Date: 2022-03-04T17:38:52+00:00

Actual source code: nn.c

      2: #include <../src/ksp/pc/impls/is/nn/nn.h>

      4: /* -------------------------------------------------------------------------- */
      5: /*
      6:    PCSetUp_NN - Prepares for the use of the NN preconditioner
      7:                     by setting data structures and options.

      9:    Input Parameter:
     10: .  pc - the preconditioner context

     12:    Application Interface Routine: PCSetUp()

     14:    Notes:
     15:    The interface routine PCSetUp() is not usually called directly by
     16:    the user, but instead is called by PCApply() if necessary.
     17: */
     18: static PetscErrorCode PCSetUp_NN(PC pc)
     19: {

     23:   if (!pc->setupcalled) {
     24:     /* Set up all the "iterative substructuring" common block */
     25:     PCISSetUp(pc,PETSC_TRUE,PETSC_TRUE);
     26:     /* Create the coarse matrix. */
     27:     PCNNCreateCoarseMatrix(pc);
     28:   }
     29:   return(0);
     30: }

     32: /* -------------------------------------------------------------------------- */
     33: /*
     34:    PCApply_NN - Applies the NN preconditioner to a vector.

     36:    Input Parameters:
     37: .  pc - the preconditioner context
     38: .  r - input vector (global)

     40:    Output Parameter:
     41: .  z - output vector (global)

     43:    Application Interface Routine: PCApply()
     44:  */
     45: static PetscErrorCode PCApply_NN(PC pc,Vec r,Vec z)
     46: {
     47:   PC_IS          *pcis = (PC_IS*)(pc->data);
     49:   PetscScalar    m_one = -1.0;
     50:   Vec            w     = pcis->vec1_global;

     53:   /*
     54:     Dirichlet solvers.
     55:     Solving $ B_I^{(i)}r_I^{(i)} $ at each processor.
     56:     Storing the local results at vec2_D
     57:   */
     58:   VecScatterBegin(pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);
     59:   VecScatterEnd  (pcis->global_to_D,r,pcis->vec1_D,INSERT_VALUES,SCATTER_FORWARD);
     60:   KSPSolve(pcis->ksp_D,pcis->vec1_D,pcis->vec2_D);

     62:   /*
     63:     Computing $ r_B - \sum_j \tilde R_j^T A_{BI}^{(j)} (B_I^{(j)}r_I^{(j)}) $ .
     64:     Storing the result in the interface portion of the global vector w.
     65:   */
     66:   MatMult(pcis->A_BI,pcis->vec2_D,pcis->vec1_B);
     67:   VecScale(pcis->vec1_B,m_one);
     68:   VecCopy(r,w);
     69:   VecScatterBegin(pcis->global_to_B,pcis->vec1_B,w,ADD_VALUES,SCATTER_REVERSE);
     70:   VecScatterEnd  (pcis->global_to_B,pcis->vec1_B,w,ADD_VALUES,SCATTER_REVERSE);

     72:   /*
     73:     Apply the interface preconditioner
     74:   */
     75:   PCNNApplyInterfacePreconditioner(pc,w,z,pcis->work_N,pcis->vec1_B,pcis->vec2_B,pcis->vec3_B,pcis->vec1_D,
     76:                                           pcis->vec3_D,pcis->vec1_N,pcis->vec2_N);

     78:   /*
     79:     Computing $ t_I^{(i)} = A_{IB}^{(i)} \tilde R_i z_B $
     80:     The result is stored in vec1_D.
     81:   */
     82:   VecScatterBegin(pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);
     83:   VecScatterEnd  (pcis->global_to_B,z,pcis->vec1_B,INSERT_VALUES,SCATTER_FORWARD);
     84:   MatMult(pcis->A_IB,pcis->vec1_B,pcis->vec1_D);

