Actual source code: mg.c


  2: /*
  3:     Defines the multigrid preconditioner interface.
  4: */
  5: #include <petsc/private/pcmgimpl.h>
  6: #include <petsc/private/kspimpl.h>
  7: #include <petscdm.h>
  8: PETSC_INTERN PetscErrorCode PCPreSolveChangeRHS(PC, PetscBool *);

 10: /*
 11:    Contains the list of registered coarse space construction routines
 12: */
 13: PetscFunctionList PCMGCoarseList = NULL;

 15: PetscErrorCode PCMGMCycle_Private(PC pc, PC_MG_Levels **mglevelsin, PetscBool transpose, PetscBool matapp, PCRichardsonConvergedReason *reason)
 16: {
 17:   PC_MG        *mg = (PC_MG *)pc->data;
 18:   PC_MG_Levels *mgc, *mglevels = *mglevelsin;
 19:   PetscInt      cycles = (mglevels->level == 1) ? 1 : (PetscInt)mglevels->cycles;

 21:   PetscFunctionBegin;
 22:   if (mglevels->eventsmoothsolve) PetscCall(PetscLogEventBegin(mglevels->eventsmoothsolve, 0, 0, 0, 0));
 23:   if (!transpose) {
 24:     if (matapp) {
 25:       PetscCall(KSPMatSolve(mglevels->smoothd, mglevels->B, mglevels->X)); /* pre-smooth */
 26:       PetscCall(KSPCheckSolve(mglevels->smoothd, pc, NULL));
 27:     } else {
 28:       PetscCall(KSPSolve(mglevels->smoothd, mglevels->b, mglevels->x)); /* pre-smooth */
 29:       PetscCall(KSPCheckSolve(mglevels->smoothd, pc, mglevels->x));
 30:     }
 31:   } else {
 32:     PetscCheck(!matapp, PetscObjectComm((PetscObject)pc), PETSC_ERR_SUP, "Not supported");
 33:     PetscCall(KSPSolveTranspose(mglevels->smoothu, mglevels->b, mglevels->x)); /* transpose of post-smooth */
 34:     PetscCall(KSPCheckSolve(mglevels->smoothu, pc, mglevels->x));
 35:   }
 36:   if (mglevels->eventsmoothsolve) PetscCall(PetscLogEventEnd(mglevels->eventsmoothsolve, 0, 0, 0, 0));
 37:   if (mglevels->level) { /* not the coarsest grid */
 38:     if (mglevels->eventresidual) PetscCall(PetscLogEventBegin(mglevels->eventresidual, 0, 0, 0, 0));
 39:     if (matapp && !mglevels->R) PetscCall(MatDuplicate(mglevels->B, MAT_DO_NOT_COPY_VALUES, &mglevels->R));
 40:     if (!transpose) {
 41:       if (matapp) PetscCall((*mglevels->matresidual)(mglevels->A, mglevels->B, mglevels->X, mglevels->R));
 42:       else PetscCall((*mglevels->residual)(mglevels->A, mglevels->b, mglevels->x, mglevels->r));
 43:     } else {
 44:       if (matapp) PetscCall((*mglevels->matresidualtranspose)(mglevels->A, mglevels->B, mglevels->X, mglevels->R));
 45:       else PetscCall((*mglevels->residualtranspose)(mglevels->A, mglevels->b, mglevels->x, mglevels->r));
 46:     }
 47:     if (mglevels->eventresidual) PetscCall(PetscLogEventEnd(mglevels->eventresidual, 0, 0, 0, 0));

 49:     /* if on finest level and have convergence criteria set */
 50:     if (mglevels->level == mglevels->levels - 1 && mg->ttol && reason) {
 51:       PetscReal rnorm;
 52:       PetscCall(VecNorm(mglevels->r, NORM_2, &rnorm));
 53:       if (rnorm <= mg->ttol) {
 54:         if (rnorm < mg->abstol) {
 55:           *reason = PCRICHARDSON_CONVERGED_ATOL;
 56:           PetscCall(PetscInfo(pc, "Linear solver has converged. Residual norm %g is less than absolute tolerance %g\n", (double)rnorm, (double)mg->abstol));
 57:         } else {
 58:           *reason = PCRICHARDSON_CONVERGED_RTOL;
 59:           PetscCall(PetscInfo(pc, "Linear solver has converged. Residual norm %g is less than relative tolerance times initial residual norm %g\n", (double)rnorm, (double)mg->ttol));
 60:         }
 61:         PetscFunctionReturn(PETSC_SUCCESS);
 62:       }
 63:     }

 65:     mgc = *(mglevelsin - 1);
 66:     if (mglevels->eventinterprestrict) PetscCall(PetscLogEventBegin(mglevels->eventinterprestrict, 0, 0, 0, 0));
 67:     if (!transpose) {
 68:       if (matapp) PetscCall(MatMatRestrict(mglevels->restrct, mglevels->R, &mgc->B));
 69:       else PetscCall(MatRestrict(mglevels->restrct, mglevels->r, mgc->b));
 70:     } else {
 71:       if (matapp) PetscCall(MatMatRestrict(mglevels->interpolate, mglevels->R, &mgc->B));
 72:       else PetscCall(MatRestrict(mglevels->interpolate, mglevels->r, mgc->b));
 73:     }
 74:     if (mglevels->eventinterprestrict) PetscCall(PetscLogEventEnd(mglevels->eventinterprestrict, 0, 0, 0, 0));
 75:     if (matapp) {
 76:       if (!mgc->X) {
 77:         PetscCall(MatDuplicate(mgc->B, MAT_DO_NOT_COPY_VALUES, &mgc->X));
 78:       } else {
 79:         PetscCall(MatZeroEntries(mgc->X));
 80:       }
 81:     } else {
 82:       PetscCall(VecZeroEntries(mgc->x));
 83:     }
 84:     while (cycles--) PetscCall(PCMGMCycle_Private(pc, mglevelsin - 1, transpose, matapp, reason));
 85:     if (mglevels->eventinterprestrict) PetscCall(PetscLogEventBegin(mglevels->eventinterprestrict, 0, 0, 0, 0));
 86:     if (!transpose) {
 87:       if (matapp) PetscCall(MatMatInterpolateAdd(mglevels->interpolate, mgc->X, mglevels->X, &mglevels->X));
 88:       else PetscCall(MatInterpolateAdd(mglevels->interpolate, mgc->x, mglevels->x, mglevels->x));
 89:     } else {
 90:       PetscCall(MatInterpolateAdd(mglevels->restrct, mgc->x, mglevels->x, mglevels->x));
 91:     }
 92:     if (mglevels->eventinterprestrict) PetscCall(PetscLogEventEnd(mglevels->eventinterprestrict, 0, 0, 0, 0));
 93:     if (mglevels->eventsmoothsolve) PetscCall(PetscLogEventBegin(mglevels->eventsmoothsolve, 0, 0, 0, 0));
 94:     if (!transpose) {
 95:       if (matapp) {
 96:         PetscCall(KSPMatSolve(mglevels->smoothu, mglevels->B, mglevels->X)); /* post smooth */
 97:         PetscCall(KSPCheckSolve(mglevels->smoothu, pc, NULL));
 98:       } else {
 99:         PetscCall(KSPSolve(mglevels->smoothu, mglevels->b, mglevels->x)); /* post smooth */
100:         PetscCall(KSPCheckSolve(mglevels->smoothu, pc, mglevels->x));
101:       }
102:     } else {
103:       PetscCheck(!matapp, PetscObjectComm((PetscObject)pc), PETSC_ERR_SUP, "Not supported");
104:       PetscCall(KSPSolveTranspose(mglevels->smoothd, mglevels->b, mglevels->x)); /* post smooth */
105:       PetscCall(KSPCheckSolve(mglevels->smoothd, pc, mglevels->x));
106:     }
107:     if (mglevels->cr) {
108:       PetscCheck(!matapp, PetscObjectComm((PetscObject)pc), PETSC_ERR_SUP, "Not supported");
109:       /* TODO Turn on copy and turn off noisy if we have an exact solution
110:       PetscCall(VecCopy(mglevels->x, mglevels->crx));
111:       PetscCall(VecCopy(mglevels->b, mglevels->crb)); */
112:       PetscCall(KSPSetNoisy_Private(mglevels->crx));
113:       PetscCall(KSPSolve(mglevels->cr, mglevels->crb, mglevels->crx)); /* compatible relaxation */
114:       PetscCall(KSPCheckSolve(mglevels->cr, pc, mglevels->crx));
115:     }
116:     if (mglevels->eventsmoothsolve) PetscCall(PetscLogEventEnd(mglevels->eventsmoothsolve, 0, 0, 0, 0));
117:   }
118:   PetscFunctionReturn(PETSC_SUCCESS);
119: }

121: static PetscErrorCode PCApplyRichardson_MG(PC pc, Vec b, Vec x, Vec w, PetscReal rtol, PetscReal abstol, PetscReal dtol, PetscInt its, PetscBool zeroguess, PetscInt *outits, PCRichardsonConvergedReason *reason)
122: {
123:   PC_MG         *mg       = (PC_MG *)pc->data;
124:   PC_MG_Levels **mglevels = mg->levels;
125:   PC             tpc;
126:   PetscBool      changeu, changed;
127:   PetscInt       levels = mglevels[0]->levels, i;

129:   PetscFunctionBegin;
130:   /* When the DM is supplying the matrix then it will not exist until here */
131:   for (i = 0; i < levels; i++) {
132:     if (!mglevels[i]->A) {
133:       PetscCall(KSPGetOperators(mglevels[i]->smoothu, &mglevels[i]->A, NULL));
134:       PetscCall(PetscObjectReference((PetscObject)mglevels[i]->A));
135:     }
136:   }

138:   PetscCall(KSPGetPC(mglevels[levels - 1]->smoothd, &tpc));
139:   PetscCall(PCPreSolveChangeRHS(tpc, &changed));
140:   PetscCall(KSPGetPC(mglevels[levels - 1]->smoothu, &tpc));
141:   PetscCall(PCPreSolveChangeRHS(tpc, &changeu));
142:   if (!changed && !changeu) {
143:     PetscCall(VecDestroy(&mglevels[levels - 1]->b));
144:     mglevels[levels - 1]->b = b;
145:   } else { /* if the smoother changes the rhs during PreSolve, we cannot use the input vector */
146:     if (!mglevels[levels - 1]->b) {
147:       Vec *vec;

149:       PetscCall(KSPCreateVecs(mglevels[levels - 1]->smoothd, 1, &vec, 0, NULL));
150:       mglevels[levels - 1]->b = *vec;
151:       PetscCall(PetscFree(vec));
152:     }
153:     PetscCall(VecCopy(b, mglevels[levels - 1]->b));
154:   }
155:   mglevels[levels - 1]->x = x;

157:   mg->rtol   = rtol;
158:   mg->abstol = abstol;
159:   mg->dtol   = dtol;
160:   if (rtol) {
161:     /* compute initial residual norm for relative convergence test */
162:     PetscReal rnorm;
163:     if (zeroguess) {
164:       PetscCall(VecNorm(b, NORM_2, &rnorm));
165:     } else {
166:       PetscCall((*mglevels[levels - 1]->residual)(mglevels[levels - 1]->A, b, x, w));
167:       PetscCall(VecNorm(w, NORM_2, &rnorm));
168:     }
169:     mg->ttol = PetscMax(rtol * rnorm, abstol);
170:   } else if (abstol) mg->ttol = abstol;
171:   else mg->ttol = 0.0;

173:   /* since smoother is applied to full system, not just residual we need to make sure that smoothers don't
174:      stop prematurely due to small residual */
175:   for (i = 1; i < levels; i++) {
176:     PetscCall(KSPSetTolerances(mglevels[i]->smoothu, 0, PETSC_DEFAULT, PETSC_DEFAULT, PETSC_DEFAULT));
177:     if (mglevels[i]->smoothu != mglevels[i]->smoothd) {
178:       /* For Richardson the initial guess is nonzero since it is solving in each cycle the original system not just applying as a preconditioner */
179:       PetscCall(KSPSetInitialGuessNonzero(mglevels[i]->smoothd, PETSC_TRUE));
180:       PetscCall(KSPSetTolerances(mglevels[i]->smoothd, 0, PETSC_DEFAULT, PETSC_DEFAULT, PETSC_DEFAULT));
181:     }
182:   }

184:   *reason = (PCRichardsonConvergedReason)0;
185:   for (i = 0; i < its; i++) {
186:     PetscCall(PCMGMCycle_Private(pc, mglevels + levels - 1, PETSC_FALSE, PETSC_FALSE, reason));
187:     if (*reason) break;
188:   }
189:   if (!*reason) *reason = PCRICHARDSON_CONVERGED_ITS;
190:   *outits = i;
191:   if (!changed && !changeu) mglevels[levels - 1]->b = NULL;
192:   PetscFunctionReturn(PETSC_SUCCESS);
193: }

195: PetscErrorCode PCReset_MG(PC pc)
196: {
197:   PC_MG         *mg       = (PC_MG *)pc->data;
198:   PC_MG_Levels **mglevels = mg->levels;
199:   PetscInt       i, n;

