Actual source code: gasm.c

petsc-3.6.1 2015-07-22
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  1: /*
  2:   This file defines an "generalized" additive Schwarz preconditioner for any Mat implementation.
  3:   In this version each processor may intersect multiple subdomains and any subdomain may
  4:   intersect multiple processors.  Intersections of subdomains with processors are called *local
  5:   subdomains*.

  7:        N    - total number of distinct global subdomains          (set explicitly in PCGASMSetTotalSubdomains() or implicitly PCGASMSetSubdomains() and then calculated in PCSetUp_GASM())
  8:        n    - actual number of local subdomains on this processor (set in PCGASMSetSubdomains() or calculated in PCGASMSetTotalSubdomains())
  9:        nmax - maximum number of local subdomains per processor    (calculated in PCSetUp_GASM())
 10: */
 11: #include <petsc/private/pcimpl.h>     /*I "petscpc.h" I*/
 12: #include <petscdm.h>

 14: typedef struct {
 15:   PetscInt    N,n,nmax;
 16:   PetscInt    overlap;                /* overlap requested by user */
 17:   PCGASMType  type;                   /* use reduced interpolation, restriction or both */
 18:   PetscBool   type_set;               /* if user set this value (so won't change it for symmetric problems) */
 19:   PetscBool   same_subdomain_solvers; /* flag indicating whether all local solvers are same */
 20:   PetscBool   sort_indices;           /* flag to sort subdomain indices */
 21:   PetscBool   user_subdomains;        /* whether the user set explicit subdomain index sets -- keep them on PCReset() */
 22:   PetscBool   dm_subdomains;          /* whether DM is allowed to define subdomains */
 23:   IS          *ois;                   /* index sets that define the outer (conceptually, overlapping) subdomains */
 24:   IS          *iis;                   /* index sets that define the inner (conceptually, nonoverlapping) subdomains */
 25:   KSP         *ksp;                /* linear solvers for each subdomain */
 26:   Mat         *pmat;               /* subdomain block matrices */
 27:   Vec         gx,gy;               /* Merged work vectors */
 28:   Vec         *x,*y;               /* Split work vectors; storage aliases pieces of storage of the above merged vectors. */
 29:   VecScatter  gorestriction;       /* merged restriction to disjoint union of outer subdomains */
 30:   VecScatter  girestriction;       /* merged restriction to disjoint union of inner subdomains */
 31: } PC_GASM;

 35: static PetscErrorCode  PCGASMComputeGlobalSubdomainNumbering_Private(PC pc,PetscInt **numbering,PetscInt **permutation)
 36: {
 37:   PC_GASM        *osm = (PC_GASM*)pc->data;
 38:   PetscInt       i;

 42:   /* Determine the number of globally-distinct subdomains and compute a global numbering for them. */
 43:   PetscMalloc2(osm->n,numbering,osm->n,permutation);
 44:   PetscObjectsListGetGlobalNumbering(PetscObjectComm((PetscObject)pc),osm->n,(PetscObject*)osm->iis,NULL,*numbering);
 45:   for (i = 0; i < osm->n; ++i) (*permutation)[i] = i;
 46:   PetscSortIntWithPermutation(osm->n,*numbering,*permutation);
 47:   return(0);
 48: }

 52: static PetscErrorCode  PCGASMSubdomainView_Private(PC pc, PetscInt i, PetscViewer viewer)
 53: {
 54:   PC_GASM        *osm = (PC_GASM*)pc->data;
 55:   PetscInt       j,nidx;
 56:   const PetscInt *idx;
 57:   PetscViewer    sviewer;
 58:   char           *cidx;

 62:   if (i < 0 || i > osm->n) SETERRQ2(PetscObjectComm((PetscObject)viewer), PETSC_ERR_ARG_WRONG, "Invalid subdomain %D: must nonnegative and less than %D", i, osm->n);
 63:   /* Inner subdomains. */
 64:   ISGetLocalSize(osm->iis[i], &nidx);
 65:   /*
 66:    No more than 15 characters per index plus a space.
 67:    PetscViewerStringSPrintf requires a string of size at least 2, so use (nidx+1) instead of nidx,
 68:    in case nidx == 0. That will take care of the space for the trailing '\0' as well.
 69:    For nidx == 0, the whole string 16 '\0'.
 70:    */
 71:   PetscMalloc1(16*(nidx+1)+1, &cidx);
 72:   PetscViewerStringOpen(PETSC_COMM_SELF, cidx, 16*(nidx+1)+1, &sviewer);
 73:   ISGetIndices(osm->iis[i], &idx);
 74:   for (j = 0; j < nidx; ++j) {
 75:     PetscViewerStringSPrintf(sviewer, "%D ", idx[j]);
 76:   }
 77:   ISRestoreIndices(osm->iis[i],&idx);
 78:   PetscViewerDestroy(&sviewer);
 79:   PetscViewerASCIIPrintf(viewer, "Inner subdomain:\n");
 80:   PetscViewerFlush(viewer);
 81:   PetscViewerASCIISynchronizedAllow(viewer,PETSC_TRUE);
 82:   PetscViewerASCIISynchronizedPrintf(viewer, "%s", cidx);
 83:   PetscViewerFlush(viewer);
 84:   PetscViewerASCIISynchronizedAllow(viewer,PETSC_FALSE);
 85:   PetscViewerASCIIPrintf(viewer, "\n");
 86:   PetscViewerFlush(viewer);
 87:   PetscFree(cidx);
 88:   /* Outer subdomains. */
 89:   ISGetLocalSize(osm->ois[i], &nidx);
 90:   /*
 91:    No more than 15 characters per index plus a space.
 92:    PetscViewerStringSPrintf requires a string of size at least 2, so use (nidx+1) instead of nidx,
 93:    in case nidx == 0. That will take care of the space for the trailing '\0' as well.
 94:    For nidx == 0, the whole string 16 '\0'.
 95:    */
 96:   PetscMalloc1(16*(nidx+1)+1, &cidx);
 97:   PetscViewerStringOpen(PETSC_COMM_SELF, cidx, 16*(nidx+1)+1, &sviewer);
 98:   ISGetIndices(osm->ois[i], &idx);
 99:   for (j = 0; j < nidx; ++j) {
100:     PetscViewerStringSPrintf(sviewer,"%D ", idx[j]);
101:   }
102:   PetscViewerDestroy(&sviewer);
103:   ISRestoreIndices(osm->ois[i],&idx);
104:   PetscViewerASCIIPrintf(viewer, "Outer subdomain:\n");
105:   PetscViewerFlush(viewer);
106:   PetscViewerASCIISynchronizedAllow(viewer,PETSC_TRUE);
107:   PetscViewerASCIISynchronizedPrintf(viewer, "%s", cidx);
108:   PetscViewerFlush(viewer);
109:   PetscViewerASCIISynchronizedAllow(viewer,PETSC_FALSE);
110:   PetscViewerASCIIPrintf(viewer, "\n");
111:   PetscViewerFlush(viewer);
112:   PetscFree(cidx);
113:   return(0);
114: }

118: static PetscErrorCode  PCGASMPrintSubdomains(PC pc)
119: {
120:   PC_GASM        *osm = (PC_GASM*)pc->data;
121:   const char     *prefix;
122:   char           fname[PETSC_MAX_PATH_LEN+1];
123:   PetscInt       l, d, count;
124:   PetscBool      doprint,found;
125:   PetscViewer    viewer, sviewer = NULL;
126:   PetscInt       *numbering,*permutation;/* global numbering of locally-supported subdomains and the permutation from the local ordering */

130:   PCGetOptionsPrefix(pc,&prefix);
131:   doprint  = PETSC_FALSE;
132:   PetscOptionsGetBool(prefix,"-pc_gasm_print_subdomains",&doprint,NULL);
133:   if (!doprint) return(0);
134:   PetscOptionsGetString(prefix,"-pc_gasm_print_subdomains",fname,PETSC_MAX_PATH_LEN,&found);
135:   if (!found) { PetscStrcpy(fname,"stdout"); };
136:   PetscViewerASCIIOpen(PetscObjectComm((PetscObject)pc),fname,&viewer);
137:   /*
138:    Make sure the viewer has a name. Otherwise this may cause a deadlock or other weird errors when creating a subcomm viewer:
139:    the subcomm viewer will attempt to inherit the viewer's name, which, if not set, will be constructed collectively on the comm.
140:   */
141:   PetscObjectName((PetscObject)viewer);
142:   l    = 0;
143:   PCGASMComputeGlobalSubdomainNumbering_Private(pc,&numbering,&permutation);
144:   for (count = 0; count < osm->N; ++count) {
145:     /* Now let subdomains go one at a time in the global numbering order and print their subdomain/solver info. */
146:     if (l<osm->n) {
147:       d = permutation[l]; /* d is the local number of the l-th smallest (in the global ordering) among the locally supported subdomains */
148:       if (numbering[d] == count) {
149:         PetscViewerGetSubcomm(viewer,((PetscObject)osm->ois[d])->comm, &sviewer);
150:         PCGASMSubdomainView_Private(pc,d,sviewer);
151:         PetscViewerRestoreSubcomm(viewer,((PetscObject)osm->ois[d])->comm, &sviewer);
152:         ++l;
153:       }
154:     }
155:     MPI_Barrier(PetscObjectComm((PetscObject)pc));
156:   }
157:   PetscFree2(numbering,permutation);
158:   PetscViewerDestroy(&viewer);
159:   return(0);
160: }


165: static PetscErrorCode PCView_GASM(PC pc,PetscViewer viewer)
166: {
167:   PC_GASM        *osm = (PC_GASM*)pc->data;
168:   const char     *prefix;
170:   PetscMPIInt    rank, size;
171:   PetscInt       bsz;
172:   PetscBool      iascii,view_subdomains=PETSC_FALSE;
173:   PetscViewer    sviewer;
174:   PetscInt       count, l;
175:   char           overlap[256]     = "user-defined overlap";
176:   char           gsubdomains[256] = "unknown total number of subdomains";
177:   char           msubdomains[256] = "unknown max number of local subdomains";
178:   PetscInt       *numbering,*permutation;/* global numbering of locally-supported subdomains and the permutation from the local ordering */

181:   MPI_Comm_size(PetscObjectComm((PetscObject)pc), &size);
182:   MPI_Comm_rank(PetscObjectComm((PetscObject)pc), &rank);

184:   if (osm->overlap >= 0) {
185:     PetscSNPrintf(overlap,sizeof(overlap),"requested amount of overlap = %D",osm->overlap);
186:   }
187:   if (osm->N != PETSC_DETERMINE) {
188:     PetscSNPrintf(gsubdomains, sizeof(gsubdomains), "total number of subdomains = %D",osm->N);
189:   }
190:   if (osm->nmax != PETSC_DETERMINE) {
191:     PetscSNPrintf(msubdomains,sizeof(msubdomains),"max number of local subdomains = %D",osm->nmax);
192:   }

