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(PetscSpaceSumSetInterleave(sp, PETSC_TRUE, PETSC_FALSE));
 72:     PetscCall(PetscSpaceCreate(PetscObjectComm((PetscObject)sp), &subsp));
 73:     PetscCall(PetscObjectGetOptionsPrefix((PetscObject)sp, &prefix));
 74:     PetscCall(PetscObjectSetOptionsPrefix((PetscObject)subsp, prefix));
 75:     PetscCall(PetscObjectAppendOptionsPrefix((PetscObject)subsp, "sumcomp_"));
 76:     if (((PetscObject)sp)->name) {
 77:       PetscCall(PetscObjectGetName((PetscObject)sp, &name));
 78:       PetscCall(PetscSNPrintf(subname, PETSC_MAX_PATH_LEN - 1, "%s sum component", name));
 79:       PetscCall(PetscObjectSetName((PetscObject)subsp, subname));
 80:     } else PetscCall(PetscObjectSetName((PetscObject)subsp, "sum component"));
 81:     PetscCall(PetscSpaceSetType(subsp, PETSCSPACEPOLYNOMIAL));
 82:     PetscCall(PetscSpaceSetDegree(subsp, degree, PETSC_DETERMINE));
 83:     PetscCall(PetscSpaceSetNumComponents(subsp, 1));
 84:     PetscCall(PetscSpaceSetNumVariables(subsp, Nv));
 85:     PetscCall(PetscSpacePolynomialSetTensor(subsp, tensor));
 86:     PetscCall(PetscSpaceSetUp(subsp));
 87:     for (PetscInt i = 0; i < Nc; i++) PetscCall(PetscSpaceSumSetSubspace(sp, i, subsp));
 88:     PetscCall(PetscSpaceDestroy(&subsp));
 89:     PetscCall(PetscSpaceSetUp(sp));
 90:     PetscFunctionReturn(PETSC_SUCCESS);
 91:   }
 92:   if (poly->tensor) {
 93:     sp->maxDegree = PETSC_DETERMINE;
 94:     PetscCall(PetscSpaceSetType(sp, PETSCSPACETENSOR));
 95:     PetscCall(PetscSpaceSetUp(sp));
 96:     PetscFunctionReturn(PETSC_SUCCESS);
 97:   }
 98:   PetscCheck(sp->degree >= 0, PetscObjectComm((PetscObject)sp), PETSC_ERR_ARG_OUTOFRANGE, "Negative degree %" PetscInt_FMT " invalid", sp->degree);
 99:   sp->maxDegree     = sp->degree;
100:   poly->setupCalled = PETSC_TRUE;
101:   PetscFunctionReturn(PETSC_SUCCESS);
102: }

104: static PetscErrorCode PetscSpaceGetDimension_Polynomial(PetscSpace sp, PetscInt *dim)
105: {
106:   PetscInt deg = sp->degree;
107:   PetscInt n   = sp->Nv;

109:   PetscFunctionBegin;
110:   PetscCall(PetscDTBinomialInt(n + deg, n, dim));
111:   *dim *= sp->Nc;
112:   PetscFunctionReturn(PETSC_SUCCESS);
113: }

115: static PetscErrorCode CoordinateBasis(PetscInt dim, PetscInt npoints, const PetscReal points[], PetscInt jet, PetscInt Njet, PetscReal pScalar[])
116: {
117:   PetscFunctionBegin;
118:   PetscCall(PetscArrayzero(pScalar, (1 + dim) * Njet * npoints));
119:   for (PetscInt b = 0; b < 1 + dim; b++) {
120:     for (PetscInt j = 0; j < PetscMin(1 + dim, Njet); j++) {
121:       if (j == 0) {
122:         if (b == 0) {
123:           for (PetscInt pt = 0; pt < npoints; pt++) pScalar[b * Njet * npoints + j * npoints + pt] = 1.;
124:         } else {
125:           for (PetscInt pt = 0; pt < npoints; pt++) pScalar[b * Njet * npoints + j * npoints + pt] = points[pt * dim + (b - 1)];
126:         }
127:       } else if (j == b) {
128:         for (PetscInt pt = 0; pt < npoints; pt++) pScalar[b * Njet * npoints + j * npoints + pt] = 1.;
129:       }
130:     }
131:   }
132:   PetscFunctionReturn(PETSC_SUCCESS);
133: }

