Date: 2015-10-02T22:20:08+00:00

Actual source code: bddcfetidp.c
petsc-3.6.2 2015-10-02
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      1: #include <../src/ksp/pc/impls/bddc/bddc.h>
      2: #include <../src/ksp/pc/impls/bddc/bddcprivate.h>

      6: PetscErrorCode PCBDDCCreateFETIDPMatContext(PC pc, FETIDPMat_ctx *fetidpmat_ctx)
      7: {
      8:   FETIDPMat_ctx  newctx;

     12:   PetscNew(&newctx);
     13:   newctx->lambda_local    = 0;
     14:   newctx->temp_solution_B = 0;
     15:   newctx->temp_solution_D = 0;
     16:   newctx->B_delta         = 0;
     17:   newctx->B_Ddelta        = 0; /* theoretically belongs to the FETIDP preconditioner */
     18:   newctx->l2g_lambda      = 0;
     19:   /* increase the reference count for BDDC preconditioner */
     20:   PetscObjectReference((PetscObject)pc);
     21:   newctx->pc              = pc;
     22:   *fetidpmat_ctx          = newctx;
     23:   return(0);
     24: }

     28: PetscErrorCode PCBDDCCreateFETIDPPCContext(PC pc, FETIDPPC_ctx *fetidppc_ctx)
     29: {
     30:   FETIDPPC_ctx   newctx;

     34:   PetscNew(&newctx);
     35:   newctx->lambda_local    = 0;
     36:   newctx->B_Ddelta        = 0;
     37:   newctx->l2g_lambda      = 0;
     38:   /* increase the reference count for BDDC preconditioner */
     39:   PetscObjectReference((PetscObject)pc);
     40:   newctx->pc              = pc;
     41:   *fetidppc_ctx           = newctx;
     42:   return(0);
     43: }

     47: PetscErrorCode PCBDDCDestroyFETIDPMat(Mat A)
     48: {
     49:   FETIDPMat_ctx  mat_ctx;

     53:   MatShellGetContext(A,(void**)&mat_ctx);
     54:   VecDestroy(&mat_ctx->lambda_local);
     55:   VecDestroy(&mat_ctx->temp_solution_D);
     56:   VecDestroy(&mat_ctx->temp_solution_B);
     57:   MatDestroy(&mat_ctx->B_delta);
     58:   MatDestroy(&mat_ctx->B_Ddelta);
     59:   VecScatterDestroy(&mat_ctx->l2g_lambda);
     60:   PCDestroy(&mat_ctx->pc); /* decrease PCBDDC reference count */
     61:   PetscFree(mat_ctx);
     62:   return(0);
     63: }

     67: PetscErrorCode PCBDDCDestroyFETIDPPC(PC pc)
     68: {
     69:   FETIDPPC_ctx   pc_ctx;

     73:   PCShellGetContext(pc,(void**)&pc_ctx);
     74:   VecDestroy(&pc_ctx->lambda_local);
     75:   MatDestroy(&pc_ctx->B_Ddelta);
     76:   VecScatterDestroy(&pc_ctx->l2g_lambda);
     77:   MatDestroy(&pc_ctx->S_j);
     78:   PCDestroy(&pc_ctx->pc); /* decrease PCBDDC reference count */
     79:   PetscFree(pc_ctx);
     80:   return(0);
     81: }

     85: PetscErrorCode PCBDDCSetupFETIDPMatContext(FETIDPMat_ctx fetidpmat_ctx )
     86: {
     88:   PC_IS          *pcis=(PC_IS*)fetidpmat_ctx->pc->data;
     89:   PC_BDDC        *pcbddc=(PC_BDDC*)fetidpmat_ctx->pc->data;
     90:   PCBDDCGraph    mat_graph=pcbddc->mat_graph;
     91:   Mat_IS         *matis  = (Mat_IS*)fetidpmat_ctx->pc->pmat->data;
     92:   MPI_Comm       comm;
     93:   Mat            ScalingMat;
     94:   Vec            lambda_global;
     95:   IS             IS_l2g_lambda;
     96:   IS             subset,subset_mult,subset_n;
     97:   PetscBool      skip_node,fully_redundant;
     98:   PetscInt       i,j,k,s,n_boundary_dofs,n_global_lambda,n_vertices,partial_sum;
     99:   PetscInt       cum,n_local_lambda,n_lambda_for_dof,dual_size,n_neg_values,n_pos_values;
    100:   PetscMPIInt    rank,size,buf_size,neigh;
    101:   PetscScalar    scalar_value;
    102:   PetscInt       *vertex_indices;
    103:   PetscInt       *dual_dofs_boundary_indices,*aux_local_numbering_1;
    104:   const PetscInt *aux_global_numbering;
    105:   PetscInt       *aux_sums,*cols_B_delta,*l2g_indices;
    106:   PetscScalar    *array,*scaling_factors,*vals_B_delta;
    107:   PetscInt       *aux_local_numbering_2;
    108:   /* For communication of scaling factors */
    109:   PetscInt       *ptrs_buffer,neigh_position;
    110:   PetscScalar    **all_factors,*send_buffer,*recv_buffer;
    111:   MPI_Request    *send_reqs,*recv_reqs;
    112:   /* tests */
    113:   Vec            test_vec;
    114:   PetscBool      test_fetidp;
    115:   PetscViewer    viewer;