     86:   /*
     87:     Dirichlet solvers.
     88:     Computing $ B_I^{(i)}t_I^{(i)} $ and sticking into the global vector the blocks
     89:     $ B_I^{(i)}r_I^{(i)} - B_I^{(i)}t_I^{(i)} $.
     90:   */
     91:   VecScatterBegin(pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);
     92:   VecScatterEnd  (pcis->global_to_D,pcis->vec2_D,z,INSERT_VALUES,SCATTER_REVERSE);
     93:   KSPSolve(pcis->ksp_D,pcis->vec1_D,pcis->vec2_D);
     94:   VecScale(pcis->vec2_D,m_one);
     95:   VecScatterBegin(pcis->global_to_D,pcis->vec2_D,z,ADD_VALUES,SCATTER_REVERSE);
     96:   VecScatterEnd  (pcis->global_to_D,pcis->vec2_D,z,ADD_VALUES,SCATTER_REVERSE);
     97:   return(0);
     98: }

    100: /* -------------------------------------------------------------------------- */
    101: /*
    102:    PCDestroy_NN - Destroys the private context for the NN preconditioner
    103:    that was created with PCCreate_NN().

    105:    Input Parameter:
    106: .  pc - the preconditioner context

    108:    Application Interface Routine: PCDestroy()
    109: */
    110: static PetscErrorCode PCDestroy_NN(PC pc)
    111: {
    112:   PC_NN          *pcnn = (PC_NN*)pc->data;

    116:   PCISDestroy(pc);

    118:   MatDestroy(&pcnn->coarse_mat);
    119:   VecDestroy(&pcnn->coarse_x);
    120:   VecDestroy(&pcnn->coarse_b);
    121:   KSPDestroy(&pcnn->ksp_coarse);
    122:   if (pcnn->DZ_IN) {
    123:     PetscFree(pcnn->DZ_IN[0]);
    124:     PetscFree(pcnn->DZ_IN);
    125:   }

    127:   /*
    128:       Free the private data structure that was hanging off the PC
    129:   */
    130:   PetscFree(pc->data);
    131:   return(0);
    132: }

    134: /* -------------------------------------------------------------------------- */
    135: /*MC
    136:    PCNN - Balancing Neumann-Neumann for scalar elliptic PDEs.

    138:    Options Database Keys:
    139: +    -pc_nn_turn_off_first_balancing - do not balance the residual before solving the local Neumann problems
    140:                                        (this skips the first coarse grid solve in the preconditioner)
    141: .    -pc_nn_turn_off_second_balancing - do not balance the solution solving the local Neumann problems
    142:                                        (this skips the second coarse grid solve in the preconditioner)
    143: .    -pc_is_damp_fixed <fact> -
    144: .    -pc_is_remove_nullspace_fixed -
    145: .    -pc_is_set_damping_factor_floating <fact> -
    146: .    -pc_is_not_damp_floating -
    147: -    -pc_is_not_remove_nullspace_floating -

    149:    Level: intermediate

    151:    Notes:
    152:     The matrix used with this preconditioner must be of type MATIS

    154:           Unlike more 'conventional' Neumann-Neumann preconditioners this iterates over ALL the
    155:           degrees of freedom, NOT just those on the interface (this allows the use of approximate solvers
    156:           on the subdomains; though in our experience using approximate solvers is slower.).

    158:           Options for the coarse grid preconditioner can be set with -nn_coarse_pc_xxx
    159:           Options for the Dirichlet subproblem preconditioner can be set with -is_localD_pc_xxx
    160:           Options for the Neumann subproblem preconditioner can be set with -is_localN_pc_xxx

    162:    Contributed by Paulo Goldfeld

    164: .seealso:  PCCreate(), PCSetType(), PCType (for list of available types), PC,  MATIS
    165: M*/

    167: PETSC_EXTERN PetscErrorCode PCCreate_NN(PC pc)
    168: {
    170:   PC_NN          *pcnn;

    173:   /*
    174:      Creates the private data structure for this preconditioner and
    175:      attach it to the PC object.
    176:   */
    177:   PetscNewLog(pc,&pcnn);
    178:   pc->data = (void*)pcnn;

    180:   PCISCreate(pc);
    181:   pcnn->coarse_mat = NULL;
    182:   pcnn->coarse_x   = NULL;
    183:   pcnn->coarse_b   = NULL;
    184:   pcnn->ksp_coarse = NULL;
    185:   pcnn->DZ_IN      = NULL;

