIndices->nNodes;
2294: PetscReal *newNodeVec = lag->intNodeIndices->nodeVec;
2295: const PetscReal *oldNodeVec = trimmedlag->allNodeIndices->nodeVec;
2297: for (PetscInt n = 0; n < nNodes; n++) {
2298: PetscReal *w = &newNodeVec[n * Nk];
2299: const PetscReal *v = &oldNodeVec[n * Nk];
2301: for (PetscInt j = 0; j < Nk; j++) {
2302: w[j] = 0.;
2303: for (PetscInt i = 0; i < Nk; i++) w[j] += v[i] * T[i * Nk + j];
2304: }
2305: }
2306: }
2307: PetscCall(PetscFree2(T, work));
2308: }
2309: sp->intMat = intMat;
2310: PetscCall(MatGetSize(sp->intMat, &nDofs, NULL));
2311: PetscCall(PetscDualSpaceDestroy(&trimmedsp));
2312: PetscCall(PetscSectionSetDof(section, 0, nDofs));
2313: }
2314: PetscCall(PetscDualSpaceSectionSetUp_Internal(sp, section));
2315: PetscCall(PetscDualSpaceCreateAllDataFromInteriorData(sp));
2316: PetscCall(PetscDualSpaceLagrangeCreateAllNodeIdx(sp));
2317: }
2318: }
2319: } else {
2320: PetscQuadrature intNodesTrace = NULL;
2321: PetscQuadrature intNodesFiber = NULL;
2322: PetscQuadrature intNodes = NULL;
2323: PetscLagNodeIndices intNodeIndices = NULL;
2324: Mat intMat = NULL;
2326: if (PetscAbsInt(formDegree) < dim) { /* get the trace k-forms on the first facet, and the 0-forms on the edge,
2327: and wedge them together to create some of the k-form dofs */
2328: PetscDualSpace trace, fiber;
2329: PetscDualSpace_Lag *tracel, *fiberl;
2330: Mat intMatTrace, intMatFiber;
2332: if (sp->pointSpaces[tensorf]) {
2333: PetscCall(PetscObjectReference((PetscObject)sp->pointSpaces[tensorf]));
2334: trace = sp->pointSpaces[tensorf];
2335: } else {
2336: PetscCall(PetscDualSpaceCreateFacetSubspace_Lagrange(sp, NULL, tensorf, formDegree, Ncopies, PETSC_TRUE, &trace));
2337: }
2338: PetscCall(PetscDualSpaceCreateEdgeSubspace_Lagrange(sp, order, 0, 1, PETSC_TRUE, &fiber));
2339: tracel = (PetscDualSpace_Lag *)trace->data;
2340: fiberl = (PetscDualSpace_Lag *)fiber->data;
2341: PetscCall(PetscLagNodeIndicesCreateTensorVertices(dm, tracel->vertIndices, &lag->vertIndices));
2342: PetscCall(PetscDualSpaceGetInteriorData(trace, &intNodesTrace, &intMatTrace));
2343: PetscCall(PetscDualSpaceGetInteriorData(fiber, &intNodesFiber, &intMatFiber));
2344: if (intNodesTrace && intNodesFiber) {
2345: PetscCall(PetscQuadratureCreateTensor(intNodesTrace, intNodesFiber, &intNodes));
2346: PetscCall(MatTensorAltV(intMatTrace, intMatFiber, dim - 1, formDegree, 1, 0, &intMat));
2347: PetscCall(PetscLagNodeIndicesTensor(tracel->intNodeIndices, dim - 1, formDegree, fiberl->intNodeIndices, 1, 0, &intNodeIndices));
2348: }
2349: PetscCall(PetscObjectReference((PetscObject)intNodesTrace));
2350: PetscCall(PetscObjectReference((PetscObject)intNodesFiber));
2351: PetscCall(PetscDualSpaceDestroy(&fiber));
2352: PetscCall(PetscDualSpaceDestroy(&trace));
2353: }
2354: if (PetscAbsInt(formDegree) > 0) { /* get the trace (k-1)-forms on the first facet, and the 1-forms on the edge,
2355: and wedge them together to create the remaining k-form dofs */
2356: PetscDualSpace trace, fiber;
2357: PetscDualSpace_Lag *tracel, *fiberl;
2358: PetscQuadrature intNodesTrace2, intNodesFiber2, intNodes2;
2359: PetscLagNodeIndices intNodeIndices2;
2360: Mat intMatTrace, intMatFiber, intMat2;
2361: PetscInt traceDegree = formDegree > 0 ? formDegree - 1 : formDegree + 1;
2362: PetscInt fiberDegree = formDegree > 0 ? 1 : -1;
2364: PetscCall(PetscDualSpaceCreateFacetSubspace_Lagrange(sp, NULL, tensorf, traceDegree, Ncopies, PETSC_TRUE, &trace));
2365: PetscCall(PetscDualSpaceCreateEdgeSubspace_Lagrange(sp, order, fiberDegree, 1, PETSC_TRUE, &fiber));
2366: tracel = (PetscDualSpace_Lag *)trace->data;
2367: fiberl = (PetscDualSpace_Lag *)fiber->data;
2368: if (!lag->vertIndices) PetscCall(PetscLagNodeIndicesCreateTensorVertices(dm, tracel->vertIndices, &lag->vertIndices));
2369: PetscCall(PetscDualSpaceGetInteriorData(trace, &intNodesTrace2, &intMatTrace));
2370: PetscCall(PetscDualSpaceGetInteriorData(fiber, &intNodesFiber2, &intMatFiber));
2371: if (intNodesTrace2 && intNodesFiber2) {
2372: PetscCall(PetscQuadratureCreateTensor(intNodesTrace2, intNodesFiber2, &intNodes2));
2373: PetscCall(MatTensorAltV(intMatTrace, intMatFiber, dim - 1, traceDegree, 1, fiberDegree, &intMat2));
2374: PetscCall(PetscLagNodeIndicesTensor(tracel->intNodeIndices, dim - 1, traceDegree, fiberl->intNodeIndices, 1, fiberDegree, &intNodeIndices2));
2375: if (!intMat) {
2376: intMat = intMat2;
2377: intNodes = intNodes2;
2378: intNodeIndices = intNodeIndices2;
2379: } else {
2380: /* merge the matrices, quadrature points, and nodes */
2381: PetscInt nM;
2382: PetscInt nDof, nDof2;
2383: PetscInt *toMerged = NULL, *toMerged2 = NULL;
2384: PetscQuadrature merged = NULL;
2385: PetscLagNodeIndices intNodeIndicesMerged = NULL;
2386: Mat matMerged = NULL;
2388: PetscCall(MatGetSize(intMat, &nDof, NULL));
2389: PetscCall(MatGetSize(intMat2, &nDof2, NULL));
2390: PetscCall(PetscQuadraturePointsMerge(intNodes, intNodes2, &merged, &toMerged, &toMerged2));
2391: PetscCall(PetscQuadratureGetData(merged, NULL, NULL, &nM, NULL, NULL));