    118:   PetscObjectGetComm((PetscObject)(fetidpmat_ctx->pc),&comm);
    119:   MPI_Comm_rank(comm,&rank);
    120:   MPI_Comm_size(comm,&size);

    122:   /* Default type of lagrange multipliers is non-redundant */
    123:   fully_redundant = PETSC_FALSE;
    124:   PetscOptionsGetBool(NULL,"-fetidp_fullyredundant",&fully_redundant,NULL);

    126:   /* Evaluate local and global number of lagrange multipliers */
    127:   VecSet(pcis->vec1_N,0.0);
    128:   n_local_lambda = 0;
    129:   partial_sum = 0;
    130:   n_boundary_dofs = 0;
    131:   s = 0;
    132:   /* Get Vertices used to define the BDDC */
    133:   n_vertices = pcbddc->n_vertices;
    134:   vertex_indices = pcbddc->local_primal_ref_node;
    135:   dual_size = pcis->n_B-n_vertices;
    136:   PetscMalloc1(dual_size,&dual_dofs_boundary_indices);
    137:   PetscMalloc1(dual_size,&aux_local_numbering_1);
    138:   PetscMalloc1(dual_size,&aux_local_numbering_2);

    140:   VecGetArray(pcis->vec1_N,&array);
    141:   for (i=0;i<pcis->n;i++){
    142:     j = mat_graph->count[i]; /* RECALL: mat_graph->count[i] does not count myself */
    143:     if ( j > 0 ) {
    144:       n_boundary_dofs++;
    145:     }
    146:     skip_node = PETSC_FALSE;
    147:     if ( s < n_vertices && vertex_indices[s]==i) { /* it works for a sorted set of vertices */
    148:       skip_node = PETSC_TRUE;
    149:       s++;
    150:     }
    151:     if (j < 1) {
    152:       skip_node = PETSC_TRUE;
    153:     }
    154:     if ( !skip_node ) {
    155:       if (fully_redundant) {
    156:         /* fully redundant set of lagrange multipliers */
    157:         n_lambda_for_dof = (j*(j+1))/2;
    158:       } else {
    159:         n_lambda_for_dof = j;
    160:       }
    161:       n_local_lambda += j;
    162:       /* needed to evaluate global number of lagrange multipliers */
    163:       array[i]=(1.0*n_lambda_for_dof)/(j+1.0); /* already scaled for the next global sum */
    164:       /* store some data needed */
    165:       dual_dofs_boundary_indices[partial_sum] = n_boundary_dofs-1;
    166:       aux_local_numbering_1[partial_sum] = i;
    167:       aux_local_numbering_2[partial_sum] = n_lambda_for_dof;
    168:       partial_sum++;
    169:     }
    170:   }
    171:   VecRestoreArray(pcis->vec1_N,&array);

    173:   VecSet(pcis->vec1_global,0.0);
    174:   VecScatterBegin(matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);
    175:   VecScatterEnd(matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);
    176:   VecSum(pcis->vec1_global,&scalar_value);
    177:   fetidpmat_ctx->n_lambda = (PetscInt)PetscRealPart(scalar_value);

    179:   /* compute global ordering of lagrange multipliers and associate l2g map */
    180:   ISCreateGeneral(comm,partial_sum,aux_local_numbering_1,PETSC_COPY_VALUES,&subset_n);
    181:   ISLocalToGlobalMappingApplyIS(matis->mapping,subset_n,&subset);
    182:   ISDestroy(&subset_n);
    183:   ISCreateGeneral(comm,partial_sum,aux_local_numbering_2,PETSC_OWN_POINTER,&subset_mult);
    184:   PCBDDCSubsetNumbering(subset,subset_mult,&i,&subset_n);
    185:   ISDestroy(&subset);
    186:   if (i != fetidpmat_ctx->n_lambda) {
    187:     SETERRQ3(PETSC_COMM_WORLD,PETSC_ERR_PLIB,"Error in %s: global number of multipliers mismatch! (%d!=%d)\n",__FUNCT__,fetidpmat_ctx->n_lambda,i);
    188:   }