194:   PCGetOptionsPrefix(pc,&prefix);
195:   PetscOptionsGetBool(prefix,"-pc_gasm_view_subdomains",&view_subdomains,NULL);

197:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
198:   if (iascii) {
199:     /*
200:      Make sure the viewer has a name. Otherwise this may cause a deadlock when creating a subcomm viewer:
201:      the subcomm viewer will attempt to inherit the viewer's name, which, if not set, will be constructed
202:      collectively on the comm.
203:      */
204:     PetscObjectName((PetscObject)viewer);
205:     PetscViewerASCIIPrintf(viewer,"Generalized additive Schwarz:\n");
206:     PetscViewerASCIIPrintf(viewer,"Restriction/interpolation type: %s\n",PCGASMTypes[osm->type]);
207:     PetscViewerASCIIPrintf(viewer,"%s\n",overlap);
208:     PetscViewerASCIIPrintf(viewer,"%s\n",gsubdomains);
209:     PetscViewerASCIIPrintf(viewer,"%s\n",msubdomains);
210:     PetscViewerASCIISynchronizedAllow(viewer,PETSC_TRUE);
211:     PetscViewerASCIISynchronizedPrintf(viewer,"[%d|%d] number of locally-supported subdomains = %D\n",rank,size,osm->n);
212:     PetscViewerFlush(viewer);
213:     PetscViewerASCIISynchronizedAllow(viewer,PETSC_FALSE);
214:     /* Cannot take advantage of osm->same_subdomain_solvers without a global numbering of subdomains. */
215:     PetscViewerASCIIPrintf(viewer,"Subdomain solver info is as follows:\n");
216:     PetscViewerASCIIPushTab(viewer);
217:     PetscViewerASCIIPrintf(viewer,"- - - - - - - - - - - - - - - - - -\n");
218:     /* Make sure that everybody waits for the banner to be printed. */
219:     MPI_Barrier(PetscObjectComm((PetscObject)viewer));
220:     /* Now let subdomains go one at a time in the global numbering order and print their subdomain/solver info. */
221:     PCGASMComputeGlobalSubdomainNumbering_Private(pc,&numbering,&permutation);
222:     l = 0;
223:     for (count = 0; count < osm->N; ++count) {
224:       PetscMPIInt srank, ssize;
225:       if (l<osm->n) {
226:         PetscInt d = permutation[l]; /* d is the local number of the l-th smallest (in the global ordering) among the locally supported subdomains */
227:         if (numbering[d] == count) {
228:           MPI_Comm_size(((PetscObject)osm->ois[d])->comm, &ssize);
229:           MPI_Comm_rank(((PetscObject)osm->ois[d])->comm, &srank);
230:           PetscViewerGetSubcomm(viewer,((PetscObject)osm->ois[d])->comm, &sviewer);
231:           ISGetLocalSize(osm->ois[d],&bsz);
232:           PetscViewerASCIISynchronizedAllow(sviewer,PETSC_TRUE);
233:           PetscViewerASCIISynchronizedPrintf(sviewer,"[%d|%d] (subcomm [%d|%d]) local subdomain number %D, local size = %D\n",rank,size,srank,ssize,d,bsz);
234:           PetscViewerFlush(sviewer);
235:           PetscViewerASCIISynchronizedAllow(sviewer,PETSC_FALSE);
236:           if (view_subdomains) {
237:             PCGASMSubdomainView_Private(pc,d,sviewer);
238:           }
239:           if (!pc->setupcalled) {
240:             PetscViewerASCIIPrintf(sviewer, "Solver not set up yet: PCSetUp() not yet called\n");
241:           } else {
242:             KSPView(osm->ksp[d],sviewer);
243:           }
244:           PetscViewerASCIIPrintf(sviewer,"- - - - - - - - - - - - - - - - - -\n");
245:           PetscViewerFlush(sviewer);
246:           PetscViewerRestoreSubcomm(viewer,((PetscObject)osm->ois[d])->comm, &sviewer);
247:           ++l;
248:         }
249:       }
250:       MPI_Barrier(PetscObjectComm((PetscObject)pc));
251:     }
252:     PetscFree2(numbering,permutation);
253:     PetscViewerASCIIPopTab(viewer);
254:   }
255:   return(0);
256: }

258: PETSC_INTERN PetscErrorCode  PCGASMCreateLocalSubdomains(Mat A, PetscInt nloc, IS *iis[]);

262: static PetscErrorCode PCSetUp_GASM(PC pc)
263: {
264:   PC_GASM        *osm = (PC_GASM*)pc->data;
266:   PetscBool      symset,flg;
267:   PetscInt       i;
268:   PetscMPIInt    rank, size;
269:   MatReuse       scall = MAT_REUSE_MATRIX;
270:   KSP            ksp;
271:   PC             subpc;
272:   const char     *prefix,*pprefix;
273:   Vec            x,y;
274:   PetscInt       oni;       /* Number of indices in the i-th local outer subdomain.               */
275:   const PetscInt *oidxi;    /* Indices from the i-th subdomain local outer subdomain.             */
276:   PetscInt       on;        /* Number of indices in the disjoint union of local outer subdomains. */
277:   PetscInt       *oidx;     /* Indices in the disjoint union of local outer subdomains. */
278:   IS             gois;      /* Disjoint union the global indices of outer subdomains.             */
279:   IS             goid;      /* Identity IS of the size of the disjoint union of outer subdomains. */
280:   PetscScalar    *gxarray, *gyarray;
281:   PetscInt       gofirst;   /* Start of locally-owned indices in the vectors -- osm->gx,osm->gy -- over the disjoint union of outer subdomains. */
282:   PetscInt       num_subdomains    = 0;
283:   DM             *subdomain_dm     = NULL;
284:   char           **subdomain_names = NULL;


288:   MPI_Comm_size(PetscObjectComm((PetscObject)pc),&size);
289:   MPI_Comm_rank(PetscObjectComm((PetscObject)pc),&rank);
290:   if (!pc->setupcalled) {

292:     if (!osm->type_set) {
293:       MatIsSymmetricKnown(pc->pmat,&symset,&flg);
294:       if (symset && flg) osm->type = PC_GASM_BASIC;
295:     }

297:     if (osm->n == PETSC_DETERMINE) {
298:       if (osm->N != PETSC_DETERMINE) {
299:         /* No local subdomains given, but the desired number of total subdomains is known, so construct them accordingly. */
300:         PCGASMCreateSubdomains(pc->pmat,osm->N,&osm->n,&osm->iis);
301:       } else if (osm->dm_subdomains && pc->dm) {
302:         /* try pc->dm next, if allowed */
303:         PetscInt  d;
304:         IS        *inner_subdomain_is, *outer_subdomain_is;
305:         DMCreateDomainDecomposition(pc->dm, &num_subdomains, &subdomain_names, &inner_subdomain_is, &outer_subdomain_is, &subdomain_dm);
306:         if (num_subdomains) {
307:           PCGASMSetSubdomains(pc, num_subdomains, inner_subdomain_is, outer_subdomain_is);
308:         }
309:         for (d = 0; d < num_subdomains; ++d) {
310:           if (inner_subdomain_is) {ISDestroy(&inner_subdomain_is[d]);}
311:           if (outer_subdomain_is) {ISDestroy(&outer_subdomain_is[d]);}
312:         }
313:         PetscFree(inner_subdomain_is);
314:         PetscFree(outer_subdomain_is);
315:       } else {
316:         /* still no subdomains; use one per processor */
317:         osm->nmax = osm->n = 1;
318:         MPI_Comm_size(PetscObjectComm((PetscObject)pc),&size);
319:         osm->N    = size;
320:         PCGASMCreateLocalSubdomains(pc->pmat,osm->n,&osm->iis);
321:       }
322:     }
323:     if (!osm->iis) {
324:       /*
325:        osm->n was set in PCGASMSetSubdomains(), but the actual subdomains have not been supplied.
326:        We create the requisite number of local inner subdomains and then expand them into
327:        out subdomains, if necessary.
328:        */
329:       PCGASMCreateLocalSubdomains(pc->pmat,osm->n,&osm->iis);
330:     }
331:     if (!osm->ois) {
332:       /*
333:         Initially make outer subdomains the same as inner subdomains. If nonzero additional overlap
334:         has been requested, copy the inner subdomains over so they can be modified.
335:       */
336:       PetscMalloc1(osm->n,&osm->ois);
337:       for (i=0; i<osm->n; ++i) {
338:         if (osm->overlap > 0) { /* With positive overlap, osm->iis[i] will be modified */
339:           ISDuplicate(osm->iis[i],(osm->ois)+i);
340:           ISCopy(osm->iis[i],osm->ois[i]);
341:         } else {
342:           PetscObjectReference((PetscObject)((osm->iis)[i]));
343:           osm->ois[i] = osm->iis[i];
344:         }
345:       }
346:       if (osm->overlap > 0) {
347:         /* Extend the "overlapping" regions by a number of steps */
348:         MatIncreaseOverlap(pc->pmat,osm->n,osm->ois,osm->overlap);
349:       }
350:     }

352:     /* Now the subdomains are defined.  Determine their global and max local numbers, if necessary. */
353:     if (osm->nmax == PETSC_DETERMINE) {
354:       PetscMPIInt inwork,outwork;
355:       /* determine global number of subdomains and the max number of local subdomains */
356:       inwork = osm->n;
357:       MPI_Allreduce(&inwork,&outwork,1,MPI_INT,MPI_MAX,PetscObjectComm((PetscObject)pc));
358:       osm->nmax  = outwork;
359:     }
360:     if (osm->N == PETSC_DETERMINE) {
361:       /* Determine the number of globally-distinct subdomains and compute a global numbering for them. */
362:       PetscObjectsListGetGlobalNumbering(PetscObjectComm((PetscObject)pc),osm->n,(PetscObject*)osm->ois,&osm->N,NULL);
363:     }


366:     if (osm->sort_indices) {
367:       for (i=0; i<osm->n; i++) {
368:         ISSort(osm->ois[i]);
369:         ISSort(osm->iis[i]);
370:       }
371:     }

373:     PCGetOptionsPrefix(pc,&prefix);
374:     PCGASMPrintSubdomains(pc);

