Actual source code: gasm.c
petsc-3.10.5 2019-03-28
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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:   PetscMalloc1(16*(nidx+1)+1, &cidx);
     74:   PetscViewerStringOpen(PETSC_COMM_SELF, cidx, 16*(nidx+1)+1, &sviewer);
     75:   ISGetIndices(osm->iis[i], &idx);
     76:   for (j = 0; j < nidx; ++j) {
     77:     PetscViewerStringSPrintf(sviewer, "%D ", idx[j]);
     78:   }
     79:   ISRestoreIndices(osm->iis[i],&idx);
     80:   PetscViewerDestroy(&sviewer);
     81:   PetscViewerASCIIPrintf(viewer, "Inner subdomain:\n");
     82:   PetscViewerFlush(viewer);
     83:   PetscViewerASCIIPushSynchronized(viewer);
     84:   PetscViewerASCIISynchronizedPrintf(viewer, "%s", cidx);
     85:   PetscViewerFlush(viewer);
     86:   PetscViewerASCIIPopSynchronized(viewer);
     87:   PetscViewerASCIIPrintf(viewer, "\n");
     88:   PetscViewerFlush(viewer);
     89:   PetscFree(cidx);
     90:   /* Outer subdomains. */
     91:   ISGetLocalSize(osm->ois[i], &nidx);
     92:   /*
     93:    No more than 15 characters per index plus a space.
     94:    PetscViewerStringSPrintf requires a string of size at least 2, so use (nidx+1) instead of nidx,
     95:    in case nidx == 0. That will take care of the space for the trailing '\0' as well.
     96:    For nidx == 0, the whole string 16 '\0'.
     97:    */
     98:   PetscMalloc1(16*(nidx+1)+1, &cidx);
     99:   PetscViewerStringOpen(PETSC_COMM_SELF, cidx, 16*(nidx+1)+1, &sviewer);
    100:   ISGetIndices(osm->ois[i], &idx);
    101:   for (j = 0; j < nidx; ++j) {
    102:     PetscViewerStringSPrintf(sviewer,"%D ", idx[j]);
    103:   }
    104:   PetscViewerDestroy(&sviewer);
    105:   ISRestoreIndices(osm->ois[i],&idx);
    106:   PetscViewerASCIIPrintf(viewer, "Outer subdomain:\n");
    107:   PetscViewerFlush(viewer);
    108:   PetscViewerASCIIPushSynchronized(viewer);
    109:   PetscViewerASCIISynchronizedPrintf(viewer, "%s", cidx);
    110:   PetscViewerFlush(viewer);
    111:   PetscViewerASCIIPopSynchronized(viewer);
    112:   PetscViewerASCIIPrintf(viewer, "\n");
    113:   PetscViewerFlush(viewer);
    114:   PetscFree(cidx);
    115:   return(0);
    116: }

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

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

    163: static PetscErrorCode PCView_GASM(PC pc,PetscViewer viewer)
    164: {
    165:   PC_GASM        *osm = (PC_GASM*)pc->data;
    166:   const char     *prefix;
    168:   PetscMPIInt    rank, size;
    169:   PetscInt       bsz;
    170:   PetscBool      iascii,view_subdomains=PETSC_FALSE;
    171:   PetscViewer    sviewer;
    172:   PetscInt       count, l;
    173:   char           overlap[256]     = "user-defined overlap";
    174:   char           gsubdomains[256] = "unknown total number of subdomains";
    175:   char           msubdomains[256] = "unknown max number of local subdomains";
    176:   PetscInt       *numbering,*permutation;/* global numbering of locally-supported subdomains and the permutation from the local ordering */

    179:   MPI_Comm_size(PetscObjectComm((PetscObject)pc), &size);
    180:   MPI_Comm_rank(PetscObjectComm((PetscObject)pc), &rank);

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

    192:   PCGetOptionsPrefix(pc,&prefix);
    193:   PetscOptionsGetBool(NULL,prefix,"-pc_gasm_view_subdomains",&view_subdomains,NULL);

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

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

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

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

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

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

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

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

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

    431:     /*
    432:        Merge the ISs, create merged vectors and restrictions.
    433:      */
    434:     /* Merge outer subdomain ISs and construct a restriction onto the disjoint union of local outer subdomains. */
    435:     on = 0;
    436:     for (i=0; i<osm->n; i++) {
    437:       ISGetLocalSize(osm->ois[i],&oni);
    438:       on  += oni;
    439:     }
    440:     PetscMalloc1(on, &oidx);
    441:     on   = 0;
    442:     /* Merge local indices together */
    443:     for (i=0; i<osm->n; i++) {
    444:       ISGetLocalSize(osm->ois[i],&oni);
    445:       ISGetIndices(osm->ois[i],&oidxi);
    446:       PetscMemcpy(oidx+on,oidxi,sizeof(PetscInt)*oni);
    447:       ISRestoreIndices(osm->ois[i],&oidxi);
    448:       on  += oni;
    449:     }
    450:     ISCreateGeneral(((PetscObject)(pc))->comm,on,oidx,PETSC_OWN_POINTER,&gois);
    451:     nTotalInnerIndices = 0;
    452:     for(i=0; i<osm->n; i++){
    453:       ISGetLocalSize(osm->iis[i],&nInnerIndices);
    454:       nTotalInnerIndices += nInnerIndices;
    455:     }
    456:     VecCreateMPI(((PetscObject)(pc))->comm,nTotalInnerIndices,PETSC_DETERMINE,&x);
    457:     VecDuplicate(x,&y);

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

    470:     /* Merge inner subdomain ISs and construct a restriction onto the disjoint union of local inner subdomains. */
    471:     {
    472:       PetscInt        ini;           /* Number of indices the i-th a local inner subdomain. */
    473:       PetscInt        in;            /* Number of indices in the disjoint uniont of local inner subdomains. */
    474:       PetscInt       *iidx;          /* Global indices in the merged local inner subdomain. */
    475:       PetscInt       *ioidx;         /* Global indices of the disjoint union of inner subdomains within the disjoint union of outer subdomains. */
    476:       IS              giis;          /* IS for the disjoint union of inner subdomains. */
    477:       IS              giois;         /* IS for the disjoint union of inner subdomains within the disjoint union of outer subdomains. */
    478:       PetscScalar    *array;
    479:       const PetscInt *indices;
    480:       PetscInt        k;
    481:       on = 0;
    482:       for (i=0; i<osm->n; i++) {
    483:         ISGetLocalSize(osm->ois[i],&oni);
    484:         on  += oni;
    485:       }
    486:       PetscMalloc1(on, &iidx);
    487:       PetscMalloc1(on, &ioidx);
    488:       VecGetArray(y,&array);
    489:       /* set communicator id to determine where overlap is */
    490:       in   = 0;
    491:       for (i=0; i<osm->n; i++) {
    492:         ISGetLocalSize(osm->iis[i],&ini);
    493:         for (k = 0; k < ini; ++k){
    494:           array[in+k] = numbering[i];
    495:         }
    496:         in += ini;
    497:       }
    498:       VecRestoreArray(y,&array);
    499:       VecScatterBegin(osm->gorestriction,y,osm->gy,INSERT_VALUES,SCATTER_FORWARD);
    500:       VecScatterEnd(osm->gorestriction,y,osm->gy,INSERT_VALUES,SCATTER_FORWARD);
    501:       VecGetOwnershipRange(osm->gy,&gostart, NULL);
    502:       VecGetArray(osm->gy,&array);
    503:       on  = 0;
    504:       in  = 0;
    505:       for (i=0; i<osm->n; i++) {
    506:             ISGetLocalSize(osm->ois[i],&oni);
    507:             ISGetIndices(osm->ois[i],&indices);
    508:             for (k=0; k<oni; k++) {
    509:           /*  skip overlapping indices to get inner domain */
    510:           if(PetscRealPart(array[on+k]) != numbering[i]) continue;
    511:           iidx[in]    = indices[k];
    512:           ioidx[in++] = gostart+on+k;
    513:             }
    514:             ISRestoreIndices(osm->ois[i], &indices);
    515:             on += oni;
    516:       }
    517:       VecRestoreArray(osm->gy,&array);
    518:       ISCreateGeneral(PetscObjectComm((PetscObject)pc),in,iidx,PETSC_OWN_POINTER,&giis);
    519:       ISCreateGeneral(PetscObjectComm((PetscObject)pc),in,ioidx,PETSC_OWN_POINTER,&giois);
    520:       VecScatterCreate(y,giis,osm->gy,giois,&osm->girestriction);
    521:       VecDestroy(&y);
    522:       ISDestroy(&giis);
    523:       ISDestroy(&giois);
    524:     }
    525:     ISDestroy(&goid);
    526:     PetscFree(numbering);