    190:   /* init data for scaling factors exchange */
    191:   partial_sum = 0;
    192:   j = 0;
    193:   PetscMalloc1(pcis->n_neigh,&ptrs_buffer);
    194:   PetscMalloc1(pcis->n_neigh-1,&send_reqs);
    195:   PetscMalloc1(pcis->n_neigh-1,&recv_reqs);
    196:   PetscMalloc1(pcis->n,&all_factors);
    197:   ptrs_buffer[0]=0;
    198:   for (i=1;i<pcis->n_neigh;i++) {
    199:     partial_sum += pcis->n_shared[i];
    200:     ptrs_buffer[i] = ptrs_buffer[i-1]+pcis->n_shared[i];
    201:   }
    202:   PetscMalloc1(partial_sum,&send_buffer);
    203:   PetscMalloc1(partial_sum,&recv_buffer);
    204:   PetscMalloc1(partial_sum,&all_factors[0]);
    205:   for (i=0;i<pcis->n-1;i++) {
    206:     j = mat_graph->count[i];
    207:     all_factors[i+1]=all_factors[i]+j;
    208:   }
    209:   /* scatter B scaling to N vec */
    210:   VecScatterBegin(pcis->N_to_B,pcis->D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);
    211:   VecScatterEnd(pcis->N_to_B,pcis->D,pcis->vec1_N,INSERT_VALUES,SCATTER_REVERSE);
    212:   /* communications */
    213:   VecGetArrayRead(pcis->vec1_N,(const PetscScalar**)&array);
    214:   for (i=1;i<pcis->n_neigh;i++) {
    215:     for (j=0;j<pcis->n_shared[i];j++) {
    216:       send_buffer[ptrs_buffer[i-1]+j]=array[pcis->shared[i][j]];
    217:     }
    218:     PetscMPIIntCast(ptrs_buffer[i]-ptrs_buffer[i-1],&buf_size);
    219:     PetscMPIIntCast(pcis->neigh[i],&neigh);
    220:     MPI_Isend(&send_buffer[ptrs_buffer[i-1]],buf_size,MPIU_SCALAR,neigh,0,comm,&send_reqs[i-1]);
    221:     MPI_Irecv(&recv_buffer[ptrs_buffer[i-1]],buf_size,MPIU_SCALAR,neigh,0,comm,&recv_reqs[i-1]);
    222:   }
    223:   VecRestoreArrayRead(pcis->vec1_N,(const PetscScalar**)&array);
    224:   MPI_Waitall((pcis->n_neigh-1),recv_reqs,MPI_STATUSES_IGNORE);
    225:   /* put values in correct places */
    226:   for (i=1;i<pcis->n_neigh;i++) {
    227:     for (j=0;j<pcis->n_shared[i];j++) {
    228:       k = pcis->shared[i][j];
    229:       neigh_position = 0;
    230:       while(mat_graph->neighbours_set[k][neigh_position] != pcis->neigh[i]) {neigh_position++;}
    231:       all_factors[k][neigh_position]=recv_buffer[ptrs_buffer[i-1]+j];
    232:     }
    233:   }
    234:   MPI_Waitall((pcis->n_neigh-1),send_reqs,MPI_STATUSES_IGNORE);
    235:   PetscFree(send_reqs);
    236:   PetscFree(recv_reqs);
    237:   PetscFree(send_buffer);
    238:   PetscFree(recv_buffer);
    239:   PetscFree(ptrs_buffer);

    241:   /* Compute B and B_delta (local actions) */
    242:   PetscMalloc1(pcis->n_neigh,&aux_sums);
    243:   PetscMalloc1(n_local_lambda,&l2g_indices);
    244:   PetscMalloc1(n_local_lambda,&vals_B_delta);
    245:   PetscMalloc1(n_local_lambda,&cols_B_delta);
    246:   PetscMalloc1(n_local_lambda,&scaling_factors);
    247:   ISGetIndices(subset_n,&aux_global_numbering);
    248:   n_global_lambda=0;
    249:   partial_sum=0;
    250:   cum = 0;
    251:   for (i=0;i<dual_size;i++) {
    252:     n_global_lambda = aux_global_numbering[cum];
    253:     j = mat_graph->count[aux_local_numbering_1[i]];
    254:     aux_sums[0]=0;
    255:     for (s=1;s<j;s++) {
    256:       aux_sums[s]=aux_sums[s-1]+j-s+1;
    257:     }
    258:     array = all_factors[aux_local_numbering_1[i]];
    259:     n_neg_values = 0;
    260:     while(n_neg_values < j && mat_graph->neighbours_set[aux_local_numbering_1[i]][n_neg_values] < rank) {n_neg_values++;}
    261:     n_pos_values = j - n_neg_values;
    262:     if (fully_redundant) {
    263:       for (s=0;s<n_neg_values;s++) {
    264:         l2g_indices    [partial_sum+s]=aux_sums[s]+n_neg_values-s-1+n_global_lambda;
    265:         cols_B_delta   [partial_sum+s]=dual_dofs_boundary_indices[i];
    266:         vals_B_delta   [partial_sum+s]=-1.0;
    267:         scaling_factors[partial_sum+s]=array[s];
    268:       }
    269:       for (s=0;s<n_pos_values;s++) {
    270:         l2g_indices    [partial_sum+s+n_neg_values]=aux_sums[n_neg_values]+s+n_global_lambda;
    271:         cols_B_delta   [partial_sum+s+n_neg_values]=dual_dofs_boundary_indices[i];
    272:         vals_B_delta   [partial_sum+s+n_neg_values]=1.0;
    273:         scaling_factors[partial_sum+s+n_neg_values]=array[s+n_neg_values];
    274:       }
    275:       partial_sum += j;
    276:     } else {
    277:       /* l2g_indices and default cols and vals of B_delta */
    278:       for (s=0;s<j;s++) {
    279:         l2g_indices    [partial_sum+s]=n_global_lambda+s;
    280:         cols_B_delta   [partial_sum+s]=dual_dofs_boundary_indices[i];
    281:         vals_B_delta   [partial_sum+s]=0.0;
    282:       }
    283:       /* B_delta */
    284:       if ( n_neg_values > 0 ) { /* there's a rank next to me to the left */
    285:         vals_B_delta   [partial_sum+n_neg_values-1]=-1.0;
    286:       }
    287:       if ( n_neg_values < j ) { /* there's a rank next to me to the right */
    288:         vals_B_delta   [partial_sum+n_neg_values]=1.0;
    289:       }
    290:       /* scaling as in Klawonn-Widlund 1999*/
    291:       for (s=0;s<n_neg_values;s++) {
    292:         scalar_value = 0.0;
    293:         for (k=0;k<s+1;k++) {
    294:           scalar_value += array[k];
    295:         }
    296:         scaling_factors[partial_sum+s] = -scalar_value;
    297:       }
    298:       for (s=0;s<n_pos_values;s++) {
    299:         scalar_value = 0.0;
    300:         for (k=s+n_neg_values;k<j;k++) {
    301:           scalar_value += array[k];
    302:         }
    303:         scaling_factors[partial_sum+s+n_neg_values] = scalar_value;
    304:       }
    305:       partial_sum += j;
    306:     }
    307:     cum += aux_local_numbering_2[i];
    308:   }
    309:   ISRestoreIndices(subset_n,&aux_global_numbering);
    310:   ISDestroy(&subset_mult);
    311:   ISDestroy(&subset_n);
    312:   PetscFree(aux_sums);
    313:   PetscFree(aux_local_numbering_1);
    314:   PetscFree(dual_dofs_boundary_indices);
    315:   PetscFree(all_factors[0]);
    316:   PetscFree(all_factors);

