Actual source code: spacepoly.c
1: #include <petsc/private/petscfeimpl.h>
3: static PetscErrorCode PetscSpaceSetFromOptions_Polynomial(PetscSpace sp, PetscOptionItems *PetscOptionsObject)
4: {
5: PetscSpace_Poly *poly = (PetscSpace_Poly *)sp->data;
7: PetscFunctionBegin;
8: PetscOptionsHeadBegin(PetscOptionsObject, "PetscSpace polynomial options");
9: PetscCall(PetscOptionsBool("-petscspace_poly_tensor", "Use the tensor product polynomials", "PetscSpacePolynomialSetTensor", poly->tensor, &poly->tensor, NULL));
10: PetscOptionsHeadEnd();
11: PetscFunctionReturn(PETSC_SUCCESS);
12: }
14: static PetscErrorCode PetscSpacePolynomialView_Ascii(PetscSpace sp, PetscViewer v)
15: {
16: PetscSpace_Poly *poly = (PetscSpace_Poly *)sp->data;
18: PetscFunctionBegin;
19: PetscCall(PetscViewerASCIIPrintf(v, "%s space of degree %" PetscInt_FMT "\n", poly->tensor ? "Tensor polynomial" : "Polynomial", sp->degree));
20: PetscFunctionReturn(PETSC_SUCCESS);
21: }
23: static PetscErrorCode PetscSpaceView_Polynomial(PetscSpace sp, PetscViewer viewer)
24: {
25: PetscBool iascii;
27: PetscFunctionBegin;
30: PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
31: if (iascii) PetscCall(PetscSpacePolynomialView_Ascii(sp, viewer));
32: PetscFunctionReturn(PETSC_SUCCESS);
33: }
35: static PetscErrorCode PetscSpaceDestroy_Polynomial(PetscSpace sp)
36: {
37: PetscSpace_Poly *poly = (PetscSpace_Poly *)sp->data;
39: PetscFunctionBegin;
40: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscSpacePolynomialGetTensor_C", NULL));
41: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscSpacePolynomialSetTensor_C", NULL));
42: if (poly->subspaces) {
43: PetscInt d;
45: for (d = 0; d < sp->Nv; ++d) PetscCall(PetscSpaceDestroy(&poly->subspaces[d]));
46: }
47: PetscCall(PetscFree(poly->subspaces));
48: PetscCall(PetscFree(poly));
49: PetscFunctionReturn(PETSC_SUCCESS);
50: }
52: static PetscErrorCode PetscSpaceSetUp_Polynomial(PetscSpace sp)
53: {
54: PetscSpace_Poly *poly = (PetscSpace_Poly *)sp->data;
56: PetscFunctionBegin;
57: if (poly->setupCalled) PetscFunctionReturn(PETSC_SUCCESS);
58: if (sp->Nv <= 1) poly->tensor = PETSC_FALSE;
59: if (sp->Nc != 1) {
60: PetscInt Nc = sp->Nc;
61: PetscBool tensor = poly->tensor;
62: PetscInt Nv = sp->Nv;
63: PetscInt degree = sp->degree;
64: const char *prefix;
65: const char *name;
66: char subname[PETSC_MAX_PATH_LEN];
67: PetscSpace subsp;
69: PetscCall(PetscSpaceSetType(sp, PETSCSPACESUM));
70: PetscCall(PetscSpaceSumSetNumSubspaces(sp, Nc));
71: PetscCall(PetscSpaceCreate(PetscObjectComm((PetscObject)sp), &subsp));
72: PetscCall(PetscObjectGetOptionsPrefix((PetscObject)sp, &prefix));
73: PetscCall(PetscObjectSetOptionsPrefix((PetscObject)subsp, prefix));
74: PetscCall(PetscObjectAppendOptionsPrefix((PetscObject)subsp, "sumcomp_"));
75: if (((PetscObject)sp)->name) {
76: PetscCall(PetscObjectGetName((PetscObject)sp, &name));
77: PetscCall(PetscSNPrintf(subname, PETSC_MAX_PATH_LEN - 1, "%s sum component", name));
78: PetscCall(PetscObjectSetName((PetscObject)subsp, subname));
79: } else PetscCall(PetscObjectSetName((PetscObject)subsp, "sum component"));
80: PetscCall(PetscSpaceSetType(subsp, PETSCSPACEPOLYNOMIAL));
81: PetscCall(PetscSpaceSetDegree(subsp, degree, PETSC_DETERMINE));
