Actual source code: asm.c

petsc-3.9.1 2018-04-29
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  2: /*
  3:   This file defines an additive Schwarz preconditioner for any Mat implementation.

  5:   Note that each processor may have any number of subdomains. But in order to
  6:   deal easily with the VecScatter(), we treat each processor as if it has the
  7:   same number of subdomains.

  9:        n - total number of true subdomains on all processors
 10:        n_local_true - actual number of subdomains on this processor
 11:        n_local = maximum over all processors of n_local_true
 12: */
 13:  #include <petsc/private/pcimpl.h>
 14:  #include <petscdm.h>

 16: typedef struct {
 17:   PetscInt   n, n_local, n_local_true;
 18:   PetscInt   overlap;             /* overlap requested by user */
 19:   KSP        *ksp;                /* linear solvers for each block */
 20:   VecScatter restriction;         /* mapping from global to overlapping (process) subdomain*/
 21:   VecScatter *lrestriction;       /* mapping from subregion to overlapping (process) subdomain */
 22:   VecScatter *lprolongation;      /* mapping from non-overlapping subregion to overlapping (process) subdomain; used for restrict additive version of algorithms */
 23:   Vec        lx, ly;              /* work vectors */
 24:   Vec        *x,*y;                    /* work vectors */
 25:   IS         lis;                 /* index set that defines each overlapping multiplicative (process) subdomain */
 26:   IS         *is;                 /* index set that defines each overlapping subdomain */
 27:   IS         *is_local;           /* index set that defines each non-overlapping subdomain, may be NULL */
 28:   Mat        *mat,*pmat;          /* mat is not currently used */
 29:   PCASMType  type;                /* use reduced interpolation, restriction or both */
 30:   PetscBool  type_set;            /* if user set this value (so won't change it for symmetric problems) */
 31:   PetscBool  same_local_solves;   /* flag indicating whether all local solvers are same */
 32:   PetscBool  sort_indices;        /* flag to sort subdomain indices */
 33:   PetscBool  dm_subdomains;       /* whether DM is allowed to define subdomains */
 34:   PCCompositeType loctype;        /* the type of composition for local solves */
 35:   MatType    sub_mat_type;        /* the type of Mat used for subdomain solves (can be MATSAME or NULL) */
 36:   /* For multiplicative solve */
 37:   Mat       *lmats;               /* submatrices for overlapping multiplicative (process) subdomain */
 38: } PC_ASM;

 40: static PetscErrorCode PCView_ASM(PC pc,PetscViewer viewer)
 41: {
 42:   PC_ASM         *osm = (PC_ASM*)pc->data;
 44:   PetscMPIInt    rank;
 45:   PetscInt       i,bsz;
 46:   PetscBool      iascii,isstring;
 47:   PetscViewer    sviewer;

 50:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
 51:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSTRING,&isstring);
 52:   if (iascii) {
 53:     char overlaps[256] = "user-defined overlap",blocks[256] = "total subdomain blocks not yet set";
 54:     if (osm->overlap >= 0) {PetscSNPrintf(overlaps,sizeof(overlaps),"amount of overlap = %D",osm->overlap);}
 55:     if (osm->n > 0) {PetscSNPrintf(blocks,sizeof(blocks),"total subdomain blocks = %D",osm->n);}
 56:     PetscViewerASCIIPrintf(viewer,"  %s, %s\n",blocks,overlaps);
 57:     PetscViewerASCIIPrintf(viewer,"  restriction/interpolation type - %s\n",PCASMTypes[osm->type]);
 58:     if (osm->dm_subdomains) {PetscViewerASCIIPrintf(viewer,"  Additive Schwarz: using DM to define subdomains\n");}
 59:     if (osm->loctype != PC_COMPOSITE_ADDITIVE) {PetscViewerASCIIPrintf(viewer,"  Additive Schwarz: local solve composition type - %s\n",PCCompositeTypes[osm->loctype]);}
 60:     MPI_Comm_rank(PetscObjectComm((PetscObject)pc),&rank);
 61:     if (osm->same_local_solves) {
 62:       if (osm->ksp) {
 63:         PetscViewerASCIIPrintf(viewer,"  Local solve is same for all blocks, in the following KSP and PC objects:\n");
 64:         PetscViewerGetSubViewer(viewer,PETSC_COMM_SELF,&sviewer);
 65:         if (!rank) {
 66:           PetscViewerASCIIPushTab(viewer);
 67:           KSPView(osm->ksp[0],sviewer);
 68:           PetscViewerASCIIPopTab(viewer);
 69:         }
 70:         PetscViewerRestoreSubViewer(viewer,PETSC_COMM_SELF,&sviewer);
 71:       }
 72:     } else {
 73:       PetscViewerASCIIPushSynchronized(viewer);
 74:       PetscViewerASCIISynchronizedPrintf(viewer,"  [%d] number of local blocks = %D\n",(int)rank,osm->n_local_true);
 75:       PetscViewerFlush(viewer);
 76:       PetscViewerASCIIPrintf(viewer,"  Local solve info for each block is in the following KSP and PC objects:\n");
 77:       PetscViewerASCIIPushTab(viewer);
 78:       PetscViewerASCIIPrintf(viewer,"- - - - - - - - - - - - - - - - - -\n");
 79:       PetscViewerGetSubViewer(viewer,PETSC_COMM_SELF,&sviewer);
 80:       for (i=0; i<osm->n_local_true; i++) {
 81:         ISGetLocalSize(osm->is[i],&bsz);
 82:         PetscViewerASCIISynchronizedPrintf(sviewer,"[%d] local block number %D, size = %D\n",(int)rank,i,bsz);
 83:         KSPView(osm->ksp[i],sviewer);
 84:         PetscViewerASCIISynchronizedPrintf(sviewer,"- - - - - - - - - - - - - - - - - -\n");
 85:       }
 86:       PetscViewerRestoreSubViewer(viewer,PETSC_COMM_SELF,&sviewer);
 87:       PetscViewerASCIIPopTab(viewer);
 88:       PetscViewerFlush(viewer);
 89:       PetscViewerASCIIPopSynchronized(viewer);
 90:     }
 91:   } else if (isstring) {
 92:     PetscViewerStringSPrintf(viewer," blocks=%D, overlap=%D, type=%s",osm->n,osm->overlap,PCASMTypes[osm->type]);
 93:     PetscViewerGetSubViewer(viewer,PETSC_COMM_SELF,&sviewer);
 94:     if (osm->ksp) {KSPView(osm->ksp[0],sviewer);}
 95:     PetscViewerRestoreSubViewer(viewer,PETSC_COMM_SELF,&sviewer);
 96:   }
 97:   return(0);
 98: }

100: static PetscErrorCode PCASMPrintSubdomains(PC pc)
101: {
102:   PC_ASM         *osm = (PC_ASM*)pc->data;
103:   const char     *prefix;
104:   char           fname[PETSC_MAX_PATH_LEN+1];
105:   PetscViewer    viewer, sviewer;
106:   char           *s;
107:   PetscInt       i,j,nidx;
108:   const PetscInt *idx;
109:   PetscMPIInt    rank, size;

113:   MPI_Comm_size(PetscObjectComm((PetscObject)pc), &size);
114:   MPI_Comm_rank(PetscObjectComm((PetscObject)pc), &rank);
115:   PCGetOptionsPrefix(pc,&prefix);
116:   PetscOptionsGetString(NULL,prefix,"-pc_asm_print_subdomains",fname,PETSC_MAX_PATH_LEN,NULL);
117:   if (fname[0] == 0) { PetscStrcpy(fname,"stdout"); };
118:   PetscViewerASCIIOpen(PetscObjectComm((PetscObject)pc),fname,&viewer);
119:   for (i=0; i<osm->n_local; i++) {
120:     if (i < osm->n_local_true) {
121:       ISGetLocalSize(osm->is[i],&nidx);
122:       ISGetIndices(osm->is[i],&idx);
123:       /* Print to a string viewer; no more than 15 characters per index plus 512 char for the header.*/
124:       PetscMalloc1(16*(nidx+1)+512, &s);
125:       PetscViewerStringOpen(PETSC_COMM_SELF, s, 16*(nidx+1)+512, &sviewer);
126:       PetscViewerStringSPrintf(sviewer, "[%D:%D] Subdomain %D with overlap:\n", rank, size, i);
127:       for (j=0; j<nidx; j++) {
128:         PetscViewerStringSPrintf(sviewer,"%D ",idx[j]);
129:       }
130:       ISRestoreIndices(osm->is[i],&idx);
131:       PetscViewerStringSPrintf(sviewer,"\n");
132:       PetscViewerDestroy(&sviewer);
133:       PetscViewerASCIIPushSynchronized(viewer);
134:       PetscViewerASCIISynchronizedPrintf(viewer, s);
135:       PetscViewerFlush(viewer);
136:       PetscViewerASCIIPopSynchronized(viewer);
137:       PetscFree(s);
138:       if (osm->is_local) {
139:         /* Print to a string viewer; no more than 15 characters per index plus 512 char for the header.*/
140:         PetscMalloc1(16*(nidx+1)+512, &s);
141:         PetscViewerStringOpen(PETSC_COMM_SELF, s, 16*(nidx+1)+512, &sviewer);
142:         PetscViewerStringSPrintf(sviewer, "[%D:%D] Subdomain %D without overlap:\n", rank, size, i);
143:         ISGetLocalSize(osm->is_local[i],&nidx);
144:         ISGetIndices(osm->is_local[i],&idx);
145:         for (j=0; j<nidx; j++) {
146:           PetscViewerStringSPrintf(sviewer,"%D ",idx[j]);
147:         }
148:         ISRestoreIndices(osm->is_local[i],&idx);
149:         PetscViewerStringSPrintf(sviewer,"\n");
150:         PetscViewerDestroy(&sviewer);
151:         PetscViewerASCIIPushSynchronized(viewer);
152:         PetscViewerASCIISynchronizedPrintf(viewer, s);
153:         PetscViewerFlush(viewer);
154:         PetscViewerASCIIPopSynchronized(viewer);
155:         PetscFree(s);
156:       }
157:     } else {
158:       /* Participate in collective viewer calls. */
159:       PetscViewerASCIIPushSynchronized(viewer);
160:       PetscViewerFlush(viewer);
161:       PetscViewerASCIIPopSynchronized(viewer);
162:       /* Assume either all ranks have is_local or none do. */
163:       if (osm->is_local) {
164:         PetscViewerASCIIPushSynchronized(viewer);
165:         PetscViewerFlush(viewer);
166:         PetscViewerASCIIPopSynchronized(viewer);
167:       }
168:     }
169:   }
170:   PetscViewerFlush(viewer);
171:   PetscViewerDestroy(&viewer);
172:   return(0);
173: }