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

    570:   } else { /* if (pc->setupcalled) */
    571:     /*
    572:        Destroy the submatrices from the previous iteration
    573:     */
    574:     if (pc->flag == DIFFERENT_NONZERO_PATTERN) {
    575:       MatDestroyMatrices(osm->n,&osm->pmat);
    576:       scall = MAT_INITIAL_MATRIX;
    577:     }
    578:     if(osm->permutationIS){
    579:       MatCreateSubMatrix(pc->pmat,osm->permutationIS,osm->permutationIS,scall,&osm->permutationP);
    580:       PetscObjectReference((PetscObject)osm->permutationP);
    581:       osm->pcmat = pc->pmat;
    582:       pc->pmat   = osm->permutationP;
    583:     }

    585:   }

    588:   /*
    589:      Extract out the submatrices.
    590:   */
    591:   if (size > 1) {
    592:     MatCreateSubMatricesMPI(pc->pmat,osm->n,osm->ois,osm->ois,scall,&osm->pmat);
    593:   } else {
    594:     MatCreateSubMatrices(pc->pmat,osm->n,osm->ois,osm->ois,scall,&osm->pmat);
    595:   }
    596:   if (scall == MAT_INITIAL_MATRIX) {
    597:     PetscObjectGetOptionsPrefix((PetscObject)pc->pmat,&pprefix);
    598:     for (i=0; i<osm->n; i++) {
    599:       PetscLogObjectParent((PetscObject)pc,(PetscObject)osm->pmat[i]);
    600:       PetscObjectSetOptionsPrefix((PetscObject)osm->pmat[i],pprefix);
    601:     }
    602:   }

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

    608:   /*
    609:      Loop over submatrices putting them into local ksps
    610:   */
    611:   for (i=0; i<osm->n; i++) {
    612:     KSPSetOperators(osm->ksp[i],osm->pmat[i],osm->pmat[i]);
    613:     if (!pc->setupcalled) {
    614:       KSPSetFromOptions(osm->ksp[i]);
    615:     }
    616:   }
    617:   if(osm->pcmat){
    618:     MatDestroy(&pc->pmat);
    619:     pc->pmat   = osm->pcmat;
    620:     osm->pcmat = 0;
    621:   }
    622:   return(0);
    623: }

    625: static PetscErrorCode PCSetUpOnBlocks_GASM(PC pc)
    626: {
    627:   PC_GASM        *osm = (PC_GASM*)pc->data;
    629:   PetscInt       i;

    632:   for (i=0; i<osm->n; i++) {
    633:     KSPSetUp(osm->ksp[i]);
    634:   }
    635:   return(0);
    636: }

    638: static PetscErrorCode PCApply_GASM(PC pc,Vec xin,Vec yout)
    639: {
    640:   PC_GASM        *osm = (PC_GASM*)pc->data;
    642:   PetscInt       i;
    643:   Vec            x,y;
    644:   ScatterMode    forward = SCATTER_FORWARD,reverse = SCATTER_REVERSE;

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

    693: static PetscErrorCode PCApplyTranspose_GASM(PC pc,Vec xin,Vec yout)
    694: {
    695:   PC_GASM        *osm = (PC_GASM*)pc->data;
    697:   PetscInt       i;
    698:   Vec            x,y;
    699:   ScatterMode    forward = SCATTER_FORWARD,reverse = SCATTER_REVERSE;

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

    715:      Note: these are reversed from the PCApply_GASM() because we are applying the
    716:      transpose of the three terms
    717:   */
    718:   if (!(osm->type & PC_GASM_INTERPOLATE)) {
    719:     /* have to zero the work RHS since scatter may leave some slots empty */
    720:     VecZeroEntries(osm->gx);
    721:     VecScatterBegin(osm->girestriction,x,osm->gx,INSERT_VALUES,forward);
    722:   } else {
    723:     VecScatterBegin(osm->gorestriction,x,osm->gx,INSERT_VALUES,forward);
    724:   }
    725:   VecZeroEntries(osm->gy);
    726:   if (!(osm->type & PC_GASM_INTERPOLATE)) {
    727:     VecScatterEnd(osm->girestriction,x,osm->gx,INSERT_VALUES,forward);
    728:   } else {
    729:     VecScatterEnd(osm->gorestriction,x,osm->gx,INSERT_VALUES,forward);
    730:   }
    731:   /* do the local solves */
    732:   for (i=0; i<osm->n; ++i) { /* Note that the solves are local, so we can go to osm->n, rather than osm->nmax. */
    733:     KSPSolveTranspose(osm->ksp[i],osm->x[i],osm->y[i]);
    734:   }
    735:   VecZeroEntries(y);
    736:   if (!(osm->type & PC_GASM_RESTRICT)) {
    737:     VecScatterBegin(osm->girestriction,osm->gy,y,ADD_VALUES,reverse);
    738:     VecScatterEnd(osm->girestriction,osm->gy,y,ADD_VALUES,reverse);
    739:   } else {
    740:     VecScatterBegin(osm->gorestriction,osm->gy,y,ADD_VALUES,reverse);
    741:     VecScatterEnd(osm->gorestriction,osm->gy,y,ADD_VALUES,reverse);
    742:   }
    743:   if(osm->pctoouter){
    744:    VecScatterBegin(osm->pctoouter,y,yout,INSERT_VALUES,SCATTER_FORWARD);
    745:    VecScatterEnd(osm->pctoouter,y,yout,INSERT_VALUES,SCATTER_FORWARD);
    746:   }
    747:   return(0);
    748: }

    750: static PetscErrorCode PCReset_GASM(PC pc)
    751: {
    752:   PC_GASM        *osm = (PC_GASM*)pc->data;
    754:   PetscInt       i;

    757:   if (osm->ksp) {
    758:     for (i=0; i<osm->n; i++) {
    759:       KSPReset(osm->ksp[i]);
    760:     }
    761:   }
    762:   if (osm->pmat) {
    763:     if (osm->n > 0) {
    764:       PetscMPIInt size;
    765:       MPI_Comm_size(PetscObjectComm((PetscObject)pc),&size);
    766:       if (size > 1) {
    767:         /* osm->pmat is created by MatCreateSubMatricesMPI(), cannot use MatDestroySubMatrices() */
    768:         MatDestroyMatrices(osm->n,&osm->pmat);
    769:       } else {
    770:         MatDestroySubMatrices(osm->n,&osm->pmat);
    771:       }
    772:     }
    773:   }
    774:   if (osm->x) {
    775:     for (i=0; i<osm->n; i++) {
    776:       VecDestroy(&osm->x[i]);
    777:       VecDestroy(&osm->y[i]);
    778:     }
    779:   }
    780:   VecDestroy(&osm->gx);
    781:   VecDestroy(&osm->gy);

    783:   VecScatterDestroy(&osm->gorestriction);
    784:   VecScatterDestroy(&osm->girestriction);
    785:   if (!osm->user_subdomains) {
    786:     PCGASMDestroySubdomains(osm->n,&osm->ois,&osm->iis);
    787:     osm->N    = PETSC_DETERMINE;
    788:     osm->nmax = PETSC_DETERMINE;
    789:   }
    790:   if(osm->pctoouter){
    791:         VecScatterDestroy(&(osm->pctoouter));
    792:   }
    793:   if(osm->permutationIS){
    794:         ISDestroy(&(osm->permutationIS));
    795:   }
    796:   if(osm->pcx){
    797:         VecDestroy(&(osm->pcx));
    798:   }
    799:   if(osm->pcy){
    800:         VecDestroy(&(osm->pcy));
    801:   }
    802:   if(osm->permutationP){
    803:     MatDestroy(&(osm->permutationP));
    804:   }
    805:   if(osm->pcmat){
    806:         MatDestroy(&osm->pcmat);
    807:   }
    808:   return(0);
    809: }