    318:   /* Local to global mapping of fetidpmat */
    319:   VecCreate(PETSC_COMM_SELF,&fetidpmat_ctx->lambda_local);
    320:   VecSetSizes(fetidpmat_ctx->lambda_local,n_local_lambda,n_local_lambda);
    321:   VecSetType(fetidpmat_ctx->lambda_local,VECSEQ);
    322:   VecCreate(comm,&lambda_global);
    323:   VecSetSizes(lambda_global,PETSC_DECIDE,fetidpmat_ctx->n_lambda);
    324:   VecSetType(lambda_global,VECMPI);
    325:   ISCreateGeneral(comm,n_local_lambda,l2g_indices,PETSC_OWN_POINTER,&IS_l2g_lambda);
    326:   VecScatterCreate(fetidpmat_ctx->lambda_local,(IS)0,lambda_global,IS_l2g_lambda,&fetidpmat_ctx->l2g_lambda);
    327:   ISDestroy(&IS_l2g_lambda);

    329:   /* Create local part of B_delta */
    330:   MatCreate(PETSC_COMM_SELF,&fetidpmat_ctx->B_delta);
    331:   MatSetSizes(fetidpmat_ctx->B_delta,n_local_lambda,pcis->n_B,n_local_lambda,pcis->n_B);
    332:   MatSetType(fetidpmat_ctx->B_delta,MATSEQAIJ);
    333:   MatSeqAIJSetPreallocation(fetidpmat_ctx->B_delta,1,NULL);
    334:   MatSetOption(fetidpmat_ctx->B_delta,MAT_IGNORE_ZERO_ENTRIES,PETSC_TRUE);
    335:   for (i=0;i<n_local_lambda;i++) {
    336:     MatSetValue(fetidpmat_ctx->B_delta,i,cols_B_delta[i],vals_B_delta[i],INSERT_VALUES);
    337:   }
    338:   PetscFree(vals_B_delta);
    339:   MatAssemblyBegin(fetidpmat_ctx->B_delta,MAT_FINAL_ASSEMBLY);
    340:   MatAssemblyEnd  (fetidpmat_ctx->B_delta,MAT_FINAL_ASSEMBLY);

    342:   if (fully_redundant) {
    343:     MatCreate(PETSC_COMM_SELF,&ScalingMat);
    344:     MatSetSizes(ScalingMat,n_local_lambda,n_local_lambda,n_local_lambda,n_local_lambda);
    345:     MatSetType(ScalingMat,MATSEQAIJ);
    346:     MatSeqAIJSetPreallocation(ScalingMat,1,NULL);
    347:     for (i=0;i<n_local_lambda;i++) {
    348:       MatSetValue(ScalingMat,i,i,scaling_factors[i],INSERT_VALUES);
    349:     }
    350:     MatAssemblyBegin(ScalingMat,MAT_FINAL_ASSEMBLY);
    351:     MatAssemblyEnd  (ScalingMat,MAT_FINAL_ASSEMBLY);
    352:     MatMatMult(ScalingMat,fetidpmat_ctx->B_delta,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&fetidpmat_ctx->B_Ddelta);
    353:     MatDestroy(&ScalingMat);
    354:   } else {
    355:     MatCreate(PETSC_COMM_SELF,&fetidpmat_ctx->B_Ddelta);
    356:     MatSetSizes(fetidpmat_ctx->B_Ddelta,n_local_lambda,pcis->n_B,n_local_lambda,pcis->n_B);
    357:     MatSetType(fetidpmat_ctx->B_Ddelta,MATSEQAIJ);
    358:     MatSeqAIJSetPreallocation(fetidpmat_ctx->B_Ddelta,1,NULL);
    359:     for (i=0;i<n_local_lambda;i++) {
    360:       MatSetValue(fetidpmat_ctx->B_Ddelta,i,cols_B_delta[i],scaling_factors[i],INSERT_VALUES);
    361:     }
    362:     MatAssemblyBegin(fetidpmat_ctx->B_Ddelta,MAT_FINAL_ASSEMBLY);
    363:     MatAssemblyEnd  (fetidpmat_ctx->B_Ddelta,MAT_FINAL_ASSEMBLY);
    364:   }
    365:   PetscFree(scaling_factors);
    366:   PetscFree(cols_B_delta);

