Actual source code: gasm.c

petsc-master 2020-11-24
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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,sizeof(fname),&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: }

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

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

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

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

198:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
199:   if (iascii) {
200:     /*
201:      Make sure the viewer has a name. Otherwise this may cause a deadlock when creating a subcomm viewer:
202:      the subcomm viewer will attempt to inherit the viewer's name, which, if not set, will be constructed
203:      collectively on the comm.
204:      */
205:     PetscObjectName((PetscObject)viewer);
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:     PetscViewerASCIIPushSynchronized(viewer);
211:     PetscViewerASCIISynchronizedPrintf(viewer,"  [%d|%d] number of locally-supported subdomains = %D\n",rank,size,osm->n);
212:     PetscViewerFlush(viewer);
213:     PetscViewerASCIIPopSynchronized(viewer);
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:           PetscViewerGetSubViewer(viewer,((PetscObject)osm->ois[d])->comm, &sviewer);
231:           ISGetLocalSize(osm->ois[d],&bsz);
232:           PetscViewerASCIISynchronizedPrintf(sviewer,"  [%d|%d] (subcomm [%d|%d]) local subdomain number %D, local size = %D\n",rank,size,srank,ssize,d,bsz);
233:           PetscViewerFlush(sviewer);
234:           if (view_subdomains) {
235:             PCGASMSubdomainView_Private(pc,d,sviewer);
236:           }
237:           if (!pc->setupcalled) {
238:             PetscViewerASCIIPrintf(sviewer, "  Solver not set up yet: PCSetUp() not yet called\n");
239:           } else {
240:             KSPView(osm->ksp[d],sviewer);
241:           }
242:           PetscViewerASCIIPrintf(sviewer,"  - - - - - - - - - - - - - - - - - -\n");
243:           PetscViewerFlush(sviewer);
244:           PetscViewerRestoreSubViewer(viewer,((PetscObject)osm->ois[d])->comm, &sviewer);
245:           ++l;
246:         }
247:       }
248:       MPI_Barrier(PetscObjectComm((PetscObject)pc));
249:     }
250:     PetscFree2(numbering,permutation);
251:     PetscViewerASCIIPopTab(viewer);
252:   }
253:   PetscViewerFlush(viewer);
254:   PetscViewerASCIIPopSynchronized(viewer);
255:   return(0);
256: }

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

260: PetscErrorCode PCGASMSetHierarchicalPartitioning(PC pc)
261: {
262:    PC_GASM              *osm = (PC_GASM*)pc->data;
263:    MatPartitioning       part;
264:    MPI_Comm              comm;
265:    PetscMPIInt           size;
266:    PetscInt              nlocalsubdomains,fromrows_localsize;
267:    IS                    partitioning,fromrows,isn;
268:    Vec                   outervec;
269:    PetscErrorCode        ierr;

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

313: static PetscErrorCode PCSetUp_GASM(PC pc)
314: {
315:   PC_GASM        *osm = (PC_GASM*)pc->data;
317:   PetscInt       i,nInnerIndices,nTotalInnerIndices;
318:   PetscMPIInt    rank, size;
319:   MatReuse       scall = MAT_REUSE_MATRIX;
320:   KSP            ksp;
321:   PC             subpc;
322:   const char     *prefix,*pprefix;
323:   Vec            x,y;
324:   PetscInt       oni;       /* Number of indices in the i-th local outer subdomain.               */
325:   const PetscInt *oidxi;    /* Indices from the i-th subdomain local outer subdomain.             */
326:   PetscInt       on;        /* Number of indices in the disjoint union of local outer subdomains. */
327:   PetscInt       *oidx;     /* Indices in the disjoint union of local outer subdomains. */
328:   IS             gois;      /* Disjoint union the global indices of outer subdomains.             */
329:   IS             goid;      /* Identity IS of the size of the disjoint union of outer subdomains. */
330:   PetscScalar    *gxarray, *gyarray;
331:   PetscInt       gostart;   /* Start of locally-owned indices in the vectors -- osm->gx,osm->gy -- over the disjoint union of outer subdomains. */
332:   PetscInt       num_subdomains    = 0;
333:   DM             *subdomain_dm     = NULL;
334:   char           **subdomain_names = NULL;
335:   PetscInt       *numbering;


339:   MPI_Comm_size(PetscObjectComm((PetscObject)pc),&size);
340:   MPI_Comm_rank(PetscObjectComm((PetscObject)pc),&rank);
341:   if (!pc->setupcalled) {
342:         /* use a hierarchical partitioning */
343:     if (osm->hierarchicalpartitioning){
344:       PCGASMSetHierarchicalPartitioning(pc);
345:     }
346:     if (osm->n == PETSC_DETERMINE) {
347:       if (osm->N != PETSC_DETERMINE) {
348:            /* No local subdomains given, but the desired number of total subdomains is known, so construct them accordingly. */
349:            PCGASMCreateSubdomains(pc->pmat,osm->N,&osm->n,&osm->iis);
350:       } else if (osm->dm_subdomains && pc->dm) {
351:         /* try pc->dm next, if allowed */
352:         PetscInt  d;
353:         IS       *inner_subdomain_is, *outer_subdomain_is;
354:         DMCreateDomainDecomposition(pc->dm, &num_subdomains, &subdomain_names, &inner_subdomain_is, &outer_subdomain_is, &subdomain_dm);
355:         if (num_subdomains) {
356:           PCGASMSetSubdomains(pc, num_subdomains, inner_subdomain_is, outer_subdomain_is);
357:         }
358:         for (d = 0; d < num_subdomains; ++d) {
359:           if (inner_subdomain_is) {ISDestroy(&inner_subdomain_is[d]);}
360:           if (outer_subdomain_is) {ISDestroy(&outer_subdomain_is[d]);}
361:         }
362:         PetscFree(inner_subdomain_is);
363:         PetscFree(outer_subdomain_is);
364:       } else {
365:         /* still no subdomains; use one per processor */
366:         osm->nmax = osm->n = 1;
367:         MPI_Comm_size(PetscObjectComm((PetscObject)pc),&size);
368:         osm->N    = size;
369:         PCGASMCreateLocalSubdomains(pc->pmat,osm->n,&osm->iis);
370:       }
371:     }
372:     if (!osm->iis) {
373:       /*
374:        osm->n was set in PCGASMSetSubdomains(), but the actual subdomains have not been supplied.
375:        We create the requisite number of local inner subdomains and then expand them into
376:        out subdomains, if necessary.
377:        */
378:       PCGASMCreateLocalSubdomains(pc->pmat,osm->n,&osm->iis);
379:     }
380:     if (!osm->ois) {
381:       /*
382:             Initially make outer subdomains the same as inner subdomains. If nonzero additional overlap
383:             has been requested, copy the inner subdomains over so they can be modified.
384:       */
385:       PetscMalloc1(osm->n,&osm->ois);
386:       for (i=0; i<osm->n; ++i) {
387:         if (osm->overlap > 0 && osm->N>1) { /* With positive overlap, osm->iis[i] will be modified */
388:           ISDuplicate(osm->iis[i],(osm->ois)+i);
389:           ISCopy(osm->iis[i],osm->ois[i]);
390:         } else {
391:           PetscObjectReference((PetscObject)((osm->iis)[i]));
392:           osm->ois[i] = osm->iis[i];
393:         }
394:       }
395:       if (osm->overlap>0 && osm->N>1) {
396:         /* Extend the "overlapping" regions by a number of steps */
397:         MatIncreaseOverlapSplit(pc->pmat,osm->n,osm->ois,osm->overlap);
398:       }
399:     }

401:     /* Now the subdomains are defined.  Determine their global and max local numbers, if necessary. */
402:     if (osm->nmax == PETSC_DETERMINE) {
403:       PetscMPIInt inwork,outwork;
404:       /* determine global number of subdomains and the max number of local subdomains */
405:       inwork     = osm->n;
406:       MPIU_Allreduce(&inwork,&outwork,1,MPI_INT,MPI_MAX,PetscObjectComm((PetscObject)pc));
407:       osm->nmax  = outwork;
408:     }
409:     if (osm->N == PETSC_DETERMINE) {
410:       /* Determine the number of globally-distinct subdomains and compute a global numbering for them. */
411:       PetscObjectsListGetGlobalNumbering(PetscObjectComm((PetscObject)pc),osm->n,(PetscObject*)osm->ois,&osm->N,NULL);
412:     }

414:     if (osm->sort_indices) {
415:       for (i=0; i<osm->n; i++) {
416:         ISSort(osm->ois[i]);
417:         ISSort(osm->iis[i]);
418:       }
419:     }
420:     PCGetOptionsPrefix(pc,&prefix);
421:     PCGASMPrintSubdomains(pc);

423:     /*
424:        Merge the ISs, create merged vectors and restrictions.
425:      */
426:     /* Merge outer subdomain ISs and construct a restriction onto the disjoint union of local outer subdomains. */
427:     on = 0;
428:     for (i=0; i<osm->n; i++) {
429:       ISGetLocalSize(osm->ois[i],&oni);
430:       on  += oni;
431:     }
432:     PetscMalloc1(on, &oidx);
433:     on   = 0;
434:     /* Merge local indices together */
435:     for (i=0; i<osm->n; i++) {
436:       ISGetLocalSize(osm->ois[i],&oni);
437:       ISGetIndices(osm->ois[i],&oidxi);
438:       PetscArraycpy(oidx+on,oidxi,oni);
439:       ISRestoreIndices(osm->ois[i],&oidxi);
440:       on  += oni;
441:     }
442:     ISCreateGeneral(((PetscObject)(pc))->comm,on,oidx,PETSC_OWN_POINTER,&gois);
443:     nTotalInnerIndices = 0;
444:     for (i=0; i<osm->n; i++){
445:       ISGetLocalSize(osm->iis[i],&nInnerIndices);
446:       nTotalInnerIndices += nInnerIndices;
447:     }
448:     VecCreateMPI(((PetscObject)(pc))->comm,nTotalInnerIndices,PETSC_DETERMINE,&x);
449:     VecDuplicate(x,&y);

