Actual source code: dmplexts.c
1: #include <petsc/private/dmpleximpl.h>
2: #include <petsc/private/tsimpl.h>
3: #include <petsc/private/snesimpl.h>
4: #include <petscds.h>
5: #include <petscfv.h>
7: static PetscErrorCode DMTSConvertPlex(DM dm, DM *plex, PetscBool copy)
8: {
9: PetscBool isPlex;
11: PetscFunctionBegin;
12: PetscCall(PetscObjectTypeCompare((PetscObject)dm, DMPLEX, &isPlex));
13: if (isPlex) {
14: *plex = dm;
15: PetscCall(PetscObjectReference((PetscObject)dm));
16: } else {
17: PetscCall(PetscObjectQuery((PetscObject)dm, "dm_plex", (PetscObject *)plex));
18: if (!*plex) {
19: PetscCall(DMConvert(dm, DMPLEX, plex));
20: PetscCall(PetscObjectCompose((PetscObject)dm, "dm_plex", (PetscObject)*plex));
21: if (copy) {
22: PetscCall(DMCopyDMTS(dm, *plex));
23: PetscCall(DMCopyDMSNES(dm, *plex));
24: PetscCall(DMCopyAuxiliaryVec(dm, *plex));
25: }
26: } else {
27: PetscCall(PetscObjectReference((PetscObject)*plex));
28: }
29: }
30: PetscFunctionReturn(PETSC_SUCCESS);
31: }
33: /*@
34: DMPlexTSComputeRHSFunctionFVM - Form the local forcing F from the local input X using pointwise functions specified by the user
36: Input Parameters:
37: + dm - The mesh
38: . t - The time
39: . locX - Local solution
40: - user - The user context
42: Output Parameter:
43: . F - Global output vector
45: Level: developer
47: .seealso: [](chapter_ts), `DMPLEX`, `TS`, `DMPlexComputeJacobianActionFEM()`
48: @*/
49: PetscErrorCode DMPlexTSComputeRHSFunctionFVM(DM dm, PetscReal time, Vec locX, Vec F, void *user)
50: {
51: Vec locF;
52: IS cellIS;
53: DM plex;
54: PetscInt depth;
55: PetscFormKey key = {NULL, 0, 0, 0};
57: PetscFunctionBegin;
58: PetscCall(DMTSConvertPlex(dm, &plex, PETSC_TRUE));
59: PetscCall(DMPlexGetDepth(plex, &depth));
60: PetscCall(DMGetStratumIS(plex, "dim", depth, &cellIS));
61: if (!cellIS) PetscCall(DMGetStratumIS(plex, "depth", depth, &cellIS));
62: PetscCall(DMGetLocalVector(plex, &locF));
63: PetscCall(VecZeroEntries(locF));
64: PetscCall(DMPlexComputeResidual_Internal(plex, key, cellIS, time, locX, NULL, time, locF, user));
65: PetscCall(DMLocalToGlobalBegin(plex, locF, ADD_VALUES, F));
66: PetscCall(DMLocalToGlobalEnd(plex, locF, ADD_VALUES, F));
67: PetscCall(DMRestoreLocalVector(plex, &locF));
68: PetscCall(ISDestroy(&cellIS));
69: PetscCall(DMDestroy(&plex));
70: PetscFunctionReturn(PETSC_SUCCESS);
71: }
73: /*@
74: DMPlexTSComputeBoundary - Insert the essential boundary values for the local input X and/or its time derivative X_t using pointwise functions specified by the user
76: Input Parameters:
77: + dm - The mesh
78: . t - The time
79: . locX - Local solution
80: . locX_t - Local solution time derivative, or NULL
81: - user - The user context
83: Level: developer
85: .seealso: [](chapter_ts), `DMPLEX`, `TS`, `DMPlexComputeJacobianActionFEM()`
86: @*/
87: PetscErrorCode DMPlexTSComputeBoundary(DM dm, PetscReal time, Vec locX, Vec locX_t, void *user)