    187:   /*
    188:       Set the pointers for the functions that are provided above.
    189:       Now when the user-level routines (such as PCApply(), PCDestroy(), etc.)
    190:       are called, they will automatically call these functions.  Note we
    191:       choose not to provide a couple of these functions since they are
    192:       not needed.
    193:   */
    194:   pc->ops->apply               = PCApply_NN;
    195:   pc->ops->applytranspose      = NULL;
    196:   pc->ops->setup               = PCSetUp_NN;
    197:   pc->ops->destroy             = PCDestroy_NN;
    198:   pc->ops->view                = NULL;
    199:   pc->ops->applyrichardson     = NULL;
    200:   pc->ops->applysymmetricleft  = NULL;
    201:   pc->ops->applysymmetricright = NULL;
    202:   return(0);
    203: }

    205: /* -------------------------------------------------------------------------- */
    206: /*
    207:    PCNNCreateCoarseMatrix -
    208: */
    209: PetscErrorCode PCNNCreateCoarseMatrix(PC pc)
    210: {
    211:   MPI_Request    *send_request, *recv_request;
    213:   PetscInt       i, j, k;
    214:   PetscScalar    *mat;     /* Sub-matrix with this subdomain's contribution to the coarse matrix             */
    215:   PetscScalar    **DZ_OUT; /* proc[k].DZ_OUT[i][] = bit of vector to be sent from processor k to processor i */

    217:   /* aliasing some names */
    218:   PC_IS       *pcis     = (PC_IS*)(pc->data);
    219:   PC_NN       *pcnn     = (PC_NN*)pc->data;
    220:   PetscInt    n_neigh   = pcis->n_neigh;
    221:   PetscInt    *neigh    = pcis->neigh;
    222:   PetscInt    *n_shared = pcis->n_shared;
    223:   PetscInt    **shared  = pcis->shared;
    224:   PetscScalar **DZ_IN;   /* Must be initialized after memory allocation. */

    227:   /* Allocate memory for mat (the +1 is to handle the case n_neigh equal to zero) */
    228:   PetscMalloc1(n_neigh*n_neigh+1,&mat);

    230:   /* Allocate memory for DZ */
    231:   /* Notice that DZ_OUT[0] is allocated some space that is never used. */
    232:   /* This is just in order to DZ_OUT and DZ_IN to have exactly the same form. */
    233:   {
    234:     PetscInt size_of_Z = 0;
    235:     PetscMalloc ((n_neigh+1)*sizeof(PetscScalar*),&pcnn->DZ_IN);
    236:     DZ_IN = pcnn->DZ_IN;
    237:     PetscMalloc ((n_neigh+1)*sizeof(PetscScalar*),&DZ_OUT);
    238:     for (i=0; i<n_neigh; i++) size_of_Z += n_shared[i];
    239:     PetscMalloc ((size_of_Z+1)*sizeof(PetscScalar),&DZ_IN[0]);
    240:     PetscMalloc ((size_of_Z+1)*sizeof(PetscScalar),&DZ_OUT[0]);
    241:   }
    242:   for (i=1; i<n_neigh; i++) {
    243:     DZ_IN[i]  = DZ_IN [i-1] + n_shared[i-1];
    244:     DZ_OUT[i] = DZ_OUT[i-1] + n_shared[i-1];
    245:   }

    247:   /* Set the values of DZ_OUT, in order to send this info to the neighbours */
    248:   /* First, set the auxiliary array pcis->work_N. */
    249:   PCISScatterArrayNToVecB(pcis->work_N,pcis->D,INSERT_VALUES,SCATTER_REVERSE,pc);
    250:   for (i=1; i<n_neigh; i++) {
    251:     for (j=0; j<n_shared[i]; j++) {
    252:       DZ_OUT[i][j] = pcis->work_N[shared[i][j]];
    253:     }
    254:   }