2392: PetscCall(MatricesMerge(intMat, intMat2, dim, formDegree, nM, toMerged, toMerged2, &matMerged));
2393: PetscCall(PetscLagNodeIndicesMerge(intNodeIndices, intNodeIndices2, &intNodeIndicesMerged));
2394: PetscCall(PetscFree(toMerged));
2395: PetscCall(PetscFree(toMerged2));
2396: PetscCall(MatDestroy(&intMat));
2397: PetscCall(MatDestroy(&intMat2));
2398: PetscCall(PetscQuadratureDestroy(&intNodes));
2399: PetscCall(PetscQuadratureDestroy(&intNodes2));
2400: PetscCall(PetscLagNodeIndicesDestroy(&intNodeIndices));
2401: PetscCall(PetscLagNodeIndicesDestroy(&intNodeIndices2));
2402: intNodes = merged;
2403: intMat = matMerged;
2404: intNodeIndices = intNodeIndicesMerged;
2405: if (!trimmed) {
2406: /* I think users expect that, when a node has a full basis for the k-forms,
2407: * they should be consecutive dofs. That isn't the case for trimmed spaces,
2408: * but is for some of the nodes in untrimmed spaces, so in that case we
2409: * sort them to group them by node */
2410: Mat intMatPerm;
2412: PetscCall(MatPermuteByNodeIdx(intMat, intNodeIndices, &intMatPerm));
2413: PetscCall(MatDestroy(&intMat));
2414: intMat = intMatPerm;
2415: }
2416: }
2417: }
2418: PetscCall(PetscDualSpaceDestroy(&fiber));
2419: PetscCall(PetscDualSpaceDestroy(&trace));
2420: }
2421: PetscCall(PetscQuadratureDestroy(&intNodesTrace));
2422: PetscCall(PetscQuadratureDestroy(&intNodesFiber));
2423: sp->intNodes = intNodes;
2424: sp->intMat = intMat;
2425: lag->intNodeIndices = intNodeIndices;
2426: {
2427: PetscInt nDofs = 0;
2429: if (intMat) PetscCall(MatGetSize(intMat, &nDofs, NULL));
2430: PetscCall(PetscSectionSetDof(section, 0, nDofs));
2431: }
2432: PetscCall(PetscDualSpaceSectionSetUp_Internal(sp, section));
2433: if (continuous) {
2434: PetscCall(PetscDualSpaceCreateAllDataFromInteriorData(sp));
2435: PetscCall(PetscDualSpaceLagrangeCreateAllNodeIdx(sp));
2436: } else {
2437: PetscCall(PetscObjectReference((PetscObject)intNodes));
2438: sp->allNodes = intNodes;
2439: PetscCall(PetscObjectReference((PetscObject)intMat));
2440: sp->allMat = intMat;
2441: PetscCall(PetscLagNodeIndicesReference(intNodeIndices));
2442: lag->allNodeIndices = intNodeIndices;
2443: }
2444: }
2445: PetscCall(PetscSectionGetStorageSize(section, &sp->spdim));
2446: PetscCall(PetscSectionGetConstrainedStorageSize(section, &sp->spintdim));
2447: // TODO: fix this, computing functionals from moments should be no different for nodal vs modal
2448: if (lag->useMoments) {
2449: PetscCall(PetscDualSpaceComputeFunctionalsFromAllData_Moments(sp));
2450: } else {
2451: PetscCall(PetscDualSpaceComputeFunctionalsFromAllData(sp));
2452: }
2453: PetscCall(PetscFree2(pStratStart, pStratEnd));
2454: PetscCall(DMDestroy(&dmint));
2455: PetscFunctionReturn(PETSC_SUCCESS);
2456: }
2458: /* Create a matrix that represents the transformation that DMPlexVecGetClosure() would need
2459: * to get the representation of the dofs for a mesh point if the mesh point had this orientation
2460: * relative to the cell */
2461: PetscErrorCode PetscDualSpaceCreateInteriorSymmetryMatrix_Lagrange(PetscDualSpace sp, PetscInt ornt, Mat *symMat)
2462: {
2463: PetscDualSpace_Lag *lag;
2464: DM dm;
2465: PetscLagNodeIndices vertIndices, intNodeIndices;
2466: PetscLagNodeIndices ni;
2467: PetscInt nodeIdxDim, nodeVecDim, nNodes;
2468: PetscInt formDegree;
2469: PetscInt *perm, *permOrnt;
2470: PetscInt *nnz;
2471: PetscInt n;
2472: PetscInt maxGroupSize;
2473: PetscScalar *V, *W, *work;
2474: Mat A;
2476: PetscFunctionBegin;
2477: if (!sp->spintdim) {
2478: *symMat = NULL;
2479: PetscFunctionReturn(PETSC_SUCCESS);
2480: }
2481: lag = (PetscDualSpace_Lag *)sp->data;
2482: vertIndices = lag->vertIndices;
2483: intNodeIndices = lag->intNodeIndices;
2484: PetscCall(PetscDualSpaceGetDM(sp, &dm));
2485: PetscCall(PetscDualSpaceGetFormDegree(sp, &formDegree));
2486: PetscCall(PetscNew(&ni));
2487: ni->refct = 1;
2488: ni->nodeIdxDim = nodeIdxDim = intNodeIndices->nodeIdxDim;
2489: ni->nodeVecDim = nodeVecDim = intNodeIndices->nodeVecDim;
2490: ni->nNodes = nNodes = intNodeIndices->nNodes;
2491: PetscCall(PetscMalloc1(nNodes * nodeIdxDim, &ni->nodeIdx));
2492: PetscCall(PetscMalloc1(nNodes * nodeVecDim, &ni->nodeVec));
2493: /* push forward the dofs by the symmetry of the reference element induced by ornt */
2494: PetscCall(PetscLagNodeIndicesPushForward(dm, vertIndices, 0, vertIndices, intNodeIndices, ornt, formDegree, ni->nodeIdx, ni->nodeVec));
2495: /* get the revlex order for both the original and transformed dofs */
2496: PetscCall(PetscLagNodeIndicesGetPermutation(intNodeIndices, &perm));
2497: PetscCall(PetscLagNodeIndicesGetPermutation(ni, &permOrnt));
2498: PetscCall(PetscMalloc1(nNodes, &nnz));
2499: for (n = 0, maxGroupSize = 0; n < nNodes;) { /* incremented in the loop */
2500: PetscInt *nind = &(ni->nodeIdx[permOrnt[n] * nodeIdxDim]);
2501: PetscInt m, nEnd;
2502: PetscInt groupSize;
2503: /* for each group of dofs that have the same nodeIdx coordinate */