88: {
89: DM plex;
90: Vec faceGeometryFVM = NULL;
91: PetscInt Nf, f;
93: PetscFunctionBegin;
94: PetscCall(DMTSConvertPlex(dm, &plex, PETSC_TRUE));
95: PetscCall(DMGetNumFields(plex, &Nf));
96: if (!locX_t) {
97: /* This is the RHS part */
98: for (f = 0; f < Nf; f++) {
99: PetscObject obj;
100: PetscClassId id;
102: PetscCall(DMGetField(plex, f, NULL, &obj));
103: PetscCall(PetscObjectGetClassId(obj, &id));
104: if (id == PETSCFV_CLASSID) {
105: PetscCall(DMPlexGetGeometryFVM(plex, &faceGeometryFVM, NULL, NULL));
106: break;
107: }
108: }
109: }
110: PetscCall(DMPlexInsertBoundaryValues(plex, PETSC_TRUE, locX, time, faceGeometryFVM, NULL, NULL));
111: PetscCall(DMPlexInsertTimeDerivativeBoundaryValues(plex, PETSC_TRUE, locX_t, time, faceGeometryFVM, NULL, NULL));
112: PetscCall(DMDestroy(&plex));
113: PetscFunctionReturn(PETSC_SUCCESS);
114: }
116: /*@
117: DMPlexTSComputeIFunctionFEM - Form the local residual F from the local input X using pointwise functions specified by the user
119: Input Parameters:
120: + dm - The mesh
121: . t - The time
122: . locX - Local solution
123: . locX_t - Local solution time derivative, or NULL
124: - user - The user context
126: Output Parameter:
127: . locF - Local output vector
129: Level: developer
131: .seealso: [](chapter_ts), `DMPLEX`, `TS`, `DMPlexTSComputeIFunctionFEM()`, `DMPlexTSComputeRHSFunctionFEM()`
132: @*/
133: PetscErrorCode DMPlexTSComputeIFunctionFEM(DM dm, PetscReal time, Vec locX, Vec locX_t, Vec locF, void *user)
134: {
135: DM plex;
136: IS allcellIS;
137: PetscInt Nds, s;
139: PetscFunctionBegin;
140: PetscCall(DMTSConvertPlex(dm, &plex, PETSC_TRUE));
141: PetscCall(DMPlexGetAllCells_Internal(plex, &allcellIS));
142: PetscCall(DMGetNumDS(dm, &Nds));
143: for (s = 0; s < Nds; ++s) {
144: PetscDS ds;
145: IS cellIS;
146: PetscFormKey key;
148: PetscCall(DMGetRegionNumDS(dm, s, &key.label, NULL, &ds));
149: key.value = 0;
150: key.field = 0;
151: key.part = 0;
152: if (!key.label) {
153: PetscCall(PetscObjectReference((PetscObject)allcellIS));
154: cellIS = allcellIS;
155: } else {
156: IS pointIS;
158: key.value = 1;
159: PetscCall(DMLabelGetStratumIS(key.label, key.value, &pointIS));
160: PetscCall(ISIntersect_Caching_Internal(allcellIS, pointIS, &cellIS));
161: PetscCall(ISDestroy(&pointIS));
162: }
163: PetscCall(DMPlexComputeResidual_Internal(plex, key, cellIS, time, locX, locX_t, time, locF, user));
164: PetscCall(ISDestroy(&cellIS));
165: }
166: PetscCall(ISDestroy(&allcellIS));
167: PetscCall(DMDestroy(&plex));
168: PetscFunctionReturn(PETSC_SUCCESS);
169: }
171: /*@
172: DMPlexTSComputeIJacobianFEM - Form the local Jacobian J from the local input X using pointwise functions specified by the user
174: Input Parameters:
175: + dm - The mesh
176: . t - The time
177: . locX - Local solution
178: . locX_t - Local solution time derivative, or NULL
179: . X_tshift - The multiplicative parameter for dF/du_t