    256:   /* Non-blocking send/receive the common-interface chunks of scaled nullspaces */
    257:   /* Notice that send_request[] and recv_request[] could have one less element. */
    258:   /* We make them longer to have request[i] corresponding to neigh[i].          */
    259:   {
    260:     PetscMPIInt tag;
    261:     PetscObjectGetNewTag((PetscObject)pc,&tag);
    262:     PetscMalloc2(n_neigh+1,&send_request,n_neigh+1,&recv_request);
    263:     for (i=1; i<n_neigh; i++) {
    264:       MPI_Isend((void*)(DZ_OUT[i]),n_shared[i],MPIU_SCALAR,neigh[i],tag,PetscObjectComm((PetscObject)pc),&(send_request[i]));
    265:       MPI_Irecv((void*)(DZ_IN [i]),n_shared[i],MPIU_SCALAR,neigh[i],tag,PetscObjectComm((PetscObject)pc),&(recv_request[i]));
    266:     }
    267:   }

    269:   /* Set DZ_IN[0][] (recall that neigh[0]==rank, always) */
    270:   for (j=0; j<n_shared[0]; j++) DZ_IN[0][j] = pcis->work_N[shared[0][j]];

    272:   /* Start computing with local D*Z while communication goes on.    */
    273:   /* Apply Schur complement. The result is "stored" in vec (more    */
    274:   /* precisely, vec points to the result, stored in pc_nn->vec1_B)  */
    275:   /* and also scattered to pcnn->work_N.                            */
    276:   PCNNApplySchurToChunk(pc,n_shared[0],shared[0],DZ_IN[0],pcis->work_N,pcis->vec1_B,pcis->vec2_B,pcis->vec1_D,pcis->vec2_D);

    278:   /* Compute the first column, while completing the receiving. */
    279:   for (i=0; i<n_neigh; i++) {
    280:     MPI_Status  stat;
    281:     PetscMPIInt ind=0;
    282:     if (i>0) {MPI_Waitany(n_neigh-1,recv_request+1,&ind,&stat); ind++;}
    283:     mat[ind*n_neigh+0] = 0.0;
    284:     for (k=0; k<n_shared[ind]; k++) mat[ind*n_neigh+0] += DZ_IN[ind][k] * pcis->work_N[shared[ind][k]];
    285:   }

    287:   /* Compute the remaining of the columns */
    288:   for (j=1; j<n_neigh; j++) {
    289:     PCNNApplySchurToChunk(pc,n_shared[j],shared[j],DZ_IN[j],pcis->work_N,pcis->vec1_B,pcis->vec2_B,pcis->vec1_D,pcis->vec2_D);
    290:     for (i=0; i<n_neigh; i++) {
    291:       mat[i*n_neigh+j] = 0.0;
    292:       for (k=0; k<n_shared[i]; k++) mat[i*n_neigh+j] += DZ_IN[i][k] * pcis->work_N[shared[i][k]];
    293:     }
    294:   }

    296:   /* Complete the sending. */
    297:   if (n_neigh>1) {
    298:     MPI_Status *stat;
    299:     PetscMalloc1(n_neigh-1,&stat);
    300:     if (n_neigh-1) {MPI_Waitall(n_neigh-1,&(send_request[1]),stat);}
    301:     PetscFree(stat);
    302:   }

    304:   /* Free the memory for the MPI requests */
    305:   PetscFree2(send_request,recv_request);

    307:   /* Free the memory for DZ_OUT */
    308:   if (DZ_OUT) {
    309:     PetscFree(DZ_OUT[0]);
    310:     PetscFree(DZ_OUT);
    311:   }

    313:   {
    314:     PetscMPIInt size;
    315:     MPI_Comm_size(PetscObjectComm((PetscObject)pc),&size);
    316:     /* Create the global coarse vectors (rhs and solution). */
    317:     VecCreateMPI(PetscObjectComm((PetscObject)pc),1,size,&(pcnn->coarse_b));
    318:     VecDuplicate(pcnn->coarse_b,&(pcnn->coarse_x));
    319:     /* Create and set the global coarse AIJ matrix. */
    320:     MatCreate(PetscObjectComm((PetscObject)pc),&(pcnn->coarse_mat));
    321:     MatSetSizes(pcnn->coarse_mat,1,1,size,size);
    322:     MatSetType(pcnn->coarse_mat,MATAIJ);
    323:     MatSeqAIJSetPreallocation(pcnn->coarse_mat,1,NULL);
    324:     MatMPIAIJSetPreallocation(pcnn->coarse_mat,1,NULL,n_neigh,NULL);
    325:     MatSetOption(pcnn->coarse_mat,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);
    326:     MatSetOption(pcnn->coarse_mat,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_FALSE);
    327:     MatSetValues(pcnn->coarse_mat,n_neigh,neigh,n_neigh,neigh,mat,ADD_VALUES);
    328:     MatAssemblyBegin(pcnn->coarse_mat,MAT_FINAL_ASSEMBLY);
    329:     MatAssemblyEnd  (pcnn->coarse_mat,MAT_FINAL_ASSEMBLY);
    330:   }