    811: static PetscErrorCode PCDestroy_GASM(PC pc)
    812: {
    813:   PC_GASM        *osm = (PC_GASM*)pc->data;
    815:   PetscInt       i;

    818:   PCReset_GASM(pc);
    819:   /* PCReset will not destroy subdomains, if user_subdomains is true. */
    820:   PCGASMDestroySubdomains(osm->n,&osm->ois,&osm->iis);
    821:   if (osm->ksp) {
    822:     for (i=0; i<osm->n; i++) {
    823:       KSPDestroy(&osm->ksp[i]);
    824:     }
    825:     PetscFree(osm->ksp);
    826:   }
    827:   PetscFree(osm->x);
    828:   PetscFree(osm->y);
    829:   PetscFree(pc->data);
    830:   return(0);
    831: }

    833: static PetscErrorCode PCSetFromOptions_GASM(PetscOptionItems *PetscOptionsObject,PC pc)
    834: {
    835:   PC_GASM        *osm = (PC_GASM*)pc->data;
    837:   PetscInt       blocks,ovl;
    838:   PetscBool      symset,flg;
    839:   PCGASMType     gasmtype;

    842:   /* set the type to symmetric if matrix is symmetric */
    843:   if (!osm->type_set && pc->pmat) {
    844:     MatIsSymmetricKnown(pc->pmat,&symset,&flg);
    845:     if (symset && flg) osm->type = PC_GASM_BASIC;
    846:   }
    847:   PetscOptionsHead(PetscOptionsObject,"Generalized additive Schwarz options");
    848:   PetscOptionsBool("-pc_gasm_use_dm_subdomains","If subdomains aren't set, use DMCreateDomainDecomposition() to define subdomains.","PCGASMSetUseDMSubdomains",osm->dm_subdomains,&osm->dm_subdomains,&flg);
    849:   PetscOptionsInt("-pc_gasm_total_subdomains","Total number of subdomains across communicator","PCGASMSetTotalSubdomains",osm->N,&blocks,&flg);
    850:   if (flg) {
    851:     PCGASMSetTotalSubdomains(pc,blocks);
    852:   }
    853:   PetscOptionsInt("-pc_gasm_overlap","Number of overlapping degrees of freedom","PCGASMSetOverlap",osm->overlap,&ovl,&flg);
    854:   if (flg) {
    855:     PCGASMSetOverlap(pc,ovl);
    856:     osm->dm_subdomains = PETSC_FALSE;
    857:   }
    858:   flg  = PETSC_FALSE;
    859:   PetscOptionsEnum("-pc_gasm_type","Type of restriction/extension","PCGASMSetType",PCGASMTypes,(PetscEnum)osm->type,(PetscEnum*)&gasmtype,&flg);
    860:   if (flg) {PCGASMSetType(pc,gasmtype);}
    861:   PetscOptionsBool("-pc_gasm_use_hierachical_partitioning","use hierarchical partitioning",NULL,osm->hierarchicalpartitioning,&osm->hierarchicalpartitioning,&flg);
    862:   PetscOptionsTail();
    863:   return(0);
    864: }

    866: /*------------------------------------------------------------------------------------*/

    868: /*@
    869:     PCGASMSetTotalSubdomains - sets the total number of subdomains to use across the
    870:                                communicator.
    871:     Logically collective on pc

    873:     Input Parameters:
    874: +   pc  - the preconditioner
    875: -   N   - total number of subdomains

    878:     Level: beginner

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

    882: .seealso: PCGASMSetSubdomains(), PCGASMSetOverlap()
    883:           PCGASMCreateSubdomains2D()
    884: @*/
    885: PetscErrorCode  PCGASMSetTotalSubdomains(PC pc,PetscInt N)
    886: {
    887:   PC_GASM        *osm = (PC_GASM*)pc->data;
    888:   PetscMPIInt    size,rank;

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

    895:   PCGASMDestroySubdomains(osm->n,&osm->iis,&osm->ois);
    896:   osm->ois = osm->iis = NULL;

    898:   MPI_Comm_size(PetscObjectComm((PetscObject)pc),&size);
    899:   MPI_Comm_rank(PetscObjectComm((PetscObject)pc),&rank);
    900:   osm->N    = N;
    901:   osm->n    = PETSC_DETERMINE;
    902:   osm->nmax = PETSC_DETERMINE;
    903:   osm->dm_subdomains = PETSC_FALSE;
    904:   return(0);
    905: }

    908: static PetscErrorCode  PCGASMSetSubdomains_GASM(PC pc,PetscInt n,IS iis[],IS ois[])
    909: {
    910:   PC_GASM         *osm = (PC_GASM*)pc->data;
    911:   PetscErrorCode  ierr;
    912:   PetscInt        i;

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

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

    978: static PetscErrorCode  PCGASMSetOverlap_GASM(PC pc,PetscInt ovl)
    979: {
    980:   PC_GASM *osm = (PC_GASM*)pc->data;

    983:   if (ovl < 0) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_OUTOFRANGE,"Negative overlap value requested");
    984:   if (pc->setupcalled && ovl != osm->overlap) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONGSTATE,"PCGASMSetOverlap() should be called before PCSetUp().");
    985:   if (!pc->setupcalled) osm->overlap = ovl;
    986:   return(0);
    987: }

    989: static PetscErrorCode  PCGASMSetType_GASM(PC pc,PCGASMType type)
    990: {
    991:   PC_GASM *osm = (PC_GASM*)pc->data;

    994:   osm->type     = type;
    995:   osm->type_set = PETSC_TRUE;
    996:   return(0);
    997: }

    999: static PetscErrorCode  PCGASMSetSortIndices_GASM(PC pc,PetscBool doSort)
    1000: {
    1001:   PC_GASM *osm = (PC_GASM*)pc->data;

    1004:   osm->sort_indices = doSort;
    1005:   return(0);
    1006: }

    1008: /*
    1009:    FIXME: This routine might need to be modified now that multiple ranks per subdomain are allowed.
    1010:         In particular, it would upset the global subdomain number calculation.
    1011: */
    1012: static PetscErrorCode  PCGASMGetSubKSP_GASM(PC pc,PetscInt *n,PetscInt *first,KSP **ksp)
    1013: {
    1014:   PC_GASM        *osm = (PC_GASM*)pc->data;

    1018:   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");

    1020:   if (n) *n = osm->n;
    1021:   if (first) {
    1022:     MPI_Scan(&osm->n,first,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)pc));
    1023:     *first -= osm->n;
    1024:   }
    1025:   if (ksp) {
    1026:     /* Assume that local solves are now different; not necessarily
    1027:        true, though!  This flag is used only for PCView_GASM() */
    1028:     *ksp                        = osm->ksp;
    1029:     osm->same_subdomain_solvers = PETSC_FALSE;
    1030:   }
    1031:   return(0);
    1032: } /* PCGASMGetSubKSP_GASM() */

    1034: /*@C
    1035:     PCGASMSetSubdomains - Sets the subdomains for this processor
    1036:     for the additive Schwarz preconditioner.

    1038:     Collective on pc

    1040:     Input Parameters:
    1041: +   pc  - the preconditioner object
    1042: .   n   - the number of subdomains for this processor
    1043: .   iis - the index sets that define the inner subdomains (or NULL for PETSc to determine subdomains)
    1044: -   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)

    1046:     Notes:
    1047:     The IS indices use the parallel, global numbering of the vector entries.
    1048:     Inner subdomains are those where the correction is applied.
    1049:     Outer subdomains are those where the residual necessary to obtain the
    1050:     corrections is obtained (see PCGASMType for the use of inner/outer subdomains).
    1051:     Both inner and outer subdomains can extend over several processors.
    1052:     This processor's portion of a subdomain is known as a local subdomain.

    1054:     Inner subdomains can not overlap with each other, do not have any entities from remote processors,
    1055:     and  have to cover the entire local subdomain owned by the current processor. The index sets on each
    1056:     process should be ordered such that the ith local subdomain is connected to the ith remote subdomain
    1057:     on another MPI process.

    1059:     By default the GASM preconditioner uses 1 (local) subdomain per processor.