135: static PetscErrorCode PetscSpaceEvaluate_Polynomial(PetscSpace sp, PetscInt npoints, const PetscReal points[], PetscReal B[], PetscReal D[], PetscReal H[])
136: {
137:   PetscSpace_Poly *poly = (PetscSpace_Poly *)sp->data;
138:   DM               dm   = sp->dm;
139:   PetscInt         dim  = sp->Nv;
140:   PetscInt         Nb, jet, Njet;
141:   PetscReal       *pScalar;

143:   PetscFunctionBegin;
144:   if (!poly->setupCalled) {
145:     PetscCall(PetscSpaceSetUp(sp));
146:     PetscCall(PetscSpaceEvaluate(sp, npoints, points, B, D, H));
147:     PetscFunctionReturn(PETSC_SUCCESS);
148:   }
149:   PetscCheck(!poly->tensor && sp->Nc == 1, PETSC_COMM_SELF, PETSC_ERR_PLIB, "tensor and multicomponent spaces should have been converted");
150:   PetscCall(PetscDTBinomialInt(dim + sp->degree, dim, &Nb));
151:   if (H) {
152:     jet = 2;
153:   } else if (D) {
154:     jet = 1;
155:   } else {
156:     jet = 0;
157:   }
158:   PetscCall(PetscDTBinomialInt(dim + jet, dim, &Njet));
159:   PetscCall(DMGetWorkArray(dm, Nb * Njet * npoints, MPIU_REAL, &pScalar));
160:   // Why are we handling the case degree == 1 specially?  Because we don't want numerical noise when we evaluate hat
161:   // functions at the vertices of a simplex, which happens when we invert the Vandermonde matrix of the PKD basis.
162:   // We don't make any promise about which basis is used.
163:   if (sp->degree == 1) {
164:     PetscCall(CoordinateBasis(dim, npoints, points, jet, Njet, pScalar));
165:   } else {
166:     PetscCall(PetscDTPKDEvalJet(dim, npoints, points, sp->degree, jet, pScalar));
167:   }
168:   if (B) {
169:     PetscInt p_strl = Nb;
170:     PetscInt b_strl = 1;

172:     PetscInt b_strr = Njet * npoints;
173:     PetscInt p_strr = 1;

175:     PetscCall(PetscArrayzero(B, npoints * Nb));
176:     for (PetscInt b = 0; b < Nb; b++) {
177:       for (PetscInt p = 0; p < npoints; p++) B[p * p_strl + b * b_strl] = pScalar[b * b_strr + p * p_strr];
178:     }
179:   }
180:   if (D) {
181:     PetscInt p_strl = dim * Nb;
182:     PetscInt b_strl = dim;
183:     PetscInt d_strl = 1;

185:     PetscInt b_strr = Njet * npoints;
186:     PetscInt d_strr = npoints;
187:     PetscInt p_strr = 1;

189:     PetscCall(PetscArrayzero(D, npoints * Nb * dim));
190:     for (PetscInt d = 0; d < dim; d++) {
191:       for (PetscInt b = 0; b < Nb; b++) {
192:         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];
193:       }
194:     }
195:   }
196:   if (H) {
197:     PetscInt p_strl  = dim * dim * Nb;
198:     PetscInt b_strl  = dim * dim;
199:     PetscInt d1_strl = dim;
200:     PetscInt d2_strl = 1;

202:     PetscInt b_strr = Njet * npoints;
203:     PetscInt j_strr = npoints;
204:     PetscInt p_strr = 1;