451:     VecCreateMPI(PetscObjectComm((PetscObject)pc),on,PETSC_DECIDE,&osm->gx);
452:     VecDuplicate(osm->gx,&osm->gy);
453:     VecGetOwnershipRange(osm->gx, &gostart, NULL);
454:     ISCreateStride(PetscObjectComm((PetscObject)pc),on,gostart,1, &goid);
455:     /* gois might indices not on local */
456:     VecScatterCreate(x,gois,osm->gx,goid, &(osm->gorestriction));
457:     PetscMalloc1(osm->n,&numbering);
458:     PetscObjectsListGetGlobalNumbering(PetscObjectComm((PetscObject)pc),osm->n,(PetscObject*)osm->ois,NULL,numbering);
459:     VecDestroy(&x);
460:     ISDestroy(&gois);

462:     /* Merge inner subdomain ISs and construct a restriction onto the disjoint union of local inner subdomains. */
463:     {
464:       PetscInt        ini;           /* Number of indices the i-th a local inner subdomain. */
465:       PetscInt        in;            /* Number of indices in the disjoint union of local inner subdomains. */
466:       PetscInt       *iidx;          /* Global indices in the merged local inner subdomain. */
467:       PetscInt       *ioidx;         /* Global indices of the disjoint union of inner subdomains within the disjoint union of outer subdomains. */
468:       IS              giis;          /* IS for the disjoint union of inner subdomains. */
469:       IS              giois;         /* IS for the disjoint union of inner subdomains within the disjoint union of outer subdomains. */
470:       PetscScalar    *array;
471:       const PetscInt *indices;
472:       PetscInt        k;
473:       on = 0;
474:       for (i=0; i<osm->n; i++) {
475:         ISGetLocalSize(osm->ois[i],&oni);
476:         on  += oni;
477:       }
478:       PetscMalloc1(on, &iidx);
479:       PetscMalloc1(on, &ioidx);
480:       VecGetArray(y,&array);
481:       /* set communicator id to determine where overlap is */
482:       in   = 0;
483:       for (i=0; i<osm->n; i++) {
484:         ISGetLocalSize(osm->iis[i],&ini);
485:         for (k = 0; k < ini; ++k){
486:           array[in+k] = numbering[i];
487:         }
488:         in += ini;
489:       }
490:       VecRestoreArray(y,&array);
491:       VecScatterBegin(osm->gorestriction,y,osm->gy,INSERT_VALUES,SCATTER_FORWARD);
492:       VecScatterEnd(osm->gorestriction,y,osm->gy,INSERT_VALUES,SCATTER_FORWARD);
493:       VecGetOwnershipRange(osm->gy,&gostart, NULL);
494:       VecGetArray(osm->gy,&array);
495:       on  = 0;
496:       in  = 0;
497:       for (i=0; i<osm->n; i++) {
498:         ISGetLocalSize(osm->ois[i],&oni);
499:         ISGetIndices(osm->ois[i],&indices);
500:         for (k=0; k<oni; k++) {
501:           /*  skip overlapping indices to get inner domain */
502:           if (PetscRealPart(array[on+k]) != numbering[i]) continue;
503:           iidx[in]    = indices[k];
504:           ioidx[in++] = gostart+on+k;
505:         }
506:         ISRestoreIndices(osm->ois[i], &indices);
507:         on += oni;
508:       }
509:       VecRestoreArray(osm->gy,&array);
510:       ISCreateGeneral(PetscObjectComm((PetscObject)pc),in,iidx,PETSC_OWN_POINTER,&giis);
511:       ISCreateGeneral(PetscObjectComm((PetscObject)pc),in,ioidx,PETSC_OWN_POINTER,&giois);
512:       VecScatterCreate(y,giis,osm->gy,giois,&osm->girestriction);
513:       VecDestroy(&y);
514:       ISDestroy(&giis);
515:       ISDestroy(&giois);
516:     }
517:     ISDestroy(&goid);
518:     PetscFree(numbering);

520:     /* Create the subdomain work vectors. */
521:     PetscMalloc1(osm->n,&osm->x);
522:     PetscMalloc1(osm->n,&osm->y);
523:     VecGetArray(osm->gx, &gxarray);
524:     VecGetArray(osm->gy, &gyarray);
525:     for (i=0, on=0; i<osm->n; ++i, on += oni) {
526:       PetscInt oNi;
527:       ISGetLocalSize(osm->ois[i],&oni);
528:       /* on a sub communicator */
529:       ISGetSize(osm->ois[i],&oNi);
530:       VecCreateMPIWithArray(((PetscObject)(osm->ois[i]))->comm,1,oni,oNi,gxarray+on,&osm->x[i]);
531:       VecCreateMPIWithArray(((PetscObject)(osm->ois[i]))->comm,1,oni,oNi,gyarray+on,&osm->y[i]);
532:     }
533:     VecRestoreArray(osm->gx, &gxarray);
534:     VecRestoreArray(osm->gy, &gyarray);
535:     /* Create the subdomain solvers */
536:     PetscMalloc1(osm->n,&osm->ksp);
537:     for (i=0; i<osm->n; i++) {
538:       char subprefix[PETSC_MAX_PATH_LEN+1];
539:       KSPCreate(((PetscObject)(osm->ois[i]))->comm,&ksp);
540:       KSPSetErrorIfNotConverged(ksp,pc->erroriffailure);
541:       PetscLogObjectParent((PetscObject)pc,(PetscObject)ksp);
542:       PetscObjectIncrementTabLevel((PetscObject)ksp,(PetscObject)pc,1);
543:       KSPSetType(ksp,KSPPREONLY);
544:       KSPGetPC(ksp,&subpc); /* Why do we need this here? */
545:       if (subdomain_dm) {
546:         KSPSetDM(ksp,subdomain_dm[i]);
547:         DMDestroy(subdomain_dm+i);
548:       }
549:       PCGetOptionsPrefix(pc,&prefix);
550:       KSPSetOptionsPrefix(ksp,prefix);
551:       if (subdomain_names && subdomain_names[i]) {
552:         PetscSNPrintf(subprefix,PETSC_MAX_PATH_LEN,"sub_%s_",subdomain_names[i]);
553:         KSPAppendOptionsPrefix(ksp,subprefix);
554:         PetscFree(subdomain_names[i]);
555:       }
556:       KSPAppendOptionsPrefix(ksp,"sub_");
557:       osm->ksp[i] = ksp;
558:     }
559:     PetscFree(subdomain_dm);
560:     PetscFree(subdomain_names);
561:     scall = MAT_INITIAL_MATRIX;
562:   } else { /* if (pc->setupcalled) */
563:     /*
564:        Destroy the submatrices from the previous iteration
565:     */
566:     if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
567:       MatDestroyMatrices(osm->n,&osm->pmat);
568:       scall = MAT_INITIAL_MATRIX;
569:     }
570:     if (osm->permutationIS){
571:       MatCreateSubMatrix(pc->pmat,osm->permutationIS,osm->permutationIS,scall,&osm->permutationP);
572:       PetscObjectReference((PetscObject)osm->permutationP);
573:       osm->pcmat = pc->pmat;
574:       pc->pmat   = osm->permutationP;
575:     }
576:   }

578:   /*
579:      Extract the submatrices.
580:   */
581:   if (size > 1) {
582:     MatCreateSubMatricesMPI(pc->pmat,osm->n,osm->ois,osm->ois,scall,&osm->pmat);
583:   } else {
584:     MatCreateSubMatrices(pc->pmat,osm->n,osm->ois,osm->ois,scall,&osm->pmat);
585:   }
586:   if (scall == MAT_INITIAL_MATRIX) {
587:     PetscObjectGetOptionsPrefix((PetscObject)pc->pmat,&pprefix);
588:     for (i=0; i<osm->n; i++) {
589:       PetscLogObjectParent((PetscObject)pc,(PetscObject)osm->pmat[i]);
590:       PetscObjectSetOptionsPrefix((PetscObject)osm->pmat[i],pprefix);
591:     }
592:   }

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

598:   /*
599:      Loop over submatrices putting them into local ksps
600:   */
601:   for (i=0; i<osm->n; i++) {
602:     KSPSetOperators(osm->ksp[i],osm->pmat[i],osm->pmat[i]);
603:     if (!pc->setupcalled) {
604:       KSPSetFromOptions(osm->ksp[i]);
605:     }
606:   }
607:   if (osm->pcmat){
608:     MatDestroy(&pc->pmat);
609:     pc->pmat   = osm->pcmat;
610:     osm->pcmat = NULL;
611:   }
612:   return(0);
613: }

615: static PetscErrorCode PCSetUpOnBlocks_GASM(PC pc)
616: {
617:   PC_GASM        *osm = (PC_GASM*)pc->data;
619:   PetscInt       i;

622:   for (i=0; i<osm->n; i++) {
623:     KSPSetUp(osm->ksp[i]);
624:   }
625:   return(0);
626: }

628: static PetscErrorCode PCApply_GASM(PC pc,Vec xin,Vec yout)
629: {
630:   PC_GASM        *osm = (PC_GASM*)pc->data;
632:   PetscInt       i;
633:   Vec            x,y;
634:   ScatterMode    forward = SCATTER_FORWARD,reverse = SCATTER_REVERSE;