    1062:     Level: advanced

    1064: .keywords: PC, GASM, set, subdomains, additive Schwarz

    1066: .seealso: PCGASMSetNumSubdomains(), PCGASMSetOverlap(), PCGASMGetSubKSP(),
    1067:           PCGASMCreateSubdomains2D(), PCGASMGetSubdomains()
    1068: @*/
    1069: PetscErrorCode  PCGASMSetSubdomains(PC pc,PetscInt n,IS iis[],IS ois[])
    1070: {
    1071:   PC_GASM *osm = (PC_GASM*)pc->data;

    1076:   PetscTryMethod(pc,"PCGASMSetSubdomains_C",(PC,PetscInt,IS[],IS[]),(pc,n,iis,ois));
    1077:   osm->dm_subdomains = PETSC_FALSE;
    1078:   return(0);
    1079: }

    1082: /*@
    1083:     PCGASMSetOverlap - Sets the overlap between a pair of subdomains for the
    1084:     additive Schwarz preconditioner.  Either all or no processors in the
    1085:     pc communicator must call this routine.

    1087:     Logically Collective on pc

    1089:     Input Parameters:
    1090: +   pc  - the preconditioner context
    1091: -   ovl - the amount of overlap between subdomains (ovl >= 0, default value = 0)

    1093:     Options Database Key:
    1094: .   -pc_gasm_overlap <overlap> - Sets overlap

    1096:     Notes:
    1097:     By default the GASM preconditioner uses 1 subdomain per processor.  To use
    1098:     multiple subdomain per perocessor or "straddling" subdomains that intersect
    1099:     multiple processors use PCGASMSetSubdomains() (or option -pc_gasm_total_subdomains <n>).

    1101:     The overlap defaults to 0, so if one desires that no additional
    1102:     overlap be computed beyond what may have been set with a call to
    1103:     PCGASMSetSubdomains(), then ovl must be set to be 0.  In particular, if one does
    1104:     not explicitly set the subdomains in application code, then all overlap would be computed
    1105:     internally by PETSc, and using an overlap of 0 would result in an GASM
    1106:     variant that is equivalent to the block Jacobi preconditioner.

    1108:     Note that one can define initial index sets with any overlap via
    1109:     PCGASMSetSubdomains(); the routine PCGASMSetOverlap() merely allows
    1110:     PETSc to extend that overlap further, if desired.

    1112:     Level: intermediate

    1114: .keywords: PC, GASM, set, overlap

    1116: .seealso: PCGASMSetSubdomains(), PCGASMGetSubKSP(),
    1117:           PCGASMCreateSubdomains2D(), PCGASMGetSubdomains()
    1118: @*/
    1119: PetscErrorCode  PCGASMSetOverlap(PC pc,PetscInt ovl)
    1120: {
    1122:   PC_GASM *osm = (PC_GASM*)pc->data;

    1127:   PetscTryMethod(pc,"PCGASMSetOverlap_C",(PC,PetscInt),(pc,ovl));
    1128:   osm->dm_subdomains = PETSC_FALSE;
    1129:   return(0);
    1130: }

    1132: /*@
    1133:     PCGASMSetType - Sets the type of restriction and interpolation used
    1134:     for local problems in the additive Schwarz method.

    1136:     Logically Collective on PC

    1138:     Input Parameters:
    1139: +   pc  - the preconditioner context
    1140: -   type - variant of GASM, one of
    1141: .vb
    1142:       PC_GASM_BASIC       - full interpolation and restriction
    1143:       PC_GASM_RESTRICT    - full restriction, local processor interpolation
    1144:       PC_GASM_INTERPOLATE - full interpolation, local processor restriction
    1145:       PC_GASM_NONE        - local processor restriction and interpolation
    1146: .ve

    1148:     Options Database Key:
    1149: .   -pc_gasm_type [basic,restrict,interpolate,none] - Sets GASM type

    1151:     Level: intermediate

    1153: .keywords: PC, GASM, set, type

    1155: .seealso: PCGASMSetSubdomains(), PCGASMGetSubKSP(),
    1156:           PCGASMCreateSubdomains2D()
    1157: @*/
    1158: PetscErrorCode  PCGASMSetType(PC pc,PCGASMType type)
    1159: {

    1165:   PetscTryMethod(pc,"PCGASMSetType_C",(PC,PCGASMType),(pc,type));
    1166:   return(0);
    1167: }

    1169: /*@
    1170:     PCGASMSetSortIndices - Determines whether subdomain indices are sorted.

    1172:     Logically Collective on PC

    1174:     Input Parameters:
    1175: +   pc  - the preconditioner context
    1176: -   doSort - sort the subdomain indices

    1178:     Level: intermediate

    1180: .keywords: PC, GASM, set, type

    1182: .seealso: PCGASMSetSubdomains(), PCGASMGetSubKSP(),
    1183:           PCGASMCreateSubdomains2D()
    1184: @*/
    1185: PetscErrorCode  PCGASMSetSortIndices(PC pc,PetscBool doSort)
    1186: {

    1192:   PetscTryMethod(pc,"PCGASMSetSortIndices_C",(PC,PetscBool),(pc,doSort));
    1193:   return(0);
    1194: }

    1196: /*@C
    1197:    PCGASMGetSubKSP - Gets the local KSP contexts for all blocks on
    1198:    this processor.

    1200:    Collective on PC iff first_local is requested

    1202:    Input Parameter:
    1203: .  pc - the preconditioner context

    1205:    Output Parameters:
    1206: +  n_local - the number of blocks on this processor or NULL
    1207: .  first_local - the global number of the first block on this processor or NULL,
    1208:                  all processors must request or all must pass NULL
    1209: -  ksp - the array of KSP contexts

    1211:    Note:
    1212:    After PCGASMGetSubKSP() the array of KSPes is not to be freed

    1214:    Currently for some matrix implementations only 1 block per processor
    1215:    is supported.

    1217:    You must call KSPSetUp() before calling PCGASMGetSubKSP().

    1219:    Level: advanced

    1221: .keywords: PC, GASM, additive Schwarz, get, sub, KSP, context

    1223: .seealso: PCGASMSetSubdomains(), PCGASMSetOverlap(),
    1224:           PCGASMCreateSubdomains2D(),
    1225: @*/
    1226: PetscErrorCode  PCGASMGetSubKSP(PC pc,PetscInt *n_local,PetscInt *first_local,KSP *ksp[])
    1227: {

    1232:   PetscUseMethod(pc,"PCGASMGetSubKSP_C",(PC,PetscInt*,PetscInt*,KSP **),(pc,n_local,first_local,ksp));
    1233:   return(0);
    1234: }

    1236: /* -------------------------------------------------------------------------------------*/
    1237: /*MC
    1238:    PCGASM - Use the (restricted) additive Schwarz method, each block is (approximately) solved with
    1239:            its own KSP object.

    1241:    Options Database Keys:
    1242: +  -pc_gasm_total_subdomains <n>  - Sets total number of local subdomains to be distributed among processors
    1243: .  -pc_gasm_view_subdomains       - activates the printing of subdomain indices in PCView(), -ksp_view or -snes_view
    1244: .  -pc_gasm_print_subdomains      - activates the printing of subdomain indices in PCSetUp()
    1245: .  -pc_gasm_overlap <ovl>         - Sets overlap by which to (automatically) extend local subdomains
    1246: -  -pc_gasm_type [basic,restrict,interpolate,none] - Sets GASM type

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

    1252:    Notes:
    1253:     Blocks can be shared by multiple processes.

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

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

    1263:    Level: beginner

    1265:    Concepts: additive Schwarz method

    1267:     References:
    1268: +   1. - M Dryja, OB Widlund, An additive variant of the Schwarz alternating method for the case of many subregions
    1269:      Courant Institute, New York University Technical report
    1270: -   2. - Barry Smith, Petter Bjorstad, and William Gropp, Domain Decompositions: Parallel Multilevel Methods for Elliptic Partial Differential Equations,
    1271:     Cambridge University Press.