2504: for (nEnd = n + 1; nEnd < nNodes; nEnd++) {
2505: PetscInt *mind = &(ni->nodeIdx[permOrnt[nEnd] * nodeIdxDim]);
2506: PetscInt d;
2508: /* compare the oriented permutation indices */
2509: for (d = 0; d < nodeIdxDim; d++)
2510: if (mind[d] != nind[d]) break;
2511: if (d < nodeIdxDim) break;
2512: }
2513: /* permOrnt[[n, nEnd)] is a group of dofs that, under the symmetry are at the same location */
2515: /* the symmetry had better map the group of dofs with the same permuted nodeIdx
2516: * to a group of dofs with the same size, otherwise we messed up */
2517: if (PetscDefined(USE_DEBUG)) {
2518: PetscInt m;
2519: PetscInt *nind = &(intNodeIndices->nodeIdx[perm[n] * nodeIdxDim]);
2521: for (m = n + 1; m < nEnd; m++) {
2522: PetscInt *mind = &(intNodeIndices->nodeIdx[perm[m] * nodeIdxDim]);
2523: PetscInt d;
2525: /* compare the oriented permutation indices */
2526: for (d = 0; d < nodeIdxDim; d++)
2527: if (mind[d] != nind[d]) break;
2528: if (d < nodeIdxDim) break;
2529: }
2530: PetscCheck(m >= nEnd, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Dofs with same index after symmetry not same block size");
2531: }
2532: groupSize = nEnd - n;
2533: /* each pushforward dof vector will be expressed in a basis of the unpermuted dofs */
2534: for (m = n; m < nEnd; m++) nnz[permOrnt[m]] = groupSize;
2536: maxGroupSize = PetscMax(maxGroupSize, nEnd - n);
2537: n = nEnd;
2538: }
2539: PetscCheck(maxGroupSize <= nodeVecDim, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Dofs are not in blocks that can be solved");
2540: PetscCall(MatCreateSeqAIJ(PETSC_COMM_SELF, nNodes, nNodes, 0, nnz, &A));
2541: PetscCall(PetscObjectSetOptionsPrefix((PetscObject)A, "lag_"));
2542: PetscCall(PetscFree(nnz));
2543: PetscCall(PetscMalloc3(maxGroupSize * nodeVecDim, &V, maxGroupSize * nodeVecDim, &W, nodeVecDim * 2, &work));
2544: for (n = 0; n < nNodes;) { /* incremented in the loop */
2545: PetscInt *nind = &(ni->nodeIdx[permOrnt[n] * nodeIdxDim]);
2546: PetscInt nEnd;
2547: PetscInt m;
2548: PetscInt groupSize;
2549: for (nEnd = n + 1; nEnd < nNodes; nEnd++) {
2550: PetscInt *mind = &(ni->nodeIdx[permOrnt[nEnd] * nodeIdxDim]);
2551: PetscInt d;
2553: /* compare the oriented permutation indices */
2554: for (d = 0; d < nodeIdxDim; d++)
2555: if (mind[d] != nind[d]) break;
2556: if (d < nodeIdxDim) break;
2557: }
2558: groupSize = nEnd - n;
2559: /* get all of the vectors from the original and all of the pushforward vectors */
2560: for (m = n; m < nEnd; m++) {
2561: PetscInt d;
2563: for (d = 0; d < nodeVecDim; d++) {
2564: V[(m - n) * nodeVecDim + d] = intNodeIndices->nodeVec[perm[m] * nodeVecDim + d];
2565: W[(m - n) * nodeVecDim + d] = ni->nodeVec[permOrnt[m] * nodeVecDim + d];
2566: }
2567: }
2568: /* now we have to solve for W in terms of V: the systems isn't always square, but the span
2569: * of V and W should always be the same, so the solution of the normal equations works */
2570: {
2571: char transpose = 'N';
2572: PetscBLASInt bm, bn, bnrhs, blda, bldb, blwork, info;
2574: PetscCall(PetscBLASIntCast(nodeVecDim, &bm));
2575: PetscCall(PetscBLASIntCast(groupSize, &bn));
2576: PetscCall(PetscBLASIntCast(groupSize, &bnrhs));
2577: PetscCall(PetscBLASIntCast(bm, &blda));
2578: PetscCall(PetscBLASIntCast(bm, &bldb));
2579: PetscCall(PetscBLASIntCast(2 * nodeVecDim, &blwork));
2580: PetscCallBLAS("LAPACKgels", LAPACKgels_(&transpose, &bm, &bn, &bnrhs, V, &blda, W, &bldb, work, &blwork, &info));
2581: PetscCheck(info == 0, PETSC_COMM_SELF, PETSC_ERR_LIB, "Bad argument to GELS");
2582: /* repack */
2583: {
2584: PetscInt i, j;
2586: for (i = 0; i < groupSize; i++) {
2587: for (j = 0; j < groupSize; j++) {
2588: /* notice the different leading dimension */
2589: V[i * groupSize + j] = W[i * nodeVecDim + j];
2590: }
2591: }
2592: }
2593: if (PetscDefined(USE_DEBUG)) {
2594: PetscReal res;
2596: /* check that the normal error is 0 */
2597: for (m = n; m < nEnd; m++) {
2598: PetscInt d;
2600: for (d = 0; d < nodeVecDim; d++) W[(m - n) * nodeVecDim + d] = ni->nodeVec[permOrnt[m] * nodeVecDim + d];
2601: }
2602: res = 0.;
2603: for (PetscInt i = 0; i < groupSize; i++) {
2604: for (PetscInt j = 0; j < nodeVecDim; j++) {
2605: for (PetscInt k = 0; k < groupSize; k++) W[i * nodeVecDim + j] -= V[i * groupSize + k] * intNodeIndices->nodeVec[perm[n + k] * nodeVecDim + j];
2606: res += PetscAbsScalar(W[i * nodeVecDim + j]);
2607: }
2608: }
2609: PetscCheck(res <= PETSC_SMALL, PETSC_COMM_SELF, PETSC_ERR_LIB, "Dof block did not solve");
2610: }
2611: }
2612: PetscCall(MatSetValues(A, groupSize, &permOrnt[n], groupSize, &perm[n], V, INSERT_VALUES));
2613: n = nEnd;
2614: }
2615: PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
2616: PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
2617: *symMat = A;
2618: PetscCall(PetscFree3(V, W, work));
2619: PetscCall(PetscLagNodeIndicesDestroy(&ni));
2620: PetscFunctionReturn(PETSC_SUCCESS);
2621: }
2623: // get the symmetries of closure points
2624: PETSC_INTERN PetscErrorCode PetscDualSpaceGetBoundarySymmetries_Internal(PetscDualSpace sp, PetscInt ***symperms, PetscScalar ***symflips)