82: PetscCall(PetscSpaceSetNumComponents(subsp, 1));
83: PetscCall(PetscSpaceSetNumVariables(subsp, Nv));
84: PetscCall(PetscSpacePolynomialSetTensor(subsp, tensor));
85: PetscCall(PetscSpaceSetUp(subsp));
86: for (PetscInt i = 0; i < Nc; i++) PetscCall(PetscSpaceSumSetSubspace(sp, i, subsp));
87: PetscCall(PetscSpaceDestroy(&subsp));
88: PetscCall(PetscSpaceSetUp(sp));
89: PetscFunctionReturn(PETSC_SUCCESS);
90: }
91: if (poly->tensor) {
92: sp->maxDegree = PETSC_DETERMINE;
93: PetscCall(PetscSpaceSetType(sp, PETSCSPACETENSOR));
94: PetscCall(PetscSpaceSetUp(sp));
95: PetscFunctionReturn(PETSC_SUCCESS);
96: }
97: PetscCheck(sp->degree >= 0, PetscObjectComm((PetscObject)sp), PETSC_ERR_ARG_OUTOFRANGE, "Negative degree %" PetscInt_FMT " invalid", sp->degree);
98: sp->maxDegree = sp->degree;
99: poly->setupCalled = PETSC_TRUE;
100: PetscFunctionReturn(PETSC_SUCCESS);
101: }
103: static PetscErrorCode PetscSpaceGetDimension_Polynomial(PetscSpace sp, PetscInt *dim)
104: {
105: PetscInt deg = sp->degree;
106: PetscInt n = sp->Nv;
108: PetscFunctionBegin;
109: PetscCall(PetscDTBinomialInt(n + deg, n, dim));
110: *dim *= sp->Nc;
111: PetscFunctionReturn(PETSC_SUCCESS);
112: }
114: static PetscErrorCode CoordinateBasis(PetscInt dim, PetscInt npoints, const PetscReal points[], PetscInt jet, PetscInt Njet, PetscReal pScalar[])
115: {
116: PetscFunctionBegin;
117: PetscCall(PetscArrayzero(pScalar, (1 + dim) * Njet * npoints));
118: for (PetscInt b = 0; b < 1 + dim; b++) {
119: for (PetscInt j = 0; j < PetscMin(1 + dim, Njet); j++) {
120: if (j == 0) {
121: if (b == 0) {
122: for (PetscInt pt = 0; pt < npoints; pt++) pScalar[b * Njet * npoints + j * npoints + pt] = 1.;
123: } else {
124: for (PetscInt pt = 0; pt < npoints; pt++) pScalar[b * Njet * npoints + j * npoints + pt] = points[pt * dim + (b - 1)];
125: }
126: } else if (j == b) {
127: for (PetscInt pt = 0; pt < npoints; pt++) pScalar[b * Njet * npoints + j * npoints + pt] = 1.;
128: }
129: }
130: }
131: PetscFunctionReturn(PETSC_SUCCESS);
132: }
134: static PetscErrorCode PetscSpaceEvaluate_Polynomial(PetscSpace sp, PetscInt npoints, const PetscReal points[], PetscReal B[], PetscReal D[], PetscReal H[])
135: {
136: PetscSpace_Poly *poly = (PetscSpace_Poly *)sp->data;
137: DM dm = sp->dm;
138: PetscInt dim = sp->Nv;
139: PetscInt Nb, jet, Njet;
140: PetscReal *pScalar;
142: PetscFunctionBegin;
143: if (!poly->setupCalled) {
144: PetscCall(PetscSpaceSetUp(sp));
145: PetscCall(PetscSpaceEvaluate(sp, npoints, points, B, D, H));
146: PetscFunctionReturn(PETSC_SUCCESS);
147: }
148: PetscCheck(!poly->tensor && sp->Nc == 1, PETSC_COMM_SELF, PETSC_ERR_PLIB, "tensor and multicomponent spaces should have been converted");
149: PetscCall(PetscDTBinomialInt(dim + sp->degree, dim, &Nb));
150: if (H) {
151: jet = 2;
152: } else if (D) {
153: jet = 1;
154: } else {
155: jet = 0;
156: }
157: PetscCall(PetscDTBinomialInt(dim + jet, dim, &Njet));
158: PetscCall(DMGetWorkArray(dm, Nb * Njet * npoints, MPIU_REAL, &pScalar));
159: // Why are we handling the case degree == 1 specially? Because we don't want numerical noise when we evaluate hat
160: // functions at the vertices of a simplex, which happens when we invert the Vandermonde matrix of the PKD basis.
161: // We don't make any promise about which basis is used.