637:   if (osm->pctoouter) {
638:     VecScatterBegin(osm->pctoouter,xin,osm->pcx,INSERT_VALUES,SCATTER_REVERSE);
639:     VecScatterEnd(osm->pctoouter,xin,osm->pcx,INSERT_VALUES,SCATTER_REVERSE);
640:     x = osm->pcx;
641:     y = osm->pcy;
642:   } else {
643:     x = xin;
644:     y = yout;
645:   }
646:   /*
647:      support for limiting the restriction or interpolation only to the inner
648:      subdomain values (leaving the other values 0).
649:   */
650:   if (!(osm->type & PC_GASM_RESTRICT)) {
651:     /* have to zero the work RHS since scatter may leave some slots empty */
652:     VecZeroEntries(osm->gx);
653:     VecScatterBegin(osm->girestriction,x,osm->gx,INSERT_VALUES,forward);
654:   } else {
655:     VecScatterBegin(osm->gorestriction,x,osm->gx,INSERT_VALUES,forward);
656:   }
657:   VecZeroEntries(osm->gy);
658:   if (!(osm->type & PC_GASM_RESTRICT)) {
659:     VecScatterEnd(osm->girestriction,x,osm->gx,INSERT_VALUES,forward);
660:   } else {
661:     VecScatterEnd(osm->gorestriction,x,osm->gx,INSERT_VALUES,forward);
662:   }
663:   /* do the subdomain solves */
664:   for (i=0; i<osm->n; ++i) {
665:     KSPSolve(osm->ksp[i],osm->x[i],osm->y[i]);
666:     KSPCheckSolve(osm->ksp[i],pc,osm->y[i]);
667:   }
668:   /* do we need to zero y? */
669:   VecZeroEntries(y);
670:   if (!(osm->type & PC_GASM_INTERPOLATE)) {
671:     VecScatterBegin(osm->girestriction,osm->gy,y,ADD_VALUES,reverse);
672:     VecScatterEnd(osm->girestriction,osm->gy,y,ADD_VALUES,reverse);
673:   } else {
674:     VecScatterBegin(osm->gorestriction,osm->gy,y,ADD_VALUES,reverse);
675:     VecScatterEnd(osm->gorestriction,osm->gy,y,ADD_VALUES,reverse);
676:   }
677:   if (osm->pctoouter) {
678:     VecScatterBegin(osm->pctoouter,y,yout,INSERT_VALUES,SCATTER_FORWARD);
679:     VecScatterEnd(osm->pctoouter,y,yout,INSERT_VALUES,SCATTER_FORWARD);
680:   }
681:   return(0);
682: }

684: static PetscErrorCode PCMatApply_GASM(PC pc,Mat Xin,Mat Yout)
685: {
686:   PC_GASM        *osm = (PC_GASM*)pc->data;
687:   Mat            X,Y,O=NULL,Z,W;
688:   Vec            x,y;
689:   PetscInt       i,m,M,N;
690:   ScatterMode    forward = SCATTER_FORWARD,reverse = SCATTER_REVERSE;

694:   if (osm->n != 1) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_SUP,"Not yet implemented");
695:   MatGetSize(Xin,NULL,&N);
696:   if (osm->pctoouter) {
697:     VecGetLocalSize(osm->pcx,&m);
698:     VecGetSize(osm->pcx,&M);
699:     MatCreateDense(PetscObjectComm((PetscObject)osm->ois[0]),m,PETSC_DECIDE,M,N,NULL,&O);
700:     for (i = 0; i < N; ++i) {
701:       MatDenseGetColumnVecRead(Xin,i,&x);
702:       MatDenseGetColumnVecWrite(O,i,&y);
703:       VecScatterBegin(osm->pctoouter,x,y,INSERT_VALUES,SCATTER_REVERSE);
704:       VecScatterEnd(osm->pctoouter,x,y,INSERT_VALUES,SCATTER_REVERSE);
705:       MatDenseRestoreColumnVecWrite(O,i,&y);
706:       MatDenseRestoreColumnVecRead(Xin,i,&x);
707:     }
708:     X = Y = O;
709:   } else {
710:     X = Xin;
711:     Y = Yout;
712:   }
713:   /*
714:      support for limiting the restriction or interpolation only to the inner
715:      subdomain values (leaving the other values 0).
716:   */
717:   VecGetLocalSize(osm->x[0],&m);
718:   VecGetSize(osm->x[0],&M);
719:   MatCreateDense(PetscObjectComm((PetscObject)osm->ois[0]),m,PETSC_DECIDE,M,N,NULL,&Z);
720:   for (i = 0; i < N; ++i) {
721:     MatDenseGetColumnVecRead(X,i,&x);
722:     MatDenseGetColumnVecWrite(Z,i,&y);
723:     if (!(osm->type & PC_GASM_RESTRICT)) {
724:       /* have to zero the work RHS since scatter may leave some slots empty */
725:       VecZeroEntries(y);
726:       VecScatterBegin(osm->girestriction,x,y,INSERT_VALUES,forward);
727:       VecScatterEnd(osm->girestriction,x,y,INSERT_VALUES,forward);
728:     } else {
729:       VecScatterBegin(osm->gorestriction,x,y,INSERT_VALUES,forward);
730:       VecScatterEnd(osm->gorestriction,x,y,INSERT_VALUES,forward);
731:     }
732:     MatDenseRestoreColumnVecWrite(Z,i,&y);
733:     MatDenseRestoreColumnVecRead(X,i,&x);
734:   }
735:   MatCreateDense(PetscObjectComm((PetscObject)osm->ois[0]),m,PETSC_DECIDE,M,N,NULL,&W);
736:   MatSetOption(Z,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);
737:   MatAssemblyBegin(Z,MAT_FINAL_ASSEMBLY);
738:   MatAssemblyEnd(Z,MAT_FINAL_ASSEMBLY);
739:   /* do the subdomain solve */
740:   KSPMatSolve(osm->ksp[0],Z,W);
741:   KSPCheckSolve(osm->ksp[0],pc,NULL);
742:   MatDestroy(&Z);
743:   /* do we need to zero y? */
744:   MatZeroEntries(Y);
745:   for (i = 0; i < N; ++i) {
746:     MatDenseGetColumnVecWrite(Y,i,&y);
747:     MatDenseGetColumnVecRead(W,i,&x);
748:     if (!(osm->type & PC_GASM_INTERPOLATE)) {
749:       VecScatterBegin(osm->girestriction,x,y,ADD_VALUES,reverse);
750:       VecScatterEnd(osm->girestriction,x,y,ADD_VALUES,reverse);
751:     } else {
752:       VecScatterBegin(osm->gorestriction,x,y,ADD_VALUES,reverse);
753:       VecScatterEnd(osm->gorestriction,x,y,ADD_VALUES,reverse);
754:     }
755:     MatDenseRestoreColumnVecRead(W,i,&x);
756:     if (osm->pctoouter) {
757:       MatDenseGetColumnVecWrite(Yout,i,&x);
758:       VecScatterBegin(osm->pctoouter,y,x,INSERT_VALUES,SCATTER_FORWARD);
759:       VecScatterEnd(osm->pctoouter,y,x,INSERT_VALUES,SCATTER_FORWARD);
760:       MatDenseRestoreColumnVecRead(Yout,i,&x);
761:     }
762:     MatDenseRestoreColumnVecWrite(Y,i,&y);
763:   }
764:   MatDestroy(&W);
765:   MatDestroy(&O);
766:   return(0);
767: }

769: static PetscErrorCode PCApplyTranspose_GASM(PC pc,Vec xin,Vec yout)
770: {
771:   PC_GASM        *osm = (PC_GASM*)pc->data;
773:   PetscInt       i;
774:   Vec            x,y;
775:   ScatterMode    forward = SCATTER_FORWARD,reverse = SCATTER_REVERSE;

778:   if (osm->pctoouter){
779:    VecScatterBegin(osm->pctoouter,xin,osm->pcx,INSERT_VALUES,SCATTER_REVERSE);
780:    VecScatterEnd(osm->pctoouter,xin,osm->pcx,INSERT_VALUES,SCATTER_REVERSE);
781:    x = osm->pcx;
782:    y = osm->pcy;
783:   }else{
784:         x = xin;
785:         y = yout;
786:   }
787:   /*
788:      Support for limiting the restriction or interpolation to only local
789:      subdomain values (leaving the other values 0).

791:      Note: these are reversed from the PCApply_GASM() because we are applying the
792:      transpose of the three terms
793:   */
794:   if (!(osm->type & PC_GASM_INTERPOLATE)) {
795:     /* have to zero the work RHS since scatter may leave some slots empty */
796:     VecZeroEntries(osm->gx);
797:     VecScatterBegin(osm->girestriction,x,osm->gx,INSERT_VALUES,forward);
798:   } else {
799:     VecScatterBegin(osm->gorestriction,x,osm->gx,INSERT_VALUES,forward);
800:   }
801:   VecZeroEntries(osm->gy);
802:   if (!(osm->type & PC_GASM_INTERPOLATE)) {
803:     VecScatterEnd(osm->girestriction,x,osm->gx,INSERT_VALUES,forward);
804:   } else {
805:     VecScatterEnd(osm->gorestriction,x,osm->gx,INSERT_VALUES,forward);
806:   }
807:   /* do the local solves */
808:   for (i=0; i<osm->n; ++i) { /* Note that the solves are local, so we can go to osm->n, rather than osm->nmax. */
809:     KSPSolveTranspose(osm->ksp[i],osm->x[i],osm->y[i]);
810:     KSPCheckSolve(osm->ksp[i],pc,osm->y[i]);
811:   }
812:   VecZeroEntries(y);
813:   if (!(osm->type & PC_GASM_RESTRICT)) {
814:     VecScatterBegin(osm->girestriction,osm->gy,y,ADD_VALUES,reverse);
815:     VecScatterEnd(osm->girestriction,osm->gy,y,ADD_VALUES,reverse);
816:   } else {
817:     VecScatterBegin(osm->gorestriction,osm->gy,y,ADD_VALUES,reverse);
818:     VecScatterEnd(osm->gorestriction,osm->gy,y,ADD_VALUES,reverse);
819:   }
820:   if (osm->pctoouter){
821:    VecScatterBegin(osm->pctoouter,y,yout,INSERT_VALUES,SCATTER_FORWARD);
822:    VecScatterEnd(osm->pctoouter,y,yout,INSERT_VALUES,SCATTER_FORWARD);
823:   }
824:   return(0);
825: }

827: static PetscErrorCode PCReset_GASM(PC pc)
828: {
829:   PC_GASM        *osm = (PC_GASM*)pc->data;
831:   PetscInt       i;

834:   if (osm->ksp) {
835:     for (i=0; i<osm->n; i++) {
836:       KSPReset(osm->ksp[i]);
837:     }
838:   }
839:   if (osm->pmat) {
840:     if (osm->n > 0) {
841:       PetscMPIInt size;
842:       MPI_Comm_size(PetscObjectComm((PetscObject)pc),&size);
843:       if (size > 1) {
844:         /* osm->pmat is created by MatCreateSubMatricesMPI(), cannot use MatDestroySubMatrices() */
845:         MatDestroyMatrices(osm->n,&osm->pmat);
846:       } else {
847:         MatDestroySubMatrices(osm->n,&osm->pmat);
848:       }
849:     }
850:   }
851:   if (osm->x) {
852:     for (i=0; i<osm->n; i++) {
853:       VecDestroy(&osm->x[i]);
854:       VecDestroy(&osm->y[i]);
855:     }
856:   }
857:   VecDestroy(&osm->gx);
858:   VecDestroy(&osm->gy);