180: - user - The user context
182: Output Parameter:
183: . locF - Local output vector
185: Level: developer
187: .seealso: [](chapter_ts), `TS`, `DM`, `DMPlexTSComputeIFunctionFEM()`, `DMPlexTSComputeRHSFunctionFEM()`
188: @*/
189: PetscErrorCode DMPlexTSComputeIJacobianFEM(DM dm, PetscReal time, Vec locX, Vec locX_t, PetscReal X_tShift, Mat Jac, Mat JacP, void *user)
190: {
191: DM plex;
192: IS allcellIS;
193: PetscBool hasJac, hasPrec;
194: PetscInt Nds, s;
196: PetscFunctionBegin;
197: PetscCall(DMTSConvertPlex(dm, &plex, PETSC_TRUE));
198: PetscCall(DMPlexGetAllCells_Internal(plex, &allcellIS));
199: PetscCall(DMGetNumDS(dm, &Nds));
200: for (s = 0; s < Nds; ++s) {
201: PetscDS ds;
202: IS cellIS;
203: PetscFormKey key;
205: PetscCall(DMGetRegionNumDS(dm, s, &key.label, NULL, &ds));
206: key.value = 0;
207: key.field = 0;
208: key.part = 0;
209: if (!key.label) {
210: PetscCall(PetscObjectReference((PetscObject)allcellIS));
211: cellIS = allcellIS;
212: } else {
213: IS pointIS;
215: key.value = 1;
216: PetscCall(DMLabelGetStratumIS(key.label, key.value, &pointIS));
217: PetscCall(ISIntersect_Caching_Internal(allcellIS, pointIS, &cellIS));
218: PetscCall(ISDestroy(&pointIS));
219: }
220: if (!s) {
221: PetscCall(PetscDSHasJacobian(ds, &hasJac));
222: PetscCall(PetscDSHasJacobianPreconditioner(ds, &hasPrec));
223: if (hasJac && hasPrec) PetscCall(MatZeroEntries(Jac));
224: PetscCall(MatZeroEntries(JacP));
225: }
226: PetscCall(DMPlexComputeJacobian_Internal(plex, key, cellIS, time, X_tShift, locX, locX_t, Jac, JacP, user));
227: PetscCall(ISDestroy(&cellIS));
228: }
229: PetscCall(ISDestroy(&allcellIS));
230: PetscCall(DMDestroy(&plex));
231: PetscFunctionReturn(PETSC_SUCCESS);
232: }
234: /*@
235: DMPlexTSComputeRHSFunctionFEM - Form the local residual G from the local input X using pointwise functions specified by the user
237: Input Parameters:
238: + dm - The mesh
239: . t - The time
240: . locX - Local solution
241: - user - The user context
243: Output Parameter:
244: . locG - Local output vector
246: Level: developer
248: .seealso: [](chapter_ts), `TS`, `DM`, `DMPlexTSComputeIFunctionFEM()`, `DMPlexTSComputeIJacobianFEM()`
249: @*/
250: PetscErrorCode DMPlexTSComputeRHSFunctionFEM(DM dm, PetscReal time, Vec locX, Vec locG, void *user)
251: {
252: DM plex;
253: IS allcellIS;
254: PetscInt Nds, s;
256: PetscFunctionBegin;
257: PetscCall(DMTSConvertPlex(dm, &plex, PETSC_TRUE));
258: PetscCall(DMPlexGetAllCells_Internal(plex, &allcellIS));
259: PetscCall(DMGetNumDS(dm, &Nds));
260: for (s = 0; s < Nds; ++s) {
261: PetscDS ds;
262: IS cellIS;
263: PetscFormKey key;
265: PetscCall(DMGetRegionNumDS(dm, s, &key.label, NULL, &ds));
266: key.value = 0;
267: key.field = 0;
268: key.part = 100;
269: if (!key.label) {
270: PetscCall(PetscObjectReference((PetscObject)allcellIS));
271: cellIS = allcellIS;
272: } else {
273: IS pointIS;
275: key.value = 1;
