xref: /petsc/src/ksp/pc/impls/mg/mg.c (revision bcee047adeeb73090d7e36cc71e39fc287cdbb97)
1 
2 /*
3     Defines the multigrid preconditioner interface.
4 */
5 #include <petsc/private/pcmgimpl.h> /*I "petscksp.h" I*/
6 #include <petsc/private/kspimpl.h>
7 #include <petscdm.h>
8 PETSC_INTERN PetscErrorCode PCPreSolveChangeRHS(PC, PetscBool *);
9 
10 /*
11    Contains the list of registered coarse space construction routines
12 */
13 PetscFunctionList PCMGCoarseList = NULL;
14 
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;
20 
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));
48 
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     }
64 
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 }
120 
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;
128 
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   }
137 
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;
148 
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;
156 
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;
172 
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   }
183 
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 }
194 
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;
200 
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));
224 
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 }
236 
237 /* Implementing CR
238 
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
240 
241   Inj^T (Inj Inj^T)^{-1} Inj
242 
243 and if Inj is a VecScatter, as it is now in PETSc, we have
244 
245   Inj^T Inj
246 
247 and
248 
249   S = I - Inj^T Inj
250 
251 since
252 
253   Inj S = Inj - (Inj Inj^T) Inj = 0.
254 
255 Brannick suggests
256 
257   A \to S^T A S  \qquad\mathrm{and}\qquad M \to S^T M S
258 
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
260 
261   M^{-1} A \to S M^{-1} A S
262 
263 In fact, since it is somewhat hard in PETSc to do the symmetric application, we will just apply S on the left.
264 
265   Check: || Inj P - I ||_F < tol
266   Check: In general, Inj Inj^T = I
267 */
268 
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;
275 
276 static PetscErrorCode CRSetup_Private(PC pc)
277 {
278   CRContext *ctx;
279   Mat        It;
280 
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 }
291 
292 static PetscErrorCode CRApply_Private(PC pc, Vec x, Vec y)
293 {
294   CRContext *ctx;
295 
296   PetscFunctionBeginUser;
297   PetscCall(PCShellGetContext(pc, &ctx));
298   PetscCall(MatMult(ctx->S, x, y));
299   PetscFunctionReturn(PETSC_SUCCESS);
300 }
301 
302 static PetscErrorCode CRDestroy_Private(PC pc)
303 {
304   CRContext *ctx;
305 
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 }
314 
315 static PetscErrorCode CreateCR_Private(PC pc, PetscInt l, PC *cr)
316 {
317   CRContext *ctx;
318 
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 }
332 
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;
345 
346   PetscFunctionBegin;
347   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
348   PetscValidLogicalCollectiveInt(pc, levels, 2);
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   }
364 
365   mg->nlevels = levels;
366 
367   PetscCall(PetscMalloc1(levels, &mglevels));
368 
369   PetscCall(PCGetOptionsPrefix(pc, &prefix));
370 
371   mg->stageApply = 0;
372   for (i = 0; i < levels; i++) {
373     PetscCall(PetscNew(&mglevels[i]));
374 
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;
384 
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];
394 
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));
401 
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_"));
406 
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 }
430 
431 /*@C
432    PCMGSetLevels - Sets the number of levels to use with `PCMG`.
433    Must be called before any other `PCMG` routine.
434 
435    Logically Collective
436 
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.
444 
445    Level: intermediate
446 
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.
450 
451      You can free the information in comms after this routine is called.
452 
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.
459 
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.
467 
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.
471 
472 .seealso: `PCMGSetType()`, `PCMGGetLevels()`
473 @*/
474 PetscErrorCode PCMGSetLevels(PC pc, PetscInt levels, MPI_Comm *comms)
475 {
476   PetscFunctionBegin;
477   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
478   if (comms) PetscValidPointer(comms, 3);
479   PetscTryMethod(pc, "PCMGSetLevels_C", (PC, PetscInt, MPI_Comm *), (pc, levels, comms));
480   PetscFunctionReturn(PETSC_SUCCESS);
481 }
482 
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;
488 
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 }
517 
518 /*
519    PCApply_MG - Runs either an additive, multiplicative, Kaskadic
520              or full cycle of multigrid.