162: if (sp->degree == 1) {
163: PetscCall(CoordinateBasis(dim, npoints, points, jet, Njet, pScalar));
164: } else {
165: PetscCall(PetscDTPKDEvalJet(dim, npoints, points, sp->degree, jet, pScalar));
166: }
167: if (B) {
168: PetscInt p_strl = Nb;
169: PetscInt b_strl = 1;
171: PetscInt b_strr = Njet * npoints;
172: PetscInt p_strr = 1;
174: PetscCall(PetscArrayzero(B, npoints * Nb));
175: for (PetscInt b = 0; b < Nb; b++) {
176: for (PetscInt p = 0; p < npoints; p++) B[p * p_strl + b * b_strl] = pScalar[b * b_strr + p * p_strr];
177: }
178: }
179: if (D) {
180: PetscInt p_strl = dim * Nb;
181: PetscInt b_strl = dim;
182: PetscInt d_strl = 1;
184: PetscInt b_strr = Njet * npoints;
185: PetscInt d_strr = npoints;
186: PetscInt p_strr = 1;
188: PetscCall(PetscArrayzero(D, npoints * Nb * dim));
189: for (PetscInt d = 0; d < dim; d++) {
190: for (PetscInt b = 0; b < Nb; b++) {
191: for (PetscInt p = 0; p < npoints; p++) D[p * p_strl + b * b_strl + d * d_strl] = pScalar[b * b_strr + (1 + d) * d_strr + p * p_strr];
192: }
193: }
194: }
195: if (H) {
196: PetscInt p_strl = dim * dim * Nb;
197: PetscInt b_strl = dim * dim;
198: PetscInt d1_strl = dim;
199: PetscInt d2_strl = 1;
201: PetscInt b_strr = Njet * npoints;
202: PetscInt j_strr = npoints;
203: PetscInt p_strr = 1;
205: PetscInt *derivs;
206: PetscCall(PetscCalloc1(dim, &derivs));
207: PetscCall(PetscArrayzero(H, npoints * Nb * dim * dim));
208: for (PetscInt d1 = 0; d1 < dim; d1++) {
209: for (PetscInt d2 = 0; d2 < dim; d2++) {
210: PetscInt j;
211: derivs[d1]++;
212: derivs[d2]++;
213: PetscCall(PetscDTGradedOrderToIndex(dim, derivs, &j));
214: derivs[d1]--;
215: derivs[d2]--;
216: for (PetscInt b = 0; b < Nb; b++) {
217: for (PetscInt p = 0; p < npoints; p++) H[p * p_strl + b * b_strl + d1 * d1_strl + d2 * d2_strl] = pScalar[b * b_strr + j * j_strr + p * p_strr];
218: }
219: }
220: }
221: PetscCall(PetscFree(derivs));
222: }
223: PetscCall(DMRestoreWorkArray(dm, Nb * Njet * npoints, MPIU_REAL, &pScalar));
224: PetscFunctionReturn(PETSC_SUCCESS);
225: }
227: /*@
228: PetscSpacePolynomialSetTensor - Set whether a function space is a space of tensor polynomials (the space is spanned
229: by polynomials whose degree in each variable is bounded by the given order), as opposed to polynomials (the space is
230: spanned by polynomials whose total degree---summing over all variables---is bounded by the given order).
232: Input Parameters:
233: + sp - the function space object
234: - tensor - `PETSC_TRUE` for a tensor polynomial space, `PETSC_FALSE` for a polynomial space
236: Options Database Key:
237: . -petscspace_poly_tensor <bool> - Whether to use tensor product polynomials in higher dimension
239: Level: intermediate
241: .seealso: `PetscSpace`, `PetscSpacePolynomialGetTensor()`, `PetscSpaceSetDegree()`, `PetscSpaceSetNumVariables()`
242: @*/
243: PetscErrorCode PetscSpacePolynomialSetTensor(PetscSpace sp, PetscBool tensor)
244: {
245: PetscFunctionBegin;
247: PetscTryMethod(sp, "PetscSpacePolynomialSetTensor_C", (PetscSpace, PetscBool), (sp, tensor));
248: PetscFunctionReturn(PETSC_SUCCESS);
249: }
251: /*@
252: PetscSpacePolynomialGetTensor - Get whether a function space is a space of tensor polynomials (the space is spanned
253: by polynomials whose degree in each variable is bounded by the given order), as opposed to polynomials (the space is
254: spanned by polynomials whose total degree---summing over all variables---is bounded by the given order).