175: static PetscErrorCode PCSetUp_ASM(PC pc)
176: {
177:   PC_ASM         *osm = (PC_ASM*)pc->data;
179:   PetscBool      symset,flg;
180:   PetscInt       i,m,m_local;
181:   MatReuse       scall = MAT_REUSE_MATRIX;
182:   IS             isl;
183:   KSP            ksp;
184:   PC             subpc;
185:   const char     *prefix,*pprefix;
186:   Vec            vec;
187:   DM             *domain_dm = NULL;

190:   if (!pc->setupcalled) {
191:     PetscInt m;

193:     if (!osm->type_set) {
194:       MatIsSymmetricKnown(pc->pmat,&symset,&flg);
195:       if (symset && flg) osm->type = PC_ASM_BASIC;
196:     }

198:     /* Note: if subdomains have been set either via PCASMSetTotalSubdomains() or via PCASMSetLocalSubdomains(), osm->n_local_true will not be PETSC_DECIDE */
199:     if (osm->n_local_true == PETSC_DECIDE) {
200:       /* no subdomains given */
201:       /* try pc->dm first, if allowed */
202:       if (osm->dm_subdomains && pc->dm) {
203:         PetscInt  num_domains, d;
204:         char      **domain_names;
205:         IS        *inner_domain_is, *outer_domain_is;
206:         DMCreateDomainDecomposition(pc->dm, &num_domains, &domain_names, &inner_domain_is, &outer_domain_is, &domain_dm);
207:         osm->overlap = -1; /* We do not want to increase the overlap of the IS. 
208:                               A future improvement of this code might allow one to use 
209:                               DM-defined subdomains and also increase the overlap, 
210:                               but that is not currently supported */
211:         if (num_domains) {
212:           PCASMSetLocalSubdomains(pc, num_domains, outer_domain_is, inner_domain_is);
213:         }
214:         for (d = 0; d < num_domains; ++d) {
215:           if (domain_names)    {PetscFree(domain_names[d]);}
216:           if (inner_domain_is) {ISDestroy(&inner_domain_is[d]);}
217:           if (outer_domain_is) {ISDestroy(&outer_domain_is[d]);}
218:         }
219:         PetscFree(domain_names);
220:         PetscFree(inner_domain_is);
221:         PetscFree(outer_domain_is);
222:       }
223:       if (osm->n_local_true == PETSC_DECIDE) {
224:         /* still no subdomains; use one subdomain per processor */
225:         osm->n_local_true = 1;
226:       }
227:     }
228:     { /* determine the global and max number of subdomains */
229:       struct {PetscInt max,sum;} inwork,outwork;
230:       PetscMPIInt size;

232:       inwork.max   = osm->n_local_true;
233:       inwork.sum   = osm->n_local_true;
234:       MPIU_Allreduce(&inwork,&outwork,1,MPIU_2INT,MPIU_MAXSUM_OP,PetscObjectComm((PetscObject)pc));
235:       osm->n_local = outwork.max;
236:       osm->n       = outwork.sum;

238:       MPI_Comm_size(PetscObjectComm((PetscObject)pc),&size);
239:       if (outwork.max == 1 && outwork.sum == size) {
240:         /* osm->n_local_true = 1 on all processes, set this option may enable use of optimized MatCreateSubMatrices() implementation */
241:         MatSetOption(pc->pmat,MAT_SUBMAT_SINGLEIS,PETSC_TRUE);
242:       }
243:     }
244:     if (!osm->is) { /* create the index sets */
245:       PCASMCreateSubdomains(pc->pmat,osm->n_local_true,&osm->is);
246:     }
247:     if (osm->n_local_true > 1 && !osm->is_local) {
248:       PetscMalloc1(osm->n_local_true,&osm->is_local);
249:       for (i=0; i<osm->n_local_true; i++) {
250:         if (osm->overlap > 0) { /* With positive overlap, osm->is[i] will be modified */
251:           ISDuplicate(osm->is[i],&osm->is_local[i]);
252:           ISCopy(osm->is[i],osm->is_local[i]);
253:         } else {
254:           PetscObjectReference((PetscObject)osm->is[i]);
255:           osm->is_local[i] = osm->is[i];
256:         }
257:       }
258:     }
259:     PCGetOptionsPrefix(pc,&prefix);
260:     flg  = PETSC_FALSE;
261:     PetscOptionsGetBool(NULL,prefix,"-pc_asm_print_subdomains",&flg,NULL);
262:     if (flg) { PCASMPrintSubdomains(pc); }

264:     if (osm->overlap > 0) {
265:       /* Extend the "overlapping" regions by a number of steps */
266:       MatIncreaseOverlap(pc->pmat,osm->n_local_true,osm->is,osm->overlap);
267:     }
268:     if (osm->sort_indices) {
269:       for (i=0; i<osm->n_local_true; i++) {
270:         ISSort(osm->is[i]);
271:         if (osm->is_local) {
272:           ISSort(osm->is_local[i]);
273:         }
274:       }
275:     }

277:     if (!osm->ksp) {
278:       /* Create the local solvers */
279:       PetscMalloc1(osm->n_local_true,&osm->ksp);
280:       if (domain_dm) {
281:         PetscInfo(pc,"Setting up ASM subproblems using the embedded DM\n");
282:       }
283:       for (i=0; i<osm->n_local_true; i++) {
284:         KSPCreate(PETSC_COMM_SELF,&ksp);
285:         KSPSetErrorIfNotConverged(ksp,pc->erroriffailure);
286:         PetscLogObjectParent((PetscObject)pc,(PetscObject)ksp);
287:         PetscObjectIncrementTabLevel((PetscObject)ksp,(PetscObject)pc,1);
288:         KSPSetType(ksp,KSPPREONLY);
289:         KSPGetPC(ksp,&subpc);
290:         PCGetOptionsPrefix(pc,&prefix);
291:         KSPSetOptionsPrefix(ksp,prefix);
292:         KSPAppendOptionsPrefix(ksp,"sub_");
293:         if (domain_dm) {
294:           KSPSetDM(ksp, domain_dm[i]);
295:           KSPSetDMActive(ksp, PETSC_FALSE);
296:           DMDestroy(&domain_dm[i]);
297:         }
298:         osm->ksp[i] = ksp;
299:       }
300:       if (domain_dm) {
301:         PetscFree(domain_dm);
302:       }
303:     }
304: 
305:     ISConcatenate(PETSC_COMM_SELF, osm->n_local_true, osm->is, &osm->lis);
306:     ISSortRemoveDups(osm->lis);
307:     ISGetLocalSize(osm->lis, &m);
308:     VecCreateSeq(PETSC_COMM_SELF, m, &osm->lx);
309:     VecDuplicate(osm->lx, &osm->ly);
310: 
311:     scall = MAT_INITIAL_MATRIX;
312:   } else {
313:     /*
314:        Destroy the blocks from the previous iteration
315:     */
316:     if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
317:       MatDestroyMatrices(osm->n_local_true,&osm->pmat);
318:       scall = MAT_INITIAL_MATRIX;
319:     }
320:   }

322:   /*
323:      Extract out the submatrices
324:   */
325:   MatCreateSubMatrices(pc->pmat,osm->n_local_true,osm->is,osm->is,scall,&osm->pmat);
326:   if (scall == MAT_INITIAL_MATRIX) {
327:     PetscObjectGetOptionsPrefix((PetscObject)pc->pmat,&pprefix);
328:     for (i=0; i<osm->n_local_true; i++) {
329:       PetscLogObjectParent((PetscObject)pc,(PetscObject)osm->pmat[i]);
330:       PetscObjectSetOptionsPrefix((PetscObject)osm->pmat[i],pprefix);
331:     }
332:   }

334:   /* Convert the types of the submatrices (if needbe) */
335:   if (osm->sub_mat_type) {
336:     for (i=0; i<osm->n_local_true; i++) {
337:       MatConvert(osm->pmat[i],osm->sub_mat_type,MAT_INPLACE_MATRIX,&(osm->pmat[i]));
338:     }
339:   }

341:   if(!pc->setupcalled){
342:     /* Create the local work vectors (from the local matrices) and scatter contexts */
343:     MatCreateVecs(pc->pmat,&vec,0);
344: 
345:     if (osm->is_local && (osm->type == PC_ASM_INTERPOLATE || osm->type == PC_ASM_NONE )) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Cannot use interpolate or none PCASMType if is_local was provided to PCASMSetLocalSubdomains()");
346:     if (osm->is_local && osm->type == PC_ASM_RESTRICT && osm->loctype == PC_COMPOSITE_ADDITIVE) {
347:       PetscMalloc1(osm->n_local_true,&osm->lprolongation);
348:     }
349:     PetscMalloc1(osm->n_local_true,&osm->lrestriction);
350:     PetscMalloc1(osm->n_local_true,&osm->x);
351:     PetscMalloc1(osm->n_local_true,&osm->y);
352: 
353:     ISGetLocalSize(osm->lis,&m);
354:     ISCreateStride(PETSC_COMM_SELF,m,0,1,&isl);
355:     VecScatterCreate(vec,osm->lis,osm->lx,isl,&osm->restriction);
356:     ISDestroy(&isl);
357: 
358: 
359:     for (i=0; i<osm->n_local_true; ++i) {
360:       ISLocalToGlobalMapping ltog;
361:       IS                     isll;
362:       const PetscInt         *idx_is;
363:       PetscInt               *idx_lis,nout;

