Actual source code: gasm.c

petsc-master 2019-06-26
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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>
 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:   PetscBool   hierarchicalpartitioning;
 24:   IS          *ois;                     /* index sets that define the outer (conceptually, overlapping) subdomains */
 25:   IS          *iis;                     /* index sets that define the inner (conceptually, nonoverlapping) subdomains */
 26:   KSP         *ksp;                     /* linear solvers for each subdomain */
 27:   Mat         *pmat;                    /* subdomain block matrices */
 28:   Vec         gx,gy;                    /* Merged work vectors */
 29:   Vec         *x,*y;                    /* Split work vectors; storage aliases pieces of storage of the above merged vectors. */
 30:   VecScatter  gorestriction;            /* merged restriction to disjoint union of outer subdomains */
 31:   VecScatter  girestriction;            /* merged restriction to disjoint union of inner subdomains */
 32:   VecScatter  pctoouter;
 33:   IS          permutationIS;
 34:   Mat         permutationP;
 35:   Mat         pcmat;
 36:   Vec         pcx,pcy;
 37: } PC_GASM;

 39: static PetscErrorCode  PCGASMComputeGlobalSubdomainNumbering_Private(PC pc,PetscInt **numbering,PetscInt **permutation)
 40: {
 41:   PC_GASM        *osm = (PC_GASM*)pc->data;
 42:   PetscInt       i;

 46:   /* Determine the number of globally-distinct subdomains and compute a global numbering for them. */
 47:   PetscMalloc2(osm->n,numbering,osm->n,permutation);
 48:   PetscObjectsListGetGlobalNumbering(PetscObjectComm((PetscObject)pc),osm->n,(PetscObject*)osm->iis,NULL,*numbering);
 49:   for (i = 0; i < osm->n; ++i) (*permutation)[i] = i;
 50:   PetscSortIntWithPermutation(osm->n,*numbering,*permutation);
 51:   return(0);
 52: }

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

 64:   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);
 65:   /* Inner subdomains. */
 66:   ISGetLocalSize(osm->iis[i], &nidx);
 67:   /*
 68:    No more than 15 characters per index plus a space.
 69:    PetscViewerStringSPrintf requires a string of size at least 2, so use (nidx+1) instead of nidx,
 70:    in case nidx == 0. That will take care of the space for the trailing '\0' as well.
 71:    For nidx == 0, the whole string 16 '\0'.
 72:    */
 73: #define len  16*(nidx+1)+1
 74:   PetscMalloc1(len, &cidx);
 75:   PetscViewerStringOpen(PETSC_COMM_SELF, cidx, len, &sviewer);
 76: #undef len
 77:   ISGetIndices(osm->iis[i], &idx);
 78:   for (j = 0; j < nidx; ++j) {
 79:     PetscViewerStringSPrintf(sviewer, "%D ", idx[j]);
 80:   }
 81:   ISRestoreIndices(osm->iis[i],&idx);
 82:   PetscViewerDestroy(&sviewer);
 83:   PetscViewerASCIIPrintf(viewer, "Inner subdomain:\n");
 84:   PetscViewerFlush(viewer);
 85:   PetscViewerASCIIPushSynchronized(viewer);
 86:   PetscViewerASCIISynchronizedPrintf(viewer, "%s", cidx);
 87:   PetscViewerFlush(viewer);
 88:   PetscViewerASCIIPopSynchronized(viewer);
 89:   PetscViewerASCIIPrintf(viewer, "\n");
 90:   PetscViewerFlush(viewer);
 91:   PetscFree(cidx);
 92:   /* Outer subdomains. */
 93:   ISGetLocalSize(osm->ois[i], &nidx);
 94:   /*
 95:    No more than 15 characters per index plus a space.
 96:    PetscViewerStringSPrintf requires a string of size at least 2, so use (nidx+1) instead of nidx,
 97:    in case nidx == 0. That will take care of the space for the trailing '\0' as well.
 98:    For nidx == 0, the whole string 16 '\0'.
 99:    */
100: #define len  16*(nidx+1)+1
101:   PetscMalloc1(len, &cidx);
102:   PetscViewerStringOpen(PETSC_COMM_SELF, cidx, len, &sviewer);
103: #undef len
104:   ISGetIndices(osm->ois[i], &idx);
105:   for (j = 0; j < nidx; ++j) {
106:     PetscViewerStringSPrintf(sviewer,"%D ", idx[j]);
107:   }
108:   PetscViewerDestroy(&sviewer);
109:   ISRestoreIndices(osm->ois[i],&idx);
110:   PetscViewerASCIIPrintf(viewer, "Outer subdomain:\n");
111:   PetscViewerFlush(viewer);
112:   PetscViewerASCIIPushSynchronized(viewer);
113:   PetscViewerASCIISynchronizedPrintf(viewer, "%s", cidx);
114:   PetscViewerFlush(viewer);
115:   PetscViewerASCIIPopSynchronized(viewer);
116:   PetscViewerASCIIPrintf(viewer, "\n");
117:   PetscViewerFlush(viewer);
118:   PetscFree(cidx);
119:   return(0);
120: }

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

134:   PCGetOptionsPrefix(pc,&prefix);
135:   doprint  = PETSC_FALSE;
136:   PetscOptionsGetBool(NULL,prefix,"-pc_gasm_print_subdomains",&doprint,NULL);
137:   if (!doprint) return(0);
138:   PetscOptionsGetString(NULL,prefix,"-pc_gasm_print_subdomains",fname,PETSC_MAX_PATH_LEN,&found);
139:   if (!found) { PetscStrcpy(fname,"stdout"); };
140:   PetscViewerASCIIOpen(PetscObjectComm((PetscObject)pc),fname,&viewer);
141:   /*
142:    Make sure the viewer has a name. Otherwise this may cause a deadlock or other weird errors when creating a subcomm viewer:
143:    the subcomm viewer will attempt to inherit the viewer's name, which, if not set, will be constructed collectively on the comm.
144:   */
145:   PetscObjectName((PetscObject)viewer);
146:   l    = 0;
147:   PCGASMComputeGlobalSubdomainNumbering_Private(pc,&numbering,&permutation);
148:   for (count = 0; count < osm->N; ++count) {
149:     /* Now let subdomains go one at a time in the global numbering order and print their subdomain/solver info. */
150:     if (l<osm->n) {
151:       d = permutation[l]; /* d is the local number of the l-th smallest (in the global ordering) among the locally supported subdomains */
152:       if (numbering[d] == count) {
153:         PetscViewerGetSubViewer(viewer,((PetscObject)osm->ois[d])->comm, &sviewer);
154:         PCGASMSubdomainView_Private(pc,d,sviewer);
155:         PetscViewerRestoreSubViewer(viewer,((PetscObject)osm->ois[d])->comm, &sviewer);
156:         ++l;
157:       }
158:     }
159:     MPI_Barrier(PetscObjectComm((PetscObject)pc));
160:   }
161:   PetscFree2(numbering,permutation);
162:   PetscViewerDestroy(&viewer);
163:   return(0);
164: }


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

183:   MPI_Comm_size(PetscObjectComm((PetscObject)pc), &size);
184:   MPI_Comm_rank(PetscObjectComm((PetscObject)pc), &rank);

186:   if (osm->overlap >= 0) {
187:     PetscSNPrintf(overlap,sizeof(overlap),"requested amount of overlap = %D",osm->overlap);
188:   }
189:   if (osm->N != PETSC_DETERMINE) {
190:     PetscSNPrintf(gsubdomains, sizeof(gsubdomains), "total number of subdomains = %D",osm->N);
191:   }
192:   if (osm->nmax != PETSC_DETERMINE) {
193:     PetscSNPrintf(msubdomains,sizeof(msubdomains),"max number of local subdomains = %D",osm->nmax);
194:   }

196:   PCGetOptionsPrefix(pc,&prefix);
197:   PetscOptionsGetBool(NULL,prefix,"-pc_gasm_view_subdomains",&view_subdomains,NULL);

199:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
200:   if (iascii) {
201:     /*
202:      Make sure the viewer has a name. Otherwise this may cause a deadlock when creating a subcomm viewer:
203:      the subcomm viewer will attempt to inherit the viewer's name, which, if not set, will be constructed
204:      collectively on the comm.
205:      */
206:     PetscObjectName((PetscObject)viewer);
207:     PetscViewerASCIIPrintf(viewer,"  Restriction/interpolation type: %s\n",PCGASMTypes[osm->type]);
208:     PetscViewerASCIIPrintf(viewer,"  %s\n",overlap);
209:     PetscViewerASCIIPrintf(viewer,"  %s\n",gsubdomains);
210:     PetscViewerASCIIPrintf(viewer,"  %s\n",msubdomains);
211:     PetscViewerASCIIPushSynchronized(viewer);
212:     PetscViewerASCIISynchronizedPrintf(viewer,"  [%d|%d] number of locally-supported subdomains = %D\n",rank,size,osm->n);
213:     PetscViewerFlush(viewer);
214:     PetscViewerASCIIPopSynchronized(viewer);
215:     /* Cannot take advantage of osm->same_subdomain_solvers without a global numbering of subdomains. */
216:     PetscViewerASCIIPrintf(viewer,"  Subdomain solver info is as follows:\n");
217:     PetscViewerASCIIPushTab(viewer);
218:     PetscViewerASCIIPrintf(viewer,"  - - - - - - - - - - - - - - - - - -\n");
219:     /* Make sure that everybody waits for the banner to be printed. */
220:     MPI_Barrier(PetscObjectComm((PetscObject)viewer));
221:     /* Now let subdomains go one at a time in the global numbering order and print their subdomain/solver info. */
222:     PCGASMComputeGlobalSubdomainNumbering_Private(pc,&numbering,&permutation);
223:     l = 0;
224:     for (count = 0; count < osm->N; ++count) {
225:       PetscMPIInt srank, ssize;
226:       if (l<osm->n) {
227:         PetscInt d = permutation[l]; /* d is the local number of the l-th smallest (in the global ordering) among the locally supported subdomains */
228:         if (numbering[d] == count) {
229:           MPI_Comm_size(((PetscObject)osm->ois[d])->comm, &ssize);
230:           MPI_Comm_rank(((PetscObject)osm->ois[d])->comm, &srank);
231:           PetscViewerGetSubViewer(viewer,((PetscObject)osm->ois[d])->comm, &sviewer);
232:           ISGetLocalSize(osm->ois[d],&bsz);
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:           if (view_subdomains) {
236:             PCGASMSubdomainView_Private(pc,d,sviewer);
237:           }
238:           if (!pc->setupcalled) {
239:             PetscViewerASCIIPrintf(sviewer, "  Solver not set up yet: PCSetUp() not yet called\n");
240:           } else {
241:             KSPView(osm->ksp[d],sviewer);
242:           }
243:           PetscViewerASCIIPrintf(sviewer,"  - - - - - - - - - - - - - - - - - -\n");
244:           PetscViewerFlush(sviewer);
245:           PetscViewerRestoreSubViewer(viewer,((PetscObject)osm->ois[d])->comm, &sviewer);
246:           ++l;
247:         }
248:       }
249:       MPI_Barrier(PetscObjectComm((PetscObject)pc));
250:     }
251:     PetscFree2(numbering,permutation);
252:     PetscViewerASCIIPopTab(viewer);
253:   }
254:   PetscViewerFlush(viewer);
255:   PetscViewerASCIIPopSynchronized(viewer);
256:   return(0);
257: }