256: Input Parameter:
257: . sp - the function space object
259: Output Parameter:
260: . tensor - `PETSC_TRUE` for a tensor polynomial space, `PETSC_FALSE` for a polynomial space
262: Level: intermediate
264: .seealso: `PetscSpace`, `PetscSpacePolynomialSetTensor()`, `PetscSpaceSetDegree()`, `PetscSpaceSetNumVariables()`
265: @*/
266: PetscErrorCode PetscSpacePolynomialGetTensor(PetscSpace sp, PetscBool *tensor)
267: {
268: PetscFunctionBegin;
271: PetscTryMethod(sp, "PetscSpacePolynomialGetTensor_C", (PetscSpace, PetscBool *), (sp, tensor));
272: PetscFunctionReturn(PETSC_SUCCESS);
273: }
275: static PetscErrorCode PetscSpacePolynomialSetTensor_Polynomial(PetscSpace sp, PetscBool tensor)
276: {
277: PetscSpace_Poly *poly = (PetscSpace_Poly *)sp->data;
279: PetscFunctionBegin;
280: poly->tensor = tensor;
281: PetscFunctionReturn(PETSC_SUCCESS);
282: }
284: static PetscErrorCode PetscSpacePolynomialGetTensor_Polynomial(PetscSpace sp, PetscBool *tensor)
285: {
286: PetscSpace_Poly *poly = (PetscSpace_Poly *)sp->data;
288: PetscFunctionBegin;
291: *tensor = poly->tensor;
292: PetscFunctionReturn(PETSC_SUCCESS);
293: }
295: static PetscErrorCode PetscSpaceGetHeightSubspace_Polynomial(PetscSpace sp, PetscInt height, PetscSpace *subsp)
296: {
297: PetscSpace_Poly *poly = (PetscSpace_Poly *)sp->data;
298: PetscInt Nc, dim, order;
299: PetscBool tensor;
301: PetscFunctionBegin;
302: PetscCall(PetscSpaceGetNumComponents(sp, &Nc));
303: PetscCall(PetscSpaceGetNumVariables(sp, &dim));
304: PetscCall(PetscSpaceGetDegree(sp, &order, NULL));
305: PetscCall(PetscSpacePolynomialGetTensor(sp, &tensor));
306: PetscCheck(height <= dim && height >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Asked for space at height %" PetscInt_FMT " for dimension %" PetscInt_FMT " space", height, dim);
307: if (!poly->subspaces) PetscCall(PetscCalloc1(dim, &poly->subspaces));
308: if (height <= dim) {
309: if (!poly->subspaces[height - 1]) {
310: PetscSpace sub;
311: const char *name;
313: PetscCall(PetscSpaceCreate(PetscObjectComm((PetscObject)sp), &sub));
314: PetscCall(PetscObjectGetName((PetscObject)sp, &name));
315: PetscCall(PetscObjectSetName((PetscObject)sub, name));
316: PetscCall(PetscSpaceSetType(sub, PETSCSPACEPOLYNOMIAL));
317: PetscCall(PetscSpaceSetNumComponents(sub, Nc));
318: PetscCall(PetscSpaceSetDegree(sub, order, PETSC_DETERMINE));
319: PetscCall(PetscSpaceSetNumVariables(sub, dim - height));
320: PetscCall(PetscSpacePolynomialSetTensor(sub, tensor));
321: PetscCall(PetscSpaceSetUp(sub));
322: poly->subspaces[height - 1] = sub;
323: }
324: *subsp = poly->subspaces[height - 1];
325: } else {
326: *subsp = NULL;
327: }
328: PetscFunctionReturn(PETSC_SUCCESS);
329: }
331: static PetscErrorCode PetscSpaceInitialize_Polynomial(PetscSpace sp)
332: {
333: PetscFunctionBegin;
334: sp->ops->setfromoptions = PetscSpaceSetFromOptions_Polynomial;
335: sp->ops->setup = PetscSpaceSetUp_Polynomial;
336: sp->ops->view = PetscSpaceView_Polynomial;
337: sp->ops->destroy = PetscSpaceDestroy_Polynomial;
338: sp->ops->getdimension = PetscSpaceGetDimension_Polynomial;
339: sp->ops->evaluate = PetscSpaceEvaluate_Polynomial;
340: sp->ops->getheightsubspace = PetscSpaceGetHeightSubspace_Polynomial;
341: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscSpacePolynomialGetTensor_C", PetscSpacePolynomialGetTensor_Polynomial));
342: PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscSpacePolynomialSetTensor_C", PetscSpacePolynomialSetTensor_Polynomial));
343: PetscFunctionReturn(PETSC_SUCCESS);
344: }
346: /*MC
347: PETSCSPACEPOLYNOMIAL = "poly" - A `PetscSpace` object that encapsulates a polynomial space, e.g. P1 is the space of
348: linear polynomials. The space is replicated for each component.
350: Level: intermediate
352: .seealso: `PetscSpace`, `PetscSpaceType`, `PetscSpaceCreate()`, `PetscSpaceSetType()`
353: M*/
355: PETSC_EXTERN PetscErrorCode PetscSpaceCreate_Polynomial(PetscSpace sp)
356: {
357: PetscSpace_Poly *poly;
359: PetscFunctionBegin;
361: PetscCall(PetscNew(&poly));
362: sp->data = poly;
364: poly->tensor = PETSC_FALSE;
365: poly->subspaces = NULL;
367: PetscCall(PetscSpaceInitialize_Polynomial(sp));
368: PetscFunctionReturn(PETSC_SUCCESS);
369: }