521 
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;
532 
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   }
543 
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;
561 
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;
575 
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   }
588 
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;
594 
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   }
607 
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 }
629 
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 }
636 
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 }
643 
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 }
650 
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;
661 
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;
673 
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];
703 
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     }
717 
718 #if defined(PETSC_USE_LOG)
719     {
720       const char   *sname = "MG Apply";
721       PetscStageLog stageLog;
722       PetscInt      st;
723 
724       PetscCall(PetscLogGetStageLog(&stageLog));
725       for (st = 0; st < stageLog->numStages; ++st) {
726         PetscBool same;
727 
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 }
742 
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};
747 
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;
755 
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 }
832 
833 #include <petsc/private/kspimpl.h>
834 
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;
851 
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));
868 
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   }
878 
879   /* Create CR solvers */
880   PetscCall(PCMGGetAdaptCR(pc, &doCR));
881   if (doCR) {
882     const char *prefix;
883 
884     PetscCall(PCGetOptionsPrefix(pc, &prefix));
885     for (i = 1; i < n; ++i) {
886       PC   ipc, cr;
887       char crprefix[128];
888 
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));
898 
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));
905 
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   }
912 
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   }
923 
924   for (i = n - 1; i > 0; i--) {
925     if (!(mglevels[i]->interpolate || mglevels[i]->restrct)) {
926       missinginterpolate = PETSC_TRUE;
927       break;
928     }
929   }
930 
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   }
936 
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   }
950 
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       }
1009 
1010       for (i = n - 2; i > -1; i--) PetscCall(DMDestroy(&dms[i]));
1011       PetscCall(PetscFree(dms));
1012     }
1013   }
1014 
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;
1019 
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   }
1054 
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   }
1063 
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   }
1077 
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   }
1127 
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;
1137 
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) 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;
1162 
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       }
1169 
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) 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;
1178 
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       }
1185 
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) pc->failedreason = PC_SUBPC_ERROR;
1190       if (mglevels[i]->eventsmoothsetup) PetscCall(PetscLogEventEnd(mglevels[i]->eventsmoothsetup, 0, 0, 0, 0));
1191     }
1192   }
1193 
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) pc->failedreason = PC_SUBPC_ERROR;
1197   if (mglevels[0]->eventsmoothsetup) PetscCall(PetscLogEventEnd(mglevels[0]->eventsmoothsetup, 0, 0, 0, 0));
1198 
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.
1203 
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));
1213 
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 }
1223 
1224 /* -------------------------------------------------------------------------------------*/
1225 
1226 PetscErrorCode PCMGGetLevels_MG(PC pc, PetscInt *levels)
1227 {
1228   PC_MG *mg = (PC_MG *)pc->data;
1229 
1230   PetscFunctionBegin;
1231   *levels = mg->nlevels;
1232   PetscFunctionReturn(PETSC_SUCCESS);
1233 }
1234 
1235 /*@
1236    PCMGGetLevels - Gets the number of levels to use with `PCMG`.
1237 
1238    Not Collective
1239 
1240    Input Parameter:
1241 .  pc - the preconditioner context
1242 
1243    Output parameter:
1244 .  levels - the number of levels
1245 
1246    Level: advanced
1247 
1248 .seealso: `PCMG`, `PCMGSetLevels()`
1249 @*/
1250 PetscErrorCode PCMGGetLevels(PC pc, PetscInt *levels)
1251 {
1252   PetscFunctionBegin;
1253   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
1254   PetscValidIntPointer(levels, 2);
1255   *levels = 0;
1256   PetscTryMethod(pc, "PCMGGetLevels_C", (PC, PetscInt *), (pc, levels));
1257   PetscFunctionReturn(PETSC_SUCCESS);
1258 }
1259 
1260 /*@
1261    PCMGGetGridComplexity - compute operator and grid complexity of the `PCMG` hierarchy
1262 
1263    Input Parameter:
1264 .  pc - the preconditioner context
1265 
1266    Output Parameters:
1267 +  gc - grid complexity = sum_i(n_i) / n_0
1268 -  oc - operator complexity = sum_i(nnz_i) / nnz_0
1269 
1270    Level: advanced
1271 
1272    Note:
1273    This is often call the operator complexity in multigrid literature
1274 
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;
1284 
1285   PetscFunctionBegin;
1286   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
1287   if (gc) PetscValidRealPointer(gc, 2);
1288   if (oc) PetscValidRealPointer(oc, 3);
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 }
1312 
1313 /*@
1314    PCMGSetType - Determines the form of multigrid to use:
1315    multiplicative, additive, full, or the Kaskade algorithm.