    1273: .seealso:  PCCreate(), PCSetType(), PCType (for list of available types), PC,
    1274:            PCBJACOBI,  PCGASMGetSubKSP(), PCGASMSetSubdomains(),
    1275:            PCSetModifySubmatrices(), PCGASMSetOverlap(), PCGASMSetType()

    1277: M*/

    1279: PETSC_EXTERN PetscErrorCode PCCreate_GASM(PC pc)
    1280: {
    1282:   PC_GASM        *osm;

    1285:   PetscNewLog(pc,&osm);

    1287:   osm->N                        = PETSC_DETERMINE;
    1288:   osm->n                        = PETSC_DECIDE;
    1289:   osm->nmax                     = PETSC_DETERMINE;
    1290:   osm->overlap                  = 0;
    1291:   osm->ksp                      = 0;
    1292:   osm->gorestriction            = 0;
    1293:   osm->girestriction            = 0;
    1294:   osm->pctoouter                = 0;
    1295:   osm->gx                       = 0;
    1296:   osm->gy                       = 0;
    1297:   osm->x                        = 0;
    1298:   osm->y                        = 0;
    1299:   osm->pcx                      = 0;
    1300:   osm->pcy                      = 0;
    1301:   osm->permutationIS            = 0;
    1302:   osm->permutationP             = 0;
    1303:   osm->pcmat                    = 0;
    1304:   osm->ois                      = 0;
    1305:   osm->iis                      = 0;
    1306:   osm->pmat                     = 0;
    1307:   osm->type                     = PC_GASM_RESTRICT;
    1308:   osm->same_subdomain_solvers   = PETSC_TRUE;
    1309:   osm->sort_indices             = PETSC_TRUE;
    1310:   osm->dm_subdomains            = PETSC_FALSE;
    1311:   osm->hierarchicalpartitioning = PETSC_FALSE;

    1313:   pc->data                 = (void*)osm;
    1314:   pc->ops->apply           = PCApply_GASM;
    1315:   pc->ops->applytranspose  = PCApplyTranspose_GASM;
    1316:   pc->ops->setup           = PCSetUp_GASM;
    1317:   pc->ops->reset           = PCReset_GASM;
    1318:   pc->ops->destroy         = PCDestroy_GASM;
    1319:   pc->ops->setfromoptions  = PCSetFromOptions_GASM;
    1320:   pc->ops->setuponblocks   = PCSetUpOnBlocks_GASM;
    1321:   pc->ops->view            = PCView_GASM;
    1322:   pc->ops->applyrichardson = 0;

    1324:   PetscObjectComposeFunction((PetscObject)pc,"PCGASMSetSubdomains_C",PCGASMSetSubdomains_GASM);
    1325:   PetscObjectComposeFunction((PetscObject)pc,"PCGASMSetOverlap_C",PCGASMSetOverlap_GASM);
    1326:   PetscObjectComposeFunction((PetscObject)pc,"PCGASMSetType_C",PCGASMSetType_GASM);
    1327:   PetscObjectComposeFunction((PetscObject)pc,"PCGASMSetSortIndices_C",PCGASMSetSortIndices_GASM);
    1328:   PetscObjectComposeFunction((PetscObject)pc,"PCGASMGetSubKSP_C",PCGASMGetSubKSP_GASM);
    1329:   return(0);
    1330: }

    1333: PetscErrorCode  PCGASMCreateLocalSubdomains(Mat A, PetscInt nloc, IS *iis[])
    1334: {
    1335:   MatPartitioning mpart;
    1336:   const char      *prefix;
    1337:   PetscInt        i,j,rstart,rend,bs;
    1338:   PetscBool       hasop, isbaij = PETSC_FALSE,foundpart = PETSC_FALSE;
    1339:   Mat             Ad     = NULL, adj;
    1340:   IS              ispart,isnumb,*is;
    1341:   PetscErrorCode  ierr;

    1344:   if (nloc < 1) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"number of local subdomains must > 0, got nloc = %D",nloc);

    1346:   /* Get prefix, row distribution, and block size */
    1347:   MatGetOptionsPrefix(A,&prefix);
    1348:   MatGetOwnershipRange(A,&rstart,&rend);
    1349:   MatGetBlockSize(A,&bs);
    1350:   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);

    1352:   /* Get diagonal block from matrix if possible */
    1353:   MatHasOperation(A,MATOP_GET_DIAGONAL_BLOCK,&hasop);
    1354:   if (hasop) {
    1355:     MatGetDiagonalBlock(A,&Ad);
    1356:   }
    1357:   if (Ad) {
    1358:     PetscObjectTypeCompare((PetscObject)Ad,MATSEQBAIJ,&isbaij);
    1359:     if (!isbaij) {PetscObjectTypeCompare((PetscObject)Ad,MATSEQSBAIJ,&isbaij);}
    1360:   }
    1361:   if (Ad && nloc > 1) {
    1362:     PetscBool  match,done;
    1363:     /* Try to setup a good matrix partitioning if available */
    1364:     MatPartitioningCreate(PETSC_COMM_SELF,&mpart);
    1365:     PetscObjectSetOptionsPrefix((PetscObject)mpart,prefix);
    1366:     MatPartitioningSetFromOptions(mpart);
    1367:     PetscObjectTypeCompare((PetscObject)mpart,MATPARTITIONINGCURRENT,&match);
    1368:     if (!match) {
    1369:       PetscObjectTypeCompare((PetscObject)mpart,MATPARTITIONINGSQUARE,&match);
    1370:     }
    1371:     if (!match) { /* assume a "good" partitioner is available */
    1372:       PetscInt       na;
    1373:       const PetscInt *ia,*ja;
    1374:       MatGetRowIJ(Ad,0,PETSC_TRUE,isbaij,&na,&ia,&ja,&done);
    1375:       if (done) {
    1376:         /* Build adjacency matrix by hand. Unfortunately a call to
    1377:            MatConvert(Ad,MATMPIADJ,MAT_INITIAL_MATRIX,&adj) will
    1378:            remove the block-aij structure and we cannot expect
    1379:            MatPartitioning to split vertices as we need */
    1380:         PetscInt       i,j,len,nnz,cnt,*iia=0,*jja=0;
    1381:         const PetscInt *row;
    1382:         nnz = 0;
    1383:         for (i=0; i<na; i++) { /* count number of nonzeros */
    1384:           len = ia[i+1] - ia[i];
    1385:           row = ja + ia[i];
    1386:           for (j=0; j<len; j++) {
    1387:             if (row[j] == i) { /* don't count diagonal */
    1388:               len--; break;
    1389:             }
    1390:           }
    1391:           nnz += len;
    1392:         }
    1393:         PetscMalloc1(na+1,&iia);
    1394:         PetscMalloc1(nnz,&jja);
    1395:         nnz    = 0;
    1396:         iia[0] = 0;
    1397:         for (i=0; i<na; i++) { /* fill adjacency */
    1398:           cnt = 0;
    1399:           len = ia[i+1] - ia[i];
    1400:           row = ja + ia[i];
    1401:           for (j=0; j<len; j++) {
    1402:             if (row[j] != i) jja[nnz+cnt++] = row[j]; /* if not diagonal */
    1403:           }
    1404:           nnz += cnt;
    1405:           iia[i+1] = nnz;
    1406:         }
    1407:         /* Partitioning of the adjacency matrix */
    1408:         MatCreateMPIAdj(PETSC_COMM_SELF,na,na,iia,jja,NULL,&adj);
    1409:         MatPartitioningSetAdjacency(mpart,adj);
    1410:         MatPartitioningSetNParts(mpart,nloc);
    1411:         MatPartitioningApply(mpart,&ispart);
    1412:         ISPartitioningToNumbering(ispart,&isnumb);
    1413:         MatDestroy(&adj);
    1414:         foundpart = PETSC_TRUE;
    1415:       }
    1416:       MatRestoreRowIJ(Ad,0,PETSC_TRUE,isbaij,&na,&ia,&ja,&done);
    1417:     }
    1418:     MatPartitioningDestroy(&mpart);
    1419:   }
    1420:   PetscMalloc1(nloc,&is);
    1421:   if (!foundpart) {

    1423:     /* Partitioning by contiguous chunks of rows */

    1425:     PetscInt mbs   = (rend-rstart)/bs;
    1426:     PetscInt start = rstart;
    1427:     for (i=0; i<nloc; i++) {
    1428:       PetscInt count = (mbs/nloc + ((mbs % nloc) > i)) * bs;
    1429:       ISCreateStride(PETSC_COMM_SELF,count,start,1,&is[i]);
    1430:       start += count;
    1431:     }