206:     PetscInt *derivs;
207:     PetscCall(PetscCalloc1(dim, &derivs));
208:     PetscCall(PetscArrayzero(H, npoints * Nb * dim * dim));
209:     for (PetscInt d1 = 0; d1 < dim; d1++) {
210:       for (PetscInt d2 = 0; d2 < dim; d2++) {
211:         PetscInt j;
212:         derivs[d1]++;
213:         derivs[d2]++;
214:         PetscCall(PetscDTGradedOrderToIndex(dim, derivs, &j));
215:         derivs[d1]--;
216:         derivs[d2]--;
217:         for (PetscInt b = 0; b < Nb; b++) {
218:           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];
219:         }
220:       }
221:     }
222:     PetscCall(PetscFree(derivs));
223:   }
224:   PetscCall(DMRestoreWorkArray(dm, Nb * Njet * npoints, MPIU_REAL, &pScalar));
225:   PetscFunctionReturn(PETSC_SUCCESS);
226: }

228: /*@
229:   PetscSpacePolynomialSetTensor - Set whether a function space is a space of tensor polynomials.

231:   Input Parameters:
232: + sp     - the function space object
233: - tensor - `PETSC_TRUE` for a tensor polynomial space, `PETSC_FALSE` for a polynomial space

235:   Options Database Key:
236: . -petscspace_poly_tensor <bool> - Whether to use tensor product polynomials in higher dimension

238:   Level: intermediate

240:   Notes:
241:   It is a tensor space if it is spanned by polynomials whose degree in each variable is
242:   bounded by the given order, as opposed to the space spanned by polynomials
243:   whose total degree---summing over all variables---is bounded by the given order.

245: .seealso: `PetscSpace`, `PetscSpacePolynomialGetTensor()`, `PetscSpaceSetDegree()`, `PetscSpaceSetNumVariables()`
246: @*/
247: PetscErrorCode PetscSpacePolynomialSetTensor(PetscSpace sp, PetscBool tensor)
248: {
249:   PetscFunctionBegin;
251:   PetscTryMethod(sp, "PetscSpacePolynomialSetTensor_C", (PetscSpace, PetscBool), (sp, tensor));
252:   PetscFunctionReturn(PETSC_SUCCESS);
253: }

255: /*@
256:   PetscSpacePolynomialGetTensor - Get whether a function space is a space of tensor
257:   polynomials.

259:   Input Parameter:
260: . sp - the function space object

262:   Output Parameter:
263: . tensor - `PETSC_TRUE` for a tensor polynomial space, `PETSC_FALSE` for a polynomial space

265:   Level: intermediate

267:   Notes:
268:   The space is a tensor space if it is spanned by polynomials whose degree in each variable is
269:   bounded by the given order, as opposed to the space spanned by polynomials
270:   whose total degree---summing over all variables---is bounded by the given order.

272: .seealso: `PetscSpace`, `PetscSpacePolynomialSetTensor()`, `PetscSpaceSetDegree()`, `PetscSpaceSetNumVariables()`
273: @*/
274: PetscErrorCode PetscSpacePolynomialGetTensor(PetscSpace sp, PetscBool *tensor)
275: {
276:   PetscFunctionBegin;
278:   PetscAssertPointer(tensor, 2);
279:   PetscTryMethod(sp, "PetscSpacePolynomialGetTensor_C", (PetscSpace, PetscBool *), (sp, tensor));
280:   PetscFunctionReturn(PETSC_SUCCESS);
281: }

283: static PetscErrorCode PetscSpacePolynomialSetTensor_Polynomial(PetscSpace sp, PetscBool tensor)
284: {
285:   PetscSpace_Poly *poly = (PetscSpace_Poly *)sp->data;

287:   PetscFunctionBegin;
288:   poly->tensor = tensor;
289:   PetscFunctionReturn(PETSC_SUCCESS);
290: }

292: static PetscErrorCode PetscSpacePolynomialGetTensor_Polynomial(PetscSpace sp, PetscBool *tensor)
293: {
294:   PetscSpace_Poly *poly = (PetscSpace_Poly *)sp->data;

296:   PetscFunctionBegin;
298:   PetscAssertPointer(tensor, 2);
299:   *tensor = poly->tensor;
300:   PetscFunctionReturn(PETSC_SUCCESS);
301: }