276: PetscCall(DMLabelGetStratumIS(key.label, key.value, &pointIS));
277: PetscCall(ISIntersect_Caching_Internal(allcellIS, pointIS, &cellIS));
278: PetscCall(ISDestroy(&pointIS));
279: }
280: PetscCall(DMPlexComputeResidual_Internal(plex, key, cellIS, time, locX, NULL, time, locG, user));
281: PetscCall(ISDestroy(&cellIS));
282: }
283: PetscCall(ISDestroy(&allcellIS));
284: PetscCall(DMDestroy(&plex));
285: PetscFunctionReturn(PETSC_SUCCESS);
286: }
288: /*@C
289: DMTSCheckResidual - Check the residual of the exact solution
291: Input Parameters:
292: + ts - the `TS` object
293: . dm - the `DM`
294: . t - the time
295: . u - a `DM` vector
296: . u_t - a `DM` vector
297: - tol - A tolerance for the check, or -1 to print the results instead
299: Output Parameters:
300: . residual - The residual norm of the exact solution, or NULL
302: Level: developer
304: .seealso: [](chapter_ts), `DM`, `DMTSCheckFromOptions()`, `DMTSCheckJacobian()`, `DNSNESCheckFromOptions()`, `DMSNESCheckDiscretization()`, `DMSNESCheckJacobian()`
305: @*/
306: PetscErrorCode DMTSCheckResidual(TS ts, DM dm, PetscReal t, Vec u, Vec u_t, PetscReal tol, PetscReal *residual)
307: {
308: MPI_Comm comm;
309: Vec r;
310: PetscReal res;
312: PetscFunctionBegin;
317: PetscCall(PetscObjectGetComm((PetscObject)ts, &comm));
318: PetscCall(DMComputeExactSolution(dm, t, u, u_t));
319: PetscCall(VecDuplicate(u, &r));
320: PetscCall(TSComputeIFunction(ts, t, u, u_t, r, PETSC_FALSE));
321: PetscCall(VecNorm(r, NORM_2, &res));
322: if (tol >= 0.0) {
323: PetscCheck(res <= tol, comm, PETSC_ERR_ARG_WRONG, "L_2 Residual %g exceeds tolerance %g", (double)res, (double)tol);
324: } else if (residual) {
325: *residual = res;
326: } else {
327: PetscCall(PetscPrintf(comm, "L_2 Residual: %g\n", (double)res));
328: PetscCall(VecChop(r, 1.0e-10));
329: PetscCall(PetscObjectCompose((PetscObject)r, "__Vec_bc_zero__", (PetscObject)dm));
330: PetscCall(PetscObjectSetName((PetscObject)r, "Initial Residual"));
331: PetscCall(PetscObjectSetOptionsPrefix((PetscObject)r, "res_"));
332: PetscCall(VecViewFromOptions(r, NULL, "-vec_view"));
333: PetscCall(PetscObjectCompose((PetscObject)r, "__Vec_bc_zero__", NULL));
334: }
335: PetscCall(VecDestroy(&r));
336: PetscFunctionReturn(PETSC_SUCCESS);
337: }
339: /*@C
340: DMTSCheckJacobian - Check the Jacobian of the exact solution against the residual using the Taylor Test
342: Input Parameters:
343: + ts - the TS object
344: . dm - the DM
345: . t - the time
346: . u - a DM vector
347: . u_t - a DM vector
348: - tol - A tolerance for the check, or -1 to print the results instead
350: Output Parameters:
351: + isLinear - Flag indicaing that the function looks linear, or NULL
352: - convRate - The rate of convergence of the linear model, or NULL
354: Level: developer
356: .seealso: [](chapter_ts), `DNTSCheckFromOptions()`, `DMTSCheckResidual()`, `DNSNESCheckFromOptions()`, `DMSNESCheckDiscretization()`, `DMSNESCheckResidual()`