    332:   {
    333:     PetscMPIInt rank;
    334:     PetscScalar one = 1.0;
    335:     MPI_Comm_rank(PetscObjectComm((PetscObject)pc),&rank);
    336:     /* "Zero out" rows of not-purely-Neumann subdomains */
    337:     if (pcis->pure_neumann) {  /* does NOT zero the row; create an empty index set. The reason is that MatZeroRows() is collective. */
    338:       MatZeroRows(pcnn->coarse_mat,0,NULL,one,NULL,NULL);
    339:     } else { /* here it DOES zero the row, since it's not a floating subdomain. */
    340:       PetscInt row = (PetscInt) rank;
    341:       MatZeroRows(pcnn->coarse_mat,1,&row,one,NULL,NULL);
    342:     }
    343:   }

    345:   /* Create the coarse linear solver context */
    346:   {
    347:     PC  pc_ctx, inner_pc;
    348:     KSP inner_ksp;

    350:     KSPCreate(PetscObjectComm((PetscObject)pc),&pcnn->ksp_coarse);
    351:     PetscObjectIncrementTabLevel((PetscObject)pcnn->ksp_coarse,(PetscObject)pc,2);
    352:     KSPSetOperators(pcnn->ksp_coarse,pcnn->coarse_mat,pcnn->coarse_mat);
    353:     KSPGetPC(pcnn->ksp_coarse,&pc_ctx);
    354:     PCSetType(pc_ctx,PCREDUNDANT);
    355:     KSPSetType(pcnn->ksp_coarse,KSPPREONLY);
    356:     PCRedundantGetKSP(pc_ctx,&inner_ksp);
    357:     KSPGetPC(inner_ksp,&inner_pc);
    358:     PCSetType(inner_pc,PCLU);
    359:     KSPSetOptionsPrefix(pcnn->ksp_coarse,"nn_coarse_");
    360:     KSPSetFromOptions(pcnn->ksp_coarse);
    361:     /* the vectors in the following line are dummy arguments, just telling the KSP the vector size. Values are not used */
    362:     KSPSetUp(pcnn->ksp_coarse);
    363:   }

    365:   /* Free the memory for mat */
    366:   PetscFree(mat);

    368:   /* for DEBUGGING, save the coarse matrix to a file. */
    369:   {
    370:     PetscBool flg = PETSC_FALSE;
    371:     PetscOptionsGetBool(NULL,NULL,"-pc_nn_save_coarse_matrix",&flg,NULL);
    372:     if (flg) {
    373:       PetscViewer viewer;
    374:       PetscViewerASCIIOpen(PETSC_COMM_WORLD,"coarse.m",&viewer);
    375:       PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);
    376:       MatView(pcnn->coarse_mat,viewer);
    377:       PetscViewerPopFormat(viewer);
    378:       PetscViewerDestroy(&viewer);
    379:     }
    380:   }

    382:   /*  Set the variable pcnn->factor_coarse_rhs. */
    383:   pcnn->factor_coarse_rhs = (pcis->pure_neumann) ? 1.0 : 0.0;

    385:   /* See historical note 02, at the bottom of this file. */
    386:   return(0);
    387: }

    389: /* -------------------------------------------------------------------------- */
    390: /*
    391:    PCNNApplySchurToChunk -

    393:    Input parameters:
    394: .  pcnn
    395: .  n - size of chunk
    396: .  idx - indices of chunk
    397: .  chunk - values