201:   PetscFunctionBegin;
202:   if (mglevels) {
203:     n = mglevels[0]->levels;
204:     for (i = 0; i < n - 1; i++) {
205:       PetscCall(VecDestroy(&mglevels[i + 1]->r));
206:       PetscCall(VecDestroy(&mglevels[i]->b));
207:       PetscCall(VecDestroy(&mglevels[i]->x));
208:       PetscCall(MatDestroy(&mglevels[i + 1]->R));
209:       PetscCall(MatDestroy(&mglevels[i]->B));
210:       PetscCall(MatDestroy(&mglevels[i]->X));
211:       PetscCall(VecDestroy(&mglevels[i]->crx));
212:       PetscCall(VecDestroy(&mglevels[i]->crb));
213:       PetscCall(MatDestroy(&mglevels[i + 1]->restrct));
214:       PetscCall(MatDestroy(&mglevels[i + 1]->interpolate));
215:       PetscCall(MatDestroy(&mglevels[i + 1]->inject));
216:       PetscCall(VecDestroy(&mglevels[i + 1]->rscale));
217:     }
218:     PetscCall(VecDestroy(&mglevels[n - 1]->crx));
219:     PetscCall(VecDestroy(&mglevels[n - 1]->crb));
220:     /* this is not null only if the smoother on the finest level
221:        changes the rhs during PreSolve */
222:     PetscCall(VecDestroy(&mglevels[n - 1]->b));
223:     PetscCall(MatDestroy(&mglevels[n - 1]->B));

225:     for (i = 0; i < n; i++) {
226:       PetscCall(MatDestroy(&mglevels[i]->coarseSpace));
227:       PetscCall(MatDestroy(&mglevels[i]->A));
228:       if (mglevels[i]->smoothd != mglevels[i]->smoothu) PetscCall(KSPReset(mglevels[i]->smoothd));
229:       PetscCall(KSPReset(mglevels[i]->smoothu));
230:       if (mglevels[i]->cr) PetscCall(KSPReset(mglevels[i]->cr));
231:     }
232:     mg->Nc = 0;
233:   }
234:   PetscFunctionReturn(PETSC_SUCCESS);
235: }

237: /* Implementing CR

239: We only want to make corrections that ``do not change'' the coarse solution. What we mean by not changing is that if I prolong my coarse solution to the fine grid and then inject that fine solution back to the coarse grid, I get the same answer. Injection is what Brannick calls R. We want the complementary projector to Inj, which we will call S, after Brannick, so that Inj S = 0. Now the orthogonal projector onto the range of Inj^T is

241:   Inj^T (Inj Inj^T)^{-1} Inj

243: and if Inj is a VecScatter, as it is now in PETSc, we have

245:   Inj^T Inj

247: and

249:   S = I - Inj^T Inj

251: since

253:   Inj S = Inj - (Inj Inj^T) Inj = 0.

255: Brannick suggests

257:   A \to S^T A S  \qquad\mathrm{and}\qquad M \to S^T M S

259: but I do not think his :math:`S^T S = I` is correct. Our S is an orthogonal projector, so :math:`S^T S = S^2 = S`. We will use

261:   M^{-1} A \to S M^{-1} A S

263: In fact, since it is somewhat hard in PETSc to do the symmetric application, we will just apply S on the left.

265:   Check: || Inj P - I ||_F < tol
266:   Check: In general, Inj Inj^T = I
267: */

269: typedef struct {
270:   PC       mg;  /* The PCMG object */
271:   PetscInt l;   /* The multigrid level for this solver */
272:   Mat      Inj; /* The injection matrix */
273:   Mat      S;   /* I - Inj^T Inj */
274: } CRContext;

276: static PetscErrorCode CRSetup_Private(PC pc)
277: {
278:   CRContext *ctx;
279:   Mat        It;

281:   PetscFunctionBeginUser;
282:   PetscCall(PCShellGetContext(pc, &ctx));
283:   PetscCall(PCMGGetInjection(ctx->mg, ctx->l, &It));
284:   PetscCheck(It, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "CR requires that injection be defined for this PCMG");
285:   PetscCall(MatCreateTranspose(It, &ctx->Inj));
286:   PetscCall(MatCreateNormal(ctx->Inj, &ctx->S));
287:   PetscCall(MatScale(ctx->S, -1.0));
288:   PetscCall(MatShift(ctx->S, 1.0));
289:   PetscFunctionReturn(PETSC_SUCCESS);
290: }

292: static PetscErrorCode CRApply_Private(PC pc, Vec x, Vec y)
293: {
294:   CRContext *ctx;

296:   PetscFunctionBeginUser;
297:   PetscCall(PCShellGetContext(pc, &ctx));
298:   PetscCall(MatMult(ctx->S, x, y));
299:   PetscFunctionReturn(PETSC_SUCCESS);
300: }

302: static PetscErrorCode CRDestroy_Private(PC pc)
303: {
304:   CRContext *ctx;

306:   PetscFunctionBeginUser;
307:   PetscCall(PCShellGetContext(pc, &ctx));
308:   PetscCall(MatDestroy(&ctx->Inj));
309:   PetscCall(MatDestroy(&ctx->S));
310:   PetscCall(PetscFree(ctx));
311:   PetscCall(PCShellSetContext(pc, NULL));
312:   PetscFunctionReturn(PETSC_SUCCESS);
313: }

315: static PetscErrorCode CreateCR_Private(PC pc, PetscInt l, PC *cr)
316: {
317:   CRContext *ctx;

319:   PetscFunctionBeginUser;
320:   PetscCall(PCCreate(PetscObjectComm((PetscObject)pc), cr));
321:   PetscCall(PetscObjectSetName((PetscObject)*cr, "S (complementary projector to injection)"));
322:   PetscCall(PetscCalloc1(1, &ctx));
323:   ctx->mg = pc;
324:   ctx->l  = l;
325:   PetscCall(PCSetType(*cr, PCSHELL));
326:   PetscCall(PCShellSetContext(*cr, ctx));
327:   PetscCall(PCShellSetApply(*cr, CRApply_Private));
328:   PetscCall(PCShellSetSetUp(*cr, CRSetup_Private));
329:   PetscCall(PCShellSetDestroy(*cr, CRDestroy_Private));
330:   PetscFunctionReturn(PETSC_SUCCESS);
331: }

333: PetscErrorCode PCMGSetLevels_MG(PC pc, PetscInt levels, MPI_Comm *comms)
334: {
335:   PC_MG         *mg = (PC_MG *)pc->data;
336:   MPI_Comm       comm;
337:   PC_MG_Levels **mglevels = mg->levels;
338:   PCMGType       mgtype   = mg->am;
339:   PetscInt       mgctype  = (PetscInt)PC_MG_CYCLE_V;
340:   PetscInt       i;
341:   PetscMPIInt    size;
342:   const char    *prefix;
343:   PC             ipc;
344:   PetscInt       n;

346:   PetscFunctionBegin;
349:   if (mg->nlevels == levels) PetscFunctionReturn(PETSC_SUCCESS);
350:   PetscCall(PetscObjectGetComm((PetscObject)pc, &comm));
351:   if (mglevels) {
352:     mgctype = mglevels[0]->cycles;
353:     /* changing the number of levels so free up the previous stuff */
354:     PetscCall(PCReset_MG(pc));
355:     n = mglevels[0]->levels;
356:     for (i = 0; i < n; i++) {
357:       if (mglevels[i]->smoothd != mglevels[i]->smoothu) PetscCall(KSPDestroy(&mglevels[i]->smoothd));
358:       PetscCall(KSPDestroy(&mglevels[i]->smoothu));
359:       PetscCall(KSPDestroy(&mglevels[i]->cr));
360:       PetscCall(PetscFree(mglevels[i]));
361:     }
362:     PetscCall(PetscFree(mg->levels));
363:   }

365:   mg->nlevels = levels;

367:   PetscCall(PetscMalloc1(levels, &mglevels));

369:   PetscCall(PCGetOptionsPrefix(pc, &prefix));

371:   mg->stageApply = 0;
372:   for (i = 0; i < levels; i++) {
373:     PetscCall(PetscNew(&mglevels[i]));

375:     mglevels[i]->level               = i;
376:     mglevels[i]->levels              = levels;
377:     mglevels[i]->cycles              = mgctype;
378:     mg->default_smoothu              = 2;
379:     mg->default_smoothd              = 2;
380:     mglevels[i]->eventsmoothsetup    = 0;
381:     mglevels[i]->eventsmoothsolve    = 0;
382:     mglevels[i]->eventresidual       = 0;
383:     mglevels[i]->eventinterprestrict = 0;

385:     if (comms) comm = comms[i];
386:     if (comm != MPI_COMM_NULL) {
387:       PetscCall(KSPCreate(comm, &mglevels[i]->smoothd));
388:       PetscCall(KSPSetErrorIfNotConverged(mglevels[i]->smoothd, pc->erroriffailure));
389:       PetscCall(PetscObjectIncrementTabLevel((PetscObject)mglevels[i]->smoothd, (PetscObject)pc, levels - i));
390:       PetscCall(KSPSetOptionsPrefix(mglevels[i]->smoothd, prefix));
391:       PetscCall(PetscObjectComposedDataSetInt((PetscObject)mglevels[i]->smoothd, PetscMGLevelId, mglevels[i]->level));
392:       if (i || levels == 1) {
393:         char tprefix[128];

395:         PetscCall(KSPSetType(mglevels[i]->smoothd, KSPCHEBYSHEV));
396:         PetscCall(KSPSetConvergenceTest(mglevels[i]->smoothd, KSPConvergedSkip, NULL, NULL));
397:         PetscCall(KSPSetNormType(mglevels[i]->smoothd, KSP_NORM_NONE));
398:         PetscCall(KSPGetPC(mglevels[i]->smoothd, &ipc));
399:         PetscCall(PCSetType(ipc, PCSOR));
400:         PetscCall(KSPSetTolerances(mglevels[i]->smoothd, PETSC_DEFAULT, PETSC_DEFAULT, PETSC_DEFAULT, mg->default_smoothd));

402:         PetscCall(PetscSNPrintf(tprefix, 128, "mg_levels_%d_", (int)i));
403:         PetscCall(KSPAppendOptionsPrefix(mglevels[i]->smoothd, tprefix));
404:       } else {
405:         PetscCall(KSPAppendOptionsPrefix(mglevels[0]->smoothd, "mg_coarse_"));

407:         /* coarse solve is (redundant) LU by default; set shifttype NONZERO to avoid annoying zero-pivot in LU preconditioner */
408:         PetscCall(KSPSetType(mglevels[0]->smoothd, KSPPREONLY));
409:         PetscCall(KSPGetPC(mglevels[0]->smoothd, &ipc));
410:         PetscCallMPI(MPI_Comm_size(comm, &size));
411:         if (size > 1) {
412:           PetscCall(PCSetType(ipc, PCREDUNDANT));
413:         } else {
414:           PetscCall(PCSetType(ipc, PCLU));
415:         }
416:         PetscCall(PCFactorSetShiftType(ipc, MAT_SHIFT_INBLOCKS));
417:       }
418:     }
419:     mglevels[i]->smoothu = mglevels[i]->smoothd;
420:     mg->rtol             = 0.0;
421:     mg->abstol           = 0.0;
422:     mg->dtol             = 0.0;
423:     mg->ttol             = 0.0;
424:     mg->cyclesperpcapply = 1;
425:   }
426:   mg->levels = mglevels;
427:   PetscCall(PCMGSetType(pc, mgtype));
428:   PetscFunctionReturn(PETSC_SUCCESS);
429: }

431: /*@C
432:    PCMGSetLevels - Sets the number of levels to use with `PCMG`.
433:    Must be called before any other `PCMG` routine.

435:    Logically Collective

437:    Input Parameters:
438: +  pc - the preconditioner context
439: .  levels - the number of levels
440: -  comms - optional communicators for each level; this is to allow solving the coarser problems
441:            on smaller sets of processes. For processes that are not included in the computation
442:            you must pass `MPI_COMM_NULL`. Use comms = `NULL` to specify that all processes
443:            should participate in each level of problem.

445:    Level: intermediate

447:    Notes:
448:      If the number of levels is one then the multigrid uses the `-mg_levels` prefix
449:      for setting the level options rather than the `-mg_coarse` prefix.

451:      You can free the information in comms after this routine is called.

453:      The array of MPI communicators must contain `MPI_COMM_NULL` for those ranks that at each level
454:      are not participating in the coarser solve. For example, with 2 levels and 1 and 2 ranks on
455:      the two levels, rank 0 in the original communicator will pass in an array of 2 communicators
456:      of size 2 and 1, while rank 1 in the original communicator will pass in array of 2 communicators
457:      the first of size 2 and the second of value `MPI_COMM_NULL` since the rank 1 does not participate
458:      in the coarse grid solve.

460:      Since each coarser level may have a new `MPI_Comm` with fewer ranks than the previous, one
461:      must take special care in providing the restriction and interpolation operation. We recommend
462:      providing these as two step operations; first perform a standard restriction or interpolation on
463:      the full number of ranks for that level and then use an MPI call to copy the resulting vector
464:      array entries (after calls to VecGetArray()) to the smaller or larger number of ranks, note in both
465:      cases the MPI calls must be made on the larger of the two communicators. Traditional MPI send and
466:      receives or `MPI_AlltoAllv()` could be used to do the reshuffling of the vector entries.

468:    Fortran Note:
469:      Use comms = `PETSC_NULL_MPI_COMM` as the equivalent of `NULL` in the C interface. Note `PETSC_NULL_MPI_COMM`
470:      is not `MPI_COMM_NULL`. It is more like `PETSC_NULL_INTEGER`, `PETSC_NULL_REAL` etc.