2625: {
2626: PetscInt closureSize = 0;
2627: PetscInt *closure = NULL;
2628: PetscInt r;
2630: PetscFunctionBegin;
2631: PetscCall(DMPlexGetTransitiveClosure(sp->dm, 0, PETSC_TRUE, &closureSize, &closure));
2632: for (r = 0; r < closureSize; r++) {
2633: PetscDualSpace psp;
2634: PetscInt point = closure[2 * r];
2635: PetscInt pspintdim;
2636: const PetscInt ***psymperms = NULL;
2637: const PetscScalar ***psymflips = NULL;
2639: if (!point) continue;
2640: PetscCall(PetscDualSpaceGetPointSubspace(sp, point, &psp));
2641: if (!psp) continue;
2642: PetscCall(PetscDualSpaceGetInteriorDimension(psp, &pspintdim));
2643: if (!pspintdim) continue;
2644: PetscCall(PetscDualSpaceGetSymmetries(psp, &psymperms, &psymflips));
2645: symperms[r] = (PetscInt **)(psymperms ? psymperms[0] : NULL);
2646: symflips[r] = (PetscScalar **)(psymflips ? psymflips[0] : NULL);
2647: }
2648: PetscCall(DMPlexRestoreTransitiveClosure(sp->dm, 0, PETSC_TRUE, &closureSize, &closure));
2649: PetscFunctionReturn(PETSC_SUCCESS);
2650: }
2652: #define BaryIndex(perEdge, a, b, c) (((b) * (2 * perEdge + 1 - (b))) / 2) + (c)
2654: #define CartIndex(perEdge, a, b) (perEdge * (a) + b)
2656: /* the existing interface for symmetries is insufficient for all cases:
2657: * - it should be sufficient for form degrees that are scalar (0 and n)
2658: * - it should be sufficient for hypercube dofs
2659: * - it isn't sufficient for simplex cells with non-scalar form degrees if
2660: * there are any dofs in the interior
2661: *
2662: * We compute the general transformation matrices, and if they fit, we return them,
2663: * otherwise we error (but we should probably change the interface to allow for
2664: * these symmetries)
2665: */
2666: static PetscErrorCode PetscDualSpaceGetSymmetries_Lagrange(PetscDualSpace sp, const PetscInt ****perms, const PetscScalar ****flips)
2667: {
2668: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2669: PetscInt dim, order, Nc;
2671: PetscFunctionBegin;
2672: PetscCall(PetscDualSpaceGetOrder(sp, &order));
2673: PetscCall(PetscDualSpaceGetNumComponents(sp, &Nc));
2674: PetscCall(DMGetDimension(sp->dm, &dim));
2675: if (!lag->symComputed) { /* store symmetries */
2676: PetscInt pStart, pEnd, p;
2677: PetscInt numPoints;
2678: PetscInt numFaces;
2679: PetscInt spintdim;
2680: PetscInt ***symperms;
2681: PetscScalar ***symflips;
2683: PetscCall(DMPlexGetChart(sp->dm, &pStart, &pEnd));
2684: numPoints = pEnd - pStart;
2685: {
2686: DMPolytopeType ct;
2687: /* The number of arrangements is no longer based on the number of faces */
2688: PetscCall(DMPlexGetCellType(sp->dm, 0, &ct));
2689: numFaces = DMPolytopeTypeGetNumArrangements(ct) / 2;
2690: }
2691: PetscCall(PetscCalloc1(numPoints, &symperms));
2692: PetscCall(PetscCalloc1(numPoints, &symflips));
2693: spintdim = sp->spintdim;
2694: /* The nodal symmetry behavior is not present when tensorSpace != tensorCell: someone might want this for the "S"
2695: * family of FEEC spaces. Most used in particular are discontinuous polynomial L2 spaces in tensor cells, where
2696: * the symmetries are not necessary for FE assembly. So for now we assume this is the case and don't return
2697: * symmetries if tensorSpace != tensorCell */
2698: if (spintdim && 0 < dim && dim < 3 && (lag->tensorSpace == lag->tensorCell)) { /* compute self symmetries */
2699: PetscInt **cellSymperms;
2700: PetscScalar **cellSymflips;
2701: PetscInt ornt;
2702: PetscInt nCopies = Nc / lag->intNodeIndices->nodeVecDim;
2703: PetscInt nNodes = lag->intNodeIndices->nNodes;
2705: lag->numSelfSym = 2 * numFaces;
2706: lag->selfSymOff = numFaces;
2707: PetscCall(PetscCalloc1(2 * numFaces, &cellSymperms));
2708: PetscCall(PetscCalloc1(2 * numFaces, &cellSymflips));
2709: /* we want to be able to index symmetries directly with the orientations, which range from [-numFaces,numFaces) */
2710: symperms[0] = &cellSymperms[numFaces];
2711: symflips[0] = &cellSymflips[numFaces];
2712: PetscCheck(lag->intNodeIndices->nodeVecDim * nCopies == Nc, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Node indices incompatible with dofs");
2713: PetscCheck(nNodes * nCopies == spintdim, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Node indices incompatible with dofs");
2714: 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 */
2715: Mat symMat;
2716: PetscInt *perm;
2717: PetscScalar *flips;
2718: PetscInt i;
2720: if (!ornt) continue;
2721: PetscCall(PetscMalloc1(spintdim, &perm));
2722: PetscCall(PetscCalloc1(spintdim, &flips));
2723: for (i = 0; i < spintdim; i++) perm[i] = -1;
2724: PetscCall(PetscDualSpaceCreateInteriorSymmetryMatrix_Lagrange(sp, ornt, &symMat));
2725: for (i = 0; i < nNodes; i++) {
2726: PetscInt ncols;
2727: PetscInt j, k;
2728: const PetscInt *cols;
2729: const PetscScalar *vals;
2730: PetscBool nz_seen = PETSC_FALSE;
2732: PetscCall(MatGetRow(symMat, i, &ncols, &cols, &vals));
2733: for (j = 0; j < ncols; j++) {
2734: if (PetscAbsScalar(vals[j]) > PETSC_SMALL) {