    399:    Output parameters:
    400: .  array_N - result of Schur complement applied to chunk, scattered to big array
    401: .  vec1_B  - result of Schur complement applied to chunk
    402: .  vec2_B  - garbage (used as work space)
    403: .  vec1_D  - garbage (used as work space)
    404: .  vec2_D  - garbage (used as work space)

    406: */
    407: PetscErrorCode PCNNApplySchurToChunk(PC pc, PetscInt n, PetscInt *idx, PetscScalar *chunk, PetscScalar *array_N, Vec vec1_B, Vec vec2_B, Vec vec1_D, Vec vec2_D)
    408: {
    410:   PetscInt       i;
    411:   PC_IS          *pcis = (PC_IS*)(pc->data);

    414:   PetscArrayzero(array_N, pcis->n);
    415:   for (i=0; i<n; i++) array_N[idx[i]] = chunk[i];
    416:   PCISScatterArrayNToVecB(array_N,vec2_B,INSERT_VALUES,SCATTER_FORWARD,pc);
    417:   PCISApplySchur(pc,vec2_B,vec1_B,(Vec)0,vec1_D,vec2_D);
    418:   PCISScatterArrayNToVecB(array_N,vec1_B,INSERT_VALUES,SCATTER_REVERSE,pc);
    419:   return(0);
    420: }

    422: /* -------------------------------------------------------------------------- */
    423: /*
    424:    PCNNApplyInterfacePreconditioner - Apply the interface preconditioner, i.e.,
    425:                                       the preconditioner for the Schur complement.

    427:    Input parameter:
    428: .  r - global vector of interior and interface nodes. The values on the interior nodes are NOT used.

    430:    Output parameters:
    431: .  z - global vector of interior and interface nodes. The values on the interface are the result of
    432:        the application of the interface preconditioner to the interface part of r. The values on the
    433:        interior nodes are garbage.
    434: .  work_N - array of local nodes (interior and interface, including ghosts); returns garbage (used as work space)
    435: .  vec1_B - vector of local interface nodes (including ghosts); returns garbage (used as work space)
    436: .  vec2_B - vector of local interface nodes (including ghosts); returns garbage (used as work space)
    437: .  vec3_B - vector of local interface nodes (including ghosts); returns garbage (used as work space)
    438: .  vec1_D - vector of local interior nodes; returns garbage (used as work space)
    439: .  vec2_D - vector of local interior nodes; returns garbage (used as work space)
    440: .  vec1_N - vector of local nodes (interior and interface, including ghosts); returns garbage (used as work space)
    441: .  vec2_N - vector of local nodes (interior and interface, including ghosts); returns garbage (used as work space)

    443: */
    444: PetscErrorCode PCNNApplyInterfacePreconditioner(PC pc, Vec r, Vec z, PetscScalar *work_N, Vec vec1_B, Vec vec2_B, Vec vec3_B, Vec vec1_D,Vec vec2_D, Vec vec1_N, Vec vec2_N)
    445: {
    447:   PC_IS          *pcis = (PC_IS*)(pc->data);

    450:   /*
    451:     First balancing step.
    452:   */
    453:   {
    454:     PetscBool flg = PETSC_FALSE;
    455:     PetscOptionsGetBool(NULL,NULL,"-pc_nn_turn_off_first_balancing",&flg,NULL);
    456:     if (!flg) {
    457:       PCNNBalancing(pc,r,(Vec)0,z,vec1_B,vec2_B,(Vec)0,vec1_D,vec2_D,work_N);
    458:     } else {
    459:       VecCopy(r,z);
    460:     }
    461:   }

    463:   /*
    464:     Extract the local interface part of z and scale it by D
    465:   */
    466:   VecScatterBegin(pcis->global_to_B,z,vec1_B,INSERT_VALUES,SCATTER_FORWARD);
    467:   VecScatterEnd  (pcis->global_to_B,z,vec1_B,INSERT_VALUES,SCATTER_FORWARD);
    468:   VecPointwiseMult(vec2_B,pcis->D,vec1_B);

    470:   /* Neumann Solver */
    471:   PCISApplyInvSchur(pc,vec2_B,vec1_B,vec1_N,vec2_N);