357: @*/
358: PetscErrorCode DMTSCheckJacobian(TS ts, DM dm, PetscReal t, Vec u, Vec u_t, PetscReal tol, PetscBool *isLinear, PetscReal *convRate)
359: {
360: MPI_Comm comm;
361: PetscDS ds;
362: Mat J, M;
363: MatNullSpace nullspace;
364: PetscReal dt, shift, slope, intercept;
365: PetscBool hasJac, hasPrec, isLin = PETSC_FALSE;
367: PetscFunctionBegin;
373: PetscCall(PetscObjectGetComm((PetscObject)ts, &comm));
374: PetscCall(DMComputeExactSolution(dm, t, u, u_t));
375: /* Create and view matrices */
376: PetscCall(TSGetTimeStep(ts, &dt));
377: shift = 1.0 / dt;
378: PetscCall(DMCreateMatrix(dm, &J));
379: PetscCall(DMGetDS(dm, &ds));
380: PetscCall(PetscDSHasJacobian(ds, &hasJac));
381: PetscCall(PetscDSHasJacobianPreconditioner(ds, &hasPrec));
382: if (hasJac && hasPrec) {
383: PetscCall(DMCreateMatrix(dm, &M));
384: PetscCall(TSComputeIJacobian(ts, t, u, u_t, shift, J, M, PETSC_FALSE));
385: PetscCall(PetscObjectSetName((PetscObject)M, "Preconditioning Matrix"));
386: PetscCall(PetscObjectSetOptionsPrefix((PetscObject)M, "jacpre_"));
387: PetscCall(MatViewFromOptions(M, NULL, "-mat_view"));
388: PetscCall(MatDestroy(&M));
389: } else {
390: PetscCall(TSComputeIJacobian(ts, t, u, u_t, shift, J, J, PETSC_FALSE));
391: }
392: PetscCall(PetscObjectSetName((PetscObject)J, "Jacobian"));
393: PetscCall(PetscObjectSetOptionsPrefix((PetscObject)J, "jac_"));
394: PetscCall(MatViewFromOptions(J, NULL, "-mat_view"));
395: /* Check nullspace */
396: PetscCall(MatGetNullSpace(J, &nullspace));
397: if (nullspace) {
398: PetscBool isNull;
399: PetscCall(MatNullSpaceTest(nullspace, J, &isNull));
400: PetscCheck(isNull, comm, PETSC_ERR_PLIB, "The null space calculated for the system operator is invalid.");
401: }
402: /* Taylor test */
403: {
404: PetscRandom rand;
405: Vec du, uhat, uhat_t, r, rhat, df;
406: PetscReal h;
407: PetscReal *es, *hs, *errors;
408: PetscReal hMax = 1.0, hMin = 1e-6, hMult = 0.1;
409: PetscInt Nv, v;
411: /* Choose a perturbation direction */
412: PetscCall(PetscRandomCreate(comm, &rand));
413: PetscCall(VecDuplicate(u, &du));
414: PetscCall(VecSetRandom(du, rand));
415: PetscCall(PetscRandomDestroy(&rand));
416: PetscCall(VecDuplicate(u, &df));
417: PetscCall(MatMult(J, du, df));
418: /* Evaluate residual at u, F(u), save in vector r */
419: PetscCall(VecDuplicate(u, &r));
420: PetscCall(TSComputeIFunction(ts, t, u, u_t, r, PETSC_FALSE));
421: /* Look at the convergence of our Taylor approximation as we approach u */
422: for (h = hMax, Nv = 0; h >= hMin; h *= hMult, ++Nv)
423: ;
424: PetscCall(PetscCalloc3(Nv, &es, Nv, &hs, Nv, &errors));
425: PetscCall(VecDuplicate(u, &uhat));
426: PetscCall(VecDuplicate(u, &uhat_t));
427: PetscCall(VecDuplicate(u, &rhat));
428: for (h = hMax, Nv = 0; h >= hMin; h *= hMult, ++Nv) {
429: PetscCall(VecWAXPY(uhat, h, du, u));
430: PetscCall(VecWAXPY(uhat_t, h * shift, du, u_t));