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



263: PetscErrorCode PCGASMSetHierarchicalPartitioning(PC pc)
264: {
265:    PC_GASM              *osm = (PC_GASM*)pc->data;
266:    MatPartitioning       part;
267:    MPI_Comm              comm;
268:    PetscMPIInt           size;
269:    PetscInt              nlocalsubdomains,fromrows_localsize;
270:    IS                    partitioning,fromrows,isn;
271:    Vec                   outervec;
272:    PetscErrorCode        ierr;

275:    PetscObjectGetComm((PetscObject)pc,&comm);
276:    MPI_Comm_size(comm,&size);
277:    /* we do not need a hierarchical partitioning when
278:     * the total number of subdomains is consistent with
279:     * the number of MPI tasks.
280:     * For the following cases, we do not need to use HP
281:     * */
282:    if(osm->N==PETSC_DETERMINE || osm->N>=size || osm->N==1) return(0);
283:    if(size%osm->N != 0) SETERRQ2(PETSC_COMM_WORLD,PETSC_ERR_ARG_INCOMP,"have to specify the total number of subdomains %D to be a factor of the number of processors %d \n",osm->N,size);
284:    nlocalsubdomains = size/osm->N;
285:    osm->n           = 1;
286:    MatPartitioningCreate(comm,&part);
287:    MatPartitioningSetAdjacency(part,pc->pmat);
288:    MatPartitioningSetType(part,MATPARTITIONINGHIERARCH);
289:    MatPartitioningHierarchicalSetNcoarseparts(part,osm->N);
290:    MatPartitioningHierarchicalSetNfineparts(part,nlocalsubdomains);
291:    MatPartitioningSetFromOptions(part);
292:    /* get new processor owner number of each vertex */
293:    MatPartitioningApply(part,&partitioning);
294:    ISBuildTwoSided(partitioning,NULL,&fromrows);
295:    ISPartitioningToNumbering(partitioning,&isn);
296:    ISDestroy(&isn);
297:    ISGetLocalSize(fromrows,&fromrows_localsize);
298:    MatPartitioningDestroy(&part);
299:    MatCreateVecs(pc->pmat,&outervec,NULL);
300:    VecCreateMPI(comm,fromrows_localsize,PETSC_DETERMINE,&(osm->pcx));
301:    VecDuplicate(osm->pcx,&(osm->pcy));
302:    VecScatterCreate(osm->pcx,NULL,outervec,fromrows,&(osm->pctoouter));
303:    MatCreateSubMatrix(pc->pmat,fromrows,fromrows,MAT_INITIAL_MATRIX,&(osm->permutationP));
304:    PetscObjectReference((PetscObject)fromrows);
305:    osm->permutationIS = fromrows;
306:    osm->pcmat =  pc->pmat;
307:    PetscObjectReference((PetscObject)osm->permutationP);
308:    pc->pmat = osm->permutationP;
309:    VecDestroy(&outervec);
310:    ISDestroy(&fromrows);
311:    ISDestroy(&partitioning);
312:    osm->n           = PETSC_DETERMINE;
313:    return(0);
314: }



318: static PetscErrorCode PCSetUp_GASM(PC pc)
319: {
320:   PC_GASM        *osm = (PC_GASM*)pc->data;
322:   PetscBool      symset,flg;
323:   PetscInt       i,nInnerIndices,nTotalInnerIndices;
324:   PetscMPIInt    rank, size;
325:   MatReuse       scall = MAT_REUSE_MATRIX;
326:   KSP            ksp;
327:   PC             subpc;
328:   const char     *prefix,*pprefix;
329:   Vec            x,y;
330:   PetscInt       oni;       /* Number of indices in the i-th local outer subdomain.               */
331:   const PetscInt *oidxi;    /* Indices from the i-th subdomain local outer subdomain.             */
332:   PetscInt       on;        /* Number of indices in the disjoint union of local outer subdomains. */
333:   PetscInt       *oidx;     /* Indices in the disjoint union of local outer subdomains. */
334:   IS             gois;      /* Disjoint union the global indices of outer subdomains.             */
335:   IS             goid;      /* Identity IS of the size of the disjoint union of outer subdomains. */
336:   PetscScalar    *gxarray, *gyarray;
337:   PetscInt       gostart;   /* Start of locally-owned indices in the vectors -- osm->gx,osm->gy -- over the disjoint union of outer subdomains. */
338:   PetscInt       num_subdomains    = 0;
339:   DM             *subdomain_dm     = NULL;
340:   char           **subdomain_names = NULL;
341:   PetscInt       *numbering;


345:   MPI_Comm_size(PetscObjectComm((PetscObject)pc),&size);
346:   MPI_Comm_rank(PetscObjectComm((PetscObject)pc),&rank);
347:   if (!pc->setupcalled) {
348:         /* use a hierarchical partitioning */
349:     if(osm->hierarchicalpartitioning){
350:       PCGASMSetHierarchicalPartitioning(pc);
351:     }
352:     if (!osm->type_set) {
353:       MatIsSymmetricKnown(pc->pmat,&symset,&flg);
354:       if (symset && flg) osm->type = PC_GASM_BASIC;
355:     }

357:     if (osm->n == PETSC_DETERMINE) {
358:       if (osm->N != PETSC_DETERMINE) {
359:            /* No local subdomains given, but the desired number of total subdomains is known, so construct them accordingly. */
360:            PCGASMCreateSubdomains(pc->pmat,osm->N,&osm->n,&osm->iis);
361:       } else if (osm->dm_subdomains && pc->dm) {
362:         /* try pc->dm next, if allowed */
363:         PetscInt  d;
364:         IS       *inner_subdomain_is, *outer_subdomain_is;
365:         DMCreateDomainDecomposition(pc->dm, &num_subdomains, &subdomain_names, &inner_subdomain_is, &outer_subdomain_is, &subdomain_dm);
366:         if (num_subdomains) {
367:           PCGASMSetSubdomains(pc, num_subdomains, inner_subdomain_is, outer_subdomain_is);
368:         }
369:         for (d = 0; d < num_subdomains; ++d) {
370:           if (inner_subdomain_is) {ISDestroy(&inner_subdomain_is[d]);}
371:           if (outer_subdomain_is) {ISDestroy(&outer_subdomain_is[d]);}
372:         }
373:         PetscFree(inner_subdomain_is);
374:         PetscFree(outer_subdomain_is);
375:       } else {
376:         /* still no subdomains; use one per processor */
377:         osm->nmax = osm->n = 1;
378:         MPI_Comm_size(PetscObjectComm((PetscObject)pc),&size);
379:         osm->N    = size;
380:         PCGASMCreateLocalSubdomains(pc->pmat,osm->n,&osm->iis);
381:       }
382:     }
383:     if (!osm->iis) {
384:       /*
385:        osm->n was set in PCGASMSetSubdomains(), but the actual subdomains have not been supplied.
386:        We create the requisite number of local inner subdomains and then expand them into
387:        out subdomains, if necessary.
388:        */
389:       PCGASMCreateLocalSubdomains(pc->pmat,osm->n,&osm->iis);
390:     }
391:     if (!osm->ois) {
392:       /*
393:             Initially make outer subdomains the same as inner subdomains. If nonzero additional overlap
394:             has been requested, copy the inner subdomains over so they can be modified.
395:       */
396:       PetscMalloc1(osm->n,&osm->ois);
397:       for (i=0; i<osm->n; ++i) {
398:         if (osm->overlap > 0 && osm->N>1) { /* With positive overlap, osm->iis[i] will be modified */
399:           ISDuplicate(osm->iis[i],(osm->ois)+i);
400:           ISCopy(osm->iis[i],osm->ois[i]);
401:         } else {
402:           PetscObjectReference((PetscObject)((osm->iis)[i]));
403:           osm->ois[i] = osm->iis[i];
404:         }
405:       }
406:       if (osm->overlap>0 && osm->N>1) {
407:            /* Extend the "overlapping" regions by a number of steps */
408:            MatIncreaseOverlapSplit(pc->pmat,osm->n,osm->ois,osm->overlap);
409:       }
410:     }

412:     /* Now the subdomains are defined.  Determine their global and max local numbers, if necessary. */
413:     if (osm->nmax == PETSC_DETERMINE) {
414:       PetscMPIInt inwork,outwork;
415:       /* determine global number of subdomains and the max number of local subdomains */
416:       inwork = osm->n;
417:       MPIU_Allreduce(&inwork,&outwork,1,MPI_INT,MPI_MAX,PetscObjectComm((PetscObject)pc));
418:       osm->nmax  = outwork;
419:     }
420:     if (osm->N == PETSC_DETERMINE) {
421:       /* Determine the number of globally-distinct subdomains and compute a global numbering for them. */
422:       PetscObjectsListGetGlobalNumbering(PetscObjectComm((PetscObject)pc),osm->n,(PetscObject*)osm->ois,&osm->N,NULL);
423:     }


426:     if (osm->sort_indices) {
427:       for (i=0; i<osm->n; i++) {
428:         ISSort(osm->ois[i]);
429:         ISSort(osm->iis[i]);
430:       }
431:     }
432:     PCGetOptionsPrefix(pc,&prefix);
433:     PCGASMPrintSubdomains(pc);

435:     /*
436:        Merge the ISs, create merged vectors and restrictions.
437:      */
438:     /* Merge outer subdomain ISs and construct a restriction onto the disjoint union of local outer subdomains. */
439:     on = 0;
440:     for (i=0; i<osm->n; i++) {
441:       ISGetLocalSize(osm->ois[i],&oni);
442:       on  += oni;
443:     }
444:     PetscMalloc1(on, &oidx);
445:     on   = 0;
446:     /* Merge local indices together */
447:     for (i=0; i<osm->n; i++) {
448:       ISGetLocalSize(osm->ois[i],&oni);
449:       ISGetIndices(osm->ois[i],&oidxi);
450:       PetscArraycpy(oidx+on,oidxi,oni);
451:       ISRestoreIndices(osm->ois[i],&oidxi);
452:       on  += oni;
453:     }
454:     ISCreateGeneral(((PetscObject)(pc))->comm,on,oidx,PETSC_OWN_POINTER,&gois);
455:     nTotalInnerIndices = 0;
456:     for(i=0; i<osm->n; i++){
457:       ISGetLocalSize(osm->iis[i],&nInnerIndices);
458:       nTotalInnerIndices += nInnerIndices;
459:     }
460:     VecCreateMPI(((PetscObject)(pc))->comm,nTotalInnerIndices,PETSC_DETERMINE,&x);
461:     VecDuplicate(x,&y);