472: .seealso: `PCMGSetType()`, `PCMGGetLevels()`
473: @*/
474: PetscErrorCode PCMGSetLevels(PC pc, PetscInt levels, MPI_Comm *comms)
475: {
476:   PetscFunctionBegin;
479:   PetscTryMethod(pc, "PCMGSetLevels_C", (PC, PetscInt, MPI_Comm *), (pc, levels, comms));
480:   PetscFunctionReturn(PETSC_SUCCESS);
481: }

483: PetscErrorCode PCDestroy_MG(PC pc)
484: {
485:   PC_MG         *mg       = (PC_MG *)pc->data;
486:   PC_MG_Levels **mglevels = mg->levels;
487:   PetscInt       i, n;

489:   PetscFunctionBegin;
490:   PetscCall(PCReset_MG(pc));
491:   if (mglevels) {
492:     n = mglevels[0]->levels;
493:     for (i = 0; i < n; i++) {
494:       if (mglevels[i]->smoothd != mglevels[i]->smoothu) PetscCall(KSPDestroy(&mglevels[i]->smoothd));
495:       PetscCall(KSPDestroy(&mglevels[i]->smoothu));
496:       PetscCall(KSPDestroy(&mglevels[i]->cr));
497:       PetscCall(PetscFree(mglevels[i]));
498:     }
499:     PetscCall(PetscFree(mg->levels));
500:   }
501:   PetscCall(PetscFree(pc->data));
502:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCGetInterpolations_C", NULL));
503:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCGetCoarseOperators_C", NULL));
504:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCMGSetGalerkin_C", NULL));
505:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCMGGetLevels_C", NULL));
506:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCMGSetLevels_C", NULL));
507:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCGetInterpolations_C", NULL));
508:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCGetCoarseOperators_C", NULL));
509:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCMGSetAdaptInterpolation_C", NULL));
510:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCMGGetAdaptInterpolation_C", NULL));
511:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCMGSetAdaptCR_C", NULL));
512:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCMGGetAdaptCR_C", NULL));
513:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCMGSetAdaptCoarseSpaceType_C", NULL));
514:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCMGGetAdaptCoarseSpaceType_C", NULL));
515:   PetscFunctionReturn(PETSC_SUCCESS);
516: }

518: /*
519:    PCApply_MG - Runs either an additive, multiplicative, Kaskadic
520:              or full cycle of multigrid.

522:   Note:
523:   A simple wrapper which calls PCMGMCycle(),PCMGACycle(), or PCMGFCycle().
524: */
525: static PetscErrorCode PCApply_MG_Internal(PC pc, Vec b, Vec x, Mat B, Mat X, PetscBool transpose)
526: {
527:   PC_MG         *mg       = (PC_MG *)pc->data;
528:   PC_MG_Levels **mglevels = mg->levels;
529:   PC             tpc;
530:   PetscInt       levels = mglevels[0]->levels, i;
531:   PetscBool      changeu, changed, matapp;

533:   PetscFunctionBegin;
534:   matapp = (PetscBool)(B && X);
535:   if (mg->stageApply) PetscCall(PetscLogStagePush(mg->stageApply));
536:   /* When the DM is supplying the matrix then it will not exist until here */
537:   for (i = 0; i < levels; i++) {
538:     if (!mglevels[i]->A) {
539:       PetscCall(KSPGetOperators(mglevels[i]->smoothu, &mglevels[i]->A, NULL));
540:       PetscCall(PetscObjectReference((PetscObject)mglevels[i]->A));
541:     }
542:   }

544:   PetscCall(KSPGetPC(mglevels[levels - 1]->smoothd, &tpc));
545:   PetscCall(PCPreSolveChangeRHS(tpc, &changed));
546:   PetscCall(KSPGetPC(mglevels[levels - 1]->smoothu, &tpc));
547:   PetscCall(PCPreSolveChangeRHS(tpc, &changeu));
548:   if (!changeu && !changed) {
549:     if (matapp) {
550:       PetscCall(MatDestroy(&mglevels[levels - 1]->B));
551:       mglevels[levels - 1]->B = B;
552:     } else {
553:       PetscCall(VecDestroy(&mglevels[levels - 1]->b));
554:       mglevels[levels - 1]->b = b;
555:     }
556:   } else { /* if the smoother changes the rhs during PreSolve, we cannot use the input vector */
557:     if (matapp) {
558:       if (mglevels[levels - 1]->B) {
559:         PetscInt  N1, N2;
560:         PetscBool flg;

562:         PetscCall(MatGetSize(mglevels[levels - 1]->B, NULL, &N1));
563:         PetscCall(MatGetSize(B, NULL, &N2));
564:         PetscCall(PetscObjectTypeCompare((PetscObject)mglevels[levels - 1]->B, ((PetscObject)B)->type_name, &flg));
565:         if (N1 != N2 || !flg) PetscCall(MatDestroy(&mglevels[levels - 1]->B));
566:       }
567:       if (!mglevels[levels - 1]->B) {
568:         PetscCall(MatDuplicate(B, MAT_COPY_VALUES, &mglevels[levels - 1]->B));
569:       } else {
570:         PetscCall(MatCopy(B, mglevels[levels - 1]->B, SAME_NONZERO_PATTERN));
571:       }
572:     } else {
573:       if (!mglevels[levels - 1]->b) {
574:         Vec *vec;

576:         PetscCall(KSPCreateVecs(mglevels[levels - 1]->smoothd, 1, &vec, 0, NULL));
577:         mglevels[levels - 1]->b = *vec;
578:         PetscCall(PetscFree(vec));
579:       }
580:       PetscCall(VecCopy(b, mglevels[levels - 1]->b));
581:     }
582:   }
583:   if (matapp) {
584:     mglevels[levels - 1]->X = X;
585:   } else {
586:     mglevels[levels - 1]->x = x;
587:   }

589:   /* If coarser Xs are present, it means we have already block applied the PC at least once
590:      Reset operators if sizes/type do no match */
591:   if (matapp && levels > 1 && mglevels[levels - 2]->X) {
592:     PetscInt  Xc, Bc;
593:     PetscBool flg;

595:     PetscCall(MatGetSize(mglevels[levels - 2]->X, NULL, &Xc));
596:     PetscCall(MatGetSize(mglevels[levels - 1]->B, NULL, &Bc));
597:     PetscCall(PetscObjectTypeCompare((PetscObject)mglevels[levels - 2]->X, ((PetscObject)mglevels[levels - 1]->X)->type_name, &flg));
598:     if (Xc != Bc || !flg) {
599:       PetscCall(MatDestroy(&mglevels[levels - 1]->R));
600:       for (i = 0; i < levels - 1; i++) {
601:         PetscCall(MatDestroy(&mglevels[i]->R));
602:         PetscCall(MatDestroy(&mglevels[i]->B));
603:         PetscCall(MatDestroy(&mglevels[i]->X));
604:       }
605:     }
606:   }

608:   if (mg->am == PC_MG_MULTIPLICATIVE) {
609:     if (matapp) PetscCall(MatZeroEntries(X));
610:     else PetscCall(VecZeroEntries(x));
611:     for (i = 0; i < mg->cyclesperpcapply; i++) PetscCall(PCMGMCycle_Private(pc, mglevels + levels - 1, transpose, matapp, NULL));
612:   } else if (mg->am == PC_MG_ADDITIVE) {
613:     PetscCall(PCMGACycle_Private(pc, mglevels, transpose, matapp));
614:   } else if (mg->am == PC_MG_KASKADE) {
615:     PetscCall(PCMGKCycle_Private(pc, mglevels, transpose, matapp));
616:   } else {
617:     PetscCall(PCMGFCycle_Private(pc, mglevels, transpose, matapp));
618:   }
619:   if (mg->stageApply) PetscCall(PetscLogStagePop());
620:   if (!changeu && !changed) {
621:     if (matapp) {
622:       mglevels[levels - 1]->B = NULL;
623:     } else {
624:       mglevels[levels - 1]->b = NULL;
625:     }
626:   }
627:   PetscFunctionReturn(PETSC_SUCCESS);
628: }

630: static PetscErrorCode PCApply_MG(PC pc, Vec b, Vec x)
631: {
632:   PetscFunctionBegin;
633:   PetscCall(PCApply_MG_Internal(pc, b, x, NULL, NULL, PETSC_FALSE));
634:   PetscFunctionReturn(PETSC_SUCCESS);
635: }

637: static PetscErrorCode PCApplyTranspose_MG(PC pc, Vec b, Vec x)
638: {
639:   PetscFunctionBegin;
640:   PetscCall(PCApply_MG_Internal(pc, b, x, NULL, NULL, PETSC_TRUE));
641:   PetscFunctionReturn(PETSC_SUCCESS);
642: }

644: static PetscErrorCode PCMatApply_MG(PC pc, Mat b, Mat x)
645: {
646:   PetscFunctionBegin;
647:   PetscCall(PCApply_MG_Internal(pc, NULL, NULL, b, x, PETSC_FALSE));
648:   PetscFunctionReturn(PETSC_SUCCESS);
649: }

651: PetscErrorCode PCSetFromOptions_MG(PC pc, PetscOptionItems *PetscOptionsObject)
652: {
653:   PetscInt            levels, cycles;
654:   PetscBool           flg, flg2;
655:   PC_MG              *mg = (PC_MG *)pc->data;
656:   PC_MG_Levels      **mglevels;
657:   PCMGType            mgtype;
658:   PCMGCycleType       mgctype;
659:   PCMGGalerkinType    gtype;
660:   PCMGCoarseSpaceType coarseSpaceType;

662:   PetscFunctionBegin;
663:   levels = PetscMax(mg->nlevels, 1);
664:   PetscOptionsHeadBegin(PetscOptionsObject, "Multigrid options");
665:   PetscCall(PetscOptionsInt("-pc_mg_levels", "Number of Levels", "PCMGSetLevels", levels, &levels, &flg));
666:   if (!flg && !mg->levels && pc->dm) {
667:     PetscCall(DMGetRefineLevel(pc->dm, &levels));
668:     levels++;
669:     mg->usedmfornumberoflevels = PETSC_TRUE;
670:   }
671:   PetscCall(PCMGSetLevels(pc, levels, NULL));
672:   mglevels = mg->levels;

674:   mgctype = (PCMGCycleType)mglevels[0]->cycles;
675:   PetscCall(PetscOptionsEnum("-pc_mg_cycle_type", "V cycle or for W-cycle", "PCMGSetCycleType", PCMGCycleTypes, (PetscEnum)mgctype, (PetscEnum *)&mgctype, &flg));
676:   if (flg) PetscCall(PCMGSetCycleType(pc, mgctype));
677:   gtype = mg->galerkin;
678:   PetscCall(PetscOptionsEnum("-pc_mg_galerkin", "Use Galerkin process to compute coarser operators", "PCMGSetGalerkin", PCMGGalerkinTypes, (PetscEnum)gtype, (PetscEnum *)&gtype, &flg));
679:   if (flg) PetscCall(PCMGSetGalerkin(pc, gtype));
680:   coarseSpaceType = mg->coarseSpaceType;
681:   PetscCall(PetscOptionsEnum("-pc_mg_adapt_interp_coarse_space", "Type of adaptive coarse space: none, polynomial, harmonic, eigenvector, generalized_eigenvector, gdsw", "PCMGSetAdaptCoarseSpaceType", PCMGCoarseSpaceTypes, (PetscEnum)coarseSpaceType, (PetscEnum *)&coarseSpaceType, &flg));
682:   if (flg) PetscCall(PCMGSetAdaptCoarseSpaceType(pc, coarseSpaceType));
683:   PetscCall(PetscOptionsInt("-pc_mg_adapt_interp_n", "Size of the coarse space for adaptive interpolation", "PCMGSetCoarseSpace", mg->Nc, &mg->Nc, &flg));
684:   PetscCall(PetscOptionsBool("-pc_mg_mesp_monitor", "Monitor the multilevel eigensolver", "PCMGSetAdaptInterpolation", PETSC_FALSE, &mg->mespMonitor, &flg));
685:   flg2 = PETSC_FALSE;
686:   PetscCall(PetscOptionsBool("-pc_mg_adapt_cr", "Monitor coarse space quality using Compatible Relaxation (CR)", "PCMGSetAdaptCR", PETSC_FALSE, &flg2, &flg));
687:   if (flg) PetscCall(PCMGSetAdaptCR(pc, flg2));
688:   flg = PETSC_FALSE;
689:   PetscCall(PetscOptionsBool("-pc_mg_distinct_smoothup", "Create separate smoothup KSP and append the prefix _up", "PCMGSetDistinctSmoothUp", PETSC_FALSE, &flg, NULL));
690:   if (flg) PetscCall(PCMGSetDistinctSmoothUp(pc));
691:   mgtype = mg->am;
692:   PetscCall(PetscOptionsEnum("-pc_mg_type", "Multigrid type", "PCMGSetType", PCMGTypes, (PetscEnum)mgtype, (PetscEnum *)&mgtype, &flg));
693:   if (flg) PetscCall(PCMGSetType(pc, mgtype));
694:   if (mg->am == PC_MG_MULTIPLICATIVE) {
695:     PetscCall(PetscOptionsInt("-pc_mg_multiplicative_cycles", "Number of cycles for each preconditioner step", "PCMGMultiplicativeSetCycles", mg->cyclesperpcapply, &cycles, &flg));
696:     if (flg) PetscCall(PCMGMultiplicativeSetCycles(pc, cycles));
697:   }
698:   flg = PETSC_FALSE;
699:   PetscCall(PetscOptionsBool("-pc_mg_log", "Log times for each multigrid level", "None", flg, &flg, NULL));
700:   if (flg) {
701:     PetscInt i;
702:     char     eventname[128];

704:     levels = mglevels[0]->levels;
705:     for (i = 0; i < levels; i++) {
706:       PetscCall(PetscSNPrintf(eventname, PETSC_STATIC_ARRAY_LENGTH(eventname), "MGSetup Level %d", (int)i));
707:       PetscCall(PetscLogEventRegister(eventname, ((PetscObject)pc)->classid, &mglevels[i]->eventsmoothsetup));
708:       PetscCall(PetscSNPrintf(eventname, PETSC_STATIC_ARRAY_LENGTH(eventname), "MGSmooth Level %d", (int)i));
709:       PetscCall(PetscLogEventRegister(eventname, ((PetscObject)pc)->classid, &mglevels[i]->eventsmoothsolve));
710:       if (i) {
711:         PetscCall(PetscSNPrintf(eventname, PETSC_STATIC_ARRAY_LENGTH(eventname), "MGResid Level %d", (int)i));
712:         PetscCall(PetscLogEventRegister(eventname, ((PetscObject)pc)->classid, &mglevels[i]->eventresidual));
713:         PetscCall(PetscSNPrintf(eventname, PETSC_STATIC_ARRAY_LENGTH(eventname), "MGInterp Level %d", (int)i));
714:         PetscCall(PetscLogEventRegister(eventname, ((PetscObject)pc)->classid, &mglevels[i]->eventinterprestrict));
715:       }
716:     }