    473:   /*
    474:     Second balancing step.
    475:   */
    476:   {
    477:     PetscBool flg = PETSC_FALSE;
    478:     PetscOptionsGetBool(NULL,NULL,"-pc_turn_off_second_balancing",&flg,NULL);
    479:     if (!flg) {
    480:       PCNNBalancing(pc,r,vec1_B,z,vec2_B,vec3_B,(Vec)0,vec1_D,vec2_D,work_N);
    481:     } else {
    482:       VecPointwiseMult(vec2_B,pcis->D,vec1_B);
    483:       VecSet(z,0.0);
    484:       VecScatterBegin(pcis->global_to_B,vec2_B,z,ADD_VALUES,SCATTER_REVERSE);
    485:       VecScatterEnd  (pcis->global_to_B,vec2_B,z,ADD_VALUES,SCATTER_REVERSE);
    486:     }
    487:   }
    488:   return(0);
    489: }

    491: /* -------------------------------------------------------------------------- */
    492: /*
    493:    PCNNBalancing - Computes z, as given in equations (15) and (16) (if the
    494:                    input argument u is provided), or s, as given in equations
    495:                    (12) and (13), if the input argument u is a null vector.
    496:                    Notice that the input argument u plays the role of u_i in
    497:                    equation (14). The equation numbers refer to [Man93].

    499:    Input Parameters:
    500: .  pcnn - NN preconditioner context.
    501: .  r - MPI vector of all nodes (interior and interface). It's preserved.
    502: .  u - (Optional) sequential vector of local interface nodes. It's preserved UNLESS vec3_B is null.

    504:    Output Parameters:
    505: .  z - MPI vector of interior and interface nodes. Returns s or z (see description above).
    506: .  vec1_B - Sequential vector of local interface nodes. Workspace.
    507: .  vec2_B - Sequential vector of local interface nodes. Workspace.
    508: .  vec3_B - (Optional) sequential vector of local interface nodes. Workspace.
    509: .  vec1_D - Sequential vector of local interior nodes. Workspace.
    510: .  vec2_D - Sequential vector of local interior nodes. Workspace.
    511: .  work_N - Array of all local nodes (interior and interface). Workspace.

    513: */
    514: PetscErrorCode PCNNBalancing(PC pc, Vec r, Vec u, Vec z, Vec vec1_B, Vec vec2_B, Vec vec3_B,Vec vec1_D, Vec vec2_D, PetscScalar *work_N)
    515: {
    517:   PetscInt       k;
    518:   PetscScalar    value;
    519:   PetscScalar    *lambda;
    520:   PC_NN          *pcnn = (PC_NN*)(pc->data);
    521:   PC_IS          *pcis = (PC_IS*)(pc->data);