463:     VecCreateMPI(PetscObjectComm((PetscObject)pc),on,PETSC_DECIDE,&osm->gx);
464:     VecDuplicate(osm->gx,&osm->gy);
465:     VecGetOwnershipRange(osm->gx, &gostart, NULL);
466:     ISCreateStride(PetscObjectComm((PetscObject)pc),on,gostart,1, &goid);
467:     /* gois might indices not on local */
468:     VecScatterCreate(x,gois,osm->gx,goid, &(osm->gorestriction));
469:     PetscMalloc1(osm->n,&numbering);
470:     PetscObjectsListGetGlobalNumbering(PetscObjectComm((PetscObject)pc),osm->n,(PetscObject*)osm->ois,NULL,numbering);
471:     VecDestroy(&x);
472:     ISDestroy(&gois);

474:     /* Merge inner subdomain ISs and construct a restriction onto the disjoint union of local inner subdomains. */
475:     {
476:       PetscInt        ini;           /* Number of indices the i-th a local inner subdomain. */
477:       PetscInt        in;            /* Number of indices in the disjoint uniont of local inner subdomains. */
478:       PetscInt       *iidx;          /* Global indices in the merged local inner subdomain. */
479:       PetscInt       *ioidx;         /* Global indices of the disjoint union of inner subdomains within the disjoint union of outer subdomains. */
480:       IS              giis;          /* IS for the disjoint union of inner subdomains. */
481:       IS              giois;         /* IS for the disjoint union of inner subdomains within the disjoint union of outer subdomains. */
482:       PetscScalar    *array;
483:       const PetscInt *indices;
484:       PetscInt        k;
485:       on = 0;
486:       for (i=0; i<osm->n; i++) {
487:         ISGetLocalSize(osm->ois[i],&oni);
488:         on  += oni;
489:       }
490:       PetscMalloc1(on, &iidx);
491:       PetscMalloc1(on, &ioidx);
492:       VecGetArray(y,&array);
493:       /* set communicator id to determine where overlap is */
494:       in   = 0;
495:       for (i=0; i<osm->n; i++) {
496:         ISGetLocalSize(osm->iis[i],&ini);
497:         for (k = 0; k < ini; ++k){
498:           array[in+k] = numbering[i];
499:         }
500:         in += ini;
501:       }
502:       VecRestoreArray(y,&array);
503:       VecScatterBegin(osm->gorestriction,y,osm->gy,INSERT_VALUES,SCATTER_FORWARD);
504:       VecScatterEnd(osm->gorestriction,y,osm->gy,INSERT_VALUES,SCATTER_FORWARD);
505:       VecGetOwnershipRange(osm->gy,&gostart, NULL);
506:       VecGetArray(osm->gy,&array);
507:       on  = 0;
508:       in  = 0;
509:       for (i=0; i<osm->n; i++) {
510:             ISGetLocalSize(osm->ois[i],&oni);
511:             ISGetIndices(osm->ois[i],&indices);
512:             for (k=0; k<oni; k++) {
513:           /*  skip overlapping indices to get inner domain */
514:           if(PetscRealPart(array[on+k]) != numbering[i]) continue;
515:           iidx[in]    = indices[k];
516:           ioidx[in++] = gostart+on+k;
517:             }
518:             ISRestoreIndices(osm->ois[i], &indices);
519:             on += oni;
520:       }
521:       VecRestoreArray(osm->gy,&array);
522:       ISCreateGeneral(PetscObjectComm((PetscObject)pc),in,iidx,PETSC_OWN_POINTER,&giis);
523:       ISCreateGeneral(PetscObjectComm((PetscObject)pc),in,ioidx,PETSC_OWN_POINTER,&giois);
524:       VecScatterCreate(y,giis,osm->gy,giois,&osm->girestriction);
525:       VecDestroy(&y);
526:       ISDestroy(&giis);
527:       ISDestroy(&giois);
528:     }
529:     ISDestroy(&goid);
530:     PetscFree(numbering);

532:     /* Create the subdomain work vectors. */
533:     PetscMalloc1(osm->n,&osm->x);
534:     PetscMalloc1(osm->n,&osm->y);
535:     VecGetArray(osm->gx, &gxarray);
536:     VecGetArray(osm->gy, &gyarray);
537:     for (i=0, on=0; i<osm->n; ++i, on += oni) {
538:       PetscInt oNi;
539:       ISGetLocalSize(osm->ois[i],&oni);
540:       /* on a sub communicator */
541:       ISGetSize(osm->ois[i],&oNi);
542:       VecCreateMPIWithArray(((PetscObject)(osm->ois[i]))->comm,1,oni,oNi,gxarray+on,&osm->x[i]);
543:       VecCreateMPIWithArray(((PetscObject)(osm->ois[i]))->comm,1,oni,oNi,gyarray+on,&osm->y[i]);
544:     }
545:     VecRestoreArray(osm->gx, &gxarray);
546:     VecRestoreArray(osm->gy, &gyarray);
547:     /* Create the subdomain solvers */
548:     PetscMalloc1(osm->n,&osm->ksp);
549:     for (i=0; i<osm->n; i++) {
550:       char subprefix[PETSC_MAX_PATH_LEN+1];
551:       KSPCreate(((PetscObject)(osm->ois[i]))->comm,&ksp);
552:       KSPSetErrorIfNotConverged(ksp,pc->erroriffailure);
553:       PetscLogObjectParent((PetscObject)pc,(PetscObject)ksp);
554:       PetscObjectIncrementTabLevel((PetscObject)ksp,(PetscObject)pc,1);
555:       KSPSetType(ksp,KSPPREONLY);
556:       KSPGetPC(ksp,&subpc); /* Why do we need this here? */
557:       if (subdomain_dm) {
558:             KSPSetDM(ksp,subdomain_dm[i]);
559:             DMDestroy(subdomain_dm+i);
560:       }
561:       PCGetOptionsPrefix(pc,&prefix);
562:       KSPSetOptionsPrefix(ksp,prefix);
563:       if (subdomain_names && subdomain_names[i]) {
564:              PetscSNPrintf(subprefix,PETSC_MAX_PATH_LEN,"sub_%s_",subdomain_names[i]);
565:              KSPAppendOptionsPrefix(ksp,subprefix);
566:              PetscFree(subdomain_names[i]);
567:       }
568:       KSPAppendOptionsPrefix(ksp,"sub_");
569:       osm->ksp[i] = ksp;
570:     }
571:     PetscFree(subdomain_dm);
572:     PetscFree(subdomain_names);
573:     scall = MAT_INITIAL_MATRIX;

575:   } else { /* if (pc->setupcalled) */
576:     /*
577:        Destroy the submatrices from the previous iteration
578:     */
579:     if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
580:       MatDestroyMatrices(osm->n,&osm->pmat);
581:       scall = MAT_INITIAL_MATRIX;
582:     }
583:     if(osm->permutationIS){
584:       MatCreateSubMatrix(pc->pmat,osm->permutationIS,osm->permutationIS,scall,&osm->permutationP);
585:       PetscObjectReference((PetscObject)osm->permutationP);
586:       osm->pcmat = pc->pmat;
587:       pc->pmat   = osm->permutationP;
588:     }

590:   }


593:   /*
594:      Extract out the submatrices.
595:   */
596:   if (size > 1) {
597:     MatCreateSubMatricesMPI(pc->pmat,osm->n,osm->ois,osm->ois,scall,&osm->pmat);
598:   } else {
599:     MatCreateSubMatrices(pc->pmat,osm->n,osm->ois,osm->ois,scall,&osm->pmat);
600:   }
601:   if (scall == MAT_INITIAL_MATRIX) {
602:     PetscObjectGetOptionsPrefix((PetscObject)pc->pmat,&pprefix);
603:     for (i=0; i<osm->n; i++) {
604:       PetscLogObjectParent((PetscObject)pc,(PetscObject)osm->pmat[i]);
605:       PetscObjectSetOptionsPrefix((PetscObject)osm->pmat[i],pprefix);
606:     }
607:   }

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

613:   /*
614:      Loop over submatrices putting them into local ksps
615:   */
616:   for (i=0; i<osm->n; i++) {
617:     KSPSetOperators(osm->ksp[i],osm->pmat[i],osm->pmat[i]);
618:     if (!pc->setupcalled) {
619:       KSPSetFromOptions(osm->ksp[i]);
620:     }
621:   }
622:   if(osm->pcmat){
623:     MatDestroy(&pc->pmat);
624:     pc->pmat   = osm->pcmat;
625:     osm->pcmat = 0;
626:   }
627:   return(0);
628: }

630: static PetscErrorCode PCSetUpOnBlocks_GASM(PC pc)
631: {
632:   PC_GASM        *osm = (PC_GASM*)pc->data;
634:   PetscInt       i;

637:   for (i=0; i<osm->n; i++) {
638:     KSPSetUp(osm->ksp[i]);
639:   }
640:   return(0);
641: }

643: static PetscErrorCode PCApply_GASM(PC pc,Vec xin,Vec yout)
644: {
645:   PC_GASM        *osm = (PC_GASM*)pc->data;
647:   PetscInt       i;
648:   Vec            x,y;
649:   ScatterMode    forward = SCATTER_FORWARD,reverse = SCATTER_REVERSE;

652:   if(osm->pctoouter){
653:     VecScatterBegin(osm->pctoouter,xin,osm->pcx,INSERT_VALUES,SCATTER_REVERSE);
654:     VecScatterEnd(osm->pctoouter,xin,osm->pcx,INSERT_VALUES,SCATTER_REVERSE);
655:     x = osm->pcx;
656:     y = osm->pcy;
657:   }else{
658:         x = xin;
659:         y = yout;
660:   }
661:   /*
662:      Support for limiting the restriction or interpolation only to the inner
663:      subdomain values (leaving the other values 0).
664:   */
665:   if (!(osm->type & PC_GASM_RESTRICT)) {
666:     /* have to zero the work RHS since scatter may leave some slots empty */
667:     VecZeroEntries(osm->gx);
668:     VecScatterBegin(osm->girestriction,x,osm->gx,INSERT_VALUES,forward);
669:   } else {
670:     VecScatterBegin(osm->gorestriction,x,osm->gx,INSERT_VALUES,forward);
671:   }
672:   VecZeroEntries(osm->gy);
673:   if (!(osm->type & PC_GASM_RESTRICT)) {
674:     VecScatterEnd(osm->girestriction,x,osm->gx,INSERT_VALUES,forward);
675:   } else {
676:     VecScatterEnd(osm->gorestriction,x,osm->gx,INSERT_VALUES,forward);
677:   }
678:   /* do the subdomain solves */
679:   for (i=0; i<osm->n; ++i) {
680:     KSPSolve(osm->ksp[i],osm->x[i],osm->y[i]);
681:     KSPCheckSolve(osm->ksp[i],pc,osm->y[i]);
682:   }
683:   /* Do we need to zero y ?? */
684:   VecZeroEntries(y);
685:   if (!(osm->type & PC_GASM_INTERPOLATE)) {
686:     VecScatterBegin(osm->girestriction,osm->gy,y,ADD_VALUES,reverse);
687:     VecScatterEnd(osm->girestriction,osm->gy,y,ADD_VALUES,reverse);
688:   } else {
689:     VecScatterBegin(osm->gorestriction,osm->gy,y,ADD_VALUES,reverse);
690:     VecScatterEnd(osm->gorestriction,osm->gy,y,ADD_VALUES,reverse);
691:   }
692:   if(osm->pctoouter){
693:     VecScatterBegin(osm->pctoouter,y,yout,INSERT_VALUES,SCATTER_FORWARD);
694:     VecScatterEnd(osm->pctoouter,y,yout,INSERT_VALUES,SCATTER_FORWARD);
695:   }
696:   return(0);
697: }

699: static PetscErrorCode PCApplyTranspose_GASM(PC pc,Vec xin,Vec yout)
700: {
701:   PC_GASM        *osm = (PC_GASM*)pc->data;
703:   PetscInt       i;
704:   Vec            x,y;
705:   ScatterMode    forward = SCATTER_FORWARD,reverse = SCATTER_REVERSE;

708:   if(osm->pctoouter){
709:    VecScatterBegin(osm->pctoouter,xin,osm->pcx,INSERT_VALUES,SCATTER_REVERSE);
710:    VecScatterEnd(osm->pctoouter,xin,osm->pcx,INSERT_VALUES,SCATTER_REVERSE);
711:    x = osm->pcx;
712:    y = osm->pcy;
713:   }else{
714:         x = xin;
715:         y = yout;
716:   }
717:   /*
718:      Support for limiting the restriction or interpolation to only local
719:      subdomain values (leaving the other values 0).