376:     /*
377:      Merge the ISs, create merged vectors and restrictions.
378:      */
379:     /* Merge outer subdomain ISs and construct a restriction onto the disjoint union of local outer subdomains. */
380:     on = 0;
381:     for (i=0; i<osm->n; i++) {
382:       ISGetLocalSize(osm->ois[i],&oni);
383:       on  += oni;
384:     }
385:     PetscMalloc1(on, &oidx);
386:     on   = 0;
387:     for (i=0; i<osm->n; i++) {
388:       ISGetLocalSize(osm->ois[i],&oni);
389:       ISGetIndices(osm->ois[i],&oidxi);
390:       PetscMemcpy(oidx+on, oidxi, sizeof(PetscInt)*oni);
391:       ISRestoreIndices(osm->ois[i], &oidxi);
392:       on  += oni;
393:     }
394:     ISCreateGeneral(((PetscObject)(pc))->comm, on, oidx, PETSC_OWN_POINTER, &gois);
395:     MatCreateVecs(pc->pmat,&x,&y);
396:     VecCreateMPI(PetscObjectComm((PetscObject)pc), on, PETSC_DECIDE, &osm->gx);
397:     VecDuplicate(osm->gx,&osm->gy);
398:     VecGetOwnershipRange(osm->gx, &gofirst, NULL);
399:     ISCreateStride(PetscObjectComm((PetscObject)pc),on,gofirst,1, &goid);
400:     VecScatterCreate(x,gois,osm->gx,goid, &(osm->gorestriction));
401:     VecDestroy(&x);
402:     ISDestroy(&gois);

404:     /* Merge inner subdomain ISs and construct a restriction onto the disjoint union of local inner subdomains. */
405:     {
406:       PetscInt ini;           /* Number of indices the i-th a local inner subdomain. */
407:       PetscInt in;            /* Number of indices in the disjoint uniont of local inner subdomains. */
408:       PetscInt *iidx;         /* Global indices in the merged local inner subdomain. */
409:       PetscInt *ioidx;        /* Global indices of the disjoint union of inner subdomains within the disjoint union of outer subdomains. */
410:       IS       giis;          /* IS for the disjoint union of inner subdomains. */
411:       IS       giois;         /* IS for the disjoint union of inner subdomains within the disjoint union of outer subdomains. */
412:       /**/
413:       in = 0;
414:       for (i=0; i<osm->n; i++) {
415:         ISGetLocalSize(osm->iis[i],&ini);
416:         in  += ini;
417:       }
418:       PetscMalloc1(in, &iidx);
419:       PetscMalloc1(in, &ioidx);
420:       VecGetOwnershipRange(osm->gx,&gofirst, NULL);
421:       in   = 0;
422:       on   = 0;
423:       for (i=0; i<osm->n; i++) {
424:         const PetscInt         *iidxi; /* Global indices of the i-th local inner subdomain. */
425:         ISLocalToGlobalMapping ltogi; /* Map from global to local indices of the i-th outer local subdomain. */
426:         PetscInt               *ioidxi; /* Local indices of the i-th local inner subdomain within the local outer subdomain. */
427:         PetscInt               ioni;  /* Number of indices in ioidxi; if ioni != ini the inner subdomain is not a subdomain of the outer subdomain (error). */
428:         PetscInt               k;
429:         ISGetLocalSize(osm->iis[i],&ini);
430:         ISGetLocalSize(osm->ois[i],&oni);
431:         ISGetIndices(osm->iis[i],&iidxi);
432:         PetscMemcpy(iidx+in, iidxi, sizeof(PetscInt)*ini);
433:         ISLocalToGlobalMappingCreateIS(osm->ois[i],&ltogi);
434:         ioidxi = ioidx+in;
435:         ISGlobalToLocalMappingApply(ltogi,IS_GTOLM_DROP,ini,iidxi,&ioni,ioidxi);
436:         ISLocalToGlobalMappingDestroy(&ltogi);
437:         ISRestoreIndices(osm->iis[i], &iidxi);
438:         if (ioni != ini) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Inner subdomain %D contains %D indices outside of its outer subdomain", i, ini - ioni);
439:         for (k = 0; k < ini; ++k) ioidxi[k] += gofirst+on;
440:         in += ini;
441:         on += oni;
442:       }
443:       ISCreateGeneral(PetscObjectComm((PetscObject)pc), in, iidx,  PETSC_OWN_POINTER, &giis);
444:       ISCreateGeneral(PetscObjectComm((PetscObject)pc), in, ioidx, PETSC_OWN_POINTER, &giois);
445:       VecScatterCreate(y,giis,osm->gy,giois,&osm->girestriction);
446:       VecDestroy(&y);
447:       ISDestroy(&giis);
448:       ISDestroy(&giois);
449:     }
450:     ISDestroy(&goid);

452:     /* Create the subdomain work vectors. */
453:     PetscMalloc1(osm->n,&osm->x);
454:     PetscMalloc1(osm->n,&osm->y);
455:     VecGetArray(osm->gx, &gxarray);
456:     VecGetArray(osm->gy, &gyarray);
457:     for (i=0, on=0; i<osm->n; ++i, on += oni) {
458:       PetscInt oNi;
459:       ISGetLocalSize(osm->ois[i],&oni);
460:       ISGetSize(osm->ois[i],&oNi);
461:       VecCreateMPIWithArray(((PetscObject)(osm->ois[i]))->comm,1,oni,oNi,gxarray+on,&osm->x[i]);
462:       VecCreateMPIWithArray(((PetscObject)(osm->ois[i]))->comm,1,oni,oNi,gyarray+on,&osm->y[i]);
463:     }
464:     VecRestoreArray(osm->gx, &gxarray);
465:     VecRestoreArray(osm->gy, &gyarray);
466:     /* Create the subdomain solvers */
467:     PetscMalloc1(osm->n,&osm->ksp);
468:     for (i=0; i<osm->n; i++) {
469:       char subprefix[PETSC_MAX_PATH_LEN+1];
470:       KSPCreate(((PetscObject)(osm->ois[i]))->comm,&ksp);
471:       PetscLogObjectParent((PetscObject)pc,(PetscObject)ksp);
472:       PetscObjectIncrementTabLevel((PetscObject)ksp,(PetscObject)pc,1);
473:       KSPSetType(ksp,KSPPREONLY);
474:       KSPGetPC(ksp,&subpc); /* Why do we need this here? */
475:       if (subdomain_dm) {
476:         KSPSetDM(ksp,subdomain_dm[i]);
477:         DMDestroy(subdomain_dm+i);
478:       }
479:       PCGetOptionsPrefix(pc,&prefix);
480:       KSPSetOptionsPrefix(ksp,prefix);
481:       if (subdomain_names && subdomain_names[i]) {
482:         PetscSNPrintf(subprefix,PETSC_MAX_PATH_LEN,"sub_%s_",subdomain_names[i]);
483:         KSPAppendOptionsPrefix(ksp,subprefix);
484:         PetscFree(subdomain_names[i]);
485:       }
486:       KSPAppendOptionsPrefix(ksp,"sub_");
487:       osm->ksp[i] = ksp;
488:     }
489:     PetscFree(subdomain_dm);
490:     PetscFree(subdomain_names);
491:     scall = MAT_INITIAL_MATRIX;

493:   } else { /*if (pc->setupcalled)*/
494:     /*
495:        Destroy the submatrices from the previous iteration
496:     */
497:     if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
498:       MatDestroyMatrices(osm->n,&osm->pmat);
499:       scall = MAT_INITIAL_MATRIX;
500:     }
501:   }

503:   /*
504:      Extract out the submatrices.
505:   */
506:   if (size > 1) {
507:     MatGetSubMatricesMPI(pc->pmat,osm->n,osm->ois,osm->ois,scall,&osm->pmat);
508:   } else {
509:     MatGetSubMatrices(pc->pmat,osm->n,osm->ois,osm->ois,scall,&osm->pmat);
510:   }
511:   if (scall == MAT_INITIAL_MATRIX) {
512:     PetscObjectGetOptionsPrefix((PetscObject)pc->pmat,&pprefix);
513:     for (i=0; i<osm->n; i++) {
514:       PetscLogObjectParent((PetscObject)pc,(PetscObject)osm->pmat[i]);
515:       PetscObjectSetOptionsPrefix((PetscObject)osm->pmat[i],pprefix);
516:     }
517:   }

519:   /* Return control to the user so that the submatrices can be modified (e.g., to apply
520:      different boundary conditions for the submatrices than for the global problem) */
521:   PCModifySubMatrices(pc,osm->n,osm->ois,osm->ois,osm->pmat,pc->modifysubmatricesP);

523:   /*
524:      Loop over submatrices putting them into local ksps
525:   */
526:   for (i=0; i<osm->n; i++) {
527:     KSPSetOperators(osm->ksp[i],osm->pmat[i],osm->pmat[i]);
528:     if (!pc->setupcalled) {
529:       KSPSetFromOptions(osm->ksp[i]);
530:     }
531:   }
532:   return(0);
533: }

537: static PetscErrorCode PCSetUpOnBlocks_GASM(PC pc)
538: {
539:   PC_GASM        *osm = (PC_GASM*)pc->data;
541:   PetscInt       i;

544:   for (i=0; i<osm->n; i++) {
545:     KSPSetUp(osm->ksp[i]);
546:   }
547:   return(0);
548: }

552: static PetscErrorCode PCApply_GASM(PC pc,Vec x,Vec y)
553: {
554:   PC_GASM        *osm = (PC_GASM*)pc->data;
556:   PetscInt       i;
557:   ScatterMode    forward = SCATTER_FORWARD,reverse = SCATTER_REVERSE;

560:   /*
561:      Support for limiting the restriction or interpolation only to the inner
562:      subdomain values (leaving the other values 0).
563:   */
564:   if (!(osm->type & PC_GASM_RESTRICT)) {
565:     /* have to zero the work RHS since scatter may leave some slots empty */
566:     VecZeroEntries(osm->gx);
567:     VecScatterBegin(osm->girestriction,x,osm->gx,INSERT_VALUES,forward);
568:   } else {
569:     VecScatterBegin(osm->gorestriction,x,osm->gx,INSERT_VALUES,forward);
570:   }
571:   VecZeroEntries(osm->gy);
572:   if (!(osm->type & PC_GASM_RESTRICT)) {
573:     VecScatterEnd(osm->girestriction,x,osm->gx,INSERT_VALUES,forward);
574:   } else {
575:     VecScatterEnd(osm->gorestriction,x,osm->gx,INSERT_VALUES,forward);
576:   }
577:   /* do the subdomain solves */
578:   for (i=0; i<osm->n; ++i) {
579:     KSPSolve(osm->ksp[i],osm->x[i],osm->y[i]);
580:   }
581:   VecZeroEntries(y);
582:   if (!(osm->type & PC_GASM_INTERPOLATE)) {
583:     VecScatterBegin(osm->girestriction,osm->gy,y,ADD_VALUES,reverse);
584:     VecScatterEnd(osm->girestriction,osm->gy,y,ADD_VALUES,reverse);  return(0);
585:   } else {
586:     VecScatterBegin(osm->gorestriction,osm->gy,y,ADD_VALUES,reverse);
587:     VecScatterEnd(osm->gorestriction,osm->gy,y,ADD_VALUES,reverse);  return(0);
588:   }
589: }

593: static PetscErrorCode PCApplyTranspose_GASM(PC pc,Vec x,Vec y)
594: {
595:   PC_GASM        *osm = (PC_GASM*)pc->data;
597:   PetscInt       i;
598:   ScatterMode    forward = SCATTER_FORWARD,reverse = SCATTER_REVERSE;

601:   /*
602:      Support for limiting the restriction or interpolation to only local
603:      subdomain values (leaving the other values 0).