718: #if defined(PETSC_USE_LOG)
719:     {
720:       const char   *sname = "MG Apply";
721:       PetscStageLog stageLog;
722:       PetscInt      st;

724:       PetscCall(PetscLogGetStageLog(&stageLog));
725:       for (st = 0; st < stageLog->numStages; ++st) {
726:         PetscBool same;

728:         PetscCall(PetscStrcmp(stageLog->stageInfo[st].name, sname, &same));
729:         if (same) mg->stageApply = st;
730:       }
731:       if (!mg->stageApply) PetscCall(PetscLogStageRegister(sname, &mg->stageApply));
732:     }
733: #endif
734:   }
735:   PetscOptionsHeadEnd();
736:   /* Check option consistency */
737:   PetscCall(PCMGGetGalerkin(pc, &gtype));
738:   PetscCall(PCMGGetAdaptInterpolation(pc, &flg));
739:   PetscCheck(!flg || !(gtype >= PC_MG_GALERKIN_NONE), PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_INCOMP, "Must use Galerkin coarse operators when adapting the interpolator");
740:   PetscFunctionReturn(PETSC_SUCCESS);
741: }

743: const char *const PCMGTypes[]            = {"MULTIPLICATIVE", "ADDITIVE", "FULL", "KASKADE", "PCMGType", "PC_MG", NULL};
744: const char *const PCMGCycleTypes[]       = {"invalid", "v", "w", "PCMGCycleType", "PC_MG_CYCLE", NULL};
745: const char *const PCMGGalerkinTypes[]    = {"both", "pmat", "mat", "none", "external", "PCMGGalerkinType", "PC_MG_GALERKIN", NULL};
746: const char *const PCMGCoarseSpaceTypes[] = {"none", "polynomial", "harmonic", "eigenvector", "generalized_eigenvector", "gdsw", "PCMGCoarseSpaceType", "PCMG_ADAPT_NONE", NULL};

748: #include <petscdraw.h>
749: PetscErrorCode PCView_MG(PC pc, PetscViewer viewer)
750: {
751:   PC_MG         *mg       = (PC_MG *)pc->data;
752:   PC_MG_Levels **mglevels = mg->levels;
753:   PetscInt       levels   = mglevels ? mglevels[0]->levels : 0, i;
754:   PetscBool      iascii, isbinary, isdraw;

756:   PetscFunctionBegin;
757:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
758:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERBINARY, &isbinary));
759:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERDRAW, &isdraw));
760:   if (iascii) {
761:     const char *cyclename = levels ? (mglevels[0]->cycles == PC_MG_CYCLE_V ? "v" : "w") : "unknown";
762:     PetscCall(PetscViewerASCIIPrintf(viewer, "  type is %s, levels=%" PetscInt_FMT " cycles=%s\n", PCMGTypes[mg->am], levels, cyclename));
763:     if (mg->am == PC_MG_MULTIPLICATIVE) PetscCall(PetscViewerASCIIPrintf(viewer, "    Cycles per PCApply=%" PetscInt_FMT "\n", mg->cyclesperpcapply));
764:     if (mg->galerkin == PC_MG_GALERKIN_BOTH) {
765:       PetscCall(PetscViewerASCIIPrintf(viewer, "    Using Galerkin computed coarse grid matrices\n"));
766:     } else if (mg->galerkin == PC_MG_GALERKIN_PMAT) {
767:       PetscCall(PetscViewerASCIIPrintf(viewer, "    Using Galerkin computed coarse grid matrices for pmat\n"));
768:     } else if (mg->galerkin == PC_MG_GALERKIN_MAT) {
769:       PetscCall(PetscViewerASCIIPrintf(viewer, "    Using Galerkin computed coarse grid matrices for mat\n"));
770:     } else if (mg->galerkin == PC_MG_GALERKIN_EXTERNAL) {
771:       PetscCall(PetscViewerASCIIPrintf(viewer, "    Using externally compute Galerkin coarse grid matrices\n"));
772:     } else {
773:       PetscCall(PetscViewerASCIIPrintf(viewer, "    Not using Galerkin computed coarse grid matrices\n"));
774:     }
775:     if (mg->view) PetscCall((*mg->view)(pc, viewer));
776:     for (i = 0; i < levels; i++) {
777:       if (i) {
778:         PetscCall(PetscViewerASCIIPrintf(viewer, "Down solver (pre-smoother) on level %" PetscInt_FMT " -------------------------------\n", i));
779:       } else {
780:         PetscCall(PetscViewerASCIIPrintf(viewer, "Coarse grid solver -- level %" PetscInt_FMT " -------------------------------\n", i));
781:       }
782:       PetscCall(PetscViewerASCIIPushTab(viewer));
783:       PetscCall(KSPView(mglevels[i]->smoothd, viewer));
784:       PetscCall(PetscViewerASCIIPopTab(viewer));
785:       if (i && mglevels[i]->smoothd == mglevels[i]->smoothu) {
786:         PetscCall(PetscViewerASCIIPrintf(viewer, "Up solver (post-smoother) same as down solver (pre-smoother)\n"));
787:       } else if (i) {
788:         PetscCall(PetscViewerASCIIPrintf(viewer, "Up solver (post-smoother) on level %" PetscInt_FMT " -------------------------------\n", i));
789:         PetscCall(PetscViewerASCIIPushTab(viewer));
790:         PetscCall(KSPView(mglevels[i]->smoothu, viewer));
791:         PetscCall(PetscViewerASCIIPopTab(viewer));
792:       }
793:       if (i && mglevels[i]->cr) {
794:         PetscCall(PetscViewerASCIIPrintf(viewer, "CR solver on level %" PetscInt_FMT " -------------------------------\n", i));
795:         PetscCall(PetscViewerASCIIPushTab(viewer));
796:         PetscCall(KSPView(mglevels[i]->cr, viewer));
797:         PetscCall(PetscViewerASCIIPopTab(viewer));
798:       }
799:     }
800:   } else if (isbinary) {
801:     for (i = levels - 1; i >= 0; i--) {
802:       PetscCall(KSPView(mglevels[i]->smoothd, viewer));
803:       if (i && mglevels[i]->smoothd != mglevels[i]->smoothu) PetscCall(KSPView(mglevels[i]->smoothu, viewer));
804:     }
805:   } else if (isdraw) {
806:     PetscDraw draw;
807:     PetscReal x, w, y, bottom, th;
808:     PetscCall(PetscViewerDrawGetDraw(viewer, 0, &draw));
809:     PetscCall(PetscDrawGetCurrentPoint(draw, &x, &y));
810:     PetscCall(PetscDrawStringGetSize(draw, NULL, &th));
811:     bottom = y - th;
812:     for (i = levels - 1; i >= 0; i--) {
813:       if (!mglevels[i]->smoothu || (mglevels[i]->smoothu == mglevels[i]->smoothd)) {
814:         PetscCall(PetscDrawPushCurrentPoint(draw, x, bottom));
815:         PetscCall(KSPView(mglevels[i]->smoothd, viewer));
816:         PetscCall(PetscDrawPopCurrentPoint(draw));
817:       } else {
818:         w = 0.5 * PetscMin(1.0 - x, x);
819:         PetscCall(PetscDrawPushCurrentPoint(draw, x + w, bottom));
820:         PetscCall(KSPView(mglevels[i]->smoothd, viewer));
821:         PetscCall(PetscDrawPopCurrentPoint(draw));
822:         PetscCall(PetscDrawPushCurrentPoint(draw, x - w, bottom));
823:         PetscCall(KSPView(mglevels[i]->smoothu, viewer));
824:         PetscCall(PetscDrawPopCurrentPoint(draw));
825:       }
826:       PetscCall(PetscDrawGetBoundingBox(draw, NULL, &bottom, NULL, NULL));
827:       bottom -= th;
828:     }
829:   }
830:   PetscFunctionReturn(PETSC_SUCCESS);
831: }

833: #include <petsc/private/kspimpl.h>

835: /*
836:     Calls setup for the KSP on each level
837: */
838: PetscErrorCode PCSetUp_MG(PC pc)
839: {
840:   PC_MG         *mg       = (PC_MG *)pc->data;
841:   PC_MG_Levels **mglevels = mg->levels;
842:   PetscInt       i, n;
843:   PC             cpc;
844:   PetscBool      dump = PETSC_FALSE, opsset, use_amat, missinginterpolate = PETSC_FALSE;
845:   Mat            dA, dB;
846:   Vec            tvec;
847:   DM            *dms;
848:   PetscViewer    viewer = NULL;
849:   PetscBool      dAeqdB = PETSC_FALSE, needRestricts = PETSC_FALSE, doCR = PETSC_FALSE;
850:   PetscBool      adaptInterpolation = mg->adaptInterpolation;

852:   PetscFunctionBegin;
853:   PetscCheck(mglevels, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "Must set MG levels with PCMGSetLevels() before setting up");
854:   n = mglevels[0]->levels;
855:   /* FIX: Move this to PCSetFromOptions_MG? */
856:   if (mg->usedmfornumberoflevels) {
857:     PetscInt levels;
858:     PetscCall(DMGetRefineLevel(pc->dm, &levels));
859:     levels++;
860:     if (levels > n) { /* the problem is now being solved on a finer grid */
861:       PetscCall(PCMGSetLevels(pc, levels, NULL));
862:       n = levels;
863:       PetscCall(PCSetFromOptions(pc)); /* it is bad to call this here, but otherwise will never be called for the new hierarchy */
864:       mglevels = mg->levels;
865:     }
866:   }
867:   PetscCall(KSPGetPC(mglevels[0]->smoothd, &cpc));

869:   /* If user did not provide fine grid operators OR operator was not updated since last global KSPSetOperators() */
870:   /* so use those from global PC */
871:   /* Is this what we always want? What if user wants to keep old one? */
872:   PetscCall(KSPGetOperatorsSet(mglevels[n - 1]->smoothd, NULL, &opsset));
873:   if (opsset) {
874:     Mat mmat;
875:     PetscCall(KSPGetOperators(mglevels[n - 1]->smoothd, NULL, &mmat));
876:     if (mmat == pc->pmat) opsset = PETSC_FALSE;
877:   }

879:   /* Create CR solvers */
880:   PetscCall(PCMGGetAdaptCR(pc, &doCR));
881:   if (doCR) {
882:     const char *prefix;

884:     PetscCall(PCGetOptionsPrefix(pc, &prefix));
885:     for (i = 1; i < n; ++i) {
886:       PC   ipc, cr;
887:       char crprefix[128];

889:       PetscCall(KSPCreate(PetscObjectComm((PetscObject)pc), &mglevels[i]->cr));
890:       PetscCall(KSPSetErrorIfNotConverged(mglevels[i]->cr, PETSC_FALSE));
891:       PetscCall(PetscObjectIncrementTabLevel((PetscObject)mglevels[i]->cr, (PetscObject)pc, n - i));
892:       PetscCall(KSPSetOptionsPrefix(mglevels[i]->cr, prefix));
893:       PetscCall(PetscObjectComposedDataSetInt((PetscObject)mglevels[i]->cr, PetscMGLevelId, mglevels[i]->level));
894:       PetscCall(KSPSetType(mglevels[i]->cr, KSPCHEBYSHEV));
895:       PetscCall(KSPSetConvergenceTest(mglevels[i]->cr, KSPConvergedSkip, NULL, NULL));
896:       PetscCall(KSPSetNormType(mglevels[i]->cr, KSP_NORM_PRECONDITIONED));
897:       PetscCall(KSPGetPC(mglevels[i]->cr, &ipc));

899:       PetscCall(PCSetType(ipc, PCCOMPOSITE));
900:       PetscCall(PCCompositeSetType(ipc, PC_COMPOSITE_MULTIPLICATIVE));
901:       PetscCall(PCCompositeAddPCType(ipc, PCSOR));
902:       PetscCall(CreateCR_Private(pc, i, &cr));
903:       PetscCall(PCCompositeAddPC(ipc, cr));
904:       PetscCall(PCDestroy(&cr));

906:       PetscCall(KSPSetTolerances(mglevels[i]->cr, PETSC_DEFAULT, PETSC_DEFAULT, PETSC_DEFAULT, mg->default_smoothd));
907:       PetscCall(KSPSetInitialGuessNonzero(mglevels[i]->cr, PETSC_TRUE));
908:       PetscCall(PetscSNPrintf(crprefix, 128, "mg_levels_%d_cr_", (int)i));
909:       PetscCall(KSPAppendOptionsPrefix(mglevels[i]->cr, crprefix));
910:     }
911:   }

913:   if (!opsset) {
914:     PetscCall(PCGetUseAmat(pc, &use_amat));
915:     if (use_amat) {
916:       PetscCall(PetscInfo(pc, "Using outer operators to define finest grid operator \n  because PCMGGetSmoother(pc,nlevels-1,&ksp);KSPSetOperators(ksp,...); was not called.\n"));
917:       PetscCall(KSPSetOperators(mglevels[n - 1]->smoothd, pc->mat, pc->pmat));
918:     } else {
919:       PetscCall(PetscInfo(pc, "Using matrix (pmat) operators to define finest grid operator \n  because PCMGGetSmoother(pc,nlevels-1,&ksp);KSPSetOperators(ksp,...); was not called.\n"));
920:       PetscCall(KSPSetOperators(mglevels[n - 1]->smoothd, pc->pmat, pc->pmat));
921:     }
922:   }