303: static PetscErrorCode PetscSpaceGetHeightSubspace_Polynomial(PetscSpace sp, PetscInt height, PetscSpace *subsp)
304: {
305:   PetscSpace_Poly *poly = (PetscSpace_Poly *)sp->data;
306:   PetscInt         Nc, dim, order;
307:   PetscBool        tensor;

309:   PetscFunctionBegin;
310:   PetscCall(PetscSpaceGetNumComponents(sp, &Nc));
311:   PetscCall(PetscSpaceGetNumVariables(sp, &dim));
312:   PetscCall(PetscSpaceGetDegree(sp, &order, NULL));
313:   PetscCall(PetscSpacePolynomialGetTensor(sp, &tensor));
314:   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);
315:   if (!poly->subspaces) PetscCall(PetscCalloc1(dim, &poly->subspaces));
316:   if (height <= dim) {
317:     if (!poly->subspaces[height - 1]) {
318:       PetscSpace  sub;
319:       const char *name;

321:       PetscCall(PetscSpaceCreate(PetscObjectComm((PetscObject)sp), &sub));
322:       PetscCall(PetscObjectGetName((PetscObject)sp, &name));
323:       PetscCall(PetscObjectSetName((PetscObject)sub, name));
324:       PetscCall(PetscSpaceSetType(sub, PETSCSPACEPOLYNOMIAL));
325:       PetscCall(PetscSpaceSetNumComponents(sub, Nc));
326:       PetscCall(PetscSpaceSetDegree(sub, order, PETSC_DETERMINE));
327:       PetscCall(PetscSpaceSetNumVariables(sub, dim - height));
328:       PetscCall(PetscSpacePolynomialSetTensor(sub, tensor));
329:       PetscCall(PetscSpaceSetUp(sub));
330:       poly->subspaces[height - 1] = sub;
331:     }
332:     *subsp = poly->subspaces[height - 1];
333:   } else {
334:     *subsp = NULL;
335:   }
336:   PetscFunctionReturn(PETSC_SUCCESS);
337: }

339: static PetscErrorCode PetscSpaceInitialize_Polynomial(PetscSpace sp)
340: {
341:   PetscFunctionBegin;
342:   sp->ops->setfromoptions    = PetscSpaceSetFromOptions_Polynomial;
343:   sp->ops->setup             = PetscSpaceSetUp_Polynomial;
344:   sp->ops->view              = PetscSpaceView_Polynomial;
345:   sp->ops->destroy           = PetscSpaceDestroy_Polynomial;
346:   sp->ops->getdimension      = PetscSpaceGetDimension_Polynomial;
347:   sp->ops->evaluate          = PetscSpaceEvaluate_Polynomial;
348:   sp->ops->getheightsubspace = PetscSpaceGetHeightSubspace_Polynomial;
349:   PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscSpacePolynomialGetTensor_C", PetscSpacePolynomialGetTensor_Polynomial));
350:   PetscCall(PetscObjectComposeFunction((PetscObject)sp, "PetscSpacePolynomialSetTensor_C", PetscSpacePolynomialSetTensor_Polynomial));
351:   PetscFunctionReturn(PETSC_SUCCESS);
352: }

354: /*MC
355:   PETSCSPACEPOLYNOMIAL = "poly" - A `PetscSpace` object that encapsulates a polynomial space, e.g. P1 is the space of
356:   linear polynomials. The space is replicated for each component.

358:   Level: intermediate

360: .seealso: `PetscSpace`, `PetscSpaceType`, `PetscSpaceCreate()`, `PetscSpaceSetType()`
361: M*/

363: PETSC_EXTERN PetscErrorCode PetscSpaceCreate_Polynomial(PetscSpace sp)
364: {
365:   PetscSpace_Poly *poly;

367:   PetscFunctionBegin;
369:   PetscCall(PetscNew(&poly));
370:   sp->data = poly;

372:   poly->tensor    = PETSC_FALSE;
373:   poly->subspaces = NULL;

375:   PetscCall(PetscSpaceInitialize_Polynomial(sp));
376:   PetscFunctionReturn(PETSC_SUCCESS);
377: }