605:      Note: these are reversed from the PCApply_GASM() because we are applying the
606:      transpose of the three terms
607:   */
608:   if (!(osm->type & PC_GASM_INTERPOLATE)) {
609:     /* have to zero the work RHS since scatter may leave some slots empty */
610:     VecZeroEntries(osm->gx);
611:     VecScatterBegin(osm->girestriction,x,osm->gx,INSERT_VALUES,forward);
612:   } else {
613:     VecScatterBegin(osm->gorestriction,x,osm->gx,INSERT_VALUES,forward);
614:   }
615:   VecZeroEntries(osm->gy);
616:   if (!(osm->type & PC_GASM_INTERPOLATE)) {
617:     VecScatterEnd(osm->girestriction,x,osm->gx,INSERT_VALUES,forward);
618:   } else {
619:     VecScatterEnd(osm->gorestriction,x,osm->gx,INSERT_VALUES,forward);
620:   }
621:   /* do the local solves */
622:   for (i=0; i<osm->n; ++i) { /* Note that the solves are local, so we can go to osm->n, rather than osm->nmax. */
623:     KSPSolveTranspose(osm->ksp[i],osm->x[i],osm->y[i]);
624:   }
625:   VecZeroEntries(y);
626:   if (!(osm->type & PC_GASM_RESTRICT)) {
627:     VecScatterBegin(osm->girestriction,osm->gy,y,ADD_VALUES,reverse);
628:     VecScatterEnd(osm->girestriction,osm->gy,y,ADD_VALUES,reverse);
629:   } else {
630:     VecScatterBegin(osm->gorestriction,osm->gy,y,ADD_VALUES,reverse);
631:     VecScatterEnd(osm->gorestriction,osm->gy,y,ADD_VALUES,reverse);
632:   }
633:   return(0);
634: }

638: static PetscErrorCode PCReset_GASM(PC pc)
639: {
640:   PC_GASM        *osm = (PC_GASM*)pc->data;
642:   PetscInt       i;

645:   if (osm->ksp) {
646:     for (i=0; i<osm->n; i++) {
647:       KSPReset(osm->ksp[i]);
648:     }
649:   }
650:   if (osm->pmat) {
651:     if (osm->n > 0) {
652:       MatDestroyMatrices(osm->n,&osm->pmat);
653:     }
654:   }
655:   if (osm->x) {
656:     for (i=0; i<osm->n; i++) {
657:       VecDestroy(&osm->x[i]);
658:       VecDestroy(&osm->y[i]);
659:     }
660:   }
661:   VecDestroy(&osm->gx);
662:   VecDestroy(&osm->gy);

664:   VecScatterDestroy(&osm->gorestriction);
665:   VecScatterDestroy(&osm->girestriction);
666:   if (!osm->user_subdomains) {
667:     PCGASMDestroySubdomains(osm->n,&osm->ois,&osm->iis);
668:     osm->N    = PETSC_DETERMINE;
669:     osm->nmax = PETSC_DETERMINE;
670:   }
671:   return(0);
672: }

676: static PetscErrorCode PCDestroy_GASM(PC pc)
677: {
678:   PC_GASM        *osm = (PC_GASM*)pc->data;
680:   PetscInt       i;

683:   PCReset_GASM(pc);

685:   /* PCReset will not destroy subdomains, if user_subdomains is true. */
686:   PCGASMDestroySubdomains(osm->n,&osm->ois,&osm->iis);

688:   if (osm->ksp) {
689:     for (i=0; i<osm->n; i++) {
690:       KSPDestroy(&osm->ksp[i]);
691:     }
692:     PetscFree(osm->ksp);
693:   }
694:   PetscFree(osm->x);
695:   PetscFree(osm->y);
696:   PetscFree(pc->data);
697:   return(0);
698: }

702: static PetscErrorCode PCSetFromOptions_GASM(PetscOptions *PetscOptionsObject,PC pc)
703: {
704:   PC_GASM        *osm = (PC_GASM*)pc->data;
706:   PetscInt       blocks,ovl;
707:   PetscBool      symset,flg;
708:   PCGASMType     gasmtype;

711:   /* set the type to symmetric if matrix is symmetric */
712:   if (!osm->type_set && pc->pmat) {
713:     MatIsSymmetricKnown(pc->pmat,&symset,&flg);
714:     if (symset && flg) osm->type = PC_GASM_BASIC;
715:   }
716:   PetscOptionsHead(PetscOptionsObject,"Generalized additive Schwarz options");
717:   PetscOptionsBool("-pc_gasm_use_dm_subdomains","If subdomains aren't set, use DMCreateDomainDecomposition() to define subdomains.","PCGASMSetUseDMSubdomains",osm->dm_subdomains,&osm->dm_subdomains,&flg);
718:   PetscOptionsInt("-pc_gasm_total_subdomains","Total number of subdomains across communicator","PCGASMSetTotalSubdomains",osm->N,&blocks,&flg);
719:   if (flg) {
720:     PCGASMSetTotalSubdomains(pc,blocks);
721:   }
722:   PetscOptionsInt("-pc_gasm_overlap","Number of overlapping degrees of freedom","PCGASMSetOverlap",osm->overlap,&ovl,&flg);
723:   if (flg) {
724:     PCGASMSetOverlap(pc,ovl);
725:     osm->dm_subdomains = PETSC_FALSE;
726:   }
727:   flg  = PETSC_FALSE;
728:   PetscOptionsEnum("-pc_gasm_type","Type of restriction/extension","PCGASMSetType",PCGASMTypes,(PetscEnum)osm->type,(PetscEnum*)&gasmtype,&flg);
729:   if (flg) {PCGASMSetType(pc,gasmtype);}
730:   PetscOptionsTail();
731:   return(0);
732: }

734: /*------------------------------------------------------------------------------------*/

738: /*@
739:     PCGASMSetTotalSubdomains - sets the total number of subdomains to use across the
740:                                communicator.
741:     Logically collective on pc

743:     Input Parameters:
744: +   pc  - the preconditioner
745: -   N   - total number of subdomains


748:     Level: beginner

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

752: .seealso: PCGASMSetSubdomains(), PCGASMSetOverlap()
753:           PCGASMCreateSubdomains2D()
754: @*/
755: PetscErrorCode  PCGASMSetTotalSubdomains(PC pc,PetscInt N)
756: {
757:   PC_GASM        *osm = (PC_GASM*)pc->data;
758:   PetscMPIInt    size,rank;

762:   if (N < 1) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Total number of subdomains must be 1 or more, got N = %D",N);
763:   if (pc->setupcalled) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONGSTATE,"PCGASMSetTotalSubdomains() should be called before calling PCSetUp().");

765:   PCGASMDestroySubdomains(osm->n,&osm->iis,&osm->ois);
766:   osm->ois = osm->iis = NULL;

768:   MPI_Comm_size(PetscObjectComm((PetscObject)pc),&size);
769:   MPI_Comm_rank(PetscObjectComm((PetscObject)pc),&rank);
770:   osm->N    = N;
771:   osm->n    = PETSC_DETERMINE;
772:   osm->nmax = PETSC_DETERMINE;
773:   osm->dm_subdomains = PETSC_FALSE;
774:   return(0);
775: }

779: static PetscErrorCode  PCGASMSetSubdomains_GASM(PC pc,PetscInt n,IS iis[],IS ois[])
780: {
781:   PC_GASM        *osm = (PC_GASM*)pc->data;
783:   PetscInt       i;

786:   if (n < 1) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Each process must have 1 or more subdomains, got n = %D",n);
787:   if (pc->setupcalled) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONGSTATE,"PCGASMSetSubdomains() should be called before calling PCSetUp().");

789:   PCGASMDestroySubdomains(osm->n,&osm->iis,&osm->ois);
790:   osm->iis  = osm->ois = NULL;
791:   osm->n    = n;
792:   osm->N    = PETSC_DETERMINE;
793:   osm->nmax = PETSC_DETERMINE;
794:   if (ois) {
795:     PetscMalloc1(n,&osm->ois);
796:     for (i=0; i<n; i++) {
797:       PetscObjectReference((PetscObject)ois[i]);
798:       osm->ois[i] = ois[i];
799:     }
800:     /*
801:        Since the user set the outer subdomains, even if nontrivial overlap was requested via PCGASMSetOverlap(),
802:        it will be ignored.  To avoid confusion later on (e.g., when viewing the PC), the overlap size is set to -1.
803:     */
804:     osm->overlap = -1;
805:     if (!iis) {
806:       PetscMalloc1(n,&osm->iis);
807:       for (i=0; i<n; i++) {
808:         for (i=0; i<n; i++) {
809:           PetscObjectReference((PetscObject)ois[i]);
810:           osm->iis[i] = ois[i];
811:         }
812:       }
813:     }
814:   }
815:   if (iis) {
816:     PetscMalloc1(n,&osm->iis);
817:     for (i=0; i<n; i++) {
818:       PetscObjectReference((PetscObject)iis[i]);
819:       osm->iis[i] = iis[i];
820:     }
821:     if (!ois) {
822:       PetscMalloc1(n,&osm->ois);
823:       for (i=0; i<n; i++) {
824:         for (i=0; i<n; i++) {
825:           PetscObjectReference((PetscObject)iis[i]);
826:           osm->ois[i] = iis[i];
827:         }
828:       }
829:       /* If necessary, osm->ois[i] will be expanded using the requested overlap size in PCSetUp_GASM(). */
830:     }
831:   }
832:   if (iis)  osm->user_subdomains = PETSC_TRUE;
833:   return(0);
834: }


839: static PetscErrorCode  PCGASMSetOverlap_GASM(PC pc,PetscInt ovl)
840: {
841:   PC_GASM *osm = (PC_GASM*)pc->data;

844:   if (ovl < 0) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_OUTOFRANGE,"Negative overlap value requested");
845:   if (pc->setupcalled && ovl != osm->overlap) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONGSTATE,"PCGASMSetOverlap() should be called before PCSetUp().");
846:   if (!pc->setupcalled) osm->overlap = ovl;
847:   return(0);
848: }