860:   VecScatterDestroy(&osm->gorestriction);
861:   VecScatterDestroy(&osm->girestriction);
862:   if (!osm->user_subdomains) {
863:     PCGASMDestroySubdomains(osm->n,&osm->ois,&osm->iis);
864:     osm->N    = PETSC_DETERMINE;
865:     osm->nmax = PETSC_DETERMINE;
866:   }
867:   if (osm->pctoouter){
868:         VecScatterDestroy(&(osm->pctoouter));
869:   }
870:   if (osm->permutationIS){
871:         ISDestroy(&(osm->permutationIS));
872:   }
873:   if (osm->pcx){
874:         VecDestroy(&(osm->pcx));
875:   }
876:   if (osm->pcy){
877:         VecDestroy(&(osm->pcy));
878:   }
879:   if (osm->permutationP){
880:     MatDestroy(&(osm->permutationP));
881:   }
882:   if (osm->pcmat){
883:         MatDestroy(&osm->pcmat);
884:   }
885:   return(0);
886: }

888: static PetscErrorCode PCDestroy_GASM(PC pc)
889: {
890:   PC_GASM        *osm = (PC_GASM*)pc->data;
892:   PetscInt       i;

895:   PCReset_GASM(pc);
896:   /* PCReset will not destroy subdomains, if user_subdomains is true. */
897:   PCGASMDestroySubdomains(osm->n,&osm->ois,&osm->iis);
898:   if (osm->ksp) {
899:     for (i=0; i<osm->n; i++) {
900:       KSPDestroy(&osm->ksp[i]);
901:     }
902:     PetscFree(osm->ksp);
903:   }
904:   PetscFree(osm->x);
905:   PetscFree(osm->y);
906:   PetscFree(pc->data);
907:   return(0);
908: }

910: static PetscErrorCode PCSetFromOptions_GASM(PetscOptionItems *PetscOptionsObject,PC pc)
911: {
912:   PC_GASM        *osm = (PC_GASM*)pc->data;
914:   PetscInt       blocks,ovl;
915:   PetscBool      flg;
916:   PCGASMType     gasmtype;

919:   PetscOptionsHead(PetscOptionsObject,"Generalized additive Schwarz options");
920:   PetscOptionsBool("-pc_gasm_use_dm_subdomains","If subdomains aren't set, use DMCreateDomainDecomposition() to define subdomains.","PCGASMSetUseDMSubdomains",osm->dm_subdomains,&osm->dm_subdomains,&flg);
921:   PetscOptionsInt("-pc_gasm_total_subdomains","Total number of subdomains across communicator","PCGASMSetTotalSubdomains",osm->N,&blocks,&flg);
922:   if (flg) {
923:     PCGASMSetTotalSubdomains(pc,blocks);
924:   }
925:   PetscOptionsInt("-pc_gasm_overlap","Number of overlapping degrees of freedom","PCGASMSetOverlap",osm->overlap,&ovl,&flg);
926:   if (flg) {
927:     PCGASMSetOverlap(pc,ovl);
928:     osm->dm_subdomains = PETSC_FALSE;
929:   }
930:   flg  = PETSC_FALSE;
931:   PetscOptionsEnum("-pc_gasm_type","Type of restriction/extension","PCGASMSetType",PCGASMTypes,(PetscEnum)osm->type,(PetscEnum*)&gasmtype,&flg);
932:   if (flg) {PCGASMSetType(pc,gasmtype);}
933:   PetscOptionsBool("-pc_gasm_use_hierachical_partitioning","use hierarchical partitioning",NULL,osm->hierarchicalpartitioning,&osm->hierarchicalpartitioning,&flg);
934:   PetscOptionsTail();
935:   return(0);
936: }

938: /*------------------------------------------------------------------------------------*/

940: /*@
941:     PCGASMSetTotalSubdomains - sets the total number of subdomains to use across the
942:                                communicator.
943:     Logically collective on pc

945:     Input Parameters:
946: +   pc  - the preconditioner
947: -   N   - total number of subdomains


950:     Level: beginner

952: .seealso: PCGASMSetSubdomains(), PCGASMSetOverlap()
953:           PCGASMCreateSubdomains2D()
954: @*/
955: PetscErrorCode  PCGASMSetTotalSubdomains(PC pc,PetscInt N)
956: {
957:   PC_GASM        *osm = (PC_GASM*)pc->data;
958:   PetscMPIInt    size,rank;

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

965:   PCGASMDestroySubdomains(osm->n,&osm->iis,&osm->ois);
966:   osm->ois = osm->iis = NULL;

968:   MPI_Comm_size(PetscObjectComm((PetscObject)pc),&size);
969:   MPI_Comm_rank(PetscObjectComm((PetscObject)pc),&rank);
970:   osm->N    = N;
971:   osm->n    = PETSC_DETERMINE;
972:   osm->nmax = PETSC_DETERMINE;
973:   osm->dm_subdomains = PETSC_FALSE;
974:   return(0);
975: }

977: static PetscErrorCode  PCGASMSetSubdomains_GASM(PC pc,PetscInt n,IS iis[],IS ois[])
978: {
979:   PC_GASM         *osm = (PC_GASM*)pc->data;
980:   PetscErrorCode  ierr;
981:   PetscInt        i;

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

987:   PCGASMDestroySubdomains(osm->n,&osm->iis,&osm->ois);
988:   osm->iis  = osm->ois = NULL;
989:   osm->n    = n;
990:   osm->N    = PETSC_DETERMINE;
991:   osm->nmax = PETSC_DETERMINE;
992:   if (ois) {
993:     PetscMalloc1(n,&osm->ois);
994:     for (i=0; i<n; i++) {
995:       PetscObjectReference((PetscObject)ois[i]);
996:       osm->ois[i] = ois[i];
997:     }
998:     /*
999:        Since the user set the outer subdomains, even if nontrivial overlap was requested via PCGASMSetOverlap(),
1000:        it will be ignored.  To avoid confusion later on (e.g., when viewing the PC), the overlap size is set to -1.
1001:     */
1002:     osm->overlap = -1;
1003:     /* inner subdomains must be provided  */
1004:     if (!iis) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_NULL,"inner indices have to be provided \n");
1005:   }/* end if */
1006:   if (iis) {
1007:     PetscMalloc1(n,&osm->iis);
1008:     for (i=0; i<n; i++) {
1009:       PetscObjectReference((PetscObject)iis[i]);
1010:       osm->iis[i] = iis[i];
1011:     }
1012:     if (!ois) {
1013:       osm->ois = NULL;
1014:       /* if user does not provide outer indices, we will create the corresponding outer indices using  osm->overlap =1 in PCSetUp_GASM */
1015:     }
1016:   }
1017:   if (PetscDefined(USE_DEBUG)) {
1018:     PetscInt        j,rstart,rend,*covered,lsize;
1019:     const PetscInt  *indices;
1020:     /* check if the inner indices cover and only cover the local portion of the preconditioning matrix */
1021:     MatGetOwnershipRange(pc->pmat,&rstart,&rend);
1022:     PetscCalloc1(rend-rstart,&covered);
1023:     /* check if the current processor owns indices from others */
1024:     for (i=0; i<n; i++) {
1025:       ISGetIndices(osm->iis[i],&indices);
1026:       ISGetLocalSize(osm->iis[i],&lsize);
1027:       for (j=0; j<lsize; j++) {
1028:         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]);
1029:         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]);
1030:         else covered[indices[j]-rstart] = 1;
1031:       }
1032:     ISRestoreIndices(osm->iis[i],&indices);
1033:     }
1034:     /* check if we miss any indices */
1035:     for (i=rstart; i<rend; i++) {
1036:       if (!covered[i-rstart]) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_NULL,"local entity %d was not covered by inner subdomains",i);
1037:     }
1038:     PetscFree(covered);
1039:   }
1040:   if (iis)  osm->user_subdomains = PETSC_TRUE;
1041:   return(0);
1042: }

1044: static PetscErrorCode  PCGASMSetOverlap_GASM(PC pc,PetscInt ovl)
1045: {
1046:   PC_GASM *osm = (PC_GASM*)pc->data;

1049:   if (ovl < 0) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_OUTOFRANGE,"Negative overlap value requested");
1050:   if (pc->setupcalled && ovl != osm->overlap) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONGSTATE,"PCGASMSetOverlap() should be called before PCSetUp().");
1051:   if (!pc->setupcalled) osm->overlap = ovl;
1052:   return(0);
1053: }

1055: static PetscErrorCode  PCGASMSetType_GASM(PC pc,PCGASMType type)
1056: {
1057:   PC_GASM *osm = (PC_GASM*)pc->data;

1060:   osm->type     = type;
1061:   osm->type_set = PETSC_TRUE;
1062:   return(0);
1063: }

1065: static PetscErrorCode  PCGASMSetSortIndices_GASM(PC pc,PetscBool doSort)
1066: {
1067:   PC_GASM *osm = (PC_GASM*)pc->data;

1070:   osm->sort_indices = doSort;
1071:   return(0);
1072: }

1074: /*
1075:    FIXME: This routine might need to be modified now that multiple ranks per subdomain are allowed.
1076:         In particular, it would upset the global subdomain number calculation.
1077: */
1078: static PetscErrorCode  PCGASMGetSubKSP_GASM(PC pc,PetscInt *n,PetscInt *first,KSP **ksp)
1079: {
1080:   PC_GASM        *osm = (PC_GASM*)pc->data;

1084:   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");

1086:   if (n) *n = osm->n;
1087:   if (first) {
1088:     MPI_Scan(&osm->n,first,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)pc));
1089:     *first -= osm->n;
1090:   }
1091:   if (ksp) {
1092:     /* Assume that local solves are now different; not necessarily
1093:        true, though!  This flag is used only for PCView_GASM() */
1094:     *ksp                        = osm->ksp;
1095:     osm->same_subdomain_solvers = PETSC_FALSE;
1096:   }
1097:   return(0);
1098: } /* PCGASMGetSubKSP_GASM() */

1100: /*@C
1101:     PCGASMSetSubdomains - Sets the subdomains for this processor
1102:     for the additive Schwarz preconditioner.