721:      Note: these are reversed from the PCApply_GASM() because we are applying the
722:      transpose of the three terms
723:   */
724:   if (!(osm->type & PC_GASM_INTERPOLATE)) {
725:     /* have to zero the work RHS since scatter may leave some slots empty */
726:     VecZeroEntries(osm->gx);
727:     VecScatterBegin(osm->girestriction,x,osm->gx,INSERT_VALUES,forward);
728:   } else {
729:     VecScatterBegin(osm->gorestriction,x,osm->gx,INSERT_VALUES,forward);
730:   }
731:   VecZeroEntries(osm->gy);
732:   if (!(osm->type & PC_GASM_INTERPOLATE)) {
733:     VecScatterEnd(osm->girestriction,x,osm->gx,INSERT_VALUES,forward);
734:   } else {
735:     VecScatterEnd(osm->gorestriction,x,osm->gx,INSERT_VALUES,forward);
736:   }
737:   /* do the local solves */
738:   for (i=0; i<osm->n; ++i) { /* Note that the solves are local, so we can go to osm->n, rather than osm->nmax. */
739:     KSPSolveTranspose(osm->ksp[i],osm->x[i],osm->y[i]);
740:     KSPCheckSolve(osm->ksp[i],pc,osm->y[i]);
741:   }
742:   VecZeroEntries(y);
743:   if (!(osm->type & PC_GASM_RESTRICT)) {
744:     VecScatterBegin(osm->girestriction,osm->gy,y,ADD_VALUES,reverse);
745:     VecScatterEnd(osm->girestriction,osm->gy,y,ADD_VALUES,reverse);
746:   } else {
747:     VecScatterBegin(osm->gorestriction,osm->gy,y,ADD_VALUES,reverse);
748:     VecScatterEnd(osm->gorestriction,osm->gy,y,ADD_VALUES,reverse);
749:   }
750:   if(osm->pctoouter){
751:    VecScatterBegin(osm->pctoouter,y,yout,INSERT_VALUES,SCATTER_FORWARD);
752:    VecScatterEnd(osm->pctoouter,y,yout,INSERT_VALUES,SCATTER_FORWARD);
753:   }
754:   return(0);
755: }

757: static PetscErrorCode PCReset_GASM(PC pc)
758: {
759:   PC_GASM        *osm = (PC_GASM*)pc->data;
761:   PetscInt       i;

764:   if (osm->ksp) {
765:     for (i=0; i<osm->n; i++) {
766:       KSPReset(osm->ksp[i]);
767:     }
768:   }
769:   if (osm->pmat) {
770:     if (osm->n > 0) {
771:       PetscMPIInt size;
772:       MPI_Comm_size(PetscObjectComm((PetscObject)pc),&size);
773:       if (size > 1) {
774:         /* osm->pmat is created by MatCreateSubMatricesMPI(), cannot use MatDestroySubMatrices() */
775:         MatDestroyMatrices(osm->n,&osm->pmat);
776:       } else {
777:         MatDestroySubMatrices(osm->n,&osm->pmat);
778:       }
779:     }
780:   }
781:   if (osm->x) {
782:     for (i=0; i<osm->n; i++) {
783:       VecDestroy(&osm->x[i]);
784:       VecDestroy(&osm->y[i]);
785:     }
786:   }
787:   VecDestroy(&osm->gx);
788:   VecDestroy(&osm->gy);

790:   VecScatterDestroy(&osm->gorestriction);
791:   VecScatterDestroy(&osm->girestriction);
792:   if (!osm->user_subdomains) {
793:     PCGASMDestroySubdomains(osm->n,&osm->ois,&osm->iis);
794:     osm->N    = PETSC_DETERMINE;
795:     osm->nmax = PETSC_DETERMINE;
796:   }
797:   if(osm->pctoouter){
798:         VecScatterDestroy(&(osm->pctoouter));
799:   }
800:   if(osm->permutationIS){
801:         ISDestroy(&(osm->permutationIS));
802:   }
803:   if(osm->pcx){
804:         VecDestroy(&(osm->pcx));
805:   }
806:   if(osm->pcy){
807:         VecDestroy(&(osm->pcy));
808:   }
809:   if(osm->permutationP){
810:     MatDestroy(&(osm->permutationP));
811:   }
812:   if(osm->pcmat){
813:         MatDestroy(&osm->pcmat);
814:   }
815:   return(0);
816: }

818: static PetscErrorCode PCDestroy_GASM(PC pc)
819: {
820:   PC_GASM        *osm = (PC_GASM*)pc->data;
822:   PetscInt       i;

825:   PCReset_GASM(pc);
826:   /* PCReset will not destroy subdomains, if user_subdomains is true. */
827:   PCGASMDestroySubdomains(osm->n,&osm->ois,&osm->iis);
828:   if (osm->ksp) {
829:     for (i=0; i<osm->n; i++) {
830:       KSPDestroy(&osm->ksp[i]);
831:     }
832:     PetscFree(osm->ksp);
833:   }
834:   PetscFree(osm->x);
835:   PetscFree(osm->y);
836:   PetscFree(pc->data);
837:   return(0);
838: }

840: static PetscErrorCode PCSetFromOptions_GASM(PetscOptionItems *PetscOptionsObject,PC pc)
841: {
842:   PC_GASM        *osm = (PC_GASM*)pc->data;
844:   PetscInt       blocks,ovl;
845:   PetscBool      symset,flg;
846:   PCGASMType     gasmtype;

849:   /* set the type to symmetric if matrix is symmetric */
850:   if (!osm->type_set && pc->pmat) {
851:     MatIsSymmetricKnown(pc->pmat,&symset,&flg);
852:     if (symset && flg) osm->type = PC_GASM_BASIC;
853:   }
854:   PetscOptionsHead(PetscOptionsObject,"Generalized additive Schwarz options");
855:   PetscOptionsBool("-pc_gasm_use_dm_subdomains","If subdomains aren't set, use DMCreateDomainDecomposition() to define subdomains.","PCGASMSetUseDMSubdomains",osm->dm_subdomains,&osm->dm_subdomains,&flg);
856:   PetscOptionsInt("-pc_gasm_total_subdomains","Total number of subdomains across communicator","PCGASMSetTotalSubdomains",osm->N,&blocks,&flg);
857:   if (flg) {
858:     PCGASMSetTotalSubdomains(pc,blocks);
859:   }
860:   PetscOptionsInt("-pc_gasm_overlap","Number of overlapping degrees of freedom","PCGASMSetOverlap",osm->overlap,&ovl,&flg);
861:   if (flg) {
862:     PCGASMSetOverlap(pc,ovl);
863:     osm->dm_subdomains = PETSC_FALSE;
864:   }
865:   flg  = PETSC_FALSE;
866:   PetscOptionsEnum("-pc_gasm_type","Type of restriction/extension","PCGASMSetType",PCGASMTypes,(PetscEnum)osm->type,(PetscEnum*)&gasmtype,&flg);
867:   if (flg) {PCGASMSetType(pc,gasmtype);}
868:   PetscOptionsBool("-pc_gasm_use_hierachical_partitioning","use hierarchical partitioning",NULL,osm->hierarchicalpartitioning,&osm->hierarchicalpartitioning,&flg);
869:   PetscOptionsTail();
870:   return(0);
871: }

873: /*------------------------------------------------------------------------------------*/

875: /*@
876:     PCGASMSetTotalSubdomains - sets the total number of subdomains to use across the
877:                                communicator.
878:     Logically collective on pc

880:     Input Parameters:
881: +   pc  - the preconditioner
882: -   N   - total number of subdomains


885:     Level: beginner

887: .seealso: PCGASMSetSubdomains(), PCGASMSetOverlap()
888:           PCGASMCreateSubdomains2D()
889: @*/
890: PetscErrorCode  PCGASMSetTotalSubdomains(PC pc,PetscInt N)
891: {
892:   PC_GASM        *osm = (PC_GASM*)pc->data;
893:   PetscMPIInt    size,rank;

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

900:   PCGASMDestroySubdomains(osm->n,&osm->iis,&osm->ois);
901:   osm->ois = osm->iis = NULL;

903:   MPI_Comm_size(PetscObjectComm((PetscObject)pc),&size);
904:   MPI_Comm_rank(PetscObjectComm((PetscObject)pc),&rank);
905:   osm->N    = N;
906:   osm->n    = PETSC_DETERMINE;
907:   osm->nmax = PETSC_DETERMINE;
908:   osm->dm_subdomains = PETSC_FALSE;
909:   return(0);
910: }


913: static PetscErrorCode  PCGASMSetSubdomains_GASM(PC pc,PetscInt n,IS iis[],IS ois[])
914: {
915:   PC_GASM         *osm = (PC_GASM*)pc->data;
916:   PetscErrorCode  ierr;
917:   PetscInt        i;