924:   for (i = n - 1; i > 0; i--) {
925:     if (!(mglevels[i]->interpolate || mglevels[i]->restrct)) {
926:       missinginterpolate = PETSC_TRUE;
927:       break;
928:     }
929:   }

931:   PetscCall(KSPGetOperators(mglevels[n - 1]->smoothd, &dA, &dB));
932:   if (dA == dB) dAeqdB = PETSC_TRUE;
933:   if (mg->galerkin == PC_MG_GALERKIN_NONE || ((mg->galerkin == PC_MG_GALERKIN_PMAT || mg->galerkin == PC_MG_GALERKIN_MAT) && !dAeqdB)) {
934:     needRestricts = PETSC_TRUE; /* user must compute either mat, pmat, or both so must restrict x to coarser levels */
935:   }

937:   if (pc->dm && !pc->setupcalled) {
938:     /* finest smoother also gets DM but it is not active, independent of whether galerkin==PC_MG_GALERKIN_EXTERNAL */
939:     PetscCall(KSPSetDM(mglevels[n - 1]->smoothd, pc->dm));
940:     PetscCall(KSPSetDMActive(mglevels[n - 1]->smoothd, PETSC_FALSE));
941:     if (mglevels[n - 1]->smoothd != mglevels[n - 1]->smoothu) {
942:       PetscCall(KSPSetDM(mglevels[n - 1]->smoothu, pc->dm));
943:       PetscCall(KSPSetDMActive(mglevels[n - 1]->smoothu, PETSC_FALSE));
944:     }
945:     if (mglevels[n - 1]->cr) {
946:       PetscCall(KSPSetDM(mglevels[n - 1]->cr, pc->dm));
947:       PetscCall(KSPSetDMActive(mglevels[n - 1]->cr, PETSC_FALSE));
948:     }
949:   }

951:   /*
952:    Skipping if user has provided all interpolation/restriction needed (since DM might not be able to produce them (when coming from SNES/TS)
953:    Skipping for externally managed hierarchy (such as ML and GAMG). Cleaner logic here would be great. Wrap ML/GAMG as DMs?
954:   */
955:   if (missinginterpolate && mg->galerkin != PC_MG_GALERKIN_EXTERNAL && !pc->setupcalled) {
956:     /* first see if we can compute a coarse space */
957:     if (mg->coarseSpaceType == PCMG_ADAPT_GDSW) {
958:       for (i = n - 2; i > -1; i--) {
959:         if (!mglevels[i + 1]->restrct && !mglevels[i + 1]->interpolate) {
960:           PetscCall(PCMGComputeCoarseSpace_Internal(pc, i + 1, mg->coarseSpaceType, mg->Nc, NULL, &mglevels[i + 1]->coarseSpace));
961:           PetscCall(PCMGSetInterpolation(pc, i + 1, mglevels[i + 1]->coarseSpace));
962:         }
963:       }
964:     } else { /* construct the interpolation from the DMs */
965:       Mat p;
966:       Vec rscale;
967:       PetscCall(PetscMalloc1(n, &dms));
968:       dms[n - 1] = pc->dm;
969:       /* Separately create them so we do not get DMKSP interference between levels */
970:       for (i = n - 2; i > -1; i--) PetscCall(DMCoarsen(dms[i + 1], MPI_COMM_NULL, &dms[i]));
971:       for (i = n - 2; i > -1; i--) {
972:         DMKSP     kdm;
973:         PetscBool dmhasrestrict, dmhasinject;
974:         PetscCall(KSPSetDM(mglevels[i]->smoothd, dms[i]));
975:         if (!needRestricts) PetscCall(KSPSetDMActive(mglevels[i]->smoothd, PETSC_FALSE));
976:         if (mglevels[i]->smoothd != mglevels[i]->smoothu) {
977:           PetscCall(KSPSetDM(mglevels[i]->smoothu, dms[i]));
978:           if (!needRestricts) PetscCall(KSPSetDMActive(mglevels[i]->smoothu, PETSC_FALSE));
979:         }
980:         if (mglevels[i]->cr) {
981:           PetscCall(KSPSetDM(mglevels[i]->cr, dms[i]));
982:           if (!needRestricts) PetscCall(KSPSetDMActive(mglevels[i]->cr, PETSC_FALSE));
983:         }
984:         PetscCall(DMGetDMKSPWrite(dms[i], &kdm));
985:         /* Ugly hack so that the next KSPSetUp() will use the RHS that we set. A better fix is to change dmActive to take
986:          * a bitwise OR of computing the matrix, RHS, and initial iterate. */
987:         kdm->ops->computerhs = NULL;
988:         kdm->rhsctx          = NULL;
989:         if (!mglevels[i + 1]->interpolate) {
990:           PetscCall(DMCreateInterpolation(dms[i], dms[i + 1], &p, &rscale));
991:           PetscCall(PCMGSetInterpolation(pc, i + 1, p));
992:           if (rscale) PetscCall(PCMGSetRScale(pc, i + 1, rscale));
993:           PetscCall(VecDestroy(&rscale));
994:           PetscCall(MatDestroy(&p));
995:         }
996:         PetscCall(DMHasCreateRestriction(dms[i], &dmhasrestrict));
997:         if (dmhasrestrict && !mglevels[i + 1]->restrct) {
998:           PetscCall(DMCreateRestriction(dms[i], dms[i + 1], &p));
999:           PetscCall(PCMGSetRestriction(pc, i + 1, p));
1000:           PetscCall(MatDestroy(&p));
1001:         }
1002:         PetscCall(DMHasCreateInjection(dms[i], &dmhasinject));
1003:         if (dmhasinject && !mglevels[i + 1]->inject) {
1004:           PetscCall(DMCreateInjection(dms[i], dms[i + 1], &p));
1005:           PetscCall(PCMGSetInjection(pc, i + 1, p));
1006:           PetscCall(MatDestroy(&p));
1007:         }
1008:       }

1010:       for (i = n - 2; i > -1; i--) PetscCall(DMDestroy(&dms[i]));
1011:       PetscCall(PetscFree(dms));
1012:     }
1013:   }

1015:   if (mg->galerkin < PC_MG_GALERKIN_NONE) {
1016:     Mat       A, B;
1017:     PetscBool doA = PETSC_FALSE, doB = PETSC_FALSE;
1018:     MatReuse  reuse = MAT_INITIAL_MATRIX;

1020:     if (mg->galerkin == PC_MG_GALERKIN_PMAT || mg->galerkin == PC_MG_GALERKIN_BOTH) doB = PETSC_TRUE;
1021:     if (mg->galerkin == PC_MG_GALERKIN_MAT || (mg->galerkin == PC_MG_GALERKIN_BOTH && dA != dB)) doA = PETSC_TRUE;
1022:     if (pc->setupcalled) reuse = MAT_REUSE_MATRIX;
1023:     for (i = n - 2; i > -1; i--) {
1024:       PetscCheck(mglevels[i + 1]->restrct || mglevels[i + 1]->interpolate, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "Must provide interpolation or restriction for each MG level except level 0");
1025:       if (!mglevels[i + 1]->interpolate) PetscCall(PCMGSetInterpolation(pc, i + 1, mglevels[i + 1]->restrct));
1026:       if (!mglevels[i + 1]->restrct) PetscCall(PCMGSetRestriction(pc, i + 1, mglevels[i + 1]->interpolate));
1027:       if (reuse == MAT_REUSE_MATRIX) PetscCall(KSPGetOperators(mglevels[i]->smoothd, &A, &B));
1028:       if (doA) PetscCall(MatGalerkin(mglevels[i + 1]->restrct, dA, mglevels[i + 1]->interpolate, reuse, 1.0, &A));
1029:       if (doB) PetscCall(MatGalerkin(mglevels[i + 1]->restrct, dB, mglevels[i + 1]->interpolate, reuse, 1.0, &B));
1030:       /* the management of the PetscObjectReference() and PetscObjecDereference() below is rather delicate */
1031:       if (!doA && dAeqdB) {
1032:         if (reuse == MAT_INITIAL_MATRIX) PetscCall(PetscObjectReference((PetscObject)B));
1033:         A = B;
1034:       } else if (!doA && reuse == MAT_INITIAL_MATRIX) {
1035:         PetscCall(KSPGetOperators(mglevels[i]->smoothd, &A, NULL));
1036:         PetscCall(PetscObjectReference((PetscObject)A));
1037:       }
1038:       if (!doB && dAeqdB) {
1039:         if (reuse == MAT_INITIAL_MATRIX) PetscCall(PetscObjectReference((PetscObject)A));
1040:         B = A;
1041:       } else if (!doB && reuse == MAT_INITIAL_MATRIX) {
1042:         PetscCall(KSPGetOperators(mglevels[i]->smoothd, NULL, &B));
1043:         PetscCall(PetscObjectReference((PetscObject)B));
1044:       }
1045:       if (reuse == MAT_INITIAL_MATRIX) {
1046:         PetscCall(KSPSetOperators(mglevels[i]->smoothd, A, B));
1047:         PetscCall(PetscObjectDereference((PetscObject)A));
1048:         PetscCall(PetscObjectDereference((PetscObject)B));
1049:       }
1050:       dA = A;
1051:       dB = B;
1052:     }
1053:   }

1055:   /* Adapt interpolation matrices */
1056:   if (adaptInterpolation) {
1057:     for (i = 0; i < n; ++i) {
1058:       if (!mglevels[i]->coarseSpace) PetscCall(PCMGComputeCoarseSpace_Internal(pc, i, mg->coarseSpaceType, mg->Nc, !i ? NULL : mglevels[i - 1]->coarseSpace, &mglevels[i]->coarseSpace));
1059:       if (i) PetscCall(PCMGAdaptInterpolator_Internal(pc, i, mglevels[i - 1]->smoothu, mglevels[i]->smoothu, mglevels[i - 1]->coarseSpace, mglevels[i]->coarseSpace));
1060:     }
1061:     for (i = n - 2; i > -1; --i) PetscCall(PCMGRecomputeLevelOperators_Internal(pc, i));
1062:   }

1064:   if (needRestricts && pc->dm) {
1065:     for (i = n - 2; i >= 0; i--) {
1066:       DM  dmfine, dmcoarse;
1067:       Mat Restrict, Inject;
1068:       Vec rscale;
1069:       PetscCall(KSPGetDM(mglevels[i + 1]->smoothd, &dmfine));
1070:       PetscCall(KSPGetDM(mglevels[i]->smoothd, &dmcoarse));
1071:       PetscCall(PCMGGetRestriction(pc, i + 1, &Restrict));
1072:       PetscCall(PCMGGetRScale(pc, i + 1, &rscale));
1073:       PetscCall(PCMGGetInjection(pc, i + 1, &Inject));
1074:       PetscCall(DMRestrict(dmfine, Restrict, rscale, Inject, dmcoarse));
1075:     }
1076:   }

1078:   if (!pc->setupcalled) {
1079:     for (i = 0; i < n; i++) PetscCall(KSPSetFromOptions(mglevels[i]->smoothd));
1080:     for (i = 1; i < n; i++) {
1081:       if (mglevels[i]->smoothu && (mglevels[i]->smoothu != mglevels[i]->smoothd)) PetscCall(KSPSetFromOptions(mglevels[i]->smoothu));
1082:       if (mglevels[i]->cr) PetscCall(KSPSetFromOptions(mglevels[i]->cr));
1083:     }
1084:     /* insure that if either interpolation or restriction is set the other other one is set */
1085:     for (i = 1; i < n; i++) {
1086:       PetscCall(PCMGGetInterpolation(pc, i, NULL));
1087:       PetscCall(PCMGGetRestriction(pc, i, NULL));
1088:     }
1089:     for (i = 0; i < n - 1; i++) {
1090:       if (!mglevels[i]->b) {
1091:         Vec *vec;
1092:         PetscCall(KSPCreateVecs(mglevels[i]->smoothd, 1, &vec, 0, NULL));
1093:         PetscCall(PCMGSetRhs(pc, i, *vec));
1094:         PetscCall(VecDestroy(vec));
1095:         PetscCall(PetscFree(vec));
1096:       }
1097:       if (!mglevels[i]->r && i) {
1098:         PetscCall(VecDuplicate(mglevels[i]->b, &tvec));
1099:         PetscCall(PCMGSetR(pc, i, tvec));
1100:         PetscCall(VecDestroy(&tvec));
1101:       }
1102:       if (!mglevels[i]->x) {
1103:         PetscCall(VecDuplicate(mglevels[i]->b, &tvec));
1104:         PetscCall(PCMGSetX(pc, i, tvec));
1105:         PetscCall(VecDestroy(&tvec));
1106:       }
1107:       if (doCR) {
1108:         PetscCall(VecDuplicate(mglevels[i]->b, &mglevels[i]->crx));
1109:         PetscCall(VecDuplicate(mglevels[i]->b, &mglevels[i]->crb));
1110:         PetscCall(VecZeroEntries(mglevels[i]->crb));
1111:       }
1112:     }
1113:     if (n != 1 && !mglevels[n - 1]->r) {
1114:       /* PCMGSetR() on the finest level if user did not supply it */
1115:       Vec *vec;
1116:       PetscCall(KSPCreateVecs(mglevels[n - 1]->smoothd, 1, &vec, 0, NULL));
1117:       PetscCall(PCMGSetR(pc, n - 1, *vec));
1118:       PetscCall(VecDestroy(vec));
1119:       PetscCall(PetscFree(vec));
1120:     }
1121:     if (doCR) {
1122:       PetscCall(VecDuplicate(mglevels[n - 1]->r, &mglevels[n - 1]->crx));
1123:       PetscCall(VecDuplicate(mglevels[n - 1]->r, &mglevels[n - 1]->crb));
1124:       PetscCall(VecZeroEntries(mglevels[n - 1]->crb));
1125:     }
1126:   }