1104:     Collective on pc

1106:     Input Parameters:
1107: +   pc  - the preconditioner object
1108: .   n   - the number of subdomains for this processor
1109: .   iis - the index sets that define the inner subdomains (or NULL for PETSc to determine subdomains)
1110: -   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)

1112:     Notes:
1113:     The IS indices use the parallel, global numbering of the vector entries.
1114:     Inner subdomains are those where the correction is applied.
1115:     Outer subdomains are those where the residual necessary to obtain the
1116:     corrections is obtained (see PCGASMType for the use of inner/outer subdomains).
1117:     Both inner and outer subdomains can extend over several processors.
1118:     This processor's portion of a subdomain is known as a local subdomain.

1120:     Inner subdomains can not overlap with each other, do not have any entities from remote processors,
1121:     and  have to cover the entire local subdomain owned by the current processor. The index sets on each
1122:     process should be ordered such that the ith local subdomain is connected to the ith remote subdomain
1123:     on another MPI process.

1125:     By default the GASM preconditioner uses 1 (local) subdomain per processor.


1128:     Level: advanced

1130: .seealso: PCGASMSetNumSubdomains(), PCGASMSetOverlap(), PCGASMGetSubKSP(),
1131:           PCGASMCreateSubdomains2D(), PCGASMGetSubdomains()
1132: @*/
1133: PetscErrorCode  PCGASMSetSubdomains(PC pc,PetscInt n,IS iis[],IS ois[])
1134: {
1135:   PC_GASM *osm = (PC_GASM*)pc->data;

1140:   PetscTryMethod(pc,"PCGASMSetSubdomains_C",(PC,PetscInt,IS[],IS[]),(pc,n,iis,ois));
1141:   osm->dm_subdomains = PETSC_FALSE;
1142:   return(0);
1143: }

1145: /*@
1146:     PCGASMSetOverlap - Sets the overlap between a pair of subdomains for the
1147:     additive Schwarz preconditioner.  Either all or no processors in the
1148:     pc communicator must call this routine.

1150:     Logically Collective on pc

1152:     Input Parameters:
1153: +   pc  - the preconditioner context
1154: -   ovl - the amount of overlap between subdomains (ovl >= 0, default value = 0)

1156:     Options Database Key:
1157: .   -pc_gasm_overlap <overlap> - Sets overlap

1159:     Notes:
1160:     By default the GASM preconditioner uses 1 subdomain per processor.  To use
1161:     multiple subdomain per perocessor or "straddling" subdomains that intersect
1162:     multiple processors use PCGASMSetSubdomains() (or option -pc_gasm_total_subdomains <n>).

1164:     The overlap defaults to 0, so if one desires that no additional
1165:     overlap be computed beyond what may have been set with a call to
1166:     PCGASMSetSubdomains(), then ovl must be set to be 0.  In particular, if one does
1167:     not explicitly set the subdomains in application code, then all overlap would be computed
1168:     internally by PETSc, and using an overlap of 0 would result in an GASM
1169:     variant that is equivalent to the block Jacobi preconditioner.

1171:     Note that one can define initial index sets with any overlap via
1172:     PCGASMSetSubdomains(); the routine PCGASMSetOverlap() merely allows
1173:     PETSc to extend that overlap further, if desired.

1175:     Level: intermediate

1177: .seealso: PCGASMSetSubdomains(), PCGASMGetSubKSP(),
1178:           PCGASMCreateSubdomains2D(), PCGASMGetSubdomains()
1179: @*/
1180: PetscErrorCode  PCGASMSetOverlap(PC pc,PetscInt ovl)
1181: {
1183:   PC_GASM *osm = (PC_GASM*)pc->data;

1188:   PetscTryMethod(pc,"PCGASMSetOverlap_C",(PC,PetscInt),(pc,ovl));
1189:   osm->dm_subdomains = PETSC_FALSE;
1190:   return(0);
1191: }

1193: /*@
1194:     PCGASMSetType - Sets the type of restriction and interpolation used
1195:     for local problems in the additive Schwarz method.

1197:     Logically Collective on PC

1199:     Input Parameters:
1200: +   pc  - the preconditioner context
1201: -   type - variant of GASM, one of
1202: .vb
1203:       PC_GASM_BASIC       - full interpolation and restriction
1204:       PC_GASM_RESTRICT    - full restriction, local processor interpolation
1205:       PC_GASM_INTERPOLATE - full interpolation, local processor restriction
1206:       PC_GASM_NONE        - local processor restriction and interpolation
1207: .ve

1209:     Options Database Key:
1210: .   -pc_gasm_type [basic,restrict,interpolate,none] - Sets GASM type

1212:     Level: intermediate

1214: .seealso: PCGASMSetSubdomains(), PCGASMGetSubKSP(),
1215:           PCGASMCreateSubdomains2D()
1216: @*/
1217: PetscErrorCode  PCGASMSetType(PC pc,PCGASMType type)
1218: {

1224:   PetscTryMethod(pc,"PCGASMSetType_C",(PC,PCGASMType),(pc,type));
1225:   return(0);
1226: }

1228: /*@
1229:     PCGASMSetSortIndices - Determines whether subdomain indices are sorted.

1231:     Logically Collective on PC

1233:     Input Parameters:
1234: +   pc  - the preconditioner context
1235: -   doSort - sort the subdomain indices

1237:     Level: intermediate

1239: .seealso: PCGASMSetSubdomains(), PCGASMGetSubKSP(),
1240:           PCGASMCreateSubdomains2D()
1241: @*/
1242: PetscErrorCode  PCGASMSetSortIndices(PC pc,PetscBool doSort)
1243: {

1249:   PetscTryMethod(pc,"PCGASMSetSortIndices_C",(PC,PetscBool),(pc,doSort));
1250:   return(0);
1251: }

1253: /*@C
1254:    PCGASMGetSubKSP - Gets the local KSP contexts for all blocks on
1255:    this processor.

1257:    Collective on PC iff first_local is requested

1259:    Input Parameter:
1260: .  pc - the preconditioner context

1262:    Output Parameters:
1263: +  n_local - the number of blocks on this processor or NULL
1264: .  first_local - the global number of the first block on this processor or NULL,
1265:                  all processors must request or all must pass NULL
1266: -  ksp - the array of KSP contexts

1268:    Note:
1269:    After PCGASMGetSubKSP() the array of KSPes is not to be freed

1271:    Currently for some matrix implementations only 1 block per processor
1272:    is supported.

1274:    You must call KSPSetUp() before calling PCGASMGetSubKSP().

1276:    Level: advanced

1278: .seealso: PCGASMSetSubdomains(), PCGASMSetOverlap(),
1279:           PCGASMCreateSubdomains2D(),
1280: @*/
1281: PetscErrorCode  PCGASMGetSubKSP(PC pc,PetscInt *n_local,PetscInt *first_local,KSP *ksp[])
1282: {

1287:   PetscUseMethod(pc,"PCGASMGetSubKSP_C",(PC,PetscInt*,PetscInt*,KSP **),(pc,n_local,first_local,ksp));
1288:   return(0);
1289: }

1291: /* -------------------------------------------------------------------------------------*/
1292: /*MC
1293:    PCGASM - Use the (restricted) additive Schwarz method, each block is (approximately) solved with
1294:            its own KSP object.

1296:    Options Database Keys:
1297: +  -pc_gasm_total_subdomains <n>  - Sets total number of local subdomains to be distributed among processors
1298: .  -pc_gasm_view_subdomains       - activates the printing of subdomain indices in PCView(), -ksp_view or -snes_view
1299: .  -pc_gasm_print_subdomains      - activates the printing of subdomain indices in PCSetUp()
1300: .  -pc_gasm_overlap <ovl>         - Sets overlap by which to (automatically) extend local subdomains
1301: -  -pc_gasm_type [basic,restrict,interpolate,none] - Sets GASM type

1303:      IMPORTANT: If you run with, for example, 3 blocks on 1 processor or 3 blocks on 3 processors you
1304:       will get a different convergence rate due to the default option of -pc_gasm_type restrict. Use
1305:       -pc_gasm_type basic to use the standard GASM.

1307:    Notes:
1308:     Blocks can be shared by multiple processes.

1310:      To set options on the solvers for each block append -sub_ to all the KSP, and PC
1311:         options database keys. For example, -sub_pc_type ilu -sub_pc_factor_levels 1 -sub_ksp_type preonly

1313:      To set the options on the solvers separate for each block call PCGASMGetSubKSP()
1314:          and set the options directly on the resulting KSP object (you can access its PC
1315:          with KSPGetPC())


1318:    Level: beginner

1320:     References:
1321: +   1. - M Dryja, OB Widlund, An additive variant of the Schwarz alternating method for the case of many subregions
1322:      Courant Institute, New York University Technical report
1323: -   2. - Barry Smith, Petter Bjorstad, and William Gropp, Domain Decompositions: Parallel Multilevel Methods for Elliptic Partial Differential Equations,
1324:     Cambridge University Press.