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

923:   PCGASMDestroySubdomains(osm->n,&osm->iis,&osm->ois);
924:   osm->iis  = osm->ois = NULL;
925:   osm->n    = n;
926:   osm->N    = PETSC_DETERMINE;
927:   osm->nmax = PETSC_DETERMINE;
928:   if (ois) {
929:     PetscMalloc1(n,&osm->ois);
930:     for (i=0; i<n; i++) {
931:       PetscObjectReference((PetscObject)ois[i]);
932:       osm->ois[i] = ois[i];
933:     }
934:     /*
935:        Since the user set the outer subdomains, even if nontrivial overlap was requested via PCGASMSetOverlap(),
936:        it will be ignored.  To avoid confusion later on (e.g., when viewing the PC), the overlap size is set to -1.
937:     */
938:     osm->overlap = -1;
939:     /* inner subdomains must be provided  */
940:     if (!iis) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_NULL,"inner indices have to be provided \n");
941:   }/* end if */
942:   if (iis) {
943:     PetscMalloc1(n,&osm->iis);
944:     for (i=0; i<n; i++) {
945:       PetscObjectReference((PetscObject)iis[i]);
946:       osm->iis[i] = iis[i];
947:     }
948:     if (!ois) {
949:       osm->ois = NULL;
950:       /* if user does not provide outer indices, we will create the corresponding outer indices using  osm->overlap =1 in PCSetUp_GASM */
951:     }
952:   }
953: #if defined(PETSC_USE_DEBUG)
954:   {
955:     PetscInt        j,rstart,rend,*covered,lsize;
956:     const PetscInt  *indices;
957:     /* check if the inner indices cover and only cover the local portion of the preconditioning matrix */
958:     MatGetOwnershipRange(pc->pmat,&rstart,&rend);
959:     PetscCalloc1(rend-rstart,&covered);
960:     /* check if the current processor owns indices from others */
961:     for (i=0; i<n; i++) {
962:       ISGetIndices(osm->iis[i],&indices);
963:       ISGetLocalSize(osm->iis[i],&lsize);
964:       for (j=0; j<lsize; j++) {
965:         if (indices[j]<rstart || indices[j]>=rend) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"inner subdomains can not own an index %d from other processors", indices[j]);
966:         else if (covered[indices[j]-rstart]==1) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"inner subdomains can not have an overlapping index %d ",indices[j]);
967:         else covered[indices[j]-rstart] = 1;
968:       }
969:     ISRestoreIndices(osm->iis[i],&indices);
970:     }
971:     /* check if we miss any indices */
972:     for (i=rstart; i<rend; i++) {
973:       if (!covered[i-rstart]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_NULL,"local entity %d was not covered by inner subdomains",i);
974:     }
975:     PetscFree(covered);
976:   }
977: #endif
978:   if (iis)  osm->user_subdomains = PETSC_TRUE;
979:   return(0);
980: }


983: static PetscErrorCode  PCGASMSetOverlap_GASM(PC pc,PetscInt ovl)
984: {
985:   PC_GASM *osm = (PC_GASM*)pc->data;

988:   if (ovl < 0) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_OUTOFRANGE,"Negative overlap value requested");
989:   if (pc->setupcalled && ovl != osm->overlap) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONGSTATE,"PCGASMSetOverlap() should be called before PCSetUp().");
990:   if (!pc->setupcalled) osm->overlap = ovl;
991:   return(0);
992: }

994: static PetscErrorCode  PCGASMSetType_GASM(PC pc,PCGASMType type)
995: {
996:   PC_GASM *osm = (PC_GASM*)pc->data;

999:   osm->type     = type;
1000:   osm->type_set = PETSC_TRUE;
1001:   return(0);
1002: }

1004: static PetscErrorCode  PCGASMSetSortIndices_GASM(PC pc,PetscBool doSort)
1005: {
1006:   PC_GASM *osm = (PC_GASM*)pc->data;

1009:   osm->sort_indices = doSort;
1010:   return(0);
1011: }

1013: /*
1014:    FIXME: This routine might need to be modified now that multiple ranks per subdomain are allowed.
1015:         In particular, it would upset the global subdomain number calculation.
1016: */
1017: static PetscErrorCode  PCGASMGetSubKSP_GASM(PC pc,PetscInt *n,PetscInt *first,KSP **ksp)
1018: {
1019:   PC_GASM        *osm = (PC_GASM*)pc->data;

1023:   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");

1025:   if (n) *n = osm->n;
1026:   if (first) {
1027:     MPI_Scan(&osm->n,first,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)pc));
1028:     *first -= osm->n;
1029:   }
1030:   if (ksp) {
1031:     /* Assume that local solves are now different; not necessarily
1032:        true, though!  This flag is used only for PCView_GASM() */
1033:     *ksp                        = osm->ksp;
1034:     osm->same_subdomain_solvers = PETSC_FALSE;
1035:   }
1036:   return(0);
1037: } /* PCGASMGetSubKSP_GASM() */

1039: /*@C
1040:     PCGASMSetSubdomains - Sets the subdomains for this processor
1041:     for the additive Schwarz preconditioner.

1043:     Collective on pc

1045:     Input Parameters:
1046: +   pc  - the preconditioner object
1047: .   n   - the number of subdomains for this processor
1048: .   iis - the index sets that define the inner subdomains (or NULL for PETSc to determine subdomains)
1049: -   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)

1051:     Notes:
1052:     The IS indices use the parallel, global numbering of the vector entries.
1053:     Inner subdomains are those where the correction is applied.
1054:     Outer subdomains are those where the residual necessary to obtain the
1055:     corrections is obtained (see PCGASMType for the use of inner/outer subdomains).
1056:     Both inner and outer subdomains can extend over several processors.
1057:     This processor's portion of a subdomain is known as a local subdomain.

1059:     Inner subdomains can not overlap with each other, do not have any entities from remote processors,
1060:     and  have to cover the entire local subdomain owned by the current processor. The index sets on each
1061:     process should be ordered such that the ith local subdomain is connected to the ith remote subdomain
1062:     on another MPI process.

1064:     By default the GASM preconditioner uses 1 (local) subdomain per processor.


1067:     Level: advanced

1069: .seealso: PCGASMSetNumSubdomains(), PCGASMSetOverlap(), PCGASMGetSubKSP(),
1070:           PCGASMCreateSubdomains2D(), PCGASMGetSubdomains()
1071: @*/
1072: PetscErrorCode  PCGASMSetSubdomains(PC pc,PetscInt n,IS iis[],IS ois[])
1073: {
1074:   PC_GASM *osm = (PC_GASM*)pc->data;

1079:   PetscTryMethod(pc,"PCGASMSetSubdomains_C",(PC,PetscInt,IS[],IS[]),(pc,n,iis,ois));
1080:   osm->dm_subdomains = PETSC_FALSE;
1081:   return(0);
1082: }


1085: /*@
1086:     PCGASMSetOverlap - Sets the overlap between a pair of subdomains for the
1087:     additive Schwarz preconditioner.  Either all or no processors in the
1088:     pc communicator must call this routine.

1090:     Logically Collective on pc

1092:     Input Parameters:
1093: +   pc  - the preconditioner context
1094: -   ovl - the amount of overlap between subdomains (ovl >= 0, default value = 0)

1096:     Options Database Key:
1097: .   -pc_gasm_overlap <overlap> - Sets overlap

1099:     Notes:
1100:     By default the GASM preconditioner uses 1 subdomain per processor.  To use
1101:     multiple subdomain per perocessor or "straddling" subdomains that intersect
1102:     multiple processors use PCGASMSetSubdomains() (or option -pc_gasm_total_subdomains <n>).

1104:     The overlap defaults to 0, so if one desires that no additional
1105:     overlap be computed beyond what may have been set with a call to
1106:     PCGASMSetSubdomains(), then ovl must be set to be 0.  In particular, if one does
1107:     not explicitly set the subdomains in application code, then all overlap would be computed
1108:     internally by PETSc, and using an overlap of 0 would result in an GASM
1109:     variant that is equivalent to the block Jacobi preconditioner.

1111:     Note that one can define initial index sets with any overlap via
1112:     PCGASMSetSubdomains(); the routine PCGASMSetOverlap() merely allows
1113:     PETSc to extend that overlap further, if desired.

1115:     Level: intermediate

1117: .seealso: PCGASMSetSubdomains(), PCGASMGetSubKSP(),
1118:           PCGASMCreateSubdomains2D(), PCGASMGetSubdomains()
1119: @*/
1120: PetscErrorCode  PCGASMSetOverlap(PC pc,PetscInt ovl)
1121: {
1123:   PC_GASM *osm = (PC_GASM*)pc->data;

1128:   PetscTryMethod(pc,"PCGASMSetOverlap_C",(PC,PetscInt),(pc,ovl));
1129:   osm->dm_subdomains = PETSC_FALSE;
1130:   return(0);
1131: }

1133: /*@
1134:     PCGASMSetType - Sets the type of restriction and interpolation used
1135:     for local problems in the additive Schwarz method.

1137:     Logically Collective on PC

1139:     Input Parameters:
1140: +   pc  - the preconditioner context
1141: -   type - variant of GASM, one of
1142: .vb
1143:       PC_GASM_BASIC       - full interpolation and restriction
1144:       PC_GASM_RESTRICT    - full restriction, local processor interpolation
1145:       PC_GASM_INTERPOLATE - full interpolation, local processor restriction
1146:       PC_GASM_NONE        - local processor restriction and interpolation
1147: .ve

1149:     Options Database Key:
1150: .   -pc_gasm_type [basic,restrict,interpolate,none] - Sets GASM type

1152:     Level: intermediate

1154: .seealso: PCGASMSetSubdomains(), PCGASMGetSubKSP(),
1155:           PCGASMCreateSubdomains2D()
1156: @*/
1157: PetscErrorCode  PCGASMSetType(PC pc,PCGASMType type)
1158: {

1164:   PetscTryMethod(pc,"PCGASMSetType_C",(PC,PCGASMType),(pc,type));
1165:   return(0);
1166: }

1168: /*@
1169:     PCGASMSetSortIndices - Determines whether subdomain indices are sorted.

1171:     Logically Collective on PC

1173:     Input Parameters:
1174: +   pc  - the preconditioner context
1175: -   doSort - sort the subdomain indices

1177:     Level: intermediate

1179: .seealso: PCGASMSetSubdomains(), PCGASMGetSubKSP(),
1180:           PCGASMCreateSubdomains2D()
1181: @*/
1182: PetscErrorCode  PCGASMSetSortIndices(PC pc,PetscBool doSort)
1183: {

1189:   PetscTryMethod(pc,"PCGASMSetSortIndices_C",(PC,PetscBool),(pc,doSort));
1190:   return(0);
1191: }

1193: /*@C
1194:    PCGASMGetSubKSP - Gets the local KSP contexts for all blocks on
1195:    this processor.

1197:    Collective on PC iff first_local is requested

1199:    Input Parameter:
1200: .  pc - the preconditioner context

1202:    Output Parameters:
1203: +  n_local - the number of blocks on this processor or NULL
1204: .  first_local - the global number of the first block on this processor or NULL,
1205:                  all processors must request or all must pass NULL
1206: -  ksp - the array of KSP contexts

1208:    Note:
1209:    After PCGASMGetSubKSP() the array of KSPes is not to be freed

1211:    Currently for some matrix implementations only 1 block per processor
1212:    is supported.

1214:    You must call KSPSetUp() before calling PCGASMGetSubKSP().

1216:    Level: advanced

1218: .seealso: PCGASMSetSubdomains(), PCGASMSetOverlap(),
1219:           PCGASMCreateSubdomains2D(),
1220: @*/
1221: PetscErrorCode  PCGASMGetSubKSP(PC pc,PetscInt *n_local,PetscInt *first_local,KSP *ksp[])
1222: {

1227:   PetscUseMethod(pc,"PCGASMGetSubKSP_C",(PC,PetscInt*,PetscInt*,KSP **),(pc,n_local,first_local,ksp));
1228:   return(0);
1229: }

1231: /* -------------------------------------------------------------------------------------*/
1232: /*MC
1233:    PCGASM - Use the (restricted) additive Schwarz method, each block is (approximately) solved with
1234:            its own KSP object.