2735: 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");
2736: nz_seen = PETSC_TRUE;
2737: 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");
2738: 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");
2739: 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");
2740: for (k = 0; k < nCopies; k++) perm[cols[j] * nCopies + k] = i * nCopies + k;
2741: if (PetscRealPart(vals[j]) < 0.) {
2742: for (k = 0; k < nCopies; k++) flips[i * nCopies + k] = -1.;
2743: } else {
2744: for (k = 0; k < nCopies; k++) flips[i * nCopies + k] = 1.;
2745: }
2746: }
2747: }
2748: PetscCall(MatRestoreRow(symMat, i, &ncols, &cols, &vals));
2749: }
2750: PetscCall(MatDestroy(&symMat));
2751: /* if there were no sign flips, keep NULL */
2752: for (i = 0; i < spintdim; i++)
2753: if (flips[i] != 1.) break;
2754: if (i == spintdim) {
2755: PetscCall(PetscFree(flips));
2756: flips = NULL;
2757: }
2758: /* if the permutation is identity, keep NULL */
2759: for (i = 0; i < spintdim; i++)
2760: if (perm[i] != i) break;
2761: if (i == spintdim) {
2762: PetscCall(PetscFree(perm));
2763: perm = NULL;
2764: }
2765: symperms[0][ornt] = perm;
2766: symflips[0][ornt] = flips;
2767: }
2768: /* if no orientations produced non-identity permutations, keep NULL */
2769: for (ornt = -numFaces; ornt < numFaces; ornt++)
2770: if (symperms[0][ornt]) break;
2771: if (ornt == numFaces) {
2772: PetscCall(PetscFree(cellSymperms));
2773: symperms[0] = NULL;
2774: }
2775: /* if no orientations produced sign flips, keep NULL */
2776: for (ornt = -numFaces; ornt < numFaces; ornt++)
2777: if (symflips[0][ornt]) break;
2778: if (ornt == numFaces) {
2779: PetscCall(PetscFree(cellSymflips));
2780: symflips[0] = NULL;
2781: }
2782: }
2783: PetscCall(PetscDualSpaceGetBoundarySymmetries_Internal(sp, symperms, symflips));
2784: for (p = 0; p < pEnd; p++)
2785: if (symperms[p]) break;
2786: if (p == pEnd) {
2787: PetscCall(PetscFree(symperms));
2788: symperms = NULL;
2789: }
2790: for (p = 0; p < pEnd; p++)
2791: if (symflips[p]) break;
2792: if (p == pEnd) {
2793: PetscCall(PetscFree(symflips));
2794: symflips = NULL;
2795: }
2796: lag->symperms = symperms;
2797: lag->symflips = symflips;
2798: lag->symComputed = PETSC_TRUE;
2799: }
2800: if (perms) *perms = (const PetscInt ***)lag->symperms;
2801: if (flips) *flips = (const PetscScalar ***)lag->symflips;
2802: PetscFunctionReturn(PETSC_SUCCESS);
2803: }
2805: static PetscErrorCode PetscDualSpaceLagrangeGetContinuity_Lagrange(PetscDualSpace sp, PetscBool *continuous)
2806: {
2807: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2809: PetscFunctionBegin;
2811: PetscAssertPointer(continuous, 2);
2812: *continuous = lag->continuous;
2813: PetscFunctionReturn(PETSC_SUCCESS);
2814: }
2816: static PetscErrorCode PetscDualSpaceLagrangeSetContinuity_Lagrange(PetscDualSpace sp, PetscBool continuous)
2817: {
2818: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2820: PetscFunctionBegin;
2822: lag->continuous = continuous;
2823: PetscFunctionReturn(PETSC_SUCCESS);
2824: }
2826: /*@
2827: PetscDualSpaceLagrangeGetContinuity - Retrieves the flag for element continuity
2829: Not Collective
2831: Input Parameter:
2832: . sp - the `PetscDualSpace`
2834: Output Parameter:
2835: . continuous - flag for element continuity
2837: Level: intermediate
2839: .seealso: `PETSCDUALSPACELAGRANGE`, `PetscDualSpace`, `PetscDualSpaceLagrangeSetContinuity()`
2840: @*/
2841: PetscErrorCode PetscDualSpaceLagrangeGetContinuity(PetscDualSpace sp, PetscBool *continuous)
2842: {
2843: PetscFunctionBegin;
2845: PetscAssertPointer(continuous, 2);
2846: PetscTryMethod(sp, "PetscDualSpaceLagrangeGetContinuity_C", (PetscDualSpace, PetscBool *), (sp, continuous));
2847: PetscFunctionReturn(PETSC_SUCCESS);
2848: }
2850: /*@
2851: PetscDualSpaceLagrangeSetContinuity - Indicate whether the element is continuous
2853: Logically Collective
2855: Input Parameters:
2856: + sp - the `PetscDualSpace`
2857: - continuous - flag for element continuity
2859: Options Database Key:
2860: . -petscdualspace_lagrange_continuity <bool> - use a continuous element
2862: Level: intermediate
2864: .seealso: `PETSCDUALSPACELAGRANGE`, `PetscDualSpace`, `PetscDualSpaceLagrangeGetContinuity()`
2865: @*/
2866: PetscErrorCode PetscDualSpaceLagrangeSetContinuity(PetscDualSpace sp, PetscBool continuous)
2867: {
2868: PetscFunctionBegin;
2871: PetscTryMethod(sp, "PetscDualSpaceLagrangeSetContinuity_C", (PetscDualSpace, PetscBool), (sp, continuous));
2872: PetscFunctionReturn(PETSC_SUCCESS);
2873: }
2875: static PetscErrorCode PetscDualSpaceLagrangeGetTensor_Lagrange(PetscDualSpace sp, PetscBool *tensor)
2876: {
2877: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2879: PetscFunctionBegin;
2880: *tensor = lag->tensorSpace;
2881: PetscFunctionReturn(PETSC_SUCCESS);
2882: }
2884: static PetscErrorCode PetscDualSpaceLagrangeSetTensor_Lagrange(PetscDualSpace sp, PetscBool tensor)
2885: {
2886: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2888: PetscFunctionBegin;