1326: .seealso:  PCCreate(), PCSetType(), PCType (for list of available types), PC,
1327:            PCBJACOBI,  PCGASMGetSubKSP(), PCGASMSetSubdomains(),
1328:            PCSetModifySubMatrices(), PCGASMSetOverlap(), PCGASMSetType()

1330: M*/

1332: PETSC_EXTERN PetscErrorCode PCCreate_GASM(PC pc)
1333: {
1335:   PC_GASM        *osm;

1338:   PetscNewLog(pc,&osm);

1340:   osm->N                        = PETSC_DETERMINE;
1341:   osm->n                        = PETSC_DECIDE;
1342:   osm->nmax                     = PETSC_DETERMINE;
1343:   osm->overlap                  = 0;
1344:   osm->ksp                      = NULL;
1345:   osm->gorestriction            = NULL;
1346:   osm->girestriction            = NULL;
1347:   osm->pctoouter                = NULL;
1348:   osm->gx                       = NULL;
1349:   osm->gy                       = NULL;
1350:   osm->x                        = NULL;
1351:   osm->y                        = NULL;
1352:   osm->pcx                      = NULL;
1353:   osm->pcy                      = NULL;
1354:   osm->permutationIS            = NULL;
1355:   osm->permutationP             = NULL;
1356:   osm->pcmat                    = NULL;
1357:   osm->ois                      = NULL;
1358:   osm->iis                      = NULL;
1359:   osm->pmat                     = NULL;
1360:   osm->type                     = PC_GASM_RESTRICT;
1361:   osm->same_subdomain_solvers   = PETSC_TRUE;
1362:   osm->sort_indices             = PETSC_TRUE;
1363:   osm->dm_subdomains            = PETSC_FALSE;
1364:   osm->hierarchicalpartitioning = PETSC_FALSE;

1366:   pc->data                 = (void*)osm;
1367:   pc->ops->apply           = PCApply_GASM;
1368:   pc->ops->matapply        = PCMatApply_GASM;
1369:   pc->ops->applytranspose  = PCApplyTranspose_GASM;
1370:   pc->ops->setup           = PCSetUp_GASM;
1371:   pc->ops->reset           = PCReset_GASM;
1372:   pc->ops->destroy         = PCDestroy_GASM;
1373:   pc->ops->setfromoptions  = PCSetFromOptions_GASM;
1374:   pc->ops->setuponblocks   = PCSetUpOnBlocks_GASM;
1375:   pc->ops->view            = PCView_GASM;
1376:   pc->ops->applyrichardson = NULL;

1378:   PetscObjectComposeFunction((PetscObject)pc,"PCGASMSetSubdomains_C",PCGASMSetSubdomains_GASM);
1379:   PetscObjectComposeFunction((PetscObject)pc,"PCGASMSetOverlap_C",PCGASMSetOverlap_GASM);
1380:   PetscObjectComposeFunction((PetscObject)pc,"PCGASMSetType_C",PCGASMSetType_GASM);
1381:   PetscObjectComposeFunction((PetscObject)pc,"PCGASMSetSortIndices_C",PCGASMSetSortIndices_GASM);
1382:   PetscObjectComposeFunction((PetscObject)pc,"PCGASMGetSubKSP_C",PCGASMGetSubKSP_GASM);
1383:   return(0);
1384: }

1386: PetscErrorCode  PCGASMCreateLocalSubdomains(Mat A, PetscInt nloc, IS *iis[])
1387: {
1388:   MatPartitioning mpart;
1389:   const char      *prefix;
1390:   PetscInt        i,j,rstart,rend,bs;
1391:   PetscBool       hasop, isbaij = PETSC_FALSE,foundpart = PETSC_FALSE;
1392:   Mat             Ad     = NULL, adj;
1393:   IS              ispart,isnumb,*is;
1394:   PetscErrorCode  ierr;

1397:   if (nloc < 1) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"number of local subdomains must > 0, got nloc = %D",nloc);

1399:   /* Get prefix, row distribution, and block size */
1400:   MatGetOptionsPrefix(A,&prefix);
1401:   MatGetOwnershipRange(A,&rstart,&rend);
1402:   MatGetBlockSize(A,&bs);
1403:   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);

1405:   /* Get diagonal block from matrix if possible */
1406:   MatHasOperation(A,MATOP_GET_DIAGONAL_BLOCK,&hasop);
1407:   if (hasop) {
1408:     MatGetDiagonalBlock(A,&Ad);
1409:   }
1410:   if (Ad) {
1411:     PetscObjectBaseTypeCompare((PetscObject)Ad,MATSEQBAIJ,&isbaij);
1412:     if (!isbaij) {PetscObjectBaseTypeCompare((PetscObject)Ad,MATSEQSBAIJ,&isbaij);}
1413:   }
1414:   if (Ad && nloc > 1) {
1415:     PetscBool  match,done;
1416:     /* Try to setup a good matrix partitioning if available */
1417:     MatPartitioningCreate(PETSC_COMM_SELF,&mpart);
1418:     PetscObjectSetOptionsPrefix((PetscObject)mpart,prefix);
1419:     MatPartitioningSetFromOptions(mpart);
1420:     PetscObjectTypeCompare((PetscObject)mpart,MATPARTITIONINGCURRENT,&match);
1421:     if (!match) {
1422:       PetscObjectTypeCompare((PetscObject)mpart,MATPARTITIONINGSQUARE,&match);
1423:     }
1424:     if (!match) { /* assume a "good" partitioner is available */
1425:       PetscInt       na;
1426:       const PetscInt *ia,*ja;
1427:       MatGetRowIJ(Ad,0,PETSC_TRUE,isbaij,&na,&ia,&ja,&done);
1428:       if (done) {
1429:         /* Build adjacency matrix by hand. Unfortunately a call to
1430:            MatConvert(Ad,MATMPIADJ,MAT_INITIAL_MATRIX,&adj) will
1431:            remove the block-aij structure and we cannot expect
1432:            MatPartitioning to split vertices as we need */
1433:         PetscInt       i,j,len,nnz,cnt,*iia=NULL,*jja=NULL;
1434:         const PetscInt *row;
1435:         nnz = 0;
1436:         for (i=0; i<na; i++) { /* count number of nonzeros */
1437:           len = ia[i+1] - ia[i];
1438:           row = ja + ia[i];
1439:           for (j=0; j<len; j++) {
1440:             if (row[j] == i) { /* don't count diagonal */
1441:               len--; break;
1442:             }
1443:           }
1444:           nnz += len;
1445:         }
1446:         PetscMalloc1(na+1,&iia);
1447:         PetscMalloc1(nnz,&jja);
1448:         nnz    = 0;
1449:         iia[0] = 0;
1450:         for (i=0; i<na; i++) { /* fill adjacency */
1451:           cnt = 0;
1452:           len = ia[i+1] - ia[i];
1453:           row = ja + ia[i];
1454:           for (j=0; j<len; j++) {
1455:             if (row[j] != i) jja[nnz+cnt++] = row[j]; /* if not diagonal */
1456:           }
1457:           nnz += cnt;
1458:           iia[i+1] = nnz;
1459:         }
1460:         /* Partitioning of the adjacency matrix */
1461:         MatCreateMPIAdj(PETSC_COMM_SELF,na,na,iia,jja,NULL,&adj);
1462:         MatPartitioningSetAdjacency(mpart,adj);
1463:         MatPartitioningSetNParts(mpart,nloc);
1464:         MatPartitioningApply(mpart,&ispart);
1465:         ISPartitioningToNumbering(ispart,&isnumb);
1466:         MatDestroy(&adj);
1467:         foundpart = PETSC_TRUE;
1468:       }
1469:       MatRestoreRowIJ(Ad,0,PETSC_TRUE,isbaij,&na,&ia,&ja,&done);
1470:     }
1471:     MatPartitioningDestroy(&mpart);
1472:   }
1473:   PetscMalloc1(nloc,&is);
1474:   if (!foundpart) {

1476:     /* Partitioning by contiguous chunks of rows */

1478:     PetscInt mbs   = (rend-rstart)/bs;
1479:     PetscInt start = rstart;
1480:     for (i=0; i<nloc; i++) {
1481:       PetscInt count = (mbs/nloc + ((mbs % nloc) > i)) * bs;
1482:       ISCreateStride(PETSC_COMM_SELF,count,start,1,&is[i]);
1483:       start += count;
1484:     }

1486:   } else {

1488:     /* Partitioning by adjacency of diagonal block  */

1490:     const PetscInt *numbering;
1491:     PetscInt       *count,nidx,*indices,*newidx,start=0;
1492:     /* Get node count in each partition */
1493:     PetscMalloc1(nloc,&count);
1494:     ISPartitioningCount(ispart,nloc,count);
1495:     if (isbaij && bs > 1) { /* adjust for the block-aij case */
1496:       for (i=0; i<nloc; i++) count[i] *= bs;
1497:     }
1498:     /* Build indices from node numbering */
1499:     ISGetLocalSize(isnumb,&nidx);
1500:     PetscMalloc1(nidx,&indices);
1501:     for (i=0; i<nidx; i++) indices[i] = i; /* needs to be initialized */
1502:     ISGetIndices(isnumb,&numbering);
1503:     PetscSortIntWithPermutation(nidx,numbering,indices);
1504:     ISRestoreIndices(isnumb,&numbering);
1505:     if (isbaij && bs > 1) { /* adjust for the block-aij case */
1506:       PetscMalloc1(nidx*bs,&newidx);
1507:       for (i=0; i<nidx; i++) {
1508:         for (j=0; j<bs; j++) newidx[i*bs+j] = indices[i]*bs + j;
1509:       }
1510:       PetscFree(indices);
1511:       nidx   *= bs;
1512:       indices = newidx;
1513:     }
1514:     /* Shift to get global indices */
1515:     for (i=0; i<nidx; i++) indices[i] += rstart;

1517:     /* Build the index sets for each block */
1518:     for (i=0; i<nloc; i++) {
1519:       ISCreateGeneral(PETSC_COMM_SELF,count[i],&indices[start],PETSC_COPY_VALUES,&is[i]);
1520:       ISSort(is[i]);
1521:       start += count[i];
1522:     }

1524:     PetscFree(count);
1525:     PetscFree(indices);
1526:     ISDestroy(&isnumb);
1527:     ISDestroy(&ispart);
1528:   }
1529:   *iis = is;
1530:   return(0);
1531: }

1533: PETSC_INTERN PetscErrorCode  PCGASMCreateStraddlingSubdomains(Mat A,PetscInt N,PetscInt *n,IS *iis[])
1534: {
1535:   PetscErrorCode  ierr;

1538:   MatSubdomainsCreateCoalesce(A,N,n,iis);
1539:   return(0);
1540: }

1542: /*@C
1543:    PCGASMCreateSubdomains - Creates n index sets defining n nonoverlapping subdomains for the additive
1544:    Schwarz preconditioner for a any problem based on its matrix.