365:       ISGetLocalSize(osm->is[i],&m);
366:       MatCreateVecs(osm->pmat[i],&osm->x[i],NULL);
367:       VecDuplicate(osm->x[i],&osm->y[i]);
368: 
369:       /* generate a scatter from ly to y[i] picking all the overlapping is[i] entries */
370:       ISLocalToGlobalMappingCreateIS(osm->lis,&ltog);
371:       ISGetLocalSize(osm->is[i],&m);
372:       ISGetIndices(osm->is[i], &idx_is);
373:       PetscMalloc1(m,&idx_lis);
374:       ISGlobalToLocalMappingApply(ltog,IS_GTOLM_DROP,m,idx_is,&nout,idx_lis);
375:       if (nout != m) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"is not a subset of lis");
376:       ISRestoreIndices(osm->is[i], &idx_is);
377:       ISCreateGeneral(PETSC_COMM_SELF,m,idx_lis,PETSC_OWN_POINTER,&isll);
378:       ISLocalToGlobalMappingDestroy(&ltog);
379:       ISCreateStride(PETSC_COMM_SELF,m,0,1,&isl);
380:       VecScatterCreate(osm->ly,isll,osm->y[i],isl,&osm->lrestriction[i]);
381:       ISDestroy(&isll);
382:       ISDestroy(&isl);
383:       if (osm->lprolongation) { /* generate a scatter from y[i] to ly picking only the the non-overalapping is_local[i] entries */
384:         ISLocalToGlobalMapping ltog;
385:         IS                     isll,isll_local;
386:         const PetscInt         *idx_local;
387:         PetscInt               *idx1, *idx2, nout;
388: 
389:         ISGetLocalSize(osm->is_local[i],&m_local);
390:         ISGetIndices(osm->is_local[i], &idx_local);
391: 
392:         ISLocalToGlobalMappingCreateIS(osm->is[i],&ltog);
393:         PetscMalloc1(m_local,&idx1);
394:         ISGlobalToLocalMappingApply(ltog,IS_GTOLM_DROP,m_local,idx_local,&nout,idx1);
395:         ISLocalToGlobalMappingDestroy(&ltog);
396:         if (nout != m_local) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"is_local not a subset of is");
397:         ISCreateGeneral(PETSC_COMM_SELF,m_local,idx1,PETSC_OWN_POINTER,&isll);
398: 
399:         ISLocalToGlobalMappingCreateIS(osm->lis,&ltog);
400:         PetscMalloc1(m_local,&idx2);
401:               ISGlobalToLocalMappingApply(ltog,IS_GTOLM_DROP,m_local,idx_local,&nout,idx2);
402:         ISLocalToGlobalMappingDestroy(&ltog);
403:         if (nout != m_local) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"is_local not a subset of lis");
404:         ISCreateGeneral(PETSC_COMM_SELF,m_local,idx2,PETSC_OWN_POINTER,&isll_local);
405: 
406:         ISRestoreIndices(osm->is_local[i], &idx_local);
407:         VecScatterCreate(osm->y[i],isll,osm->ly,isll_local,&osm->lprolongation[i]);
408: 
409:         ISDestroy(&isll);
410:         ISDestroy(&isll_local);
411:       }
412:     }
413:     VecDestroy(&vec);
414:   }

416:   if (osm->loctype == PC_COMPOSITE_MULTIPLICATIVE) {
417:     IS      *cis;
418:     PetscInt c;

420:     PetscMalloc1(osm->n_local_true, &cis);
421:     for (c = 0; c < osm->n_local_true; ++c) cis[c] = osm->lis;
422:     MatCreateSubMatrices(pc->pmat, osm->n_local_true, osm->is, cis, scall, &osm->lmats);
423:     PetscFree(cis);
424:   }

426:   /* Return control to the user so that the submatrices can be modified (e.g., to apply
427:      different boundary conditions for the submatrices than for the global problem) */
428:   PCModifySubMatrices(pc,osm->n_local_true,osm->is,osm->is,osm->pmat,pc->modifysubmatricesP);

430:   /*
431:      Loop over subdomains putting them into local ksp
432:   */
433:   for (i=0; i<osm->n_local_true; i++) {
434:     KSPSetOperators(osm->ksp[i],osm->pmat[i],osm->pmat[i]);
435:     if (!pc->setupcalled) {
436:       KSPSetFromOptions(osm->ksp[i]);
437:     }
438:   }
439:   return(0);
440: }

442: static PetscErrorCode PCSetUpOnBlocks_ASM(PC pc)
443: {
444:   PC_ASM             *osm = (PC_ASM*)pc->data;
445:   PetscErrorCode     ierr;
446:   PetscInt           i;
447:   KSPConvergedReason reason;

450:   for (i=0; i<osm->n_local_true; i++) {
451:     KSPSetUp(osm->ksp[i]);
452:     KSPGetConvergedReason(osm->ksp[i],&reason);
453:     if (reason == KSP_DIVERGED_PCSETUP_FAILED) {
454:       pc->failedreason = PC_SUBPC_ERROR;
455:     }
456:   }
457:   return(0);
458: }

460: static PetscErrorCode PCApply_ASM(PC pc,Vec x,Vec y)
461: {
462:   PC_ASM         *osm = (PC_ASM*)pc->data;
464:   PetscInt       i,n_local_true = osm->n_local_true;
465:   ScatterMode    forward = SCATTER_FORWARD,reverse = SCATTER_REVERSE;

468:   /*
469:      Support for limiting the restriction or interpolation to only local
470:      subdomain values (leaving the other values 0).
471:   */
472:   if (!(osm->type & PC_ASM_RESTRICT)) {
473:     forward = SCATTER_FORWARD_LOCAL;
474:     /* have to zero the work RHS since scatter may leave some slots empty */
475:     VecSet(osm->lx, 0.0);
476:   }
477:   if (!(osm->type & PC_ASM_INTERPOLATE)) {
478:     reverse = SCATTER_REVERSE_LOCAL;
479:   }
480: 
481:   if(osm->loctype == PC_COMPOSITE_MULTIPLICATIVE || osm->loctype == PC_COMPOSITE_ADDITIVE){
482:     /* zero the global and the local solutions */
483:     VecZeroEntries(y);
484:     VecSet(osm->ly, 0.0);
485: 
486:     /* Copy the global RHS to local RHS including the ghost nodes */
487:     VecScatterBegin(osm->restriction, x, osm->lx, INSERT_VALUES, forward);
488:     VecScatterEnd(osm->restriction, x, osm->lx, INSERT_VALUES, forward);
489: 
490:     /* Restrict local RHS to the overlapping 0-block RHS */
491:     VecScatterBegin(osm->lrestriction[0], osm->lx, osm->x[0], INSERT_VALUES, forward);
492:     VecScatterEnd(osm->lrestriction[0], osm->lx, osm->x[0],  INSERT_VALUES, forward);
493: 
494:     /* do the local solves */
495:     for (i = 0; i < n_local_true; ++i) {
496: 
497:       /* solve the overlapping i-block */
498:       KSPSolve(osm->ksp[i], osm->x[i], osm->y[i]);

500:       if (osm->lprolongation) { /* interpolate the non-overalapping i-block solution to the local solution (only for restrictive additive) */
501:          VecScatterBegin(osm->lprolongation[i], osm->y[i], osm->ly, ADD_VALUES, forward);
502:          VecScatterEnd(osm->lprolongation[i], osm->y[i], osm->ly, ADD_VALUES, forward);
503:       }
504:       else{ /* interpolate the overalapping i-block solution to the local solution */
505:         VecScatterBegin(osm->lrestriction[i], osm->y[i], osm->ly, ADD_VALUES, reverse);
506:         VecScatterEnd(osm->lrestriction[i], osm->y[i], osm->ly, ADD_VALUES, reverse);
507:       }
508: 
509:       if (i < n_local_true-1) {
510:         /* Restrict local RHS to the overlapping (i+1)-block RHS */
511:         VecScatterBegin(osm->lrestriction[i+1], osm->lx, osm->x[i+1], INSERT_VALUES, forward);
512:         VecScatterEnd(osm->lrestriction[i+1], osm->lx, osm->x[i+1], INSERT_VALUES, forward);
513: 
514:         if ( osm->loctype == PC_COMPOSITE_MULTIPLICATIVE){
515:           /* udpdate the overlapping (i+1)-block RHS using the current local solution */
516:           MatMult(osm->lmats[i+1], osm->ly, osm->y[i+1]);
517:           VecAXPBY(osm->x[i+1],-1.,1., osm->y[i+1]);
518:         }
519:       }
520:     }
521:     /* Add the local solution to the global solution including the ghost nodes */
522:     VecScatterBegin(osm->restriction, osm->ly, y,  ADD_VALUES, reverse);
523:     VecScatterEnd(osm->restriction,  osm->ly, y, ADD_VALUES, reverse);
524:   }else{
525:     SETERRQ1(PetscObjectComm((PetscObject) pc), PETSC_ERR_ARG_WRONG, "Invalid local composition type: %s", PCCompositeTypes[osm->loctype]);
526:   }
527:   return(0);
528: }

530: static PetscErrorCode PCApplyTranspose_ASM(PC pc,Vec x,Vec y)
531: {
532:   PC_ASM         *osm = (PC_ASM*)pc->data;
534:   PetscInt       i,n_local_true = osm->n_local_true;
535:   ScatterMode    forward = SCATTER_FORWARD,reverse = SCATTER_REVERSE;

538:   /*
539:      Support for limiting the restriction or interpolation to only local
540:      subdomain values (leaving the other values 0).

542:      Note: these are reversed from the PCApply_ASM() because we are applying the
543:      transpose of the three terms
544:   */
545: 
546:   if (!(osm->type & PC_ASM_INTERPOLATE)) {
547:     forward = SCATTER_FORWARD_LOCAL;
548:     /* have to zero the work RHS since scatter may leave some slots empty */
549:     VecSet(osm->lx, 0.0);
550:   }
551:   if (!(osm->type & PC_ASM_RESTRICT)) reverse = SCATTER_REVERSE_LOCAL;

553:   /* zero the global and the local solutions */
554:   VecZeroEntries(y);
555:   VecSet(osm->ly, 0.0);
556: 
557:   /* Copy the global RHS to local RHS including the ghost nodes */
558:   VecScatterBegin(osm->restriction, x, osm->lx, INSERT_VALUES, forward);
559:   VecScatterEnd(osm->restriction, x, osm->lx, INSERT_VALUES, forward);
560: 
561:   /* Restrict local RHS to the overlapping 0-block RHS */
562:   VecScatterBegin(osm->lrestriction[0], osm->lx, osm->x[0], INSERT_VALUES, forward);
563:   VecScatterEnd(osm->lrestriction[0], osm->lx, osm->x[0],  INSERT_VALUES, forward);
564: 
565:   /* do the local solves */
566:   for (i = 0; i < n_local_true; ++i) {
567: 
568:     /* solve the overlapping i-block */
569:     KSPSolve(osm->ksp[i], osm->x[i], osm->y[i]);