1128:   if (pc->dm) {
1129:     /* need to tell all the coarser levels to rebuild the matrix using the DM for that level */
1130:     for (i = 0; i < n - 1; i++) {
1131:       if (mglevels[i]->smoothd->setupstage != KSP_SETUP_NEW) mglevels[i]->smoothd->setupstage = KSP_SETUP_NEWMATRIX;
1132:     }
1133:   }
1134:   // We got here (PCSetUp_MG) because the matrix has changed, which means the smoother needs to be set up again (e.g.,
1135:   // new diagonal for Jacobi). Setting it here allows it to be logged under PCSetUp rather than deep inside a PCApply.
1136:   if (mglevels[n - 1]->smoothd->setupstage != KSP_SETUP_NEW) mglevels[n - 1]->smoothd->setupstage = KSP_SETUP_NEWMATRIX;

1138:   for (i = 1; i < n; i++) {
1139:     if (mglevels[i]->smoothu == mglevels[i]->smoothd || mg->am == PC_MG_FULL || mg->am == PC_MG_KASKADE || mg->cyclesperpcapply > 1) {
1140:       /* if doing only down then initial guess is zero */
1141:       PetscCall(KSPSetInitialGuessNonzero(mglevels[i]->smoothd, PETSC_TRUE));
1142:     }
1143:     if (mglevels[i]->cr) PetscCall(KSPSetInitialGuessNonzero(mglevels[i]->cr, PETSC_TRUE));
1144:     if (mglevels[i]->eventsmoothsetup) PetscCall(PetscLogEventBegin(mglevels[i]->eventsmoothsetup, 0, 0, 0, 0));
1145:     PetscCall(KSPSetUp(mglevels[i]->smoothd));
1146:     if (mglevels[i]->smoothd->reason == KSP_DIVERGED_PC_FAILED) pc->failedreason = PC_SUBPC_ERROR;
1147:     if (mglevels[i]->eventsmoothsetup) PetscCall(PetscLogEventEnd(mglevels[i]->eventsmoothsetup, 0, 0, 0, 0));
1148:     if (!mglevels[i]->residual) {
1149:       Mat mat;
1150:       PetscCall(KSPGetOperators(mglevels[i]->smoothd, &mat, NULL));
1151:       PetscCall(PCMGSetResidual(pc, i, PCMGResidualDefault, mat));
1152:     }
1153:     if (!mglevels[i]->residualtranspose) {
1154:       Mat mat;
1155:       PetscCall(KSPGetOperators(mglevels[i]->smoothd, &mat, NULL));
1156:       PetscCall(PCMGSetResidualTranspose(pc, i, PCMGResidualTransposeDefault, mat));
1157:     }
1158:   }
1159:   for (i = 1; i < n; i++) {
1160:     if (mglevels[i]->smoothu && mglevels[i]->smoothu != mglevels[i]->smoothd) {
1161:       Mat downmat, downpmat;

1163:       /* check if operators have been set for up, if not use down operators to set them */
1164:       PetscCall(KSPGetOperatorsSet(mglevels[i]->smoothu, &opsset, NULL));
1165:       if (!opsset) {
1166:         PetscCall(KSPGetOperators(mglevels[i]->smoothd, &downmat, &downpmat));
1167:         PetscCall(KSPSetOperators(mglevels[i]->smoothu, downmat, downpmat));
1168:       }

1170:       PetscCall(KSPSetInitialGuessNonzero(mglevels[i]->smoothu, PETSC_TRUE));
1171:       if (mglevels[i]->eventsmoothsetup) PetscCall(PetscLogEventBegin(mglevels[i]->eventsmoothsetup, 0, 0, 0, 0));
1172:       PetscCall(KSPSetUp(mglevels[i]->smoothu));
1173:       if (mglevels[i]->smoothu->reason == KSP_DIVERGED_PC_FAILED) pc->failedreason = PC_SUBPC_ERROR;
1174:       if (mglevels[i]->eventsmoothsetup) PetscCall(PetscLogEventEnd(mglevels[i]->eventsmoothsetup, 0, 0, 0, 0));
1175:     }
1176:     if (mglevels[i]->cr) {
1177:       Mat downmat, downpmat;

1179:       /* check if operators have been set for up, if not use down operators to set them */
1180:       PetscCall(KSPGetOperatorsSet(mglevels[i]->cr, &opsset, NULL));
1181:       if (!opsset) {
1182:         PetscCall(KSPGetOperators(mglevels[i]->smoothd, &downmat, &downpmat));
1183:         PetscCall(KSPSetOperators(mglevels[i]->cr, downmat, downpmat));
1184:       }

1186:       PetscCall(KSPSetInitialGuessNonzero(mglevels[i]->cr, PETSC_TRUE));
1187:       if (mglevels[i]->eventsmoothsetup) PetscCall(PetscLogEventBegin(mglevels[i]->eventsmoothsetup, 0, 0, 0, 0));
1188:       PetscCall(KSPSetUp(mglevels[i]->cr));
1189:       if (mglevels[i]->cr->reason == KSP_DIVERGED_PC_FAILED) pc->failedreason = PC_SUBPC_ERROR;
1190:       if (mglevels[i]->eventsmoothsetup) PetscCall(PetscLogEventEnd(mglevels[i]->eventsmoothsetup, 0, 0, 0, 0));
1191:     }
1192:   }

1194:   if (mglevels[0]->eventsmoothsetup) PetscCall(PetscLogEventBegin(mglevels[0]->eventsmoothsetup, 0, 0, 0, 0));
1195:   PetscCall(KSPSetUp(mglevels[0]->smoothd));
1196:   if (mglevels[0]->smoothd->reason == KSP_DIVERGED_PC_FAILED) pc->failedreason = PC_SUBPC_ERROR;
1197:   if (mglevels[0]->eventsmoothsetup) PetscCall(PetscLogEventEnd(mglevels[0]->eventsmoothsetup, 0, 0, 0, 0));

1199:     /*
1200:      Dump the interpolation/restriction matrices plus the
1201:    Jacobian/stiffness on each level. This allows MATLAB users to
1202:    easily check if the Galerkin condition A_c = R A_f R^T is satisfied.

1204:    Only support one or the other at the same time.
1205:   */
1206: #if defined(PETSC_USE_SOCKET_VIEWER)
1207:   PetscCall(PetscOptionsGetBool(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, "-pc_mg_dump_matlab", &dump, NULL));
1208:   if (dump) viewer = PETSC_VIEWER_SOCKET_(PetscObjectComm((PetscObject)pc));
1209:   dump = PETSC_FALSE;
1210: #endif
1211:   PetscCall(PetscOptionsGetBool(((PetscObject)pc)->options, ((PetscObject)pc)->prefix, "-pc_mg_dump_binary", &dump, NULL));
1212:   if (dump) viewer = PETSC_VIEWER_BINARY_(PetscObjectComm((PetscObject)pc));

1214:   if (viewer) {
1215:     for (i = 1; i < n; i++) PetscCall(MatView(mglevels[i]->restrct, viewer));
1216:     for (i = 0; i < n; i++) {
1217:       PetscCall(KSPGetPC(mglevels[i]->smoothd, &pc));
1218:       PetscCall(MatView(pc->mat, viewer));
1219:     }
1220:   }
1221:   PetscFunctionReturn(PETSC_SUCCESS);
1222: }

1224: /* -------------------------------------------------------------------------------------*/

1226: PetscErrorCode PCMGGetLevels_MG(PC pc, PetscInt *levels)
1227: {
1228:   PC_MG *mg = (PC_MG *)pc->data;

1230:   PetscFunctionBegin;
1231:   *levels = mg->nlevels;
1232:   PetscFunctionReturn(PETSC_SUCCESS);
1233: }

1235: /*@
1236:    PCMGGetLevels - Gets the number of levels to use with `PCMG`.

1238:    Not Collective

1240:    Input Parameter:
1241: .  pc - the preconditioner context

1243:    Output parameter:
1244: .  levels - the number of levels

1246:    Level: advanced

1248: .seealso: `PCMG`, `PCMGSetLevels()`
1249: @*/
1250: PetscErrorCode PCMGGetLevels(PC pc, PetscInt *levels)
1251: {
1252:   PetscFunctionBegin;
1255:   *levels = 0;
1256:   PetscTryMethod(pc, "PCMGGetLevels_C", (PC, PetscInt *), (pc, levels));
1257:   PetscFunctionReturn(PETSC_SUCCESS);
1258: }

1260: /*@
1261:    PCMGGetGridComplexity - compute operator and grid complexity of the `PCMG` hierarchy

1263:    Input Parameter:
1264: .  pc - the preconditioner context

1266:    Output Parameters:
1267: +  gc - grid complexity = sum_i(n_i) / n_0
1268: -  oc - operator complexity = sum_i(nnz_i) / nnz_0

1270:    Level: advanced

1272:    Note:
1273:    This is often call the operator complexity in multigrid literature

1275: .seealso: `PCMG`, `PCMGGetLevels()`, `PCMGSetLevels()`
1276: @*/
1277: PetscErrorCode PCMGGetGridComplexity(PC pc, PetscReal *gc, PetscReal *oc)
1278: {
1279:   PC_MG         *mg       = (PC_MG *)pc->data;
1280:   PC_MG_Levels **mglevels = mg->levels;
1281:   PetscInt       lev, N;
1282:   PetscLogDouble nnz0 = 0, sgc = 0, soc = 0, n0 = 0;
1283:   MatInfo        info;

1285:   PetscFunctionBegin;
1289:   if (!pc->setupcalled) {
1290:     if (gc) *gc = 0;
1291:     if (oc) *oc = 0;
1292:     PetscFunctionReturn(PETSC_SUCCESS);
1293:   }
1294:   PetscCheck(mg->nlevels > 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "MG has no levels");
1295:   for (lev = 0; lev < mg->nlevels; lev++) {
1296:     Mat dB;
1297:     PetscCall(KSPGetOperators(mglevels[lev]->smoothd, NULL, &dB));
1298:     PetscCall(MatGetInfo(dB, MAT_GLOBAL_SUM, &info)); /* global reduction */
1299:     PetscCall(MatGetSize(dB, &N, NULL));
1300:     sgc += N;
1301:     soc += info.nz_used;
1302:     if (lev == mg->nlevels - 1) {
1303:       nnz0 = info.nz_used;
1304:       n0   = N;
1305:     }
1306:   }
1307:   PetscCheck(n0 > 0 && gc, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Number for grid points on finest level is not available");
1308:   *gc = (PetscReal)(sgc / n0);
1309:   if (nnz0 > 0 && oc) *oc = (PetscReal)(soc / nnz0);
1310:   PetscFunctionReturn(PETSC_SUCCESS);
1311: }

1313: /*@
1314:    PCMGSetType - Determines the form of multigrid to use:
1315:    multiplicative, additive, full, or the Kaskade algorithm.

1317:    Logically Collective

1319:    Input Parameters:
1320: +  pc - the preconditioner context
1321: -  form - multigrid form, one of `PC_MG_MULTIPLICATIVE`, `PC_MG_ADDITIVE`, `PC_MG_FULL`, `PC_MG_KASKADE`

1323:    Options Database Key:
1324: .  -pc_mg_type <form> - Sets <form>, one of multiplicative, additive, full, kaskade

1326:    Level: advanced

1328: .seealso: `PCMGType`, `PCMG`, `PCMGGetLevels()`, `PCMGSetLevels()`, `PCMGGetType()`, `PCMGCycleType`
1329: @*/
1330: PetscErrorCode PCMGSetType(PC pc, PCMGType form)
1331: {
1332:   PC_MG *mg = (PC_MG *)pc->data;

1334:   PetscFunctionBegin;
1337:   mg->am = form;
1338:   if (form == PC_MG_MULTIPLICATIVE) pc->ops->applyrichardson = PCApplyRichardson_MG;
1339:   else pc->ops->applyrichardson = NULL;
1340:   PetscFunctionReturn(PETSC_SUCCESS);
1341: }

1343: /*@
1344:    PCMGGetType - Finds the form of multigrid the `PCMG` is using  multiplicative, additive, full, or the Kaskade algorithm.

1346:    Logically Collective

1348:    Input Parameter:
1349: .  pc - the preconditioner context

1351:    Output Parameter:
1352: .  type - one of `PC_MG_MULTIPLICATIVE`, `PC_MG_ADDITIVE`, `PC_MG_FULL`, `PC_MG_KASKADE`, `PCMGCycleType`

1354:    Level: advanced

1356: .seealso: `PCMGType`, `PCMG`, `PCMGGetLevels()`, `PCMGSetLevels()`, `PCMGSetType()`
1357: @*/
1358: PetscErrorCode PCMGGetType(PC pc, PCMGType *type)
1359: {
1360:   PC_MG *mg = (PC_MG *)pc->data;

1362:   PetscFunctionBegin;
1364:   *type = mg->am;
1365:   PetscFunctionReturn(PETSC_SUCCESS);
1366: }

1368: /*@
1369:    PCMGSetCycleType - Sets the type cycles to use.  Use `PCMGSetCycleTypeOnLevel()` for more
1370:    complicated cycling.