852: static PetscErrorCode  PCGASMSetType_GASM(PC pc,PCGASMType type)
853: {
854:   PC_GASM *osm = (PC_GASM*)pc->data;

857:   osm->type     = type;
858:   osm->type_set = PETSC_TRUE;
859:   return(0);
860: }

864: static PetscErrorCode  PCGASMSetSortIndices_GASM(PC pc,PetscBool doSort)
865: {
866:   PC_GASM *osm = (PC_GASM*)pc->data;

869:   osm->sort_indices = doSort;
870:   return(0);
871: }

875: /*
876:    FIXME: This routine might need to be modified now that multiple ranks per subdomain are allowed.
877:         In particular, it would upset the global subdomain number calculation.
878: */
879: static PetscErrorCode  PCGASMGetSubKSP_GASM(PC pc,PetscInt *n,PetscInt *first,KSP **ksp)
880: {
881:   PC_GASM        *osm = (PC_GASM*)pc->data;

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

887:   if (n) *n = osm->n;
888:   if (first) {
889:     MPI_Scan(&osm->n,first,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)pc));
890:     *first -= osm->n;
891:   }
892:   if (ksp) {
893:     /* Assume that local solves are now different; not necessarily
894:        true, though!  This flag is used only for PCView_GASM() */
895:     *ksp                        = osm->ksp;
896:     osm->same_subdomain_solvers = PETSC_FALSE;
897:   }
898:   return(0);
899: } /* PCGASMGetSubKSP_GASM() */

903: /*@C
904:     PCGASMSetSubdomains - Sets the subdomains for this processor
905:     for the additive Schwarz preconditioner.

907:     Collective on pc

909:     Input Parameters:
910: +   pc  - the preconditioner object
911: .   n   - the number of subdomains for this processor
912: .   iis - the index sets that define the inner subdomains (or NULL for PETSc to determine subdomains)
913: -   ois - the index sets that define the outer subdomains (or NULL to use the same as iis, or to construct by expanding iis by the requested overlap)

915:     Notes:
916:     The IS indices use the parallel, global numbering of the vector entries.
917:     Inner subdomains are those where the correction is applied.
918:     Outer subdomains are those where the residual necessary to obtain the
919:     corrections is obtained (see PCGASMType for the use of inner/outer subdomains).
920:     Both inner and outer subdomains can extend over several processors.
921:     This processor's portion of a subdomain is known as a local subdomain.

923:     By default the GASM preconditioner uses 1 (local) subdomain per processor.


926:     Level: advanced

928: .keywords: PC, GASM, set, subdomains, additive Schwarz

930: .seealso: PCGASMSetNumSubdomains(), PCGASMSetOverlap(), PCGASMGetSubKSP(),
931:           PCGASMCreateSubdomains2D(), PCGASMGetSubdomains()
932: @*/
933: PetscErrorCode  PCGASMSetSubdomains(PC pc,PetscInt n,IS iis[],IS ois[])
934: {
935:   PC_GASM *osm = (PC_GASM*)pc->data;

940:   PetscTryMethod(pc,"PCGASMSetSubdomains_C",(PC,PetscInt,IS[],IS[]),(pc,n,iis,ois));
941:   osm->dm_subdomains = PETSC_FALSE;
942:   return(0);
943: }


948: /*@
949:     PCGASMSetOverlap - Sets the overlap between a pair of subdomains for the
950:     additive Schwarz preconditioner.  Either all or no processors in the
951:     pc communicator must call this routine.

953:     Logically Collective on pc

955:     Input Parameters:
956: +   pc  - the preconditioner context
957: -   ovl - the amount of overlap between subdomains (ovl >= 0, default value = 0)

959:     Options Database Key:
960: .   -pc_gasm_overlap <overlap> - Sets overlap

962:     Notes:
963:     By default the GASM preconditioner uses 1 subdomain per processor.  To use
964:     multiple subdomain per perocessor or "straddling" subdomains that intersect
965:     multiple processors use PCGASMSetSubdomains() (or option -pc_gasm_total_subdomains <n>).

967:     The overlap defaults to 0, so if one desires that no additional
968:     overlap be computed beyond what may have been set with a call to
969:     PCGASMSetSubdomains(), then ovl must be set to be 0.  In particular, if one does
970:     not explicitly set the subdomains in application code, then all overlap would be computed
971:     internally by PETSc, and using an overlap of 0 would result in an GASM
972:     variant that is equivalent to the block Jacobi preconditioner.

974:     Note that one can define initial index sets with any overlap via
975:     PCGASMSetSubdomains(); the routine PCGASMSetOverlap() merely allows
976:     PETSc to extend that overlap further, if desired.

978:     Level: intermediate

980: .keywords: PC, GASM, set, overlap

982: .seealso: PCGASMSetSubdomains(), PCGASMGetSubKSP(),
983:           PCGASMCreateSubdomains2D(), PCGASMGetSubdomains()
984: @*/
985: PetscErrorCode  PCGASMSetOverlap(PC pc,PetscInt ovl)
986: {
988:   PC_GASM *osm = (PC_GASM*)pc->data;

993:   PetscTryMethod(pc,"PCGASMSetOverlap_C",(PC,PetscInt),(pc,ovl));
994:   osm->dm_subdomains = PETSC_FALSE;
995:   return(0);
996: }

1000: /*@
1001:     PCGASMSetType - Sets the type of restriction and interpolation used
1002:     for local problems in the additive Schwarz method.

1004:     Logically Collective on PC

1006:     Input Parameters:
1007: +   pc  - the preconditioner context
1008: -   type - variant of GASM, one of
1009: .vb
1010:       PC_GASM_BASIC       - full interpolation and restriction
1011:       PC_GASM_RESTRICT    - full restriction, local processor interpolation
1012:       PC_GASM_INTERPOLATE - full interpolation, local processor restriction
1013:       PC_GASM_NONE        - local processor restriction and interpolation
1014: .ve

1016:     Options Database Key:
1017: .   -pc_gasm_type [basic,restrict,interpolate,none] - Sets GASM type

1019:     Level: intermediate

1021: .keywords: PC, GASM, set, type

1023: .seealso: PCGASMSetSubdomains(), PCGASMGetSubKSP(),
1024:           PCGASMCreateSubdomains2D()
1025: @*/
1026: PetscErrorCode  PCGASMSetType(PC pc,PCGASMType type)
1027: {

1033:   PetscTryMethod(pc,"PCGASMSetType_C",(PC,PCGASMType),(pc,type));
1034:   return(0);
1035: }

1039: /*@
1040:     PCGASMSetSortIndices - Determines whether subdomain indices are sorted.

1042:     Logically Collective on PC

1044:     Input Parameters:
1045: +   pc  - the preconditioner context
1046: -   doSort - sort the subdomain indices

1048:     Level: intermediate

1050: .keywords: PC, GASM, set, type

1052: .seealso: PCGASMSetSubdomains(), PCGASMGetSubKSP(),
1053:           PCGASMCreateSubdomains2D()
1054: @*/
1055: PetscErrorCode  PCGASMSetSortIndices(PC pc,PetscBool doSort)
1056: {

1062:   PetscTryMethod(pc,"PCGASMSetSortIndices_C",(PC,PetscBool),(pc,doSort));
1063:   return(0);
1064: }

1068: /*@C
1069:    PCGASMGetSubKSP - Gets the local KSP contexts for all blocks on
1070:    this processor.

1072:    Collective on PC iff first_local is requested

1074:    Input Parameter:
1075: .  pc - the preconditioner context

1077:    Output Parameters:
1078: +  n_local - the number of blocks on this processor or NULL
1079: .  first_local - the global number of the first block on this processor or NULL,
1080:                  all processors must request or all must pass NULL
1081: -  ksp - the array of KSP contexts

1083:    Note:
1084:    After PCGASMGetSubKSP() the array of KSPes is not to be freed

1086:    Currently for some matrix implementations only 1 block per processor
1087:    is supported.

1089:    You must call KSPSetUp() before calling PCGASMGetSubKSP().

1091:    Level: advanced

1093: .keywords: PC, GASM, additive Schwarz, get, sub, KSP, context

1095: .seealso: PCGASMSetSubdomains(), PCGASMSetOverlap(),
1096:           PCGASMCreateSubdomains2D(),
1097: @*/
1098: PetscErrorCode  PCGASMGetSubKSP(PC pc,PetscInt *n_local,PetscInt *first_local,KSP *ksp[])
1099: {

1104:   PetscUseMethod(pc,"PCGASMGetSubKSP_C",(PC,PetscInt*,PetscInt*,KSP **),(pc,n_local,first_local,ksp));
1105:   return(0);
1106: }

1108: /* -------------------------------------------------------------------------------------*/
1109: /*MC
1110:    PCGASM - Use the (restricted) additive Schwarz method, each block is (approximately) solved with
1111:            its own KSP object.

1113:    Options Database Keys:
1114: +  -pc_gasm_total_subdomains <n>  - Sets total number of local subdomains to be distributed among processors
1115: .  -pc_gasm_view_subdomains       - activates the printing of subdomain indices in PCView(), -ksp_view or -snes_view
1116: .  -pc_gasm_print_subdomains      - activates the printing of subdomain indices in PCSetUp()
1117: .  -pc_gasm_overlap <ovl>         - Sets overlap by which to (automatically) extend local subdomains
1118: -  -pc_gasm_type [basic,restrict,interpolate,none] - Sets GASM type

1120:      IMPORTANT: If you run with, for example, 3 blocks on 1 processor or 3 blocks on 3 processors you
1121:       will get a different convergence rate due to the default option of -pc_gasm_type restrict. Use
1122:       -pc_gasm_type basic to use the standard GASM.

1124:    Notes: Each processor can have one or more blocks, but a block cannot be shared by more
1125:      than one processor. Defaults to one block per processor.

1127:      To set options on the solvers for each block append -sub_ to all the KSP, and PC
1128:         options database keys. For example, -sub_pc_type ilu -sub_pc_factor_levels 1 -sub_ksp_type preonly

1130:      To set the options on the solvers separate for each block call PCGASMGetSubKSP()
1131:          and set the options directly on the resulting KSP object (you can access its PC
1132:          with KSPGetPC())


1135:    Level: beginner

1137:    Concepts: additive Schwarz method

1139:     References:
1140:     An additive variant of the Schwarz alternating method for the case of many subregions
1141:     M Dryja, OB Widlund - Courant Institute, New York University Technical report

1143:     Domain Decompositions: Parallel Multilevel Methods for Elliptic Partial Differential Equations,
1144:     Barry Smith, Petter Bjorstad, and William Gropp, Cambridge University Press, ISBN 0-521-49589-X.