1546:    Collective

1548:    Input Parameters:
1549: +  A       - The global matrix operator
1550: -  N       - the number of global subdomains requested

1552:    Output Parameters:
1553: +  n   - the number of subdomains created on this processor
1554: -  iis - the array of index sets defining the local inner subdomains (on which the correction is applied)

1556:    Level: advanced

1558:    Note: When N >= A's communicator size, each subdomain is local -- contained within a single processor.
1559:          When N < size, the subdomains are 'straddling' (processor boundaries) and are no longer local.
1560:          The resulting subdomains can be use in PCGASMSetSubdomains(pc,n,iss,NULL).  The overlapping
1561:          outer subdomains will be automatically generated from these according to the requested amount of
1562:          overlap; this is currently supported only with local subdomains.


1565: .seealso: PCGASMSetSubdomains(), PCGASMDestroySubdomains()
1566: @*/
1567: PetscErrorCode  PCGASMCreateSubdomains(Mat A,PetscInt N,PetscInt *n,IS *iis[])
1568: {
1569:   PetscMPIInt     size;
1570:   PetscErrorCode  ierr;


1576:   if (N < 1) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Number of subdomains must be > 0, N = %D",N);
1577:   MPI_Comm_size(PetscObjectComm((PetscObject)A),&size);
1578:   if (N >= size) {
1579:     *n = N/size + (N%size);
1580:     PCGASMCreateLocalSubdomains(A,*n,iis);
1581:   } else {
1582:     PCGASMCreateStraddlingSubdomains(A,N,n,iis);
1583:   }
1584:   return(0);
1585: }

1587: /*@C
1588:    PCGASMDestroySubdomains - Destroys the index sets created with
1589:    PCGASMCreateSubdomains() or PCGASMCreateSubdomains2D. Should be
1590:    called after setting subdomains with PCGASMSetSubdomains().

1592:    Collective

1594:    Input Parameters:
1595: +  n   - the number of index sets
1596: .  iis - the array of inner subdomains,
1597: -  ois - the array of outer subdomains, can be NULL

1599:    Level: intermediate

1601:    Notes:
1602:     this is merely a convenience subroutine that walks each list,
1603:    destroys each IS on the list, and then frees the list. At the end the
1604:    list pointers are set to NULL.

1606: .seealso: PCGASMCreateSubdomains(), PCGASMSetSubdomains()
1607: @*/
1608: PetscErrorCode  PCGASMDestroySubdomains(PetscInt n,IS **iis,IS **ois)
1609: {
1610:   PetscInt       i;

1614:   if (n <= 0) return(0);
1615:   if (ois) {
1617:     if (*ois) {
1619:       for (i=0; i<n; i++) {
1620:         ISDestroy(&(*ois)[i]);
1621:       }
1622:       PetscFree((*ois));
1623:     }
1624:   }
1625:   if (iis) {
1627:     if (*iis) {
1629:       for (i=0; i<n; i++) {
1630:         ISDestroy(&(*iis)[i]);
1631:       }
1632:       PetscFree((*iis));
1633:     }
1634:   }
1635:   return(0);
1636: }

1638: #define PCGASMLocalSubdomainBounds2D(M,N,xleft,ylow,xright,yhigh,first,last,xleft_loc,ylow_loc,xright_loc,yhigh_loc,n) \
1639:   {                                                                                                       \
1640:     PetscInt first_row = first/M, last_row = last/M+1;                                                     \
1641:     /*                                                                                                    \
1642:      Compute ylow_loc and yhigh_loc so that (ylow_loc,xleft) and (yhigh_loc,xright) are the corners       \
1643:      of the bounding box of the intersection of the subdomain with the local ownership range (local       \
1644:      subdomain).                                                                                          \
1645:      Also compute xleft_loc and xright_loc as the lower and upper bounds on the first and last rows       \
1646:      of the intersection.                                                                                 \
1647:     */                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             \
1648:     /* ylow_loc is the grid row containing the first element of the local sumbdomain */                   \
1649:     *ylow_loc = PetscMax(first_row,ylow);                                                                    \
1650:     /* xleft_loc is the offset of first element of the local subdomain within its grid row (might actually be outside the local subdomain) */ \
1651:     *xleft_loc = *ylow_loc==first_row ? PetscMax(first%M,xleft) : xleft;                                                                            \
1652:     /* yhigh_loc is the grid row above the last local subdomain element */                                                                    \
1653:     *yhigh_loc = PetscMin(last_row,yhigh);                                                                                                     \
1654:     /* xright is the offset of the end of the  local subdomain within its grid row (might actually be outside the local subdomain) */         \
1655:     *xright_loc = *yhigh_loc==last_row ? PetscMin(xright,last%M) : xright;                                                                          \
1656:     /* Now compute the size of the local subdomain n. */ \
1657:     *n = 0;                                               \
1658:     if (*ylow_loc < *yhigh_loc) {                           \
1659:       PetscInt width = xright-xleft;                     \
1660:       *n += width*(*yhigh_loc-*ylow_loc-1);                 \
1661:       *n += PetscMin(PetscMax(*xright_loc-xleft,0),width); \
1662:       *n -= PetscMin(PetscMax(*xleft_loc-xleft,0), width); \
1663:     } \
1664:   }

1666: /*@
1667:    PCGASMCreateSubdomains2D - Creates the index sets for the overlapping Schwarz
1668:    preconditioner for a two-dimensional problem on a regular grid.

1670:    Collective

1672:    Input Parameters:
1673: +  M, N               - the global number of grid points in the x and y directions
1674: .  Mdomains, Ndomains - the global number of subdomains in the x and y directions
1675: .  dof                - degrees of freedom per node
1676: -  overlap            - overlap in mesh lines

1678:    Output Parameters:
1679: +  Nsub - the number of local subdomains created
1680: .  iis  - array of index sets defining inner (nonoverlapping) subdomains
1681: -  ois  - array of index sets defining outer (overlapping, if overlap > 0) subdomains


1684:    Level: advanced

1686: .seealso: PCGASMSetSubdomains(), PCGASMGetSubKSP(), PCGASMSetOverlap()
1687: @*/
1688: PetscErrorCode  PCGASMCreateSubdomains2D(PC pc,PetscInt M,PetscInt N,PetscInt Mdomains,PetscInt Ndomains,PetscInt dof,PetscInt overlap,PetscInt *nsub,IS **iis,IS **ois)
1689: {
1691:   PetscMPIInt    size, rank;
1692:   PetscInt       i, j;
1693:   PetscInt       maxheight, maxwidth;
1694:   PetscInt       xstart, xleft, xright, xleft_loc, xright_loc;
1695:   PetscInt       ystart, ylow,  yhigh,  ylow_loc,  yhigh_loc;
1696:   PetscInt       x[2][2], y[2][2], n[2];
1697:   PetscInt       first, last;
1698:   PetscInt       nidx, *idx;
1699:   PetscInt       ii,jj,s,q,d;
1700:   PetscInt       k,kk;
1701:   PetscMPIInt    color;
1702:   MPI_Comm       comm, subcomm;
1703:   IS             **xis = NULL, **is = ois, **is_local = iis;

1706:   PetscObjectGetComm((PetscObject)pc, &comm);
1707:   MPI_Comm_size(comm, &size);
1708:   MPI_Comm_rank(comm, &rank);
1709:   MatGetOwnershipRange(pc->pmat, &first, &last);
1710:   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) "
1711:                                       "does not respect the number of degrees of freedom per grid point %D", first, last, dof);

1713:   /* Determine the number of domains with nonzero intersections with the local ownership range. */
1714:   s      = 0;
1715:   ystart = 0;
1716:   for (j=0; j<Ndomains; ++j) {
1717:     maxheight = N/Ndomains + ((N % Ndomains) > j); /* Maximal height of subdomain */
1718:     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);
1719:     /* Vertical domain limits with an overlap. */
1720:     ylow   = PetscMax(ystart - overlap,0);
1721:     yhigh  = PetscMin(ystart + maxheight + overlap,N);
1722:     xstart = 0;
1723:     for (i=0; i<Mdomains; ++i) {
1724:       maxwidth = M/Mdomains + ((M % Mdomains) > i); /* Maximal width of subdomain */
1725:       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);
1726:       /* Horizontal domain limits with an overlap. */
1727:       xleft  = PetscMax(xstart - overlap,0);
1728:       xright = PetscMin(xstart + maxwidth + overlap,M);
1729:       /*
1730:          Determine whether this subdomain intersects this processor's ownership range of pc->pmat.
1731:       */
1732:       PCGASMLocalSubdomainBounds2D(M,N,xleft,ylow,xright,yhigh,first,last,(&xleft_loc),(&ylow_loc),(&xright_loc),(&yhigh_loc),(&nidx));
1733:       if (nidx) ++s;
1734:       xstart += maxwidth;
1735:     } /* for (i = 0; i < Mdomains; ++i) */
1736:     ystart += maxheight;
1737:   } /* for (j = 0; j < Ndomains; ++j) */