1372:    Logically Collective

1374:    Input Parameters:
1375: +  pc - the multigrid context
1376: -  n - either `PC_MG_CYCLE_V` or `PC_MG_CYCLE_W`

1378:    Options Database Key:
1379: .  -pc_mg_cycle_type <v,w> - provide the cycle desired

1381:    Level: advanced

1383: .seealso: `PCMG`, `PCMGSetCycleTypeOnLevel()`, `PCMGType`, `PCMGCycleType`
1384: @*/
1385: PetscErrorCode PCMGSetCycleType(PC pc, PCMGCycleType n)
1386: {
1387:   PC_MG         *mg       = (PC_MG *)pc->data;
1388:   PC_MG_Levels **mglevels = mg->levels;
1389:   PetscInt       i, levels;

1391:   PetscFunctionBegin;
1394:   PetscCheck(mglevels, PetscObjectComm((PetscObject)pc), PETSC_ERR_ORDER, "Must set MG levels with PCMGSetLevels() before calling");
1395:   levels = mglevels[0]->levels;
1396:   for (i = 0; i < levels; i++) mglevels[i]->cycles = n;
1397:   PetscFunctionReturn(PETSC_SUCCESS);
1398: }

1400: /*@
1401:    PCMGMultiplicativeSetCycles - Sets the number of cycles to use for each preconditioner step
1402:          of multigrid when `PCMGType` is `PC_MG_MULTIPLICATIVE`

1404:    Logically Collective

1406:    Input Parameters:
1407: +  pc - the multigrid context
1408: -  n - number of cycles (default is 1)

1410:    Options Database Key:
1411: .  -pc_mg_multiplicative_cycles n - set the number of cycles

1413:    Level: advanced

1415:    Note:
1416:     This is not associated with setting a v or w cycle, that is set with `PCMGSetCycleType()`

1418: .seealso: `PCMGSetCycleTypeOnLevel()`, `PCMGSetCycleType()`, `PCMGCycleType`, `PCMGType`
1419: @*/
1420: PetscErrorCode PCMGMultiplicativeSetCycles(PC pc, PetscInt n)
1421: {
1422:   PC_MG *mg = (PC_MG *)pc->data;

1424:   PetscFunctionBegin;
1427:   mg->cyclesperpcapply = n;
1428:   PetscFunctionReturn(PETSC_SUCCESS);
1429: }

1431: PetscErrorCode PCMGSetGalerkin_MG(PC pc, PCMGGalerkinType use)
1432: {
1433:   PC_MG *mg = (PC_MG *)pc->data;

1435:   PetscFunctionBegin;
1436:   mg->galerkin = use;
1437:   PetscFunctionReturn(PETSC_SUCCESS);
1438: }

1440: /*@
1441:    PCMGSetGalerkin - Causes the coarser grid matrices to be computed from the
1442:       finest grid via the Galerkin process: A_i-1 = r_i * A_i * p_i

1444:    Logically Collective

1446:    Input Parameters:
1447: +  pc - the multigrid context
1448: -  use - one of `PC_MG_GALERKIN_BOTH`, `PC_MG_GALERKIN_PMAT`, `PC_MG_GALERKIN_MAT`, or `PC_MG_GALERKIN_NONE`

1450:    Options Database Key:
1451: .  -pc_mg_galerkin <both,pmat,mat,none> - set the matrices to form via the Galerkin process

1453:    Level: intermediate

1455:    Note:
1456:    Some codes that use `PCMG` such as `PCGAMG` use Galerkin internally while constructing the hierarchy and thus do not
1457:    use the `PCMG` construction of the coarser grids.

1459: .seealso: `PCMG`, `PCMGGetGalerkin()`, `PCMGGalerkinType`
1460: @*/
1461: PetscErrorCode PCMGSetGalerkin(PC pc, PCMGGalerkinType use)
1462: {
1463:   PetscFunctionBegin;
1465:   PetscTryMethod(pc, "PCMGSetGalerkin_C", (PC, PCMGGalerkinType), (pc, use));
1466:   PetscFunctionReturn(PETSC_SUCCESS);
1467: }

1469: /*@
1470:    PCMGGetGalerkin - Checks if Galerkin multigrid is being used, i.e. A_i-1 = r_i * A_i * p_i

1472:    Not Collective

1474:    Input Parameter:
1475: .  pc - the multigrid context

1477:    Output Parameter:
1478: .  galerkin - one of `PC_MG_GALERKIN_BOTH`,`PC_MG_GALERKIN_PMAT`,`PC_MG_GALERKIN_MAT`, `PC_MG_GALERKIN_NONE`, or `PC_MG_GALERKIN_EXTERNAL`

1480:    Level: intermediate

1482: .seealso: `PCMG`, `PCMGSetGalerkin()`, `PCMGGalerkinType`
1483: @*/
1484: PetscErrorCode PCMGGetGalerkin(PC pc, PCMGGalerkinType *galerkin)
1485: {
1486:   PC_MG *mg = (PC_MG *)pc->data;

1488:   PetscFunctionBegin;
1490:   *galerkin = mg->galerkin;
1491:   PetscFunctionReturn(PETSC_SUCCESS);
1492: }

1494: PetscErrorCode PCMGSetAdaptInterpolation_MG(PC pc, PetscBool adapt)
1495: {
1496:   PC_MG *mg = (PC_MG *)pc->data;

1498:   PetscFunctionBegin;
1499:   mg->adaptInterpolation = adapt;
1500:   PetscFunctionReturn(PETSC_SUCCESS);
1501: }

1503: PetscErrorCode PCMGGetAdaptInterpolation_MG(PC pc, PetscBool *adapt)
1504: {
1505:   PC_MG *mg = (PC_MG *)pc->data;

1507:   PetscFunctionBegin;
1508:   *adapt = mg->adaptInterpolation;
1509:   PetscFunctionReturn(PETSC_SUCCESS);
1510: }

1512: PetscErrorCode PCMGSetAdaptCoarseSpaceType_MG(PC pc, PCMGCoarseSpaceType ctype)
1513: {
1514:   PC_MG *mg = (PC_MG *)pc->data;

1516:   PetscFunctionBegin;
1517:   mg->adaptInterpolation = ctype != PCMG_ADAPT_NONE ? PETSC_TRUE : PETSC_FALSE;
1518:   mg->coarseSpaceType    = ctype;
1519:   PetscFunctionReturn(PETSC_SUCCESS);
1520: }

1522: PetscErrorCode PCMGGetAdaptCoarseSpaceType_MG(PC pc, PCMGCoarseSpaceType *ctype)
1523: {
1524:   PC_MG *mg = (PC_MG *)pc->data;

1526:   PetscFunctionBegin;
1527:   *ctype = mg->coarseSpaceType;
1528:   PetscFunctionReturn(PETSC_SUCCESS);
1529: }

1531: PetscErrorCode PCMGSetAdaptCR_MG(PC pc, PetscBool cr)
1532: {
1533:   PC_MG *mg = (PC_MG *)pc->data;

1535:   PetscFunctionBegin;
1536:   mg->compatibleRelaxation = cr;
1537:   PetscFunctionReturn(PETSC_SUCCESS);
1538: }

1540: PetscErrorCode PCMGGetAdaptCR_MG(PC pc, PetscBool *cr)
1541: {
1542:   PC_MG *mg = (PC_MG *)pc->data;

1544:   PetscFunctionBegin;
1545:   *cr = mg->compatibleRelaxation;
1546:   PetscFunctionReturn(PETSC_SUCCESS);
1547: }

1549: /*@C
1550:   PCMGSetAdaptCoarseSpaceType - Set the type of adaptive coarse space.

1552:   Adapts or creates the interpolator based upon a vector space which should be accurately captured by the next coarser mesh, and thus accurately interpolated.

1554:   Logically Collective

1556:   Input Parameters:
1557: + pc    - the multigrid context
1558: - ctype - the type of coarse space

1560:   Options Database Keys:
1561: + -pc_mg_adapt_interp_n <int>             - The number of modes to use
1562: - -pc_mg_adapt_interp_coarse_space <type> - The type of coarse space: none, polynomial, harmonic, eigenvector, generalized_eigenvector, gdsw

1564:   Level: intermediate

1566: .seealso: `PCMG`, `PCMGCoarseSpaceType`, `PCMGGetAdaptCoarseSpaceType()`, `PCMGSetGalerkin()`, `PCMGSetAdaptInterpolation()`
1567: @*/
1568: PetscErrorCode PCMGSetAdaptCoarseSpaceType(PC pc, PCMGCoarseSpaceType ctype)
1569: {
1570:   PetscFunctionBegin;
1573:   PetscTryMethod(pc, "PCMGSetAdaptCoarseSpaceType_C", (PC, PCMGCoarseSpaceType), (pc, ctype));
1574:   PetscFunctionReturn(PETSC_SUCCESS);
1575: }

1577: /*@C
1578:    PCMGGetAdaptCoarseSpaceType - Get the type of adaptive coarse space.

1580:    Not Collective

1582:    Input Parameter:
1583: .  pc    - the multigrid context

1585:    Output Parameter:
1586: .  ctype - the type of coarse space

1588:   Level: intermediate

1590: .seealso: `PCMG`, `PCMGCoarseSpaceType`, `PCMGSetAdaptCoarseSpaceType()`, `PCMGSetGalerkin()`, `PCMGSetAdaptInterpolation()`
1591: @*/
1592: PetscErrorCode PCMGGetAdaptCoarseSpaceType(PC pc, PCMGCoarseSpaceType *ctype)
1593: {
1594:   PetscFunctionBegin;
1597:   PetscUseMethod(pc, "PCMGGetAdaptCoarseSpaceType_C", (PC, PCMGCoarseSpaceType *), (pc, ctype));
1598:   PetscFunctionReturn(PETSC_SUCCESS);
1599: }

1601: /* MATT: REMOVE? */
1602: /*@
1603:    PCMGSetAdaptInterpolation - Adapt the interpolator based upon a vector space which should be accurately captured by the next coarser mesh, and thus accurately interpolated.

1605:    Logically Collective

1607:    Input Parameters:
1608: +  pc    - the multigrid context
1609: -  adapt - flag for adaptation of the interpolator

1611:    Options Database Keys:
1612: +  -pc_mg_adapt_interp                     - Turn on adaptation
1613: .  -pc_mg_adapt_interp_n <int>             - The number of modes to use, should be divisible by dimension
1614: -  -pc_mg_adapt_interp_coarse_space <type> - The type of coarse space: polynomial, harmonic, eigenvector, generalized_eigenvector

1616:   Level: intermediate

1618: .seealso: `PCMG`, `PCMGGetAdaptInterpolation()`, `PCMGSetGalerkin()`, `PCMGGetAdaptCoarseSpaceType()`, `PCMGSetAdaptCoarseSpaceType()`
1619: @*/
1620: PetscErrorCode PCMGSetAdaptInterpolation(PC pc, PetscBool adapt)
1621: {
1622:   PetscFunctionBegin;
1624:   PetscTryMethod(pc, "PCMGSetAdaptInterpolation_C", (PC, PetscBool), (pc, adapt));
1625:   PetscFunctionReturn(PETSC_SUCCESS);
1626: }

1628: /*@
1629:   PCMGGetAdaptInterpolation - Get the flag to adapt the interpolator based upon a vector space which should be accurately captured by the next coarser mesh,
1630:   and thus accurately interpolated.

1632:   Not Collective

1634:   Input Parameter:
1635: . pc    - the multigrid context

1637:   Output Parameter:
1638: . adapt - flag for adaptation of the interpolator

1640:   Level: intermediate

1642: .seealso: `PCMG`, `PCMGSetAdaptInterpolation()`, `PCMGSetGalerkin()`, `PCMGGetAdaptCoarseSpaceType()`, `PCMGSetAdaptCoarseSpaceType()`
1643: @*/
1644: PetscErrorCode PCMGGetAdaptInterpolation(PC pc, PetscBool *adapt)
1645: {
1646:   PetscFunctionBegin;
1649:   PetscUseMethod(pc, "PCMGGetAdaptInterpolation_C", (PC, PetscBool *), (pc, adapt));
1650:   PetscFunctionReturn(PETSC_SUCCESS);
1651: }

1653: /*@
1654:    PCMGSetAdaptCR - Monitor the coarse space quality using an auxiliary solve with compatible relaxation.

1656:    Logically Collective

1658:    Input Parameters:
1659: +  pc - the multigrid context
1660: -  cr - flag for compatible relaxation

1662:    Options Database Key:
1663: .  -pc_mg_adapt_cr - Turn on compatible relaxation

1665:    Level: intermediate

1667: .seealso: `PCMG`, `PCMGGetAdaptCR()`, `PCMGSetAdaptInterpolation()`, `PCMGSetGalerkin()`, `PCMGGetAdaptCoarseSpaceType()`, `PCMGSetAdaptCoarseSpaceType()`
1668: @*/
1669: PetscErrorCode PCMGSetAdaptCR(PC pc, PetscBool cr)
1670: {
1671:   PetscFunctionBegin;
1673:   PetscTryMethod(pc, "PCMGSetAdaptCR_C", (PC, PetscBool), (pc, cr));
1674:   PetscFunctionReturn(PETSC_SUCCESS);
1675: }

1677: /*@
1678:   PCMGGetAdaptCR - Get the flag to monitor coarse space quality using an auxiliary solve with compatible relaxation.

1680:   Not Collective

1682:   Input Parameter:
1683: . pc    - the multigrid context

1685:   Output Parameter:
1686: . cr - flag for compatible relaxaion

1688:   Level: intermediate

1690: .seealso: `PCMGSetAdaptCR()`, `PCMGGetAdaptInterpolation()`, `PCMGSetGalerkin()`, `PCMGGetAdaptCoarseSpaceType()`, `PCMGSetAdaptCoarseSpaceType()`
1691: @*/
1692: PetscErrorCode PCMGGetAdaptCR(PC pc, PetscBool *cr)
1693: {
1694:   PetscFunctionBegin;
1697:   PetscUseMethod(pc, "PCMGGetAdaptCR_C", (PC, PetscBool *), (pc, cr));
1698:   PetscFunctionReturn(PETSC_SUCCESS);
1699: }

1701: /*@
1702:    PCMGSetNumberSmooth - Sets the number of pre and post-smoothing steps to use
1703:    on all levels.  Use `PCMGDistinctSmoothUp()` to create separate up and down smoothers if you want different numbers of
1704:    pre- and post-smoothing steps.