1316 
1317    Logically Collective
1318 
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`
1322 
1323    Options Database Key:
1324 .  -pc_mg_type <form> - Sets <form>, one of multiplicative, additive, full, kaskade
1325 
1326    Level: advanced
1327 
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;
1333 
1334   PetscFunctionBegin;
1335   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
1336   PetscValidLogicalCollectiveEnum(pc, form, 2);
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 }
1342 
1343 /*@
1344    PCMGGetType - Finds the form of multigrid the `PCMG` is using  multiplicative, additive, full, or the Kaskade algorithm.
1345 
1346    Logically Collective
1347 
1348    Input Parameter:
1349 .  pc - the preconditioner context
1350 
1351    Output Parameter:
1352 .  type - one of `PC_MG_MULTIPLICATIVE`, `PC_MG_ADDITIVE`, `PC_MG_FULL`, `PC_MG_KASKADE`, `PCMGCycleType`
1353 
1354    Level: advanced
1355 
1356 .seealso: `PCMGType`, `PCMG`, `PCMGGetLevels()`, `PCMGSetLevels()`, `PCMGSetType()`
1357 @*/
1358 PetscErrorCode PCMGGetType(PC pc, PCMGType *type)
1359 {
1360   PC_MG *mg = (PC_MG *)pc->data;
1361 
1362   PetscFunctionBegin;
1363   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
1364   *type = mg->am;
1365   PetscFunctionReturn(PETSC_SUCCESS);
1366 }
1367 
1368 /*@
1369    PCMGSetCycleType - Sets the type cycles to use.  Use `PCMGSetCycleTypeOnLevel()` for more
1370    complicated cycling.
1371 
1372    Logically Collective
1373 
1374    Input Parameters:
1375 +  pc - the multigrid context
1376 -  n - either `PC_MG_CYCLE_V` or `PC_MG_CYCLE_W`
1377 
1378    Options Database Key:
1379 .  -pc_mg_cycle_type <v,w> - provide the cycle desired
1380 
1381    Level: advanced
1382 
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;
1390 
1391   PetscFunctionBegin;
1392   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
1393   PetscValidLogicalCollectiveEnum(pc, n, 2);
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 }
1399 
1400 /*@
1401    PCMGMultiplicativeSetCycles - Sets the number of cycles to use for each preconditioner step
1402          of multigrid when `PCMGType` is `PC_MG_MULTIPLICATIVE`
1403 
1404    Logically Collective
1405 
1406    Input Parameters:
1407 +  pc - the multigrid context
1408 -  n - number of cycles (default is 1)
1409 
1410    Options Database Key:
1411 .  -pc_mg_multiplicative_cycles n - set the number of cycles
1412 
1413    Level: advanced
1414 
1415    Note:
1416     This is not associated with setting a v or w cycle, that is set with `PCMGSetCycleType()`
1417 
1418 .seealso: `PCMGSetCycleTypeOnLevel()`, `PCMGSetCycleType()`, `PCMGCycleType`, `PCMGType`
1419 @*/
1420 PetscErrorCode PCMGMultiplicativeSetCycles(PC pc, PetscInt n)
1421 {
1422   PC_MG *mg = (PC_MG *)pc->data;
1423 
1424   PetscFunctionBegin;
1425   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
1426   PetscValidLogicalCollectiveInt(pc, n, 2);
1427   mg->cyclesperpcapply = n;
1428   PetscFunctionReturn(PETSC_SUCCESS);
1429 }
1430 
1431 PetscErrorCode PCMGSetGalerkin_MG(PC pc, PCMGGalerkinType use)
1432 {
1433   PC_MG *mg = (PC_MG *)pc->data;
1434 
1435   PetscFunctionBegin;
1436   mg->galerkin = use;
1437   PetscFunctionReturn(PETSC_SUCCESS);
1438 }
1439 
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
1443 
1444    Logically Collective
1445 
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`
1449 
1450    Options Database Key:
1451 .  -pc_mg_galerkin <both,pmat,mat,none> - set the matrices to form via the Galerkin process
1452 
1453    Level: intermediate
1454 
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.