571:     if (osm->lprolongation) { /* interpolate the non-overalapping i-block solution to the local solution */
572:      VecScatterBegin(osm->lprolongation[i], osm->y[i], osm->ly, ADD_VALUES, forward);
573:      VecScatterEnd(osm->lprolongation[i], osm->y[i], osm->ly, ADD_VALUES, forward);
574:     }
575:     else{ /* interpolate the overalapping i-block solution to the local solution */
576:       VecScatterBegin(osm->lrestriction[i], osm->y[i], osm->ly, ADD_VALUES, reverse);
577:       VecScatterEnd(osm->lrestriction[i], osm->y[i], osm->ly, ADD_VALUES, reverse);
578:     }
579: 
580:     if (i < n_local_true-1) {
581:       /* Restrict local RHS to the overlapping (i+1)-block RHS */
582:       VecScatterBegin(osm->lrestriction[i+1], osm->lx, osm->x[i+1], INSERT_VALUES, forward);
583:       VecScatterEnd(osm->lrestriction[i+1], osm->lx, osm->x[i+1], INSERT_VALUES, forward);
584:     }
585:   }
586:   /* Add the local solution to the global solution including the ghost nodes */
587:   VecScatterBegin(osm->restriction, osm->ly, y,  ADD_VALUES, reverse);
588:   VecScatterEnd(osm->restriction,  osm->ly, y, ADD_VALUES, reverse);
589: 
590:   return(0);
591: 
592: }

594: static PetscErrorCode PCReset_ASM(PC pc)
595: {
596:   PC_ASM         *osm = (PC_ASM*)pc->data;
598:   PetscInt       i;

601:   if (osm->ksp) {
602:     for (i=0; i<osm->n_local_true; i++) {
603:       KSPReset(osm->ksp[i]);
604:     }
605:   }
606:   if (osm->pmat) {
607:     if (osm->n_local_true > 0) {
608:       MatDestroySubMatrices(osm->n_local_true,&osm->pmat);
609:     }
610:   }
611:   if (osm->lrestriction) {
612:     VecScatterDestroy(&osm->restriction);
613:     for (i=0; i<osm->n_local_true; i++) {
614:       VecScatterDestroy(&osm->lrestriction[i]);
615:       if (osm->lprolongation) {VecScatterDestroy(&osm->lprolongation[i]);}
616:       VecDestroy(&osm->x[i]);
617:       VecDestroy(&osm->y[i]);
618:     }
619:     PetscFree(osm->lrestriction);
620:     if (osm->lprolongation) {PetscFree(osm->lprolongation);}
621:     PetscFree(osm->x);
622:     PetscFree(osm->y);
623: 
624:   }
625:   PCASMDestroySubdomains(osm->n_local_true,osm->is,osm->is_local);
626:   ISDestroy(&osm->lis);
627:   VecDestroy(&osm->lx);
628:   VecDestroy(&osm->ly);
629:   if (osm->loctype == PC_COMPOSITE_MULTIPLICATIVE) {
630:     MatDestroyMatrices(osm->n_local_true, &osm->lmats);
631:   }

633:   PetscFree(osm->sub_mat_type);

635:   osm->is       = 0;
636:   osm->is_local = 0;
637:   return(0);
638: }

640: static PetscErrorCode PCDestroy_ASM(PC pc)
641: {
642:   PC_ASM         *osm = (PC_ASM*)pc->data;
644:   PetscInt       i;

647:   PCReset_ASM(pc);
648:   if (osm->ksp) {
649:     for (i=0; i<osm->n_local_true; i++) {
650:       KSPDestroy(&osm->ksp[i]);
651:     }
652:     PetscFree(osm->ksp);
653:   }
654:   PetscFree(pc->data);
655:   return(0);
656: }

658: static PetscErrorCode PCSetFromOptions_ASM(PetscOptionItems *PetscOptionsObject,PC pc)
659: {
660:   PC_ASM         *osm = (PC_ASM*)pc->data;
662:   PetscInt       blocks,ovl;
663:   PetscBool      symset,flg;
664:   PCASMType      asmtype;
665:   PCCompositeType loctype;
666:   char           sub_mat_type[256];

669:   /* set the type to symmetric if matrix is symmetric */
670:   if (!osm->type_set && pc->pmat) {
671:     MatIsSymmetricKnown(pc->pmat,&symset,&flg);
672:     if (symset && flg) osm->type = PC_ASM_BASIC;
673:   }
674:   PetscOptionsHead(PetscOptionsObject,"Additive Schwarz options");
675:   PetscOptionsBool("-pc_asm_dm_subdomains","Use DMCreateDomainDecomposition() to define subdomains","PCASMSetDMSubdomains",osm->dm_subdomains,&osm->dm_subdomains,&flg);
676:   PetscOptionsInt("-pc_asm_blocks","Number of subdomains","PCASMSetTotalSubdomains",osm->n,&blocks,&flg);
677:   if (flg) {
678:     PCASMSetTotalSubdomains(pc,blocks,NULL,NULL);
679:     osm->dm_subdomains = PETSC_FALSE;
680:   }
681:   PetscOptionsInt("-pc_asm_overlap","Number of grid points overlap","PCASMSetOverlap",osm->overlap,&ovl,&flg);
682:   if (flg) {
683:     PCASMSetOverlap(pc,ovl);
684:     osm->dm_subdomains = PETSC_FALSE;
685:   }
686:   flg  = PETSC_FALSE;
687:   PetscOptionsEnum("-pc_asm_type","Type of restriction/extension","PCASMSetType",PCASMTypes,(PetscEnum)osm->type,(PetscEnum*)&asmtype,&flg);
688:   if (flg) {PCASMSetType(pc,asmtype); }
689:   flg  = PETSC_FALSE;
690:   PetscOptionsEnum("-pc_asm_local_type","Type of local solver composition","PCASMSetLocalType",PCCompositeTypes,(PetscEnum)osm->loctype,(PetscEnum*)&loctype,&flg);
691:   if (flg) {PCASMSetLocalType(pc,loctype); }
692:   PetscOptionsFList("-pc_asm_sub_mat_type","Subsolve Matrix Type","PCASMSetSubMatType",MatList,NULL,sub_mat_type,256,&flg);
693:   if(flg){
694:     PCASMSetSubMatType(pc,sub_mat_type);
695:   }
696:   PetscOptionsTail();
697:   return(0);
698: }

700: /*------------------------------------------------------------------------------------*/

702: static PetscErrorCode  PCASMSetLocalSubdomains_ASM(PC pc,PetscInt n,IS is[],IS is_local[])
703: {
704:   PC_ASM         *osm = (PC_ASM*)pc->data;
706:   PetscInt       i;

709:   if (n < 1) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Each process must have 1 or more blocks, n = %D",n);
710:   if (pc->setupcalled && (n != osm->n_local_true || is)) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONGSTATE,"PCASMSetLocalSubdomains() should be called before calling PCSetUp().");

712:   if (!pc->setupcalled) {
713:     if (is) {
714:       for (i=0; i<n; i++) {PetscObjectReference((PetscObject)is[i]);}
715:     }
716:     if (is_local) {
717:       for (i=0; i<n; i++) {PetscObjectReference((PetscObject)is_local[i]);}
718:     }
719:     PCASMDestroySubdomains(osm->n_local_true,osm->is,osm->is_local);

721:     osm->n_local_true = n;
722:     osm->is           = 0;
723:     osm->is_local     = 0;
724:     if (is) {
725:       PetscMalloc1(n,&osm->is);
726:       for (i=0; i<n; i++) osm->is[i] = is[i];
727:       /* Flag indicating that the user has set overlapping subdomains so PCASM should not increase their size. */
728:       osm->overlap = -1;
729:     }
730:     if (is_local) {
731:       PetscMalloc1(n,&osm->is_local);
732:       for (i=0; i<n; i++) osm->is_local[i] = is_local[i];
733:       if (!is) {
734:         PetscMalloc1(osm->n_local_true,&osm->is);
735:         for (i=0; i<osm->n_local_true; i++) {
736:           if (osm->overlap > 0) { /* With positive overlap, osm->is[i] will be modified */
737:             ISDuplicate(osm->is_local[i],&osm->is[i]);
738:             ISCopy(osm->is_local[i],osm->is[i]);
739:           } else {
740:             PetscObjectReference((PetscObject)osm->is_local[i]);
741:             osm->is[i] = osm->is_local[i];
742:           }
743:         }
744:       }
745:     }
746:   }
747:   return(0);
748: }

750: static PetscErrorCode  PCASMSetTotalSubdomains_ASM(PC pc,PetscInt N,IS *is,IS *is_local)
751: {
752:   PC_ASM         *osm = (PC_ASM*)pc->data;
754:   PetscMPIInt    rank,size;
755:   PetscInt       n;

758:   if (N < 1) SETERRQ1(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_OUTOFRANGE,"Number of total blocks must be > 0, N = %D",N);
759:   if (is || is_local) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Use PCASMSetLocalSubdomains() to set specific index sets\n\they cannot be set globally yet.");

761:   /*
762:      Split the subdomains equally among all processors
763:   */
764:   MPI_Comm_rank(PetscObjectComm((PetscObject)pc),&rank);
765:   MPI_Comm_size(PetscObjectComm((PetscObject)pc),&size);
766:   n    = N/size + ((N % size) > rank);
767:   if (!n) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Process %d must have at least one block: total processors %d total blocks %D",(int)rank,(int)size,N);
768:   if (pc->setupcalled && n != osm->n_local_true) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"PCASMSetTotalSubdomains() should be called before PCSetUp().");
769:   if (!pc->setupcalled) {
770:     PCASMDestroySubdomains(osm->n_local_true,osm->is,osm->is_local);

772:     osm->n_local_true = n;
773:     osm->is           = 0;
774:     osm->is_local     = 0;
775:   }
776:   return(0);
777: }

779: static PetscErrorCode  PCASMSetOverlap_ASM(PC pc,PetscInt ovl)
780: {
781:   PC_ASM *osm = (PC_ASM*)pc->data;

784:   if (ovl < 0) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_OUTOFRANGE,"Negative overlap value requested");
785:   if (pc->setupcalled && ovl != osm->overlap) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONGSTATE,"PCASMSetOverlap() should be called before PCSetUp().");
786:   if (!pc->setupcalled) osm->overlap = ovl;
787:   return(0);
788: }

790: static PetscErrorCode  PCASMSetType_ASM(PC pc,PCASMType type)
791: {
792:   PC_ASM *osm = (PC_ASM*)pc->data;

795:   osm->type     = type;
796:   osm->type_set = PETSC_TRUE;
797:   return(0);
798: }

800: static PetscErrorCode  PCASMGetType_ASM(PC pc,PCASMType *type)
801: {
802:   PC_ASM *osm = (PC_ASM*)pc->data;

805:   *type = osm->type;
806:   return(0);
807: }

809: static PetscErrorCode  PCASMSetLocalType_ASM(PC pc, PCCompositeType type)
810: {
811:   PC_ASM *osm = (PC_ASM *) pc->data;

814:   if (type != PC_COMPOSITE_ADDITIVE && type != PC_COMPOSITE_MULTIPLICATIVE) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Only supports additive or multiplicative as the local type");
815:   osm->loctype = type;
816:   return(0);
817: }