    368:   /* Create some vectors needed by fetidp */
    369:   VecDuplicate(pcis->vec1_B,&fetidpmat_ctx->temp_solution_B);
    370:   VecDuplicate(pcis->vec1_D,&fetidpmat_ctx->temp_solution_D);

    372:   test_fetidp = PETSC_FALSE;
    373:   PetscOptionsGetBool(NULL,"-fetidp_check",&test_fetidp,NULL);

    375:   if (test_fetidp && !pcbddc->use_deluxe_scaling) {

    377:     PetscReal real_value;

    379:     PetscViewerASCIIGetStdout(comm,&viewer);
    380:     PetscViewerASCIISynchronizedAllow(viewer,PETSC_TRUE);
    381:     PetscViewerASCIIPrintf(viewer,"----------FETI_DP TESTS--------------\n");
    382:     PetscViewerASCIIPrintf(viewer,"All tests should return zero!\n");
    383:     PetscViewerASCIIPrintf(viewer,"FETIDP MAT context in the ");
    384:     if (fully_redundant) {
    385:       PetscViewerASCIIPrintf(viewer,"fully redundant case for lagrange multipliers.\n");
    386:     } else {
    387:       PetscViewerASCIIPrintf(viewer,"Non-fully redundant case for lagrange multiplier.\n");
    388:     }
    389:     PetscViewerFlush(viewer);

    391:     /******************************************************************/
    392:     /* TEST A/B: Test numbering of global lambda dofs             */
    393:     /******************************************************************/

    395:     VecDuplicate(fetidpmat_ctx->lambda_local,&test_vec);
    396:     VecSet(lambda_global,1.0);
    397:     VecSet(test_vec,1.0);
    398:     VecScatterBegin(fetidpmat_ctx->l2g_lambda,lambda_global,fetidpmat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);
    399:     VecScatterEnd  (fetidpmat_ctx->l2g_lambda,lambda_global,fetidpmat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);
    400:     scalar_value = -1.0;
    401:     VecAXPY(test_vec,scalar_value,fetidpmat_ctx->lambda_local);
    402:     VecNorm(test_vec,NORM_INFINITY,&real_value);
    403:     VecDestroy(&test_vec);
    404:     PetscViewerASCIISynchronizedPrintf(viewer,"A[%04d]: CHECK glob to loc: % 1.14e\n",rank,real_value);
    405:     PetscViewerFlush(viewer);
    406:     if (fully_redundant) {
    407:       VecSet(lambda_global,0.0);
    408:       VecSet(fetidpmat_ctx->lambda_local,0.5);
    409:       VecScatterBegin(fetidpmat_ctx->l2g_lambda,fetidpmat_ctx->lambda_local,lambda_global,ADD_VALUES,SCATTER_FORWARD);
    410:       VecScatterEnd  (fetidpmat_ctx->l2g_lambda,fetidpmat_ctx->lambda_local,lambda_global,ADD_VALUES,SCATTER_FORWARD);
    411:       VecSum(lambda_global,&scalar_value);
    412:       PetscViewerASCIISynchronizedPrintf(viewer,"B[%04d]: CHECK loc to glob: % 1.14e\n",rank,PetscRealPart(scalar_value)-fetidpmat_ctx->n_lambda);
    413:       PetscViewerFlush(viewer);
    414:     }

    416:     /******************************************************************/
    417:     /* TEST C: It should holds B_delta*w=0, w\in\widehat{W}           */
    418:     /* This is the meaning of the B matrix                            */
    419:     /******************************************************************/

    421:     VecSetRandom(pcis->vec1_N,NULL);
    422:     VecSet(pcis->vec1_global,0.0);
    423:     VecScatterBegin(matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);
    424:     VecScatterEnd  (matis->ctx,pcis->vec1_N,pcis->vec1_global,ADD_VALUES,SCATTER_REVERSE);
    425:     VecScatterBegin(matis->ctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);
    426:     VecScatterEnd  (matis->ctx,pcis->vec1_global,pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);
    427:     VecScatterBegin(pcis->N_to_B,pcis->vec1_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);
    428:     VecScatterEnd  (pcis->N_to_B,pcis->vec1_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);
    429:     /* Action of B_delta */
    430:     MatMult(fetidpmat_ctx->B_delta,pcis->vec1_B,fetidpmat_ctx->lambda_local);
    431:     VecSet(lambda_global,0.0);
    432:     VecScatterBegin(fetidpmat_ctx->l2g_lambda,fetidpmat_ctx->lambda_local,lambda_global,ADD_VALUES,SCATTER_FORWARD);
    433:     VecScatterEnd  (fetidpmat_ctx->l2g_lambda,fetidpmat_ctx->lambda_local,lambda_global,ADD_VALUES,SCATTER_FORWARD);
    434:     VecNorm(lambda_global,NORM_INFINITY,&real_value);
    435:     PetscViewerASCIIPrintf(viewer,"C[coll]: CHECK infty norm of B_delta*w (w continuous): % 1.14e\n",real_value);
    436:     PetscViewerFlush(viewer);