    1433:   } else {

    1435:     /* Partitioning by adjacency of diagonal block  */

    1437:     const PetscInt *numbering;
    1438:     PetscInt       *count,nidx,*indices,*newidx,start=0;
    1439:     /* Get node count in each partition */
    1440:     PetscMalloc1(nloc,&count);
    1441:     ISPartitioningCount(ispart,nloc,count);
    1442:     if (isbaij && bs > 1) { /* adjust for the block-aij case */
    1443:       for (i=0; i<nloc; i++) count[i] *= bs;
    1444:     }
    1445:     /* Build indices from node numbering */
    1446:     ISGetLocalSize(isnumb,&nidx);
    1447:     PetscMalloc1(nidx,&indices);
    1448:     for (i=0; i<nidx; i++) indices[i] = i; /* needs to be initialized */
    1449:     ISGetIndices(isnumb,&numbering);
    1450:     PetscSortIntWithPermutation(nidx,numbering,indices);
    1451:     ISRestoreIndices(isnumb,&numbering);
    1452:     if (isbaij && bs > 1) { /* adjust for the block-aij case */
    1453:       PetscMalloc1(nidx*bs,&newidx);
    1454:       for (i=0; i<nidx; i++) {
    1455:         for (j=0; j<bs; j++) newidx[i*bs+j] = indices[i]*bs + j;
    1456:       }
    1457:       PetscFree(indices);
    1458:       nidx   *= bs;
    1459:       indices = newidx;
    1460:     }
    1461:     /* Shift to get global indices */
    1462:     for (i=0; i<nidx; i++) indices[i] += rstart;

    1464:     /* Build the index sets for each block */
    1465:     for (i=0; i<nloc; i++) {
    1466:       ISCreateGeneral(PETSC_COMM_SELF,count[i],&indices[start],PETSC_COPY_VALUES,&is[i]);
    1467:       ISSort(is[i]);
    1468:       start += count[i];
    1469:     }

    1471:     PetscFree(count);
    1472:     PetscFree(indices);
    1473:     ISDestroy(&isnumb);
    1474:     ISDestroy(&ispart);
    1475:   }
    1476:   *iis = is;
    1477:   return(0);
    1478: }

    1480: PETSC_INTERN PetscErrorCode  PCGASMCreateStraddlingSubdomains(Mat A,PetscInt N,PetscInt *n,IS *iis[])
    1481: {
    1482:   PetscErrorCode  ierr;

    1485:   MatSubdomainsCreateCoalesce(A,N,n,iis);
    1486:   return(0);
    1487: }

    1491: /*@C
    1492:    PCGASMCreateSubdomains - Creates n index sets defining n nonoverlapping subdomains for the additive
    1493:    Schwarz preconditioner for a any problem based on its matrix.

    1495:    Collective

    1497:    Input Parameters:
    1498: +  A       - The global matrix operator
    1499: -  N       - the number of global subdomains requested

    1501:    Output Parameters:
    1502: +  n   - the number of subdomains created on this processor
    1503: -  iis - the array of index sets defining the local inner subdomains (on which the correction is applied)

    1505:    Level: advanced

    1507:    Note: When N >= A's communicator size, each subdomain is local -- contained within a single processor.
    1508:          When N < size, the subdomains are 'straddling' (processor boundaries) and are no longer local.
    1509:          The resulting subdomains can be use in PCGASMSetSubdomains(pc,n,iss,NULL).  The overlapping
    1510:          outer subdomains will be automatically generated from these according to the requested amount of
    1511:          overlap; this is currently supported only with local subdomains.

    1514: .keywords: PC, GASM, additive Schwarz, create, subdomains, unstructured grid

    1516: .seealso: PCGASMSetSubdomains(), PCGASMDestroySubdomains()
    1517: @*/
    1518: PetscErrorCode  PCGASMCreateSubdomains(Mat A,PetscInt N,PetscInt *n,IS *iis[])
    1519: {
    1520:   PetscMPIInt     size;
    1521:   PetscErrorCode  ierr;

    1527:   if (N < 1) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Number of subdomains must be > 0, N = %D",N);
    1528:   MPI_Comm_size(PetscObjectComm((PetscObject)A),&size);
    1529:   if (N >= size) {
    1530:     *n = N/size + (N%size);
    1531:     PCGASMCreateLocalSubdomains(A,*n,iis);
    1532:   } else {
    1533:     PCGASMCreateStraddlingSubdomains(A,N,n,iis);
    1534:   }
    1535:   return(0);
    1536: }

    1538: /*@C
    1539:    PCGASMDestroySubdomains - Destroys the index sets created with
    1540:    PCGASMCreateSubdomains() or PCGASMCreateSubdomains2D. Should be
    1541:    called after setting subdomains with PCGASMSetSubdomains().

    1543:    Collective

    1545:    Input Parameters:
    1546: +  n   - the number of index sets
    1547: .  iis - the array of inner subdomains,
    1548: -  ois - the array of outer subdomains, can be NULL

    1550:    Level: intermediate

    1552:    Notes:
    1553:     this is merely a convenience subroutine that walks each list,
    1554:    destroys each IS on the list, and then frees the list. At the end the
    1555:    list pointers are set to NULL.

    1557: .keywords: PC, GASM, additive Schwarz, create, subdomains, unstructured grid

    1559: .seealso: PCGASMCreateSubdomains(), PCGASMSetSubdomains()
    1560: @*/
    1561: PetscErrorCode  PCGASMDestroySubdomains(PetscInt n,IS **iis,IS **ois)
    1562: {
    1563:   PetscInt       i;

    1567:   if (n <= 0) return(0);
    1568:   if (ois) {
    1570:     if (*ois) {
    1572:       for (i=0; i<n; i++) {
    1573:         ISDestroy(&(*ois)[i]);
    1574:       }
    1575:       PetscFree((*ois));
    1576:     }
    1577:   }
    1578:   if (iis) {
    1580:     if (*iis) {
    1582:       for (i=0; i<n; i++) {
    1583:         ISDestroy(&(*iis)[i]);
    1584:       }
    1585:       PetscFree((*iis));
    1586:     }
    1587:   }
    1588:   return(0);
    1589: }

    1592: #define PCGASMLocalSubdomainBounds2D(M,N,xleft,ylow,xright,yhigh,first,last,xleft_loc,ylow_loc,xright_loc,yhigh_loc,n) \
    1593:   {                                                                                                       \
    1594:     PetscInt first_row = first/M, last_row = last/M+1;                                                     \
    1595:     /*                                                                                                    \
    1596:      Compute ylow_loc and yhigh_loc so that (ylow_loc,xleft) and (yhigh_loc,xright) are the corners       \
    1597:      of the bounding box of the intersection of the subdomain with the local ownership range (local       \
    1598:      subdomain).                                                                                          \
    1599:      Also compute xleft_loc and xright_loc as the lower and upper bounds on the first and last rows       \
    1600:      of the intersection.                                                                                 \
    1601:     */                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             \
    1602:     /* ylow_loc is the grid row containing the first element of the local sumbdomain */                   \
    1603:     *ylow_loc = PetscMax(first_row,ylow);                                                                    \
    1604:     /* xleft_loc is the offset of first element of the local subdomain within its grid row (might actually be outside the local subdomain) */ \
    1605:     *xleft_loc = *ylow_loc==first_row ? PetscMax(first%M,xleft) : xleft;                                                                            \
    1606:     /* yhigh_loc is the grid row above the last local subdomain element */                                                                    \
    1607:     *yhigh_loc = PetscMin(last_row,yhigh);                                                                                                     \
    1608:     /* xright is the offset of the end of the  local subdomain within its grid row (might actually be outside the local subdomain) */         \
    1609:     *xright_loc = *yhigh_loc==last_row ? PetscMin(xright,last%M) : xright;                                                                          \
    1610:     /* Now compute the size of the local subdomain n. */ \
    1611:     *n = 0;                                               \
    1612:     if (*ylow_loc < *yhigh_loc) {                           \
    1613:       PetscInt width = xright-xleft;                     \
    1614:       *n += width*(*yhigh_loc-*ylow_loc-1);                 \
    1615:       *n += PetscMin(PetscMax(*xright_loc-xleft,0),width); \
    1616:       *n -= PetscMin(PetscMax(*xleft_loc-xleft,0), width); \
    1617:     } \
    1618:   }

    1622: /*@
    1623:    PCGASMCreateSubdomains2D - Creates the index sets for the overlapping Schwarz
    1624:    preconditioner for a two-dimensional problem on a regular grid.