1236:    Options Database Keys:
1237: +  -pc_gasm_total_subdomains <n>  - Sets total number of local subdomains to be distributed among processors
1238: .  -pc_gasm_view_subdomains       - activates the printing of subdomain indices in PCView(), -ksp_view or -snes_view
1239: .  -pc_gasm_print_subdomains      - activates the printing of subdomain indices in PCSetUp()
1240: .  -pc_gasm_overlap <ovl>         - Sets overlap by which to (automatically) extend local subdomains
1241: -  -pc_gasm_type [basic,restrict,interpolate,none] - Sets GASM type

1243:      IMPORTANT: If you run with, for example, 3 blocks on 1 processor or 3 blocks on 3 processors you
1244:       will get a different convergence rate due to the default option of -pc_gasm_type restrict. Use
1245:       -pc_gasm_type basic to use the standard GASM.

1247:    Notes:
1248:     Blocks can be shared by multiple processes.

1250:      To set options on the solvers for each block append -sub_ to all the KSP, and PC
1251:         options database keys. For example, -sub_pc_type ilu -sub_pc_factor_levels 1 -sub_ksp_type preonly

1253:      To set the options on the solvers separate for each block call PCGASMGetSubKSP()
1254:          and set the options directly on the resulting KSP object (you can access its PC
1255:          with KSPGetPC())


1258:    Level: beginner

1260:     References:
1261: +   1. - M Dryja, OB Widlund, An additive variant of the Schwarz alternating method for the case of many subregions
1262:      Courant Institute, New York University Technical report
1263: -   2. - Barry Smith, Petter Bjorstad, and William Gropp, Domain Decompositions: Parallel Multilevel Methods for Elliptic Partial Differential Equations,
1264:     Cambridge University Press.

1266: .seealso:  PCCreate(), PCSetType(), PCType (for list of available types), PC,
1267:            PCBJACOBI,  PCGASMGetSubKSP(), PCGASMSetSubdomains(),
1268:            PCSetModifySubmatrices(), PCGASMSetOverlap(), PCGASMSetType()

1270: M*/

1272: PETSC_EXTERN PetscErrorCode PCCreate_GASM(PC pc)
1273: {
1275:   PC_GASM        *osm;

1278:   PetscNewLog(pc,&osm);

1280:   osm->N                        = PETSC_DETERMINE;
1281:   osm->n                        = PETSC_DECIDE;
1282:   osm->nmax                     = PETSC_DETERMINE;
1283:   osm->overlap                  = 0;
1284:   osm->ksp                      = 0;
1285:   osm->gorestriction            = 0;
1286:   osm->girestriction            = 0;
1287:   osm->pctoouter                = 0;
1288:   osm->gx                       = 0;
1289:   osm->gy                       = 0;
1290:   osm->x                        = 0;
1291:   osm->y                        = 0;
1292:   osm->pcx                      = 0;
1293:   osm->pcy                      = 0;
1294:   osm->permutationIS            = 0;
1295:   osm->permutationP             = 0;
1296:   osm->pcmat                    = 0;
1297:   osm->ois                      = 0;
1298:   osm->iis                      = 0;
1299:   osm->pmat                     = 0;
1300:   osm->type                     = PC_GASM_RESTRICT;
1301:   osm->same_subdomain_solvers   = PETSC_TRUE;
1302:   osm->sort_indices             = PETSC_TRUE;
1303:   osm->dm_subdomains            = PETSC_FALSE;
1304:   osm->hierarchicalpartitioning = PETSC_FALSE;

1306:   pc->data                 = (void*)osm;
1307:   pc->ops->apply           = PCApply_GASM;
1308:   pc->ops->applytranspose  = PCApplyTranspose_GASM;
1309:   pc->ops->setup           = PCSetUp_GASM;
1310:   pc->ops->reset           = PCReset_GASM;
1311:   pc->ops->destroy         = PCDestroy_GASM;
1312:   pc->ops->setfromoptions  = PCSetFromOptions_GASM;
1313:   pc->ops->setuponblocks   = PCSetUpOnBlocks_GASM;
1314:   pc->ops->view            = PCView_GASM;
1315:   pc->ops->applyrichardson = 0;

1317:   PetscObjectComposeFunction((PetscObject)pc,"PCGASMSetSubdomains_C",PCGASMSetSubdomains_GASM);
1318:   PetscObjectComposeFunction((PetscObject)pc,"PCGASMSetOverlap_C",PCGASMSetOverlap_GASM);
1319:   PetscObjectComposeFunction((PetscObject)pc,"PCGASMSetType_C",PCGASMSetType_GASM);
1320:   PetscObjectComposeFunction((PetscObject)pc,"PCGASMSetSortIndices_C",PCGASMSetSortIndices_GASM);
1321:   PetscObjectComposeFunction((PetscObject)pc,"PCGASMGetSubKSP_C",PCGASMGetSubKSP_GASM);
1322:   return(0);
1323: }


1326: PetscErrorCode  PCGASMCreateLocalSubdomains(Mat A, PetscInt nloc, IS *iis[])
1327: {
1328:   MatPartitioning mpart;
1329:   const char      *prefix;
1330:   PetscInt        i,j,rstart,rend,bs;
1331:   PetscBool       hasop, isbaij = PETSC_FALSE,foundpart = PETSC_FALSE;
1332:   Mat             Ad     = NULL, adj;
1333:   IS              ispart,isnumb,*is;
1334:   PetscErrorCode  ierr;

1337:   if (nloc < 1) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"number of local subdomains must > 0, got nloc = %D",nloc);

1339:   /* Get prefix, row distribution, and block size */
1340:   MatGetOptionsPrefix(A,&prefix);
1341:   MatGetOwnershipRange(A,&rstart,&rend);
1342:   MatGetBlockSize(A,&bs);
1343:   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);

1345:   /* Get diagonal block from matrix if possible */
1346:   MatHasOperation(A,MATOP_GET_DIAGONAL_BLOCK,&hasop);
1347:   if (hasop) {
1348:     MatGetDiagonalBlock(A,&Ad);
1349:   }
1350:   if (Ad) {
1351:     PetscObjectTypeCompare((PetscObject)Ad,MATSEQBAIJ,&isbaij);
1352:     if (!isbaij) {PetscObjectTypeCompare((PetscObject)Ad,MATSEQSBAIJ,&isbaij);}
1353:   }
1354:   if (Ad && nloc > 1) {
1355:     PetscBool  match,done;
1356:     /* Try to setup a good matrix partitioning if available */
1357:     MatPartitioningCreate(PETSC_COMM_SELF,&mpart);
1358:     PetscObjectSetOptionsPrefix((PetscObject)mpart,prefix);
1359:     MatPartitioningSetFromOptions(mpart);
1360:     PetscObjectTypeCompare((PetscObject)mpart,MATPARTITIONINGCURRENT,&match);
1361:     if (!match) {
1362:       PetscObjectTypeCompare((PetscObject)mpart,MATPARTITIONINGSQUARE,&match);
1363:     }
1364:     if (!match) { /* assume a "good" partitioner is available */
1365:       PetscInt       na;
1366:       const PetscInt *ia,*ja;
1367:       MatGetRowIJ(Ad,0,PETSC_TRUE,isbaij,&na,&ia,&ja,&done);
1368:       if (done) {
1369:         /* Build adjacency matrix by hand. Unfortunately a call to
1370:            MatConvert(Ad,MATMPIADJ,MAT_INITIAL_MATRIX,&adj) will
1371:            remove the block-aij structure and we cannot expect
1372:            MatPartitioning to split vertices as we need */
1373:         PetscInt       i,j,len,nnz,cnt,*iia=0,*jja=0;
1374:         const PetscInt *row;
1375:         nnz = 0;
1376:         for (i=0; i<na; i++) { /* count number of nonzeros */
1377:           len = ia[i+1] - ia[i];
1378:           row = ja + ia[i];
1379:           for (j=0; j<len; j++) {
1380:             if (row[j] == i) { /* don't count diagonal */
1381:               len--; break;
1382:             }
1383:           }
1384:           nnz += len;
1385:         }
1386:         PetscMalloc1(na+1,&iia);
1387:         PetscMalloc1(nnz,&jja);
1388:         nnz    = 0;
1389:         iia[0] = 0;
1390:         for (i=0; i<na; i++) { /* fill adjacency */
1391:           cnt = 0;
1392:           len = ia[i+1] - ia[i];
1393:           row = ja + ia[i];
1394:           for (j=0; j<len; j++) {
1395:             if (row[j] != i) jja[nnz+cnt++] = row[j]; /* if not diagonal */
1396:           }
1397:           nnz += cnt;
1398:           iia[i+1] = nnz;
1399:         }
1400:         /* Partitioning of the adjacency matrix */
1401:         MatCreateMPIAdj(PETSC_COMM_SELF,na,na,iia,jja,NULL,&adj);
1402:         MatPartitioningSetAdjacency(mpart,adj);
1403:         MatPartitioningSetNParts(mpart,nloc);
1404:         MatPartitioningApply(mpart,&ispart);
1405:         ISPartitioningToNumbering(ispart,&isnumb);
1406:         MatDestroy(&adj);
1407:         foundpart = PETSC_TRUE;
1408:       }
1409:       MatRestoreRowIJ(Ad,0,PETSC_TRUE,isbaij,&na,&ia,&ja,&done);
1410:     }
1411:     MatPartitioningDestroy(&mpart);
1412:   }
1413:   PetscMalloc1(nloc,&is);
1414:   if (!foundpart) {

1416:     /* Partitioning by contiguous chunks of rows */

1418:     PetscInt mbs   = (rend-rstart)/bs;
1419:     PetscInt start = rstart;
1420:     for (i=0; i<nloc; i++) {
1421:       PetscInt count = (mbs/nloc + ((mbs % nloc) > i)) * bs;
1422:       ISCreateStride(PETSC_COMM_SELF,count,start,1,&is[i]);
1423:       start += count;
1424:     }

1426:   } else {

1428:     /* Partitioning by adjacency of diagonal block  */

1430:     const PetscInt *numbering;
1431:     PetscInt       *count,nidx,*indices,*newidx,start=0;
1432:     /* Get node count in each partition */
1433:     PetscMalloc1(nloc,&count);
1434:     ISPartitioningCount(ispart,nloc,count);
1435:     if (isbaij && bs > 1) { /* adjust for the block-aij case */
1436:       for (i=0; i<nloc; i++) count[i] *= bs;
1437:     }
1438:     /* Build indices from node numbering */
1439:     ISGetLocalSize(isnumb,&nidx);
1440:     PetscMalloc1(nidx,&indices);
1441:     for (i=0; i<nidx; i++) indices[i] = i; /* needs to be initialized */
1442:     ISGetIndices(isnumb,&numbering);
1443:     PetscSortIntWithPermutation(nidx,numbering,indices);
1444:     ISRestoreIndices(isnumb,&numbering);
1445:     if (isbaij && bs > 1) { /* adjust for the block-aij case */
1446:       PetscMalloc1(nidx*bs,&newidx);
1447:       for (i=0; i<nidx; i++) {
1448:         for (j=0; j<bs; j++) newidx[i*bs+j] = indices[i]*bs + j;
1449:       }
1450:       PetscFree(indices);
1451:       nidx   *= bs;
1452:       indices = newidx;
1453:     }
1454:     /* Shift to get global indices */
1455:     for (i=0; i<nidx; i++) indices[i] += rstart;