819: static PetscErrorCode  PCASMGetLocalType_ASM(PC pc, PCCompositeType *type)
820: {
821:   PC_ASM *osm = (PC_ASM *) pc->data;

824:   *type = osm->loctype;
825:   return(0);
826: }

828: static PetscErrorCode  PCASMSetSortIndices_ASM(PC pc,PetscBool  doSort)
829: {
830:   PC_ASM *osm = (PC_ASM*)pc->data;

833:   osm->sort_indices = doSort;
834:   return(0);
835: }

837: static PetscErrorCode  PCASMGetSubKSP_ASM(PC pc,PetscInt *n_local,PetscInt *first_local,KSP **ksp)
838: {
839:   PC_ASM         *osm = (PC_ASM*)pc->data;

843:   if (osm->n_local_true < 1) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ORDER,"Need to call PCSetUP() on PC (or KSPSetUp() on the outer KSP object) before calling here");

845:   if (n_local) *n_local = osm->n_local_true;
846:   if (first_local) {
847:     MPI_Scan(&osm->n_local_true,first_local,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)pc));
848:     *first_local -= osm->n_local_true;
849:   }
850:   if (ksp) {
851:     /* Assume that local solves are now different; not necessarily
852:        true though!  This flag is used only for PCView_ASM() */
853:     *ksp                   = osm->ksp;
854:     osm->same_local_solves = PETSC_FALSE;
855:   }
856:   return(0);
857: }

859: static PetscErrorCode  PCASMGetSubMatType_ASM(PC pc,MatType *sub_mat_type)
860: {
861:   PC_ASM         *osm = (PC_ASM*)pc->data;

866:   *sub_mat_type = osm->sub_mat_type;
867:   return(0);
868: }

870: static PetscErrorCode PCASMSetSubMatType_ASM(PC pc,MatType sub_mat_type)
871: {
872:   PetscErrorCode    ierr;
873:   PC_ASM            *osm = (PC_ASM*)pc->data;

877:   PetscFree(osm->sub_mat_type);
878:   PetscStrallocpy(sub_mat_type,(char**)&osm->sub_mat_type);
879:   return(0);
880: }

882: /*@C
883:     PCASMSetLocalSubdomains - Sets the local subdomains (for this processor only) for the additive Schwarz preconditioner.

885:     Collective on PC

887:     Input Parameters:
888: +   pc - the preconditioner context
889: .   n - the number of subdomains for this processor (default value = 1)
890: .   is - the index set that defines the subdomains for this processor
891:          (or NULL for PETSc to determine subdomains)
892: -   is_local - the index sets that define the local part of the subdomains for this processor, not used unless PCASMType is PC_ASM_RESTRICT
893:          (or NULL to not provide these)

895:     Notes:
896:     The IS numbering is in the parallel, global numbering of the vector for both is and is_local

898:     By default the ASM preconditioner uses 1 block per processor.

900:     Use PCASMSetTotalSubdomains() to set the subdomains for all processors.

902:     If is_local is provided and PCASMType is PC_ASM_RESTRICT then the solution only over the is_local region is interpolated
903:     back to form the global solution (this is the standard restricted additive Schwarz method)

905:     If the is_local is provided and PCASMType is PC_ASM_INTERPOLATE or PC_ASM_NONE then an error is generated since there is
906:     no code to handle that case.

908:     Level: advanced

910: .keywords: PC, ASM, set, local, subdomains, additive Schwarz

912: .seealso: PCASMSetTotalSubdomains(), PCASMSetOverlap(), PCASMGetSubKSP(),
913:           PCASMCreateSubdomains2D(), PCASMGetLocalSubdomains(), PCASMType, PCASMSetType()
914: @*/
915: PetscErrorCode  PCASMSetLocalSubdomains(PC pc,PetscInt n,IS is[],IS is_local[])
916: {

921:   PetscTryMethod(pc,"PCASMSetLocalSubdomains_C",(PC,PetscInt,IS[],IS[]),(pc,n,is,is_local));
922:   return(0);
923: }

925: /*@C
926:     PCASMSetTotalSubdomains - Sets the subdomains for all processors for the
927:     additive Schwarz preconditioner.  Either all or no processors in the
928:     PC communicator must call this routine, with the same index sets.

930:     Collective on PC

932:     Input Parameters:
933: +   pc - the preconditioner context
934: .   N  - the number of subdomains for all processors
935: .   is - the index sets that define the subdomains for all processors
936:          (or NULL to ask PETSc to determine the subdomains)
937: -   is_local - the index sets that define the local part of the subdomains for this processor
938:          (or NULL to not provide this information)

940:     Options Database Key:
941:     To set the total number of subdomain blocks rather than specify the
942:     index sets, use the option
943: .    -pc_asm_blocks <blks> - Sets total blocks

945:     Notes:
946:     Currently you cannot use this to set the actual subdomains with the argument is or is_local.

948:     By default the ASM preconditioner uses 1 block per processor.

950:     These index sets cannot be destroyed until after completion of the
951:     linear solves for which the ASM preconditioner is being used.

953:     Use PCASMSetLocalSubdomains() to set local subdomains.

955:     The IS numbering is in the parallel, global numbering of the vector for both is and is_local

957:     Level: advanced

959: .keywords: PC, ASM, set, total, global, subdomains, additive Schwarz

961: .seealso: PCASMSetLocalSubdomains(), PCASMSetOverlap(), PCASMGetSubKSP(),
962:           PCASMCreateSubdomains2D()
963: @*/
964: PetscErrorCode  PCASMSetTotalSubdomains(PC pc,PetscInt N,IS is[],IS is_local[])
965: {

970:   PetscTryMethod(pc,"PCASMSetTotalSubdomains_C",(PC,PetscInt,IS[],IS[]),(pc,N,is,is_local));
971:   return(0);
972: }

974: /*@
975:     PCASMSetOverlap - Sets the overlap between a pair of subdomains for the
976:     additive Schwarz preconditioner.  Either all or no processors in the
977:     PC communicator must call this routine.

979:     Logically Collective on PC

981:     Input Parameters:
982: +   pc  - the preconditioner context
983: -   ovl - the amount of overlap between subdomains (ovl >= 0, default value = 1)

985:     Options Database Key:
986: .   -pc_asm_overlap <ovl> - Sets overlap

988:     Notes:
989:     By default the ASM preconditioner uses 1 block per processor.  To use
990:     multiple blocks per perocessor, see PCASMSetTotalSubdomains() and
991:     PCASMSetLocalSubdomains() (and the option -pc_asm_blocks <blks>).

993:     The overlap defaults to 1, so if one desires that no additional
994:     overlap be computed beyond what may have been set with a call to
995:     PCASMSetTotalSubdomains() or PCASMSetLocalSubdomains(), then ovl
996:     must be set to be 0.  In particular, if one does not explicitly set
997:     the subdomains an application code, then all overlap would be computed
998:     internally by PETSc, and using an overlap of 0 would result in an ASM
999:     variant that is equivalent to the block Jacobi preconditioner.

1001:     The default algorithm used by PETSc to increase overlap is fast, but not scalable,
1002:     use the option -mat_increase_overlap_scalable when the problem and number of processes is large.

1004:     Note that one can define initial index sets with any overlap via
1005:     PCASMSetLocalSubdomains(); the routine
1006:     PCASMSetOverlap() merely allows PETSc to extend that overlap further
1007:     if desired.

1009:     Level: intermediate

1011: .keywords: PC, ASM, set, overlap

1013: .seealso: PCASMSetTotalSubdomains(), PCASMSetLocalSubdomains(), PCASMGetSubKSP(),
1014:           PCASMCreateSubdomains2D(), PCASMGetLocalSubdomains(), MatIncreaseOverlap()
1015: @*/
1016: PetscErrorCode  PCASMSetOverlap(PC pc,PetscInt ovl)
1017: {

1023:   PetscTryMethod(pc,"PCASMSetOverlap_C",(PC,PetscInt),(pc,ovl));
1024:   return(0);
1025: }

1027: /*@
1028:     PCASMSetType - Sets the type of restriction and interpolation used
1029:     for local problems in the additive Schwarz method.

1031:     Logically Collective on PC

1033:     Input Parameters:
1034: +   pc  - the preconditioner context
1035: -   type - variant of ASM, one of
1036: .vb
1037:       PC_ASM_BASIC       - full interpolation and restriction
1038:       PC_ASM_RESTRICT    - full restriction, local processor interpolation
1039:       PC_ASM_INTERPOLATE - full interpolation, local processor restriction
1040:       PC_ASM_NONE        - local processor restriction and interpolation
1041: .ve

1043:     Options Database Key:
1044: .   -pc_asm_type [basic,restrict,interpolate,none] - Sets ASM type

1046:     Notes: if the is_local arguments are passed to PCASMSetLocalSubdomains() then they are used when PC_ASM_RESTRICT has been selected
1047:     to limit the local processor interpolation

1049:     Level: intermediate

1051: .keywords: PC, ASM, set, type

1053: .seealso: PCASMSetTotalSubdomains(), PCASMSetTotalSubdomains(), PCASMGetSubKSP(),
1054:           PCASMCreateSubdomains2D(), PCASMType, PCASMSetLocalType(), PCASMGetLocalType()
1055: @*/
1056: PetscErrorCode  PCASMSetType(PC pc,PCASMType type)
1057: {

1063:   PetscTryMethod(pc,"PCASMSetType_C",(PC,PCASMType),(pc,type));
1064:   return(0);
1065: }

1067: /*@
1068:     PCASMGetType - Gets the type of restriction and interpolation used
1069:     for local problems in the additive Schwarz method.

1071:     Logically Collective on PC

1073:     Input Parameter:
1074: .   pc  - the preconditioner context

1076:     Output Parameter:
1077: .   type - variant of ASM, one of

1079: .vb
1080:       PC_ASM_BASIC       - full interpolation and restriction
1081:       PC_ASM_RESTRICT    - full restriction, local processor interpolation
1082:       PC_ASM_INTERPOLATE - full interpolation, local processor restriction
1083:       PC_ASM_NONE        - local processor restriction and interpolation
1084: .ve

1086:     Options Database Key:
1087: .   -pc_asm_type [basic,restrict,interpolate,none] - Sets ASM type

1089:     Level: intermediate

1091: .keywords: PC, ASM, set, type

1093: .seealso: PCASMSetTotalSubdomains(), PCASMSetTotalSubdomains(), PCASMGetSubKSP(),
1094:           PCASMCreateSubdomains2D(), PCASMType, PCASMSetType(), PCASMSetLocalType(), PCASMGetLocalType()
1095: @*/
1096: PetscErrorCode  PCASMGetType(PC pc,PCASMType *type)
1097: {

1102:   PetscUseMethod(pc,"PCASMGetType_C",(PC,PCASMType*),(pc,type));
1103:   return(0);
1104: }

1106: /*@
1107:   PCASMSetLocalType - Sets the type of composition used for local problems in the additive Schwarz method.