    438:     /******************************************************************/
    439:     /* TEST D: It should holds E_Dw = w - P_Dw w\in\widetilde{W}     */
    440:     /* E_D = R_D^TR                                                   */
    441:     /* P_D = B_{D,delta}^T B_{delta}                                  */
    442:     /* eq.44 Mandel Tezaur and Dohrmann 2005                          */
    443:     /******************************************************************/

    445:     /* compute a random vector in \widetilde{W} */
    446:     VecSetRandom(pcis->vec1_N,NULL);
    447:     scalar_value = 0.0;  /* set zero at vertices */
    448:     VecGetArray(pcis->vec1_N,&array);
    449:     for (i=0;i<n_vertices;i++) { array[vertex_indices[i]]=scalar_value; }
    450:     VecRestoreArray(pcis->vec1_N,&array);
    451:     /* store w for final comparison */
    452:     VecDuplicate(pcis->vec1_B,&test_vec);
    453:     VecScatterBegin(pcis->N_to_B,pcis->vec1_N,test_vec,INSERT_VALUES,SCATTER_FORWARD);
    454:     VecScatterEnd  (pcis->N_to_B,pcis->vec1_N,test_vec,INSERT_VALUES,SCATTER_FORWARD);

    456:     /* Jump operator P_D : results stored in pcis->vec1_B */

    458:     VecScatterBegin(pcis->N_to_B,pcis->vec1_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);
    459:     VecScatterEnd  (pcis->N_to_B,pcis->vec1_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);
    460:     /* Action of B_delta */
    461:     MatMult(fetidpmat_ctx->B_delta,pcis->vec1_B,fetidpmat_ctx->lambda_local);
    462:     VecSet(lambda_global,0.0);
    463:     VecScatterBegin(fetidpmat_ctx->l2g_lambda,fetidpmat_ctx->lambda_local,lambda_global,ADD_VALUES,SCATTER_FORWARD);
    464:     VecScatterEnd  (fetidpmat_ctx->l2g_lambda,fetidpmat_ctx->lambda_local,lambda_global,ADD_VALUES,SCATTER_FORWARD);
    465:     /* Action of B_Ddelta^T */
    466:     VecScatterBegin(fetidpmat_ctx->l2g_lambda,lambda_global,fetidpmat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);
    467:     VecScatterEnd  (fetidpmat_ctx->l2g_lambda,lambda_global,fetidpmat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);
    468:     MatMultTranspose(fetidpmat_ctx->B_Ddelta,fetidpmat_ctx->lambda_local,pcis->vec1_B);

    470:     /* Average operator E_D : results stored in pcis->vec2_B */
    471:     VecScatterBegin(pcis->N_to_B,pcis->vec1_N,pcis->vec2_B,INSERT_VALUES,SCATTER_FORWARD);
    472:     VecScatterEnd  (pcis->N_to_B,pcis->vec1_N,pcis->vec2_B,INSERT_VALUES,SCATTER_FORWARD);
    473:     PCBDDCScalingExtension(fetidpmat_ctx->pc,pcis->vec2_B,pcis->vec1_global);
    474:     VecScatterBegin(pcis->global_to_B,pcis->vec1_global,pcis->vec2_B,INSERT_VALUES,SCATTER_FORWARD);
    475:     VecScatterEnd  (pcis->global_to_B,pcis->vec1_global,pcis->vec2_B,INSERT_VALUES,SCATTER_FORWARD);

    477:     /* test E_D=I-P_D */
    478:     scalar_value = 1.0;
    479:     VecAXPY(pcis->vec1_B,scalar_value,pcis->vec2_B);
    480:     scalar_value = -1.0;
    481:     VecAXPY(pcis->vec1_B,scalar_value,test_vec);
    482:     VecNorm(pcis->vec1_B,NORM_INFINITY,&real_value);
    483:     VecDestroy(&test_vec);
    484:     PetscViewerASCIISynchronizedPrintf(viewer,"D[%04d] CHECK infty norm of E_D + P_D - I: % 1.14e\n",rank,real_value);
    485:     PetscViewerFlush(viewer);

    487:     /******************************************************************/
    488:     /* TEST E: It should holds R_D^TP_Dw=0 w\in\widetilde{W}          */
    489:     /* eq.48 Mandel Tezaur and Dohrmann 2005                          */
    490:     /******************************************************************/

    492:     VecSetRandom(pcis->vec1_N,NULL);
    493:     VecGetArray(pcis->vec1_N,&array);
    494:     scalar_value = 0.0;  /* set zero at vertices */
    495:     for (i=0;i<n_vertices;i++) { array[vertex_indices[i]]=scalar_value; }
    496:     VecRestoreArray(pcis->vec1_N,&array);