1457:     /* Build the index sets for each block */
1458:     for (i=0; i<nloc; i++) {
1459:       ISCreateGeneral(PETSC_COMM_SELF,count[i],&indices[start],PETSC_COPY_VALUES,&is[i]);
1460:       ISSort(is[i]);
1461:       start += count[i];
1462:     }

1464:     PetscFree(count);
1465:     PetscFree(indices);
1466:     ISDestroy(&isnumb);
1467:     ISDestroy(&ispart);
1468:   }
1469:   *iis = is;
1470:   return(0);
1471: }

1473: PETSC_INTERN PetscErrorCode  PCGASMCreateStraddlingSubdomains(Mat A,PetscInt N,PetscInt *n,IS *iis[])
1474: {
1475:   PetscErrorCode  ierr;

1478:   MatSubdomainsCreateCoalesce(A,N,n,iis);
1479:   return(0);
1480: }



1484: /*@C
1485:    PCGASMCreateSubdomains - Creates n index sets defining n nonoverlapping subdomains for the additive
1486:    Schwarz preconditioner for a any problem based on its matrix.

1488:    Collective

1490:    Input Parameters:
1491: +  A       - The global matrix operator
1492: -  N       - the number of global subdomains requested

1494:    Output Parameters:
1495: +  n   - the number of subdomains created on this processor
1496: -  iis - the array of index sets defining the local inner subdomains (on which the correction is applied)

1498:    Level: advanced

1500:    Note: When N >= A's communicator size, each subdomain is local -- contained within a single processor.
1501:          When N < size, the subdomains are 'straddling' (processor boundaries) and are no longer local.
1502:          The resulting subdomains can be use in PCGASMSetSubdomains(pc,n,iss,NULL).  The overlapping
1503:          outer subdomains will be automatically generated from these according to the requested amount of
1504:          overlap; this is currently supported only with local subdomains.


1507: .seealso: PCGASMSetSubdomains(), PCGASMDestroySubdomains()
1508: @*/
1509: PetscErrorCode  PCGASMCreateSubdomains(Mat A,PetscInt N,PetscInt *n,IS *iis[])
1510: {
1511:   PetscMPIInt     size;
1512:   PetscErrorCode  ierr;


1518:   if (N < 1) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Number of subdomains must be > 0, N = %D",N);
1519:   MPI_Comm_size(PetscObjectComm((PetscObject)A),&size);
1520:   if (N >= size) {
1521:     *n = N/size + (N%size);
1522:     PCGASMCreateLocalSubdomains(A,*n,iis);
1523:   } else {
1524:     PCGASMCreateStraddlingSubdomains(A,N,n,iis);
1525:   }
1526:   return(0);
1527: }

1529: /*@C
1530:    PCGASMDestroySubdomains - Destroys the index sets created with
1531:    PCGASMCreateSubdomains() or PCGASMCreateSubdomains2D. Should be
1532:    called after setting subdomains with PCGASMSetSubdomains().

1534:    Collective

1536:    Input Parameters:
1537: +  n   - the number of index sets
1538: .  iis - the array of inner subdomains,
1539: -  ois - the array of outer subdomains, can be NULL

1541:    Level: intermediate

1543:    Notes:
1544:     this is merely a convenience subroutine that walks each list,
1545:    destroys each IS on the list, and then frees the list. At the end the
1546:    list pointers are set to NULL.

1548: .seealso: PCGASMCreateSubdomains(), PCGASMSetSubdomains()
1549: @*/
1550: PetscErrorCode  PCGASMDestroySubdomains(PetscInt n,IS **iis,IS **ois)
1551: {
1552:   PetscInt       i;

1556:   if (n <= 0) return(0);
1557:   if (ois) {
1559:     if (*ois) {
1561:       for (i=0; i<n; i++) {
1562:         ISDestroy(&(*ois)[i]);
1563:       }
1564:       PetscFree((*ois));
1565:     }
1566:   }
1567:   if (iis) {
1569:     if (*iis) {
1571:       for (i=0; i<n; i++) {
1572:         ISDestroy(&(*iis)[i]);
1573:       }
1574:       PetscFree((*iis));
1575:     }
1576:   }
1577:   return(0);
1578: }


1581: #define PCGASMLocalSubdomainBounds2D(M,N,xleft,ylow,xright,yhigh,first,last,xleft_loc,ylow_loc,xright_loc,yhigh_loc,n) \
1582:   {                                                                                                       \
1583:     PetscInt first_row = first/M, last_row = last/M+1;                                                     \
1584:     /*                                                                                                    \
1585:      Compute ylow_loc and yhigh_loc so that (ylow_loc,xleft) and (yhigh_loc,xright) are the corners       \
1586:      of the bounding box of the intersection of the subdomain with the local ownership range (local       \
1587:      subdomain).                                                                                          \
1588:      Also compute xleft_loc and xright_loc as the lower and upper bounds on the first and last rows       \
1589:      of the intersection.                                                                                 \
1590:     */                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             \
1591:     /* ylow_loc is the grid row containing the first element of the local sumbdomain */                   \
1592:     *ylow_loc = PetscMax(first_row,ylow);                                                                    \
1593:     /* xleft_loc is the offset of first element of the local subdomain within its grid row (might actually be outside the local subdomain) */ \
1594:     *xleft_loc = *ylow_loc==first_row ? PetscMax(first%M,xleft) : xleft;                                                                            \
1595:     /* yhigh_loc is the grid row above the last local subdomain element */                                                                    \
1596:     *yhigh_loc = PetscMin(last_row,yhigh);                                                                                                     \
1597:     /* xright is the offset of the end of the  local subdomain within its grid row (might actually be outside the local subdomain) */         \
1598:     *xright_loc = *yhigh_loc==last_row ? PetscMin(xright,last%M) : xright;                                                                          \
1599:     /* Now compute the size of the local subdomain n. */ \
1600:     *n = 0;                                               \
1601:     if (*ylow_loc < *yhigh_loc) {                           \
1602:       PetscInt width = xright-xleft;                     \
1603:       *n += width*(*yhigh_loc-*ylow_loc-1);                 \
1604:       *n += PetscMin(PetscMax(*xright_loc-xleft,0),width); \
1605:       *n -= PetscMin(PetscMax(*xleft_loc-xleft,0), width); \
1606:     } \
1607:   }



1611: /*@
1612:    PCGASMCreateSubdomains2D - Creates the index sets for the overlapping Schwarz
1613:    preconditioner for a two-dimensional problem on a regular grid.

1615:    Collective

1617:    Input Parameters:
1618: +  M, N               - the global number of grid points in the x and y directions
1619: .  Mdomains, Ndomains - the global number of subdomains in the x and y directions
1620: .  dof                - degrees of freedom per node
1621: -  overlap            - overlap in mesh lines

1623:    Output Parameters:
1624: +  Nsub - the number of local subdomains created
1625: .  iis  - array of index sets defining inner (nonoverlapping) subdomains
1626: -  ois  - array of index sets defining outer (overlapping, if overlap > 0) subdomains


1629:    Level: advanced

1631: .seealso: PCGASMSetSubdomains(), PCGASMGetSubKSP(), PCGASMSetOverlap()
1632: @*/
1633: PetscErrorCode  PCGASMCreateSubdomains2D(PC pc,PetscInt M,PetscInt N,PetscInt Mdomains,PetscInt Ndomains,PetscInt dof,PetscInt overlap,PetscInt *nsub,IS **iis,IS **ois)
1634: {
1636:   PetscMPIInt    size, rank;
1637:   PetscInt       i, j;
1638:   PetscInt       maxheight, maxwidth;
1639:   PetscInt       xstart, xleft, xright, xleft_loc, xright_loc;
1640:   PetscInt       ystart, ylow,  yhigh,  ylow_loc,  yhigh_loc;
1641:   PetscInt       x[2][2], y[2][2], n[2];
1642:   PetscInt       first, last;
1643:   PetscInt       nidx, *idx;
1644:   PetscInt       ii,jj,s,q,d;
1645:   PetscInt       k,kk;
1646:   PetscMPIInt    color;
1647:   MPI_Comm       comm, subcomm;
1648:   IS             **xis = 0, **is = ois, **is_local = iis;

1651:   PetscObjectGetComm((PetscObject)pc, &comm);
1652:   MPI_Comm_size(comm, &size);
1653:   MPI_Comm_rank(comm, &rank);
1654:   MatGetOwnershipRange(pc->pmat, &first, &last);
1655:   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) "
1656:                                       "does not respect the number of degrees of freedom per grid point %D", first, last, dof);

1658:   /* Determine the number of domains with nonzero intersections with the local ownership range. */
1659:   s      = 0;
1660:   ystart = 0;
1661:   for (j=0; j<Ndomains; ++j) {
1662:     maxheight = N/Ndomains + ((N % Ndomains) > j); /* Maximal height of subdomain */
1663:     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);
1664:     /* Vertical domain limits with an overlap. */
1665:     ylow   = PetscMax(ystart - overlap,0);
1666:     yhigh  = PetscMin(ystart + maxheight + overlap,N);
1667:     xstart = 0;
1668:     for (i=0; i<Mdomains; ++i) {
1669:       maxwidth = M/Mdomains + ((M % Mdomains) > i); /* Maximal width of subdomain */
1670:       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);
1671:       /* Horizontal domain limits with an overlap. */
1672:       xleft  = PetscMax(xstart - overlap,0);
1673:       xright = PetscMin(xstart + maxwidth + overlap,M);
1674:       /*
1675:          Determine whether this subdomain intersects this processor's ownership range of pc->pmat.
1676:       */
1677:       PCGASMLocalSubdomainBounds2D(M,N,xleft,ylow,xright,yhigh,first,last,(&xleft_loc),(&ylow_loc),(&xright_loc),(&yhigh_loc),(&nidx));
1678:       if (nidx) ++s;
1679:       xstart += maxwidth;
1680:     } /* for (i = 0; i < Mdomains; ++i) */
1681:     ystart += maxheight;
1682:   } /* for (j = 0; j < Ndomains; ++j) */