1706:    Logically Collective

1708:    Input Parameters:
1709: +  mg - the multigrid context
1710: -  n - the number of smoothing steps

1712:    Options Database Key:
1713: .  -mg_levels_ksp_max_it <n> - Sets number of pre and post-smoothing steps

1715:    Level: advanced

1717:    Note:
1718:    This does not set a value on the coarsest grid, since we assume that there is no separate smooth up on the coarsest grid.

1720: .seealso: `PCMG`, `PCMGSetDistinctSmoothUp()`
1721: @*/
1722: PetscErrorCode PCMGSetNumberSmooth(PC pc, PetscInt n)
1723: {
1724:   PC_MG         *mg       = (PC_MG *)pc->data;
1725:   PC_MG_Levels **mglevels = mg->levels;
1726:   PetscInt       i, levels;

1728:   PetscFunctionBegin;
1731:   PetscCheck(mglevels, PetscObjectComm((PetscObject)pc), PETSC_ERR_ORDER, "Must set MG levels with PCMGSetLevels() before calling");
1732:   levels = mglevels[0]->levels;

1734:   for (i = 1; i < levels; i++) {
1735:     PetscCall(KSPSetTolerances(mglevels[i]->smoothu, PETSC_DEFAULT, PETSC_DEFAULT, PETSC_DEFAULT, n));
1736:     PetscCall(KSPSetTolerances(mglevels[i]->smoothd, PETSC_DEFAULT, PETSC_DEFAULT, PETSC_DEFAULT, n));
1737:     mg->default_smoothu = n;
1738:     mg->default_smoothd = n;
1739:   }
1740:   PetscFunctionReturn(PETSC_SUCCESS);
1741: }

1743: /*@
1744:    PCMGSetDistinctSmoothUp - sets the up (post) smoother to be a separate `KSP` from the down (pre) smoother on all levels
1745:        and adds the suffix _up to the options name

1747:    Logically Collective

1749:    Input Parameter:
1750: .  pc - the preconditioner context

1752:    Options Database Key:
1753: .  -pc_mg_distinct_smoothup <bool> - use distinct smoothing objects

1755:    Level: advanced

1757:    Note:
1758:    This does not set a value on the coarsest grid, since we assume that there is no separate smooth up on the coarsest grid.

1760: .seealso: `PCMG`, `PCMGSetNumberSmooth()`
1761: @*/
1762: PetscErrorCode PCMGSetDistinctSmoothUp(PC pc)
1763: {
1764:   PC_MG         *mg       = (PC_MG *)pc->data;
1765:   PC_MG_Levels **mglevels = mg->levels;
1766:   PetscInt       i, levels;
1767:   KSP            subksp;

1769:   PetscFunctionBegin;
1771:   PetscCheck(mglevels, PetscObjectComm((PetscObject)pc), PETSC_ERR_ORDER, "Must set MG levels with PCMGSetLevels() before calling");
1772:   levels = mglevels[0]->levels;

1774:   for (i = 1; i < levels; i++) {
1775:     const char *prefix = NULL;
1776:     /* make sure smoother up and down are different */
1777:     PetscCall(PCMGGetSmootherUp(pc, i, &subksp));
1778:     PetscCall(KSPGetOptionsPrefix(mglevels[i]->smoothd, &prefix));
1779:     PetscCall(KSPSetOptionsPrefix(subksp, prefix));
1780:     PetscCall(KSPAppendOptionsPrefix(subksp, "up_"));
1781:   }
1782:   PetscFunctionReturn(PETSC_SUCCESS);
1783: }

1785: /* No new matrices are created, and the coarse operator matrices are the references to the original ones */
1786: PetscErrorCode PCGetInterpolations_MG(PC pc, PetscInt *num_levels, Mat *interpolations[])
1787: {
1788:   PC_MG         *mg       = (PC_MG *)pc->data;
1789:   PC_MG_Levels **mglevels = mg->levels;
1790:   Mat           *mat;
1791:   PetscInt       l;

1793:   PetscFunctionBegin;
1794:   PetscCheck(mglevels, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "Must set MG levels before calling");
1795:   PetscCall(PetscMalloc1(mg->nlevels, &mat));
1796:   for (l = 1; l < mg->nlevels; l++) {
1797:     mat[l - 1] = mglevels[l]->interpolate;
1798:     PetscCall(PetscObjectReference((PetscObject)mat[l - 1]));
1799:   }
1800:   *num_levels     = mg->nlevels;
1801:   *interpolations = mat;
1802:   PetscFunctionReturn(PETSC_SUCCESS);
1803: }

1805: /* No new matrices are created, and the coarse operator matrices are the references to the original ones */
1806: PetscErrorCode PCGetCoarseOperators_MG(PC pc, PetscInt *num_levels, Mat *coarseOperators[])
1807: {
1808:   PC_MG         *mg       = (PC_MG *)pc->data;
1809:   PC_MG_Levels **mglevels = mg->levels;
1810:   PetscInt       l;
1811:   Mat           *mat;

1813:   PetscFunctionBegin;
1814:   PetscCheck(mglevels, PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONGSTATE, "Must set MG levels before calling");
1815:   PetscCall(PetscMalloc1(mg->nlevels, &mat));
1816:   for (l = 0; l < mg->nlevels - 1; l++) {
1817:     PetscCall(KSPGetOperators(mglevels[l]->smoothd, NULL, &(mat[l])));
1818:     PetscCall(PetscObjectReference((PetscObject)mat[l]));
1819:   }
1820:   *num_levels      = mg->nlevels;
1821:   *coarseOperators = mat;
1822:   PetscFunctionReturn(PETSC_SUCCESS);
1823: }

1825: /*@C
1826:    PCMGRegisterCoarseSpaceConstructor -  Adds a method to the `PCMG` package for coarse space construction.

1828:    Not Collective

1830:    Input Parameters:
1831: +  name     - name of the constructor
1832: -  function - constructor routine

1834:    Calling sequence of `function`:
1835: $  PetscErrorCode my_csp(PC pc, PetscInt l, DM dm, KSP smooth, PetscInt Nc, Mat initGuess, Mat *coarseSp)
1836: +  pc        - The `PC` object
1837: .  l         - The multigrid level, 0 is the coarse level
1838: .  dm        - The `DM` for this level
1839: .  smooth    - The level smoother
1840: .  Nc        - The size of the coarse space
1841: .  initGuess - Basis for an initial guess for the space
1842: -  coarseSp  - A basis for the computed coarse space

1844:   Level: advanced

1846:   Developer Note:
1847:   How come this is not used by `PCGAMG`?

1849: .seealso: `PCMG`, `PCMGGetCoarseSpaceConstructor()`, `PCRegister()`
1850: @*/
1851: PetscErrorCode PCMGRegisterCoarseSpaceConstructor(const char name[], PetscErrorCode (*function)(PC, PetscInt, DM, KSP, PetscInt, Mat, Mat *))
1852: {
1853:   PetscFunctionBegin;
1854:   PetscCall(PCInitializePackage());
1855:   PetscCall(PetscFunctionListAdd(&PCMGCoarseList, name, function));
1856:   PetscFunctionReturn(PETSC_SUCCESS);
1857: }

1859: /*@C
1860:   PCMGGetCoarseSpaceConstructor -  Returns the given coarse space construction method.

1862:   Not Collective

1864:   Input Parameter:
1865: . name     - name of the constructor

1867:   Output Parameter:
1868: . function - constructor routine

1870:   Level: advanced

1872: .seealso: `PCMG`, `PCMGRegisterCoarseSpaceConstructor()`, `PCRegister()`
1873: @*/
1874: PetscErrorCode PCMGGetCoarseSpaceConstructor(const char name[], PetscErrorCode (**function)(PC, PetscInt, DM, KSP, PetscInt, Mat, Mat *))
1875: {
1876:   PetscFunctionBegin;
1877:   PetscCall(PetscFunctionListFind(PCMGCoarseList, name, function));
1878:   PetscFunctionReturn(PETSC_SUCCESS);
1879: }

1881: /*MC
1882:    PCMG - Use multigrid preconditioning. This preconditioner requires you provide additional
1883:     information about the coarser grid matrices and restriction/interpolation operators.

1885:    Options Database Keys:
1886: +  -pc_mg_levels <nlevels> - number of levels including finest
1887: .  -pc_mg_cycle_type <v,w> - provide the cycle desired
1888: .  -pc_mg_type <additive,multiplicative,full,kaskade> - multiplicative is the default
1889: .  -pc_mg_log - log information about time spent on each level of the solver
1890: .  -pc_mg_distinct_smoothup - configure up (after interpolation) and down (before restriction) smoothers separately (with different options prefixes)
1891: .  -pc_mg_galerkin <both,pmat,mat,none> - use Galerkin process to compute coarser operators, i.e. Acoarse = R A R'
1892: .  -pc_mg_multiplicative_cycles - number of cycles to use as the preconditioner (defaults to 1)
1893: .  -pc_mg_dump_matlab - dumps the matrices for each level and the restriction/interpolation matrices
1894:                         to the Socket viewer for reading from MATLAB.
1895: -  -pc_mg_dump_binary - dumps the matrices for each level and the restriction/interpolation matrices
1896:                         to the binary output file called binaryoutput

1898:    Level: intermediate

1900:    Notes:
1901:     If one uses a Krylov method such `KSPGMRES` or `KSPCG` as the smoother then one must use `KSPFGMRES`, `KSPGCR`, or `KSPRICHARDSON` as the outer Krylov method

1903:        When run with a single level the smoother options are used on that level NOT the coarse grid solver options

1905:        When run with `KSPRICHARDSON` the convergence test changes slightly if monitor is turned on. The iteration count may change slightly. This
1906:        is because without monitoring the residual norm is computed WITHIN each multigrid cycle on the finest level after the pre-smoothing
1907:        (because the residual has just been computed for the multigrid algorithm and is hence available for free) while with monitoring the
1908:        residual is computed at the end of each cycle.

1910: .seealso: `PCCreate()`, `PCSetType()`, `PCType`, `PC`, `PCMGType`, `PCEXOTIC`, `PCGAMG`, `PCML`, `PCHYPRE`
1911:           `PCMGSetLevels()`, `PCMGGetLevels()`, `PCMGSetType()`, `PCMGSetCycleType()`,
1912:           `PCMGSetDistinctSmoothUp()`, `PCMGGetCoarseSolve()`, `PCMGSetResidual()`, `PCMGSetInterpolation()`,
1913:           `PCMGSetRestriction()`, `PCMGGetSmoother()`, `PCMGGetSmootherUp()`, `PCMGGetSmootherDown()`,
1914:           `PCMGSetCycleTypeOnLevel()`, `PCMGSetRhs()`, `PCMGSetX()`, `PCMGSetR()`,
1915:           `PCMGSetAdaptCR()`, `PCMGGetAdaptInterpolation()`, `PCMGSetGalerkin()`, `PCMGGetAdaptCoarseSpaceType()`, `PCMGSetAdaptCoarseSpaceType()`
1916: M*/

1918: PETSC_EXTERN PetscErrorCode PCCreate_MG(PC pc)
1919: {
1920:   PC_MG *mg;

1922:   PetscFunctionBegin;
1923:   PetscCall(PetscNew(&mg));
1924:   pc->data               = mg;
1925:   mg->nlevels            = -1;
1926:   mg->am                 = PC_MG_MULTIPLICATIVE;
1927:   mg->galerkin           = PC_MG_GALERKIN_NONE;
1928:   mg->adaptInterpolation = PETSC_FALSE;
1929:   mg->Nc                 = -1;
1930:   mg->eigenvalue         = -1;

1932:   pc->useAmat = PETSC_TRUE;

1934:   pc->ops->apply          = PCApply_MG;
1935:   pc->ops->applytranspose = PCApplyTranspose_MG;
1936:   pc->ops->matapply       = PCMatApply_MG;
1937:   pc->ops->setup          = PCSetUp_MG;
1938:   pc->ops->reset          = PCReset_MG;
1939:   pc->ops->destroy        = PCDestroy_MG;
1940:   pc->ops->setfromoptions = PCSetFromOptions_MG;
1941:   pc->ops->view           = PCView_MG;

1943:   PetscCall(PetscObjectComposedDataRegister(&mg->eigenvalue));
1944:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCMGSetGalerkin_C", PCMGSetGalerkin_MG));
1945:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCMGGetLevels_C", PCMGGetLevels_MG));
1946:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCMGSetLevels_C", PCMGSetLevels_MG));
1947:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCGetInterpolations_C", PCGetInterpolations_MG));
1948:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCGetCoarseOperators_C", PCGetCoarseOperators_MG));
1949:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCMGSetAdaptInterpolation_C", PCMGSetAdaptInterpolation_MG));
1950:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCMGGetAdaptInterpolation_C", PCMGGetAdaptInterpolation_MG));
1951:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCMGSetAdaptCR_C", PCMGSetAdaptCR_MG));
1952:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCMGGetAdaptCR_C", PCMGGetAdaptCR_MG));
1953:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCMGSetAdaptCoarseSpaceType_C", PCMGSetAdaptCoarseSpaceType_MG));
1954:   PetscCall(PetscObjectComposeFunction((PetscObject)pc, "PCMGGetAdaptCoarseSpaceType_C", PCMGGetAdaptCoarseSpaceType_MG));
1955:   PetscFunctionReturn(PETSC_SUCCESS);
1956: }