1458 
1459 .seealso: `PCMG`, `PCMGGetGalerkin()`, `PCMGGalerkinType`
1460 @*/
1461 PetscErrorCode PCMGSetGalerkin(PC pc, PCMGGalerkinType use)
1462 {
1463   PetscFunctionBegin;
1464   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
1465   PetscTryMethod(pc, "PCMGSetGalerkin_C", (PC, PCMGGalerkinType), (pc, use));
1466   PetscFunctionReturn(PETSC_SUCCESS);
1467 }
1468 
1469 /*@
1470    PCMGGetGalerkin - Checks if Galerkin multigrid is being used, i.e. A_i-1 = r_i * A_i * p_i
1471 
1472    Not Collective
1473 
1474    Input Parameter:
1475 .  pc - the multigrid context
1476 
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`
1479 
1480    Level: intermediate
1481 
1482 .seealso: `PCMG`, `PCMGSetGalerkin()`, `PCMGGalerkinType`
1483 @*/
1484 PetscErrorCode PCMGGetGalerkin(PC pc, PCMGGalerkinType *galerkin)
1485 {
1486   PC_MG *mg = (PC_MG *)pc->data;
1487 
1488   PetscFunctionBegin;
1489   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
1490   *galerkin = mg->galerkin;
1491   PetscFunctionReturn(PETSC_SUCCESS);
1492 }
1493 
1494 PetscErrorCode PCMGSetAdaptInterpolation_MG(PC pc, PetscBool adapt)
1495 {
1496   PC_MG *mg = (PC_MG *)pc->data;
1497 
1498   PetscFunctionBegin;
1499   mg->adaptInterpolation = adapt;
1500   PetscFunctionReturn(PETSC_SUCCESS);
1501 }
1502 
1503 PetscErrorCode PCMGGetAdaptInterpolation_MG(PC pc, PetscBool *adapt)
1504 {
1505   PC_MG *mg = (PC_MG *)pc->data;
1506 
1507   PetscFunctionBegin;
1508   *adapt = mg->adaptInterpolation;
1509   PetscFunctionReturn(PETSC_SUCCESS);
1510 }
1511 
1512 PetscErrorCode PCMGSetAdaptCoarseSpaceType_MG(PC pc, PCMGCoarseSpaceType ctype)
1513 {
1514   PC_MG *mg = (PC_MG *)pc->data;
1515 
1516   PetscFunctionBegin;
1517   mg->adaptInterpolation = ctype != PCMG_ADAPT_NONE ? PETSC_TRUE : PETSC_FALSE;
1518   mg->coarseSpaceType    = ctype;
1519   PetscFunctionReturn(PETSC_SUCCESS);
1520 }
1521 
1522 PetscErrorCode PCMGGetAdaptCoarseSpaceType_MG(PC pc, PCMGCoarseSpaceType *ctype)
1523 {
1524   PC_MG *mg = (PC_MG *)pc->data;
1525 
1526   PetscFunctionBegin;
1527   *ctype = mg->coarseSpaceType;
1528   PetscFunctionReturn(PETSC_SUCCESS);
1529 }
1530 
1531 PetscErrorCode PCMGSetAdaptCR_MG(PC pc, PetscBool cr)
1532 {
1533   PC_MG *mg = (PC_MG *)pc->data;
1534 
1535   PetscFunctionBegin;
1536   mg->compatibleRelaxation = cr;
1537   PetscFunctionReturn(PETSC_SUCCESS);
1538 }
1539 
1540 PetscErrorCode PCMGGetAdaptCR_MG(PC pc, PetscBool *cr)
1541 {
1542   PC_MG *mg = (PC_MG *)pc->data;
1543 
1544   PetscFunctionBegin;
1545   *cr = mg->compatibleRelaxation;
1546   PetscFunctionReturn(PETSC_SUCCESS);
1547 }
1548 
1549 /*@C
1550   PCMGSetAdaptCoarseSpaceType - Set the type of adaptive coarse space.
1551 
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.