1146: .seealso:  PCCreate(), PCSetType(), PCType (for list of available types), PC,
1147:            PCBJACOBI,  PCGASMGetSubKSP(), PCGASMSetSubdomains(),
1148:            PCSetModifySubmatrices(), PCGASMSetOverlap(), PCGASMSetType()

1150: M*/

1154: PETSC_EXTERN PetscErrorCode PCCreate_GASM(PC pc)
1155: {
1157:   PC_GASM        *osm;

1160:   PetscNewLog(pc,&osm);

1162:   osm->N                      = PETSC_DETERMINE;
1163:   osm->n                      = PETSC_DECIDE;
1164:   osm->nmax                   = PETSC_DETERMINE;
1165:   osm->overlap                = 0;
1166:   osm->ksp                    = 0;
1167:   osm->gorestriction          = 0;
1168:   osm->girestriction          = 0;
1169:   osm->gx                     = 0;
1170:   osm->gy                     = 0;
1171:   osm->x                      = 0;
1172:   osm->y                      = 0;
1173:   osm->ois                    = 0;
1174:   osm->iis                    = 0;
1175:   osm->pmat                   = 0;
1176:   osm->type                   = PC_GASM_RESTRICT;
1177:   osm->same_subdomain_solvers = PETSC_TRUE;
1178:   osm->sort_indices           = PETSC_TRUE;
1179:   osm->dm_subdomains          = PETSC_FALSE;

1181:   pc->data                 = (void*)osm;
1182:   pc->ops->apply           = PCApply_GASM;
1183:   pc->ops->applytranspose  = PCApplyTranspose_GASM;
1184:   pc->ops->setup           = PCSetUp_GASM;
1185:   pc->ops->reset           = PCReset_GASM;
1186:   pc->ops->destroy         = PCDestroy_GASM;
1187:   pc->ops->setfromoptions  = PCSetFromOptions_GASM;
1188:   pc->ops->setuponblocks   = PCSetUpOnBlocks_GASM;
1189:   pc->ops->view            = PCView_GASM;
1190:   pc->ops->applyrichardson = 0;

1192:   PetscObjectComposeFunction((PetscObject)pc,"PCGASMSetSubdomains_C",PCGASMSetSubdomains_GASM);
1193:   PetscObjectComposeFunction((PetscObject)pc,"PCGASMSetOverlap_C",PCGASMSetOverlap_GASM);
1194:   PetscObjectComposeFunction((PetscObject)pc,"PCGASMSetType_C",PCGASMSetType_GASM);
1195:   PetscObjectComposeFunction((PetscObject)pc,"PCGASMSetSortIndices_C",PCGASMSetSortIndices_GASM);
1196:   PetscObjectComposeFunction((PetscObject)pc,"PCGASMGetSubKSP_C",PCGASMGetSubKSP_GASM);
1197:   return(0);
1198: }


1203: PetscErrorCode  PCGASMCreateLocalSubdomains(Mat A, PetscInt nloc, IS *iis[])
1204: {
1205:   MatPartitioning mpart;
1206:   const char      *prefix;
1207:   PetscErrorCode  (*f)(Mat,MatReuse,Mat*);
1208:   PetscMPIInt     size;
1209:   PetscInt        i,j,rstart,rend,bs;
1210:   PetscBool       isbaij = PETSC_FALSE,foundpart = PETSC_FALSE;
1211:   Mat             Ad     = NULL, adj;
1212:   IS              ispart,isnumb,*is;
1213:   PetscErrorCode  ierr;

1216:   if (nloc < 1) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"number of local subdomains must > 0, got nloc = %D",nloc);

1218:   /* Get prefix, row distribution, and block size */
1219:   MatGetOptionsPrefix(A,&prefix);
1220:   MatGetOwnershipRange(A,&rstart,&rend);
1221:   MatGetBlockSize(A,&bs);
1222:   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);

1224:   /* Get diagonal block from matrix if possible */
1225:   MPI_Comm_size(PetscObjectComm((PetscObject)A),&size);
1226:   PetscObjectQueryFunction((PetscObject)A,"MatGetDiagonalBlock_C",&f);
1227:   if (f) {
1228:     MatGetDiagonalBlock(A,&Ad);
1229:   } else if (size == 1) {
1230:     Ad = A;
1231:   }
1232:   if (Ad) {
1233:     PetscObjectTypeCompare((PetscObject)Ad,MATSEQBAIJ,&isbaij);
1234:     if (!isbaij) {PetscObjectTypeCompare((PetscObject)Ad,MATSEQSBAIJ,&isbaij);}
1235:   }
1236:   if (Ad && nloc > 1) {
1237:     PetscBool  match,done;
1238:     /* Try to setup a good matrix partitioning if available */
1239:     MatPartitioningCreate(PETSC_COMM_SELF,&mpart);
1240:     PetscObjectSetOptionsPrefix((PetscObject)mpart,prefix);
1241:     MatPartitioningSetFromOptions(mpart);
1242:     PetscObjectTypeCompare((PetscObject)mpart,MATPARTITIONINGCURRENT,&match);
1243:     if (!match) {
1244:       PetscObjectTypeCompare((PetscObject)mpart,MATPARTITIONINGSQUARE,&match);
1245:     }
1246:     if (!match) { /* assume a "good" partitioner is available */
1247:       PetscInt       na;
1248:       const PetscInt *ia,*ja;
1249:       MatGetRowIJ(Ad,0,PETSC_TRUE,isbaij,&na,&ia,&ja,&done);
1250:       if (done) {
1251:         /* Build adjacency matrix by hand. Unfortunately a call to
1252:            MatConvert(Ad,MATMPIADJ,MAT_INITIAL_MATRIX,&adj) will
1253:            remove the block-aij structure and we cannot expect
1254:            MatPartitioning to split vertices as we need */
1255:         PetscInt       i,j,len,nnz,cnt,*iia=0,*jja=0;
1256:         const PetscInt *row;
1257:         nnz = 0;
1258:         for (i=0; i<na; i++) { /* count number of nonzeros */
1259:           len = ia[i+1] - ia[i];
1260:           row = ja + ia[i];
1261:           for (j=0; j<len; j++) {
1262:             if (row[j] == i) { /* don't count diagonal */
1263:               len--; break;
1264:             }
1265:           }
1266:           nnz += len;
1267:         }
1268:         PetscMalloc1(na+1,&iia);
1269:         PetscMalloc1(nnz,&jja);
1270:         nnz    = 0;
1271:         iia[0] = 0;
1272:         for (i=0; i<na; i++) { /* fill adjacency */
1273:           cnt = 0;
1274:           len = ia[i+1] - ia[i];
1275:           row = ja + ia[i];
1276:           for (j=0; j<len; j++) {
1277:             if (row[j] != i) jja[nnz+cnt++] = row[j]; /* if not diagonal */
1278:           }
1279:           nnz += cnt;
1280:           iia[i+1] = nnz;
1281:         }
1282:         /* Partitioning of the adjacency matrix */
1283:         MatCreateMPIAdj(PETSC_COMM_SELF,na,na,iia,jja,NULL,&adj);
1284:         MatPartitioningSetAdjacency(mpart,adj);
1285:         MatPartitioningSetNParts(mpart,nloc);
1286:         MatPartitioningApply(mpart,&ispart);
1287:         ISPartitioningToNumbering(ispart,&isnumb);
1288:         MatDestroy(&adj);
1289:         foundpart = PETSC_TRUE;
1290:       }
1291:       MatRestoreRowIJ(Ad,0,PETSC_TRUE,isbaij,&na,&ia,&ja,&done);
1292:     }
1293:     MatPartitioningDestroy(&mpart);
1294:   }
1295:   PetscMalloc1(nloc,&is);
1296:   if (!foundpart) {

1298:     /* Partitioning by contiguous chunks of rows */

1300:     PetscInt mbs   = (rend-rstart)/bs;
1301:     PetscInt start = rstart;
1302:     for (i=0; i<nloc; i++) {
1303:       PetscInt count = (mbs/nloc + ((mbs % nloc) > i)) * bs;
1304:       ISCreateStride(PETSC_COMM_SELF,count,start,1,&is[i]);
1305:       start += count;
1306:     }

1308:   } else {

1310:     /* Partitioning by adjacency of diagonal block  */

1312:     const PetscInt *numbering;
1313:     PetscInt       *count,nidx,*indices,*newidx,start=0;
1314:     /* Get node count in each partition */
1315:     PetscMalloc1(nloc,&count);
1316:     ISPartitioningCount(ispart,nloc,count);
1317:     if (isbaij && bs > 1) { /* adjust for the block-aij case */
1318:       for (i=0; i<nloc; i++) count[i] *= bs;
1319:     }
1320:     /* Build indices from node numbering */
1321:     ISGetLocalSize(isnumb,&nidx);
1322:     PetscMalloc1(nidx,&indices);
1323:     for (i=0; i<nidx; i++) indices[i] = i; /* needs to be initialized */
1324:     ISGetIndices(isnumb,&numbering);
1325:     PetscSortIntWithPermutation(nidx,numbering,indices);
1326:     ISRestoreIndices(isnumb,&numbering);
1327:     if (isbaij && bs > 1) { /* adjust for the block-aij case */
1328:       PetscMalloc1(nidx*bs,&newidx);
1329:       for (i=0; i<nidx; i++) {
1330:         for (j=0; j<bs; j++) newidx[i*bs+j] = indices[i]*bs + j;
1331:       }
1332:       PetscFree(indices);
1333:       nidx   *= bs;
1334:       indices = newidx;
1335:     }
1336:     /* Shift to get global indices */
1337:     for (i=0; i<nidx; i++) indices[i] += rstart;

1339:     /* Build the index sets for each block */
1340:     for (i=0; i<nloc; i++) {
1341:       ISCreateGeneral(PETSC_COMM_SELF,count[i],&indices[start],PETSC_COPY_VALUES,&is[i]);
1342:       ISSort(is[i]);
1343:       start += count[i];
1344:     }

1346:     PetscFree(count);
1347:     PetscFree(indices);
1348:     ISDestroy(&isnumb);
1349:     ISDestroy(&ispart);
1350:   }
1351:   *iis = is;
1352:   return(0);
1353: }

1357: PETSC_INTERN PetscErrorCode  PCGASMCreateStraddlingSubdomains(Mat A,PetscInt N,PetscInt *n,IS *iis[])
1358: {
1359:   PetscErrorCode  ierr;

1362:   MatSubdomainsCreateCoalesce(A,N,n,iis);
1363:   return(0);
1364: }



1370: /*@C
1371:    PCGASMCreateSubdomains - Creates n index sets defining n nonoverlapping subdomains for the additive
1372:    Schwarz preconditioner for a any problem based on its matrix.