    1626:    Collective

    1628:    Input Parameters:
    1629: +  M, N               - the global number of grid points in the x and y directions
    1630: .  Mdomains, Ndomains - the global number of subdomains in the x and y directions
    1631: .  dof                - degrees of freedom per node
    1632: -  overlap            - overlap in mesh lines

    1634:    Output Parameters:
    1635: +  Nsub - the number of local subdomains created
    1636: .  iis  - array of index sets defining inner (nonoverlapping) subdomains
    1637: -  ois  - array of index sets defining outer (overlapping, if overlap > 0) subdomains

    1640:    Level: advanced

    1642: .keywords: PC, GASM, additive Schwarz, create, subdomains, 2D, regular grid

    1644: .seealso: PCGASMSetSubdomains(), PCGASMGetSubKSP(), PCGASMSetOverlap()
    1645: @*/
    1646: PetscErrorCode  PCGASMCreateSubdomains2D(PC pc,PetscInt M,PetscInt N,PetscInt Mdomains,PetscInt Ndomains,PetscInt dof,PetscInt overlap,PetscInt *nsub,IS **iis,IS **ois)
    1647: {
    1649:   PetscMPIInt    size, rank;
    1650:   PetscInt       i, j;
    1651:   PetscInt       maxheight, maxwidth;
    1652:   PetscInt       xstart, xleft, xright, xleft_loc, xright_loc;
    1653:   PetscInt       ystart, ylow,  yhigh,  ylow_loc,  yhigh_loc;
    1654:   PetscInt       x[2][2], y[2][2], n[2];
    1655:   PetscInt       first, last;
    1656:   PetscInt       nidx, *idx;
    1657:   PetscInt       ii,jj,s,q,d;
    1658:   PetscInt       k,kk;
    1659:   PetscMPIInt    color;
    1660:   MPI_Comm       comm, subcomm;
    1661:   IS             **xis = 0, **is = ois, **is_local = iis;

    1664:   PetscObjectGetComm((PetscObject)pc, &comm);
    1665:   MPI_Comm_size(comm, &size);
    1666:   MPI_Comm_rank(comm, &rank);
    1667:   MatGetOwnershipRange(pc->pmat, &first, &last);
    1668:   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) "
    1669:                                       "does not respect the number of degrees of freedom per grid point %D", first, last, dof);

    1671:   /* Determine the number of domains with nonzero intersections with the local ownership range. */
    1672:   s      = 0;
    1673:   ystart = 0;
    1674:   for (j=0; j<Ndomains; ++j) {
    1675:     maxheight = N/Ndomains + ((N % Ndomains) > j); /* Maximal height of subdomain */
    1676:     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);
    1677:     /* Vertical domain limits with an overlap. */
    1678:     ylow   = PetscMax(ystart - overlap,0);
    1679:     yhigh  = PetscMin(ystart + maxheight + overlap,N);
    1680:     xstart = 0;
    1681:     for (i=0; i<Mdomains; ++i) {
    1682:       maxwidth = M/Mdomains + ((M % Mdomains) > i); /* Maximal width of subdomain */
    1683:       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);
    1684:       /* Horizontal domain limits with an overlap. */
    1685:       xleft  = PetscMax(xstart - overlap,0);
    1686:       xright = PetscMin(xstart + maxwidth + overlap,M);
    1687:       /*
    1688:          Determine whether this subdomain intersects this processor's ownership range of pc->pmat.
    1689:       */
    1690:       PCGASMLocalSubdomainBounds2D(M,N,xleft,ylow,xright,yhigh,first,last,(&xleft_loc),(&ylow_loc),(&xright_loc),(&yhigh_loc),(&nidx));
    1691:       if (nidx) ++s;
    1692:       xstart += maxwidth;
    1693:     } /* for (i = 0; i < Mdomains; ++i) */
    1694:     ystart += maxheight;
    1695:   } /* for (j = 0; j < Ndomains; ++j) */

    1697:   /* Now we can allocate the necessary number of ISs. */
    1698:   *nsub  = s;
    1699:   PetscMalloc1(*nsub,is);
    1700:   PetscMalloc1(*nsub,is_local);
    1701:   s      = 0;
    1702:   ystart = 0;
    1703:   for (j=0; j<Ndomains; ++j) {
    1704:     maxheight = N/Ndomains + ((N % Ndomains) > j); /* Maximal height of subdomain */
    1705:     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);
    1706:     /* Vertical domain limits with an overlap. */
    1707:     y[0][0] = PetscMax(ystart - overlap,0);
    1708:     y[0][1] = PetscMin(ystart + maxheight + overlap,N);
    1709:     /* Vertical domain limits without an overlap. */
    1710:     y[1][0] = ystart;
    1711:     y[1][1] = PetscMin(ystart + maxheight,N);
    1712:     xstart  = 0;
    1713:     for (i=0; i<Mdomains; ++i) {
    1714:       maxwidth = M/Mdomains + ((M % Mdomains) > i); /* Maximal width of subdomain */
    1715:       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);
    1716:       /* Horizontal domain limits with an overlap. */
    1717:       x[0][0] = PetscMax(xstart - overlap,0);
    1718:       x[0][1] = PetscMin(xstart + maxwidth + overlap,M);
    1719:       /* Horizontal domain limits without an overlap. */
    1720:       x[1][0] = xstart;
    1721:       x[1][1] = PetscMin(xstart+maxwidth,M);
    1722:       /*
    1723:          Determine whether this domain intersects this processor's ownership range of pc->pmat.
    1724:          Do this twice: first for the domains with overlaps, and once without.
    1725:          During the first pass create the subcommunicators, and use them on the second pass as well.
    1726:       */
    1727:       for (q = 0; q < 2; ++q) {
    1728:         PetscBool split = PETSC_FALSE;
    1729:         /*
    1730:           domain limits, (xleft, xright) and (ylow, yheigh) are adjusted
    1731:           according to whether the domain with an overlap or without is considered.
    1732:         */
    1733:         xleft = x[q][0]; xright = x[q][1];
    1734:         ylow  = y[q][0]; yhigh  = y[q][1];
    1735:         PCGASMLocalSubdomainBounds2D(M,N,xleft,ylow,xright,yhigh,first,last,(&xleft_loc),(&ylow_loc),(&xright_loc),(&yhigh_loc),(&nidx));
    1736:         nidx *= dof;
    1737:         n[q]  = nidx;
    1738:         /*
    1739:          Based on the counted number of indices in the local domain *with an overlap*,
    1740:          construct a subcommunicator of all the processors supporting this domain.
    1741:          Observe that a domain with an overlap might have nontrivial local support,
    1742:          while the domain without an overlap might not.  Hence, the decision to participate
    1743:          in the subcommunicator must be based on the domain with an overlap.
    1744:          */
    1745:         if (q == 0) {
    1746:           if (nidx) color = 1;
    1747:           else color = MPI_UNDEFINED;
    1748:           MPI_Comm_split(comm, color, rank, &subcomm);
    1749:           split = PETSC_TRUE;
    1750:         }
    1751:         /*
    1752:          Proceed only if the number of local indices *with an overlap* is nonzero.
    1753:          */
    1754:         if (n[0]) {
    1755:           if (q == 0) xis = is;
    1756:           if (q == 1) {
    1757:             /*
    1758:              The IS for the no-overlap subdomain shares a communicator with the overlapping domain.
    1759:              Moreover, if the overlap is zero, the two ISs are identical.
    1760:              */
    1761:             if (overlap == 0) {
    1762:               (*is_local)[s] = (*is)[s];
    1763:               PetscObjectReference((PetscObject)(*is)[s]);
    1764:               continue;
    1765:             } else {
    1766:               xis     = is_local;
    1767:               subcomm = ((PetscObject)(*is)[s])->comm;
    1768:             }
    1769:           } /* if (q == 1) */
    1770:           idx  = NULL;
    1771:           PetscMalloc1(nidx,&idx);
    1772:           if (nidx) {
    1773:             k = 0;
    1774:             for (jj=ylow_loc; jj<yhigh_loc; ++jj) {
    1775:               PetscInt x0 = (jj==ylow_loc) ? xleft_loc : xleft;
    1776:               PetscInt x1 = (jj==yhigh_loc-1) ? xright_loc : xright;
    1777:               kk = dof*(M*jj + x0);
    1778:               for (ii=x0; ii<x1; ++ii) {
    1779:                 for (d = 0; d < dof; ++d) {
    1780:                   idx[k++] = kk++;
    1781:                 }
    1782:               }
    1783:             }
    1784:           }
    1785:           ISCreateGeneral(subcomm,nidx,idx,PETSC_OWN_POINTER,(*xis)+s);
    1786:           if (split) {
    1787:             MPI_Comm_free(&subcomm);
    1788:           }
    1789:         }/* if (n[0]) */
    1790:       }/* for (q = 0; q < 2; ++q) */
    1791:       if (n[0]) ++s;
    1792:       xstart += maxwidth;
    1793:     } /* for (i = 0; i < Mdomains; ++i) */
    1794:     ystart += maxheight;
    1795:   } /* for (j = 0; j < Ndomains; ++j) */
    1796:   return(0);
    1797: }