2889: lag->tensorSpace = tensor;
2890: PetscFunctionReturn(PETSC_SUCCESS);
2891: }
2893: static PetscErrorCode PetscDualSpaceLagrangeGetTrimmed_Lagrange(PetscDualSpace sp, PetscBool *trimmed)
2894: {
2895: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2897: PetscFunctionBegin;
2898: *trimmed = lag->trimmed;
2899: PetscFunctionReturn(PETSC_SUCCESS);
2900: }
2902: static PetscErrorCode PetscDualSpaceLagrangeSetTrimmed_Lagrange(PetscDualSpace sp, PetscBool trimmed)
2903: {
2904: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2906: PetscFunctionBegin;
2907: lag->trimmed = trimmed;
2908: PetscFunctionReturn(PETSC_SUCCESS);
2909: }
2911: static PetscErrorCode PetscDualSpaceLagrangeGetNodeType_Lagrange(PetscDualSpace sp, PetscDTNodeType *nodeType, PetscBool *boundary, PetscReal *exponent)
2912: {
2913: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2915: PetscFunctionBegin;
2916: if (nodeType) *nodeType = lag->nodeType;
2917: if (boundary) *boundary = lag->endNodes;
2918: if (exponent) *exponent = lag->nodeExponent;
2919: PetscFunctionReturn(PETSC_SUCCESS);
2920: }
2922: static PetscErrorCode PetscDualSpaceLagrangeSetNodeType_Lagrange(PetscDualSpace sp, PetscDTNodeType nodeType, PetscBool boundary, PetscReal exponent)
2923: {
2924: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2926: PetscFunctionBegin;
2927: PetscCheck(nodeType != PETSCDTNODES_GAUSSJACOBI || exponent > -1., PetscObjectComm((PetscObject)sp), PETSC_ERR_ARG_OUTOFRANGE, "Exponent must be > -1");
2928: lag->nodeType = nodeType;
2929: lag->endNodes = boundary;
2930: lag->nodeExponent = exponent;
2931: PetscFunctionReturn(PETSC_SUCCESS);
2932: }
2934: static PetscErrorCode PetscDualSpaceLagrangeGetUseMoments_Lagrange(PetscDualSpace sp, PetscBool *useMoments)
2935: {
2936: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2938: PetscFunctionBegin;
2939: *useMoments = lag->useMoments;
2940: PetscFunctionReturn(PETSC_SUCCESS);
2941: }
2943: static PetscErrorCode PetscDualSpaceLagrangeSetUseMoments_Lagrange(PetscDualSpace sp, PetscBool useMoments)
2944: {
2945: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2947: PetscFunctionBegin;
2948: lag->useMoments = useMoments;
2949: PetscFunctionReturn(PETSC_SUCCESS);
2950: }
2952: static PetscErrorCode PetscDualSpaceLagrangeGetMomentOrder_Lagrange(PetscDualSpace sp, PetscInt *momentOrder)
2953: {
2954: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2956: PetscFunctionBegin;
2957: *momentOrder = lag->momentOrder;
2958: PetscFunctionReturn(PETSC_SUCCESS);
2959: }
2961: static PetscErrorCode PetscDualSpaceLagrangeSetMomentOrder_Lagrange(PetscDualSpace sp, PetscInt momentOrder)
2962: {
2963: PetscDualSpace_Lag *lag = (PetscDualSpace_Lag *)sp->data;
2965: PetscFunctionBegin;
2966: lag->momentOrder = momentOrder;
2967: PetscFunctionReturn(PETSC_SUCCESS);
2968: }
2970: /*@
2971: PetscDualSpaceLagrangeGetTensor - Get the tensor nature of the dual space
2973: Not Collective
2975: Input Parameter:
2976: . sp - The `PetscDualSpace`
2978: Output Parameter:
2979: . tensor - Whether the dual space has tensor layout (vs. simplicial)
2981: Level: intermediate
2983: .seealso: `PETSCDUALSPACELAGRANGE`, `PetscDualSpace`, `PetscDualSpaceLagrangeSetTensor()`, `PetscDualSpaceCreate()`
2984: @*/
2985: PetscErrorCode PetscDualSpaceLagrangeGetTensor(PetscDualSpace sp, PetscBool *tensor)
2986: {
2987: PetscFunctionBegin;
2989: PetscAssertPointer(tensor, 2);
2990: PetscTryMethod(sp, "PetscDualSpaceLagrangeGetTensor_C", (PetscDualSpace, PetscBool *), (sp, tensor));
2991: PetscFunctionReturn(PETSC_SUCCESS);
2992: }
2994: /*@
2995: PetscDualSpaceLagrangeSetTensor - Set the tensor nature of the dual space
2997: Not Collective
2999: Input Parameters:
3000: + sp - The `PetscDualSpace`
3001: - tensor - Whether the dual space has tensor layout (vs. simplicial)
3003: Level: intermediate
3005: .seealso: `PETSCDUALSPACELAGRANGE`, `PetscDualSpace`, `PetscDualSpaceLagrangeGetTensor()`, `PetscDualSpaceCreate()`
3006: @*/
3007: PetscErrorCode PetscDualSpaceLagrangeSetTensor(PetscDualSpace sp, PetscBool tensor)
3008: {
3009: PetscFunctionBegin;
3011: PetscTryMethod(sp, "PetscDualSpaceLagrangeSetTensor_C", (PetscDualSpace, PetscBool), (sp, tensor));
3012: PetscFunctionReturn(PETSC_SUCCESS);
3013: }
3015: /*@
3016: PetscDualSpaceLagrangeGetTrimmed - Get the trimmed nature of the dual space
3018: Not Collective
3020: Input Parameter:
3021: . sp - The `PetscDualSpace`
3023: Output Parameter:
3024: . 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)
3026: Level: intermediate
3028: .seealso: `PETSCDUALSPACELAGRANGE`, `PetscDualSpace`, `PetscDualSpaceLagrangeSetTrimmed()`, `PetscDualSpaceCreate()`
3029: @*/
3030: PetscErrorCode PetscDualSpaceLagrangeGetTrimmed(PetscDualSpace sp, PetscBool *trimmed)
3031: {
3032: PetscFunctionBegin;
3034: PetscAssertPointer(trimmed, 2);
3035: PetscTryMethod(sp, "PetscDualSpaceLagrangeGetTrimmed_C", (PetscDualSpace, PetscBool *), (sp, trimmed));
3036: PetscFunctionReturn(PETSC_SUCCESS);
3037: }
3039: /*@