1109:   Logically Collective on PC

1111:   Input Parameters:
1112: + pc  - the preconditioner context
1113: - type - type of composition, one of
1114: .vb
1115:   PC_COMPOSITE_ADDITIVE       - local additive combination
1116:   PC_COMPOSITE_MULTIPLICATIVE - local multiplicative combination
1117: .ve

1119:   Options Database Key:
1120: . -pc_asm_local_type [additive,multiplicative] - Sets local solver composition type

1122:   Level: intermediate

1124: .seealso: PCASMSetType(), PCASMGetType(), PCASMGetLocalType(), PCASM, PCASMType, PCASMSetType(), PCASMGetType(), PCCompositeType
1125: @*/
1126: PetscErrorCode PCASMSetLocalType(PC pc, PCCompositeType type)
1127: {

1133:   PetscTryMethod(pc, "PCASMSetLocalType_C", (PC, PCCompositeType), (pc, type));
1134:   return(0);
1135: }

1137: /*@
1138:   PCASMGetLocalType - Gets the type of composition used for local problems in the additive Schwarz method.

1140:   Logically Collective on PC

1142:   Input Parameter:
1143: . pc  - the preconditioner context

1145:   Output Parameter:
1146: . type - type of composition, one of
1147: .vb
1148:   PC_COMPOSITE_ADDITIVE       - local additive combination
1149:   PC_COMPOSITE_MULTIPLICATIVE - local multiplicative combination
1150: .ve

1152:   Options Database Key:
1153: . -pc_asm_local_type [additive,multiplicative] - Sets local solver composition type

1155:   Level: intermediate

1157: .seealso: PCASMSetType(), PCASMGetType(), PCASMSetLocalType(), PCASMCreate(), PCASMType, PCASMSetType(), PCASMGetType(), PCCompositeType
1158: @*/
1159: PetscErrorCode PCASMGetLocalType(PC pc, PCCompositeType *type)
1160: {

1166:   PetscUseMethod(pc, "PCASMGetLocalType_C", (PC, PCCompositeType *), (pc, type));
1167:   return(0);
1168: }

1170: /*@
1171:     PCASMSetSortIndices - Determines whether subdomain indices are sorted.

1173:     Logically Collective on PC

1175:     Input Parameters:
1176: +   pc  - the preconditioner context
1177: -   doSort - sort the subdomain indices

1179:     Level: intermediate

1181: .keywords: PC, ASM, set, type

1183: .seealso: PCASMSetLocalSubdomains(), PCASMSetTotalSubdomains(), PCASMGetSubKSP(),
1184:           PCASMCreateSubdomains2D()
1185: @*/
1186: PetscErrorCode  PCASMSetSortIndices(PC pc,PetscBool doSort)
1187: {

1193:   PetscTryMethod(pc,"PCASMSetSortIndices_C",(PC,PetscBool),(pc,doSort));
1194:   return(0);
1195: }

1197: /*@C
1198:    PCASMGetSubKSP - Gets the local KSP contexts for all blocks on
1199:    this processor.

1201:    Collective on PC iff first_local is requested

1203:    Input Parameter:
1204: .  pc - the preconditioner context

1206:    Output Parameters:
1207: +  n_local - the number of blocks on this processor or NULL
1208: .  first_local - the global number of the first block on this processor or NULL,
1209:                  all processors must request or all must pass NULL
1210: -  ksp - the array of KSP contexts

1212:    Note:
1213:    After PCASMGetSubKSP() the array of KSPes is not to be freed.

1215:    You must call KSPSetUp() before calling PCASMGetSubKSP().

1217:    Fortran note:
1218:    The output argument 'ksp' must be an array of sufficient length or PETSC_NULL_KSP. The latter can be used to learn the necessary length.

1220:    Level: advanced

1222: .keywords: PC, ASM, additive Schwarz, get, sub, KSP, context

1224: .seealso: PCASMSetTotalSubdomains(), PCASMSetTotalSubdomains(), PCASMSetOverlap(),
1225:           PCASMCreateSubdomains2D(),
1226: @*/
1227: PetscErrorCode  PCASMGetSubKSP(PC pc,PetscInt *n_local,PetscInt *first_local,KSP *ksp[])
1228: {

1233:   PetscUseMethod(pc,"PCASMGetSubKSP_C",(PC,PetscInt*,PetscInt*,KSP **),(pc,n_local,first_local,ksp));
1234:   return(0);
1235: }

1237: /* -------------------------------------------------------------------------------------*/
1238: /*MC
1239:    PCASM - Use the (restricted) additive Schwarz method, each block is (approximately) solved with
1240:            its own KSP object.

1242:    Options Database Keys:
1243: +  -pc_asm_blocks <blks> - Sets total blocks
1244: .  -pc_asm_overlap <ovl> - Sets overlap
1245: .  -pc_asm_type [basic,restrict,interpolate,none] - Sets ASM type, default is restrict
1246: -  -pc_asm_local_type [additive, multiplicative] - Sets ASM type, default is additive

1248:      IMPORTANT: If you run with, for example, 3 blocks on 1 processor or 3 blocks on 3 processors you
1249:       will get a different convergence rate due to the default option of -pc_asm_type restrict. Use
1250:       -pc_asm_type basic to use the standard ASM.

1252:    Notes: Each processor can have one or more blocks, but a block cannot be shared by more
1253:      than one processor. Use PCGASM for subdomains shared by multiple processes. Defaults to one block per processor.

1255:      To set options on the solvers for each block append -sub_ to all the KSP, and PC
1256:         options database keys. For example, -sub_pc_type ilu -sub_pc_factor_levels 1 -sub_ksp_type preonly

1258:      To set the options on the solvers separate for each block call PCASMGetSubKSP()
1259:          and set the options directly on the resulting KSP object (you can access its PC
1260:          with KSPGetPC())

1262:    Level: beginner

1264:    Concepts: additive Schwarz method

1266:     References:
1267: +   1. - M Dryja, OB Widlund, An additive variant of the Schwarz alternating method for the case of many subregions
1268:      Courant Institute, New York University Technical report
1269: -   1. - Barry Smith, Petter Bjorstad, and William Gropp, Domain Decompositions: Parallel Multilevel Methods for Elliptic Partial Differential Equations,
1270:     Cambridge University Press.

1272: .seealso:  PCCreate(), PCSetType(), PCType (for list of available types), PC,
1273:            PCBJACOBI, PCASMGetSubKSP(), PCASMSetLocalSubdomains(), PCASMType, PCASMGetType(), PCASMSetLocalType(), PCASMGetLocalType()
1274:            PCASMSetTotalSubdomains(), PCSetModifySubmatrices(), PCASMSetOverlap(), PCASMSetType(), PCCompositeType

1276: M*/

1278: PETSC_EXTERN PetscErrorCode PCCreate_ASM(PC pc)
1279: {
1281:   PC_ASM         *osm;

1284:   PetscNewLog(pc,&osm);

1286:   osm->n                 = PETSC_DECIDE;
1287:   osm->n_local           = 0;
1288:   osm->n_local_true      = PETSC_DECIDE;
1289:   osm->overlap           = 1;
1290:   osm->ksp               = 0;
1291:   osm->restriction       = 0;
1292:   osm->lprolongation     = 0;
1293:   osm->lrestriction      = 0;
1294:   osm->x                 = 0;
1295:   osm->y                 = 0;
1296:   osm->is                = 0;
1297:   osm->is_local          = 0;
1298:   osm->mat               = 0;
1299:   osm->pmat              = 0;
1300:   osm->type              = PC_ASM_RESTRICT;
1301:   osm->loctype           = PC_COMPOSITE_ADDITIVE;
1302:   osm->same_local_solves = PETSC_TRUE;
1303:   osm->sort_indices      = PETSC_TRUE;
1304:   osm->dm_subdomains     = PETSC_FALSE;
1305:   osm->sub_mat_type      = NULL;

1307:   pc->data                 = (void*)osm;
1308:   pc->ops->apply           = PCApply_ASM;
1309:   pc->ops->applytranspose  = PCApplyTranspose_ASM;
1310:   pc->ops->setup           = PCSetUp_ASM;
1311:   pc->ops->reset           = PCReset_ASM;
1312:   pc->ops->destroy         = PCDestroy_ASM;
1313:   pc->ops->setfromoptions  = PCSetFromOptions_ASM;
1314:   pc->ops->setuponblocks   = PCSetUpOnBlocks_ASM;
1315:   pc->ops->view            = PCView_ASM;
1316:   pc->ops->applyrichardson = 0;

1318:   PetscObjectComposeFunction((PetscObject)pc,"PCASMSetLocalSubdomains_C",PCASMSetLocalSubdomains_ASM);
1319:   PetscObjectComposeFunction((PetscObject)pc,"PCASMSetTotalSubdomains_C",PCASMSetTotalSubdomains_ASM);
1320:   PetscObjectComposeFunction((PetscObject)pc,"PCASMSetOverlap_C",PCASMSetOverlap_ASM);
1321:   PetscObjectComposeFunction((PetscObject)pc,"PCASMSetType_C",PCASMSetType_ASM);
1322:   PetscObjectComposeFunction((PetscObject)pc,"PCASMGetType_C",PCASMGetType_ASM);
1323:   PetscObjectComposeFunction((PetscObject)pc,"PCASMSetLocalType_C",PCASMSetLocalType_ASM);
1324:   PetscObjectComposeFunction((PetscObject)pc,"PCASMGetLocalType_C",PCASMGetLocalType_ASM);
1325:   PetscObjectComposeFunction((PetscObject)pc,"PCASMSetSortIndices_C",PCASMSetSortIndices_ASM);
1326:   PetscObjectComposeFunction((PetscObject)pc,"PCASMGetSubKSP_C",PCASMGetSubKSP_ASM);
1327:   PetscObjectComposeFunction((PetscObject)pc,"PCASMGetSubMatType_C",PCASMGetSubMatType_ASM);
1328:   PetscObjectComposeFunction((PetscObject)pc,"PCASMSetSubMatType_C",PCASMSetSubMatType_ASM);
1329:   return(0);
1330: }

1332: /*@C
1333:    PCASMCreateSubdomains - Creates the index sets for the overlapping Schwarz
1334:    preconditioner for a any problem on a general grid.