1374:    Collective

1376:    Input Parameters:
1377: +  A       - The global matrix operator
1378: -  N       - the number of global subdomains requested

1380:    Output Parameters:
1381: +  n   - the number of subdomains created on this processor
1382: -  iis - the array of index sets defining the local inner subdomains (on which the correction is applied)

1384:    Level: advanced

1386:    Note: When N >= A's communicator size, each subdomain is local -- contained within a single processor.
1387:          When N < size, the subdomains are 'straddling' (processor boundaries) and are no longer local.
1388:          The resulting subdomains can be use in PCGASMSetSubdomains(pc,n,iss,NULL).  The overlapping
1389:          outer subdomains will be automatically generated from these according to the requested amount of
1390:          overlap; this is currently supported only with local subdomains.


1393: .keywords: PC, GASM, additive Schwarz, create, subdomains, unstructured grid

1395: .seealso: PCGASMSetSubdomains(), PCGASMDestroySubdomains()
1396: @*/
1397: PetscErrorCode  PCGASMCreateSubdomains(Mat A,PetscInt N,PetscInt *n,IS *iis[])
1398: {
1399:   PetscMPIInt     size;
1400:   PetscErrorCode  ierr;


1406:   if (N < 1) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Number of subdomains must be > 0, N = %D",N);
1407:   MPI_Comm_size(PetscObjectComm((PetscObject)A),&size);
1408:   if (N >= size) {
1409:     *n = N/size + (N%size);
1410:     PCGASMCreateLocalSubdomains(A,*n,iis);
1411:   } else {
1412:     PCGASMCreateStraddlingSubdomains(A,N,n,iis);
1413:   }
1414:   return(0);
1415: }

1419: /*@C
1420:    PCGASMDestroySubdomains - Destroys the index sets created with
1421:    PCGASMCreateSubdomains() or PCGASMCreateSubdomains2D. Should be
1422:    called after setting subdomains with PCGASMSetSubdomains().

1424:    Collective

1426:    Input Parameters:
1427: +  n   - the number of index sets
1428: .  iis - the array of inner subdomains,
1429: -  ois - the array of outer subdomains, can be NULL

1431:    Level: intermediate

1433:    Notes: this is merely a convenience subroutine that walks each list,
1434:    destroys each IS on the list, and then frees the list. At the end the
1435:    list pointers are set to NULL.

1437: .keywords: PC, GASM, additive Schwarz, create, subdomains, unstructured grid

1439: .seealso: PCGASMCreateSubdomains(), PCGASMSetSubdomains()
1440: @*/
1441: PetscErrorCode  PCGASMDestroySubdomains(PetscInt n,IS **iis,IS **ois)
1442: {
1443:   PetscInt       i;

1447:   if (n <= 0) return(0);
1448:   if (iis) {
1450:     if (*iis) {
1452:       for (i=0; i<n; i++) {
1453:         ISDestroy(&(*iis)[i]);
1454:       }
1455:       PetscFree((*iis));
1456:     }
1457:   }
1458:   if (ois) {
1460:     if (*ois) {
1462:       for (i=0; i<n; i++) {
1463:         ISDestroy(&(*ois)[i]);
1464:       }
1465:       PetscFree((*ois));
1466:     }
1467:   }
1468:   return(0);
1469: }


1472: #define PCGASMLocalSubdomainBounds2D(M,N,xleft,ylow,xright,yhigh,first,last,xleft_loc,ylow_loc,xright_loc,yhigh_loc,n) \
1473:   {                                                                                                       \
1474:     PetscInt first_row = first/M, last_row = last/M+1;                                                     \
1475:     /*                                                                                                    \
1476:      Compute ylow_loc and yhigh_loc so that (ylow_loc,xleft) and (yhigh_loc,xright) are the corners       \
1477:      of the bounding box of the intersection of the subdomain with the local ownership range (local       \
1478:      subdomain).                                                                                          \
1479:      Also compute xleft_loc and xright_loc as the lower and upper bounds on the first and last rows       \
1480:      of the intersection.                                                                                 \
1481:     */                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             \
1482:     /* ylow_loc is the grid row containing the first element of the local sumbdomain */                   \
1483:     *ylow_loc = PetscMax(first_row,ylow);                                                                    \
1484:     /* xleft_loc is the offset of first element of the local subdomain within its grid row (might actually be outside the local subdomain) */ \
1485:     *xleft_loc = *ylow_loc==first_row ? PetscMax(first%M,xleft) : xleft;                                                                            \
1486:     /* yhigh_loc is the grid row above the last local subdomain element */                                                                    \
1487:     *yhigh_loc = PetscMin(last_row,yhigh);                                                                                                     \
1488:     /* xright is the offset of the end of the  local subdomain within its grid row (might actually be outside the local subdomain) */         \
1489:     *xright_loc = *yhigh_loc==last_row ? PetscMin(xright,last%M) : xright;                                                                          \
1490:     /* Now compute the size of the local subdomain n. */ \
1491:     *n = 0;                                               \
1492:     if (*ylow_loc < *yhigh_loc) {                           \
1493:       PetscInt width = xright-xleft;                     \
1494:       *n += width*(*yhigh_loc-*ylow_loc-1);                 \
1495:       *n += PetscMin(PetscMax(*xright_loc-xleft,0),width); \
1496:       *n -= PetscMin(PetscMax(*xleft_loc-xleft,0), width); \
1497:     } \
1498:   }



1504: /*@
1505:    PCGASMCreateSubdomains2D - Creates the index sets for the overlapping Schwarz
1506:    preconditioner for a two-dimensional problem on a regular grid.

1508:    Collective

1510:    Input Parameters:
1511: +  M, N               - the global number of grid points in the x and y directions
1512: .  Mdomains, Ndomains - the global number of subdomains in the x and y directions
1513: .  dof                - degrees of freedom per node
1514: -  overlap            - overlap in mesh lines

1516:    Output Parameters:
1517: +  Nsub - the number of local subdomains created
1518: .  iis  - array of index sets defining inner (nonoverlapping) subdomains
1519: -  ois  - array of index sets defining outer (overlapping, if overlap > 0) subdomains


1522:    Level: advanced

1524: .keywords: PC, GASM, additive Schwarz, create, subdomains, 2D, regular grid

1526: .seealso: PCGASMSetSubdomains(), PCGASMGetSubKSP(), PCGASMSetOverlap()
1527: @*/
1528: PetscErrorCode  PCGASMCreateSubdomains2D(PC pc,PetscInt M,PetscInt N,PetscInt Mdomains,PetscInt Ndomains,PetscInt dof,PetscInt overlap,PetscInt *nsub,IS **iis,IS **ois)
1529: {
1531:   PetscMPIInt    size, rank;
1532:   PetscInt       i, j;
1533:   PetscInt       maxheight, maxwidth;
1534:   PetscInt       xstart, xleft, xright, xleft_loc, xright_loc;
1535:   PetscInt       ystart, ylow,  yhigh,  ylow_loc,  yhigh_loc;
1536:   PetscInt       x[2][2], y[2][2], n[2];
1537:   PetscInt       first, last;
1538:   PetscInt       nidx, *idx;
1539:   PetscInt       ii,jj,s,q,d;
1540:   PetscInt       k,kk;
1541:   PetscMPIInt    color;
1542:   MPI_Comm       comm, subcomm;
1543:   IS             **xis = 0, **is = ois, **is_local = iis;

1546:   PetscObjectGetComm((PetscObject)pc, &comm);
1547:   MPI_Comm_size(comm, &size);
1548:   MPI_Comm_rank(comm, &rank);
1549:   MatGetOwnershipRange(pc->pmat, &first, &last);
1550:   if (first%dof || last%dof) SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Matrix row partitioning unsuitable for domain decomposition: local row range (%D,%D) "
1551:                                       "does not respect the number of degrees of freedom per grid point %D", first, last, dof);

1553:   /* Determine the number of domains with nonzero intersections with the local ownership range. */
1554:   s      = 0;
1555:   ystart = 0;
1556:   for (j=0; j<Ndomains; ++j) {
1557:     maxheight = N/Ndomains + ((N % Ndomains) > j); /* Maximal height of subdomain */
1558:     if (maxheight < 2) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Too many %D subdomains in the vertical directon for mesh height %D", Ndomains, N);
1559:     /* Vertical domain limits with an overlap. */
1560:     ylow   = PetscMax(ystart - overlap,0);
1561:     yhigh  = PetscMin(ystart + maxheight + overlap,N);
1562:     xstart = 0;
1563:     for (i=0; i<Mdomains; ++i) {
1564:       maxwidth = M/Mdomains + ((M % Mdomains) > i); /* Maximal width of subdomain */
1565:       if (maxwidth < 2) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Too many %D subdomains in the horizontal direction for mesh width %D", Mdomains, M);
1566:       /* Horizontal domain limits with an overlap. */
1567:       xleft  = PetscMax(xstart - overlap,0);
1568:       xright = PetscMin(xstart + maxwidth + overlap,M);
1569:       /*
1570:          Determine whether this subdomain intersects this processor's ownership range of pc->pmat.
1571:       */
1572:       PCGASMLocalSubdomainBounds2D(M,N,xleft,ylow,xright,yhigh,first,last,(&xleft_loc),(&ylow_loc),(&xright_loc),(&yhigh_loc),(&nidx));
1573:       if (nidx) ++s;
1574:       xstart += maxwidth;
1575:     } /* for (i = 0; i < Mdomains; ++i) */
1576:     ystart += maxheight;
1577:   } /* for (j = 0; j < Ndomains; ++j) */