    524:   PetscLogEventBegin(PC_ApplyCoarse,pc,0,0,0);
    525:   if (u) {
    526:     if (!vec3_B) vec3_B = u;
    527:     VecPointwiseMult(vec1_B,pcis->D,u);
    528:     VecSet(z,0.0);
    529:     VecScatterBegin(pcis->global_to_B,vec1_B,z,ADD_VALUES,SCATTER_REVERSE);
    530:     VecScatterEnd  (pcis->global_to_B,vec1_B,z,ADD_VALUES,SCATTER_REVERSE);
    531:     VecScatterBegin(pcis->global_to_B,z,vec2_B,INSERT_VALUES,SCATTER_FORWARD);
    532:     VecScatterEnd  (pcis->global_to_B,z,vec2_B,INSERT_VALUES,SCATTER_FORWARD);
    533:     PCISApplySchur(pc,vec2_B,vec3_B,(Vec)0,vec1_D,vec2_D);
    534:     VecScale(vec3_B,-1.0);
    535:     VecCopy(r,z);
    536:     VecScatterBegin(pcis->global_to_B,vec3_B,z,ADD_VALUES,SCATTER_REVERSE);
    537:     VecScatterEnd  (pcis->global_to_B,vec3_B,z,ADD_VALUES,SCATTER_REVERSE);
    538:   } else {
    539:     VecCopy(r,z);
    540:   }
    541:   VecScatterBegin(pcis->global_to_B,z,vec2_B,INSERT_VALUES,SCATTER_FORWARD);
    542:   VecScatterEnd  (pcis->global_to_B,z,vec2_B,INSERT_VALUES,SCATTER_FORWARD);
    543:   PCISScatterArrayNToVecB(work_N,vec2_B,INSERT_VALUES,SCATTER_REVERSE,pc);
    544:   for (k=0, value=0.0; k<pcis->n_shared[0]; k++) value += pcnn->DZ_IN[0][k] * work_N[pcis->shared[0][k]];
    545:   value *= pcnn->factor_coarse_rhs;  /* This factor is set in CreateCoarseMatrix(). */
    546:   {
    547:     PetscMPIInt rank;
    548:     MPI_Comm_rank(PetscObjectComm((PetscObject)pc),&rank);
    549:     VecSetValue(pcnn->coarse_b,rank,value,INSERT_VALUES);
    550:     /*
    551:        Since we are only inserting local values (one value actually) we don't need to do the
    552:        reduction that tells us there is no data that needs to be moved. Hence we comment out these
    553:        VecAssemblyBegin(pcnn->coarse_b);
    554:        VecAssemblyEnd  (pcnn->coarse_b);
    555:     */
    556:   }
    557:   KSPSolve(pcnn->ksp_coarse,pcnn->coarse_b,pcnn->coarse_x);
    558:   if (!u) { VecScale(pcnn->coarse_x,-1.0); }
    559:   VecGetArray(pcnn->coarse_x,&lambda);
    560:   for (k=0; k<pcis->n_shared[0]; k++) work_N[pcis->shared[0][k]] = *lambda * pcnn->DZ_IN[0][k];
    561:   VecRestoreArray(pcnn->coarse_x,&lambda);
    562:   PCISScatterArrayNToVecB(work_N,vec2_B,INSERT_VALUES,SCATTER_FORWARD,pc);
    563:   VecSet(z,0.0);
    564:   VecScatterBegin(pcis->global_to_B,vec2_B,z,ADD_VALUES,SCATTER_REVERSE);
    565:   VecScatterEnd  (pcis->global_to_B,vec2_B,z,ADD_VALUES,SCATTER_REVERSE);
    566:   if (!u) {
    567:     VecScatterBegin(pcis->global_to_B,z,vec2_B,INSERT_VALUES,SCATTER_FORWARD);
    568:     VecScatterEnd  (pcis->global_to_B,z,vec2_B,INSERT_VALUES,SCATTER_FORWARD);
    569:     PCISApplySchur(pc,vec2_B,vec1_B,(Vec)0,vec1_D,vec2_D);
    570:     VecCopy(r,z);
    571:   }
    572:   VecScatterBegin(pcis->global_to_B,vec1_B,z,ADD_VALUES,SCATTER_REVERSE);
    573:   VecScatterEnd  (pcis->global_to_B,vec1_B,z,ADD_VALUES,SCATTER_REVERSE);
    574:   PetscLogEventEnd(PC_ApplyCoarse,pc,0,0,0);
    575:   return(0);
    576: }

    578: /*  -------   E N D   O F   T H E   C O D E   -------  */
    579: /*                                                     */
    580: /*  From now on, "footnotes" (or "historical notes").  */
    581: /*                                                     */
    582: /*  -------------------------------------------------  */

    584: /* --------------------------------------------------------------------------
    585:    Historical note 01
    586:    -------------------------------------------------------------------------- */
    587: /*
    588:    We considered the possibility of an alternative D_i that would still
    589:    provide a partition of unity (i.e., $ \sum_i  N_i D_i N_i^T = I $).
    590:    The basic principle was still the pseudo-inverse of the counting
    591:    function; the difference was that we would not count subdomains
    592:    that do not contribute to the coarse space (i.e., not pure-Neumann
    593:    subdomains).

    595:    This turned out to be a bad idea:  we would solve trivial Neumann
    596:    problems in the not pure-Neumann subdomains, since we would be scaling
    597:    the balanced residual by zero.
    598: */

    600: /* --------------------------------------------------------------------------
    601:    Historical note 02
    602:    -------------------------------------------------------------------------- */
    603: /*
    604:    We tried an alternative coarse problem, that would eliminate exactly a
    605:    constant error. Turned out not to improve the overall convergence.
    606: */