    1799: /*@C
    1800:     PCGASMGetSubdomains - Gets the subdomains supported on this processor
    1801:     for the additive Schwarz preconditioner.

    1803:     Not Collective

    1805:     Input Parameter:
    1806: .   pc - the preconditioner context

    1808:     Output Parameters:
    1809: +   n   - the number of subdomains for this processor (default value = 1)
    1810: .   iis - the index sets that define the inner subdomains (without overlap) supported on this processor (can be NULL)
    1811: -   ois - the index sets that define the outer subdomains (with overlap) supported on this processor (can be NULL)

    1814:     Notes:
    1815:     The user is responsible for destroying the ISs and freeing the returned arrays.
    1816:     The IS numbering is in the parallel, global numbering of the vector.

    1818:     Level: advanced

    1820: .keywords: PC, GASM, get, subdomains, additive Schwarz

    1822: .seealso: PCGASMSetOverlap(), PCGASMGetSubKSP(), PCGASMCreateSubdomains2D(),
    1823:           PCGASMSetSubdomains(), PCGASMGetSubmatrices()
    1824: @*/
    1825: PetscErrorCode  PCGASMGetSubdomains(PC pc,PetscInt *n,IS *iis[],IS *ois[])
    1826: {
    1827:   PC_GASM        *osm;
    1829:   PetscBool      match;
    1830:   PetscInt       i;

    1834:   PetscObjectTypeCompare((PetscObject)pc,PCGASM,&match);
    1835:   if (!match) SETERRQ2(PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "Incorrect object type: expected %s, got %s instead", PCGASM, ((PetscObject)pc)->type_name);
    1836:   osm = (PC_GASM*)pc->data;
    1837:   if (n) *n = osm->n;
    1838:   if (iis) {
    1839:     PetscMalloc1(osm->n, iis);
    1840:   }
    1841:   if (ois) {
    1842:     PetscMalloc1(osm->n, ois);
    1843:   }
    1844:   if (iis || ois) {
    1845:     for (i = 0; i < osm->n; ++i) {
    1846:       if (iis) (*iis)[i] = osm->iis[i];
    1847:       if (ois) (*ois)[i] = osm->ois[i];
    1848:     }
    1849:   }
    1850:   return(0);
    1851: }

    1853: /*@C
    1854:     PCGASMGetSubmatrices - Gets the local submatrices (for this processor
    1855:     only) for the additive Schwarz preconditioner.

    1857:     Not Collective

    1859:     Input Parameter:
    1860: .   pc - the preconditioner context

    1862:     Output Parameters:
    1863: +   n   - the number of matrices for this processor (default value = 1)
    1864: -   mat - the matrices

    1866:     Notes:
    1867:     matrices returned by this routine have the same communicators as the index sets (IS)
    1868:            used to define subdomains in PCGASMSetSubdomains()
    1869:     Level: advanced

    1871: .keywords: PC, GASM, set, local, subdomains, additive Schwarz, block Jacobi

    1873: .seealso: PCGASMSetOverlap(), PCGASMGetSubKSP(),
    1874:           PCGASMCreateSubdomains2D(), PCGASMSetSubdomains(), PCGASMGetSubdomains()
    1875: @*/
    1876: PetscErrorCode  PCGASMGetSubmatrices(PC pc,PetscInt *n,Mat *mat[])
    1877: {
    1878:   PC_GASM        *osm;
    1880:   PetscBool      match;

    1886:   if (!pc->setupcalled) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONGSTATE,"Must call after KSPSetUP() or PCSetUp().");
    1887:   PetscObjectTypeCompare((PetscObject)pc,PCGASM,&match);
    1888:   if (!match) SETERRQ2(PetscObjectComm((PetscObject)pc), PETSC_ERR_ARG_WRONG, "Expected %s, got %s instead", PCGASM, ((PetscObject)pc)->type_name);
    1889:   osm = (PC_GASM*)pc->data;
    1890:   if (n) *n = osm->n;
    1891:   if (mat) *mat = osm->pmat;
    1892:   return(0);
    1893: }

    1895: /*@
    1896:     PCGASMSetUseDMSubdomains - Indicates whether to use DMCreateDomainDecomposition() to define the subdomains, whenever possible.
    1897:     Logically Collective

    1899:     Input Parameter:
    1900: +   pc  - the preconditioner
    1901: -   flg - boolean indicating whether to use subdomains defined by the DM

    1903:     Options Database Key:
    1904: .   -pc_gasm_dm_subdomains -pc_gasm_overlap -pc_gasm_total_subdomains

    1906:     Level: intermediate

    1908:     Notes:
    1909:     PCGASMSetSubdomains(), PCGASMSetTotalSubdomains() or PCGASMSetOverlap() take precedence over PCGASMSetUseDMSubdomains(),
    1910:     so setting PCGASMSetSubdomains() with nontrivial subdomain ISs or any of PCGASMSetTotalSubdomains() and PCGASMSetOverlap()
    1911:     automatically turns the latter off.

    1913: .keywords: PC, ASM, DM, set, subdomains, additive Schwarz

    1915: .seealso: PCGASMGetUseDMSubdomains(), PCGASMSetSubdomains(), PCGASMSetOverlap()
    1916:           PCGASMCreateSubdomains2D()
    1917: @*/
    1918: PetscErrorCode  PCGASMSetUseDMSubdomains(PC pc,PetscBool flg)
    1919: {
    1920:   PC_GASM        *osm = (PC_GASM*)pc->data;
    1922:   PetscBool      match;

    1927:   if (pc->setupcalled) SETERRQ(((PetscObject)pc)->comm,PETSC_ERR_ARG_WRONGSTATE,"Not for a setup PC.");
    1928:   PetscObjectTypeCompare((PetscObject)pc,PCGASM,&match);
    1929:   if (match) {
    1930:     if (!osm->user_subdomains && osm->N == PETSC_DETERMINE && osm->overlap < 0) {
    1931:       osm->dm_subdomains = flg;
    1932:     }
    1933:   }
    1934:   return(0);
    1935: }

    1937: /*@
    1938:     PCGASMGetUseDMSubdomains - Returns flag indicating whether to use DMCreateDomainDecomposition() to define the subdomains, whenever possible.
    1939:     Not Collective

    1941:     Input Parameter:
    1942: .   pc  - the preconditioner

    1944:     Output Parameter:
    1945: .   flg - boolean indicating whether to use subdomains defined by the DM

    1947:     Level: intermediate

    1949: .keywords: PC, ASM, DM, set, subdomains, additive Schwarz

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

    1963:   PetscObjectTypeCompare((PetscObject)pc,PCGASM,&match);
    1964:   if (match) {
    1965:     if (flg) *flg = osm->dm_subdomains;
    1966:   }
    1967:   return(0);
    1968: }