1553 
1554   Logically Collective
1555 
1556   Input Parameters:
1557 + pc    - the multigrid context
1558 - ctype - the type of coarse space
1559 
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
1563 
1564   Level: intermediate
1565 
1566 .seealso: `PCMG`, `PCMGCoarseSpaceType`, `PCMGGetAdaptCoarseSpaceType()`, `PCMGSetGalerkin()`, `PCMGSetAdaptInterpolation()`
1567 @*/
1568 PetscErrorCode PCMGSetAdaptCoarseSpaceType(PC pc, PCMGCoarseSpaceType ctype)
1569 {
1570   PetscFunctionBegin;
1571   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
1572   PetscValidLogicalCollectiveEnum(pc, ctype, 2);
1573   PetscTryMethod(pc, "PCMGSetAdaptCoarseSpaceType_C", (PC, PCMGCoarseSpaceType), (pc, ctype));
1574   PetscFunctionReturn(PETSC_SUCCESS);
1575 }
1576 
1577 /*@C
1578    PCMGGetAdaptCoarseSpaceType - Get the type of adaptive coarse space.
1579 
1580    Not Collective
1581 
1582    Input Parameter:
1583 .  pc    - the multigrid context
1584 
1585    Output Parameter:
1586 .  ctype - the type of coarse space
1587 
1588   Level: intermediate
1589 
1590 .seealso: `PCMG`, `PCMGCoarseSpaceType`, `PCMGSetAdaptCoarseSpaceType()`, `PCMGSetGalerkin()`, `PCMGSetAdaptInterpolation()`
1591 @*/
1592 PetscErrorCode PCMGGetAdaptCoarseSpaceType(PC pc, PCMGCoarseSpaceType *ctype)
1593 {
1594   PetscFunctionBegin;
1595   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
1596   PetscValidPointer(ctype, 2);
1597   PetscUseMethod(pc, "PCMGGetAdaptCoarseSpaceType_C", (PC, PCMGCoarseSpaceType *), (pc, ctype));
1598   PetscFunctionReturn(PETSC_SUCCESS);
1599 }
1600 
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.
1604 
1605    Logically Collective
1606 
1607    Input Parameters:
1608 +  pc    - the multigrid context
1609 -  adapt - flag for adaptation of the interpolator
1610 
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
1615 
1616   Level: intermediate
1617 
1618 .seealso: `PCMG`, `PCMGGetAdaptInterpolation()`, `PCMGSetGalerkin()`, `PCMGGetAdaptCoarseSpaceType()`, `PCMGSetAdaptCoarseSpaceType()`
1619 @*/
1620 PetscErrorCode PCMGSetAdaptInterpolation(PC pc, PetscBool adapt)
1621 {
1622   PetscFunctionBegin;
1623   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
1624   PetscTryMethod(pc, "PCMGSetAdaptInterpolation_C", (PC, PetscBool), (pc, adapt));
1625   PetscFunctionReturn(PETSC_SUCCESS);
1626 }
1627 
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.
1631 
1632   Not Collective
1633 
1634   Input Parameter:
1635 . pc    - the multigrid context
1636 
1637   Output Parameter:
1638 . adapt - flag for adaptation of the interpolator
1639 
1640   Level: intermediate
1641 
1642 .seealso: `PCMG`, `PCMGSetAdaptInterpolation()`, `PCMGSetGalerkin()`, `PCMGGetAdaptCoarseSpaceType()`, `PCMGSetAdaptCoarseSpaceType()`
1643 @*/
1644 PetscErrorCode PCMGGetAdaptInterpolation(PC pc, PetscBool *adapt)
1645 {
1646   PetscFunctionBegin;
1647   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
1648   PetscValidBoolPointer(adapt, 2);
1649   PetscUseMethod(pc, "PCMGGetAdaptInterpolation_C", (PC, PetscBool *), (pc, adapt));
1650   PetscFunctionReturn(PETSC_SUCCESS);
1651 }
1652 
1653 /*@
1654    PCMGSetAdaptCR - Monitor the coarse space quality using an auxiliary solve with compatible relaxation.
1655 
1656    Logically Collective
1657 
1658    Input Parameters:
1659 +  pc - the multigrid context
1660 -  cr - flag for compatible relaxation
1661 
1662    Options Database Key:
1663 .  -pc_mg_adapt_cr - Turn on compatible relaxation
1664 
1665    Level: intermediate
1666 
1667 .seealso: `PCMG`, `PCMGGetAdaptCR()`, `PCMGSetAdaptInterpolation()`, `PCMGSetGalerkin()`, `PCMGGetAdaptCoarseSpaceType()`, `PCMGSetAdaptCoarseSpaceType()`
1668 @*/
1669 PetscErrorCode PCMGSetAdaptCR(PC pc, PetscBool cr)
1670 {
1671   PetscFunctionBegin;
1672   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
1673   PetscTryMethod(pc, "PCMGSetAdaptCR_C", (PC, PetscBool), (pc, cr));
1674   PetscFunctionReturn(PETSC_SUCCESS);
1675 }
1676 
1677 /*@
1678   PCMGGetAdaptCR - Get the flag to monitor coarse space quality using an auxiliary solve with compatible relaxation.