    498:     /* Jump operator P_D : results stored in pcis->vec1_B */

    500:     VecScatterBegin(pcis->N_to_B,pcis->vec1_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);
    501:     VecScatterEnd  (pcis->N_to_B,pcis->vec1_N,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);
    502:     /* Action of B_delta */
    503:     MatMult(fetidpmat_ctx->B_delta,pcis->vec1_B,fetidpmat_ctx->lambda_local);
    504:     VecSet(lambda_global,0.0);
    505:     VecScatterBegin(fetidpmat_ctx->l2g_lambda,fetidpmat_ctx->lambda_local,lambda_global,ADD_VALUES,SCATTER_FORWARD);
    506:     VecScatterEnd  (fetidpmat_ctx->l2g_lambda,fetidpmat_ctx->lambda_local,lambda_global,ADD_VALUES,SCATTER_FORWARD);
    507:     /* Action of B_Ddelta^T */
    508:     VecScatterBegin(fetidpmat_ctx->l2g_lambda,lambda_global,fetidpmat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);
    509:     VecScatterEnd  (fetidpmat_ctx->l2g_lambda,lambda_global,fetidpmat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);
    510:     MatMultTranspose(fetidpmat_ctx->B_Ddelta,fetidpmat_ctx->lambda_local,pcis->vec1_B);
    511:     /* scaling */
    512:     PCBDDCScalingExtension(fetidpmat_ctx->pc,pcis->vec1_B,pcis->vec1_global);
    513:     VecNorm(pcis->vec1_global,NORM_INFINITY,&real_value);
    514:     PetscViewerASCIIPrintf(viewer,"E[coll]: CHECK infty norm of R^T_D P_D: % 1.14e\n",real_value);
    515:     PetscViewerFlush(viewer);

    517:     if (!fully_redundant) {
    518:       /******************************************************************/
    519:       /* TEST F: It should holds B_{delta}B^T_{D,delta}=I               */
    520:       /* Corollary thm 14 Mandel Tezaur and Dohrmann 2005               */
    521:       /******************************************************************/
    522:       VecDuplicate(lambda_global,&test_vec);
    523:       VecSetRandom(lambda_global,NULL);
    524:       /* Action of B_Ddelta^T */
    525:       VecScatterBegin(fetidpmat_ctx->l2g_lambda,lambda_global,fetidpmat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);
    526:       VecScatterEnd  (fetidpmat_ctx->l2g_lambda,lambda_global,fetidpmat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);
    527:       MatMultTranspose(fetidpmat_ctx->B_Ddelta,fetidpmat_ctx->lambda_local,pcis->vec1_B);
    528:       /* Action of B_delta */
    529:       MatMult(fetidpmat_ctx->B_delta,pcis->vec1_B,fetidpmat_ctx->lambda_local);
    530:       VecSet(test_vec,0.0);
    531:       VecScatterBegin(fetidpmat_ctx->l2g_lambda,fetidpmat_ctx->lambda_local,test_vec,ADD_VALUES,SCATTER_FORWARD);
    532:       VecScatterEnd  (fetidpmat_ctx->l2g_lambda,fetidpmat_ctx->lambda_local,test_vec,ADD_VALUES,SCATTER_FORWARD);
    533:       scalar_value = -1.0;
    534:       VecAXPY(lambda_global,scalar_value,test_vec);
    535:       VecNorm(lambda_global,NORM_INFINITY,&real_value);
    536:       PetscViewerASCIIPrintf(viewer,"E[coll]: CHECK infty norm of P^T_D - I: % 1.14e\n",real_value);
    537:       PetscViewerFlush(viewer);
    538:       PetscViewerFlush(viewer);
    539:       VecDestroy(&test_vec);
    540:     }
    541:   }
    542:   /* final cleanup */
    543:   VecDestroy(&lambda_global);

    545:   return(0);
    546: }

    550: PetscErrorCode PCBDDCSetupFETIDPPCContext(Mat fetimat, FETIDPPC_ctx fetidppc_ctx)
    551: {
    552:   FETIDPMat_ctx  mat_ctx;
    553:   PC_IS          *pcis;

    557:   MatShellGetContext(fetimat,(void**)&mat_ctx);
    558:   /* get references from objects created when setting up feti mat context */
    559:   PetscObjectReference((PetscObject)mat_ctx->lambda_local);
    560:   fetidppc_ctx->lambda_local = mat_ctx->lambda_local;
    561:   PetscObjectReference((PetscObject)mat_ctx->B_Ddelta);
    562:   fetidppc_ctx->B_Ddelta = mat_ctx->B_Ddelta;
    563:   PetscObjectReference((PetscObject)mat_ctx->l2g_lambda);
    564:   fetidppc_ctx->l2g_lambda = mat_ctx->l2g_lambda;
    565:   /* create local Schur complement matrix */
    566:   pcis = (PC_IS*)fetidppc_ctx->pc->data;
    567:   MatCreateSchurComplement(pcis->A_II,pcis->A_II,pcis->A_IB,pcis->A_BI,pcis->A_BB,&fetidppc_ctx->S_j);
    568:   MatSchurComplementSetKSP(fetidppc_ctx->S_j,pcis->ksp_D);
    569:   return(0);
    570: }

    574: PetscErrorCode FETIDPMatMult(Mat fetimat, Vec x, Vec y)
    575: {
    576:   FETIDPMat_ctx  mat_ctx;
    577:   PC_IS          *pcis;