1739:   /* Now we can allocate the necessary number of ISs. */
1740:   *nsub  = s;
1741:   PetscMalloc1(*nsub,is);
1742:   PetscMalloc1(*nsub,is_local);
1743:   s      = 0;
1744:   ystart = 0;
1745:   for (j=0; j<Ndomains; ++j) {
1746:     maxheight = N/Ndomains + ((N % Ndomains) > j); /* Maximal height of subdomain */
1747:     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);
1748:     /* Vertical domain limits with an overlap. */
1749:     y[0][0] = PetscMax(ystart - overlap,0);
1750:     y[0][1] = PetscMin(ystart + maxheight + overlap,N);
1751:     /* Vertical domain limits without an overlap. */
1752:     y[1][0] = ystart;
1753:     y[1][1] = PetscMin(ystart + maxheight,N);
1754:     xstart  = 0;
1755:     for (i=0; i<Mdomains; ++i) {
1756:       maxwidth = M/Mdomains + ((M % Mdomains) > i); /* Maximal width of subdomain */
1757:       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);
1758:       /* Horizontal domain limits with an overlap. */
1759:       x[0][0] = PetscMax(xstart - overlap,0);
1760:       x[0][1] = PetscMin(xstart + maxwidth + overlap,M);
1761:       /* Horizontal domain limits without an overlap. */
1762:       x[1][0] = xstart;
1763:       x[1][1] = PetscMin(xstart+maxwidth,M);
1764:       /*
1765:          Determine whether this domain intersects this processor's ownership range of pc->pmat.
1766:          Do this twice: first for the domains with overlaps, and once without.
1767:          During the first pass create the subcommunicators, and use them on the second pass as well.
1768:       */
1769:       for (q = 0; q < 2; ++q) {
1770:         PetscBool split = PETSC_FALSE;
1771:         /*
1772:           domain limits, (xleft, xright) and (ylow, yheigh) are adjusted
1773:           according to whether the domain with an overlap or without is considered.
1774:         */
1775:         xleft = x[q][0]; xright = x[q][1];
1776:         ylow  = y[q][0]; yhigh  = y[q][1];
1777:         PCGASMLocalSubdomainBounds2D(M,N,xleft,ylow,xright,yhigh,first,last,(&xleft_loc),(&ylow_loc),(&xright_loc),(&yhigh_loc),(&nidx));
1778:         nidx *= dof;
1779:         n[q]  = nidx;
1780:         /*
1781:          Based on the counted number of indices in the local domain *with an overlap*,
1782:          construct a subcommunicator of all the processors supporting this domain.
1783:          Observe that a domain with an overlap might have nontrivial local support,
1784:          while the domain without an overlap might not.  Hence, the decision to participate
1785:          in the subcommunicator must be based on the domain with an overlap.
1786:          */
1787:         if (q == 0) {
1788:           if (nidx) color = 1;
1789:           else color = MPI_UNDEFINED;
1790:           MPI_Comm_split(comm, color, rank, &subcomm);
1791:           split = PETSC_TRUE;
1792:         }
1793:         /*
1794:          Proceed only if the number of local indices *with an overlap* is nonzero.
1795:          */
1796:         if (n[0]) {
1797:           if (q == 0) xis = is;
1798:           if (q == 1) {
1799:             /*
1800:              The IS for the no-overlap subdomain shares a communicator with the overlapping domain.
1801:              Moreover, if the overlap is zero, the two ISs are identical.
1802:              */
1803:             if (overlap == 0) {
1804:               (*is_local)[s] = (*is)[s];
1805:               PetscObjectReference((PetscObject)(*is)[s]);
1806:               continue;
1807:             } else {
1808:               xis     = is_local;
1809:               subcomm = ((PetscObject)(*is)[s])->comm;
1810:             }
1811:           } /* if (q == 1) */
1812:           idx  = NULL;
1813:           PetscMalloc1(nidx,&idx);
1814:           if (nidx) {
1815:             k = 0;
1816:             for (jj=ylow_loc; jj<yhigh_loc; ++jj) {
1817:               PetscInt x0 = (jj==ylow_loc) ? xleft_loc : xleft;
1818:               PetscInt x1 = (jj==yhigh_loc-1) ? xright_loc : xright;
1819:               kk = dof*(M*jj + x0);
1820:               for (ii=x0; ii<x1; ++ii) {
1821:                 for (d = 0; d < dof; ++d) {
1822:                   idx[k++] = kk++;
1823:                 }
1824:               }
1825:             }
1826:           }
1827:           ISCreateGeneral(subcomm,nidx,idx,PETSC_OWN_POINTER,(*xis)+s);
1828:           if (split) {
1829:             MPI_Comm_free(&subcomm);
1830:           }
1831:         }/* if (n[0]) */
1832:       }/* for (q = 0; q < 2; ++q) */
1833:       if (n[0]) ++s;
1834:       xstart += maxwidth;
1835:     } /* for (i = 0; i < Mdomains; ++i) */
1836:     ystart += maxheight;
1837:   } /* for (j = 0; j < Ndomains; ++j) */
1838:   return(0);
1839: }

1841: /*@C
1842:     PCGASMGetSubdomains - Gets the subdomains supported on this processor
1843:     for the additive Schwarz preconditioner.

1845:     Not Collective

1847:     Input Parameter:
1848: .   pc - the preconditioner context

1850:     Output Parameters:
1851: +   n   - the number of subdomains for this processor (default value = 1)
1852: .   iis - the index sets that define the inner subdomains (without overlap) supported on this processor (can be NULL)
1853: -   ois - the index sets that define the outer subdomains (with overlap) supported on this processor (can be NULL)


1856:     Notes:
1857:     The user is responsible for destroying the ISs and freeing the returned arrays.
1858:     The IS numbering is in the parallel, global numbering of the vector.

1860:     Level: advanced

1862: .seealso: PCGASMSetOverlap(), PCGASMGetSubKSP(), PCGASMCreateSubdomains2D(),
1863:           PCGASMSetSubdomains(), PCGASMGetSubmatrices()
1864: @*/
1865: PetscErrorCode  PCGASMGetSubdomains(PC pc,PetscInt *n,IS *iis[],IS *ois[])
1866: {
1867:   PC_GASM        *osm;
1869:   PetscBool      match;
1870:   PetscInt       i;

1874:   PetscObjectTypeCompare((PetscObject)pc,PCGASM,&match);
1875:   if (!match) SETERRQ2(PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "Incorrect object type: expected %s, got %s instead", PCGASM, ((PetscObject)pc)->type_name);
1876:   osm = (PC_GASM*)pc->data;
1877:   if (n) *n = osm->n;
1878:   if (iis) {
1879:     PetscMalloc1(osm->n, iis);
1880:   }
1881:   if (ois) {
1882:     PetscMalloc1(osm->n, ois);
1883:   }
1884:   if (iis || ois) {
1885:     for (i = 0; i < osm->n; ++i) {
1886:       if (iis) (*iis)[i] = osm->iis[i];
1887:       if (ois) (*ois)[i] = osm->ois[i];
1888:     }
1889:   }
1890:   return(0);
1891: }

1893: /*@C
1894:     PCGASMGetSubmatrices - Gets the local submatrices (for this processor
1895:     only) for the additive Schwarz preconditioner.

1897:     Not Collective

1899:     Input Parameter:
1900: .   pc - the preconditioner context

1902:     Output Parameters:
1903: +   n   - the number of matrices for this processor (default value = 1)
1904: -   mat - the matrices

1906:     Notes:
1907:     matrices returned by this routine have the same communicators as the index sets (IS)
1908:            used to define subdomains in PCGASMSetSubdomains()
1909:     Level: advanced

1911: .seealso: PCGASMSetOverlap(), PCGASMGetSubKSP(),
1912:           PCGASMCreateSubdomains2D(), PCGASMSetSubdomains(), PCGASMGetSubdomains()
1913: @*/
1914: PetscErrorCode  PCGASMGetSubmatrices(PC pc,PetscInt *n,Mat *mat[])
1915: {
1916:   PC_GASM        *osm;
1918:   PetscBool      match;

1924:   if (!pc->setupcalled) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONGSTATE,"Must call after KSPSetUp() or PCSetUp().");
1925:   PetscObjectTypeCompare((PetscObject)pc,PCGASM,&match);
1926:   if (!match) SETERRQ2(PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "Expected %s, got %s instead", PCGASM, ((PetscObject)pc)->type_name);
1927:   osm = (PC_GASM*)pc->data;
1928:   if (n) *n = osm->n;
1929:   if (mat) *mat = osm->pmat;
1930:   return(0);
1931: }

1933: /*@
1934:     PCGASMSetUseDMSubdomains - Indicates whether to use DMCreateDomainDecomposition() to define the subdomains, whenever possible.
1935:     Logically Collective

1937:     Input Parameter:
1938: +   pc  - the preconditioner
1939: -   flg - boolean indicating whether to use subdomains defined by the DM

1941:     Options Database Key:
1942: .   -pc_gasm_dm_subdomains -pc_gasm_overlap -pc_gasm_total_subdomains

1944:     Level: intermediate

1946:     Notes:
1947:     PCGASMSetSubdomains(), PCGASMSetTotalSubdomains() or PCGASMSetOverlap() take precedence over PCGASMSetUseDMSubdomains(),
1948:     so setting PCGASMSetSubdomains() with nontrivial subdomain ISs or any of PCGASMSetTotalSubdomains() and PCGASMSetOverlap()
1949:     automatically turns the latter off.

1951: .seealso: PCGASMGetUseDMSubdomains(), PCGASMSetSubdomains(), PCGASMSetOverlap()
1952:           PCGASMCreateSubdomains2D()
1953: @*/
1954: PetscErrorCode  PCGASMSetUseDMSubdomains(PC pc,PetscBool flg)
1955: {
1956:   PC_GASM        *osm = (PC_GASM*)pc->data;
1958:   PetscBool      match;

1963:   if (pc->setupcalled) SETERRQ(((PetscObject)pc)->comm,PETSC_ERR_ARG_WRONGSTATE,"Not for a setup PC.");
1964:   PetscObjectTypeCompare((PetscObject)pc,PCGASM,&match);
1965:   if (match) {
1966:     if (!osm->user_subdomains && osm->N == PETSC_DETERMINE && osm->overlap < 0) {
1967:       osm->dm_subdomains = flg;
1968:     }
1969:   }
1970:   return(0);
1971: }

1973: /*@
1974:     PCGASMGetUseDMSubdomains - Returns flag indicating whether to use DMCreateDomainDecomposition() to define the subdomains, whenever possible.
1975:     Not Collective

1977:     Input Parameter:
1978: .   pc  - the preconditioner

1980:     Output Parameter:
1981: .   flg - boolean indicating whether to use subdomains defined by the DM

1983:     Level: intermediate

1985: .seealso: PCGASMSetUseDMSubdomains(), PCGASMSetOverlap()
1986:           PCGASMCreateSubdomains2D()
1987: @*/
1988: PetscErrorCode  PCGASMGetUseDMSubdomains(PC pc,PetscBool* flg)
1989: {
1990:   PC_GASM        *osm = (PC_GASM*)pc->data;
1992:   PetscBool      match;

1997:   PetscObjectTypeCompare((PetscObject)pc,PCGASM,&match);
1998:   if (match) {
1999:     if (flg) *flg = osm->dm_subdomains;
2000:   }
2001:   return(0);
2002: }