3040: PetscDualSpaceLagrangeSetTrimmed - Set the trimmed nature of the dual space
3042: Not Collective
3044: Input Parameters:
3045: + sp - The `PetscDualSpace`
3046: - 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)
3048: Level: intermediate
3050: .seealso: `PETSCDUALSPACELAGRANGE`, `PetscDualSpace`, `PetscDualSpaceLagrangeGetTrimmed()`, `PetscDualSpaceCreate()`
3051: @*/
3052: PetscErrorCode PetscDualSpaceLagrangeSetTrimmed(PetscDualSpace sp, PetscBool trimmed)
3053: {
3054: PetscFunctionBegin;
3056: PetscTryMethod(sp, "PetscDualSpaceLagrangeSetTrimmed_C", (PetscDualSpace, PetscBool), (sp, trimmed));
3057: PetscFunctionReturn(PETSC_SUCCESS);
3058: }
3060: /*@
3061: PetscDualSpaceLagrangeGetNodeType - Get a description of how nodes are laid out for Lagrange polynomials in this
3062: dual space
3064: Not Collective
3066: Input Parameter:
3067: . sp - The `PetscDualSpace`
3069: Output Parameters:
3070: + nodeType - The type of nodes
3071: . boundary - Whether the node type is one that includes endpoints (if nodeType is `PETSCDTNODES_GAUSSJACOBI`, nodes that
3072: include the boundary are Gauss-Lobatto-Jacobi nodes)
3073: - exponent - If nodeType is `PETSCDTNODES_GAUSJACOBI`, indicates the exponent used for both ends of the 1D Jacobi weight function
3074: '0' is Gauss-Legendre, '-0.5' is Gauss-Chebyshev of the first type, '0.5' is Gauss-Chebyshev of the second type
3076: Level: advanced
3078: .seealso: `PETSCDUALSPACELAGRANGE`, `PetscDualSpace`, `PetscDTNodeType`, `PetscDualSpaceLagrangeSetNodeType()`
3079: @*/
3080: PetscErrorCode PetscDualSpaceLagrangeGetNodeType(PetscDualSpace sp, PetscDTNodeType *nodeType, PetscBool *boundary, PetscReal *exponent)
3081: {
3082: PetscFunctionBegin;
3084: if (nodeType) PetscAssertPointer(nodeType, 2);
3085: if (boundary) PetscAssertPointer(boundary, 3);
3086: if (exponent) PetscAssertPointer(exponent, 4);
3087: PetscTryMethod(sp, "PetscDualSpaceLagrangeGetNodeType_C", (PetscDualSpace, PetscDTNodeType *, PetscBool *, PetscReal *), (sp, nodeType, boundary, exponent));
3088: PetscFunctionReturn(PETSC_SUCCESS);
3089: }
3091: /*@
3092: PetscDualSpaceLagrangeSetNodeType - Set a description of how nodes are laid out for Lagrange polynomials in this
3093: dual space
3095: Logically Collective
3097: Input Parameters:
3098: + sp - The `PetscDualSpace`
3099: . nodeType - The type of nodes
3100: . boundary - Whether the node type is one that includes endpoints (if nodeType is `PETSCDTNODES_GAUSSJACOBI`, nodes that
3101: include the boundary are Gauss-Lobatto-Jacobi nodes)
3102: - exponent - If nodeType is `PETSCDTNODES_GAUSJACOBI`, indicates the exponent used for both ends of the 1D Jacobi weight function
3103: '0' is Gauss-Legendre, '-0.5' is Gauss-Chebyshev of the first type, '0.5' is Gauss-Chebyshev of the second type
3105: Level: advanced
3107: .seealso: `PETSCDUALSPACELAGRANGE`, `PetscDualSpace`, `PetscDTNodeType`, `PetscDualSpaceLagrangeGetNodeType()`
3108: @*/
3109: PetscErrorCode PetscDualSpaceLagrangeSetNodeType(PetscDualSpace sp, PetscDTNodeType nodeType, PetscBool boundary, PetscReal exponent)
3110: {
3111: PetscFunctionBegin;
3113: PetscTryMethod(sp, "PetscDualSpaceLagrangeSetNodeType_C", (PetscDualSpace, PetscDTNodeType, PetscBool, PetscReal), (sp, nodeType, boundary, exponent));
3114: PetscFunctionReturn(PETSC_SUCCESS);
3115: }
3117: /*@
3118: PetscDualSpaceLagrangeGetUseMoments - Get the flag for using moment functionals
3120: Not Collective
3122: Input Parameter:
3123: . sp - The `PetscDualSpace`
3125: Output Parameter:
3126: . useMoments - Moment flag
3128: Level: advanced
3130: .seealso: `PETSCDUALSPACELAGRANGE`, `PetscDualSpace`, `PetscDualSpaceLagrangeSetUseMoments()`
3131: @*/
3132: PetscErrorCode PetscDualSpaceLagrangeGetUseMoments(PetscDualSpace sp, PetscBool *useMoments)
3133: {
3134: PetscFunctionBegin;
3136: PetscAssertPointer(useMoments, 2);
3137: PetscUseMethod(sp, "PetscDualSpaceLagrangeGetUseMoments_C", (PetscDualSpace, PetscBool *), (sp, useMoments));
3138: PetscFunctionReturn(PETSC_SUCCESS);
3139: }
3141: /*@
3142: PetscDualSpaceLagrangeSetUseMoments - Set the flag for moment functionals
3144: Logically Collective
3146: Input Parameters:
3147: + sp - The `PetscDualSpace`
3148: - useMoments - The flag for moment functionals
3150: Level: advanced
3152: .seealso: `PETSCDUALSPACELAGRANGE`, `PetscDualSpace`, `PetscDualSpaceLagrangeGetUseMoments()`
3153: @*/
3154: PetscErrorCode PetscDualSpaceLagrangeSetUseMoments(PetscDualSpace sp, PetscBool useMoments)
3155: {
3156: PetscFunctionBegin;
3158: PetscTryMethod(sp, "PetscDualSpaceLagrangeSetUseMoments_C", (PetscDualSpace, PetscBool), (sp, useMoments));
3159: PetscFunctionReturn(PETSC_SUCCESS);
3160: }
3162: /*@
3163: PetscDualSpaceLagrangeGetMomentOrder - Get the order for moment integration
3165: Not Collective
3167: Input Parameter:
3168: . sp - The `PetscDualSpace`
3170: Output Parameter:
3171: . order - Moment integration order
3173: Level: advanced
3175: .seealso: `PETSCDUALSPACELAGRANGE`, `PetscDualSpace`, `PetscDualSpaceLagrangeSetMomentOrder()`