    581:   MatShellGetContext(fetimat,(void**)&mat_ctx);
    582:   pcis = (PC_IS*)mat_ctx->pc->data;
    583:   /* Application of B_delta^T */
    584:   VecScatterBegin(mat_ctx->l2g_lambda,x,mat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);
    585:   VecScatterEnd(mat_ctx->l2g_lambda,x,mat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);
    586:   MatMultTranspose(mat_ctx->B_delta,mat_ctx->lambda_local,pcis->vec1_B);
    587:   /* Application of \widetilde{S}^-1 */
    588:   VecSet(pcis->vec1_D,0.0);
    589:   PCBDDCApplyInterfacePreconditioner(mat_ctx->pc,PETSC_FALSE);
    590:   /* Application of B_delta */
    591:   MatMult(mat_ctx->B_delta,pcis->vec1_B,mat_ctx->lambda_local);
    592:   VecSet(y,0.0);
    593:   VecScatterBegin(mat_ctx->l2g_lambda,mat_ctx->lambda_local,y,ADD_VALUES,SCATTER_FORWARD);
    594:   VecScatterEnd(mat_ctx->l2g_lambda,mat_ctx->lambda_local,y,ADD_VALUES,SCATTER_FORWARD);
    595:   return(0);
    596: }

    600: PetscErrorCode FETIDPMatMultTranspose(Mat fetimat, Vec x, Vec y)
    601: {
    602:   FETIDPMat_ctx  mat_ctx;
    603:   PC_IS          *pcis;

    607:   MatShellGetContext(fetimat,(void**)&mat_ctx);
    608:   pcis = (PC_IS*)mat_ctx->pc->data;
    609:   /* Application of B_delta^T */
    610:   VecScatterBegin(mat_ctx->l2g_lambda,x,mat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);
    611:   VecScatterEnd(mat_ctx->l2g_lambda,x,mat_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);
    612:   MatMultTranspose(mat_ctx->B_delta,mat_ctx->lambda_local,pcis->vec1_B);
    613:   /* Application of \widetilde{S}^-1 */
    614:   VecSet(pcis->vec1_D,0.0);
    615:   PCBDDCApplyInterfacePreconditioner(mat_ctx->pc,PETSC_TRUE);
    616:   /* Application of B_delta */
    617:   MatMult(mat_ctx->B_delta,pcis->vec1_B,mat_ctx->lambda_local);
    618:   VecSet(y,0.0);
    619:   VecScatterBegin(mat_ctx->l2g_lambda,mat_ctx->lambda_local,y,ADD_VALUES,SCATTER_FORWARD);
    620:   VecScatterEnd(mat_ctx->l2g_lambda,mat_ctx->lambda_local,y,ADD_VALUES,SCATTER_FORWARD);
    621:   return(0);
    622: }

    626: PetscErrorCode FETIDPPCApply(PC fetipc, Vec x, Vec y)
    627: {
    628:   FETIDPPC_ctx   pc_ctx;
    629:   PC_IS          *pcis;

    633:   PCShellGetContext(fetipc,(void**)&pc_ctx);
    634:   pcis = (PC_IS*)pc_ctx->pc->data;
    635:   /* Application of B_Ddelta^T */
    636:   VecScatterBegin(pc_ctx->l2g_lambda,x,pc_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);
    637:   VecScatterEnd(pc_ctx->l2g_lambda,x,pc_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);
    638:   VecSet(pcis->vec2_B,0.0);
    639:   MatMultTranspose(pc_ctx->B_Ddelta,pc_ctx->lambda_local,pcis->vec2_B);
    640:   /* Application of local Schur complement */
    641:   MatMult(pc_ctx->S_j,pcis->vec2_B,pcis->vec1_B);
    642:   /* Application of B_Ddelta */
    643:   MatMult(pc_ctx->B_Ddelta,pcis->vec1_B,pc_ctx->lambda_local);
    644:   VecSet(y,0.0);
    645:   VecScatterBegin(pc_ctx->l2g_lambda,pc_ctx->lambda_local,y,ADD_VALUES,SCATTER_FORWARD);
    646:   VecScatterEnd(pc_ctx->l2g_lambda,pc_ctx->lambda_local,y,ADD_VALUES,SCATTER_FORWARD);
    647:   return(0);
    648: }

    652: PetscErrorCode FETIDPPCApplyTranspose(PC fetipc, Vec x, Vec y)
    653: {
    654:   FETIDPPC_ctx   pc_ctx;
    655:   PC_IS          *pcis;

    659:   PCShellGetContext(fetipc,(void**)&pc_ctx);
    660:   pcis = (PC_IS*)pc_ctx->pc->data;
    661:   /* Application of B_Ddelta^T */
    662:   VecScatterBegin(pc_ctx->l2g_lambda,x,pc_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);
    663:   VecScatterEnd(pc_ctx->l2g_lambda,x,pc_ctx->lambda_local,INSERT_VALUES,SCATTER_REVERSE);
    664:   VecSet(pcis->vec2_B,0.0);
    665:   MatMultTranspose(pc_ctx->B_Ddelta,pc_ctx->lambda_local,pcis->vec2_B);
    666:   /* Application of local Schur complement */
    667:   MatMultTranspose(pc_ctx->S_j,pcis->vec2_B,pcis->vec1_B);
    668:   /* Application of B_Ddelta */
    669:   MatMult(pc_ctx->B_Ddelta,pcis->vec1_B,pc_ctx->lambda_local);
    670:   VecSet(y,0.0);
    671:   VecScatterBegin(pc_ctx->l2g_lambda,pc_ctx->lambda_local,y,ADD_VALUES,SCATTER_FORWARD);
    672:   VecScatterEnd(pc_ctx->l2g_lambda,pc_ctx->lambda_local,y,ADD_VALUES,SCATTER_FORWARD);
    673:   return(0);
    674: }