1684:   /* Now we can allocate the necessary number of ISs. */
1685:   *nsub  = s;
1686:   PetscMalloc1(*nsub,is);
1687:   PetscMalloc1(*nsub,is_local);
1688:   s      = 0;
1689:   ystart = 0;
1690:   for (j=0; j<Ndomains; ++j) {
1691:     maxheight = N/Ndomains + ((N % Ndomains) > j); /* Maximal height of subdomain */
1692:     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);
1693:     /* Vertical domain limits with an overlap. */
1694:     y[0][0] = PetscMax(ystart - overlap,0);
1695:     y[0][1] = PetscMin(ystart + maxheight + overlap,N);
1696:     /* Vertical domain limits without an overlap. */
1697:     y[1][0] = ystart;
1698:     y[1][1] = PetscMin(ystart + maxheight,N);
1699:     xstart  = 0;
1700:     for (i=0; i<Mdomains; ++i) {
1701:       maxwidth = M/Mdomains + ((M % Mdomains) > i); /* Maximal width of subdomain */
1702:       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);
1703:       /* Horizontal domain limits with an overlap. */
1704:       x[0][0] = PetscMax(xstart - overlap,0);
1705:       x[0][1] = PetscMin(xstart + maxwidth + overlap,M);
1706:       /* Horizontal domain limits without an overlap. */
1707:       x[1][0] = xstart;
1708:       x[1][1] = PetscMin(xstart+maxwidth,M);
1709:       /*
1710:          Determine whether this domain intersects this processor's ownership range of pc->pmat.
1711:          Do this twice: first for the domains with overlaps, and once without.
1712:          During the first pass create the subcommunicators, and use them on the second pass as well.
1713:       */
1714:       for (q = 0; q < 2; ++q) {
1715:         PetscBool split = PETSC_FALSE;
1716:         /*
1717:           domain limits, (xleft, xright) and (ylow, yheigh) are adjusted
1718:           according to whether the domain with an overlap or without is considered.
1719:         */
1720:         xleft = x[q][0]; xright = x[q][1];
1721:         ylow  = y[q][0]; yhigh  = y[q][1];
1722:         PCGASMLocalSubdomainBounds2D(M,N,xleft,ylow,xright,yhigh,first,last,(&xleft_loc),(&ylow_loc),(&xright_loc),(&yhigh_loc),(&nidx));
1723:         nidx *= dof;
1724:         n[q]  = nidx;
1725:         /*
1726:          Based on the counted number of indices in the local domain *with an overlap*,
1727:          construct a subcommunicator of all the processors supporting this domain.
1728:          Observe that a domain with an overlap might have nontrivial local support,
1729:          while the domain without an overlap might not.  Hence, the decision to participate
1730:          in the subcommunicator must be based on the domain with an overlap.
1731:          */
1732:         if (q == 0) {
1733:           if (nidx) color = 1;
1734:           else color = MPI_UNDEFINED;
1735:           MPI_Comm_split(comm, color, rank, &subcomm);
1736:           split = PETSC_TRUE;
1737:         }
1738:         /*
1739:          Proceed only if the number of local indices *with an overlap* is nonzero.
1740:          */
1741:         if (n[0]) {
1742:           if (q == 0) xis = is;
1743:           if (q == 1) {
1744:             /*
1745:              The IS for the no-overlap subdomain shares a communicator with the overlapping domain.
1746:              Moreover, if the overlap is zero, the two ISs are identical.
1747:              */
1748:             if (overlap == 0) {
1749:               (*is_local)[s] = (*is)[s];
1750:               PetscObjectReference((PetscObject)(*is)[s]);
1751:               continue;
1752:             } else {
1753:               xis     = is_local;
1754:               subcomm = ((PetscObject)(*is)[s])->comm;
1755:             }
1756:           } /* if (q == 1) */
1757:           idx  = NULL;
1758:           PetscMalloc1(nidx,&idx);
1759:           if (nidx) {
1760:             k = 0;
1761:             for (jj=ylow_loc; jj<yhigh_loc; ++jj) {
1762:               PetscInt x0 = (jj==ylow_loc) ? xleft_loc : xleft;
1763:               PetscInt x1 = (jj==yhigh_loc-1) ? xright_loc : xright;
1764:               kk = dof*(M*jj + x0);
1765:               for (ii=x0; ii<x1; ++ii) {
1766:                 for (d = 0; d < dof; ++d) {
1767:                   idx[k++] = kk++;
1768:                 }
1769:               }
1770:             }
1771:           }
1772:           ISCreateGeneral(subcomm,nidx,idx,PETSC_OWN_POINTER,(*xis)+s);
1773:           if (split) {
1774:             MPI_Comm_free(&subcomm);
1775:           }
1776:         }/* if (n[0]) */
1777:       }/* for (q = 0; q < 2; ++q) */
1778:       if (n[0]) ++s;
1779:       xstart += maxwidth;
1780:     } /* for (i = 0; i < Mdomains; ++i) */
1781:     ystart += maxheight;
1782:   } /* for (j = 0; j < Ndomains; ++j) */
1783:   return(0);
1784: }

1786: /*@C
1787:     PCGASMGetSubdomains - Gets the subdomains supported on this processor
1788:     for the additive Schwarz preconditioner.

1790:     Not Collective

1792:     Input Parameter:
1793: .   pc - the preconditioner context

1795:     Output Parameters:
1796: +   n   - the number of subdomains for this processor (default value = 1)
1797: .   iis - the index sets that define the inner subdomains (without overlap) supported on this processor (can be NULL)
1798: -   ois - the index sets that define the outer subdomains (with overlap) supported on this processor (can be NULL)


1801:     Notes:
1802:     The user is responsible for destroying the ISs and freeing the returned arrays.
1803:     The IS numbering is in the parallel, global numbering of the vector.

1805:     Level: advanced

1807: .seealso: PCGASMSetOverlap(), PCGASMGetSubKSP(), PCGASMCreateSubdomains2D(),
1808:           PCGASMSetSubdomains(), PCGASMGetSubmatrices()
1809: @*/
1810: PetscErrorCode  PCGASMGetSubdomains(PC pc,PetscInt *n,IS *iis[],IS *ois[])
1811: {
1812:   PC_GASM        *osm;
1814:   PetscBool      match;
1815:   PetscInt       i;

1819:   PetscObjectTypeCompare((PetscObject)pc,PCGASM,&match);
1820:   if (!match) SETERRQ2(PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "Incorrect object type: expected %s, got %s instead", PCGASM, ((PetscObject)pc)->type_name);
1821:   osm = (PC_GASM*)pc->data;
1822:   if (n) *n = osm->n;
1823:   if (iis) {
1824:     PetscMalloc1(osm->n, iis);
1825:   }
1826:   if (ois) {
1827:     PetscMalloc1(osm->n, ois);
1828:   }
1829:   if (iis || ois) {
1830:     for (i = 0; i < osm->n; ++i) {
1831:       if (iis) (*iis)[i] = osm->iis[i];
1832:       if (ois) (*ois)[i] = osm->ois[i];
1833:     }
1834:   }
1835:   return(0);
1836: }

1838: /*@C
1839:     PCGASMGetSubmatrices - Gets the local submatrices (for this processor
1840:     only) for the additive Schwarz preconditioner.

1842:     Not Collective

1844:     Input Parameter:
1845: .   pc - the preconditioner context

1847:     Output Parameters:
1848: +   n   - the number of matrices for this processor (default value = 1)
1849: -   mat - the matrices

1851:     Notes:
1852:     matrices returned by this routine have the same communicators as the index sets (IS)
1853:            used to define subdomains in PCGASMSetSubdomains()
1854:     Level: advanced

1856: .seealso: PCGASMSetOverlap(), PCGASMGetSubKSP(),
1857:           PCGASMCreateSubdomains2D(), PCGASMSetSubdomains(), PCGASMGetSubdomains()
1858: @*/
1859: PetscErrorCode  PCGASMGetSubmatrices(PC pc,PetscInt *n,Mat *mat[])
1860: {
1861:   PC_GASM        *osm;
1863:   PetscBool      match;

1869:   if (!pc->setupcalled) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONGSTATE,"Must call after KSPSetUP() or PCSetUp().");
1870:   PetscObjectTypeCompare((PetscObject)pc,PCGASM,&match);
1871:   if (!match) SETERRQ2(PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "Expected %s, got %s instead", PCGASM, ((PetscObject)pc)->type_name);
1872:   osm = (PC_GASM*)pc->data;
1873:   if (n) *n = osm->n;
1874:   if (mat) *mat = osm->pmat;
1875:   return(0);
1876: }

1878: /*@
1879:     PCGASMSetUseDMSubdomains - Indicates whether to use DMCreateDomainDecomposition() to define the subdomains, whenever possible.
1880:     Logically Collective

1882:     Input Parameter:
1883: +   pc  - the preconditioner
1884: -   flg - boolean indicating whether to use subdomains defined by the DM

1886:     Options Database Key:
1887: .   -pc_gasm_dm_subdomains -pc_gasm_overlap -pc_gasm_total_subdomains

1889:     Level: intermediate

1891:     Notes:
1892:     PCGASMSetSubdomains(), PCGASMSetTotalSubdomains() or PCGASMSetOverlap() take precedence over PCGASMSetUseDMSubdomains(),
1893:     so setting PCGASMSetSubdomains() with nontrivial subdomain ISs or any of PCGASMSetTotalSubdomains() and PCGASMSetOverlap()
1894:     automatically turns the latter off.

1896: .seealso: PCGASMGetUseDMSubdomains(), PCGASMSetSubdomains(), PCGASMSetOverlap()
1897:           PCGASMCreateSubdomains2D()
1898: @*/
1899: PetscErrorCode  PCGASMSetUseDMSubdomains(PC pc,PetscBool flg)
1900: {
1901:   PC_GASM        *osm = (PC_GASM*)pc->data;
1903:   PetscBool      match;

1908:   if (pc->setupcalled) SETERRQ(((PetscObject)pc)->comm,PETSC_ERR_ARG_WRONGSTATE,"Not for a setup PC.");
1909:   PetscObjectTypeCompare((PetscObject)pc,PCGASM,&match);
1910:   if (match) {
1911:     if (!osm->user_subdomains && osm->N == PETSC_DETERMINE && osm->overlap < 0) {
1912:       osm->dm_subdomains = flg;
1913:     }
1914:   }
1915:   return(0);
1916: }

1918: /*@
1919:     PCGASMGetUseDMSubdomains - Returns flag indicating whether to use DMCreateDomainDecomposition() to define the subdomains, whenever possible.
1920:     Not Collective

1922:     Input Parameter:
1923: .   pc  - the preconditioner

1925:     Output Parameter:
1926: .   flg - boolean indicating whether to use subdomains defined by the DM

1928:     Level: intermediate

1930: .seealso: PCGASMSetUseDMSubdomains(), PCGASMSetOverlap()
1931:           PCGASMCreateSubdomains2D()
1932: @*/
1933: PetscErrorCode  PCGASMGetUseDMSubdomains(PC pc,PetscBool* flg)
1934: {
1935:   PC_GASM        *osm = (PC_GASM*)pc->data;
1937:   PetscBool      match;

1942:   PetscObjectTypeCompare((PetscObject)pc,PCGASM,&match);
1943:   if (match) {
1944:     if (flg) *flg = osm->dm_subdomains;
1945:   }
1946:   return(0);
1947: }