1679 
1680   Not Collective
1681 
1682   Input Parameter:
1683 . pc    - the multigrid context
1684 
1685   Output Parameter:
1686 . cr - flag for compatible relaxaion
1687 
1688   Level: intermediate
1689 
1690 .seealso: `PCMGSetAdaptCR()`, `PCMGGetAdaptInterpolation()`, `PCMGSetGalerkin()`, `PCMGGetAdaptCoarseSpaceType()`, `PCMGSetAdaptCoarseSpaceType()`
1691 @*/
1692 PetscErrorCode PCMGGetAdaptCR(PC pc, PetscBool *cr)
1693 {
1694   PetscFunctionBegin;
1695   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
1696   PetscValidBoolPointer(cr, 2);
1697   PetscUseMethod(pc, "PCMGGetAdaptCR_C", (PC, PetscBool *), (pc, cr));
1698   PetscFunctionReturn(PETSC_SUCCESS);
1699 }
1700 
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.
1705 
1706    Logically Collective
1707 
1708    Input Parameters:
1709 +  mg - the multigrid context
1710 -  n - the number of smoothing steps
1711 
1712    Options Database Key:
1713 .  -mg_levels_ksp_max_it <n> - Sets number of pre and post-smoothing steps
1714 
1715    Level: advanced
1716 
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.
1719 
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;
1727 
1728   PetscFunctionBegin;
1729   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
1730   PetscValidLogicalCollectiveInt(pc, n, 2);
1731   PetscCheck(mglevels, PetscObjectComm((PetscObject)pc), PETSC_ERR_ORDER, "Must set MG levels with PCMGSetLevels() before calling");
1732   levels = mglevels[0]->levels;
1733 
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 }
1742 
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
1746 
1747    Logically Collective
1748 
1749    Input Parameter:
1750 .  pc - the preconditioner context
1751 
1752    Options Database Key:
1753 .  -pc_mg_distinct_smoothup <bool> - use distinct smoothing objects
1754 
1755    Level: advanced
1756 
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.
1759 
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;
1768 
1769   PetscFunctionBegin;
1770   PetscValidHeaderSpecific(pc, PC_CLASSID, 1);
1771   PetscCheck(mglevels, PetscObjectComm((PetscObject)pc), PETSC_ERR_ORDER, "Must set MG levels with PCMGSetLevels() before calling");
1772   levels = mglevels[0]->levels;
1773 
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 }
1784 
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;
1792 
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 }
1804 
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;
1812 
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 }
1824 
1825 /*@C
1826    PCMGRegisterCoarseSpaceConstructor -  Adds a method to the `PCMG` package for coarse space construction.
1827 
1828    Not Collective
1829 
1830    Input Parameters:
1831 +  name     - name of the constructor
1832 -  function - constructor routine
1833 
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
1843 
1844   Level: advanced
1845 
1846   Developer Note:
1847   How come this is not used by `PCGAMG`?
1848 
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 }
1858 
1859 /*@C
1860   PCMGGetCoarseSpaceConstructor -  Returns the given coarse space construction method.
1861 
1862   Not Collective
1863 
1864   Input Parameter:
1865 . name     - name of the constructor
1866 
1867   Output Parameter:
1868 . function - constructor routine
1869 
1870   Level: advanced
1871 
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 }
1880 
1881 /*MC
1882    PCMG - Use multigrid preconditioning. This preconditioner requires you provide additional
1883     information about the coarser grid matrices and restriction/interpolation operators.
1884 
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
1897 
1898    Level: intermediate
1899 
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
1902 
1903        When run with a single level the smoother options are used on that level NOT the coarse grid solver options
1904 
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.
1909 
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*/
1917 
1918 PETSC_EXTERN PetscErrorCode PCCreate_MG(PC pc)
1919 {
1920   PC_MG *mg;
1921 
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;
1931 
1932   pc->useAmat = PETSC_TRUE;
1933 
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;
1942 
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 }
1957