1336:    Collective

1338:    Input Parameters:
1339: +  A - The global matrix operator
1340: -  n - the number of local blocks

1342:    Output Parameters:
1343: .  outis - the array of index sets defining the subdomains

1345:    Level: advanced

1347:    Note: this generates nonoverlapping subdomains; the PCASM will generate the overlap
1348:     from these if you use PCASMSetLocalSubdomains()

1350:     In the Fortran version you must provide the array outis[] already allocated of length n.

1352: .keywords: PC, ASM, additive Schwarz, create, subdomains, unstructured grid

1354: .seealso: PCASMSetLocalSubdomains(), PCASMDestroySubdomains()
1355: @*/
1356: PetscErrorCode  PCASMCreateSubdomains(Mat A, PetscInt n, IS* outis[])
1357: {
1358:   MatPartitioning mpart;
1359:   const char      *prefix;
1360:   PetscInt        i,j,rstart,rend,bs;
1361:   PetscBool       hasop, isbaij = PETSC_FALSE,foundpart = PETSC_FALSE;
1362:   Mat             Ad     = NULL, adj;
1363:   IS              ispart,isnumb,*is;
1364:   PetscErrorCode  ierr;

1369:   if (n < 1) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"number of local blocks must be > 0, n = %D",n);

1371:   /* Get prefix, row distribution, and block size */
1372:   MatGetOptionsPrefix(A,&prefix);
1373:   MatGetOwnershipRange(A,&rstart,&rend);
1374:   MatGetBlockSize(A,&bs);
1375:   if (rstart/bs*bs != rstart || rend/bs*bs != rend) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"bad row distribution [%D,%D) for matrix block size %D",rstart,rend,bs);

1377:   /* Get diagonal block from matrix if possible */
1378:   MatHasOperation(A,MATOP_GET_DIAGONAL_BLOCK,&hasop);
1379:   if (hasop) {
1380:     MatGetDiagonalBlock(A,&Ad);
1381:   }
1382:   if (Ad) {
1383:     PetscObjectTypeCompare((PetscObject)Ad,MATSEQBAIJ,&isbaij);
1384:     if (!isbaij) {PetscObjectTypeCompare((PetscObject)Ad,MATSEQSBAIJ,&isbaij);}
1385:   }
1386:   if (Ad && n > 1) {
1387:     PetscBool match,done;
1388:     /* Try to setup a good matrix partitioning if available */
1389:     MatPartitioningCreate(PETSC_COMM_SELF,&mpart);
1390:     PetscObjectSetOptionsPrefix((PetscObject)mpart,prefix);
1391:     MatPartitioningSetFromOptions(mpart);
1392:     PetscObjectTypeCompare((PetscObject)mpart,MATPARTITIONINGCURRENT,&match);
1393:     if (!match) {
1394:       PetscObjectTypeCompare((PetscObject)mpart,MATPARTITIONINGSQUARE,&match);
1395:     }
1396:     if (!match) { /* assume a "good" partitioner is available */
1397:       PetscInt       na;
1398:       const PetscInt *ia,*ja;
1399:       MatGetRowIJ(Ad,0,PETSC_TRUE,isbaij,&na,&ia,&ja,&done);
1400:       if (done) {
1401:         /* Build adjacency matrix by hand. Unfortunately a call to
1402:            MatConvert(Ad,MATMPIADJ,MAT_INITIAL_MATRIX,&adj) will
1403:            remove the block-aij structure and we cannot expect
1404:            MatPartitioning to split vertices as we need */
1405:         PetscInt       i,j,len,nnz,cnt,*iia=0,*jja=0;
1406:         const PetscInt *row;
1407:         nnz = 0;
1408:         for (i=0; i<na; i++) { /* count number of nonzeros */
1409:           len = ia[i+1] - ia[i];
1410:           row = ja + ia[i];
1411:           for (j=0; j<len; j++) {
1412:             if (row[j] == i) { /* don't count diagonal */
1413:               len--; break;
1414:             }
1415:           }
1416:           nnz += len;
1417:         }
1418:         PetscMalloc1(na+1,&iia);
1419:         PetscMalloc1(nnz,&jja);
1420:         nnz    = 0;
1421:         iia[0] = 0;
1422:         for (i=0; i<na; i++) { /* fill adjacency */
1423:           cnt = 0;
1424:           len = ia[i+1] - ia[i];
1425:           row = ja + ia[i];
1426:           for (j=0; j<len; j++) {
1427:             if (row[j] != i) { /* if not diagonal */
1428:               jja[nnz+cnt++] = row[j];
1429:             }
1430:           }
1431:           nnz     += cnt;
1432:           iia[i+1] = nnz;
1433:         }
1434:         /* Partitioning of the adjacency matrix */
1435:         MatCreateMPIAdj(PETSC_COMM_SELF,na,na,iia,jja,NULL,&adj);
1436:         MatPartitioningSetAdjacency(mpart,adj);
1437:         MatPartitioningSetNParts(mpart,n);
1438:         MatPartitioningApply(mpart,&ispart);
1439:         ISPartitioningToNumbering(ispart,&isnumb);
1440:         MatDestroy(&adj);
1441:         foundpart = PETSC_TRUE;
1442:       }
1443:       MatRestoreRowIJ(Ad,0,PETSC_TRUE,isbaij,&na,&ia,&ja,&done);
1444:     }
1445:     MatPartitioningDestroy(&mpart);
1446:   }

1448:   PetscMalloc1(n,&is);
1449:   *outis = is;

1451:   if (!foundpart) {

1453:     /* Partitioning by contiguous chunks of rows */

1455:     PetscInt mbs   = (rend-rstart)/bs;
1456:     PetscInt start = rstart;
1457:     for (i=0; i<n; i++) {
1458:       PetscInt count = (mbs/n + ((mbs % n) > i)) * bs;
1459:       ISCreateStride(PETSC_COMM_SELF,count,start,1,&is[i]);
1460:       start += count;
1461:     }

1463:   } else {

1465:     /* Partitioning by adjacency of diagonal block  */

1467:     const PetscInt *numbering;
1468:     PetscInt       *count,nidx,*indices,*newidx,start=0;
1469:     /* Get node count in each partition */
1470:     PetscMalloc1(n,&count);
1471:     ISPartitioningCount(ispart,n,count);
1472:     if (isbaij && bs > 1) { /* adjust for the block-aij case */
1473:       for (i=0; i<n; i++) count[i] *= bs;
1474:     }
1475:     /* Build indices from node numbering */
1476:     ISGetLocalSize(isnumb,&nidx);
1477:     PetscMalloc1(nidx,&indices);
1478:     for (i=0; i<nidx; i++) indices[i] = i; /* needs to be initialized */
1479:     ISGetIndices(isnumb,&numbering);
1480:     PetscSortIntWithPermutation(nidx,numbering,indices);
1481:     ISRestoreIndices(isnumb,&numbering);
1482:     if (isbaij && bs > 1) { /* adjust for the block-aij case */
1483:       PetscMalloc1(nidx*bs,&newidx);
1484:       for (i=0; i<nidx; i++) {
1485:         for (j=0; j<bs; j++) newidx[i*bs+j] = indices[i]*bs + j;
1486:       }
1487:       PetscFree(indices);
1488:       nidx   *= bs;
1489:       indices = newidx;
1490:     }
1491:     /* Shift to get global indices */
1492:     for (i=0; i<nidx; i++) indices[i] += rstart;

1494:     /* Build the index sets for each block */
1495:     for (i=0; i<n; i++) {
1496:       ISCreateGeneral(PETSC_COMM_SELF,count[i],&indices[start],PETSC_COPY_VALUES,&is[i]);
1497:       ISSort(is[i]);
1498:       start += count[i];
1499:     }

1501:     PetscFree(count);
1502:     PetscFree(indices);
1503:     ISDestroy(&isnumb);
1504:     ISDestroy(&ispart);

1506:   }
1507:   return(0);
1508: }

1510: /*@C
1511:    PCASMDestroySubdomains - Destroys the index sets created with
1512:    PCASMCreateSubdomains(). Should be called after setting subdomains
1513:    with PCASMSetLocalSubdomains().

1515:    Collective

1517:    Input Parameters:
1518: +  n - the number of index sets
1519: .  is - the array of index sets
1520: -  is_local - the array of local index sets, can be NULL

1522:    Level: advanced

1524: .keywords: PC, ASM, additive Schwarz, create, subdomains, unstructured grid

1526: .seealso: PCASMCreateSubdomains(), PCASMSetLocalSubdomains()
1527: @*/
1528: PetscErrorCode  PCASMDestroySubdomains(PetscInt n, IS is[], IS is_local[])
1529: {
1530:   PetscInt       i;

1534:   if (n <= 0) return(0);
1535:   if (is) {
1537:     for (i=0; i<n; i++) { ISDestroy(&is[i]); }
1538:     PetscFree(is);
1539:   }
1540:   if (is_local) {
1542:     for (i=0; i<n; i++) { ISDestroy(&is_local[i]); }
1543:     PetscFree(is_local);
1544:   }
1545:   return(0);
1546: }

1548: /*@
1549:    PCASMCreateSubdomains2D - Creates the index sets for the overlapping Schwarz
1550:    preconditioner for a two-dimensional problem on a regular grid.

1552:    Not Collective

1554:    Input Parameters:
1555: +  m, n - the number of mesh points in the x and y directions
1556: .  M, N - the number of subdomains in the x and y directions
1557: .  dof - degrees of freedom per node
1558: -  overlap - overlap in mesh lines

1560:    Output Parameters:
1561: +  Nsub - the number of subdomains created
1562: .  is - array of index sets defining overlapping (if overlap > 0) subdomains
1563: -  is_local - array of index sets defining non-overlapping subdomains

1565:    Note:
1566:    Presently PCAMSCreateSubdomains2d() is valid only for sequential
1567:    preconditioners.  More general related routines are
1568:    PCASMSetTotalSubdomains() and PCASMSetLocalSubdomains().