431: /* F(\hat u, \hat u_t) \approx F(u, u_t) + J(u, u_t) (uhat - u) + J_t(u, u_t) (uhat_t - u_t) = F(u) + h * J(u) du + h * shift * J_t(u) du = F(u) + h F' du */
432: PetscCall(TSComputeIFunction(ts, t, uhat, uhat_t, rhat, PETSC_FALSE));
433: PetscCall(VecAXPBYPCZ(rhat, -1.0, -h, 1.0, r, df));
434: PetscCall(VecNorm(rhat, NORM_2, &errors[Nv]));
436: es[Nv] = PetscLog10Real(errors[Nv]);
437: hs[Nv] = PetscLog10Real(h);
438: }
439: PetscCall(VecDestroy(&uhat));
440: PetscCall(VecDestroy(&uhat_t));
441: PetscCall(VecDestroy(&rhat));
442: PetscCall(VecDestroy(&df));
443: PetscCall(VecDestroy(&r));
444: PetscCall(VecDestroy(&du));
445: for (v = 0; v < Nv; ++v) {
446: if ((tol >= 0) && (errors[v] > tol)) break;
447: else if (errors[v] > PETSC_SMALL) break;
448: }
449: if (v == Nv) isLin = PETSC_TRUE;
450: PetscCall(PetscLinearRegression(Nv, hs, es, &slope, &intercept));
451: PetscCall(PetscFree3(es, hs, errors));
452: /* Slope should be about 2 */
453: if (tol >= 0) {
454: PetscCheck(isLin || PetscAbsReal(2 - slope) <= tol, comm, PETSC_ERR_ARG_WRONG, "Taylor approximation convergence rate should be 2, not %0.2f", (double)slope);
455: } else if (isLinear || convRate) {
456: if (isLinear) *isLinear = isLin;
457: if (convRate) *convRate = slope;
458: } else {
459: if (!isLin) PetscCall(PetscPrintf(comm, "Taylor approximation converging at order %3.2f\n", (double)slope));
460: else PetscCall(PetscPrintf(comm, "Function appears to be linear\n"));
461: }
462: }
463: PetscCall(MatDestroy(&J));
464: PetscFunctionReturn(PETSC_SUCCESS);
465: }
467: /*@C
468: DMTSCheckFromOptions - Check the residual and Jacobian functions using the exact solution by outputting some diagnostic information
470: Input Parameters:
471: + ts - the `TS` object
472: - u - representative `TS` vector
474: Note:
475: The user must call `PetscDSSetExactSolution()` beforehand
477: Level: developer
478: @*/
479: PetscErrorCode DMTSCheckFromOptions(TS ts, Vec u)
480: {
481: DM dm;
482: SNES snes;
483: Vec sol, u_t;
484: PetscReal t;
485: PetscBool check;
487: PetscFunctionBegin;
488: PetscCall(PetscOptionsHasName(((PetscObject)ts)->options, ((PetscObject)ts)->prefix, "-dmts_check", &check));
489: if (!check) PetscFunctionReturn(PETSC_SUCCESS);
490: PetscCall(VecDuplicate(u, &sol));
491: PetscCall(VecCopy(u, sol));
492: PetscCall(TSSetSolution(ts, u));
493: PetscCall(TSGetDM(ts, &dm));
494: PetscCall(TSSetUp(ts));
495: PetscCall(TSGetSNES(ts, &snes));
496: PetscCall(SNESSetSolution(snes, u));
498: PetscCall(TSGetTime(ts, &t));
499: PetscCall(DMSNESCheckDiscretization(snes, dm, t, sol, -1.0, NULL));
500: PetscCall(DMGetGlobalVector(dm, &u_t));
501: PetscCall(DMTSCheckResidual(ts, dm, t, sol, u_t, -1.0, NULL));
502: PetscCall(DMTSCheckJacobian(ts, dm, t, sol, u_t, -1.0, NULL, NULL));
503: PetscCall(DMRestoreGlobalVector(dm, &u_t));
505: PetscCall(VecDestroy(&sol));
506: PetscFunctionReturn(PETSC_SUCCESS);
507: }