3176: @*/
3177: PetscErrorCode PetscDualSpaceLagrangeGetMomentOrder(PetscDualSpace sp, PetscInt *order)
3178: {
3179: PetscFunctionBegin;
3181: PetscAssertPointer(order, 2);
3182: PetscUseMethod(sp, "PetscDualSpaceLagrangeGetMomentOrder_C", (PetscDualSpace, PetscInt *), (sp, order));
3183: PetscFunctionReturn(PETSC_SUCCESS);
3184: }
3186: /*@
3187: PetscDualSpaceLagrangeSetMomentOrder - Set the order for moment integration
3189: Logically Collective
3191: Input Parameters:
3192: + sp - The `PetscDualSpace`
3193: - order - The order for moment integration
3195: Level: advanced
3197: .seealso: `PETSCDUALSPACELAGRANGE`, `PetscDualSpace`, `PetscDualSpaceLagrangeGetMomentOrder()`
3198: @*/
3199: PetscErrorCode PetscDualSpaceLagrangeSetMomentOrder(PetscDualSpace sp, PetscInt order)
3200: {
3201: PetscFunctionBegin;
3203: PetscTryMethod(sp, "PetscDualSpaceLagrangeSetMomentOrder_C", (PetscDualSpace, PetscInt), (sp, order));
3204: PetscFunctionReturn(PETSC_SUCCESS);
3205: }
3207: static PetscErrorCode PetscDualSpaceInitialize_Lagrange(PetscDualSpace sp)
3208: {
3209: PetscFunctionBegin;
3210: sp->ops->destroy = PetscDualSpaceDestroy_Lagrange;
3211: sp->ops->view = PetscDualSpaceView_Lagrange;
3212: sp->ops->setfromoptions = PetscDualSpaceSetFromOptions_Lagrange;
3213: sp->ops->duplicate = PetscDualSpaceDuplicate_Lagrange;
3214: sp->ops->setup = PetscDualSpaceSetUp_Lagrange;
3215: sp->ops->createheightsubspace = NULL;
3216: sp->ops->createpointsubspace = NULL;
3217: sp->ops->getsymmetries = PetscDualSpaceGetSymmetries_Lagrange;
3218: sp->ops->apply = PetscDualSpaceApplyDefault;
3219: sp->ops->applyall = PetscDualSpaceApplyAllDefault;
3220: sp->ops->applyint = PetscDualSpaceApplyInteriorDefault;
3221: sp->ops->createalldata = PetscDualSpaceCreateAllDataDefault;
3222: sp->ops->createintdata = PetscDualSpaceCreateInteriorDataDefault;
3223: PetscFunctionReturn(PETSC_SUCCESS);
3224: }
3226: /*MC
3227: PETSCDUALSPACELAGRANGE = "lagrange" - A `PetscDualSpaceType` that encapsulates a dual space of pointwise evaluation functionals
3229: Level: intermediate
3231: Developer Note:
3232: This `PetscDualSpace` seems to manage directly trimmed and untrimmed polynomials as well as tensor and non-tensor polynomials while for `PetscSpace` there seems to
3233: be different `PetscSpaceType` for them.
3235: .seealso: `PetscDualSpace`, `PetscDualSpaceType`, `PetscDualSpaceCreate()`, `PetscDualSpaceSetType()`,
3236: `PetscDualSpaceLagrangeSetMomentOrder()`, `PetscDualSpaceLagrangeGetMomentOrder()`, `PetscDualSpaceLagrangeSetUseMoments()`, `PetscDualSpaceLagrangeGetUseMoments()`,
3237: `PetscDualSpaceLagrangeSetNodeType, PetscDualSpaceLagrangeGetNodeType, PetscDualSpaceLagrangeGetContinuity, PetscDualSpaceLagrangeSetContinuity,
3238: `PetscDualSpaceLagrangeGetTensor()`, `PetscDualSpaceLagrangeSetTensor()`, `PetscDualSpaceLagrangeGetTrimmed()`, `PetscDualSpaceLagrangeSetTrimmed()`
3239: M*/
3240: PETSC_EXTERN PetscErrorCode PetscDualSpaceCreate_Lagrange(PetscDualSpace sp)
3241: {
3242: PetscDualSpace_Lag *lag;
3244: PetscFunctionBegin;
3246: PetscCall(PetscNew(&lag));
3247: sp->data = lag;
3249: lag->tensorCell = PETSC_FALSE;
3250: lag->tensorSpace = PETSC_FALSE;
3251: lag->continuous = PETSC_TRUE;
3252: lag->numCopies = PETSC_DEFAULT;
3253: lag->numNodeSkip = PETSC_DEFAULT;
3254: lag->nodeType = PETSCDTNODES_DEFAULT;
3255: lag->useMoments = PETSC_FALSE;
3256: lag->momentOrder = 0;
3258: PetscCall(PetscDualSpaceInitialize_Lagrange(sp));
3259: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetContinuity_C", PetscDualSpaceLagrangeGetContinuity_Lagrange));
3260: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetContinuity_C", PetscDualSpaceLagrangeSetContinuity_Lagrange));
3261: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetTensor_C", PetscDualSpaceLagrangeGetTensor_Lagrange));
3262: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetTensor_C", PetscDualSpaceLagrangeSetTensor_Lagrange));
3263: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetTrimmed_C", PetscDualSpaceLagrangeGetTrimmed_Lagrange));
3264: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetTrimmed_C", PetscDualSpaceLagrangeSetTrimmed_Lagrange));
3265: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetNodeType_C", PetscDualSpaceLagrangeGetNodeType_Lagrange));
3266: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetNodeType_C", PetscDualSpaceLagrangeSetNodeType_Lagrange));
3267: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetUseMoments_C", PetscDualSpaceLagrangeGetUseMoments_Lagrange));
3268: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetUseMoments_C", PetscDualSpaceLagrangeSetUseMoments_Lagrange));
3269: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeGetMomentOrder_C", PetscDualSpaceLagrangeGetMomentOrder_Lagrange));
3270: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscDualSpaceLagrangeSetMomentOrder_C", PetscDualSpaceLagrangeSetMomentOrder_Lagrange));
3271: PetscFunctionReturn(PETSC_SUCCESS);
3272: }