1570:    Level: advanced

1572: .keywords: PC, ASM, additive Schwarz, create, subdomains, 2D, regular grid

1574: .seealso: PCASMSetTotalSubdomains(), PCASMSetLocalSubdomains(), PCASMGetSubKSP(),
1575:           PCASMSetOverlap()
1576: @*/
1577: PetscErrorCode  PCASMCreateSubdomains2D(PetscInt m,PetscInt n,PetscInt M,PetscInt N,PetscInt dof,PetscInt overlap,PetscInt *Nsub,IS **is,IS **is_local)
1578: {
1579:   PetscInt       i,j,height,width,ystart,xstart,yleft,yright,xleft,xright,loc_outer;
1581:   PetscInt       nidx,*idx,loc,ii,jj,count;

1584:   if (dof != 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP," ");

1586:   *Nsub     = N*M;
1587:   PetscMalloc1(*Nsub,is);
1588:   PetscMalloc1(*Nsub,is_local);
1589:   ystart    = 0;
1590:   loc_outer = 0;
1591:   for (i=0; i<N; i++) {
1592:     height = n/N + ((n % N) > i); /* height of subdomain */
1593:     if (height < 2) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Too many N subdomains for mesh dimension n");
1594:     yleft  = ystart - overlap; if (yleft < 0) yleft = 0;
1595:     yright = ystart + height + overlap; if (yright > n) yright = n;
1596:     xstart = 0;
1597:     for (j=0; j<M; j++) {
1598:       width = m/M + ((m % M) > j); /* width of subdomain */
1599:       if (width < 2) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Too many M subdomains for mesh dimension m");
1600:       xleft  = xstart - overlap; if (xleft < 0) xleft = 0;
1601:       xright = xstart + width + overlap; if (xright > m) xright = m;
1602:       nidx   = (xright - xleft)*(yright - yleft);
1603:       PetscMalloc1(nidx,&idx);
1604:       loc    = 0;
1605:       for (ii=yleft; ii<yright; ii++) {
1606:         count = m*ii + xleft;
1607:         for (jj=xleft; jj<xright; jj++) idx[loc++] = count++;
1608:       }
1609:       ISCreateGeneral(PETSC_COMM_SELF,nidx,idx,PETSC_COPY_VALUES,(*is)+loc_outer);
1610:       if (overlap == 0) {
1611:         PetscObjectReference((PetscObject)(*is)[loc_outer]);

1613:         (*is_local)[loc_outer] = (*is)[loc_outer];
1614:       } else {
1615:         for (loc=0,ii=ystart; ii<ystart+height; ii++) {
1616:           for (jj=xstart; jj<xstart+width; jj++) {
1617:             idx[loc++] = m*ii + jj;
1618:           }
1619:         }
1620:         ISCreateGeneral(PETSC_COMM_SELF,loc,idx,PETSC_COPY_VALUES,*is_local+loc_outer);
1621:       }
1622:       PetscFree(idx);
1623:       xstart += width;
1624:       loc_outer++;
1625:     }
1626:     ystart += height;
1627:   }
1628:   for (i=0; i<*Nsub; i++) { ISSort((*is)[i]); }
1629:   return(0);
1630: }

1632: /*@C
1633:     PCASMGetLocalSubdomains - Gets the local subdomains (for this processor
1634:     only) for the additive Schwarz preconditioner.

1636:     Not Collective

1638:     Input Parameter:
1639: .   pc - the preconditioner context

1641:     Output Parameters:
1642: +   n - the number of subdomains for this processor (default value = 1)
1643: .   is - the index sets that define the subdomains for this processor
1644: -   is_local - the index sets that define the local part of the subdomains for this processor (can be NULL)


1647:     Notes:
1648:     The IS numbering is in the parallel, global numbering of the vector.

1650:     Level: advanced

1652: .keywords: PC, ASM, set, local, subdomains, additive Schwarz

1654: .seealso: PCASMSetTotalSubdomains(), PCASMSetOverlap(), PCASMGetSubKSP(),
1655:           PCASMCreateSubdomains2D(), PCASMSetLocalSubdomains(), PCASMGetLocalSubmatrices()
1656: @*/
1657: PetscErrorCode  PCASMGetLocalSubdomains(PC pc,PetscInt *n,IS *is[],IS *is_local[])
1658: {
1659:   PC_ASM         *osm = (PC_ASM*)pc->data;
1661:   PetscBool      match;

1667:   PetscObjectTypeCompare((PetscObject)pc,PCASM,&match);
1668:   if (!match) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONG,"PC is not a PCASM");
1669:   if (n) *n = osm->n_local_true;
1670:   if (is) *is = osm->is;
1671:   if (is_local) *is_local = osm->is_local;
1672:   return(0);
1673: }

1675: /*@C
1676:     PCASMGetLocalSubmatrices - Gets the local submatrices (for this processor
1677:     only) for the additive Schwarz preconditioner.

1679:     Not Collective

1681:     Input Parameter:
1682: .   pc - the preconditioner context

1684:     Output Parameters:
1685: +   n - the number of matrices for this processor (default value = 1)
1686: -   mat - the matrices

1688:     Level: advanced

1690:     Notes: Call after PCSetUp() (or KSPSetUp()) but before PCApply() (or KSPApply()) and before PCSetUpOnBlocks())

1692:            Usually one would use PCSetModifySubmatrices() to change the submatrices in building the preconditioner.

1694: .keywords: PC, ASM, set, local, subdomains, additive Schwarz, block Jacobi

1696: .seealso: PCASMSetTotalSubdomains(), PCASMSetOverlap(), PCASMGetSubKSP(),
1697:           PCASMCreateSubdomains2D(), PCASMSetLocalSubdomains(), PCASMGetLocalSubdomains(), PCSetModifySubmatrices()
1698: @*/
1699: PetscErrorCode  PCASMGetLocalSubmatrices(PC pc,PetscInt *n,Mat *mat[])
1700: {
1701:   PC_ASM         *osm;
1703:   PetscBool      match;

1709:   if (!pc->setupcalled) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONGSTATE,"Must call after KSPSetUP() or PCSetUp().");
1710:   PetscObjectTypeCompare((PetscObject)pc,PCASM,&match);
1711:   if (!match) {
1712:     if (n) *n = 0;
1713:     if (mat) *mat = NULL;
1714:   } else {
1715:     osm = (PC_ASM*)pc->data;
1716:     if (n) *n = osm->n_local_true;
1717:     if (mat) *mat = osm->pmat;
1718:   }
1719:   return(0);
1720: }

1722: /*@
1723:     PCASMSetDMSubdomains - Indicates whether to use DMCreateDomainDecomposition() to define the subdomains, whenever possible.

1725:     Logically Collective

1727:     Input Parameter:
1728: +   pc  - the preconditioner
1729: -   flg - boolean indicating whether to use subdomains defined by the DM

1731:     Options Database Key:
1732: .   -pc_asm_dm_subdomains

1734:     Level: intermediate

1736:     Notes:
1737:     PCASMSetTotalSubdomains() and PCASMSetOverlap() take precedence over PCASMSetDMSubdomains(),
1738:     so setting either of the first two effectively turns the latter off.

1740: .keywords: PC, ASM, DM, set, subdomains, additive Schwarz

1742: .seealso: PCASMGetDMSubdomains(), PCASMSetTotalSubdomains(), PCASMSetOverlap()
1743:           PCASMCreateSubdomains2D(), PCASMSetLocalSubdomains(), PCASMGetLocalSubdomains()
1744: @*/
1745: PetscErrorCode  PCASMSetDMSubdomains(PC pc,PetscBool flg)
1746: {
1747:   PC_ASM         *osm = (PC_ASM*)pc->data;
1749:   PetscBool      match;

1754:   if (pc->setupcalled) SETERRQ(((PetscObject)pc)->comm,PETSC_ERR_ARG_WRONGSTATE,"Not for a setup PC.");
1755:   PetscObjectTypeCompare((PetscObject)pc,PCASM,&match);
1756:   if (match) {
1757:     osm->dm_subdomains = flg;
1758:   }
1759:   return(0);
1760: }

1762: /*@
1763:     PCASMGetDMSubdomains - Returns flag indicating whether to use DMCreateDomainDecomposition() to define the subdomains, whenever possible.
1764:     Not Collective

1766:     Input Parameter:
1767: .   pc  - the preconditioner

1769:     Output Parameter:
1770: .   flg - boolean indicating whether to use subdomains defined by the DM

1772:     Level: intermediate

1774: .keywords: PC, ASM, DM, set, subdomains, additive Schwarz

1776: .seealso: PCASMSetDMSubdomains(), PCASMSetTotalSubdomains(), PCASMSetOverlap()
1777:           PCASMCreateSubdomains2D(), PCASMSetLocalSubdomains(), PCASMGetLocalSubdomains()
1778: @*/
1779: PetscErrorCode  PCASMGetDMSubdomains(PC pc,PetscBool* flg)
1780: {
1781:   PC_ASM         *osm = (PC_ASM*)pc->data;
1783:   PetscBool      match;

1788:   PetscObjectTypeCompare((PetscObject)pc,PCASM,&match);
1789:   if (match) {
1790:     if (flg) *flg = osm->dm_subdomains;
1791:   }
1792:   return(0);
1793: }

1795: /*@
1796:      PCASMGetSubMatType - Gets the matrix type used for ASM subsolves, as a string.

1798:    Not Collective

1800:    Input Parameter:
1801: .  pc - the PC

1803:    Output Parameter:
1804: .  -pc_asm_sub_mat_type - name of matrix type

1806:    Level: advanced

1808: .keywords: PC, PCASM, MatType, set

1810: .seealso: PCASMSetSubMatType(), PCASM, PCSetType(), VecSetType(), MatType, Mat
1811: @*/
1812: PetscErrorCode  PCASMGetSubMatType(PC pc,MatType *sub_mat_type){

1815:   PetscTryMethod(pc,"PCASMGetSubMatType_C",(PC,MatType*),(pc,sub_mat_type));
1816:   return(0);
1817: }

1819: /*@
1820:      PCASMSetSubMatType - Set the type of matrix used for ASM subsolves

1822:    Collective on Mat

1824:    Input Parameters:
1825: +  pc             - the PC object
1826: -  sub_mat_type   - matrix type

1828:    Options Database Key:
1829: .  -pc_asm_sub_mat_type  <sub_mat_type> - Sets the matrix type used for subsolves, for example, seqaijviennacl. If you specify a base name like aijviennacl, the corresponding sequential type is assumed.

1831:    Notes:
1832:    See "${PETSC_DIR}/include/petscmat.h" for available types

1834:   Level: advanced

1836: .keywords: PC, PCASM, MatType, set

1838: .seealso: PCASMGetSubMatType(), PCASM, PCSetType(), VecSetType(), MatType, Mat
1839: @*/
1840: PetscErrorCode PCASMSetSubMatType(PC pc,MatType sub_mat_type)
1841: {

1844:   PetscTryMethod(pc,"PCASMSetSubMatType_C",(PC,MatType),(pc,sub_mat_type));
1845:   return(0);
1846: }