1579:   /* Now we can allocate the necessary number of ISs. */
1580:   *nsub  = s;
1581:   PetscMalloc1(*nsub,is);
1582:   PetscMalloc1(*nsub,is_local);
1583:   s      = 0;
1584:   ystart = 0;
1585:   for (j=0; j<Ndomains; ++j) {
1586:     maxheight = N/Ndomains + ((N % Ndomains) > j); /* Maximal height of subdomain */
1587:     if (maxheight < 2) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Too many %D subdomains in the vertical directon for mesh height %D", Ndomains, N);
1588:     /* Vertical domain limits with an overlap. */
1589:     y[0][0] = PetscMax(ystart - overlap,0);
1590:     y[0][1] = PetscMin(ystart + maxheight + overlap,N);
1591:     /* Vertical domain limits without an overlap. */
1592:     y[1][0] = ystart;
1593:     y[1][1] = PetscMin(ystart + maxheight,N);
1594:     xstart  = 0;
1595:     for (i=0; i<Mdomains; ++i) {
1596:       maxwidth = M/Mdomains + ((M % Mdomains) > i); /* Maximal width of subdomain */
1597:       if (maxwidth < 2) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Too many %D subdomains in the horizontal direction for mesh width %D", Mdomains, M);
1598:       /* Horizontal domain limits with an overlap. */
1599:       x[0][0] = PetscMax(xstart - overlap,0);
1600:       x[0][1] = PetscMin(xstart + maxwidth + overlap,M);
1601:       /* Horizontal domain limits without an overlap. */
1602:       x[1][0] = xstart;
1603:       x[1][1] = PetscMin(xstart+maxwidth,M);
1604:       /*
1605:          Determine whether this domain intersects this processor's ownership range of pc->pmat.
1606:          Do this twice: first for the domains with overlaps, and once without.
1607:          During the first pass create the subcommunicators, and use them on the second pass as well.
1608:       */
1609:       for (q = 0; q < 2; ++q) {
1610:         /*
1611:           domain limits, (xleft, xright) and (ylow, yheigh) are adjusted
1612:           according to whether the domain with an overlap or without is considered.
1613:         */
1614:         xleft = x[q][0]; xright = x[q][1];
1615:         ylow  = y[q][0]; yhigh  = y[q][1];
1616:         PCGASMLocalSubdomainBounds2D(M,N,xleft,ylow,xright,yhigh,first,last,(&xleft_loc),(&ylow_loc),(&xright_loc),(&yhigh_loc),(&nidx));
1617:         nidx *= dof;
1618:         n[q]  = nidx;
1619:         /*
1620:          Based on the counted number of indices in the local domain *with an overlap*,
1621:          construct a subcommunicator of all the processors supporting this domain.
1622:          Observe that a domain with an overlap might have nontrivial local support,
1623:          while the domain without an overlap might not.  Hence, the decision to participate
1624:          in the subcommunicator must be based on the domain with an overlap.
1625:          */
1626:         if (q == 0) {
1627:           if (nidx) color = 1;
1628:           else color = MPI_UNDEFINED;

1630:           MPI_Comm_split(comm, color, rank, &subcomm);
1631:         }
1632:         /*
1633:          Proceed only if the number of local indices *with an overlap* is nonzero.
1634:          */
1635:         if (n[0]) {
1636:           if (q == 0) xis = is;
1637:           if (q == 1) {
1638:             /*
1639:              The IS for the no-overlap subdomain shares a communicator with the overlapping domain.
1640:              Moreover, if the overlap is zero, the two ISs are identical.
1641:              */
1642:             if (overlap == 0) {
1643:               (*is_local)[s] = (*is)[s];
1644:               PetscObjectReference((PetscObject)(*is)[s]);
1645:               continue;
1646:             } else {
1647:               xis     = is_local;
1648:               subcomm = ((PetscObject)(*is)[s])->comm;
1649:             }
1650:           } /* if (q == 1) */
1651:           idx  = NULL;
1652:           PetscMalloc1(nidx,&idx);
1653:           if (nidx) {
1654:             k = 0;
1655:             for (jj=ylow_loc; jj<yhigh_loc; ++jj) {
1656:               PetscInt x0 = (jj==ylow_loc) ? xleft_loc : xleft;
1657:               PetscInt x1 = (jj==yhigh_loc-1) ? xright_loc : xright;
1658:               kk = dof*(M*jj + x0);
1659:               for (ii=x0; ii<x1; ++ii) {
1660:                 for (d = 0; d < dof; ++d) {
1661:                   idx[k++] = kk++;
1662:                 }
1663:               }
1664:             }
1665:           }
1666:           ISCreateGeneral(subcomm,nidx,idx,PETSC_OWN_POINTER,(*xis)+s);
1667:         }/* if (n[0]) */
1668:       }/* for (q = 0; q < 2; ++q) */
1669:       if (n[0]) ++s;
1670:       xstart += maxwidth;
1671:     } /* for (i = 0; i < Mdomains; ++i) */
1672:     ystart += maxheight;
1673:   } /* for (j = 0; j < Ndomains; ++j) */
1674:   return(0);
1675: }

1679: /*@C
1680:     PCGASMGetSubdomains - Gets the subdomains supported on this processor
1681:     for the additive Schwarz preconditioner.

1683:     Not Collective

1685:     Input Parameter:
1686: .   pc - the preconditioner context

1688:     Output Parameters:
1689: +   n   - the number of subdomains for this processor (default value = 1)
1690: .   iis - the index sets that define the inner subdomains (without overlap) supported on this processor (can be NULL)
1691: -   ois - the index sets that define the outer subdomains (with overlap) supported on this processor (can be NULL)


1694:     Notes:
1695:     The user is responsible for destroying the ISs and freeing the returned arrays.
1696:     The IS numbering is in the parallel, global numbering of the vector.

1698:     Level: advanced

1700: .keywords: PC, GASM, get, subdomains, additive Schwarz

1702: .seealso: PCGASMSetOverlap(), PCGASMGetSubKSP(), PCGASMCreateSubdomains2D(),
1703:           PCGASMSetSubdomains(), PCGASMGetSubmatrices()
1704: @*/
1705: PetscErrorCode  PCGASMGetSubdomains(PC pc,PetscInt *n,IS *iis[],IS *ois[])
1706: {
1707:   PC_GASM        *osm;
1709:   PetscBool      match;
1710:   PetscInt       i;

1714:   PetscObjectTypeCompare((PetscObject)pc,PCGASM,&match);
1715:   if (!match) SETERRQ2(PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "Incorrect object type: expected %s, got %s instead", PCGASM, ((PetscObject)pc)->type_name);
1716:   osm = (PC_GASM*)pc->data;
1717:   if (n) *n = osm->n;
1718:   if (iis) {
1719:     PetscMalloc1(osm->n, iis);
1720:   }
1721:   if (ois) {
1722:     PetscMalloc1(osm->n, ois);
1723:   }
1724:   if (iis || ois) {
1725:     for (i = 0; i < osm->n; ++i) {
1726:       if (iis) (*iis)[i] = osm->iis[i];
1727:       if (ois) (*ois)[i] = osm->ois[i];
1728:     }
1729:   }
1730:   return(0);
1731: }

1735: /*@C
1736:     PCGASMGetSubmatrices - Gets the local submatrices (for this processor
1737:     only) for the additive Schwarz preconditioner.

1739:     Not Collective

1741:     Input Parameter:
1742: .   pc - the preconditioner context

1744:     Output Parameters:
1745: +   n   - the number of matrices for this processor (default value = 1)
1746: -   mat - the matrices

1748:     Notes: matrices returned by this routine have the same communicators as the index sets (IS)
1749:            used to define subdomains in PCGASMSetSubdomains()
1750:     Level: advanced

1752: .keywords: PC, GASM, set, local, subdomains, additive Schwarz, block Jacobi

1754: .seealso: PCGASMSetOverlap(), PCGASMGetSubKSP(),
1755:           PCGASMCreateSubdomains2D(), PCGASMSetSubdomains(), PCGASMGetSubdomains()
1756: @*/
1757: PetscErrorCode  PCGASMGetSubmatrices(PC pc,PetscInt *n,Mat *mat[])
1758: {
1759:   PC_GASM        *osm;
1761:   PetscBool      match;

1767:   if (!pc->setupcalled) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONGSTATE,"Must call after KSPSetUP() or PCSetUp().");
1768:   PetscObjectTypeCompare((PetscObject)pc,PCGASM,&match);
1769:   if (!match) SETERRQ2(PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "Expected %s, got %s instead", PCGASM, ((PetscObject)pc)->type_name);
1770:   osm = (PC_GASM*)pc->data;
1771:   if (n) *n = osm->n;
1772:   if (mat) *mat = osm->pmat;
1773:   return(0);
1774: }

1778: /*@
1779:     PCGASMSetUseDMSubdomains - Indicates whether to use DMCreateDomainDecomposition() to define the subdomains, whenever possible.
1780:     Logically Collective

1782:     Input Parameter:
1783: +   pc  - the preconditioner
1784: -   flg - boolean indicating whether to use subdomains defined by the DM

1786:     Options Database Key:
1787: .   -pc_gasm_dm_subdomains -pc_gasm_overlap -pc_gasm_total_subdomains

1789:     Level: intermediate

1791:     Notes:
1792:     PCGASMSetSubdomains(), PCGASMSetTotalSubdomains() or PCGASMSetOverlap() take precedence over PCGASMSetUseDMSubdomains(),
1793:     so setting PCGASMSetSubdomains() with nontrivial subdomain ISs or any of PCGASMSetTotalSubdomains() and PCGASMSetOverlap()
1794:     automatically turns the latter off.

1796: .keywords: PC, ASM, DM, set, subdomains, additive Schwarz

1798: .seealso: PCGASMGetUseDMSubdomains(), PCGASMSetSubdomains(), PCGASMSetOverlap()
1799:           PCGASMCreateSubdomains2D()
1800: @*/
1801: PetscErrorCode  PCGASMSetUseDMSubdomains(PC pc,PetscBool flg)
1802: {
1803:   PC_GASM        *osm = (PC_GASM*)pc->data;
1805:   PetscBool      match;

1810:   if (pc->setupcalled) SETERRQ(((PetscObject)pc)->comm,PETSC_ERR_ARG_WRONGSTATE,"Not for a setup PC.");
1811:   PetscObjectTypeCompare((PetscObject)pc,PCGASM,&match);
1812:   if (match) {
1813:     if (!osm->user_subdomains && osm->N == PETSC_DETERMINE && osm->overlap < 0) {
1814:       osm->dm_subdomains = flg;
1815:     }
1816:   }
1817:   return(0);
1818: }

1822: /*@
1823:     PCGASMGetUseDMSubdomains - Returns flag indicating whether to use DMCreateDomainDecomposition() to define the subdomains, whenever possible.
1824:     Not Collective

1826:     Input Parameter:
1827: .   pc  - the preconditioner

1829:     Output Parameter:
1830: .   flg - boolean indicating whether to use subdomains defined by the DM

1832:     Level: intermediate

1834: .keywords: PC, ASM, DM, set, subdomains, additive Schwarz

1836: .seealso: PCGASMSetUseDMSubdomains(), PCGASMSetOverlap()
1837:           PCGASMCreateSubdomains2D()
1838: @*/
1839: PetscErrorCode  PCGASMGetUseDMSubdomains(PC pc,PetscBool* flg)
1840: {
1841:   PC_GASM        *osm = (PC_GASM*)pc->data;
1843:   PetscBool      match;

1848:   PetscObjectTypeCompare((PetscObject)pc,PCGASM,&match);
1849:   if (match) {
1850:     if (flg) *flg = osm->dm_subdomains;
1851:   }
1852:   return(0);
1853: }